Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 697.16 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.a.43.16 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.23501 | − | 0.0687789i | 0.999527 | − | 0.0307589i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | 2.13605 | + | 2.13605i | 0.807352 | + | 0.807352i | 0.984232 | − | 0.176880i | \(-0.0566006\pi\) |
−0.176880 | + | 0.984232i | \(0.556601\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −0.0687789 | − | 2.23501i | −0.0217498 | − | 0.706772i | ||||
\(11\) | − | 2.07347i | − | 0.625174i | −0.949889 | − | 0.312587i | \(-0.898804\pi\) | ||
0.949889 | − | 0.312587i | \(-0.101196\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | − | 4.31443i | − | 1.19661i | −0.801269 | − | 0.598304i | \(-0.795842\pi\) | ||
0.801269 | − | 0.598304i | \(-0.204158\pi\) | |||||||
\(14\) | 2.13605 | − | 2.13605i | 0.570884 | − | 0.570884i | ||||
\(15\) | 1.62902 | + | 1.53176i | 0.420612 | + | 0.395498i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.62056 | 0.635579 | 0.317790 | − | 0.948161i | \(-0.397059\pi\) | ||||
0.317790 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.48007 | − | 1.48007i | −0.339551 | − | 0.339551i | 0.516647 | − | 0.856198i | \(-0.327180\pi\) |
−0.856198 | + | 0.516647i | \(0.827180\pi\) | |||||||
\(20\) | −2.23501 | + | 0.0687789i | −0.499763 | + | 0.0153794i | ||||
\(21\) | 3.02083i | 0.659200i | ||||||||
\(22\) | −2.07347 | −0.442065 | ||||||||
\(23\) | 3.49438i | 0.728628i | 0.931276 | + | 0.364314i | \(0.118697\pi\) | ||||
−0.931276 | + | 0.364314i | \(0.881303\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 4.99054 | − | 0.307443i | 0.998108 | − | 0.0614886i | ||||
\(26\) | −4.31443 | −0.846129 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.13605 | − | 2.13605i | −0.403676 | − | 0.403676i | ||||
\(29\) | −0.364989 | + | 0.364989i | −0.0677767 | + | 0.0677767i | −0.740183 | − | 0.672406i | \(-0.765261\pi\) |
0.672406 | + | 0.740183i | \(0.265261\pi\) | |||||||
\(30\) | 1.53176 | − | 1.62902i | 0.279659 | − | 0.297418i | ||||
\(31\) | 0.391381 | + | 0.391381i | 0.0702942 | + | 0.0702942i | 0.741380 | − | 0.671086i | \(-0.234172\pi\) |
−0.671086 | + | 0.741380i | \(0.734172\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.46616 | − | 1.46616i | 0.255226 | − | 0.255226i | ||||
\(34\) | − | 2.62056i | − | 0.449422i | ||||||
\(35\) | 4.92101 | + | 4.62718i | 0.831803 | + | 0.782137i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 5.47103 | − | 2.65855i | 0.899431 | − | 0.437062i | ||||
\(38\) | −1.48007 | + | 1.48007i | −0.240099 | + | 0.240099i | ||||
\(39\) | 3.05076 | − | 3.05076i | 0.488513 | − | 0.488513i | ||||
\(40\) | 0.0687789 | + | 2.23501i | 0.0108749 | + | 0.353386i | ||||
\(41\) | 3.80013i | 0.593481i | 0.954958 | + | 0.296740i | \(0.0958996\pi\) | ||||
−0.954958 | + | 0.296740i | \(0.904100\pi\) | |||||||
\(42\) | 3.02083 | 0.466125 | ||||||||
\(43\) | 6.28607i | 0.958617i | 0.877647 | + | 0.479308i | \(0.159112\pi\) | ||||
−0.877647 | + | 0.479308i | \(0.840888\pi\) | |||||||
\(44\) | 2.07347i | 0.312587i | ||||||||
\(45\) | 0.0687789 | + | 2.23501i | 0.0102530 | + | 0.333176i | ||||
\(46\) | 3.49438 | 0.515218 | ||||||||
\(47\) | 3.37898 | + | 3.37898i | 0.492876 | + | 0.492876i | 0.909211 | − | 0.416336i | \(-0.136686\pi\) |
−0.416336 | + | 0.909211i | \(0.636686\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 2.12544i | 0.303634i | ||||||||
\(50\) | −0.307443 | − | 4.99054i | −0.0434790 | − | 0.705769i | ||||
\(51\) | 1.85302 | + | 1.85302i | 0.259474 | + | 0.259474i | ||||
\(52\) | 4.31443i | 0.598304i | ||||||||
\(53\) | −1.87850 | + | 1.87850i | −0.258031 | + | 0.258031i | −0.824253 | − | 0.566222i | \(-0.808405\pi\) |
0.566222 | + | 0.824253i | \(0.308405\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | −0.142611 | − | 4.63422i | −0.0192296 | − | 0.624878i | ||||
\(56\) | −2.13605 | + | 2.13605i | −0.285442 | + | 0.285442i | ||||
\(57\) | − | 2.09313i | − | 0.277242i | ||||||
\(58\) | 0.364989 | + | 0.364989i | 0.0479254 | + | 0.0479254i | ||||
\(59\) | 0.917356 | + | 0.917356i | 0.119430 | + | 0.119430i | 0.764296 | − | 0.644866i | \(-0.223087\pi\) |
−0.644866 | + | 0.764296i | \(0.723087\pi\) | |||||||
\(60\) | −1.62902 | − | 1.53176i | −0.210306 | − | 0.197749i | ||||
\(61\) | 5.87589 | + | 5.87589i | 0.752331 | + | 0.752331i | 0.974914 | − | 0.222583i | \(-0.0714489\pi\) |
−0.222583 | + | 0.974914i | \(0.571449\pi\) | |||||||
\(62\) | 0.391381 | − | 0.391381i | 0.0497055 | − | 0.0497055i | ||||
\(63\) | −2.13605 | + | 2.13605i | −0.269117 | + | 0.269117i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.296742 | − | 9.64280i | −0.0368063 | − | 1.19604i | ||||
\(66\) | −1.46616 | − | 1.46616i | −0.180472 | − | 0.180472i | ||||
\(67\) | 3.05783 | − | 3.05783i | 0.373573 | − | 0.373573i | −0.495204 | − | 0.868777i | \(-0.664907\pi\) |
0.868777 | + | 0.495204i | \(0.164907\pi\) | |||||||
\(68\) | −2.62056 | −0.317790 | ||||||||
\(69\) | −2.47090 | + | 2.47090i | −0.297461 | + | 0.297461i | ||||
\(70\) | 4.62718 | − | 4.92101i | 0.553054 | − | 0.588174i | ||||
\(71\) | −9.16581 | −1.08778 | −0.543891 | − | 0.839156i | \(-0.683049\pi\) | ||||
−0.543891 | + | 0.839156i | \(0.683049\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.50139 | − | 8.50139i | −0.995012 | − | 0.995012i | 0.00497545 | − | 0.999988i | \(-0.498416\pi\) |
−0.999988 | + | 0.00497545i | \(0.998416\pi\) | |||||||
\(74\) | −2.65855 | − | 5.47103i | −0.309050 | − | 0.635994i | ||||
\(75\) | 3.74624 | + | 3.31145i | 0.432578 | + | 0.382373i | ||||
\(76\) | 1.48007 | + | 1.48007i | 0.169776 | + | 0.169776i | ||||
\(77\) | 4.42903 | − | 4.42903i | 0.504735 | − | 0.504735i | ||||
\(78\) | −3.05076 | − | 3.05076i | −0.345431 | − | 0.345431i | ||||
\(79\) | −9.01137 | − | 9.01137i | −1.01386 | − | 1.01386i | −0.999903 | − | 0.0139555i | \(-0.995558\pi\) |
−0.0139555 | − | 0.999903i | \(-0.504442\pi\) | |||||||
\(80\) | 2.23501 | − | 0.0687789i | 0.249882 | − | 0.00768972i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 3.80013 | 0.419654 | ||||||||
\(83\) | −0.381394 | + | 0.381394i | −0.0418634 | + | 0.0418634i | −0.727729 | − | 0.685865i | \(-0.759424\pi\) |
0.685865 | + | 0.727729i | \(0.259424\pi\) | |||||||
\(84\) | − | 3.02083i | − | 0.329600i | ||||||
\(85\) | 5.85698 | − | 0.180239i | 0.635278 | − | 0.0195497i | ||||
\(86\) | 6.28607 | 0.677844 | ||||||||
\(87\) | −0.516172 | −0.0553395 | ||||||||
\(88\) | 2.07347 | 0.221032 | ||||||||
\(89\) | −3.68659 | + | 3.68659i | −0.390778 | + | 0.390778i | −0.874965 | − | 0.484187i | \(-0.839116\pi\) |
0.484187 | + | 0.874965i | \(0.339116\pi\) | |||||||
\(90\) | 2.23501 | − | 0.0687789i | 0.235591 | − | 0.00724994i | ||||
\(91\) | 9.21585 | − | 9.21585i | 0.966084 | − | 0.966084i | ||||
\(92\) | − | 3.49438i | − | 0.364314i | ||||||
\(93\) | 0.553497i | 0.0573950i | ||||||||
\(94\) | 3.37898 | − | 3.37898i | 0.348516 | − | 0.348516i | ||||
\(95\) | −3.40977 | − | 3.20617i | −0.349835 | − | 0.328946i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 14.1415 | 1.43586 | 0.717928 | − | 0.696117i | \(-0.245091\pi\) | ||||
0.717928 | + | 0.696117i | \(0.245091\pi\) | |||||||
\(98\) | 2.12544 | 0.214702 | ||||||||
\(99\) | 2.07347 | 0.208391 | ||||||||
\(100\) | −4.99054 | + | 0.307443i | −0.499054 | + | 0.0307443i | ||||
\(101\) | − | 7.64384i | − | 0.760591i | −0.924865 | − | 0.380295i | \(-0.875822\pi\) | ||
0.924865 | − | 0.380295i | \(-0.124178\pi\) | |||||||
\(102\) | 1.85302 | − | 1.85302i | 0.183476 | − | 0.183476i | ||||
\(103\) | −9.85885 | −0.971422 | −0.485711 | − | 0.874120i | \(-0.661439\pi\) | ||||
−0.485711 | + | 0.874120i | \(0.661439\pi\) | |||||||
\(104\) | 4.31443 | 0.423065 | ||||||||
\(105\) | 0.207770 | + | 6.75159i | 0.0202763 | + | 0.658888i | ||||
\(106\) | 1.87850 | + | 1.87850i | 0.182456 | + | 0.182456i | ||||
\(107\) | 4.17096 | + | 4.17096i | 0.403222 | + | 0.403222i | 0.879367 | − | 0.476145i | \(-0.157966\pi\) |
−0.476145 | + | 0.879367i | \(0.657966\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 0.461041 | + | 0.461041i | 0.0441597 | + | 0.0441597i | 0.728842 | − | 0.684682i | \(-0.240059\pi\) |
−0.684682 | + | 0.728842i | \(0.740059\pi\) | |||||||
\(110\) | −4.63422 | + | 0.142611i | −0.441856 | + | 0.0135974i | ||||
\(111\) | 5.74848 | + | 1.98872i | 0.545621 | + | 0.188761i | ||||
\(112\) | 2.13605 | + | 2.13605i | 0.201838 | + | 0.201838i | ||||
\(113\) | −17.3203 | −1.62936 | −0.814678 | − | 0.579913i | \(-0.803086\pi\) | ||||
−0.814678 | + | 0.579913i | \(0.803086\pi\) | |||||||
\(114\) | −2.09313 | −0.196040 | ||||||||
\(115\) | 0.240340 | + | 7.80997i | 0.0224118 | + | 0.728284i | ||||
\(116\) | 0.364989 | − | 0.364989i | 0.0338884 | − | 0.0338884i | ||||
\(117\) | 4.31443 | 0.398869 | ||||||||
\(118\) | 0.917356 | − | 0.917356i | 0.0844495 | − | 0.0844495i | ||||
\(119\) | 5.59765 | + | 5.59765i | 0.513136 | + | 0.513136i | ||||
\(120\) | −1.53176 | + | 1.62902i | −0.139830 | + | 0.148709i | ||||
\(121\) | 6.70073 | 0.609158 | ||||||||
\(122\) | 5.87589 | − | 5.87589i | 0.531978 | − | 0.531978i | ||||
\(123\) | −2.68710 | + | 2.68710i | −0.242287 | + | 0.242287i | ||||
\(124\) | −0.391381 | − | 0.391381i | −0.0351471 | − | 0.0351471i | ||||
\(125\) | 11.1328 | − | 1.03038i | 0.995744 | − | 0.0921602i | ||||
\(126\) | 2.13605 | + | 2.13605i | 0.190295 | + | 0.190295i | ||||
\(127\) | −6.18161 | − | 6.18161i | −0.548529 | − | 0.548529i | 0.377486 | − | 0.926015i | \(-0.376789\pi\) |
−0.926015 | + | 0.377486i | \(0.876789\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.44492 | + | 4.44492i | −0.391354 | + | 0.391354i | ||||
\(130\) | −9.64280 | + | 0.296742i | −0.845729 | + | 0.0260260i | ||||
\(131\) | 1.03836 | + | 1.03836i | 0.0907217 | + | 0.0907217i | 0.751011 | − | 0.660289i | \(-0.229566\pi\) |
−0.660289 | + | 0.751011i | \(0.729566\pi\) | |||||||
\(132\) | −1.46616 | + | 1.46616i | −0.127613 | + | 0.127613i | ||||
\(133\) | − | 6.32301i | − | 0.548275i | ||||||
\(134\) | −3.05783 | − | 3.05783i | −0.264156 | − | 0.264156i | ||||
\(135\) | −1.53176 | + | 1.62902i | −0.131833 | + | 0.140204i | ||||
\(136\) | 2.62056i | 0.224711i | ||||||||
\(137\) | −13.3475 | − | 13.3475i | −1.14035 | − | 1.14035i | −0.988386 | − | 0.151966i | \(-0.951440\pi\) |
−0.151966 | − | 0.988386i | \(-0.548560\pi\) | |||||||
\(138\) | 2.47090 | + | 2.47090i | 0.210337 | + | 0.210337i | ||||
\(139\) | 12.1026 | 1.02653 | 0.513267 | − | 0.858229i | \(-0.328435\pi\) | ||||
0.513267 | + | 0.858229i | \(0.328435\pi\) | |||||||
\(140\) | −4.92101 | − | 4.62718i | −0.415902 | − | 0.391068i | ||||
\(141\) | 4.77861i | 0.402431i | ||||||||
\(142\) | 9.16581i | 0.769177i | ||||||||
\(143\) | −8.94583 | −0.748088 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −0.790650 | + | 0.840857i | −0.0656599 | + | 0.0698294i | ||||
\(146\) | −8.50139 | + | 8.50139i | −0.703580 | + | 0.703580i | ||||
\(147\) | −1.50291 | + | 1.50291i | −0.123958 | + | 0.123958i | ||||
\(148\) | −5.47103 | + | 2.65855i | −0.449716 | + | 0.218531i | ||||
\(149\) | 1.78006i | 0.145828i | 0.997338 | + | 0.0729141i | \(0.0232299\pi\) | ||||
−0.997338 | + | 0.0729141i | \(0.976770\pi\) | |||||||
\(150\) | 3.31145 | − | 3.74624i | 0.270379 | − | 0.305879i | ||||
\(151\) | 14.7620i | 1.20132i | 0.799506 | + | 0.600658i | \(0.205095\pi\) | ||||
−0.799506 | + | 0.600658i | \(0.794905\pi\) | |||||||
\(152\) | 1.48007 | − | 1.48007i | 0.120049 | − | 0.120049i | ||||
\(153\) | 2.62056i | 0.211860i | ||||||||
\(154\) | −4.42903 | − | 4.42903i | −0.356902 | − | 0.356902i | ||||
\(155\) | 0.901660 | + | 0.847823i | 0.0724231 | + | 0.0680988i | ||||
\(156\) | −3.05076 | + | 3.05076i | −0.244257 | + | 0.244257i | ||||
\(157\) | 3.02964 | + | 3.02964i | 0.241792 | + | 0.241792i | 0.817591 | − | 0.575799i | \(-0.195309\pi\) |
−0.575799 | + | 0.817591i | \(0.695309\pi\) | |||||||
\(158\) | −9.01137 | + | 9.01137i | −0.716906 | + | 0.716906i | ||||
\(159\) | −2.65660 | −0.210682 | ||||||||
\(160\) | −0.0687789 | − | 2.23501i | −0.00543745 | − | 0.176693i | ||||
\(161\) | −7.46418 | + | 7.46418i | −0.588260 | + | 0.588260i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 6.39530 | 0.500918 | 0.250459 | − | 0.968127i | \(-0.419418\pi\) | ||||
0.250459 | + | 0.968127i | \(0.419418\pi\) | |||||||
\(164\) | − | 3.80013i | − | 0.296740i | ||||||
\(165\) | 3.17605 | − | 3.37773i | 0.247255 | − | 0.262956i | ||||
\(166\) | 0.381394 | + | 0.381394i | 0.0296019 | + | 0.0296019i | ||||
\(167\) | −7.40255 | −0.572826 | −0.286413 | − | 0.958106i | \(-0.592463\pi\) | ||||
−0.286413 | + | 0.958106i | \(0.592463\pi\) | |||||||
\(168\) | −3.02083 | −0.233062 | ||||||||
\(169\) | −5.61431 | −0.431870 | ||||||||
\(170\) | −0.180239 | − | 5.85698i | −0.0138237 | − | 0.449210i | ||||
\(171\) | 1.48007 | − | 1.48007i | 0.113184 | − | 0.113184i | ||||
\(172\) | − | 6.28607i | − | 0.479308i | ||||||
\(173\) | −16.3983 | − | 16.3983i | −1.24674 | − | 1.24674i | −0.957152 | − | 0.289586i | \(-0.906483\pi\) |
−0.289586 | − | 0.957152i | \(-0.593517\pi\) | |||||||
\(174\) | 0.516172i | 0.0391309i | ||||||||
\(175\) | 11.3168 | + | 10.0033i | 0.855467 | + | 0.756181i | ||||
\(176\) | − | 2.07347i | − | 0.156293i | ||||||
\(177\) | 1.29734i | 0.0975139i | ||||||||
\(178\) | 3.68659 | + | 3.68659i | 0.276322 | + | 0.276322i | ||||
\(179\) | −16.2448 | + | 16.2448i | −1.21419 | + | 1.21419i | −0.244559 | + | 0.969634i | \(0.578643\pi\) |
−0.969634 | + | 0.244559i | \(0.921357\pi\) | |||||||
\(180\) | −0.0687789 | − | 2.23501i | −0.00512648 | − | 0.166588i | ||||
\(181\) | −5.45708 | −0.405621 | −0.202811 | − | 0.979218i | \(-0.565008\pi\) | ||||
−0.202811 | + | 0.979218i | \(0.565008\pi\) | |||||||
\(182\) | −9.21585 | − | 9.21585i | −0.683124 | − | 0.683124i | ||||
\(183\) | 8.30976i | 0.614275i | ||||||||
\(184\) | −3.49438 | −0.257609 | ||||||||
\(185\) | 12.0449 | − | 6.31817i | 0.885562 | − | 0.464521i | ||||
\(186\) | 0.553497 | 0.0405844 | ||||||||
\(187\) | − | 5.43364i | − | 0.397347i | ||||||
\(188\) | −3.37898 | − | 3.37898i | −0.246438 | − | 0.246438i | ||||
\(189\) | −3.02083 | −0.219733 | ||||||||
\(190\) | −3.20617 | + | 3.40977i | −0.232600 | + | 0.247370i | ||||
\(191\) | −8.47691 | + | 8.47691i | −0.613367 | + | 0.613367i | −0.943822 | − | 0.330455i | \(-0.892798\pi\) |
0.330455 | + | 0.943822i | \(0.392798\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 0.815237i | 0.0586820i | 0.999569 | + | 0.0293410i | \(0.00934088\pi\) | ||||
−0.999569 | + | 0.0293410i | \(0.990659\pi\) | |||||||
\(194\) | − | 14.1415i | − | 1.01530i | ||||||
\(195\) | 6.60866 | − | 7.02831i | 0.473256 | − | 0.503308i | ||||
\(196\) | − | 2.12544i | − | 0.151817i | ||||||
\(197\) | −12.1517 | − | 12.1517i | −0.865772 | − | 0.865772i | 0.126229 | − | 0.992001i | \(-0.459713\pi\) |
−0.992001 | + | 0.126229i | \(0.959713\pi\) | |||||||
\(198\) | − | 2.07347i | − | 0.147355i | ||||||
\(199\) | 6.43148 | − | 6.43148i | 0.455915 | − | 0.455915i | −0.441397 | − | 0.897312i | \(-0.645517\pi\) |
0.897312 | + | 0.441397i | \(0.145517\pi\) | |||||||
\(200\) | 0.307443 | + | 4.99054i | 0.0217395 | + | 0.352884i | ||||
\(201\) | 4.32442 | 0.305021 | ||||||||
\(202\) | −7.64384 | −0.537819 | ||||||||
\(203\) | −1.55927 | −0.109439 | ||||||||
\(204\) | −1.85302 | − | 1.85302i | −0.129737 | − | 0.129737i | ||||
\(205\) | 0.261369 | + | 8.49333i | 0.0182548 | + | 0.593200i | ||||
\(206\) | 9.85885i | 0.686899i | ||||||||
\(207\) | −3.49438 | −0.242876 | ||||||||
\(208\) | − | 4.31443i | − | 0.299152i | ||||||
\(209\) | −3.06887 | + | 3.06887i | −0.212279 | + | 0.212279i | ||||
\(210\) | 6.75159 | − | 0.207770i | 0.465904 | − | 0.0143375i | ||||
\(211\) | −1.84896 | −0.127287 | −0.0636437 | − | 0.997973i | \(-0.520272\pi\) | ||||
−0.0636437 | + | 0.997973i | \(0.520272\pi\) | |||||||
\(212\) | 1.87850 | − | 1.87850i | 0.129016 | − | 0.129016i | ||||
\(213\) | −6.48120 | − | 6.48120i | −0.444085 | − | 0.444085i | ||||
\(214\) | 4.17096 | − | 4.17096i | 0.285121 | − | 0.285121i | ||||
\(215\) | 0.432349 | + | 14.0494i | 0.0294860 | + | 0.958163i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 1.67202i | 0.113504i | ||||||||
\(218\) | 0.461041 | − | 0.461041i | 0.0312256 | − | 0.0312256i | ||||
\(219\) | − | 12.0228i | − | 0.812424i | ||||||
\(220\) | 0.142611 | + | 4.63422i | 0.00961482 | + | 0.312439i | ||||
\(221\) | − | 11.3062i | − | 0.760539i | ||||||
\(222\) | 1.98872 | − | 5.74848i | 0.133474 | − | 0.385812i | ||||
\(223\) | 4.85478 | − | 4.85478i | 0.325100 | − | 0.325100i | −0.525620 | − | 0.850720i | \(-0.676166\pi\) |
0.850720 | + | 0.525620i | \(0.176166\pi\) | |||||||
\(224\) | 2.13605 | − | 2.13605i | 0.142721 | − | 0.142721i | ||||
\(225\) | 0.307443 | + | 4.99054i | 0.0204962 | + | 0.332703i | ||||
\(226\) | 17.3203i | 1.15213i | ||||||||
\(227\) | −19.5601 | −1.29825 | −0.649123 | − | 0.760683i | \(-0.724864\pi\) | ||||
−0.649123 | + | 0.760683i | \(0.724864\pi\) | |||||||
\(228\) | 2.09313i | 0.138621i | ||||||||
\(229\) | 5.52626i | 0.365186i | 0.983189 | + | 0.182593i | \(0.0584490\pi\) | ||||
−0.983189 | + | 0.182593i | \(0.941551\pi\) | |||||||
\(230\) | 7.80997 | − | 0.240340i | 0.514974 | − | 0.0158475i | ||||
\(231\) | 6.26360 | 0.412115 | ||||||||
\(232\) | −0.364989 | − | 0.364989i | −0.0239627 | − | 0.0239627i | ||||
\(233\) | −8.07622 | − | 8.07622i | −0.529091 | − | 0.529091i | 0.391210 | − | 0.920301i | \(-0.372056\pi\) |
−0.920301 | + | 0.391210i | \(0.872056\pi\) | |||||||
\(234\) | − | 4.31443i | − | 0.282043i | ||||||
\(235\) | 7.78447 | + | 7.31966i | 0.507803 | + | 0.477482i | ||||
\(236\) | −0.917356 | − | 0.917356i | −0.0597148 | − | 0.0597148i | ||||
\(237\) | − | 12.7440i | − | 0.827812i | ||||||
\(238\) | 5.59765 | − | 5.59765i | 0.362842 | − | 0.362842i | ||||
\(239\) | 1.04218 | + | 1.04218i | 0.0674129 | + | 0.0674129i | 0.740009 | − | 0.672597i | \(-0.234821\pi\) |
−0.672597 | + | 0.740009i | \(0.734821\pi\) | |||||||
\(240\) | 1.62902 | + | 1.53176i | 0.105153 | + | 0.0988745i | ||||
\(241\) | 2.39676 | − | 2.39676i | 0.154389 | − | 0.154389i | −0.625686 | − | 0.780075i | \(-0.715181\pi\) |
0.780075 | + | 0.625686i | \(0.215181\pi\) | |||||||
\(242\) | − | 6.70073i | − | 0.430739i | ||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −5.87589 | − | 5.87589i | −0.376165 | − | 0.376165i | ||||
\(245\) | 0.146186 | + | 4.75038i | 0.00933945 | + | 0.303491i | ||||
\(246\) | 2.68710 | + | 2.68710i | 0.171323 | + | 0.171323i | ||||
\(247\) | −6.38566 | + | 6.38566i | −0.406310 | + | 0.406310i | ||||
\(248\) | −0.391381 | + | 0.391381i | −0.0248527 | + | 0.0248527i | ||||
\(249\) | −0.539372 | −0.0341813 | ||||||||
\(250\) | −1.03038 | − | 11.1328i | −0.0651671 | − | 0.704097i | ||||
\(251\) | 14.2994 | + | 14.2994i | 0.902571 | + | 0.902571i | 0.995658 | − | 0.0930871i | \(-0.0296735\pi\) |
−0.0930871 | + | 0.995658i | \(0.529674\pi\) | |||||||
\(252\) | 2.13605 | − | 2.13605i | 0.134559 | − | 0.134559i | ||||
\(253\) | 7.24548 | 0.455519 | ||||||||
\(254\) | −6.18161 | + | 6.18161i | −0.387869 | + | 0.387869i | ||||
\(255\) | 4.26896 | + | 4.01406i | 0.267332 | + | 0.251370i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.9481 | −1.43146 | −0.715731 | − | 0.698376i | \(-0.753906\pi\) | ||||
−0.715731 | + | 0.698376i | \(0.753906\pi\) | |||||||
\(258\) | 4.44492 | + | 4.44492i | 0.276729 | + | 0.276729i | ||||
\(259\) | 17.3652 | + | 6.00760i | 1.07902 | + | 0.373294i | ||||
\(260\) | 0.296742 | + | 9.64280i | 0.0184032 | + | 0.598021i | ||||
\(261\) | −0.364989 | − | 0.364989i | −0.0225922 | − | 0.0225922i | ||||
\(262\) | 1.03836 | − | 1.03836i | 0.0641499 | − | 0.0641499i | ||||
\(263\) | −0.797307 | − | 0.797307i | −0.0491641 | − | 0.0491641i | 0.682097 | − | 0.731261i | \(-0.261068\pi\) |
−0.731261 | + | 0.682097i | \(0.761068\pi\) | |||||||
\(264\) | 1.46616 | + | 1.46616i | 0.0902361 | + | 0.0902361i | ||||
\(265\) | −4.06926 | + | 4.32766i | −0.249973 | + | 0.265846i | ||||
\(266\) | −6.32301 | −0.387689 | ||||||||
\(267\) | −5.21363 | −0.319069 | ||||||||
\(268\) | −3.05783 | + | 3.05783i | −0.186787 | + | 0.186787i | ||||
\(269\) | 17.8697i | 1.08954i | 0.838587 | + | 0.544768i | \(0.183382\pi\) | ||||
−0.838587 | + | 0.544768i | \(0.816618\pi\) | |||||||
\(270\) | 1.62902 | + | 1.53176i | 0.0991393 | + | 0.0932197i | ||||
\(271\) | −20.7623 | −1.26122 | −0.630610 | − | 0.776100i | \(-0.717195\pi\) | ||||
−0.630610 | + | 0.776100i | \(0.717195\pi\) | |||||||
\(272\) | 2.62056 | 0.158895 | ||||||||
\(273\) | 13.0332 | 0.788804 | ||||||||
\(274\) | −13.3475 | + | 13.3475i | −0.806350 | + | 0.806350i | ||||
\(275\) | −0.637473 | − | 10.3477i | −0.0384411 | − | 0.623991i | ||||
\(276\) | 2.47090 | − | 2.47090i | 0.148731 | − | 0.148731i | ||||
\(277\) | 17.8467i | 1.07230i | 0.844122 | + | 0.536152i | \(0.180122\pi\) | ||||
−0.844122 | + | 0.536152i | \(0.819878\pi\) | |||||||
\(278\) | − | 12.1026i | − | 0.725869i | ||||||
\(279\) | −0.391381 | + | 0.391381i | −0.0234314 | + | 0.0234314i | ||||
\(280\) | −4.62718 | + | 4.92101i | −0.276527 | + | 0.294087i | ||||
\(281\) | −10.2645 | + | 10.2645i | −0.612330 | + | 0.612330i | −0.943553 | − | 0.331223i | \(-0.892539\pi\) |
0.331223 | + | 0.943553i | \(0.392539\pi\) | |||||||
\(282\) | 4.77861 | 0.284562 | ||||||||
\(283\) | −9.49377 | −0.564346 | −0.282173 | − | 0.959364i | \(-0.591055\pi\) | ||||
−0.282173 | + | 0.959364i | \(0.591055\pi\) | |||||||
\(284\) | 9.16581 | 0.543891 | ||||||||
\(285\) | −0.143963 | − | 4.67818i | −0.00852766 | − | 0.277111i | ||||
\(286\) | 8.94583i | 0.528978i | ||||||||
\(287\) | −8.11728 | + | 8.11728i | −0.479148 | + | 0.479148i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −10.1327 | −0.596039 | ||||||||
\(290\) | 0.840857 | + | 0.790650i | 0.0493768 | + | 0.0464286i | ||||
\(291\) | 9.99958 | + | 9.99958i | 0.586186 | + | 0.586186i | ||||
\(292\) | 8.50139 | + | 8.50139i | 0.497506 | + | 0.497506i | ||||
\(293\) | −1.37161 | + | 1.37161i | −0.0801303 | + | 0.0801303i | −0.746036 | − | 0.665906i | \(-0.768045\pi\) |
0.665906 | + | 0.746036i | \(0.268045\pi\) | |||||||
\(294\) | 1.50291 | + | 1.50291i | 0.0876517 | + | 0.0876517i | ||||
\(295\) | 2.11340 | + | 1.98721i | 0.123047 | + | 0.115700i | ||||
\(296\) | 2.65855 | + | 5.47103i | 0.154525 | + | 0.317997i | ||||
\(297\) | 1.46616 | + | 1.46616i | 0.0850754 | + | 0.0850754i | ||||
\(298\) | 1.78006 | 0.103116 | ||||||||
\(299\) | 15.0763 | 0.871882 | ||||||||
\(300\) | −3.74624 | − | 3.31145i | −0.216289 | − | 0.191187i | ||||
\(301\) | −13.4274 | + | 13.4274i | −0.773941 | + | 0.773941i | ||||
\(302\) | 14.7620 | 0.849459 | ||||||||
\(303\) | 5.40501 | − | 5.40501i | 0.310510 | − | 0.310510i | ||||
\(304\) | −1.48007 | − | 1.48007i | −0.0848878 | − | 0.0848878i | ||||
\(305\) | 13.5368 | + | 12.7285i | 0.775115 | + | 0.728834i | ||||
\(306\) | 2.62056 | 0.149807 | ||||||||
\(307\) | −12.9742 | + | 12.9742i | −0.740476 | + | 0.740476i | −0.972670 | − | 0.232194i | \(-0.925410\pi\) |
0.232194 | + | 0.972670i | \(0.425410\pi\) | |||||||
\(308\) | −4.42903 | + | 4.42903i | −0.252368 | + | 0.252368i | ||||
\(309\) | −6.97126 | − | 6.97126i | −0.396581 | − | 0.396581i | ||||
\(310\) | 0.847823 | − | 0.901660i | 0.0481531 | − | 0.0512109i | ||||
\(311\) | 21.1073 | + | 21.1073i | 1.19689 | + | 1.19689i | 0.975094 | + | 0.221794i | \(0.0711911\pi\) |
0.221794 | + | 0.975094i | \(0.428809\pi\) | |||||||
\(312\) | 3.05076 | + | 3.05076i | 0.172715 | + | 0.172715i | ||||
\(313\) | − | 27.9746i | − | 1.58122i | −0.612323 | − | 0.790608i | \(-0.709765\pi\) | ||
0.612323 | − | 0.790608i | \(-0.290235\pi\) | |||||||
\(314\) | 3.02964 | − | 3.02964i | 0.170973 | − | 0.170973i | ||||
\(315\) | −4.62718 | + | 4.92101i | −0.260712 | + | 0.277268i | ||||
\(316\) | 9.01137 | + | 9.01137i | 0.506929 | + | 0.506929i | ||||
\(317\) | −4.72175 | + | 4.72175i | −0.265200 | + | 0.265200i | −0.827163 | − | 0.561963i | \(-0.810046\pi\) |
0.561963 | + | 0.827163i | \(0.310046\pi\) | |||||||
\(318\) | 2.65660i | 0.148975i | ||||||||
\(319\) | 0.756793 | + | 0.756793i | 0.0423722 | + | 0.0423722i | ||||
\(320\) | −2.23501 | + | 0.0687789i | −0.124941 | + | 0.00384486i | ||||
\(321\) | 5.89863i | 0.329229i | ||||||||
\(322\) | 7.46418 | + | 7.46418i | 0.415962 | + | 0.415962i | ||||
\(323\) | −3.87861 | − | 3.87861i | −0.215812 | − | 0.215812i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.32644 | − | 21.5313i | −0.0735778 | − | 1.19434i | ||||
\(326\) | − | 6.39530i | − | 0.354203i | ||||||
\(327\) | 0.652011i | 0.0360563i | ||||||||
\(328\) | −3.80013 | −0.209827 | ||||||||
\(329\) | 14.4354i | 0.795848i | ||||||||
\(330\) | −3.37773 | − | 3.17605i | −0.185938 | − | 0.174836i | ||||
\(331\) | 5.59691 | − | 5.59691i | 0.307634 | − | 0.307634i | −0.536357 | − | 0.843991i | \(-0.680200\pi\) |
0.843991 | + | 0.536357i | \(0.180200\pi\) | |||||||
\(332\) | 0.381394 | − | 0.381394i | 0.0209317 | − | 0.0209317i | ||||
\(333\) | 2.65855 | + | 5.47103i | 0.145687 | + | 0.299810i | ||||
\(334\) | 7.40255i | 0.405049i | ||||||||
\(335\) | 6.62397 | − | 7.04459i | 0.361906 | − | 0.384887i | ||||
\(336\) | 3.02083i | 0.164800i | ||||||||
\(337\) | 15.5752 | − | 15.5752i | 0.848433 | − | 0.848433i | −0.141505 | − | 0.989938i | \(-0.545194\pi\) |
0.989938 | + | 0.141505i | \(0.0451941\pi\) | |||||||
\(338\) | 5.61431i | 0.305378i | ||||||||
\(339\) | −12.2473 | − | 12.2473i | −0.665182 | − | 0.665182i | ||||
\(340\) | −5.85698 | + | 0.180239i | −0.317639 | + | 0.00977485i | ||||
\(341\) | 0.811517 | − | 0.811517i | 0.0439461 | − | 0.0439461i | ||||
\(342\) | −1.48007 | − | 1.48007i | −0.0800330 | − | 0.0800330i | ||||
\(343\) | 10.4123 | − | 10.4123i | 0.562212 | − | 0.562212i | ||||
\(344\) | −6.28607 | −0.338922 | ||||||||
\(345\) | −5.35254 | + | 5.69243i | −0.288171 | + | 0.306470i | ||||
\(346\) | −16.3983 | + | 16.3983i | −0.881577 | + | 0.881577i | ||||
\(347\) | 7.34661i | 0.394386i | 0.980365 | + | 0.197193i | \(0.0631826\pi\) | ||||
−0.980365 | + | 0.197193i | \(0.936817\pi\) | |||||||
\(348\) | 0.516172 | 0.0276697 | ||||||||
\(349\) | − | 5.62756i | − | 0.301236i | −0.988592 | − | 0.150618i | \(-0.951874\pi\) | ||
0.988592 | − | 0.150618i | \(-0.0481264\pi\) | |||||||
\(350\) | 10.0033 | − | 11.3168i | 0.534701 | − | 0.604907i | ||||
\(351\) | 3.05076 | + | 3.05076i | 0.162838 | + | 0.162838i | ||||
\(352\) | −2.07347 | −0.110516 | ||||||||
\(353\) | 25.6724 | 1.36640 | 0.683201 | − | 0.730231i | \(-0.260587\pi\) | ||||
0.683201 | + | 0.730231i | \(0.260587\pi\) | |||||||
\(354\) | 1.29734 | 0.0689527 | ||||||||
\(355\) | −20.4857 | + | 0.630414i | −1.08727 | + | 0.0334589i | ||||
\(356\) | 3.68659 | − | 3.68659i | 0.195389 | − | 0.195389i | ||||
\(357\) | 7.91628i | 0.418974i | ||||||||
\(358\) | 16.2448 | + | 16.2448i | 0.858564 | + | 0.858564i | ||||
\(359\) | − | 29.6458i | − | 1.56465i | −0.622872 | − | 0.782324i | \(-0.714034\pi\) | ||
0.622872 | − | 0.782324i | \(-0.285966\pi\) | |||||||
\(360\) | −2.23501 | + | 0.0687789i | −0.117795 | + | 0.00362497i | ||||
\(361\) | − | 14.6188i | − | 0.769410i | ||||||
\(362\) | 5.45708i | 0.286818i | ||||||||
\(363\) | 4.73813 | + | 4.73813i | 0.248688 | + | 0.248688i | ||||
\(364\) | −9.21585 | + | 9.21585i | −0.483042 | + | 0.483042i | ||||
\(365\) | −19.5854 | − | 18.4160i | −1.02515 | − | 0.963936i | ||||
\(366\) | 8.30976 | 0.434358 | ||||||||
\(367\) | −22.3758 | − | 22.3758i | −1.16801 | − | 1.16801i | −0.982677 | − | 0.185329i | \(-0.940665\pi\) |
−0.185329 | − | 0.982677i | \(-0.559335\pi\) | |||||||
\(368\) | 3.49438i | 0.182157i | ||||||||
\(369\) | −3.80013 | −0.197827 | ||||||||
\(370\) | −6.31817 | − | 12.0449i | −0.328466 | − | 0.626187i | ||||
\(371\) | −8.02514 | −0.416644 | ||||||||
\(372\) | − | 0.553497i | − | 0.0286975i | ||||||
\(373\) | −2.58745 | − | 2.58745i | −0.133973 | − | 0.133973i | 0.636940 | − | 0.770913i | \(-0.280200\pi\) |
−0.770913 | + | 0.636940i | \(0.780200\pi\) | |||||||
\(374\) | −5.43364 | −0.280967 | ||||||||
\(375\) | 8.60064 | + | 7.14346i | 0.444135 | + | 0.368887i | ||||
\(376\) | −3.37898 | + | 3.37898i | −0.174258 | + | 0.174258i | ||||
\(377\) | 1.57472 | + | 1.57472i | 0.0811022 | + | 0.0811022i | ||||
\(378\) | 3.02083i | 0.155375i | ||||||||
\(379\) | 30.1390i | 1.54814i | 0.633102 | + | 0.774069i | \(0.281781\pi\) | ||||
−0.633102 | + | 0.774069i | \(0.718219\pi\) | |||||||
\(380\) | 3.40977 | + | 3.20617i | 0.174917 | + | 0.164473i | ||||
\(381\) | − | 8.74212i | − | 0.447872i | ||||||
\(382\) | 8.47691 | + | 8.47691i | 0.433716 | + | 0.433716i | ||||
\(383\) | 27.3379i | 1.39690i | 0.715658 | + | 0.698451i | \(0.246127\pi\) | ||||
−0.715658 | + | 0.698451i | \(0.753873\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 9.59431 | − | 10.2036i | 0.488971 | − | 0.520022i | ||||
\(386\) | 0.815237 | 0.0414945 | ||||||||
\(387\) | −6.28607 | −0.319539 | ||||||||
\(388\) | −14.1415 | −0.717928 | ||||||||
\(389\) | 7.29908 | + | 7.29908i | 0.370078 | + | 0.370078i | 0.867506 | − | 0.497428i | \(-0.165722\pi\) |
−0.497428 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(390\) | −7.02831 | − | 6.60866i | −0.355893 | − | 0.334642i | ||||
\(391\) | 9.15723i | 0.463101i | ||||||||
\(392\) | −2.12544 | −0.107351 | ||||||||
\(393\) | 1.46846i | 0.0740739i | ||||||||
\(394\) | −12.1517 | + | 12.1517i | −0.612194 | + | 0.612194i | ||||
\(395\) | −20.7603 | − | 19.5207i | −1.04456 | − | 0.982193i | ||||
\(396\) | −2.07347 | −0.104196 | ||||||||
\(397\) | 23.8828 | − | 23.8828i | 1.19864 | − | 1.19864i | 0.224069 | − | 0.974573i | \(-0.428066\pi\) |
0.974573 | − | 0.224069i | \(-0.0719342\pi\) | |||||||
\(398\) | −6.43148 | − | 6.43148i | −0.322381 | − | 0.322381i | ||||
\(399\) | 4.47104 | − | 4.47104i | 0.223832 | − | 0.223832i | ||||
\(400\) | 4.99054 | − | 0.307443i | 0.249527 | − | 0.0153722i | ||||
\(401\) | 9.30160 | + | 9.30160i | 0.464500 | + | 0.464500i | 0.900127 | − | 0.435627i | \(-0.143473\pi\) |
−0.435627 | + | 0.900127i | \(0.643473\pi\) | |||||||
\(402\) | − | 4.32442i | − | 0.215683i | ||||||
\(403\) | 1.68859 | − | 1.68859i | 0.0841146 | − | 0.0841146i | ||||
\(404\) | 7.64384i | 0.380295i | ||||||||
\(405\) | −2.23501 | + | 0.0687789i | −0.111059 | + | 0.00341765i | ||||
\(406\) | 1.55927i | 0.0773853i | ||||||||
\(407\) | −5.51241 | − | 11.3440i | −0.273240 | − | 0.562301i | ||||
\(408\) | −1.85302 | + | 1.85302i | −0.0917379 | + | 0.0917379i | ||||
\(409\) | −24.5847 | + | 24.5847i | −1.21563 | + | 1.21563i | −0.246487 | + | 0.969146i | \(0.579276\pi\) |
−0.969146 | + | 0.246487i | \(0.920724\pi\) | |||||||
\(410\) | 8.49333 | − | 0.261369i | 0.419456 | − | 0.0129081i | ||||
\(411\) | − | 18.8762i | − | 0.931093i | ||||||
\(412\) | 9.85885 | 0.485711 | ||||||||
\(413\) | 3.91904i | 0.192844i | ||||||||
\(414\) | 3.49438i | 0.171739i | ||||||||
\(415\) | −0.826187 | + | 0.878651i | −0.0405559 | + | 0.0431313i | ||||
\(416\) | −4.31443 | −0.211532 | ||||||||
\(417\) | 8.55786 | + | 8.55786i | 0.419080 | + | 0.419080i | ||||
\(418\) | 3.06887 | + | 3.06887i | 0.150104 | + | 0.150104i | ||||
\(419\) | − | 23.6748i | − | 1.15659i | −0.815829 | − | 0.578294i | \(-0.803719\pi\) | ||
0.815829 | − | 0.578294i | \(-0.196281\pi\) | |||||||
\(420\) | −0.207770 | − | 6.75159i | −0.0101381 | − | 0.329444i | ||||
\(421\) | −26.6921 | − | 26.6921i | −1.30089 | − | 1.30089i | −0.927790 | − | 0.373102i | \(-0.878294\pi\) |
−0.373102 | − | 0.927790i | \(-0.621706\pi\) | |||||||
\(422\) | 1.84896i | 0.0900058i | ||||||||
\(423\) | −3.37898 | + | 3.37898i | −0.164292 | + | 0.164292i | ||||
\(424\) | −1.87850 | − | 1.87850i | −0.0912279 | − | 0.0912279i | ||||
\(425\) | 13.0780 | − | 0.805673i | 0.634376 | − | 0.0390809i | ||||
\(426\) | −6.48120 | + | 6.48120i | −0.314015 | + | 0.314015i | ||||
\(427\) | 25.1024i | 1.21479i | ||||||||
\(428\) | −4.17096 | − | 4.17096i | −0.201611 | − | 0.201611i | ||||
\(429\) | −6.32566 | − | 6.32566i | −0.305406 | − | 0.305406i | ||||
\(430\) | 14.0494 | − | 0.432349i | 0.677524 | − | 0.0208497i | ||||
\(431\) | 25.8053 | + | 25.8053i | 1.24300 | + | 1.24300i | 0.958752 | + | 0.284245i | \(0.0917428\pi\) |
0.284245 | + | 0.958752i | \(0.408257\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −2.62555 | + | 2.62555i | −0.126176 | + | 0.126176i | −0.767375 | − | 0.641199i | \(-0.778437\pi\) |
0.641199 | + | 0.767375i | \(0.278437\pi\) | |||||||
\(434\) | 1.67202 | 0.0802597 | ||||||||
\(435\) | −1.15365 | + | 0.0355018i | −0.0553133 | + | 0.00170218i | ||||
\(436\) | −0.461041 | − | 0.461041i | −0.0220799 | − | 0.0220799i | ||||
\(437\) | 5.17192 | − | 5.17192i | 0.247407 | − | 0.247407i | ||||
\(438\) | −12.0228 | −0.574471 | ||||||||
\(439\) | 4.04448 | − | 4.04448i | 0.193033 | − | 0.193033i | −0.603973 | − | 0.797005i | \(-0.706416\pi\) |
0.797005 | + | 0.603973i | \(0.206416\pi\) | |||||||
\(440\) | 4.63422 | − | 0.142611i | 0.220928 | − | 0.00679871i | ||||
\(441\) | −2.12544 | −0.101211 | ||||||||
\(442\) | −11.3062 | −0.537782 | ||||||||
\(443\) | 0.534873 | + | 0.534873i | 0.0254126 | + | 0.0254126i | 0.719699 | − | 0.694286i | \(-0.244280\pi\) |
−0.694286 | + | 0.719699i | \(0.744280\pi\) | |||||||
\(444\) | −5.74848 | − | 1.98872i | −0.272811 | − | 0.0943806i | ||||
\(445\) | −7.98601 | + | 8.49313i | −0.378573 | + | 0.402613i | ||||
\(446\) | −4.85478 | − | 4.85478i | −0.229881 | − | 0.229881i | ||||
\(447\) | −1.25869 | + | 1.25869i | −0.0595341 | + | 0.0595341i | ||||
\(448\) | −2.13605 | − | 2.13605i | −0.100919 | − | 0.100919i | ||||
\(449\) | −15.2168 | − | 15.2168i | −0.718124 | − | 0.718124i | 0.250097 | − | 0.968221i | \(-0.419538\pi\) |
−0.968221 | + | 0.250097i | \(0.919538\pi\) | |||||||
\(450\) | 4.99054 | − | 0.307443i | 0.235256 | − | 0.0144930i | ||||
\(451\) | 7.87944 | 0.371029 | ||||||||
\(452\) | 17.3203 | 0.814678 | ||||||||
\(453\) | −10.4383 | + | 10.4383i | −0.490435 | + | 0.490435i | ||||
\(454\) | 19.5601i | 0.917999i | ||||||||
\(455\) | 19.9637 | − | 21.2314i | 0.935911 | − | 0.995342i | ||||
\(456\) | 2.09313 | 0.0980200 | ||||||||
\(457\) | −26.8366 | −1.25536 | −0.627682 | − | 0.778470i | \(-0.715996\pi\) | ||||
−0.627682 | + | 0.778470i | \(0.715996\pi\) | |||||||
\(458\) | 5.52626 | 0.258225 | ||||||||
\(459\) | −1.85302 | + | 1.85302i | −0.0864914 | + | 0.0864914i | ||||
\(460\) | −0.240340 | − | 7.80997i | −0.0112059 | − | 0.364142i | ||||
\(461\) | 9.31792 | − | 9.31792i | 0.433979 | − | 0.433979i | −0.456001 | − | 0.889980i | \(-0.650718\pi\) |
0.889980 | + | 0.456001i | \(0.150718\pi\) | |||||||
\(462\) | − | 6.26360i | − | 0.291409i | ||||||
\(463\) | − | 31.8446i | − | 1.47995i | −0.672637 | − | 0.739973i | \(-0.734838\pi\) | ||
0.672637 | − | 0.739973i | \(-0.265162\pi\) | |||||||
\(464\) | −0.364989 | + | 0.364989i | −0.0169442 | + | 0.0169442i | ||||
\(465\) | 0.0380689 | + | 1.23707i | 0.00176540 | + | 0.0573678i | ||||
\(466\) | −8.07622 | + | 8.07622i | −0.374124 | + | 0.374124i | ||||
\(467\) | 24.6295 | 1.13972 | 0.569859 | − | 0.821743i | \(-0.306998\pi\) | ||||
0.569859 | + | 0.821743i | \(0.306998\pi\) | |||||||
\(468\) | −4.31443 | −0.199435 | ||||||||
\(469\) | 13.0634 | 0.603210 | ||||||||
\(470\) | 7.31966 | − | 7.78447i | 0.337631 | − | 0.359071i | ||||
\(471\) | 4.28456i | 0.197422i | ||||||||
\(472\) | −0.917356 | + | 0.917356i | −0.0422248 | + | 0.0422248i | ||||
\(473\) | 13.0340 | 0.599302 | ||||||||
\(474\) | −12.7440 | −0.585351 | ||||||||
\(475\) | −7.84138 | − | 6.93131i | −0.359787 | − | 0.318030i | ||||
\(476\) | −5.59765 | − | 5.59765i | −0.256568 | − | 0.256568i | ||||
\(477\) | −1.87850 | − | 1.87850i | −0.0860105 | − | 0.0860105i | ||||
\(478\) | 1.04218 | − | 1.04218i | 0.0476681 | − | 0.0476681i | ||||
\(479\) | −3.98964 | − | 3.98964i | −0.182291 | − | 0.182291i | 0.610062 | − | 0.792353i | \(-0.291144\pi\) |
−0.792353 | + | 0.610062i | \(0.791144\pi\) | |||||||
\(480\) | 1.53176 | − | 1.62902i | 0.0699148 | − | 0.0743545i | ||||
\(481\) | −11.4701 | − | 23.6044i | −0.522992 | − | 1.07627i | ||||
\(482\) | −2.39676 | − | 2.39676i | −0.109169 | − | 0.109169i | ||||
\(483\) | −10.5559 | −0.480312 | ||||||||
\(484\) | −6.70073 | −0.304579 | ||||||||
\(485\) | 31.6065 | − | 0.972640i | 1.43518 | − | 0.0441653i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 33.5571 | 1.52062 | 0.760309 | − | 0.649561i | \(-0.225047\pi\) | ||||
0.760309 | + | 0.649561i | \(0.225047\pi\) | |||||||
\(488\) | −5.87589 | + | 5.87589i | −0.265989 | + | 0.265989i | ||||
\(489\) | 4.52216 | + | 4.52216i | 0.204499 | + | 0.204499i | ||||
\(490\) | 4.75038 | − | 0.146186i | 0.214600 | − | 0.00660399i | ||||
\(491\) | 31.9342 | 1.44117 | 0.720585 | − | 0.693366i | \(-0.243873\pi\) | ||||
0.720585 | + | 0.693366i | \(0.243873\pi\) | |||||||
\(492\) | 2.68710 | − | 2.68710i | 0.121144 | − | 0.121144i | ||||
\(493\) | −0.956475 | + | 0.956475i | −0.0430775 | + | 0.0430775i | ||||
\(494\) | 6.38566 | + | 6.38566i | 0.287304 | + | 0.287304i | ||||
\(495\) | 4.63422 | − | 0.142611i | 0.208293 | − | 0.00640988i | ||||
\(496\) | 0.391381 | + | 0.391381i | 0.0175735 | + | 0.0175735i | ||||
\(497\) | −19.5786 | − | 19.5786i | −0.878222 | − | 0.878222i | ||||
\(498\) | 0.539372i | 0.0241698i | ||||||||
\(499\) | −25.1910 | + | 25.1910i | −1.12770 | + | 1.12770i | −0.137154 | + | 0.990550i | \(0.543796\pi\) |
−0.990550 | + | 0.137154i | \(0.956204\pi\) | |||||||
\(500\) | −11.1328 | + | 1.03038i | −0.497872 | + | 0.0460801i | ||||
\(501\) | −5.23439 | − | 5.23439i | −0.233855 | − | 0.233855i | ||||
\(502\) | 14.2994 | − | 14.2994i | 0.638214 | − | 0.638214i | ||||
\(503\) | − | 6.19986i | − | 0.276438i | −0.990402 | − | 0.138219i | \(-0.955862\pi\) | ||
0.990402 | − | 0.138219i | \(-0.0441378\pi\) | |||||||
\(504\) | −2.13605 | − | 2.13605i | −0.0951473 | − | 0.0951473i | ||||
\(505\) | −0.525735 | − | 17.0841i | −0.0233949 | − | 0.760231i | ||||
\(506\) | − | 7.24548i | − | 0.322101i | ||||||
\(507\) | −3.96992 | − | 3.96992i | −0.176310 | − | 0.176310i | ||||
\(508\) | 6.18161 | + | 6.18161i | 0.274265 | + | 0.274265i | ||||
\(509\) | −2.76652 | −0.122624 | −0.0613120 | − | 0.998119i | \(-0.519528\pi\) | ||||
−0.0613120 | + | 0.998119i | \(0.519528\pi\) | |||||||
\(510\) | 4.01406 | − | 4.26896i | 0.177746 | − | 0.189033i | ||||
\(511\) | − | 36.3188i | − | 1.60665i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.09313 | 0.0924141 | ||||||||
\(514\) | 22.9481i | 1.01220i | ||||||||
\(515\) | −22.0346 | + | 0.678081i | −0.970962 | + | 0.0298798i | ||||
\(516\) | 4.44492 | − | 4.44492i | 0.195677 | − | 0.195677i | ||||
\(517\) | 7.00621 | − | 7.00621i | 0.308133 | − | 0.308133i | ||||
\(518\) | 6.00760 | − | 17.3652i | 0.263959 | − | 0.762983i | ||||
\(519\) | − | 23.1907i | − | 1.01796i | ||||||
\(520\) | 9.64280 | − | 0.296742i | 0.422865 | − | 0.0130130i | ||||
\(521\) | − | 9.79854i | − | 0.429282i | −0.976693 | − | 0.214641i | \(-0.931142\pi\) | ||
0.976693 | − | 0.214641i | \(-0.0688581\pi\) | |||||||
\(522\) | −0.364989 | + | 0.364989i | −0.0159751 | + | 0.0159751i | ||||
\(523\) | 10.5951i | 0.463289i | 0.972800 | + | 0.231645i | \(0.0744107\pi\) | ||||
−0.972800 | + | 0.231645i | \(0.925589\pi\) | |||||||
\(524\) | −1.03836 | − | 1.03836i | −0.0453608 | − | 0.0453608i | ||||
\(525\) | 0.928735 | + | 15.0756i | 0.0405333 | + | 0.657953i | ||||
\(526\) | −0.797307 | + | 0.797307i | −0.0347642 | + | 0.0347642i | ||||
\(527\) | 1.02564 | + | 1.02564i | 0.0446775 | + | 0.0446775i | ||||
\(528\) | 1.46616 | − | 1.46616i | 0.0638065 | − | 0.0638065i | ||||
\(529\) | 10.7893 | 0.469101 | ||||||||
\(530\) | 4.32766 | + | 4.06926i | 0.187982 | + | 0.176757i | ||||
\(531\) | −0.917356 | + | 0.917356i | −0.0398099 | + | 0.0398099i | ||||
\(532\) | 6.32301i | 0.274137i | ||||||||
\(533\) | 16.3954 | 0.710163 | ||||||||
\(534\) | 5.21363i | 0.225616i | ||||||||
\(535\) | 9.60901 | + | 9.03526i | 0.415434 | + | 0.390629i | ||||
\(536\) | 3.05783 | + | 3.05783i | 0.132078 | + | 0.132078i | ||||
\(537\) | −22.9736 | −0.991385 | ||||||||
\(538\) | 17.8697 | 0.770418 | ||||||||
\(539\) | 4.40703 | 0.189824 | ||||||||
\(540\) | 1.53176 | − | 1.62902i | 0.0659163 | − | 0.0701021i | ||||
\(541\) | 23.3766 | − | 23.3766i | 1.00504 | − | 1.00504i | 0.00505037 | − | 0.999987i | \(-0.498392\pi\) |
0.999987 | − | 0.00505037i | \(-0.00160759\pi\) | |||||||
\(542\) | 20.7623i | 0.891818i | ||||||||
\(543\) | −3.85874 | − | 3.85874i | −0.165594 | − | 0.165594i | ||||
\(544\) | − | 2.62056i | − | 0.112356i | ||||||
\(545\) | 1.06214 | + | 0.998722i | 0.0454971 | + | 0.0427805i | ||||
\(546\) | − | 13.0332i | − | 0.557769i | ||||||
\(547\) | − | 17.2554i | − | 0.737787i | −0.929472 | − | 0.368894i | \(-0.879737\pi\) | ||
0.929472 | − | 0.368894i | \(-0.120263\pi\) | |||||||
\(548\) | 13.3475 | + | 13.3475i | 0.570176 | + | 0.570176i | ||||
\(549\) | −5.87589 | + | 5.87589i | −0.250777 | + | 0.250777i | ||||
\(550\) | −10.3477 | + | 0.637473i | −0.441228 | + | 0.0271820i | ||||
\(551\) | 1.08042 | 0.0460273 | ||||||||
\(552\) | −2.47090 | − | 2.47090i | −0.105168 | − | 0.105168i | ||||
\(553\) | − | 38.4975i | − | 1.63708i | ||||||
\(554\) | 17.8467 | 0.758233 | ||||||||
\(555\) | 12.9847 | + | 4.04944i | 0.551169 | + | 0.171889i | ||||
\(556\) | −12.1026 | −0.513267 | ||||||||
\(557\) | 17.6010i | 0.745779i | 0.927876 | + | 0.372889i | \(0.121633\pi\) | ||||
−0.927876 | + | 0.372889i | \(0.878367\pi\) | |||||||
\(558\) | 0.391381 | + | 0.391381i | 0.0165685 | + | 0.0165685i | ||||
\(559\) | 27.1208 | 1.14709 | ||||||||
\(560\) | 4.92101 | + | 4.62718i | 0.207951 | + | 0.195534i | ||||
\(561\) | 3.84217 | − | 3.84217i | 0.162216 | − | 0.162216i | ||||
\(562\) | 10.2645 | + | 10.2645i | 0.432983 | + | 0.432983i | ||||
\(563\) | − | 24.3413i | − | 1.02586i | −0.858429 | − | 0.512932i | \(-0.828559\pi\) | ||
0.858429 | − | 0.512932i | \(-0.171441\pi\) | |||||||
\(564\) | − | 4.77861i | − | 0.201216i | ||||||
\(565\) | −38.7110 | + | 1.19127i | −1.62859 | + | 0.0501172i | ||||
\(566\) | 9.49377i | 0.399053i | ||||||||
\(567\) | −2.13605 | − | 2.13605i | −0.0897058 | − | 0.0897058i | ||||
\(568\) | − | 9.16581i | − | 0.384589i | ||||||
\(569\) | −3.96188 | + | 3.96188i | −0.166090 | + | 0.166090i | −0.785259 | − | 0.619168i | \(-0.787470\pi\) |
0.619168 | + | 0.785259i | \(0.287470\pi\) | |||||||
\(570\) | −4.67818 | + | 0.143963i | −0.195947 | + | 0.00602997i | ||||
\(571\) | −12.7277 | −0.532638 | −0.266319 | − | 0.963885i | \(-0.585807\pi\) | ||||
−0.266319 | + | 0.963885i | \(0.585807\pi\) | |||||||
\(572\) | 8.94583 | 0.374044 | ||||||||
\(573\) | −11.9882 | −0.500812 | ||||||||
\(574\) | 8.11728 | + | 8.11728i | 0.338809 | + | 0.338809i | ||||
\(575\) | 1.07432 | + | 17.4388i | 0.0448024 | + | 0.727250i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | −30.3340 | −1.26282 | −0.631410 | − | 0.775449i | \(-0.717524\pi\) | ||||
−0.631410 | + | 0.775449i | \(0.717524\pi\) | |||||||
\(578\) | 10.1327i | 0.421463i | ||||||||
\(579\) | −0.576459 | + | 0.576459i | −0.0239568 | + | 0.0239568i | ||||
\(580\) | 0.790650 | − | 0.840857i | 0.0328300 | − | 0.0349147i | ||||
\(581\) | −1.62935 | −0.0675970 | ||||||||
\(582\) | 9.99958 | − | 9.99958i | 0.414496 | − | 0.414496i | ||||
\(583\) | 3.89500 | + | 3.89500i | 0.161315 | + | 0.161315i | ||||
\(584\) | 8.50139 | − | 8.50139i | 0.351790 | − | 0.351790i | ||||
\(585\) | 9.64280 | − | 0.296742i | 0.398681 | − | 0.0122688i | ||||
\(586\) | 1.37161 | + | 1.37161i | 0.0566606 | + | 0.0566606i | ||||
\(587\) | − | 25.0340i | − | 1.03327i | −0.856207 | − | 0.516633i | \(-0.827185\pi\) | ||
0.856207 | − | 0.516633i | \(-0.172815\pi\) | |||||||
\(588\) | 1.50291 | − | 1.50291i | 0.0619791 | − | 0.0619791i | ||||
\(589\) | − | 1.15854i | − | 0.0477369i | ||||||
\(590\) | 1.98721 | − | 2.11340i | 0.0818120 | − | 0.0870071i | ||||
\(591\) | − | 17.1851i | − | 0.706900i | ||||||
\(592\) | 5.47103 | − | 2.65855i | 0.224858 | − | 0.109266i | ||||
\(593\) | 16.2930 | − | 16.2930i | 0.669073 | − | 0.669073i | −0.288428 | − | 0.957502i | \(-0.593133\pi\) |
0.957502 | + | 0.288428i | \(0.0931327\pi\) | |||||||
\(594\) | 1.46616 | − | 1.46616i | 0.0601574 | − | 0.0601574i | ||||
\(595\) | 12.8958 | + | 12.1258i | 0.528677 | + | 0.497110i | ||||
\(596\) | − | 1.78006i | − | 0.0729141i | ||||||
\(597\) | 9.09548 | 0.372253 | ||||||||
\(598\) | − | 15.0763i | − | 0.616514i | ||||||
\(599\) | 18.7185i | 0.764818i | 0.923993 | + | 0.382409i | \(0.124905\pi\) | ||||
−0.923993 | + | 0.382409i | \(0.875095\pi\) | |||||||
\(600\) | −3.31145 | + | 3.74624i | −0.135189 | + | 0.152940i | ||||
\(601\) | −34.1418 | −1.39267 | −0.696337 | − | 0.717715i | \(-0.745188\pi\) | ||||
−0.696337 | + | 0.717715i | \(0.745188\pi\) | |||||||
\(602\) | 13.4274 | + | 13.4274i | 0.547259 | + | 0.547259i | ||||
\(603\) | 3.05783 | + | 3.05783i | 0.124524 | + | 0.124524i | ||||
\(604\) | − | 14.7620i | − | 0.600658i | ||||||
\(605\) | 14.9762 | − | 0.460869i | 0.608869 | − | 0.0187370i | ||||
\(606\) | −5.40501 | − | 5.40501i | −0.219564 | − | 0.219564i | ||||
\(607\) | 15.4550i | 0.627298i | 0.949539 | + | 0.313649i | \(0.101551\pi\) | ||||
−0.949539 | + | 0.313649i | \(0.898449\pi\) | |||||||
\(608\) | −1.48007 | + | 1.48007i | −0.0600247 | + | 0.0600247i | ||||
\(609\) | −1.10257 | − | 1.10257i | −0.0446784 | − | 0.0446784i | ||||
\(610\) | 12.7285 | − | 13.5368i | 0.515363 | − | 0.548089i | ||||
\(611\) | 14.5784 | − | 14.5784i | 0.589779 | − | 0.589779i | ||||
\(612\) | − | 2.62056i | − | 0.105930i | ||||||
\(613\) | 25.2055 | + | 25.2055i | 1.01804 | + | 1.01804i | 0.999834 | + | 0.0182063i | \(0.00579555\pi\) |
0.0182063 | + | 0.999834i | \(0.494204\pi\) | |||||||
\(614\) | 12.9742 | + | 12.9742i | 0.523596 | + | 0.523596i | ||||
\(615\) | −5.82087 | + | 6.19050i | −0.234720 | + | 0.249625i | ||||
\(616\) | 4.42903 | + | 4.42903i | 0.178451 | + | 0.178451i | ||||
\(617\) | −14.0812 | + | 14.0812i | −0.566887 | + | 0.566887i | −0.931255 | − | 0.364368i | \(-0.881285\pi\) |
0.364368 | + | 0.931255i | \(0.381285\pi\) | |||||||
\(618\) | −6.97126 | + | 6.97126i | −0.280425 | + | 0.280425i | ||||
\(619\) | 11.5159 | 0.462861 | 0.231431 | − | 0.972851i | \(-0.425659\pi\) | ||||
0.231431 | + | 0.972851i | \(0.425659\pi\) | |||||||
\(620\) | −0.901660 | − | 0.847823i | −0.0362115 | − | 0.0340494i | ||||
\(621\) | −2.47090 | − | 2.47090i | −0.0991538 | − | 0.0991538i | ||||
\(622\) | 21.1073 | − | 21.1073i | 0.846327 | − | 0.846327i | ||||
\(623\) | −15.7495 | −0.630991 | ||||||||
\(624\) | 3.05076 | − | 3.05076i | 0.122128 | − | 0.122128i | ||||
\(625\) | 24.8110 | − | 3.06861i | 0.992438 | − | 0.122745i | ||||
\(626\) | −27.9746 | −1.11809 | ||||||||
\(627\) | −4.34004 | −0.173325 | ||||||||
\(628\) | −3.02964 | − | 3.02964i | −0.120896 | − | 0.120896i | ||||
\(629\) | 14.3372 | − | 6.96688i | 0.571660 | − | 0.277788i | ||||
\(630\) | 4.92101 | + | 4.62718i | 0.196058 | + | 0.184351i | ||||
\(631\) | 24.9435 | + | 24.9435i | 0.992985 | + | 0.992985i | 0.999976 | − | 0.00699059i | \(-0.00222519\pi\) |
−0.00699059 | + | 0.999976i | \(0.502225\pi\) | |||||||
\(632\) | 9.01137 | − | 9.01137i | 0.358453 | − | 0.358453i | ||||
\(633\) | −1.30741 | − | 1.30741i | −0.0519649 | − | 0.0519649i | ||||
\(634\) | 4.72175 | + | 4.72175i | 0.187525 | + | 0.187525i | ||||
\(635\) | −14.2411 | − | 13.3908i | −0.565142 | − | 0.531398i | ||||
\(636\) | 2.65660 | 0.105341 | ||||||||
\(637\) | 9.17007 | 0.363331 | ||||||||
\(638\) | 0.756793 | − | 0.756793i | 0.0299617 | − | 0.0299617i | ||||
\(639\) | − | 9.16581i | − | 0.362594i | ||||||
\(640\) | 0.0687789 | + | 2.23501i | 0.00271873 | + | 0.0883465i | ||||
\(641\) | 41.0494 | 1.62136 | 0.810678 | − | 0.585492i | \(-0.199099\pi\) | ||||
0.810678 | + | 0.585492i | \(0.199099\pi\) | |||||||
\(642\) | 5.89863 | 0.232800 | ||||||||
\(643\) | 16.4624 | 0.649212 | 0.324606 | − | 0.945849i | \(-0.394768\pi\) | ||||
0.324606 | + | 0.945849i | \(0.394768\pi\) | |||||||
\(644\) | 7.46418 | − | 7.46418i | 0.294130 | − | 0.294130i | ||||
\(645\) | −9.62873 | + | 10.2402i | −0.379131 | + | 0.403206i | ||||
\(646\) | −3.87861 | + | 3.87861i | −0.152602 | + | 0.152602i | ||||
\(647\) | 40.3405i | 1.58595i | 0.609256 | + | 0.792974i | \(0.291468\pi\) | ||||
−0.609256 | + | 0.792974i | \(0.708532\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 1.90211 | − | 1.90211i | 0.0746643 | − | 0.0746643i | ||||
\(650\) | −21.5313 | + | 1.32644i | −0.844528 | + | 0.0520273i | ||||
\(651\) | −1.18230 | + | 1.18230i | −0.0463379 | + | 0.0463379i | ||||
\(652\) | −6.39530 | −0.250459 | ||||||||
\(653\) | −34.2938 | −1.34202 | −0.671009 | − | 0.741449i | \(-0.734139\pi\) | ||||
−0.671009 | + | 0.741449i | \(0.734139\pi\) | |||||||
\(654\) | 0.652011 | 0.0254956 | ||||||||
\(655\) | 2.39216 | + | 2.24932i | 0.0934692 | + | 0.0878883i | ||||
\(656\) | 3.80013i | 0.148370i | ||||||||
\(657\) | 8.50139 | − | 8.50139i | 0.331671 | − | 0.331671i | ||||
\(658\) | 14.4354 | 0.562750 | ||||||||
\(659\) | −35.9415 | −1.40008 | −0.700040 | − | 0.714104i | \(-0.746835\pi\) | ||||
−0.700040 | + | 0.714104i | \(0.746835\pi\) | |||||||
\(660\) | −3.17605 | + | 3.37773i | −0.123627 | + | 0.131478i | ||||
\(661\) | 15.5165 | + | 15.5165i | 0.603520 | + | 0.603520i | 0.941245 | − | 0.337725i | \(-0.109657\pi\) |
−0.337725 | + | 0.941245i | \(0.609657\pi\) | |||||||
\(662\) | −5.59691 | − | 5.59691i | −0.217530 | − | 0.217530i | ||||
\(663\) | 7.99471 | − | 7.99471i | 0.310489 | − | 0.310489i | ||||
\(664\) | −0.381394 | − | 0.381394i | −0.0148009 | − | 0.0148009i | ||||
\(665\) | −0.434890 | − | 14.1320i | −0.0168643 | − | 0.548015i | ||||
\(666\) | 5.47103 | − | 2.65855i | 0.211998 | − | 0.103017i | ||||
\(667\) | −1.27541 | − | 1.27541i | −0.0493841 | − | 0.0493841i | ||||
\(668\) | 7.40255 | 0.286413 | ||||||||
\(669\) | 6.86570 | 0.265443 | ||||||||
\(670\) | −7.04459 | − | 6.62397i | −0.272156 | − | 0.255906i | ||||
\(671\) | 12.1835 | − | 12.1835i | 0.470337 | − | 0.470337i | ||||
\(672\) | 3.02083 | 0.116531 | ||||||||
\(673\) | 32.7754 | − | 32.7754i | 1.26340 | − | 1.26340i | 0.313966 | − | 0.949434i | \(-0.398342\pi\) |
0.949434 | − | 0.313966i | \(-0.101658\pi\) | |||||||
\(674\) | −15.5752 | − | 15.5752i | −0.599933 | − | 0.599933i | ||||
\(675\) | −3.31145 | + | 3.74624i | −0.127458 | + | 0.144193i | ||||
\(676\) | 5.61431 | 0.215935 | ||||||||
\(677\) | 5.04971 | − | 5.04971i | 0.194076 | − | 0.194076i | −0.603379 | − | 0.797455i | \(-0.706179\pi\) |
0.797455 | + | 0.603379i | \(0.206179\pi\) | |||||||
\(678\) | −12.2473 | + | 12.2473i | −0.470355 | + | 0.470355i | ||||
\(679\) | 30.2071 | + | 30.2071i | 1.15924 | + | 1.15924i | ||||
\(680\) | 0.180239 | + | 5.85698i | 0.00691186 | + | 0.224605i | ||||
\(681\) | −13.8310 | − | 13.8310i | −0.530007 | − | 0.530007i | ||||
\(682\) | −0.811517 | − | 0.811517i | −0.0310746 | − | 0.0310746i | ||||
\(683\) | − | 35.9730i | − | 1.37647i | −0.725488 | − | 0.688235i | \(-0.758386\pi\) | ||
0.725488 | − | 0.688235i | \(-0.241614\pi\) | |||||||
\(684\) | −1.48007 | + | 1.48007i | −0.0565919 | + | 0.0565919i | ||||
\(685\) | −30.7498 | − | 28.9137i | −1.17489 | − | 1.10474i | ||||
\(686\) | −10.4123 | − | 10.4123i | −0.397544 | − | 0.397544i | ||||
\(687\) | −3.90766 | + | 3.90766i | −0.149086 | + | 0.149086i | ||||
\(688\) | 6.28607i | 0.239654i | ||||||||
\(689\) | 8.10465 | + | 8.10465i | 0.308762 | + | 0.308762i | ||||
\(690\) | 5.69243 | + | 5.35254i | 0.216707 | + | 0.203768i | ||||
\(691\) | 18.4832i | 0.703135i | 0.936163 | + | 0.351567i | \(0.114351\pi\) | ||||
−0.936163 | + | 0.351567i | \(0.885649\pi\) | |||||||
\(692\) | 16.3983 | + | 16.3983i | 0.623369 | + | 0.623369i | ||||
\(693\) | 4.42903 | + | 4.42903i | 0.168245 | + | 0.168245i | ||||
\(694\) | 7.34661 | 0.278873 | ||||||||
\(695\) | 27.0495 | − | 0.832407i | 1.02605 | − | 0.0315750i | ||||
\(696\) | − | 0.516172i | − | 0.0195655i | ||||||
\(697\) | 9.95847i | 0.377204i | ||||||||
\(698\) | −5.62756 | −0.213006 | ||||||||
\(699\) | − | 11.4215i | − | 0.432001i | ||||||
\(700\) | −11.3168 | − | 10.0033i | −0.427734 | − | 0.378091i | ||||
\(701\) | −14.1983 | + | 14.1983i | −0.536264 | + | 0.536264i | −0.922429 | − | 0.386166i | \(-0.873799\pi\) |
0.386166 | + | 0.922429i | \(0.373799\pi\) | |||||||
\(702\) | 3.05076 | − | 3.05076i | 0.115144 | − | 0.115144i | ||||
\(703\) | −12.0323 | − | 4.16266i | −0.453808 | − | 0.156998i | ||||
\(704\) | 2.07347i | 0.0781467i | ||||||||
\(705\) | 0.328667 | + | 10.6802i | 0.0123783 | + | 0.402241i | ||||
\(706\) | − | 25.6724i | − | 0.966192i | ||||||
\(707\) | 16.3276 | − | 16.3276i | 0.614064 | − | 0.614064i | ||||
\(708\) | − | 1.29734i | − | 0.0487569i | ||||||
\(709\) | −19.8820 | − | 19.8820i | −0.746684 | − | 0.746684i | 0.227171 | − | 0.973855i | \(-0.427053\pi\) |
−0.973855 | + | 0.227171i | \(0.927053\pi\) | |||||||
\(710\) | 0.630414 | + | 20.4857i | 0.0236590 | + | 0.768814i | ||||
\(711\) | 9.01137 | − | 9.01137i | 0.337953 | − | 0.337953i | ||||
\(712\) | −3.68659 | − | 3.68659i | −0.138161 | − | 0.138161i | ||||
\(713\) | −1.36764 | + | 1.36764i | −0.0512183 | + | 0.0512183i | ||||
\(714\) | 7.91628 | 0.296259 | ||||||||
\(715\) | −19.9940 | + | 0.615285i | −0.747734 | + | 0.0230103i | ||||
\(716\) | 16.2448 | − | 16.2448i | 0.607097 | − | 0.607097i | ||||
\(717\) | 1.47386i | 0.0550424i | ||||||||
\(718\) | −29.6458 | −1.10637 | ||||||||
\(719\) | − | 5.03356i | − | 0.187720i | −0.995585 | − | 0.0938601i | \(-0.970079\pi\) | ||
0.995585 | − | 0.0938601i | \(-0.0299206\pi\) | |||||||
\(720\) | 0.0687789 | + | 2.23501i | 0.00256324 | + | 0.0832939i | ||||
\(721\) | −21.0590 | − | 21.0590i | −0.784279 | − | 0.784279i | ||||
\(722\) | −14.6188 | −0.544055 | ||||||||
\(723\) | 3.38953 | 0.126058 | ||||||||
\(724\) | 5.45708 | 0.202811 | ||||||||
\(725\) | −1.70928 | + | 1.93370i | −0.0634810 | + | 0.0718160i | ||||
\(726\) | 4.73813 | − | 4.73813i | 0.175849 | − | 0.175849i | ||||
\(727\) | − | 6.59381i | − | 0.244551i | −0.992496 | − | 0.122275i | \(-0.960981\pi\) | ||
0.992496 | − | 0.122275i | \(-0.0390191\pi\) | |||||||
\(728\) | 9.21585 | + | 9.21585i | 0.341562 | + | 0.341562i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −18.4160 | + | 19.5854i | −0.681606 | + | 0.724888i | ||||
\(731\) | 16.4730i | 0.609277i | ||||||||
\(732\) | − | 8.30976i | − | 0.307138i | ||||||
\(733\) | −32.6674 | − | 32.6674i | −1.20660 | − | 1.20660i | −0.972122 | − | 0.234474i | \(-0.924663\pi\) |
−0.234474 | − | 0.972122i | \(-0.575337\pi\) | |||||||
\(734\) | −22.3758 | + | 22.3758i | −0.825904 | + | 0.825904i | ||||
\(735\) | −3.25566 | + | 3.46240i | −0.120087 | + | 0.127712i | ||||
\(736\) | 3.49438 | 0.128805 | ||||||||
\(737\) | −6.34031 | − | 6.34031i | −0.233548 | − | 0.233548i | ||||
\(738\) | 3.80013i | 0.139885i | ||||||||
\(739\) | 2.57619 | 0.0947665 | 0.0473833 | − | 0.998877i | \(-0.484912\pi\) | ||||
0.0473833 | + | 0.998877i | \(0.484912\pi\) | |||||||
\(740\) | −12.0449 | + | 6.31817i | −0.442781 | + | 0.232261i | ||||
\(741\) | −9.03068 | −0.331750 | ||||||||
\(742\) | 8.02514i | 0.294612i | ||||||||
\(743\) | 16.2323 | + | 16.2323i | 0.595504 | + | 0.595504i | 0.939113 | − | 0.343609i | \(-0.111649\pi\) |
−0.343609 | + | 0.939113i | \(0.611649\pi\) | |||||||
\(744\) | −0.553497 | −0.0202922 | ||||||||
\(745\) | 0.122431 | + | 3.97845i | 0.00448551 | + | 0.145759i | ||||
\(746\) | −2.58745 | + | 2.58745i | −0.0947334 | + | 0.0947334i | ||||
\(747\) | −0.381394 | − | 0.381394i | −0.0139545 | − | 0.0139545i | ||||
\(748\) | 5.43364i | 0.198674i | ||||||||
\(749\) | 17.8188i | 0.651084i | ||||||||
\(750\) | 7.14346 | − | 8.60064i | 0.260842 | − | 0.314051i | ||||
\(751\) | 9.18070i | 0.335009i | 0.985871 | + | 0.167504i | \(0.0535708\pi\) | ||||
−0.985871 | + | 0.167504i | \(0.946429\pi\) | |||||||
\(752\) | 3.37898 | + | 3.37898i | 0.123219 | + | 0.123219i | ||||
\(753\) | 20.2224i | 0.736946i | ||||||||
\(754\) | 1.57472 | − | 1.57472i | 0.0573479 | − | 0.0573479i | ||||
\(755\) | 1.01532 | + | 32.9933i | 0.0369511 | + | 1.20075i | ||||
\(756\) | 3.02083 | 0.109867 | ||||||||
\(757\) | 7.11882 | 0.258738 | 0.129369 | − | 0.991597i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991597i | \(0.458705\pi\) | |||||||
\(758\) | 30.1390 | 1.09470 | ||||||||
\(759\) | 5.12333 | + | 5.12333i | 0.185965 | + | 0.185965i | ||||
\(760\) | 3.20617 | − | 3.40977i | 0.116300 | − | 0.123685i | ||||
\(761\) | − | 7.70500i | − | 0.279306i | −0.990200 | − | 0.139653i | \(-0.955401\pi\) | ||
0.990200 | − | 0.139653i | \(-0.0445987\pi\) | |||||||
\(762\) | −8.74212 | −0.316694 | ||||||||
\(763\) | 1.96962i | 0.0713049i | ||||||||
\(764\) | 8.47691 | − | 8.47691i | 0.306684 | − | 0.306684i | ||||
\(765\) | 0.180239 | + | 5.85698i | 0.00651656 | + | 0.211759i | ||||
\(766\) | 27.3379 | 0.987759 | ||||||||
\(767\) | 3.95787 | − | 3.95787i | 0.142910 | − | 0.142910i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | 30.6954 | − | 30.6954i | 1.10690 | − | 1.10690i | 0.113349 | − | 0.993555i | \(-0.463842\pi\) |
0.993555 | − | 0.113349i | \(-0.0361579\pi\) | |||||||
\(770\) | −10.2036 | − | 9.59431i | −0.367711 | − | 0.345755i | ||||
\(771\) | −16.2267 | − | 16.2267i | −0.584392 | − | 0.584392i | ||||
\(772\) | − | 0.815237i | − | 0.0293410i | ||||||
\(773\) | −26.9674 | + | 26.9674i | −0.969949 | + | 0.969949i | −0.999561 | − | 0.0296121i | \(-0.990573\pi\) |
0.0296121 | + | 0.999561i | \(0.490573\pi\) | |||||||
\(774\) | 6.28607i | 0.225948i | ||||||||
\(775\) | 2.07353 | + | 1.83288i | 0.0744835 | + | 0.0658389i | ||||
\(776\) | 14.1415i | 0.507652i | ||||||||
\(777\) | 8.03103 | + | 16.5271i | 0.288112 | + | 0.592905i | ||||
\(778\) | 7.29908 | − | 7.29908i | 0.261685 | − | 0.261685i | ||||
\(779\) | 5.62445 | − | 5.62445i | 0.201517 | − | 0.201517i | ||||
\(780\) | −6.60866 | + | 7.02831i | −0.236628 | + | 0.251654i | ||||
\(781\) | 19.0050i | 0.680052i | ||||||||
\(782\) | 9.15723 | 0.327462 | ||||||||
\(783\) | − | 0.516172i | − | 0.0184465i | ||||||
\(784\) | 2.12544i | 0.0759086i | ||||||||
\(785\) | 6.97966 | + | 6.56290i | 0.249115 | + | 0.234240i | ||||
\(786\) | 1.46846 | 0.0523782 | ||||||||
\(787\) | 5.73093 | + | 5.73093i | 0.204286 | + | 0.204286i | 0.801833 | − | 0.597548i | \(-0.203858\pi\) |
−0.597548 | + | 0.801833i | \(0.703858\pi\) | |||||||
\(788\) | 12.1517 | + | 12.1517i | 0.432886 | + | 0.432886i | ||||
\(789\) | − | 1.12756i | − | 0.0401423i | ||||||
\(790\) | −19.5207 | + | 20.7603i | −0.694515 | + | 0.738618i | ||||
\(791\) | −36.9971 | − | 36.9971i | −1.31546 | − | 1.31546i | ||||
\(792\) | 2.07347i | 0.0736774i | ||||||||
\(793\) | 25.3511 | − | 25.3511i | 0.900245 | − | 0.900245i | ||||
\(794\) | −23.8828 | − | 23.8828i | −0.847568 | − | 0.847568i | ||||
\(795\) | −5.93752 | + | 0.182718i | −0.210582 | + | 0.00648033i | ||||
\(796\) | −6.43148 | + | 6.43148i | −0.227958 | + | 0.227958i | ||||
\(797\) | 53.4909i | 1.89474i | 0.320135 | + | 0.947372i | \(0.396272\pi\) | ||||
−0.320135 | + | 0.947372i | \(0.603728\pi\) | |||||||
\(798\) | −4.47104 | − | 4.47104i | −0.158273 | − | 0.158273i | ||||
\(799\) | 8.85483 | + | 8.85483i | 0.313261 | + | 0.313261i | ||||
\(800\) | −0.307443 | − | 4.99054i | −0.0108698 | − | 0.176442i | ||||
\(801\) | −3.68659 | − | 3.68659i | −0.130259 | − | 0.130259i | ||||
\(802\) | 9.30160 | − | 9.30160i | 0.328451 | − | 0.328451i | ||||
\(803\) | −17.6273 | + | 17.6273i | −0.622056 | + | 0.622056i | ||||
\(804\) | −4.32442 | −0.152511 | ||||||||
\(805\) | −16.1691 | + | 17.1959i | −0.569887 | + | 0.606075i | ||||
\(806\) | −1.68859 | − | 1.68859i | −0.0594780 | − | 0.0594780i | ||||
\(807\) | −12.6358 | + | 12.6358i | −0.444801 | + | 0.444801i | ||||
\(808\) | 7.64384 | 0.268909 | ||||||||
\(809\) | 18.8689 | − | 18.8689i | 0.663396 | − | 0.663396i | −0.292783 | − | 0.956179i | \(-0.594581\pi\) |
0.956179 | + | 0.292783i | \(0.0945815\pi\) | |||||||
\(810\) | 0.0687789 | + | 2.23501i | 0.00241665 | + | 0.0785302i | ||||
\(811\) | −7.19705 | −0.252723 | −0.126361 | − | 0.991984i | \(-0.540330\pi\) | ||||
−0.126361 | + | 0.991984i | \(0.540330\pi\) | |||||||
\(812\) | 1.55927 | 0.0547197 | ||||||||
\(813\) | −14.6812 | − | 14.6812i | −0.514891 | − | 0.514891i | ||||
\(814\) | −11.3440 | + | 5.51241i | −0.397607 | + | 0.193210i | ||||
\(815\) | 14.2936 | − | 0.439862i | 0.500681 | − | 0.0154077i | ||||
\(816\) | 1.85302 | + | 1.85302i | 0.0648685 | + | 0.0648685i | ||||
\(817\) | 9.30382 | − | 9.30382i | 0.325499 | − | 0.325499i | ||||
\(818\) | 24.5847 | + | 24.5847i | 0.859583 | + | 0.859583i | ||||
\(819\) | 9.21585 | + | 9.21585i | 0.322028 | + | 0.322028i | ||||
\(820\) | −0.261369 | − | 8.49333i | −0.00912739 | − | 0.296600i | ||||
\(821\) | 18.4340 | 0.643352 | 0.321676 | − | 0.946850i | \(-0.395754\pi\) | ||||
0.321676 | + | 0.946850i | \(0.395754\pi\) | |||||||
\(822\) | −18.8762 | −0.658382 | ||||||||
\(823\) | −34.1801 | + | 34.1801i | −1.19144 | + | 1.19144i | −0.214782 | + | 0.976662i | \(0.568904\pi\) |
−0.976662 | + | 0.214782i | \(0.931096\pi\) | |||||||
\(824\) | − | 9.85885i | − | 0.343449i | ||||||
\(825\) | 6.86618 | − | 7.76770i | 0.239050 | − | 0.270437i | ||||
\(826\) | 3.91904 | 0.136361 | ||||||||
\(827\) | 22.3642 | 0.777681 | 0.388840 | − | 0.921305i | \(-0.372876\pi\) | ||||
0.388840 | + | 0.921305i | \(0.372876\pi\) | |||||||
\(828\) | 3.49438 | 0.121438 | ||||||||
\(829\) | −13.4981 | + | 13.4981i | −0.468809 | + | 0.468809i | −0.901529 | − | 0.432719i | \(-0.857554\pi\) |
0.432719 | + | 0.901529i | \(0.357554\pi\) | |||||||
\(830\) | 0.878651 | + | 0.826187i | 0.0304984 | + | 0.0286774i | ||||
\(831\) | −12.6195 | + | 12.6195i | −0.437766 | + | 0.437766i | ||||
\(832\) | 4.31443i | 0.149576i | ||||||||
\(833\) | 5.56984i | 0.192984i | ||||||||
\(834\) | 8.55786 | − | 8.55786i | 0.296335 | − | 0.296335i | ||||
\(835\) | −16.5448 | + | 0.509139i | −0.572555 | + | 0.0176195i | ||||
\(836\) | 3.06887 | − | 3.06887i | 0.106139 | − | 0.106139i | ||||
\(837\) | −0.553497 | −0.0191317 | ||||||||
\(838\) | −23.6748 | −0.817831 | ||||||||
\(839\) | 17.9355 | 0.619202 | 0.309601 | − | 0.950867i | \(-0.399805\pi\) | ||||
0.309601 | + | 0.950867i | \(0.399805\pi\) | |||||||
\(840\) | −6.75159 | + | 0.207770i | −0.232952 | + | 0.00716874i | ||||
\(841\) | 28.7336i | 0.990813i | ||||||||
\(842\) | −26.6921 | + | 26.6921i | −0.919870 | + | 0.919870i | ||||
\(843\) | −14.5162 | −0.499965 | ||||||||
\(844\) | 1.84896 | 0.0636437 | ||||||||
\(845\) | −12.5480 | + | 0.386146i | −0.431666 | + | 0.0132838i | ||||
\(846\) | 3.37898 | + | 3.37898i | 0.116172 | + | 0.116172i | ||||
\(847\) | 14.3131 | + | 14.3131i | 0.491805 | + | 0.491805i | ||||
\(848\) | −1.87850 | + | 1.87850i | −0.0645079 | + | 0.0645079i | ||||
\(849\) | −6.71311 | − | 6.71311i | −0.230393 | − | 0.230393i | ||||
\(850\) | −0.805673 | − | 13.0780i | −0.0276344 | − | 0.448572i | ||||
\(851\) | 9.28997 | + | 19.1178i | 0.318456 | + | 0.655351i | ||||
\(852\) | 6.48120 | + | 6.48120i | 0.222042 | + | 0.222042i | ||||
\(853\) | 48.5949 | 1.66386 | 0.831929 | − | 0.554883i | \(-0.187237\pi\) | ||||
0.831929 | + | 0.554883i | \(0.187237\pi\) | |||||||
\(854\) | 25.1024 | 0.858987 | ||||||||
\(855\) | 3.20617 | − | 3.40977i | 0.109649 | − | 0.116612i | ||||
\(856\) | −4.17096 | + | 4.17096i | −0.142560 | + | 0.142560i | ||||
\(857\) | −27.6764 | −0.945409 | −0.472704 | − | 0.881221i | \(-0.656722\pi\) | ||||
−0.472704 | + | 0.881221i | \(0.656722\pi\) | |||||||
\(858\) | −6.32566 | + | 6.32566i | −0.215954 | + | 0.215954i | ||||
\(859\) | 1.92645 | + | 1.92645i | 0.0657295 | + | 0.0657295i | 0.739207 | − | 0.673478i | \(-0.235200\pi\) |
−0.673478 | + | 0.739207i | \(0.735200\pi\) | |||||||
\(860\) | −0.432349 | − | 14.0494i | −0.0147430 | − | 0.479081i | ||||
\(861\) | −11.4796 | −0.391222 | ||||||||
\(862\) | 25.8053 | − | 25.8053i | 0.878931 | − | 0.878931i | ||||
\(863\) | 4.85716 | − | 4.85716i | 0.165340 | − | 0.165340i | −0.619588 | − | 0.784927i | \(-0.712700\pi\) |
0.784927 | + | 0.619588i | \(0.212700\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | −37.7782 | − | 35.5224i | −1.28450 | − | 1.20780i | ||||
\(866\) | 2.62555 | + | 2.62555i | 0.0892197 | + | 0.0892197i | ||||
\(867\) | −7.16488 | − | 7.16488i | −0.243332 | − | 0.243332i | ||||
\(868\) | − | 1.67202i | − | 0.0567522i | ||||||
\(869\) | −18.6848 | + | 18.6848i | −0.633838 | + | 0.633838i | ||||
\(870\) | 0.0355018 | + | 1.15365i | 0.00120362 | + | 0.0391124i | ||||
\(871\) | −13.1928 | − | 13.1928i | −0.447021 | − | 0.447021i | ||||
\(872\) | −0.461041 | + | 0.461041i | −0.0156128 | + | 0.0156128i | ||||
\(873\) | 14.1415i | 0.478619i | ||||||||
\(874\) | −5.17192 | − | 5.17192i | −0.174943 | − | 0.174943i | ||||
\(875\) | 25.9811 | + | 21.5792i | 0.878322 | + | 0.729510i | ||||
\(876\) | 12.0228i | 0.406212i | ||||||||
\(877\) | 41.2031 | + | 41.2031i | 1.39133 | + | 1.39133i | 0.822353 | + | 0.568978i | \(0.192661\pi\) |
0.568978 | + | 0.822353i | \(0.307339\pi\) | |||||||
\(878\) | −4.04448 | − | 4.04448i | −0.136495 | − | 0.136495i | ||||
\(879\) | −1.93975 | −0.0654261 | ||||||||
\(880\) | −0.142611 | − | 4.63422i | −0.00480741 | − | 0.156220i | ||||
\(881\) | − | 4.54000i | − | 0.152957i | −0.997071 | − | 0.0764783i | \(-0.975632\pi\) | ||
0.997071 | − | 0.0764783i | \(-0.0243676\pi\) | |||||||
\(882\) | 2.12544i | 0.0715673i | ||||||||
\(883\) | −0.358056 | −0.0120495 | −0.00602477 | − | 0.999982i | \(-0.501918\pi\) | ||||
−0.00602477 | + | 0.999982i | \(0.501918\pi\) | |||||||
\(884\) | 11.3062i | 0.380269i | ||||||||
\(885\) | 0.0892295 | + | 2.89956i | 0.00299942 | + | 0.0974678i | ||||
\(886\) | 0.534873 | − | 0.534873i | 0.0179694 | − | 0.0179694i | ||||
\(887\) | −15.5018 | + | 15.5018i | −0.520498 | + | 0.520498i | −0.917722 | − | 0.397223i | \(-0.869974\pi\) |
0.397223 | + | 0.917722i | \(0.369974\pi\) | |||||||
\(888\) | −1.98872 | + | 5.74848i | −0.0667372 | + | 0.192906i | ||||
\(889\) | − | 26.4085i | − | 0.885712i | ||||||
\(890\) | 8.49313 | + | 7.98601i | 0.284690 | + | 0.267692i | ||||
\(891\) | 2.07347i | 0.0694638i | ||||||||
\(892\) | −4.85478 | + | 4.85478i | −0.162550 | + | 0.162550i | ||||
\(893\) | − | 10.0023i | − | 0.334713i | ||||||
\(894\) | 1.25869 | + | 1.25869i | 0.0420970 | + | 0.0420970i | ||||
\(895\) | −35.1900 | + | 37.4246i | −1.17627 | + | 1.25097i | ||||
\(896\) | −2.13605 | + | 2.13605i | −0.0713605 | + | 0.0713605i | ||||
\(897\) | 10.6605 | + | 10.6605i | 0.355945 | + | 0.355945i | ||||
\(898\) | −15.2168 | + | 15.2168i | −0.507790 | + | 0.507790i | ||||
\(899\) | −0.285700 | −0.00952862 | ||||||||
\(900\) | −0.307443 | − | 4.99054i | −0.0102481 | − | 0.166351i | ||||
\(901\) | −4.92271 | + | 4.92271i | −0.163999 | + | 0.163999i | ||||
\(902\) | − | 7.87944i | − | 0.262357i | ||||||
\(903\) | −18.9892 | −0.631920 | ||||||||
\(904\) | − | 17.3203i | − | 0.576064i | ||||||
\(905\) | −12.1966 | + | 0.375332i | −0.405429 | + | 0.0124765i | ||||
\(906\) | 10.4383 | + | 10.4383i | 0.346790 | + | 0.346790i | ||||
\(907\) | −28.0078 | −0.929984 | −0.464992 | − | 0.885315i | \(-0.653943\pi\) | ||||
−0.464992 | + | 0.885315i | \(0.653943\pi\) | |||||||
\(908\) | 19.5601 | 0.649123 | ||||||||
\(909\) | 7.64384 | 0.253530 | ||||||||
\(910\) | −21.2314 | − | 19.9637i | −0.703813 | − | 0.661789i | ||||
\(911\) | −28.1566 | + | 28.1566i | −0.932870 | + | 0.932870i | −0.997884 | − | 0.0650140i | \(-0.979291\pi\) |
0.0650140 | + | 0.997884i | \(0.479291\pi\) | |||||||
\(912\) | − | 2.09313i | − | 0.0693106i | ||||||
\(913\) | 0.790807 | + | 0.790807i | 0.0261719 | + | 0.0261719i | ||||
\(914\) | 26.8366i | 0.887676i | ||||||||
\(915\) | 0.571537 | + | 18.5724i | 0.0188944 | + | 0.613985i | ||||
\(916\) | − | 5.52626i | − | 0.182593i | ||||||
\(917\) | 4.43597i | 0.146489i | ||||||||
\(918\) | 1.85302 | + | 1.85302i | 0.0611586 | + | 0.0611586i | ||||
\(919\) | −23.6708 | + | 23.6708i | −0.780828 | + | 0.780828i | −0.979970 | − | 0.199143i | \(-0.936184\pi\) |
0.199143 | + | 0.979970i | \(0.436184\pi\) | |||||||
\(920\) | −7.80997 | + | 0.240340i | −0.257487 | + | 0.00792376i | ||||
\(921\) | −18.3483 | −0.604596 | ||||||||
\(922\) | −9.31792 | − | 9.31792i | −0.306869 | − | 0.306869i | ||||
\(923\) | 39.5452i | 1.30165i | ||||||||
\(924\) | −6.26360 | −0.206057 | ||||||||
\(925\) | 26.4860 | − | 14.9496i | 0.870855 | − | 0.491540i | ||||
\(926\) | −31.8446 | −1.04648 | ||||||||
\(927\) | − | 9.85885i | − | 0.323807i | ||||||
\(928\) | 0.364989 | + | 0.364989i | 0.0119813 | + | 0.0119813i | ||||
\(929\) | 23.2278 | 0.762081 | 0.381040 | − | 0.924558i | \(-0.375566\pi\) | ||||
0.381040 | + | 0.924558i | \(0.375566\pi\) | |||||||
\(930\) | 1.23707 | − | 0.0380689i | 0.0405652 | − | 0.00124833i | ||||
\(931\) | 3.14580 | − | 3.14580i | 0.103099 | − | 0.103099i | ||||
\(932\) | 8.07622 | + | 8.07622i | 0.264545 | + | 0.264545i | ||||
\(933\) | 29.8503i | 0.977254i | ||||||||
\(934\) | − | 24.6295i | − | 0.805902i | ||||||
\(935\) | −0.373720 | − | 12.1442i | −0.0122220 | − | 0.397159i | ||||
\(936\) | 4.31443i | 0.141022i | ||||||||
\(937\) | 12.8916 | + | 12.8916i | 0.421152 | + | 0.421152i | 0.885600 | − | 0.464449i | \(-0.153747\pi\) |
−0.464449 | + | 0.885600i | \(0.653747\pi\) | |||||||
\(938\) | − | 13.0634i | − | 0.426534i | ||||||
\(939\) | 19.7810 | − | 19.7810i | 0.645529 | − | 0.645529i | ||||
\(940\) | −7.78447 | − | 7.31966i | −0.253901 | − | 0.238741i | ||||
\(941\) | 13.8545 | 0.451643 | 0.225821 | − | 0.974169i | \(-0.427493\pi\) | ||||
0.225821 | + | 0.974169i | \(0.427493\pi\) | |||||||
\(942\) | 4.28456 | 0.139599 | ||||||||
\(943\) | −13.2791 | −0.432427 | ||||||||
\(944\) | 0.917356 | + | 0.917356i | 0.0298574 | + | 0.0298574i | ||||
\(945\) | −6.75159 | + | 0.207770i | −0.219629 | + | 0.00675875i | ||||
\(946\) | − | 13.0340i | − | 0.423771i | ||||||
\(947\) | −45.6796 | −1.48439 | −0.742194 | − | 0.670185i | \(-0.766215\pi\) | ||||
−0.742194 | + | 0.670185i | \(0.766215\pi\) | |||||||
\(948\) | 12.7440i | 0.413906i | ||||||||
\(949\) | −36.6786 | + | 36.6786i | −1.19064 | + | 1.19064i | ||||
\(950\) | −6.93131 | + | 7.84138i | −0.224881 | + | 0.254408i | ||||
\(951\) | −6.67756 | −0.216535 | ||||||||
\(952\) | −5.59765 | + | 5.59765i | −0.181421 | + | 0.181421i | ||||
\(953\) | −9.42694 | − | 9.42694i | −0.305368 | − | 0.305368i | 0.537741 | − | 0.843110i | \(-0.319278\pi\) |
−0.843110 | + | 0.537741i | \(0.819278\pi\) | |||||||
\(954\) | −1.87850 | + | 1.87850i | −0.0608186 | + | 0.0608186i | ||||
\(955\) | −18.3629 | + | 19.5290i | −0.594211 | + | 0.631944i | ||||
\(956\) | −1.04218 | − | 1.04218i | −0.0337065 | − | 0.0337065i | ||||
\(957\) | 1.07027i | 0.0345968i | ||||||||
\(958\) | −3.98964 | + | 3.98964i | −0.128899 | + | 0.128899i | ||||
\(959\) | − | 57.0218i | − | 1.84133i | ||||||
\(960\) | −1.62902 | − | 1.53176i | −0.0525765 | − | 0.0494372i | ||||
\(961\) | − | 30.6936i | − | 0.990117i | ||||||
\(962\) | −23.6044 | + | 11.4701i | −0.761035 | + | 0.369811i | ||||
\(963\) | −4.17096 | + | 4.17096i | −0.134407 | + | 0.134407i | ||||
\(964\) | −2.39676 | + | 2.39676i | −0.0771944 | + | 0.0771944i | ||||
\(965\) | 0.0560711 | + | 1.82206i | 0.00180499 | + | 0.0586543i | ||||
\(966\) | 10.5559i | 0.339632i | ||||||||
\(967\) | 44.8271 | 1.44154 | 0.720772 | − | 0.693173i | \(-0.243788\pi\) | ||||
0.720772 | + | 0.693173i | \(0.243788\pi\) | |||||||
\(968\) | 6.70073i | 0.215370i | ||||||||
\(969\) | − | 5.48518i | − | 0.176209i | ||||||
\(970\) | −0.972640 | − | 31.6065i | −0.0312296 | − | 1.01482i | ||||
\(971\) | 14.5531 | 0.467030 | 0.233515 | − | 0.972353i | \(-0.424977\pi\) | ||||
0.233515 | + | 0.972353i | \(0.424977\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 25.8519 | + | 25.8519i | 0.828774 | + | 0.828774i | ||||
\(974\) | − | 33.5571i | − | 1.07524i | ||||||
\(975\) | 14.2870 | − | 16.1629i | 0.457551 | − | 0.517627i | ||||
\(976\) | 5.87589 | + | 5.87589i | 0.188083 | + | 0.188083i | ||||
\(977\) | 3.38584i | 0.108323i | 0.998532 | + | 0.0541613i | \(0.0172485\pi\) | ||||
−0.998532 | + | 0.0541613i | \(0.982751\pi\) | |||||||
\(978\) | 4.52216 | − | 4.52216i | 0.144603 | − | 0.144603i | ||||
\(979\) | 7.64403 | + | 7.64403i | 0.244304 | + | 0.244304i | ||||
\(980\) | −0.146186 | − | 4.75038i | −0.00466973 | − | 0.151745i | ||||
\(981\) | −0.461041 | + | 0.461041i | −0.0147199 | + | 0.0147199i | ||||
\(982\) | − | 31.9342i | − | 1.01906i | ||||||
\(983\) | 22.1865 | + | 22.1865i | 0.707640 | + | 0.707640i | 0.966038 | − | 0.258398i | \(-0.0831947\pi\) |
−0.258398 | + | 0.966038i | \(0.583195\pi\) | |||||||
\(984\) | −2.68710 | − | 2.68710i | −0.0856615 | − | 0.0856615i | ||||
\(985\) | −27.9949 | − | 26.3234i | −0.891993 | − | 0.838733i | ||||
\(986\) | 0.956475 | + | 0.956475i | 0.0304604 | + | 0.0304604i | ||||
\(987\) | −10.2074 | + | 10.2074i | −0.324904 | + | 0.324904i | ||||
\(988\) | 6.38566 | − | 6.38566i | 0.203155 | − | 0.203155i | ||||
\(989\) | −21.9659 | −0.698475 | ||||||||
\(990\) | −0.142611 | − | 4.63422i | −0.00453247 | − | 0.147285i | ||||
\(991\) | −0.255920 | − | 0.255920i | −0.00812958 | − | 0.00812958i | 0.703030 | − | 0.711160i | \(-0.251830\pi\) |
−0.711160 | + | 0.703030i | \(0.751830\pi\) | |||||||
\(992\) | 0.391381 | − | 0.391381i | 0.0124264 | − | 0.0124264i | ||||
\(993\) | 7.91522 | 0.251182 | ||||||||
\(994\) | −19.5786 | + | 19.5786i | −0.620997 | + | 0.620997i | ||||
\(995\) | 13.9321 | − | 14.8168i | 0.441676 | − | 0.469723i | ||||
\(996\) | 0.539372 | 0.0170907 | ||||||||
\(997\) | −35.1093 | −1.11192 | −0.555962 | − | 0.831208i | \(-0.687650\pi\) | ||||
−0.555962 | + | 0.831208i | \(0.687650\pi\) | |||||||
\(998\) | 25.1910 | + | 25.1910i | 0.797407 | + | 0.797407i | ||||
\(999\) | −1.98872 | + | 5.74848i | −0.0629204 | + | 0.181874i |
(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.l.a.697.16 | yes | 36 | |
5.3 | odd | 4 | 1110.2.o.a.253.3 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.o.a.487.3 | yes | 36 | ||
185.43 | even | 4 | inner | 1110.2.l.a.43.16 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.16 | ✓ | 36 | 185.43 | even | 4 | inner | |
1110.2.l.a.697.16 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.253.3 | yes | 36 | 5.3 | odd | 4 | ||
1110.2.o.a.487.3 | yes | 36 | 37.6 | odd | 4 |