Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(141,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 141.4 | ||
Root | \(0.500000 - 0.691860i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.141 |
Dual form | 280.2.b.c.141.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.635665 | + | 1.26330i | −0.449483 | + | 0.893289i | ||||
\(3\) | − | 0.414214i | − | 0.239146i | −0.992825 | − | 0.119573i | \(-0.961847\pi\) | ||
0.992825 | − | 0.119573i | \(-0.0381526\pi\) | |||||||
\(4\) | −1.19186 | − | 1.60607i | −0.595930 | − | 0.803037i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0.523276 | + | 0.263301i | 0.213627 | + | 0.107492i | ||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.78658 | − | 0.484753i | 0.985204 | − | 0.171386i | ||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | −1.26330 | − | 0.635665i | −0.399491 | − | 0.201015i | ||||
\(11\) | 6.37109i | 1.92096i | 0.278357 | + | 0.960478i | \(0.410210\pi\) | ||||
−0.278357 | + | 0.960478i | \(0.589790\pi\) | |||||||
\(12\) | −0.665257 | + | 0.493684i | −0.192043 | + | 0.142514i | ||||
\(13\) | − | 0.573155i | − | 0.158965i | −0.996836 | − | 0.0794823i | \(-0.974673\pi\) | ||
0.996836 | − | 0.0794823i | \(-0.0253267\pi\) | |||||||
\(14\) | 0.635665 | − | 1.26330i | 0.169889 | − | 0.337631i | ||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | −1.15894 | + | 3.82843i | −0.289735 | + | 0.957107i | ||||
\(17\) | 0.638991 | 0.154978 | 0.0774890 | − | 0.996993i | \(-0.475310\pi\) | ||||
0.0774890 | + | 0.996993i | \(0.475310\pi\) | |||||||
\(18\) | −1.79793 | + | 3.57316i | −0.423777 | + | 0.842201i | ||||
\(19\) | 6.11582i | 1.40306i | 0.712638 | + | 0.701532i | \(0.247500\pi\) | ||||
−0.712638 | + | 0.701532i | \(0.752500\pi\) | |||||||
\(20\) | 1.60607 | − | 1.19186i | 0.359129 | − | 0.266508i | ||||
\(21\) | 0.414214i | 0.0903888i | ||||||||
\(22\) | −8.04860 | − | 4.04988i | −1.71597 | − | 0.863437i | ||||
\(23\) | 4.62636 | 0.964663 | 0.482331 | − | 0.875989i | \(-0.339790\pi\) | ||||
0.482331 | + | 0.875989i | \(0.339790\pi\) | |||||||
\(24\) | −0.200791 | − | 1.15424i | −0.0409863 | − | 0.235608i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.724068 | + | 0.364335i | 0.142001 | + | 0.0714519i | ||||
\(27\) | − | 2.41421i | − | 0.464616i | ||||||
\(28\) | 1.19186 | + | 1.60607i | 0.225240 | + | 0.303519i | ||||
\(29\) | 1.60850i | 0.298690i | 0.988785 | + | 0.149345i | \(0.0477166\pi\) | ||||
−0.988785 | + | 0.149345i | \(0.952283\pi\) | |||||||
\(30\) | −0.263301 | + | 0.523276i | −0.0480720 | + | 0.0955368i | ||||
\(31\) | −4.08370 | −0.733454 | −0.366727 | − | 0.930329i | \(-0.619522\pi\) | ||||
−0.366727 | + | 0.930329i | \(0.619522\pi\) | |||||||
\(32\) | −4.09976 | − | 3.89769i | −0.724742 | − | 0.689021i | ||||
\(33\) | 2.63899 | 0.459389 | ||||||||
\(34\) | −0.406184 | + | 0.807238i | −0.0696600 | + | 0.138440i | ||||
\(35\) | − | 1.00000i | − | 0.169031i | ||||||
\(36\) | −3.37109 | − | 4.54266i | −0.561848 | − | 0.757110i | ||||
\(37\) | − | 2.96951i | − | 0.488184i | −0.969752 | − | 0.244092i | \(-0.921510\pi\) | ||
0.969752 | − | 0.244092i | \(-0.0784898\pi\) | |||||||
\(38\) | −7.72612 | − | 3.88761i | −1.25334 | − | 0.630654i | ||||
\(39\) | −0.237409 | −0.0380158 | ||||||||
\(40\) | 0.484753 | + | 2.78658i | 0.0766461 | + | 0.440597i | ||||
\(41\) | 8.11582 | 1.26748 | 0.633739 | − | 0.773547i | \(-0.281519\pi\) | ||||
0.633739 | + | 0.773547i | \(0.281519\pi\) | |||||||
\(42\) | −0.523276 | − | 0.263301i | −0.0807433 | − | 0.0406282i | ||||
\(43\) | − | 2.08370i | − | 0.317761i | −0.987298 | − | 0.158881i | \(-0.949212\pi\) | ||
0.987298 | − | 0.158881i | \(-0.0507885\pi\) | |||||||
\(44\) | 10.2324 | − | 7.59344i | 1.54260 | − | 1.14475i | ||||
\(45\) | 2.82843i | 0.421637i | ||||||||
\(46\) | −2.94082 | + | 5.84449i | −0.433600 | + | 0.861722i | ||||
\(47\) | −8.45479 | −1.23326 | −0.616629 | − | 0.787254i | \(-0.711502\pi\) | ||||
−0.616629 | + | 0.787254i | \(0.711502\pi\) | |||||||
\(48\) | 1.58579 | + | 0.480049i | 0.228889 | + | 0.0692892i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.635665 | − | 1.26330i | 0.0898966 | − | 0.178658i | ||||
\(51\) | − | 0.264679i | − | 0.0370624i | ||||||
\(52\) | −0.920529 | + | 0.683121i | −0.127654 | + | 0.0947318i | ||||
\(53\) | − | 0.317883i | − | 0.0436646i | −0.999762 | − | 0.0218323i | \(-0.993050\pi\) | ||
0.999762 | − | 0.0218323i | \(-0.00694999\pi\) | |||||||
\(54\) | 3.04988 | + | 1.53463i | 0.415036 | + | 0.208837i | ||||
\(55\) | −6.37109 | −0.859077 | ||||||||
\(56\) | −2.78658 | + | 0.484753i | −0.372372 | + | 0.0647778i | ||||
\(57\) | 2.53325 | 0.335538 | ||||||||
\(58\) | −2.03202 | − | 1.02247i | −0.266817 | − | 0.134256i | ||||
\(59\) | − | 6.37887i | − | 0.830458i | −0.909717 | − | 0.415229i | \(-0.863701\pi\) | ||
0.909717 | − | 0.415229i | \(-0.136299\pi\) | |||||||
\(60\) | −0.493684 | − | 0.665257i | −0.0637344 | − | 0.0858843i | ||||
\(61\) | − | 8.44700i | − | 1.08153i | −0.841174 | − | 0.540764i | \(-0.818135\pi\) | ||
0.841174 | − | 0.540764i | \(-0.181865\pi\) | |||||||
\(62\) | 2.59587 | − | 5.15894i | 0.329675 | − | 0.655186i | ||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 7.53003 | − | 2.70160i | 0.941254 | − | 0.337700i | ||||
\(65\) | 0.573155 | 0.0710912 | ||||||||
\(66\) | −1.67751 | + | 3.33384i | −0.206488 | + | 0.410367i | ||||
\(67\) | 4.31788i | 0.527513i | 0.964589 | + | 0.263757i | \(0.0849616\pi\) | ||||
−0.964589 | + | 0.263757i | \(0.915038\pi\) | |||||||
\(68\) | −0.761588 | − | 1.02627i | −0.0923561 | − | 0.124453i | ||||
\(69\) | − | 1.91630i | − | 0.230696i | ||||||
\(70\) | 1.26330 | + | 0.635665i | 0.150993 | + | 0.0759765i | ||||
\(71\) | 13.1917 | 1.56557 | 0.782785 | − | 0.622292i | \(-0.213798\pi\) | ||||
0.782785 | + | 0.622292i | \(0.213798\pi\) | |||||||
\(72\) | 7.88163 | − | 1.37109i | 0.928859 | − | 0.161584i | ||||
\(73\) | 15.1917 | 1.77806 | 0.889029 | − | 0.457851i | \(-0.151381\pi\) | ||||
0.889029 | + | 0.457851i | \(0.151381\pi\) | |||||||
\(74\) | 3.75138 | + | 1.88761i | 0.436089 | + | 0.219430i | ||||
\(75\) | 0.414214i | 0.0478293i | ||||||||
\(76\) | 9.82245 | − | 7.28919i | 1.12671 | − | 0.836128i | ||||
\(77\) | − | 6.37109i | − | 0.726053i | ||||||
\(78\) | 0.150912 | − | 0.299919i | 0.0170875 | − | 0.0339591i | ||||
\(79\) | −3.80801 | −0.428435 | −0.214217 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214217 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(80\) | −3.82843 | − | 1.15894i | −0.428031 | − | 0.129574i | ||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −5.15894 | + | 10.2527i | −0.569710 | + | 1.13222i | ||||
\(83\) | − | 12.4243i | − | 1.36374i | −0.731472 | − | 0.681872i | \(-0.761166\pi\) | ||
0.731472 | − | 0.681872i | \(-0.238834\pi\) | |||||||
\(84\) | 0.665257 | − | 0.493684i | 0.0725855 | − | 0.0538654i | ||||
\(85\) | 0.638991i | 0.0693083i | ||||||||
\(86\) | 2.63234 | + | 1.32453i | 0.283852 | + | 0.142828i | ||||
\(87\) | 0.666261 | 0.0714307 | ||||||||
\(88\) | 3.08840 | + | 17.7535i | 0.329225 | + | 1.89253i | ||||
\(89\) | −6.54011 | −0.693250 | −0.346625 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346625 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(90\) | −3.57316 | − | 1.79793i | −0.376644 | − | 0.189519i | ||||
\(91\) | 0.573155i | 0.0600830i | ||||||||
\(92\) | −5.51397 | − | 7.43027i | −0.574871 | − | 0.774659i | ||||
\(93\) | 1.69152i | 0.175403i | ||||||||
\(94\) | 5.37441 | − | 10.6809i | 0.554328 | − | 1.10166i | ||||
\(95\) | −6.11582 | −0.627469 | ||||||||
\(96\) | −1.61448 | + | 1.69818i | −0.164777 | + | 0.173319i | ||||
\(97\) | −17.3559 | −1.76223 | −0.881113 | − | 0.472907i | \(-0.843205\pi\) | ||||
−0.881113 | + | 0.472907i | \(0.843205\pi\) | |||||||
\(98\) | −0.635665 | + | 1.26330i | −0.0642119 | + | 0.127613i | ||||
\(99\) | 18.0202i | 1.81109i | ||||||||
\(100\) | 1.19186 | + | 1.60607i | 0.119186 | + | 0.160607i | ||||
\(101\) | − | 13.3617i | − | 1.32954i | −0.747049 | − | 0.664768i | \(-0.768530\pi\) | ||
0.747049 | − | 0.664768i | \(-0.231470\pi\) | |||||||
\(102\) | 0.334369 | + | 0.168247i | 0.0331075 | + | 0.0166589i | ||||
\(103\) | −14.8181 | −1.46007 | −0.730035 | − | 0.683410i | \(-0.760496\pi\) | ||||
−0.730035 | + | 0.683410i | \(0.760496\pi\) | |||||||
\(104\) | −0.277839 | − | 1.59714i | −0.0272443 | − | 0.156613i | ||||
\(105\) | −0.414214 | −0.0404231 | ||||||||
\(106\) | 0.401582 | + | 0.202067i | 0.0390051 | + | 0.0196265i | ||||
\(107\) | 2.57153i | 0.248599i | 0.992245 | + | 0.124300i | \(0.0396684\pi\) | ||||
−0.992245 | + | 0.124300i | \(0.960332\pi\) | |||||||
\(108\) | −3.87740 | + | 2.87740i | −0.373103 | + | 0.276878i | ||||
\(109\) | 13.6442i | 1.30688i | 0.756979 | + | 0.653440i | \(0.226675\pi\) | ||||
−0.756979 | + | 0.653440i | \(0.773325\pi\) | |||||||
\(110\) | 4.04988 | − | 8.04860i | 0.386141 | − | 0.767404i | ||||
\(111\) | −1.23001 | −0.116747 | ||||||||
\(112\) | 1.15894 | − | 3.82843i | 0.109510 | − | 0.361752i | ||||
\(113\) | 1.83005 | 0.172157 | 0.0860783 | − | 0.996288i | \(-0.472566\pi\) | ||||
0.0860783 | + | 0.996288i | \(0.472566\pi\) | |||||||
\(114\) | −1.61030 | + | 3.20026i | −0.150819 | + | 0.299732i | ||||
\(115\) | 4.62636i | 0.431410i | ||||||||
\(116\) | 2.58336 | − | 1.91710i | 0.239859 | − | 0.177998i | ||||
\(117\) | − | 1.62113i | − | 0.149873i | ||||||
\(118\) | 8.05844 | + | 4.05483i | 0.741839 | + | 0.373277i | ||||
\(119\) | −0.638991 | −0.0585762 | ||||||||
\(120\) | 1.15424 | − | 0.200791i | 0.105367 | − | 0.0183296i | ||||
\(121\) | −29.5908 | −2.69007 | ||||||||
\(122\) | 10.6711 | + | 5.36947i | 0.966117 | + | 0.486129i | ||||
\(123\) | − | 3.36168i | − | 0.303113i | ||||||
\(124\) | 4.86720 | + | 6.55872i | 0.437087 | + | 0.588990i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.79793 | − | 3.57316i | 0.160173 | − | 0.318322i | ||||
\(127\) | 3.91375 | 0.347289 | 0.173645 | − | 0.984808i | \(-0.444446\pi\) | ||||
0.173645 | + | 0.984808i | \(0.444446\pi\) | |||||||
\(128\) | −1.37364 | + | 11.2300i | −0.121414 | + | 0.992602i | ||||
\(129\) | −0.863096 | −0.0759914 | ||||||||
\(130\) | −0.364335 | + | 0.724068i | −0.0319543 | + | 0.0635049i | ||||
\(131\) | − | 10.1970i | − | 0.890913i | −0.895304 | − | 0.445456i | \(-0.853041\pi\) | ||
0.895304 | − | 0.445456i | \(-0.146959\pi\) | |||||||
\(132\) | −3.14531 | − | 4.23841i | −0.273764 | − | 0.368906i | ||||
\(133\) | − | 6.11582i | − | 0.530308i | ||||||
\(134\) | −5.45479 | − | 2.74473i | −0.471222 | − | 0.237108i | ||||
\(135\) | 2.41421 | 0.207782 | ||||||||
\(136\) | 1.78060 | − | 0.309753i | 0.152685 | − | 0.0265611i | ||||
\(137\) | −3.51217 | −0.300065 | −0.150032 | − | 0.988681i | \(-0.547938\pi\) | ||||
−0.150032 | + | 0.988681i | \(0.547938\pi\) | |||||||
\(138\) | 2.42087 | + | 1.21813i | 0.206078 | + | 0.103694i | ||||
\(139\) | − | 1.87802i | − | 0.159292i | −0.996823 | − | 0.0796459i | \(-0.974621\pi\) | ||
0.996823 | − | 0.0796459i | \(-0.0253790\pi\) | |||||||
\(140\) | −1.60607 | + | 1.19186i | −0.135738 | + | 0.100731i | ||||
\(141\) | 3.50209i | 0.294929i | ||||||||
\(142\) | −8.38552 | + | 16.6651i | −0.703698 | + | 1.39851i | ||||
\(143\) | 3.65162 | 0.305364 | ||||||||
\(144\) | −3.27798 | + | 10.8284i | −0.273165 | + | 0.902369i | ||||
\(145\) | −1.60850 | −0.133578 | ||||||||
\(146\) | −9.65685 | + | 19.1917i | −0.799207 | + | 1.58832i | ||||
\(147\) | − | 0.414214i | − | 0.0341638i | ||||||
\(148\) | −4.76924 | + | 3.53923i | −0.392029 | + | 0.290923i | ||||
\(149\) | 8.99907i | 0.737233i | 0.929582 | + | 0.368616i | \(0.120168\pi\) | ||||
−0.929582 | + | 0.368616i | \(0.879832\pi\) | |||||||
\(150\) | −0.523276 | − | 0.263301i | −0.0427253 | − | 0.0214984i | ||||
\(151\) | −10.8732 | −0.884846 | −0.442423 | − | 0.896806i | \(-0.645881\pi\) | ||||
−0.442423 | + | 0.896806i | \(0.645881\pi\) | |||||||
\(152\) | 2.96466 | + | 17.0422i | 0.240466 | + | 1.38230i | ||||
\(153\) | 1.80734 | 0.146115 | ||||||||
\(154\) | 8.04860 | + | 4.04988i | 0.648575 | + | 0.326349i | ||||
\(155\) | − | 4.08370i | − | 0.328011i | ||||||
\(156\) | 0.282958 | + | 0.381296i | 0.0226548 | + | 0.0305281i | ||||
\(157\) | 11.3390i | 0.904948i | 0.891777 | + | 0.452474i | \(0.149459\pi\) | ||||
−0.891777 | + | 0.452474i | \(0.850541\pi\) | |||||||
\(158\) | 2.42062 | − | 4.81067i | 0.192574 | − | 0.382716i | ||||
\(159\) | −0.131672 | −0.0104422 | ||||||||
\(160\) | 3.89769 | − | 4.09976i | 0.308139 | − | 0.324114i | ||||
\(161\) | −4.62636 | −0.364608 | ||||||||
\(162\) | −4.75813 | + | 9.45616i | −0.373834 | + | 0.742946i | ||||
\(163\) | − | 24.0656i | − | 1.88496i | −0.334260 | − | 0.942481i | \(-0.608486\pi\) | ||
0.334260 | − | 0.942481i | \(-0.391514\pi\) | |||||||
\(164\) | −9.67291 | − | 13.0346i | −0.755328 | − | 1.01783i | ||||
\(165\) | 2.63899i | 0.205445i | ||||||||
\(166\) | 15.6956 | + | 7.89769i | 1.21822 | + | 0.612980i | ||||
\(167\) | 13.7328 | 1.06267 | 0.531337 | − | 0.847161i | \(-0.321690\pi\) | ||||
0.531337 | + | 0.847161i | \(0.321690\pi\) | |||||||
\(168\) | 0.200791 | + | 1.15424i | 0.0154914 | + | 0.0890514i | ||||
\(169\) | 12.6715 | 0.974730 | ||||||||
\(170\) | −0.807238 | − | 0.406184i | −0.0619123 | − | 0.0311529i | ||||
\(171\) | 17.2981i | 1.32282i | ||||||||
\(172\) | −3.34657 | + | 2.48348i | −0.255174 | + | 0.189363i | ||||
\(173\) | 19.1648i | 1.45708i | 0.685005 | + | 0.728538i | \(0.259800\pi\) | ||||
−0.685005 | + | 0.728538i | \(0.740200\pi\) | |||||||
\(174\) | −0.423519 | + | 0.841688i | −0.0321069 | + | 0.0638082i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −24.3912 | − | 7.38372i | −1.83856 | − | 0.556569i | ||||
\(177\) | −2.64222 | −0.198601 | ||||||||
\(178\) | 4.15732 | − | 8.26213i | 0.311604 | − | 0.619273i | ||||
\(179\) | 8.08115i | 0.604013i | 0.953306 | + | 0.302007i | \(0.0976565\pi\) | ||||
−0.953306 | + | 0.302007i | \(0.902344\pi\) | |||||||
\(180\) | 4.54266 | − | 3.37109i | 0.338590 | − | 0.251266i | ||||
\(181\) | − | 18.4243i | − | 1.36947i | −0.728794 | − | 0.684733i | \(-0.759919\pi\) | ||
0.728794 | − | 0.684733i | \(-0.240081\pi\) | |||||||
\(182\) | −0.724068 | − | 0.364335i | −0.0536715 | − | 0.0270063i | ||||
\(183\) | −3.49886 | −0.258643 | ||||||||
\(184\) | 12.8917 | − | 2.24264i | 0.950390 | − | 0.165330i | ||||
\(185\) | 2.96951 | 0.218322 | ||||||||
\(186\) | −2.13690 | − | 1.07524i | −0.156685 | − | 0.0788406i | ||||
\(187\) | 4.07107i | 0.297706i | ||||||||
\(188\) | 10.0769 | + | 13.5790i | 0.734935 | + | 0.990351i | ||||
\(189\) | 2.41421i | 0.175608i | ||||||||
\(190\) | 3.88761 | − | 7.72612i | 0.282037 | − | 0.560511i | ||||
\(191\) | 17.0860 | 1.23630 | 0.618150 | − | 0.786061i | \(-0.287883\pi\) | ||||
0.618150 | + | 0.786061i | \(0.287883\pi\) | |||||||
\(192\) | −1.11904 | − | 3.11904i | −0.0807598 | − | 0.225097i | ||||
\(193\) | 20.5975 | 1.48264 | 0.741320 | − | 0.671152i | \(-0.234200\pi\) | ||||
0.741320 | + | 0.671152i | \(0.234200\pi\) | |||||||
\(194\) | 11.0325 | − | 21.9257i | 0.792091 | − | 1.57418i | ||||
\(195\) | − | 0.237409i | − | 0.0170012i | ||||||
\(196\) | −1.19186 | − | 1.60607i | −0.0851328 | − | 0.114720i | ||||
\(197\) | − | 15.0662i | − | 1.07342i | −0.843766 | − | 0.536712i | \(-0.819666\pi\) | ||
0.843766 | − | 0.536712i | \(-0.180334\pi\) | |||||||
\(198\) | −22.7649 | − | 11.4548i | −1.61783 | − | 0.814056i | ||||
\(199\) | −13.4032 | −0.950128 | −0.475064 | − | 0.879951i | \(-0.657575\pi\) | ||||
−0.475064 | + | 0.879951i | \(0.657575\pi\) | |||||||
\(200\) | −2.78658 | + | 0.484753i | −0.197041 | + | 0.0342772i | ||||
\(201\) | 1.78853 | 0.126153 | ||||||||
\(202\) | 16.8798 | + | 8.49356i | 1.18766 | + | 0.597604i | ||||
\(203\) | − | 1.60850i | − | 0.112894i | ||||||
\(204\) | −0.425093 | + | 0.315460i | −0.0297625 | + | 0.0220866i | ||||
\(205\) | 8.11582i | 0.566833i | ||||||||
\(206\) | 9.41934 | − | 18.7197i | 0.656277 | − | 1.30426i | ||||
\(207\) | 13.0853 | 0.909493 | ||||||||
\(208\) | 2.19428 | + | 0.664253i | 0.152146 | + | 0.0460577i | ||||
\(209\) | −38.9644 | −2.69522 | ||||||||
\(210\) | 0.263301 | − | 0.523276i | 0.0181695 | − | 0.0361095i | ||||
\(211\) | − | 5.54266i | − | 0.381573i | −0.981632 | − | 0.190786i | \(-0.938896\pi\) | ||
0.981632 | − | 0.190786i | \(-0.0611037\pi\) | |||||||
\(212\) | −0.510544 | + | 0.378872i | −0.0350643 | + | 0.0260211i | ||||
\(213\) | − | 5.46419i | − | 0.374400i | ||||||
\(214\) | −3.24862 | − | 1.63463i | −0.222071 | − | 0.111741i | ||||
\(215\) | 2.08370 | 0.142107 | ||||||||
\(216\) | −1.17030 | − | 6.72739i | −0.0796286 | − | 0.457741i | ||||
\(217\) | 4.08370 | 0.277220 | ||||||||
\(218\) | −17.2368 | − | 8.67316i | −1.16742 | − | 0.587420i | ||||
\(219\) | − | 6.29262i | − | 0.425216i | ||||||
\(220\) | 7.59344 | + | 10.2324i | 0.511950 | + | 0.689870i | ||||
\(221\) | − | 0.366241i | − | 0.0246360i | ||||||
\(222\) | 0.781874 | − | 1.55387i | 0.0524760 | − | 0.104289i | ||||
\(223\) | 18.0052 | 1.20572 | 0.602860 | − | 0.797847i | \(-0.294028\pi\) | ||||
0.602860 | + | 0.797847i | \(0.294028\pi\) | |||||||
\(224\) | 4.09976 | + | 3.89769i | 0.273927 | + | 0.260425i | ||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | −1.16330 | + | 2.31190i | −0.0773815 | + | 0.153786i | ||||
\(227\) | 10.3532i | 0.687168i | 0.939122 | + | 0.343584i | \(0.111641\pi\) | ||||
−0.939122 | + | 0.343584i | \(0.888359\pi\) | |||||||
\(228\) | −3.01928 | − | 4.06859i | −0.199957 | − | 0.269449i | ||||
\(229\) | − | 18.2089i | − | 1.20328i | −0.798768 | − | 0.601640i | \(-0.794514\pi\) | ||
0.798768 | − | 0.601640i | \(-0.205486\pi\) | |||||||
\(230\) | −5.84449 | − | 2.94082i | −0.385374 | − | 0.193912i | ||||
\(231\) | −2.63899 | −0.173633 | ||||||||
\(232\) | 0.779723 | + | 4.48220i | 0.0511913 | + | 0.294271i | ||||
\(233\) | −21.8243 | −1.42975 | −0.714877 | − | 0.699250i | \(-0.753517\pi\) | ||||
−0.714877 | + | 0.699250i | \(0.753517\pi\) | |||||||
\(234\) | 2.04797 | + | 1.03049i | 0.133880 | + | 0.0673655i | ||||
\(235\) | − | 8.45479i | − | 0.551529i | ||||||
\(236\) | −10.2449 | + | 7.60272i | −0.666888 | + | 0.494895i | ||||
\(237\) | 1.57733i | 0.102459i | ||||||||
\(238\) | 0.406184 | − | 0.807238i | 0.0263290 | − | 0.0523255i | ||||
\(239\) | 19.1924 | 1.24145 | 0.620727 | − | 0.784027i | \(-0.286838\pi\) | ||||
0.620727 | + | 0.784027i | \(0.286838\pi\) | |||||||
\(240\) | −0.480049 | + | 1.58579i | −0.0309871 | + | 0.102362i | ||||
\(241\) | 10.5369 | 0.678739 | 0.339370 | − | 0.940653i | \(-0.389786\pi\) | ||||
0.339370 | + | 0.940653i | \(0.389786\pi\) | |||||||
\(242\) | 18.8098 | − | 37.3820i | 1.20914 | − | 2.40301i | ||||
\(243\) | − | 10.3431i | − | 0.663513i | ||||||
\(244\) | −13.5665 | + | 10.0676i | −0.868506 | + | 0.644515i | ||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 4.24682 | + | 2.13690i | 0.270767 | + | 0.136244i | ||||
\(247\) | 3.50531 | 0.223038 | ||||||||
\(248\) | −11.3795 | + | 1.97958i | −0.722602 | + | 0.125704i | ||||
\(249\) | −5.14631 | −0.326134 | ||||||||
\(250\) | 1.26330 | + | 0.635665i | 0.0798982 | + | 0.0402030i | ||||
\(251\) | 6.57153i | 0.414791i | 0.978257 | + | 0.207396i | \(0.0664988\pi\) | ||||
−0.978257 | + | 0.207396i | \(0.933501\pi\) | |||||||
\(252\) | 3.37109 | + | 4.54266i | 0.212359 | + | 0.286161i | ||||
\(253\) | 29.4749i | 1.85307i | ||||||||
\(254\) | −2.48783 | + | 4.94424i | −0.156101 | + | 0.310229i | ||||
\(255\) | 0.264679 | 0.0165748 | ||||||||
\(256\) | −13.3137 | − | 8.87385i | −0.832107 | − | 0.554615i | ||||
\(257\) | 19.3779 | 1.20876 | 0.604381 | − | 0.796695i | \(-0.293420\pi\) | ||||
0.604381 | + | 0.796695i | \(0.293420\pi\) | |||||||
\(258\) | 0.548640 | − | 1.09035i | 0.0341569 | − | 0.0678823i | ||||
\(259\) | 2.96951i | 0.184516i | ||||||||
\(260\) | −0.683121 | − | 0.920529i | −0.0423653 | − | 0.0570888i | ||||
\(261\) | 4.54952i | 0.281608i | ||||||||
\(262\) | 12.8818 | + | 6.48185i | 0.795842 | + | 0.400450i | ||||
\(263\) | 17.5096 | 1.07969 | 0.539845 | − | 0.841765i | \(-0.318483\pi\) | ||||
0.539845 | + | 0.841765i | \(0.318483\pi\) | |||||||
\(264\) | 7.35375 | − | 1.27926i | 0.452592 | − | 0.0787329i | ||||
\(265\) | 0.317883 | 0.0195274 | ||||||||
\(266\) | 7.72612 | + | 3.88761i | 0.473719 | + | 0.238365i | ||||
\(267\) | 2.70900i | 0.165788i | ||||||||
\(268\) | 6.93484 | − | 5.14631i | 0.423613 | − | 0.314361i | ||||
\(269\) | 0.661029i | 0.0403037i | 0.999797 | + | 0.0201518i | \(0.00641496\pi\) | ||||
−0.999797 | + | 0.0201518i | \(0.993585\pi\) | |||||||
\(270\) | −1.53463 | + | 3.04988i | −0.0933947 | + | 0.185610i | ||||
\(271\) | 10.5722 | 0.642217 | 0.321108 | − | 0.947042i | \(-0.395945\pi\) | ||||
0.321108 | + | 0.947042i | \(0.395945\pi\) | |||||||
\(272\) | −0.740553 | + | 2.44633i | −0.0449026 | + | 0.148331i | ||||
\(273\) | 0.237409 | 0.0143686 | ||||||||
\(274\) | 2.23256 | − | 4.43692i | 0.134874 | − | 0.268044i | ||||
\(275\) | − | 6.37109i | − | 0.384191i | ||||||
\(276\) | −3.07772 | + | 2.28396i | −0.185257 | + | 0.137478i | ||||
\(277\) | − | 15.0211i | − | 0.902530i | −0.892390 | − | 0.451265i | \(-0.850973\pi\) | ||
0.892390 | − | 0.451265i | \(-0.149027\pi\) | |||||||
\(278\) | 2.37251 | + | 1.19379i | 0.142294 | + | 0.0715990i | ||||
\(279\) | −11.5504 | −0.691507 | ||||||||
\(280\) | −0.484753 | − | 2.78658i | −0.0289695 | − | 0.166530i | ||||
\(281\) | −1.97567 | −0.117858 | −0.0589292 | − | 0.998262i | \(-0.518769\pi\) | ||||
−0.0589292 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(282\) | −4.42419 | − | 2.22616i | −0.263457 | − | 0.132566i | ||||
\(283\) | − | 19.0669i | − | 1.13341i | −0.823921 | − | 0.566705i | \(-0.808218\pi\) | ||
0.823921 | − | 0.566705i | \(-0.191782\pi\) | |||||||
\(284\) | −15.7227 | − | 21.1869i | −0.932970 | − | 1.25721i | ||||
\(285\) | 2.53325i | 0.150057i | ||||||||
\(286\) | −2.32121 | + | 4.61310i | −0.137256 | + | 0.272778i | ||||
\(287\) | −8.11582 | −0.479061 | ||||||||
\(288\) | −11.5959 | − | 11.0243i | −0.683293 | − | 0.649615i | ||||
\(289\) | −16.5917 | −0.975982 | ||||||||
\(290\) | 1.02247 | − | 2.03202i | 0.0600412 | − | 0.119324i | ||||
\(291\) | 7.18905i | 0.421430i | ||||||||
\(292\) | −18.1064 | − | 24.3990i | −1.05960 | − | 1.42785i | ||||
\(293\) | 28.7640i | 1.68041i | 0.542270 | + | 0.840204i | \(0.317565\pi\) | ||||
−0.542270 | + | 0.840204i | \(0.682435\pi\) | |||||||
\(294\) | 0.523276 | + | 0.263301i | 0.0305181 | + | 0.0153560i | ||||
\(295\) | 6.37887 | 0.371392 | ||||||||
\(296\) | −1.43948 | − | 8.27476i | −0.0836678 | − | 0.480961i | ||||
\(297\) | 15.3812 | 0.892506 | ||||||||
\(298\) | −11.3685 | − | 5.72040i | −0.658562 | − | 0.331374i | ||||
\(299\) | − | 2.65162i | − | 0.153347i | ||||||
\(300\) | 0.665257 | − | 0.493684i | 0.0384086 | − | 0.0285029i | ||||
\(301\) | 2.08370i | 0.120102i | ||||||||
\(302\) | 6.91170 | − | 13.7361i | 0.397724 | − | 0.790423i | ||||
\(303\) | −5.53459 | −0.317954 | ||||||||
\(304\) | −23.4140 | − | 7.08787i | −1.34288 | − | 0.406517i | ||||
\(305\) | 8.44700 | 0.483674 | ||||||||
\(306\) | −1.14886 | + | 2.28321i | −0.0656761 | + | 0.130523i | ||||
\(307\) | − | 12.5142i | − | 0.714222i | −0.934062 | − | 0.357111i | \(-0.883762\pi\) | ||
0.934062 | − | 0.357111i | \(-0.116238\pi\) | |||||||
\(308\) | −10.2324 | + | 7.59344i | −0.583047 | + | 0.432677i | ||||
\(309\) | 6.13785i | 0.349170i | ||||||||
\(310\) | 5.15894 | + | 2.59587i | 0.293008 | + | 0.147435i | ||||
\(311\) | 18.0617 | 1.02418 | 0.512092 | − | 0.858931i | \(-0.328871\pi\) | ||||
0.512092 | + | 0.858931i | \(0.328871\pi\) | |||||||
\(312\) | −0.661558 | + | 0.115085i | −0.0374533 | + | 0.00651538i | ||||
\(313\) | −15.7853 | −0.892238 | −0.446119 | − | 0.894974i | \(-0.647194\pi\) | ||||
−0.446119 | + | 0.894974i | \(0.647194\pi\) | |||||||
\(314\) | −14.3245 | − | 7.20779i | −0.808380 | − | 0.406759i | ||||
\(315\) | − | 2.82843i | − | 0.159364i | ||||||
\(316\) | 4.53861 | + | 6.11594i | 0.255317 | + | 0.344049i | ||||
\(317\) | 28.0844i | 1.57738i | 0.614793 | + | 0.788688i | \(0.289239\pi\) | ||||
−0.614793 | + | 0.788688i | \(0.710761\pi\) | |||||||
\(318\) | 0.0836990 | − | 0.166341i | 0.00469361 | − | 0.00932793i | ||||
\(319\) | −10.2479 | −0.573771 | ||||||||
\(320\) | 2.70160 | + | 7.53003i | 0.151024 | + | 0.420941i | ||||
\(321\) | 1.06516 | 0.0594516 | ||||||||
\(322\) | 2.94082 | − | 5.84449i | 0.163885 | − | 0.325700i | ||||
\(323\) | 3.90795i | 0.217444i | ||||||||
\(324\) | −8.92140 | − | 12.0219i | −0.495634 | − | 0.667884i | ||||
\(325\) | 0.573155i | 0.0317929i | ||||||||
\(326\) | 30.4021 | + | 15.2977i | 1.68382 | + | 0.847258i | ||||
\(327\) | 5.65162 | 0.312535 | ||||||||
\(328\) | 22.6154 | − | 3.93416i | 1.24872 | − | 0.217228i | ||||
\(329\) | 8.45479 | 0.466127 | ||||||||
\(330\) | −3.33384 | − | 1.67751i | −0.183522 | − | 0.0923441i | ||||
\(331\) | 15.8852i | 0.873132i | 0.899672 | + | 0.436566i | \(0.143805\pi\) | ||||
−0.899672 | + | 0.436566i | \(0.856195\pi\) | |||||||
\(332\) | −19.9543 | + | 14.8080i | −1.09514 | + | 0.812695i | ||||
\(333\) | − | 8.39903i | − | 0.460264i | ||||||
\(334\) | −8.72944 | + | 17.3486i | −0.477654 | + | 0.949274i | ||||
\(335\) | −4.31788 | −0.235911 | ||||||||
\(336\) | −1.58579 | − | 0.480049i | −0.0865117 | − | 0.0261888i | ||||
\(337\) | −8.44311 | −0.459925 | −0.229963 | − | 0.973199i | \(-0.573860\pi\) | ||||
−0.229963 | + | 0.973199i | \(0.573860\pi\) | |||||||
\(338\) | −8.05483 | + | 16.0079i | −0.438125 | + | 0.870716i | ||||
\(339\) | − | 0.758031i | − | 0.0411706i | ||||||
\(340\) | 1.02627 | − | 0.761588i | 0.0556571 | − | 0.0413029i | ||||
\(341\) | − | 26.0176i | − | 1.40893i | ||||||
\(342\) | −21.8528 | − | 10.9958i | −1.18166 | − | 0.594586i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.01008 | − | 5.80639i | −0.0544598 | − | 0.313060i | ||||
\(345\) | 1.91630 | 0.103170 | ||||||||
\(346\) | −24.2110 | − | 12.1824i | −1.30159 | − | 0.654931i | ||||
\(347\) | 2.89656i | 0.155495i | 0.996973 | + | 0.0777477i | \(0.0247729\pi\) | ||||
−0.996973 | + | 0.0777477i | \(0.975227\pi\) | |||||||
\(348\) | −0.794090 | − | 1.07006i | −0.0425677 | − | 0.0573615i | ||||
\(349\) | 4.86671i | 0.260509i | 0.991481 | + | 0.130254i | \(0.0415794\pi\) | ||||
−0.991481 | + | 0.130254i | \(0.958421\pi\) | |||||||
\(350\) | −0.635665 | + | 1.26330i | −0.0339777 | + | 0.0675263i | ||||
\(351\) | −1.38372 | −0.0738575 | ||||||||
\(352\) | 24.8325 | − | 26.1199i | 1.32358 | − | 1.39220i | ||||
\(353\) | −3.46742 | −0.184552 | −0.0922760 | − | 0.995733i | \(-0.529414\pi\) | ||||
−0.0922760 | + | 0.995733i | \(0.529414\pi\) | |||||||
\(354\) | 1.67956 | − | 3.33791i | 0.0892678 | − | 0.177408i | ||||
\(355\) | 13.1917i | 0.700144i | ||||||||
\(356\) | 7.79489 | + | 10.5039i | 0.413128 | + | 0.556705i | ||||
\(357\) | 0.264679i | 0.0140083i | ||||||||
\(358\) | −10.2089 | − | 5.13690i | −0.539558 | − | 0.271494i | ||||
\(359\) | 33.8444 | 1.78624 | 0.893120 | − | 0.449819i | \(-0.148511\pi\) | ||||
0.893120 | + | 0.449819i | \(0.148511\pi\) | |||||||
\(360\) | 1.37109 | + | 7.88163i | 0.0722627 | + | 0.415398i | ||||
\(361\) | −18.4032 | −0.968590 | ||||||||
\(362\) | 23.2754 | + | 11.7117i | 1.22333 | + | 0.615552i | ||||
\(363\) | 12.2569i | 0.643320i | ||||||||
\(364\) | 0.920529 | − | 0.683121i | 0.0482488 | − | 0.0358052i | ||||
\(365\) | 15.1917i | 0.795172i | ||||||||
\(366\) | 2.22411 | − | 4.42012i | 0.116256 | − | 0.231043i | ||||
\(367\) | −0.762206 | −0.0397868 | −0.0198934 | − | 0.999802i | \(-0.506333\pi\) | ||||
−0.0198934 | + | 0.999802i | \(0.506333\pi\) | |||||||
\(368\) | −5.36168 | + | 17.7117i | −0.279497 | + | 0.923285i | ||||
\(369\) | 22.9550 | 1.19499 | ||||||||
\(370\) | −1.88761 | + | 3.75138i | −0.0981322 | + | 0.195025i | ||||
\(371\) | 0.317883i | 0.0165037i | ||||||||
\(372\) | 2.71671 | − | 2.01606i | 0.140855 | − | 0.104528i | ||||
\(373\) | − | 19.2621i | − | 0.997355i | −0.866788 | − | 0.498678i | \(-0.833819\pi\) | ||
0.866788 | − | 0.498678i | \(-0.166181\pi\) | |||||||
\(374\) | −5.14298 | − | 2.58784i | −0.265937 | − | 0.133814i | ||||
\(375\) | −0.414214 | −0.0213899 | ||||||||
\(376\) | −23.5599 | + | 4.09848i | −1.21501 | + | 0.211363i | ||||
\(377\) | 0.921918 | 0.0474812 | ||||||||
\(378\) | −3.04988 | − | 1.53463i | −0.156869 | − | 0.0789329i | ||||
\(379\) | − | 0.317883i | − | 0.0163286i | −0.999967 | − | 0.00816428i | \(-0.997401\pi\) | ||
0.999967 | − | 0.00816428i | \(-0.00259880\pi\) | |||||||
\(380\) | 7.28919 | + | 9.82245i | 0.373928 | + | 0.503881i | ||||
\(381\) | − | 1.62113i | − | 0.0830529i | ||||||
\(382\) | −10.8610 | + | 21.5848i | −0.555696 | + | 1.10437i | ||||
\(383\) | −34.9835 | −1.78757 | −0.893787 | − | 0.448492i | \(-0.851961\pi\) | ||||
−0.893787 | + | 0.448492i | \(0.851961\pi\) | |||||||
\(384\) | 4.65162 | + | 0.568980i | 0.237377 | + | 0.0290357i | ||||
\(385\) | 6.37109 | 0.324701 | ||||||||
\(386\) | −13.0931 | + | 26.0208i | −0.666422 | + | 1.32443i | ||||
\(387\) | − | 5.89359i | − | 0.299588i | ||||||
\(388\) | 20.6858 | + | 27.8749i | 1.05016 | + | 1.41513i | ||||
\(389\) | − | 25.9718i | − | 1.31682i | −0.752658 | − | 0.658411i | \(-0.771229\pi\) | ||
0.752658 | − | 0.658411i | \(-0.228771\pi\) | |||||||
\(390\) | 0.299919 | + | 0.150912i | 0.0151870 | + | 0.00764175i | ||||
\(391\) | 2.95620 | 0.149502 | ||||||||
\(392\) | 2.78658 | − | 0.484753i | 0.140743 | − | 0.0244837i | ||||
\(393\) | −4.22372 | −0.213059 | ||||||||
\(394\) | 19.0332 | + | 9.57707i | 0.958877 | + | 0.482486i | ||||
\(395\) | − | 3.80801i | − | 0.191602i | ||||||
\(396\) | 28.9417 | − | 21.4775i | 1.45437 | − | 1.07928i | ||||
\(397\) | − | 24.9314i | − | 1.25127i | −0.780116 | − | 0.625634i | \(-0.784840\pi\) | ||
0.780116 | − | 0.625634i | \(-0.215160\pi\) | |||||||
\(398\) | 8.51995 | − | 16.9323i | 0.427067 | − | 0.848739i | ||||
\(399\) | −2.53325 | −0.126821 | ||||||||
\(400\) | 1.15894 | − | 3.82843i | 0.0579471 | − | 0.191421i | ||||
\(401\) | −7.53905 | −0.376482 | −0.188241 | − | 0.982123i | \(-0.560279\pi\) | ||||
−0.188241 | + | 0.982123i | \(0.560279\pi\) | |||||||
\(402\) | −1.13690 | + | 2.25945i | −0.0567036 | + | 0.112691i | ||||
\(403\) | 2.34059i | 0.116593i | ||||||||
\(404\) | −21.4598 | + | 15.9252i | −1.06767 | + | 0.792311i | ||||
\(405\) | 7.48528i | 0.371947i | ||||||||
\(406\) | 2.03202 | + | 1.02247i | 0.100847 | + | 0.0507441i | ||||
\(407\) | 18.9190 | 0.937779 | ||||||||
\(408\) | −0.128304 | − | 0.737548i | −0.00635198 | − | 0.0365141i | ||||
\(409\) | 16.7064 | 0.826081 | 0.413040 | − | 0.910713i | \(-0.364467\pi\) | ||||
0.413040 | + | 0.910713i | \(0.364467\pi\) | |||||||
\(410\) | −10.2527 | − | 5.15894i | −0.506346 | − | 0.254782i | ||||
\(411\) | 1.45479i | 0.0717593i | ||||||||
\(412\) | 17.6611 | + | 23.7989i | 0.870099 | + | 1.17249i | ||||
\(413\) | 6.37887i | 0.313884i | ||||||||
\(414\) | −8.31788 | + | 16.5307i | −0.408802 | + | 0.812440i | ||||
\(415\) | 12.4243 | 0.609885 | ||||||||
\(416\) | −2.23398 | + | 2.34980i | −0.109530 | + | 0.115208i | ||||
\(417\) | −0.777902 | −0.0380940 | ||||||||
\(418\) | 24.7683 | − | 49.2238i | 1.21146 | − | 2.40761i | ||||
\(419\) | − | 1.40320i | − | 0.0685510i | −0.999412 | − | 0.0342755i | \(-0.989088\pi\) | ||
0.999412 | − | 0.0342755i | \(-0.0109124\pi\) | |||||||
\(420\) | 0.493684 | + | 0.665257i | 0.0240893 | + | 0.0324612i | ||||
\(421\) | 12.5538i | 0.611835i | 0.952058 | + | 0.305917i | \(0.0989631\pi\) | ||||
−0.952058 | + | 0.305917i | \(0.901037\pi\) | |||||||
\(422\) | 7.00205 | + | 3.52328i | 0.340854 | + | 0.171510i | ||||
\(423\) | −23.9137 | −1.16273 | ||||||||
\(424\) | −0.154095 | − | 0.885806i | −0.00748351 | − | 0.0430186i | ||||
\(425\) | −0.638991 | −0.0309956 | ||||||||
\(426\) | 6.90292 | + | 3.47340i | 0.334448 | + | 0.168287i | ||||
\(427\) | 8.44700i | 0.408779i | ||||||||
\(428\) | 4.13007 | − | 3.06491i | 0.199634 | − | 0.148148i | ||||
\(429\) | − | 1.51255i | − | 0.0730267i | ||||||
\(430\) | −1.32453 | + | 2.63234i | −0.0638747 | + | 0.126943i | ||||
\(431\) | −2.28283 | −0.109960 | −0.0549800 | − | 0.998487i | \(-0.517510\pi\) | ||||
−0.0549800 | + | 0.998487i | \(0.517510\pi\) | |||||||
\(432\) | 9.24264 | + | 2.79793i | 0.444687 | + | 0.134616i | ||||
\(433\) | 20.0357 | 0.962856 | 0.481428 | − | 0.876486i | \(-0.340118\pi\) | ||||
0.481428 | + | 0.876486i | \(0.340118\pi\) | |||||||
\(434\) | −2.59587 | + | 5.15894i | −0.124606 | + | 0.247637i | ||||
\(435\) | 0.666261i | 0.0319448i | ||||||||
\(436\) | 21.9136 | − | 16.2620i | 1.04947 | − | 0.778808i | ||||
\(437\) | 28.2940i | 1.35348i | ||||||||
\(438\) | 7.94948 | + | 4.00000i | 0.379841 | + | 0.191127i | ||||
\(439\) | −7.05681 | −0.336803 | −0.168402 | − | 0.985718i | \(-0.553861\pi\) | ||||
−0.168402 | + | 0.985718i | \(0.553861\pi\) | |||||||
\(440\) | −17.7535 | + | 3.08840i | −0.846366 | + | 0.147234i | ||||
\(441\) | 2.82843 | 0.134687 | ||||||||
\(442\) | 0.462673 | + | 0.232807i | 0.0220071 | + | 0.0110735i | ||||
\(443\) | − | 6.36075i | − | 0.302208i | −0.988518 | − | 0.151104i | \(-0.951717\pi\) | ||
0.988518 | − | 0.151104i | \(-0.0482829\pi\) | |||||||
\(444\) | 1.46600 | + | 1.97549i | 0.0695732 | + | 0.0937524i | ||||
\(445\) | − | 6.54011i | − | 0.310031i | ||||||
\(446\) | −11.4453 | + | 22.7460i | −0.541951 | + | 1.07706i | ||||
\(447\) | 3.72754 | 0.176306 | ||||||||
\(448\) | −7.53003 | + | 2.70160i | −0.355760 | + | 0.127639i | ||||
\(449\) | −1.29907 | −0.0613069 | −0.0306534 | − | 0.999530i | \(-0.509759\pi\) | ||||
−0.0306534 | + | 0.999530i | \(0.509759\pi\) | |||||||
\(450\) | 1.79793 | − | 3.57316i | 0.0847554 | − | 0.168440i | ||||
\(451\) | 51.7066i | 2.43477i | ||||||||
\(452\) | −2.18116 | − | 2.93919i | −0.102593 | − | 0.138248i | ||||
\(453\) | 4.50382i | 0.211608i | ||||||||
\(454\) | −13.0792 | − | 6.58118i | −0.613839 | − | 0.308870i | ||||
\(455\) | −0.573155 | −0.0268699 | ||||||||
\(456\) | 7.05911 | − | 1.22800i | 0.330573 | − | 0.0575065i | ||||
\(457\) | −9.46809 | −0.442899 | −0.221449 | − | 0.975172i | \(-0.571079\pi\) | ||||
−0.221449 | + | 0.975172i | \(0.571079\pi\) | |||||||
\(458\) | 23.0034 | + | 11.5748i | 1.07488 | + | 0.540854i | ||||
\(459\) | − | 1.54266i | − | 0.0720052i | ||||||
\(460\) | 7.43027 | − | 5.51397i | 0.346438 | − | 0.257090i | ||||
\(461\) | 41.7160i | 1.94291i | 0.237230 | + | 0.971454i | \(0.423761\pi\) | ||||
−0.237230 | + | 0.971454i | \(0.576239\pi\) | |||||||
\(462\) | 1.67751 | − | 3.33384i | 0.0780450 | − | 0.155104i | ||||
\(463\) | −20.6108 | −0.957865 | −0.478932 | − | 0.877852i | \(-0.658976\pi\) | ||||
−0.478932 | + | 0.877852i | \(0.658976\pi\) | |||||||
\(464\) | −6.15801 | − | 1.86415i | −0.285879 | − | 0.0865412i | ||||
\(465\) | −1.69152 | −0.0784425 | ||||||||
\(466\) | 13.8729 | − | 27.5706i | 0.642650 | − | 1.27718i | ||||
\(467\) | − | 4.26373i | − | 0.197302i | −0.995122 | − | 0.0986509i | \(-0.968547\pi\) | ||
0.995122 | − | 0.0986509i | \(-0.0314527\pi\) | |||||||
\(468\) | −2.60365 | + | 1.93216i | −0.120354 | + | 0.0893140i | ||||
\(469\) | − | 4.31788i | − | 0.199381i | ||||||
\(470\) | 10.6809 | + | 5.37441i | 0.492675 | + | 0.247903i | ||||
\(471\) | 4.69676 | 0.216415 | ||||||||
\(472\) | −3.09218 | − | 17.7752i | −0.142329 | − | 0.818171i | ||||
\(473\) | 13.2754 | 0.610405 | ||||||||
\(474\) | −1.99264 | − | 1.00265i | −0.0915251 | − | 0.0460534i | ||||
\(475\) | − | 6.11582i | − | 0.280613i | ||||||
\(476\) | 0.761588 | + | 1.02627i | 0.0349073 | + | 0.0470388i | ||||
\(477\) | − | 0.899110i | − | 0.0411674i | ||||||
\(478\) | −12.1999 | + | 24.2458i | −0.558012 | + | 1.10898i | ||||
\(479\) | −28.6080 | −1.30713 | −0.653565 | − | 0.756870i | \(-0.726728\pi\) | ||||
−0.653565 | + | 0.756870i | \(0.726728\pi\) | |||||||
\(480\) | −1.69818 | − | 1.61448i | −0.0775107 | − | 0.0736904i | ||||
\(481\) | −1.70199 | −0.0776040 | ||||||||
\(482\) | −6.69792 | + | 13.3112i | −0.305082 | + | 0.606310i | ||||
\(483\) | 1.91630i | 0.0871947i | ||||||||
\(484\) | 35.2680 | + | 47.5249i | 1.60309 | + | 2.16022i | ||||
\(485\) | − | 17.3559i | − | 0.788091i | ||||||
\(486\) | 13.0665 | + | 6.57478i | 0.592709 | + | 0.298238i | ||||
\(487\) | −21.2949 | −0.964964 | −0.482482 | − | 0.875906i | \(-0.660265\pi\) | ||||
−0.482482 | + | 0.875906i | \(0.660265\pi\) | |||||||
\(488\) | −4.09471 | − | 23.5382i | −0.185359 | − | 1.06553i | ||||
\(489\) | −9.96829 | −0.450782 | ||||||||
\(490\) | −1.26330 | − | 0.635665i | −0.0570701 | − | 0.0287164i | ||||
\(491\) | − | 20.9018i | − | 0.943285i | −0.881790 | − | 0.471642i | \(-0.843661\pi\) | ||
0.881790 | − | 0.471642i | \(-0.156339\pi\) | |||||||
\(492\) | −5.39911 | + | 4.00665i | −0.243410 | + | 0.180634i | ||||
\(493\) | 1.02781i | 0.0462905i | ||||||||
\(494\) | −2.22820 | + | 4.42826i | −0.100252 | + | 0.199237i | ||||
\(495\) | −18.0202 | −0.809946 | ||||||||
\(496\) | 4.73277 | − | 15.6341i | 0.212508 | − | 0.701994i | ||||
\(497\) | −13.1917 | −0.591730 | ||||||||
\(498\) | 3.27133 | − | 6.50134i | 0.146592 | − | 0.291332i | ||||
\(499\) | − | 37.2449i | − | 1.66731i | −0.552284 | − | 0.833656i | \(-0.686244\pi\) | ||
0.552284 | − | 0.833656i | \(-0.313756\pi\) | |||||||
\(500\) | −1.60607 | + | 1.19186i | −0.0718258 | + | 0.0533016i | ||||
\(501\) | − | 5.68830i | − | 0.254134i | ||||||
\(502\) | −8.30182 | − | 4.17729i | −0.370529 | − | 0.186442i | ||||
\(503\) | −2.27182 | −0.101295 | −0.0506477 | − | 0.998717i | \(-0.516129\pi\) | ||||
−0.0506477 | + | 0.998717i | \(0.516129\pi\) | |||||||
\(504\) | −7.88163 | + | 1.37109i | −0.351076 | + | 0.0610731i | ||||
\(505\) | 13.3617 | 0.594587 | ||||||||
\(506\) | −37.2357 | − | 18.7362i | −1.65533 | − | 0.832926i | ||||
\(507\) | − | 5.24870i | − | 0.233103i | ||||||
\(508\) | −4.66464 | − | 6.28577i | −0.206960 | − | 0.278886i | ||||
\(509\) | 11.1716i | 0.495171i | 0.968866 | + | 0.247586i | \(0.0796372\pi\) | ||||
−0.968866 | + | 0.247586i | \(0.920363\pi\) | |||||||
\(510\) | −0.168247 | + | 0.334369i | −0.00745011 | + | 0.0148061i | ||||
\(511\) | −15.1917 | −0.672043 | ||||||||
\(512\) | 19.6734 | − | 11.1784i | 0.869450 | − | 0.494021i | ||||
\(513\) | 14.7649 | 0.651886 | ||||||||
\(514\) | −12.3179 | + | 24.4802i | −0.543319 | + | 1.07977i | ||||
\(515\) | − | 14.8181i | − | 0.652963i | ||||||
\(516\) | 1.02869 | + | 1.38620i | 0.0452855 | + | 0.0610239i | ||||
\(517\) | − | 53.8662i | − | 2.36903i | ||||||
\(518\) | −3.75138 | − | 1.88761i | −0.164826 | − | 0.0829369i | ||||
\(519\) | 7.93834 | 0.348454 | ||||||||
\(520\) | 1.59714 | − | 0.277839i | 0.0700393 | − | 0.0121840i | ||||
\(521\) | −26.9593 | −1.18111 | −0.590554 | − | 0.806998i | \(-0.701091\pi\) | ||||
−0.590554 | + | 0.806998i | \(0.701091\pi\) | |||||||
\(522\) | −5.74741 | − | 2.89197i | −0.251557 | − | 0.126578i | ||||
\(523\) | 16.5339i | 0.722979i | 0.932376 | + | 0.361489i | \(0.117732\pi\) | ||||
−0.932376 | + | 0.361489i | \(0.882268\pi\) | |||||||
\(524\) | −16.3771 | + | 12.1533i | −0.715436 | + | 0.530921i | ||||
\(525\) | − | 0.414214i | − | 0.0180778i | ||||||
\(526\) | −11.1303 | + | 22.1199i | −0.485302 | + | 0.964474i | ||||
\(527\) | −2.60945 | −0.113669 | ||||||||
\(528\) | −3.05844 | + | 10.1032i | −0.133101 | + | 0.439685i | ||||
\(529\) | −1.59680 | −0.0694259 | ||||||||
\(530\) | −0.202067 | + | 0.401582i | −0.00877724 | + | 0.0174436i | ||||
\(531\) | − | 18.0422i | − | 0.782964i | ||||||
\(532\) | −9.82245 | + | 7.28919i | −0.425857 | + | 0.316027i | ||||
\(533\) | − | 4.65162i | − | 0.201484i | ||||||
\(534\) | −3.42228 | − | 1.72202i | −0.148097 | − | 0.0745190i | ||||
\(535\) | −2.57153 | −0.111177 | ||||||||
\(536\) | 2.09311 | + | 12.0321i | 0.0904084 | + | 0.519708i | ||||
\(537\) | 3.34732 | 0.144448 | ||||||||
\(538\) | −0.835079 | − | 0.420193i | −0.0360028 | − | 0.0181158i | ||||
\(539\) | 6.37109i | 0.274422i | ||||||||
\(540\) | −2.87740 | − | 3.87740i | −0.123824 | − | 0.166857i | ||||
\(541\) | − | 19.9011i | − | 0.855616i | −0.903870 | − | 0.427808i | \(-0.859286\pi\) | ||
0.903870 | − | 0.427808i | \(-0.140714\pi\) | |||||||
\(542\) | −6.72040 | + | 13.3559i | −0.288666 | + | 0.573685i | ||||
\(543\) | −7.63159 | −0.327503 | ||||||||
\(544\) | −2.61971 | − | 2.49059i | −0.112319 | − | 0.106783i | ||||
\(545\) | −13.6442 | −0.584454 | ||||||||
\(546\) | −0.150912 | + | 0.299919i | −0.00645846 | + | 0.0128353i | ||||
\(547\) | 5.29610i | 0.226445i | 0.993570 | + | 0.113223i | \(0.0361173\pi\) | ||||
−0.993570 | + | 0.113223i | \(0.963883\pi\) | |||||||
\(548\) | 4.18601 | + | 5.64080i | 0.178817 | + | 0.240963i | ||||
\(549\) | − | 23.8917i | − | 1.01967i | ||||||
\(550\) | 8.04860 | + | 4.04988i | 0.343194 | + | 0.172687i | ||||
\(551\) | −9.83727 | −0.419082 | ||||||||
\(552\) | −0.928932 | − | 5.33992i | −0.0395380 | − | 0.227282i | ||||
\(553\) | 3.80801 | 0.161933 | ||||||||
\(554\) | 18.9762 | + | 9.54838i | 0.806220 | + | 0.405672i | ||||
\(555\) | − | 1.23001i | − | 0.0522110i | ||||||
\(556\) | −3.01624 | + | 2.23834i | −0.127917 | + | 0.0949267i | ||||
\(557\) | − | 0.114759i | − | 0.00486248i | −0.999997 | − | 0.00243124i | \(-0.999226\pi\) | ||
0.999997 | − | 0.00243124i | \(-0.000773889\pi\) | |||||||
\(558\) | 7.34222 | − | 14.5917i | 0.310821 | − | 0.617716i | ||||
\(559\) | −1.19428 | −0.0505128 | ||||||||
\(560\) | 3.82843 | + | 1.15894i | 0.161781 | + | 0.0489742i | ||||
\(561\) | 1.68629 | 0.0711953 | ||||||||
\(562\) | 1.25586 | − | 2.49586i | 0.0529754 | − | 0.105282i | ||||
\(563\) | 6.67149i | 0.281170i | 0.990069 | + | 0.140585i | \(0.0448983\pi\) | ||||
−0.990069 | + | 0.140585i | \(0.955102\pi\) | |||||||
\(564\) | 5.62461 | − | 4.17400i | 0.236839 | − | 0.175757i | ||||
\(565\) | 1.83005i | 0.0769908i | ||||||||
\(566\) | 24.0872 | + | 12.1202i | 1.01246 | + | 0.509448i | ||||
\(567\) | −7.48528 | −0.314352 | ||||||||
\(568\) | 36.7598 | − | 6.39473i | 1.54241 | − | 0.268317i | ||||
\(569\) | 22.9536 | 0.962267 | 0.481134 | − | 0.876647i | \(-0.340225\pi\) | ||||
0.481134 | + | 0.876647i | \(0.340225\pi\) | |||||||
\(570\) | −3.20026 | − | 1.61030i | −0.134044 | − | 0.0674481i | ||||
\(571\) | − | 18.4294i | − | 0.771246i | −0.922656 | − | 0.385623i | \(-0.873986\pi\) | ||
0.922656 | − | 0.385623i | \(-0.126014\pi\) | |||||||
\(572\) | −4.35222 | − | 5.86477i | −0.181975 | − | 0.245218i | ||||
\(573\) | − | 7.07725i | − | 0.295656i | ||||||
\(574\) | 5.15894 | − | 10.2527i | 0.215330 | − | 0.427940i | ||||
\(575\) | −4.62636 | −0.192933 | ||||||||
\(576\) | 21.2981 | − | 7.64129i | 0.887422 | − | 0.318387i | ||||
\(577\) | 10.7201 | 0.446285 | 0.223143 | − | 0.974786i | \(-0.428368\pi\) | ||||
0.223143 | + | 0.974786i | \(0.428368\pi\) | |||||||
\(578\) | 10.5468 | − | 20.9603i | 0.438687 | − | 0.871834i | ||||
\(579\) | − | 8.53176i | − | 0.354568i | ||||||
\(580\) | 1.91710 | + | 2.58336i | 0.0796033 | + | 0.107268i | ||||
\(581\) | 12.4243i | 0.515447i | ||||||||
\(582\) | −9.08194 | − | 4.56983i | −0.376458 | − | 0.189426i | ||||
\(583\) | 2.02526 | 0.0838778 | ||||||||
\(584\) | 42.3329 | − | 7.36423i | 1.75175 | − | 0.304734i | ||||
\(585\) | 1.62113 | 0.0670254 | ||||||||
\(586\) | −36.3375 | − | 18.2842i | −1.50109 | − | 0.755315i | ||||
\(587\) | 33.8444i | 1.39691i | 0.715655 | + | 0.698454i | \(0.246128\pi\) | ||||
−0.715655 | + | 0.698454i | \(0.753872\pi\) | |||||||
\(588\) | −0.665257 | + | 0.493684i | −0.0274347 | + | 0.0203592i | ||||
\(589\) | − | 24.9752i | − | 1.02908i | ||||||
\(590\) | −4.05483 | + | 8.05844i | −0.166935 | + | 0.331761i | ||||
\(591\) | −6.24063 | −0.256705 | ||||||||
\(592\) | 11.3685 | + | 3.44148i | 0.467244 | + | 0.141444i | ||||
\(593\) | −2.26336 | −0.0929452 | −0.0464726 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464726 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(594\) | −9.77727 | + | 19.4310i | −0.401166 | + | 0.797265i | ||||
\(595\) | − | 0.638991i | − | 0.0261961i | ||||||
\(596\) | 14.4532 | − | 10.7256i | 0.592025 | − | 0.439339i | ||||
\(597\) | 5.55179i | 0.227220i | ||||||||
\(598\) | 3.34980 | + | 1.68554i | 0.136983 | + | 0.0689270i | ||||
\(599\) | −26.3290 | −1.07577 | −0.537887 | − | 0.843017i | \(-0.680777\pi\) | ||||
−0.537887 | + | 0.843017i | \(0.680777\pi\) | |||||||
\(600\) | 0.200791 | + | 1.15424i | 0.00819727 | + | 0.0471216i | ||||
\(601\) | −1.06516 | −0.0434489 | −0.0217245 | − | 0.999764i | \(-0.506916\pi\) | ||||
−0.0217245 | + | 0.999764i | \(0.506916\pi\) | |||||||
\(602\) | −2.63234 | − | 1.32453i | −0.107286 | − | 0.0539840i | ||||
\(603\) | 12.2128i | 0.497344i | ||||||||
\(604\) | 12.9593 | + | 17.4631i | 0.527306 | + | 0.710564i | ||||
\(605\) | − | 29.5908i | − | 1.20304i | ||||||
\(606\) | 3.51815 | − | 6.99185i | 0.142915 | − | 0.284025i | ||||
\(607\) | −6.42494 | −0.260780 | −0.130390 | − | 0.991463i | \(-0.541623\pi\) | ||||
−0.130390 | + | 0.991463i | \(0.541623\pi\) | |||||||
\(608\) | 23.8376 | − | 25.0734i | 0.966741 | − | 1.01686i | ||||
\(609\) | −0.666261 | −0.0269983 | ||||||||
\(610\) | −5.36947 | + | 10.6711i | −0.217403 | + | 0.432061i | ||||
\(611\) | 4.84591i | 0.196044i | ||||||||
\(612\) | −2.15409 | − | 2.90272i | −0.0870741 | − | 0.117335i | ||||
\(613\) | 5.46419i | 0.220697i | 0.993893 | + | 0.110348i | \(0.0351966\pi\) | ||||
−0.993893 | + | 0.110348i | \(0.964803\pi\) | |||||||
\(614\) | 15.8092 | + | 7.95482i | 0.638006 | + | 0.321031i | ||||
\(615\) | 3.36168 | 0.135556 | ||||||||
\(616\) | −3.08840 | − | 17.7535i | −0.124435 | − | 0.715310i | ||||
\(617\) | −34.9485 | −1.40698 | −0.703488 | − | 0.710707i | \(-0.748375\pi\) | ||||
−0.703488 | + | 0.710707i | \(0.748375\pi\) | |||||||
\(618\) | −7.75396 | − | 3.90162i | −0.311910 | − | 0.156946i | ||||
\(619\) | 1.00848i | 0.0405341i | 0.999795 | + | 0.0202671i | \(0.00645165\pi\) | ||||
−0.999795 | + | 0.0202671i | \(0.993548\pi\) | |||||||
\(620\) | −6.55872 | + | 4.86720i | −0.263405 | + | 0.195471i | ||||
\(621\) | − | 11.1690i | − | 0.448197i | ||||||
\(622\) | −11.4812 | + | 22.8173i | −0.460353 | + | 0.914892i | ||||
\(623\) | 6.54011 | 0.262024 | ||||||||
\(624\) | 0.275143 | − | 0.908902i | 0.0110145 | − | 0.0363852i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.0342 | − | 19.9416i | 0.401046 | − | 0.797026i | ||||
\(627\) | 16.1396i | 0.644553i | ||||||||
\(628\) | 18.2112 | − | 13.5145i | 0.726707 | − | 0.539286i | ||||
\(629\) | − | 1.89749i | − | 0.0756578i | ||||||
\(630\) | 3.57316 | + | 1.79793i | 0.142358 | + | 0.0716314i | ||||
\(631\) | −38.7566 | −1.54287 | −0.771437 | − | 0.636306i | \(-0.780462\pi\) | ||||
−0.771437 | + | 0.636306i | \(0.780462\pi\) | |||||||
\(632\) | −10.6113 | + | 1.84594i | −0.422096 | + | 0.0734277i | ||||
\(633\) | −2.29585 | −0.0912517 | ||||||||
\(634\) | −35.4790 | − | 17.8523i | −1.40905 | − | 0.709004i | ||||
\(635\) | 3.91375i | 0.155312i | ||||||||
\(636\) | 0.156934 | + | 0.211474i | 0.00622284 | + | 0.00838550i | ||||
\(637\) | − | 0.573155i | − | 0.0227092i | ||||||
\(638\) | 6.51422 | − | 12.9461i | 0.257900 | − | 0.512543i | ||||
\(639\) | 37.3118 | 1.47603 | ||||||||
\(640\) | −11.2300 | − | 1.37364i | −0.443905 | − | 0.0542979i | ||||
\(641\) | 25.5096 | 1.00757 | 0.503785 | − | 0.863829i | \(-0.331941\pi\) | ||||
0.503785 | + | 0.863829i | \(0.331941\pi\) | |||||||
\(642\) | −0.677088 | + | 1.34562i | −0.0267225 | + | 0.0531075i | ||||
\(643\) | 28.9041i | 1.13987i | 0.821691 | + | 0.569933i | \(0.193031\pi\) | ||||
−0.821691 | + | 0.569933i | \(0.806969\pi\) | |||||||
\(644\) | 5.51397 | + | 7.43027i | 0.217281 | + | 0.292794i | ||||
\(645\) | − | 0.863096i | − | 0.0339844i | ||||||
\(646\) | −4.93692 | − | 2.48415i | −0.194240 | − | 0.0977375i | ||||
\(647\) | −36.9077 | −1.45099 | −0.725496 | − | 0.688226i | \(-0.758390\pi\) | ||||
−0.725496 | + | 0.688226i | \(0.758390\pi\) | |||||||
\(648\) | 20.8583 | − | 3.62851i | 0.819392 | − | 0.142541i | ||||
\(649\) | 40.6404 | 1.59527 | ||||||||
\(650\) | −0.724068 | − | 0.364335i | −0.0284003 | − | 0.0142904i | ||||
\(651\) | − | 1.69152i | − | 0.0662960i | ||||||
\(652\) | −38.6511 | + | 28.6828i | −1.51369 | + | 1.12330i | ||||
\(653\) | 26.8139i | 1.04931i | 0.851315 | + | 0.524655i | \(0.175806\pi\) | ||||
−0.851315 | + | 0.524655i | \(0.824194\pi\) | |||||||
\(654\) | −3.59254 | + | 7.13970i | −0.140479 | + | 0.279184i | ||||
\(655\) | 10.1970 | 0.398428 | ||||||||
\(656\) | −9.40576 | + | 31.0708i | −0.367233 | + | 1.21311i | ||||
\(657\) | 42.9687 | 1.67637 | ||||||||
\(658\) | −5.37441 | + | 10.6809i | −0.209516 | + | 0.416386i | ||||
\(659\) | − | 29.6783i | − | 1.15610i | −0.816000 | − | 0.578052i | \(-0.803813\pi\) | ||
0.816000 | − | 0.578052i | \(-0.196187\pi\) | |||||||
\(660\) | 4.23841 | − | 3.14531i | 0.164980 | − | 0.122431i | ||||
\(661\) | − | 32.6812i | − | 1.27115i | −0.772039 | − | 0.635575i | \(-0.780763\pi\) | ||
0.772039 | − | 0.635575i | \(-0.219237\pi\) | |||||||
\(662\) | −20.0678 | − | 10.0977i | −0.779959 | − | 0.392458i | ||||
\(663\) | −0.151702 | −0.00589162 | ||||||||
\(664\) | −6.02271 | − | 34.6213i | −0.233726 | − | 1.34357i | ||||
\(665\) | 6.11582 | 0.237161 | ||||||||
\(666\) | 10.6105 | + | 5.33897i | 0.411149 | + | 0.206881i | ||||
\(667\) | 7.44148i | 0.288135i | ||||||||
\(668\) | −16.3675 | − | 22.0558i | −0.633279 | − | 0.853366i | ||||
\(669\) | − | 7.45801i | − | 0.288343i | ||||||
\(670\) | 2.74473 | − | 5.45479i | 0.106038 | − | 0.210737i | ||||
\(671\) | 53.8166 | 2.07757 | ||||||||
\(672\) | 1.61448 | − | 1.69818i | 0.0622798 | − | 0.0655085i | ||||
\(673\) | −33.6084 | −1.29551 | −0.647754 | − | 0.761850i | \(-0.724291\pi\) | ||||
−0.647754 | + | 0.761850i | \(0.724291\pi\) | |||||||
\(674\) | 5.36699 | − | 10.6662i | 0.206729 | − | 0.410846i | ||||
\(675\) | 2.41421i | 0.0929231i | ||||||||
\(676\) | −15.1026 | − | 20.3513i | −0.580871 | − | 0.782744i | ||||
\(677\) | 18.5122i | 0.711480i | 0.934585 | + | 0.355740i | \(0.115771\pi\) | ||||
−0.934585 | + | 0.355740i | \(0.884229\pi\) | |||||||
\(678\) | 0.957622 | + | 0.481854i | 0.0367772 | + | 0.0185055i | ||||
\(679\) | 17.3559 | 0.666058 | ||||||||
\(680\) | 0.309753 | + | 1.78060i | 0.0118785 | + | 0.0682828i | ||||
\(681\) | 4.28845 | 0.164334 | ||||||||
\(682\) | 32.8681 | + | 16.5385i | 1.25858 | + | 0.633291i | ||||
\(683\) | − | 37.9217i | − | 1.45103i | −0.688205 | − | 0.725516i | \(-0.741601\pi\) | ||
0.688205 | − | 0.725516i | \(-0.258399\pi\) | |||||||
\(684\) | 27.7821 | − | 20.6170i | 1.06227 | − | 0.788309i | ||||
\(685\) | − | 3.51217i | − | 0.134193i | ||||||
\(686\) | 0.635665 | − | 1.26330i | 0.0242698 | − | 0.0482331i | ||||
\(687\) | −7.54238 | −0.287760 | ||||||||
\(688\) | 7.97729 | + | 2.41489i | 0.304131 | + | 0.0920667i | ||||
\(689\) | −0.182196 | −0.00694113 | ||||||||
\(690\) | −1.21813 | + | 2.42087i | −0.0463733 | + | 0.0921608i | ||||
\(691\) | 12.2822i | 0.467235i | 0.972329 | + | 0.233618i | \(0.0750564\pi\) | ||||
−0.972329 | + | 0.233618i | \(0.924944\pi\) | |||||||
\(692\) | 30.7801 | − | 22.8418i | 1.17009 | − | 0.868315i | ||||
\(693\) | − | 18.0202i | − | 0.684529i | ||||||
\(694\) | −3.65922 | − | 1.84124i | −0.138902 | − | 0.0698925i | ||||
\(695\) | 1.87802 | 0.0712374 | ||||||||
\(696\) | 1.85659 | − | 0.322972i | 0.0703738 | − | 0.0122422i | ||||
\(697\) | 5.18593 | 0.196431 | ||||||||
\(698\) | −6.14812 | − | 3.09360i | −0.232710 | − | 0.117094i | ||||
\(699\) | 9.03990i | 0.341920i | ||||||||
\(700\) | −1.19186 | − | 1.60607i | −0.0450481 | − | 0.0607039i | ||||
\(701\) | − | 33.4919i | − | 1.26497i | −0.774572 | − | 0.632485i | \(-0.782035\pi\) | ||
0.774572 | − | 0.632485i | \(-0.217965\pi\) | |||||||
\(702\) | 0.879582 | − | 1.74805i | 0.0331977 | − | 0.0659760i | ||||
\(703\) | 18.1609 | 0.684953 | ||||||||
\(704\) | 17.2121 | + | 47.9745i | 0.648707 | + | 1.80811i | ||||
\(705\) | −3.50209 | −0.131896 | ||||||||
\(706\) | 2.20412 | − | 4.38039i | 0.0829530 | − | 0.164858i | ||||
\(707\) | 13.3617i | 0.502518i | ||||||||
\(708\) | 3.14915 | + | 4.24359i | 0.118352 | + | 0.159484i | ||||
\(709\) | 24.2644i | 0.911269i | 0.890167 | + | 0.455635i | \(0.150588\pi\) | ||||
−0.890167 | + | 0.455635i | \(0.849412\pi\) | |||||||
\(710\) | −16.6651 | − | 8.38552i | −0.625431 | − | 0.314703i | ||||
\(711\) | −10.7707 | −0.403932 | ||||||||
\(712\) | −18.2245 | + | 3.17034i | −0.682993 | + | 0.118813i | ||||
\(713\) | −18.8927 | −0.707536 | ||||||||
\(714\) | −0.334369 | − | 0.168247i | −0.0125134 | − | 0.00629649i | ||||
\(715\) | 3.65162i | 0.136563i | ||||||||
\(716\) | 12.9789 | − | 9.63159i | 0.485045 | − | 0.359949i | ||||
\(717\) | − | 7.94975i | − | 0.296889i | ||||||
\(718\) | −21.5137 | + | 42.7557i | −0.802885 | + | 1.59563i | ||||
\(719\) | 48.3258 | 1.80225 | 0.901124 | − | 0.433561i | \(-0.142743\pi\) | ||||
0.901124 | + | 0.433561i | \(0.142743\pi\) | |||||||
\(720\) | −10.8284 | − | 3.27798i | −0.403552 | − | 0.122163i | ||||
\(721\) | 14.8181 | 0.551855 | ||||||||
\(722\) | 11.6983 | − | 23.2488i | 0.435365 | − | 0.865230i | ||||
\(723\) | − | 4.36451i | − | 0.162318i | ||||||
\(724\) | −29.5908 | + | 21.9592i | −1.09973 | + | 0.816106i | ||||
\(725\) | − | 1.60850i | − | 0.0597381i | ||||||
\(726\) | −15.4841 | − | 7.79128i | −0.574671 | − | 0.289162i | ||||
\(727\) | −21.6926 | −0.804533 | −0.402267 | − | 0.915523i | \(-0.631778\pi\) | ||||
−0.402267 | + | 0.915523i | \(0.631778\pi\) | |||||||
\(728\) | 0.277839 | + | 1.59714i | 0.0102974 | + | 0.0591940i | ||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | −19.1917 | − | 9.65685i | −0.710318 | − | 0.357416i | ||||
\(731\) | − | 1.33146i | − | 0.0492460i | ||||||
\(732\) | 4.17015 | + | 5.61943i | 0.154133 | + | 0.207700i | ||||
\(733\) | 39.6832i | 1.46573i | 0.680372 | + | 0.732867i | \(0.261818\pi\) | ||||
−0.680372 | + | 0.732867i | \(0.738182\pi\) | |||||||
\(734\) | 0.484508 | − | 0.962896i | 0.0178835 | − | 0.0355411i | ||||
\(735\) | 0.414214 | 0.0152785 | ||||||||
\(736\) | −18.9670 | − | 18.0321i | −0.699131 | − | 0.664673i | ||||
\(737\) | −27.5096 | −1.01333 | ||||||||
\(738\) | −14.5917 | + | 28.9991i | −0.537128 | + | 1.06747i | ||||
\(739\) | 7.62891i | 0.280634i | 0.990107 | + | 0.140317i | \(0.0448122\pi\) | ||||
−0.990107 | + | 0.140317i | \(0.955188\pi\) | |||||||
\(740\) | −3.53923 | − | 4.76924i | −0.130105 | − | 0.175321i | ||||
\(741\) | − | 1.45195i | − | 0.0533386i | ||||||
\(742\) | −0.401582 | − | 0.202067i | −0.0147426 | − | 0.00741813i | ||||
\(743\) | −18.0916 | −0.663717 | −0.331858 | − | 0.943329i | \(-0.607676\pi\) | ||||
−0.331858 | + | 0.943329i | \(0.607676\pi\) | |||||||
\(744\) | 0.819971 | + | 4.71356i | 0.0300616 | + | 0.172808i | ||||
\(745\) | −8.99907 | −0.329700 | ||||||||
\(746\) | 24.3339 | + | 12.2443i | 0.890926 | + | 0.448294i | ||||
\(747\) | − | 35.1412i | − | 1.28575i | ||||||
\(748\) | 6.53843 | − | 4.85214i | 0.239069 | − | 0.177412i | ||||
\(749\) | − | 2.57153i | − | 0.0939618i | ||||||
\(750\) | 0.263301 | − | 0.523276i | 0.00961440 | − | 0.0191074i | ||||
\(751\) | −46.8933 | −1.71116 | −0.855581 | − | 0.517669i | \(-0.826800\pi\) | ||||
−0.855581 | + | 0.517669i | \(0.826800\pi\) | |||||||
\(752\) | 9.79860 | − | 32.3685i | 0.357318 | − | 1.18036i | ||||
\(753\) | 2.72202 | 0.0991959 | ||||||||
\(754\) | −0.586031 | + | 1.16466i | −0.0213420 | + | 0.0424144i | ||||
\(755\) | − | 10.8732i | − | 0.395715i | ||||||
\(756\) | 3.87740 | − | 2.87740i | 0.141020 | − | 0.104650i | ||||
\(757\) | − | 14.0299i | − | 0.509924i | −0.966951 | − | 0.254962i | \(-0.917937\pi\) | ||
0.966951 | − | 0.254962i | \(-0.0820629\pi\) | |||||||
\(758\) | 0.401582 | + | 0.202067i | 0.0145861 | + | 0.00733942i | ||||
\(759\) | 12.2089 | 0.443156 | ||||||||
\(760\) | −17.0422 | + | 2.96466i | −0.618185 | + | 0.107539i | ||||
\(761\) | 39.9447 | 1.44799 | 0.723996 | − | 0.689804i | \(-0.242303\pi\) | ||||
0.723996 | + | 0.689804i | \(0.242303\pi\) | |||||||
\(762\) | 2.04797 | + | 1.03049i | 0.0741902 | + | 0.0373309i | ||||
\(763\) | − | 13.6442i | − | 0.493954i | ||||||
\(764\) | −20.3641 | − | 27.4414i | −0.736747 | − | 0.992793i | ||||
\(765\) | 1.80734i | 0.0653445i | ||||||||
\(766\) | 22.2378 | − | 44.1947i | 0.803484 | − | 1.59682i | ||||
\(767\) | −3.65608 | −0.132014 | ||||||||
\(768\) | −3.67567 | + | 5.51472i | −0.132634 | + | 0.198995i | ||||
\(769\) | 21.6005 | 0.778932 | 0.389466 | − | 0.921041i | \(-0.372660\pi\) | ||||
0.389466 | + | 0.921041i | \(0.372660\pi\) | |||||||
\(770\) | −4.04988 | + | 8.04860i | −0.145947 | + | 0.290052i | ||||
\(771\) | − | 8.02661i | − | 0.289071i | ||||||
\(772\) | −24.5493 | − | 33.0811i | −0.883549 | − | 1.19061i | ||||
\(773\) | − | 7.55852i | − | 0.271861i | −0.990718 | − | 0.135930i | \(-0.956598\pi\) | ||
0.990718 | − | 0.135930i | \(-0.0434024\pi\) | |||||||
\(774\) | 7.44538 | + | 3.74635i | 0.267619 | + | 0.134660i | ||||
\(775\) | 4.08370 | 0.146691 | ||||||||
\(776\) | −48.3636 | + | 8.41332i | −1.73615 | + | 0.302021i | ||||
\(777\) | 1.23001 | 0.0441263 | ||||||||
\(778\) | 32.8102 | + | 16.5094i | 1.17630 | + | 0.591890i | ||||
\(779\) | 49.6348i | 1.77835i | ||||||||
\(780\) | −0.381296 | + | 0.282958i | −0.0136526 | + | 0.0101315i | ||||
\(781\) | 84.0457i | 3.00739i | ||||||||
\(782\) | −1.87915 | + | 3.73457i | −0.0671984 | + | 0.133548i | ||||
\(783\) | 3.88325 | 0.138776 | ||||||||
\(784\) | −1.15894 | + | 3.82843i | −0.0413908 | + | 0.136730i | ||||
\(785\) | −11.3390 | −0.404705 | ||||||||
\(786\) | 2.68487 | − | 5.33583i | 0.0957662 | − | 0.190323i | ||||
\(787\) | − | 33.0164i | − | 1.17691i | −0.808531 | − | 0.588453i | \(-0.799737\pi\) | ||
0.808531 | − | 0.588453i | \(-0.200263\pi\) | |||||||
\(788\) | −24.1975 | + | 17.9568i | −0.861999 | + | 0.639685i | ||||
\(789\) | − | 7.25272i | − | 0.258204i | ||||||
\(790\) | 4.81067 | + | 2.42062i | 0.171156 | + | 0.0861218i | ||||
\(791\) | −1.83005 | −0.0650691 | ||||||||
\(792\) | 8.73532 | + | 50.2146i | 0.310396 | + | 1.78430i | ||||
\(793\) | −4.84144 | −0.171925 | ||||||||
\(794\) | 31.4958 | + | 15.8480i | 1.11774 | + | 0.562424i | ||||
\(795\) | − | 0.131672i | − | 0.00466991i | ||||||
\(796\) | 15.9747 | + | 21.5265i | 0.566210 | + | 0.762988i | ||||
\(797\) | 52.2029i | 1.84912i | 0.381035 | + | 0.924561i | \(0.375568\pi\) | ||||
−0.381035 | + | 0.924561i | \(0.624432\pi\) | |||||||
\(798\) | 1.61030 | − | 3.20026i | 0.0570040 | − | 0.113288i | ||||
\(799\) | −5.40253 | −0.191128 | ||||||||
\(800\) | 4.09976 | + | 3.89769i | 0.144948 | + | 0.137804i | ||||
\(801\) | −18.4982 | −0.653602 | ||||||||
\(802\) | 4.79231 | − | 9.52409i | 0.169222 | − | 0.336307i | ||||
\(803\) | 96.7879i | 3.41557i | ||||||||
\(804\) | −2.13167 | − | 2.87250i | −0.0751783 | − | 0.101305i | ||||
\(805\) | − | 4.62636i | − | 0.163058i | ||||||
\(806\) | −2.95687 | − | 1.48783i | −0.104151 | − | 0.0524067i | ||||
\(807\) | 0.273807 | 0.00963847 | ||||||||
\(808\) | −6.47711 | − | 37.2334i | −0.227864 | − | 1.30987i | ||||
\(809\) | 24.8852 | 0.874918 | 0.437459 | − | 0.899238i | \(-0.355878\pi\) | ||||
0.437459 | + | 0.899238i | \(0.355878\pi\) | |||||||
\(810\) | −9.45616 | − | 4.75813i | −0.332256 | − | 0.167184i | ||||
\(811\) | − | 29.2632i | − | 1.02757i | −0.857919 | − | 0.513785i | \(-0.828243\pi\) | ||
0.857919 | − | 0.513785i | \(-0.171757\pi\) | |||||||
\(812\) | −2.58336 | + | 1.91710i | −0.0906583 | + | 0.0672771i | ||||
\(813\) | − | 4.37916i | − | 0.153584i | ||||||
\(814\) | −12.0261 | + | 23.9004i | −0.421516 | + | 0.837708i | ||||
\(815\) | 24.0656 | 0.842980 | ||||||||
\(816\) | 1.01330 | + | 0.306747i | 0.0354727 | + | 0.0107383i | ||||
\(817\) | 12.7435 | 0.445839 | ||||||||
\(818\) | −10.6197 | + | 21.1053i | −0.371309 | + | 0.737929i | ||||
\(819\) | 1.62113i | 0.0566468i | ||||||||
\(820\) | 13.0346 | − | 9.67291i | 0.455188 | − | 0.337793i | ||||
\(821\) | 10.7833i | 0.376340i | 0.982136 | + | 0.188170i | \(0.0602556\pi\) | ||||
−0.982136 | + | 0.188170i | \(0.939744\pi\) | |||||||
\(822\) | −1.83783 | − | 0.924757i | −0.0641018 | − | 0.0322546i | ||||
\(823\) | 17.2874 | 0.602600 | 0.301300 | − | 0.953529i | \(-0.402579\pi\) | ||||
0.301300 | + | 0.953529i | \(0.402579\pi\) | |||||||
\(824\) | −41.2918 | + | 7.18311i | −1.43847 | + | 0.250236i | ||||
\(825\) | −2.63899 | −0.0918779 | ||||||||
\(826\) | −8.05844 | − | 4.05483i | −0.280389 | − | 0.141085i | ||||
\(827\) | − | 8.53905i | − | 0.296932i | −0.988918 | − | 0.148466i | \(-0.952566\pi\) | ||
0.988918 | − | 0.148466i | \(-0.0474335\pi\) | |||||||
\(828\) | −15.5959 | − | 21.0160i | −0.541994 | − | 0.730356i | ||||
\(829\) | 48.6955i | 1.69127i | 0.533765 | + | 0.845633i | \(0.320777\pi\) | ||||
−0.533765 | + | 0.845633i | \(0.679223\pi\) | |||||||
\(830\) | −7.89769 | + | 15.6956i | −0.274133 | + | 0.544803i | ||||
\(831\) | −6.22194 | −0.215837 | ||||||||
\(832\) | −1.54844 | − | 4.31588i | −0.0536824 | − | 0.149626i | ||||
\(833\) | 0.638991 | 0.0221397 | ||||||||
\(834\) | 0.494485 | − | 0.982725i | 0.0171226 | − | 0.0340290i | ||||
\(835\) | 13.7328i | 0.475242i | ||||||||
\(836\) | 46.4401 | + | 62.5797i | 1.60616 | + | 2.16436i | ||||
\(837\) | 9.85892i | 0.340774i | ||||||||
\(838\) | 1.77267 | + | 0.891968i | 0.0612359 | + | 0.0308125i | ||||
\(839\) | −4.54882 | −0.157043 | −0.0785214 | − | 0.996912i | \(-0.525020\pi\) | ||||
−0.0785214 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(840\) | −1.15424 | + | 0.200791i | −0.0398250 | + | 0.00692795i | ||||
\(841\) | 26.4127 | 0.910784 | ||||||||
\(842\) | −15.8592 | − | 7.98001i | −0.546545 | − | 0.275009i | ||||
\(843\) | 0.818348i | 0.0281854i | ||||||||
\(844\) | −8.90192 | + | 6.60607i | −0.306417 | + | 0.227390i | ||||
\(845\) | 12.6715i | 0.435913i | ||||||||
\(846\) | 15.2011 | − | 30.2103i | 0.522626 | − | 1.03865i | ||||
\(847\) | 29.5908 | 1.01675 | ||||||||
\(848\) | 1.21699 | + | 0.368408i | 0.0417917 | + | 0.0126512i | ||||
\(849\) | −7.89777 | −0.271051 | ||||||||
\(850\) | 0.406184 | − | 0.807238i | 0.0139320 | − | 0.0276880i | ||||
\(851\) | − | 13.7380i | − | 0.470933i | ||||||
\(852\) | −8.77589 | + | 6.51255i | −0.300657 | + | 0.223116i | ||||
\(853\) | 33.4183i | 1.14422i | 0.820177 | + | 0.572110i | \(0.193875\pi\) | ||||
−0.820177 | + | 0.572110i | \(0.806125\pi\) | |||||||
\(854\) | −10.6711 | − | 5.36947i | −0.365158 | − | 0.183739i | ||||
\(855\) | −17.2981 | −0.591584 | ||||||||
\(856\) | 1.24656 | + | 7.16578i | 0.0426065 | + | 0.244921i | ||||
\(857\) | −16.4925 | −0.563373 | −0.281687 | − | 0.959506i | \(-0.590894\pi\) | ||||
−0.281687 | + | 0.959506i | \(0.590894\pi\) | |||||||
\(858\) | 1.91081 | + | 0.961476i | 0.0652339 | + | 0.0328243i | ||||
\(859\) | − | 22.4600i | − | 0.766326i | −0.923681 | − | 0.383163i | \(-0.874835\pi\) | ||
0.923681 | − | 0.383163i | \(-0.125165\pi\) | |||||||
\(860\) | −2.48348 | − | 3.34657i | −0.0846858 | − | 0.114117i | ||||
\(861\) | 3.36168i | 0.114566i | ||||||||
\(862\) | 1.45111 | − | 2.88390i | 0.0494252 | − | 0.0982260i | ||||
\(863\) | 35.0034 | 1.19153 | 0.595764 | − | 0.803159i | \(-0.296849\pi\) | ||||
0.595764 | + | 0.803159i | \(0.296849\pi\) | |||||||
\(864\) | −9.40986 | + | 9.89769i | −0.320130 | + | 0.336726i | ||||
\(865\) | −19.1648 | −0.651624 | ||||||||
\(866\) | −12.7360 | + | 25.3112i | −0.432787 | + | 0.860108i | ||||
\(867\) | 6.87250i | 0.233402i | ||||||||
\(868\) | −4.86720 | − | 6.55872i | −0.165203 | − | 0.222617i | ||||
\(869\) | − | 24.2612i | − | 0.823004i | ||||||
\(870\) | −0.841688 | − | 0.423519i | −0.0285359 | − | 0.0143586i | ||||
\(871\) | 2.47482 | 0.0838560 | ||||||||
\(872\) | 6.61407 | + | 38.0207i | 0.223981 | + | 1.28754i | ||||
\(873\) | −49.0899 | −1.66144 | ||||||||
\(874\) | −35.7438 | − | 17.9855i | −1.20905 | − | 0.608368i | ||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | −10.1064 | + | 7.49992i | −0.341464 | + | 0.253399i | ||||
\(877\) | 13.9841i | 0.472211i | 0.971727 | + | 0.236106i | \(0.0758711\pi\) | ||||
−0.971727 | + | 0.236106i | \(0.924129\pi\) | |||||||
\(878\) | 4.48577 | − | 8.91488i | 0.151387 | − | 0.300863i | ||||
\(879\) | 11.9144 | 0.401863 | ||||||||
\(880\) | 7.38372 | − | 24.3912i | 0.248905 | − | 0.822229i | ||||
\(881\) | −4.22514 | −0.142349 | −0.0711743 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711743 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(882\) | −1.79793 | + | 3.57316i | −0.0605395 | + | 0.120314i | ||||
\(883\) | 15.4565i | 0.520154i | 0.965588 | + | 0.260077i | \(0.0837479\pi\) | ||||
−0.965588 | + | 0.260077i | \(0.916252\pi\) | |||||||
\(884\) | −0.588210 | + | 0.436508i | −0.0197836 | + | 0.0146813i | ||||
\(885\) | − | 2.64222i | − | 0.0888171i | ||||||
\(886\) | 8.03554 | + | 4.04331i | 0.269959 | + | 0.135838i | ||||
\(887\) | 26.5127 | 0.890208 | 0.445104 | − | 0.895479i | \(-0.353167\pi\) | ||||
0.445104 | + | 0.895479i | \(0.353167\pi\) | |||||||
\(888\) | −3.42752 | + | 0.596250i | −0.115020 | + | 0.0200089i | ||||
\(889\) | −3.91375 | −0.131263 | ||||||||
\(890\) | 8.26213 | + | 4.15732i | 0.276947 | + | 0.139354i | ||||
\(891\) | 47.6894i | 1.59765i | ||||||||
\(892\) | −21.4597 | − | 28.9177i | −0.718524 | − | 0.968237i | ||||
\(893\) | − | 51.7079i | − | 1.73034i | ||||||
\(894\) | −2.36947 | + | 4.70900i | −0.0792468 | + | 0.157493i | ||||
\(895\) | −8.08115 | −0.270123 | ||||||||
\(896\) | 1.37364 | − | 11.2300i | 0.0458901 | − | 0.375168i | ||||
\(897\) | −1.09834 | −0.0366724 | ||||||||
\(898\) | 0.825773 | − | 1.64112i | 0.0275564 | − | 0.0547648i | ||||
\(899\) | − | 6.56862i | − | 0.219076i | ||||||
\(900\) | 3.37109 | + | 4.54266i | 0.112370 | + | 0.151422i | ||||
\(901\) | − | 0.203125i | − | 0.00676706i | ||||||
\(902\) | −65.3210 | − | 32.8681i | −2.17495 | − | 1.09439i | ||||
\(903\) | 0.863096 | 0.0287220 | ||||||||
\(904\) | 5.09958 | − | 0.887122i | 0.169609 | − | 0.0295052i | ||||
\(905\) | 18.4243 | 0.612444 | ||||||||
\(906\) | −5.68968 | − | 2.86292i | −0.189027 | − | 0.0951141i | ||||
\(907\) | 41.8112i | 1.38832i | 0.719821 | + | 0.694160i | \(0.244224\pi\) | ||||
−0.719821 | + | 0.694160i | \(0.755776\pi\) | |||||||
\(908\) | 16.6280 | − | 12.3396i | 0.551821 | − | 0.409504i | ||||
\(909\) | − | 37.7925i | − | 1.25350i | ||||||
\(910\) | 0.364335 | − | 0.724068i | 0.0120776 | − | 0.0240026i | ||||
\(911\) | −8.07470 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(912\) | −2.93589 | + | 9.69838i | −0.0972171 | + | 0.321145i | ||||
\(913\) | 79.1563 | 2.61969 | ||||||||
\(914\) | 6.01854 | − | 11.9610i | 0.199075 | − | 0.395636i | ||||
\(915\) | − | 3.49886i | − | 0.115669i | ||||||
\(916\) | −29.2449 | + | 21.7025i | −0.966277 | + | 0.717070i | ||||
\(917\) | 10.1970i | 0.336733i | ||||||||
\(918\) | 1.94885 | + | 0.980616i | 0.0643215 | + | 0.0323651i | ||||
\(919\) | −12.7176 | −0.419514 | −0.209757 | − | 0.977754i | \(-0.567267\pi\) | ||||
−0.209757 | + | 0.977754i | \(0.567267\pi\) | |||||||
\(920\) | 2.24264 | + | 12.8917i | 0.0739377 | + | 0.425027i | ||||
\(921\) | −5.18354 | −0.170803 | ||||||||
\(922\) | −52.6998 | − | 26.5174i | −1.73558 | − | 0.873304i | ||||
\(923\) | − | 7.56091i | − | 0.248870i | ||||||
\(924\) | 3.14531 | + | 4.23841i | 0.103473 | + | 0.139434i | ||||
\(925\) | 2.96951i | 0.0976367i | ||||||||
\(926\) | 13.1016 | − | 26.0376i | 0.430544 | − | 0.855650i | ||||
\(927\) | −41.9119 | −1.37657 | ||||||||
\(928\) | 6.26942 | − | 6.59445i | 0.205804 | − | 0.216473i | ||||
\(929\) | −40.7169 | −1.33588 | −0.667939 | − | 0.744216i | \(-0.732823\pi\) | ||||
−0.667939 | + | 0.744216i | \(0.732823\pi\) | |||||||
\(930\) | 1.07524 | − | 2.13690i | 0.0352586 | − | 0.0700718i | ||||
\(931\) | 6.11582i | 0.200438i | ||||||||
\(932\) | 26.0114 | + | 35.0513i | 0.852033 | + | 1.14814i | ||||
\(933\) | − | 7.48139i | − | 0.244930i | ||||||
\(934\) | 5.38637 | + | 2.71030i | 0.176248 | + | 0.0886838i | ||||
\(935\) | −4.07107 | −0.133138 | ||||||||
\(936\) | −0.785846 | − | 4.51740i | −0.0256862 | − | 0.147656i | ||||
\(937\) | −3.65363 | −0.119359 | −0.0596794 | − | 0.998218i | \(-0.519008\pi\) | ||||
−0.0596794 | + | 0.998218i | \(0.519008\pi\) | |||||||
\(938\) | 5.45479 | + | 2.74473i | 0.178105 | + | 0.0896185i | ||||
\(939\) | 6.53849i | 0.213375i | ||||||||
\(940\) | −13.5790 | + | 10.0769i | −0.442898 | + | 0.328673i | ||||
\(941\) | − | 12.5502i | − | 0.409124i | −0.978854 | − | 0.204562i | \(-0.934423\pi\) | ||
0.978854 | − | 0.204562i | \(-0.0655770\pi\) | |||||||
\(942\) | −2.98556 | + | 5.93342i | −0.0972749 | + | 0.193321i | ||||
\(943\) | 37.5467 | 1.22269 | ||||||||
\(944\) | 24.4210 | + | 7.39274i | 0.794837 | + | 0.240613i | ||||
\(945\) | −2.41421 | −0.0785344 | ||||||||
\(946\) | −8.43873 | + | 16.7709i | −0.274367 | + | 0.545268i | ||||
\(947\) | − | 50.0396i | − | 1.62607i | −0.582215 | − | 0.813035i | \(-0.697814\pi\) | ||
0.582215 | − | 0.813035i | \(-0.302186\pi\) | |||||||
\(948\) | 2.53331 | − | 1.87996i | 0.0822780 | − | 0.0610581i | ||||
\(949\) | − | 8.70722i | − | 0.282648i | ||||||
\(950\) | 7.72612 | + | 3.88761i | 0.250668 | + | 0.126131i | ||||
\(951\) | 11.6329 | 0.377224 | ||||||||
\(952\) | −1.78060 | + | 0.309753i | −0.0577095 | + | 0.0100391i | ||||
\(953\) | −37.1736 | −1.20417 | −0.602086 | − | 0.798431i | \(-0.705663\pi\) | ||||
−0.602086 | + | 0.798431i | \(0.705663\pi\) | |||||||
\(954\) | 1.13585 | + | 0.571533i | 0.0367744 | + | 0.0185041i | ||||
\(955\) | 17.0860i | 0.552890i | ||||||||
\(956\) | −22.8746 | − | 30.8244i | −0.739819 | − | 0.996932i | ||||
\(957\) | 4.24481i | 0.137215i | ||||||||
\(958\) | 18.1851 | − | 36.1405i | 0.587533 | − | 1.16765i | ||||
\(959\) | 3.51217 | 0.113414 | ||||||||
\(960\) | 3.11904 | − | 1.11904i | 0.100667 | − | 0.0361169i | ||||
\(961\) | −14.3234 | −0.462045 | ||||||||
\(962\) | 1.08189 | − | 2.15012i | 0.0348817 | − | 0.0693227i | ||||
\(963\) | 7.27339i | 0.234382i | ||||||||
\(964\) | −12.5585 | − | 16.9230i | −0.404481 | − | 0.545052i | ||||
\(965\) | 20.5975i | 0.663057i | ||||||||
\(966\) | −2.42087 | − | 1.21813i | −0.0778901 | − | 0.0391926i | ||||
\(967\) | 36.9518 | 1.18829 | 0.594145 | − | 0.804358i | \(-0.297491\pi\) | ||||
0.594145 | + | 0.804358i | \(0.297491\pi\) | |||||||
\(968\) | −82.4570 | + | 14.3442i | −2.65027 | + | 0.461040i | ||||
\(969\) | 1.61873 | 0.0520010 | ||||||||
\(970\) | 21.9257 | + | 11.0325i | 0.703993 | + | 0.354234i | ||||
\(971\) | − | 15.1668i | − | 0.486724i | −0.969935 | − | 0.243362i | \(-0.921750\pi\) | ||
0.969935 | − | 0.243362i | \(-0.0782504\pi\) | |||||||
\(972\) | −16.6118 | + | 12.3276i | −0.532825 | + | 0.395407i | ||||
\(973\) | 1.87802i | 0.0602066i | ||||||||
\(974\) | 13.5364 | − | 26.9019i | 0.433735 | − | 0.861991i | ||||
\(975\) | 0.237409 | 0.00760316 | ||||||||
\(976\) | 32.3387 | + | 9.78958i | 1.03514 | + | 0.313357i | ||||
\(977\) | −32.5314 | −1.04077 | −0.520386 | − | 0.853931i | \(-0.674212\pi\) | ||||
−0.520386 | + | 0.853931i | \(0.674212\pi\) | |||||||
\(978\) | 6.33649 | − | 12.5930i | 0.202619 | − | 0.402678i | ||||
\(979\) | − | 41.6676i | − | 1.33170i | ||||||
\(980\) | 1.60607 | − | 1.19186i | 0.0513041 | − | 0.0380726i | ||||
\(981\) | 38.5917i | 1.23214i | ||||||||
\(982\) | 26.4053 | + | 13.2865i | 0.842626 | + | 0.423991i | ||||
\(983\) | 25.7172 | 0.820251 | 0.410126 | − | 0.912029i | \(-0.365485\pi\) | ||||
0.410126 | + | 0.912029i | \(0.365485\pi\) | |||||||
\(984\) | −1.62958 | − | 9.36759i | −0.0519492 | − | 0.298628i | ||||
\(985\) | 15.0662 | 0.480050 | ||||||||
\(986\) | −1.29844 | − | 0.653346i | −0.0413507 | − | 0.0208068i | ||||
\(987\) | − | 3.50209i | − | 0.111473i | ||||||
\(988\) | −4.17784 | − | 5.62979i | −0.132915 | − | 0.179107i | ||||
\(989\) | − | 9.63994i | − | 0.306532i | ||||||
\(990\) | 11.4548 | − | 22.7649i | 0.364057 | − | 0.723516i | ||||
\(991\) | −6.65917 | −0.211535 | −0.105768 | − | 0.994391i | \(-0.533730\pi\) | ||||
−0.105768 | + | 0.994391i | \(0.533730\pi\) | |||||||
\(992\) | 16.7422 | + | 15.9170i | 0.531565 | + | 0.505365i | ||||
\(993\) | 6.57988 | 0.208806 | ||||||||
\(994\) | 8.38552 | − | 16.6651i | 0.265973 | − | 0.528586i | ||||
\(995\) | − | 13.4032i | − | 0.424910i | ||||||
\(996\) | 6.13368 | + | 8.26535i | 0.194353 | + | 0.261898i | ||||
\(997\) | 5.50077i | 0.174211i | 0.996199 | + | 0.0871056i | \(0.0277618\pi\) | ||||
−0.996199 | + | 0.0871056i | \(0.972238\pi\) | |||||||
\(998\) | 47.0516 | + | 23.6753i | 1.48939 | + | 0.749429i | ||||
\(999\) | −7.16902 | −0.226818 |
(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 | 280.2.b.c.141.4 | yes | 8 | |
4.3 | odd | 2 | 1120.2.b.c.561.5 | 8 | |||
8.3 | odd | 2 | 1120.2.b.c.561.4 | 8 | |||
8.5 | even | 2 | inner | 280.2.b.c.141.3 | ✓ | 8 | |
16.3 | odd | 4 | 8960.2.a.bv.1.1 | 4 | |||
16.5 | even | 4 | 8960.2.a.bu.1.1 | 4 | |||
16.11 | odd | 4 | 8960.2.a.bs.1.4 | 4 | |||
16.13 | even | 4 | 8960.2.a.bt.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.b.c.141.3 | ✓ | 8 | 8.5 | even | 2 | inner | |
280.2.b.c.141.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1120.2.b.c.561.4 | 8 | 8.3 | odd | 2 | |||
1120.2.b.c.561.5 | 8 | 4.3 | odd | 2 | |||
8960.2.a.bs.1.4 | 4 | 16.11 | odd | 4 | |||
8960.2.a.bt.1.4 | 4 | 16.13 | even | 4 | |||
8960.2.a.bu.1.1 | 4 | 16.5 | even | 4 | |||
8960.2.a.bv.1.1 | 4 | 16.3 | odd | 4 |