Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,2,Mod(11,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.e (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: | \(0.479102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.8 | ||
Root | \(1.17915 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.11 |
Dual form | 60.2.e.a.11.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17915 | + | 0.780776i | 0.833783 | + | 0.552092i | ||||
\(3\) | −1.51022 | + | 0.848071i | −0.871928 | + | 0.489634i | ||||
\(4\) | 0.780776 | + | 1.84130i | 0.390388 | + | 0.920650i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −2.44293 | − | 0.179147i | −0.997322 | − | 0.0731366i | ||||
\(7\) | − | 3.02045i | − | 1.14162i | −0.821081 | − | 0.570811i | \(-0.806629\pi\) | ||
0.821081 | − | 0.570811i | \(-0.193371\pi\) | |||||||
\(8\) | −0.516994 | + | 2.78078i | −0.182785 | + | 0.983153i | ||||
\(9\) | 1.56155 | − | 2.56155i | 0.520518 | − | 0.853851i | ||||
\(10\) | 0.780776 | − | 1.17915i | 0.246903 | − | 0.372879i | ||||
\(11\) | 1.32431 | 0.399294 | 0.199647 | − | 0.979868i | \(-0.436021\pi\) | ||||
0.199647 | + | 0.979868i | \(0.436021\pi\) | |||||||
\(12\) | −2.74070 | − | 2.11862i | −0.791172 | − | 0.611594i | ||||
\(13\) | −5.12311 | −1.42089 | −0.710447 | − | 0.703751i | \(-0.751507\pi\) | ||||
−0.710447 | + | 0.703751i | \(0.751507\pi\) | |||||||
\(14\) | 2.35829 | − | 3.56155i | 0.630281 | − | 0.951865i | ||||
\(15\) | 0.848071 | + | 1.51022i | 0.218971 | + | 0.389938i | ||||
\(16\) | −2.78078 | + | 2.87529i | −0.695194 | + | 0.718822i | ||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 3.84130 | − | 1.80122i | 0.905403 | − | 0.424553i | ||||
\(19\) | 1.32431i | 0.303817i | 0.988395 | + | 0.151908i | \(0.0485419\pi\) | ||||
−0.988395 | + | 0.151908i | \(0.951458\pi\) | |||||||
\(20\) | 1.84130 | − | 0.780776i | 0.411727 | − | 0.174587i | ||||
\(21\) | 2.56155 | + | 4.56155i | 0.558977 | + | 0.995412i | ||||
\(22\) | 1.56155 | + | 1.03399i | 0.332924 | + | 0.220447i | ||||
\(23\) | 0.371834 | 0.0775328 | 0.0387664 | − | 0.999248i | \(-0.487657\pi\) | ||||
0.0387664 | + | 0.999248i | \(0.487657\pi\) | |||||||
\(24\) | −1.57752 | − | 4.63804i | −0.322010 | − | 0.946736i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −6.04090 | − | 4.00000i | −1.18472 | − | 0.784465i | ||||
\(27\) | −0.185917 | + | 5.19283i | −0.0357798 | + | 0.999360i | ||||
\(28\) | 5.56155 | − | 2.35829i | 1.05103 | − | 0.445676i | ||||
\(29\) | 3.12311i | 0.579946i | 0.957035 | + | 0.289973i | \(0.0936464\pi\) | ||||
−0.957035 | + | 0.289973i | \(0.906354\pi\) | |||||||
\(30\) | −0.179147 | + | 2.44293i | −0.0327077 | + | 0.446016i | ||||
\(31\) | − | 4.71659i | − | 0.847124i | −0.905867 | − | 0.423562i | \(-0.860780\pi\) | ||
0.905867 | − | 0.423562i | \(-0.139220\pi\) | |||||||
\(32\) | −5.52390 | + | 1.21922i | −0.976497 | + | 0.215530i | ||||
\(33\) | −2.00000 | + | 1.12311i | −0.348155 | + | 0.195508i | ||||
\(34\) | −1.56155 | + | 2.35829i | −0.267804 | + | 0.404444i | ||||
\(35\) | −3.02045 | −0.510549 | ||||||||
\(36\) | 5.93581 | + | 0.875288i | 0.989302 | + | 0.145881i | ||||
\(37\) | 5.12311 | 0.842233 | 0.421117 | − | 0.907006i | \(-0.361638\pi\) | ||||
0.421117 | + | 0.907006i | \(0.361638\pi\) | |||||||
\(38\) | −1.03399 | + | 1.56155i | −0.167735 | + | 0.253317i | ||||
\(39\) | 7.73704 | − | 4.34475i | 1.23892 | − | 0.695718i | ||||
\(40\) | 2.78078 | + | 0.516994i | 0.439679 | + | 0.0817439i | ||||
\(41\) | − | 1.12311i | − | 0.175400i | −0.996147 | − | 0.0876998i | \(-0.972048\pi\) | ||
0.996147 | − | 0.0876998i | \(-0.0279516\pi\) | |||||||
\(42\) | −0.541105 | + | 7.37874i | −0.0834943 | + | 1.13856i | ||||
\(43\) | 7.73704i | 1.17989i | 0.807445 | + | 0.589944i | \(0.200850\pi\) | ||||
−0.807445 | + | 0.589944i | \(0.799150\pi\) | |||||||
\(44\) | 1.03399 | + | 2.43845i | 0.155879 | + | 0.367610i | ||||
\(45\) | −2.56155 | − | 1.56155i | −0.381854 | − | 0.232783i | ||||
\(46\) | 0.438447 | + | 0.290319i | 0.0646455 | + | 0.0428052i | ||||
\(47\) | 3.02045 | 0.440578 | 0.220289 | − | 0.975435i | \(-0.429300\pi\) | ||||
0.220289 | + | 0.975435i | \(0.429300\pi\) | |||||||
\(48\) | 1.76115 | − | 6.70062i | 0.254200 | − | 0.967152i | ||||
\(49\) | −2.12311 | −0.303301 | ||||||||
\(50\) | −1.17915 | − | 0.780776i | −0.166757 | − | 0.110418i | ||||
\(51\) | −1.69614 | − | 3.02045i | −0.237507 | − | 0.422947i | ||||
\(52\) | −4.00000 | − | 9.43318i | −0.554700 | − | 1.30815i | ||||
\(53\) | − | 12.2462i | − | 1.68215i | −0.540921 | − | 0.841073i | \(-0.681924\pi\) | ||
0.540921 | − | 0.841073i | \(-0.318076\pi\) | |||||||
\(54\) | −4.27366 | + | 5.97795i | −0.581571 | + | 0.813495i | ||||
\(55\) | − | 1.32431i | − | 0.178570i | ||||||
\(56\) | 8.39919 | + | 1.56155i | 1.12239 | + | 0.208671i | ||||
\(57\) | −1.12311 | − | 2.00000i | −0.148759 | − | 0.264906i | ||||
\(58\) | −2.43845 | + | 3.68260i | −0.320184 | + | 0.483549i | ||||
\(59\) | −14.1498 | −1.84214 | −0.921071 | − | 0.389394i | \(-0.872685\pi\) | ||||
−0.921071 | + | 0.389394i | \(0.872685\pi\) | |||||||
\(60\) | −2.11862 | + | 2.74070i | −0.273513 | + | 0.353823i | ||||
\(61\) | 3.12311 | 0.399873 | 0.199936 | − | 0.979809i | \(-0.435926\pi\) | ||||
0.199936 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(62\) | 3.68260 | − | 5.56155i | 0.467691 | − | 0.706318i | ||||
\(63\) | −7.73704 | − | 4.71659i | −0.974775 | − | 0.594234i | ||||
\(64\) | −7.46543 | − | 2.87529i | −0.933179 | − | 0.359411i | ||||
\(65\) | 5.12311i | 0.635443i | ||||||||
\(66\) | −3.23519 | − | 0.237246i | −0.398224 | − | 0.0292030i | ||||
\(67\) | − | 4.34475i | − | 0.530796i | −0.964139 | − | 0.265398i | \(-0.914497\pi\) | ||
0.964139 | − | 0.265398i | \(-0.0855034\pi\) | |||||||
\(68\) | −3.68260 | + | 1.56155i | −0.446581 | + | 0.189366i | ||||
\(69\) | −0.561553 | + | 0.315342i | −0.0676030 | + | 0.0379627i | ||||
\(70\) | −3.56155 | − | 2.35829i | −0.425687 | − | 0.281870i | ||||
\(71\) | 3.39228 | 0.402590 | 0.201295 | − | 0.979531i | \(-0.435485\pi\) | ||||
0.201295 | + | 0.979531i | \(0.435485\pi\) | |||||||
\(72\) | 6.31579 | + | 5.66664i | 0.744323 | + | 0.667819i | ||||
\(73\) | 8.24621 | 0.965146 | 0.482573 | − | 0.875856i | \(-0.339702\pi\) | ||||
0.482573 | + | 0.875856i | \(0.339702\pi\) | |||||||
\(74\) | 6.04090 | + | 4.00000i | 0.702240 | + | 0.464991i | ||||
\(75\) | 1.51022 | − | 0.848071i | 0.174386 | − | 0.0979267i | ||||
\(76\) | −2.43845 | + | 1.03399i | −0.279709 | + | 0.118607i | ||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 12.5154 | + | 0.917790i | 1.41709 | + | 0.103919i | ||||
\(79\) | 8.10887i | 0.912319i | 0.889898 | + | 0.456160i | \(0.150775\pi\) | ||||
−0.889898 | + | 0.456160i | \(0.849225\pi\) | |||||||
\(80\) | 2.87529 | + | 2.78078i | 0.321467 | + | 0.310900i | ||||
\(81\) | −4.12311 | − | 8.00000i | −0.458123 | − | 0.888889i | ||||
\(82\) | 0.876894 | − | 1.32431i | 0.0968368 | − | 0.146245i | ||||
\(83\) | 15.1022 | 1.65769 | 0.828843 | − | 0.559481i | \(-0.189000\pi\) | ||||
0.828843 | + | 0.559481i | \(0.189000\pi\) | |||||||
\(84\) | −6.39919 | + | 8.27814i | −0.698209 | + | 0.903219i | ||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | −6.04090 | + | 9.12311i | −0.651407 | + | 0.983770i | ||||
\(87\) | −2.64861 | − | 4.71659i | −0.283961 | − | 0.505671i | ||||
\(88\) | −0.684658 | + | 3.68260i | −0.0729848 | + | 0.392567i | ||||
\(89\) | 10.2462i | 1.08610i | 0.839702 | + | 0.543048i | \(0.182730\pi\) | ||||
−0.839702 | + | 0.543048i | \(0.817270\pi\) | |||||||
\(90\) | −1.80122 | − | 3.84130i | −0.189866 | − | 0.404909i | ||||
\(91\) | 15.4741i | 1.62212i | ||||||||
\(92\) | 0.290319 | + | 0.684658i | 0.0302679 | + | 0.0713806i | ||||
\(93\) | 4.00000 | + | 7.12311i | 0.414781 | + | 0.738632i | ||||
\(94\) | 3.56155 | + | 2.35829i | 0.367346 | + | 0.243240i | ||||
\(95\) | 1.32431 | 0.135871 | ||||||||
\(96\) | 7.30834 | − | 6.52596i | 0.745904 | − | 0.666053i | ||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −2.50345 | − | 1.65767i | −0.252887 | − | 0.167450i | ||||
\(99\) | 2.06798 | − | 3.39228i | 0.207839 | − | 0.340937i | ||||
\(100\) | −0.780776 | − | 1.84130i | −0.0780776 | − | 0.184130i | ||||
\(101\) | − | 0.876894i | − | 0.0872543i | −0.999048 | − | 0.0436271i | \(-0.986109\pi\) | ||
0.999048 | − | 0.0436271i | \(-0.0138914\pi\) | |||||||
\(102\) | 0.358294 | − | 4.88586i | 0.0354764 | − | 0.483772i | ||||
\(103\) | − | 9.80501i | − | 0.966117i | −0.875588 | − | 0.483058i | \(-0.839526\pi\) | ||
0.875588 | − | 0.483058i | \(-0.160474\pi\) | |||||||
\(104\) | 2.64861 | − | 14.2462i | 0.259718 | − | 1.39696i | ||||
\(105\) | 4.56155 | − | 2.56155i | 0.445162 | − | 0.249982i | ||||
\(106\) | 9.56155 | − | 14.4401i | 0.928700 | − | 1.40255i | ||||
\(107\) | −3.02045 | −0.291998 | −0.145999 | − | 0.989285i | \(-0.546640\pi\) | ||||
−0.145999 | + | 0.989285i | \(0.546640\pi\) | |||||||
\(108\) | −9.70671 | + | 3.71211i | −0.934029 | + | 0.357198i | ||||
\(109\) | −0.876894 | −0.0839912 | −0.0419956 | − | 0.999118i | \(-0.513372\pi\) | ||||
−0.0419956 | + | 0.999118i | \(0.513372\pi\) | |||||||
\(110\) | 1.03399 | − | 1.56155i | 0.0985868 | − | 0.148888i | ||||
\(111\) | −7.73704 | + | 4.34475i | −0.734367 | + | 0.412386i | ||||
\(112\) | 8.68466 | + | 8.39919i | 0.820623 | + | 0.793649i | ||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0.237246 | − | 3.23519i | 0.0222201 | − | 0.303003i | ||||
\(115\) | − | 0.371834i | − | 0.0346737i | ||||||
\(116\) | −5.75058 | + | 2.43845i | −0.533928 | + | 0.226404i | ||||
\(117\) | −8.00000 | + | 13.1231i | −0.739600 | + | 1.21323i | ||||
\(118\) | −16.6847 | − | 11.0478i | −1.53595 | − | 1.01703i | ||||
\(119\) | 6.04090 | 0.553768 | ||||||||
\(120\) | −4.63804 | + | 1.57752i | −0.423393 | + | 0.144007i | ||||
\(121\) | −9.24621 | −0.840565 | ||||||||
\(122\) | 3.68260 | + | 2.43845i | 0.333407 | + | 0.220767i | ||||
\(123\) | 0.952473 | + | 1.69614i | 0.0858816 | + | 0.152936i | ||||
\(124\) | 8.68466 | − | 3.68260i | 0.779905 | − | 0.330707i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −5.44050 | − | 11.6024i | −0.484679 | − | 1.03363i | ||||
\(127\) | 15.1022i | 1.34011i | 0.742313 | + | 0.670054i | \(0.233729\pi\) | ||||
−0.742313 | + | 0.670054i | \(0.766271\pi\) | |||||||
\(128\) | −6.55789 | − | 9.21922i | −0.579641 | − | 0.814872i | ||||
\(129\) | −6.56155 | − | 11.6847i | −0.577713 | − | 1.02878i | ||||
\(130\) | −4.00000 | + | 6.04090i | −0.350823 | + | 0.529822i | ||||
\(131\) | 5.46026 | 0.477065 | 0.238532 | − | 0.971135i | \(-0.423334\pi\) | ||||
0.238532 | + | 0.971135i | \(0.423334\pi\) | |||||||
\(132\) | −3.62953 | − | 2.80571i | −0.315910 | − | 0.244205i | ||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 3.39228 | − | 5.12311i | 0.293049 | − | 0.442569i | ||||
\(135\) | 5.19283 | + | 0.185917i | 0.446927 | + | 0.0160012i | ||||
\(136\) | −5.56155 | − | 1.03399i | −0.476899 | − | 0.0886637i | ||||
\(137\) | − | 8.24621i | − | 0.704521i | −0.935902 | − | 0.352261i | \(-0.885413\pi\) | ||
0.935902 | − | 0.352261i | \(-0.114587\pi\) | |||||||
\(138\) | −0.908365 | − | 0.0666131i | −0.0773251 | − | 0.00567048i | ||||
\(139\) | − | 17.5420i | − | 1.48790i | −0.668237 | − | 0.743949i | \(-0.732951\pi\) | ||
0.668237 | − | 0.743949i | \(-0.267049\pi\) | |||||||
\(140\) | −2.35829 | − | 5.56155i | −0.199312 | − | 0.470037i | ||||
\(141\) | −4.56155 | + | 2.56155i | −0.384152 | + | 0.215722i | ||||
\(142\) | 4.00000 | + | 2.64861i | 0.335673 | + | 0.222267i | ||||
\(143\) | −6.78456 | −0.567354 | ||||||||
\(144\) | 3.02287 | + | 11.6130i | 0.251906 | + | 0.967752i | ||||
\(145\) | 3.12311 | 0.259360 | ||||||||
\(146\) | 9.72350 | + | 6.43845i | 0.804722 | + | 0.532850i | ||||
\(147\) | 3.20636 | − | 1.80054i | 0.264457 | − | 0.148506i | ||||
\(148\) | 4.00000 | + | 9.43318i | 0.328798 | + | 0.775402i | ||||
\(149\) | − | 14.0000i | − | 1.14692i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 2.44293 | + | 0.179147i | 0.199464 | + | 0.0146273i | ||||
\(151\) | − | 7.36520i | − | 0.599372i | −0.954038 | − | 0.299686i | \(-0.903118\pi\) | ||
0.954038 | − | 0.299686i | \(-0.0968819\pi\) | |||||||
\(152\) | −3.68260 | − | 0.684658i | −0.298698 | − | 0.0555331i | ||||
\(153\) | 5.12311 | + | 3.12311i | 0.414179 | + | 0.252488i | ||||
\(154\) | 3.12311 | − | 4.71659i | 0.251667 | − | 0.380074i | ||||
\(155\) | −4.71659 | −0.378846 | ||||||||
\(156\) | 14.0409 | + | 10.8539i | 1.12417 | + | 0.869010i | ||||
\(157\) | −3.36932 | −0.268901 | −0.134450 | − | 0.990920i | \(-0.542927\pi\) | ||||
−0.134450 | + | 0.990920i | \(0.542927\pi\) | |||||||
\(158\) | −6.33122 | + | 9.56155i | −0.503684 | + | 0.760676i | ||||
\(159\) | 10.3857 | + | 18.4945i | 0.823636 | + | 1.46671i | ||||
\(160\) | 1.21922 | + | 5.52390i | 0.0963881 | + | 0.436703i | ||||
\(161\) | − | 1.12311i | − | 0.0885131i | ||||||
\(162\) | 1.38446 | − | 12.6524i | 0.108774 | − | 0.994067i | ||||
\(163\) | − | 15.6829i | − | 1.22838i | −0.789159 | − | 0.614189i | \(-0.789483\pi\) | ||
0.789159 | − | 0.614189i | \(-0.210517\pi\) | |||||||
\(164\) | 2.06798 | − | 0.876894i | 0.161482 | − | 0.0684739i | ||||
\(165\) | 1.12311 | + | 2.00000i | 0.0874337 | + | 0.155700i | ||||
\(166\) | 17.8078 | + | 11.7915i | 1.38215 | + | 0.915196i | ||||
\(167\) | −9.06134 | −0.701188 | −0.350594 | − | 0.936528i | \(-0.614020\pi\) | ||||
−0.350594 | + | 0.936528i | \(0.614020\pi\) | |||||||
\(168\) | −14.0090 | + | 4.76481i | −1.08082 | + | 0.367613i | ||||
\(169\) | 13.2462 | 1.01894 | ||||||||
\(170\) | 2.35829 | + | 1.56155i | 0.180873 | + | 0.119766i | ||||
\(171\) | 3.39228 | + | 2.06798i | 0.259414 | + | 0.158142i | ||||
\(172\) | −14.2462 | + | 6.04090i | −1.08626 | + | 0.460614i | ||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 0.559496 | − | 7.62953i | 0.0424153 | − | 0.578393i | ||||
\(175\) | 3.02045i | 0.228324i | ||||||||
\(176\) | −3.68260 | + | 3.80776i | −0.277587 | + | 0.287021i | ||||
\(177\) | 21.3693 | − | 12.0000i | 1.60622 | − | 0.901975i | ||||
\(178\) | −8.00000 | + | 12.0818i | −0.599625 | + | 0.905569i | ||||
\(179\) | −10.0138 | −0.748468 | −0.374234 | − | 0.927334i | \(-0.622094\pi\) | ||||
−0.374234 | + | 0.927334i | \(0.622094\pi\) | |||||||
\(180\) | 0.875288 | − | 5.93581i | 0.0652401 | − | 0.442429i | ||||
\(181\) | −12.2462 | −0.910254 | −0.455127 | − | 0.890427i | \(-0.650406\pi\) | ||||
−0.455127 | + | 0.890427i | \(0.650406\pi\) | |||||||
\(182\) | −12.0818 | + | 18.2462i | −0.895562 | + | 1.35250i | ||||
\(183\) | −4.71659 | + | 2.64861i | −0.348660 | + | 0.195791i | ||||
\(184\) | −0.192236 | + | 1.03399i | −0.0141718 | + | 0.0762266i | ||||
\(185\) | − | 5.12311i | − | 0.376658i | ||||||
\(186\) | −0.844964 | + | 11.5223i | −0.0619558 | + | 0.844856i | ||||
\(187\) | 2.64861i | 0.193686i | ||||||||
\(188\) | 2.35829 | + | 5.56155i | 0.171996 | + | 0.405618i | ||||
\(189\) | 15.6847 | + | 0.561553i | 1.14089 | + | 0.0408470i | ||||
\(190\) | 1.56155 | + | 1.03399i | 0.113287 | + | 0.0750133i | ||||
\(191\) | −24.9073 | −1.80223 | −0.901113 | − | 0.433585i | \(-0.857248\pi\) | ||||
−0.901113 | + | 0.433585i | \(0.857248\pi\) | |||||||
\(192\) | 13.7129 | − | 1.98889i | 0.989645 | − | 0.143535i | ||||
\(193\) | −0.246211 | −0.0177227 | −0.00886134 | − | 0.999961i | \(-0.502821\pi\) | ||||
−0.00886134 | + | 0.999961i | \(0.502821\pi\) | |||||||
\(194\) | −7.07488 | − | 4.68466i | −0.507947 | − | 0.336339i | ||||
\(195\) | −4.34475 | − | 7.73704i | −0.311134 | − | 0.554061i | ||||
\(196\) | −1.65767 | − | 3.90928i | −0.118405 | − | 0.279234i | ||||
\(197\) | 4.24621i | 0.302530i | 0.988493 | + | 0.151265i | \(0.0483347\pi\) | ||||
−0.988493 | + | 0.151265i | \(0.951665\pi\) | |||||||
\(198\) | 5.08706 | − | 2.38537i | 0.361522 | − | 0.169521i | ||||
\(199\) | 5.46026i | 0.387067i | 0.981094 | + | 0.193534i | \(0.0619949\pi\) | ||||
−0.981094 | + | 0.193534i | \(0.938005\pi\) | |||||||
\(200\) | 0.516994 | − | 2.78078i | 0.0365570 | − | 0.196631i | ||||
\(201\) | 3.68466 | + | 6.56155i | 0.259896 | + | 0.462816i | ||||
\(202\) | 0.684658 | − | 1.03399i | 0.0481724 | − | 0.0727511i | ||||
\(203\) | 9.43318 | 0.662079 | ||||||||
\(204\) | 4.23725 | − | 5.48140i | 0.296667 | − | 0.383775i | ||||
\(205\) | −1.12311 | −0.0784411 | ||||||||
\(206\) | 7.65552 | − | 11.5616i | 0.533385 | − | 0.805532i | ||||
\(207\) | 0.580639 | − | 0.952473i | 0.0403572 | − | 0.0662014i | ||||
\(208\) | 14.2462 | − | 14.7304i | 0.987797 | − | 1.02137i | ||||
\(209\) | 1.75379i | 0.121312i | ||||||||
\(210\) | 7.37874 | + | 0.541105i | 0.509182 | + | 0.0373398i | ||||
\(211\) | − | 16.7984i | − | 1.15645i | −0.815878 | − | 0.578224i | \(-0.803746\pi\) | ||
0.815878 | − | 0.578224i | \(-0.196254\pi\) | |||||||
\(212\) | 22.5490 | − | 9.56155i | 1.54867 | − | 0.656690i | ||||
\(213\) | −5.12311 | + | 2.87689i | −0.351029 | + | 0.197122i | ||||
\(214\) | −3.56155 | − | 2.35829i | −0.243463 | − | 0.161210i | ||||
\(215\) | 7.73704 | 0.527662 | ||||||||
\(216\) | −14.3440 | − | 3.20165i | −0.975983 | − | 0.217845i | ||||
\(217\) | −14.2462 | −0.967096 | ||||||||
\(218\) | −1.03399 | − | 0.684658i | −0.0700305 | − | 0.0463709i | ||||
\(219\) | −12.4536 | + | 6.99337i | −0.841538 | + | 0.472568i | ||||
\(220\) | 2.43845 | − | 1.03399i | 0.164400 | − | 0.0697114i | ||||
\(221\) | − | 10.2462i | − | 0.689235i | ||||||
\(222\) | −12.5154 | − | 0.917790i | −0.839978 | − | 0.0615980i | ||||
\(223\) | 8.31768i | 0.556993i | 0.960437 | + | 0.278496i | \(0.0898360\pi\) | ||||
−0.960437 | + | 0.278496i | \(0.910164\pi\) | |||||||
\(224\) | 3.68260 | + | 16.6847i | 0.246054 | + | 1.11479i | ||||
\(225\) | −1.56155 | + | 2.56155i | −0.104104 | + | 0.170770i | ||||
\(226\) | −10.9309 | + | 16.5081i | −0.727111 | + | 1.09810i | ||||
\(227\) | 21.8868 | 1.45268 | 0.726339 | − | 0.687337i | \(-0.241220\pi\) | ||||
0.726339 | + | 0.687337i | \(0.241220\pi\) | |||||||
\(228\) | 2.80571 | − | 3.62953i | 0.185812 | − | 0.240371i | ||||
\(229\) | −16.2462 | −1.07358 | −0.536790 | − | 0.843716i | \(-0.680363\pi\) | ||||
−0.536790 | + | 0.843716i | \(0.680363\pi\) | |||||||
\(230\) | 0.290319 | − | 0.438447i | 0.0191431 | − | 0.0289104i | ||||
\(231\) | 3.39228 | + | 6.04090i | 0.223196 | + | 0.397462i | ||||
\(232\) | −8.68466 | − | 1.61463i | −0.570176 | − | 0.106005i | ||||
\(233\) | − | 10.0000i | − | 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | −19.6794 | + | 9.22786i | −1.28648 | + | 0.603244i | ||||
\(235\) | − | 3.02045i | − | 0.197032i | ||||||
\(236\) | −11.0478 | − | 26.0540i | −0.719151 | − | 1.69597i | ||||
\(237\) | −6.87689 | − | 12.2462i | −0.446702 | − | 0.795477i | ||||
\(238\) | 7.12311 | + | 4.71659i | 0.461722 | + | 0.305731i | ||||
\(239\) | 17.3790 | 1.12416 | 0.562078 | − | 0.827084i | \(-0.310002\pi\) | ||||
0.562078 | + | 0.827084i | \(0.310002\pi\) | |||||||
\(240\) | −6.70062 | − | 1.76115i | −0.432523 | − | 0.113682i | ||||
\(241\) | 13.3693 | 0.861193 | 0.430597 | − | 0.902544i | \(-0.358303\pi\) | ||||
0.430597 | + | 0.902544i | \(0.358303\pi\) | |||||||
\(242\) | −10.9026 | − | 7.21922i | −0.700849 | − | 0.464069i | ||||
\(243\) | 13.0114 | + | 8.58511i | 0.834680 | + | 0.550735i | ||||
\(244\) | 2.43845 | + | 5.75058i | 0.156106 | + | 0.368143i | ||||
\(245\) | 2.12311i | 0.135640i | ||||||||
\(246\) | −0.201201 | + | 2.74367i | −0.0128281 | + | 0.174930i | ||||
\(247\) | − | 6.78456i | − | 0.431691i | ||||||
\(248\) | 13.1158 | + | 2.43845i | 0.832853 | + | 0.154842i | ||||
\(249\) | −22.8078 | + | 12.8078i | −1.44538 | + | 0.811659i | ||||
\(250\) | −0.780776 | + | 1.17915i | −0.0493806 | + | 0.0745758i | ||||
\(251\) | 18.7033 | 1.18054 | 0.590272 | − | 0.807205i | \(-0.299021\pi\) | ||||
0.590272 | + | 0.807205i | \(0.299021\pi\) | |||||||
\(252\) | 2.64376 | − | 17.9288i | 0.166541 | − | 1.12941i | ||||
\(253\) | 0.492423 | 0.0309583 | ||||||||
\(254\) | −11.7915 | + | 17.8078i | −0.739863 | + | 1.11736i | ||||
\(255\) | −3.02045 | + | 1.69614i | −0.189148 | + | 0.106216i | ||||
\(256\) | −0.534565 | − | 15.9911i | −0.0334103 | − | 0.999442i | ||||
\(257\) | 30.4924i | 1.90207i | 0.309091 | + | 0.951033i | \(0.399975\pi\) | ||||
−0.309091 | + | 0.951033i | \(0.600025\pi\) | |||||||
\(258\) | 1.38607 | − | 18.9010i | 0.0862929 | − | 1.17673i | ||||
\(259\) | − | 15.4741i | − | 0.961512i | ||||||
\(260\) | −9.43318 | + | 4.00000i | −0.585021 | + | 0.248069i | ||||
\(261\) | 8.00000 | + | 4.87689i | 0.495188 | + | 0.301872i | ||||
\(262\) | 6.43845 | + | 4.26324i | 0.397769 | + | 0.263384i | ||||
\(263\) | −23.7917 | −1.46706 | −0.733531 | − | 0.679656i | \(-0.762129\pi\) | ||||
−0.733531 | + | 0.679656i | \(0.762129\pi\) | |||||||
\(264\) | −2.08912 | − | 6.14219i | −0.128576 | − | 0.378026i | ||||
\(265\) | −12.2462 | −0.752279 | ||||||||
\(266\) | 4.71659 | + | 3.12311i | 0.289193 | + | 0.191490i | ||||
\(267\) | −8.68951 | − | 15.4741i | −0.531789 | − | 0.946998i | ||||
\(268\) | 8.00000 | − | 3.39228i | 0.488678 | − | 0.207217i | ||||
\(269\) | 14.0000i | 0.853595i | 0.904347 | + | 0.426798i | \(0.140358\pi\) | ||||
−0.904347 | + | 0.426798i | \(0.859642\pi\) | |||||||
\(270\) | 5.97795 | + | 4.27366i | 0.363806 | + | 0.260087i | ||||
\(271\) | 15.3110i | 0.930080i | 0.885290 | + | 0.465040i | \(0.153960\pi\) | ||||
−0.885290 | + | 0.465040i | \(0.846040\pi\) | |||||||
\(272\) | −5.75058 | − | 5.56155i | −0.348680 | − | 0.337219i | ||||
\(273\) | −13.1231 | − | 23.3693i | −0.794246 | − | 1.41438i | ||||
\(274\) | 6.43845 | − | 9.72350i | 0.388961 | − | 0.587418i | ||||
\(275\) | −1.32431 | −0.0798587 | ||||||||
\(276\) | −1.01909 | − | 0.787776i | −0.0613418 | − | 0.0474186i | ||||
\(277\) | 23.3693 | 1.40413 | 0.702063 | − | 0.712115i | \(-0.252262\pi\) | ||||
0.702063 | + | 0.712115i | \(0.252262\pi\) | |||||||
\(278\) | 13.6964 | − | 20.6847i | 0.821457 | − | 1.24058i | ||||
\(279\) | −12.0818 | − | 7.36520i | −0.723318 | − | 0.440943i | ||||
\(280\) | 1.56155 | − | 8.39919i | 0.0933206 | − | 0.501948i | ||||
\(281\) | 13.6155i | 0.812234i | 0.913821 | + | 0.406117i | \(0.133118\pi\) | ||||
−0.913821 | + | 0.406117i | \(0.866882\pi\) | |||||||
\(282\) | −7.37874 | − | 0.541105i | −0.439398 | − | 0.0322223i | ||||
\(283\) | 23.2111i | 1.37976i | 0.723925 | + | 0.689879i | \(0.242336\pi\) | ||||
−0.723925 | + | 0.689879i | \(0.757664\pi\) | |||||||
\(284\) | 2.64861 | + | 6.24621i | 0.157166 | + | 0.370644i | ||||
\(285\) | −2.00000 | + | 1.12311i | −0.118470 | + | 0.0665270i | ||||
\(286\) | −8.00000 | − | 5.29723i | −0.473050 | − | 0.313232i | ||||
\(287\) | −3.39228 | −0.200240 | ||||||||
\(288\) | −5.50276 | + | 16.0536i | −0.324253 | + | 0.945970i | ||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 3.68260 | + | 2.43845i | 0.216250 | + | 0.143191i | ||||
\(291\) | 9.06134 | − | 5.08842i | 0.531185 | − | 0.298289i | ||||
\(292\) | 6.43845 | + | 15.1838i | 0.376782 | + | 0.888562i | ||||
\(293\) | 2.49242i | 0.145609i | 0.997346 | + | 0.0728044i | \(0.0231949\pi\) | ||||
−0.997346 | + | 0.0728044i | \(0.976805\pi\) | |||||||
\(294\) | 5.18660 | + | 0.380349i | 0.302489 | + | 0.0221824i | ||||
\(295\) | 14.1498i | 0.823831i | ||||||||
\(296\) | −2.64861 | + | 14.2462i | −0.153948 | + | 0.828044i | ||||
\(297\) | −0.246211 | + | 6.87689i | −0.0142866 | + | 0.399038i | ||||
\(298\) | 10.9309 | − | 16.5081i | 0.633208 | − | 0.956286i | ||||
\(299\) | −1.90495 | −0.110166 | ||||||||
\(300\) | 2.74070 | + | 2.11862i | 0.158234 | + | 0.122319i | ||||
\(301\) | 23.3693 | 1.34699 | ||||||||
\(302\) | 5.75058 | − | 8.68466i | 0.330908 | − | 0.499746i | ||||
\(303\) | 0.743668 | + | 1.32431i | 0.0427226 | + | 0.0760794i | ||||
\(304\) | −3.80776 | − | 3.68260i | −0.218390 | − | 0.211212i | ||||
\(305\) | − | 3.12311i | − | 0.178829i | ||||||
\(306\) | 3.60245 | + | 7.68260i | 0.205938 | + | 0.439185i | ||||
\(307\) | 11.1293i | 0.635184i | 0.948227 | + | 0.317592i | \(0.102874\pi\) | ||||
−0.948227 | + | 0.317592i | \(0.897126\pi\) | |||||||
\(308\) | 7.36520 | − | 3.12311i | 0.419671 | − | 0.177955i | ||||
\(309\) | 8.31534 | + | 14.8078i | 0.473043 | + | 0.842384i | ||||
\(310\) | −5.56155 | − | 3.68260i | −0.315875 | − | 0.209158i | ||||
\(311\) | 20.7713 | 1.17783 | 0.588916 | − | 0.808194i | \(-0.299555\pi\) | ||||
0.588916 | + | 0.808194i | \(0.299555\pi\) | |||||||
\(312\) | 8.08179 | + | 23.7612i | 0.457541 | + | 1.34521i | ||||
\(313\) | −22.4924 | −1.27135 | −0.635673 | − | 0.771958i | \(-0.719278\pi\) | ||||
−0.635673 | + | 0.771958i | \(0.719278\pi\) | |||||||
\(314\) | −3.97292 | − | 2.63068i | −0.224205 | − | 0.148458i | ||||
\(315\) | −4.71659 | + | 7.73704i | −0.265750 | + | 0.435933i | ||||
\(316\) | −14.9309 | + | 6.33122i | −0.839927 | + | 0.356159i | ||||
\(317\) | − | 16.7386i | − | 0.940135i | −0.882630 | − | 0.470068i | \(-0.844230\pi\) | ||
0.882630 | − | 0.470068i | \(-0.155770\pi\) | |||||||
\(318\) | −2.19387 | + | 29.9166i | −0.123026 | + | 1.67764i | ||||
\(319\) | 4.13595i | 0.231569i | ||||||||
\(320\) | −2.87529 | + | 7.46543i | −0.160734 | + | 0.417330i | ||||
\(321\) | 4.56155 | − | 2.56155i | 0.254601 | − | 0.142972i | ||||
\(322\) | 0.876894 | − | 1.32431i | 0.0488674 | − | 0.0738007i | ||||
\(323\) | −2.64861 | −0.147373 | ||||||||
\(324\) | 11.5112 | − | 13.8381i | 0.639510 | − | 0.768783i | ||||
\(325\) | 5.12311 | 0.284179 | ||||||||
\(326\) | 12.2448 | − | 18.4924i | 0.678178 | − | 1.02420i | ||||
\(327\) | 1.32431 | − | 0.743668i | 0.0732343 | − | 0.0411249i | ||||
\(328\) | 3.12311 | + | 0.580639i | 0.172445 | + | 0.0320604i | ||||
\(329\) | − | 9.12311i | − | 0.502973i | ||||||
\(330\) | −0.237246 | + | 3.23519i | −0.0130600 | + | 0.178091i | ||||
\(331\) | − | 3.22925i | − | 0.177496i | −0.996054 | − | 0.0887479i | \(-0.971713\pi\) | ||
0.996054 | − | 0.0887479i | \(-0.0282865\pi\) | |||||||
\(332\) | 11.7915 | + | 27.8078i | 0.647141 | + | 1.52615i | ||||
\(333\) | 8.00000 | − | 13.1231i | 0.438397 | − | 0.719142i | ||||
\(334\) | −10.6847 | − | 7.07488i | −0.584638 | − | 0.387120i | ||||
\(335\) | −4.34475 | −0.237379 | ||||||||
\(336\) | −20.2389 | − | 5.31946i | −1.10412 | − | 0.290200i | ||||
\(337\) | −1.50758 | −0.0821230 | −0.0410615 | − | 0.999157i | \(-0.513074\pi\) | ||||
−0.0410615 | + | 0.999157i | \(0.513074\pi\) | |||||||
\(338\) | 15.6192 | + | 10.3423i | 0.849574 | + | 0.562549i | ||||
\(339\) | −11.8730 | − | 21.1431i | −0.644852 | − | 1.14834i | ||||
\(340\) | 1.56155 | + | 3.68260i | 0.0846871 | + | 0.199717i | ||||
\(341\) | − | 6.24621i | − | 0.338251i | ||||||
\(342\) | 2.38537 | + | 5.08706i | 0.128986 | + | 0.275077i | ||||
\(343\) | − | 14.7304i | − | 0.795367i | ||||||
\(344\) | −21.5150 | − | 4.00000i | −1.16001 | − | 0.215666i | ||||
\(345\) | 0.315342 | + | 0.561553i | 0.0169774 | + | 0.0302330i | ||||
\(346\) | −1.56155 | + | 2.35829i | −0.0839496 | + | 0.126783i | ||||
\(347\) | −22.6305 | −1.21487 | −0.607434 | − | 0.794370i | \(-0.707801\pi\) | ||||
−0.607434 | + | 0.794370i | \(0.707801\pi\) | |||||||
\(348\) | 6.61668 | − | 8.55950i | 0.354691 | − | 0.458837i | ||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | −2.35829 | + | 3.56155i | −0.126056 | + | 0.190373i | ||||
\(351\) | 0.952473 | − | 26.6034i | 0.0508392 | − | 1.41998i | ||||
\(352\) | −7.31534 | + | 1.61463i | −0.389909 | + | 0.0860599i | ||||
\(353\) | − | 20.2462i | − | 1.07760i | −0.842435 | − | 0.538799i | \(-0.818878\pi\) | ||
0.842435 | − | 0.538799i | \(-0.181122\pi\) | |||||||
\(354\) | 34.5669 | + | 2.53489i | 1.83721 | + | 0.134728i | ||||
\(355\) | − | 3.39228i | − | 0.180044i | ||||||
\(356\) | −18.8664 | + | 8.00000i | −0.999915 | + | 0.423999i | ||||
\(357\) | −9.12311 | + | 5.12311i | −0.482846 | + | 0.271144i | ||||
\(358\) | −11.8078 | − | 7.81855i | −0.624060 | − | 0.413223i | ||||
\(359\) | 21.5150 | 1.13552 | 0.567758 | − | 0.823195i | \(-0.307811\pi\) | ||||
0.567758 | + | 0.823195i | \(0.307811\pi\) | |||||||
\(360\) | 5.66664 | − | 6.31579i | 0.298658 | − | 0.332871i | ||||
\(361\) | 17.2462 | 0.907695 | ||||||||
\(362\) | −14.4401 | − | 9.56155i | −0.758954 | − | 0.502544i | ||||
\(363\) | 13.9638 | − | 7.84144i | 0.732912 | − | 0.411569i | ||||
\(364\) | −28.4924 | + | 12.0818i | −1.49341 | + | 0.633258i | ||||
\(365\) | − | 8.24621i | − | 0.431626i | ||||||
\(366\) | −7.62953 | − | 0.559496i | −0.398802 | − | 0.0292453i | ||||
\(367\) | − | 10.9663i | − | 0.572436i | −0.958165 | − | 0.286218i | \(-0.907602\pi\) | ||
0.958165 | − | 0.286218i | \(-0.0923981\pi\) | |||||||
\(368\) | −1.03399 | + | 1.06913i | −0.0539003 | + | 0.0557323i | ||||
\(369\) | −2.87689 | − | 1.75379i | −0.149765 | − | 0.0912986i | ||||
\(370\) | 4.00000 | − | 6.04090i | 0.207950 | − | 0.314051i | ||||
\(371\) | −36.9890 | −1.92038 | ||||||||
\(372\) | −9.99267 | + | 12.9268i | −0.518096 | + | 0.670221i | ||||
\(373\) | −9.12311 | −0.472377 | −0.236188 | − | 0.971707i | \(-0.575898\pi\) | ||||
−0.236188 | + | 0.971707i | \(0.575898\pi\) | |||||||
\(374\) | −2.06798 | + | 3.12311i | −0.106932 | + | 0.161492i | ||||
\(375\) | −0.848071 | − | 1.51022i | −0.0437942 | − | 0.0779876i | ||||
\(376\) | −1.56155 | + | 8.39919i | −0.0805309 | + | 0.433155i | ||||
\(377\) | − | 16.0000i | − | 0.824042i | ||||||
\(378\) | 18.0561 | + | 12.9084i | 0.928704 | + | 0.663935i | ||||
\(379\) | 18.7033i | 0.960725i | 0.877070 | + | 0.480363i | \(0.159495\pi\) | ||||
−0.877070 | + | 0.480363i | \(0.840505\pi\) | |||||||
\(380\) | 1.03399 | + | 2.43845i | 0.0530424 | + | 0.125090i | ||||
\(381\) | −12.8078 | − | 22.8078i | −0.656162 | − | 1.16848i | ||||
\(382\) | −29.3693 | − | 19.4470i | −1.50266 | − | 0.994995i | ||||
\(383\) | −15.1022 | −0.771688 | −0.385844 | − | 0.922564i | \(-0.626090\pi\) | ||||
−0.385844 | + | 0.922564i | \(0.626090\pi\) | |||||||
\(384\) | 17.7224 | + | 8.36154i | 0.904394 | + | 0.426698i | ||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | −0.290319 | − | 0.192236i | −0.0147769 | − | 0.00978455i | ||||
\(387\) | 19.8188 | + | 12.0818i | 1.00745 | + | 0.614152i | ||||
\(388\) | −4.68466 | − | 11.0478i | −0.237827 | − | 0.560867i | ||||
\(389\) | − | 20.7386i | − | 1.05149i | −0.850642 | − | 0.525745i | \(-0.823787\pi\) | ||
0.850642 | − | 0.525745i | \(-0.176213\pi\) | |||||||
\(390\) | 0.917790 | − | 12.5154i | 0.0464741 | − | 0.633741i | ||||
\(391\) | 0.743668i | 0.0376089i | ||||||||
\(392\) | 1.09763 | − | 5.90388i | 0.0554388 | − | 0.298191i | ||||
\(393\) | −8.24621 | + | 4.63068i | −0.415966 | + | 0.233587i | ||||
\(394\) | −3.31534 | + | 5.00691i | −0.167024 | + | 0.252244i | ||||
\(395\) | 8.10887 | 0.408002 | ||||||||
\(396\) | 7.86084 | + | 1.15915i | 0.395022 | + | 0.0582495i | ||||
\(397\) | 14.8769 | 0.746650 | 0.373325 | − | 0.927701i | \(-0.378218\pi\) | ||||
0.373325 | + | 0.927701i | \(0.378218\pi\) | |||||||
\(398\) | −4.26324 | + | 6.43845i | −0.213697 | + | 0.322730i | ||||
\(399\) | −6.04090 | + | 3.39228i | −0.302423 | + | 0.169827i | ||||
\(400\) | 2.78078 | − | 2.87529i | 0.139039 | − | 0.143764i | ||||
\(401\) | 24.0000i | 1.19850i | 0.800561 | + | 0.599251i | \(0.204535\pi\) | ||||
−0.800561 | + | 0.599251i | \(0.795465\pi\) | |||||||
\(402\) | −0.778351 | + | 10.6139i | −0.0388206 | + | 0.529375i | ||||
\(403\) | 24.1636i | 1.20367i | ||||||||
\(404\) | 1.61463 | − | 0.684658i | 0.0803307 | − | 0.0340630i | ||||
\(405\) | −8.00000 | + | 4.12311i | −0.397523 | + | 0.204879i | ||||
\(406\) | 11.1231 | + | 7.36520i | 0.552030 | + | 0.365529i | ||||
\(407\) | 6.78456 | 0.336298 | ||||||||
\(408\) | 9.27608 | − | 3.15504i | 0.459235 | − | 0.156198i | ||||
\(409\) | 25.3693 | 1.25443 | 0.627216 | − | 0.778845i | \(-0.284194\pi\) | ||||
0.627216 | + | 0.778845i | \(0.284194\pi\) | |||||||
\(410\) | −1.32431 | − | 0.876894i | −0.0654029 | − | 0.0433067i | ||||
\(411\) | 6.99337 | + | 12.4536i | 0.344957 | + | 0.614292i | ||||
\(412\) | 18.0540 | − | 7.65552i | 0.889456 | − | 0.377161i | ||||
\(413\) | 42.7386i | 2.10303i | ||||||||
\(414\) | 1.42833 | − | 0.669757i | 0.0701984 | − | 0.0329167i | ||||
\(415\) | − | 15.1022i | − | 0.741340i | ||||||
\(416\) | 28.2995 | − | 6.24621i | 1.38750 | − | 0.306246i | ||||
\(417\) | 14.8769 | + | 26.4924i | 0.728525 | + | 1.29734i | ||||
\(418\) | −1.36932 | + | 2.06798i | −0.0669755 | + | 0.101148i | ||||
\(419\) | 7.36520 | 0.359814 | 0.179907 | − | 0.983684i | \(-0.442420\pi\) | ||||
0.179907 | + | 0.983684i | \(0.442420\pi\) | |||||||
\(420\) | 8.27814 | + | 6.39919i | 0.403932 | + | 0.312249i | ||||
\(421\) | −25.3693 | −1.23642 | −0.618212 | − | 0.786011i | \(-0.712143\pi\) | ||||
−0.618212 | + | 0.786011i | \(0.712143\pi\) | |||||||
\(422\) | 13.1158 | − | 19.8078i | 0.638466 | − | 0.964227i | ||||
\(423\) | 4.71659 | − | 7.73704i | 0.229328 | − | 0.376188i | ||||
\(424\) | 34.0540 | + | 6.33122i | 1.65381 | + | 0.307471i | ||||
\(425\) | − | 2.00000i | − | 0.0970143i | ||||||
\(426\) | −8.28711 | − | 0.607718i | −0.401512 | − | 0.0294440i | ||||
\(427\) | − | 9.43318i | − | 0.456503i | ||||||
\(428\) | −2.35829 | − | 5.56155i | −0.113992 | − | 0.268828i | ||||
\(429\) | 10.2462 | − | 5.75379i | 0.494692 | − | 0.277796i | ||||
\(430\) | 9.12311 | + | 6.04090i | 0.439955 | + | 0.291318i | ||||
\(431\) | −16.6354 | −0.801297 | −0.400648 | − | 0.916232i | \(-0.631215\pi\) | ||||
−0.400648 | + | 0.916232i | \(0.631215\pi\) | |||||||
\(432\) | −14.4139 | − | 14.9747i | −0.693488 | − | 0.720468i | ||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | −16.7984 | − | 11.1231i | −0.806348 | − | 0.533926i | ||||
\(435\) | −4.71659 | + | 2.64861i | −0.226143 | + | 0.126991i | ||||
\(436\) | −0.684658 | − | 1.61463i | −0.0327892 | − | 0.0773266i | ||||
\(437\) | 0.492423i | 0.0235558i | ||||||||
\(438\) | −20.1449 | − | 1.47729i | −0.962561 | − | 0.0705875i | ||||
\(439\) | 9.27015i | 0.442440i | 0.975224 | + | 0.221220i | \(0.0710039\pi\) | ||||
−0.975224 | + | 0.221220i | \(0.928996\pi\) | |||||||
\(440\) | 3.68260 | + | 0.684658i | 0.175561 | + | 0.0326398i | ||||
\(441\) | −3.31534 | + | 5.43845i | −0.157873 | + | 0.258974i | ||||
\(442\) | 8.00000 | − | 12.0818i | 0.380521 | − | 0.574672i | ||||
\(443\) | −16.5896 | −0.788195 | −0.394097 | − | 0.919069i | \(-0.628943\pi\) | ||||
−0.394097 | + | 0.919069i | \(0.628943\pi\) | |||||||
\(444\) | −14.0409 | − | 10.8539i | −0.666351 | − | 0.515105i | ||||
\(445\) | 10.2462 | 0.485717 | ||||||||
\(446\) | −6.49424 | + | 9.80776i | −0.307511 | + | 0.464411i | ||||
\(447\) | 11.8730 | + | 21.1431i | 0.561573 | + | 1.00004i | ||||
\(448\) | −8.68466 | + | 22.5490i | −0.410312 | + | 1.06534i | ||||
\(449\) | − | 27.3693i | − | 1.29164i | −0.763491 | − | 0.645819i | \(-0.776516\pi\) | ||
0.763491 | − | 0.645819i | \(-0.223484\pi\) | |||||||
\(450\) | −3.84130 | + | 1.80122i | −0.181081 | + | 0.0849105i | ||||
\(451\) | − | 1.48734i | − | 0.0700359i | ||||||
\(452\) | −25.7782 | + | 10.9309i | −1.21250 | + | 0.514145i | ||||
\(453\) | 6.24621 | + | 11.1231i | 0.293473 | + | 0.522609i | ||||
\(454\) | 25.8078 | + | 17.0887i | 1.21122 | + | 0.802012i | ||||
\(455\) | 15.4741 | 0.725436 | ||||||||
\(456\) | 6.14219 | − | 2.08912i | 0.287634 | − | 0.0978319i | ||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | −19.1567 | − | 12.6847i | −0.895133 | − | 0.592715i | ||||
\(459\) | −10.3857 | − | 0.371834i | −0.484761 | − | 0.0173557i | ||||
\(460\) | 0.684658 | − | 0.290319i | 0.0319224 | − | 0.0135362i | ||||
\(461\) | 41.8617i | 1.94970i | 0.222872 | + | 0.974848i | \(0.428457\pi\) | ||||
−0.222872 | + | 0.974848i | \(0.571543\pi\) | |||||||
\(462\) | −0.716589 | + | 9.77172i | −0.0333387 | + | 0.454622i | ||||
\(463\) | 3.02045i | 0.140372i | 0.997534 | + | 0.0701861i | \(0.0223593\pi\) | ||||
−0.997534 | + | 0.0701861i | \(0.977641\pi\) | |||||||
\(464\) | −8.97983 | − | 8.68466i | −0.416878 | − | 0.403175i | ||||
\(465\) | 7.12311 | − | 4.00000i | 0.330326 | − | 0.185496i | ||||
\(466\) | 7.80776 | − | 11.7915i | 0.361688 | − | 0.546229i | ||||
\(467\) | 2.27678 | 0.105357 | 0.0526784 | − | 0.998612i | \(-0.483224\pi\) | ||||
0.0526784 | + | 0.998612i | \(0.483224\pi\) | |||||||
\(468\) | −30.4098 | − | 4.48419i | −1.40569 | − | 0.207282i | ||||
\(469\) | −13.1231 | −0.605969 | ||||||||
\(470\) | 2.35829 | − | 3.56155i | 0.108780 | − | 0.164282i | ||||
\(471\) | 5.08842 | − | 2.85742i | 0.234462 | − | 0.131663i | ||||
\(472\) | 7.31534 | − | 39.3473i | 0.336716 | − | 1.81111i | ||||
\(473\) | 10.2462i | 0.471121i | ||||||||
\(474\) | 1.45268 | − | 19.8094i | 0.0667239 | − | 0.909876i | ||||
\(475\) | − | 1.32431i | − | 0.0607634i | ||||||
\(476\) | 4.71659 | + | 11.1231i | 0.216184 | + | 0.509827i | ||||
\(477\) | −31.3693 | − | 19.1231i | −1.43630 | − | 0.875587i | ||||
\(478\) | 20.4924 | + | 13.5691i | 0.937302 | + | 0.620637i | ||||
\(479\) | 25.6509 | 1.17202 | 0.586010 | − | 0.810304i | \(-0.300698\pi\) | ||||
0.586010 | + | 0.810304i | \(0.300698\pi\) | |||||||
\(480\) | −6.52596 | − | 7.30834i | −0.297868 | − | 0.333579i | ||||
\(481\) | −26.2462 | −1.19672 | ||||||||
\(482\) | 15.7644 | + | 10.4384i | 0.718048 | + | 0.475458i | ||||
\(483\) | 0.952473 | + | 1.69614i | 0.0433390 | + | 0.0771771i | ||||
\(484\) | −7.21922 | − | 17.0251i | −0.328147 | − | 0.773866i | ||||
\(485\) | 6.00000i | 0.272446i | ||||||||
\(486\) | 8.63928 | + | 20.2821i | 0.391886 | + | 0.920014i | ||||
\(487\) | − | 25.2791i | − | 1.14550i | −0.819728 | − | 0.572752i | \(-0.805876\pi\) | ||
0.819728 | − | 0.572752i | \(-0.194124\pi\) | |||||||
\(488\) | −1.61463 | + | 8.68466i | −0.0730907 | + | 0.393136i | ||||
\(489\) | 13.3002 | + | 23.6847i | 0.601455 | + | 1.07106i | ||||
\(490\) | −1.65767 | + | 2.50345i | −0.0748859 | + | 0.113095i | ||||
\(491\) | 26.9752 | 1.21737 | 0.608687 | − | 0.793410i | \(-0.291696\pi\) | ||||
0.608687 | + | 0.793410i | \(0.291696\pi\) | |||||||
\(492\) | −2.37944 | + | 3.07810i | −0.107273 | + | 0.138771i | ||||
\(493\) | −6.24621 | −0.281315 | ||||||||
\(494\) | 5.29723 | − | 8.00000i | 0.238334 | − | 0.359937i | ||||
\(495\) | −3.39228 | − | 2.06798i | −0.152472 | − | 0.0929486i | ||||
\(496\) | 13.5616 | + | 13.1158i | 0.608932 | + | 0.588916i | ||||
\(497\) | − | 10.2462i | − | 0.459605i | ||||||
\(498\) | −36.8937 | − | 2.70552i | −1.65325 | − | 0.121237i | ||||
\(499\) | 32.2725i | 1.44471i | 0.691521 | + | 0.722357i | \(0.256941\pi\) | ||||
−0.691521 | + | 0.722357i | \(0.743059\pi\) | |||||||
\(500\) | −1.84130 | + | 0.780776i | −0.0823455 | + | 0.0349174i | ||||
\(501\) | 13.6847 | − | 7.68466i | 0.611385 | − | 0.343325i | ||||
\(502\) | 22.0540 | + | 14.6031i | 0.984317 | + | 0.651769i | ||||
\(503\) | 14.3586 | 0.640217 | 0.320109 | − | 0.947381i | \(-0.396281\pi\) | ||||
0.320109 | + | 0.947381i | \(0.396281\pi\) | |||||||
\(504\) | 17.1158 | − | 19.0765i | 0.762397 | − | 0.849736i | ||||
\(505\) | −0.876894 | −0.0390213 | ||||||||
\(506\) | 0.580639 | + | 0.384472i | 0.0258125 | + | 0.0170919i | ||||
\(507\) | −20.0047 | + | 11.2337i | −0.888442 | + | 0.498907i | ||||
\(508\) | −27.8078 | + | 11.7915i | −1.23377 | + | 0.523162i | ||||
\(509\) | 11.1231i | 0.493023i | 0.969140 | + | 0.246511i | \(0.0792843\pi\) | ||||
−0.969140 | + | 0.246511i | \(0.920716\pi\) | |||||||
\(510\) | −4.88586 | − | 0.358294i | −0.216350 | − | 0.0158655i | ||||
\(511\) | − | 24.9073i | − | 1.10183i | ||||||
\(512\) | 11.8551 | − | 19.2732i | 0.523927 | − | 0.851763i | ||||
\(513\) | −6.87689 | − | 0.246211i | −0.303622 | − | 0.0108705i | ||||
\(514\) | −23.8078 | + | 35.9551i | −1.05012 | + | 1.58591i | ||||
\(515\) | −9.80501 | −0.432060 | ||||||||
\(516\) | 16.3919 | − | 21.2049i | 0.721612 | − | 0.933494i | ||||
\(517\) | 4.00000 | 0.175920 | ||||||||
\(518\) | 12.0818 | − | 18.2462i | 0.530843 | − | 0.801692i | ||||
\(519\) | −1.69614 | − | 3.02045i | −0.0744523 | − | 0.132583i | ||||
\(520\) | −14.2462 | − | 2.64861i | −0.624738 | − | 0.116149i | ||||
\(521\) | − | 38.2462i | − | 1.67560i | −0.545980 | − | 0.837798i | \(-0.683842\pi\) | ||
0.545980 | − | 0.837798i | \(-0.316158\pi\) | |||||||
\(522\) | 5.62541 | + | 11.9968i | 0.246218 | + | 0.525085i | ||||
\(523\) | − | 35.2929i | − | 1.54325i | −0.636077 | − | 0.771625i | \(-0.719444\pi\) | ||
0.636077 | − | 0.771625i | \(-0.280556\pi\) | |||||||
\(524\) | 4.26324 | + | 10.0540i | 0.186241 | + | 0.439210i | ||||
\(525\) | −2.56155 | − | 4.56155i | −0.111795 | − | 0.199082i | ||||
\(526\) | −28.0540 | − | 18.5760i | −1.22321 | − | 0.809954i | ||||
\(527\) | 9.43318 | 0.410916 | ||||||||
\(528\) | 2.33230 | − | 8.87368i | 0.101500 | − | 0.386177i | ||||
\(529\) | −22.8617 | −0.993989 | ||||||||
\(530\) | −14.4401 | − | 9.56155i | −0.627237 | − | 0.415327i | ||||
\(531\) | −22.0956 | + | 36.2454i | −0.958868 | + | 1.57292i | ||||
\(532\) | 3.12311 | + | 7.36520i | 0.135404 | + | 0.319322i | ||||
\(533\) | 5.75379i | 0.249224i | ||||||||
\(534\) | 1.83558 | − | 25.0308i | 0.0794333 | − | 1.08319i | ||||
\(535\) | 3.02045i | 0.130585i | ||||||||
\(536\) | 12.0818 | + | 2.24621i | 0.521854 | + | 0.0970215i | ||||
\(537\) | 15.1231 | − | 8.49242i | 0.652610 | − | 0.366475i | ||||
\(538\) | −10.9309 | + | 16.5081i | −0.471263 | + | 0.711713i | ||||
\(539\) | −2.81164 | −0.121106 | ||||||||
\(540\) | 3.71211 | + | 9.70671i | 0.159744 | + | 0.417710i | ||||
\(541\) | −26.9848 | −1.16017 | −0.580085 | − | 0.814556i | \(-0.696980\pi\) | ||||
−0.580085 | + | 0.814556i | \(0.696980\pi\) | |||||||
\(542\) | −11.9545 | + | 18.0540i | −0.513490 | + | 0.775485i | ||||
\(543\) | 18.4945 | − | 10.3857i | 0.793676 | − | 0.445691i | ||||
\(544\) | −2.43845 | − | 11.0478i | −0.104548 | − | 0.473671i | ||||
\(545\) | 0.876894i | 0.0375620i | ||||||||
\(546\) | 2.77214 | − | 37.8021i | 0.118637 | − | 1.61778i | ||||
\(547\) | 5.83209i | 0.249362i | 0.992197 | + | 0.124681i | \(0.0397908\pi\) | ||||
−0.992197 | + | 0.124681i | \(0.960209\pi\) | |||||||
\(548\) | 15.1838 | − | 6.43845i | 0.648618 | − | 0.275037i | ||||
\(549\) | 4.87689 | − | 8.00000i | 0.208141 | − | 0.341432i | ||||
\(550\) | −1.56155 | − | 1.03399i | −0.0665848 | − | 0.0440894i | ||||
\(551\) | −4.13595 | −0.176197 | ||||||||
\(552\) | −0.586575 | − | 1.72458i | −0.0249663 | − | 0.0734031i | ||||
\(553\) | 24.4924 | 1.04152 | ||||||||
\(554\) | 27.5559 | + | 18.2462i | 1.17074 | + | 0.775207i | ||||
\(555\) | 4.34475 | + | 7.73704i | 0.184425 | + | 0.328419i | ||||
\(556\) | 32.3002 | − | 13.6964i | 1.36983 | − | 0.580858i | ||||
\(557\) | 36.2462i | 1.53580i | 0.640569 | + | 0.767901i | \(0.278699\pi\) | ||||
−0.640569 | + | 0.767901i | \(0.721301\pi\) | |||||||
\(558\) | −8.49563 | − | 18.1178i | −0.359649 | − | 0.766989i | ||||
\(559\) | − | 39.6377i | − | 1.67649i | ||||||
\(560\) | 8.39919 | − | 8.68466i | 0.354931 | − | 0.366994i | ||||
\(561\) | −2.24621 | − | 4.00000i | −0.0948351 | − | 0.168880i | ||||
\(562\) | −10.6307 | + | 16.0547i | −0.448428 | + | 0.677227i | ||||
\(563\) | −7.90007 | −0.332948 | −0.166474 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166474 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(564\) | −8.27814 | − | 6.39919i | −0.348573 | − | 0.269455i | ||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | −18.1227 | + | 27.3693i | −0.761753 | + | 1.15042i | ||||
\(567\) | −24.1636 | + | 12.4536i | −1.01478 | + | 0.523003i | ||||
\(568\) | −1.75379 | + | 9.43318i | −0.0735873 | + | 0.395807i | ||||
\(569\) | − | 13.1231i | − | 0.550149i | −0.961423 | − | 0.275075i | \(-0.911297\pi\) | ||
0.961423 | − | 0.275075i | \(-0.0887026\pi\) | |||||||
\(570\) | −3.23519 | − | 0.237246i | −0.135507 | − | 0.00993714i | ||||
\(571\) | 33.0161i | 1.38168i | 0.723007 | + | 0.690841i | \(0.242759\pi\) | ||||
−0.723007 | + | 0.690841i | \(0.757241\pi\) | |||||||
\(572\) | −5.29723 | − | 12.4924i | −0.221488 | − | 0.522334i | ||||
\(573\) | 37.6155 | − | 21.1231i | 1.57141 | − | 0.882430i | ||||
\(574\) | −4.00000 | − | 2.64861i | −0.166957 | − | 0.110551i | ||||
\(575\) | −0.371834 | −0.0155066 | ||||||||
\(576\) | −19.0229 | + | 14.6332i | −0.792620 | + | 0.609716i | ||||
\(577\) | −32.2462 | −1.34243 | −0.671214 | − | 0.741264i | \(-0.734227\pi\) | ||||
−0.671214 | + | 0.741264i | \(0.734227\pi\) | |||||||
\(578\) | 15.3289 | + | 10.1501i | 0.637599 | + | 0.422188i | ||||
\(579\) | 0.371834 | − | 0.208805i | 0.0154529 | − | 0.00867762i | ||||
\(580\) | 2.43845 | + | 5.75058i | 0.101251 | + | 0.238780i | ||||
\(581\) | − | 45.6155i | − | 1.89245i | ||||||
\(582\) | 14.6576 | + | 1.07488i | 0.607576 | + | 0.0445554i | ||||
\(583\) | − | 16.2177i | − | 0.671670i | ||||||
\(584\) | −4.26324 | + | 22.9309i | −0.176414 | + | 0.948886i | ||||
\(585\) | 13.1231 | + | 8.00000i | 0.542574 | + | 0.330759i | ||||
\(586\) | −1.94602 | + | 2.93893i | −0.0803895 | + | 0.121406i | ||||
\(587\) | 1.85917 | 0.0767362 | 0.0383681 | − | 0.999264i | \(-0.487784\pi\) | ||||
0.0383681 | + | 0.999264i | \(0.487784\pi\) | |||||||
\(588\) | 5.81880 | + | 4.49806i | 0.239963 | + | 0.185497i | ||||
\(589\) | 6.24621 | 0.257371 | ||||||||
\(590\) | −11.0478 | + | 16.6847i | −0.454831 | + | 0.686897i | ||||
\(591\) | −3.60109 | − | 6.41273i | −0.148129 | − | 0.263784i | ||||
\(592\) | −14.2462 | + | 14.7304i | −0.585516 | + | 0.605416i | ||||
\(593\) | 8.24621i | 0.338631i | 0.985562 | + | 0.169316i | \(0.0541557\pi\) | ||||
−0.985562 | + | 0.169316i | \(0.945844\pi\) | |||||||
\(594\) | −5.65964 | + | 7.91664i | −0.232218 | + | 0.324823i | ||||
\(595\) | − | 6.04090i | − | 0.247653i | ||||||
\(596\) | 25.7782 | − | 10.9309i | 1.05592 | − | 0.447746i | ||||
\(597\) | −4.63068 | − | 8.24621i | −0.189521 | − | 0.337495i | ||||
\(598\) | −2.24621 | − | 1.48734i | −0.0918544 | − | 0.0608217i | ||||
\(599\) | −44.1912 | −1.80560 | −0.902802 | − | 0.430056i | \(-0.858494\pi\) | ||||
−0.902802 | + | 0.430056i | \(0.858494\pi\) | |||||||
\(600\) | 1.57752 | + | 4.63804i | 0.0644019 | + | 0.189347i | ||||
\(601\) | 23.1231 | 0.943211 | 0.471606 | − | 0.881810i | \(-0.343675\pi\) | ||||
0.471606 | + | 0.881810i | \(0.343675\pi\) | |||||||
\(602\) | 27.5559 | + | 18.2462i | 1.12309 | + | 0.743660i | ||||
\(603\) | −11.1293 | − | 6.78456i | −0.453221 | − | 0.276289i | ||||
\(604\) | 13.5616 | − | 5.75058i | 0.551812 | − | 0.233988i | ||||
\(605\) | 9.24621i | 0.375912i | ||||||||
\(606\) | −0.157093 | + | 2.14219i | −0.00638148 | + | 0.0870206i | ||||
\(607\) | 4.50778i | 0.182965i | 0.995807 | + | 0.0914827i | \(0.0291606\pi\) | ||||
−0.995807 | + | 0.0914827i | \(0.970839\pi\) | |||||||
\(608\) | −1.61463 | − | 7.31534i | −0.0654817 | − | 0.296676i | ||||
\(609\) | −14.2462 | + | 8.00000i | −0.577286 | + | 0.324176i | ||||
\(610\) | 2.43845 | − | 3.68260i | 0.0987298 | − | 0.149104i | ||||
\(611\) | −15.4741 | −0.626014 | ||||||||
\(612\) | −1.75058 | + | 11.8716i | −0.0707629 | + | 0.479882i | ||||
\(613\) | 9.12311 | 0.368479 | 0.184239 | − | 0.982881i | \(-0.441018\pi\) | ||||
0.184239 | + | 0.982881i | \(0.441018\pi\) | |||||||
\(614\) | −8.68951 | + | 13.1231i | −0.350680 | + | 0.529605i | ||||
\(615\) | 1.69614 | − | 0.952473i | 0.0683950 | − | 0.0384074i | ||||
\(616\) | 11.1231 | + | 2.06798i | 0.448163 | + | 0.0833211i | ||||
\(617\) | − | 14.0000i | − | 0.563619i | −0.959470 | − | 0.281809i | \(-0.909065\pi\) | ||
0.959470 | − | 0.281809i | \(-0.0909346\pi\) | |||||||
\(618\) | −1.75654 | + | 23.9530i | −0.0706584 | + | 0.963529i | ||||
\(619\) | − | 28.1365i | − | 1.13090i | −0.824782 | − | 0.565451i | \(-0.808702\pi\) | ||
0.824782 | − | 0.565451i | \(-0.191298\pi\) | |||||||
\(620\) | −3.68260 | − | 8.68466i | −0.147897 | − | 0.348784i | ||||
\(621\) | −0.0691303 | + | 1.93087i | −0.00277410 | + | 0.0774831i | ||||
\(622\) | 24.4924 | + | 16.2177i | 0.982057 | + | 0.650272i | ||||
\(623\) | 30.9481 | 1.23991 | ||||||||
\(624\) | −9.02255 | + | 34.3280i | −0.361191 | + | 1.37422i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −26.5219 | − | 17.5616i | −1.06003 | − | 0.701901i | ||||
\(627\) | −1.48734 | − | 2.64861i | −0.0593985 | − | 0.105775i | ||||
\(628\) | −2.63068 | − | 6.20393i | −0.104976 | − | 0.247564i | ||||
\(629\) | 10.2462i | 0.408543i | ||||||||
\(630\) | −11.6024 | + | 5.44050i | −0.462253 | + | 0.216755i | ||||
\(631\) | 39.8007i | 1.58444i | 0.610235 | + | 0.792220i | \(0.291075\pi\) | ||||
−0.610235 | + | 0.792220i | \(0.708925\pi\) | |||||||
\(632\) | −22.5490 | − | 4.19224i | −0.896949 | − | 0.166758i | ||||
\(633\) | 14.2462 | + | 25.3693i | 0.566236 | + | 1.00834i | ||||
\(634\) | 13.0691 | − | 19.7373i | 0.519041 | − | 0.783869i | ||||
\(635\) | 15.1022 | 0.599314 | ||||||||
\(636\) | −25.9451 | + | 33.5632i | −1.02879 | + | 1.33087i | ||||
\(637\) | 10.8769 | 0.430958 | ||||||||
\(638\) | −3.22925 | + | 4.87689i | −0.127847 | + | 0.193078i | ||||
\(639\) | 5.29723 | − | 8.68951i | 0.209555 | − | 0.343752i | ||||
\(640\) | −9.21922 | + | 6.55789i | −0.364422 | + | 0.259223i | ||||
\(641\) | − | 6.38447i | − | 0.252171i | −0.992019 | − | 0.126086i | \(-0.959759\pi\) | ||
0.992019 | − | 0.126086i | \(-0.0402414\pi\) | |||||||
\(642\) | 7.37874 | + | 0.541105i | 0.291216 | + | 0.0213557i | ||||
\(643\) | 3.60109i | 0.142013i | 0.997476 | + | 0.0710065i | \(0.0226211\pi\) | ||||
−0.997476 | + | 0.0710065i | \(0.977379\pi\) | |||||||
\(644\) | 2.06798 | − | 0.876894i | 0.0814896 | − | 0.0345545i | ||||
\(645\) | −11.6847 | + | 6.56155i | −0.460083 | + | 0.258361i | ||||
\(646\) | −3.12311 | − | 2.06798i | −0.122877 | − | 0.0813634i | ||||
\(647\) | −36.6172 | −1.43957 | −0.719786 | − | 0.694197i | \(-0.755760\pi\) | ||||
−0.719786 | + | 0.694197i | \(0.755760\pi\) | |||||||
\(648\) | 24.3778 | − | 7.32948i | 0.957652 | − | 0.287929i | ||||
\(649\) | −18.7386 | −0.735556 | ||||||||
\(650\) | 6.04090 | + | 4.00000i | 0.236943 | + | 0.156893i | ||||
\(651\) | 21.5150 | − | 12.0818i | 0.843238 | − | 0.473523i | ||||
\(652\) | 28.8769 | − | 12.2448i | 1.13091 | − | 0.479544i | ||||
\(653\) | − | 38.9848i | − | 1.52559i | −0.646638 | − | 0.762797i | \(-0.723825\pi\) | ||
0.646638 | − | 0.762797i | \(-0.276175\pi\) | |||||||
\(654\) | 2.14219 | + | 0.157093i | 0.0837663 | + | 0.00614283i | ||||
\(655\) | − | 5.46026i | − | 0.213350i | ||||||
\(656\) | 3.22925 | + | 3.12311i | 0.126081 | + | 0.121937i | ||||
\(657\) | 12.8769 | − | 21.1231i | 0.502375 | − | 0.824091i | ||||
\(658\) | 7.12311 | − | 10.7575i | 0.277688 | − | 0.419370i | ||||
\(659\) | 24.7442 | 0.963898 | 0.481949 | − | 0.876199i | \(-0.339929\pi\) | ||||
0.481949 | + | 0.876199i | \(0.339929\pi\) | |||||||
\(660\) | −2.80571 | + | 3.62953i | −0.109212 | + | 0.141279i | ||||
\(661\) | 28.1080 | 1.09327 | 0.546636 | − | 0.837370i | \(-0.315908\pi\) | ||||
0.546636 | + | 0.837370i | \(0.315908\pi\) | |||||||
\(662\) | 2.52132 | − | 3.80776i | 0.0979940 | − | 0.147993i | ||||
\(663\) | 8.68951 | + | 15.4741i | 0.337473 | + | 0.600963i | ||||
\(664\) | −7.80776 | + | 41.9960i | −0.303000 | + | 1.62976i | ||||
\(665\) | − | 4.00000i | − | 0.155113i | ||||||
\(666\) | 19.6794 | − | 9.22786i | 0.762561 | − | 0.357572i | ||||
\(667\) | 1.16128i | 0.0449648i | ||||||||
\(668\) | −7.07488 | − | 16.6847i | −0.273735 | − | 0.645549i | ||||
\(669\) | −7.05398 | − | 12.5616i | −0.272722 | − | 0.485658i | ||||
\(670\) | −5.12311 | − | 3.39228i | −0.197923 | − | 0.131055i | ||||
\(671\) | 4.13595 | 0.159667 | ||||||||
\(672\) | −19.7113 | − | 22.0745i | −0.760381 | − | 0.851541i | ||||
\(673\) | 22.4924 | 0.867019 | 0.433510 | − | 0.901149i | \(-0.357275\pi\) | ||||
0.433510 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(674\) | −1.77766 | − | 1.17708i | −0.0684727 | − | 0.0453395i | ||||
\(675\) | 0.185917 | − | 5.19283i | 0.00715595 | − | 0.199872i | ||||
\(676\) | 10.3423 | + | 24.3903i | 0.397782 | + | 0.938087i | ||||
\(677\) | 1.50758i | 0.0579409i | 0.999580 | + | 0.0289705i | \(0.00922287\pi\) | ||||
−0.999580 | + | 0.0289705i | \(0.990777\pi\) | |||||||
\(678\) | 2.50806 | − | 34.2010i | 0.0963215 | − | 1.31348i | ||||
\(679\) | 18.1227i | 0.695485i | ||||||||
\(680\) | −1.03399 | + | 5.56155i | −0.0396516 | + | 0.213276i | ||||
\(681\) | −33.0540 | + | 18.5616i | −1.26663 | + | 0.711280i | ||||
\(682\) | 4.87689 | − | 7.36520i | 0.186746 | − | 0.282028i | ||||
\(683\) | 7.90007 | 0.302288 | 0.151144 | − | 0.988512i | \(-0.451704\pi\) | ||||
0.151144 | + | 0.988512i | \(0.451704\pi\) | |||||||
\(684\) | −1.15915 | + | 7.86084i | −0.0443212 | + | 0.300567i | ||||
\(685\) | −8.24621 | −0.315072 | ||||||||
\(686\) | 11.5012 | − | 17.3693i | 0.439116 | − | 0.663164i | ||||
\(687\) | 24.5354 | − | 13.7779i | 0.936085 | − | 0.525661i | ||||
\(688\) | −22.2462 | − | 21.5150i | −0.848129 | − | 0.820251i | ||||
\(689\) | 62.7386i | 2.39015i | ||||||||
\(690\) | −0.0666131 | + | 0.908365i | −0.00253592 | + | 0.0345809i | ||||
\(691\) | − | 18.2857i | − | 0.695621i | −0.937565 | − | 0.347811i | \(-0.886925\pi\) | ||
0.937565 | − | 0.347811i | \(-0.113075\pi\) | |||||||
\(692\) | −3.68260 | + | 1.56155i | −0.139991 | + | 0.0593613i | ||||
\(693\) | −10.2462 | − | 6.24621i | −0.389221 | − | 0.237274i | ||||
\(694\) | −26.6847 | − | 17.6693i | −1.01294 | − | 0.670719i | ||||
\(695\) | −17.5420 | −0.665408 | ||||||||
\(696\) | 14.4851 | − | 4.92676i | 0.549056 | − | 0.186748i | ||||
\(697\) | 2.24621 | 0.0850813 | ||||||||
\(698\) | −16.5081 | − | 10.9309i | −0.624839 | − | 0.413740i | ||||
\(699\) | 8.48071 | + | 15.1022i | 0.320770 | + | 0.571219i | ||||
\(700\) | −5.56155 | + | 2.35829i | −0.210207 | + | 0.0891352i | ||||
\(701\) | 17.5076i | 0.661252i | 0.943762 | + | 0.330626i | \(0.107260\pi\) | ||||
−0.943762 | + | 0.330626i | \(0.892740\pi\) | |||||||
\(702\) | 21.8944 | − | 30.6256i | 0.826351 | − | 1.15589i | ||||
\(703\) | 6.78456i | 0.255885i | ||||||||
\(704\) | −9.88653 | − | 3.80776i | −0.372612 | − | 0.143511i | ||||
\(705\) | 2.56155 | + | 4.56155i | 0.0964737 | + | 0.171798i | ||||
\(706\) | 15.8078 | − | 23.8733i | 0.594933 | − | 0.898482i | ||||
\(707\) | −2.64861 | −0.0996114 | ||||||||
\(708\) | 38.7803 | + | 29.9780i | 1.45745 | + | 1.12664i | ||||
\(709\) | 6.49242 | 0.243828 | 0.121914 | − | 0.992541i | \(-0.461097\pi\) | ||||
0.121914 | + | 0.992541i | \(0.461097\pi\) | |||||||
\(710\) | 2.64861 | − | 4.00000i | 0.0994007 | − | 0.150117i | ||||
\(711\) | 20.7713 | + | 12.6624i | 0.778985 | + | 0.474878i | ||||
\(712\) | −28.4924 | − | 5.29723i | −1.06780 | − | 0.198522i | ||||
\(713\) | − | 1.75379i | − | 0.0656799i | ||||||
\(714\) | −14.7575 | − | 1.08221i | −0.552285 | − | 0.0405007i | ||||
\(715\) | 6.78456i | 0.253728i | ||||||||
\(716\) | −7.81855 | − | 18.4384i | −0.292193 | − | 0.689077i | ||||
\(717\) | −26.2462 | + | 14.7386i | −0.980183 | + | 0.550424i | ||||
\(718\) | 25.3693 | + | 16.7984i | 0.946774 | + | 0.626910i | ||||
\(719\) | −30.9481 | −1.15417 | −0.577086 | − | 0.816684i | \(-0.695810\pi\) | ||||
−0.577086 | + | 0.816684i | \(0.695810\pi\) | |||||||
\(720\) | 11.6130 | − | 3.02287i | 0.432792 | − | 0.112656i | ||||
\(721\) | −29.6155 | −1.10294 | ||||||||
\(722\) | 20.3358 | + | 13.4654i | 0.756821 | + | 0.501132i | ||||
\(723\) | −20.1907 | + | 11.3381i | −0.750899 | + | 0.421669i | ||||
\(724\) | −9.56155 | − | 22.5490i | −0.355352 | − | 0.838025i | ||||
\(725\) | − | 3.12311i | − | 0.115989i | ||||||
\(726\) | 22.5878 | + | 1.65643i | 0.838314 | + | 0.0614760i | ||||
\(727\) | 10.9663i | 0.406717i | 0.979104 | + | 0.203359i | \(0.0651857\pi\) | ||||
−0.979104 | + | 0.203359i | \(0.934814\pi\) | |||||||
\(728\) | −43.0299 | − | 8.00000i | −1.59480 | − | 0.296500i | ||||
\(729\) | −26.9309 | − | 1.93087i | −0.997440 | − | 0.0715137i | ||||
\(730\) | 6.43845 | − | 9.72350i | 0.238298 | − | 0.359883i | ||||
\(731\) | −15.4741 | −0.572329 | ||||||||
\(732\) | −8.55950 | − | 6.61668i | −0.316368 | − | 0.244560i | ||||
\(733\) | −26.8769 | −0.992721 | −0.496360 | − | 0.868117i | \(-0.665331\pi\) | ||||
−0.496360 | + | 0.868117i | \(0.665331\pi\) | |||||||
\(734\) | 8.56222 | − | 12.9309i | 0.316037 | − | 0.477287i | ||||
\(735\) | −1.80054 | − | 3.20636i | −0.0664140 | − | 0.118269i | ||||
\(736\) | −2.05398 | + | 0.453349i | −0.0757105 | + | 0.0167107i | ||||
\(737\) | − | 5.75379i | − | 0.211944i | ||||||
\(738\) | −2.02297 | − | 4.31419i | −0.0744664 | − | 0.158807i | ||||
\(739\) | 26.9752i | 0.992300i | 0.868237 | + | 0.496150i | \(0.165253\pi\) | ||||
−0.868237 | + | 0.496150i | \(0.834747\pi\) | |||||||
\(740\) | 9.43318 | − | 4.00000i | 0.346771 | − | 0.147043i | ||||
\(741\) | 5.75379 | + | 10.2462i | 0.211371 | + | 0.376404i | ||||
\(742\) | −43.6155 | − | 28.8802i | −1.60118 | − | 1.06022i | ||||
\(743\) | −9.80501 | −0.359711 | −0.179856 | − | 0.983693i | \(-0.557563\pi\) | ||||
−0.179856 | + | 0.983693i | \(0.557563\pi\) | |||||||
\(744\) | −21.8757 | + | 7.44050i | −0.802004 | + | 0.272782i | ||||
\(745\) | −14.0000 | −0.512920 | ||||||||
\(746\) | −10.7575 | − | 7.12311i | −0.393860 | − | 0.260795i | ||||
\(747\) | 23.5829 | − | 38.6852i | 0.862855 | − | 1.41542i | ||||
\(748\) | −4.87689 | + | 2.06798i | −0.178317 | + | 0.0756127i | ||||
\(749\) | 9.12311i | 0.333351i | ||||||||
\(750\) | 0.179147 | − | 2.44293i | 0.00654153 | − | 0.0892032i | ||||
\(751\) | − | 11.5012i | − | 0.419683i | −0.977735 | − | 0.209842i | \(-0.932705\pi\) | ||
0.977735 | − | 0.209842i | \(-0.0672948\pi\) | |||||||
\(752\) | −8.39919 | + | 8.68466i | −0.306287 | + | 0.316697i | ||||
\(753\) | −28.2462 | + | 15.8617i | −1.02935 | + | 0.578034i | ||||
\(754\) | 12.4924 | − | 18.8664i | 0.454947 | − | 0.687072i | ||||
\(755\) | −7.36520 | −0.268047 | ||||||||
\(756\) | 11.2122 | + | 29.3186i | 0.407785 | + | 1.06631i | ||||
\(757\) | 10.8769 | 0.395327 | 0.197664 | − | 0.980270i | \(-0.436665\pi\) | ||||
0.197664 | + | 0.980270i | \(0.436665\pi\) | |||||||
\(758\) | −14.6031 | + | 22.0540i | −0.530409 | + | 0.801036i | ||||
\(759\) | −0.743668 | + | 0.417609i | −0.0269934 | + | 0.0151582i | ||||
\(760\) | −0.684658 | + | 3.68260i | −0.0248352 | + | 0.133582i | ||||
\(761\) | − | 31.2311i | − | 1.13212i | −0.824362 | − | 0.566062i | \(-0.808466\pi\) | ||
0.824362 | − | 0.566062i | \(-0.191534\pi\) | |||||||
\(762\) | 2.70552 | − | 36.8937i | 0.0980108 | − | 1.33652i | ||||
\(763\) | 2.64861i | 0.0958863i | ||||||||
\(764\) | −19.4470 | − | 45.8617i | −0.703568 | − | 1.65922i | ||||
\(765\) | 3.12311 | − | 5.12311i | 0.112916 | − | 0.185226i | ||||
\(766\) | −17.8078 | − | 11.7915i | −0.643421 | − | 0.426043i | ||||
\(767\) | 72.4908 | 2.61749 | ||||||||
\(768\) | 14.3689 | + | 23.6967i | 0.518492 | + | 0.855083i | ||||
\(769\) | 38.9848 | 1.40583 | 0.702915 | − | 0.711274i | \(-0.251882\pi\) | ||||
0.702915 | + | 0.711274i | \(0.251882\pi\) | |||||||
\(770\) | −4.71659 | − | 3.12311i | −0.169974 | − | 0.112549i | ||||
\(771\) | −25.8597 | − | 46.0504i | −0.931315 | − | 1.65846i | ||||
\(772\) | −0.192236 | − | 0.453349i | −0.00691872 | − | 0.0163164i | ||||
\(773\) | − | 0.246211i | − | 0.00885560i | −0.999990 | − | 0.00442780i | \(-0.998591\pi\) | ||
0.999990 | − | 0.00442780i | \(-0.00140942\pi\) | |||||||
\(774\) | 13.9361 | + | 29.7203i | 0.500924 | + | 1.06827i | ||||
\(775\) | 4.71659i | 0.169425i | ||||||||
\(776\) | 3.10196 | − | 16.6847i | 0.111354 | − | 0.598944i | ||||
\(777\) | 13.1231 | + | 23.3693i | 0.470789 | + | 0.838370i | ||||
\(778\) | 16.1922 | − | 24.4539i | 0.580520 | − | 0.876715i | ||||
\(779\) | 1.48734 | 0.0532894 | ||||||||
\(780\) | 10.8539 | − | 14.0409i | 0.388633 | − | 0.502745i | ||||
\(781\) | 4.49242 | 0.160752 | ||||||||
\(782\) | −0.580639 | + | 0.876894i | −0.0207636 | + | 0.0313577i | ||||
\(783\) | −16.2177 | − | 0.580639i | −0.579575 | − | 0.0207503i | ||||
\(784\) | 5.90388 | − | 6.10454i | 0.210853 | − | 0.218019i | ||||
\(785\) | 3.36932i | 0.120256i | ||||||||
\(786\) | −13.3390 | − | 0.978190i | −0.475787 | − | 0.0348909i | ||||
\(787\) | 42.0775i | 1.49990i | 0.661495 | + | 0.749950i | \(0.269922\pi\) | ||||
−0.661495 | + | 0.749950i | \(0.730078\pi\) | |||||||
\(788\) | −7.81855 | + | 3.31534i | −0.278524 | + | 0.118104i | ||||
\(789\) | 35.9309 | − | 20.1771i | 1.27917 | − | 0.718323i | ||||
\(790\) | 9.56155 | + | 6.33122i | 0.340185 | + | 0.225255i | ||||
\(791\) | 42.2863 | 1.50353 | ||||||||
\(792\) | 8.36405 | + | 7.50437i | 0.297203 | + | 0.266656i | ||||
\(793\) | −16.0000 | −0.568177 | ||||||||
\(794\) | 17.5420 | + | 11.6155i | 0.622544 | + | 0.412220i | ||||
\(795\) | 18.4945 | − | 10.3857i | 0.655933 | − | 0.368341i | ||||
\(796\) | −10.0540 | + | 4.26324i | −0.356354 | + | 0.151107i | ||||
\(797\) | 12.7386i | 0.451226i | 0.974217 | + | 0.225613i | \(0.0724384\pi\) | ||||
−0.974217 | + | 0.225613i | \(0.927562\pi\) | |||||||
\(798\) | −9.77172 | − | 0.716589i | −0.345915 | − | 0.0253670i | ||||
\(799\) | 6.04090i | 0.213712i | ||||||||
\(800\) | 5.52390 | − | 1.21922i | 0.195299 | − | 0.0431061i | ||||
\(801\) | 26.2462 | + | 16.0000i | 0.927364 | + | 0.565332i | ||||
\(802\) | −18.7386 | + | 28.2995i | −0.661684 | + | 0.999291i | ||||
\(803\) | 10.9205 | 0.385377 | ||||||||
\(804\) | −9.20490 | + | 11.9077i | −0.324632 | + | 0.419951i | ||||
\(805\) | −1.12311 | −0.0395843 | ||||||||
\(806\) | −18.8664 | + | 28.4924i | −0.664539 | + | 1.00360i | ||||
\(807\) | −11.8730 | − | 21.1431i | −0.417949 | − | 0.744274i | ||||
\(808\) | 2.43845 | + | 0.453349i | 0.0857843 | + | 0.0159488i | ||||
\(809\) | − | 29.7538i | − | 1.04609i | −0.852306 | − | 0.523044i | \(-0.824796\pi\) | ||
0.852306 | − | 0.523044i | \(-0.175204\pi\) | |||||||
\(810\) | −12.6524 | − | 1.38446i | −0.444560 | − | 0.0486451i | ||||
\(811\) | − | 46.2592i | − | 1.62438i | −0.583393 | − | 0.812190i | \(-0.698275\pi\) | ||
0.583393 | − | 0.812190i | \(-0.301725\pi\) | |||||||
\(812\) | 7.36520 | + | 17.3693i | 0.258468 | + | 0.609544i | ||||
\(813\) | −12.9848 | − | 23.1231i | −0.455398 | − | 0.810963i | ||||
\(814\) | 8.00000 | + | 5.29723i | 0.280400 | + | 0.185668i | ||||
\(815\) | −15.6829 | −0.549347 | ||||||||
\(816\) | 13.4012 | + | 3.52230i | 0.469137 | + | 0.123305i | ||||
\(817\) | −10.2462 | −0.358470 | ||||||||
\(818\) | 29.9142 | + | 19.8078i | 1.04592 | + | 0.692562i | ||||
\(819\) | 39.6377 | + | 24.1636i | 1.38505 | + | 0.844344i | ||||
\(820\) | −0.876894 | − | 2.06798i | −0.0306225 | − | 0.0722168i | ||||
\(821\) | 53.2311i | 1.85778i | 0.370360 | + | 0.928888i | \(0.379234\pi\) | ||||
−0.370360 | + | 0.928888i | \(0.620766\pi\) | |||||||
\(822\) | −1.47729 | + | 20.1449i | −0.0515263 | + | 0.702635i | ||||
\(823\) | 48.2814i | 1.68298i | 0.540270 | + | 0.841492i | \(0.318322\pi\) | ||||
−0.540270 | + | 0.841492i | \(0.681678\pi\) | |||||||
\(824\) | 27.2655 | + | 5.06913i | 0.949840 | + | 0.176592i | ||||
\(825\) | 2.00000 | − | 1.12311i | 0.0696311 | − | 0.0391015i | ||||
\(826\) | −33.3693 | + | 50.3951i | −1.16107 | + | 1.75347i | ||||
\(827\) | −17.7509 | −0.617258 | −0.308629 | − | 0.951183i | \(-0.599870\pi\) | ||||
−0.308629 | + | 0.951183i | \(0.599870\pi\) | |||||||
\(828\) | 2.20714 | + | 0.325462i | 0.0767033 | + | 0.0113106i | ||||
\(829\) | −8.87689 | −0.308307 | −0.154154 | − | 0.988047i | \(-0.549265\pi\) | ||||
−0.154154 | + | 0.988047i | \(0.549265\pi\) | |||||||
\(830\) | 11.7915 | − | 17.8078i | 0.409288 | − | 0.618117i | ||||
\(831\) | −35.2929 | + | 19.8188i | −1.22430 | + | 0.687508i | ||||
\(832\) | 38.2462 | + | 14.7304i | 1.32595 | + | 0.510685i | ||||
\(833\) | − | 4.24621i | − | 0.147122i | ||||||
\(834\) | −3.14261 | + | 42.8540i | −0.108820 | + | 1.48391i | ||||
\(835\) | 9.06134i | 0.313581i | ||||||||
\(836\) | −3.22925 | + | 1.36932i | −0.111686 | + | 0.0473588i | ||||
\(837\) | 24.4924 | + | 0.876894i | 0.846582 | + | 0.0303099i | ||||
\(838\) | 8.68466 | + | 5.75058i | 0.300007 | + | 0.198650i | ||||
\(839\) | −17.7051 | −0.611247 | −0.305624 | − | 0.952152i | \(-0.598865\pi\) | ||||
−0.305624 | + | 0.952152i | \(0.598865\pi\) | |||||||
\(840\) | 4.76481 | + | 14.0090i | 0.164402 | + | 0.483355i | ||||
\(841\) | 19.2462 | 0.663662 | ||||||||
\(842\) | −29.9142 | − | 19.8078i | −1.03091 | − | 0.682621i | ||||
\(843\) | −11.5469 | − | 20.5625i | −0.397697 | − | 0.708210i | ||||
\(844\) | 30.9309 | − | 13.1158i | 1.06468 | − | 0.451464i | ||||
\(845\) | − | 13.2462i | − | 0.455684i | ||||||
\(846\) | 11.6024 | − | 5.44050i | 0.398900 | − | 0.187048i | ||||
\(847\) | 27.9277i | 0.959607i | ||||||||
\(848\) | 35.2114 | + | 34.0540i | 1.20916 | + | 1.16942i | ||||
\(849\) | −19.6847 | − | 35.0540i | −0.675576 | − | 1.20305i | ||||
\(850\) | 1.56155 | − | 2.35829i | 0.0535608 | − | 0.0808888i | ||||
\(851\) | 1.90495 | 0.0653007 | ||||||||
\(852\) | −9.29723 | − | 7.18697i | −0.318518 | − | 0.246221i | ||||
\(853\) | −7.86174 | −0.269181 | −0.134590 | − | 0.990901i | \(-0.542972\pi\) | ||||
−0.134590 | + | 0.990901i | \(0.542972\pi\) | |||||||
\(854\) | 7.36520 | − | 11.1231i | 0.252032 | − | 0.380625i | ||||
\(855\) | 2.06798 | − | 3.39228i | 0.0707233 | − | 0.116014i | ||||
\(856\) | 1.56155 | − | 8.39919i | 0.0533728 | − | 0.287078i | ||||
\(857\) | − | 20.7386i | − | 0.708418i | −0.935166 | − | 0.354209i | \(-0.884750\pi\) | ||
0.935166 | − | 0.354209i | \(-0.115250\pi\) | |||||||
\(858\) | 16.5742 | + | 1.21544i | 0.565834 | + | 0.0414943i | ||||
\(859\) | − | 33.4337i | − | 1.14074i | −0.821386 | − | 0.570372i | \(-0.806799\pi\) | ||
0.821386 | − | 0.570372i | \(-0.193201\pi\) | |||||||
\(860\) | 6.04090 | + | 14.2462i | 0.205993 | + | 0.485792i | ||||
\(861\) | 5.12311 | − | 2.87689i | 0.174595 | − | 0.0980443i | ||||
\(862\) | −19.6155 | − | 12.9885i | −0.668108 | − | 0.442390i | ||||
\(863\) | 10.5487 | 0.359081 | 0.179541 | − | 0.983751i | \(-0.442539\pi\) | ||||
0.179541 | + | 0.983751i | \(0.442539\pi\) | |||||||
\(864\) | −5.30423 | − | 28.9113i | −0.180453 | − | 0.983584i | ||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 21.2247 | + | 14.0540i | 0.721243 | + | 0.477574i | ||||
\(867\) | −19.6329 | + | 11.0249i | −0.666769 | + | 0.374426i | ||||
\(868\) | −11.1231 | − | 26.2316i | −0.377543 | − | 0.890357i | ||||
\(869\) | 10.7386i | 0.364283i | ||||||||
\(870\) | −7.62953 | − | 0.559496i | −0.258665 | − | 0.0189687i | ||||
\(871\) | 22.2586i | 0.754205i | ||||||||
\(872\) | 0.453349 | − | 2.43845i | 0.0153523 | − | 0.0825762i | ||||
\(873\) | −9.36932 | + | 15.3693i | −0.317103 | + | 0.520173i | ||||
\(874\) | −0.384472 | + | 0.580639i | −0.0130050 | + | 0.0196404i | ||||
\(875\) | 3.02045 | 0.102110 | ||||||||
\(876\) | −22.6004 | − | 17.4706i | −0.763596 | − | 0.590277i | ||||
\(877\) | 37.6155 | 1.27019 | 0.635093 | − | 0.772436i | \(-0.280962\pi\) | ||||
0.635093 | + | 0.772436i | \(0.280962\pi\) | |||||||
\(878\) | −7.23791 | + | 10.9309i | −0.244268 | + | 0.368899i | ||||
\(879\) | −2.11375 | − | 3.76412i | −0.0712950 | − | 0.126960i | ||||
\(880\) | 3.80776 | + | 3.68260i | 0.128360 | + | 0.124140i | ||||
\(881\) | 0.630683i | 0.0212483i | 0.999944 | + | 0.0106241i | \(0.00338183\pi\) | ||||
−0.999944 | + | 0.0106241i | \(0.996618\pi\) | |||||||
\(882\) | −8.15549 | + | 3.82419i | −0.274610 | + | 0.128767i | ||||
\(883\) | − | 22.4674i | − | 0.756090i | −0.925787 | − | 0.378045i | \(-0.876597\pi\) | ||
0.925787 | − | 0.378045i | \(-0.123403\pi\) | |||||||
\(884\) | 18.8664 | − | 8.00000i | 0.634544 | − | 0.269069i | ||||
\(885\) | −12.0000 | − | 21.3693i | −0.403376 | − | 0.718322i | ||||
\(886\) | −19.5616 | − | 12.9527i | −0.657183 | − | 0.435156i | ||||
\(887\) | −51.6737 | −1.73503 | −0.867516 | − | 0.497409i | \(-0.834285\pi\) | ||||
−0.867516 | + | 0.497409i | \(0.834285\pi\) | |||||||
\(888\) | −8.08179 | − | 23.7612i | −0.271207 | − | 0.797373i | ||||
\(889\) | 45.6155 | 1.52990 | ||||||||
\(890\) | 12.0818 | + | 8.00000i | 0.404983 | + | 0.268161i | ||||
\(891\) | −5.46026 | − | 10.5945i | −0.182925 | − | 0.354928i | ||||
\(892\) | −15.3153 | + | 6.49424i | −0.512796 | + | 0.217443i | ||||
\(893\) | 4.00000i | 0.133855i | ||||||||
\(894\) | −2.50806 | + | 34.2010i | −0.0838821 | + | 1.14385i | ||||
\(895\) | 10.0138i | 0.334725i | ||||||||
\(896\) | −27.8462 | + | 19.8078i | −0.930276 | + | 0.661731i | ||||
\(897\) | 2.87689 | − | 1.61553i | 0.0960567 | − | 0.0539409i | ||||
\(898\) | 21.3693 | − | 32.2725i | 0.713103 | − | 1.07695i | ||||
\(899\) | 14.7304 | 0.491287 | ||||||||
\(900\) | −5.93581 | − | 0.875288i | −0.197860 | − | 0.0291763i | ||||
\(901\) | 24.4924 | 0.815961 | ||||||||
\(902\) | 1.16128 | − | 1.75379i | 0.0386663 | − | 0.0583948i | ||||
\(903\) | −35.2929 | + | 19.8188i | −1.17447 | + | 0.659529i | ||||
\(904\) | −38.9309 | − | 7.23791i | −1.29482 | − | 0.240729i | ||||
\(905\) | 12.2462i | 0.407078i | ||||||||
\(906\) | −1.31946 | + | 17.9927i | −0.0438360 | + | 0.597767i | ||||
\(907\) | − | 46.2134i | − | 1.53449i | −0.641353 | − | 0.767246i | \(-0.721627\pi\) | ||
0.641353 | − | 0.767246i | \(-0.278373\pi\) | |||||||
\(908\) | 17.0887 | + | 40.3002i | 0.567108 | + | 1.33741i | ||||
\(909\) | −2.24621 | − | 1.36932i | −0.0745021 | − | 0.0454174i | ||||
\(910\) | 18.2462 | + | 12.0818i | 0.604856 | + | 0.400507i | ||||
\(911\) | −14.3128 | −0.474204 | −0.237102 | − | 0.971485i | \(-0.576198\pi\) | ||||
−0.237102 | + | 0.971485i | \(0.576198\pi\) | |||||||
\(912\) | 8.87368 | + | 2.33230i | 0.293837 | + | 0.0772302i | ||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | −11.7915 | − | 7.80776i | −0.390027 | − | 0.258258i | ||||
\(915\) | 2.64861 | + | 4.71659i | 0.0875605 | + | 0.155926i | ||||
\(916\) | −12.6847 | − | 29.9142i | −0.419113 | − | 0.988392i | ||||
\(917\) | − | 16.4924i | − | 0.544628i | ||||||
\(918\) | −11.9559 | − | 8.54732i | −0.394603 | − | 0.282104i | ||||
\(919\) | − | 49.9775i | − | 1.64861i | −0.566148 | − | 0.824303i | \(-0.691567\pi\) | ||
0.566148 | − | 0.824303i | \(-0.308433\pi\) | |||||||
\(920\) | 1.03399 | + | 0.192236i | 0.0340896 | + | 0.00633783i | ||||
\(921\) | −9.43845 | − | 16.8078i | −0.311007 | − | 0.553835i | ||||
\(922\) | −32.6847 | + | 49.3612i | −1.07641 | + | 1.62562i | ||||
\(923\) | −17.3790 | −0.572037 | ||||||||
\(924\) | −8.47449 | + | 10.9628i | −0.278790 | + | 0.360650i | ||||
\(925\) | −5.12311 | −0.168447 | ||||||||
\(926\) | −2.35829 | + | 3.56155i | −0.0774984 | + | 0.117040i | ||||
\(927\) | −25.1161 | − | 15.3110i | −0.824920 | − | 0.502881i | ||||
\(928\) | −3.80776 | − | 17.2517i | −0.124996 | − | 0.566316i | ||||
\(929\) | − | 33.1231i | − | 1.08673i | −0.839495 | − | 0.543367i | \(-0.817149\pi\) | ||
0.839495 | − | 0.543367i | \(-0.182851\pi\) | |||||||
\(930\) | 11.5223 | + | 0.844964i | 0.377831 | + | 0.0277075i | ||||
\(931\) | − | 2.81164i | − | 0.0921479i | ||||||
\(932\) | 18.4130 | − | 7.80776i | 0.603138 | − | 0.255752i | ||||
\(933\) | −31.3693 | + | 17.6155i | −1.02699 | + | 0.576707i | ||||
\(934\) | 2.68466 | + | 1.77766i | 0.0878447 | + | 0.0581667i | ||||
\(935\) | 2.64861 | 0.0866189 | ||||||||
\(936\) | −32.3565 | − | 29.0308i | −1.05760 | − | 0.948901i | ||||
\(937\) | −22.4924 | −0.734795 | −0.367398 | − | 0.930064i | \(-0.619751\pi\) | ||||
−0.367398 | + | 0.930064i | \(0.619751\pi\) | |||||||
\(938\) | −15.4741 | − | 10.2462i | −0.505246 | − | 0.334551i | ||||
\(939\) | 33.9686 | − | 19.0752i | 1.10852 | − | 0.622494i | ||||
\(940\) | 5.56155 | − | 2.35829i | 0.181398 | − | 0.0769191i | ||||
\(941\) | 0.876894i | 0.0285859i | 0.999898 | + | 0.0142930i | \(0.00454975\pi\) | ||||
−0.999898 | + | 0.0142930i | \(0.995450\pi\) | |||||||
\(942\) | 8.23100 | + | 0.603604i | 0.268181 | + | 0.0196665i | ||||
\(943\) | − | 0.417609i | − | 0.0135992i | ||||||
\(944\) | 39.3473 | − | 40.6847i | 1.28065 | − | 1.32417i | ||||
\(945\) | 0.561553 | − | 15.6847i | 0.0182673 | − | 0.510222i | ||||
\(946\) | −8.00000 | + | 12.0818i | −0.260102 | + | 0.392813i | ||||
\(947\) | 32.4813 | 1.05550 | 0.527750 | − | 0.849400i | \(-0.323036\pi\) | ||||
0.527750 | + | 0.849400i | \(0.323036\pi\) | |||||||
\(948\) | 17.1796 | − | 22.2240i | 0.557969 | − | 0.721801i | ||||
\(949\) | −42.2462 | −1.37137 | ||||||||
\(950\) | 1.03399 | − | 1.56155i | 0.0335470 | − | 0.0506635i | ||||
\(951\) | 14.1955 | + | 25.2791i | 0.460322 | + | 0.819731i | ||||
\(952\) | −3.12311 | + | 16.7984i | −0.101220 | + | 0.544439i | ||||
\(953\) | − | 22.4924i | − | 0.728601i | −0.931281 | − | 0.364301i | \(-0.881308\pi\) | ||
0.931281 | − | 0.364301i | \(-0.118692\pi\) | |||||||
\(954\) | −22.0582 | − | 47.0414i | −0.714160 | − | 1.52302i | ||||
\(955\) | 24.9073i | 0.805980i | ||||||||
\(956\) | 13.5691 | + | 32.0000i | 0.438857 | + | 1.03495i | ||||
\(957\) | −3.50758 | − | 6.24621i | −0.113384 | − | 0.201911i | ||||
\(958\) | 30.2462 | + | 20.0276i | 0.977211 | + | 0.647063i | ||||
\(959\) | −24.9073 | −0.804297 | ||||||||
\(960\) | −1.98889 | − | 13.7129i | −0.0641910 | − | 0.442583i | ||||
\(961\) | 8.75379 | 0.282380 | ||||||||
\(962\) | −30.9481 | − | 20.4924i | −0.997808 | − | 0.660702i | ||||
\(963\) | −4.71659 | + | 7.73704i | −0.151990 | + | 0.249323i | ||||
\(964\) | 10.4384 | + | 24.6169i | 0.336200 | + | 0.792858i | ||||
\(965\) | 0.246211i | 0.00792582i | ||||||||
\(966\) | −0.201201 | + | 2.74367i | −0.00647354 | + | 0.0882761i | ||||
\(967\) | 26.4404i | 0.850265i | 0.905131 | + | 0.425132i | \(0.139772\pi\) | ||||
−0.905131 | + | 0.425132i | \(0.860228\pi\) | |||||||
\(968\) | 4.78023 | − | 25.7116i | 0.153643 | − | 0.826404i | ||||
\(969\) | 4.00000 | − | 2.24621i | 0.128499 | − | 0.0721587i | ||||
\(970\) | −4.68466 | + | 7.07488i | −0.150415 | + | 0.227161i | ||||
\(971\) | 52.6261 | 1.68885 | 0.844427 | − | 0.535671i | \(-0.179941\pi\) | ||||
0.844427 | + | 0.535671i | \(0.179941\pi\) | |||||||
\(972\) | −5.64879 | + | 30.6609i | −0.181185 | + | 0.983449i | ||||
\(973\) | −52.9848 | −1.69862 | ||||||||
\(974\) | 19.7373 | − | 29.8078i | 0.632424 | − | 0.955102i | ||||
\(975\) | −7.73704 | + | 4.34475i | −0.247783 | + | 0.139144i | ||||
\(976\) | −8.68466 | + | 8.97983i | −0.277989 | + | 0.287437i | ||||
\(977\) | 31.7538i | 1.01589i | 0.861388 | + | 0.507947i | \(0.169595\pi\) | ||||
−0.861388 | + | 0.507947i | \(0.830405\pi\) | |||||||
\(978\) | −2.80954 | + | 38.3122i | −0.0898393 | + | 1.22509i | ||||
\(979\) | 13.5691i | 0.433671i | ||||||||
\(980\) | −3.90928 | + | 1.65767i | −0.124877 | + | 0.0529524i | ||||
\(981\) | −1.36932 | + | 2.24621i | −0.0437189 | + | 0.0717160i | ||||
\(982\) | 31.8078 | + | 21.0616i | 1.01503 | + | 0.672103i | ||||
\(983\) | 40.0095 | 1.27610 | 0.638052 | − | 0.769993i | \(-0.279740\pi\) | ||||
0.638052 | + | 0.769993i | \(0.279740\pi\) | |||||||
\(984\) | −5.20901 | + | 1.77172i | −0.166057 | + | 0.0564804i | ||||
\(985\) | 4.24621 | 0.135296 | ||||||||
\(986\) | −7.36520 | − | 4.87689i | −0.234556 | − | 0.155312i | ||||
\(987\) | 7.73704 | + | 13.7779i | 0.246273 | + | 0.438556i | ||||
\(988\) | 12.4924 | − | 5.29723i | 0.397437 | − | 0.168527i | ||||
\(989\) | 2.87689i | 0.0914799i | ||||||||
\(990\) | −2.38537 | − | 5.08706i | −0.0758122 | − | 0.161677i | ||||
\(991\) | − | 33.0161i | − | 1.04879i | −0.851475 | − | 0.524396i | \(-0.824291\pi\) | ||
0.851475 | − | 0.524396i | \(-0.175709\pi\) | |||||||
\(992\) | 5.75058 | + | 26.0540i | 0.182581 | + | 0.827215i | ||||
\(993\) | 2.73863 | + | 4.87689i | 0.0869079 | + | 0.154764i | ||||
\(994\) | 8.00000 | − | 12.0818i | 0.253745 | − | 0.383211i | ||||
\(995\) | 5.46026 | 0.173102 | ||||||||
\(996\) | −41.3907 | − | 31.9960i | −1.31151 | − | 1.01383i | ||||
\(997\) | −33.6155 | −1.06461 | −0.532307 | − | 0.846551i | \(-0.678675\pi\) | ||||
−0.532307 | + | 0.846551i | \(0.678675\pi\) | |||||||
\(998\) | −25.1976 | + | 38.0540i | −0.797615 | + | 1.20458i | ||||
\(999\) | −0.952473 | + | 26.6034i | −0.0301349 | + | 0.841694i |
(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 | 60.2.e.a.11.8 | yes | 8 | |
3.2 | odd | 2 | inner | 60.2.e.a.11.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 60.2.e.a.11.2 | yes | 8 | |
5.2 | odd | 4 | 300.2.h.b.299.4 | 8 | |||
5.3 | odd | 4 | 300.2.h.a.299.5 | 8 | |||
5.4 | even | 2 | 300.2.e.c.251.1 | 8 | |||
8.3 | odd | 2 | 960.2.h.g.191.2 | 8 | |||
8.5 | even | 2 | 960.2.h.g.191.7 | 8 | |||
12.11 | even | 2 | inner | 60.2.e.a.11.7 | yes | 8 | |
15.2 | even | 4 | 300.2.h.a.299.6 | 8 | |||
15.8 | even | 4 | 300.2.h.b.299.3 | 8 | |||
15.14 | odd | 2 | 300.2.e.c.251.8 | 8 | |||
20.3 | even | 4 | 300.2.h.a.299.8 | 8 | |||
20.7 | even | 4 | 300.2.h.b.299.1 | 8 | |||
20.19 | odd | 2 | 300.2.e.c.251.7 | 8 | |||
24.5 | odd | 2 | 960.2.h.g.191.1 | 8 | |||
24.11 | even | 2 | 960.2.h.g.191.8 | 8 | |||
60.23 | odd | 4 | 300.2.h.b.299.2 | 8 | |||
60.47 | odd | 4 | 300.2.h.a.299.7 | 8 | |||
60.59 | even | 2 | 300.2.e.c.251.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.e.a.11.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
60.2.e.a.11.2 | yes | 8 | 4.3 | odd | 2 | inner | |
60.2.e.a.11.7 | yes | 8 | 12.11 | even | 2 | inner | |
60.2.e.a.11.8 | yes | 8 | 1.1 | even | 1 | trivial | |
300.2.e.c.251.1 | 8 | 5.4 | even | 2 | |||
300.2.e.c.251.2 | 8 | 60.59 | even | 2 | |||
300.2.e.c.251.7 | 8 | 20.19 | odd | 2 | |||
300.2.e.c.251.8 | 8 | 15.14 | odd | 2 | |||
300.2.h.a.299.5 | 8 | 5.3 | odd | 4 | |||
300.2.h.a.299.6 | 8 | 15.2 | even | 4 | |||
300.2.h.a.299.7 | 8 | 60.47 | odd | 4 | |||
300.2.h.a.299.8 | 8 | 20.3 | even | 4 | |||
300.2.h.b.299.1 | 8 | 20.7 | even | 4 | |||
300.2.h.b.299.2 | 8 | 60.23 | odd | 4 | |||
300.2.h.b.299.3 | 8 | 15.8 | even | 4 | |||
300.2.h.b.299.4 | 8 | 5.2 | odd | 4 | |||
960.2.h.g.191.1 | 8 | 24.5 | odd | 2 | |||
960.2.h.g.191.2 | 8 | 8.3 | odd | 2 | |||
960.2.h.g.191.7 | 8 | 8.5 | even | 2 | |||
960.2.h.g.191.8 | 8 | 24.11 | even | 2 |