Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.e.47.1 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.42268 | + | 0.987925i | −0.821382 | + | 0.570379i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.16582 | − | 0.556076i | 0.968584 | − | 0.248685i | ||||
\(6\) | 1.70455 | + | 0.307415i | 0.695880 | + | 0.125502i | ||||
\(7\) | 3.32202 | − | 3.32202i | 1.25561 | − | 1.25561i | 0.302437 | − | 0.953169i | \(-0.402200\pi\) |
0.953169 | − | 0.302437i | \(-0.0978001\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.04801 | − | 2.81099i | 0.349337 | − | 0.936997i | ||||
\(10\) | −1.92467 | − | 1.13826i | −0.608635 | − | 0.359950i | ||||
\(11\) | 1.84760i | 0.557071i | 0.960426 | + | 0.278536i | \(0.0898490\pi\) | ||||
−0.960426 | + | 0.278536i | \(0.910151\pi\) | |||||||
\(12\) | −0.987925 | − | 1.42268i | −0.285189 | − | 0.410691i | ||||
\(13\) | −1.71935 | − | 1.71935i | −0.476861 | − | 0.476861i | 0.427265 | − | 0.904126i | \(-0.359477\pi\) |
−0.904126 | + | 0.427265i | \(0.859477\pi\) | |||||||
\(14\) | −4.69805 | −1.25561 | ||||||||
\(15\) | −2.53190 | + | 2.93078i | −0.653733 | + | 0.756725i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.948261 | − | 0.948261i | −0.229987 | − | 0.229987i | 0.582700 | − | 0.812687i | \(-0.301996\pi\) |
−0.812687 | + | 0.582700i | \(0.801996\pi\) | |||||||
\(18\) | −2.72873 | + | 1.24662i | −0.643167 | + | 0.293830i | ||||
\(19\) | − | 1.25446i | − | 0.287794i | −0.989593 | − | 0.143897i | \(-0.954037\pi\) | ||
0.989593 | − | 0.143897i | \(-0.0459633\pi\) | |||||||
\(20\) | 0.556076 | + | 2.16582i | 0.124342 | + | 0.484292i | ||||
\(21\) | −1.44425 | + | 8.00806i | −0.315161 | + | 1.74750i | ||||
\(22\) | 1.30645 | − | 1.30645i | 0.278536 | − | 0.278536i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | −0.307415 | + | 1.70455i | −0.0627508 | + | 0.347940i | ||||
\(25\) | 4.38156 | − | 2.40872i | 0.876312 | − | 0.481745i | ||||
\(26\) | 2.43152i | 0.476861i | ||||||||
\(27\) | 1.28607 | + | 5.03448i | 0.247504 | + | 0.968887i | ||||
\(28\) | 3.32202 | + | 3.32202i | 0.627803 | + | 0.627803i | ||||
\(29\) | −6.59528 | −1.22471 | −0.612356 | − | 0.790582i | \(-0.709778\pi\) | ||||
−0.612356 | + | 0.790582i | \(0.709778\pi\) | |||||||
\(30\) | 3.86270 | − | 0.282055i | 0.705229 | − | 0.0514959i | ||||
\(31\) | −4.74469 | −0.852171 | −0.426086 | − | 0.904683i | \(-0.640108\pi\) | ||||
−0.426086 | + | 0.904683i | \(0.640108\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1.82529 | − | 2.62853i | −0.317741 | − | 0.457568i | ||||
\(34\) | 1.34104i | 0.229987i | ||||||||
\(35\) | 5.34761 | − | 9.04220i | 0.903910 | − | 1.52841i | ||||
\(36\) | 2.81099 | + | 1.04801i | 0.468499 | + | 0.174668i | ||||
\(37\) | 6.93789 | − | 6.93789i | 1.14058 | − | 1.14058i | 0.152239 | − | 0.988344i | \(-0.451352\pi\) |
0.988344 | − | 0.152239i | \(-0.0486483\pi\) | |||||||
\(38\) | −0.887039 | + | 0.887039i | −0.143897 | + | 0.143897i | ||||
\(39\) | 4.14466 | + | 0.747487i | 0.663676 | + | 0.119694i | ||||
\(40\) | 1.13826 | − | 1.92467i | 0.179975 | − | 0.304317i | ||||
\(41\) | − | 0.505725i | − | 0.0789810i | −0.999220 | − | 0.0394905i | \(-0.987427\pi\) | ||
0.999220 | − | 0.0394905i | \(-0.0125735\pi\) | |||||||
\(42\) | 6.68380 | − | 4.64132i | 1.03133 | − | 0.716171i | ||||
\(43\) | 6.74120 | + | 6.74120i | 1.02802 | + | 1.02802i | 0.999596 | + | 0.0284272i | \(0.00904988\pi\) |
0.0284272 | + | 0.999596i | \(0.490950\pi\) | |||||||
\(44\) | −1.84760 | −0.278536 | ||||||||
\(45\) | 0.706675 | − | 6.67088i | 0.105345 | − | 0.994436i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −7.17165 | − | 7.17165i | −1.04609 | − | 1.04609i | −0.998885 | − | 0.0472070i | \(-0.984968\pi\) |
−0.0472070 | − | 0.998885i | \(-0.515032\pi\) | |||||||
\(48\) | 1.42268 | − | 0.987925i | 0.205345 | − | 0.142595i | ||||
\(49\) | − | 15.0717i | − | 2.15309i | ||||||
\(50\) | −4.80145 | − | 1.39501i | −0.679028 | − | 0.197284i | ||||
\(51\) | 2.28588 | + | 0.412257i | 0.320087 | + | 0.0577275i | ||||
\(52\) | 1.71935 | − | 1.71935i | 0.238430 | − | 0.238430i | ||||
\(53\) | 7.30308 | − | 7.30308i | 1.00315 | − | 1.00315i | 0.00315967 | − | 0.999995i | \(-0.498994\pi\) |
0.999995 | − | 0.00315967i | \(-0.00100576\pi\) | |||||||
\(54\) | 2.65053 | − | 4.46931i | 0.360691 | − | 0.608196i | ||||
\(55\) | 1.02740 | + | 4.00156i | 0.138535 | + | 0.539570i | ||||
\(56\) | − | 4.69805i | − | 0.627803i | ||||||
\(57\) | 1.23932 | + | 1.78469i | 0.164151 | + | 0.236388i | ||||
\(58\) | 4.66357 | + | 4.66357i | 0.612356 | + | 0.612356i | ||||
\(59\) | 7.06183 | 0.919371 | 0.459686 | − | 0.888082i | \(-0.347962\pi\) | ||||
0.459686 | + | 0.888082i | \(0.347962\pi\) | |||||||
\(60\) | −2.93078 | − | 2.53190i | −0.378363 | − | 0.326867i | ||||
\(61\) | 3.82384 | 0.489593 | 0.244796 | − | 0.969574i | \(-0.421279\pi\) | ||||
0.244796 | + | 0.969574i | \(0.421279\pi\) | |||||||
\(62\) | 3.35500 | + | 3.35500i | 0.426086 | + | 0.426086i | ||||
\(63\) | −5.85667 | − | 12.8197i | −0.737870 | − | 1.61513i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −4.67988 | − | 2.76771i | −0.580468 | − | 0.343292i | ||||
\(66\) | −0.567979 | + | 3.14932i | −0.0699134 | + | 0.387655i | ||||
\(67\) | −2.57400 | + | 2.57400i | −0.314464 | + | 0.314464i | −0.846636 | − | 0.532172i | \(-0.821376\pi\) |
0.532172 | + | 0.846636i | \(0.321376\pi\) | |||||||
\(68\) | 0.948261 | − | 0.948261i | 0.114994 | − | 0.114994i | ||||
\(69\) | −0.307415 | + | 1.70455i | −0.0370084 | + | 0.205204i | ||||
\(70\) | −10.1751 | + | 2.61247i | −1.21616 | + | 0.312250i | ||||
\(71\) | 11.8194i | 1.40271i | 0.712812 | + | 0.701355i | \(0.247421\pi\) | ||||
−0.712812 | + | 0.701355i | \(0.752579\pi\) | |||||||
\(72\) | −1.24662 | − | 2.72873i | −0.146915 | − | 0.321583i | ||||
\(73\) | −3.30214 | − | 3.30214i | −0.386486 | − | 0.386486i | 0.486946 | − | 0.873432i | \(-0.338111\pi\) |
−0.873432 | + | 0.486946i | \(0.838111\pi\) | |||||||
\(74\) | −9.81166 | −1.14058 | ||||||||
\(75\) | −3.85390 | + | 7.75548i | −0.445010 | + | 0.895526i | ||||
\(76\) | 1.25446 | 0.143897 | ||||||||
\(77\) | 6.13775 | + | 6.13775i | 0.699462 | + | 0.699462i | ||||
\(78\) | −2.40216 | − | 3.45927i | −0.271991 | − | 0.391685i | ||||
\(79\) | 7.20508i | 0.810635i | 0.914176 | + | 0.405318i | \(0.132839\pi\) | ||||
−0.914176 | + | 0.405318i | \(0.867161\pi\) | |||||||
\(80\) | −2.16582 | + | 0.556076i | −0.242146 | + | 0.0621712i | ||||
\(81\) | −6.80335 | − | 5.89189i | −0.755928 | − | 0.654655i | ||||
\(82\) | −0.357602 | + | 0.357602i | −0.0394905 | + | 0.0394905i | ||||
\(83\) | 11.2118 | − | 11.2118i | 1.23065 | − | 1.23065i | 0.266940 | − | 0.963713i | \(-0.413988\pi\) |
0.963713 | − | 0.266940i | \(-0.0860125\pi\) | |||||||
\(84\) | −8.00806 | − | 1.44425i | −0.873752 | − | 0.157581i | ||||
\(85\) | −2.58107 | − | 1.52646i | −0.279956 | − | 0.165568i | ||||
\(86\) | − | 9.53349i | − | 1.02802i | ||||||
\(87\) | 9.38294 | − | 6.51564i | 1.00596 | − | 0.698550i | ||||
\(88\) | 1.30645 | + | 1.30645i | 0.139268 | + | 0.139268i | ||||
\(89\) | −9.35985 | −0.992142 | −0.496071 | − | 0.868282i | \(-0.665224\pi\) | ||||
−0.496071 | + | 0.868282i | \(0.665224\pi\) | |||||||
\(90\) | −5.21672 | + | 4.21733i | −0.549890 | + | 0.444545i | ||||
\(91\) | −11.4234 | −1.19750 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 6.75015 | − | 4.68739i | 0.699958 | − | 0.486060i | ||||
\(94\) | 10.1422i | 1.04609i | ||||||||
\(95\) | −0.697577 | − | 2.71694i | −0.0715699 | − | 0.278752i | ||||
\(96\) | −1.70455 | − | 0.307415i | −0.173970 | − | 0.0313754i | ||||
\(97\) | −5.09832 | + | 5.09832i | −0.517656 | + | 0.517656i | −0.916861 | − | 0.399206i | \(-0.869286\pi\) |
0.399206 | + | 0.916861i | \(0.369286\pi\) | |||||||
\(98\) | −10.6573 | + | 10.6573i | −1.07655 | + | 1.07655i | ||||
\(99\) | 5.19358 | + | 1.93630i | 0.521974 | + | 0.194605i | ||||
\(100\) | 2.40872 | + | 4.38156i | 0.240872 | + | 0.438156i | ||||
\(101\) | − | 12.0814i | − | 1.20214i | −0.799196 | − | 0.601071i | \(-0.794741\pi\) | ||
0.799196 | − | 0.601071i | \(-0.205259\pi\) | |||||||
\(102\) | −1.32485 | − | 1.90787i | −0.131180 | − | 0.188907i | ||||
\(103\) | 9.21304 | + | 9.21304i | 0.907788 | + | 0.907788i | 0.996093 | − | 0.0883058i | \(-0.0281453\pi\) |
−0.0883058 | + | 0.996093i | \(0.528145\pi\) | |||||||
\(104\) | −2.43152 | −0.238430 | ||||||||
\(105\) | 1.32511 | + | 18.1471i | 0.129317 | + | 1.77098i | ||||
\(106\) | −10.3281 | −1.00315 | ||||||||
\(107\) | 8.07473 | + | 8.07473i | 0.780614 | + | 0.780614i | 0.979934 | − | 0.199321i | \(-0.0638735\pi\) |
−0.199321 | + | 0.979934i | \(0.563874\pi\) | |||||||
\(108\) | −5.03448 | + | 1.28607i | −0.484443 | + | 0.123752i | ||||
\(109\) | 13.1231i | 1.25697i | 0.777823 | + | 0.628484i | \(0.216324\pi\) | ||||
−0.777823 | + | 0.628484i | \(0.783676\pi\) | |||||||
\(110\) | 2.10305 | − | 3.55602i | 0.200518 | − | 0.339053i | ||||
\(111\) | −3.01625 | + | 16.7245i | −0.286290 | + | 1.58742i | ||||
\(112\) | −3.32202 | + | 3.32202i | −0.313902 | + | 0.313902i | ||||
\(113\) | −2.14024 | + | 2.14024i | −0.201337 | + | 0.201337i | −0.800573 | − | 0.599236i | \(-0.795471\pi\) |
0.599236 | + | 0.800573i | \(0.295471\pi\) | |||||||
\(114\) | 0.385641 | − | 2.13830i | 0.0361186 | − | 0.200270i | ||||
\(115\) | 1.13826 | − | 1.92467i | 0.106143 | − | 0.179477i | ||||
\(116\) | − | 6.59528i | − | 0.612356i | ||||||
\(117\) | −6.63496 | + | 3.03118i | −0.613402 | + | 0.280232i | ||||
\(118\) | −4.99347 | − | 4.99347i | −0.459686 | − | 0.459686i | ||||
\(119\) | −6.30029 | −0.577546 | ||||||||
\(120\) | 0.282055 | + | 3.86270i | 0.0257480 | + | 0.352615i | ||||
\(121\) | 7.58639 | 0.689672 | ||||||||
\(122\) | −2.70387 | − | 2.70387i | −0.244796 | − | 0.244796i | ||||
\(123\) | 0.499619 | + | 0.719483i | 0.0450491 | + | 0.0648736i | ||||
\(124\) | − | 4.74469i | − | 0.426086i | ||||||
\(125\) | 8.15024 | − | 7.65334i | 0.728979 | − | 0.684536i | ||||
\(126\) | −4.92360 | + | 13.2062i | −0.438629 | + | 1.17650i | ||||
\(127\) | 1.46864 | − | 1.46864i | 0.130321 | − | 0.130321i | −0.638938 | − | 0.769258i | \(-0.720626\pi\) |
0.769258 | + | 0.638938i | \(0.220626\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −16.2503 | − | 2.93074i | −1.43076 | − | 0.258037i | ||||
\(130\) | 1.35211 | + | 5.26624i | 0.118588 | + | 0.461880i | ||||
\(131\) | 3.62572i | 0.316781i | 0.987377 | + | 0.158390i | \(0.0506304\pi\) | ||||
−0.987377 | + | 0.158390i | \(0.949370\pi\) | |||||||
\(132\) | 2.62853 | − | 1.82529i | 0.228784 | − | 0.158871i | ||||
\(133\) | −4.16735 | − | 4.16735i | −0.361355 | − | 0.361355i | ||||
\(134\) | 3.64019 | 0.314464 | ||||||||
\(135\) | 5.58496 | + | 10.1886i | 0.480676 | + | 0.876898i | ||||
\(136\) | −1.34104 | −0.114994 | ||||||||
\(137\) | −4.25154 | − | 4.25154i | −0.363233 | − | 0.363233i | 0.501769 | − | 0.865002i | \(-0.332683\pi\) |
−0.865002 | + | 0.501769i | \(0.832683\pi\) | |||||||
\(138\) | 1.42268 | − | 0.987925i | 0.121106 | − | 0.0840977i | ||||
\(139\) | 9.87234i | 0.837361i | 0.908134 | + | 0.418680i | \(0.137507\pi\) | ||||
−0.908134 | + | 0.418680i | \(0.862493\pi\) | |||||||
\(140\) | 9.04220 | + | 5.34761i | 0.764205 | + | 0.451955i | ||||
\(141\) | 17.2880 | + | 3.11788i | 1.45591 | + | 0.262573i | ||||
\(142\) | 8.35761 | − | 8.35761i | 0.701355 | − | 0.701355i | ||||
\(143\) | 3.17666 | − | 3.17666i | 0.265645 | − | 0.265645i | ||||
\(144\) | −1.04801 | + | 2.81099i | −0.0873341 | + | 0.234249i | ||||
\(145\) | −14.2842 | + | 3.66748i | −1.18624 | + | 0.304567i | ||||
\(146\) | 4.66993i | 0.386486i | ||||||||
\(147\) | 14.8897 | + | 21.4421i | 1.22808 | + | 1.76851i | ||||
\(148\) | 6.93789 | + | 6.93789i | 0.570291 | + | 0.570291i | ||||
\(149\) | −2.39241 | −0.195994 | −0.0979968 | − | 0.995187i | \(-0.531244\pi\) | ||||
−0.0979968 | + | 0.995187i | \(0.531244\pi\) | |||||||
\(150\) | 8.20907 | − | 2.75884i | 0.670268 | − | 0.225258i | ||||
\(151\) | 10.6559 | 0.867165 | 0.433582 | − | 0.901114i | \(-0.357249\pi\) | ||||
0.433582 | + | 0.901114i | \(0.357249\pi\) | |||||||
\(152\) | −0.887039 | − | 0.887039i | −0.0719484 | − | 0.0719484i | ||||
\(153\) | −3.65934 | + | 1.67177i | −0.295840 | + | 0.135154i | ||||
\(154\) | − | 8.68009i | − | 0.699462i | ||||||
\(155\) | −10.2761 | + | 2.63841i | −0.825400 | + | 0.211922i | ||||
\(156\) | −0.747487 | + | 4.14466i | −0.0598468 | + | 0.331838i | ||||
\(157\) | 0.651151 | − | 0.651151i | 0.0519675 | − | 0.0519675i | −0.680645 | − | 0.732613i | \(-0.738301\pi\) |
0.732613 | + | 0.680645i | \(0.238301\pi\) | |||||||
\(158\) | 5.09476 | − | 5.09476i | 0.405318 | − | 0.405318i | ||||
\(159\) | −3.17502 | + | 17.6048i | −0.251795 | + | 1.39615i | ||||
\(160\) | 1.92467 | + | 1.13826i | 0.152159 | + | 0.0899874i | ||||
\(161\) | − | 4.69805i | − | 0.370258i | ||||||
\(162\) | 0.644498 | + | 8.97689i | 0.0506366 | + | 0.705291i | ||||
\(163\) | −4.88731 | − | 4.88731i | −0.382804 | − | 0.382804i | 0.489307 | − | 0.872111i | \(-0.337250\pi\) |
−0.872111 | + | 0.489307i | \(0.837250\pi\) | |||||||
\(164\) | 0.505725 | 0.0394905 | ||||||||
\(165\) | −5.41490 | − | 4.67792i | −0.421550 | − | 0.364176i | ||||
\(166\) | −15.8559 | −1.23065 | ||||||||
\(167\) | −3.50266 | − | 3.50266i | −0.271044 | − | 0.271044i | 0.558477 | − | 0.829520i | \(-0.311386\pi\) |
−0.829520 | + | 0.558477i | \(0.811386\pi\) | |||||||
\(168\) | 4.64132 | + | 6.68380i | 0.358085 | + | 0.515666i | ||||
\(169\) | − | 7.08770i | − | 0.545208i | ||||||
\(170\) | 0.745722 | + | 2.90446i | 0.0571943 | + | 0.222762i | ||||
\(171\) | −3.52629 | − | 1.31469i | −0.269662 | − | 0.100537i | ||||
\(172\) | −6.74120 | + | 6.74120i | −0.514012 | + | 0.514012i | ||||
\(173\) | −1.69609 | + | 1.69609i | −0.128952 | + | 0.128952i | −0.768637 | − | 0.639685i | \(-0.779065\pi\) |
0.639685 | + | 0.768637i | \(0.279065\pi\) | |||||||
\(174\) | −11.2420 | − | 2.02749i | −0.852253 | − | 0.153703i | ||||
\(175\) | 6.55380 | − | 22.5575i | 0.495421 | − | 1.70518i | ||||
\(176\) | − | 1.84760i | − | 0.139268i | ||||||
\(177\) | −10.0467 | + | 6.97655i | −0.755155 | + | 0.524390i | ||||
\(178\) | 6.61841 | + | 6.61841i | 0.496071 | + | 0.496071i | ||||
\(179\) | −15.4433 | −1.15429 | −0.577145 | − | 0.816642i | \(-0.695833\pi\) | ||||
−0.577145 | + | 0.816642i | \(0.695833\pi\) | |||||||
\(180\) | 6.67088 | + | 0.706675i | 0.497218 | + | 0.0526725i | ||||
\(181\) | 15.1508 | 1.12615 | 0.563076 | − | 0.826405i | \(-0.309618\pi\) | ||||
0.563076 | + | 0.826405i | \(0.309618\pi\) | |||||||
\(182\) | 8.07757 | + | 8.07757i | 0.598749 | + | 0.598749i | ||||
\(183\) | −5.44009 | + | 3.77767i | −0.402143 | + | 0.279253i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 11.1682 | − | 18.8842i | 0.821105 | − | 1.38840i | ||||
\(186\) | −8.08756 | − | 1.45859i | −0.593009 | − | 0.106949i | ||||
\(187\) | 1.75200 | − | 1.75200i | 0.128119 | − | 0.128119i | ||||
\(188\) | 7.17165 | − | 7.17165i | 0.523046 | − | 0.523046i | ||||
\(189\) | 20.9970 | + | 12.4523i | 1.52731 | + | 0.905772i | ||||
\(190\) | −1.42791 | + | 2.41443i | −0.103591 | + | 0.175161i | ||||
\(191\) | − | 5.46374i | − | 0.395342i | −0.980268 | − | 0.197671i | \(-0.936662\pi\) | ||
0.980268 | − | 0.197671i | \(-0.0633378\pi\) | |||||||
\(192\) | 0.987925 | + | 1.42268i | 0.0712973 | + | 0.102673i | ||||
\(193\) | −15.8524 | − | 15.8524i | −1.14108 | − | 1.14108i | −0.988253 | − | 0.152829i | \(-0.951162\pi\) |
−0.152829 | − | 0.988253i | \(-0.548838\pi\) | |||||||
\(194\) | 7.21011 | 0.517656 | ||||||||
\(195\) | 9.39224 | − | 0.685822i | 0.672592 | − | 0.0491128i | ||||
\(196\) | 15.0717 | 1.07655 | ||||||||
\(197\) | 15.9133 | + | 15.9133i | 1.13378 | + | 1.13378i | 0.989544 | + | 0.144232i | \(0.0460712\pi\) |
0.144232 | + | 0.989544i | \(0.453929\pi\) | |||||||
\(198\) | −2.30324 | − | 5.04158i | −0.163684 | − | 0.358290i | ||||
\(199\) | 18.2044i | 1.29048i | 0.763981 | + | 0.645238i | \(0.223242\pi\) | ||||
−0.763981 | + | 0.645238i | \(0.776758\pi\) | |||||||
\(200\) | 1.39501 | − | 4.80145i | 0.0986418 | − | 0.339514i | ||||
\(201\) | 1.11905 | − | 6.20489i | 0.0789316 | − | 0.437659i | ||||
\(202\) | −8.54283 | + | 8.54283i | −0.601071 | + | 0.601071i | ||||
\(203\) | −21.9097 | + | 21.9097i | −1.53776 | + | 1.53776i | ||||
\(204\) | −0.412257 | + | 2.28588i | −0.0288638 | + | 0.160043i | ||||
\(205\) | −0.281222 | − | 1.09531i | −0.0196414 | − | 0.0764998i | ||||
\(206\) | − | 13.0292i | − | 0.907788i | ||||||
\(207\) | −1.24662 | − | 2.72873i | −0.0866459 | − | 0.189660i | ||||
\(208\) | 1.71935 | + | 1.71935i | 0.119215 | + | 0.119215i | ||||
\(209\) | 2.31774 | 0.160321 | ||||||||
\(210\) | 11.8950 | − | 13.7690i | 0.820831 | − | 0.950149i | ||||
\(211\) | −24.0819 | −1.65787 | −0.828935 | − | 0.559346i | \(-0.811052\pi\) | ||||
−0.828935 | + | 0.559346i | \(0.811052\pi\) | |||||||
\(212\) | 7.30308 | + | 7.30308i | 0.501577 | + | 0.501577i | ||||
\(213\) | −11.6767 | − | 16.8152i | −0.800076 | − | 1.15216i | ||||
\(214\) | − | 11.4194i | − | 0.780614i | ||||||
\(215\) | 18.3488 | + | 10.8516i | 1.25138 | + | 0.740073i | ||||
\(216\) | 4.46931 | + | 2.65053i | 0.304098 | + | 0.180346i | ||||
\(217\) | −15.7620 | + | 15.7620i | −1.06999 | + | 1.06999i | ||||
\(218\) | 9.27945 | − | 9.27945i | 0.628484 | − | 0.628484i | ||||
\(219\) | 7.96014 | + | 1.43561i | 0.537896 | + | 0.0970093i | ||||
\(220\) | −4.00156 | + | 1.02740i | −0.269785 | + | 0.0692676i | ||||
\(221\) | 3.26078i | 0.219344i | ||||||||
\(222\) | 13.9588 | − | 9.69318i | 0.936854 | − | 0.650564i | ||||
\(223\) | −2.75191 | − | 2.75191i | −0.184282 | − | 0.184282i | 0.608937 | − | 0.793219i | \(-0.291596\pi\) |
−0.793219 | + | 0.608937i | \(0.791596\pi\) | |||||||
\(224\) | 4.69805 | 0.313902 | ||||||||
\(225\) | −2.17899 | − | 14.8409i | −0.145266 | − | 0.989393i | ||||
\(226\) | 3.02676 | 0.201337 | ||||||||
\(227\) | 5.47594 | + | 5.47594i | 0.363451 | + | 0.363451i | 0.865082 | − | 0.501631i | \(-0.167266\pi\) |
−0.501631 | + | 0.865082i | \(0.667266\pi\) | |||||||
\(228\) | −1.78469 | + | 1.23932i | −0.118194 | + | 0.0820756i | ||||
\(229\) | 27.5633i | 1.82144i | 0.413030 | + | 0.910718i | \(0.364471\pi\) | ||||
−0.413030 | + | 0.910718i | \(0.635529\pi\) | |||||||
\(230\) | −2.16582 | + | 0.556076i | −0.142810 | + | 0.0366666i | ||||
\(231\) | −14.7957 | − | 2.66839i | −0.973483 | − | 0.175567i | ||||
\(232\) | −4.66357 | + | 4.66357i | −0.306178 | + | 0.306178i | ||||
\(233\) | −4.58254 | + | 4.58254i | −0.300212 | + | 0.300212i | −0.841097 | − | 0.540885i | \(-0.818090\pi\) |
0.540885 | + | 0.841097i | \(0.318090\pi\) | |||||||
\(234\) | 6.83499 | + | 2.54826i | 0.446817 | + | 0.166585i | ||||
\(235\) | −19.5205 | − | 11.5445i | −1.27338 | − | 0.753081i | ||||
\(236\) | 7.06183i | 0.459686i | ||||||||
\(237\) | −7.11808 | − | 10.2505i | −0.462369 | − | 0.665841i | ||||
\(238\) | 4.45497 | + | 4.45497i | 0.288773 | + | 0.288773i | ||||
\(239\) | −5.95432 | −0.385153 | −0.192576 | − | 0.981282i | \(-0.561684\pi\) | ||||
−0.192576 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(240\) | 2.53190 | − | 2.93078i | 0.163433 | − | 0.189181i | ||||
\(241\) | 16.3480 | 1.05307 | 0.526534 | − | 0.850154i | \(-0.323491\pi\) | ||||
0.526534 | + | 0.850154i | \(0.323491\pi\) | |||||||
\(242\) | −5.36439 | − | 5.36439i | −0.344836 | − | 0.344836i | ||||
\(243\) | 15.4997 | + | 1.66105i | 0.994307 | + | 0.106557i | ||||
\(244\) | 3.82384i | 0.244796i | ||||||||
\(245\) | −8.38099 | − | 32.6425i | −0.535442 | − | 2.08545i | ||||
\(246\) | 0.155468 | − | 0.862035i | 0.00991225 | − | 0.0549613i | ||||
\(247\) | −2.15686 | + | 2.15686i | −0.137237 | + | 0.137237i | ||||
\(248\) | −3.35500 | + | 3.35500i | −0.213043 | + | 0.213043i | ||||
\(249\) | −4.87433 | + | 27.0271i | −0.308898 | + | 1.71277i | ||||
\(250\) | −11.1748 | − | 0.351357i | −0.706758 | − | 0.0222217i | ||||
\(251\) | 22.8963i | 1.44520i | 0.691266 | + | 0.722601i | \(0.257053\pi\) | ||||
−0.691266 | + | 0.722601i | \(0.742947\pi\) | |||||||
\(252\) | 12.8197 | − | 5.85667i | 0.807564 | − | 0.368935i | ||||
\(253\) | 1.30645 | + | 1.30645i | 0.0821357 | + | 0.0821357i | ||||
\(254\) | −2.07697 | −0.130321 | ||||||||
\(255\) | 5.18005 | − | 0.378248i | 0.324387 | − | 0.0236868i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.1981 | − | 13.1981i | −0.823275 | − | 0.823275i | 0.163301 | − | 0.986576i | \(-0.447786\pi\) |
−0.986576 | + | 0.163301i | \(0.947786\pi\) | |||||||
\(258\) | 9.41837 | + | 13.5631i | 0.586362 | + | 0.844400i | ||||
\(259\) | − | 46.0957i | − | 2.86424i | ||||||
\(260\) | 2.76771 | − | 4.67988i | 0.171646 | − | 0.290234i | ||||
\(261\) | −6.91192 | + | 18.5393i | −0.427837 | + | 1.14755i | ||||
\(262\) | 2.56377 | − | 2.56377i | 0.158390 | − | 0.158390i | ||||
\(263\) | −16.5451 | + | 16.5451i | −1.02021 | + | 1.02021i | −0.0204218 | + | 0.999791i | \(0.506501\pi\) |
−0.999791 | + | 0.0204218i | \(0.993499\pi\) | |||||||
\(264\) | −3.14932 | − | 0.567979i | −0.193827 | − | 0.0349567i | ||||
\(265\) | 11.7561 | − | 19.8782i | 0.722171 | − | 1.22111i | ||||
\(266\) | 5.89353i | 0.361355i | ||||||||
\(267\) | 13.3160 | − | 9.24683i | 0.814928 | − | 0.565897i | ||||
\(268\) | −2.57400 | − | 2.57400i | −0.157232 | − | 0.157232i | ||||
\(269\) | 9.22484 | 0.562449 | 0.281224 | − | 0.959642i | \(-0.409260\pi\) | ||||
0.281224 | + | 0.959642i | \(0.409260\pi\) | |||||||
\(270\) | 3.25529 | − | 11.1536i | 0.198111 | − | 0.678787i | ||||
\(271\) | 12.2145 | 0.741979 | 0.370990 | − | 0.928637i | \(-0.379019\pi\) | ||||
0.370990 | + | 0.928637i | \(0.379019\pi\) | |||||||
\(272\) | 0.948261 | + | 0.948261i | 0.0574968 | + | 0.0574968i | ||||
\(273\) | 16.2518 | − | 11.2855i | 0.983604 | − | 0.683028i | ||||
\(274\) | 6.01258i | 0.363233i | ||||||||
\(275\) | 4.45035 | + | 8.09535i | 0.268366 | + | 0.488168i | ||||
\(276\) | −1.70455 | − | 0.307415i | −0.102602 | − | 0.0185042i | ||||
\(277\) | −7.60344 | + | 7.60344i | −0.456846 | + | 0.456846i | −0.897619 | − | 0.440773i | \(-0.854705\pi\) |
0.440773 | + | 0.897619i | \(0.354705\pi\) | |||||||
\(278\) | 6.98080 | − | 6.98080i | 0.418680 | − | 0.418680i | ||||
\(279\) | −4.97248 | + | 13.3373i | −0.297695 | + | 0.798482i | ||||
\(280\) | −2.61247 | − | 10.1751i | −0.156125 | − | 0.608080i | ||||
\(281\) | 7.76150i | 0.463012i | 0.972833 | + | 0.231506i | \(0.0743653\pi\) | ||||
−0.972833 | + | 0.231506i | \(0.925635\pi\) | |||||||
\(282\) | −10.0198 | − | 14.4291i | −0.596669 | − | 0.859241i | ||||
\(283\) | −21.0879 | − | 21.0879i | −1.25355 | − | 1.25355i | −0.954118 | − | 0.299430i | \(-0.903204\pi\) |
−0.299430 | − | 0.954118i | \(-0.596796\pi\) | |||||||
\(284\) | −11.8194 | −0.701355 | ||||||||
\(285\) | 3.67656 | + | 3.17617i | 0.217781 | + | 0.188140i | ||||
\(286\) | −4.49247 | −0.265645 | ||||||||
\(287\) | −1.68003 | − | 1.68003i | −0.0991691 | − | 0.0991691i | ||||
\(288\) | 2.72873 | − | 1.24662i | 0.160792 | − | 0.0734576i | ||||
\(289\) | − | 15.2016i | − | 0.894212i | ||||||
\(290\) | 12.6937 | + | 7.50715i | 0.745402 | + | 0.440835i | ||||
\(291\) | 2.21650 | − | 12.2900i | 0.129933 | − | 0.720453i | ||||
\(292\) | 3.30214 | − | 3.30214i | 0.193243 | − | 0.193243i | ||||
\(293\) | −14.1881 | + | 14.1881i | −0.828875 | + | 0.828875i | −0.987361 | − | 0.158486i | \(-0.949339\pi\) |
0.158486 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(294\) | 4.63325 | − | 25.6904i | 0.270217 | − | 1.49830i | ||||
\(295\) | 15.2946 | − | 3.92691i | 0.890489 | − | 0.228634i | ||||
\(296\) | − | 9.81166i | − | 0.570291i | ||||||
\(297\) | −9.30169 | + | 2.37614i | −0.539739 | + | 0.137878i | ||||
\(298\) | 1.69169 | + | 1.69169i | 0.0979968 | + | 0.0979968i | ||||
\(299\) | −2.43152 | −0.140619 | ||||||||
\(300\) | −7.75548 | − | 3.85390i | −0.447763 | − | 0.222505i | ||||
\(301\) | 44.7888 | 2.58158 | ||||||||
\(302\) | −7.53486 | − | 7.53486i | −0.433582 | − | 0.433582i | ||||
\(303\) | 11.9355 | + | 17.1879i | 0.685676 | + | 0.987418i | ||||
\(304\) | 1.25446i | 0.0719484i | ||||||||
\(305\) | 8.28176 | − | 2.12635i | 0.474212 | − | 0.121754i | ||||
\(306\) | 3.76966 | + | 1.40543i | 0.215497 | + | 0.0803429i | ||||
\(307\) | −12.0813 | + | 12.0813i | −0.689518 | + | 0.689518i | −0.962125 | − | 0.272607i | \(-0.912114\pi\) |
0.272607 | + | 0.962125i | \(0.412114\pi\) | |||||||
\(308\) | −6.13775 | + | 6.13775i | −0.349731 | + | 0.349731i | ||||
\(309\) | −22.2090 | − | 4.00537i | −1.26342 | − | 0.227858i | ||||
\(310\) | 9.13197 | + | 5.40069i | 0.518661 | + | 0.306739i | ||||
\(311\) | 24.1187i | 1.36765i | 0.729647 | + | 0.683824i | \(0.239685\pi\) | ||||
−0.729647 | + | 0.683824i | \(0.760315\pi\) | |||||||
\(312\) | 3.45927 | − | 2.40216i | 0.195842 | − | 0.135996i | ||||
\(313\) | 5.08762 | + | 5.08762i | 0.287569 | + | 0.287569i | 0.836118 | − | 0.548549i | \(-0.184820\pi\) |
−0.548549 | + | 0.836118i | \(0.684820\pi\) | |||||||
\(314\) | −0.920866 | −0.0519675 | ||||||||
\(315\) | −19.8132 | − | 24.5084i | −1.11635 | − | 1.38089i | ||||
\(316\) | −7.20508 | −0.405318 | ||||||||
\(317\) | 10.9530 | + | 10.9530i | 0.615184 | + | 0.615184i | 0.944292 | − | 0.329108i | \(-0.106748\pi\) |
−0.329108 | + | 0.944292i | \(0.606748\pi\) | |||||||
\(318\) | 14.6935 | − | 10.2034i | 0.823973 | − | 0.572178i | ||||
\(319\) | − | 12.1854i | − | 0.682252i | ||||||
\(320\) | −0.556076 | − | 2.16582i | −0.0310856 | − | 0.121073i | ||||
\(321\) | −19.4649 | − | 3.51049i | −1.08643 | − | 0.195937i | ||||
\(322\) | −3.32202 | + | 3.32202i | −0.185129 | + | 0.185129i | ||||
\(323\) | −1.18956 | + | 1.18956i | −0.0661888 | + | 0.0661888i | ||||
\(324\) | 5.89189 | − | 6.80335i | 0.327327 | − | 0.377964i | ||||
\(325\) | −11.6748 | − | 3.39199i | −0.647604 | − | 0.188154i | ||||
\(326\) | 6.91170i | 0.382804i | ||||||||
\(327\) | −12.9647 | − | 18.6699i | −0.716947 | − | 1.03245i | ||||
\(328\) | −0.357602 | − | 0.357602i | −0.0197453 | − | 0.0197453i | ||||
\(329\) | −47.6487 | −2.62696 | ||||||||
\(330\) | 0.521123 | + | 7.13671i | 0.0286869 | + | 0.392863i | ||||
\(331\) | 24.6028 | 1.35229 | 0.676146 | − | 0.736767i | \(-0.263649\pi\) | ||||
0.676146 | + | 0.736767i | \(0.263649\pi\) | |||||||
\(332\) | 11.2118 | + | 11.2118i | 0.615327 | + | 0.615327i | ||||
\(333\) | −12.2314 | − | 26.7733i | −0.670276 | − | 1.46717i | ||||
\(334\) | 4.95351i | 0.271044i | ||||||||
\(335\) | −4.14349 | + | 7.00617i | −0.226383 | + | 0.382788i | ||||
\(336\) | 1.44425 | − | 8.00806i | 0.0787903 | − | 0.436876i | ||||
\(337\) | −13.0595 | + | 13.0595i | −0.711398 | + | 0.711398i | −0.966828 | − | 0.255430i | \(-0.917783\pi\) |
0.255430 | + | 0.966828i | \(0.417783\pi\) | |||||||
\(338\) | −5.01176 | + | 5.01176i | −0.272604 | + | 0.272604i | ||||
\(339\) | 0.930471 | − | 5.15926i | 0.0505362 | − | 0.280213i | ||||
\(340\) | 1.52646 | − | 2.58107i | 0.0827838 | − | 0.139978i | ||||
\(341\) | − | 8.76627i | − | 0.474720i | ||||||
\(342\) | 1.56383 | + | 3.42309i | 0.0845625 | + | 0.185099i | ||||
\(343\) | −26.8142 | − | 26.8142i | −1.44783 | − | 1.44783i | ||||
\(344\) | 9.53349 | 0.514012 | ||||||||
\(345\) | 0.282055 | + | 3.86270i | 0.0151853 | + | 0.207961i | ||||
\(346\) | 2.39864 | 0.128952 | ||||||||
\(347\) | −7.05463 | − | 7.05463i | −0.378712 | − | 0.378712i | 0.491925 | − | 0.870637i | \(-0.336293\pi\) |
−0.870637 | + | 0.491925i | \(0.836293\pi\) | |||||||
\(348\) | 6.51564 | + | 9.38294i | 0.349275 | + | 0.502978i | ||||
\(349\) | − | 28.6619i | − | 1.53424i | −0.641505 | − | 0.767119i | \(-0.721689\pi\) | ||
0.641505 | − | 0.767119i | \(-0.278311\pi\) | |||||||
\(350\) | −20.5848 | + | 11.3163i | −1.10030 | + | 0.604881i | ||||
\(351\) | 6.44482 | − | 10.8672i | 0.343999 | − | 0.580049i | ||||
\(352\) | −1.30645 | + | 1.30645i | −0.0696339 | + | 0.0696339i | ||||
\(353\) | −4.92849 | + | 4.92849i | −0.262317 | + | 0.262317i | −0.825995 | − | 0.563678i | \(-0.809386\pi\) |
0.563678 | + | 0.825995i | \(0.309386\pi\) | |||||||
\(354\) | 12.0372 | + | 2.17091i | 0.639772 | + | 0.115383i | ||||
\(355\) | 6.57252 | + | 25.5988i | 0.348833 | + | 1.35864i | ||||
\(356\) | − | 9.35985i | − | 0.496071i | ||||||
\(357\) | 8.96326 | − | 6.22421i | 0.474386 | − | 0.329420i | ||||
\(358\) | 10.9201 | + | 10.9201i | 0.577145 | + | 0.577145i | ||||
\(359\) | −9.91548 | −0.523319 | −0.261660 | − | 0.965160i | \(-0.584270\pi\) | ||||
−0.261660 | + | 0.965160i | \(0.584270\pi\) | |||||||
\(360\) | −4.21733 | − | 5.21672i | −0.222273 | − | 0.274945i | ||||
\(361\) | 17.4263 | 0.917175 | ||||||||
\(362\) | −10.7133 | − | 10.7133i | −0.563076 | − | 0.563076i | ||||
\(363\) | −10.7930 | + | 7.49478i | −0.566484 | + | 0.393374i | ||||
\(364\) | − | 11.4234i | − | 0.598749i | ||||||
\(365\) | −8.98808 | − | 5.31560i | −0.470458 | − | 0.278231i | ||||
\(366\) | 6.51794 | + | 1.17551i | 0.340698 | + | 0.0614447i | ||||
\(367\) | 9.89573 | − | 9.89573i | 0.516553 | − | 0.516553i | −0.399974 | − | 0.916527i | \(-0.630981\pi\) |
0.916527 | + | 0.399974i | \(0.130981\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | −1.42159 | − | 0.530005i | −0.0740050 | − | 0.0275910i | ||||
\(370\) | −21.2503 | + | 5.45603i | −1.10475 | + | 0.283646i | ||||
\(371\) | − | 48.5220i | − | 2.51913i | ||||||
\(372\) | 4.68739 | + | 6.75015i | 0.243030 | + | 0.349979i | ||||
\(373\) | 23.6341 | + | 23.6341i | 1.22373 | + | 1.22373i | 0.966297 | + | 0.257430i | \(0.0828756\pi\) |
0.257430 | + | 0.966297i | \(0.417124\pi\) | |||||||
\(374\) | −2.47771 | −0.128119 | ||||||||
\(375\) | −4.03421 | + | 18.9400i | −0.208326 | + | 0.978059i | ||||
\(376\) | −10.1422 | −0.523046 | ||||||||
\(377\) | 11.3396 | + | 11.3396i | 0.584017 | + | 0.584017i | ||||
\(378\) | −6.04202 | − | 23.6522i | −0.310768 | − | 1.21654i | ||||
\(379\) | 24.1573i | 1.24088i | 0.784255 | + | 0.620439i | \(0.213046\pi\) | ||||
−0.784255 | + | 0.620439i | \(0.786954\pi\) | |||||||
\(380\) | 2.71694 | − | 0.697577i | 0.139376 | − | 0.0357850i | ||||
\(381\) | −0.638491 | + | 3.54030i | −0.0327109 | + | 0.181375i | ||||
\(382\) | −3.86345 | + | 3.86345i | −0.197671 | + | 0.197671i | ||||
\(383\) | 16.8899 | − | 16.8899i | 0.863033 | − | 0.863033i | −0.128656 | − | 0.991689i | \(-0.541066\pi\) |
0.991689 | + | 0.128656i | \(0.0410663\pi\) | |||||||
\(384\) | 0.307415 | − | 1.70455i | 0.0156877 | − | 0.0869850i | ||||
\(385\) | 16.7063 | + | 9.88021i | 0.851433 | + | 0.503542i | ||||
\(386\) | 22.4187i | 1.14108i | ||||||||
\(387\) | 26.0143 | − | 11.8846i | 1.32238 | − | 0.604129i | ||||
\(388\) | −5.09832 | − | 5.09832i | −0.258828 | − | 0.258828i | ||||
\(389\) | 0.696017 | 0.0352895 | 0.0176447 | − | 0.999844i | \(-0.494383\pi\) | ||||
0.0176447 | + | 0.999844i | \(0.494383\pi\) | |||||||
\(390\) | −7.12627 | − | 6.15637i | −0.360853 | − | 0.311740i | ||||
\(391\) | −1.34104 | −0.0678195 | ||||||||
\(392\) | −10.6573 | − | 10.6573i | −0.538273 | − | 0.538273i | ||||
\(393\) | −3.58194 | − | 5.15822i | −0.180685 | − | 0.260198i | ||||
\(394\) | − | 22.5048i | − | 1.13378i | ||||||
\(395\) | 4.00658 | + | 15.6049i | 0.201593 | + | 0.785169i | ||||
\(396\) | −1.93630 | + | 5.19358i | −0.0973026 | + | 0.260987i | ||||
\(397\) | −22.8095 | + | 22.8095i | −1.14478 | + | 1.14478i | −0.157213 | + | 0.987565i | \(0.550251\pi\) |
−0.987565 | + | 0.157213i | \(0.949749\pi\) | |||||||
\(398\) | 12.8725 | − | 12.8725i | 0.645238 | − | 0.645238i | ||||
\(399\) | 10.0458 | + | 1.81176i | 0.502920 | + | 0.0907014i | ||||
\(400\) | −4.38156 | + | 2.40872i | −0.219078 | + | 0.120436i | ||||
\(401\) | 25.2746i | 1.26216i | 0.775720 | + | 0.631078i | \(0.217387\pi\) | ||||
−0.775720 | + | 0.631078i | \(0.782613\pi\) | |||||||
\(402\) | −5.17881 | + | 3.59623i | −0.258295 | + | 0.179364i | ||||
\(403\) | 8.15776 | + | 8.15776i | 0.406367 | + | 0.406367i | ||||
\(404\) | 12.0814 | 0.601071 | ||||||||
\(405\) | −18.0112 | − | 8.97760i | −0.894983 | − | 0.446101i | ||||
\(406\) | 30.9849 | 1.53776 | ||||||||
\(407\) | 12.8184 | + | 12.8184i | 0.635386 | + | 0.635386i | ||||
\(408\) | 1.90787 | − | 1.32485i | 0.0944536 | − | 0.0655898i | ||||
\(409\) | − | 1.78568i | − | 0.0882962i | −0.999025 | − | 0.0441481i | \(-0.985943\pi\) | ||
0.999025 | − | 0.0441481i | \(-0.0140574\pi\) | |||||||
\(410\) | −0.575648 | + | 0.973355i | −0.0284292 | + | 0.0480706i | ||||
\(411\) | 10.2488 | + | 1.84836i | 0.505534 | + | 0.0911728i | ||||
\(412\) | −9.21304 | + | 9.21304i | −0.453894 | + | 0.453894i | ||||
\(413\) | 23.4595 | − | 23.4595i | 1.15437 | − | 1.15437i | ||||
\(414\) | −1.04801 | + | 2.81099i | −0.0515069 | + | 0.138153i | ||||
\(415\) | 18.0481 | − | 30.5173i | 0.885947 | − | 1.49804i | ||||
\(416\) | − | 2.43152i | − | 0.119215i | ||||||
\(417\) | −9.75313 | − | 14.0451i | −0.477613 | − | 0.687793i | ||||
\(418\) | −1.63889 | − | 1.63889i | −0.0801607 | − | 0.0801607i | ||||
\(419\) | 35.8107 | 1.74946 | 0.874732 | − | 0.484606i | \(-0.161037\pi\) | ||||
0.874732 | + | 0.484606i | \(0.161037\pi\) | |||||||
\(420\) | −18.1471 | + | 1.32511i | −0.885490 | + | 0.0646586i | ||||
\(421\) | 20.9681 | 1.02192 | 0.510962 | − | 0.859603i | \(-0.329289\pi\) | ||||
0.510962 | + | 0.859603i | \(0.329289\pi\) | |||||||
\(422\) | 17.0285 | + | 17.0285i | 0.828935 | + | 0.828935i | ||||
\(423\) | −27.6754 | + | 12.6435i | −1.34562 | + | 0.614747i | ||||
\(424\) | − | 10.3281i | − | 0.501577i | ||||||
\(425\) | −6.43896 | − | 1.87076i | −0.312335 | − | 0.0907453i | ||||
\(426\) | −3.63348 | + | 20.1469i | −0.176043 | + | 0.976119i | ||||
\(427\) | 12.7029 | − | 12.7029i | 0.614736 | − | 0.614736i | ||||
\(428\) | −8.07473 | + | 8.07473i | −0.390307 | + | 0.390307i | ||||
\(429\) | −1.38105 | + | 7.65765i | −0.0666779 | + | 0.369715i | ||||
\(430\) | −5.30135 | − | 20.6478i | −0.255654 | − | 0.995727i | ||||
\(431\) | − | 20.7370i | − | 0.998867i | −0.866352 | − | 0.499434i | \(-0.833541\pi\) | ||
0.866352 | − | 0.499434i | \(-0.166459\pi\) | |||||||
\(432\) | −1.28607 | − | 5.03448i | −0.0618761 | − | 0.242222i | ||||
\(433\) | 18.7131 | + | 18.7131i | 0.899293 | + | 0.899293i | 0.995374 | − | 0.0960806i | \(-0.0306307\pi\) |
−0.0960806 | + | 0.995374i | \(0.530631\pi\) | |||||||
\(434\) | 22.2908 | 1.06999 | ||||||||
\(435\) | 16.6986 | − | 19.3293i | 0.800635 | − | 0.926771i | ||||
\(436\) | −13.1231 | −0.628484 | ||||||||
\(437\) | −0.887039 | − | 0.887039i | −0.0424328 | − | 0.0424328i | ||||
\(438\) | −4.61354 | − | 6.64379i | −0.220443 | − | 0.317453i | ||||
\(439\) | − | 17.8021i | − | 0.849646i | −0.905276 | − | 0.424823i | \(-0.860336\pi\) | ||
0.905276 | − | 0.424823i | \(-0.139664\pi\) | |||||||
\(440\) | 3.55602 | + | 2.10305i | 0.169526 | + | 0.100259i | ||||
\(441\) | −42.3663 | − | 15.7952i | −2.01744 | − | 0.752154i | ||||
\(442\) | 2.30572 | − | 2.30572i | 0.109672 | − | 0.109672i | ||||
\(443\) | 29.1309 | − | 29.1309i | 1.38405 | − | 1.38405i | 0.546759 | − | 0.837290i | \(-0.315861\pi\) |
0.837290 | − | 0.546759i | \(-0.184139\pi\) | |||||||
\(444\) | −16.7245 | − | 3.01625i | −0.793709 | − | 0.143145i | ||||
\(445\) | −20.2718 | + | 5.20479i | −0.960974 | + | 0.246731i | ||||
\(446\) | 3.89179i | 0.184282i | ||||||||
\(447\) | 3.40362 | − | 2.36352i | 0.160986 | − | 0.111791i | ||||
\(448\) | −3.32202 | − | 3.32202i | −0.156951 | − | 0.156951i | ||||
\(449\) | −5.24969 | −0.247748 | −0.123874 | − | 0.992298i | \(-0.539532\pi\) | ||||
−0.123874 | + | 0.992298i | \(0.539532\pi\) | |||||||
\(450\) | −8.95332 | + | 12.0349i | −0.422063 | + | 0.567329i | ||||
\(451\) | 0.934376 | 0.0439981 | ||||||||
\(452\) | −2.14024 | − | 2.14024i | −0.100668 | − | 0.100668i | ||||
\(453\) | −15.1599 | + | 10.5272i | −0.712274 | + | 0.494612i | ||||
\(454\) | − | 7.74414i | − | 0.363451i | ||||||
\(455\) | −24.7411 | + | 6.35229i | −1.15988 | + | 0.297800i | ||||
\(456\) | 2.13830 | + | 0.385641i | 0.100135 | + | 0.0180593i | ||||
\(457\) | −8.60192 | + | 8.60192i | −0.402381 | + | 0.402381i | −0.879071 | − | 0.476691i | \(-0.841836\pi\) |
0.476691 | + | 0.879071i | \(0.341836\pi\) | |||||||
\(458\) | 19.4902 | − | 19.4902i | 0.910718 | − | 0.910718i | ||||
\(459\) | 3.55447 | − | 5.99353i | 0.165909 | − | 0.279754i | ||||
\(460\) | 1.92467 | + | 1.13826i | 0.0897383 | + | 0.0530717i | ||||
\(461\) | 1.17403i | 0.0546799i | 0.999626 | + | 0.0273400i | \(0.00870366\pi\) | ||||
−0.999626 | + | 0.0273400i | \(0.991296\pi\) | |||||||
\(462\) | 8.57528 | + | 12.3490i | 0.398958 | + | 0.574525i | ||||
\(463\) | 7.56540 | + | 7.56540i | 0.351594 | + | 0.351594i | 0.860702 | − | 0.509108i | \(-0.170025\pi\) |
−0.509108 | + | 0.860702i | \(0.670025\pi\) | |||||||
\(464\) | 6.59528 | 0.306178 | ||||||||
\(465\) | 12.0131 | − | 13.9057i | 0.557093 | − | 0.644859i | ||||
\(466\) | 6.48069 | 0.300212 | ||||||||
\(467\) | −21.1971 | − | 21.1971i | −0.980883 | − | 0.980883i | 0.0189378 | − | 0.999821i | \(-0.493972\pi\) |
−0.999821 | + | 0.0189378i | \(0.993972\pi\) | |||||||
\(468\) | −3.03118 | − | 6.63496i | −0.140116 | − | 0.306701i | ||||
\(469\) | 17.1018i | 0.789687i | ||||||||
\(470\) | 5.63986 | + | 21.9663i | 0.260147 | + | 1.01323i | ||||
\(471\) | −0.283088 | + | 1.56966i | −0.0130440 | + | 0.0723263i | ||||
\(472\) | 4.99347 | − | 4.99347i | 0.229843 | − | 0.229843i | ||||
\(473\) | −12.4550 | + | 12.4550i | −0.572682 | + | 0.572682i | ||||
\(474\) | −2.21495 | + | 12.2814i | −0.101736 | + | 0.564105i | ||||
\(475\) | −3.02165 | − | 5.49650i | −0.138643 | − | 0.252197i | ||||
\(476\) | − | 6.30029i | − | 0.288773i | ||||||
\(477\) | −12.8752 | − | 28.1826i | −0.589515 | − | 1.29039i | ||||
\(478\) | 4.21034 | + | 4.21034i | 0.192576 | + | 0.192576i | ||||
\(479\) | 8.11220 | 0.370656 | 0.185328 | − | 0.982677i | \(-0.440665\pi\) | ||||
0.185328 | + | 0.982677i | \(0.440665\pi\) | |||||||
\(480\) | −3.86270 | + | 0.282055i | −0.176307 | + | 0.0128740i | ||||
\(481\) | −23.8573 | −1.08780 | ||||||||
\(482\) | −11.5598 | − | 11.5598i | −0.526534 | − | 0.526534i | ||||
\(483\) | 4.64132 | + | 6.68380i | 0.211187 | + | 0.304123i | ||||
\(484\) | 7.58639i | 0.344836i | ||||||||
\(485\) | −8.20699 | + | 13.8771i | −0.372660 | + | 0.630126i | ||||
\(486\) | −9.78541 | − | 12.1345i | −0.443875 | − | 0.550432i | ||||
\(487\) | 8.77478 | − | 8.77478i | 0.397623 | − | 0.397623i | −0.479771 | − | 0.877394i | \(-0.659280\pi\) |
0.877394 | + | 0.479771i | \(0.159280\pi\) | |||||||
\(488\) | 2.70387 | − | 2.70387i | 0.122398 | − | 0.122398i | ||||
\(489\) | 11.7814 | + | 2.12476i | 0.532771 | + | 0.0960851i | ||||
\(490\) | −17.1555 | + | 29.0080i | −0.775006 | + | 1.31045i | ||||
\(491\) | 34.5844i | 1.56077i | 0.625299 | + | 0.780385i | \(0.284977\pi\) | ||||
−0.625299 | + | 0.780385i | \(0.715023\pi\) | |||||||
\(492\) | −0.719483 | + | 0.499619i | −0.0324368 | + | 0.0225245i | ||||
\(493\) | 6.25404 | + | 6.25404i | 0.281668 | + | 0.281668i | ||||
\(494\) | 3.05026 | 0.137237 | ||||||||
\(495\) | 12.3251 | + | 1.30565i | 0.553971 | + | 0.0586846i | ||||
\(496\) | 4.74469 | 0.213043 | ||||||||
\(497\) | 39.2645 | + | 39.2645i | 1.76125 | + | 1.76125i | ||||
\(498\) | 22.5577 | − | 15.6644i | 1.01084 | − | 0.701938i | ||||
\(499\) | 14.6311i | 0.654977i | 0.944855 | + | 0.327489i | \(0.106202\pi\) | ||||
−0.944855 | + | 0.327489i | \(0.893798\pi\) | |||||||
\(500\) | 7.65334 | + | 8.15024i | 0.342268 | + | 0.364490i | ||||
\(501\) | 8.44351 | + | 1.52278i | 0.377228 | + | 0.0680329i | ||||
\(502\) | 16.1901 | − | 16.1901i | 0.722601 | − | 0.722601i | ||||
\(503\) | −10.2330 | + | 10.2330i | −0.456268 | + | 0.456268i | −0.897428 | − | 0.441160i | \(-0.854567\pi\) |
0.441160 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(504\) | −13.2062 | − | 4.92360i | −0.588250 | − | 0.219315i | ||||
\(505\) | −6.71817 | − | 26.1661i | −0.298955 | − | 1.16438i | ||||
\(506\) | − | 1.84760i | − | 0.0821357i | ||||||
\(507\) | 7.00211 | + | 10.0835i | 0.310975 | + | 0.447824i | ||||
\(508\) | 1.46864 | + | 1.46864i | 0.0651603 | + | 0.0651603i | ||||
\(509\) | −6.98622 | −0.309659 | −0.154829 | − | 0.987941i | \(-0.549483\pi\) | ||||
−0.154829 | + | 0.987941i | \(0.549483\pi\) | |||||||
\(510\) | −3.93031 | − | 3.39538i | −0.174037 | − | 0.150350i | ||||
\(511\) | −21.9396 | −0.970549 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 6.31557 | − | 1.61333i | 0.278839 | − | 0.0712302i | ||||
\(514\) | 18.6649i | 0.823275i | ||||||||
\(515\) | 25.0769 | + | 14.8306i | 1.10502 | + | 0.653516i | ||||
\(516\) | 2.93074 | − | 16.2503i | 0.129019 | − | 0.715381i | ||||
\(517\) | 13.2503 | − | 13.2503i | 0.582748 | − | 0.582748i | ||||
\(518\) | −32.5946 | + | 32.5946i | −1.43212 | + | 1.43212i | ||||
\(519\) | 0.737378 | − | 4.08861i | 0.0323673 | − | 0.179470i | ||||
\(520\) | −5.26624 | + | 1.35211i | −0.230940 | + | 0.0592940i | ||||
\(521\) | − | 28.2975i | − | 1.23973i | −0.784707 | − | 0.619867i | \(-0.787187\pi\) | ||
0.784707 | − | 0.619867i | \(-0.212813\pi\) | |||||||
\(522\) | 17.9967 | − | 8.22178i | 0.787695 | − | 0.359858i | ||||
\(523\) | −9.90039 | − | 9.90039i | −0.432914 | − | 0.432914i | 0.456705 | − | 0.889618i | \(-0.349030\pi\) |
−0.889618 | + | 0.456705i | \(0.849030\pi\) | |||||||
\(524\) | −3.62572 | −0.158390 | ||||||||
\(525\) | 12.9611 | + | 38.5666i | 0.565671 | + | 1.68318i | ||||
\(526\) | 23.3983 | 1.02021 | ||||||||
\(527\) | 4.49920 | + | 4.49920i | 0.195988 | + | 0.195988i | ||||
\(528\) | 1.82529 | + | 2.62853i | 0.0794354 | + | 0.114392i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −22.3688 | + | 5.74322i | −0.971640 | + | 0.249469i | ||||
\(531\) | 7.40086 | − | 19.8507i | 0.321170 | − | 0.861449i | ||||
\(532\) | 4.16735 | − | 4.16735i | 0.180678 | − | 0.180678i | ||||
\(533\) | −0.869517 | + | 0.869517i | −0.0376630 | + | 0.0376630i | ||||
\(534\) | −15.9544 | − | 2.87736i | −0.690412 | − | 0.124516i | ||||
\(535\) | 21.9786 | + | 12.9983i | 0.950217 | + | 0.561964i | ||||
\(536\) | 3.64019i | 0.157232i | ||||||||
\(537\) | 21.9709 | − | 15.2569i | 0.948113 | − | 0.658382i | ||||
\(538\) | −6.52295 | − | 6.52295i | −0.281224 | − | 0.281224i | ||||
\(539\) | 27.8463 | 1.19943 | ||||||||
\(540\) | −10.1886 | + | 5.58496i | −0.438449 | + | 0.240338i | ||||
\(541\) | 3.24241 | 0.139402 | 0.0697011 | − | 0.997568i | \(-0.477795\pi\) | ||||
0.0697011 | + | 0.997568i | \(0.477795\pi\) | |||||||
\(542\) | −8.63697 | − | 8.63697i | −0.370990 | − | 0.370990i | ||||
\(543\) | −21.5547 | + | 14.9679i | −0.925001 | + | 0.642333i | ||||
\(544\) | − | 1.34104i | − | 0.0574968i | ||||||
\(545\) | 7.29746 | + | 28.4223i | 0.312589 | + | 1.21748i | ||||
\(546\) | −19.4718 | − | 3.51173i | −0.833316 | − | 0.150288i | ||||
\(547\) | −28.5515 | + | 28.5515i | −1.22077 | + | 1.22077i | −0.253416 | + | 0.967357i | \(0.581554\pi\) |
−0.967357 | + | 0.253416i | \(0.918446\pi\) | |||||||
\(548\) | 4.25154 | − | 4.25154i | 0.181617 | − | 0.181617i | ||||
\(549\) | 4.00742 | − | 10.7488i | 0.171033 | − | 0.458747i | ||||
\(550\) | 2.57741 | − | 8.87115i | 0.109901 | − | 0.378267i | ||||
\(551\) | 8.27353i | 0.352464i | ||||||||
\(552\) | 0.987925 | + | 1.42268i | 0.0420489 | + | 0.0605531i | ||||
\(553\) | 23.9354 | + | 23.9354i | 1.01784 | + | 1.01784i | ||||
\(554\) | 10.7529 | 0.456846 | ||||||||
\(555\) | 2.76743 | + | 37.8995i | 0.117471 | + | 1.60874i | ||||
\(556\) | −9.87234 | −0.418680 | ||||||||
\(557\) | 6.90279 | + | 6.90279i | 0.292481 | + | 0.292481i | 0.838059 | − | 0.545579i | \(-0.183690\pi\) |
−0.545579 | + | 0.838059i | \(0.683690\pi\) | |||||||
\(558\) | 12.9470 | − | 5.91481i | 0.548088 | − | 0.250394i | ||||
\(559\) | − | 23.1809i | − | 0.980448i | ||||||
\(560\) | −5.34761 | + | 9.04220i | −0.225978 | + | 0.382103i | ||||
\(561\) | −0.761684 | + | 4.22338i | −0.0321583 | + | 0.178311i | ||||
\(562\) | 5.48821 | − | 5.48821i | 0.231506 | − | 0.231506i | ||||
\(563\) | 6.94658 | − | 6.94658i | 0.292764 | − | 0.292764i | −0.545407 | − | 0.838171i | \(-0.683625\pi\) |
0.838171 | + | 0.545407i | \(0.183625\pi\) | |||||||
\(564\) | −3.11788 | + | 17.2880i | −0.131286 | + | 0.727955i | ||||
\(565\) | −3.44524 | + | 5.82552i | −0.144942 | + | 0.245081i | ||||
\(566\) | 29.8229i | 1.25355i | ||||||||
\(567\) | −42.1739 | + | 3.02788i | −1.77114 | + | 0.127159i | ||||
\(568\) | 8.35761 | + | 8.35761i | 0.350678 | + | 0.350678i | ||||
\(569\) | 28.0632 | 1.17647 | 0.588236 | − | 0.808689i | \(-0.299823\pi\) | ||||
0.588236 | + | 0.808689i | \(0.299823\pi\) | |||||||
\(570\) | −0.353827 | − | 4.84561i | −0.0148202 | − | 0.202960i | ||||
\(571\) | −23.3485 | −0.977103 | −0.488552 | − | 0.872535i | \(-0.662475\pi\) | ||||
−0.488552 | + | 0.872535i | \(0.662475\pi\) | |||||||
\(572\) | 3.17666 | + | 3.17666i | 0.132823 | + | 0.132823i | ||||
\(573\) | 5.39776 | + | 7.77313i | 0.225495 | + | 0.324727i | ||||
\(574\) | 2.37592i | 0.0991691i | ||||||||
\(575\) | 1.39501 | − | 4.80145i | 0.0581757 | − | 0.200234i | ||||
\(576\) | −2.81099 | − | 1.04801i | −0.117125 | − | 0.0436671i | ||||
\(577\) | −10.4763 | + | 10.4763i | −0.436134 | + | 0.436134i | −0.890709 | − | 0.454575i | \(-0.849791\pi\) |
0.454575 | + | 0.890709i | \(0.349791\pi\) | |||||||
\(578\) | −10.7492 | + | 10.7492i | −0.447106 | + | 0.447106i | ||||
\(579\) | 38.2138 | + | 6.89185i | 1.58811 | + | 0.286415i | ||||
\(580\) | −3.66748 | − | 14.2842i | −0.152284 | − | 0.593119i | ||||
\(581\) | − | 74.4916i | − | 3.09043i | ||||||
\(582\) | −10.2576 | + | 7.12304i | −0.425193 | + | 0.295260i | ||||
\(583\) | 13.4931 | + | 13.4931i | 0.558828 | + | 0.558828i | ||||
\(584\) | −4.66993 | −0.193243 | ||||||||
\(585\) | −12.6846 | + | 10.2545i | −0.524442 | + | 0.423973i | ||||
\(586\) | 20.0649 | 0.828875 | ||||||||
\(587\) | 20.7853 | + | 20.7853i | 0.857899 | + | 0.857899i | 0.991090 | − | 0.133191i | \(-0.0425224\pi\) |
−0.133191 | + | 0.991090i | \(0.542522\pi\) | |||||||
\(588\) | −21.4421 | + | 14.8897i | −0.884256 | + | 0.614039i | ||||
\(589\) | 5.95204i | 0.245249i | ||||||||
\(590\) | −13.5917 | − | 8.03820i | −0.559561 | − | 0.330928i | ||||
\(591\) | −38.3606 | − | 6.91832i | −1.57794 | − | 0.284582i | ||||
\(592\) | −6.93789 | + | 6.93789i | −0.285146 | + | 0.285146i | ||||
\(593\) | 10.7822 | − | 10.7822i | 0.442772 | − | 0.442772i | −0.450171 | − | 0.892942i | \(-0.648637\pi\) |
0.892942 | + | 0.450171i | \(0.148637\pi\) | |||||||
\(594\) | 8.25747 | + | 4.89710i | 0.338808 | + | 0.200931i | ||||
\(595\) | −13.6453 | + | 3.50344i | −0.559402 | + | 0.143627i | ||||
\(596\) | − | 2.39241i | − | 0.0979968i | ||||||
\(597\) | −17.9846 | − | 25.8990i | −0.736060 | − | 1.05997i | ||||
\(598\) | 1.71935 | + | 1.71935i | 0.0703093 | + | 0.0703093i | ||||
\(599\) | −39.1541 | −1.59979 | −0.799896 | − | 0.600139i | \(-0.795112\pi\) | ||||
−0.799896 | + | 0.600139i | \(0.795112\pi\) | |||||||
\(600\) | 2.75884 | + | 8.20907i | 0.112629 | + | 0.335134i | ||||
\(601\) | −46.8771 | −1.91216 | −0.956078 | − | 0.293113i | \(-0.905309\pi\) | ||||
−0.956078 | + | 0.293113i | \(0.905309\pi\) | |||||||
\(602\) | −31.6705 | − | 31.6705i | −1.29079 | − | 1.29079i | ||||
\(603\) | 4.53792 | + | 9.93308i | 0.184798 | + | 0.404506i | ||||
\(604\) | 10.6559i | 0.433582i | ||||||||
\(605\) | 16.4308 | − | 4.21861i | 0.668005 | − | 0.171511i | ||||
\(606\) | 3.71400 | − | 20.5933i | 0.150871 | − | 0.836547i | ||||
\(607\) | −28.6698 | + | 28.6698i | −1.16367 | + | 1.16367i | −0.180005 | + | 0.983666i | \(0.557611\pi\) |
−0.983666 | + | 0.180005i | \(0.942389\pi\) | |||||||
\(608\) | 0.887039 | − | 0.887039i | 0.0359742 | − | 0.0359742i | ||||
\(609\) | 9.52524 | − | 52.8154i | 0.385982 | − | 2.14019i | ||||
\(610\) | −7.35964 | − | 4.35253i | −0.297983 | − | 0.176229i | ||||
\(611\) | 24.6611i | 0.997681i | ||||||||
\(612\) | −1.67177 | − | 3.65934i | −0.0675772 | − | 0.147920i | ||||
\(613\) | 13.3096 | + | 13.3096i | 0.537571 | + | 0.537571i | 0.922815 | − | 0.385244i | \(-0.125883\pi\) |
−0.385244 | + | 0.922815i | \(0.625883\pi\) | |||||||
\(614\) | 17.0856 | 0.689518 | ||||||||
\(615\) | 1.48217 | + | 1.28045i | 0.0597669 | + | 0.0516325i | ||||
\(616\) | 8.68009 | 0.349731 | ||||||||
\(617\) | 20.0482 | + | 20.0482i | 0.807111 | + | 0.807111i | 0.984196 | − | 0.177084i | \(-0.0566666\pi\) |
−0.177084 | + | 0.984196i | \(0.556667\pi\) | |||||||
\(618\) | 12.8719 | + | 18.5363i | 0.517783 | + | 0.745640i | ||||
\(619\) | − | 41.4746i | − | 1.66700i | −0.552517 | − | 0.833502i | \(-0.686332\pi\) | ||
0.552517 | − | 0.833502i | \(-0.313668\pi\) | |||||||
\(620\) | −2.63841 | − | 10.2761i | −0.105961 | − | 0.412700i | ||||
\(621\) | 4.46931 | + | 2.65053i | 0.179347 | + | 0.106362i | ||||
\(622\) | 17.0545 | − | 17.0545i | 0.683824 | − | 0.683824i | ||||
\(623\) | −31.0936 | + | 31.0936i | −1.24574 | + | 1.24574i | ||||
\(624\) | −4.14466 | − | 0.747487i | −0.165919 | − | 0.0299234i | ||||
\(625\) | 13.3961 | − | 21.1079i | 0.535844 | − | 0.844317i | ||||
\(626\) | − | 7.19498i | − | 0.287569i | ||||||
\(627\) | −3.29739 | + | 2.28975i | −0.131685 | + | 0.0914439i | ||||
\(628\) | 0.651151 | + | 0.651151i | 0.0259837 | + | 0.0259837i | ||||
\(629\) | −13.1579 | −0.524638 | ||||||||
\(630\) | −3.31999 | + | 31.3401i | −0.132272 | + | 1.24862i | ||||
\(631\) | −0.161420 | −0.00642604 | −0.00321302 | − | 0.999995i | \(-0.501023\pi\) | ||||
−0.00321302 | + | 0.999995i | \(0.501023\pi\) | |||||||
\(632\) | 5.09476 | + | 5.09476i | 0.202659 | + | 0.202659i | ||||
\(633\) | 34.2608 | − | 23.7911i | 1.36174 | − | 0.945613i | ||||
\(634\) | − | 15.4899i | − | 0.615184i | ||||||
\(635\) | 2.36413 | − | 3.99748i | 0.0938177 | − | 0.158635i | ||||
\(636\) | −17.6048 | − | 3.17502i | −0.698076 | − | 0.125898i | ||||
\(637\) | −25.9134 | + | 25.9134i | −1.02673 | + | 1.02673i | ||||
\(638\) | −8.61639 | + | 8.61639i | −0.341126 | + | 0.341126i | ||||
\(639\) | 33.2244 | + | 12.3869i | 1.31434 | + | 0.490018i | ||||
\(640\) | −1.13826 | + | 1.92467i | −0.0449937 | + | 0.0760793i | ||||
\(641\) | 31.1595i | 1.23073i | 0.788244 | + | 0.615363i | \(0.210991\pi\) | ||||
−0.788244 | + | 0.615363i | \(0.789009\pi\) | |||||||
\(642\) | 11.2815 | + | 16.2461i | 0.445245 | + | 0.641182i | ||||
\(643\) | −26.5729 | − | 26.5729i | −1.04793 | − | 1.04793i | −0.998792 | − | 0.0491393i | \(-0.984352\pi\) |
−0.0491393 | − | 0.998792i | \(-0.515648\pi\) | |||||||
\(644\) | 4.69805 | 0.185129 | ||||||||
\(645\) | −36.8250 | + | 2.68897i | −1.44998 | + | 0.105878i | ||||
\(646\) | 1.68229 | 0.0661888 | ||||||||
\(647\) | 16.8647 | + | 16.8647i | 0.663020 | + | 0.663020i | 0.956091 | − | 0.293071i | \(-0.0946771\pi\) |
−0.293071 | + | 0.956091i | \(0.594677\pi\) | |||||||
\(648\) | −8.97689 | + | 0.644498i | −0.352646 | + | 0.0253183i | ||||
\(649\) | 13.0474i | 0.512155i | ||||||||
\(650\) | 5.85686 | + | 10.6539i | 0.229725 | + | 0.417879i | ||||
\(651\) | 6.85252 | − | 37.9958i | 0.268571 | − | 1.48917i | ||||
\(652\) | 4.88731 | − | 4.88731i | 0.191402 | − | 0.191402i | ||||
\(653\) | −21.5295 | + | 21.5295i | −0.842515 | + | 0.842515i | −0.989185 | − | 0.146670i | \(-0.953144\pi\) |
0.146670 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(654\) | −4.03425 | + | 22.3690i | −0.157752 | + | 0.874699i | ||||
\(655\) | 2.01618 | + | 7.85266i | 0.0787785 | + | 0.306829i | ||||
\(656\) | 0.505725i | 0.0197453i | ||||||||
\(657\) | −12.7430 | + | 5.82161i | −0.497150 | + | 0.227123i | ||||
\(658\) | 33.6927 | + | 33.6927i | 1.31348 | + | 1.31348i | ||||
\(659\) | 3.43028 | 0.133625 | 0.0668124 | − | 0.997766i | \(-0.478717\pi\) | ||||
0.0668124 | + | 0.997766i | \(0.478717\pi\) | |||||||
\(660\) | 4.67792 | − | 5.41490i | 0.182088 | − | 0.210775i | ||||
\(661\) | −9.37004 | −0.364452 | −0.182226 | − | 0.983257i | \(-0.558330\pi\) | ||||
−0.182226 | + | 0.983257i | \(0.558330\pi\) | |||||||
\(662\) | −17.3968 | − | 17.3968i | −0.676146 | − | 0.676146i | ||||
\(663\) | −3.22140 | − | 4.63903i | −0.125109 | − | 0.180165i | ||||
\(664\) | − | 15.8559i | − | 0.615327i | ||||||
\(665\) | −11.3431 | − | 6.70837i | −0.439867 | − | 0.260140i | ||||
\(666\) | −10.2827 | + | 27.5805i | −0.398447 | + | 1.06872i | ||||
\(667\) | −4.66357 | + | 4.66357i | −0.180574 | + | 0.180574i | ||||
\(668\) | 3.50266 | − | 3.50266i | 0.135522 | − | 0.135522i | ||||
\(669\) | 6.63376 | + | 1.19640i | 0.256476 | + | 0.0462553i | ||||
\(670\) | 7.88400 | − | 2.02422i | 0.304585 | − | 0.0782025i | ||||
\(671\) | 7.06492i | 0.272738i | ||||||||
\(672\) | −6.68380 | + | 4.64132i | −0.257833 | + | 0.179043i | ||||
\(673\) | 2.35869 | + | 2.35869i | 0.0909206 | + | 0.0909206i | 0.751104 | − | 0.660184i | \(-0.229522\pi\) |
−0.660184 | + | 0.751104i | \(0.729522\pi\) | |||||||
\(674\) | 18.4690 | 0.711398 | ||||||||
\(675\) | 17.7617 | + | 18.9611i | 0.683647 | + | 0.729813i | ||||
\(676\) | 7.08770 | 0.272604 | ||||||||
\(677\) | −19.9993 | − | 19.9993i | −0.768634 | − | 0.768634i | 0.209232 | − | 0.977866i | \(-0.432904\pi\) |
−0.977866 | + | 0.209232i | \(0.932904\pi\) | |||||||
\(678\) | −4.30609 | + | 2.99021i | −0.165375 | + | 0.114838i | ||||
\(679\) | 33.8734i | 1.29994i | ||||||||
\(680\) | −2.90446 | + | 0.745722i | −0.111381 | + | 0.0285971i | ||||
\(681\) | −13.2003 | − | 2.38067i | −0.505836 | − | 0.0912273i | ||||
\(682\) | −6.19869 | + | 6.19869i | −0.237360 | + | 0.237360i | ||||
\(683\) | 11.5301 | − | 11.5301i | 0.441189 | − | 0.441189i | −0.451223 | − | 0.892411i | \(-0.649012\pi\) |
0.892411 | + | 0.451223i | \(0.149012\pi\) | |||||||
\(684\) | 1.31469 | − | 3.52629i | 0.0502684 | − | 0.134831i | ||||
\(685\) | −11.5722 | − | 6.84389i | −0.442153 | − | 0.261492i | ||||
\(686\) | 37.9210i | 1.44783i | ||||||||
\(687\) | −27.2305 | − | 39.2136i | −1.03891 | − | 1.49609i | ||||
\(688\) | −6.74120 | − | 6.74120i | −0.257006 | − | 0.257006i | ||||
\(689\) | −25.1130 | −0.956730 | ||||||||
\(690\) | 2.53190 | − | 2.93078i | 0.0963877 | − | 0.111573i | ||||
\(691\) | −26.9565 | −1.02548 | −0.512738 | − | 0.858545i | \(-0.671369\pi\) | ||||
−0.512738 | + | 0.858545i | \(0.671369\pi\) | |||||||
\(692\) | −1.69609 | − | 1.69609i | −0.0644758 | − | 0.0644758i | ||||
\(693\) | 23.6856 | − | 10.8207i | 0.899742 | − | 0.411046i | ||||
\(694\) | 9.97675i | 0.378712i | ||||||||
\(695\) | 5.48977 | + | 21.3817i | 0.208239 | + | 0.811055i | ||||
\(696\) | 2.02749 | − | 11.2420i | 0.0768517 | − | 0.426127i | ||||
\(697\) | −0.479560 | + | 0.479560i | −0.0181646 | + | 0.0181646i | ||||
\(698\) | −20.2671 | + | 20.2671i | −0.767119 | + | 0.767119i | ||||
\(699\) | 1.99226 | − | 11.0467i | 0.0753543 | − | 0.417824i | ||||
\(700\) | 22.5575 | + | 6.55380i | 0.852592 | + | 0.247710i | ||||
\(701\) | − | 14.1410i | − | 0.534099i | −0.963683 | − | 0.267050i | \(-0.913951\pi\) | ||
0.963683 | − | 0.267050i | \(-0.0860488\pi\) | |||||||
\(702\) | −12.2415 | + | 3.12711i | −0.462024 | + | 0.118025i | ||||
\(703\) | −8.70333 | − | 8.70333i | −0.328252 | − | 0.328252i | ||||
\(704\) | 1.84760 | 0.0696339 | ||||||||
\(705\) | 39.1764 | − | 2.86067i | 1.47547 | − | 0.107739i | ||||
\(706\) | 6.96994 | 0.262317 | ||||||||
\(707\) | −40.1346 | − | 40.1346i | −1.50942 | − | 1.50942i | ||||
\(708\) | −6.97655 | − | 10.0467i | −0.262195 | − | 0.377578i | ||||
\(709\) | 46.4972i | 1.74624i | 0.487506 | + | 0.873120i | \(0.337907\pi\) | ||||
−0.487506 | + | 0.873120i | \(0.662093\pi\) | |||||||
\(710\) | 13.4536 | − | 22.7486i | 0.504905 | − | 0.853738i | ||||
\(711\) | 20.2534 | + | 7.55100i | 0.759563 | + | 0.283185i | ||||
\(712\) | −6.61841 | + | 6.61841i | −0.248036 | + | 0.248036i | ||||
\(713\) | −3.35500 | + | 3.35500i | −0.125646 | + | 0.125646i | ||||
\(714\) | −10.7392 | − | 1.93680i | −0.401903 | − | 0.0724830i | ||||
\(715\) | 5.11361 | − | 8.64653i | 0.191238 | − | 0.323362i | ||||
\(716\) | − | 15.4433i | − | 0.577145i | ||||||
\(717\) | 8.47106 | − | 5.88242i | 0.316357 | − | 0.219683i | ||||
\(718\) | 7.01130 | + | 7.01130i | 0.261660 | + | 0.261660i | ||||
\(719\) | 5.67119 | 0.211500 | 0.105750 | − | 0.994393i | \(-0.466276\pi\) | ||||
0.105750 | + | 0.994393i | \(0.466276\pi\) | |||||||
\(720\) | −0.706675 | + | 6.67088i | −0.0263362 | + | 0.248609i | ||||
\(721\) | 61.2118 | 2.27965 | ||||||||
\(722\) | −12.3223 | − | 12.3223i | −0.458587 | − | 0.458587i | ||||
\(723\) | −23.2579 | + | 16.1506i | −0.864972 | + | 0.600648i | ||||
\(724\) | 15.1508i | 0.563076i | ||||||||
\(725\) | −28.8976 | + | 15.8862i | −1.07323 | + | 0.589999i | ||||
\(726\) | 12.9314 | + | 2.33217i | 0.479929 | + | 0.0865550i | ||||
\(727\) | 4.22102 | − | 4.22102i | 0.156549 | − | 0.156549i | −0.624487 | − | 0.781036i | \(-0.714692\pi\) |
0.781036 | + | 0.624487i | \(0.214692\pi\) | |||||||
\(728\) | −8.07757 | + | 8.07757i | −0.299375 | + | 0.299375i | ||||
\(729\) | −23.6920 | + | 12.9494i | −0.877483 | + | 0.479608i | ||||
\(730\) | 2.59684 | + | 10.1142i | 0.0961132 | + | 0.374344i | ||||
\(731\) | − | 12.7848i | − | 0.472864i | ||||||
\(732\) | −3.77767 | − | 5.44009i | −0.139627 | − | 0.201071i | ||||
\(733\) | −0.654319 | − | 0.654319i | −0.0241678 | − | 0.0241678i | 0.694920 | − | 0.719087i | \(-0.255440\pi\) |
−0.719087 | + | 0.694920i | \(0.755440\pi\) | |||||||
\(734\) | −13.9947 | −0.516553 | ||||||||
\(735\) | 44.1718 | + | 38.1599i | 1.62930 | + | 1.40755i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −4.75572 | − | 4.75572i | −0.175179 | − | 0.175179i | ||||
\(738\) | 0.630446 | + | 1.37999i | 0.0232070 | + | 0.0507980i | ||||
\(739\) | 28.6232i | 1.05292i | 0.850199 | + | 0.526461i | \(0.176481\pi\) | ||||
−0.850199 | + | 0.526461i | \(0.823519\pi\) | |||||||
\(740\) | 18.8842 | + | 11.1682i | 0.694198 | + | 0.410552i | ||||
\(741\) | 0.937694 | − | 5.19932i | 0.0344471 | − | 0.191002i | ||||
\(742\) | −34.3102 | + | 34.3102i | −1.25957 | + | 1.25957i | ||||
\(743\) | 3.48132 | − | 3.48132i | 0.127717 | − | 0.127717i | −0.640359 | − | 0.768076i | \(-0.721214\pi\) |
0.768076 | + | 0.640359i | \(0.221214\pi\) | |||||||
\(744\) | 1.45859 | − | 8.08756i | 0.0534744 | − | 0.296505i | ||||
\(745\) | −5.18153 | + | 1.33036i | −0.189836 | + | 0.0487407i | ||||
\(746\) | − | 33.4237i | − | 1.22373i | ||||||
\(747\) | −19.7662 | − | 43.2663i | −0.723206 | − | 1.58303i | ||||
\(748\) | 1.75200 | + | 1.75200i | 0.0640596 | + | 0.0640596i | ||||
\(749\) | 53.6489 | 1.96029 | ||||||||
\(750\) | 16.2453 | − | 10.5400i | 0.593193 | − | 0.384867i | ||||
\(751\) | 1.84306 | 0.0672543 | 0.0336271 | − | 0.999434i | \(-0.489294\pi\) | ||||
0.0336271 | + | 0.999434i | \(0.489294\pi\) | |||||||
\(752\) | 7.17165 | + | 7.17165i | 0.261523 | + | 0.261523i | ||||
\(753\) | −22.6198 | − | 32.5740i | −0.824312 | − | 1.18706i | ||||
\(754\) | − | 16.0366i | − | 0.584017i | ||||||
\(755\) | 23.0788 | − | 5.92549i | 0.839922 | − | 0.215651i | ||||
\(756\) | −12.4523 | + | 20.9970i | −0.452886 | + | 0.763654i | ||||
\(757\) | 35.9978 | − | 35.9978i | 1.30836 | − | 1.30836i | 0.385768 | − | 0.922596i | \(-0.373937\pi\) |
0.922596 | − | 0.385768i | \(-0.126063\pi\) | |||||||
\(758\) | 17.0818 | − | 17.0818i | 0.620439 | − | 0.620439i | ||||
\(759\) | −3.14932 | − | 0.567979i | −0.114313 | − | 0.0206163i | ||||
\(760\) | −2.41443 | − | 1.42791i | −0.0875806 | − | 0.0517956i | ||||
\(761\) | − | 15.0705i | − | 0.546305i | −0.961971 | − | 0.273152i | \(-0.911934\pi\) | ||
0.961971 | − | 0.273152i | \(-0.0880663\pi\) | |||||||
\(762\) | 2.95485 | − | 2.05189i | 0.107043 | − | 0.0743320i | ||||
\(763\) | 43.5953 | + | 43.5953i | 1.57826 | + | 1.57826i | ||||
\(764\) | 5.46374 | 0.197671 | ||||||||
\(765\) | −6.99584 | + | 5.65562i | −0.252935 | + | 0.204479i | ||||
\(766\) | −23.8859 | −0.863033 | ||||||||
\(767\) | −12.1417 | − | 12.1417i | −0.438412 | − | 0.438412i | ||||
\(768\) | −1.42268 | + | 0.987925i | −0.0513364 | + | 0.0356487i | ||||
\(769\) | − | 20.8224i | − | 0.750876i | −0.926847 | − | 0.375438i | \(-0.877492\pi\) | ||
0.926847 | − | 0.375438i | \(-0.122508\pi\) | |||||||
\(770\) | −4.82679 | − | 18.7995i | −0.173946 | − | 0.677488i | ||||
\(771\) | 31.8153 | + | 5.73788i | 1.14580 | + | 0.206645i | ||||
\(772\) | 15.8524 | − | 15.8524i | 0.570541 | − | 0.570541i | ||||
\(773\) | 18.5904 | − | 18.5904i | 0.668650 | − | 0.668650i | −0.288753 | − | 0.957404i | \(-0.593241\pi\) |
0.957404 | + | 0.288753i | \(0.0932408\pi\) | |||||||
\(774\) | −26.7986 | − | 9.99119i | −0.963255 | − | 0.359126i | ||||
\(775\) | −20.7891 | + | 11.4286i | −0.746767 | + | 0.410529i | ||||
\(776\) | 7.21011i | 0.258828i | ||||||||
\(777\) | 45.5390 | + | 65.5792i | 1.63370 | + | 2.35264i | ||||
\(778\) | −0.492158 | − | 0.492158i | −0.0176447 | − | 0.0176447i | ||||
\(779\) | −0.634414 | −0.0227302 | ||||||||
\(780\) | 0.685822 | + | 9.39224i | 0.0245564 | + | 0.336296i | ||||
\(781\) | −21.8376 | −0.781409 | ||||||||
\(782\) | 0.948261 | + | 0.948261i | 0.0339097 | + | 0.0339097i | ||||
\(783\) | −8.48200 | − | 33.2038i | −0.303122 | − | 1.18661i | ||||
\(784\) | 15.0717i | 0.538273i | ||||||||
\(785\) | 1.04819 | − | 1.77237i | 0.0374114 | − | 0.0632584i | ||||
\(786\) | −1.11460 | + | 6.18023i | −0.0397565 | + | 0.220441i | ||||
\(787\) | −12.5673 | + | 12.5673i | −0.447976 | + | 0.447976i | −0.894681 | − | 0.446705i | \(-0.852597\pi\) |
0.446705 | + | 0.894681i | \(0.352597\pi\) | |||||||
\(788\) | −15.9133 | + | 15.9133i | −0.566888 | + | 0.566888i | ||||
\(789\) | 7.19298 | − | 39.8836i | 0.256077 | − | 1.41989i | ||||
\(790\) | 8.20127 | − | 13.8674i | 0.291788 | − | 0.493381i | ||||
\(791\) | 14.2199i | 0.505600i | ||||||||
\(792\) | 5.04158 | − | 2.30324i | 0.179145 | − | 0.0818422i | ||||
\(793\) | −6.57451 | − | 6.57451i | −0.233468 | − | 0.233468i | ||||
\(794\) | 32.2575 | 1.14478 | ||||||||
\(795\) | 2.91309 | + | 39.8944i | 0.103317 | + | 1.41491i | ||||
\(796\) | −18.2044 | −0.645238 | ||||||||
\(797\) | −29.2967 | − | 29.2967i | −1.03774 | − | 1.03774i | −0.999259 | − | 0.0384846i | \(-0.987747\pi\) |
−0.0384846 | − | 0.999259i | \(-0.512253\pi\) | |||||||
\(798\) | −5.82236 | − | 8.38458i | −0.206109 | − | 0.296811i | ||||
\(799\) | 13.6012i | 0.481175i | ||||||||
\(800\) | 4.80145 | + | 1.39501i | 0.169757 | + | 0.0493209i | ||||
\(801\) | −9.80922 | + | 26.3105i | −0.346592 | + | 0.929635i | ||||
\(802\) | 17.8719 | − | 17.8719i | 0.631078 | − | 0.631078i | ||||
\(803\) | 6.10102 | − | 6.10102i | 0.215300 | − | 0.215300i | ||||
\(804\) | 6.20489 | + | 1.11905i | 0.218830 | + | 0.0394658i | ||||
\(805\) | −2.61247 | − | 10.1751i | −0.0920776 | − | 0.358626i | ||||
\(806\) | − | 11.5368i | − | 0.406367i | ||||||
\(807\) | −13.1240 | + | 9.11345i | −0.461985 | + | 0.320809i | ||||
\(808\) | −8.54283 | − | 8.54283i | −0.300536 | − | 0.300536i | ||||
\(809\) | −7.19305 | −0.252894 | −0.126447 | − | 0.991973i | \(-0.540357\pi\) | ||||
−0.126447 | + | 0.991973i | \(0.540357\pi\) | |||||||
\(810\) | 6.38771 | + | 19.0840i | 0.224441 | + | 0.670542i | ||||
\(811\) | 9.26127 | 0.325207 | 0.162604 | − | 0.986691i | \(-0.448011\pi\) | ||||
0.162604 | + | 0.986691i | \(0.448011\pi\) | |||||||
\(812\) | −21.9097 | − | 21.9097i | −0.768878 | − | 0.768878i | ||||
\(813\) | −17.3773 | + | 12.0670i | −0.609448 | + | 0.423209i | ||||
\(814\) | − | 18.1280i | − | 0.635386i | ||||||
\(815\) | −13.3028 | − | 7.86732i | −0.465975 | − | 0.275580i | ||||
\(816\) | −2.28588 | − | 0.412257i | −0.0800217 | − | 0.0144319i | ||||
\(817\) | 8.45658 | − | 8.45658i | 0.295858 | − | 0.295858i | ||||
\(818\) | −1.26267 | + | 1.26267i | −0.0441481 | + | 0.0441481i | ||||
\(819\) | −11.9718 | + | 32.1111i | −0.418330 | + | 1.12205i | ||||
\(820\) | 1.09531 | − | 0.281222i | 0.0382499 | − | 0.00982070i | ||||
\(821\) | 24.0845i | 0.840555i | 0.907396 | + | 0.420277i | \(0.138067\pi\) | ||||
−0.907396 | + | 0.420277i | \(0.861933\pi\) | |||||||
\(822\) | −5.93998 | − | 8.55395i | −0.207181 | − | 0.298353i | ||||
\(823\) | −14.2232 | − | 14.2232i | −0.495791 | − | 0.495791i | 0.414334 | − | 0.910125i | \(-0.364015\pi\) |
−0.910125 | + | 0.414334i | \(0.864015\pi\) | |||||||
\(824\) | 13.0292 | 0.453894 | ||||||||
\(825\) | −14.3290 | − | 7.12045i | −0.498871 | − | 0.247902i | ||||
\(826\) | −33.1768 | −1.15437 | ||||||||
\(827\) | −0.719388 | − | 0.719388i | −0.0250156 | − | 0.0250156i | 0.694488 | − | 0.719504i | \(-0.255631\pi\) |
−0.719504 | + | 0.694488i | \(0.755631\pi\) | |||||||
\(828\) | 2.72873 | − | 1.24662i | 0.0948298 | − | 0.0433229i | ||||
\(829\) | 7.68796i | 0.267014i | 0.991048 | + | 0.133507i | \(0.0426238\pi\) | ||||
−0.991048 | + | 0.133507i | \(0.957376\pi\) | |||||||
\(830\) | −34.3409 | + | 8.81706i | −1.19199 | + | 0.306045i | ||||
\(831\) | 3.30560 | − | 18.3288i | 0.114670 | − | 0.635821i | ||||
\(832\) | −1.71935 | + | 1.71935i | −0.0596076 | + | 0.0596076i | ||||
\(833\) | −14.2919 | + | 14.2919i | −0.495184 | + | 0.495184i | ||||
\(834\) | −3.03491 | + | 16.8279i | −0.105090 | + | 0.582703i | ||||
\(835\) | −9.53387 | − | 5.63838i | −0.329933 | − | 0.195124i | ||||
\(836\) | 2.31774i | 0.0801607i | ||||||||
\(837\) | −6.10200 | − | 23.8871i | −0.210916 | − | 0.825657i | ||||
\(838\) | −25.3220 | − | 25.3220i | −0.874732 | − | 0.874732i | ||||
\(839\) | 38.2353 | 1.32003 | 0.660014 | − | 0.751253i | \(-0.270550\pi\) | ||||
0.660014 | + | 0.751253i | \(0.270550\pi\) | |||||||
\(840\) | 13.7690 | + | 11.8950i | 0.475074 | + | 0.410416i | ||||
\(841\) | 14.4977 | 0.499921 | ||||||||
\(842\) | −14.8267 | − | 14.8267i | −0.510962 | − | 0.510962i | ||||
\(843\) | −7.66777 | − | 11.0421i | −0.264092 | − | 0.380310i | ||||
\(844\) | − | 24.0819i | − | 0.828935i | ||||||
\(845\) | −3.94130 | − | 15.3507i | −0.135585 | − | 0.528080i | ||||
\(846\) | 28.5098 | + | 10.6292i | 0.980186 | + | 0.365438i | ||||
\(847\) | 25.2022 | − | 25.2022i | 0.865956 | − | 0.865956i | ||||
\(848\) | −7.30308 | + | 7.30308i | −0.250789 | + | 0.250789i | ||||
\(849\) | 50.8346 | + | 9.16800i | 1.74464 | + | 0.314645i | ||||
\(850\) | 3.23020 | + | 5.87586i | 0.110795 | + | 0.201540i | ||||
\(851\) | − | 9.81166i | − | 0.336339i | ||||||
\(852\) | 16.8152 | − | 11.6767i | 0.576081 | − | 0.400038i | ||||
\(853\) | −0.699678 | − | 0.699678i | −0.0239565 | − | 0.0239565i | 0.695027 | − | 0.718984i | \(-0.255392\pi\) |
−0.718984 | + | 0.695027i | \(0.755392\pi\) | |||||||
\(854\) | −17.9646 | −0.614736 | ||||||||
\(855\) | −8.36837 | − | 0.886498i | −0.286192 | − | 0.0303176i | ||||
\(856\) | 11.4194 | 0.390307 | ||||||||
\(857\) | −14.0885 | − | 14.0885i | −0.481253 | − | 0.481253i | 0.424278 | − | 0.905532i | \(-0.360528\pi\) |
−0.905532 | + | 0.424278i | \(0.860528\pi\) | |||||||
\(858\) | 6.39133 | − | 4.43822i | 0.218196 | − | 0.151518i | ||||
\(859\) | − | 14.8178i | − | 0.505577i | −0.967522 | − | 0.252789i | \(-0.918652\pi\) | ||
0.967522 | − | 0.252789i | \(-0.0813477\pi\) | |||||||
\(860\) | −10.8516 | + | 18.3488i | −0.370037 | + | 0.625690i | ||||
\(861\) | 4.04988 | + | 0.730394i | 0.138020 | + | 0.0248918i | ||||
\(862\) | −14.6633 | + | 14.6633i | −0.499434 | + | 0.499434i | ||||
\(863\) | −8.29672 | + | 8.29672i | −0.282424 | + | 0.282424i | −0.834075 | − | 0.551651i | \(-0.813998\pi\) |
0.551651 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(864\) | −2.65053 | + | 4.46931i | −0.0901728 | + | 0.152049i | ||||
\(865\) | −2.73028 | + | 4.61659i | −0.0928323 | + | 0.156969i | ||||
\(866\) | − | 26.4643i | − | 0.899293i | ||||||
\(867\) | 15.0180 | + | 21.6269i | 0.510039 | + | 0.734490i | ||||
\(868\) | −15.7620 | − | 15.7620i | −0.534996 | − | 0.534996i | ||||
\(869\) | −13.3121 | −0.451582 | ||||||||
\(870\) | −25.4756 | + | 1.86023i | −0.863703 | + | 0.0630677i | ||||
\(871\) | 8.85120 | 0.299912 | ||||||||
\(872\) | 9.27945 | + | 9.27945i | 0.314242 | + | 0.314242i | ||||
\(873\) | 8.98824 | + | 19.6744i | 0.304206 | + | 0.665878i | ||||
\(874\) | 1.25446i | 0.0424328i | ||||||||
\(875\) | 1.65069 | − | 52.4998i | 0.0558035 | − | 1.77482i | ||||
\(876\) | −1.43561 | + | 7.96014i | −0.0485047 | + | 0.268948i | ||||
\(877\) | −5.35773 | + | 5.35773i | −0.180918 | + | 0.180918i | −0.791756 | − | 0.610838i | \(-0.790833\pi\) |
0.610838 | + | 0.791756i | \(0.290833\pi\) | |||||||
\(878\) | −12.5880 | + | 12.5880i | −0.424823 | + | 0.424823i | ||||
\(879\) | 6.16827 | − | 34.2017i | 0.208050 | − | 1.15360i | ||||
\(880\) | −1.02740 | − | 4.00156i | −0.0346338 | − | 0.134893i | ||||
\(881\) | − | 13.0986i | − | 0.441305i | −0.975353 | − | 0.220652i | \(-0.929181\pi\) | ||
0.975353 | − | 0.220652i | \(-0.0708186\pi\) | |||||||
\(882\) | 18.7886 | + | 41.1264i | 0.632644 | + | 1.38480i | ||||
\(883\) | −26.7110 | − | 26.7110i | −0.898897 | − | 0.898897i | 0.0964414 | − | 0.995339i | \(-0.469254\pi\) |
−0.995339 | + | 0.0964414i | \(0.969254\pi\) | |||||||
\(884\) | −3.26078 | −0.109672 | ||||||||
\(885\) | −17.8798 | + | 20.6967i | −0.601024 | + | 0.695711i | ||||
\(886\) | −41.1973 | −1.38405 | ||||||||
\(887\) | 1.13171 | + | 1.13171i | 0.0379992 | + | 0.0379992i | 0.725851 | − | 0.687852i | \(-0.241446\pi\) |
−0.687852 | + | 0.725851i | \(0.741446\pi\) | |||||||
\(888\) | 9.69318 | + | 13.9588i | 0.325282 | + | 0.468427i | ||||
\(889\) | − | 9.75769i | − | 0.327263i | ||||||
\(890\) | 18.0146 | + | 10.6540i | 0.603852 | + | 0.357121i | ||||
\(891\) | 10.8858 | − | 12.5698i | 0.364689 | − | 0.421106i | ||||
\(892\) | 2.75191 | − | 2.75191i | 0.0921408 | − | 0.0921408i | ||||
\(893\) | −8.99657 | + | 8.99657i | −0.301059 | + | 0.301059i | ||||
\(894\) | −4.07798 | − | 0.735462i | −0.136388 | − | 0.0245975i | ||||
\(895\) | −33.4475 | + | 8.58768i | −1.11803 | + | 0.287054i | ||||
\(896\) | 4.69805i | 0.156951i | ||||||||
\(897\) | 3.45927 | − | 2.40216i | 0.115502 | − | 0.0802058i | ||||
\(898\) | 3.71209 | + | 3.71209i | 0.123874 | + | 0.123874i | ||||
\(899\) | 31.2925 | 1.04366 | ||||||||
\(900\) | 14.8409 | − | 2.17899i | 0.494696 | − | 0.0726328i | ||||
\(901\) | −13.8504 | −0.461425 | ||||||||
\(902\) | −0.660704 | − | 0.660704i | −0.0219990 | − | 0.0219990i | ||||
\(903\) | −63.7199 | + | 44.2480i | −2.12047 | + | 1.47248i | ||||
\(904\) | 3.02676i | 0.100668i | ||||||||
\(905\) | 32.8140 | − | 8.42501i | 1.09077 | − | 0.280057i | ||||
\(906\) | 18.1635 | + | 3.27578i | 0.603443 | + | 0.108831i | ||||
\(907\) | 18.6482 | − | 18.6482i | 0.619203 | − | 0.619203i | −0.326124 | − | 0.945327i | \(-0.605743\pi\) |
0.945327 | + | 0.326124i | \(0.105743\pi\) | |||||||
\(908\) | −5.47594 | + | 5.47594i | −0.181725 | + | 0.181725i | ||||
\(909\) | −33.9607 | − | 12.6614i | −1.12640 | − | 0.419952i | ||||
\(910\) | 21.9863 | + | 13.0028i | 0.728839 | + | 0.431039i | ||||
\(911\) | − | 6.38602i | − | 0.211578i | −0.994389 | − | 0.105789i | \(-0.966263\pi\) | ||
0.994389 | − | 0.105789i | \(-0.0337369\pi\) | |||||||
\(912\) | −1.23932 | − | 1.78469i | −0.0410378 | − | 0.0590971i | ||||
\(913\) | 20.7148 | + | 20.7148i | 0.685561 | + | 0.685561i | ||||
\(914\) | 12.1649 | 0.402381 | ||||||||
\(915\) | −9.68158 | + | 11.2069i | −0.320063 | + | 0.370487i | ||||
\(916\) | −27.5633 | −0.910718 | ||||||||
\(917\) | 12.0447 | + | 12.0447i | 0.397752 | + | 0.397752i | ||||
\(918\) | −6.75146 | + | 1.72468i | −0.222831 | + | 0.0569228i | ||||
\(919\) | 8.47456i | 0.279550i | 0.990183 | + | 0.139775i | \(0.0446379\pi\) | ||||
−0.990183 | + | 0.139775i | \(0.955362\pi\) | |||||||
\(920\) | −0.556076 | − | 2.16582i | −0.0183333 | − | 0.0714050i | ||||
\(921\) | 5.25237 | − | 29.1233i | 0.173071 | − | 0.959644i | ||||
\(922\) | 0.830163 | − | 0.830163i | 0.0273400 | − | 0.0273400i | ||||
\(923\) | 20.3217 | − | 20.3217i | 0.668898 | − | 0.668898i | ||||
\(924\) | 2.66839 | − | 14.7957i | 0.0877836 | − | 0.486742i | ||||
\(925\) | 13.6873 | − | 47.1102i | 0.450036 | − | 1.54898i | ||||
\(926\) | − | 10.6991i | − | 0.351594i | ||||||
\(927\) | 35.5531 | − | 16.2424i | 1.16772 | − | 0.533471i | ||||
\(928\) | −4.66357 | − | 4.66357i | −0.153089 | − | 0.153089i | ||||
\(929\) | 24.0411 | 0.788764 | 0.394382 | − | 0.918947i | \(-0.370959\pi\) | ||||
0.394382 | + | 0.918947i | \(0.370959\pi\) | |||||||
\(930\) | −18.3273 | + | 1.33826i | −0.600976 | + | 0.0438833i | ||||
\(931\) | −18.9068 | −0.619646 | ||||||||
\(932\) | −4.58254 | − | 4.58254i | −0.150106 | − | 0.150106i | ||||
\(933\) | −23.8275 | − | 34.3131i | −0.780077 | − | 1.12336i | ||||
\(934\) | 29.9772i | 0.980883i | ||||||||
\(935\) | 2.82028 | − | 4.76877i | 0.0922329 | − | 0.155955i | ||||
\(936\) | −2.54826 | + | 6.83499i | −0.0832925 | + | 0.223409i | ||||
\(937\) | −11.1439 | + | 11.1439i | −0.364055 | + | 0.364055i | −0.865303 | − | 0.501249i | \(-0.832874\pi\) |
0.501249 | + | 0.865303i | \(0.332874\pi\) | |||||||
\(938\) | 12.0928 | − | 12.0928i | 0.394843 | − | 0.394843i | ||||
\(939\) | −12.2642 | − | 2.21184i | −0.400227 | − | 0.0721808i | ||||
\(940\) | 11.5445 | − | 19.5205i | 0.376541 | − | 0.636688i | ||||
\(941\) | 49.5446i | 1.61511i | 0.589794 | + | 0.807554i | \(0.299209\pi\) | ||||
−0.589794 | + | 0.807554i | \(0.700791\pi\) | |||||||
\(942\) | 1.31009 | − | 0.909747i | 0.0426852 | − | 0.0296411i | ||||
\(943\) | −0.357602 | − | 0.357602i | −0.0116451 | − | 0.0116451i | ||||
\(944\) | −7.06183 | −0.229843 | ||||||||
\(945\) | 52.4002 | + | 15.2935i | 1.70458 | + | 0.497498i | ||||
\(946\) | 17.6140 | 0.572682 | ||||||||
\(947\) | −13.1798 | − | 13.1798i | −0.428286 | − | 0.428286i | 0.459758 | − | 0.888044i | \(-0.347936\pi\) |
−0.888044 | + | 0.459758i | \(0.847936\pi\) | |||||||
\(948\) | 10.2505 | − | 7.11808i | 0.332921 | − | 0.231185i | ||||
\(949\) | 11.3550i | 0.368600i | ||||||||
\(950\) | −1.74998 | + | 6.02325i | −0.0567769 | + | 0.195420i | ||||
\(951\) | −26.4034 | − | 4.76184i | −0.856188 | − | 0.154413i | ||||
\(952\) | −4.45497 | + | 4.45497i | −0.144387 | + | 0.144387i | ||||
\(953\) | 38.2438 | − | 38.2438i | 1.23884 | − | 1.23884i | 0.278361 | − | 0.960477i | \(-0.410209\pi\) |
0.960477 | − | 0.278361i | \(-0.0897912\pi\) | |||||||
\(954\) | −10.8240 | + | 29.0322i | −0.350439 | + | 0.939953i | ||||
\(955\) | −3.03826 | − | 11.8335i | −0.0983156 | − | 0.382922i | ||||
\(956\) | − | 5.95432i | − | 0.192576i | ||||||
\(957\) | 12.0383 | + | 17.3359i | 0.389142 | + | 0.560389i | ||||
\(958\) | −5.73619 | − | 5.73619i | −0.185328 | − | 0.185328i | ||||
\(959\) | −28.2474 | −0.912156 | ||||||||
\(960\) | 2.93078 | + | 2.53190i | 0.0945906 | + | 0.0817167i | ||||
\(961\) | −8.48794 | −0.273804 | ||||||||
\(962\) | 16.8696 | + | 16.8696i | 0.543899 | + | 0.543899i | ||||
\(963\) | 31.1604 | − | 14.2356i | 1.00413 | − | 0.458736i | ||||
\(964\) | 16.3480i | 0.526534i | ||||||||
\(965\) | −43.1486 | − | 25.5183i | −1.38900 | − | 0.821464i | ||||
\(966\) | 1.44425 | − | 8.00806i | 0.0464680 | − | 0.257655i | ||||
\(967\) | −8.40687 | + | 8.40687i | −0.270347 | + | 0.270347i | −0.829240 | − | 0.558893i | \(-0.811226\pi\) |
0.558893 | + | 0.829240i | \(0.311226\pi\) | |||||||
\(968\) | 5.36439 | − | 5.36439i | 0.172418 | − | 0.172418i | ||||
\(969\) | 0.517161 | − | 2.86755i | 0.0166136 | − | 0.0921189i | ||||
\(970\) | 15.6158 | − | 4.00937i | 0.501393 | − | 0.128733i | ||||
\(971\) | − | 5.54281i | − | 0.177877i | −0.996037 | − | 0.0889386i | \(-0.971653\pi\) | ||
0.996037 | − | 0.0889386i | \(-0.0283475\pi\) | |||||||
\(972\) | −1.66105 | + | 15.4997i | −0.0532783 | + | 0.497153i | ||||
\(973\) | 32.7961 | + | 32.7961i | 1.05140 | + | 1.05140i | ||||
\(974\) | −12.4094 | −0.397623 | ||||||||
\(975\) | 19.9605 | − | 6.70817i | 0.639249 | − | 0.214833i | ||||
\(976\) | −3.82384 | −0.122398 | ||||||||
\(977\) | 31.9373 | + | 31.9373i | 1.02177 | + | 1.02177i | 0.999758 | + | 0.0220078i | \(0.00700586\pi\) |
0.0220078 | + | 0.999758i | \(0.492994\pi\) | |||||||
\(978\) | −6.82824 | − | 9.83311i | −0.218343 | − | 0.314428i | ||||
\(979\) | − | 17.2932i | − | 0.552694i | ||||||
\(980\) | 32.6425 | − | 8.38099i | 1.04273 | − | 0.267721i | ||||
\(981\) | 36.8890 | + | 13.7532i | 1.17778 | + | 0.439105i | ||||
\(982\) | 24.4548 | − | 24.4548i | 0.780385 | − | 0.780385i | ||||
\(983\) | 23.3509 | − | 23.3509i | 0.744777 | − | 0.744777i | −0.228716 | − | 0.973493i | \(-0.573453\pi\) |
0.973493 | + | 0.228716i | \(0.0734529\pi\) | |||||||
\(984\) | 0.862035 | + | 0.155468i | 0.0274807 | + | 0.00495613i | ||||
\(985\) | 43.3144 | + | 25.6164i | 1.38011 | + | 0.816205i | ||||
\(986\) | − | 8.84455i | − | 0.281668i | ||||||
\(987\) | 67.7887 | − | 47.0734i | 2.15774 | − | 1.49836i | ||||
\(988\) | −2.15686 | − | 2.15686i | −0.0686187 | − | 0.0686187i | ||||
\(989\) | 9.53349 | 0.303147 | ||||||||
\(990\) | −7.79192 | − | 9.63839i | −0.247643 | − | 0.306328i | ||||
\(991\) | −48.3027 | −1.53439 | −0.767193 | − | 0.641416i | \(-0.778347\pi\) | ||||
−0.767193 | + | 0.641416i | \(0.778347\pi\) | |||||||
\(992\) | −3.35500 | − | 3.35500i | −0.106521 | − | 0.106521i | ||||
\(993\) | −35.0018 | + | 24.3057i | −1.11075 | + | 0.771319i | ||||
\(994\) | − | 55.5283i | − | 1.76125i | ||||||
\(995\) | 10.1230 | + | 39.4275i | 0.320922 | + | 1.24994i | ||||
\(996\) | −27.0271 | − | 4.87433i | −0.856387 | − | 0.154449i | ||||
\(997\) | 31.8848 | − | 31.8848i | 1.00980 | − | 1.00980i | 0.00985083 | − | 0.999951i | \(-0.496864\pi\) |
0.999951 | − | 0.00985083i | \(-0.00313567\pi\) | |||||||
\(998\) | 10.3457 | − | 10.3457i | 0.327489 | − | 0.327489i | ||||
\(999\) | 43.8513 | + | 26.0061i | 1.38739 | + | 0.822796i |
(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 | 690.2.i.e.323.1 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.e.323.14 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.e.47.14 | yes | 32 | |
15.2 | even | 4 | inner | 690.2.i.e.47.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.e.47.1 | ✓ | 32 | 15.2 | even | 4 | inner | |
690.2.i.e.47.14 | yes | 32 | 5.2 | odd | 4 | inner | |
690.2.i.e.323.1 | yes | 32 | 1.1 | even | 1 | trivial | |
690.2.i.e.323.14 | yes | 32 | 3.2 | odd | 2 | inner |