Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(77,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.s (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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.3 | ||
Root | \(1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.77 |
Dual form | 390.2.s.a.233.3 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.618034 | − | 1.61803i | −0.356822 | − | 0.934172i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.707107 | + | 2.12132i | 0.316228 | + | 0.948683i | ||||
\(6\) | 0.707107 | − | 1.58114i | 0.288675 | − | 0.645497i | ||||
\(7\) | −3.16228 | + | 3.16228i | −1.19523 | + | 1.19523i | −0.219650 | + | 0.975579i | \(0.570491\pi\) |
−0.975579 | + | 0.219650i | \(0.929509\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(10\) | −1.00000 | + | 2.00000i | −0.316228 | + | 0.632456i | ||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 1.61803 | − | 0.618034i | 0.467086 | − | 0.178411i | ||||
\(13\) | 3.58114 | − | 0.418861i | 0.993229 | − | 0.116171i | ||||
\(14\) | −4.47214 | −1.19523 | ||||||||
\(15\) | 2.99535 | − | 2.45517i | 0.773397 | − | 0.633922i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.23607 | + | 2.23607i | −0.542326 | + | 0.542326i | −0.924210 | − | 0.381884i | \(-0.875275\pi\) |
0.381884 | + | 0.924210i | \(0.375275\pi\) | |||||||
\(18\) | −2.99535 | − | 0.166925i | −0.706011 | − | 0.0393447i | ||||
\(19\) | 6.32456 | 1.45095 | 0.725476 | − | 0.688247i | \(-0.241620\pi\) | ||||
0.725476 | + | 0.688247i | \(0.241620\pi\) | |||||||
\(20\) | −2.12132 | + | 0.707107i | −0.474342 | + | 0.158114i | ||||
\(21\) | 7.07107 | + | 3.16228i | 1.54303 | + | 0.690066i | ||||
\(22\) | −4.00000 | − | 4.00000i | −0.852803 | − | 0.852803i | ||||
\(23\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(24\) | 1.58114 | + | 0.707107i | 0.322749 | + | 0.144338i | ||||
\(25\) | −4.00000 | + | 3.00000i | −0.800000 | + | 0.600000i | ||||
\(26\) | 2.82843 | + | 2.23607i | 0.554700 | + | 0.438529i | ||||
\(27\) | 4.61803 | + | 2.38197i | 0.888741 | + | 0.458410i | ||||
\(28\) | −3.16228 | − | 3.16228i | −0.597614 | − | 0.597614i | ||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 3.85410 | + | 0.381966i | 0.703660 | + | 0.0697371i | ||||
\(31\) | − | 3.16228i | − | 0.567962i | −0.958830 | − | 0.283981i | \(-0.908345\pi\) | ||
0.958830 | − | 0.283981i | \(-0.0916552\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 3.49613 | + | 9.15298i | 0.608598 | + | 1.59333i | ||||
\(34\) | −3.16228 | −0.542326 | ||||||||
\(35\) | −8.94427 | − | 4.47214i | −1.51186 | − | 0.755929i | ||||
\(36\) | −2.00000 | − | 2.23607i | −0.333333 | − | 0.372678i | ||||
\(37\) | −3.16228 | + | 3.16228i | −0.519875 | + | 0.519875i | −0.917534 | − | 0.397658i | \(-0.869823\pi\) |
0.397658 | + | 0.917534i | \(0.369823\pi\) | |||||||
\(38\) | 4.47214 | + | 4.47214i | 0.725476 | + | 0.725476i | ||||
\(39\) | −2.89100 | − | 5.53553i | −0.462930 | − | 0.886395i | ||||
\(40\) | −2.00000 | − | 1.00000i | −0.316228 | − | 0.158114i | ||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 2.76393 | + | 7.23607i | 0.426484 | + | 1.11655i | ||||
\(43\) | −5.00000 | + | 5.00000i | −0.762493 | + | 0.762493i | −0.976772 | − | 0.214280i | \(-0.931260\pi\) |
0.214280 | + | 0.976772i | \(0.431260\pi\) | |||||||
\(44\) | − | 5.65685i | − | 0.852803i | ||||||
\(45\) | −5.82378 | − | 3.32920i | −0.868158 | − | 0.496288i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | + | 1.41421i | 0.206284 | + | 0.206284i | 0.802686 | − | 0.596402i | \(-0.203403\pi\) |
−0.596402 | + | 0.802686i | \(0.703403\pi\) | |||||||
\(48\) | 0.618034 | + | 1.61803i | 0.0892055 | + | 0.233543i | ||||
\(49\) | − | 13.0000i | − | 1.85714i | ||||||
\(50\) | −4.94975 | − | 0.707107i | −0.700000 | − | 0.100000i | ||||
\(51\) | 5.00000 | + | 2.23607i | 0.700140 | + | 0.313112i | ||||
\(52\) | 0.418861 | + | 3.58114i | 0.0580856 | + | 0.496615i | ||||
\(53\) | 4.47214 | + | 4.47214i | 0.614295 | + | 0.614295i | 0.944062 | − | 0.329767i | \(-0.106970\pi\) |
−0.329767 | + | 0.944062i | \(0.606970\pi\) | |||||||
\(54\) | 1.58114 | + | 4.94975i | 0.215166 | + | 0.673575i | ||||
\(55\) | −4.00000 | − | 12.0000i | −0.539360 | − | 1.61808i | ||||
\(56\) | − | 4.47214i | − | 0.597614i | ||||||
\(57\) | −3.90879 | − | 10.2333i | −0.517732 | − | 1.35544i | ||||
\(58\) | 3.16228 | + | 3.16228i | 0.415227 | + | 0.415227i | ||||
\(59\) | − | 2.82843i | − | 0.368230i | −0.982905 | − | 0.184115i | \(-0.941058\pi\) | ||
0.982905 | − | 0.184115i | \(-0.0589419\pi\) | |||||||
\(60\) | 2.45517 | + | 2.99535i | 0.316961 | + | 0.386698i | ||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 2.23607 | − | 2.23607i | 0.283981 | − | 0.283981i | ||||
\(63\) | 0.746512 | − | 13.3956i | 0.0940517 | − | 1.68769i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 3.42079 | + | 7.30056i | 0.424296 | + | 0.905523i | ||||
\(66\) | −4.00000 | + | 8.94427i | −0.492366 | + | 1.10096i | ||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | −2.23607 | − | 2.23607i | −0.271163 | − | 0.271163i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.16228 | − | 9.48683i | −0.377964 | − | 1.13389i | ||||
\(71\) | −1.41421 | −0.167836 | −0.0839181 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839181 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(72\) | 0.166925 | − | 2.99535i | 0.0196723 | − | 0.353006i | ||||
\(73\) | −3.16228 | − | 3.16228i | −0.370117 | − | 0.370117i | 0.497403 | − | 0.867520i | \(-0.334287\pi\) |
−0.867520 | + | 0.497403i | \(0.834287\pi\) | |||||||
\(74\) | −4.47214 | −0.519875 | ||||||||
\(75\) | 7.32624 | + | 4.61803i | 0.845961 | + | 0.533245i | ||||
\(76\) | 6.32456i | 0.725476i | ||||||||
\(77\) | 17.8885 | − | 17.8885i | 2.03859 | − | 2.03859i | ||||
\(78\) | 1.86997 | − | 5.95846i | 0.211732 | − | 0.674662i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | −0.707107 | − | 2.12132i | −0.0790569 | − | 0.237171i | ||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 4.00000 | + | 4.00000i | 0.441726 | + | 0.441726i | ||||
\(83\) | −2.82843 | + | 2.82843i | −0.310460 | + | 0.310460i | −0.845088 | − | 0.534628i | \(-0.820452\pi\) |
0.534628 | + | 0.845088i | \(0.320452\pi\) | |||||||
\(84\) | −3.16228 | + | 7.07107i | −0.345033 | + | 0.771517i | ||||
\(85\) | −6.32456 | − | 3.16228i | −0.685994 | − | 0.342997i | ||||
\(86\) | −7.07107 | −0.762493 | ||||||||
\(87\) | −2.76393 | − | 7.23607i | −0.296325 | − | 0.775788i | ||||
\(88\) | 4.00000 | − | 4.00000i | 0.426401 | − | 0.426401i | ||||
\(89\) | 2.82843i | 0.299813i | 0.988700 | + | 0.149906i | \(0.0478972\pi\) | ||||
−0.988700 | + | 0.149906i | \(0.952103\pi\) | |||||||
\(90\) | −1.76393 | − | 6.47214i | −0.185935 | − | 0.682223i | ||||
\(91\) | −10.0000 | + | 12.6491i | −1.04828 | + | 1.32599i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.11667 | + | 1.95440i | −0.530574 | + | 0.202661i | ||||
\(94\) | 2.00000i | 0.206284i | ||||||||
\(95\) | 4.47214 | + | 13.4164i | 0.458831 | + | 1.37649i | ||||
\(96\) | −0.707107 | + | 1.58114i | −0.0721688 | + | 0.161374i | ||||
\(97\) | −9.48683 | + | 9.48683i | −0.963242 | + | 0.963242i | −0.999348 | − | 0.0361060i | \(-0.988505\pi\) |
0.0361060 | + | 0.999348i | \(0.488505\pi\) | |||||||
\(98\) | 9.19239 | − | 9.19239i | 0.928571 | − | 0.928571i | ||||
\(99\) | 12.6491 | − | 11.3137i | 1.27128 | − | 1.13707i | ||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | − | 4.47214i | − | 0.444994i | −0.974933 | − | 0.222497i | \(-0.928579\pi\) | ||
0.974933 | − | 0.222497i | \(-0.0714208\pi\) | |||||||
\(102\) | 1.95440 | + | 5.11667i | 0.193514 | + | 0.506626i | ||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | −2.23607 | + | 2.82843i | −0.219265 | + | 0.277350i | ||||
\(105\) | −1.70820 | + | 17.2361i | −0.166704 | + | 1.68207i | ||||
\(106\) | 6.32456i | 0.614295i | ||||||||
\(107\) | 2.23607 | − | 2.23607i | 0.216169 | − | 0.216169i | −0.590713 | − | 0.806882i | \(-0.701153\pi\) |
0.806882 | + | 0.590713i | \(0.201153\pi\) | |||||||
\(108\) | −2.38197 | + | 4.61803i | −0.229205 | + | 0.444371i | ||||
\(109\) | −3.16228 | −0.302891 | −0.151446 | − | 0.988466i | \(-0.548393\pi\) | ||||
−0.151446 | + | 0.988466i | \(0.548393\pi\) | |||||||
\(110\) | 5.65685 | − | 11.3137i | 0.539360 | − | 1.07872i | ||||
\(111\) | 7.07107 | + | 3.16228i | 0.671156 | + | 0.300150i | ||||
\(112\) | 3.16228 | − | 3.16228i | 0.298807 | − | 0.298807i | ||||
\(113\) | 6.70820 | + | 6.70820i | 0.631055 | + | 0.631055i | 0.948333 | − | 0.317278i | \(-0.102769\pi\) |
−0.317278 | + | 0.948333i | \(0.602769\pi\) | |||||||
\(114\) | 4.47214 | − | 10.0000i | 0.418854 | − | 0.936586i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.47214i | 0.415227i | ||||||||
\(117\) | −7.16995 | + | 8.09888i | −0.662862 | + | 0.748742i | ||||
\(118\) | 2.00000 | − | 2.00000i | 0.184115 | − | 0.184115i | ||||
\(119\) | − | 14.1421i | − | 1.29641i | ||||||
\(120\) | −0.381966 | + | 3.85410i | −0.0348686 | + | 0.351830i | ||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | 7.07107 | + | 7.07107i | 0.640184 | + | 0.640184i | ||||
\(123\) | −3.49613 | − | 9.15298i | −0.315235 | − | 0.825297i | ||||
\(124\) | 3.16228 | 0.283981 | ||||||||
\(125\) | −9.19239 | − | 6.36396i | −0.822192 | − | 0.569210i | ||||
\(126\) | 10.0000 | − | 8.94427i | 0.890871 | − | 0.796819i | ||||
\(127\) | −2.00000 | − | 2.00000i | −0.177471 | − | 0.177471i | 0.612781 | − | 0.790253i | \(-0.290051\pi\) |
−0.790253 | + | 0.612781i | \(0.790051\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 11.1803 | + | 5.00000i | 0.984374 | + | 0.440225i | ||||
\(130\) | −2.74342 | + | 7.58114i | −0.240614 | + | 0.664910i | ||||
\(131\) | 17.8885i | 1.56293i | 0.623949 | + | 0.781465i | \(0.285527\pi\) | ||||
−0.623949 | + | 0.781465i | \(0.714473\pi\) | |||||||
\(132\) | −9.15298 | + | 3.49613i | −0.796665 | + | 0.304299i | ||||
\(133\) | −20.0000 | + | 20.0000i | −1.73422 | + | 1.73422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.78747 | + | 11.4806i | −0.153841 | + | 0.988096i | ||||
\(136\) | − | 3.16228i | − | 0.271163i | ||||||
\(137\) | 12.7279 | + | 12.7279i | 1.08742 | + | 1.08742i | 0.995793 | + | 0.0916263i | \(0.0292065\pi\) |
0.0916263 | + | 0.995793i | \(0.470793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 4.47214 | − | 8.94427i | 0.377964 | − | 0.755929i | ||||
\(141\) | 1.41421 | − | 3.16228i | 0.119098 | − | 0.266312i | ||||
\(142\) | −1.00000 | − | 1.00000i | −0.0839181 | − | 0.0839181i | ||||
\(143\) | −20.2580 | + | 2.36944i | −1.69406 | + | 0.198142i | ||||
\(144\) | 2.23607 | − | 2.00000i | 0.186339 | − | 0.166667i | ||||
\(145\) | 3.16228 | + | 9.48683i | 0.262613 | + | 0.787839i | ||||
\(146\) | − | 4.47214i | − | 0.370117i | ||||||
\(147\) | −21.0344 | + | 8.03444i | −1.73489 | + | 0.662670i | ||||
\(148\) | −3.16228 | − | 3.16228i | −0.259938 | − | 0.259938i | ||||
\(149\) | 4.24264i | 0.347571i | 0.984784 | + | 0.173785i | \(0.0555999\pi\) | ||||
−0.984784 | + | 0.173785i | \(0.944400\pi\) | |||||||
\(150\) | 1.91499 | + | 8.44588i | 0.156358 | + | 0.689603i | ||||
\(151\) | − | 22.1359i | − | 1.80140i | −0.434444 | − | 0.900699i | \(-0.643055\pi\) | ||
0.434444 | − | 0.900699i | \(-0.356945\pi\) | |||||||
\(152\) | −4.47214 | + | 4.47214i | −0.362738 | + | 0.362738i | ||||
\(153\) | 0.527864 | − | 9.47214i | 0.0426753 | − | 0.765777i | ||||
\(154\) | 25.2982 | 2.03859 | ||||||||
\(155\) | 6.70820 | − | 2.23607i | 0.538816 | − | 0.179605i | ||||
\(156\) | 5.53553 | − | 2.89100i | 0.443197 | − | 0.231465i | ||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.47214 | − | 10.0000i | 0.354663 | − | 0.793052i | ||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.03166 | − | 5.61745i | 0.552460 | − | 0.441348i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 5.65685i | 0.441726i | ||||||||
\(165\) | −16.9443 | + | 13.8885i | −1.31911 | + | 1.08122i | ||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 12.7279 | + | 12.7279i | 0.984916 | + | 0.984916i | 0.999888 | − | 0.0149717i | \(-0.00476583\pi\) |
−0.0149717 | + | 0.999888i | \(0.504766\pi\) | |||||||
\(168\) | −7.23607 | + | 2.76393i | −0.558275 | + | 0.213242i | ||||
\(169\) | 12.6491 | − | 3.00000i | 0.973009 | − | 0.230769i | ||||
\(170\) | −2.23607 | − | 6.70820i | −0.171499 | − | 0.514496i | ||||
\(171\) | −14.1421 | + | 12.6491i | −1.08148 | + | 0.967302i | ||||
\(172\) | −5.00000 | − | 5.00000i | −0.381246 | − | 0.381246i | ||||
\(173\) | −13.4164 | − | 13.4164i | −1.02003 | − | 1.02003i | −0.999795 | − | 0.0202354i | \(-0.993558\pi\) |
−0.0202354 | − | 0.999795i | \(-0.506442\pi\) | |||||||
\(174\) | 3.16228 | − | 7.07107i | 0.239732 | − | 0.536056i | ||||
\(175\) | 3.16228 | − | 22.1359i | 0.239046 | − | 1.67332i | ||||
\(176\) | 5.65685 | 0.426401 | ||||||||
\(177\) | −4.57649 | + | 1.74806i | −0.343990 | + | 0.131393i | ||||
\(178\) | −2.00000 | + | 2.00000i | −0.149906 | + | 0.149906i | ||||
\(179\) | 17.8885 | 1.33705 | 0.668526 | − | 0.743689i | \(-0.266925\pi\) | ||||
0.668526 | + | 0.743689i | \(0.266925\pi\) | |||||||
\(180\) | 3.32920 | − | 5.82378i | 0.248144 | − | 0.434079i | ||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | −16.0153 | + | 1.87320i | −1.18714 | + | 0.138851i | ||||
\(183\) | −6.18034 | − | 16.1803i | −0.456864 | − | 1.19609i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.94427 | − | 4.47214i | −0.657596 | − | 0.328798i | ||||
\(186\) | −5.00000 | − | 2.23607i | −0.366618 | − | 0.163956i | ||||
\(187\) | 12.6491 | − | 12.6491i | 0.924995 | − | 0.924995i | ||||
\(188\) | −1.41421 | + | 1.41421i | −0.103142 | + | 0.103142i | ||||
\(189\) | −22.1359 | + | 7.07107i | −1.61015 | + | 0.514344i | ||||
\(190\) | −6.32456 | + | 12.6491i | −0.458831 | + | 0.917663i | ||||
\(191\) | − | 8.94427i | − | 0.647185i | −0.946197 | − | 0.323592i | \(-0.895109\pi\) | ||
0.946197 | − | 0.323592i | \(-0.104891\pi\) | |||||||
\(192\) | −1.61803 | + | 0.618034i | −0.116772 | + | 0.0446028i | ||||
\(193\) | −9.48683 | − | 9.48683i | −0.682877 | − | 0.682877i | 0.277770 | − | 0.960648i | \(-0.410405\pi\) |
−0.960648 | + | 0.277770i | \(0.910405\pi\) | |||||||
\(194\) | −13.4164 | −0.963242 | ||||||||
\(195\) | 9.69840 | − | 10.0469i | 0.694517 | − | 0.719477i | ||||
\(196\) | 13.0000 | 0.928571 | ||||||||
\(197\) | 1.41421 | + | 1.41421i | 0.100759 | + | 0.100759i | 0.755689 | − | 0.654931i | \(-0.227302\pi\) |
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(198\) | 16.9443 | + | 0.944272i | 1.20418 | + | 0.0671065i | ||||
\(199\) | 20.0000i | 1.41776i | 0.705328 | + | 0.708881i | \(0.250800\pi\) | ||||
−0.705328 | + | 0.708881i | \(0.749200\pi\) | |||||||
\(200\) | 0.707107 | − | 4.94975i | 0.0500000 | − | 0.350000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.16228 | − | 3.16228i | 0.222497 | − | 0.222497i | ||||
\(203\) | −14.1421 | + | 14.1421i | −0.992583 | + | 0.992583i | ||||
\(204\) | −2.23607 | + | 5.00000i | −0.156556 | + | 0.350070i | ||||
\(205\) | 4.00000 | + | 12.0000i | 0.279372 | + | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.58114 | + | 0.418861i | −0.248307 | + | 0.0290428i | ||||
\(209\) | −35.7771 | −2.47475 | ||||||||
\(210\) | −13.3956 | + | 10.9799i | −0.924386 | + | 0.757682i | ||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | −4.47214 | + | 4.47214i | −0.307148 | + | 0.307148i | ||||
\(213\) | 0.874032 | + | 2.28825i | 0.0598877 | + | 0.156788i | ||||
\(214\) | 3.16228 | 0.216169 | ||||||||
\(215\) | −14.1421 | − | 7.07107i | −0.964486 | − | 0.482243i | ||||
\(216\) | −4.94975 | + | 1.58114i | −0.336788 | + | 0.107583i | ||||
\(217\) | 10.0000 | + | 10.0000i | 0.678844 | + | 0.678844i | ||||
\(218\) | −2.23607 | − | 2.23607i | −0.151446 | − | 0.151446i | ||||
\(219\) | −3.16228 | + | 7.07107i | −0.213687 | + | 0.477818i | ||||
\(220\) | 12.0000 | − | 4.00000i | 0.809040 | − | 0.269680i | ||||
\(221\) | −7.07107 | + | 8.94427i | −0.475651 | + | 0.601657i | ||||
\(222\) | 2.76393 | + | 7.23607i | 0.185503 | + | 0.485653i | ||||
\(223\) | 18.9737 | + | 18.9737i | 1.27057 | + | 1.27057i | 0.945789 | + | 0.324782i | \(0.105291\pi\) |
0.324782 | + | 0.945789i | \(0.394709\pi\) | |||||||
\(224\) | 4.47214 | 0.298807 | ||||||||
\(225\) | 2.94427 | − | 14.7082i | 0.196285 | − | 0.980547i | ||||
\(226\) | 9.48683i | 0.631055i | ||||||||
\(227\) | −8.48528 | − | 8.48528i | −0.563188 | − | 0.563188i | 0.367024 | − | 0.930212i | \(-0.380377\pi\) |
−0.930212 | + | 0.367024i | \(0.880377\pi\) | |||||||
\(228\) | 10.2333 | − | 3.90879i | 0.677720 | − | 0.258866i | ||||
\(229\) | −9.48683 | −0.626908 | −0.313454 | − | 0.949603i | \(-0.601486\pi\) | ||||
−0.313454 | + | 0.949603i | \(0.601486\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −40.0000 | − | 17.8885i | −2.63181 | − | 1.17698i | ||||
\(232\) | −3.16228 | + | 3.16228i | −0.207614 | + | 0.207614i | ||||
\(233\) | −2.23607 | − | 2.23607i | −0.146490 | − | 0.146490i | 0.630058 | − | 0.776548i | \(-0.283031\pi\) |
−0.776548 | + | 0.630058i | \(0.783031\pi\) | |||||||
\(234\) | −10.7967 | + | 0.656854i | −0.705802 | + | 0.0429399i | ||||
\(235\) | −2.00000 | + | 4.00000i | −0.130466 | + | 0.260931i | ||||
\(236\) | 2.82843 | 0.184115 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.0000 | − | 10.0000i | 0.648204 | − | 0.648204i | ||||
\(239\) | 4.24264i | 0.274434i | 0.990541 | + | 0.137217i | \(0.0438157\pi\) | ||||
−0.990541 | + | 0.137217i | \(0.956184\pi\) | |||||||
\(240\) | −2.99535 | + | 2.45517i | −0.193349 | + | 0.158481i | ||||
\(241\) | 12.6491i | 0.814801i | 0.913250 | + | 0.407400i | \(0.133565\pi\) | ||||
−0.913250 | + | 0.407400i | \(0.866435\pi\) | |||||||
\(242\) | 14.8492 | + | 14.8492i | 0.954545 | + | 0.954545i | ||||
\(243\) | −15.0902 | + | 3.90983i | −0.968035 | + | 0.250816i | ||||
\(244\) | 10.0000i | 0.640184i | ||||||||
\(245\) | 27.5772 | − | 9.19239i | 1.76184 | − | 0.587280i | ||||
\(246\) | 4.00000 | − | 8.94427i | 0.255031 | − | 0.570266i | ||||
\(247\) | 22.6491 | − | 2.64911i | 1.44113 | − | 0.168559i | ||||
\(248\) | 2.23607 | + | 2.23607i | 0.141990 | + | 0.141990i | ||||
\(249\) | 6.32456 | + | 2.82843i | 0.400802 | + | 0.179244i | ||||
\(250\) | −2.00000 | − | 11.0000i | −0.126491 | − | 0.695701i | ||||
\(251\) | 17.8885i | 1.12911i | 0.825394 | + | 0.564557i | \(0.190953\pi\) | ||||
−0.825394 | + | 0.564557i | \(0.809047\pi\) | |||||||
\(252\) | 13.3956 | + | 0.746512i | 0.843845 | + | 0.0470259i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 2.82843i | − | 0.177471i | ||||||
\(255\) | −1.20788 | + | 12.1877i | −0.0756405 | + | 0.763226i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.1246 | − | 20.1246i | 1.25534 | − | 1.25534i | 0.302045 | − | 0.953294i | \(-0.402331\pi\) |
0.953294 | − | 0.302045i | \(-0.0976694\pi\) | |||||||
\(258\) | 4.37016 | + | 11.4412i | 0.272074 | + | 0.712300i | ||||
\(259\) | − | 20.0000i | − | 1.24274i | ||||||
\(260\) | −7.30056 | + | 3.42079i | −0.452762 | + | 0.212148i | ||||
\(261\) | −10.0000 | + | 8.94427i | −0.618984 | + | 0.553637i | ||||
\(262\) | −12.6491 | + | 12.6491i | −0.781465 | + | 0.781465i | ||||
\(263\) | 8.94427 | + | 8.94427i | 0.551527 | + | 0.551527i | 0.926882 | − | 0.375354i | \(-0.122479\pi\) |
−0.375354 | + | 0.926882i | \(0.622479\pi\) | |||||||
\(264\) | −8.94427 | − | 4.00000i | −0.550482 | − | 0.246183i | ||||
\(265\) | −6.32456 | + | 12.6491i | −0.388514 | + | 0.777029i | ||||
\(266\) | −28.2843 | −1.73422 | ||||||||
\(267\) | 4.57649 | − | 1.74806i | 0.280077 | − | 0.106980i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.3607 | 1.36335 | 0.681677 | − | 0.731653i | \(-0.261251\pi\) | ||||
0.681677 | + | 0.731653i | \(0.261251\pi\) | |||||||
\(270\) | −9.38197 | + | 6.85410i | −0.570968 | + | 0.417127i | ||||
\(271\) | − | 9.48683i | − | 0.576284i | −0.957588 | − | 0.288142i | \(-0.906962\pi\) | ||
0.957588 | − | 0.288142i | \(-0.0930375\pi\) | |||||||
\(272\) | 2.23607 | − | 2.23607i | 0.135582 | − | 0.135582i | ||||
\(273\) | 26.6470 | + | 8.36276i | 1.61275 | + | 0.506137i | ||||
\(274\) | 18.0000i | 1.08742i | ||||||||
\(275\) | 22.6274 | − | 16.9706i | 1.36448 | − | 1.02336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0000 | + | 10.0000i | 0.600842 | + | 0.600842i | 0.940536 | − | 0.339694i | \(-0.110324\pi\) |
−0.339694 | + | 0.940536i | \(0.610324\pi\) | |||||||
\(278\) | 2.82843 | − | 2.82843i | 0.169638 | − | 0.169638i | ||||
\(279\) | 6.32456 | + | 7.07107i | 0.378641 | + | 0.423334i | ||||
\(280\) | 9.48683 | − | 3.16228i | 0.566947 | − | 0.188982i | ||||
\(281\) | 8.48528 | 0.506189 | 0.253095 | − | 0.967442i | \(-0.418552\pi\) | ||||
0.253095 | + | 0.967442i | \(0.418552\pi\) | |||||||
\(282\) | 3.23607 | − | 1.23607i | 0.192705 | − | 0.0736068i | ||||
\(283\) | 9.00000 | − | 9.00000i | 0.534994 | − | 0.534994i | −0.387060 | − | 0.922055i | \(-0.626509\pi\) |
0.922055 | + | 0.387060i | \(0.126509\pi\) | |||||||
\(284\) | − | 1.41421i | − | 0.0839181i | ||||||
\(285\) | 18.9443 | − | 15.5279i | 1.12216 | − | 0.919791i | ||||
\(286\) | −16.0000 | − | 12.6491i | −0.946100 | − | 0.747958i | ||||
\(287\) | −17.8885 | + | 17.8885i | −1.05593 | + | 1.05593i | ||||
\(288\) | 2.99535 | + | 0.166925i | 0.176503 | + | 0.00983617i | ||||
\(289\) | 7.00000i | 0.411765i | ||||||||
\(290\) | −4.47214 | + | 8.94427i | −0.262613 | + | 0.525226i | ||||
\(291\) | 21.2132 | + | 9.48683i | 1.24354 | + | 0.556128i | ||||
\(292\) | 3.16228 | − | 3.16228i | 0.185058 | − | 0.185058i | ||||
\(293\) | −11.3137 | + | 11.3137i | −0.660954 | + | 0.660954i | −0.955605 | − | 0.294651i | \(-0.904797\pi\) |
0.294651 | + | 0.955605i | \(0.404797\pi\) | |||||||
\(294\) | −20.5548 | − | 9.19239i | −1.19878 | − | 0.536111i | ||||
\(295\) | 6.00000 | − | 2.00000i | 0.349334 | − | 0.116445i | ||||
\(296\) | − | 4.47214i | − | 0.259938i | ||||||
\(297\) | −26.1235 | − | 13.4744i | −1.51584 | − | 0.781866i | ||||
\(298\) | −3.00000 | + | 3.00000i | −0.173785 | + | 0.173785i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.61803 | + | 7.32624i | −0.266622 | + | 0.422981i | ||||
\(301\) | − | 31.6228i | − | 1.82271i | ||||||
\(302\) | 15.6525 | − | 15.6525i | 0.900699 | − | 0.900699i | ||||
\(303\) | −7.23607 | + | 2.76393i | −0.415701 | + | 0.158784i | ||||
\(304\) | −6.32456 | −0.362738 | ||||||||
\(305\) | 7.07107 | + | 21.2132i | 0.404888 | + | 1.21466i | ||||
\(306\) | 7.07107 | − | 6.32456i | 0.404226 | − | 0.361551i | ||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 17.8885 | + | 17.8885i | 1.01929 | + | 1.01929i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.32456 | + | 3.16228i | 0.359211 | + | 0.179605i | ||||
\(311\) | − | 8.94427i | − | 0.507183i | −0.967311 | − | 0.253592i | \(-0.918388\pi\) | ||
0.967311 | − | 0.253592i | \(-0.0816119\pi\) | |||||||
\(312\) | 5.95846 | + | 1.86997i | 0.337331 | + | 0.105866i | ||||
\(313\) | −1.00000 | + | 1.00000i | −0.0565233 | + | 0.0565233i | −0.734803 | − | 0.678280i | \(-0.762726\pi\) |
0.678280 | + | 0.734803i | \(0.262726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 28.9443 | − | 7.88854i | 1.63082 | − | 0.444469i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.7990 | − | 19.7990i | −1.11202 | − | 1.11202i | −0.992877 | − | 0.119145i | \(-0.961985\pi\) |
−0.119145 | − | 0.992877i | \(-0.538015\pi\) | |||||||
\(318\) | 10.2333 | − | 3.90879i | 0.573858 | − | 0.219194i | ||||
\(319\) | −25.2982 | −1.41643 | ||||||||
\(320\) | 2.12132 | − | 0.707107i | 0.118585 | − | 0.0395285i | ||||
\(321\) | −5.00000 | − | 2.23607i | −0.279073 | − | 0.124805i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.1421 | + | 14.1421i | −0.786889 | + | 0.786889i | ||||
\(324\) | 8.94427 | + | 1.00000i | 0.496904 | + | 0.0555556i | ||||
\(325\) | −13.0680 | + | 12.4189i | −0.724881 | + | 0.688874i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.95440 | + | 5.11667i | 0.108078 | + | 0.282953i | ||||
\(328\) | −4.00000 | + | 4.00000i | −0.220863 | + | 0.220863i | ||||
\(329\) | −8.94427 | −0.493114 | ||||||||
\(330\) | −21.8021 | − | 2.16073i | −1.20017 | − | 0.118944i | ||||
\(331\) | 12.6491i | 0.695258i | 0.937632 | + | 0.347629i | \(0.113013\pi\) | ||||
−0.937632 | + | 0.347629i | \(0.886987\pi\) | |||||||
\(332\) | −2.82843 | − | 2.82843i | −0.155230 | − | 0.155230i | ||||
\(333\) | 0.746512 | − | 13.3956i | 0.0409086 | − | 0.734076i | ||||
\(334\) | 18.0000i | 0.984916i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.07107 | − | 3.16228i | −0.385758 | − | 0.172516i | ||||
\(337\) | −13.0000 | − | 13.0000i | −0.708155 | − | 0.708155i | 0.257992 | − | 0.966147i | \(-0.416939\pi\) |
−0.966147 | + | 0.257992i | \(0.916939\pi\) | |||||||
\(338\) | 11.0656 | + | 6.82295i | 0.601889 | + | 0.371120i | ||||
\(339\) | 6.70820 | − | 15.0000i | 0.364340 | − | 0.814688i | ||||
\(340\) | 3.16228 | − | 6.32456i | 0.171499 | − | 0.342997i | ||||
\(341\) | 17.8885i | 0.968719i | ||||||||
\(342\) | −18.9443 | − | 1.05573i | −1.02439 | − | 0.0570872i | ||||
\(343\) | 18.9737 | + | 18.9737i | 1.02448 | + | 1.02448i | ||||
\(344\) | − | 7.07107i | − | 0.381246i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 18.9737i | − | 1.02003i | ||||||
\(347\) | −20.1246 | + | 20.1246i | −1.08035 | + | 1.08035i | −0.0838690 | + | 0.996477i | \(0.526728\pi\) |
−0.996477 | + | 0.0838690i | \(0.973272\pi\) | |||||||
\(348\) | 7.23607 | − | 2.76393i | 0.387894 | − | 0.148162i | ||||
\(349\) | −3.16228 | −0.169273 | −0.0846364 | − | 0.996412i | \(-0.526973\pi\) | ||||
−0.0846364 | + | 0.996412i | \(0.526973\pi\) | |||||||
\(350\) | 17.8885 | − | 13.4164i | 0.956183 | − | 0.717137i | ||||
\(351\) | 17.5355 | + | 6.59584i | 0.935978 | + | 0.352060i | ||||
\(352\) | 4.00000 | + | 4.00000i | 0.213201 | + | 0.213201i | ||||
\(353\) | 9.89949 | − | 9.89949i | 0.526897 | − | 0.526897i | −0.392749 | − | 0.919646i | \(-0.628476\pi\) |
0.919646 | + | 0.392749i | \(0.128476\pi\) | |||||||
\(354\) | −4.47214 | − | 2.00000i | −0.237691 | − | 0.106299i | ||||
\(355\) | −1.00000 | − | 3.00000i | −0.0530745 | − | 0.159223i | ||||
\(356\) | −2.82843 | −0.149906 | ||||||||
\(357\) | −22.8825 | + | 8.74032i | −1.21107 | + | 0.462587i | ||||
\(358\) | 12.6491 | + | 12.6491i | 0.668526 | + | 0.668526i | ||||
\(359\) | − | 32.5269i | − | 1.71670i | −0.513061 | − | 0.858352i | \(-0.671488\pi\) | ||
0.513061 | − | 0.858352i | \(-0.328512\pi\) | |||||||
\(360\) | 6.47214 | − | 1.76393i | 0.341112 | − | 0.0929674i | ||||
\(361\) | 21.0000 | 1.10526 | ||||||||
\(362\) | −15.5563 | − | 15.5563i | −0.817624 | − | 0.817624i | ||||
\(363\) | −12.9787 | − | 33.9787i | −0.681206 | − | 1.78342i | ||||
\(364\) | −12.6491 | − | 10.0000i | −0.662994 | − | 0.524142i | ||||
\(365\) | 4.47214 | − | 8.94427i | 0.234082 | − | 0.468165i | ||||
\(366\) | 7.07107 | − | 15.8114i | 0.369611 | − | 0.826475i | ||||
\(367\) | −20.0000 | − | 20.0000i | −1.04399 | − | 1.04399i | −0.998987 | − | 0.0450047i | \(-0.985670\pi\) |
−0.0450047 | − | 0.998987i | \(-0.514330\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6491 | + | 11.3137i | −0.658486 | + | 0.588968i | ||||
\(370\) | −3.16228 | − | 9.48683i | −0.164399 | − | 0.493197i | ||||
\(371\) | −28.2843 | −1.46845 | ||||||||
\(372\) | −1.95440 | − | 5.11667i | −0.101331 | − | 0.265287i | ||||
\(373\) | 16.0000 | − | 16.0000i | 0.828449 | − | 0.828449i | −0.158854 | − | 0.987302i | \(-0.550780\pi\) |
0.987302 | + | 0.158854i | \(0.0507798\pi\) | |||||||
\(374\) | 17.8885 | 0.924995 | ||||||||
\(375\) | −4.61590 | + | 18.8067i | −0.238364 | + | 0.971176i | ||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | 16.0153 | − | 1.87320i | 0.824832 | − | 0.0964749i | ||||
\(378\) | −20.6525 | − | 10.6525i | −1.06225 | − | 0.547904i | ||||
\(379\) | −6.32456 | −0.324871 | −0.162435 | − | 0.986719i | \(-0.551935\pi\) | ||||
−0.162435 | + | 0.986719i | \(0.551935\pi\) | |||||||
\(380\) | −13.4164 | + | 4.47214i | −0.688247 | + | 0.229416i | ||||
\(381\) | −2.00000 | + | 4.47214i | −0.102463 | + | 0.229114i | ||||
\(382\) | 6.32456 | − | 6.32456i | 0.323592 | − | 0.323592i | ||||
\(383\) | 11.3137 | − | 11.3137i | 0.578103 | − | 0.578103i | −0.356277 | − | 0.934380i | \(-0.615954\pi\) |
0.934380 | + | 0.356277i | \(0.115954\pi\) | |||||||
\(384\) | −1.58114 | − | 0.707107i | −0.0806872 | − | 0.0360844i | ||||
\(385\) | 50.5964 | + | 25.2982i | 2.57863 | + | 1.28932i | ||||
\(386\) | − | 13.4164i | − | 0.682877i | ||||||
\(387\) | 1.18034 | − | 21.1803i | 0.0600000 | − | 1.07666i | ||||
\(388\) | −9.48683 | − | 9.48683i | −0.481621 | − | 0.481621i | ||||
\(389\) | −13.4164 | −0.680239 | −0.340119 | − | 0.940382i | \(-0.610468\pi\) | ||||
−0.340119 | + | 0.940382i | \(0.610468\pi\) | |||||||
\(390\) | 13.9621 | − | 0.246460i | 0.706997 | − | 0.0124800i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 9.19239 | + | 9.19239i | 0.464286 | + | 0.464286i | ||||
\(393\) | 28.9443 | − | 11.0557i | 1.46005 | − | 0.557688i | ||||
\(394\) | 2.00000i | 0.100759i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.3137 | + | 12.6491i | 0.568535 | + | 0.635642i | ||||
\(397\) | 25.2982 | − | 25.2982i | 1.26968 | − | 1.26968i | 0.323429 | − | 0.946252i | \(-0.395164\pi\) |
0.946252 | − | 0.323429i | \(-0.104836\pi\) | |||||||
\(398\) | −14.1421 | + | 14.1421i | −0.708881 | + | 0.708881i | ||||
\(399\) | 44.7214 | + | 20.0000i | 2.23887 | + | 1.00125i | ||||
\(400\) | 4.00000 | − | 3.00000i | 0.200000 | − | 0.150000i | ||||
\(401\) | −8.48528 | −0.423735 | −0.211867 | − | 0.977298i | \(-0.567954\pi\) | ||||
−0.211867 | + | 0.977298i | \(0.567954\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.32456 | − | 11.3246i | −0.0659808 | − | 0.564116i | ||||
\(404\) | 4.47214 | 0.222497 | ||||||||
\(405\) | 19.6808 | − | 4.20323i | 0.977945 | − | 0.208860i | ||||
\(406\) | −20.0000 | −0.992583 | ||||||||
\(407\) | 17.8885 | − | 17.8885i | 0.886702 | − | 0.886702i | ||||
\(408\) | −5.11667 | + | 1.95440i | −0.253313 | + | 0.0967570i | ||||
\(409\) | −18.9737 | −0.938187 | −0.469094 | − | 0.883148i | \(-0.655419\pi\) | ||||
−0.469094 | + | 0.883148i | \(0.655419\pi\) | |||||||
\(410\) | −5.65685 | + | 11.3137i | −0.279372 | + | 0.558744i | ||||
\(411\) | 12.7279 | − | 28.4605i | 0.627822 | − | 1.40385i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.94427 | + | 8.94427i | 0.440119 | + | 0.440119i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | − | 4.00000i | −0.392705 | − | 0.196352i | ||||
\(416\) | −2.82843 | − | 2.23607i | −0.138675 | − | 0.109632i | ||||
\(417\) | −6.47214 | + | 2.47214i | −0.316942 | + | 0.121061i | ||||
\(418\) | −25.2982 | − | 25.2982i | −1.23738 | − | 1.23738i | ||||
\(419\) | 13.4164 | 0.655434 | 0.327717 | − | 0.944776i | \(-0.393721\pi\) | ||||
0.327717 | + | 0.944776i | \(0.393721\pi\) | |||||||
\(420\) | −17.2361 | − | 1.70820i | −0.841034 | − | 0.0833518i | ||||
\(421\) | − | 3.16228i | − | 0.154120i | −0.997026 | − | 0.0770600i | \(-0.975447\pi\) | ||
0.997026 | − | 0.0770600i | \(-0.0245533\pi\) | |||||||
\(422\) | 14.1421 | + | 14.1421i | 0.688428 | + | 0.688428i | ||||
\(423\) | −5.99070 | − | 0.333851i | −0.291278 | − | 0.0162324i | ||||
\(424\) | −6.32456 | −0.307148 | ||||||||
\(425\) | 2.23607 | − | 15.6525i | 0.108465 | − | 0.759257i | ||||
\(426\) | −1.00000 | + | 2.23607i | −0.0484502 | + | 0.108338i | ||||
\(427\) | −31.6228 | + | 31.6228i | −1.53033 | + | 1.53033i | ||||
\(428\) | 2.23607 | + | 2.23607i | 0.108084 | + | 0.108084i | ||||
\(429\) | 16.3539 | + | 31.3137i | 0.789576 | + | 1.51184i | ||||
\(430\) | −5.00000 | − | 15.0000i | −0.241121 | − | 0.723364i | ||||
\(431\) | 1.41421 | 0.0681203 | 0.0340601 | − | 0.999420i | \(-0.489156\pi\) | ||||
0.0340601 | + | 0.999420i | \(0.489156\pi\) | |||||||
\(432\) | −4.61803 | − | 2.38197i | −0.222185 | − | 0.114602i | ||||
\(433\) | 21.0000 | − | 21.0000i | 1.00920 | − | 1.00920i | 0.00923827 | − | 0.999957i | \(-0.497059\pi\) |
0.999957 | − | 0.00923827i | \(-0.00294067\pi\) | |||||||
\(434\) | 14.1421i | 0.678844i | ||||||||
\(435\) | 13.3956 | − | 10.9799i | 0.642271 | − | 0.526444i | ||||
\(436\) | − | 3.16228i | − | 0.151446i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −7.23607 | + | 2.76393i | −0.345753 | + | 0.132066i | ||||
\(439\) | 16.0000i | 0.763638i | 0.924237 | + | 0.381819i | \(0.124702\pi\) | ||||
−0.924237 | + | 0.381819i | \(0.875298\pi\) | |||||||
\(440\) | 11.3137 | + | 5.65685i | 0.539360 | + | 0.269680i | ||||
\(441\) | 26.0000 | + | 29.0689i | 1.23810 | + | 1.38423i | ||||
\(442\) | −11.3246 | + | 1.32456i | −0.538654 | + | 0.0630027i | ||||
\(443\) | 11.1803 | + | 11.1803i | 0.531194 | + | 0.531194i | 0.920928 | − | 0.389734i | \(-0.127433\pi\) |
−0.389734 | + | 0.920928i | \(0.627433\pi\) | |||||||
\(444\) | −3.16228 | + | 7.07107i | −0.150075 | + | 0.335578i | ||||
\(445\) | −6.00000 | + | 2.00000i | −0.284427 | + | 0.0948091i | ||||
\(446\) | 26.8328i | 1.27057i | ||||||||
\(447\) | 6.86474 | − | 2.62210i | 0.324691 | − | 0.124021i | ||||
\(448\) | 3.16228 | + | 3.16228i | 0.149404 | + | 0.149404i | ||||
\(449\) | − | 31.1127i | − | 1.46830i | −0.678988 | − | 0.734150i | \(-0.737581\pi\) | ||
0.678988 | − | 0.734150i | \(-0.262419\pi\) | |||||||
\(450\) | 12.4822 | − | 8.31836i | 0.588416 | − | 0.392131i | ||||
\(451\) | −32.0000 | −1.50682 | ||||||||
\(452\) | −6.70820 | + | 6.70820i | −0.315527 | + | 0.315527i | ||||
\(453\) | −35.8167 | + | 13.6808i | −1.68282 | + | 0.642778i | ||||
\(454\) | − | 12.0000i | − | 0.563188i | ||||||
\(455\) | −33.9039 | − | 12.2689i | −1.58944 | − | 0.575176i | ||||
\(456\) | 10.0000 | + | 4.47214i | 0.468293 | + | 0.209427i | ||||
\(457\) | 22.1359 | − | 22.1359i | 1.03548 | − | 1.03548i | 0.0361286 | − | 0.999347i | \(-0.488497\pi\) |
0.999347 | − | 0.0361286i | \(-0.0115026\pi\) | |||||||
\(458\) | −6.70820 | − | 6.70820i | −0.313454 | − | 0.313454i | ||||
\(459\) | −15.6525 | + | 5.00000i | −0.730595 | + | 0.233380i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41421 | 0.0658665 | 0.0329332 | − | 0.999458i | \(-0.489515\pi\) | ||||
0.0329332 | + | 0.999458i | \(0.489515\pi\) | |||||||
\(462\) | −15.6352 | − | 40.9334i | −0.727414 | − | 1.90439i | ||||
\(463\) | 18.9737 | + | 18.9737i | 0.881781 | + | 0.881781i | 0.993716 | − | 0.111935i | \(-0.0357047\pi\) |
−0.111935 | + | 0.993716i | \(0.535705\pi\) | |||||||
\(464\) | −4.47214 | −0.207614 | ||||||||
\(465\) | −7.76393 | − | 9.47214i | −0.360044 | − | 0.439260i | ||||
\(466\) | − | 3.16228i | − | 0.146490i | ||||||
\(467\) | −6.70820 | + | 6.70820i | −0.310419 | + | 0.310419i | −0.845072 | − | 0.534653i | \(-0.820442\pi\) |
0.534653 | + | 0.845072i | \(0.320442\pi\) | |||||||
\(468\) | −8.09888 | − | 7.16995i | −0.374371 | − | 0.331431i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.24264 | + | 1.41421i | −0.195698 | + | 0.0652328i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | + | 2.00000i | 0.0920575 | + | 0.0920575i | ||||
\(473\) | 28.2843 | − | 28.2843i | 1.30051 | − | 1.30051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.2982 | + | 18.9737i | −1.16076 | + | 0.870572i | ||||
\(476\) | 14.1421 | 0.648204 | ||||||||
\(477\) | −18.9443 | − | 1.05573i | −0.867399 | − | 0.0483385i | ||||
\(478\) | −3.00000 | + | 3.00000i | −0.137217 | + | 0.137217i | ||||
\(479\) | − | 18.3848i | − | 0.840022i | −0.907519 | − | 0.420011i | \(-0.862026\pi\) | ||
0.907519 | − | 0.420011i | \(-0.137974\pi\) | |||||||
\(480\) | −3.85410 | − | 0.381966i | −0.175915 | − | 0.0174343i | ||||
\(481\) | −10.0000 | + | 12.6491i | −0.455961 | + | 0.576750i | ||||
\(482\) | −8.94427 | + | 8.94427i | −0.407400 | + | 0.407400i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.0000i | 0.954545i | ||||||||
\(485\) | −26.8328 | − | 13.4164i | −1.21842 | − | 0.609208i | ||||
\(486\) | −13.4350 | − | 7.90569i | −0.609425 | − | 0.358610i | ||||
\(487\) | 3.16228 | − | 3.16228i | 0.143296 | − | 0.143296i | −0.631819 | − | 0.775116i | \(-0.717692\pi\) |
0.775116 | + | 0.631819i | \(0.217692\pi\) | |||||||
\(488\) | −7.07107 | + | 7.07107i | −0.320092 | + | 0.320092i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.0000 | + | 13.0000i | 1.17456 | + | 0.587280i | ||||
\(491\) | − | 22.3607i | − | 1.00912i | −0.863376 | − | 0.504562i | \(-0.831654\pi\) | ||
0.863376 | − | 0.504562i | \(-0.168346\pi\) | |||||||
\(492\) | 9.15298 | − | 3.49613i | 0.412648 | − | 0.157618i | ||||
\(493\) | −10.0000 | + | 10.0000i | −0.450377 | + | 0.450377i | ||||
\(494\) | 17.8885 | + | 14.1421i | 0.804844 | + | 0.636285i | ||||
\(495\) | 32.9443 | + | 18.8328i | 1.48073 | + | 0.846472i | ||||
\(496\) | 3.16228i | 0.141990i | ||||||||
\(497\) | 4.47214 | − | 4.47214i | 0.200603 | − | 0.200603i | ||||
\(498\) | 2.47214 | + | 6.47214i | 0.110779 | + | 0.290023i | ||||
\(499\) | −12.6491 | −0.566252 | −0.283126 | − | 0.959083i | \(-0.591371\pi\) | ||||
−0.283126 | + | 0.959083i | \(0.591371\pi\) | |||||||
\(500\) | 6.36396 | − | 9.19239i | 0.284605 | − | 0.411096i | ||||
\(501\) | 12.7279 | − | 28.4605i | 0.568642 | − | 1.27152i | ||||
\(502\) | −12.6491 | + | 12.6491i | −0.564557 | + | 0.564557i | ||||
\(503\) | 4.47214 | + | 4.47214i | 0.199403 | + | 0.199403i | 0.799744 | − | 0.600341i | \(-0.204969\pi\) |
−0.600341 | + | 0.799744i | \(0.704969\pi\) | |||||||
\(504\) | 8.94427 | + | 10.0000i | 0.398410 | + | 0.445435i | ||||
\(505\) | 9.48683 | − | 3.16228i | 0.422159 | − | 0.140720i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6717 | − | 18.6126i | −0.562769 | − | 0.826614i | ||||
\(508\) | 2.00000 | − | 2.00000i | 0.0887357 | − | 0.0887357i | ||||
\(509\) | 24.0416i | 1.06563i | 0.846233 | + | 0.532813i | \(0.178865\pi\) | ||||
−0.846233 | + | 0.532813i | \(0.821135\pi\) | |||||||
\(510\) | −9.47214 | + | 7.76393i | −0.419433 | + | 0.343793i | ||||
\(511\) | 20.0000 | 0.884748 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 29.2070 | + | 15.0649i | 1.28952 | + | 0.665131i | ||||
\(514\) | 28.4605 | 1.25534 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.00000 | + | 11.1803i | −0.220113 | + | 0.492187i | ||||
\(517\) | −8.00000 | − | 8.00000i | −0.351840 | − | 0.351840i | ||||
\(518\) | 14.1421 | − | 14.1421i | 0.621370 | − | 0.621370i | ||||
\(519\) | −13.4164 | + | 30.0000i | −0.588915 | + | 1.31685i | ||||
\(520\) | −7.58114 | − | 2.74342i | −0.332455 | − | 0.120307i | ||||
\(521\) | − | 26.8328i | − | 1.17557i | −0.809018 | − | 0.587784i | \(-0.800001\pi\) | ||
0.809018 | − | 0.587784i | \(-0.199999\pi\) | |||||||
\(522\) | −13.3956 | − | 0.746512i | −0.586310 | − | 0.0326740i | ||||
\(523\) | −15.0000 | + | 15.0000i | −0.655904 | + | 0.655904i | −0.954408 | − | 0.298504i | \(-0.903512\pi\) |
0.298504 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(524\) | −17.8885 | −0.781465 | ||||||||
\(525\) | −37.7711 | + | 8.56409i | −1.64847 | + | 0.373768i | ||||
\(526\) | 12.6491i | 0.551527i | ||||||||
\(527\) | 7.07107 | + | 7.07107i | 0.308021 | + | 0.308021i | ||||
\(528\) | −3.49613 | − | 9.15298i | −0.152149 | − | 0.398332i | ||||
\(529\) | − | 23.0000i | − | 1.00000i | ||||||
\(530\) | −13.4164 | + | 4.47214i | −0.582772 | + | 0.194257i | ||||
\(531\) | 5.65685 | + | 6.32456i | 0.245487 | + | 0.274462i | ||||
\(532\) | −20.0000 | − | 20.0000i | −0.867110 | − | 0.867110i | ||||
\(533\) | 20.2580 | − | 2.36944i | 0.877471 | − | 0.102632i | ||||
\(534\) | 4.47214 | + | 2.00000i | 0.193528 | + | 0.0865485i | ||||
\(535\) | 6.32456 | + | 3.16228i | 0.273434 | + | 0.136717i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.0557 | − | 28.9443i | −0.477090 | − | 1.24904i | ||||
\(538\) | 15.8114 | + | 15.8114i | 0.681677 | + | 0.681677i | ||||
\(539\) | 73.5391i | 3.16755i | ||||||||
\(540\) | −11.4806 | − | 1.78747i | −0.494048 | − | 0.0769205i | ||||
\(541\) | 41.1096i | 1.76744i | 0.468016 | + | 0.883720i | \(0.344969\pi\) | ||||
−0.468016 | + | 0.883720i | \(0.655031\pi\) | |||||||
\(542\) | 6.70820 | − | 6.70820i | 0.288142 | − | 0.288142i | ||||
\(543\) | 13.5967 | + | 35.5967i | 0.583492 | + | 1.52760i | ||||
\(544\) | 3.16228 | 0.135582 | ||||||||
\(545\) | −2.23607 | − | 6.70820i | −0.0957826 | − | 0.287348i | ||||
\(546\) | 12.9289 | + | 24.7557i | 0.553307 | + | 1.05944i | ||||
\(547\) | 5.00000 | + | 5.00000i | 0.213785 | + | 0.213785i | 0.805873 | − | 0.592088i | \(-0.201696\pi\) |
−0.592088 | + | 0.805873i | \(0.701696\pi\) | |||||||
\(548\) | −12.7279 | + | 12.7279i | −0.543710 | + | 0.543710i | ||||
\(549\) | −22.3607 | + | 20.0000i | −0.954331 | + | 0.853579i | ||||
\(550\) | 28.0000 | + | 4.00000i | 1.19392 | + | 0.170561i | ||||
\(551\) | 28.2843 | 1.20495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.1421i | 0.600842i | ||||||||
\(555\) | −1.70820 | + | 17.2361i | −0.0725092 | + | 0.731630i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 12.7279 | + | 12.7279i | 0.539299 | + | 0.539299i | 0.923323 | − | 0.384024i | \(-0.125462\pi\) |
−0.384024 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(558\) | −0.527864 | + | 9.47214i | −0.0223463 | + | 0.400987i | ||||
\(559\) | −15.8114 | + | 20.0000i | −0.668750 | + | 0.845910i | ||||
\(560\) | 8.94427 | + | 4.47214i | 0.377964 | + | 0.188982i | ||||
\(561\) | −28.2843 | − | 12.6491i | −1.19416 | − | 0.534046i | ||||
\(562\) | 6.00000 | + | 6.00000i | 0.253095 | + | 0.253095i | ||||
\(563\) | −20.1246 | − | 20.1246i | −0.848151 | − | 0.848151i | 0.141751 | − | 0.989902i | \(-0.454727\pi\) |
−0.989902 | + | 0.141751i | \(0.954727\pi\) | |||||||
\(564\) | 3.16228 | + | 1.41421i | 0.133156 | + | 0.0595491i | ||||
\(565\) | −9.48683 | + | 18.9737i | −0.399114 | + | 0.798228i | ||||
\(566\) | 12.7279 | 0.534994 | ||||||||
\(567\) | 25.1220 | + | 31.4465i | 1.05502 | + | 1.32063i | ||||
\(568\) | 1.00000 | − | 1.00000i | 0.0419591 | − | 0.0419591i | ||||
\(569\) | −8.94427 | −0.374963 | −0.187482 | − | 0.982268i | \(-0.560033\pi\) | ||||
−0.187482 | + | 0.982268i | \(0.560033\pi\) | |||||||
\(570\) | 24.3755 | + | 2.41577i | 1.02098 | + | 0.101185i | ||||
\(571\) | −10.0000 | −0.418487 | −0.209243 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209243 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(572\) | −2.36944 | − | 20.2580i | −0.0990711 | − | 0.847029i | ||||
\(573\) | −14.4721 | + | 5.52786i | −0.604582 | + | 0.230930i | ||||
\(574\) | −25.2982 | −1.05593 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.00000 | + | 2.23607i | 0.0833333 | + | 0.0931695i | ||||
\(577\) | 9.48683 | − | 9.48683i | 0.394942 | − | 0.394942i | −0.481503 | − | 0.876445i | \(-0.659909\pi\) |
0.876445 | + | 0.481503i | \(0.159909\pi\) | |||||||
\(578\) | −4.94975 | + | 4.94975i | −0.205882 | + | 0.205882i | ||||
\(579\) | −9.48683 | + | 21.2132i | −0.394259 | + | 0.881591i | ||||
\(580\) | −9.48683 | + | 3.16228i | −0.393919 | + | 0.131306i | ||||
\(581\) | − | 17.8885i | − | 0.742142i | ||||||
\(582\) | 8.29180 | + | 21.7082i | 0.343706 | + | 0.899834i | ||||
\(583\) | −25.2982 | − | 25.2982i | −1.04775 | − | 1.04775i | ||||
\(584\) | 4.47214 | 0.185058 | ||||||||
\(585\) | −22.2502 | − | 9.48298i | −0.919934 | − | 0.392073i | ||||
\(586\) | −16.0000 | −0.660954 | ||||||||
\(587\) | −8.48528 | − | 8.48528i | −0.350225 | − | 0.350225i | 0.509968 | − | 0.860193i | \(-0.329657\pi\) |
−0.860193 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(588\) | −8.03444 | − | 21.0344i | −0.331335 | − | 0.867446i | ||||
\(589\) | − | 20.0000i | − | 0.824086i | ||||||
\(590\) | 5.65685 | + | 2.82843i | 0.232889 | + | 0.116445i | ||||
\(591\) | 1.41421 | − | 3.16228i | 0.0581730 | − | 0.130079i | ||||
\(592\) | 3.16228 | − | 3.16228i | 0.129969 | − | 0.129969i | ||||
\(593\) | 4.24264 | − | 4.24264i | 0.174224 | − | 0.174224i | −0.614608 | − | 0.788833i | \(-0.710686\pi\) |
0.788833 | + | 0.614608i | \(0.210686\pi\) | |||||||
\(594\) | −8.94427 | − | 28.0000i | −0.366988 | − | 1.14885i | ||||
\(595\) | 30.0000 | − | 10.0000i | 1.22988 | − | 0.409960i | ||||
\(596\) | −4.24264 | −0.173785 | ||||||||
\(597\) | 32.3607 | − | 12.3607i | 1.32443 | − | 0.505889i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.94427 | −0.365453 | −0.182727 | − | 0.983164i | \(-0.558492\pi\) | ||||
−0.182727 | + | 0.983164i | \(0.558492\pi\) | |||||||
\(600\) | −8.44588 | + | 1.91499i | −0.344801 | + | 0.0781791i | ||||
\(601\) | −40.0000 | −1.63163 | −0.815817 | − | 0.578310i | \(-0.803712\pi\) | ||||
−0.815817 | + | 0.578310i | \(0.803712\pi\) | |||||||
\(602\) | 22.3607 | − | 22.3607i | 0.911353 | − | 0.911353i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22.1359 | 0.900699 | ||||||||
\(605\) | 14.8492 | + | 44.5477i | 0.603708 | + | 1.81112i | ||||
\(606\) | −7.07107 | − | 3.16228i | −0.287242 | − | 0.128459i | ||||
\(607\) | 30.0000 | + | 30.0000i | 1.21766 | + | 1.21766i | 0.968448 | + | 0.249214i | \(0.0801723\pi\) |
0.249214 | + | 0.968448i | \(0.419828\pi\) | |||||||
\(608\) | −4.47214 | − | 4.47214i | −0.181369 | − | 0.181369i | ||||
\(609\) | 31.6228 | + | 14.1421i | 1.28142 | + | 0.573068i | ||||
\(610\) | −10.0000 | + | 20.0000i | −0.404888 | + | 0.809776i | ||||
\(611\) | 5.65685 | + | 4.47214i | 0.228852 | + | 0.180923i | ||||
\(612\) | 9.47214 | + | 0.527864i | 0.382888 | + | 0.0213376i | ||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.9443 | − | 13.8885i | 0.683259 | − | 0.560040i | ||||
\(616\) | 25.2982i | 1.01929i | ||||||||
\(617\) | −12.7279 | − | 12.7279i | −0.512407 | − | 0.512407i | 0.402856 | − | 0.915263i | \(-0.368017\pi\) |
−0.915263 | + | 0.402856i | \(0.868017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 2.23607 | + | 6.70820i | 0.0898027 | + | 0.269408i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.32456 | − | 6.32456i | 0.253592 | − | 0.253592i | ||||
\(623\) | −8.94427 | − | 8.94427i | −0.358345 | − | 0.358345i | ||||
\(624\) | 2.89100 | + | 5.53553i | 0.115733 | + | 0.221599i | ||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | −1.41421 | −0.0565233 | ||||||||
\(627\) | 22.1115 | + | 57.8885i | 0.883047 | + | 2.31185i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 14.1421i | − | 0.563884i | ||||||
\(630\) | 26.0447 | + | 14.8886i | 1.03765 | + | 0.593178i | ||||
\(631\) | − | 15.8114i | − | 0.629441i | −0.949184 | − | 0.314721i | \(-0.898089\pi\) | ||
0.949184 | − | 0.314721i | \(-0.101911\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.3607 | − | 32.3607i | −0.491293 | − | 1.28622i | ||||
\(634\) | − | 28.0000i | − | 1.11202i | ||||||
\(635\) | 2.82843 | − | 5.65685i | 0.112243 | − | 0.224485i | ||||
\(636\) | 10.0000 | + | 4.47214i | 0.396526 | + | 0.177332i | ||||
\(637\) | −5.44520 | − | 46.5548i | −0.215746 | − | 1.84457i | ||||
\(638\) | −17.8885 | − | 17.8885i | −0.708214 | − | 0.708214i | ||||
\(639\) | 3.16228 | − | 2.82843i | 0.125098 | − | 0.111891i | ||||
\(640\) | 2.00000 | + | 1.00000i | 0.0790569 | + | 0.0395285i | ||||
\(641\) | 49.1935i | 1.94303i | 0.236986 | + | 0.971513i | \(0.423841\pi\) | ||||
−0.236986 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(642\) | −1.95440 | − | 5.11667i | −0.0771338 | − | 0.201939i | ||||
\(643\) | −18.9737 | − | 18.9737i | −0.748248 | − | 0.748248i | 0.225902 | − | 0.974150i | \(-0.427467\pi\) |
−0.974150 | + | 0.225902i | \(0.927467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.70091 | + | 27.2526i | −0.106348 | + | 1.07307i | ||||
\(646\) | −20.0000 | −0.786889 | ||||||||
\(647\) | −22.3607 | + | 22.3607i | −0.879089 | + | 0.879089i | −0.993440 | − | 0.114351i | \(-0.963521\pi\) |
0.114351 | + | 0.993440i | \(0.463521\pi\) | |||||||
\(648\) | 5.61745 | + | 7.03166i | 0.220674 | + | 0.276230i | ||||
\(649\) | 16.0000i | 0.628055i | ||||||||
\(650\) | −18.0219 | − | 0.458991i | −0.706878 | − | 0.0180031i | ||||
\(651\) | 10.0000 | − | 22.3607i | 0.391931 | − | 0.876384i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.8885 | − | 17.8885i | −0.700033 | − | 0.700033i | 0.264385 | − | 0.964417i | \(-0.414831\pi\) |
−0.964417 | + | 0.264385i | \(0.914831\pi\) | |||||||
\(654\) | −2.23607 | + | 5.00000i | −0.0874372 | + | 0.195515i | ||||
\(655\) | −37.9473 | + | 12.6491i | −1.48272 | + | 0.494242i | ||||
\(656\) | −5.65685 | −0.220863 | ||||||||
\(657\) | 13.3956 | + | 0.746512i | 0.522613 | + | 0.0291242i | ||||
\(658\) | −6.32456 | − | 6.32456i | −0.246557 | − | 0.246557i | ||||
\(659\) | −31.3050 | −1.21947 | −0.609734 | − | 0.792606i | \(-0.708724\pi\) | ||||
−0.609734 | + | 0.792606i | \(0.708724\pi\) | |||||||
\(660\) | −13.8885 | − | 16.9443i | −0.540611 | − | 0.659555i | ||||
\(661\) | − | 41.1096i | − | 1.59898i | −0.600680 | − | 0.799489i | \(-0.705104\pi\) | ||
0.600680 | − | 0.799489i | \(-0.294896\pi\) | |||||||
\(662\) | −8.94427 | + | 8.94427i | −0.347629 | + | 0.347629i | ||||
\(663\) | 18.8423 | + | 5.91336i | 0.731774 | + | 0.229656i | ||||
\(664\) | − | 4.00000i | − | 0.155230i | ||||||
\(665\) | −56.5685 | − | 28.2843i | −2.19363 | − | 1.09682i | ||||
\(666\) | 10.0000 | − | 8.94427i | 0.387492 | − | 0.346583i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −12.7279 | + | 12.7279i | −0.492458 | + | 0.492458i | ||||
\(669\) | 18.9737 | − | 42.4264i | 0.733564 | − | 1.64030i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −56.5685 | −2.18380 | ||||||||
\(672\) | −2.76393 | − | 7.23607i | −0.106621 | − | 0.279137i | ||||
\(673\) | −15.0000 | + | 15.0000i | −0.578208 | + | 0.578208i | −0.934409 | − | 0.356202i | \(-0.884072\pi\) |
0.356202 | + | 0.934409i | \(0.384072\pi\) | |||||||
\(674\) | − | 18.3848i | − | 0.708155i | ||||||
\(675\) | −25.6180 | + | 4.32624i | −0.986039 | + | 0.166517i | ||||
\(676\) | 3.00000 | + | 12.6491i | 0.115385 | + | 0.486504i | ||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 15.3500 | − | 5.86319i | 0.589514 | − | 0.225174i | ||||
\(679\) | − | 60.0000i | − | 2.30259i | ||||||
\(680\) | 6.70820 | − | 2.23607i | 0.257248 | − | 0.0857493i | ||||
\(681\) | −8.48528 | + | 18.9737i | −0.325157 | + | 0.727072i | ||||
\(682\) | −12.6491 | + | 12.6491i | −0.484359 | + | 0.484359i | ||||
\(683\) | 16.9706 | − | 16.9706i | 0.649361 | − | 0.649361i | −0.303478 | − | 0.952838i | \(-0.598148\pi\) |
0.952838 | + | 0.303478i | \(0.0981479\pi\) | |||||||
\(684\) | −12.6491 | − | 14.1421i | −0.483651 | − | 0.540738i | ||||
\(685\) | −18.0000 | + | 36.0000i | −0.687745 | + | 1.37549i | ||||
\(686\) | 26.8328i | 1.02448i | ||||||||
\(687\) | 5.86319 | + | 15.3500i | 0.223694 | + | 0.585640i | ||||
\(688\) | 5.00000 | − | 5.00000i | 0.190623 | − | 0.190623i | ||||
\(689\) | 17.8885 | + | 14.1421i | 0.681499 | + | 0.538772i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 13.4164 | − | 13.4164i | 0.510015 | − | 0.510015i | ||||
\(693\) | −4.22291 | + | 75.7771i | −0.160415 | + | 2.87853i | ||||
\(694\) | −28.4605 | −1.08035 | ||||||||
\(695\) | 8.48528 | − | 2.82843i | 0.321865 | − | 0.107288i | ||||
\(696\) | 7.07107 | + | 3.16228i | 0.268028 | + | 0.119866i | ||||
\(697\) | −12.6491 | + | 12.6491i | −0.479119 | + | 0.479119i | ||||
\(698\) | −2.23607 | − | 2.23607i | −0.0846364 | − | 0.0846364i | ||||
\(699\) | −2.23607 | + | 5.00000i | −0.0845759 | + | 0.189117i | ||||
\(700\) | 22.1359 | + | 3.16228i | 0.836660 | + | 0.119523i | ||||
\(701\) | 49.1935i | 1.85801i | 0.370064 | + | 0.929006i | \(0.379336\pi\) | ||||
−0.370064 | + | 0.929006i | \(0.620664\pi\) | |||||||
\(702\) | 7.73553 | + | 17.0635i | 0.291959 | + | 0.644019i | ||||
\(703\) | −20.0000 | + | 20.0000i | −0.754314 | + | 0.754314i | ||||
\(704\) | 5.65685i | 0.213201i | ||||||||
\(705\) | 7.70820 | + | 0.763932i | 0.290308 | + | 0.0287713i | ||||
\(706\) | 14.0000 | 0.526897 | ||||||||
\(707\) | 14.1421 | + | 14.1421i | 0.531870 | + | 0.531870i | ||||
\(708\) | −1.74806 | − | 4.57649i | −0.0656963 | − | 0.171995i | ||||
\(709\) | −47.4342 | −1.78143 | −0.890714 | − | 0.454565i | \(-0.849795\pi\) | ||||
−0.890714 | + | 0.454565i | \(0.849795\pi\) | |||||||
\(710\) | 1.41421 | − | 2.82843i | 0.0530745 | − | 0.106149i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.00000 | − | 2.00000i | −0.0749532 | − | 0.0749532i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −22.3607 | − | 10.0000i | −0.836827 | − | 0.374241i | ||||
\(715\) | −19.3509 | − | 41.2982i | −0.723682 | − | 1.54447i | ||||
\(716\) | 17.8885i | 0.668526i | ||||||||
\(717\) | 6.86474 | − | 2.62210i | 0.256368 | − | 0.0979240i | ||||
\(718\) | 23.0000 | − | 23.0000i | 0.858352 | − | 0.858352i | ||||
\(719\) | 17.8885 | 0.667130 | 0.333565 | − | 0.942727i | \(-0.391748\pi\) | ||||
0.333565 | + | 0.942727i | \(0.391748\pi\) | |||||||
\(720\) | 5.82378 | + | 3.32920i | 0.217039 | + | 0.124072i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.8492 | + | 14.8492i | 0.552632 | + | 0.552632i | ||||
\(723\) | 20.4667 | − | 7.81758i | 0.761164 | − | 0.290739i | ||||
\(724\) | − | 22.0000i | − | 0.817624i | ||||||
\(725\) | −17.8885 | + | 13.4164i | −0.664364 | + | 0.498273i | ||||
\(726\) | 14.8492 | − | 33.2039i | 0.551107 | − | 1.23231i | ||||
\(727\) | 18.0000 | + | 18.0000i | 0.667583 | + | 0.667583i | 0.957156 | − | 0.289573i | \(-0.0935133\pi\) |
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(728\) | −1.87320 | − | 16.0153i | −0.0694256 | − | 0.593568i | ||||
\(729\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(730\) | 9.48683 | − | 3.16228i | 0.351123 | − | 0.117041i | ||||
\(731\) | − | 22.3607i | − | 0.827040i | ||||||
\(732\) | 16.1803 | − | 6.18034i | 0.598043 | − | 0.228432i | ||||
\(733\) | −9.48683 | − | 9.48683i | −0.350404 | − | 0.350404i | 0.509856 | − | 0.860260i | \(-0.329699\pi\) |
−0.860260 | + | 0.509856i | \(0.829699\pi\) | |||||||
\(734\) | − | 28.2843i | − | 1.04399i | ||||||
\(735\) | −31.9172 | − | 38.9396i | −1.17728 | − | 1.43631i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −16.9443 | − | 0.944272i | −0.623727 | − | 0.0347591i | ||||
\(739\) | 44.2719 | 1.62857 | 0.814284 | − | 0.580467i | \(-0.197130\pi\) | ||||
0.814284 | + | 0.580467i | \(0.197130\pi\) | |||||||
\(740\) | 4.47214 | − | 8.94427i | 0.164399 | − | 0.328798i | ||||
\(741\) | −18.2843 | − | 35.0098i | −0.671689 | − | 1.28612i | ||||
\(742\) | −20.0000 | − | 20.0000i | −0.734223 | − | 0.734223i | ||||
\(743\) | −16.9706 | + | 16.9706i | −0.622590 | + | 0.622590i | −0.946193 | − | 0.323603i | \(-0.895106\pi\) |
0.323603 | + | 0.946193i | \(0.395106\pi\) | |||||||
\(744\) | 2.23607 | − | 5.00000i | 0.0819782 | − | 0.183309i | ||||
\(745\) | −9.00000 | + | 3.00000i | −0.329734 | + | 0.109911i | ||||
\(746\) | 22.6274 | 0.828449 | ||||||||
\(747\) | 0.667701 | − | 11.9814i | 0.0244299 | − | 0.438377i | ||||
\(748\) | 12.6491 | + | 12.6491i | 0.462497 | + | 0.462497i | ||||
\(749\) | 14.1421i | 0.516742i | ||||||||
\(750\) | −16.5623 | + | 10.0344i | −0.604770 | + | 0.366406i | ||||
\(751\) | 48.0000 | 1.75154 | 0.875772 | − | 0.482724i | \(-0.160353\pi\) | ||||
0.875772 | + | 0.482724i | \(0.160353\pi\) | |||||||
\(752\) | −1.41421 | − | 1.41421i | −0.0515711 | − | 0.0515711i | ||||
\(753\) | 28.9443 | − | 11.0557i | 1.05479 | − | 0.402893i | ||||
\(754\) | 12.6491 | + | 10.0000i | 0.460653 | + | 0.364179i | ||||
\(755\) | 46.9574 | − | 15.6525i | 1.70896 | − | 0.569652i | ||||
\(756\) | −7.07107 | − | 22.1359i | −0.257172 | − | 0.805076i | ||||
\(757\) | −18.0000 | − | 18.0000i | −0.654221 | − | 0.654221i | 0.299786 | − | 0.954007i | \(-0.403085\pi\) |
−0.954007 | + | 0.299786i | \(0.903085\pi\) | |||||||
\(758\) | −4.47214 | − | 4.47214i | −0.162435 | − | 0.162435i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.6491 | − | 6.32456i | −0.458831 | − | 0.229416i | ||||
\(761\) | 36.7696 | 1.33290 | 0.666448 | − | 0.745552i | \(-0.267814\pi\) | ||||
0.666448 | + | 0.745552i | \(0.267814\pi\) | |||||||
\(762\) | −4.57649 | + | 1.74806i | −0.165789 | + | 0.0633257i | ||||
\(763\) | 10.0000 | − | 10.0000i | 0.362024 | − | 0.362024i | ||||
\(764\) | 8.94427 | 0.323592 | ||||||||
\(765\) | 20.4667 | − | 5.57804i | 0.739975 | − | 0.201675i | ||||
\(766\) | 16.0000 | 0.578103 | ||||||||
\(767\) | −1.18472 | − | 10.1290i | −0.0427777 | − | 0.365737i | ||||
\(768\) | −0.618034 | − | 1.61803i | −0.0223014 | − | 0.0583858i | ||||
\(769\) | 50.5964 | 1.82455 | 0.912277 | − | 0.409573i | \(-0.134322\pi\) | ||||
0.912277 | + | 0.409573i | \(0.134322\pi\) | |||||||
\(770\) | 17.8885 | + | 53.6656i | 0.644658 | + | 1.93398i | ||||
\(771\) | −45.0000 | − | 20.1246i | −1.62064 | − | 0.724770i | ||||
\(772\) | 9.48683 | − | 9.48683i | 0.341439 | − | 0.341439i | ||||
\(773\) | 4.24264 | − | 4.24264i | 0.152597 | − | 0.152597i | −0.626680 | − | 0.779277i | \(-0.715587\pi\) |
0.779277 | + | 0.626680i | \(0.215587\pi\) | |||||||
\(774\) | 15.8114 | − | 14.1421i | 0.568329 | − | 0.508329i | ||||
\(775\) | 9.48683 | + | 12.6491i | 0.340777 | + | 0.454369i | ||||
\(776\) | − | 13.4164i | − | 0.481621i | ||||||
\(777\) | −32.3607 | + | 12.3607i | −1.16093 | + | 0.443437i | ||||
\(778\) | −9.48683 | − | 9.48683i | −0.340119 | − | 0.340119i | ||||
\(779\) | 35.7771 | 1.28185 | ||||||||
\(780\) | 10.0469 | + | 9.69840i | 0.359738 | + | 0.347258i | ||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.6525 | + | 10.6525i | 0.738059 | + | 0.380688i | ||||
\(784\) | 13.0000i | 0.464286i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 28.2843 | + | 12.6491i | 1.00887 | + | 0.451179i | ||||
\(787\) | 12.6491 | − | 12.6491i | 0.450892 | − | 0.450892i | −0.444758 | − | 0.895651i | \(-0.646710\pi\) |
0.895651 | + | 0.444758i | \(0.146710\pi\) | |||||||
\(788\) | −1.41421 | + | 1.41421i | −0.0503793 | + | 0.0503793i | ||||
\(789\) | 8.94427 | − | 20.0000i | 0.318425 | − | 0.712019i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.4264 | −1.50851 | ||||||||
\(792\) | −0.944272 | + | 16.9443i | −0.0335532 | + | 0.602088i | ||||
\(793\) | 35.8114 | − | 4.18861i | 1.27170 | − | 0.148742i | ||||
\(794\) | 35.7771 | 1.26968 | ||||||||
\(795\) | 24.3755 | + | 2.41577i | 0.864509 | + | 0.0856784i | ||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 13.4164 | − | 13.4164i | 0.475234 | − | 0.475234i | −0.428370 | − | 0.903603i | \(-0.640912\pi\) |
0.903603 | + | 0.428370i | \(0.140912\pi\) | |||||||
\(798\) | 17.4806 | + | 45.7649i | 0.618808 | + | 1.62006i | ||||
\(799\) | −6.32456 | −0.223747 | ||||||||
\(800\) | 4.94975 | + | 0.707107i | 0.175000 | + | 0.0250000i | ||||
\(801\) | −5.65685 | − | 6.32456i | −0.199875 | − | 0.223467i | ||||
\(802\) | −6.00000 | − | 6.00000i | −0.211867 | − | 0.211867i | ||||
\(803\) | 17.8885 | + | 17.8885i | 0.631273 | + | 0.631273i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.07107 | − | 8.94427i | 0.249068 | − | 0.315049i | ||||
\(807\) | −13.8197 | − | 36.1803i | −0.486475 | − | 1.27361i | ||||
\(808\) | 3.16228 | + | 3.16228i | 0.111249 | + | 0.111249i | ||||
\(809\) | −17.8885 | −0.628928 | −0.314464 | − | 0.949269i | \(-0.601825\pi\) | ||||
−0.314464 | + | 0.949269i | \(0.601825\pi\) | |||||||
\(810\) | 16.8885 | + | 10.9443i | 0.593403 | + | 0.384543i | ||||
\(811\) | 44.2719i | 1.55460i | 0.629132 | + | 0.777298i | \(0.283410\pi\) | ||||
−0.629132 | + | 0.777298i | \(0.716590\pi\) | |||||||
\(812\) | −14.1421 | − | 14.1421i | −0.496292 | − | 0.496292i | ||||
\(813\) | −15.3500 | + | 5.86319i | −0.538349 | + | 0.205631i | ||||
\(814\) | 25.2982 | 0.886702 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.00000 | − | 2.23607i | −0.175035 | − | 0.0782780i | ||||
\(817\) | −31.6228 | + | 31.6228i | −1.10634 | + | 1.10634i | ||||
\(818\) | −13.4164 | − | 13.4164i | −0.469094 | − | 0.469094i | ||||
\(819\) | −2.93754 | − | 48.2843i | −0.102646 | − | 1.68719i | ||||
\(820\) | −12.0000 | + | 4.00000i | −0.419058 | + | 0.139686i | ||||
\(821\) | 15.5563 | 0.542920 | 0.271460 | − | 0.962450i | \(-0.412493\pi\) | ||||
0.271460 | + | 0.962450i | \(0.412493\pi\) | |||||||
\(822\) | 29.1246 | − | 11.1246i | 1.01584 | − | 0.388015i | ||||
\(823\) | 10.0000 | − | 10.0000i | 0.348578 | − | 0.348578i | −0.511002 | − | 0.859580i | \(-0.670725\pi\) |
0.859580 | + | 0.511002i | \(0.170725\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −41.4435 | − | 26.1235i | −1.44288 | − | 0.909505i | ||||
\(826\) | 12.6491i | 0.440119i | ||||||||
\(827\) | −5.65685 | − | 5.65685i | −0.196708 | − | 0.196708i | 0.601879 | − | 0.798587i | \(-0.294419\pi\) |
−0.798587 | + | 0.601879i | \(0.794419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.0000i | − | 0.347314i | −0.984806 | − | 0.173657i | \(-0.944442\pi\) | ||
0.984806 | − | 0.173657i | \(-0.0555585\pi\) | |||||||
\(830\) | −2.82843 | − | 8.48528i | −0.0981761 | − | 0.294528i | ||||
\(831\) | 10.0000 | − | 22.3607i | 0.346896 | − | 0.775683i | ||||
\(832\) | −0.418861 | − | 3.58114i | −0.0145214 | − | 0.124154i | ||||
\(833\) | 29.0689 | + | 29.0689i | 1.00718 | + | 1.00718i | ||||
\(834\) | −6.32456 | − | 2.82843i | −0.219001 | − | 0.0979404i | ||||
\(835\) | −18.0000 | + | 36.0000i | −0.622916 | + | 1.24583i | ||||
\(836\) | − | 35.7771i | − | 1.23738i | ||||||
\(837\) | 7.53244 | − | 14.6035i | 0.260359 | − | 0.504771i | ||||
\(838\) | 9.48683 | + | 9.48683i | 0.327717 | + | 0.327717i | ||||
\(839\) | − | 18.3848i | − | 0.634713i | −0.948306 | − | 0.317356i | \(-0.897205\pi\) | ||
0.948306 | − | 0.317356i | \(-0.102795\pi\) | |||||||
\(840\) | −10.9799 | − | 13.3956i | −0.378841 | − | 0.462193i | ||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 2.23607 | − | 2.23607i | 0.0770600 | − | 0.0770600i | ||||
\(843\) | −5.24419 | − | 13.7295i | −0.180620 | − | 0.472868i | ||||
\(844\) | 20.0000i | 0.688428i | ||||||||
\(845\) | 15.3082 | + | 24.7115i | 0.526619 | + | 0.850101i | ||||
\(846\) | −4.00000 | − | 4.47214i | −0.137523 | − | 0.153755i | ||||
\(847\) | −66.4078 | + | 66.4078i | −2.28180 | + | 2.28180i | ||||
\(848\) | −4.47214 | − | 4.47214i | −0.153574 | − | 0.153574i | ||||
\(849\) | −20.1246 | − | 9.00000i | −0.690675 | − | 0.308879i | ||||
\(850\) | 12.6491 | − | 9.48683i | 0.433861 | − | 0.325396i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −2.28825 | + | 0.874032i | −0.0783940 | + | 0.0299438i | ||||
\(853\) | −37.9473 | − | 37.9473i | −1.29929 | − | 1.29929i | −0.928859 | − | 0.370433i | \(-0.879209\pi\) |
−0.370433 | − | 0.928859i | \(-0.620791\pi\) | |||||||
\(854\) | −44.7214 | −1.53033 | ||||||||
\(855\) | −36.8328 | − | 21.0557i | −1.25966 | − | 0.720091i | ||||
\(856\) | 3.16228i | 0.108084i | ||||||||
\(857\) | −20.1246 | + | 20.1246i | −0.687444 | + | 0.687444i | −0.961666 | − | 0.274223i | \(-0.911579\pi\) |
0.274223 | + | 0.961666i | \(0.411579\pi\) | |||||||
\(858\) | −10.5781 | + | 33.7061i | −0.361132 | + | 1.15071i | ||||
\(859\) | 50.0000i | 1.70598i | 0.521929 | + | 0.852989i | \(0.325213\pi\) | ||||
−0.521929 | + | 0.852989i | \(0.674787\pi\) | |||||||
\(860\) | 7.07107 | − | 14.1421i | 0.241121 | − | 0.482243i | ||||
\(861\) | 40.0000 | + | 17.8885i | 1.36320 | + | 0.609640i | ||||
\(862\) | 1.00000 | + | 1.00000i | 0.0340601 | + | 0.0340601i | ||||
\(863\) | 9.89949 | − | 9.89949i | 0.336983 | − | 0.336983i | −0.518248 | − | 0.855231i | \(-0.673415\pi\) |
0.855231 | + | 0.518248i | \(0.173415\pi\) | |||||||
\(864\) | −1.58114 | − | 4.94975i | −0.0537914 | − | 0.168394i | ||||
\(865\) | 18.9737 | − | 37.9473i | 0.645124 | − | 1.29025i | ||||
\(866\) | 29.6985 | 1.00920 | ||||||||
\(867\) | 11.3262 | − | 4.32624i | 0.384659 | − | 0.146927i | ||||
\(868\) | −10.0000 | + | 10.0000i | −0.339422 | + | 0.339422i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 17.2361 | + | 1.70820i | 0.584357 | + | 0.0579135i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.23607 | − | 2.23607i | 0.0757228 | − | 0.0757228i | ||||
\(873\) | 2.23954 | − | 40.1869i | 0.0757969 | − | 1.36012i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 49.1935 | − | 8.94427i | 1.66304 | − | 0.302372i | ||||
\(876\) | −7.07107 | − | 3.16228i | −0.238909 | − | 0.106843i | ||||
\(877\) | −6.32456 | + | 6.32456i | −0.213565 | + | 0.213565i | −0.805780 | − | 0.592215i | \(-0.798254\pi\) |
0.592215 | + | 0.805780i | \(0.298254\pi\) | |||||||
\(878\) | −11.3137 | + | 11.3137i | −0.381819 | + | 0.381819i | ||||
\(879\) | 25.2982 | + | 11.3137i | 0.853288 | + | 0.381602i | ||||
\(880\) | 4.00000 | + | 12.0000i | 0.134840 | + | 0.404520i | ||||
\(881\) | − | 31.3050i | − | 1.05469i | −0.849651 | − | 0.527345i | \(-0.823187\pi\) | ||
0.849651 | − | 0.527345i | \(-0.176813\pi\) | |||||||
\(882\) | −2.17003 | + | 38.9396i | −0.0730687 | + | 1.31116i | ||||
\(883\) | −21.0000 | + | 21.0000i | −0.706706 | + | 0.706706i | −0.965841 | − | 0.259135i | \(-0.916563\pi\) |
0.259135 | + | 0.965841i | \(0.416563\pi\) | |||||||
\(884\) | −8.94427 | − | 7.07107i | −0.300828 | − | 0.237826i | ||||
\(885\) | −6.94427 | − | 8.47214i | −0.233429 | − | 0.284788i | ||||
\(886\) | 15.8114i | 0.531194i | ||||||||
\(887\) | −35.7771 | + | 35.7771i | −1.20128 | + | 1.20128i | −0.227499 | + | 0.973778i | \(0.573055\pi\) |
−0.973778 | + | 0.227499i | \(0.926945\pi\) | |||||||
\(888\) | −7.23607 | + | 2.76393i | −0.242827 | + | 0.0927515i | ||||
\(889\) | 12.6491 | 0.424238 | ||||||||
\(890\) | −5.65685 | − | 2.82843i | −0.189618 | − | 0.0948091i | ||||
\(891\) | −5.65685 | + | 50.5964i | −0.189512 | + | 1.69504i | ||||
\(892\) | −18.9737 | + | 18.9737i | −0.635285 | + | 0.635285i | ||||
\(893\) | 8.94427 | + | 8.94427i | 0.299309 | + | 0.299309i | ||||
\(894\) | 6.70820 | + | 3.00000i | 0.224356 | + | 0.100335i | ||||
\(895\) | 12.6491 | + | 37.9473i | 0.422813 | + | 1.26844i | ||||
\(896\) | 4.47214i | 0.149404i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.0000 | − | 22.0000i | 0.734150 | − | 0.734150i | ||||
\(899\) | − | 14.1421i | − | 0.471667i | ||||||
\(900\) | 14.7082 | + | 2.94427i | 0.490273 | + | 0.0981424i | ||||
\(901\) | −20.0000 | −0.666297 | ||||||||
\(902\) | −22.6274 | − | 22.6274i | −0.753411 | − | 0.753411i | ||||
\(903\) | −51.1667 | + | 19.5440i | −1.70272 | + | 0.650382i | ||||
\(904\) | −9.48683 | −0.315527 | ||||||||
\(905\) | −15.5563 | − | 46.6690i | −0.517111 | − | 1.55133i | ||||
\(906\) | −35.0000 | − | 15.6525i | −1.16280 | − | 0.520019i | ||||
\(907\) | 33.0000 | + | 33.0000i | 1.09575 | + | 1.09575i | 0.994902 | + | 0.100845i | \(0.0321546\pi\) |
0.100845 | + | 0.994902i | \(0.467845\pi\) | |||||||
\(908\) | 8.48528 | − | 8.48528i | 0.281594 | − | 0.281594i | ||||
\(909\) | 8.94427 | + | 10.0000i | 0.296663 | + | 0.331679i | ||||
\(910\) | −15.2982 | − | 32.6491i | −0.507131 | − | 1.08231i | ||||
\(911\) | − | 44.7214i | − | 1.48168i | −0.671679 | − | 0.740842i | \(-0.734427\pi\) | ||
0.671679 | − | 0.740842i | \(-0.265573\pi\) | |||||||
\(912\) | 3.90879 | + | 10.2333i | 0.129433 | + | 0.338860i | ||||
\(913\) | 16.0000 | − | 16.0000i | 0.529523 | − | 0.529523i | ||||
\(914\) | 31.3050 | 1.03548 | ||||||||
\(915\) | 29.9535 | − | 24.5517i | 0.990233 | − | 0.811654i | ||||
\(916\) | − | 9.48683i | − | 0.313454i | ||||||
\(917\) | −56.5685 | − | 56.5685i | −1.86806 | − | 1.86806i | ||||
\(918\) | −14.6035 | − | 7.53244i | −0.481988 | − | 0.248607i | ||||
\(919\) | − | 40.0000i | − | 1.31948i | −0.751495 | − | 0.659739i | \(-0.770667\pi\) | ||
0.751495 | − | 0.659739i | \(-0.229333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.00000 | + | 1.00000i | 0.0329332 | + | 0.0329332i | ||||
\(923\) | −5.06450 | + | 0.592359i | −0.166700 | + | 0.0194977i | ||||
\(924\) | 17.8885 | − | 40.0000i | 0.588490 | − | 1.31590i | ||||
\(925\) | 3.16228 | − | 22.1359i | 0.103975 | − | 0.727825i | ||||
\(926\) | 26.8328i | 0.881781i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.16228 | − | 3.16228i | −0.103807 | − | 0.103807i | ||||
\(929\) | 2.82843i | 0.0927977i | 0.998923 | + | 0.0463988i | \(0.0147745\pi\) | ||||
−0.998923 | + | 0.0463988i | \(0.985225\pi\) | |||||||
\(930\) | 1.20788 | − | 12.1877i | 0.0396080 | − | 0.399652i | ||||
\(931\) | − | 82.2192i | − | 2.69463i | ||||||
\(932\) | 2.23607 | − | 2.23607i | 0.0732448 | − | 0.0732448i | ||||
\(933\) | −14.4721 | + | 5.52786i | −0.473796 | + | 0.180974i | ||||
\(934\) | −9.48683 | −0.310419 | ||||||||
\(935\) | 35.7771 | + | 17.8885i | 1.17004 | + | 0.585018i | ||||
\(936\) | −0.656854 | − | 10.7967i | −0.0214700 | − | 0.352901i | ||||
\(937\) | 3.00000 | + | 3.00000i | 0.0980057 | + | 0.0980057i | 0.754410 | − | 0.656404i | \(-0.227923\pi\) |
−0.656404 | + | 0.754410i | \(0.727923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.23607 | + | 1.00000i | 0.0729713 | + | 0.0326338i | ||||
\(940\) | −4.00000 | − | 2.00000i | −0.130466 | − | 0.0652328i | ||||
\(941\) | −1.41421 | −0.0461020 | −0.0230510 | − | 0.999734i | \(-0.507338\pi\) | ||||
−0.0230510 | + | 0.999734i | \(0.507338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.82843i | 0.0920575i | ||||||||
\(945\) | −30.6525 | − | 41.9574i | −0.997125 | − | 1.36488i | ||||
\(946\) | 40.0000 | 1.30051 | ||||||||
\(947\) | 36.7696 | + | 36.7696i | 1.19485 | + | 1.19485i | 0.975689 | + | 0.219161i | \(0.0703321\pi\) |
0.219161 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6491 | − | 10.0000i | −0.410608 | − | 0.324614i | ||||
\(950\) | −31.3050 | − | 4.47214i | −1.01567 | − | 0.145095i | ||||
\(951\) | −19.7990 | + | 44.2719i | −0.642026 | + | 1.43561i | ||||
\(952\) | 10.0000 | + | 10.0000i | 0.324102 | + | 0.324102i | ||||
\(953\) | 6.70820 | + | 6.70820i | 0.217300 | + | 0.217300i | 0.807360 | − | 0.590060i | \(-0.200896\pi\) |
−0.590060 | + | 0.807360i | \(0.700896\pi\) | |||||||
\(954\) | −12.6491 | − | 14.1421i | −0.409530 | − | 0.457869i | ||||
\(955\) | 18.9737 | − | 6.32456i | 0.613973 | − | 0.204658i | ||||
\(956\) | −4.24264 | −0.137217 | ||||||||
\(957\) | 15.6352 | + | 40.9334i | 0.505413 | + | 1.32319i | ||||
\(958\) | 13.0000 | − | 13.0000i | 0.420011 | − | 0.420011i | ||||
\(959\) | −80.4984 | −2.59943 | ||||||||
\(960\) | −2.45517 | − | 2.99535i | −0.0792403 | − | 0.0966746i | ||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | −16.0153 | + | 1.87320i | −0.516355 | + | 0.0603945i | ||||
\(963\) | −0.527864 | + | 9.47214i | −0.0170102 | + | 0.305235i | ||||
\(964\) | −12.6491 | −0.407400 | ||||||||
\(965\) | 13.4164 | − | 26.8328i | 0.431889 | − | 0.863779i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.6228 | − | 31.6228i | 1.01692 | − | 1.01692i | 0.0170656 | − | 0.999854i | \(-0.494568\pi\) |
0.999854 | − | 0.0170656i | \(-0.00543240\pi\) | |||||||
\(968\) | −14.8492 | + | 14.8492i | −0.477273 | + | 0.477273i | ||||
\(969\) | 31.6228 | + | 14.1421i | 1.01587 | + | 0.454311i | ||||
\(970\) | −9.48683 | − | 28.4605i | −0.304604 | − | 0.913812i | ||||
\(971\) | 31.3050i | 1.00462i | 0.864687 | + | 0.502312i | \(0.167517\pi\) | ||||
−0.864687 | + | 0.502312i | \(0.832483\pi\) | |||||||
\(972\) | −3.90983 | − | 15.0902i | −0.125408 | − | 0.484017i | ||||
\(973\) | 12.6491 | + | 12.6491i | 0.405512 | + | 0.405512i | ||||
\(974\) | 4.47214 | 0.143296 | ||||||||
\(975\) | 28.1706 | + | 13.4691i | 0.902181 | + | 0.431358i | ||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | 29.6985 | + | 29.6985i | 0.950139 | + | 0.950139i | 0.998815 | − | 0.0486759i | \(-0.0155002\pi\) |
−0.0486759 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.0000i | − | 0.511362i | ||||||
\(980\) | 9.19239 | + | 27.5772i | 0.293640 | + | 0.880920i | ||||
\(981\) | 7.07107 | − | 6.32456i | 0.225762 | − | 0.201928i | ||||
\(982\) | 15.8114 | − | 15.8114i | 0.504562 | − | 0.504562i | ||||
\(983\) | −18.3848 | + | 18.3848i | −0.586383 | + | 0.586383i | −0.936650 | − | 0.350267i | \(-0.886091\pi\) |
0.350267 | + | 0.936650i | \(0.386091\pi\) | |||||||
\(984\) | 8.94427 | + | 4.00000i | 0.285133 | + | 0.127515i | ||||
\(985\) | −2.00000 | + | 4.00000i | −0.0637253 | + | 0.127451i | ||||
\(986\) | −14.1421 | −0.450377 | ||||||||
\(987\) | 5.52786 | + | 14.4721i | 0.175954 | + | 0.460653i | ||||
\(988\) | 2.64911 | + | 22.6491i | 0.0842794 | + | 0.720564i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 9.97831 | + | 36.6119i | 0.317131 | + | 1.16360i | ||||
\(991\) | −28.0000 | −0.889449 | −0.444725 | − | 0.895667i | \(-0.646698\pi\) | ||||
−0.444725 | + | 0.895667i | \(0.646698\pi\) | |||||||
\(992\) | −2.23607 | + | 2.23607i | −0.0709952 | + | 0.0709952i | ||||
\(993\) | 20.4667 | − | 7.81758i | 0.649491 | − | 0.248083i | ||||
\(994\) | 6.32456 | 0.200603 | ||||||||
\(995\) | −42.4264 | + | 14.1421i | −1.34501 | + | 0.448336i | ||||
\(996\) | −2.82843 | + | 6.32456i | −0.0896221 | + | 0.200401i | ||||
\(997\) | 20.0000 | + | 20.0000i | 0.633406 | + | 0.633406i | 0.948921 | − | 0.315514i | \(-0.102177\pi\) |
−0.315514 | + | 0.948921i | \(0.602177\pi\) | |||||||
\(998\) | −8.94427 | − | 8.94427i | −0.283126 | − | 0.283126i | ||||
\(999\) | −22.1359 | + | 7.07107i | −0.700350 | + | 0.223719i |
(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 | 390.2.s.a.77.3 | yes | 8 | |
3.2 | odd | 2 | inner | 390.2.s.a.77.2 | yes | 8 | |
5.3 | odd | 4 | inner | 390.2.s.a.233.4 | yes | 8 | |
13.12 | even | 2 | inner | 390.2.s.a.77.1 | ✓ | 8 | |
15.8 | even | 4 | inner | 390.2.s.a.233.1 | yes | 8 | |
39.38 | odd | 2 | inner | 390.2.s.a.77.4 | yes | 8 | |
65.38 | odd | 4 | inner | 390.2.s.a.233.2 | yes | 8 | |
195.38 | even | 4 | inner | 390.2.s.a.233.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.s.a.77.1 | ✓ | 8 | 13.12 | even | 2 | inner | |
390.2.s.a.77.2 | yes | 8 | 3.2 | odd | 2 | inner | |
390.2.s.a.77.3 | yes | 8 | 1.1 | even | 1 | trivial | |
390.2.s.a.77.4 | yes | 8 | 39.38 | odd | 2 | inner | |
390.2.s.a.233.1 | yes | 8 | 15.8 | even | 4 | inner | |
390.2.s.a.233.2 | yes | 8 | 65.38 | odd | 4 | inner | |
390.2.s.a.233.3 | yes | 8 | 195.38 | even | 4 | inner | |
390.2.s.a.233.4 | yes | 8 | 5.3 | odd | 4 | inner |