Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Character | \(\chi\) | \(=\) | 1110.529 |
Dual form | 1110.2.ba.b.619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.62555 | − | 1.53544i | −0.726968 | − | 0.686672i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 2.75229 | + | 1.58904i | 1.04027 | + | 0.600599i | 0.919909 | − | 0.392131i | \(-0.128262\pi\) |
0.120359 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0.516959 | − | 2.17549i | 0.163477 | − | 0.687950i | ||||
\(11\) | −3.88035 | −1.16997 | −0.584985 | − | 0.811044i | \(-0.698900\pi\) | ||||
−0.584985 | + | 0.811044i | \(0.698900\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | −0.379707 | + | 0.657673i | −0.105312 | + | 0.182406i | −0.913866 | − | 0.406017i | \(-0.866917\pi\) |
0.808554 | + | 0.588422i | \(0.200251\pi\) | |||||||
\(14\) | 3.17807i | 0.849375i | ||||||||
\(15\) | 0.640045 | + | 2.14251i | 0.165259 | + | 0.553193i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.69434 | − | 2.93468i | −0.410937 | − | 0.711764i | 0.584055 | − | 0.811714i | \(-0.301465\pi\) |
−0.994992 | + | 0.0999499i | \(0.968132\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 4.55166 | + | 2.62790i | 1.04422 | + | 0.602882i | 0.921026 | − | 0.389501i | \(-0.127352\pi\) |
0.123196 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(20\) | 2.14251 | − | 0.640045i | 0.479079 | − | 0.143118i | ||||
\(21\) | −1.58904 | − | 2.75229i | −0.346756 | − | 0.600599i | ||||
\(22\) | −1.94018 | − | 3.36048i | −0.413647 | − | 0.716457i | ||||
\(23\) | −6.61653 | −1.37964 | −0.689821 | − | 0.723980i | \(-0.742311\pi\) | ||||
−0.689821 | + | 0.723980i | \(0.742311\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0.284822 | + | 4.99188i | 0.0569645 | + | 0.998376i | ||||
\(26\) | −0.759415 | −0.148934 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.75229 | + | 1.58904i | −0.520134 | + | 0.300300i | ||||
\(29\) | − | 1.30709i | − | 0.242721i | −0.992609 | − | 0.121360i | \(-0.961274\pi\) | ||
0.992609 | − | 0.121360i | \(-0.0387256\pi\) | |||||||
\(30\) | −1.53544 | + | 1.62555i | −0.280332 | + | 0.296783i | ||||
\(31\) | 6.12433i | 1.09996i | 0.835177 | + | 0.549981i | \(0.185365\pi\) | ||||
−0.835177 | + | 0.549981i | \(0.814635\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.36048 | + | 1.94018i | 0.584985 | + | 0.337741i | ||||
\(34\) | 1.69434 | − | 2.93468i | 0.290576 | − | 0.503293i | ||||
\(35\) | −2.03411 | − | 6.80904i | −0.343827 | − | 1.15094i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −6.05221 | − | 0.608935i | −0.994977 | − | 0.100108i | ||||
\(38\) | 5.25580i | 0.852604i | ||||||||
\(39\) | 0.657673 | − | 0.379707i | 0.105312 | − | 0.0608019i | ||||
\(40\) | 1.62555 | + | 1.53544i | 0.257022 | + | 0.242775i | ||||
\(41\) | −5.17175 | + | 8.95773i | −0.807691 | + | 1.39896i | 0.106768 | + | 0.994284i | \(0.465950\pi\) |
−0.914459 | + | 0.404678i | \(0.867384\pi\) | |||||||
\(42\) | 1.58904 | − | 2.75229i | 0.245194 | − | 0.424688i | ||||
\(43\) | −9.41844 | −1.43630 | −0.718149 | − | 0.695889i | \(-0.755011\pi\) | ||||
−0.718149 | + | 0.695889i | \(0.755011\pi\) | |||||||
\(44\) | 1.94018 | − | 3.36048i | 0.292492 | − | 0.506612i | ||||
\(45\) | 0.516959 | − | 2.17549i | 0.0770637 | − | 0.324303i | ||||
\(46\) | −3.30827 | − | 5.73009i | −0.487777 | − | 0.844855i | ||||
\(47\) | 5.34620i | 0.779824i | 0.920852 | + | 0.389912i | \(0.127495\pi\) | ||||
−0.920852 | + | 0.389912i | \(0.872505\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 1.55007 | + | 2.68480i | 0.221438 | + | 0.383543i | ||||
\(50\) | −4.18068 | + | 2.74260i | −0.591238 | + | 0.387863i | ||||
\(51\) | 3.38867i | 0.474509i | ||||||||
\(52\) | −0.379707 | − | 0.657673i | −0.0526559 | − | 0.0912028i | ||||
\(53\) | 2.76662 | − | 1.59731i | 0.380024 | − | 0.219407i | −0.297804 | − | 0.954627i | \(-0.596254\pi\) |
0.677829 | + | 0.735220i | \(0.262921\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 6.30770 | + | 5.95806i | 0.850530 | + | 0.803385i | ||||
\(56\) | −2.75229 | − | 1.58904i | −0.367790 | − | 0.212344i | ||||
\(57\) | −2.62790 | − | 4.55166i | −0.348074 | − | 0.602882i | ||||
\(58\) | 1.13197 | − | 0.653545i | 0.148635 | − | 0.0858147i | ||||
\(59\) | −5.34529 | + | 3.08610i | −0.695897 | + | 0.401776i | −0.805817 | − | 0.592164i | \(-0.798274\pi\) |
0.109920 | + | 0.993940i | \(0.464940\pi\) | |||||||
\(60\) | −2.17549 | − | 0.516959i | −0.280854 | − | 0.0667391i | ||||
\(61\) | −8.45447 | − | 4.88119i | −1.08248 | − | 0.624973i | −0.150919 | − | 0.988546i | \(-0.548223\pi\) |
−0.931565 | + | 0.363574i | \(0.881557\pi\) | |||||||
\(62\) | −5.30382 | + | 3.06216i | −0.673586 | + | 0.388895i | ||||
\(63\) | 3.17807i | 0.400399i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.62705 | − | 0.486060i | 0.201811 | − | 0.0602883i | ||||
\(66\) | 3.88035i | 0.477638i | ||||||||
\(67\) | −8.72817 | − | 5.03921i | −1.06632 | − | 0.615638i | −0.139144 | − | 0.990272i | \(-0.544435\pi\) |
−0.927173 | + | 0.374634i | \(0.877768\pi\) | |||||||
\(68\) | 3.38867 | 0.410937 | ||||||||
\(69\) | 5.73009 | + | 3.30827i | 0.689821 | + | 0.398269i | ||||
\(70\) | 4.87975 | − | 5.16611i | 0.583242 | − | 0.617469i | ||||
\(71\) | −3.22083 | + | 5.57863i | −0.382242 | + | 0.662062i | −0.991382 | − | 0.131000i | \(-0.958181\pi\) |
0.609141 | + | 0.793062i | \(0.291514\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | − | 5.84525i | − | 0.684135i | −0.939675 | − | 0.342067i | \(-0.888873\pi\) | ||
0.939675 | − | 0.342067i | \(-0.111127\pi\) | |||||||
\(74\) | −2.49875 | − | 5.54583i | −0.290474 | − | 0.644690i | ||||
\(75\) | 2.24928 | − | 4.46551i | 0.259724 | − | 0.515632i | ||||
\(76\) | −4.55166 | + | 2.62790i | −0.522111 | + | 0.301441i | ||||
\(77\) | −10.6799 | − | 6.16602i | −1.21708 | − | 0.702683i | ||||
\(78\) | 0.657673 | + | 0.379707i | 0.0744668 | + | 0.0429934i | ||||
\(79\) | 7.39006 | + | 4.26665i | 0.831446 | + | 0.480036i | 0.854348 | − | 0.519702i | \(-0.173957\pi\) |
−0.0229014 | + | 0.999738i | \(0.507290\pi\) | |||||||
\(80\) | −0.516959 | + | 2.17549i | −0.0577978 | + | 0.243227i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −10.3435 | −1.14225 | ||||||||
\(83\) | 6.05368 | − | 3.49509i | 0.664477 | − | 0.383636i | −0.129504 | − | 0.991579i | \(-0.541338\pi\) |
0.793981 | + | 0.607943i | \(0.208005\pi\) | |||||||
\(84\) | 3.17807 | 0.346756 | ||||||||
\(85\) | −1.75181 | + | 7.37202i | −0.190010 | + | 0.799608i | ||||
\(86\) | −4.70922 | − | 8.15661i | −0.507808 | − | 0.879550i | ||||
\(87\) | −0.653545 | + | 1.13197i | −0.0700674 | + | 0.121360i | ||||
\(88\) | 3.88035 | 0.413647 | ||||||||
\(89\) | −1.93582 | + | 1.11765i | −0.205197 | + | 0.118470i | −0.599077 | − | 0.800691i | \(-0.704466\pi\) |
0.393880 | + | 0.919162i | \(0.371132\pi\) | |||||||
\(90\) | 2.14251 | − | 0.640045i | 0.225840 | − | 0.0674667i | ||||
\(91\) | −2.09013 | + | 1.20674i | −0.219105 | + | 0.126500i | ||||
\(92\) | 3.30827 | − | 5.73009i | 0.344911 | − | 0.597403i | ||||
\(93\) | 3.06216 | − | 5.30382i | 0.317532 | − | 0.549981i | ||||
\(94\) | −4.62995 | + | 2.67310i | −0.477543 | + | 0.275709i | ||||
\(95\) | −3.36395 | − | 11.2606i | −0.345134 | − | 1.15531i | ||||
\(96\) | −0.866025 | + | 0.500000i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | −4.77178 | −0.484501 | −0.242250 | − | 0.970214i | \(-0.577886\pi\) | ||||
−0.242250 | + | 0.970214i | \(0.577886\pi\) | |||||||
\(98\) | −1.55007 | + | 2.68480i | −0.156581 | + | 0.271206i | ||||
\(99\) | −1.94018 | − | 3.36048i | −0.194995 | − | 0.337741i | ||||
\(100\) | −4.46551 | − | 2.24928i | −0.446551 | − | 0.224928i | ||||
\(101\) | 2.01613 | 0.200612 | 0.100306 | − | 0.994957i | \(-0.468018\pi\) | ||||
0.100306 | + | 0.994957i | \(0.468018\pi\) | |||||||
\(102\) | −2.93468 | + | 1.69434i | −0.290576 | + | 0.167764i | ||||
\(103\) | −8.06815 | −0.794978 | −0.397489 | − | 0.917607i | \(-0.630118\pi\) | ||||
−0.397489 | + | 0.917607i | \(0.630118\pi\) | |||||||
\(104\) | 0.379707 | − | 0.657673i | 0.0372334 | − | 0.0644901i | ||||
\(105\) | −1.64293 | + | 6.91386i | −0.160334 | + | 0.674724i | ||||
\(106\) | 2.76662 | + | 1.59731i | 0.268718 | + | 0.155144i | ||||
\(107\) | 4.44127 | + | 2.56417i | 0.429354 | + | 0.247887i | 0.699071 | − | 0.715052i | \(-0.253597\pi\) |
−0.269718 | + | 0.962939i | \(0.586930\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −4.29464 | + | 2.47951i | −0.411352 | + | 0.237494i | −0.691371 | − | 0.722500i | \(-0.742993\pi\) |
0.280018 | + | 0.959995i | \(0.409659\pi\) | |||||||
\(110\) | −2.00598 | + | 8.44166i | −0.191263 | + | 0.804881i | ||||
\(111\) | 4.93690 | + | 3.55346i | 0.468589 | + | 0.337279i | ||||
\(112\) | − | 3.17807i | − | 0.300300i | ||||||
\(113\) | 5.50508 | + | 9.53507i | 0.517874 | + | 0.896984i | 0.999784 | + | 0.0207636i | \(0.00660974\pi\) |
−0.481910 | + | 0.876221i | \(0.660057\pi\) | |||||||
\(114\) | 2.62790 | − | 4.55166i | 0.246125 | − | 0.426302i | ||||
\(115\) | 10.7555 | + | 10.1593i | 1.00296 | + | 0.947361i | ||||
\(116\) | 1.13197 | + | 0.653545i | 0.105101 | + | 0.0606802i | ||||
\(117\) | −0.759415 | −0.0702079 | ||||||||
\(118\) | −5.34529 | − | 3.08610i | −0.492074 | − | 0.284099i | ||||
\(119\) | − | 10.7694i | − | 0.987234i | ||||||
\(120\) | −0.640045 | − | 2.14251i | −0.0584279 | − | 0.195583i | ||||
\(121\) | 4.05712 | 0.368829 | ||||||||
\(122\) | − | 9.76238i | − | 0.883845i | ||||||
\(123\) | 8.95773 | − | 5.17175i | 0.807691 | − | 0.466321i | ||||
\(124\) | −5.30382 | − | 3.06216i | −0.476297 | − | 0.274990i | ||||
\(125\) | 7.20176 | − | 8.55188i | 0.644145 | − | 0.764903i | ||||
\(126\) | −2.75229 | + | 1.58904i | −0.245194 | + | 0.141563i | ||||
\(127\) | 13.0596 | − | 7.53996i | 1.15885 | − | 0.669063i | 0.207823 | − | 0.978166i | \(-0.433362\pi\) |
0.951029 | + | 0.309103i | \(0.100029\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 8.15661 | + | 4.70922i | 0.718149 | + | 0.414624i | ||||
\(130\) | 1.23447 | + | 1.16604i | 0.108270 | + | 0.102268i | ||||
\(131\) | 9.51251 | − | 5.49205i | 0.831112 | − | 0.479843i | −0.0231214 | − | 0.999733i | \(-0.507360\pi\) |
0.854233 | + | 0.519890i | \(0.174027\pi\) | |||||||
\(132\) | −3.36048 | + | 1.94018i | −0.292492 | + | 0.168871i | ||||
\(133\) | 8.35166 | + | 14.4655i | 0.724180 | + | 1.25432i | ||||
\(134\) | − | 10.0784i | − | 0.870644i | ||||||
\(135\) | −1.53544 | + | 1.62555i | −0.132150 | + | 0.139905i | ||||
\(136\) | 1.69434 | + | 2.93468i | 0.145288 | + | 0.251647i | ||||
\(137\) | 1.70269i | 0.145471i | 0.997351 | + | 0.0727353i | \(0.0231728\pi\) | ||||
−0.997351 | + | 0.0727353i | \(0.976827\pi\) | |||||||
\(138\) | 6.61653i | 0.563237i | ||||||||
\(139\) | 8.79340 | + | 15.2306i | 0.745846 | + | 1.29184i | 0.949798 | + | 0.312863i | \(0.101288\pi\) |
−0.203952 | + | 0.978981i | \(0.565379\pi\) | |||||||
\(140\) | 6.91386 | + | 1.64293i | 0.584328 | + | 0.138853i | ||||
\(141\) | 2.67310 | − | 4.62995i | 0.225116 | − | 0.389912i | ||||
\(142\) | −6.44165 | −0.540571 | ||||||||
\(143\) | 1.47340 | − | 2.55200i | 0.123212 | − | 0.213409i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −2.00696 | + | 2.12474i | −0.166669 | + | 0.176450i | ||||
\(146\) | 5.06214 | − | 2.92263i | 0.418945 | − | 0.241878i | ||||
\(147\) | − | 3.10014i | − | 0.255695i | ||||||
\(148\) | 3.55346 | − | 4.93690i | 0.292092 | − | 0.405810i | ||||
\(149\) | 18.0769 | 1.48092 | 0.740458 | − | 0.672103i | \(-0.234609\pi\) | ||||
0.740458 | + | 0.672103i | \(0.234609\pi\) | |||||||
\(150\) | 4.99188 | − | 0.284822i | 0.407585 | − | 0.0232556i | ||||
\(151\) | 7.75253 | − | 13.4278i | 0.630892 | − | 1.09274i | −0.356478 | − | 0.934304i | \(-0.616023\pi\) |
0.987370 | − | 0.158433i | \(-0.0506441\pi\) | |||||||
\(152\) | −4.55166 | − | 2.62790i | −0.369188 | − | 0.213151i | ||||
\(153\) | 1.69434 | − | 2.93468i | 0.136979 | − | 0.237255i | ||||
\(154\) | − | 12.3320i | − | 0.993744i | ||||||
\(155\) | 9.40356 | − | 9.95540i | 0.755312 | − | 0.799637i | ||||
\(156\) | 0.759415i | 0.0608019i | ||||||||
\(157\) | −4.26063 | + | 2.45988i | −0.340035 | + | 0.196320i | −0.660288 | − | 0.751013i | \(-0.729566\pi\) |
0.320252 | + | 0.947332i | \(0.396232\pi\) | |||||||
\(158\) | 8.53330i | 0.678873i | ||||||||
\(159\) | −3.19462 | −0.253350 | ||||||||
\(160\) | −2.14251 | + | 0.640045i | −0.169380 | + | 0.0506000i | ||||
\(161\) | −18.2106 | − | 10.5139i | −1.43520 | − | 0.828612i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −3.02056 | − | 5.23176i | −0.236588 | − | 0.409783i | 0.723145 | − | 0.690696i | \(-0.242696\pi\) |
−0.959733 | + | 0.280914i | \(0.909363\pi\) | |||||||
\(164\) | −5.17175 | − | 8.95773i | −0.403845 | − | 0.699481i | ||||
\(165\) | −2.48360 | − | 8.31368i | −0.193348 | − | 0.647219i | ||||
\(166\) | 6.05368 | + | 3.49509i | 0.469856 | + | 0.271272i | ||||
\(167\) | 9.53467 | − | 16.5145i | 0.737815 | − | 1.27793i | −0.215663 | − | 0.976468i | \(-0.569191\pi\) |
0.953477 | − | 0.301465i | \(-0.0974755\pi\) | |||||||
\(168\) | 1.58904 | + | 2.75229i | 0.122597 | + | 0.212344i | ||||
\(169\) | 6.21164 | + | 10.7589i | 0.477819 | + | 0.827606i | ||||
\(170\) | −7.26026 | + | 2.16890i | −0.556837 | + | 0.166347i | ||||
\(171\) | 5.25580i | 0.401921i | ||||||||
\(172\) | 4.70922 | − | 8.15661i | 0.359075 | − | 0.621936i | ||||
\(173\) | −17.6459 | + | 10.1879i | −1.34160 | + | 0.774571i | −0.987042 | − | 0.160465i | \(-0.948701\pi\) |
−0.354554 | + | 0.935035i | \(0.615367\pi\) | |||||||
\(174\) | −1.30709 | −0.0990903 | ||||||||
\(175\) | −7.14836 | + | 14.1917i | −0.540365 | + | 1.07279i | ||||
\(176\) | 1.94018 | + | 3.36048i | 0.146246 | + | 0.253306i | ||||
\(177\) | 6.17221 | 0.463931 | ||||||||
\(178\) | −1.93582 | − | 1.11765i | −0.145096 | − | 0.0837713i | ||||
\(179\) | − | 1.86502i | − | 0.139398i | −0.997568 | − | 0.0696989i | \(-0.977796\pi\) | ||
0.997568 | − | 0.0696989i | \(-0.0222039\pi\) | |||||||
\(180\) | 1.62555 | + | 1.53544i | 0.121161 | + | 0.114445i | ||||
\(181\) | 6.08878 | − | 10.5461i | 0.452575 | − | 0.783884i | −0.545970 | − | 0.837805i | \(-0.683839\pi\) |
0.998545 | + | 0.0539212i | \(0.0171720\pi\) | |||||||
\(182\) | −2.09013 | − | 1.20674i | −0.154931 | − | 0.0894493i | ||||
\(183\) | 4.88119 | + | 8.45447i | 0.360828 | + | 0.624973i | ||||
\(184\) | 6.61653 | 0.487777 | ||||||||
\(185\) | 8.90317 | + | 10.2827i | 0.654574 | + | 0.755998i | ||||
\(186\) | 6.12433 | 0.449057 | ||||||||
\(187\) | 6.57462 | + | 11.3876i | 0.480784 | + | 0.832742i | ||||
\(188\) | −4.62995 | − | 2.67310i | −0.337674 | − | 0.194956i | ||||
\(189\) | 1.58904 | − | 2.75229i | 0.115585 | − | 0.200200i | ||||
\(190\) | 8.06999 | − | 8.54356i | 0.585459 | − | 0.619815i | ||||
\(191\) | 21.9186i | 1.58597i | 0.609240 | + | 0.792986i | \(0.291475\pi\) | ||||
−0.609240 | + | 0.792986i | \(0.708525\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 6.01088 | 0.432672 | 0.216336 | − | 0.976319i | \(-0.430589\pi\) | ||||
0.216336 | + | 0.976319i | \(0.430589\pi\) | |||||||
\(194\) | −2.38589 | − | 4.13248i | −0.171297 | − | 0.296695i | ||||
\(195\) | −1.65210 | − | 0.392586i | −0.118309 | − | 0.0281137i | ||||
\(196\) | −3.10014 | −0.221438 | ||||||||
\(197\) | −16.0895 | + | 9.28928i | −1.14633 | + | 0.661834i | −0.947990 | − | 0.318299i | \(-0.896888\pi\) |
−0.198340 | + | 0.980133i | \(0.563555\pi\) | |||||||
\(198\) | 1.94018 | − | 3.36048i | 0.137882 | − | 0.238819i | ||||
\(199\) | 2.04121i | 0.144697i | 0.997379 | + | 0.0723487i | \(0.0230495\pi\) | ||||
−0.997379 | + | 0.0723487i | \(0.976951\pi\) | |||||||
\(200\) | −0.284822 | − | 4.99188i | −0.0201400 | − | 0.352979i | ||||
\(201\) | 5.03921 | + | 8.72817i | 0.355439 | + | 0.615638i | ||||
\(202\) | 1.00807 | + | 1.74602i | 0.0709272 | + | 0.122850i | ||||
\(203\) | 2.07701 | − | 3.59749i | 0.145778 | − | 0.252494i | ||||
\(204\) | −2.93468 | − | 1.69434i | −0.205469 | − | 0.118627i | ||||
\(205\) | 22.1610 | − | 6.62030i | 1.54779 | − | 0.462382i | ||||
\(206\) | −4.03407 | − | 6.98722i | −0.281067 | − | 0.486823i | ||||
\(207\) | −3.30827 | − | 5.73009i | −0.229940 | − | 0.398269i | ||||
\(208\) | 0.759415 | 0.0526559 | ||||||||
\(209\) | −17.6620 | − | 10.1972i | −1.22171 | − | 0.705353i | ||||
\(210\) | −6.80904 | + | 2.03411i | −0.469869 | + | 0.140367i | ||||
\(211\) | 13.3152 | 0.916658 | 0.458329 | − | 0.888783i | \(-0.348448\pi\) | ||||
0.458329 | + | 0.888783i | \(0.348448\pi\) | |||||||
\(212\) | 3.19462i | 0.219407i | ||||||||
\(213\) | 5.57863 | − | 3.22083i | 0.382242 | − | 0.220687i | ||||
\(214\) | 5.12833i | 0.350566i | ||||||||
\(215\) | 15.3101 | + | 14.4615i | 1.04414 | + | 0.986265i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −9.73177 | + | 16.8559i | −0.660636 | + | 1.14425i | ||||
\(218\) | −4.29464 | − | 2.47951i | −0.290870 | − | 0.167934i | ||||
\(219\) | −2.92263 | + | 5.06214i | −0.197493 | + | 0.342067i | ||||
\(220\) | −8.31368 | + | 2.48360i | −0.560508 | + | 0.167444i | ||||
\(221\) | 2.57341 | 0.173106 | ||||||||
\(222\) | −0.608935 | + | 6.05221i | −0.0408691 | + | 0.406197i | ||||
\(223\) | 14.8913i | 0.997193i | 0.866834 | + | 0.498597i | \(0.166151\pi\) | ||||
−0.866834 | + | 0.498597i | \(0.833849\pi\) | |||||||
\(224\) | 2.75229 | − | 1.58904i | 0.183895 | − | 0.106172i | ||||
\(225\) | −4.18068 | + | 2.74260i | −0.278712 | + | 0.182840i | ||||
\(226\) | −5.50508 | + | 9.53507i | −0.366192 | + | 0.634264i | ||||
\(227\) | 0.708052 | − | 1.22638i | 0.0469951 | − | 0.0813979i | −0.841571 | − | 0.540146i | \(-0.818369\pi\) |
0.888566 | + | 0.458749i | \(0.151702\pi\) | |||||||
\(228\) | 5.25580 | 0.348074 | ||||||||
\(229\) | −13.9106 | + | 24.0938i | −0.919237 | + | 1.59217i | −0.118661 | + | 0.992935i | \(0.537860\pi\) |
−0.800576 | + | 0.599231i | \(0.795473\pi\) | |||||||
\(230\) | −3.42048 | + | 14.3942i | −0.225540 | + | 0.949125i | ||||
\(231\) | 6.16602 | + | 10.6799i | 0.405694 | + | 0.702683i | ||||
\(232\) | 1.30709i | 0.0858147i | ||||||||
\(233\) | − | 21.1423i | − | 1.38508i | −0.721382 | − | 0.692538i | \(-0.756493\pi\) | ||
0.721382 | − | 0.692538i | \(-0.243507\pi\) | |||||||
\(234\) | −0.379707 | − | 0.657673i | −0.0248223 | − | 0.0429934i | ||||
\(235\) | 8.20879 | − | 8.69052i | 0.535483 | − | 0.566907i | ||||
\(236\) | − | 6.17221i | − | 0.401776i | ||||||
\(237\) | −4.26665 | − | 7.39006i | −0.277149 | − | 0.480036i | ||||
\(238\) | 9.32662 | − | 5.38472i | 0.604555 | − | 0.349040i | ||||
\(239\) | −5.13952 | + | 2.96731i | −0.332448 | + | 0.191939i | −0.656927 | − | 0.753954i | \(-0.728144\pi\) |
0.324479 | + | 0.945893i | \(0.394811\pi\) | |||||||
\(240\) | 1.53544 | − | 1.62555i | 0.0991125 | − | 0.104929i | ||||
\(241\) | −21.6064 | − | 12.4744i | −1.39179 | − | 0.803550i | −0.398276 | − | 0.917266i | \(-0.630391\pi\) |
−0.993513 | + | 0.113716i | \(0.963725\pi\) | |||||||
\(242\) | 2.02856 | + | 3.51357i | 0.130401 | + | 0.225861i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 8.45447 | − | 4.88119i | 0.541242 | − | 0.312486i | ||||
\(245\) | 1.60264 | − | 6.74432i | 0.102389 | − | 0.430879i | ||||
\(246\) | 8.95773 | + | 5.17175i | 0.571124 | + | 0.329738i | ||||
\(247\) | −3.45660 | + | 1.99567i | −0.219938 | + | 0.126981i | ||||
\(248\) | − | 6.12433i | − | 0.388895i | ||||||
\(249\) | −6.99018 | −0.442985 | ||||||||
\(250\) | 11.0070 | + | 1.96097i | 0.696145 | + | 0.124023i | ||||
\(251\) | − | 5.08160i | − | 0.320748i | −0.987056 | − | 0.160374i | \(-0.948730\pi\) | ||
0.987056 | − | 0.160374i | \(-0.0512700\pi\) | |||||||
\(252\) | −2.75229 | − | 1.58904i | −0.173378 | − | 0.100100i | ||||
\(253\) | 25.6745 | 1.61414 | ||||||||
\(254\) | 13.0596 | + | 7.53996i | 0.819432 | + | 0.473099i | ||||
\(255\) | 5.20312 | − | 5.50846i | 0.325832 | − | 0.344953i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.08288 | − | 8.80380i | −0.317061 | − | 0.549166i | 0.662812 | − | 0.748786i | \(-0.269363\pi\) |
−0.979873 | + | 0.199620i | \(0.936029\pi\) | |||||||
\(258\) | 9.41844i | 0.586366i | ||||||||
\(259\) | −15.6898 | − | 11.2931i | −0.974917 | − | 0.701722i | ||||
\(260\) | −0.392586 | + | 1.65210i | −0.0243472 | + | 0.102459i | ||||
\(261\) | 1.13197 | − | 0.653545i | 0.0700674 | − | 0.0404534i | ||||
\(262\) | 9.51251 | + | 5.49205i | 0.587685 | + | 0.339300i | ||||
\(263\) | 13.5376 | + | 7.81597i | 0.834767 | + | 0.481953i | 0.855482 | − | 0.517832i | \(-0.173261\pi\) |
−0.0207149 | + | 0.999785i | \(0.506594\pi\) | |||||||
\(264\) | −3.36048 | − | 1.94018i | −0.206823 | − | 0.119410i | ||||
\(265\) | −6.94986 | − | 1.65149i | −0.426926 | − | 0.101450i | ||||
\(266\) | −8.35166 | + | 14.4655i | −0.512073 | + | 0.886936i | ||||
\(267\) | 2.23530 | 0.136798 | ||||||||
\(268\) | 8.72817 | − | 5.03921i | 0.533158 | − | 0.307819i | ||||
\(269\) | −17.1683 | −1.04677 | −0.523384 | − | 0.852097i | \(-0.675330\pi\) | ||||
−0.523384 | + | 0.852097i | \(0.675330\pi\) | |||||||
\(270\) | −2.17549 | − | 0.516959i | −0.132396 | − | 0.0314611i | ||||
\(271\) | −4.20412 | − | 7.28174i | −0.255382 | − | 0.442334i | 0.709617 | − | 0.704587i | \(-0.248868\pi\) |
−0.964999 | + | 0.262253i | \(0.915535\pi\) | |||||||
\(272\) | −1.69434 | + | 2.93468i | −0.102734 | + | 0.177941i | ||||
\(273\) | 2.41347 | 0.146070 | ||||||||
\(274\) | −1.47457 | + | 0.851345i | −0.0890822 | + | 0.0514316i | ||||
\(275\) | −1.10521 | − | 19.3703i | −0.0666467 | − | 1.16807i | ||||
\(276\) | −5.73009 | + | 3.30827i | −0.344911 | + | 0.199134i | ||||
\(277\) | 14.0962 | − | 24.4154i | 0.846960 | − | 1.46698i | −0.0369475 | − | 0.999317i | \(-0.511763\pi\) |
0.883908 | − | 0.467661i | \(-0.154903\pi\) | |||||||
\(278\) | −8.79340 | + | 15.2306i | −0.527393 | + | 0.913472i | ||||
\(279\) | −5.30382 | + | 3.06216i | −0.317532 | + | 0.183327i | ||||
\(280\) | 2.03411 | + | 6.80904i | 0.121561 | + | 0.406918i | ||||
\(281\) | −18.0402 | + | 10.4155i | −1.07619 | + | 0.621339i | −0.929866 | − | 0.367898i | \(-0.880078\pi\) |
−0.146324 | + | 0.989237i | \(0.546744\pi\) | |||||||
\(282\) | 5.34620 | 0.318362 | ||||||||
\(283\) | 7.70394 | − | 13.3436i | 0.457952 | − | 0.793196i | −0.540901 | − | 0.841086i | \(-0.681917\pi\) |
0.998853 | + | 0.0478906i | \(0.0152499\pi\) | |||||||
\(284\) | −3.22083 | − | 5.57863i | −0.191121 | − | 0.331031i | ||||
\(285\) | −2.71703 | + | 11.4339i | −0.160943 | + | 0.677288i | ||||
\(286\) | 2.94680 | 0.174248 | ||||||||
\(287\) | −28.4683 | + | 16.4362i | −1.68043 | + | 0.970197i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 2.75844 | − | 4.77777i | 0.162261 | − | 0.281045i | ||||
\(290\) | −2.84356 | − | 0.675712i | −0.166980 | − | 0.0396792i | ||||
\(291\) | 4.13248 | + | 2.38589i | 0.242250 | + | 0.139863i | ||||
\(292\) | 5.06214 | + | 2.92263i | 0.296239 | + | 0.171034i | ||||
\(293\) | −10.7757 | − | 6.22135i | −0.629523 | − | 0.363455i | 0.151044 | − | 0.988527i | \(-0.451736\pi\) |
−0.780567 | + | 0.625072i | \(0.785070\pi\) | |||||||
\(294\) | 2.68480 | − | 1.55007i | 0.156581 | − | 0.0904019i | ||||
\(295\) | 13.4276 | + | 3.19078i | 0.781783 | + | 0.185774i | ||||
\(296\) | 6.05221 | + | 0.608935i | 0.351777 | + | 0.0353937i | ||||
\(297\) | 3.88035i | 0.225161i | ||||||||
\(298\) | 9.03844 | + | 15.6550i | 0.523583 | + | 0.906872i | ||||
\(299\) | 2.51235 | − | 4.35151i | 0.145293 | − | 0.251654i | ||||
\(300\) | 2.74260 | + | 4.18068i | 0.158344 | + | 0.241372i | ||||
\(301\) | −25.9223 | − | 14.9662i | −1.49414 | − | 0.862640i | ||||
\(302\) | 15.5051 | 0.892215 | ||||||||
\(303\) | −1.74602 | − | 1.00807i | −0.100306 | − | 0.0579118i | ||||
\(304\) | − | 5.25580i | − | 0.301441i | ||||||
\(305\) | 6.24837 | + | 20.9160i | 0.357780 | + | 1.19765i | ||||
\(306\) | 3.38867 | 0.193718 | ||||||||
\(307\) | − | 28.9874i | − | 1.65440i | −0.561910 | − | 0.827199i | \(-0.689933\pi\) | ||
0.561910 | − | 0.827199i | \(-0.310067\pi\) | |||||||
\(308\) | 10.6799 | − | 6.16602i | 0.608541 | − | 0.351341i | ||||
\(309\) | 6.98722 | + | 4.03407i | 0.397489 | + | 0.229490i | ||||
\(310\) | 13.3234 | + | 3.16603i | 0.756719 | + | 0.179818i | ||||
\(311\) | −0.445283 | + | 0.257084i | −0.0252497 | + | 0.0145779i | −0.512572 | − | 0.858644i | \(-0.671307\pi\) |
0.487322 | + | 0.873222i | \(0.337974\pi\) | |||||||
\(312\) | −0.657673 | + | 0.379707i | −0.0372334 | + | 0.0214967i | ||||
\(313\) | 11.2521 | + | 19.4892i | 0.636006 | + | 1.10160i | 0.986301 | + | 0.164956i | \(0.0527481\pi\) |
−0.350295 | + | 0.936640i | \(0.613919\pi\) | |||||||
\(314\) | −4.26063 | − | 2.45988i | −0.240441 | − | 0.138819i | ||||
\(315\) | 4.87975 | − | 5.16611i | 0.274943 | − | 0.291077i | ||||
\(316\) | −7.39006 | + | 4.26665i | −0.415723 | + | 0.240018i | ||||
\(317\) | 6.11367 | − | 3.52973i | 0.343378 | − | 0.198249i | −0.318387 | − | 0.947961i | \(-0.603141\pi\) |
0.661765 | + | 0.749712i | \(0.269808\pi\) | |||||||
\(318\) | −1.59731 | − | 2.76662i | −0.0895726 | − | 0.155144i | ||||
\(319\) | 5.07197i | 0.283976i | ||||||||
\(320\) | −1.62555 | − | 1.53544i | −0.0908710 | − | 0.0858339i | ||||
\(321\) | −2.56417 | − | 4.44127i | −0.143118 | − | 0.247887i | ||||
\(322\) | − | 21.0278i | − | 1.17183i | ||||||
\(323\) | − | 17.8102i | − | 0.990986i | ||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −3.39117 | − | 1.70813i | −0.188108 | − | 0.0947503i | ||||
\(326\) | 3.02056 | − | 5.23176i | 0.167293 | − | 0.289760i | ||||
\(327\) | 4.95903 | 0.274235 | ||||||||
\(328\) | 5.17175 | − | 8.95773i | 0.285562 | − | 0.494608i | ||||
\(329\) | −8.49531 | + | 14.7143i | −0.468361 | + | 0.811226i | ||||
\(330\) | 5.95806 | − | 6.30770i | 0.327981 | − | 0.347228i | ||||
\(331\) | 11.4620 | − | 6.61756i | 0.630006 | − | 0.363734i | −0.150748 | − | 0.988572i | \(-0.548168\pi\) |
0.780754 | + | 0.624838i | \(0.214835\pi\) | |||||||
\(332\) | 6.99018i | 0.383636i | ||||||||
\(333\) | −2.49875 | − | 5.54583i | −0.136931 | − | 0.303910i | ||||
\(334\) | 19.0693 | 1.04343 | ||||||||
\(335\) | 6.45065 | + | 21.5931i | 0.352437 | + | 1.17976i | ||||
\(336\) | −1.58904 | + | 2.75229i | −0.0866890 | + | 0.150150i | ||||
\(337\) | 8.19202 | + | 4.72967i | 0.446248 | + | 0.257641i | 0.706244 | − | 0.707968i | \(-0.250388\pi\) |
−0.259996 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(338\) | −6.21164 | + | 10.7589i | −0.337869 | + | 0.585206i | ||||
\(339\) | − | 11.0102i | − | 0.597989i | ||||||
\(340\) | −5.50846 | − | 5.20312i | −0.298738 | − | 0.282179i | ||||
\(341\) | − | 23.7645i | − | 1.28692i | ||||||
\(342\) | −4.55166 | + | 2.62790i | −0.246125 | + | 0.142101i | ||||
\(343\) | − | 12.3940i | − | 0.669215i | ||||||
\(344\) | 9.41844 | 0.507808 | ||||||||
\(345\) | −4.23488 | − | 14.1760i | −0.227998 | − | 0.763209i | ||||
\(346\) | −17.6459 | − | 10.1879i | −0.948652 | − | 0.547704i | ||||
\(347\) | 6.97276 | 0.374317 | 0.187159 | − | 0.982330i | \(-0.440072\pi\) | ||||
0.187159 | + | 0.982330i | \(0.440072\pi\) | |||||||
\(348\) | −0.653545 | − | 1.13197i | −0.0350337 | − | 0.0606802i | ||||
\(349\) | −4.99936 | − | 8.65914i | −0.267609 | − | 0.463513i | 0.700635 | − | 0.713520i | \(-0.252900\pi\) |
−0.968244 | + | 0.250007i | \(0.919567\pi\) | |||||||
\(350\) | −15.8646 | + | 0.905186i | −0.847996 | + | 0.0483842i | ||||
\(351\) | 0.657673 | + | 0.379707i | 0.0351040 | + | 0.0202673i | ||||
\(352\) | −1.94018 | + | 3.36048i | −0.103412 | + | 0.179114i | ||||
\(353\) | −0.898282 | − | 1.55587i | −0.0478107 | − | 0.0828106i | 0.841130 | − | 0.540834i | \(-0.181891\pi\) |
−0.888940 | + | 0.458023i | \(0.848558\pi\) | |||||||
\(354\) | 3.08610 | + | 5.34529i | 0.164025 | + | 0.284099i | ||||
\(355\) | 13.8013 | − | 4.12295i | 0.732497 | − | 0.218823i | ||||
\(356\) | − | 2.23530i | − | 0.118470i | ||||||
\(357\) | −5.38472 | + | 9.32662i | −0.284990 | + | 0.493617i | ||||
\(358\) | 1.61515 | − | 0.932508i | 0.0853634 | − | 0.0492846i | ||||
\(359\) | 36.2514 | 1.91327 | 0.956637 | − | 0.291283i | \(-0.0940822\pi\) | ||||
0.956637 | + | 0.291283i | \(0.0940822\pi\) | |||||||
\(360\) | −0.516959 | + | 2.17549i | −0.0272461 | + | 0.114658i | ||||
\(361\) | 4.31172 | + | 7.46812i | 0.226933 | + | 0.393059i | ||||
\(362\) | 12.1776 | 0.640038 | ||||||||
\(363\) | −3.51357 | − | 2.02856i | −0.184415 | − | 0.106472i | ||||
\(364\) | − | 2.41347i | − | 0.126500i | ||||||
\(365\) | −8.97506 | + | 9.50174i | −0.469776 | + | 0.497344i | ||||
\(366\) | −4.88119 | + | 8.45447i | −0.255144 | + | 0.441922i | ||||
\(367\) | −24.0265 | − | 13.8717i | −1.25417 | − | 0.724096i | −0.282236 | − | 0.959345i | \(-0.591076\pi\) |
−0.971935 | + | 0.235249i | \(0.924409\pi\) | |||||||
\(368\) | 3.30827 | + | 5.73009i | 0.172455 | + | 0.298701i | ||||
\(369\) | −10.3435 | −0.538461 | ||||||||
\(370\) | −4.45347 | + | 12.8517i | −0.231525 | + | 0.668129i | ||||
\(371\) | 10.1527 | 0.527103 | ||||||||
\(372\) | 3.06216 | + | 5.30382i | 0.158766 | + | 0.274990i | ||||
\(373\) | 13.7243 | + | 7.92370i | 0.710615 | + | 0.410274i | 0.811289 | − | 0.584646i | \(-0.198767\pi\) |
−0.100674 | + | 0.994919i | \(0.532100\pi\) | |||||||
\(374\) | −6.57462 | + | 11.3876i | −0.339966 | + | 0.588838i | ||||
\(375\) | −10.5128 | + | 3.80526i | −0.542881 | + | 0.196503i | ||||
\(376\) | − | 5.34620i | − | 0.275709i | ||||||
\(377\) | 0.859638 | + | 0.496312i | 0.0442736 | + | 0.0255614i | ||||
\(378\) | 3.17807 | 0.163462 | ||||||||
\(379\) | 12.5851 | + | 21.7980i | 0.646453 | + | 1.11969i | 0.983964 | + | 0.178367i | \(0.0570816\pi\) |
−0.337511 | + | 0.941322i | \(0.609585\pi\) | |||||||
\(380\) | 11.4339 | + | 2.71703i | 0.586549 | + | 0.139381i | ||||
\(381\) | −15.0799 | −0.772568 | ||||||||
\(382\) | −18.9820 | + | 10.9593i | −0.971205 | + | 0.560726i | ||||
\(383\) | −7.99822 | + | 13.8533i | −0.408690 | + | 0.707872i | −0.994743 | − | 0.102401i | \(-0.967348\pi\) |
0.586053 | + | 0.810273i | \(0.300681\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 7.89306 | + | 26.4215i | 0.402267 | + | 1.34656i | ||||
\(386\) | 3.00544 | + | 5.20557i | 0.152973 | + | 0.264957i | ||||
\(387\) | −4.70922 | − | 8.15661i | −0.239383 | − | 0.414624i | ||||
\(388\) | 2.38589 | − | 4.13248i | 0.121125 | − | 0.209795i | ||||
\(389\) | 5.81063 | + | 3.35477i | 0.294611 | + | 0.170093i | 0.640019 | − | 0.768359i | \(-0.278926\pi\) |
−0.345409 | + | 0.938452i | \(0.612260\pi\) | |||||||
\(390\) | −0.486060 | − | 1.62705i | −0.0246126 | − | 0.0823890i | ||||
\(391\) | 11.2106 | + | 19.4174i | 0.566946 | + | 0.981980i | ||||
\(392\) | −1.55007 | − | 2.68480i | −0.0782903 | − | 0.135603i | ||||
\(393\) | −10.9841 | −0.554074 | ||||||||
\(394\) | −16.0895 | − | 9.28928i | −0.810578 | − | 0.467987i | ||||
\(395\) | −5.46170 | − | 18.2827i | −0.274808 | − | 0.919901i | ||||
\(396\) | 3.88035 | 0.194995 | ||||||||
\(397\) | 19.4407i | 0.975703i | 0.872927 | + | 0.487851i | \(0.162219\pi\) | ||||
−0.872927 | + | 0.487851i | \(0.837781\pi\) | |||||||
\(398\) | −1.76774 | + | 1.02060i | −0.0886087 | + | 0.0511583i | ||||
\(399\) | − | 16.7033i | − | 0.836212i | ||||||
\(400\) | 4.18068 | − | 2.74260i | 0.209034 | − | 0.137130i | ||||
\(401\) | 0.994109i | 0.0496434i | 0.999692 | + | 0.0248217i | \(0.00790181\pi\) | ||||
−0.999692 | + | 0.0248217i | \(0.992098\pi\) | |||||||
\(402\) | −5.03921 | + | 8.72817i | −0.251333 | + | 0.435322i | ||||
\(403\) | −4.02780 | − | 2.32545i | −0.200639 | − | 0.115839i | ||||
\(404\) | −1.00807 | + | 1.74602i | −0.0501531 | + | 0.0868677i | ||||
\(405\) | 2.14251 | − | 0.640045i | 0.106462 | − | 0.0318041i | ||||
\(406\) | 4.15403 | 0.206161 | ||||||||
\(407\) | 23.4847 | + | 2.36288i | 1.16409 | + | 0.117124i | ||||
\(408\) | − | 3.38867i | − | 0.167764i | ||||||
\(409\) | −26.9360 | + | 15.5515i | −1.33190 | + | 0.768973i | −0.985591 | − | 0.169148i | \(-0.945898\pi\) |
−0.346309 | + | 0.938120i | \(0.612565\pi\) | |||||||
\(410\) | 16.8139 | + | 15.8819i | 0.830377 | + | 0.784349i | ||||
\(411\) | 0.851345 | − | 1.47457i | 0.0419938 | − | 0.0727353i | ||||
\(412\) | 4.03407 | − | 6.98722i | 0.198745 | − | 0.344236i | ||||
\(413\) | −19.6157 | −0.965226 | ||||||||
\(414\) | 3.30827 | − | 5.73009i | 0.162592 | − | 0.281618i | ||||
\(415\) | −15.2071 | − | 3.61364i | −0.746486 | − | 0.177386i | ||||
\(416\) | 0.379707 | + | 0.657673i | 0.0186167 | + | 0.0322451i | ||||
\(417\) | − | 17.5868i | − | 0.861229i | ||||||
\(418\) | − | 20.3944i | − | 0.997520i | ||||||
\(419\) | 19.2268 | + | 33.3019i | 0.939293 | + | 1.62690i | 0.766794 | + | 0.641893i | \(0.221851\pi\) |
0.172498 | + | 0.985010i | \(0.444816\pi\) | |||||||
\(420\) | −5.16611 | − | 4.87975i | −0.252080 | − | 0.238107i | ||||
\(421\) | 9.18954i | 0.447871i | 0.974604 | + | 0.223935i | \(0.0718905\pi\) | ||||
−0.974604 | + | 0.223935i | \(0.928110\pi\) | |||||||
\(422\) | 6.65761 | + | 11.5313i | 0.324088 | + | 0.561336i | ||||
\(423\) | −4.62995 | + | 2.67310i | −0.225116 | + | 0.129971i | ||||
\(424\) | −2.76662 | + | 1.59731i | −0.134359 | + | 0.0775722i | ||||
\(425\) | 14.1670 | − | 9.29379i | 0.687199 | − | 0.450815i | ||||
\(426\) | 5.57863 | + | 3.22083i | 0.270286 | + | 0.156050i | ||||
\(427\) | −15.5128 | − | 26.8689i | −0.750716 | − | 1.30028i | ||||
\(428\) | −4.44127 | + | 2.56417i | −0.214677 | + | 0.123944i | ||||
\(429\) | −2.55200 | + | 1.47340i | −0.123212 | + | 0.0711363i | ||||
\(430\) | −4.86895 | + | 20.4897i | −0.234801 | + | 0.988102i | ||||
\(431\) | −9.79127 | − | 5.65299i | −0.471629 | − | 0.272295i | 0.245293 | − | 0.969449i | \(-0.421116\pi\) |
−0.716921 | + | 0.697154i | \(0.754449\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 19.1591i | 0.920727i | 0.887731 | + | 0.460363i | \(0.152281\pi\) | ||||
−0.887731 | + | 0.460363i | \(0.847719\pi\) | |||||||
\(434\) | −19.4635 | −0.934280 | ||||||||
\(435\) | 2.80045 | − | 0.836597i | 0.134271 | − | 0.0401117i | ||||
\(436\) | − | 4.95903i | − | 0.237494i | ||||||
\(437\) | −30.1162 | − | 17.3876i | −1.44065 | − | 0.831761i | ||||
\(438\) | −5.84525 | −0.279297 | ||||||||
\(439\) | 28.6432 | + | 16.5371i | 1.36706 | + | 0.789274i | 0.990552 | − | 0.137138i | \(-0.0437903\pi\) |
0.376511 | + | 0.926412i | \(0.377124\pi\) | |||||||
\(440\) | −6.30770 | − | 5.95806i | −0.300708 | − | 0.284039i | ||||
\(441\) | −1.55007 | + | 2.68480i | −0.0738128 | + | 0.127848i | ||||
\(442\) | 1.28670 | + | 2.22864i | 0.0612023 | + | 0.106005i | ||||
\(443\) | 0.475614i | 0.0225971i | 0.999936 | + | 0.0112985i | \(0.00359651\pi\) | ||||
−0.999936 | + | 0.0112985i | \(0.996403\pi\) | |||||||
\(444\) | −5.54583 | + | 2.49875i | −0.263194 | + | 0.118585i | ||||
\(445\) | 4.86286 | + | 1.15556i | 0.230522 | + | 0.0547786i | ||||
\(446\) | −12.8962 | + | 7.44563i | −0.610654 | + | 0.352561i | ||||
\(447\) | −15.6550 | − | 9.03844i | −0.740458 | − | 0.427503i | ||||
\(448\) | 2.75229 | + | 1.58904i | 0.130034 | + | 0.0750749i | ||||
\(449\) | −33.9306 | − | 19.5898i | −1.60128 | − | 0.924502i | −0.991231 | − | 0.132141i | \(-0.957815\pi\) |
−0.610053 | − | 0.792360i | \(-0.708852\pi\) | |||||||
\(450\) | −4.46551 | − | 2.24928i | −0.210506 | − | 0.106032i | ||||
\(451\) | 20.0682 | − | 34.7591i | 0.944974 | − | 1.63674i | ||||
\(452\) | −11.0102 | −0.517874 | ||||||||
\(453\) | −13.4278 | + | 7.75253i | −0.630892 | + | 0.364245i | ||||
\(454\) | 1.41610 | 0.0664611 | ||||||||
\(455\) | 5.25049 | + | 1.24767i | 0.246147 | + | 0.0584915i | ||||
\(456\) | 2.62790 | + | 4.55166i | 0.123063 | + | 0.213151i | ||||
\(457\) | −6.27814 | + | 10.8741i | −0.293679 | + | 0.508667i | −0.974677 | − | 0.223618i | \(-0.928213\pi\) |
0.680998 | + | 0.732286i | \(0.261546\pi\) | |||||||
\(458\) | −27.8212 | −1.30000 | ||||||||
\(459\) | −2.93468 | + | 1.69434i | −0.136979 | + | 0.0790849i | ||||
\(460\) | −14.1760 | + | 4.23488i | −0.660958 | + | 0.197452i | ||||
\(461\) | −4.06075 | + | 2.34448i | −0.189128 | + | 0.109193i | −0.591574 | − | 0.806250i | \(-0.701493\pi\) |
0.402446 | + | 0.915444i | \(0.368160\pi\) | |||||||
\(462\) | −6.16602 | + | 10.6799i | −0.286869 | + | 0.496872i | ||||
\(463\) | −6.13895 | + | 10.6330i | −0.285301 | + | 0.494156i | −0.972682 | − | 0.232141i | \(-0.925427\pi\) |
0.687381 | + | 0.726297i | \(0.258760\pi\) | |||||||
\(464\) | −1.13197 | + | 0.653545i | −0.0525506 | + | 0.0303401i | ||||
\(465\) | −13.1214 | + | 3.91985i | −0.608491 | + | 0.181778i | ||||
\(466\) | 18.3097 | − | 10.5711i | 0.848182 | − | 0.489698i | ||||
\(467\) | 12.6856 | 0.587021 | 0.293511 | − | 0.955956i | \(-0.405176\pi\) | ||||
0.293511 | + | 0.955956i | \(0.405176\pi\) | |||||||
\(468\) | 0.379707 | − | 0.657673i | 0.0175520 | − | 0.0304009i | ||||
\(469\) | −16.0150 | − | 27.7388i | −0.739503 | − | 1.28086i | ||||
\(470\) | 11.6306 | + | 2.76377i | 0.536480 | + | 0.127483i | ||||
\(471\) | 4.91975 | 0.226690 | ||||||||
\(472\) | 5.34529 | − | 3.08610i | 0.246037 | − | 0.142049i | ||||
\(473\) | 36.5468 | 1.68043 | ||||||||
\(474\) | 4.26665 | − | 7.39006i | 0.195974 | − | 0.339436i | ||||
\(475\) | −11.8218 | + | 23.4698i | −0.542419 | + | 1.07687i | ||||
\(476\) | 9.32662 | + | 5.38472i | 0.427485 | + | 0.246808i | ||||
\(477\) | 2.76662 | + | 1.59731i | 0.126675 | + | 0.0731357i | ||||
\(478\) | −5.13952 | − | 2.96731i | −0.235076 | − | 0.135721i | ||||
\(479\) | −2.51613 | + | 1.45269i | −0.114965 | + | 0.0663750i | −0.556380 | − | 0.830928i | \(-0.687810\pi\) |
0.441415 | + | 0.897303i | \(0.354477\pi\) | |||||||
\(480\) | 2.17549 | + | 0.516959i | 0.0992970 | + | 0.0235958i | ||||
\(481\) | 2.69855 | − | 3.74915i | 0.123043 | − | 0.170947i | ||||
\(482\) | − | 24.9489i | − | 1.13639i | ||||||
\(483\) | 10.5139 | + | 18.2106i | 0.478399 | + | 0.828612i | ||||
\(484\) | −2.02856 | + | 3.51357i | −0.0922073 | + | 0.159708i | ||||
\(485\) | 7.75676 | + | 7.32680i | 0.352216 | + | 0.332693i | ||||
\(486\) | 0.866025 | + | 0.500000i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | 0.439955 | 0.0199363 | 0.00996814 | − | 0.999950i | \(-0.496827\pi\) | ||||
0.00996814 | + | 0.999950i | \(0.496827\pi\) | |||||||
\(488\) | 8.45447 | + | 4.88119i | 0.382716 | + | 0.220961i | ||||
\(489\) | 6.04111i | 0.273189i | ||||||||
\(490\) | 6.64207 | − | 1.98423i | 0.300058 | − | 0.0896383i | ||||
\(491\) | 38.7496 | 1.74875 | 0.874373 | − | 0.485254i | \(-0.161273\pi\) | ||||
0.874373 | + | 0.485254i | \(0.161273\pi\) | |||||||
\(492\) | 10.3435i | 0.466321i | ||||||||
\(493\) | −3.83589 | + | 2.21465i | −0.172760 | + | 0.0997429i | ||||
\(494\) | −3.45660 | − | 1.99567i | −0.155520 | − | 0.0897893i | ||||
\(495\) | −2.00598 | + | 8.44166i | −0.0901622 | + | 0.379424i | ||||
\(496\) | 5.30382 | − | 3.06216i | 0.238149 | − | 0.137495i | ||||
\(497\) | −17.7293 | + | 10.2360i | −0.795268 | + | 0.459148i | ||||
\(498\) | −3.49509 | − | 6.05368i | −0.156619 | − | 0.271272i | ||||
\(499\) | −32.7624 | − | 18.9154i | −1.46665 | − | 0.846768i | −0.467342 | − | 0.884077i | \(-0.654788\pi\) |
−0.999304 | + | 0.0373082i | \(0.988122\pi\) | |||||||
\(500\) | 3.80526 | + | 10.5128i | 0.170177 | + | 0.470149i | ||||
\(501\) | −16.5145 | + | 9.53467i | −0.737815 | + | 0.425978i | ||||
\(502\) | 4.40080 | − | 2.54080i | 0.196417 | − | 0.113401i | ||||
\(503\) | −13.0136 | − | 22.5402i | −0.580246 | − | 1.00502i | −0.995450 | − | 0.0952875i | \(-0.969623\pi\) |
0.415203 | − | 0.909729i | \(-0.363710\pi\) | |||||||
\(504\) | − | 3.17807i | − | 0.141563i | ||||||
\(505\) | −3.27732 | − | 3.09566i | −0.145839 | − | 0.137755i | ||||
\(506\) | 12.8372 | + | 22.2347i | 0.570685 | + | 0.988455i | ||||
\(507\) | − | 12.4233i | − | 0.551738i | ||||||
\(508\) | 15.0799i | 0.669063i | ||||||||
\(509\) | −18.3204 | − | 31.7319i | −0.812038 | − | 1.40649i | −0.911435 | − | 0.411444i | \(-0.865025\pi\) |
0.0993971 | − | 0.995048i | \(-0.468309\pi\) | |||||||
\(510\) | 7.37202 | + | 1.75181i | 0.326439 | + | 0.0775712i | ||||
\(511\) | 9.28831 | − | 16.0878i | 0.410891 | − | 0.711684i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.62790 | − | 4.55166i | 0.116025 | − | 0.200961i | ||||
\(514\) | 5.08288 | − | 8.80380i | 0.224196 | − | 0.388319i | ||||
\(515\) | 13.1152 | + | 12.3882i | 0.577924 | + | 0.545889i | ||||
\(516\) | −8.15661 | + | 4.70922i | −0.359075 | + | 0.207312i | ||||
\(517\) | − | 20.7451i | − | 0.912370i | ||||||
\(518\) | 1.93524 | − | 19.2343i | 0.0850296 | − | 0.845109i | ||||
\(519\) | 20.3758 | 0.894397 | ||||||||
\(520\) | −1.62705 | + | 0.486060i | −0.0713510 | + | 0.0213151i | ||||
\(521\) | −6.87938 | + | 11.9154i | −0.301391 | + | 0.522025i | −0.976451 | − | 0.215738i | \(-0.930784\pi\) |
0.675060 | + | 0.737763i | \(0.264118\pi\) | |||||||
\(522\) | 1.13197 | + | 0.653545i | 0.0495451 | + | 0.0286049i | ||||
\(523\) | −0.135209 | + | 0.234189i | −0.00591228 | + | 0.0102404i | −0.868966 | − | 0.494871i | \(-0.835215\pi\) |
0.863054 | + | 0.505111i | \(0.168549\pi\) | |||||||
\(524\) | 10.9841i | 0.479843i | ||||||||
\(525\) | 13.2865 | − | 8.71619i | 0.579871 | − | 0.380406i | ||||
\(526\) | 15.6319i | 0.681585i | ||||||||
\(527\) | 17.9729 | − | 10.3767i | 0.782913 | − | 0.452015i | ||||
\(528\) | − | 3.88035i | − | 0.168871i | ||||||
\(529\) | 20.7785 | 0.903414 | ||||||||
\(530\) | −2.04470 | − | 6.84449i | −0.0888160 | − | 0.297306i | ||||
\(531\) | −5.34529 | − | 3.08610i | −0.231966 | − | 0.133925i | ||||
\(532\) | −16.7033 | −0.724180 | ||||||||
\(533\) | −3.92750 | − | 6.80263i | −0.170119 | − | 0.294655i | ||||
\(534\) | 1.11765 | + | 1.93582i | 0.0483654 | + | 0.0837713i | ||||
\(535\) | −3.28237 | − | 10.9875i | −0.141909 | − | 0.475031i | ||||
\(536\) | 8.72817 | + | 5.03921i | 0.377000 | + | 0.217661i | ||||
\(537\) | −0.932508 | + | 1.61515i | −0.0402407 | + | 0.0696989i | ||||
\(538\) | −8.58413 | − | 14.8681i | −0.370088 | − | 0.641011i | ||||
\(539\) | −6.01481 | − | 10.4180i | −0.259076 | − | 0.448733i | ||||
\(540\) | −0.640045 | − | 2.14251i | −0.0275432 | − | 0.0921989i | ||||
\(541\) | − | 33.4724i | − | 1.43909i | −0.694446 | − | 0.719545i | \(-0.744350\pi\) | ||
0.694446 | − | 0.719545i | \(-0.255650\pi\) | |||||||
\(542\) | 4.20412 | − | 7.28174i | 0.180582 | − | 0.312778i | ||||
\(543\) | −10.5461 | + | 6.08878i | −0.452575 | + | 0.261295i | ||||
\(544\) | −3.38867 | −0.145288 | ||||||||
\(545\) | 10.7883 | + | 2.56361i | 0.462120 | + | 0.109813i | ||||
\(546\) | 1.20674 | + | 2.09013i | 0.0516436 | + | 0.0894493i | ||||
\(547\) | −41.8398 | −1.78894 | −0.894471 | − | 0.447126i | \(-0.852448\pi\) | ||||
−0.894471 | + | 0.447126i | \(0.852448\pi\) | |||||||
\(548\) | −1.47457 | − | 0.851345i | −0.0629906 | − | 0.0363677i | ||||
\(549\) | − | 9.76238i | − | 0.416648i | ||||||
\(550\) | 16.2225 | − | 10.6423i | 0.691731 | − | 0.453788i | ||||
\(551\) | 3.43490 | − | 5.94943i | 0.146332 | − | 0.253454i | ||||
\(552\) | −5.73009 | − | 3.30827i | −0.243889 | − | 0.140809i | ||||
\(553\) | 13.5597 | + | 23.4861i | 0.576618 | + | 0.998732i | ||||
\(554\) | 28.1925 | 1.19778 | ||||||||
\(555\) | −2.56904 | − | 13.3566i | −0.109049 | − | 0.566958i | ||||
\(556\) | −17.5868 | −0.745846 | ||||||||
\(557\) | −18.9097 | − | 32.7526i | −0.801230 | − | 1.38777i | −0.918807 | − | 0.394708i | \(-0.870846\pi\) |
0.117576 | − | 0.993064i | \(-0.462488\pi\) | |||||||
\(558\) | −5.30382 | − | 3.06216i | −0.224529 | − | 0.129632i | ||||
\(559\) | 3.57625 | − | 6.19425i | 0.151259 | − | 0.261989i | ||||
\(560\) | −4.87975 | + | 5.16611i | −0.206207 | + | 0.218308i | ||||
\(561\) | − | 13.1492i | − | 0.555162i | ||||||
\(562\) | −18.0402 | − | 10.4155i | −0.760981 | − | 0.439353i | ||||
\(563\) | −38.4439 | −1.62022 | −0.810109 | − | 0.586280i | \(-0.800592\pi\) | ||||
−0.810109 | + | 0.586280i | \(0.800592\pi\) | |||||||
\(564\) | 2.67310 | + | 4.62995i | 0.112558 | + | 0.194956i | ||||
\(565\) | 5.69180 | − | 23.9525i | 0.239456 | − | 1.00769i | ||||
\(566\) | 15.4079 | 0.647642 | ||||||||
\(567\) | −2.75229 | + | 1.58904i | −0.115585 | + | 0.0667332i | ||||
\(568\) | 3.22083 | − | 5.57863i | 0.135143 | − | 0.234074i | ||||
\(569\) | 42.4265i | 1.77861i | 0.457315 | + | 0.889305i | \(0.348811\pi\) | ||||
−0.457315 | + | 0.889305i | \(0.651189\pi\) | |||||||
\(570\) | −11.2606 | + | 3.36395i | −0.471655 | + | 0.140900i | ||||
\(571\) | −2.51703 | − | 4.35962i | −0.105334 | − | 0.182444i | 0.808540 | − | 0.588441i | \(-0.200258\pi\) |
−0.913875 | + | 0.405996i | \(0.866925\pi\) | |||||||
\(572\) | 1.47340 | + | 2.55200i | 0.0616059 | + | 0.106704i | ||||
\(573\) | 10.9593 | − | 18.9820i | 0.457831 | − | 0.792986i | ||||
\(574\) | −28.4683 | − | 16.4362i | −1.18824 | − | 0.686033i | ||||
\(575\) | −1.88454 | − | 33.0289i | −0.0785906 | − | 1.37740i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −4.83557 | − | 8.37546i | −0.201308 | − | 0.348675i | 0.747642 | − | 0.664102i | \(-0.231186\pi\) |
−0.948950 | + | 0.315427i | \(0.897852\pi\) | |||||||
\(578\) | 5.51689 | 0.229472 | ||||||||
\(579\) | −5.20557 | − | 3.00544i | −0.216336 | − | 0.124902i | ||||
\(580\) | −0.836597 | − | 2.80045i | −0.0347378 | − | 0.116282i | ||||
\(581\) | 22.2153 | 0.921646 | ||||||||
\(582\) | 4.77178i | 0.197797i | ||||||||
\(583\) | −10.7355 | + | 6.19812i | −0.444617 | + | 0.256700i | ||||
\(584\) | 5.84525i | 0.241878i | ||||||||
\(585\) | 1.23447 | + | 1.16604i | 0.0510389 | + | 0.0482098i | ||||
\(586\) | − | 12.4427i | − | 0.514003i | ||||||
\(587\) | −11.6533 | + | 20.1840i | −0.480981 | + | 0.833084i | −0.999762 | − | 0.0218233i | \(-0.993053\pi\) |
0.518780 | + | 0.854908i | \(0.326386\pi\) | |||||||
\(588\) | 2.68480 | + | 1.55007i | 0.110719 | + | 0.0639238i | ||||
\(589\) | −16.0941 | + | 27.8758i | −0.663147 | + | 1.14860i | ||||
\(590\) | 3.95049 | + | 13.2240i | 0.162639 | + | 0.544424i | ||||
\(591\) | 18.5786 | 0.764220 | ||||||||
\(592\) | 2.49875 | + | 5.54583i | 0.102698 | + | 0.227932i | ||||
\(593\) | 28.4421i | 1.16798i | 0.811762 | + | 0.583989i | \(0.198509\pi\) | ||||
−0.811762 | + | 0.583989i | \(0.801491\pi\) | |||||||
\(594\) | −3.36048 | + | 1.94018i | −0.137882 | + | 0.0796064i | ||||
\(595\) | −16.5359 | + | 17.5063i | −0.677905 | + | 0.717687i | ||||
\(596\) | −9.03844 | + | 15.6550i | −0.370229 | + | 0.641255i | ||||
\(597\) | 1.02060 | − | 1.76774i | 0.0417706 | − | 0.0723487i | ||||
\(598\) | 5.02469 | 0.205475 | ||||||||
\(599\) | 13.7454 | − | 23.8078i | 0.561623 | − | 0.972759i | −0.435733 | − | 0.900076i | \(-0.643511\pi\) |
0.997355 | − | 0.0726826i | \(-0.0231560\pi\) | |||||||
\(600\) | −2.24928 | + | 4.46551i | −0.0918264 | + | 0.182304i | ||||
\(601\) | −22.0281 | − | 38.1539i | −0.898547 | − | 1.55633i | −0.829353 | − | 0.558725i | \(-0.811291\pi\) |
−0.0691938 | − | 0.997603i | \(-0.522043\pi\) | |||||||
\(602\) | − | 29.9325i | − | 1.21996i | ||||||
\(603\) | − | 10.0784i | − | 0.410425i | ||||||
\(604\) | 7.75253 | + | 13.4278i | 0.315446 | + | 0.546368i | ||||
\(605\) | −6.59505 | − | 6.22949i | −0.268127 | − | 0.253265i | ||||
\(606\) | − | 2.01613i | − | 0.0818997i | ||||||
\(607\) | 22.3880 | + | 38.7772i | 0.908702 | + | 1.57392i | 0.815869 | + | 0.578236i | \(0.196259\pi\) |
0.0928326 | + | 0.995682i | \(0.470408\pi\) | |||||||
\(608\) | 4.55166 | − | 2.62790i | 0.184594 | − | 0.106575i | ||||
\(609\) | −3.59749 | + | 2.07701i | −0.145778 | + | 0.0841648i | ||||
\(610\) | −14.9896 | + | 15.8692i | −0.606911 | + | 0.642527i | ||||
\(611\) | −3.51605 | − | 2.02999i | −0.142244 | − | 0.0821247i | ||||
\(612\) | 1.69434 | + | 2.93468i | 0.0684895 | + | 0.118627i | ||||
\(613\) | −21.4944 | + | 12.4098i | −0.868150 | + | 0.501227i | −0.866733 | − | 0.498772i | \(-0.833784\pi\) |
−0.00141717 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(614\) | 25.1038 | − | 14.4937i | 1.01311 | − | 0.584918i | ||||
\(615\) | −22.5022 | − | 5.34716i | −0.907374 | − | 0.215618i | ||||
\(616\) | 10.6799 | + | 6.16602i | 0.430304 | + | 0.248436i | ||||
\(617\) | −34.1390 | + | 19.7101i | −1.37438 | + | 0.793500i | −0.991476 | − | 0.130287i | \(-0.958410\pi\) |
−0.382906 | + | 0.923787i | \(0.625077\pi\) | |||||||
\(618\) | 8.06815i | 0.324549i | ||||||||
\(619\) | 9.70430 | 0.390049 | 0.195024 | − | 0.980798i | \(-0.437521\pi\) | ||||
0.195024 | + | 0.980798i | \(0.437521\pi\) | |||||||
\(620\) | 3.91985 | + | 13.1214i | 0.157425 | + | 0.526969i | ||||
\(621\) | 6.61653i | 0.265512i | ||||||||
\(622\) | −0.445283 | − | 0.257084i | −0.0178542 | − | 0.0103081i | ||||
\(623\) | −7.10393 | −0.284613 | ||||||||
\(624\) | −0.657673 | − | 0.379707i | −0.0263280 | − | 0.0152005i | ||||
\(625\) | −24.8378 | + | 2.84360i | −0.993510 | + | 0.113744i | ||||
\(626\) | −11.2521 | + | 19.4892i | −0.449724 | + | 0.778945i | ||||
\(627\) | 10.1972 | + | 17.6620i | 0.407236 | + | 0.705353i | ||||
\(628\) | − | 4.91975i | − | 0.196320i | ||||||
\(629\) | 8.46745 | + | 18.7930i | 0.337619 | + | 0.749327i | ||||
\(630\) | 6.91386 | + | 1.64293i | 0.275455 | + | 0.0654560i | ||||
\(631\) | −11.6902 | + | 6.74933i | −0.465379 | + | 0.268687i | −0.714303 | − | 0.699836i | \(-0.753256\pi\) |
0.248924 | + | 0.968523i | \(0.419923\pi\) | |||||||
\(632\) | −7.39006 | − | 4.26665i | −0.293961 | − | 0.169718i | ||||
\(633\) | −11.5313 | − | 6.65761i | −0.458329 | − | 0.264616i | ||||
\(634\) | 6.11367 | + | 3.52973i | 0.242805 | + | 0.140183i | ||||
\(635\) | −32.8062 | − | 7.79570i | −1.30187 | − | 0.309363i | ||||
\(636\) | 1.59731 | − | 2.76662i | 0.0633374 | − | 0.109704i | ||||
\(637\) | −2.35429 | −0.0932804 | ||||||||
\(638\) | −4.39245 | + | 2.53598i | −0.173899 | + | 0.100401i | ||||
\(639\) | −6.44165 | −0.254828 | ||||||||
\(640\) | 0.516959 | − | 2.17549i | 0.0204346 | − | 0.0859938i | ||||
\(641\) | 8.41425 | + | 14.5739i | 0.332343 | + | 0.575635i | 0.982971 | − | 0.183762i | \(-0.0588275\pi\) |
−0.650628 | + | 0.759397i | \(0.725494\pi\) | |||||||
\(642\) | 2.56417 | − | 4.44127i | 0.101200 | − | 0.175283i | ||||
\(643\) | 18.4589 | 0.727949 | 0.363975 | − | 0.931409i | \(-0.381419\pi\) | ||||
0.363975 | + | 0.931409i | \(0.381419\pi\) | |||||||
\(644\) | 18.2106 | − | 10.5139i | 0.717599 | − | 0.414306i | ||||
\(645\) | −6.02823 | − | 20.1791i | −0.237361 | − | 0.794551i | ||||
\(646\) | 15.4241 | − | 8.90510i | 0.606852 | − | 0.350366i | ||||
\(647\) | 2.42149 | − | 4.19414i | 0.0951985 | − | 0.164889i | −0.814493 | − | 0.580173i | \(-0.802985\pi\) |
0.909691 | + | 0.415285i | \(0.136318\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 20.7416 | − | 11.9752i | 0.814179 | − | 0.470066i | ||||
\(650\) | −0.216298 | − | 3.79091i | −0.00848392 | − | 0.148692i | ||||
\(651\) | 16.8559 | − | 9.73177i | 0.660636 | − | 0.381418i | ||||
\(652\) | 6.04111 | 0.236588 | ||||||||
\(653\) | 0.412819 | − | 0.715023i | 0.0161549 | − | 0.0279810i | −0.857835 | − | 0.513925i | \(-0.828191\pi\) |
0.873990 | + | 0.485944i | \(0.161524\pi\) | |||||||
\(654\) | 2.47951 | + | 4.29464i | 0.0969566 | + | 0.167934i | ||||
\(655\) | −23.8958 | − | 5.67833i | −0.933686 | − | 0.221871i | ||||
\(656\) | 10.3435 | 0.403845 | ||||||||
\(657\) | 5.06214 | − | 2.92263i | 0.197493 | − | 0.114022i | ||||
\(658\) | −16.9906 | −0.662363 | ||||||||
\(659\) | −12.4134 | + | 21.5006i | −0.483557 | + | 0.837546i | −0.999822 | − | 0.0188834i | \(-0.993989\pi\) |
0.516264 | + | 0.856429i | \(0.327322\pi\) | |||||||
\(660\) | 8.44166 | + | 2.00598i | 0.328591 | + | 0.0780827i | ||||
\(661\) | 14.5538 | + | 8.40263i | 0.566077 | + | 0.326825i | 0.755581 | − | 0.655055i | \(-0.227355\pi\) |
−0.189504 | + | 0.981880i | \(0.560688\pi\) | |||||||
\(662\) | 11.4620 | + | 6.61756i | 0.445482 | + | 0.257199i | ||||
\(663\) | −2.22864 | − | 1.28670i | −0.0865531 | − | 0.0499715i | ||||
\(664\) | −6.05368 | + | 3.49509i | −0.234928 | + | 0.135636i | ||||
\(665\) | 8.63493 | − | 36.3379i | 0.334848 | − | 1.40912i | ||||
\(666\) | 3.55346 | − | 4.93690i | 0.137694 | − | 0.191301i | ||||
\(667\) | 8.64841i | 0.334868i | ||||||||
\(668\) | 9.53467 | + | 16.5145i | 0.368907 | + | 0.638966i | ||||
\(669\) | 7.44563 | − | 12.8962i | 0.287865 | − | 0.498597i | ||||
\(670\) | −15.4749 | + | 16.3830i | −0.597846 | + | 0.632930i | ||||
\(671\) | 32.8063 | + | 18.9407i | 1.26647 | + | 0.731199i | ||||
\(672\) | −3.17807 | −0.122597 | ||||||||
\(673\) | 1.06009 | + | 0.612042i | 0.0408634 | + | 0.0235925i | 0.520293 | − | 0.853988i | \(-0.325823\pi\) |
−0.479429 | + | 0.877581i | \(0.659156\pi\) | |||||||
\(674\) | 9.45934i | 0.364360i | ||||||||
\(675\) | 4.99188 | − | 0.284822i | 0.192138 | − | 0.0109628i | ||||
\(676\) | −12.4233 | −0.477819 | ||||||||
\(677\) | − | 19.9522i | − | 0.766825i | −0.923577 | − | 0.383412i | \(-0.874749\pi\) | ||
0.923577 | − | 0.383412i | \(-0.125251\pi\) | |||||||
\(678\) | 9.53507 | − | 5.50508i | 0.366192 | − | 0.211421i | ||||
\(679\) | −13.1333 | − | 7.58253i | −0.504011 | − | 0.290991i | ||||
\(680\) | 1.75181 | − | 7.37202i | 0.0671787 | − | 0.282704i | ||||
\(681\) | −1.22638 | + | 0.708052i | −0.0469951 | + | 0.0271326i | ||||
\(682\) | 20.5807 | − | 11.8823i | 0.788075 | − | 0.454996i | ||||
\(683\) | −7.80416 | − | 13.5172i | −0.298618 | − | 0.517221i | 0.677202 | − | 0.735797i | \(-0.263192\pi\) |
−0.975820 | + | 0.218576i | \(0.929859\pi\) | |||||||
\(684\) | −4.55166 | − | 2.62790i | −0.174037 | − | 0.100480i | ||||
\(685\) | 2.61439 | − | 2.76781i | 0.0998905 | − | 0.105752i | ||||
\(686\) | 10.7336 | − | 6.19702i | 0.409809 | − | 0.236603i | ||||
\(687\) | 24.0938 | − | 13.9106i | 0.919237 | − | 0.530722i | ||||
\(688\) | 4.70922 | + | 8.15661i | 0.179537 | + | 0.310968i | ||||
\(689\) | 2.42604i | 0.0924248i | ||||||||
\(690\) | 10.1593 | − | 10.7555i | 0.386759 | − | 0.409455i | ||||
\(691\) | −19.8289 | − | 34.3447i | −0.754328 | − | 1.30654i | −0.945707 | − | 0.325019i | \(-0.894629\pi\) |
0.191379 | − | 0.981516i | \(-0.438704\pi\) | |||||||
\(692\) | − | 20.3758i | − | 0.774571i | ||||||
\(693\) | − | 12.3320i | − | 0.468455i | ||||||
\(694\) | 3.48638 | + | 6.03859i | 0.132341 | + | 0.229222i | ||||
\(695\) | 9.09165 | − | 38.2599i | 0.344866 | − | 1.45128i | ||||
\(696\) | 0.653545 | − | 1.13197i | 0.0247726 | − | 0.0429073i | ||||
\(697\) | 35.0507 | 1.32764 | ||||||||
\(698\) | 4.99936 | − | 8.65914i | 0.189228 | − | 0.327753i | ||||
\(699\) | −10.5711 | + | 18.3097i | −0.399837 | + | 0.692538i | ||||
\(700\) | −8.71619 | − | 13.2865i | −0.329441 | − | 0.502183i | ||||
\(701\) | 30.5819 | − | 17.6564i | 1.15506 | − | 0.666875i | 0.204945 | − | 0.978773i | \(-0.434298\pi\) |
0.950115 | + | 0.311899i | \(0.100965\pi\) | |||||||
\(702\) | 0.759415i | 0.0286623i | ||||||||
\(703\) | −25.9473 | − | 18.6763i | −0.978623 | − | 0.704389i | ||||
\(704\) | −3.88035 | −0.146246 | ||||||||
\(705\) | −11.4543 | + | 3.42181i | −0.431393 | + | 0.128873i | ||||
\(706\) | 0.898282 | − | 1.55587i | 0.0338073 | − | 0.0585559i | ||||
\(707\) | 5.54898 | + | 3.20370i | 0.208691 | + | 0.120488i | ||||
\(708\) | −3.08610 | + | 5.34529i | −0.115983 | + | 0.200888i | ||||
\(709\) | − | 11.4844i | − | 0.431305i | −0.976470 | − | 0.215652i | \(-0.930812\pi\) | ||
0.976470 | − | 0.215652i | \(-0.0691878\pi\) | |||||||
\(710\) | 10.4712 | + | 9.89080i | 0.392978 | + | 0.371195i | ||||
\(711\) | 8.53330i | 0.320024i | ||||||||
\(712\) | 1.93582 | − | 1.11765i | 0.0725481 | − | 0.0418856i | ||||
\(713\) | − | 40.5218i | − | 1.51755i | ||||||
\(714\) | −10.7694 | −0.403036 | ||||||||
\(715\) | −6.31354 | + | 1.88608i | −0.236113 | + | 0.0705355i | ||||
\(716\) | 1.61515 | + | 0.932508i | 0.0603610 | + | 0.0348494i | ||||
\(717\) | 5.93461 | 0.221632 | ||||||||
\(718\) | 18.1257 | + | 31.3946i | 0.676444 | + | 1.17164i | ||||
\(719\) | 6.73406 | + | 11.6637i | 0.251138 | + | 0.434984i | 0.963839 | − | 0.266484i | \(-0.0858619\pi\) |
−0.712701 | + | 0.701468i | \(0.752529\pi\) | |||||||
\(720\) | −2.14251 | + | 0.640045i | −0.0798466 | + | 0.0238531i | ||||
\(721\) | −22.2059 | − | 12.8206i | −0.826991 | − | 0.477463i | ||||
\(722\) | −4.31172 | + | 7.46812i | −0.160466 | + | 0.277935i | ||||
\(723\) | 12.4744 | + | 21.6064i | 0.463930 | + | 0.803550i | ||||
\(724\) | 6.08878 | + | 10.5461i | 0.226288 | + | 0.391942i | ||||
\(725\) | 6.52484 | − | 0.372289i | 0.242326 | − | 0.0138264i | ||||
\(726\) | − | 4.05712i | − | 0.150574i | ||||||
\(727\) | −8.17953 | + | 14.1674i | −0.303362 | + | 0.525439i | −0.976895 | − | 0.213718i | \(-0.931443\pi\) |
0.673533 | + | 0.739157i | \(0.264776\pi\) | |||||||
\(728\) | 2.09013 | − | 1.20674i | 0.0774654 | − | 0.0447247i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −12.7163 | − | 3.02175i | −0.470651 | − | 0.111840i | ||||
\(731\) | 15.9580 | + | 27.6401i | 0.590228 | + | 1.02231i | ||||
\(732\) | −9.76238 | −0.360828 | ||||||||
\(733\) | 33.0277 | + | 19.0685i | 1.21991 | + | 0.704313i | 0.964898 | − | 0.262626i | \(-0.0845886\pi\) |
0.255008 | + | 0.966939i | \(0.417922\pi\) | |||||||
\(734\) | − | 27.7434i | − | 1.02403i | ||||||
\(735\) | −4.76009 | + | 5.03943i | −0.175579 | + | 0.185882i | ||||
\(736\) | −3.30827 | + | 5.73009i | −0.121944 | + | 0.211214i | ||||
\(737\) | 33.8684 | + | 19.5539i | 1.24756 | + | 0.720278i | ||||
\(738\) | −5.17175 | − | 8.95773i | −0.190375 | − | 0.329738i | ||||
\(739\) | −36.2617 | −1.33391 | −0.666954 | − | 0.745099i | \(-0.732402\pi\) | ||||
−0.666954 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(740\) | −13.3566 | + | 2.56904i | −0.491000 | + | 0.0944396i | ||||
\(741\) | 3.99133 | 0.146625 | ||||||||
\(742\) | 5.07636 | + | 8.79251i | 0.186359 | + | 0.322783i | ||||
\(743\) | 5.97478 | + | 3.44954i | 0.219193 | + | 0.126551i | 0.605577 | − | 0.795787i | \(-0.292942\pi\) |
−0.386383 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(744\) | −3.06216 | + | 5.30382i | −0.112264 | + | 0.194448i | ||||
\(745\) | −29.3849 | − | 27.7560i | −1.07658 | − | 1.01690i | ||||
\(746\) | 15.8474i | 0.580215i | ||||||||
\(747\) | 6.05368 | + | 3.49509i | 0.221492 | + | 0.127879i | ||||
\(748\) | −13.1492 | −0.480784 | ||||||||
\(749\) | 8.14911 | + | 14.1147i | 0.297762 | + | 0.515739i | ||||
\(750\) | −8.55188 | − | 7.20176i | −0.312270 | − | 0.262971i | ||||
\(751\) | −27.9667 | −1.02052 | −0.510260 | − | 0.860020i | \(-0.670451\pi\) | ||||
−0.510260 | + | 0.860020i | \(0.670451\pi\) | |||||||
\(752\) | 4.62995 | − | 2.67310i | 0.168837 | − | 0.0974780i | ||||
\(753\) | −2.54080 | + | 4.40080i | −0.0925919 | + | 0.160374i | ||||
\(754\) | 0.992624i | 0.0361492i | ||||||||
\(755\) | −33.2197 | + | 9.92393i | −1.20899 | + | 0.361169i | ||||
\(756\) | 1.58904 | + | 2.75229i | 0.0577927 | + | 0.100100i | ||||
\(757\) | 22.6799 | + | 39.2828i | 0.824316 | + | 1.42776i | 0.902441 | + | 0.430814i | \(0.141773\pi\) |
−0.0781247 | + | 0.996944i | \(0.524893\pi\) | |||||||
\(758\) | −12.5851 | + | 21.7980i | −0.457111 | + | 0.791740i | ||||
\(759\) | −22.2347 | − | 12.8372i | −0.807070 | − | 0.465962i | ||||
\(760\) | 3.36395 | + | 11.2606i | 0.122023 | + | 0.408465i | ||||
\(761\) | 4.81085 | + | 8.33263i | 0.174393 | + | 0.302058i | 0.939951 | − | 0.341309i | \(-0.110870\pi\) |
−0.765558 | + | 0.643367i | \(0.777537\pi\) | |||||||
\(762\) | −7.53996 | − | 13.0596i | −0.273144 | − | 0.473099i | ||||
\(763\) | −15.7601 | −0.570555 | ||||||||
\(764\) | −18.9820 | − | 10.9593i | −0.686746 | − | 0.396493i | ||||
\(765\) | −7.26026 | + | 2.16890i | −0.262495 | + | 0.0784169i | ||||
\(766\) | −15.9964 | −0.577975 | ||||||||
\(767\) | − | 4.68726i | − | 0.169247i | ||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 31.0987i | 1.12145i | 0.828002 | + | 0.560725i | \(0.189477\pi\) | ||||
−0.828002 | + | 0.560725i | \(0.810523\pi\) | |||||||
\(770\) | −18.9351 | + | 20.0463i | −0.682375 | + | 0.722420i | ||||
\(771\) | 10.1658i | 0.366111i | ||||||||
\(772\) | −3.00544 | + | 5.20557i | −0.108168 | + | 0.187353i | ||||
\(773\) | 3.09863 | + | 1.78899i | 0.111450 | + | 0.0643456i | 0.554689 | − | 0.832058i | \(-0.312837\pi\) |
−0.443239 | + | 0.896404i | \(0.646171\pi\) | |||||||
\(774\) | 4.70922 | − | 8.15661i | 0.169269 | − | 0.293183i | ||||
\(775\) | −30.5719 | + | 1.74435i | −1.09818 | + | 0.0626587i | ||||
\(776\) | 4.77178 | 0.171297 | ||||||||
\(777\) | 7.94120 | + | 17.6251i | 0.284889 | + | 0.632295i | ||||
\(778\) | 6.70954i | 0.240548i | ||||||||
\(779\) | −47.0800 | + | 27.1817i | −1.68682 | + | 0.973884i | ||||
\(780\) | 1.16604 | − | 1.23447i | 0.0417509 | − | 0.0442010i | ||||
\(781\) | 12.4979 | − | 21.6471i | 0.447211 | − | 0.774593i | ||||
\(782\) | −11.2106 | + | 19.4174i | −0.400892 | + | 0.694365i | ||||
\(783\) | −1.30709 | −0.0467116 | ||||||||
\(784\) | 1.55007 | − | 2.68480i | 0.0553596 | − | 0.0958857i | ||||
\(785\) | 10.7029 | + | 2.54331i | 0.382002 | + | 0.0907747i | ||||
\(786\) | −5.49205 | − | 9.51251i | −0.195895 | − | 0.339300i | ||||
\(787\) | 31.7684i | 1.13242i | 0.824260 | + | 0.566211i | \(0.191591\pi\) | ||||
−0.824260 | + | 0.566211i | \(0.808409\pi\) | |||||||
\(788\) | − | 18.5786i | − | 0.661834i | ||||||
\(789\) | −7.81597 | − | 13.5376i | −0.278256 | − | 0.481953i | ||||
\(790\) | 13.1024 | − | 13.8713i | 0.466163 | − | 0.493519i | ||||
\(791\) | 34.9911i | 1.24414i | ||||||||
\(792\) | 1.94018 | + | 3.36048i | 0.0689411 | + | 0.119410i | ||||
\(793\) | 6.42045 | − | 3.70685i | 0.227997 | − | 0.131634i | ||||
\(794\) | −16.8362 | + | 9.72037i | −0.597493 | + | 0.344963i | ||||
\(795\) | 5.19301 | + | 4.90516i | 0.184177 | + | 0.173968i | ||||
\(796\) | −1.76774 | − | 1.02060i | −0.0626558 | − | 0.0361744i | ||||
\(797\) | 8.31378 | + | 14.3999i | 0.294489 | + | 0.510070i | 0.974866 | − | 0.222792i | \(-0.0715172\pi\) |
−0.680377 | + | 0.732863i | \(0.738184\pi\) | |||||||
\(798\) | 14.4655 | − | 8.35166i | 0.512073 | − | 0.295645i | ||||
\(799\) | 15.6894 | − | 9.05827i | 0.555050 | − | 0.320458i | ||||
\(800\) | 4.46551 | + | 2.24928i | 0.157880 | + | 0.0795240i | ||||
\(801\) | −1.93582 | − | 1.11765i | −0.0683990 | − | 0.0394902i | ||||
\(802\) | −0.860924 | + | 0.497054i | −0.0304003 | + | 0.0175516i | ||||
\(803\) | 22.6816i | 0.800417i | ||||||||
\(804\) | −10.0784 | −0.355439 | ||||||||
\(805\) | 13.4588 | + | 45.0523i | 0.474359 | + | 1.58788i | ||||
\(806\) | − | 4.65090i | − | 0.163821i | ||||||
\(807\) | 14.8681 | + | 8.58413i | 0.523384 | + | 0.302176i | ||||
\(808\) | −2.01613 | −0.0709272 | ||||||||
\(809\) | −16.5235 | − | 9.53987i | −0.580937 | − | 0.335404i | 0.180569 | − | 0.983562i | \(-0.442206\pi\) |
−0.761506 | + | 0.648158i | \(0.775539\pi\) | |||||||
\(810\) | 1.62555 | + | 1.53544i | 0.0571160 | + | 0.0539500i | ||||
\(811\) | −26.6866 | + | 46.2226i | −0.937094 | + | 1.62309i | −0.166237 | + | 0.986086i | \(0.553162\pi\) |
−0.770857 | + | 0.637008i | \(0.780172\pi\) | |||||||
\(812\) | 2.07701 | + | 3.59749i | 0.0728889 | + | 0.126247i | ||||
\(813\) | 8.40823i | 0.294890i | ||||||||
\(814\) | 9.69602 | + | 21.5198i | 0.339845 | + | 0.754268i | ||||
\(815\) | −3.12301 | + | 13.1424i | −0.109394 | + | 0.460357i | ||||
\(816\) | 2.93468 | − | 1.69434i | 0.102734 | − | 0.0593137i | ||||
\(817\) | −42.8695 | − | 24.7507i | −1.49981 | − | 0.865918i | ||||
\(818\) | −26.9360 | − | 15.5515i | −0.941795 | − | 0.543746i | ||||
\(819\) | −2.09013 | − | 1.20674i | −0.0730351 | − | 0.0421668i | ||||
\(820\) | −5.34716 | + | 22.5022i | −0.186731 | + | 0.785809i | ||||
\(821\) | −5.62460 | + | 9.74210i | −0.196300 | + | 0.340001i | −0.947326 | − | 0.320271i | \(-0.896226\pi\) |
0.751026 | + | 0.660273i | \(0.229559\pi\) | |||||||
\(822\) | 1.70269 | 0.0593881 | ||||||||
\(823\) | −16.0481 | + | 9.26537i | −0.559401 | + | 0.322970i | −0.752905 | − | 0.658129i | \(-0.771348\pi\) |
0.193504 | + | 0.981099i | \(0.438015\pi\) | |||||||
\(824\) | 8.06815 | 0.281067 | ||||||||
\(825\) | −8.72798 | + | 17.3277i | −0.303869 | + | 0.603274i | ||||
\(826\) | −9.80786 | − | 16.9877i | −0.341259 | − | 0.591078i | ||||
\(827\) | −20.4765 | + | 35.4663i | −0.712037 | + | 1.23328i | 0.252054 | + | 0.967713i | \(0.418894\pi\) |
−0.964091 | + | 0.265572i | \(0.914439\pi\) | |||||||
\(828\) | 6.61653 | 0.229940 | ||||||||
\(829\) | 37.5169 | − | 21.6604i | 1.30301 | − | 0.752296i | 0.322094 | − | 0.946708i | \(-0.395613\pi\) |
0.980920 | + | 0.194412i | \(0.0622798\pi\) | |||||||
\(830\) | −4.47403 | − | 14.9765i | −0.155296 | − | 0.519843i | ||||
\(831\) | −24.4154 | + | 14.0962i | −0.846960 | + | 0.488993i | ||||
\(832\) | −0.379707 | + | 0.657673i | −0.0131640 | + | 0.0228007i | ||||
\(833\) | 5.25268 | − | 9.09791i | 0.181995 | − | 0.315224i | ||||
\(834\) | 15.2306 | − | 8.79340i | 0.527393 | − | 0.304491i | ||||
\(835\) | −40.8562 | + | 12.2052i | −1.41389 | + | 0.422380i | ||||
\(836\) | 17.6620 | − | 10.1972i | 0.610854 | − | 0.352677i | ||||
\(837\) | 6.12433 | 0.211688 | ||||||||
\(838\) | −19.2268 | + | 33.3019i | −0.664180 | + | 1.15039i | ||||
\(839\) | 6.10865 | + | 10.5805i | 0.210894 | + | 0.365279i | 0.951995 | − | 0.306115i | \(-0.0990292\pi\) |
−0.741101 | + | 0.671394i | \(0.765696\pi\) | |||||||
\(840\) | 1.64293 | − | 6.91386i | 0.0566866 | − | 0.238551i | ||||
\(841\) | 27.2915 | 0.941087 | ||||||||
\(842\) | −7.95838 | + | 4.59477i | −0.274264 | + | 0.158346i | ||||
\(843\) | 20.8311 | 0.717460 | ||||||||
\(844\) | −6.65761 | + | 11.5313i | −0.229165 | + | 0.396925i | ||||
\(845\) | 6.42233 | − | 27.0267i | 0.220935 | − | 0.929748i | ||||
\(846\) | −4.62995 | − | 2.67310i | −0.159181 | − | 0.0919031i | ||||
\(847\) | 11.1664 | + | 6.44691i | 0.383681 | + | 0.221519i | ||||
\(848\) | −2.76662 | − | 1.59731i | −0.0950061 | − | 0.0548518i | ||||
\(849\) | −13.3436 | + | 7.70394i | −0.457952 | + | 0.264399i | ||||
\(850\) | 15.1321 | + | 7.62207i | 0.519028 | + | 0.261435i | ||||
\(851\) | 40.0446 | + | 4.02904i | 1.37271 | + | 0.138114i | ||||
\(852\) | 6.44165i | 0.220687i | ||||||||
\(853\) | −25.4152 | − | 44.0204i | −0.870199 | − | 1.50723i | −0.861791 | − | 0.507263i | \(-0.830657\pi\) |
−0.00840753 | − | 0.999965i | \(-0.502676\pi\) | |||||||
\(854\) | 15.5128 | − | 26.8689i | 0.530836 | − | 0.919435i | ||||
\(855\) | 8.06999 | − | 8.54356i | 0.275988 | − | 0.292184i | ||||
\(856\) | −4.44127 | − | 2.56417i | −0.151799 | − | 0.0876414i | ||||
\(857\) | 52.0353 | 1.77749 | 0.888746 | − | 0.458400i | \(-0.151577\pi\) | ||||
0.888746 | + | 0.458400i | \(0.151577\pi\) | |||||||
\(858\) | −2.55200 | − | 1.47340i | −0.0871239 | − | 0.0503010i | ||||
\(859\) | 37.8302i | 1.29075i | 0.763866 | + | 0.645375i | \(0.223299\pi\) | ||||
−0.763866 | + | 0.645375i | \(0.776701\pi\) | |||||||
\(860\) | −20.1791 | + | 6.02823i | −0.688101 | + | 0.205561i | ||||
\(861\) | 32.8724 | 1.12029 | ||||||||
\(862\) | − | 11.3060i | − | 0.385083i | ||||||
\(863\) | 1.07588 | − | 0.621161i | 0.0366235 | − | 0.0211446i | −0.481576 | − | 0.876404i | \(-0.659936\pi\) |
0.518200 | + | 0.855259i | \(0.326602\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 44.3273 | + | 10.5334i | 1.50717 | + | 0.358148i | ||||
\(866\) | −16.5923 | + | 9.57954i | −0.563828 | + | 0.325526i | ||||
\(867\) | −4.77777 | + | 2.75844i | −0.162261 | + | 0.0936817i | ||||
\(868\) | −9.73177 | − | 16.8559i | −0.330318 | − | 0.572127i | ||||
\(869\) | −28.6760 | − | 16.5561i | −0.972767 | − | 0.561627i | ||||
\(870\) | 2.12474 | + | 2.00696i | 0.0720354 | + | 0.0680425i | ||||
\(871\) | 6.62831 | − | 3.82685i | 0.224592 | − | 0.129668i | ||||
\(872\) | 4.29464 | − | 2.47951i | 0.145435 | − | 0.0839669i | ||||
\(873\) | −2.38589 | − | 4.13248i | −0.0807501 | − | 0.139863i | ||||
\(874\) | − | 34.7752i | − | 1.17629i | ||||||
\(875\) | 33.4106 | − | 12.0934i | 1.12948 | − | 0.408831i | ||||
\(876\) | −2.92263 | − | 5.06214i | −0.0987464 | − | 0.171034i | ||||
\(877\) | − | 9.31872i | − | 0.314671i | −0.987545 | − | 0.157335i | \(-0.949710\pi\) | ||
0.987545 | − | 0.157335i | \(-0.0502904\pi\) | |||||||
\(878\) | 33.0743i | 1.11620i | ||||||||
\(879\) | 6.22135 | + | 10.7757i | 0.209841 | + | 0.363455i | ||||
\(880\) | 2.00598 | − | 8.44166i | 0.0676216 | − | 0.284568i | ||||
\(881\) | −6.24610 | + | 10.8186i | −0.210436 | + | 0.364486i | −0.951851 | − | 0.306561i | \(-0.900822\pi\) |
0.741415 | + | 0.671047i | \(0.234155\pi\) | |||||||
\(882\) | −3.10014 | −0.104387 | ||||||||
\(883\) | 1.69119 | − | 2.92923i | 0.0569131 | − | 0.0985764i | −0.836165 | − | 0.548478i | \(-0.815208\pi\) |
0.893078 | + | 0.449901i | \(0.148541\pi\) | |||||||
\(884\) | −1.28670 | + | 2.22864i | −0.0432766 | + | 0.0749572i | ||||
\(885\) | −10.0332 | − | 9.47708i | −0.337263 | − | 0.318568i | ||||
\(886\) | −0.411893 | + | 0.237807i | −0.0138378 | + | 0.00798927i | ||||
\(887\) | − | 1.02834i | − | 0.0345283i | −0.999851 | − | 0.0172642i | \(-0.994504\pi\) | ||
0.999851 | − | 0.0172642i | \(-0.00549563\pi\) | |||||||
\(888\) | −4.93690 | − | 3.55346i | −0.165671 | − | 0.119246i | ||||
\(889\) | 47.9251 | 1.60736 | ||||||||
\(890\) | 1.43069 | + | 4.78914i | 0.0479569 | + | 0.160532i | ||||
\(891\) | 1.94018 | − | 3.36048i | 0.0649983 | − | 0.112580i | ||||
\(892\) | −12.8962 | − | 7.44563i | −0.431797 | − | 0.249298i | ||||
\(893\) | −14.0493 | + | 24.3341i | −0.470141 | + | 0.814309i | ||||
\(894\) | − | 18.0769i | − | 0.604581i | ||||||
\(895\) | −2.86363 | + | 3.03167i | −0.0957205 | + | 0.101338i | ||||
\(896\) | 3.17807i | 0.106172i | ||||||||
\(897\) | −4.35151 | + | 2.51235i | −0.145293 | + | 0.0838848i | ||||
\(898\) | − | 39.1797i | − | 1.30744i | ||||||
\(899\) | 8.00505 | 0.266983 | ||||||||
\(900\) | −0.284822 | − | 4.99188i | −0.00949408 | − | 0.166396i | ||||
\(901\) | −9.37517 | − | 5.41276i | −0.312332 | − | 0.180325i | ||||
\(902\) | 40.1364 | 1.33640 | ||||||||
\(903\) | 14.9662 | + | 25.9223i | 0.498045 | + | 0.862640i | ||||
\(904\) | −5.50508 | − | 9.53507i | −0.183096 | − | 0.317132i | ||||
\(905\) | −26.0905 | + | 7.79419i | −0.867278 | + | 0.259088i | ||||
\(906\) | −13.4278 | − | 7.75253i | −0.446108 | − | 0.257560i | ||||
\(907\) | −9.56237 | + | 16.5625i | −0.317513 | + | 0.549949i | −0.979969 | − | 0.199152i | \(-0.936181\pi\) |
0.662455 | + | 0.749101i | \(0.269514\pi\) | |||||||
\(908\) | 0.708052 | + | 1.22638i | 0.0234975 | + | 0.0406989i | ||||
\(909\) | 1.00807 | + | 1.74602i | 0.0334354 | + | 0.0579118i | ||||
\(910\) | 1.54473 | + | 5.17089i | 0.0512074 | + | 0.171413i | ||||
\(911\) | − | 39.6440i | − | 1.31346i | −0.754124 | − | 0.656732i | \(-0.771938\pi\) | ||
0.754124 | − | 0.656732i | \(-0.228062\pi\) | |||||||
\(912\) | −2.62790 | + | 4.55166i | −0.0870185 | + | 0.150720i | ||||
\(913\) | −23.4904 | + | 13.5622i | −0.777418 | + | 0.448843i | ||||
\(914\) | −12.5563 | −0.415325 | ||||||||
\(915\) | 5.04675 | − | 21.2380i | 0.166840 | − | 0.702105i | ||||
\(916\) | −13.9106 | − | 24.0938i | −0.459619 | − | 0.796083i | ||||
\(917\) | 34.9083 | 1.15277 | ||||||||
\(918\) | −2.93468 | − | 1.69434i | −0.0968588 | − | 0.0559215i | ||||
\(919\) | 32.9069i | 1.08550i | 0.839895 | + | 0.542749i | \(0.182616\pi\) | ||||
−0.839895 | + | 0.542749i | \(0.817384\pi\) | |||||||
\(920\) | −10.7555 | − | 10.1593i | −0.354598 | − | 0.334943i | ||||
\(921\) | −14.4937 | + | 25.1038i | −0.477583 | + | 0.827199i | ||||
\(922\) | −4.06075 | − | 2.34448i | −0.133734 | − | 0.0772113i | ||||
\(923\) | −2.44594 | − | 4.23650i | −0.0805092 | − | 0.139446i | ||||
\(924\) | −12.3320 | −0.405694 | ||||||||
\(925\) | 1.31593 | − | 30.3853i | 0.0432675 | − | 0.999064i | ||||
\(926\) | −12.2779 | −0.403477 | ||||||||
\(927\) | −4.03407 | − | 6.98722i | −0.132496 | − | 0.229490i | ||||
\(928\) | −1.13197 | − | 0.653545i | −0.0371589 | − | 0.0214537i | ||||
\(929\) | −15.3383 | + | 26.5668i | −0.503235 | + | 0.871628i | 0.496758 | + | 0.867889i | \(0.334524\pi\) |
−0.999993 | + | 0.00373929i | \(0.998810\pi\) | |||||||
\(930\) | −9.95540 | − | 9.40356i | −0.326450 | − | 0.308355i | ||||
\(931\) | 16.2937i | 0.534005i | ||||||||
\(932\) | 18.3097 | + | 10.5711i | 0.599755 | + | 0.346269i | ||||
\(933\) | 0.514169 | 0.0168331 | ||||||||
\(934\) | 6.34282 | + | 10.9861i | 0.207543 | + | 0.359476i | ||||
\(935\) | 6.79762 | − | 28.6060i | 0.222306 | − | 0.935517i | ||||
\(936\) | 0.759415 | 0.0248223 | ||||||||
\(937\) | −12.2218 | + | 7.05627i | −0.399269 | + | 0.230518i | −0.686169 | − | 0.727442i | \(-0.740709\pi\) |
0.286899 | + | 0.957961i | \(0.407375\pi\) | |||||||
\(938\) | 16.0150 | − | 27.7388i | 0.522908 | − | 0.905703i | ||||
\(939\) | − | 22.5042i | − | 0.734397i | ||||||
\(940\) | 3.42181 | + | 11.4543i | 0.111607 | + | 0.373598i | ||||
\(941\) | −15.2622 | − | 26.4350i | −0.497535 | − | 0.861756i | 0.502461 | − | 0.864600i | \(-0.332428\pi\) |
−0.999996 | + | 0.00284385i | \(0.999095\pi\) | |||||||
\(942\) | 2.45988 | + | 4.26063i | 0.0801471 | + | 0.138819i | ||||
\(943\) | 34.2190 | − | 59.2691i | 1.11432 | − | 1.93007i | ||||
\(944\) | 5.34529 | + | 3.08610i | 0.173974 | + | 0.100444i | ||||
\(945\) | −6.80904 | + | 2.03411i | −0.221498 | + | 0.0661696i | ||||
\(946\) | 18.2734 | + | 31.6505i | 0.594120 | + | 1.02905i | ||||
\(947\) | 24.2928 | + | 42.0764i | 0.789411 | + | 1.36730i | 0.926328 | + | 0.376718i | \(0.122947\pi\) |
−0.136916 | + | 0.990583i | \(0.543719\pi\) | |||||||
\(948\) | 8.53330 | 0.277149 | ||||||||
\(949\) | 3.84426 | + | 2.21949i | 0.124790 | + | 0.0720475i | ||||
\(950\) | −26.2363 | + | 1.49697i | −0.851219 | + | 0.0485681i | ||||
\(951\) | −7.05946 | −0.228919 | ||||||||
\(952\) | 10.7694i | 0.349040i | ||||||||
\(953\) | 31.8214 | − | 18.3721i | 1.03080 | − | 0.595131i | 0.113585 | − | 0.993528i | \(-0.463767\pi\) |
0.917213 | + | 0.398397i | \(0.130433\pi\) | |||||||
\(954\) | 3.19462i | 0.103430i | ||||||||
\(955\) | 33.6547 | − | 35.6297i | 1.08904 | − | 1.15295i | ||||
\(956\) | − | 5.93461i | − | 0.191939i | ||||||
\(957\) | 2.53598 | − | 4.39245i | 0.0819767 | − | 0.141988i | ||||
\(958\) | −2.51613 | − | 1.45269i | −0.0812925 | − | 0.0469342i | ||||
\(959\) | −2.70564 | + | 4.68630i | −0.0873695 | + | 0.151328i | ||||
\(960\) | 0.640045 | + | 2.14251i | 0.0206574 | + | 0.0691492i | ||||
\(961\) | −6.50738 | −0.209915 | ||||||||
\(962\) | 4.59614 | + | 0.462435i | 0.148185 | + | 0.0149095i | ||||
\(963\) | 5.12833i | 0.165258i | ||||||||
\(964\) | 21.6064 | − | 12.4744i | 0.695895 | − | 0.401775i | ||||
\(965\) | −9.77098 | − | 9.22937i | −0.314539 | − | 0.297104i | ||||
\(966\) | −10.5139 | + | 18.2106i | −0.338279 | + | 0.585917i | ||||
\(967\) | 27.1750 | − | 47.0685i | 0.873890 | − | 1.51362i | 0.0159491 | − | 0.999873i | \(-0.494923\pi\) |
0.857941 | − | 0.513749i | \(-0.171744\pi\) | |||||||
\(968\) | −4.05712 | −0.130401 | ||||||||
\(969\) | −8.90510 | + | 15.4241i | −0.286073 | + | 0.495493i | ||||
\(970\) | −2.46681 | + | 10.3810i | −0.0792046 | + | 0.333312i | ||||
\(971\) | 26.2816 | + | 45.5210i | 0.843416 | + | 1.46084i | 0.886990 | + | 0.461789i | \(0.152792\pi\) |
−0.0435737 | + | 0.999050i | \(0.513874\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 55.8921i | 1.79182i | ||||||||
\(974\) | 0.219978 | + | 0.381012i | 0.00704854 | + | 0.0122084i | ||||
\(975\) | 2.08277 | + | 3.17487i | 0.0667022 | + | 0.101677i | ||||
\(976\) | 9.76238i | 0.312486i | ||||||||
\(977\) | −22.6877 | − | 39.2962i | −0.725843 | − | 1.25720i | −0.958626 | − | 0.284669i | \(-0.908116\pi\) |
0.232782 | − | 0.972529i | \(-0.425217\pi\) | |||||||
\(978\) | −5.23176 | + | 3.02056i | −0.167293 | + | 0.0965867i | ||||
\(979\) | 7.51167 | − | 4.33687i | 0.240074 | − | 0.138607i | ||||
\(980\) | 5.03943 | + | 4.76009i | 0.160979 | + | 0.152055i | ||||
\(981\) | −4.29464 | − | 2.47951i | −0.137117 | − | 0.0791648i | ||||
\(982\) | 19.3748 | + | 33.5582i | 0.618275 | + | 1.07088i | ||||
\(983\) | 3.52063 | − | 2.03263i | 0.112291 | − | 0.0648310i | −0.442803 | − | 0.896619i | \(-0.646016\pi\) |
0.555093 | + | 0.831788i | \(0.312683\pi\) | |||||||
\(984\) | −8.95773 | + | 5.17175i | −0.285562 | + | 0.164869i | ||||
\(985\) | 40.4175 | + | 9.60435i | 1.28781 | + | 0.306020i | ||||
\(986\) | −3.83589 | − | 2.21465i | −0.122160 | − | 0.0705289i | ||||
\(987\) | 14.7143 | − | 8.49531i | 0.468361 | − | 0.270409i | ||||
\(988\) | − | 3.99133i | − | 0.126981i | ||||||
\(989\) | 62.3174 | 1.98158 | ||||||||
\(990\) | −8.31368 | + | 2.48360i | −0.264226 | + | 0.0789340i | ||||
\(991\) | − | 56.8201i | − | 1.80495i | −0.430744 | − | 0.902474i | \(-0.641749\pi\) | ||
0.430744 | − | 0.902474i | \(-0.358251\pi\) | |||||||
\(992\) | 5.30382 | + | 3.06216i | 0.168397 | + | 0.0972238i | ||||
\(993\) | −13.2351 | −0.420004 | ||||||||
\(994\) | −17.7293 | − | 10.2360i | −0.562339 | − | 0.324667i | ||||
\(995\) | 3.13416 | − | 3.31809i | 0.0993596 | − | 0.105190i | ||||
\(996\) | 3.49509 | − | 6.05368i | 0.110746 | − | 0.191818i | ||||
\(997\) | 9.73005 | + | 16.8529i | 0.308154 | + | 0.533738i | 0.977959 | − | 0.208799i | \(-0.0669555\pi\) |
−0.669805 | + | 0.742537i | \(0.733622\pi\) | |||||||
\(998\) | − | 37.8307i | − | 1.19751i | ||||||
\(999\) | −0.608935 | + | 6.05221i | −0.0192659 | + | 0.191483i |
(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 | 1110.2.ba.b.529.1 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.a.529.18 | ✓ | 36 | ||
37.27 | even | 6 | 1110.2.ba.a.619.18 | yes | 36 | ||
185.64 | even | 6 | inner | 1110.2.ba.b.619.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.18 | ✓ | 36 | 5.4 | even | 2 | ||
1110.2.ba.a.619.18 | yes | 36 | 37.27 | even | 6 | ||
1110.2.ba.b.529.1 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.619.1 | yes | 36 | 185.64 | even | 6 | inner |