Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 107.3 | ||
Character | \(\chi\) | \(=\) | 750.107 |
Dual form | 750.2.l.b.743.3 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.891007 | − | 0.453990i | −0.630037 | − | 0.321020i | ||||
\(3\) | −0.368756 | − | 1.69234i | −0.212901 | − | 0.977074i | ||||
\(4\) | 0.587785 | + | 0.809017i | 0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.439743 | + | 1.67530i | −0.179524 | + | 0.683938i | ||||
\(7\) | 2.72680 | + | 2.72680i | 1.03063 | + | 1.03063i | 0.999516 | + | 0.0311178i | \(0.00990669\pi\) |
0.0311178 | + | 0.999516i | \(0.490093\pi\) | |||||||
\(8\) | −0.156434 | − | 0.987688i | −0.0553079 | − | 0.349201i | ||||
\(9\) | −2.72804 | + | 1.24812i | −0.909346 | + | 0.416040i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.335657 | + | 0.109061i | −0.101204 | + | 0.0328833i | −0.359181 | − | 0.933268i | \(-0.616944\pi\) |
0.257977 | + | 0.966151i | \(0.416944\pi\) | |||||||
\(12\) | 1.15238 | − | 1.29306i | 0.332665 | − | 0.373275i | ||||
\(13\) | 1.12512 | + | 2.20817i | 0.312052 | + | 0.612437i | 0.992760 | − | 0.120119i | \(-0.0383275\pi\) |
−0.680707 | + | 0.732555i | \(0.738327\pi\) | |||||||
\(14\) | −1.19166 | − | 3.66754i | −0.318483 | − | 0.980191i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −3.49819 | + | 0.554059i | −0.848436 | + | 0.134379i | −0.565488 | − | 0.824756i | \(-0.691312\pi\) |
−0.282948 | + | 0.959135i | \(0.591312\pi\) | |||||||
\(18\) | 2.99734 | + | 0.126420i | 0.706479 | + | 0.0297975i | ||||
\(19\) | −3.84926 | + | 5.29805i | −0.883080 | + | 1.21546i | 0.0924780 | + | 0.995715i | \(0.470521\pi\) |
−0.975558 | + | 0.219741i | \(0.929479\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.60915 | − | 5.62020i | 0.787582 | − | 1.22643i | ||||
\(22\) | 0.348585 | + | 0.0552105i | 0.0743186 | + | 0.0117709i | ||||
\(23\) | −3.55825 | + | 6.98347i | −0.741947 | + | 1.45615i | 0.142638 | + | 0.989775i | \(0.454441\pi\) |
−0.884585 | + | 0.466378i | \(0.845559\pi\) | |||||||
\(24\) | −1.61382 | + | 0.628956i | −0.329420 | + | 0.128385i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 2.47829i | − | 0.486033i | ||||||
\(27\) | 3.11823 | + | 4.15652i | 0.600103 | + | 0.799923i | ||||
\(28\) | −0.603255 | + | 3.80880i | −0.114004 | + | 0.719796i | ||||
\(29\) | −5.05137 | + | 3.67003i | −0.938015 | + | 0.681508i | −0.947942 | − | 0.318443i | \(-0.896840\pi\) |
0.00992666 | + | 0.999951i | \(0.496840\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.39184 | − | 2.46432i | −0.609193 | − | 0.442604i | 0.239937 | − | 0.970788i | \(-0.422873\pi\) |
−0.849130 | + | 0.528184i | \(0.822873\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.308344 | + | 0.527829i | 0.0536759 | + | 0.0918832i | ||||
\(34\) | 3.36845 | + | 1.09448i | 0.577684 | + | 0.187701i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.61325 | − | 1.47340i | −0.435542 | − | 0.245567i | ||||
\(37\) | −4.33521 | + | 2.20890i | −0.712704 | + | 0.363141i | −0.772452 | − | 0.635073i | \(-0.780970\pi\) |
0.0597483 | + | 0.998213i | \(0.480970\pi\) | |||||||
\(38\) | 5.83498 | − | 2.97307i | 0.946558 | − | 0.482296i | ||||
\(39\) | 3.32209 | − | 2.71836i | 0.531960 | − | 0.435286i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.06531 | + | 2.62058i | 1.25959 | + | 0.409265i | 0.861348 | − | 0.508015i | \(-0.169621\pi\) |
0.398241 | + | 0.917281i | \(0.369621\pi\) | |||||||
\(42\) | −5.76730 | + | 3.36911i | −0.889913 | + | 0.519865i | ||||
\(43\) | 5.16349 | − | 5.16349i | 0.787425 | − | 0.787425i | −0.193647 | − | 0.981071i | \(-0.562031\pi\) |
0.981071 | + | 0.193647i | \(0.0620315\pi\) | |||||||
\(44\) | −0.285527 | − | 0.207447i | −0.0430448 | − | 0.0312738i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.34085 | − | 4.60690i | 0.934908 | − | 0.679250i | ||||
\(47\) | 0.668895 | − | 4.22323i | 0.0975683 | − | 0.616022i | −0.889649 | − | 0.456644i | \(-0.849051\pi\) |
0.987218 | − | 0.159378i | \(-0.0509488\pi\) | |||||||
\(48\) | 1.72346 | + | 0.172255i | 0.248761 | + | 0.0248628i | ||||
\(49\) | 7.87088i | 1.12441i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22763 | + | 5.71582i | 0.311931 | + | 0.800375i | ||||
\(52\) | −1.12512 | + | 2.20817i | −0.156026 | + | 0.306218i | ||||
\(53\) | 4.34698 | + | 0.688494i | 0.597103 | + | 0.0945719i | 0.447668 | − | 0.894200i | \(-0.352255\pi\) |
0.149435 | + | 0.988772i | \(0.452255\pi\) | |||||||
\(54\) | −0.891339 | − | 5.11913i | −0.121296 | − | 0.696626i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.26666 | − | 3.11979i | 0.302896 | − | 0.416900i | ||||
\(57\) | 10.3855 | + | 4.56057i | 1.37560 | + | 0.604063i | ||||
\(58\) | 6.16696 | − | 0.976751i | 0.809762 | − | 0.128254i | ||||
\(59\) | 0.713107 | − | 2.19472i | 0.0928386 | − | 0.285728i | −0.893846 | − | 0.448375i | \(-0.852003\pi\) |
0.986684 | + | 0.162647i | \(0.0520031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0451729 | + | 0.139028i | 0.00578380 | + | 0.0178007i | 0.953907 | − | 0.300103i | \(-0.0970211\pi\) |
−0.948123 | + | 0.317904i | \(0.897021\pi\) | |||||||
\(62\) | 1.90338 | + | 3.73559i | 0.241729 | + | 0.474420i | ||||
\(63\) | −10.8422 | − | 4.03544i | −1.36599 | − | 0.508418i | ||||
\(64\) | −0.951057 | + | 0.309017i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0351078 | − | 0.610284i | −0.00432147 | − | 0.0751208i | ||||
\(67\) | −1.18445 | − | 7.47829i | −0.144703 | − | 0.913619i | −0.948053 | − | 0.318112i | \(-0.896951\pi\) |
0.803350 | − | 0.595507i | \(-0.203049\pi\) | |||||||
\(68\) | −2.50443 | − | 2.50443i | −0.303707 | − | 0.303707i | ||||
\(69\) | 13.1305 | + | 3.44659i | 1.58073 | + | 0.414920i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.62303 | + | 4.98667i | 0.429974 | + | 0.591809i | 0.967947 | − | 0.251153i | \(-0.0808098\pi\) |
−0.537973 | + | 0.842962i | \(0.680810\pi\) | |||||||
\(72\) | 1.65951 | + | 2.49920i | 0.195576 | + | 0.294534i | ||||
\(73\) | 9.30362 | + | 4.74043i | 1.08891 | + | 0.554825i | 0.903827 | − | 0.427898i | \(-0.140746\pi\) |
0.185079 | + | 0.982724i | \(0.440746\pi\) | |||||||
\(74\) | 4.86552 | 0.565605 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.54875 | −0.751193 | ||||||||
\(77\) | −1.21266 | − | 0.617880i | −0.138195 | − | 0.0704139i | ||||
\(78\) | −4.19411 | + | 0.913883i | −0.474890 | + | 0.103477i | ||||
\(79\) | 0.803169 | + | 1.10547i | 0.0903636 | + | 0.124375i | 0.851805 | − | 0.523859i | \(-0.175508\pi\) |
−0.761442 | + | 0.648234i | \(0.775508\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.88439 | − | 6.80984i | 0.653821 | − | 0.756649i | ||||
\(82\) | −5.99652 | − | 5.99652i | −0.662205 | − | 0.662205i | ||||
\(83\) | −0.915181 | − | 5.77823i | −0.100454 | − | 0.634243i | −0.985621 | − | 0.168969i | \(-0.945956\pi\) |
0.885167 | − | 0.465273i | \(-0.154044\pi\) | |||||||
\(84\) | 6.66824 | − | 0.383604i | 0.727565 | − | 0.0418546i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.94488 | + | 2.25653i | −0.748886 | + | 0.243328i | ||||
\(87\) | 8.07367 | + | 7.19529i | 0.865588 | + | 0.771416i | ||||
\(88\) | 0.160227 | + | 0.314463i | 0.0170803 | + | 0.0335219i | ||||
\(89\) | 0.633239 | + | 1.94891i | 0.0671232 | + | 0.206584i | 0.978992 | − | 0.203897i | \(-0.0653608\pi\) |
−0.911869 | + | 0.410481i | \(0.865361\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.95327 | + | 9.08922i | −0.309587 | + | 0.952809i | ||||
\(92\) | −7.74123 | + | 1.22609i | −0.807079 | + | 0.127829i | ||||
\(93\) | −2.91971 | + | 6.64888i | −0.302759 | + | 0.689457i | ||||
\(94\) | −2.51330 | + | 3.45926i | −0.259227 | + | 0.356795i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.45742 | − | 0.935916i | −0.148747 | − | 0.0955216i | ||||
\(97\) | −6.93926 | − | 1.09907i | −0.704575 | − | 0.111594i | −0.206142 | − | 0.978522i | \(-0.566091\pi\) |
−0.498433 | + | 0.866928i | \(0.666091\pi\) | |||||||
\(98\) | 3.57330 | − | 7.01300i | 0.360958 | − | 0.708420i | ||||
\(99\) | 0.779562 | − | 0.716464i | 0.0783490 | − | 0.0720073i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.58679i | 0.953921i | 0.878925 | + | 0.476961i | \(0.158262\pi\) | ||||
−0.878925 | + | 0.476961i | \(0.841738\pi\) | |||||||
\(102\) | 0.610091 | − | 6.10416i | 0.0604081 | − | 0.604402i | ||||
\(103\) | −1.04075 | + | 6.57102i | −0.102548 | + | 0.647462i | 0.881853 | + | 0.471524i | \(0.156296\pi\) |
−0.984401 | + | 0.175938i | \(0.943704\pi\) | |||||||
\(104\) | 2.00498 | − | 1.45670i | 0.196604 | − | 0.142841i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.56062 | − | 2.58694i | −0.345838 | − | 0.251266i | ||||
\(107\) | 10.4337 | − | 10.4337i | 1.00866 | − | 1.00866i | 0.00870186 | − | 0.999962i | \(-0.497230\pi\) |
0.999962 | − | 0.00870186i | \(-0.00276992\pi\) | |||||||
\(108\) | −1.52985 | + | 4.96584i | −0.147210 | + | 0.477838i | ||||
\(109\) | −10.5722 | − | 3.43511i | −1.01263 | − | 0.329024i | −0.244729 | − | 0.969592i | \(-0.578699\pi\) |
−0.767902 | + | 0.640568i | \(0.778699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.33685 | + | 6.52211i | 0.506551 | + | 0.619051i | ||||
\(112\) | −3.43597 | + | 1.75071i | −0.324668 | + | 0.165427i | ||||
\(113\) | 1.56816 | − | 0.799015i | 0.147520 | − | 0.0751650i | −0.378672 | − | 0.925531i | \(-0.623619\pi\) |
0.526192 | + | 0.850366i | \(0.323619\pi\) | |||||||
\(114\) | −7.18313 | − | 8.77844i | −0.672762 | − | 0.822176i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.93824 | − | 1.92945i | −0.551352 | − | 0.179145i | ||||
\(117\) | −5.82544 | − | 4.61969i | −0.538562 | − | 0.427091i | ||||
\(118\) | −1.63176 | + | 1.63176i | −0.150216 | + | 0.150216i | ||||
\(119\) | −11.0497 | − | 8.02806i | −1.01292 | − | 0.735931i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.79842 | + | 6.39242i | −0.799856 | + | 0.581129i | ||||
\(122\) | 0.0228680 | − | 0.144383i | 0.00207037 | − | 0.0130718i | ||||
\(123\) | 1.46078 | − | 14.6156i | 0.131714 | − | 1.31784i | ||||
\(124\) | − | 4.19255i | − | 0.376502i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.82841 | + | 8.51786i | 0.697410 | + | 0.758831i | ||||
\(127\) | −2.44874 | + | 4.80592i | −0.217290 | + | 0.426457i | −0.973762 | − | 0.227571i | \(-0.926922\pi\) |
0.756471 | + | 0.654027i | \(0.226922\pi\) | |||||||
\(128\) | 0.987688 | + | 0.156434i | 0.0873001 | + | 0.0138270i | ||||
\(129\) | −10.6425 | − | 6.83432i | −0.937016 | − | 0.601728i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2354 | − | 14.0878i | 0.894273 | − | 1.23086i | −0.0779865 | − | 0.996954i | \(-0.524849\pi\) |
0.972259 | − | 0.233906i | \(-0.0751509\pi\) | |||||||
\(132\) | −0.245782 | + | 0.559706i | −0.0213926 | + | 0.0487161i | ||||
\(133\) | −24.9429 | + | 3.95056i | −2.16282 | + | 0.342557i | ||||
\(134\) | −2.33973 | + | 7.20094i | −0.202122 | + | 0.622066i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.09448 | + | 3.36845i | 0.0938505 | + | 0.288842i | ||||
\(137\) | 8.13848 | + | 15.9727i | 0.695317 | + | 1.36464i | 0.920663 | + | 0.390358i | \(0.127649\pi\) |
−0.225346 | + | 0.974279i | \(0.572351\pi\) | |||||||
\(138\) | −10.1347 | − | 9.03207i | −0.862721 | − | 0.768861i | ||||
\(139\) | 17.1405 | − | 5.56927i | 1.45383 | − | 0.472379i | 0.527654 | − | 0.849459i | \(-0.323072\pi\) |
0.926181 | + | 0.377080i | \(0.123072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.39381 | + | 0.425343i | −0.622671 | + | 0.0358204i | ||||
\(142\) | −0.964240 | − | 6.08797i | −0.0809172 | − | 0.510891i | ||||
\(143\) | −0.618480 | − | 0.618480i | −0.0517199 | − | 0.0517199i | ||||
\(144\) | −0.344023 | − | 2.98021i | −0.0286686 | − | 0.248351i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.13747 | − | 8.44751i | −0.507941 | − | 0.699121i | ||||
\(147\) | 13.3202 | − | 2.90243i | 1.09863 | − | 0.239388i | ||||
\(148\) | −4.33521 | − | 2.20890i | −0.356352 | − | 0.181570i | ||||
\(149\) | 4.64891 | 0.380854 | 0.190427 | − | 0.981701i | \(-0.439013\pi\) | ||||
0.190427 | + | 0.981701i | \(0.439013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6548 | −1.19259 | −0.596295 | − | 0.802765i | \(-0.703361\pi\) | ||||
−0.596295 | + | 0.802765i | \(0.703361\pi\) | |||||||
\(152\) | 5.83498 | + | 2.97307i | 0.473279 | + | 0.241148i | ||||
\(153\) | 8.85167 | − | 5.87766i | 0.715615 | − | 0.475181i | ||||
\(154\) | 0.799974 | + | 1.10107i | 0.0644637 | + | 0.0887267i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.15188 | + | 1.08981i | 0.332416 | + | 0.0872547i | ||||
\(157\) | −3.17235 | − | 3.17235i | −0.253181 | − | 0.253181i | 0.569093 | − | 0.822273i | \(-0.307295\pi\) |
−0.822273 | + | 0.569093i | \(0.807295\pi\) | |||||||
\(158\) | −0.213757 | − | 1.34961i | −0.0170056 | − | 0.107369i | ||||
\(159\) | −0.437806 | − | 7.61046i | −0.0347203 | − | 0.603548i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.7452 | + | 9.33987i | −2.26544 | + | 0.736085i | ||||
\(162\) | −8.33463 | + | 3.39616i | −0.654831 | + | 0.266827i | ||||
\(163\) | 4.91227 | + | 9.64088i | 0.384759 | + | 0.755132i | 0.999434 | − | 0.0336487i | \(-0.0107127\pi\) |
−0.614675 | + | 0.788781i | \(0.710713\pi\) | |||||||
\(164\) | 2.62058 | + | 8.06531i | 0.204633 | + | 0.629795i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.80783 | + | 5.56392i | −0.140315 | + | 0.431844i | ||||
\(167\) | −16.5871 | + | 2.62714i | −1.28355 | + | 0.203295i | −0.760686 | − | 0.649120i | \(-0.775137\pi\) |
−0.522866 | + | 0.852415i | \(0.675137\pi\) | |||||||
\(168\) | −6.11560 | − | 2.68553i | −0.471829 | − | 0.207193i | ||||
\(169\) | 4.03108 | − | 5.54830i | 0.310083 | − | 0.426793i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.88832 | − | 19.2576i | 0.297347 | − | 1.47267i | ||||
\(172\) | 7.21237 | + | 1.14233i | 0.549938 | + | 0.0871017i | ||||
\(173\) | −7.90821 | + | 15.5207i | −0.601250 | + | 1.18002i | 0.367043 | + | 0.930204i | \(0.380370\pi\) |
−0.968293 | + | 0.249816i | \(0.919630\pi\) | |||||||
\(174\) | −3.92710 | − | 10.0764i | −0.297713 | − | 0.763892i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.352930i | − | 0.0266031i | ||||||
\(177\) | −3.97717 | − | 0.397506i | −0.298943 | − | 0.0298784i | ||||
\(178\) | 0.320566 | − | 2.02397i | 0.0240274 | − | 0.151703i | ||||
\(179\) | 5.94519 | − | 4.31943i | 0.444364 | − | 0.322849i | −0.343002 | − | 0.939334i | \(-0.611444\pi\) |
0.787367 | + | 0.616485i | \(0.211444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.543117 | − | 0.394597i | −0.0403695 | − | 0.0293302i | 0.567418 | − | 0.823430i | \(-0.307943\pi\) |
−0.607787 | + | 0.794100i | \(0.707943\pi\) | |||||||
\(182\) | 6.75780 | − | 6.75780i | 0.500922 | − | 0.500922i | ||||
\(183\) | 0.218625 | − | 0.127715i | 0.0161612 | − | 0.00944098i | ||||
\(184\) | 7.45412 | + | 2.42199i | 0.549525 | + | 0.178552i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.62001 | − | 4.59868i | 0.412079 | − | 0.337192i | ||||
\(187\) | 1.11376 | − | 0.567491i | 0.0814465 | − | 0.0414991i | ||||
\(188\) | 3.80983 | − | 1.94121i | 0.277861 | − | 0.141577i | ||||
\(189\) | −2.83122 | + | 19.8368i | −0.205941 | + | 1.44291i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4008 | + | 4.35419i | 0.969650 | + | 0.315058i | 0.750675 | − | 0.660672i | \(-0.229729\pi\) |
0.218975 | + | 0.975730i | \(0.429729\pi\) | |||||||
\(192\) | 0.873670 | + | 1.49556i | 0.0630517 | + | 0.107933i | ||||
\(193\) | 2.89340 | − | 2.89340i | 0.208271 | − | 0.208271i | −0.595261 | − | 0.803532i | \(-0.702951\pi\) |
0.803532 | + | 0.595261i | \(0.202951\pi\) | |||||||
\(194\) | 5.68396 | + | 4.12964i | 0.408085 | + | 0.296491i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.36767 | + | 4.62638i | −0.454834 | + | 0.330456i | ||||
\(197\) | 3.55739 | − | 22.4605i | 0.253454 | − | 1.60024i | −0.452353 | − | 0.891839i | \(-0.649415\pi\) |
0.705806 | − | 0.708405i | \(-0.250585\pi\) | |||||||
\(198\) | −1.01986 | + | 0.284460i | −0.0724785 | + | 0.0202157i | ||||
\(199\) | − | 6.31867i | − | 0.447919i | −0.974598 | − | 0.223959i | \(-0.928102\pi\) | ||
0.974598 | − | 0.223959i | \(-0.0718983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.2191 | + | 4.76215i | −0.861866 | + | 0.335896i | ||||
\(202\) | 4.35231 | − | 8.54189i | 0.306228 | − | 0.601006i | ||||
\(203\) | −23.7815 | − | 3.76662i | −1.66914 | − | 0.264365i | ||||
\(204\) | −3.31483 | + | 5.16187i | −0.232084 | + | 0.361403i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.91049 | − | 5.38233i | 0.272457 | − | 0.375005i | ||||
\(207\) | 0.990845 | − | 23.4923i | 0.0688685 | − | 1.63283i | ||||
\(208\) | −2.44778 | + | 0.387690i | −0.169723 | + | 0.0268815i | ||||
\(209\) | 0.714216 | − | 2.19813i | 0.0494033 | − | 0.152048i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.28435 | − | 3.95283i | −0.0884185 | − | 0.272124i | 0.897064 | − | 0.441900i | \(-0.145696\pi\) |
−0.985483 | + | 0.169776i | \(0.945696\pi\) | |||||||
\(212\) | 1.99809 | + | 3.92147i | 0.137229 | + | 0.269327i | ||||
\(213\) | 7.10313 | − | 7.97026i | 0.486699 | − | 0.546113i | ||||
\(214\) | −14.0333 | + | 4.55969i | −0.959296 | + | 0.311694i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.61755 | − | 3.73006i | 0.246143 | − | 0.253798i | ||||
\(217\) | −2.52917 | − | 15.9686i | −0.171691 | − | 1.08402i | ||||
\(218\) | 7.86037 | + | 7.86037i | 0.532371 | + | 0.532371i | ||||
\(219\) | 4.59166 | − | 17.4930i | 0.310276 | − | 1.18206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.15934 | − | 7.10123i | −0.347055 | − | 0.477680i | ||||
\(222\) | −1.79419 | − | 8.23412i | −0.120418 | − | 0.552638i | ||||
\(223\) | −13.6942 | − | 6.97753i | −0.917030 | − | 0.467250i | −0.0692509 | − | 0.997599i | \(-0.522061\pi\) |
−0.847779 | + | 0.530349i | \(0.822061\pi\) | |||||||
\(224\) | 3.85628 | 0.257658 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.75998 | −0.117072 | ||||||||
\(227\) | −12.4969 | − | 6.36747i | −0.829445 | − | 0.422624i | −0.0129084 | − | 0.999917i | \(-0.504109\pi\) |
−0.816537 | + | 0.577293i | \(0.804109\pi\) | |||||||
\(228\) | 2.41489 | + | 11.0827i | 0.159930 | + | 0.733971i | ||||
\(229\) | 10.1878 | + | 14.0224i | 0.673232 | + | 0.926624i | 0.999828 | − | 0.0185396i | \(-0.00590167\pi\) |
−0.326596 | + | 0.945164i | \(0.605902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.598489 | + | 2.28008i | −0.0393777 | + | 0.150018i | ||||
\(232\) | 4.41506 | + | 4.41506i | 0.289863 | + | 0.289863i | ||||
\(233\) | 0.384884 | + | 2.43006i | 0.0252146 | + | 0.159199i | 0.997083 | − | 0.0763263i | \(-0.0243191\pi\) |
−0.971868 | + | 0.235525i | \(0.924319\pi\) | |||||||
\(234\) | 3.09320 | + | 6.76087i | 0.202209 | + | 0.441972i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.19472 | − | 0.713107i | 0.142864 | − | 0.0464193i | ||||
\(237\) | 1.57466 | − | 1.76688i | 0.102285 | − | 0.114771i | ||||
\(238\) | 6.20067 | + | 12.1695i | 0.401930 | + | 0.788831i | ||||
\(239\) | 0.751883 | + | 2.31406i | 0.0486352 | + | 0.149684i | 0.972425 | − | 0.233217i | \(-0.0749252\pi\) |
−0.923790 | + | 0.382901i | \(0.874925\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500207 | − | 1.53948i | 0.0322212 | − | 0.0991666i | −0.933653 | − | 0.358180i | \(-0.883397\pi\) |
0.965874 | + | 0.259013i | \(0.0833974\pi\) | |||||||
\(242\) | 10.7415 | − | 1.70129i | 0.690493 | − | 0.109363i | ||||
\(243\) | −13.6945 | − | 7.44723i | −0.878501 | − | 0.477740i | ||||
\(244\) | −0.0859239 | + | 0.118264i | −0.00550072 | + | 0.00757109i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.93691 | + | 12.3594i | −0.506039 | + | 0.788008i | ||||
\(247\) | −16.0299 | − | 2.53888i | −1.01996 | − | 0.161545i | ||||
\(248\) | −1.90338 | + | 3.73559i | −0.120865 | + | 0.237210i | ||||
\(249\) | −9.44125 | + | 3.67955i | −0.598315 | + | 0.233182i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 24.7263i | − | 1.56071i | −0.625335 | − | 0.780357i | \(-0.715038\pi\) | ||
0.625335 | − | 0.780357i | \(-0.284962\pi\) | |||||||
\(252\) | −3.10814 | − | 11.1435i | −0.195794 | − | 0.701974i | ||||
\(253\) | 0.432724 | − | 2.73211i | 0.0272052 | − | 0.171767i | ||||
\(254\) | 4.36369 | − | 3.17040i | 0.273802 | − | 0.198929i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −20.2470 | + | 20.2470i | −1.26297 | + | 1.26297i | −0.313326 | + | 0.949646i | \(0.601443\pi\) |
−0.949646 | + | 0.313326i | \(0.898557\pi\) | |||||||
\(258\) | 6.37978 | + | 10.9210i | 0.397188 | + | 0.679912i | ||||
\(259\) | −17.8445 | − | 5.79802i | −1.10880 | − | 0.360272i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.19968 | − | 16.3167i | 0.569446 | − | 1.00998i | ||||
\(262\) | −15.5156 | + | 7.90558i | −0.958555 | + | 0.488408i | ||||
\(263\) | −2.68232 | + | 1.36671i | −0.165399 | + | 0.0842750i | −0.534730 | − | 0.845023i | \(-0.679587\pi\) |
0.369331 | + | 0.929298i | \(0.379587\pi\) | |||||||
\(264\) | 0.473094 | − | 0.387119i | 0.0291169 | − | 0.0238255i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 24.0178 | + | 7.80385i | 1.47262 | + | 0.478485i | ||||
\(267\) | 3.06471 | − | 1.79033i | 0.187557 | − | 0.109566i | ||||
\(268\) | 5.35387 | − | 5.35387i | 0.327039 | − | 0.327039i | ||||
\(269\) | 10.4918 | + | 7.62274i | 0.639697 | + | 0.464767i | 0.859746 | − | 0.510722i | \(-0.170622\pi\) |
−0.220049 | + | 0.975489i | \(0.570622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7784 | − | 10.0106i | 0.836981 | − | 0.608102i | −0.0845447 | − | 0.996420i | \(-0.526944\pi\) |
0.921526 | + | 0.388317i | \(0.126944\pi\) | |||||||
\(272\) | 0.554059 | − | 3.49819i | 0.0335948 | − | 0.212109i | ||||
\(273\) | 16.4711 | + | 1.64623i | 0.996876 | + | 0.0996347i | ||||
\(274\) | − | 17.9265i | − | 1.08298i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.92959 | + | 12.6487i | 0.296726 | + | 0.761361i | ||||
\(277\) | 4.82425 | − | 9.46812i | 0.289861 | − | 0.568884i | −0.699454 | − | 0.714677i | \(-0.746573\pi\) |
0.989315 | + | 0.145793i | \(0.0465735\pi\) | |||||||
\(278\) | −17.8007 | − | 2.81935i | −1.06761 | − | 0.169093i | ||||
\(279\) | 12.3288 | + | 2.48932i | 0.738108 | + | 0.149032i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4932 | + | 22.7009i | −0.983902 | + | 1.35422i | −0.0492011 | + | 0.998789i | \(0.515668\pi\) |
−0.934701 | + | 0.355436i | \(0.884332\pi\) | |||||||
\(282\) | 6.78104 | + | 2.97774i | 0.403805 | + | 0.177322i | ||||
\(283\) | 25.3567 | − | 4.01611i | 1.50730 | − | 0.238733i | 0.652539 | − | 0.757755i | \(-0.273704\pi\) |
0.854761 | + | 0.519022i | \(0.173704\pi\) | |||||||
\(284\) | −1.90474 | + | 5.86218i | −0.113025 | + | 0.347856i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.270286 | + | 0.831854i | 0.0159823 | + | 0.0491886i | ||||
\(287\) | 14.8467 | + | 29.1383i | 0.876372 | + | 1.71998i | ||||
\(288\) | −1.04646 | + | 2.81157i | −0.0616632 | + | 0.165673i | ||||
\(289\) | −4.23760 | + | 1.37688i | −0.249271 | + | 0.0809930i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.698888 | + | 12.1489i | 0.0409696 | + | 0.712181i | ||||
\(292\) | 1.63344 | + | 10.3131i | 0.0955899 | + | 0.603531i | ||||
\(293\) | 24.1559 | + | 24.1559i | 1.41120 | + | 1.41120i | 0.751709 | + | 0.659495i | \(0.229230\pi\) |
0.659495 | + | 0.751709i | \(0.270770\pi\) | |||||||
\(294\) | −13.1861 | − | 3.46116i | −0.769027 | − | 0.201859i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.85988 | + | 3.93629i | 0.166227 | + | 0.228792i | ||||
\(297\) | −1.49997 | − | 1.05509i | −0.0870370 | − | 0.0612223i | ||||
\(298\) | −4.14221 | − | 2.11056i | −0.239952 | − | 0.122262i | ||||
\(299\) | −19.4242 | −1.12333 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.1596 | 1.62309 | ||||||||
\(302\) | 13.0575 | + | 6.65314i | 0.751376 | + | 0.382845i | ||||
\(303\) | 16.2241 | − | 3.53518i | 0.932051 | − | 0.203091i | ||||
\(304\) | −3.84926 | − | 5.29805i | −0.220770 | − | 0.303864i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.5553 | + | 1.21846i | −0.603406 | + | 0.0696547i | ||||
\(307\) | 12.8970 | + | 12.8970i | 0.736071 | + | 0.736071i | 0.971815 | − | 0.235744i | \(-0.0757527\pi\) |
−0.235744 | + | 0.971815i | \(0.575753\pi\) | |||||||
\(308\) | −0.212907 | − | 1.34424i | −0.0121315 | − | 0.0765952i | ||||
\(309\) | 11.5042 | − | 0.661801i | 0.654451 | − | 0.0376485i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4255 | + | 5.01205i | −0.874699 | + | 0.284207i | −0.711755 | − | 0.702428i | \(-0.752099\pi\) |
−0.162945 | + | 0.986635i | \(0.552099\pi\) | |||||||
\(312\) | −3.20458 | − | 2.85594i | −0.181424 | − | 0.161686i | ||||
\(313\) | −2.45198 | − | 4.81228i | −0.138594 | − | 0.272006i | 0.811269 | − | 0.584674i | \(-0.198777\pi\) |
−0.949863 | + | 0.312668i | \(0.898777\pi\) | |||||||
\(314\) | 1.38637 | + | 4.26680i | 0.0782372 | + | 0.240789i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.422251 | + | 1.29956i | −0.0237535 | + | 0.0731057i | ||||
\(317\) | −8.47316 | + | 1.34202i | −0.475900 | + | 0.0753752i | −0.389777 | − | 0.920909i | \(-0.627448\pi\) |
−0.0861233 | + | 0.996284i | \(0.527448\pi\) | |||||||
\(318\) | −3.06499 | + | 6.97973i | −0.171876 | + | 0.391404i | ||||
\(319\) | 1.29527 | − | 1.78278i | 0.0725210 | − | 0.0998166i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.5049 | − | 13.8099i | −1.20028 | − | 0.770793i | ||||
\(322\) | 29.8523 | + | 4.72815i | 1.66361 | + | 0.263489i | ||||
\(323\) | 10.5300 | − | 20.6663i | 0.585905 | − | 1.14990i | ||||
\(324\) | 8.96804 | + | 0.757846i | 0.498224 | + | 0.0421025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 10.8202i | − | 0.599276i | ||||||
\(327\) | −1.91483 | + | 19.1584i | −0.105890 | + | 1.05946i | ||||
\(328\) | 1.32662 | − | 8.37596i | 0.0732504 | − | 0.462485i | ||||
\(329\) | 13.3399 | − | 9.69197i | 0.735450 | − | 0.534336i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9895 | + | 16.7029i | 1.26362 | + | 0.918073i | 0.998929 | − | 0.0462607i | \(-0.0147305\pi\) |
0.264690 | + | 0.964334i | \(0.414731\pi\) | |||||||
\(332\) | 4.13675 | − | 4.13675i | 0.227034 | − | 0.227034i | ||||
\(333\) | 9.06965 | − | 11.4368i | 0.497014 | − | 0.626734i | ||||
\(334\) | 15.9719 | + | 5.18960i | 0.873946 | + | 0.283962i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.22984 | + | 5.16925i | 0.230757 | + | 0.282005i | ||||
\(337\) | 4.22871 | − | 2.15464i | 0.230353 | − | 0.117371i | −0.335005 | − | 0.942216i | \(-0.608738\pi\) |
0.565358 | + | 0.824846i | \(0.308738\pi\) | |||||||
\(338\) | −6.11059 | + | 3.11350i | −0.332372 | + | 0.169352i | ||||
\(339\) | −1.93047 | − | 2.35921i | −0.104849 | − | 0.128135i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.40726 | + | 0.457245i | 0.0762072 | + | 0.0247612i | ||||
\(342\) | −12.2073 | + | 15.3934i | −0.660095 | + | 0.832380i | ||||
\(343\) | −2.37470 | + | 2.37470i | −0.128222 | + | 0.128222i | ||||
\(344\) | −5.90767 | − | 4.29217i | −0.318520 | − | 0.231418i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0925 | − | 10.2388i | 0.757620 | − | 0.550443i | ||||
\(347\) | −1.25574 | + | 7.92843i | −0.0674116 | + | 0.425620i | 0.930784 | + | 0.365570i | \(0.119126\pi\) |
−0.998195 | + | 0.0600500i | \(0.980874\pi\) | |||||||
\(348\) | −1.07553 | + | 10.7610i | −0.0576545 | + | 0.576851i | ||||
\(349\) | 18.9234i | 1.01295i | 0.862256 | + | 0.506474i | \(0.169051\pi\) | ||||
−0.862256 | + | 0.506474i | \(0.830949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.66994 | + | 11.5622i | −0.302639 | + | 0.617143i | ||||
\(352\) | −0.160227 | + | 0.314463i | −0.00854013 | + | 0.0167609i | ||||
\(353\) | 4.66620 | + | 0.739053i | 0.248357 | + | 0.0393358i | 0.279371 | − | 0.960183i | \(-0.409874\pi\) |
−0.0310149 | + | 0.999519i | \(0.509874\pi\) | |||||||
\(354\) | 3.36322 | + | 2.15978i | 0.178753 | + | 0.114791i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.20449 | + | 1.65784i | −0.0638379 | + | 0.0878654i | ||||
\(357\) | −9.51159 | + | 21.6602i | −0.503406 | + | 1.14638i | ||||
\(358\) | −7.25818 | + | 1.14958i | −0.383607 | + | 0.0607573i | ||||
\(359\) | 4.67561 | − | 14.3900i | 0.246769 | − | 0.759478i | −0.748571 | − | 0.663054i | \(-0.769260\pi\) |
0.995340 | − | 0.0964232i | \(-0.0307402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.38121 | − | 22.7170i | −0.388485 | − | 1.19563i | ||||
\(362\) | 0.304777 | + | 0.598158i | 0.0160187 | + | 0.0314385i | ||||
\(363\) | 14.0626 | + | 12.5327i | 0.738097 | + | 0.657795i | ||||
\(364\) | −9.08922 | + | 2.95327i | −0.476405 | + | 0.154793i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.252778 | + | 0.0145415i | −0.0132129 | + | 0.000760098i | ||||
\(367\) | 5.73021 | + | 36.1791i | 0.299114 | + | 1.88853i | 0.439193 | + | 0.898393i | \(0.355265\pi\) |
−0.140078 | + | 0.990140i | \(0.544735\pi\) | |||||||
\(368\) | −5.54211 | − | 5.54211i | −0.288902 | − | 0.288902i | ||||
\(369\) | −25.2733 | + | 2.91744i | −1.31567 | + | 0.151876i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.97595 | + | 13.7307i | 0.517926 | + | 0.712864i | ||||
\(372\) | −7.09522 | + | 1.54603i | −0.367870 | + | 0.0801577i | ||||
\(373\) | 1.97517 | + | 1.00640i | 0.102270 | + | 0.0521093i | 0.504377 | − | 0.863483i | \(-0.331722\pi\) |
−0.402107 | + | 0.915593i | \(0.631722\pi\) | |||||||
\(374\) | −1.25001 | −0.0646363 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.27588 | −0.220512 | ||||||||
\(377\) | −13.7875 | − | 7.02506i | −0.710090 | − | 0.361809i | ||||
\(378\) | 11.5283 | − | 16.3894i | 0.592954 | − | 0.842977i | ||||
\(379\) | 4.15559 | + | 5.71968i | 0.213458 | + | 0.293800i | 0.902297 | − | 0.431114i | \(-0.141879\pi\) |
−0.688839 | + | 0.724914i | \(0.741879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.03625 | + | 2.37189i | 0.462941 | + | 0.121516i | ||||
\(382\) | −9.96347 | − | 9.96347i | −0.509775 | − | 0.509775i | ||||
\(383\) | −2.17700 | − | 13.7450i | −0.111240 | − | 0.702339i | −0.978771 | − | 0.204957i | \(-0.934295\pi\) |
0.867532 | − | 0.497382i | \(-0.165705\pi\) | |||||||
\(384\) | −0.0994751 | − | 1.72919i | −0.00507632 | − | 0.0882425i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.89161 | + | 1.26446i | −0.198078 | + | 0.0643593i | ||||
\(387\) | −7.64154 | + | 20.5309i | −0.388441 | + | 1.04364i | ||||
\(388\) | −3.18963 | − | 6.26000i | −0.161929 | − | 0.317803i | ||||
\(389\) | −4.65972 | − | 14.3411i | −0.236257 | − | 0.727125i | −0.996952 | − | 0.0780155i | \(-0.975142\pi\) |
0.760695 | − | 0.649110i | \(-0.224858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.57820 | − | 26.4010i | 0.433818 | − | 1.33515i | ||||
\(392\) | 7.77397 | − | 1.23128i | 0.392645 | − | 0.0621888i | ||||
\(393\) | −27.6158 | − | 12.1268i | −1.39303 | − | 0.611719i | ||||
\(394\) | −13.3665 | + | 18.3974i | −0.673395 | + | 0.926849i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.03785 | + | 0.209552i | 0.0521538 | + | 0.0105304i | ||||
\(397\) | 13.6256 | + | 2.15808i | 0.683849 | + | 0.108311i | 0.488686 | − | 0.872460i | \(-0.337476\pi\) |
0.195163 | + | 0.980771i | \(0.437476\pi\) | |||||||
\(398\) | −2.86862 | + | 5.62998i | −0.143791 | + | 0.282205i | ||||
\(399\) | 15.8835 | + | 40.7551i | 0.795171 | + | 2.04031i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8196i | 0.789991i | 0.918683 | + | 0.394995i | \(0.129254\pi\) | ||||
−0.918683 | + | 0.394995i | \(0.870746\pi\) | |||||||
\(402\) | 13.0492 | + | 1.30423i | 0.650836 | + | 0.0650490i | ||||
\(403\) | 1.62541 | − | 10.2624i | 0.0809674 | − | 0.511208i | ||||
\(404\) | −7.75588 | + | 5.63497i | −0.385869 | + | 0.280350i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.4795 | + | 14.1527i | 0.966750 | + | 0.702385i | ||||
\(407\) | 1.21424 | − | 1.21424i | 0.0601875 | − | 0.0601875i | ||||
\(408\) | 5.29697 | − | 3.09436i | 0.262239 | − | 0.153194i | ||||
\(409\) | −5.65867 | − | 1.83861i | −0.279803 | − | 0.0909136i | 0.165754 | − | 0.986167i | \(-0.446994\pi\) |
−0.445557 | + | 0.895254i | \(0.646994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0301 | − | 19.6631i | 1.18532 | − | 0.969909i | ||||
\(412\) | −5.92780 | + | 3.02037i | −0.292042 | + | 0.148803i | ||||
\(413\) | 7.92905 | − | 4.04005i | 0.390163 | − | 0.198798i | ||||
\(414\) | −11.5481 | + | 20.4820i | −0.567559 | + | 1.00663i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.35699 | + | 0.765834i | 0.115561 | + | 0.0375481i | ||||
\(417\) | −15.7457 | − | 26.9538i | −0.771073 | − | 1.31993i | ||||
\(418\) | −1.63430 | + | 1.63430i | −0.0799363 | + | 0.0799363i | ||||
\(419\) | −3.49605 | − | 2.54003i | −0.170793 | − | 0.124088i | 0.499105 | − | 0.866542i | \(-0.333662\pi\) |
−0.669898 | + | 0.742453i | \(0.733662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2471 | + | 14.7103i | −0.986781 | + | 0.716939i | −0.959214 | − | 0.282681i | \(-0.908776\pi\) |
−0.0275674 | + | 0.999620i | \(0.508776\pi\) | |||||||
\(422\) | −0.650182 | + | 4.10508i | −0.0316503 | + | 0.199832i | ||||
\(423\) | 3.44634 | + | 12.3560i | 0.167567 | + | 0.600770i | ||||
\(424\) | − | 4.40116i | − | 0.213739i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.94736 | + | 3.87680i | −0.481951 | + | 0.187831i | ||||
\(427\) | −0.255924 | + | 0.502279i | −0.0123850 | + | 0.0243070i | ||||
\(428\) | 14.5738 | + | 2.30827i | 0.704452 | + | 0.111574i | ||||
\(429\) | −0.818612 | + | 1.27475i | −0.0395230 | + | 0.0615454i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.11469 | − | 5.66339i | 0.198198 | − | 0.272796i | −0.698337 | − | 0.715769i | \(-0.746076\pi\) |
0.896535 | + | 0.442973i | \(0.146076\pi\) | |||||||
\(432\) | −4.91667 | + | 1.68117i | −0.236553 | + | 0.0808855i | ||||
\(433\) | 9.74698 | − | 1.54377i | 0.468410 | − | 0.0741889i | 0.0822322 | − | 0.996613i | \(-0.473795\pi\) |
0.386178 | + | 0.922424i | \(0.373795\pi\) | |||||||
\(434\) | −4.99607 | + | 15.3763i | −0.239819 | + | 0.738087i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.43511 | − | 10.5722i | −0.164512 | − | 0.506315i | ||||
\(437\) | −23.3021 | − | 45.7330i | −1.11469 | − | 2.18770i | ||||
\(438\) | −12.0328 | + | 13.5018i | −0.574951 | + | 0.645139i | ||||
\(439\) | −0.555271 | + | 0.180419i | −0.0265016 | + | 0.00861091i | −0.322238 | − | 0.946659i | \(-0.604435\pi\) |
0.295736 | + | 0.955270i | \(0.404435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.82380 | − | 21.4721i | −0.467800 | − | 1.02248i | ||||
\(442\) | 1.37312 | + | 8.66953i | 0.0653126 | + | 0.412368i | ||||
\(443\) | −6.33032 | − | 6.33032i | −0.300763 | − | 0.300763i | 0.540549 | − | 0.841312i | \(-0.318216\pi\) |
−0.841312 | + | 0.540549i | \(0.818216\pi\) | |||||||
\(444\) | −2.13958 | + | 8.15120i | −0.101540 | + | 0.386839i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.03387 | + | 12.4341i | 0.427766 | + | 0.588770i | ||||
\(447\) | −1.71431 | − | 7.86754i | −0.0810842 | − | 0.372122i | ||||
\(448\) | −3.43597 | − | 1.75071i | −0.162334 | − | 0.0827134i | ||||
\(449\) | −18.3782 | −0.867322 | −0.433661 | − | 0.901076i | \(-0.642779\pi\) | ||||
−0.433661 | + | 0.901076i | \(0.642779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.99298 | −0.140934 | ||||||||
\(452\) | 1.56816 | + | 0.799015i | 0.0737598 | + | 0.0375825i | ||||
\(453\) | 5.40404 | + | 24.8009i | 0.253904 | + | 1.16525i | ||||
\(454\) | 8.24401 | + | 11.3469i | 0.386911 | + | 0.532537i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.87977 | − | 10.9711i | 0.134857 | − | 0.513769i | ||||
\(457\) | 24.7918 | + | 24.7918i | 1.15971 | + | 1.15971i | 0.984537 | + | 0.175174i | \(0.0560488\pi\) |
0.175174 | + | 0.984537i | \(0.443951\pi\) | |||||||
\(458\) | −2.71142 | − | 17.1192i | −0.126696 | − | 0.799928i | ||||
\(459\) | −13.2111 | − | 12.8126i | −0.616642 | − | 0.598042i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.133994 | − | 0.0435374i | 0.00624074 | − | 0.00202774i | −0.305895 | − | 0.952065i | \(-0.598956\pi\) |
0.312136 | + | 0.950038i | \(0.398956\pi\) | |||||||
\(462\) | 1.56839 | − | 1.75985i | 0.0729681 | − | 0.0818758i | ||||
\(463\) | 4.02806 | + | 7.90552i | 0.187200 | + | 0.367401i | 0.965464 | − | 0.260537i | \(-0.0838995\pi\) |
−0.778264 | + | 0.627937i | \(0.783899\pi\) | |||||||
\(464\) | −1.92945 | − | 5.93824i | −0.0895725 | − | 0.275676i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.760291 | − | 2.33993i | 0.0352198 | − | 0.108395i | ||||
\(467\) | 4.81480 | − | 0.762590i | 0.222803 | − | 0.0352885i | −0.0440349 | − | 0.999030i | \(-0.514021\pi\) |
0.266838 | + | 0.963742i | \(0.414021\pi\) | |||||||
\(468\) | 0.313305 | − | 7.42827i | 0.0144825 | − | 0.343372i | ||||
\(469\) | 17.1621 | − | 23.6216i | 0.792470 | − | 1.09074i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.19887 | + | 6.53851i | −0.193474 | + | 0.301279i | ||||
\(472\) | −2.27925 | − | 0.360998i | −0.104911 | − | 0.0166163i | ||||
\(473\) | −1.17002 | + | 2.29630i | −0.0537977 | + | 0.105584i | ||||
\(474\) | −2.20518 | + | 0.859427i | −0.101287 | + | 0.0394748i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 13.6581i | − | 0.626020i | ||||||
\(477\) | −12.7180 | + | 3.54732i | −0.582319 | + | 0.162420i | ||||
\(478\) | 0.380627 | − | 2.40319i | 0.0174095 | − | 0.109919i | ||||
\(479\) | −11.5308 | + | 8.37759i | −0.526854 | + | 0.382782i | −0.819180 | − | 0.573537i | \(-0.805571\pi\) |
0.292326 | + | 0.956319i | \(0.405571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.75526 | − | 7.08761i | −0.444802 | − | 0.323167i | ||||
\(482\) | −1.14460 | + | 1.14460i | −0.0521349 | + | 0.0521349i | ||||
\(483\) | 26.4062 | + | 45.2025i | 1.20152 | + | 2.05678i | ||||
\(484\) | −10.3432 | − | 3.36070i | −0.470144 | − | 0.152759i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.82090 | + | 12.8527i | 0.400124 | + | 0.583010i | ||||
\(487\) | 31.0777 | − | 15.8349i | 1.40827 | − | 0.717547i | 0.425945 | − | 0.904749i | \(-0.359942\pi\) |
0.982321 | + | 0.187202i | \(0.0599418\pi\) | |||||||
\(488\) | 0.130250 | − | 0.0663655i | 0.00589612 | − | 0.00300422i | ||||
\(489\) | 14.5042 | − | 11.8684i | 0.655904 | − | 0.536706i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.09165 | − | 1.65438i | −0.229783 | − | 0.0746610i | 0.191862 | − | 0.981422i | \(-0.438547\pi\) |
−0.421645 | + | 0.906761i | \(0.638547\pi\) | |||||||
\(492\) | 12.6829 | − | 7.40904i | 0.571789 | − | 0.334025i | ||||
\(493\) | 15.6372 | − | 15.6372i | 0.704266 | − | 0.704266i | ||||
\(494\) | 13.1301 | + | 9.53958i | 0.590751 | + | 0.429206i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.39184 | − | 2.46432i | 0.152298 | − | 0.110651i | ||||
\(497\) | −3.71838 | + | 23.4769i | −0.166792 | + | 1.05308i | ||||
\(498\) | 10.0827 | + | 1.00773i | 0.451817 | + | 0.0451576i | ||||
\(499\) | − | 8.93736i | − | 0.400091i | −0.979787 | − | 0.200046i | \(-0.935891\pi\) | ||
0.979787 | − | 0.200046i | \(-0.0641090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5626 | + | 27.1023i | 0.471903 | + | 1.21084i | ||||
\(502\) | −11.2255 | + | 22.0313i | −0.501020 | + | 0.983307i | ||||
\(503\) | −2.88408 | − | 0.456793i | −0.128595 | − | 0.0203674i | 0.0918053 | − | 0.995777i | \(-0.470736\pi\) |
−0.220400 | + | 0.975410i | \(0.570736\pi\) | |||||||
\(504\) | −2.28966 | + | 11.3400i | −0.101990 | + | 0.505123i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.62591 | + | 2.23788i | −0.0722807 | + | 0.0994859i | ||||
\(507\) | −10.8761 | − | 4.77599i | −0.483025 | − | 0.212109i | ||||
\(508\) | −5.32741 | + | 0.843778i | −0.236365 | + | 0.0374366i | ||||
\(509\) | −3.24395 | + | 9.98385i | −0.143786 | + | 0.442527i | −0.996853 | − | 0.0792745i | \(-0.974740\pi\) |
0.853067 | + | 0.521801i | \(0.174740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4429 | + | 38.2953i | 0.550441 | + | 1.69408i | ||||
\(512\) | 0.453990 | + | 0.891007i | 0.0200637 | + | 0.0393773i | ||||
\(513\) | −34.0243 | + | 0.520992i | −1.50221 | + | 0.0230023i | ||||
\(514\) | 27.2321 | − | 8.84825i | 1.20116 | − | 0.390280i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.726395 | − | 12.6270i | −0.0319777 | − | 0.555874i | ||||
\(517\) | 0.236073 | + | 1.49051i | 0.0103825 | + | 0.0655524i | ||||
\(518\) | 13.2673 | + | 13.2673i | 0.582932 | + | 0.582932i | ||||
\(519\) | 29.1826 | + | 7.66004i | 1.28097 | + | 0.336238i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1471 | + | 15.3427i | 0.488364 | + | 0.672175i | 0.980085 | − | 0.198578i | \(-0.0636322\pi\) |
−0.491722 | + | 0.870753i | \(0.663632\pi\) | |||||||
\(522\) | −15.6046 | + | 10.3617i | −0.682995 | + | 0.453520i | ||||
\(523\) | −21.7058 | − | 11.0596i | −0.949127 | − | 0.483604i | −0.0903250 | − | 0.995912i | \(-0.528791\pi\) |
−0.858802 | + | 0.512308i | \(0.828791\pi\) | |||||||
\(524\) | 17.4135 | 0.760714 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.01044 | 0.131261 | ||||||||
\(527\) | 13.2307 | + | 6.74137i | 0.576338 | + | 0.293659i | ||||
\(528\) | −0.597278 | + | 0.130145i | −0.0259932 | + | 0.00566383i | ||||
\(529\) | −22.5886 | − | 31.0905i | −0.982111 | − | 1.35176i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.793889 | + | 6.87732i | 0.0344518 | + | 0.298450i | ||||
\(532\) | −17.8571 | − | 17.8571i | −0.774205 | − | 0.774205i | ||||
\(533\) | 3.28775 | + | 20.7580i | 0.142408 | + | 0.899131i | ||||
\(534\) | −3.54347 | + | 0.203845i | −0.153341 | + | 0.00882122i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.20094 | + | 2.33973i | −0.311033 | + | 0.101061i | ||||
\(537\) | −9.50227 | − | 8.46847i | −0.410053 | − | 0.365441i | ||||
\(538\) | −5.88761 | − | 11.5551i | −0.253833 | − | 0.498175i | ||||
\(539\) | −0.858409 | − | 2.64191i | −0.0369743 | − | 0.113795i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.94591 | − | 27.5327i | 0.384615 | − | 1.18372i | −0.552144 | − | 0.833749i | \(-0.686190\pi\) |
0.936759 | − | 0.349974i | \(-0.113810\pi\) | |||||||
\(542\) | −16.8214 | + | 2.66425i | −0.722542 | + | 0.114439i | ||||
\(543\) | −0.467516 | + | 1.06465i | −0.0200630 | + | 0.0456884i | ||||
\(544\) | −2.08182 | + | 2.86537i | −0.0892571 | + | 0.122852i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.9285 | − | 8.94453i | −0.596084 | − | 0.382790i | ||||
\(547\) | −12.9801 | − | 2.05584i | −0.554988 | − | 0.0879014i | −0.127360 | − | 0.991857i | \(-0.540650\pi\) |
−0.427627 | + | 0.903955i | \(0.640650\pi\) | |||||||
\(548\) | −8.13848 | + | 15.9727i | −0.347659 | + | 0.682319i | ||||
\(549\) | −0.296757 | − | 0.322892i | −0.0126653 | − | 0.0137807i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 40.8893i | − | 1.74194i | ||||||
\(552\) | 1.35009 | − | 13.5080i | 0.0574635 | − | 0.574940i | ||||
\(553\) | −0.824307 | + | 5.20447i | −0.0350531 | + | 0.221317i | ||||
\(554\) | −8.59687 | + | 6.24599i | −0.365246 | + | 0.265367i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.5805 | + | 10.5934i | 0.618353 | + | 0.449260i | ||||
\(557\) | 24.6270 | − | 24.6270i | 1.04348 | − | 1.04348i | 0.0444707 | − | 0.999011i | \(-0.485840\pi\) |
0.999011 | − | 0.0444707i | \(-0.0141601\pi\) | |||||||
\(558\) | −9.85495 | − | 7.81518i | −0.417193 | − | 0.330843i | ||||
\(559\) | 17.2114 | + | 5.59233i | 0.727966 | + | 0.236530i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.37110 | − | 1.67560i | −0.0578877 | − | 0.0707441i | ||||
\(562\) | 25.0016 | − | 12.7389i | 1.05463 | − | 0.537359i | ||||
\(563\) | 8.71723 | − | 4.44165i | 0.367388 | − | 0.187193i | −0.260544 | − | 0.965462i | \(-0.583902\pi\) |
0.627931 | + | 0.778269i | \(0.283902\pi\) | |||||||
\(564\) | −4.69008 | − | 5.73171i | −0.197488 | − | 0.241348i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.4163 | − | 7.93332i | −1.02629 | − | 0.333462i | ||||
\(567\) | 34.6146 | − | 2.52353i | 1.45368 | − | 0.105978i | ||||
\(568\) | 4.35851 | − | 4.35851i | 0.182879 | − | 0.182879i | ||||
\(569\) | 8.66014 | + | 6.29196i | 0.363052 | + | 0.263773i | 0.754324 | − | 0.656502i | \(-0.227965\pi\) |
−0.391272 | + | 0.920275i | \(0.627965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5798 | − | 9.13980i | 0.526450 | − | 0.382489i | −0.292578 | − | 0.956242i | \(-0.594513\pi\) |
0.819028 | + | 0.573753i | \(0.194513\pi\) | |||||||
\(572\) | 0.136828 | − | 0.863895i | 0.00572105 | − | 0.0361213i | ||||
\(573\) | 2.42715 | − | 24.2844i | 0.101396 | − | 1.01450i | ||||
\(574\) | − | 32.7026i | − | 1.36498i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.20883 | − | 2.03004i | 0.0920345 | − | 0.0845852i | ||||
\(577\) | 6.76199 | − | 13.2712i | 0.281505 | − | 0.552485i | −0.706350 | − | 0.707863i | \(-0.749659\pi\) |
0.987855 | + | 0.155378i | \(0.0496594\pi\) | |||||||
\(578\) | 4.40082 | + | 0.697022i | 0.183050 | + | 0.0289923i | ||||
\(579\) | −5.96357 | − | 3.82966i | −0.247837 | − | 0.159155i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.2606 | − | 18.2516i | 0.550140 | − | 0.757203i | ||||
\(582\) | 4.89277 | − | 11.1420i | 0.202812 | − | 0.461852i | ||||
\(583\) | −1.53418 | + | 0.242990i | −0.0635392 | + | 0.0100636i | ||||
\(584\) | 3.22666 | − | 9.93064i | 0.133520 | − | 0.410933i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.5565 | − | 32.4896i | −0.436086 | − | 1.34213i | ||||
\(587\) | −11.6079 | − | 22.7817i | −0.479108 | − | 0.940302i | −0.996423 | − | 0.0845070i | \(-0.973068\pi\) |
0.517315 | − | 0.855795i | \(-0.326932\pi\) | |||||||
\(588\) | 10.1775 | + | 9.07027i | 0.419715 | + | 0.374052i | ||||
\(589\) | 26.1121 | − | 8.48435i | 1.07593 | − | 0.349592i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −39.3226 | + | 2.26211i | −1.61752 | + | 0.0930508i | ||||
\(592\) | −0.761135 | − | 4.80562i | −0.0312825 | − | 0.197510i | ||||
\(593\) | 5.46116 | + | 5.46116i | 0.224263 | + | 0.224263i | 0.810291 | − | 0.586028i | \(-0.199309\pi\) |
−0.586028 | + | 0.810291i | \(0.699309\pi\) | |||||||
\(594\) | 0.857484 | + | 1.62106i | 0.0351830 | + | 0.0665129i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.73256 | + | 3.76105i | 0.111930 | + | 0.154058i | ||||
\(597\) | −10.6933 | + | 2.33005i | −0.437650 | + | 0.0953624i | ||||
\(598\) | 17.3071 | + | 8.81838i | 0.707738 | + | 0.360611i | ||||
\(599\) | −20.6409 | −0.843363 | −0.421681 | − | 0.906744i | \(-0.638560\pi\) | ||||
−0.421681 | + | 0.906744i | \(0.638560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9854 | 0.733642 | 0.366821 | − | 0.930292i | \(-0.380446\pi\) | ||||
0.366821 | + | 0.930292i | \(0.380446\pi\) | |||||||
\(602\) | −25.0904 | − | 12.7842i | −1.02261 | − | 0.521045i | ||||
\(603\) | 12.5650 | + | 18.9227i | 0.511687 | + | 0.770594i | ||||
\(604\) | −8.61387 | − | 11.8560i | −0.350494 | − | 0.482413i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.0607 | − | 4.21573i | −0.652423 | − | 0.171252i | ||||
\(607\) | −5.54524 | − | 5.54524i | −0.225074 | − | 0.225074i | 0.585557 | − | 0.810631i | \(-0.300876\pi\) |
−0.810631 | + | 0.585557i | \(0.800876\pi\) | |||||||
\(608\) | 1.02445 | + | 6.46812i | 0.0415469 | + | 0.262317i | ||||
\(609\) | 2.39516 | + | 41.6354i | 0.0970567 | + | 1.68715i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.0782 | − | 3.27461i | 0.407721 | − | 0.132477i | ||||
\(612\) | 9.95800 | + | 3.70635i | 0.402528 | + | 0.149820i | ||||
\(613\) | 2.13588 | + | 4.19191i | 0.0862676 | + | 0.169310i | 0.930110 | − | 0.367282i | \(-0.119712\pi\) |
−0.843842 | + | 0.536592i | \(0.819712\pi\) | |||||||
\(614\) | −5.63620 | − | 17.3464i | −0.227459 | − | 0.700045i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.420571 | + | 1.29439i | −0.0169453 | + | 0.0521523i | ||||
\(617\) | 40.5328 | − | 6.41977i | 1.63179 | − | 0.258450i | 0.727733 | − | 0.685861i | \(-0.240574\pi\) |
0.904058 | + | 0.427410i | \(0.140574\pi\) | |||||||
\(618\) | −10.5508 | − | 4.63313i | −0.424414 | − | 0.186372i | ||||
\(619\) | −10.1486 | + | 13.9684i | −0.407908 | + | 0.561438i | −0.962707 | − | 0.270547i | \(-0.912795\pi\) |
0.554798 | + | 0.831985i | \(0.312795\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.1224 | + | 6.98607i | −1.61005 | + | 0.280341i | ||||
\(622\) | 16.0196 | + | 2.53726i | 0.642329 | + | 0.101735i | ||||
\(623\) | −3.58757 | + | 7.04100i | −0.143733 | + | 0.282092i | ||||
\(624\) | 1.55874 | + | 3.99951i | 0.0623994 | + | 0.160109i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.40095i | 0.215865i | ||||||||
\(627\) | −3.98336 | − | 0.398124i | −0.159080 | − | 0.0158995i | ||||
\(628\) | 0.701824 | − | 4.43114i | 0.0280058 | − | 0.176822i | ||||
\(629\) | 13.9415 | − | 10.1291i | 0.555885 | − | 0.403874i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4746 | − | 21.4146i | −1.17337 | − | 0.852501i | −0.181959 | − | 0.983306i | \(-0.558244\pi\) |
−0.991408 | + | 0.130805i | \(0.958244\pi\) | |||||||
\(632\) | 0.966214 | − | 0.966214i | 0.0384339 | − | 0.0384339i | ||||
\(633\) | −6.21593 | + | 3.63119i | −0.247061 | + | 0.144327i | ||||
\(634\) | 8.15891 | + | 2.65099i | 0.324032 | + | 0.105284i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.89965 | − | 4.82751i | 0.233936 | − | 0.191423i | ||||
\(637\) | −17.3803 | + | 8.85568i | −0.688631 | + | 0.350875i | ||||
\(638\) | −1.96346 | + | 1.00043i | −0.0777340 | + | 0.0396074i | ||||
\(639\) | −16.1077 | − | 9.08185i | −0.637212 | − | 0.359272i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1775 | + | 9.15543i | 1.11294 | + | 0.361618i | 0.807071 | − | 0.590454i | \(-0.201051\pi\) |
0.305874 | + | 0.952072i | \(0.401051\pi\) | |||||||
\(642\) | 12.8914 | + | 22.0677i | 0.508784 | + | 0.870943i | ||||
\(643\) | −16.2471 | + | 16.2471i | −0.640721 | + | 0.640721i | −0.950733 | − | 0.310012i | \(-0.899667\pi\) |
0.310012 | + | 0.950733i | \(0.399667\pi\) | |||||||
\(644\) | −24.4521 | − | 17.7655i | −0.963547 | − | 0.700058i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7646 | + | 13.6333i | −0.738284 | + | 0.536394i | ||||
\(647\) | −0.280589 | + | 1.77157i | −0.0110311 | + | 0.0696477i | −0.992590 | − | 0.121513i | \(-0.961225\pi\) |
0.981559 | + | 0.191161i | \(0.0612253\pi\) | |||||||
\(648\) | −7.64652 | − | 4.74665i | −0.300384 | − | 0.186466i | ||||
\(649\) | 0.814444i | 0.0319697i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.0916 | + | 10.1687i | −1.02261 | + | 0.398544i | ||||
\(652\) | −4.91227 | + | 9.64088i | −0.192379 | + | 0.377566i | ||||
\(653\) | −26.3159 | − | 4.16803i | −1.02982 | − | 0.163107i | −0.381416 | − | 0.924404i | \(-0.624563\pi\) |
−0.648404 | + | 0.761296i | \(0.724563\pi\) | |||||||
\(654\) | 10.4039 | − | 16.2010i | 0.406824 | − | 0.633509i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.98463 | + | 6.86076i | −0.194617 | + | 0.267868i | ||||
\(657\) | −31.2973 | − | 1.32004i | −1.22102 | − | 0.0514996i | ||||
\(658\) | −16.2860 | + | 2.57944i | −0.634893 | + | 0.100557i | ||||
\(659\) | −2.02081 | + | 6.21940i | −0.0787195 | + | 0.242274i | −0.982670 | − | 0.185363i | \(-0.940654\pi\) |
0.903951 | + | 0.427637i | \(0.140654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.97584 | + | 18.3917i | 0.232433 | + | 0.715356i | 0.997452 | + | 0.0713473i | \(0.0227299\pi\) |
−0.765018 | + | 0.644008i | \(0.777270\pi\) | |||||||
\(662\) | −12.9009 | − | 25.3194i | −0.501407 | − | 0.984066i | ||||
\(663\) | −10.1152 | + | 11.3500i | −0.392840 | + | 0.440797i | ||||
\(664\) | −5.56392 | + | 1.80783i | −0.215922 | + | 0.0701573i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.2733 | + | 6.07276i | −0.514331 | + | 0.235315i | ||||
\(667\) | −7.65551 | − | 48.3350i | −0.296422 | − | 1.87154i | ||||
\(668\) | −11.8751 | − | 11.8751i | −0.459461 | − | 0.459461i | ||||
\(669\) | −6.75856 | + | 25.7482i | −0.261301 | + | 0.995484i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0303252 | − | 0.0417390i | −0.00117069 | − | 0.00161132i | ||||
\(672\) | −1.42202 | − | 6.52614i | −0.0548558 | − | 0.251751i | ||||
\(673\) | −39.1978 | − | 19.9723i | −1.51096 | − | 0.769874i | −0.514793 | − | 0.857315i | \(-0.672131\pi\) |
−0.996170 | + | 0.0874407i | \(0.972131\pi\) | |||||||
\(674\) | −4.74599 | −0.182809 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.85808 | 0.263772 | ||||||||
\(677\) | 33.3683 | + | 17.0020i | 1.28245 | + | 0.653440i | 0.956441 | − | 0.291927i | \(-0.0942963\pi\) |
0.326008 | + | 0.945367i | \(0.394296\pi\) | |||||||
\(678\) | 0.649003 | + | 2.97849i | 0.0249248 | + | 0.114388i | ||||
\(679\) | −15.9250 | − | 21.9189i | −0.611147 | − | 0.841171i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.16764 | + | 23.4970i | −0.236344 | + | 0.900406i | ||||
\(682\) | −1.04629 | − | 1.04629i | −0.0400645 | − | 0.0400645i | ||||
\(683\) | −5.33840 | − | 33.7054i | −0.204268 | − | 1.28970i | −0.850263 | − | 0.526358i | \(-0.823557\pi\) |
0.645995 | − | 0.763342i | \(-0.276443\pi\) | |||||||
\(684\) | 17.8652 | − | 8.17363i | 0.683094 | − | 0.312526i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.19397 | − | 1.03778i | 0.121946 | − | 0.0396228i | ||||
\(687\) | 19.9738 | − | 22.4121i | 0.762049 | − | 0.855077i | ||||
\(688\) | 3.31516 | + | 6.50638i | 0.126389 | + | 0.248053i | ||||
\(689\) | 3.37056 | + | 10.3735i | 0.128408 | + | 0.395199i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.75674 | + | 30.0282i | −0.371164 | + | 1.14232i | 0.574867 | + | 0.818247i | \(0.305054\pi\) |
−0.946030 | + | 0.324078i | \(0.894946\pi\) | |||||||
\(692\) | −17.2049 | + | 2.72498i | −0.654031 | + | 0.103588i | ||||
\(693\) | 4.07936 | + | 0.172057i | 0.154962 | + | 0.00653591i | ||||
\(694\) | 4.71830 | − | 6.49419i | 0.179104 | − | 0.246516i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.84371 | − | 9.09986i | 0.221505 | − | 0.344929i | ||||
\(697\) | −29.6659 | − | 4.69862i | −1.12368 | − | 0.177973i | ||||
\(698\) | 8.59105 | − | 16.8609i | 0.325176 | − | 0.638194i | ||||
\(699\) | 3.97056 | − | 1.54745i | 0.150181 | − | 0.0585301i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 41.1349i | − | 1.55364i | −0.629720 | − | 0.776822i | \(-0.716830\pi\) | ||
0.629720 | − | 0.776822i | \(-0.283170\pi\) | |||||||
\(702\) | 10.3011 | − | 7.72787i | 0.388789 | − | 0.291670i | ||||
\(703\) | 4.98448 | − | 31.4708i | 0.187993 | − | 1.18694i | ||||
\(704\) | 0.285527 | − | 0.207447i | 0.0107612 | − | 0.00781846i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.82209 | − | 2.77691i | −0.143846 | − | 0.104510i | ||||
\(707\) | −26.1413 | + | 26.1413i | −0.983143 | + | 0.983143i | ||||
\(708\) | −2.01613 | − | 3.45125i | −0.0757710 | − | 0.129706i | ||||
\(709\) | −48.5191 | − | 15.7648i | −1.82217 | − | 0.592060i | −0.999731 | − | 0.0232123i | \(-0.992611\pi\) |
−0.822443 | − | 0.568848i | \(-0.807389\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.57083 | − | 2.01331i | −0.133917 | − | 0.0755049i | ||||
\(712\) | 1.82585 | − | 0.930319i | 0.0684268 | − | 0.0348652i | ||||
\(713\) | 29.2785 | − | 14.9181i | 1.09649 | − | 0.558689i | ||||
\(714\) | 18.3084 | − | 14.9812i | 0.685175 | − | 0.560658i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.98899 | + | 2.27086i | 0.261191 | + | 0.0848660i | ||||
\(717\) | 3.63891 | − | 2.12576i | 0.135898 | − | 0.0793881i | ||||
\(718\) | −10.6989 | + | 10.6989i | −0.399281 | + | 0.399281i | ||||
\(719\) | 29.8994 | + | 21.7232i | 1.11506 | + | 0.810138i | 0.983453 | − | 0.181164i | \(-0.0579866\pi\) |
0.131606 | + | 0.991302i | \(0.457987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.7558 | + | 15.0800i | −0.772985 | + | 0.561607i | ||||
\(722\) | −3.73661 | + | 23.5920i | −0.139062 | + | 0.878004i | ||||
\(723\) | −2.78978 | − | 0.278830i | −0.103753 | − | 0.0103698i | ||||
\(724\) | − | 0.671329i | − | 0.0249497i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.84017 | − | 17.5510i | −0.253863 | − | 0.651379i | ||||
\(727\) | −8.55075 | + | 16.7818i | −0.317130 | + | 0.622402i | −0.993458 | − | 0.114198i | \(-0.963570\pi\) |
0.676328 | + | 0.736600i | \(0.263570\pi\) | |||||||
\(728\) | 9.43931 | + | 1.49504i | 0.349844 | + | 0.0554099i | ||||
\(729\) | −7.55333 | + | 25.9219i | −0.279753 | + | 0.960072i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.2020 | + | 20.9238i | −0.562266 | + | 0.773893i | ||||
\(732\) | 0.231828 | + | 0.101802i | 0.00856862 | + | 0.00376271i | ||||
\(733\) | −34.3095 | + | 5.43410i | −1.26725 | + | 0.200713i | −0.753627 | − | 0.657302i | \(-0.771698\pi\) |
−0.513625 | + | 0.858015i | \(0.671698\pi\) | |||||||
\(734\) | 11.3193 | − | 34.8373i | 0.417804 | − | 1.28587i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.42199 | + | 7.45412i | 0.0892758 | + | 0.274763i | ||||
\(737\) | 1.21316 | + | 2.38096i | 0.0446873 | + | 0.0877038i | ||||
\(738\) | 23.8431 | + | 8.87436i | 0.877678 | + | 0.326670i | ||||
\(739\) | 2.70309 | − | 0.878288i | 0.0994348 | − | 0.0323083i | −0.258877 | − | 0.965910i | \(-0.583352\pi\) |
0.358312 | + | 0.933602i | \(0.383352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.61445 | + | 28.0643i | 0.0593083 | + | 1.03097i | ||||
\(742\) | −2.65502 | − | 16.7632i | −0.0974689 | − | 0.615395i | ||||
\(743\) | −19.3245 | − | 19.3245i | −0.708947 | − | 0.708947i | 0.257367 | − | 0.966314i | \(-0.417145\pi\) |
−0.966314 | + | 0.257367i | \(0.917145\pi\) | |||||||
\(744\) | 7.02377 | + | 1.84364i | 0.257504 | + | 0.0675913i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.30299 | − | 1.79341i | −0.0477059 | − | 0.0656615i | ||||
\(747\) | 9.70857 | + | 14.6210i | 0.355218 | + | 0.534953i | ||||
\(748\) | 1.11376 | + | 0.567491i | 0.0407233 | + | 0.0207495i | ||||
\(749\) | 56.9012 | 2.07913 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6596 | 0.498445 | 0.249222 | − | 0.968446i | \(-0.419825\pi\) | ||||
0.249222 | + | 0.968446i | \(0.419825\pi\) | |||||||
\(752\) | 3.80983 | + | 1.94121i | 0.138930 | + | 0.0707886i | ||||
\(753\) | −41.8454 | + | 9.11798i | −1.52493 | + | 0.332278i | ||||
\(754\) | 9.09541 | + | 12.5188i | 0.331235 | + | 0.455906i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −17.7124 | + | 9.36926i | −0.644195 | + | 0.340757i | ||||
\(757\) | 11.1659 | + | 11.1659i | 0.405833 | + | 0.405833i | 0.880283 | − | 0.474450i | \(-0.157353\pi\) |
−0.474450 | + | 0.880283i | \(0.657353\pi\) | |||||||
\(758\) | −1.10598 | − | 6.98287i | −0.0401710 | − | 0.253629i | ||||
\(759\) | −4.78324 | + | 0.275165i | −0.173621 | + | 0.00998786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3455 | + | 4.33621i | −0.483774 | + | 0.157188i | −0.540742 | − | 0.841188i | \(-0.681857\pi\) |
0.0569686 | + | 0.998376i | \(0.481857\pi\) | |||||||
\(762\) | −6.97454 | − | 6.21574i | −0.252661 | − | 0.225173i | ||||
\(763\) | −19.4614 | − | 38.1951i | −0.704548 | − | 1.38275i | ||||
\(764\) | 4.35419 | + | 13.4008i | 0.157529 | + | 0.484825i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.30040 | + | 13.2353i | −0.155380 | + | 0.478209i | ||||
\(767\) | 5.64864 | − | 0.894657i | 0.203961 | − | 0.0323042i | ||||
\(768\) | −0.696404 | + | 1.58588i | −0.0251293 | + | 0.0572256i | ||||
\(769\) | 13.0082 | − | 17.9042i | 0.469087 | − | 0.645643i | −0.507275 | − | 0.861784i | \(-0.669347\pi\) |
0.976362 | + | 0.216141i | \(0.0693471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.7310 | + | 26.7986i | 1.50290 | + | 0.965128i | ||||
\(772\) | 4.04150 | + | 0.640111i | 0.145457 | + | 0.0230381i | ||||
\(773\) | −19.2486 | + | 37.7774i | −0.692323 | + | 1.35876i | 0.230324 | + | 0.973114i | \(0.426021\pi\) |
−0.922647 | + | 0.385646i | \(0.873979\pi\) | |||||||
\(774\) | 16.1295 | − | 14.8239i | 0.579762 | − | 0.532836i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.02576i | 0.252210i | ||||||||
\(777\) | −3.23198 | + | 32.3370i | −0.115947 | + | 1.16008i | ||||
\(778\) | −2.35890 | + | 14.8935i | −0.0845708 | + | 0.533959i | ||||
\(779\) | −44.9294 | + | 32.6431i | −1.60976 | + | 1.16956i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.75995 | − | 1.27868i | −0.0629758 | − | 0.0457546i | ||||
\(782\) | −19.6290 | + | 19.6290i | −0.701932 | + | 0.701932i | ||||
\(783\) | −31.0059 | − | 9.55212i | −1.10806 | − | 0.341365i | ||||
\(784\) | −7.48565 | − | 2.43223i | −0.267345 | − | 0.0868655i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.1004 | + | 23.3424i | 0.681288 | + | 0.832596i | ||||
\(787\) | 25.7904 | − | 13.1408i | 0.919327 | − | 0.468420i | 0.0707509 | − | 0.997494i | \(-0.477460\pi\) |
0.848576 | + | 0.529074i | \(0.177460\pi\) | |||||||
\(788\) | 20.2619 | − | 10.3240i | 0.721800 | − | 0.367776i | ||||
\(789\) | 3.30206 | + | 4.03542i | 0.117557 | + | 0.143665i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.45480 | + | 2.09729i | 0.229506 | + | 0.0745711i | ||||
\(792\) | −0.829593 | − | 0.657885i | −0.0294783 | − | 0.0233769i | ||||
\(793\) | −0.256173 | + | 0.256173i | −0.00909695 | + | 0.00909695i | ||||
\(794\) | −11.1607 | − | 8.10876i | −0.396080 | − | 0.287769i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.11191 | − | 3.71402i | 0.181187 | − | 0.131640i | ||||
\(797\) | −2.70297 | + | 17.0659i | −0.0957441 | + | 0.604505i | 0.892432 | + | 0.451182i | \(0.148997\pi\) |
−0.988176 | + | 0.153323i | \(0.951003\pi\) | |||||||
\(798\) | 4.35009 | − | 43.5240i | 0.153991 | − | 1.54073i | ||||
\(799\) | 15.1443i | 0.535766i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.15997 | − | 4.52634i | −0.146985 | − | 0.159930i | ||||
\(802\) | 7.18193 | − | 14.0953i | 0.253603 | − | 0.497723i | ||||
\(803\) | −3.63982 | − | 0.576491i | −0.128446 | − | 0.0203439i | ||||
\(804\) | −11.0348 | − | 7.08630i | −0.389169 | − | 0.249915i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.10729 | + | 8.40597i | −0.215120 | + | 0.296088i | ||||
\(807\) | 9.03137 | − | 20.5666i | 0.317919 | − | 0.723980i | ||||
\(808\) | 9.46876 | − | 1.49970i | 0.333110 | − | 0.0527594i | ||||
\(809\) | 14.1884 | − | 43.6674i | 0.498837 | − | 1.53526i | −0.312054 | − | 0.950064i | \(-0.601017\pi\) |
0.810891 | − | 0.585198i | \(-0.198983\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2314 | + | 43.7999i | 0.499733 | + | 1.53802i | 0.809448 | + | 0.587192i | \(0.199767\pi\) |
−0.309714 | + | 0.950830i | \(0.600233\pi\) | |||||||
\(812\) | −10.9312 | − | 21.4536i | −0.383609 | − | 0.752874i | ||||
\(813\) | −22.0223 | − | 19.6264i | −0.772355 | − | 0.688326i | ||||
\(814\) | −1.63314 | + | 0.530641i | −0.0572417 | + | 0.0185989i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.12445 | + | 0.352321i | −0.214398 | + | 0.0123337i | ||||
\(817\) | 7.48082 | + | 47.2320i | 0.261721 | + | 1.65244i | ||||
\(818\) | 4.20720 | + | 4.20720i | 0.147101 | + | 0.147101i | ||||
\(819\) | −3.28782 | − | 28.4818i | −0.114886 | − | 0.995234i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3733 | + | 18.4068i | 0.466731 | + | 0.642400i | 0.975888 | − | 0.218274i | \(-0.0700425\pi\) |
−0.509156 | + | 0.860674i | \(0.670043\pi\) | |||||||
\(822\) | −30.3378 | + | 6.61051i | −1.05815 | + | 0.230568i | ||||
\(823\) | 33.1249 | + | 16.8780i | 1.15466 | + | 0.588330i | 0.923127 | − | 0.384496i | \(-0.125625\pi\) |
0.231536 | + | 0.972826i | \(0.425625\pi\) | |||||||
\(824\) | 6.65293 | 0.231766 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.89898 | −0.309635 | ||||||||
\(827\) | −9.39702 | − | 4.78802i | −0.326766 | − | 0.166496i | 0.282910 | − | 0.959147i | \(-0.408700\pi\) |
−0.609676 | + | 0.792651i | \(0.708700\pi\) | |||||||
\(828\) | 19.5881 | − | 13.0068i | 0.680732 | − | 0.452018i | ||||
\(829\) | 7.78028 | + | 10.7086i | 0.270220 | + | 0.371926i | 0.922464 | − | 0.386083i | \(-0.126172\pi\) |
−0.652244 | + | 0.758009i | \(0.726172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.8023 | − | 4.67285i | −0.617553 | − | 0.162099i | ||||
\(832\) | −1.75242 | − | 1.75242i | −0.0607541 | − | 0.0607541i | ||||
\(833\) | −4.36093 | − | 27.5338i | −0.151097 | − | 0.953990i | ||||
\(834\) | 1.79279 | + | 31.1644i | 0.0620794 | + | 1.07914i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.19813 | − | 0.714216i | 0.0760239 | − | 0.0247017i | ||||
\(837\) | −0.333542 | − | 21.7826i | −0.0115289 | − | 0.752915i | ||||
\(838\) | 1.96185 | + | 3.85035i | 0.0677711 | + | 0.133008i | ||||
\(839\) | −0.944989 | − | 2.90838i | −0.0326247 | − | 0.100408i | 0.933418 | − | 0.358790i | \(-0.116811\pi\) |
−0.966043 | + | 0.258382i | \(0.916811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.08568 | − | 9.49674i | 0.106403 | − | 0.327474i | ||||
\(842\) | 24.7186 | − | 3.91504i | 0.851860 | − | 0.134921i | ||||
\(843\) | 44.4997 | + | 19.5410i | 1.53265 | + | 0.673029i | ||||
\(844\) | 2.44299 | − | 3.36248i | 0.0840910 | − | 0.115741i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.53880 | − | 12.5739i | 0.0872858 | − | 0.432299i | ||||
\(847\) | −41.4224 | − | 6.56066i | −1.42329 | − | 0.225427i | ||||
\(848\) | −1.99809 | + | 3.92147i | −0.0686146 | + | 0.134664i | ||||
\(849\) | −16.1471 | − | 41.4312i | −0.554165 | − | 1.42192i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 38.1346i | − | 1.30724i | ||||||
\(852\) | 10.6232 | + | 1.06175i | 0.363945 | + | 0.0363751i | ||||
\(853\) | −5.89808 | + | 37.2390i | −0.201946 | + | 1.27504i | 0.653412 | + | 0.757003i | \(0.273337\pi\) |
−0.855358 | + | 0.518037i | \(0.826663\pi\) | |||||||
\(854\) | 0.456059 | − | 0.331347i | 0.0156060 | − | 0.0113384i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.9374 | − | 8.67305i | −0.408013 | − | 0.296439i | ||||
\(857\) | 3.57064 | − | 3.57064i | 0.121971 | − | 0.121971i | −0.643487 | − | 0.765457i | \(-0.722513\pi\) |
0.765457 | + | 0.643487i | \(0.222513\pi\) | |||||||
\(858\) | 1.30811 | − | 0.764167i | 0.0446582 | − | 0.0260882i | ||||
\(859\) | 33.5736 | + | 10.9087i | 1.14552 | + | 0.372201i | 0.819453 | − | 0.573147i | \(-0.194278\pi\) |
0.326064 | + | 0.945348i | \(0.394278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.8371 | − | 35.8706i | 1.49396 | − | 1.22247i | ||||
\(862\) | −6.23735 | + | 3.17809i | −0.212445 | + | 0.108246i | ||||
\(863\) | 17.9383 | − | 9.14003i | 0.610628 | − | 0.311130i | −0.121191 | − | 0.992629i | \(-0.538672\pi\) |
0.731819 | + | 0.681499i | \(0.238672\pi\) | |||||||
\(864\) | 5.14402 | + | 0.734186i | 0.175003 | + | 0.0249775i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.38548 | − | 3.04953i | −0.318932 | − | 0.103627i | ||||
\(867\) | 3.89279 | + | 6.66374i | 0.132206 | + | 0.226312i | ||||
\(868\) | 11.4322 | − | 11.4322i | 0.388035 | − | 0.388035i | ||||
\(869\) | −0.390153 | − | 0.283463i | −0.0132350 | − | 0.00961581i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1807 | − | 11.0294i | 0.514379 | − | 0.373718i | ||||
\(872\) | −1.73896 | + | 10.9794i | −0.0588887 | + | 0.371809i | ||||
\(873\) | 20.3024 | − | 5.66273i | 0.687131 | − | 0.191654i | ||||
\(874\) | 51.3273i | 1.73617i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.8510 | − | 6.56737i | 0.569343 | − | 0.221891i | ||||
\(877\) | 19.1482 | − | 37.5805i | 0.646590 | − | 1.26900i | −0.302244 | − | 0.953230i | \(-0.597736\pi\) |
0.948834 | − | 0.315774i | \(-0.102264\pi\) | |||||||
\(878\) | 0.576659 | + | 0.0913337i | 0.0194613 | + | 0.00308236i | ||||
\(879\) | 31.9724 | − | 49.7877i | 1.07840 | − | 1.67930i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.4775 | + | 30.9376i | −0.757285 | + | 1.04231i | 0.240150 | + | 0.970736i | \(0.422803\pi\) |
−0.997435 | + | 0.0715779i | \(0.977197\pi\) | |||||||
\(882\) | −0.995035 | + | 23.5917i | −0.0335046 | + | 0.794372i | ||||
\(883\) | 13.8121 | − | 2.18763i | 0.464816 | − | 0.0736196i | 0.0803657 | − | 0.996765i | \(-0.474391\pi\) |
0.384450 | + | 0.923146i | \(0.374391\pi\) | |||||||
\(884\) | 2.71243 | − | 8.34799i | 0.0912288 | − | 0.280773i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.76645 | + | 8.51427i | 0.0929408 | + | 0.286042i | ||||
\(887\) | −9.40690 | − | 18.4621i | −0.315853 | − | 0.619896i | 0.677433 | − | 0.735585i | \(-0.263092\pi\) |
−0.993285 | + | 0.115689i | \(0.963092\pi\) | |||||||
\(888\) | 5.60695 | − | 6.29142i | 0.188157 | − | 0.211126i | ||||
\(889\) | −19.7820 | + | 6.42756i | −0.663467 | + | 0.215574i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.23244 | + | 2.92753i | −0.0412884 | + | 0.0980759i | ||||
\(892\) | −2.40429 | − | 15.1801i | −0.0805017 | − | 0.508268i | ||||
\(893\) | 19.8002 | + | 19.8002i | 0.662587 | + | 0.662587i | ||||
\(894\) | −2.04433 | + | 7.78831i | −0.0683725 | + | 0.260480i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.26666 | + | 3.11979i | 0.0757239 | + | 0.104225i | ||||
\(897\) | 7.16277 | + | 32.8723i | 0.239158 | + | 1.09757i | ||||
\(898\) | 16.3751 | + | 8.34354i | 0.546445 | + | 0.278428i | ||||
\(899\) | 26.1776 | 0.873071 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5880 | −0.519312 | ||||||||
\(902\) | 2.66676 | + | 1.35878i | 0.0887935 | + | 0.0452425i | ||||
\(903\) | −10.3840 | − | 47.6557i | −0.345558 | − | 1.58588i | ||||
\(904\) | −1.03449 | − | 1.42386i | −0.0344067 | − | 0.0473567i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.44435 | − | 24.5512i | 0.214099 | − | 0.815658i | ||||
\(907\) | −8.19678 | − | 8.19678i | −0.272170 | − | 0.272170i | 0.557803 | − | 0.829973i | \(-0.311644\pi\) |
−0.829973 | + | 0.557803i | \(0.811644\pi\) | |||||||
\(908\) | −2.19408 | − | 13.8529i | −0.0728131 | − | 0.459724i | ||||
\(909\) | −11.9655 | − | 26.1531i | −0.396870 | − | 0.867445i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.38290 | − | 1.42409i | 0.145212 | − | 0.0471822i | −0.235509 | − | 0.971872i | \(-0.575676\pi\) |
0.380721 | + | 0.924690i | \(0.375676\pi\) | |||||||
\(912\) | −7.54667 | + | 8.46794i | −0.249895 | + | 0.280402i | ||||
\(913\) | 0.937368 | + | 1.83969i | 0.0310224 | + | 0.0608848i | ||||
\(914\) | −10.8344 | − | 33.3449i | −0.358371 | − | 1.10295i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.35607 | + | 16.4843i | −0.176970 | + | 0.544656i | ||||
\(917\) | 66.3247 | − | 10.5048i | 2.19023 | − | 0.346899i | ||||
\(918\) | 5.95437 | + | 17.4138i | 0.196524 | + | 0.574743i | ||||
\(919\) | 1.33595 | − | 1.83878i | 0.0440689 | − | 0.0606557i | −0.786414 | − | 0.617700i | \(-0.788065\pi\) |
0.830483 | + | 0.557044i | \(0.188065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.0703 | − | 26.5820i | 0.562485 | − | 0.875906i | ||||
\(922\) | −0.139155 | − | 0.0220400i | −0.00458284 | − | 0.000725850i | ||||
\(923\) | −6.93508 | + | 13.6109i | −0.228271 | + | 0.448007i | ||||
\(924\) | −2.19640 | + | 0.856007i | −0.0722564 | + | 0.0281606i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 8.87257i | − | 0.291571i | ||||||
\(927\) | −5.36223 | − | 19.2250i | −0.176119 | − | 0.631431i | ||||
\(928\) | −0.976751 | + | 6.16696i | −0.0320634 | + | 0.202440i | ||||
\(929\) | −12.0105 | + | 8.72617i | −0.394053 | + | 0.286296i | −0.767114 | − | 0.641510i | \(-0.778308\pi\) |
0.373061 | + | 0.927807i | \(0.378308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.7003 | − | 30.2970i | −1.36667 | − | 0.992945i | ||||
\(932\) | −1.73973 | + | 1.73973i | −0.0569868 | + | 0.0569868i | ||||
\(933\) | 14.1703 | + | 24.2570i | 0.463916 | + | 0.794138i | ||||
\(934\) | −4.63623 | − | 1.50640i | −0.151702 | − | 0.0492910i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.65152 | + | 6.47640i | −0.119354 | + | 0.211688i | ||||
\(937\) | −13.2746 | + | 6.76373i | −0.433661 | + | 0.220961i | −0.657173 | − | 0.753740i | \(-0.728248\pi\) |
0.223512 | + | 0.974701i | \(0.428248\pi\) | |||||||
\(938\) | −26.0155 | + | 13.2555i | −0.849435 | + | 0.432809i | ||||
\(939\) | −7.23984 | + | 5.92414i | −0.236263 | + | 0.193327i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.4117 | − | 9.55645i | −0.958795 | − | 0.311531i | −0.212511 | − | 0.977159i | \(-0.568164\pi\) |
−0.746284 | + | 0.665627i | \(0.768164\pi\) | |||||||
\(942\) | 6.70965 | − | 3.91961i | 0.218612 | − | 0.127708i | ||||
\(943\) | −46.9991 | + | 46.9991i | −1.53050 | + | 1.53050i | ||||
\(944\) | 1.86694 | + | 1.35641i | 0.0607636 | + | 0.0441474i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.08499 | − | 1.51484i | 0.0677890 | − | 0.0492516i | ||||
\(947\) | 1.42242 | − | 8.98080i | 0.0462224 | − | 0.291837i | −0.953739 | − | 0.300636i | \(-0.902801\pi\) |
0.999961 | + | 0.00879948i | \(0.00280100\pi\) | |||||||
\(948\) | 2.35500 | + | 0.235375i | 0.0764868 | + | 0.00764461i | ||||
\(949\) | 25.8775i | 0.840021i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.39568 | + | 13.8446i | 0.174967 | + | 0.448942i | ||||
\(952\) | −6.20067 | + | 12.1695i | −0.200965 | + | 0.394416i | ||||
\(953\) | −18.9081 | − | 2.99474i | −0.612493 | − | 0.0970093i | −0.157522 | − | 0.987516i | \(-0.550350\pi\) |
−0.454971 | + | 0.890506i | \(0.650350\pi\) | |||||||
\(954\) | 12.9423 | + | 2.61319i | 0.419023 | + | 0.0846052i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.43017 | + | 1.96845i | −0.0462549 | + | 0.0636644i | ||||
\(957\) | −3.49471 | − | 1.53462i | −0.112968 | − | 0.0496073i | ||||
\(958\) | 14.0773 | − | 2.22963i | 0.454818 | − | 0.0720361i | ||||
\(959\) | −21.3623 | + | 65.7463i | −0.689823 | + | 2.12306i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.14780 | − | 12.7656i | −0.133800 | − | 0.411794i | ||||
\(962\) | 5.47429 | + | 10.7439i | 0.176498 | + | 0.346397i | ||||
\(963\) | −15.4410 | + | 41.4861i | −0.497580 | + | 1.33687i | ||||
\(964\) | 1.53948 | − | 0.500207i | 0.0495833 | − | 0.0161106i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.00658 | − | 52.2639i | −0.0967351 | − | 1.68156i | ||||
\(967\) | 6.88343 | + | 43.4603i | 0.221356 | + | 1.39759i | 0.808686 | + | 0.588240i | \(0.200179\pi\) |
−0.587330 | + | 0.809347i | \(0.699821\pi\) | |||||||
\(968\) | 7.69010 | + | 7.69010i | 0.247169 | + | 0.247169i | ||||
\(969\) | −38.8574 | − | 10.1995i | −1.24828 | − | 0.327657i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.1657 | + | 25.0030i | 0.582965 | + | 0.802383i | 0.994017 | − | 0.109229i | \(-0.0348383\pi\) |
−0.411051 | + | 0.911612i | \(0.634838\pi\) | |||||||
\(972\) | −2.02448 | − | 15.4564i | −0.0649352 | − | 0.495765i | ||||
\(973\) | 61.9249 | + | 31.5523i | 1.98522 | + | 1.01152i | ||||
\(974\) | −34.8793 | −1.11761 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.146183 | −0.00467919 | ||||||||
\(977\) | 42.2813 | + | 21.5434i | 1.35270 | + | 0.689235i | 0.971894 | − | 0.235420i | \(-0.0756465\pi\) |
0.380806 | + | 0.924655i | \(0.375646\pi\) | |||||||
\(978\) | −18.3115 | + | 3.99001i | −0.585537 | + | 0.127587i | ||||
\(979\) | −0.425102 | − | 0.585102i | −0.0135863 | − | 0.0186999i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1287 | − | 3.82424i | 1.05772 | − | 0.122099i | ||||
\(982\) | 3.78562 | + | 3.78562i | 0.120804 | + | 0.120804i | ||||
\(983\) | 5.45227 | + | 34.4243i | 0.173900 | + | 1.09796i | 0.908015 | + | 0.418938i | \(0.137598\pi\) |
−0.734114 | + | 0.679026i | \(0.762402\pi\) | |||||||
\(984\) | −14.6642 | + | 0.843585i | −0.467477 | + | 0.0268925i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −21.0320 | + | 6.83372i | −0.669796 | + | 0.217630i | ||||
\(987\) | −21.3213 | − | 19.0016i | −0.678664 | − | 0.604828i | ||||
\(988\) | −7.36813 | − | 14.4608i | −0.234411 | − | 0.460058i | ||||
\(989\) | 17.6860 | + | 54.4321i | 0.562384 | + | 1.73084i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.45449 | − | 4.47645i | 0.0462033 | − | 0.142199i | −0.925293 | − | 0.379252i | \(-0.876181\pi\) |
0.971497 | + | 0.237053i | \(0.0761814\pi\) | |||||||
\(992\) | −4.14093 | + | 0.655859i | −0.131475 | + | 0.0208235i | ||||
\(993\) | 19.7894 | − | 45.0654i | 0.627999 | − | 1.43011i | ||||
\(994\) | 13.9714 | − | 19.2300i | 0.443146 | − | 0.609938i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.52625 | − | 5.47535i | −0.270165 | − | 0.173493i | ||||
\(997\) | 20.4803 | + | 3.24377i | 0.648619 | + | 0.102731i | 0.472070 | − | 0.881561i | \(-0.343507\pi\) |
0.176548 | + | 0.984292i | \(0.443507\pi\) | |||||||
\(998\) | −4.05748 | + | 7.96325i | −0.128437 | + | 0.252072i | ||||
\(999\) | −22.6995 | − | 11.1315i | −0.718180 | − | 0.352186i |
(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 | 750.2.l.b.107.3 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.107.9 | 80 | ||
5.2 | odd | 4 | 750.2.l.c.143.6 | 80 | |||
5.3 | odd | 4 | 750.2.l.a.143.5 | 80 | |||
5.4 | even | 2 | 150.2.l.a.17.8 | yes | 80 | ||
15.2 | even | 4 | 750.2.l.c.143.1 | 80 | |||
15.8 | even | 4 | 750.2.l.a.143.10 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.17.2 | ✓ | 80 | ||
25.3 | odd | 20 | inner | 750.2.l.b.743.9 | 80 | ||
25.4 | even | 10 | 750.2.l.c.257.1 | 80 | |||
25.21 | even | 5 | 750.2.l.a.257.10 | 80 | |||
25.22 | odd | 20 | 150.2.l.a.53.2 | yes | 80 | ||
75.29 | odd | 10 | 750.2.l.c.257.6 | 80 | |||
75.47 | even | 20 | 150.2.l.a.53.8 | yes | 80 | ||
75.53 | even | 20 | inner | 750.2.l.b.743.3 | 80 | ||
75.71 | odd | 10 | 750.2.l.a.257.5 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.2 | ✓ | 80 | 15.14 | odd | 2 | ||
150.2.l.a.17.8 | yes | 80 | 5.4 | even | 2 | ||
150.2.l.a.53.2 | yes | 80 | 25.22 | odd | 20 | ||
150.2.l.a.53.8 | yes | 80 | 75.47 | even | 20 | ||
750.2.l.a.143.5 | 80 | 5.3 | odd | 4 | |||
750.2.l.a.143.10 | 80 | 15.8 | even | 4 | |||
750.2.l.a.257.5 | 80 | 75.71 | odd | 10 | |||
750.2.l.a.257.10 | 80 | 25.21 | even | 5 | |||
750.2.l.b.107.3 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.b.107.9 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.743.3 | 80 | 75.53 | even | 20 | inner | ||
750.2.l.b.743.9 | 80 | 25.3 | odd | 20 | inner | ||
750.2.l.c.143.1 | 80 | 15.2 | even | 4 | |||
750.2.l.c.143.6 | 80 | 5.2 | odd | 4 | |||
750.2.l.c.257.1 | 80 | 25.4 | even | 10 | |||
750.2.l.c.257.6 | 80 | 75.29 | odd | 10 |