Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(27,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.27");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 183.12 | ||
Character | \(\chi\) | \(=\) | 260.183 |
Dual form | 260.2.o.a.27.12 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.769019 | − | 1.18685i | −0.543779 | − | 0.839229i | ||||
\(3\) | −0.808783 | + | 0.808783i | −0.466951 | + | 0.466951i | −0.900925 | − | 0.433974i | \(-0.857111\pi\) |
0.433974 | + | 0.900925i | \(0.357111\pi\) | |||||||
\(4\) | −0.817219 | + | 1.82542i | −0.408609 | + | 0.912709i | ||||
\(5\) | 0.885949 | − | 2.05307i | 0.396208 | − | 0.918161i | ||||
\(6\) | 1.58187 | + | 0.337933i | 0.645797 | + | 0.137961i | ||||
\(7\) | 0.771151 | + | 0.771151i | 0.291468 | + | 0.291468i | 0.837660 | − | 0.546192i | \(-0.183923\pi\) |
−0.546192 | + | 0.837660i | \(0.683923\pi\) | |||||||
\(8\) | 2.79495 | − | 0.433867i | 0.988165 | − | 0.153395i | ||||
\(9\) | 1.69174i | 0.563913i | ||||||||
\(10\) | −3.11799 | + | 0.527363i | −0.985996 | + | 0.166767i | ||||
\(11\) | 0.875946i | 0.264108i | 0.991243 | + | 0.132054i | \(0.0421572\pi\) | ||||
−0.991243 | + | 0.132054i | \(0.957843\pi\) | |||||||
\(12\) | −0.815415 | − | 2.13732i | −0.235390 | − | 0.616991i | ||||
\(13\) | 0.707107 | + | 0.707107i | 0.196116 | + | 0.196116i | ||||
\(14\) | 0.322210 | − | 1.50827i | 0.0861141 | − | 0.403102i | ||||
\(15\) | 0.943948 | + | 2.37703i | 0.243726 | + | 0.613746i | ||||
\(16\) | −2.66431 | − | 2.98353i | −0.666077 | − | 0.745883i | ||||
\(17\) | 4.91209 | − | 4.91209i | 1.19136 | − | 1.19136i | 0.214671 | − | 0.976686i | \(-0.431132\pi\) |
0.976686 | − | 0.214671i | \(-0.0688681\pi\) | |||||||
\(18\) | 2.00784 | − | 1.30098i | 0.473252 | − | 0.306644i | ||||
\(19\) | 6.89579 | 1.58200 | 0.791001 | − | 0.611815i | \(-0.209560\pi\) | ||||
0.791001 | + | 0.611815i | \(0.209560\pi\) | |||||||
\(20\) | 3.02370 | + | 3.29503i | 0.676119 | + | 0.736792i | ||||
\(21\) | −1.24739 | −0.272202 | ||||||||
\(22\) | 1.03962 | − | 0.673619i | 0.221647 | − | 0.143616i | ||||
\(23\) | 6.03681 | − | 6.03681i | 1.25876 | − | 1.25876i | 0.307077 | − | 0.951685i | \(-0.400649\pi\) |
0.951685 | − | 0.307077i | \(-0.0993509\pi\) | |||||||
\(24\) | −1.90961 | + | 2.61142i | −0.389797 | + | 0.533053i | ||||
\(25\) | −3.43019 | − | 3.63783i | −0.686038 | − | 0.727566i | ||||
\(26\) | 0.295450 | − | 1.38301i | 0.0579425 | − | 0.271230i | ||||
\(27\) | −3.79460 | − | 3.79460i | −0.730271 | − | 0.730271i | ||||
\(28\) | −2.03787 | + | 0.777475i | −0.385122 | + | 0.146929i | ||||
\(29\) | 7.85222i | 1.45812i | 0.684449 | + | 0.729060i | \(0.260043\pi\) | ||||
−0.684449 | + | 0.729060i | \(0.739957\pi\) | |||||||
\(30\) | 2.09526 | − | 2.94830i | 0.382540 | − | 0.538284i | ||||
\(31\) | 5.45839i | 0.980356i | 0.871622 | + | 0.490178i | \(0.163068\pi\) | ||||
−0.871622 | + | 0.490178i | \(0.836932\pi\) | |||||||
\(32\) | −1.49210 | + | 5.45652i | −0.263768 | + | 0.964586i | ||||
\(33\) | −0.708451 | − | 0.708451i | −0.123325 | − | 0.123325i | ||||
\(34\) | −9.60741 | − | 2.05242i | −1.64766 | − | 0.351987i | ||||
\(35\) | 2.26643 | − | 0.900026i | 0.383096 | − | 0.152132i | ||||
\(36\) | −3.08813 | − | 1.38252i | −0.514689 | − | 0.230420i | ||||
\(37\) | −2.21989 | + | 2.21989i | −0.364947 | + | 0.364947i | −0.865631 | − | 0.500683i | \(-0.833082\pi\) |
0.500683 | + | 0.865631i | \(0.333082\pi\) | |||||||
\(38\) | −5.30299 | − | 8.18426i | −0.860259 | − | 1.32766i | ||||
\(39\) | −1.14379 | −0.183153 | ||||||||
\(40\) | 1.58543 | − | 6.12262i | 0.250678 | − | 0.968071i | ||||
\(41\) | −1.36683 | −0.213463 | −0.106732 | − | 0.994288i | \(-0.534039\pi\) | ||||
−0.106732 | + | 0.994288i | \(0.534039\pi\) | |||||||
\(42\) | 0.959266 | + | 1.48046i | 0.148018 | + | 0.228440i | ||||
\(43\) | −4.34174 | + | 4.34174i | −0.662109 | + | 0.662109i | −0.955877 | − | 0.293768i | \(-0.905091\pi\) |
0.293768 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(44\) | −1.59897 | − | 0.715840i | −0.241054 | − | 0.107917i | ||||
\(45\) | 3.47326 | + | 1.49879i | 0.517763 | + | 0.223427i | ||||
\(46\) | −11.8072 | − | 2.52236i | −1.74088 | − | 0.371901i | ||||
\(47\) | 3.81120 | + | 3.81120i | 0.555921 | + | 0.555921i | 0.928144 | − | 0.372222i | \(-0.121404\pi\) |
−0.372222 | + | 0.928144i | \(0.621404\pi\) | |||||||
\(48\) | 4.56788 | + | 0.258185i | 0.659317 | + | 0.0372657i | ||||
\(49\) | − | 5.81065i | − | 0.830093i | ||||||
\(50\) | −1.67967 | + | 6.86868i | −0.237541 | + | 0.971377i | ||||
\(51\) | 7.94564i | 1.11261i | ||||||||
\(52\) | −1.86863 | + | 0.712905i | −0.259132 | + | 0.0988621i | ||||
\(53\) | −2.18578 | − | 2.18578i | −0.300240 | − | 0.300240i | 0.540867 | − | 0.841108i | \(-0.318096\pi\) |
−0.841108 | + | 0.540867i | \(0.818096\pi\) | |||||||
\(54\) | −1.58550 | + | 7.42174i | −0.215759 | + | 1.00997i | ||||
\(55\) | 1.79838 | + | 0.776043i | 0.242493 | + | 0.104642i | ||||
\(56\) | 2.48991 | + | 1.82075i | 0.332728 | + | 0.243308i | ||||
\(57\) | −5.57720 | + | 5.57720i | −0.738718 | + | 0.738718i | ||||
\(58\) | 9.31940 | − | 6.03851i | 1.22370 | − | 0.792895i | ||||
\(59\) | −0.749270 | −0.0975467 | −0.0487733 | − | 0.998810i | \(-0.515531\pi\) | ||||
−0.0487733 | + | 0.998810i | \(0.515531\pi\) | |||||||
\(60\) | −5.11049 | − | 0.219453i | −0.659761 | − | 0.0283313i | ||||
\(61\) | −4.79700 | −0.614193 | −0.307097 | − | 0.951678i | \(-0.599357\pi\) | ||||
−0.307097 | + | 0.951678i | \(0.599357\pi\) | |||||||
\(62\) | 6.47828 | − | 4.19761i | 0.822742 | − | 0.533096i | ||||
\(63\) | −1.30459 | + | 1.30459i | −0.164362 | + | 0.164362i | ||||
\(64\) | 7.62352 | − | 2.42528i | 0.952940 | − | 0.303160i | ||||
\(65\) | 2.07820 | − | 0.825279i | 0.257769 | − | 0.102363i | ||||
\(66\) | −0.296011 | + | 1.38564i | −0.0364365 | + | 0.170560i | ||||
\(67\) | −10.0709 | − | 10.0709i | −1.23035 | − | 1.23035i | −0.963828 | − | 0.266526i | \(-0.914124\pi\) |
−0.266526 | − | 0.963828i | \(-0.585876\pi\) | |||||||
\(68\) | 4.95237 | + | 12.9809i | 0.600563 | + | 1.57416i | ||||
\(69\) | 9.76494i | 1.17556i | ||||||||
\(70\) | −2.81112 | − | 1.99777i | −0.335993 | − | 0.238779i | ||||
\(71\) | 5.01480i | 0.595148i | 0.954699 | + | 0.297574i | \(0.0961775\pi\) | ||||
−0.954699 | + | 0.297574i | \(0.903823\pi\) | |||||||
\(72\) | 0.733990 | + | 4.72833i | 0.0865016 | + | 0.557239i | ||||
\(73\) | 6.85076 | + | 6.85076i | 0.801821 | + | 0.801821i | 0.983380 | − | 0.181559i | \(-0.0581144\pi\) |
−0.181559 | + | 0.983380i | \(0.558114\pi\) | |||||||
\(74\) | 4.34181 | + | 0.927534i | 0.504725 | + | 0.107824i | ||||
\(75\) | 5.71650 | + | 0.167936i | 0.660084 | + | 0.0193916i | ||||
\(76\) | −5.63537 | + | 12.5877i | −0.646421 | + | 1.44391i | ||||
\(77\) | −0.675487 | + | 0.675487i | −0.0769789 | + | 0.0769789i | ||||
\(78\) | 0.879598 | + | 1.35751i | 0.0995949 | + | 0.153708i | ||||
\(79\) | −1.62958 | −0.183342 | −0.0916710 | − | 0.995789i | \(-0.529221\pi\) | ||||
−0.0916710 | + | 0.995789i | \(0.529221\pi\) | |||||||
\(80\) | −8.48584 | + | 2.82675i | −0.948746 | + | 0.316040i | ||||
\(81\) | 1.06280 | 0.118089 | ||||||||
\(82\) | 1.05112 | + | 1.62222i | 0.116077 | + | 0.179144i | ||||
\(83\) | −2.66989 | + | 2.66989i | −0.293058 | + | 0.293058i | −0.838287 | − | 0.545229i | \(-0.816443\pi\) |
0.545229 | + | 0.838287i | \(0.316443\pi\) | |||||||
\(84\) | 1.01939 | − | 2.27701i | 0.111224 | − | 0.248442i | ||||
\(85\) | −5.73301 | − | 14.4367i | −0.621832 | − | 1.56588i | ||||
\(86\) | 8.49186 | + | 1.81410i | 0.915701 | + | 0.195620i | ||||
\(87\) | −6.35074 | − | 6.35074i | −0.680871 | − | 0.680871i | ||||
\(88\) | 0.380044 | + | 2.44823i | 0.0405129 | + | 0.260982i | ||||
\(89\) | − | 3.68804i | − | 0.390931i | −0.980711 | − | 0.195466i | \(-0.937378\pi\) | ||
0.980711 | − | 0.195466i | \(-0.0626218\pi\) | |||||||
\(90\) | −0.892160 | − | 5.27483i | −0.0940419 | − | 0.556016i | ||||
\(91\) | 1.09057i | 0.114323i | ||||||||
\(92\) | 6.08631 | + | 15.9531i | 0.634542 | + | 1.66323i | ||||
\(93\) | −4.41465 | − | 4.41465i | −0.457778 | − | 0.457778i | ||||
\(94\) | 1.59243 | − | 7.45421i | 0.164247 | − | 0.768843i | ||||
\(95\) | 6.10932 | − | 14.1575i | 0.626803 | − | 1.45253i | ||||
\(96\) | −3.20636 | − | 5.61993i | −0.327248 | − | 0.573582i | ||||
\(97\) | 6.65520 | − | 6.65520i | 0.675733 | − | 0.675733i | −0.283299 | − | 0.959032i | \(-0.591429\pi\) |
0.959032 | + | 0.283299i | \(0.0914288\pi\) | |||||||
\(98\) | −6.89636 | + | 4.46850i | −0.696638 | + | 0.451387i | ||||
\(99\) | −1.48187 | −0.148934 | ||||||||
\(100\) | 9.44378 | − | 3.28863i | 0.944378 | − | 0.328863i | ||||
\(101\) | −6.22911 | −0.619820 | −0.309910 | − | 0.950766i | \(-0.600299\pi\) | ||||
−0.309910 | + | 0.950766i | \(0.600299\pi\) | |||||||
\(102\) | 9.43027 | − | 6.11035i | 0.933736 | − | 0.605015i | ||||
\(103\) | −9.05772 | + | 9.05772i | −0.892483 | + | 0.892483i | −0.994756 | − | 0.102273i | \(-0.967388\pi\) |
0.102273 | + | 0.994756i | \(0.467388\pi\) | |||||||
\(104\) | 2.28312 | + | 1.66954i | 0.223878 | + | 0.163712i | ||||
\(105\) | −1.10512 | + | 2.56098i | −0.107849 | + | 0.249926i | ||||
\(106\) | −0.913284 | + | 4.27510i | −0.0887060 | + | 0.415235i | ||||
\(107\) | −6.98064 | − | 6.98064i | −0.674844 | − | 0.674844i | 0.283985 | − | 0.958829i | \(-0.408344\pi\) |
−0.958829 | + | 0.283985i | \(0.908344\pi\) | |||||||
\(108\) | 10.0278 | − | 3.82572i | 0.964921 | − | 0.368130i | ||||
\(109\) | − | 5.87444i | − | 0.562670i | −0.959610 | − | 0.281335i | \(-0.909223\pi\) | ||
0.959610 | − | 0.281335i | \(-0.0907772\pi\) | |||||||
\(110\) | −0.461941 | − | 2.73119i | −0.0440444 | − | 0.260409i | ||||
\(111\) | − | 3.59082i | − | 0.340825i | ||||||
\(112\) | 0.246171 | − | 4.35534i | 0.0232610 | − | 0.411541i | ||||
\(113\) | 8.29477 | + | 8.29477i | 0.780307 | + | 0.780307i | 0.979882 | − | 0.199576i | \(-0.0639564\pi\) |
−0.199576 | + | 0.979882i | \(0.563956\pi\) | |||||||
\(114\) | 10.9083 | + | 2.33032i | 1.02165 | + | 0.218254i | ||||
\(115\) | −7.04568 | − | 17.7423i | −0.657013 | − | 1.65448i | ||||
\(116\) | −14.3336 | − | 6.41698i | −1.33084 | − | 0.595802i | ||||
\(117\) | −1.19624 | + | 1.19624i | −0.110592 | + | 0.110592i | ||||
\(118\) | 0.576203 | + | 0.889270i | 0.0530438 | + | 0.0818640i | ||||
\(119\) | 7.57593 | 0.694485 | ||||||||
\(120\) | 3.66960 | + | 6.23414i | 0.334987 | + | 0.569096i | ||||
\(121\) | 10.2327 | 0.930247 | ||||||||
\(122\) | 3.68899 | + | 5.69332i | 0.333985 | + | 0.515449i | ||||
\(123\) | 1.10547 | − | 1.10547i | 0.0996768 | − | 0.0996768i | ||||
\(124\) | −9.96384 | − | 4.46070i | −0.894780 | − | 0.400582i | ||||
\(125\) | −10.5077 | + | 3.81949i | −0.939836 | + | 0.341625i | ||||
\(126\) | 2.55160 | + | 0.545094i | 0.227314 | + | 0.0485609i | ||||
\(127\) | −8.46315 | − | 8.46315i | −0.750983 | − | 0.750983i | 0.223680 | − | 0.974663i | \(-0.428193\pi\) |
−0.974663 | + | 0.223680i | \(0.928193\pi\) | |||||||
\(128\) | −8.74107 | − | 7.18288i | −0.772609 | − | 0.634883i | ||||
\(129\) | − | 7.02305i | − | 0.618345i | ||||||
\(130\) | −2.57766 | − | 1.83185i | −0.226075 | − | 0.160664i | ||||
\(131\) | − | 15.5022i | − | 1.35443i | −0.735785 | − | 0.677215i | \(-0.763187\pi\) | ||
0.735785 | − | 0.677215i | \(-0.236813\pi\) | |||||||
\(132\) | 1.87218 | − | 0.714260i | 0.162952 | − | 0.0621683i | ||||
\(133\) | 5.31770 | + | 5.31770i | 0.461103 | + | 0.461103i | ||||
\(134\) | −4.20791 | + | 19.6973i | −0.363508 | + | 1.70159i | ||||
\(135\) | −11.1524 | + | 4.42876i | −0.959846 | + | 0.381167i | ||||
\(136\) | 11.5979 | − | 15.8603i | 0.994509 | − | 1.36001i | ||||
\(137\) | −2.57473 | + | 2.57473i | −0.219974 | + | 0.219974i | −0.808487 | − | 0.588513i | \(-0.799713\pi\) |
0.588513 | + | 0.808487i | \(0.299713\pi\) | |||||||
\(138\) | 11.5895 | − | 7.50943i | 0.986564 | − | 0.639245i | ||||
\(139\) | 4.22654 | 0.358491 | 0.179245 | − | 0.983804i | \(-0.442634\pi\) | ||||
0.179245 | + | 0.983804i | \(0.442634\pi\) | |||||||
\(140\) | −0.209242 | + | 4.87270i | −0.0176842 | + | 0.411818i | ||||
\(141\) | −6.16488 | −0.519176 | ||||||||
\(142\) | 5.95181 | − | 3.85648i | 0.499465 | − | 0.323629i | ||||
\(143\) | −0.619387 | + | 0.619387i | −0.0517958 | + | 0.0517958i | ||||
\(144\) | 5.04736 | − | 4.50731i | 0.420613 | − | 0.375609i | ||||
\(145\) | 16.1212 | + | 6.95667i | 1.33879 | + | 0.577720i | ||||
\(146\) | 2.86245 | − | 13.3992i | 0.236898 | − | 1.10892i | ||||
\(147\) | 4.69956 | + | 4.69956i | 0.387613 | + | 0.387613i | ||||
\(148\) | −2.23809 | − | 5.86636i | −0.183970 | − | 0.482212i | ||||
\(149\) | − | 1.00491i | − | 0.0823258i | −0.999152 | − | 0.0411629i | \(-0.986894\pi\) | ||
0.999152 | − | 0.0411629i | \(-0.0131063\pi\) | |||||||
\(150\) | −4.19678 | − | 6.91376i | −0.342666 | − | 0.564506i | ||||
\(151\) | 16.2847i | 1.32523i | 0.748960 | + | 0.662615i | \(0.230554\pi\) | ||||
−0.748960 | + | 0.662615i | \(0.769446\pi\) | |||||||
\(152\) | 19.2734 | − | 2.99186i | 1.56328 | − | 0.242672i | ||||
\(153\) | 8.30998 | + | 8.30998i | 0.671822 | + | 0.671822i | ||||
\(154\) | 1.32116 | + | 0.282238i | 0.106462 | + | 0.0227434i | ||||
\(155\) | 11.2065 | + | 4.83585i | 0.900124 | + | 0.388425i | ||||
\(156\) | 0.934729 | − | 2.08790i | 0.0748382 | − | 0.167166i | ||||
\(157\) | −0.171561 | + | 0.171561i | −0.0136920 | + | 0.0136920i | −0.713920 | − | 0.700228i | \(-0.753082\pi\) |
0.700228 | + | 0.713920i | \(0.253082\pi\) | |||||||
\(158\) | 1.25318 | + | 1.93406i | 0.0996975 | + | 0.153866i | ||||
\(159\) | 3.53565 | 0.280395 | ||||||||
\(160\) | 9.88070 | + | 7.89758i | 0.781138 | + | 0.624359i | ||||
\(161\) | 9.31058 | 0.733777 | ||||||||
\(162\) | −0.817316 | − | 1.26139i | −0.0642144 | − | 0.0991038i | ||||
\(163\) | −8.52729 | + | 8.52729i | −0.667909 | + | 0.667909i | −0.957232 | − | 0.289323i | \(-0.906570\pi\) |
0.289323 | + | 0.957232i | \(0.406570\pi\) | |||||||
\(164\) | 1.11700 | − | 2.49504i | 0.0872230 | − | 0.194830i | ||||
\(165\) | −2.08215 | + | 0.826847i | −0.162095 | + | 0.0643700i | ||||
\(166\) | 5.22195 | + | 1.11556i | 0.405302 | + | 0.0865841i | ||||
\(167\) | −8.81617 | − | 8.81617i | −0.682216 | − | 0.682216i | 0.278283 | − | 0.960499i | \(-0.410235\pi\) |
−0.960499 | + | 0.278283i | \(0.910235\pi\) | |||||||
\(168\) | −3.48639 | + | 0.541201i | −0.268981 | + | 0.0417546i | ||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | −12.7254 | + | 17.9063i | −0.975996 | + | 1.37335i | ||||
\(171\) | 11.6659i | 0.892112i | ||||||||
\(172\) | −4.37734 | − | 11.4736i | −0.333769 | − | 0.874857i | ||||
\(173\) | 0.914606 | + | 0.914606i | 0.0695362 | + | 0.0695362i | 0.741020 | − | 0.671483i | \(-0.234343\pi\) |
−0.671483 | + | 0.741020i | \(0.734343\pi\) | |||||||
\(174\) | −2.65353 | + | 12.4212i | −0.201163 | + | 0.941650i | ||||
\(175\) | 0.160122 | − | 5.45051i | 0.0121041 | − | 0.412020i | ||||
\(176\) | 2.61341 | − | 2.33379i | 0.196993 | − | 0.175916i | ||||
\(177\) | 0.605997 | − | 0.605997i | 0.0455496 | − | 0.0455496i | ||||
\(178\) | −4.37714 | + | 2.83617i | −0.328081 | + | 0.212580i | ||||
\(179\) | 4.85523 | 0.362897 | 0.181449 | − | 0.983400i | \(-0.441921\pi\) | ||||
0.181449 | + | 0.983400i | \(0.441921\pi\) | |||||||
\(180\) | −5.57434 | + | 5.11531i | −0.415487 | + | 0.381272i | ||||
\(181\) | −16.5488 | −1.23006 | −0.615031 | − | 0.788503i | \(-0.710857\pi\) | ||||
−0.615031 | + | 0.788503i | \(0.710857\pi\) | |||||||
\(182\) | 1.29434 | − | 0.838671i | 0.0959432 | − | 0.0621664i | ||||
\(183\) | 3.87974 | − | 3.87974i | 0.286798 | − | 0.286798i | ||||
\(184\) | 14.2534 | − | 19.4918i | 1.05078 | − | 1.43695i | ||||
\(185\) | 2.59088 | + | 6.52429i | 0.190485 | + | 0.479676i | ||||
\(186\) | −1.84457 | + | 8.63448i | −0.135251 | + | 0.633111i | ||||
\(187\) | 4.30273 | + | 4.30273i | 0.314647 | + | 0.314647i | ||||
\(188\) | −10.0716 | + | 3.84246i | −0.734549 | + | 0.280240i | ||||
\(189\) | − | 5.85242i | − | 0.425701i | ||||||
\(190\) | −21.5010 | + | 3.63658i | −1.55985 | + | 0.263825i | ||||
\(191\) | − | 19.6388i | − | 1.42102i | −0.703690 | − | 0.710508i | \(-0.748465\pi\) | ||
0.703690 | − | 0.710508i | \(-0.251535\pi\) | |||||||
\(192\) | −4.20425 | + | 8.12730i | −0.303416 | + | 0.586537i | ||||
\(193\) | −13.0800 | − | 13.0800i | −0.941517 | − | 0.941517i | 0.0568651 | − | 0.998382i | \(-0.481890\pi\) |
−0.998382 | + | 0.0568651i | \(0.981890\pi\) | |||||||
\(194\) | −13.0167 | − | 2.78074i | −0.934544 | − | 0.199645i | ||||
\(195\) | −1.01334 | + | 2.34829i | −0.0725669 | + | 0.168164i | ||||
\(196\) | 10.6069 | + | 4.74857i | 0.757634 | + | 0.339184i | ||||
\(197\) | −0.774201 | + | 0.774201i | −0.0551596 | + | 0.0551596i | −0.734149 | − | 0.678989i | \(-0.762418\pi\) |
0.678989 | + | 0.734149i | \(0.262418\pi\) | |||||||
\(198\) | 1.13959 | + | 1.75876i | 0.0809870 | + | 0.124989i | ||||
\(199\) | −3.72024 | −0.263721 | −0.131860 | − | 0.991268i | \(-0.542095\pi\) | ||||
−0.131860 | + | 0.991268i | \(0.542095\pi\) | |||||||
\(200\) | −11.1656 | − | 8.67931i | −0.789524 | − | 0.613720i | ||||
\(201\) | 16.2903 | 1.14903 | ||||||||
\(202\) | 4.79031 | + | 7.39301i | 0.337045 | + | 0.520171i | ||||
\(203\) | −6.05525 | + | 6.05525i | −0.424995 | + | 0.424995i | ||||
\(204\) | −14.5041 | − | 6.49333i | −1.01549 | − | 0.454624i | ||||
\(205\) | −1.21094 | + | 2.80620i | −0.0845758 | + | 0.195993i | ||||
\(206\) | 17.7157 | + | 3.78458i | 1.23431 | + | 0.263684i | ||||
\(207\) | 10.2127 | + | 10.2127i | 0.709832 | + | 0.709832i | ||||
\(208\) | 0.225727 | − | 3.99363i | 0.0156513 | − | 0.276908i | ||||
\(209\) | 6.04034i | 0.417819i | ||||||||
\(210\) | 3.88935 | − | 0.657826i | 0.268391 | − | 0.0453943i | ||||
\(211\) | 10.1014i | 0.695411i | 0.937604 | + | 0.347706i | \(0.113039\pi\) | ||||
−0.937604 | + | 0.347706i | \(0.886961\pi\) | |||||||
\(212\) | 5.77623 | − | 2.20371i | 0.396713 | − | 0.151351i | ||||
\(213\) | −4.05589 | − | 4.05589i | −0.277905 | − | 0.277905i | ||||
\(214\) | −2.91672 | + | 13.6532i | −0.199383 | + | 0.933314i | ||||
\(215\) | 5.06733 | + | 12.7604i | 0.345589 | + | 0.870255i | ||||
\(216\) | −12.2521 | − | 8.95937i | −0.833648 | − | 0.609608i | ||||
\(217\) | −4.20924 | + | 4.20924i | −0.285742 | + | 0.285742i | ||||
\(218\) | −6.97208 | + | 4.51756i | −0.472209 | + | 0.305968i | ||||
\(219\) | −11.0816 | −0.748822 | ||||||||
\(220\) | −2.88627 | + | 2.64860i | −0.194592 | + | 0.178568i | ||||
\(221\) | 6.94675 | 0.467289 | ||||||||
\(222\) | −4.26176 | + | 2.76141i | −0.286030 | + | 0.185334i | ||||
\(223\) | −10.9738 | + | 10.9738i | −0.734860 | + | 0.734860i | −0.971578 | − | 0.236718i | \(-0.923928\pi\) |
0.236718 | + | 0.971578i | \(0.423928\pi\) | |||||||
\(224\) | −5.35844 | + | 3.05717i | −0.358026 | + | 0.204266i | ||||
\(225\) | 6.15426 | − | 5.80298i | 0.410284 | − | 0.386866i | ||||
\(226\) | 3.46580 | − | 16.2235i | 0.230541 | − | 1.07917i | ||||
\(227\) | 5.10770 | + | 5.10770i | 0.339010 | + | 0.339010i | 0.855995 | − | 0.516985i | \(-0.172946\pi\) |
−0.516985 | + | 0.855995i | \(0.672946\pi\) | |||||||
\(228\) | −5.62293 | − | 14.7385i | −0.372388 | − | 0.976082i | ||||
\(229\) | 1.18140i | 0.0780689i | 0.999238 | + | 0.0390345i | \(0.0124282\pi\) | ||||
−0.999238 | + | 0.0390345i | \(0.987572\pi\) | |||||||
\(230\) | −15.6391 | + | 22.0063i | −1.03121 | + | 1.45105i | ||||
\(231\) | − | 1.09265i | − | 0.0718908i | ||||||
\(232\) | 3.40682 | + | 21.9466i | 0.223669 | + | 1.44086i | ||||
\(233\) | −12.0874 | − | 12.0874i | −0.791870 | − | 0.791870i | 0.189928 | − | 0.981798i | \(-0.439175\pi\) |
−0.981798 | + | 0.189928i | \(0.939175\pi\) | |||||||
\(234\) | 2.33969 | + | 0.499824i | 0.152950 | + | 0.0326745i | ||||
\(235\) | 11.2012 | − | 4.44814i | 0.730686 | − | 0.290164i | ||||
\(236\) | 0.612318 | − | 1.36773i | 0.0398585 | − | 0.0890318i | ||||
\(237\) | 1.31798 | − | 1.31798i | 0.0856118 | − | 0.0856118i | ||||
\(238\) | −5.82604 | − | 8.99149i | −0.377646 | − | 0.582831i | ||||
\(239\) | 19.0528 | 1.23242 | 0.616211 | − | 0.787581i | \(-0.288667\pi\) | ||||
0.616211 | + | 0.787581i | \(0.288667\pi\) | |||||||
\(240\) | 4.57698 | − | 9.14943i | 0.295443 | − | 0.590593i | ||||
\(241\) | −0.866695 | −0.0558287 | −0.0279144 | − | 0.999610i | \(-0.508887\pi\) | ||||
−0.0279144 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(242\) | −7.86916 | − | 12.1447i | −0.505849 | − | 0.780690i | ||||
\(243\) | 10.5242 | − | 10.5242i | 0.675129 | − | 0.675129i | ||||
\(244\) | 3.92020 | − | 8.75654i | 0.250965 | − | 0.560580i | ||||
\(245\) | −11.9297 | − | 5.14794i | −0.762159 | − | 0.328890i | ||||
\(246\) | −2.16215 | − | 0.461898i | −0.137854 | − | 0.0294495i | ||||
\(247\) | 4.87606 | + | 4.87606i | 0.310256 | + | 0.310256i | ||||
\(248\) | 2.36822 | + | 15.2559i | 0.150382 | + | 0.968753i | ||||
\(249\) | − | 4.31872i | − | 0.273688i | ||||||
\(250\) | 12.6138 | + | 9.53378i | 0.797765 | + | 0.602969i | ||||
\(251\) | − | 11.9952i | − | 0.757128i | −0.925575 | − | 0.378564i | \(-0.876418\pi\) | ||
0.925575 | − | 0.378564i | \(-0.123582\pi\) | |||||||
\(252\) | −1.31528 | − | 3.44755i | −0.0828551 | − | 0.217175i | ||||
\(253\) | 5.28792 | + | 5.28792i | 0.332449 | + | 0.332449i | ||||
\(254\) | −3.53615 | + | 16.5528i | −0.221878 | + | 1.03861i | ||||
\(255\) | 16.3130 | + | 7.03943i | 1.02156 | + | 0.440826i | ||||
\(256\) | −1.80294 | + | 15.8981i | −0.112684 | + | 0.993631i | ||||
\(257\) | −9.55086 | + | 9.55086i | −0.595766 | + | 0.595766i | −0.939183 | − | 0.343417i | \(-0.888416\pi\) |
0.343417 | + | 0.939183i | \(0.388416\pi\) | |||||||
\(258\) | −8.33530 | + | 5.40086i | −0.518933 | + | 0.336243i | ||||
\(259\) | −3.42374 | −0.212741 | ||||||||
\(260\) | −0.191864 | + | 4.46802i | −0.0118989 | + | 0.277095i | ||||
\(261\) | −13.2839 | −0.822253 | ||||||||
\(262\) | −18.3987 | + | 11.9215i | −1.13668 | + | 0.736510i | ||||
\(263\) | 8.00268 | − | 8.00268i | 0.493467 | − | 0.493467i | −0.415930 | − | 0.909397i | \(-0.636544\pi\) |
0.909397 | + | 0.415930i | \(0.136544\pi\) | |||||||
\(264\) | −2.28746 | − | 1.67271i | −0.140783 | − | 0.102948i | ||||
\(265\) | −6.42406 | + | 2.55107i | −0.394627 | + | 0.156711i | ||||
\(266\) | 2.22189 | − | 10.4007i | 0.136233 | − | 0.637708i | ||||
\(267\) | 2.98282 | + | 2.98282i | 0.182546 | + | 0.182546i | ||||
\(268\) | 26.6137 | − | 10.1535i | 1.62569 | − | 0.620221i | ||||
\(269\) | − | 7.28829i | − | 0.444375i | −0.975004 | − | 0.222188i | \(-0.928680\pi\) | ||
0.975004 | − | 0.222188i | \(-0.0713197\pi\) | |||||||
\(270\) | 13.8327 | + | 9.83041i | 0.841830 | + | 0.598260i | ||||
\(271\) | − | 4.92513i | − | 0.299181i | −0.988748 | − | 0.149590i | \(-0.952205\pi\) | ||
0.988748 | − | 0.149590i | \(-0.0477955\pi\) | |||||||
\(272\) | −27.7427 | − | 1.56807i | −1.68215 | − | 0.0950781i | ||||
\(273\) | −0.882037 | − | 0.882037i | −0.0533833 | − | 0.0533833i | ||||
\(274\) | 5.03583 | + | 1.07580i | 0.304226 | + | 0.0649913i | ||||
\(275\) | 3.18654 | − | 3.00466i | 0.192156 | − | 0.181188i | ||||
\(276\) | −17.8251 | − | 7.98009i | −1.07295 | − | 0.480345i | ||||
\(277\) | −13.6222 | + | 13.6222i | −0.818482 | + | 0.818482i | −0.985888 | − | 0.167406i | \(-0.946461\pi\) |
0.167406 | + | 0.985888i | \(0.446461\pi\) | |||||||
\(278\) | −3.25029 | − | 5.01627i | −0.194940 | − | 0.300856i | ||||
\(279\) | −9.23417 | −0.552835 | ||||||||
\(280\) | 5.94406 | − | 3.49886i | 0.355226 | − | 0.209097i | ||||
\(281\) | 11.2668 | 0.672120 | 0.336060 | − | 0.941841i | \(-0.390905\pi\) | ||||
0.336060 | + | 0.941841i | \(0.390905\pi\) | |||||||
\(282\) | 4.74091 | + | 7.31678i | 0.282317 | + | 0.435708i | ||||
\(283\) | −11.8154 | + | 11.8154i | −0.702350 | + | 0.702350i | −0.964914 | − | 0.262565i | \(-0.915432\pi\) |
0.262565 | + | 0.964914i | \(0.415432\pi\) | |||||||
\(284\) | −9.15412 | − | 4.09819i | −0.543197 | − | 0.243183i | ||||
\(285\) | 6.50926 | + | 16.3915i | 0.385576 | + | 0.970948i | ||||
\(286\) | 1.21144 | + | 0.258798i | 0.0716339 | + | 0.0153031i | ||||
\(287\) | −1.05403 | − | 1.05403i | −0.0622176 | − | 0.0622176i | ||||
\(288\) | −9.23101 | − | 2.52424i | −0.543943 | − | 0.148742i | ||||
\(289\) | − | 31.2573i | − | 1.83867i | ||||||
\(290\) | −4.14097 | − | 24.4832i | −0.243166 | − | 1.43770i | ||||
\(291\) | 10.7652i | 0.631069i | ||||||||
\(292\) | −18.1041 | + | 6.90693i | −1.05946 | + | 0.404198i | ||||
\(293\) | −7.28832 | − | 7.28832i | −0.425788 | − | 0.425788i | 0.461403 | − | 0.887191i | \(-0.347346\pi\) |
−0.887191 | + | 0.461403i | \(0.847346\pi\) | |||||||
\(294\) | 1.96361 | − | 9.19172i | 0.114520 | − | 0.536072i | ||||
\(295\) | −0.663815 | + | 1.53830i | −0.0386488 | + | 0.0895635i | ||||
\(296\) | −5.24135 | + | 7.16762i | −0.304647 | + | 0.416609i | ||||
\(297\) | 3.32387 | − | 3.32387i | 0.192870 | − | 0.192870i | ||||
\(298\) | −1.19268 | + | 0.772798i | −0.0690901 | + | 0.0447670i | ||||
\(299\) | 8.53734 | 0.493727 | ||||||||
\(300\) | −4.97818 | + | 10.2978i | −0.287415 | + | 0.594541i | ||||
\(301\) | −6.69627 | −0.385967 | ||||||||
\(302\) | 19.3275 | − | 12.5233i | 1.11217 | − | 0.720632i | ||||
\(303\) | 5.03800 | − | 5.03800i | 0.289426 | − | 0.289426i | ||||
\(304\) | −18.3725 | − | 20.5738i | −1.05373 | − | 1.17999i | ||||
\(305\) | −4.24990 | + | 9.84858i | −0.243349 | + | 0.563928i | ||||
\(306\) | 3.47215 | − | 16.2532i | 0.198490 | − | 0.929135i | ||||
\(307\) | 16.3497 | + | 16.3497i | 0.933128 | + | 0.933128i | 0.997900 | − | 0.0647718i | \(-0.0206319\pi\) |
−0.0647718 | + | 0.997900i | \(0.520632\pi\) | |||||||
\(308\) | −0.681026 | − | 1.78507i | −0.0388050 | − | 0.101714i | ||||
\(309\) | − | 14.6515i | − | 0.833493i | ||||||
\(310\) | −2.87855 | − | 17.0192i | −0.163491 | − | 0.966627i | ||||
\(311\) | 21.7219i | 1.23174i | 0.787850 | + | 0.615868i | \(0.211194\pi\) | ||||
−0.787850 | + | 0.615868i | \(0.788806\pi\) | |||||||
\(312\) | −3.19685 | + | 0.496254i | −0.180986 | + | 0.0280949i | ||||
\(313\) | −1.17273 | − | 1.17273i | −0.0662866 | − | 0.0662866i | 0.673186 | − | 0.739473i | \(-0.264925\pi\) |
−0.739473 | + | 0.673186i | \(0.764925\pi\) | |||||||
\(314\) | 0.335550 | + | 0.0716830i | 0.0189362 | + | 0.00404531i | ||||
\(315\) | 1.52261 | + | 3.83420i | 0.0857893 | + | 0.216033i | ||||
\(316\) | 1.33172 | − | 2.97467i | 0.0749153 | − | 0.167338i | ||||
\(317\) | 6.45087 | − | 6.45087i | 0.362317 | − | 0.362317i | −0.502348 | − | 0.864665i | \(-0.667530\pi\) |
0.864665 | + | 0.502348i | \(0.167530\pi\) | |||||||
\(318\) | −2.71898 | − | 4.19628i | −0.152473 | − | 0.235316i | ||||
\(319\) | −6.87812 | −0.385101 | ||||||||
\(320\) | 1.77479 | − | 17.8003i | 0.0992136 | − | 0.995066i | ||||
\(321\) | 11.2917 | 0.630239 | ||||||||
\(322\) | −7.16002 | − | 11.0503i | −0.399012 | − | 0.615807i | ||||
\(323\) | 33.8728 | − | 33.8728i | 1.88473 | − | 1.88473i | ||||
\(324\) | −0.868542 | + | 1.94006i | −0.0482523 | + | 0.107781i | ||||
\(325\) | 0.146824 | − | 4.99784i | 0.00814433 | − | 0.277230i | ||||
\(326\) | 16.6783 | + | 3.56295i | 0.923723 | + | 0.197334i | ||||
\(327\) | 4.75115 | + | 4.75115i | 0.262739 | + | 0.262739i | ||||
\(328\) | −3.82023 | + | 0.593023i | −0.210937 | + | 0.0327442i | ||||
\(329\) | 5.87803i | 0.324066i | ||||||||
\(330\) | 2.58256 | + | 1.83533i | 0.142165 | + | 0.101032i | ||||
\(331\) | 32.7431i | 1.79973i | 0.436173 | + | 0.899863i | \(0.356334\pi\) | ||||
−0.436173 | + | 0.899863i | \(0.643666\pi\) | |||||||
\(332\) | −2.69178 | − | 7.05555i | −0.147731 | − | 0.387224i | ||||
\(333\) | −3.75547 | − | 3.75547i | −0.205799 | − | 0.205799i | ||||
\(334\) | −3.68365 | + | 17.2433i | −0.201561 | + | 0.943510i | ||||
\(335\) | −29.5985 | + | 11.7539i | −1.61714 | + | 0.642186i | ||||
\(336\) | 3.32343 | + | 3.72162i | 0.181308 | + | 0.203031i | ||||
\(337\) | 17.0557 | − | 17.0557i | 0.929083 | − | 0.929083i | −0.0685633 | − | 0.997647i | \(-0.521842\pi\) |
0.997647 | + | 0.0685633i | \(0.0218415\pi\) | |||||||
\(338\) | 1.18685 | − | 0.769019i | 0.0645560 | − | 0.0418291i | ||||
\(339\) | −13.4173 | −0.728730 | ||||||||
\(340\) | 31.0382 | + | 1.33283i | 1.68328 | + | 0.0722831i | ||||
\(341\) | −4.78125 | −0.258919 | ||||||||
\(342\) | 13.8456 | − | 8.97128i | 0.748686 | − | 0.485111i | ||||
\(343\) | 9.87895 | − | 9.87895i | 0.533413 | − | 0.533413i | ||||
\(344\) | −10.2512 | + | 14.0187i | −0.552708 | + | 0.755837i | ||||
\(345\) | 20.0481 | + | 8.65124i | 1.07935 | + | 0.465767i | ||||
\(346\) | 0.382149 | − | 1.78885i | 0.0205445 | − | 0.0961690i | ||||
\(347\) | −12.2761 | − | 12.2761i | −0.659016 | − | 0.659016i | 0.296131 | − | 0.955147i | \(-0.404303\pi\) |
−0.955147 | + | 0.296131i | \(0.904303\pi\) | |||||||
\(348\) | 16.7827 | − | 6.40282i | 0.899648 | − | 0.343227i | ||||
\(349\) | 30.2444i | 1.61895i | 0.587156 | + | 0.809474i | \(0.300248\pi\) | ||||
−0.587156 | + | 0.809474i | \(0.699752\pi\) | |||||||
\(350\) | −6.59207 | + | 4.00151i | −0.352361 | + | 0.213890i | ||||
\(351\) | − | 5.36638i | − | 0.286436i | ||||||
\(352\) | −4.77962 | − | 1.30700i | −0.254755 | − | 0.0696632i | ||||
\(353\) | −15.7099 | − | 15.7099i | −0.836152 | − | 0.836152i | 0.152198 | − | 0.988350i | \(-0.451365\pi\) |
−0.988350 | + | 0.152198i | \(0.951365\pi\) | |||||||
\(354\) | −1.18525 | − | 0.253203i | −0.0629954 | − | 0.0134576i | ||||
\(355\) | 10.2957 | + | 4.44286i | 0.546441 | + | 0.235803i | ||||
\(356\) | 6.73221 | + | 3.01393i | 0.356807 | + | 0.159738i | ||||
\(357\) | −6.12729 | + | 6.12729i | −0.324291 | + | 0.324291i | ||||
\(358\) | −3.73377 | − | 5.76243i | −0.197336 | − | 0.304554i | ||||
\(359\) | −35.6895 | −1.88362 | −0.941809 | − | 0.336149i | \(-0.890875\pi\) | ||||
−0.941809 | + | 0.336149i | \(0.890875\pi\) | |||||||
\(360\) | 10.3579 | + | 2.68213i | 0.545908 | + | 0.141360i | ||||
\(361\) | 28.5519 | 1.50273 | ||||||||
\(362\) | 12.7263 | + | 19.6409i | 0.668882 | + | 1.03230i | ||||
\(363\) | −8.27605 | + | 8.27605i | −0.434380 | + | 0.434380i | ||||
\(364\) | −1.99075 | − | 0.891236i | −0.104344 | − | 0.0467135i | ||||
\(365\) | 20.1345 | − | 7.99566i | 1.05389 | − | 0.418512i | ||||
\(366\) | −7.58825 | − | 1.62107i | −0.396644 | − | 0.0847345i | ||||
\(367\) | 4.41082 | + | 4.41082i | 0.230243 | + | 0.230243i | 0.812794 | − | 0.582551i | \(-0.197945\pi\) |
−0.582551 | + | 0.812794i | \(0.697945\pi\) | |||||||
\(368\) | −34.0949 | − | 1.92711i | −1.77732 | − | 0.100457i | ||||
\(369\) | − | 2.31232i | − | 0.120375i | ||||||
\(370\) | 5.75091 | − | 8.09229i | 0.298976 | − | 0.420698i | ||||
\(371\) | − | 3.37114i | − | 0.175021i | ||||||
\(372\) | 11.6663 | − | 4.45085i | 0.604871 | − | 0.230766i | ||||
\(373\) | 16.1225 | + | 16.1225i | 0.834792 | + | 0.834792i | 0.988168 | − | 0.153376i | \(-0.0490145\pi\) |
−0.153376 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(374\) | 1.79781 | − | 8.41557i | 0.0929624 | − | 0.435159i | ||||
\(375\) | 5.40931 | − | 11.5876i | 0.279335 | − | 0.598380i | ||||
\(376\) | 12.3057 | + | 8.99858i | 0.634618 | + | 0.464066i | ||||
\(377\) | −5.55236 | + | 5.55236i | −0.285961 | + | 0.285961i | ||||
\(378\) | −6.94594 | + | 4.50062i | −0.357260 | + | 0.231487i | ||||
\(379\) | 33.3029 | 1.71066 | 0.855328 | − | 0.518086i | \(-0.173355\pi\) | ||||
0.855328 | + | 0.518086i | \(0.173355\pi\) | |||||||
\(380\) | 20.8508 | + | 22.7219i | 1.06962 | + | 1.16561i | ||||
\(381\) | 13.6897 | 0.701345 | ||||||||
\(382\) | −23.3083 | + | 15.1026i | −1.19256 | + | 0.772718i | ||||
\(383\) | −1.90891 | + | 1.90891i | −0.0975409 | + | 0.0975409i | −0.754193 | − | 0.656652i | \(-0.771972\pi\) |
0.656652 | + | 0.754193i | \(0.271972\pi\) | |||||||
\(384\) | 12.8790 | − | 1.26024i | 0.657230 | − | 0.0643113i | ||||
\(385\) | 0.788375 | + | 1.98527i | 0.0401793 | + | 0.101179i | ||||
\(386\) | −5.46519 | + | 25.5827i | −0.278171 | + | 1.30212i | ||||
\(387\) | −7.34509 | − | 7.34509i | −0.373372 | − | 0.373372i | ||||
\(388\) | 6.70977 | + | 17.5873i | 0.340637 | + | 0.892859i | ||||
\(389\) | 2.08615i | 0.105772i | 0.998601 | + | 0.0528859i | \(0.0168420\pi\) | ||||
−0.998601 | + | 0.0528859i | \(0.983158\pi\) | |||||||
\(390\) | 3.56634 | − | 0.603194i | 0.180589 | − | 0.0305439i | ||||
\(391\) | − | 59.3067i | − | 2.99927i | ||||||
\(392\) | −2.52105 | − | 16.2405i | −0.127332 | − | 0.820269i | ||||
\(393\) | 12.5379 | + | 12.5379i | 0.632453 | + | 0.632453i | ||||
\(394\) | 1.51424 | + | 0.323484i | 0.0762861 | + | 0.0162969i | ||||
\(395\) | −1.44372 | + | 3.34564i | −0.0726417 | + | 0.168337i | ||||
\(396\) | 1.21101 | − | 2.70504i | 0.0608557 | − | 0.135933i | ||||
\(397\) | −23.2416 | + | 23.2416i | −1.16646 | + | 1.16646i | −0.183431 | + | 0.983033i | \(0.558720\pi\) |
−0.983033 | + | 0.183431i | \(0.941280\pi\) | |||||||
\(398\) | 2.86094 | + | 4.41536i | 0.143406 | + | 0.221322i | ||||
\(399\) | −8.60173 | −0.430625 | ||||||||
\(400\) | −1.71451 | + | 19.9264i | −0.0857254 | + | 0.996319i | ||||
\(401\) | 16.0373 | 0.800865 | 0.400432 | − | 0.916326i | \(-0.368860\pi\) | ||||
0.400432 | + | 0.916326i | \(0.368860\pi\) | |||||||
\(402\) | −12.5276 | − | 19.3341i | −0.624818 | − | 0.964299i | ||||
\(403\) | −3.85966 | + | 3.85966i | −0.192264 | + | 0.192264i | ||||
\(404\) | 5.09055 | − | 11.3707i | 0.253264 | − | 0.565715i | ||||
\(405\) | 0.941589 | − | 2.18201i | 0.0467879 | − | 0.108425i | ||||
\(406\) | 11.8433 | + | 2.53006i | 0.587771 | + | 0.125565i | ||||
\(407\) | −1.94450 | − | 1.94450i | −0.0963854 | − | 0.0963854i | ||||
\(408\) | 3.44735 | + | 22.2077i | 0.170669 | + | 1.09944i | ||||
\(409\) | 38.6612i | 1.91167i | 0.293898 | + | 0.955837i | \(0.405047\pi\) | ||||
−0.293898 | + | 0.955837i | \(0.594953\pi\) | |||||||
\(410\) | 4.26177 | − | 0.720816i | 0.210474 | − | 0.0355985i | ||||
\(411\) | − | 4.16480i | − | 0.205434i | ||||||
\(412\) | −9.13199 | − | 23.9363i | −0.449901 | − | 1.17925i | ||||
\(413\) | −0.577801 | − | 0.577801i | −0.0284317 | − | 0.0284317i | ||||
\(414\) | 4.26717 | − | 19.9747i | 0.209720 | − | 0.981703i | ||||
\(415\) | 3.11608 | + | 7.84685i | 0.152962 | + | 0.385187i | ||||
\(416\) | −4.91342 | + | 2.80327i | −0.240900 | + | 0.137442i | ||||
\(417\) | −3.41836 | + | 3.41836i | −0.167398 | + | 0.167398i | ||||
\(418\) | 7.16897 | − | 4.64514i | 0.350646 | − | 0.227201i | ||||
\(419\) | 15.9101 | 0.777261 | 0.388630 | − | 0.921394i | \(-0.372948\pi\) | ||||
0.388630 | + | 0.921394i | \(0.372948\pi\) | |||||||
\(420\) | −3.77173 | − | 4.11019i | −0.184041 | − | 0.200557i | ||||
\(421\) | 3.52390 | 0.171744 | 0.0858721 | − | 0.996306i | \(-0.472632\pi\) | ||||
0.0858721 | + | 0.996306i | \(0.472632\pi\) | |||||||
\(422\) | 11.9889 | − | 7.76819i | 0.583609 | − | 0.378150i | ||||
\(423\) | −6.44756 | + | 6.44756i | −0.313491 | + | 0.313491i | ||||
\(424\) | −7.05750 | − | 5.16082i | −0.342743 | − | 0.250632i | ||||
\(425\) | −34.7188 | − | 1.01995i | −1.68411 | − | 0.0494748i | ||||
\(426\) | −1.69467 | + | 7.93279i | −0.0821070 | + | 0.384345i | ||||
\(427\) | −3.69921 | − | 3.69921i | −0.179018 | − | 0.179018i | ||||
\(428\) | 18.4473 | − | 7.03788i | 0.891684 | − | 0.340189i | ||||
\(429\) | − | 1.00190i | − | 0.0483722i | ||||||
\(430\) | 11.2478 | − | 15.8272i | 0.542419 | − | 0.763255i | ||||
\(431\) | − | 34.0034i | − | 1.63788i | −0.573876 | − | 0.818942i | \(-0.694561\pi\) | ||
0.573876 | − | 0.818942i | \(-0.305439\pi\) | |||||||
\(432\) | −1.21134 | + | 21.4313i | −0.0582804 | + | 1.03111i | ||||
\(433\) | −20.4386 | − | 20.4386i | −0.982216 | − | 0.982216i | 0.0176285 | − | 0.999845i | \(-0.494388\pi\) |
−0.999845 | + | 0.0176285i | \(0.994388\pi\) | |||||||
\(434\) | 8.23272 | + | 1.75874i | 0.395183 | + | 0.0844224i | ||||
\(435\) | −18.6650 | + | 7.41209i | −0.894916 | + | 0.355382i | ||||
\(436\) | 10.7233 | + | 4.80071i | 0.513554 | + | 0.229912i | ||||
\(437\) | 41.6286 | − | 41.6286i | 1.99136 | − | 1.99136i | ||||
\(438\) | 8.52193 | + | 13.1521i | 0.407194 | + | 0.628433i | ||||
\(439\) | 4.50397 | 0.214963 | 0.107481 | − | 0.994207i | \(-0.465721\pi\) | ||||
0.107481 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(440\) | 5.36308 | + | 1.38875i | 0.255675 | + | 0.0662059i | ||||
\(441\) | 9.83011 | 0.468100 | ||||||||
\(442\) | −5.34218 | − | 8.24474i | −0.254102 | − | 0.392162i | ||||
\(443\) | −16.9086 | + | 16.9086i | −0.803352 | + | 0.803352i | −0.983618 | − | 0.180266i | \(-0.942304\pi\) |
0.180266 | + | 0.983618i | \(0.442304\pi\) | |||||||
\(444\) | 6.55475 | + | 2.93448i | 0.311074 | + | 0.139264i | ||||
\(445\) | −7.57180 | − | 3.26741i | −0.358938 | − | 0.154890i | ||||
\(446\) | 21.4633 | + | 4.58517i | 1.01632 | + | 0.217114i | ||||
\(447\) | 0.812758 | + | 0.812758i | 0.0384421 | + | 0.0384421i | ||||
\(448\) | 7.74914 | + | 4.00863i | 0.366112 | + | 0.189390i | ||||
\(449\) | 15.2463i | 0.719516i | 0.933046 | + | 0.359758i | \(0.117141\pi\) | ||||
−0.933046 | + | 0.359758i | \(0.882859\pi\) | |||||||
\(450\) | −11.6200 | − | 2.84156i | −0.547772 | − | 0.133953i | ||||
\(451\) | − | 1.19727i | − | 0.0563772i | ||||||
\(452\) | −21.9201 | + | 8.36279i | −1.03103 | + | 0.393353i | ||||
\(453\) | −13.1708 | − | 13.1708i | −0.618818 | − | 0.618818i | ||||
\(454\) | 2.13415 | − | 9.98999i | 0.100160 | − | 0.468853i | ||||
\(455\) | 2.23902 | + | 0.966191i | 0.104967 | + | 0.0452958i | ||||
\(456\) | −13.1682 | + | 18.0078i | −0.616659 | + | 0.843291i | ||||
\(457\) | 7.44322 | − | 7.44322i | 0.348179 | − | 0.348179i | −0.511252 | − | 0.859431i | \(-0.670818\pi\) |
0.859431 | + | 0.511252i | \(0.170818\pi\) | |||||||
\(458\) | 1.40214 | − | 0.908517i | 0.0655177 | − | 0.0424522i | ||||
\(459\) | −37.2789 | −1.74003 | ||||||||
\(460\) | 38.1450 | + | 1.63801i | 1.77852 | + | 0.0763727i | ||||
\(461\) | −21.5904 | −1.00556 | −0.502782 | − | 0.864413i | \(-0.667690\pi\) | ||||
−0.502782 | + | 0.864413i | \(0.667690\pi\) | |||||||
\(462\) | −1.29680 | + | 0.840265i | −0.0603328 | + | 0.0390927i | ||||
\(463\) | 5.31937 | − | 5.31937i | 0.247212 | − | 0.247212i | −0.572614 | − | 0.819825i | \(-0.694070\pi\) |
0.819825 | + | 0.572614i | \(0.194070\pi\) | |||||||
\(464\) | 23.4274 | − | 20.9207i | 1.08759 | − | 0.971220i | ||||
\(465\) | −12.9747 | + | 5.15243i | −0.601690 | + | 0.238938i | ||||
\(466\) | −5.05046 | + | 23.6413i | −0.233958 | + | 1.09516i | ||||
\(467\) | −12.0139 | − | 12.0139i | −0.555939 | − | 0.555939i | 0.372210 | − | 0.928149i | \(-0.378600\pi\) |
−0.928149 | + | 0.372210i | \(0.878600\pi\) | |||||||
\(468\) | −1.20605 | − | 3.16123i | −0.0557496 | − | 0.146128i | ||||
\(469\) | − | 15.5323i | − | 0.717217i | ||||||
\(470\) | −13.8932 | − | 9.87343i | −0.640846 | − | 0.455427i | ||||
\(471\) | − | 0.277511i | − | 0.0127870i | ||||||
\(472\) | −2.09417 | + | 0.325084i | −0.0963922 | + | 0.0149632i | ||||
\(473\) | −3.80313 | − | 3.80313i | −0.174868 | − | 0.174868i | ||||
\(474\) | −2.57779 | − | 0.550689i | −0.118402 | − | 0.0252940i | ||||
\(475\) | −23.6539 | − | 25.0857i | −1.08531 | − | 1.15101i | ||||
\(476\) | −6.19120 | + | 13.8293i | −0.283773 | + | 0.633863i | ||||
\(477\) | 3.69777 | − | 3.69777i | 0.169309 | − | 0.169309i | ||||
\(478\) | −14.6520 | − | 22.6128i | −0.670165 | − | 1.03428i | ||||
\(479\) | −6.77238 | −0.309438 | −0.154719 | − | 0.987959i | \(-0.549447\pi\) | ||||
−0.154719 | + | 0.987959i | \(0.549447\pi\) | |||||||
\(480\) | −14.3788 | + | 1.60391i | −0.656298 | + | 0.0732082i | ||||
\(481\) | −3.13940 | −0.143144 | ||||||||
\(482\) | 0.666505 | + | 1.02864i | 0.0303585 | + | 0.0468531i | ||||
\(483\) | −7.53025 | + | 7.53025i | −0.342638 | + | 0.342638i | ||||
\(484\) | −8.36237 | + | 18.6790i | −0.380108 | + | 0.849045i | ||||
\(485\) | −7.76742 | − | 19.5598i | −0.352700 | − | 0.888163i | ||||
\(486\) | −20.5840 | − | 4.39733i | −0.933709 | − | 0.199467i | ||||
\(487\) | 5.85296 | + | 5.85296i | 0.265223 | + | 0.265223i | 0.827172 | − | 0.561949i | \(-0.189948\pi\) |
−0.561949 | + | 0.827172i | \(0.689948\pi\) | |||||||
\(488\) | −13.4074 | + | 2.08126i | −0.606924 | + | 0.0942143i | ||||
\(489\) | − | 13.7935i | − | 0.623762i | ||||||
\(490\) | 3.06432 | + | 18.1176i | 0.138432 | + | 0.818469i | ||||
\(491\) | − | 30.1005i | − | 1.35842i | −0.733945 | − | 0.679209i | \(-0.762323\pi\) | ||
0.733945 | − | 0.679209i | \(-0.237677\pi\) | |||||||
\(492\) | 1.11453 | + | 2.92136i | 0.0502471 | + | 0.131705i | ||||
\(493\) | 38.5708 | + | 38.5708i | 1.73714 | + | 1.73714i | ||||
\(494\) | 2.03736 | − | 9.53693i | 0.0916652 | − | 0.429087i | ||||
\(495\) | −1.31286 | + | 3.04239i | −0.0590088 | + | 0.136745i | ||||
\(496\) | 16.2853 | − | 14.5428i | 0.731231 | − | 0.652992i | ||||
\(497\) | −3.86717 | + | 3.86717i | −0.173466 | + | 0.173466i | ||||
\(498\) | −5.12567 | + | 3.32118i | −0.229687 | + | 0.148826i | ||||
\(499\) | −4.19308 | −0.187708 | −0.0938541 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938541 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(500\) | 1.61492 | − | 22.3023i | 0.0722214 | − | 0.997389i | ||||
\(501\) | 14.2607 | 0.637123 | ||||||||
\(502\) | −14.2364 | + | 9.22451i | −0.635404 | + | 0.411710i | ||||
\(503\) | 6.34559 | − | 6.34559i | 0.282936 | − | 0.282936i | −0.551343 | − | 0.834279i | \(-0.685884\pi\) |
0.834279 | + | 0.551343i | \(0.185884\pi\) | |||||||
\(504\) | −3.08024 | + | 4.21227i | −0.137205 | + | 0.187630i | ||||
\(505\) | −5.51867 | + | 12.7888i | −0.245578 | + | 0.569094i | ||||
\(506\) | 2.20945 | − | 10.3425i | 0.0982219 | − | 0.459779i | ||||
\(507\) | −0.808783 | − | 0.808783i | −0.0359193 | − | 0.0359193i | ||||
\(508\) | 22.3650 | − | 8.53254i | 0.992288 | − | 0.378570i | ||||
\(509\) | 40.6251i | 1.80068i | 0.435190 | + | 0.900338i | \(0.356681\pi\) | ||||
−0.435190 | + | 0.900338i | \(0.643319\pi\) | |||||||
\(510\) | −4.19024 | − | 24.7745i | −0.185547 | − | 1.09703i | ||||
\(511\) | 10.5659i | 0.467410i | ||||||||
\(512\) | 20.2551 | − | 10.0861i | 0.895158 | − | 0.445748i | ||||
\(513\) | −26.1668 | − | 26.1668i | −1.15529 | − | 1.15529i | ||||
\(514\) | 18.6802 | + | 3.99063i | 0.823949 | + | 0.176019i | ||||
\(515\) | 10.5714 | + | 26.6208i | 0.465834 | + | 1.17305i | ||||
\(516\) | 12.8200 | + | 5.73937i | 0.564369 | + | 0.252662i | ||||
\(517\) | −3.33841 | + | 3.33841i | −0.146823 | + | 0.146823i | ||||
\(518\) | 2.63292 | + | 4.06346i | 0.115684 | + | 0.178538i | ||||
\(519\) | −1.47944 | −0.0649400 | ||||||||
\(520\) | 5.45041 | − | 3.20828i | 0.239016 | − | 0.140692i | ||||
\(521\) | −37.7559 | −1.65412 | −0.827058 | − | 0.562116i | \(-0.809987\pi\) | ||||
−0.827058 | + | 0.562116i | \(0.809987\pi\) | |||||||
\(522\) | 10.2156 | + | 15.7660i | 0.447124 | + | 0.690058i | ||||
\(523\) | 4.86113 | − | 4.86113i | 0.212563 | − | 0.212563i | −0.592793 | − | 0.805355i | \(-0.701975\pi\) |
0.805355 | + | 0.592793i | \(0.201975\pi\) | |||||||
\(524\) | 28.2979 | + | 12.6687i | 1.23620 | + | 0.553433i | ||||
\(525\) | 4.27878 | + | 4.53779i | 0.186741 | + | 0.198045i | ||||
\(526\) | −15.6522 | − | 3.34376i | −0.682468 | − | 0.145795i | ||||
\(527\) | 26.8121 | + | 26.8121i | 1.16795 | + | 1.16795i | ||||
\(528\) | −0.226156 | + | 4.00122i | −0.00984217 | + | 0.174131i | ||||
\(529\) | − | 49.8861i | − | 2.16896i | ||||||
\(530\) | 7.96796 | + | 5.66256i | 0.346106 | + | 0.245966i | ||||
\(531\) | − | 1.26757i | − | 0.0550078i | ||||||
\(532\) | −14.0527 | + | 5.36130i | −0.609264 | + | 0.232442i | ||||
\(533\) | −0.966495 | − | 0.966495i | −0.0418635 | − | 0.0418635i | ||||
\(534\) | 1.24631 | − | 5.83401i | 0.0539331 | − | 0.252462i | ||||
\(535\) | −20.5162 | + | 8.14725i | −0.886994 | + | 0.352236i | ||||
\(536\) | −32.5170 | − | 23.7782i | −1.40452 | − | 1.02706i | ||||
\(537\) | −3.92683 | + | 3.92683i | −0.169455 | + | 0.169455i | ||||
\(538\) | −8.65010 | + | 5.60484i | −0.372932 | + | 0.241642i | ||||
\(539\) | 5.08982 | 0.219234 | ||||||||
\(540\) | 1.02962 | − | 23.9771i | 0.0443076 | − | 1.03181i | ||||
\(541\) | −38.2350 | −1.64385 | −0.821925 | − | 0.569596i | \(-0.807100\pi\) | ||||
−0.821925 | + | 0.569596i | \(0.807100\pi\) | |||||||
\(542\) | −5.84539 | + | 3.78752i | −0.251081 | + | 0.162688i | ||||
\(543\) | 13.3844 | − | 13.3844i | 0.574379 | − | 0.574379i | ||||
\(544\) | 19.4736 | + | 34.1323i | 0.834925 | + | 1.46341i | ||||
\(545\) | −12.0606 | − | 5.20446i | −0.516621 | − | 0.222934i | ||||
\(546\) | −0.368541 | + | 1.72515i | −0.0157721 | + | 0.0738295i | ||||
\(547\) | −7.89796 | − | 7.89796i | −0.337692 | − | 0.337692i | 0.517806 | − | 0.855498i | \(-0.326749\pi\) |
−0.855498 | + | 0.517806i | \(0.826749\pi\) | |||||||
\(548\) | −2.59584 | − | 6.80408i | −0.110889 | − | 0.290656i | ||||
\(549\) | − | 8.11528i | − | 0.346352i | ||||||
\(550\) | −6.01659 | − | 1.47130i | −0.256548 | − | 0.0627365i | ||||
\(551\) | 54.1472i | 2.30675i | ||||||||
\(552\) | 4.23669 | + | 27.2925i | 0.180325 | + | 1.16165i | ||||
\(553\) | −1.25665 | − | 1.25665i | −0.0534383 | − | 0.0534383i | ||||
\(554\) | 26.6433 | + | 5.69177i | 1.13197 | + | 0.241820i | ||||
\(555\) | −7.37220 | − | 3.18128i | −0.312932 | − | 0.135038i | ||||
\(556\) | −3.45401 | + | 7.71521i | −0.146483 | + | 0.327198i | ||||
\(557\) | 7.49825 | − | 7.49825i | 0.317711 | − | 0.317711i | −0.530176 | − | 0.847887i | \(-0.677874\pi\) |
0.847887 | + | 0.530176i | \(0.177874\pi\) | |||||||
\(558\) | 7.10125 | + | 10.9596i | 0.300620 | + | 0.463955i | ||||
\(559\) | −6.14014 | −0.259700 | ||||||||
\(560\) | −8.72372 | − | 4.36401i | −0.368644 | − | 0.184413i | ||||
\(561\) | −6.95995 | −0.293849 | ||||||||
\(562\) | −8.66438 | − | 13.3720i | −0.365485 | − | 0.564062i | ||||
\(563\) | 1.24248 | − | 1.24248i | 0.0523644 | − | 0.0523644i | −0.680440 | − | 0.732804i | \(-0.738211\pi\) |
0.732804 | + | 0.680440i | \(0.238211\pi\) | |||||||
\(564\) | 5.03805 | − | 11.2535i | 0.212140 | − | 0.473857i | ||||
\(565\) | 24.3785 | − | 9.68100i | 1.02561 | − | 0.407283i | ||||
\(566\) | 23.1093 | + | 4.93680i | 0.971355 | + | 0.207509i | ||||
\(567\) | 0.819581 | + | 0.819581i | 0.0344192 | + | 0.0344192i | ||||
\(568\) | 2.17576 | + | 14.0161i | 0.0912928 | + | 0.588104i | ||||
\(569\) | 22.3401i | 0.936548i | 0.883583 | + | 0.468274i | \(0.155124\pi\) | ||||
−0.883583 | + | 0.468274i | \(0.844876\pi\) | |||||||
\(570\) | 14.4485 | − | 20.3309i | 0.605180 | − | 0.851567i | ||||
\(571\) | − | 40.7031i | − | 1.70337i | −0.524052 | − | 0.851686i | \(-0.675580\pi\) | ||
0.524052 | − | 0.851686i | \(-0.324420\pi\) | |||||||
\(572\) | −0.624466 | − | 1.63682i | −0.0261103 | − | 0.0684387i | ||||
\(573\) | 15.8836 | + | 15.8836i | 0.663545 | + | 0.663545i | ||||
\(574\) | −0.440406 | + | 2.06155i | −0.0183822 | + | 0.0860474i | ||||
\(575\) | −42.6683 | − | 1.25349i | −1.77939 | − | 0.0522740i | ||||
\(576\) | 4.10293 | + | 12.8970i | 0.170956 | + | 0.537375i | ||||
\(577\) | −5.55759 | + | 5.55759i | −0.231366 | + | 0.231366i | −0.813263 | − | 0.581897i | \(-0.802311\pi\) |
0.581897 | + | 0.813263i | \(0.302311\pi\) | |||||||
\(578\) | −37.0977 | + | 24.0375i | −1.54306 | + | 0.999828i | ||||
\(579\) | 21.1577 | 0.879285 | ||||||||
\(580\) | −25.8733 | + | 23.7427i | −1.07433 | + | 0.985864i | ||||
\(581\) | −4.11778 | −0.170834 | ||||||||
\(582\) | 12.7767 | − | 8.27867i | 0.529611 | − | 0.343162i | ||||
\(583\) | 1.91463 | − | 1.91463i | 0.0792958 | − | 0.0792958i | ||||
\(584\) | 22.1199 | + | 16.1752i | 0.915327 | + | 0.669336i | ||||
\(585\) | 1.39616 | + | 3.51577i | 0.0577240 | + | 0.145359i | ||||
\(586\) | −3.04527 | + | 14.2550i | −0.125799 | + | 0.588868i | ||||
\(587\) | 5.52984 | + | 5.52984i | 0.228241 | + | 0.228241i | 0.811957 | − | 0.583717i | \(-0.198402\pi\) |
−0.583717 | + | 0.811957i | \(0.698402\pi\) | |||||||
\(588\) | −12.4192 | + | 4.73809i | −0.512160 | + | 0.195396i | ||||
\(589\) | 37.6399i | 1.55092i | ||||||||
\(590\) | 2.33622 | − | 0.395137i | 0.0961807 | − | 0.0162675i | ||||
\(591\) | − | 1.25232i | − | 0.0515137i | ||||||
\(592\) | 12.5376 | + | 0.708646i | 0.515291 | + | 0.0291252i | ||||
\(593\) | 25.9213 | + | 25.9213i | 1.06446 | + | 1.06446i | 0.997774 | + | 0.0666872i | \(0.0212429\pi\) |
0.0666872 | + | 0.997774i | \(0.478757\pi\) | |||||||
\(594\) | −6.50104 | − | 1.38881i | −0.266741 | − | 0.0569835i | ||||
\(595\) | 6.71189 | − | 15.5539i | 0.275161 | − | 0.637649i | ||||
\(596\) | 1.83439 | + | 0.821235i | 0.0751395 | + | 0.0336391i | ||||
\(597\) | 3.00887 | − | 3.00887i | 0.123145 | − | 0.123145i | ||||
\(598\) | −6.56538 | − | 10.1325i | −0.268478 | − | 0.414350i | ||||
\(599\) | 12.5925 | 0.514515 | 0.257257 | − | 0.966343i | \(-0.417181\pi\) | ||||
0.257257 | + | 0.966343i | \(0.417181\pi\) | |||||||
\(600\) | 16.0502 | − | 2.01083i | 0.655247 | − | 0.0820917i | ||||
\(601\) | −8.34802 | −0.340523 | −0.170261 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170261 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(602\) | 5.14956 | + | 7.94746i | 0.209880 | + | 0.323914i | ||||
\(603\) | 17.0373 | − | 17.0373i | 0.693812 | − | 0.693812i | ||||
\(604\) | −29.7264 | − | 13.3082i | −1.20955 | − | 0.541502i | ||||
\(605\) | 9.06567 | − | 21.0085i | 0.368572 | − | 0.854116i | ||||
\(606\) | −9.85367 | − | 2.10502i | −0.400278 | − | 0.0855108i | ||||
\(607\) | 7.84172 | + | 7.84172i | 0.318286 | + | 0.318286i | 0.848108 | − | 0.529823i | \(-0.177742\pi\) |
−0.529823 | + | 0.848108i | \(0.677742\pi\) | |||||||
\(608\) | −10.2892 | + | 37.6270i | −0.417282 | + | 1.52598i | ||||
\(609\) | − | 9.79477i | − | 0.396904i | ||||||
\(610\) | 14.9570 | − | 2.52976i | 0.605592 | − | 0.102427i | ||||
\(611\) | 5.38986i | 0.218050i | ||||||||
\(612\) | −21.9603 | + | 8.37812i | −0.887691 | + | 0.338666i | ||||
\(613\) | 0.714872 | + | 0.714872i | 0.0288734 | + | 0.0288734i | 0.721396 | − | 0.692523i | \(-0.243501\pi\) |
−0.692523 | + | 0.721396i | \(0.743501\pi\) | |||||||
\(614\) | 6.83140 | − | 31.9779i | 0.275693 | − | 1.29052i | ||||
\(615\) | −1.29022 | − | 3.24900i | −0.0520265 | − | 0.131012i | ||||
\(616\) | −1.59488 | + | 2.18103i | −0.0642596 | + | 0.0878760i | ||||
\(617\) | 17.2100 | − | 17.2100i | 0.692847 | − | 0.692847i | −0.270011 | − | 0.962857i | \(-0.587027\pi\) |
0.962857 | + | 0.270011i | \(0.0870272\pi\) | |||||||
\(618\) | −17.3891 | + | 11.2673i | −0.699491 | + | 0.453236i | ||||
\(619\) | −0.361036 | −0.0145113 | −0.00725564 | − | 0.999974i | \(-0.502310\pi\) | ||||
−0.00725564 | + | 0.999974i | \(0.502310\pi\) | |||||||
\(620\) | −17.9856 | + | 16.5045i | −0.722318 | + | 0.662837i | ||||
\(621\) | −45.8146 | −1.83847 | ||||||||
\(622\) | 25.7806 | − | 16.7046i | 1.03371 | − | 0.669792i | ||||
\(623\) | 2.84403 | − | 2.84403i | 0.113944 | − | 0.113944i | ||||
\(624\) | 3.04741 | + | 3.41254i | 0.121994 | + | 0.136611i | ||||
\(625\) | −1.46761 | + | 24.9569i | −0.0587042 | + | 0.998275i | ||||
\(626\) | −0.490001 | + | 2.29370i | −0.0195844 | + | 0.0916748i | ||||
\(627\) | −4.88533 | − | 4.88533i | −0.195101 | − | 0.195101i | ||||
\(628\) | −0.172967 | − | 0.453372i | −0.00690215 | − | 0.0180915i | ||||
\(629\) | 21.8086i | 0.869566i | ||||||||
\(630\) | 3.37970 | − | 4.75568i | 0.134651 | − | 0.189471i | ||||
\(631\) | − | 7.91135i | − | 0.314946i | −0.987523 | − | 0.157473i | \(-0.949665\pi\) | ||
0.987523 | − | 0.157473i | \(-0.0503347\pi\) | |||||||
\(632\) | −4.55460 | + | 0.707021i | −0.181172 | + | 0.0281238i | ||||
\(633\) | −8.16987 | − | 8.16987i | −0.324723 | − | 0.324723i | ||||
\(634\) | −12.6171 | − | 2.69536i | −0.501087 | − | 0.107047i | ||||
\(635\) | −24.8733 | + | 9.87751i | −0.987068 | + | 0.391977i | ||||
\(636\) | −2.88940 | + | 6.45404i | −0.114572 | + | 0.255919i | ||||
\(637\) | 4.10875 | − | 4.10875i | 0.162795 | − | 0.162795i | ||||
\(638\) | 5.28941 | + | 8.16329i | 0.209410 | + | 0.323188i | ||||
\(639\) | −8.48374 | −0.335612 | ||||||||
\(640\) | −22.4911 | + | 11.5824i | −0.889038 | + | 0.457833i | ||||
\(641\) | −12.3758 | −0.488813 | −0.244407 | − | 0.969673i | \(-0.578593\pi\) | ||||
−0.244407 | + | 0.969673i | \(0.578593\pi\) | |||||||
\(642\) | −8.68350 | − | 13.4015i | −0.342710 | − | 0.528914i | ||||
\(643\) | −1.50067 | + | 1.50067i | −0.0591807 | + | 0.0591807i | −0.736078 | − | 0.676897i | \(-0.763324\pi\) |
0.676897 | + | 0.736078i | \(0.263324\pi\) | |||||||
\(644\) | −7.60878 | + | 16.9957i | −0.299828 | + | 0.669725i | ||||
\(645\) | −14.4188 | − | 6.22206i | −0.567740 | − | 0.244994i | ||||
\(646\) | −66.2506 | − | 14.1530i | −2.60660 | − | 0.556844i | ||||
\(647\) | 15.1830 | + | 15.1830i | 0.596906 | + | 0.596906i | 0.939488 | − | 0.342582i | \(-0.111301\pi\) |
−0.342582 | + | 0.939488i | \(0.611301\pi\) | |||||||
\(648\) | 2.97048 | − | 0.461115i | 0.116692 | − | 0.0181143i | ||||
\(649\) | − | 0.656320i | − | 0.0257628i | ||||||
\(650\) | −6.04459 | + | 3.66918i | −0.237088 | + | 0.143917i | ||||
\(651\) | − | 6.80873i | − | 0.266855i | ||||||
\(652\) | −8.59721 | − | 22.5345i | −0.336693 | − | 0.882520i | ||||
\(653\) | −11.8664 | − | 11.8664i | −0.464369 | − | 0.464369i | 0.435716 | − | 0.900084i | \(-0.356495\pi\) |
−0.900084 | + | 0.435716i | \(0.856495\pi\) | |||||||
\(654\) | 1.98517 | − | 9.29263i | 0.0776263 | − | 0.363370i | ||||
\(655\) | −31.8270 | − | 13.7341i | −1.24358 | − | 0.536637i | ||||
\(656\) | 3.64166 | + | 4.07798i | 0.142183 | + | 0.159219i | ||||
\(657\) | −11.5897 | + | 11.5897i | −0.452157 | + | 0.452157i | ||||
\(658\) | 6.97633 | − | 4.52032i | 0.271966 | − | 0.176220i | ||||
\(659\) | −46.7405 | −1.82075 | −0.910376 | − | 0.413782i | \(-0.864208\pi\) | ||||
−0.910376 | + | 0.413782i | \(0.864208\pi\) | |||||||
\(660\) | 0.192229 | − | 4.47651i | 0.00748251 | − | 0.174248i | ||||
\(661\) | 23.7102 | 0.922219 | 0.461109 | − | 0.887343i | \(-0.347452\pi\) | ||||
0.461109 | + | 0.887343i | \(0.347452\pi\) | |||||||
\(662\) | 38.8612 | − | 25.1801i | 1.51038 | − | 0.978653i | ||||
\(663\) | −5.61842 | + | 5.61842i | −0.218201 | + | 0.218201i | ||||
\(664\) | −6.30384 | + | 8.62059i | −0.244636 | + | 0.334544i | ||||
\(665\) | 15.6288 | − | 6.20639i | 0.606059 | − | 0.240674i | ||||
\(666\) | −1.56915 | + | 7.34521i | −0.0608032 | + | 0.284621i | ||||
\(667\) | 47.4024 | + | 47.4024i | 1.83543 | + | 1.83543i | ||||
\(668\) | 23.2979 | − | 8.88846i | 0.901425 | − | 0.343905i | ||||
\(669\) | − | 17.7509i | − | 0.686288i | ||||||
\(670\) | 36.7119 | + | 26.0899i | 1.41831 | + | 1.00794i | ||||
\(671\) | − | 4.20192i | − | 0.162213i | ||||||
\(672\) | 1.86123 | − | 6.80640i | 0.0717984 | − | 0.262563i | ||||
\(673\) | 1.49025 | + | 1.49025i | 0.0574448 | + | 0.0574448i | 0.735246 | − | 0.677801i | \(-0.237067\pi\) |
−0.677801 | + | 0.735246i | \(0.737067\pi\) | |||||||
\(674\) | −33.3587 | − | 7.12637i | −1.28493 | − | 0.274498i | ||||
\(675\) | −0.787912 | + | 26.8203i | −0.0303268 | + | 1.03231i | ||||
\(676\) | −1.82542 | − | 0.817219i | −0.0702084 | − | 0.0314315i | ||||
\(677\) | 21.9052 | − | 21.9052i | 0.841884 | − | 0.841884i | −0.147219 | − | 0.989104i | \(-0.547032\pi\) |
0.989104 | + | 0.147219i | \(0.0470323\pi\) | |||||||
\(678\) | 10.3182 | + | 15.9244i | 0.396268 | + | 0.611571i | ||||
\(679\) | 10.2643 | 0.393909 | ||||||||
\(680\) | −22.2871 | − | 37.8626i | −0.854671 | − | 1.45197i | ||||
\(681\) | −8.26205 | −0.316602 | ||||||||
\(682\) | 3.67688 | + | 5.67462i | 0.140795 | + | 0.217293i | ||||
\(683\) | 21.9173 | − | 21.9173i | 0.838644 | − | 0.838644i | −0.150037 | − | 0.988680i | \(-0.547939\pi\) |
0.988680 | + | 0.150037i | \(0.0479392\pi\) | |||||||
\(684\) | −21.2951 | − | 9.53357i | −0.814239 | − | 0.364525i | ||||
\(685\) | 3.00502 | + | 7.56718i | 0.114816 | + | 0.289127i | ||||
\(686\) | −19.3219 | − | 4.12771i | −0.737714 | − | 0.157597i | ||||
\(687\) | −0.955494 | − | 0.955494i | −0.0364544 | − | 0.0364544i | ||||
\(688\) | 24.5214 | + | 1.38600i | 0.934871 | + | 0.0528406i | ||||
\(689\) | − | 3.09116i | − | 0.117764i | ||||||
\(690\) | −5.14967 | − | 30.4470i | −0.196044 | − | 1.15910i | ||||
\(691\) | − | 1.94770i | − | 0.0740939i | −0.999314 | − | 0.0370470i | \(-0.988205\pi\) | ||
0.999314 | − | 0.0370470i | \(-0.0117951\pi\) | |||||||
\(692\) | −2.41697 | + | 0.922105i | −0.0918794 | + | 0.0350532i | ||||
\(693\) | −1.14275 | − | 1.14275i | −0.0434094 | − | 0.0434094i | ||||
\(694\) | −5.12932 | + | 24.0104i | −0.194706 | + | 0.911424i | ||||
\(695\) | 3.74450 | − | 8.67739i | 0.142037 | − | 0.329152i | ||||
\(696\) | −20.5054 | − | 14.9946i | −0.777256 | − | 0.568371i | ||||
\(697\) | −6.71400 | + | 6.71400i | −0.254311 | + | 0.254311i | ||||
\(698\) | 35.8956 | − | 23.2586i | 1.35867 | − | 0.880349i | ||||
\(699\) | 19.5521 | 0.739529 | ||||||||
\(700\) | 9.81861 | + | 4.74655i | 0.371109 | + | 0.179403i | ||||
\(701\) | 16.3253 | 0.616597 | 0.308299 | − | 0.951290i | \(-0.400240\pi\) | ||||
0.308299 | + | 0.951290i | \(0.400240\pi\) | |||||||
\(702\) | −6.36907 | + | 4.12685i | −0.240385 | + | 0.155758i | ||||
\(703\) | −15.3079 | + | 15.3079i | −0.577348 | + | 0.577348i | ||||
\(704\) | 2.12441 | + | 6.67779i | 0.0800668 | + | 0.251679i | ||||
\(705\) | −5.46177 | + | 12.6569i | −0.205702 | + | 0.476687i | ||||
\(706\) | −6.56404 | + | 30.7264i | −0.247041 | + | 1.15640i | ||||
\(707\) | −4.80359 | − | 4.80359i | −0.180657 | − | 0.180657i | ||||
\(708\) | 0.610967 | + | 1.60143i | 0.0229615 | + | 0.0601855i | ||||
\(709\) | 9.91483i | 0.372359i | 0.982516 | + | 0.186180i | \(0.0596106\pi\) | ||||
−0.982516 | + | 0.186180i | \(0.940389\pi\) | |||||||
\(710\) | −2.64462 | − | 15.6361i | −0.0992509 | − | 0.586814i | ||||
\(711\) | − | 2.75682i | − | 0.103389i | ||||||
\(712\) | −1.60012 | − | 10.3079i | −0.0599670 | − | 0.386304i | ||||
\(713\) | 32.9512 | + | 32.9512i | 1.23403 | + | 1.23403i | ||||
\(714\) | 11.9842 | + | 2.56016i | 0.448496 | + | 0.0958116i | ||||
\(715\) | 0.722900 | + | 1.82039i | 0.0270349 | + | 0.0680788i | ||||
\(716\) | −3.96779 | + | 8.86283i | −0.148283 | + | 0.331220i | ||||
\(717\) | −15.4096 | + | 15.4096i | −0.575481 | + | 0.575481i | ||||
\(718\) | 27.4459 | + | 42.3580i | 1.02427 | + | 1.58079i | ||||
\(719\) | 5.89066 | 0.219685 | 0.109842 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109842 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(720\) | −4.78212 | − | 14.3558i | −0.178219 | − | 0.535010i | ||||
\(721\) | −13.9697 | −0.520260 | ||||||||
\(722\) | −21.9570 | − | 33.8868i | −0.817153 | − | 1.26114i | ||||
\(723\) | 0.700969 | − | 0.700969i | 0.0260693 | − | 0.0260693i | ||||
\(724\) | 13.5240 | − | 30.2085i | 0.502615 | − | 1.12269i | ||||
\(725\) | 28.5650 | − | 26.9346i | 1.06088 | − | 1.00033i | ||||
\(726\) | 16.1869 | + | 3.45798i | 0.600751 | + | 0.128338i | ||||
\(727\) | 33.8770 | + | 33.8770i | 1.25643 | + | 1.25643i | 0.952786 | + | 0.303642i | \(0.0982026\pi\) |
0.303642 | + | 0.952786i | \(0.401797\pi\) | |||||||
\(728\) | 0.473164 | + | 3.04810i | 0.0175366 | + | 0.112970i | ||||
\(729\) | 20.2120i | 0.748594i | ||||||||
\(730\) | −24.9735 | − | 17.7478i | −0.924309 | − | 0.656875i | ||||
\(731\) | 42.6540i | 1.57762i | ||||||||
\(732\) | 3.91155 | + | 10.2527i | 0.144575 | + | 0.378952i | ||||
\(733\) | 24.2491 | + | 24.2491i | 0.895661 | + | 0.895661i | 0.995049 | − | 0.0993880i | \(-0.0316885\pi\) |
−0.0993880 | + | 0.995049i | \(0.531689\pi\) | |||||||
\(734\) | 1.84297 | − | 8.62697i | 0.0680252 | − | 0.318427i | ||||
\(735\) | 13.8121 | − | 5.48495i | 0.509467 | − | 0.202315i | ||||
\(736\) | 23.9325 | + | 41.9475i | 0.882163 | + | 1.54621i | ||||
\(737\) | 8.82155 | − | 8.82155i | 0.324946 | − | 0.324946i | ||||
\(738\) | −2.74437 | + | 1.77822i | −0.101022 | + | 0.0654571i | ||||
\(739\) | 11.3816 | 0.418679 | 0.209339 | − | 0.977843i | \(-0.432869\pi\) | ||||
0.209339 | + | 0.977843i | \(0.432869\pi\) | |||||||
\(740\) | −14.0269 | − | 0.602338i | −0.515638 | − | 0.0221424i | ||||
\(741\) | −7.88735 | −0.289749 | ||||||||
\(742\) | −4.00103 | + | 2.59247i | −0.146882 | + | 0.0951726i | ||||
\(743\) | 13.5560 | − | 13.5560i | 0.497323 | − | 0.497323i | −0.413281 | − | 0.910604i | \(-0.635617\pi\) |
0.910604 | + | 0.413281i | \(0.135617\pi\) | |||||||
\(744\) | −14.2541 | − | 10.4234i | −0.522581 | − | 0.382139i | ||||
\(745\) | −2.06316 | − | 0.890303i | −0.0755883 | − | 0.0326182i | ||||
\(746\) | 6.73646 | − | 31.5335i | 0.246639 | − | 1.15452i | ||||
\(747\) | −4.51676 | − | 4.51676i | −0.165259 | − | 0.165259i | ||||
\(748\) | −11.3706 | + | 4.33801i | −0.415749 | + | 0.158613i | ||||
\(749\) | − | 10.7663i | − | 0.393391i | ||||||
\(750\) | −17.9126 | + | 2.49104i | −0.654074 | + | 0.0909601i | ||||
\(751\) | − | 0.486430i | − | 0.0177501i | −0.999961 | − | 0.00887505i | \(-0.997175\pi\) | ||
0.999961 | − | 0.00887505i | \(-0.00282505\pi\) | |||||||
\(752\) | 1.21664 | − | 21.5251i | 0.0443661 | − | 0.784939i | ||||
\(753\) | 9.70149 | + | 9.70149i | 0.353542 | + | 0.353542i | ||||
\(754\) | 10.8597 | + | 2.31994i | 0.395486 | + | 0.0844871i | ||||
\(755\) | 33.4336 | + | 14.4274i | 1.21677 | + | 0.525068i | ||||
\(756\) | 10.6831 | + | 4.78271i | 0.388541 | + | 0.173945i | ||||
\(757\) | 22.6809 | − | 22.6809i | 0.824350 | − | 0.824350i | −0.162379 | − | 0.986729i | \(-0.551917\pi\) |
0.986729 | + | 0.162379i | \(0.0519166\pi\) | |||||||
\(758\) | −25.6106 | − | 39.5255i | −0.930219 | − | 1.43563i | ||||
\(759\) | −8.55356 | −0.310475 | ||||||||
\(760\) | 10.9328 | − | 42.2203i | 0.396573 | − | 1.53149i | ||||
\(761\) | 41.2722 | 1.49612 | 0.748058 | − | 0.663633i | \(-0.230986\pi\) | ||||
0.748058 | + | 0.663633i | \(0.230986\pi\) | |||||||
\(762\) | −10.5276 | − | 16.2476i | −0.381376 | − | 0.588589i | ||||
\(763\) | 4.53008 | − | 4.53008i | 0.164000 | − | 0.164000i | ||||
\(764\) | 35.8491 | + | 16.0492i | 1.29697 | + | 0.580640i | ||||
\(765\) | 24.4232 | − | 9.69875i | 0.883022 | − | 0.350659i | ||||
\(766\) | 3.73358 | + | 0.797600i | 0.134900 | + | 0.0288184i | ||||
\(767\) | −0.529814 | − | 0.529814i | −0.0191305 | − | 0.0191305i | ||||
\(768\) | −11.3999 | − | 14.3163i | −0.411359 | − | 0.516595i | ||||
\(769\) | − | 35.2742i | − | 1.27202i | −0.771681 | − | 0.636010i | \(-0.780584\pi\) | ||
0.771681 | − | 0.636010i | \(-0.219416\pi\) | |||||||
\(770\) | 1.74994 | − | 2.46239i | 0.0630634 | − | 0.0887384i | ||||
\(771\) | − | 15.4491i | − | 0.556387i | ||||||
\(772\) | 34.5656 | − | 13.1872i | 1.24404 | − | 0.474619i | ||||
\(773\) | −26.9007 | − | 26.9007i | −0.967551 | − | 0.967551i | 0.0319390 | − | 0.999490i | \(-0.489832\pi\) |
−0.999490 | + | 0.0319390i | \(0.989832\pi\) | |||||||
\(774\) | −3.06899 | + | 14.3660i | −0.110313 | + | 0.516376i | ||||
\(775\) | 19.8567 | − | 18.7233i | 0.713273 | − | 0.672561i | ||||
\(776\) | 15.7135 | − | 21.4884i | 0.564081 | − | 0.771390i | ||||
\(777\) | 2.76906 | − | 2.76906i | 0.0993396 | − | 0.0993396i | ||||
\(778\) | 2.47594 | − | 1.60429i | 0.0887667 | − | 0.0575164i | ||||
\(779\) | −9.42537 | −0.337699 | ||||||||
\(780\) | −3.45848 | − | 3.76884i | −0.123834 | − | 0.134946i | ||||
\(781\) | −4.39270 | −0.157183 | ||||||||
\(782\) | −70.3881 | + | 45.6080i | −2.51707 | + | 1.63094i | ||||
\(783\) | 29.7960 | − | 29.7960i | 1.06482 | − | 1.06482i | ||||
\(784\) | −17.3363 | + | 15.4814i | −0.619153 | + | 0.552906i | ||||
\(785\) | 0.200232 | + | 0.504220i | 0.00714658 | + | 0.0179964i | ||||
\(786\) | 5.23870 | − | 24.5225i | 0.186858 | − | 0.874687i | ||||
\(787\) | −19.9522 | − | 19.9522i | −0.711220 | − | 0.711220i | 0.255570 | − | 0.966791i | \(-0.417737\pi\) |
−0.966791 | + | 0.255570i | \(0.917737\pi\) | |||||||
\(788\) | −0.780550 | − | 2.04593i | −0.0278059 | − | 0.0728834i | ||||
\(789\) | 12.9449i | 0.460850i | ||||||||
\(790\) | 5.08102 | − | 0.859380i | 0.180775 | − | 0.0305754i | ||||
\(791\) | 12.7930i | 0.454868i | ||||||||
\(792\) | −4.14176 | + | 0.642936i | −0.147171 | + | 0.0228457i | ||||
\(793\) | −3.39199 | − | 3.39199i | −0.120453 | − | 0.120453i | ||||
\(794\) | 45.4575 | + | 9.71103i | 1.61323 | + | 0.344631i | ||||
\(795\) | 3.13241 | − | 7.25894i | 0.111095 | − | 0.257448i | ||||
\(796\) | 3.04025 | − | 6.79100i | 0.107759 | − | 0.240701i | ||||
\(797\) | 0.641383 | − | 0.641383i | 0.0227190 | − | 0.0227190i | −0.695656 | − | 0.718375i | \(-0.744886\pi\) |
0.718375 | + | 0.695656i | \(0.244886\pi\) | |||||||
\(798\) | 6.61489 | + | 10.2089i | 0.234165 | + | 0.361393i | ||||
\(799\) | 37.4420 | 1.32460 | ||||||||
\(800\) | 24.9681 | − | 13.2889i | 0.882755 | − | 0.469834i | ||||
\(801\) | 6.23920 | 0.220451 | ||||||||
\(802\) | −12.3330 | − | 19.0338i | −0.435493 | − | 0.672108i | ||||
\(803\) | −6.00090 | + | 6.00090i | −0.211767 | + | 0.211767i | ||||
\(804\) | −13.3128 | + | 29.7366i | −0.469505 | + | 1.04873i | ||||
\(805\) | 8.24870 | − | 19.1153i | 0.290729 | − | 0.673725i | ||||
\(806\) | 7.54899 | + | 1.61268i | 0.265902 | + | 0.0568042i | ||||
\(807\) | 5.89465 | + | 5.89465i | 0.207502 | + | 0.207502i | ||||
\(808\) | −17.4101 | + | 2.70261i | −0.612484 | + | 0.0950774i | ||||
\(809\) | − | 13.2680i | − | 0.466478i | −0.972419 | − | 0.233239i | \(-0.925067\pi\) | ||
0.972419 | − | 0.233239i | \(-0.0749325\pi\) | |||||||
\(810\) | −3.31381 | + | 0.560483i | −0.116435 | + | 0.0196933i | ||||
\(811\) | − | 10.2936i | − | 0.361458i | −0.983533 | − | 0.180729i | \(-0.942154\pi\) | ||
0.983533 | − | 0.180729i | \(-0.0578458\pi\) | |||||||
\(812\) | −6.10490 | − | 16.0018i | −0.214240 | − | 0.561554i | ||||
\(813\) | 3.98337 | + | 3.98337i | 0.139703 | + | 0.139703i | ||||
\(814\) | −0.812470 | + | 3.80319i | −0.0284771 | + | 0.133302i | ||||
\(815\) | 9.95238 | + | 25.0619i | 0.348617 | + | 0.877879i | ||||
\(816\) | 23.7061 | − | 21.1696i | 0.829879 | − | 0.741085i | ||||
\(817\) | −29.9397 | + | 29.9397i | −1.04746 | + | 1.04746i | ||||
\(818\) | 45.8850 | − | 29.7312i | 1.60433 | − | 1.03953i | ||||
\(819\) | −1.84496 | −0.0644683 | ||||||||
\(820\) | −4.13288 | − | 4.50375i | −0.144326 | − | 0.157278i | ||||
\(821\) | −1.68106 | −0.0586694 | −0.0293347 | − | 0.999570i | \(-0.509339\pi\) | ||||
−0.0293347 | + | 0.999570i | \(0.509339\pi\) | |||||||
\(822\) | −4.94298 | + | 3.20281i | −0.172406 | + | 0.111711i | ||||
\(823\) | −30.8205 | + | 30.8205i | −1.07434 | + | 1.07434i | −0.0773299 | + | 0.997006i | \(0.524639\pi\) |
−0.997006 | + | 0.0773299i | \(0.975361\pi\) | |||||||
\(824\) | −21.3860 | + | 29.2457i | −0.745018 | + | 1.01882i | ||||
\(825\) | −0.147103 | + | 5.00734i | −0.00512147 | + | 0.174333i | ||||
\(826\) | −0.241422 | + | 1.13010i | −0.00840015 | + | 0.0393213i | ||||
\(827\) | 2.18949 | + | 2.18949i | 0.0761362 | + | 0.0761362i | 0.744149 | − | 0.668013i | \(-0.232855\pi\) |
−0.668013 | + | 0.744149i | \(0.732855\pi\) | |||||||
\(828\) | −26.9885 | + | 10.2964i | −0.937914 | + | 0.357826i | ||||
\(829\) | − | 44.9575i | − | 1.56144i | −0.624881 | − | 0.780720i | \(-0.714853\pi\) | ||
0.624881 | − | 0.780720i | \(-0.285147\pi\) | |||||||
\(830\) | 6.91670 | − | 9.73270i | 0.240082 | − | 0.337827i | ||||
\(831\) | − | 22.0349i | − | 0.764382i | ||||||
\(832\) | 7.10557 | + | 3.67571i | 0.246341 | + | 0.127432i | ||||
\(833\) | −28.5425 | − | 28.5425i | −0.988938 | − | 0.988938i | ||||
\(834\) | 6.68586 | + | 1.42829i | 0.231512 | + | 0.0494577i | ||||
\(835\) | −25.9109 | + | 10.2895i | −0.896683 | + | 0.356084i | ||||
\(836\) | −11.0261 | − | 4.93628i | −0.381347 | − | 0.170725i | ||||
\(837\) | 20.7124 | − | 20.7124i | 0.715925 | − | 0.715925i | ||||
\(838\) | −12.2352 | − | 18.8829i | −0.422658 | − | 0.652299i | ||||
\(839\) | 20.4522 | 0.706088 | 0.353044 | − | 0.935607i | \(-0.385147\pi\) | ||||
0.353044 | + | 0.935607i | \(0.385147\pi\) | |||||||
\(840\) | −1.97764 | + | 7.63728i | −0.0682351 | + | 0.263511i | ||||
\(841\) | −32.6574 | −1.12612 | ||||||||
\(842\) | −2.70994 | − | 4.18233i | −0.0933908 | − | 0.144133i | ||||
\(843\) | −9.11239 | + | 9.11239i | −0.313847 | + | 0.313847i | ||||
\(844\) | −18.4393 | − | 8.25508i | −0.634708 | − | 0.284151i | ||||
\(845\) | 2.05307 | + | 0.885949i | 0.0706277 | + | 0.0304776i | ||||
\(846\) | 12.6106 | + | 2.69398i | 0.433561 | + | 0.0926210i | ||||
\(847\) | 7.89097 | + | 7.89097i | 0.271137 | + | 0.271137i | ||||
\(848\) | −0.697759 | + | 12.3450i | −0.0239611 | + | 0.423927i | ||||
\(849\) | − | 19.1121i | − | 0.655926i | ||||||
\(850\) | 25.4889 | + | 41.9903i | 0.874261 | + | 1.44025i | ||||
\(851\) | 26.8021i | 0.918764i | ||||||||
\(852\) | 10.7182 | − | 4.08915i | 0.367201 | − | 0.140092i | ||||
\(853\) | 10.9833 | + | 10.9833i | 0.376062 | + | 0.376062i | 0.869679 | − | 0.493618i | \(-0.164326\pi\) |
−0.493618 | + | 0.869679i | \(0.664326\pi\) | |||||||
\(854\) | −1.54564 | + | 7.23517i | −0.0528907 | + | 0.247583i | ||||
\(855\) | 23.9508 | + | 10.3354i | 0.819102 | + | 0.353462i | ||||
\(856\) | −22.5392 | − | 16.4819i | −0.770375 | − | 0.563339i | ||||
\(857\) | −26.6753 | + | 26.6753i | −0.911212 | + | 0.911212i | −0.996368 | − | 0.0851556i | \(-0.972861\pi\) |
0.0851556 | + | 0.996368i | \(0.472861\pi\) | |||||||
\(858\) | −1.18910 | + | 0.770481i | −0.0405953 | + | 0.0263038i | ||||
\(859\) | −11.5130 | −0.392817 | −0.196409 | − | 0.980522i | \(-0.562928\pi\) | ||||
−0.196409 | + | 0.980522i | \(0.562928\pi\) | |||||||
\(860\) | −27.4343 | − | 1.17808i | −0.935501 | − | 0.0401720i | ||||
\(861\) | 1.70497 | 0.0581052 | ||||||||
\(862\) | −40.3568 | + | 26.1492i | −1.37456 | + | 0.890646i | ||||
\(863\) | 2.48286 | − | 2.48286i | 0.0845177 | − | 0.0845177i | −0.663584 | − | 0.748102i | \(-0.730966\pi\) |
0.748102 | + | 0.663584i | \(0.230966\pi\) | |||||||
\(864\) | 26.3672 | − | 15.0434i | 0.897032 | − | 0.511787i | ||||
\(865\) | 2.68804 | − | 1.06745i | 0.0913962 | − | 0.0362946i | ||||
\(866\) | −8.53984 | + | 39.9752i | −0.290196 | + | 1.35841i | ||||
\(867\) | 25.2804 | + | 25.2804i | 0.858568 | + | 0.858568i | ||||
\(868\) | −4.24376 | − | 11.1235i | −0.144043 | − | 0.377556i | ||||
\(869\) | − | 1.42742i | − | 0.0484220i | ||||||
\(870\) | 23.1507 | + | 16.4524i | 0.784883 | + | 0.557790i | ||||
\(871\) | − | 14.2424i | − | 0.482584i | ||||||
\(872\) | −2.54873 | − | 16.4188i | −0.0863108 | − | 0.556010i | ||||
\(873\) | 11.2589 | + | 11.2589i | 0.381055 | + | 0.381055i | ||||
\(874\) | −81.4200 | − | 17.3936i | −2.75407 | − | 0.588348i | ||||
\(875\) | −11.0484 | − | 5.15762i | −0.373505 | − | 0.174359i | ||||
\(876\) | 9.05606 | − | 20.2285i | 0.305976 | − | 0.683457i | ||||
\(877\) | −9.52846 | + | 9.52846i | −0.321753 | + | 0.321753i | −0.849439 | − | 0.527686i | \(-0.823060\pi\) |
0.527686 | + | 0.849439i | \(0.323060\pi\) | |||||||
\(878\) | −3.46364 | − | 5.34553i | −0.116892 | − | 0.180403i | ||||
\(879\) | 11.7893 | 0.397645 | ||||||||
\(880\) | −2.47608 | − | 7.43314i | −0.0834687 | − | 0.250571i | ||||
\(881\) | 23.8353 | 0.803030 | 0.401515 | − | 0.915852i | \(-0.368484\pi\) | ||||
0.401515 | + | 0.915852i | \(0.368484\pi\) | |||||||
\(882\) | −7.55954 | − | 11.6668i | −0.254543 | − | 0.392843i | ||||
\(883\) | 18.1255 | − | 18.1255i | 0.609973 | − | 0.609973i | −0.332966 | − | 0.942939i | \(-0.608049\pi\) |
0.942939 | + | 0.332966i | \(0.108049\pi\) | |||||||
\(884\) | −5.67701 | + | 12.6807i | −0.190939 | + | 0.426499i | ||||
\(885\) | −0.707272 | − | 1.78104i | −0.0237747 | − | 0.0598689i | ||||
\(886\) | 33.0710 | + | 7.06491i | 1.11104 | + | 0.237350i | ||||
\(887\) | −40.7732 | − | 40.7732i | −1.36903 | − | 1.36903i | −0.861827 | − | 0.507202i | \(-0.830680\pi\) |
−0.507202 | − | 0.861827i | \(-0.669320\pi\) | |||||||
\(888\) | −1.55794 | − | 10.0362i | −0.0522810 | − | 0.336792i | ||||
\(889\) | − | 13.0527i | − | 0.437774i | ||||||
\(890\) | 1.94493 | + | 11.4993i | 0.0651943 | + | 0.385457i | ||||
\(891\) | 0.930958i | 0.0311883i | ||||||||
\(892\) | −11.0638 | − | 28.9998i | −0.370443 | − | 0.970984i | ||||
\(893\) | 26.2813 | + | 26.2813i | 0.879469 | + | 0.879469i | ||||
\(894\) | 0.339594 | − | 1.58965i | 0.0113577 | − | 0.0531657i | ||||
\(895\) | 4.30149 | − | 9.96813i | 0.143783 | − | 0.333198i | ||||
\(896\) | −1.20160 | − | 12.2798i | −0.0401427 | − | 0.410238i | ||||
\(897\) | −6.90486 | + | 6.90486i | −0.230546 | + | 0.230546i | ||||
\(898\) | 18.0950 | − | 11.7247i | 0.603839 | − | 0.391258i | ||||
\(899\) | −42.8605 | −1.42948 | ||||||||
\(900\) | 5.56350 | + | 15.9764i | 0.185450 | + | 0.532547i | ||||
\(901\) | −21.4735 | −0.715388 | ||||||||
\(902\) | −1.42098 | + | 0.920723i | −0.0473134 | + | 0.0306567i | ||||
\(903\) | 5.41583 | − | 5.41583i | 0.180228 | − | 0.180228i | ||||
\(904\) | 26.7823 | + | 19.5847i | 0.890767 | + | 0.651376i | ||||
\(905\) | −14.6614 | + | 33.9758i | −0.487361 | + | 1.12939i | ||||
\(906\) | −5.50315 | + | 25.7603i | −0.182830 | + | 0.855830i | ||||
\(907\) | −4.06624 | − | 4.06624i | −0.135017 | − | 0.135017i | 0.636368 | − | 0.771385i | \(-0.280436\pi\) |
−0.771385 | + | 0.636368i | \(0.780436\pi\) | |||||||
\(908\) | −13.4978 | + | 5.14958i | −0.447940 | + | 0.170895i | ||||
\(909\) | − | 10.5380i | − | 0.349524i | ||||||
\(910\) | −0.575127 | − | 3.40040i | −0.0190653 | − | 0.112722i | ||||
\(911\) | 39.9899i | 1.32492i | 0.749095 | + | 0.662462i | \(0.230489\pi\) | ||||
−0.749095 | + | 0.662462i | \(0.769511\pi\) | |||||||
\(912\) | 31.4991 | + | 1.78039i | 1.04304 | + | 0.0589545i | ||||
\(913\) | −2.33868 | − | 2.33868i | −0.0773990 | − | 0.0773990i | ||||
\(914\) | −14.5580 | − | 3.11000i | −0.481534 | − | 0.102869i | ||||
\(915\) | −4.52812 | − | 11.4026i | −0.149695 | − | 0.376959i | ||||
\(916\) | −2.15654 | − | 0.965460i | −0.0712542 | − | 0.0318997i | ||||
\(917\) | 11.9545 | − | 11.9545i | 0.394773 | − | 0.394773i | ||||
\(918\) | 28.6682 | + | 44.2444i | 0.946190 | + | 1.46028i | ||||
\(919\) | 11.6349 | 0.383799 | 0.191899 | − | 0.981415i | \(-0.438535\pi\) | ||||
0.191899 | + | 0.981415i | \(0.438535\pi\) | |||||||
\(920\) | −27.3902 | − | 46.5320i | −0.903027 | − | 1.53411i | ||||
\(921\) | −26.4468 | −0.871451 | ||||||||
\(922\) | 16.6034 | + | 25.6245i | 0.546804 | + | 0.843898i | ||||
\(923\) | −3.54600 | + | 3.54600i | −0.116718 | + | 0.116718i | ||||
\(924\) | 1.99453 | + | 0.892930i | 0.0656154 | + | 0.0293752i | ||||
\(925\) | 15.6902 | + | 0.460939i | 0.515891 | + | 0.0151556i | ||||
\(926\) | −10.4040 | − | 2.22259i | −0.341896 | − | 0.0730387i | ||||
\(927\) | −15.3233 | − | 15.3233i | −0.503283 | − | 0.503283i | ||||
\(928\) | −42.8458 | − | 11.7163i | −1.40648 | − | 0.384606i | ||||
\(929\) | − | 8.92800i | − | 0.292918i | −0.989217 | − | 0.146459i | \(-0.953212\pi\) | ||
0.989217 | − | 0.146459i | \(-0.0467877\pi\) | |||||||
\(930\) | 16.0930 | + | 11.4367i | 0.527710 | + | 0.375026i | ||||
\(931\) | − | 40.0690i | − | 1.31321i | ||||||
\(932\) | 31.9425 | − | 12.1865i | 1.04631 | − | 0.399182i | ||||
\(933\) | −17.5683 | − | 17.5683i | −0.575160 | − | 0.575160i | ||||
\(934\) | −5.01977 | + | 23.4977i | −0.164252 | + | 0.768867i | ||||
\(935\) | 12.6458 | − | 5.02180i | 0.413562 | − | 0.164231i | ||||
\(936\) | −2.82442 | + | 3.86244i | −0.0923192 | + | 0.126248i | ||||
\(937\) | 24.2793 | − | 24.2793i | 0.793171 | − | 0.793171i | −0.188837 | − | 0.982008i | \(-0.560472\pi\) |
0.982008 | + | 0.188837i | \(0.0604718\pi\) | |||||||
\(938\) | −18.4345 | + | 11.9447i | −0.601909 | + | 0.390007i | ||||
\(939\) | 1.89697 | 0.0619052 | ||||||||
\(940\) | −1.03412 | + | 24.0820i | −0.0337293 | + | 0.785468i | ||||
\(941\) | 36.8409 | 1.20098 | 0.600490 | − | 0.799632i | \(-0.294972\pi\) | ||||
0.600490 | + | 0.799632i | \(0.294972\pi\) | |||||||
\(942\) | −0.329363 | + | 0.213411i | −0.0107312 | + | 0.00695331i | ||||
\(943\) | −8.25129 | + | 8.25129i | −0.268699 | + | 0.268699i | ||||
\(944\) | 1.99629 | + | 2.23547i | 0.0649736 | + | 0.0727584i | ||||
\(945\) | −12.0154 | − | 5.18495i | −0.390862 | − | 0.168666i | ||||
\(946\) | −1.58906 | + | 7.43842i | −0.0516647 | + | 0.241844i | ||||
\(947\) | 7.31295 | + | 7.31295i | 0.237639 | + | 0.237639i | 0.815872 | − | 0.578233i | \(-0.196257\pi\) |
−0.578233 | + | 0.815872i | \(0.696257\pi\) | |||||||
\(948\) | 1.32878 | + | 3.48294i | 0.0431569 | + | 0.113120i | ||||
\(949\) | 9.68844i | 0.314500i | ||||||||
\(950\) | −11.5827 | + | 47.3649i | −0.375791 | + | 1.53672i | ||||
\(951\) | 10.4347i | 0.338369i | ||||||||
\(952\) | 21.1744 | − | 3.28695i | 0.686265 | − | 0.106531i | ||||
\(953\) | −27.6641 | − | 27.6641i | −0.896127 | − | 0.896127i | 0.0989642 | − | 0.995091i | \(-0.468447\pi\) |
−0.995091 | + | 0.0989642i | \(0.968447\pi\) | |||||||
\(954\) | −7.23236 | − | 1.54504i | −0.234156 | − | 0.0500225i | ||||
\(955\) | −40.3199 | − | 17.3990i | −1.30472 | − | 0.563018i | ||||
\(956\) | −15.5703 | + | 34.7793i | −0.503579 | + | 1.12484i | ||||
\(957\) | 5.56291 | − | 5.56291i | 0.179823 | − | 0.179823i | ||||
\(958\) | 5.20809 | + | 8.03779i | 0.168266 | + | 0.259689i | ||||
\(959\) | −3.97101 | −0.128231 | ||||||||
\(960\) | 12.9612 | + | 15.8320i | 0.418320 | + | 0.510975i | ||||
\(961\) | 1.20600 | 0.0389031 | ||||||||
\(962\) | 2.41426 | + | 3.72599i | 0.0778387 | + | 0.120131i | ||||
\(963\) | 11.8094 | − | 11.8094i | 0.380553 | − | 0.380553i | ||||
\(964\) | 0.708280 | − | 1.58208i | 0.0228121 | − | 0.0509554i | ||||
\(965\) | −38.4423 | + | 15.2659i | −1.23750 | + | 0.491427i | ||||
\(966\) | 14.7282 | + | 3.14636i | 0.473871 | + | 0.101232i | ||||
\(967\) | −18.7603 | − | 18.7603i | −0.603289 | − | 0.603289i | 0.337895 | − | 0.941184i | \(-0.390285\pi\) |
−0.941184 | + | 0.337895i | \(0.890285\pi\) | |||||||
\(968\) | 28.6000 | − | 4.43964i | 0.919238 | − | 0.142695i | ||||
\(969\) | 54.7915i | 1.76015i | ||||||||
\(970\) | −17.2412 | + | 24.2606i | −0.553580 | + | 0.778960i | ||||
\(971\) | 46.5164i | 1.49278i | 0.665508 | + | 0.746391i | \(0.268215\pi\) | ||||
−0.665508 | + | 0.746391i | \(0.731785\pi\) | |||||||
\(972\) | 10.6105 | + | 27.8117i | 0.340333 | + | 0.892061i | ||||
\(973\) | 3.25930 | + | 3.25930i | 0.104489 | + | 0.104489i | ||||
\(974\) | 2.44554 | − | 11.4476i | 0.0783601 | − | 0.366805i | ||||
\(975\) | 3.92342 | + | 4.16092i | 0.125650 | + | 0.133256i | ||||
\(976\) | 12.7807 | + | 14.3120i | 0.409100 | + | 0.458116i | ||||
\(977\) | −31.9984 | + | 31.9984i | −1.02372 | + | 1.02372i | −0.0240079 | + | 0.999712i | \(0.507643\pi\) |
−0.999712 | + | 0.0240079i | \(0.992357\pi\) | |||||||
\(978\) | −16.3707 | + | 10.6074i | −0.523479 | + | 0.339188i | ||||
\(979\) | 3.23052 | 0.103248 | ||||||||
\(980\) | 19.1463 | − | 17.5697i | 0.611606 | − | 0.561242i | ||||
\(981\) | 9.93803 | 0.317297 | ||||||||
\(982\) | −35.7248 | + | 23.1479i | −1.14002 | + | 0.738679i | ||||
\(983\) | −26.0707 | + | 26.0707i | −0.831527 | + | 0.831527i | −0.987726 | − | 0.156198i | \(-0.950076\pi\) |
0.156198 | + | 0.987726i | \(0.450076\pi\) | |||||||
\(984\) | 2.61011 | − | 3.56936i | 0.0832072 | − | 0.113787i | ||||
\(985\) | 0.903586 | + | 2.27539i | 0.0287907 | + | 0.0725000i | ||||
\(986\) | 16.1160 | − | 75.4395i | 0.513239 | − | 2.40248i | ||||
\(987\) | −4.75405 | − | 4.75405i | −0.151323 | − | 0.151323i | ||||
\(988\) | −12.8857 | + | 4.91604i | −0.409947 | + | 0.156400i | ||||
\(989\) | 52.4205i | 1.66687i | ||||||||
\(990\) | 4.62047 | − | 0.781484i | 0.146848 | − | 0.0248372i | ||||
\(991\) | 51.6625i | 1.64111i | 0.571565 | + | 0.820557i | \(0.306337\pi\) | ||||
−0.571565 | + | 0.820557i | \(0.693663\pi\) | |||||||
\(992\) | −29.7838 | − | 8.14445i | −0.945637 | − | 0.258587i | ||||
\(993\) | −26.4821 | − | 26.4821i | −0.840384 | − | 0.840384i | ||||
\(994\) | 7.56368 | + | 1.61582i | 0.239905 | + | 0.0512506i | ||||
\(995\) | −3.29594 | + | 7.63791i | −0.104488 | + | 0.242138i | ||||
\(996\) | 7.88348 | + | 3.52934i | 0.249798 | + | 0.111831i | ||||
\(997\) | 6.73844 | − | 6.73844i | 0.213409 | − | 0.213409i | −0.592305 | − | 0.805714i | \(-0.701782\pi\) |
0.805714 | + | 0.592305i | \(0.201782\pi\) | |||||||
\(998\) | 3.22456 | + | 4.97656i | 0.102072 | + | 0.157530i | ||||
\(999\) | 16.8472 | 0.533021 |
(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 | 260.2.o.a.183.12 | yes | 72 | |
4.3 | odd | 2 | inner | 260.2.o.a.183.31 | yes | 72 | |
5.2 | odd | 4 | inner | 260.2.o.a.27.31 | yes | 72 | |
20.7 | even | 4 | inner | 260.2.o.a.27.12 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.o.a.27.12 | ✓ | 72 | 20.7 | even | 4 | inner | |
260.2.o.a.27.31 | yes | 72 | 5.2 | odd | 4 | inner | |
260.2.o.a.183.12 | yes | 72 | 1.1 | even | 1 | trivial | |
260.2.o.a.183.31 | yes | 72 | 4.3 | odd | 2 | inner |