Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,2,Mod(49,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.n (of order \(8\), degree \(4\), 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: | \(3.39364208590\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Character | \(\chi\) | \(=\) | 425.274 |
Dual form | 425.2.n.e.349.4 |
$q$-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 \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.982785 | − | 0.982785i | 0.694934 | − | 0.694934i | −0.268380 | − | 0.963313i | \(-0.586488\pi\) |
0.963313 | + | 0.268380i | \(0.0864881\pi\) | |||||||
\(3\) | −0.0424107 | − | 0.102388i | −0.0244858 | − | 0.0591140i | 0.911164 | − | 0.412045i | \(-0.135185\pi\) |
−0.935650 | + | 0.352931i | \(0.885185\pi\) | |||||||
\(4\) | 0.0682683i | 0.0341341i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.142306 | − | 0.0589452i | −0.0580964 | − | 0.0240643i | ||||
\(7\) | −1.58527 | − | 0.656642i | −0.599177 | − | 0.248187i | 0.0624163 | − | 0.998050i | \(-0.480119\pi\) |
−0.661593 | + | 0.749863i | \(0.730119\pi\) | |||||||
\(8\) | 2.03266 | + | 2.03266i | 0.718655 | + | 0.718655i | ||||
\(9\) | 2.11264 | − | 2.11264i | 0.704212 | − | 0.704212i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.35924 | + | 2.21987i | 1.61587 | + | 0.669316i | 0.993545 | − | 0.113442i | \(-0.0361876\pi\) |
0.622327 | + | 0.782758i | \(0.286188\pi\) | |||||||
\(12\) | 0.00698988 | − | 0.00289530i | 0.00201781 | − | 0.000835803i | ||||
\(13\) | 1.25411 | 0.347827 | 0.173913 | − | 0.984761i | \(-0.444359\pi\) | ||||
0.173913 | + | 0.984761i | \(0.444359\pi\) | |||||||
\(14\) | −2.20332 | + | 0.912645i | −0.588862 | + | 0.243915i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.85880 | 0.964701 | ||||||||
\(17\) | −1.85005 | − | 3.68474i | −0.448703 | − | 0.893681i | ||||
\(18\) | − | 4.15253i | − | 0.978761i | ||||||
\(19\) | −1.99782 | − | 1.99782i | −0.458331 | − | 0.458331i | 0.439776 | − | 0.898107i | \(-0.355058\pi\) |
−0.898107 | + | 0.439776i | \(0.855058\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.190162i | 0.0414968i | ||||||||
\(22\) | 7.44863 | − | 3.08532i | 1.58805 | − | 0.657793i | ||||
\(23\) | 0.785431 | − | 1.89620i | 0.163774 | − | 0.395385i | −0.820594 | − | 0.571512i | \(-0.806357\pi\) |
0.984367 | + | 0.176127i | \(0.0563570\pi\) | |||||||
\(24\) | 0.121915 | − | 0.294328i | 0.0248857 | − | 0.0600794i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23252 | − | 1.23252i | 0.241716 | − | 0.241716i | ||||
\(27\) | −0.613073 | − | 0.253943i | −0.117986 | − | 0.0488714i | ||||
\(28\) | 0.0448278 | − | 0.108224i | 0.00847165 | − | 0.0204524i | ||||
\(29\) | 1.99220 | + | 4.80961i | 0.369943 | + | 0.893122i | 0.993759 | + | 0.111550i | \(0.0355816\pi\) |
−0.623816 | + | 0.781572i | \(0.714418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.64434 | + | 1.09532i | −0.474937 | + | 0.196725i | −0.607295 | − | 0.794477i | \(-0.707745\pi\) |
0.132358 | + | 0.991202i | \(0.457745\pi\) | |||||||
\(32\) | −0.272952 | + | 0.272952i | −0.0482516 | + | 0.0482516i | ||||
\(33\) | − | 0.642871i | − | 0.111909i | ||||||
\(34\) | −5.43951 | − | 1.80310i | −0.932868 | − | 0.309230i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.144226 | + | 0.144226i | 0.0240377 | + | 0.0240377i | ||||
\(37\) | 2.41443 | + | 5.82896i | 0.396931 | + | 0.958275i | 0.988390 | + | 0.151940i | \(0.0485521\pi\) |
−0.591459 | + | 0.806335i | \(0.701448\pi\) | |||||||
\(38\) | −3.92685 | −0.637019 | ||||||||
\(39\) | −0.0531875 | − | 0.128406i | −0.00851682 | − | 0.0205614i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.61688 | + | 8.73191i | −0.564861 | + | 1.36370i | 0.340977 | + | 0.940072i | \(0.389242\pi\) |
−0.905838 | + | 0.423624i | \(0.860758\pi\) | |||||||
\(42\) | 0.186889 | + | 0.186889i | 0.0288375 | + | 0.0288375i | ||||
\(43\) | −5.25643 | − | 5.25643i | −0.801597 | − | 0.801597i | 0.181748 | − | 0.983345i | \(-0.441825\pi\) |
−0.983345 | + | 0.181748i | \(0.941825\pi\) | |||||||
\(44\) | −0.151547 | + | 0.365866i | −0.0228465 | + | 0.0551564i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.09165 | − | 2.63546i | −0.160954 | − | 0.388578i | ||||
\(47\) | −7.63491 | −1.11367 | −0.556833 | − | 0.830624i | \(-0.687984\pi\) | ||||
−0.556833 | + | 0.830624i | \(0.687984\pi\) | |||||||
\(48\) | −0.163655 | − | 0.395097i | −0.0236215 | − | 0.0570273i | ||||
\(49\) | −2.86784 | − | 2.86784i | −0.409691 | − | 0.409691i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.298813 | + | 0.345696i | −0.0418422 | + | 0.0484072i | ||||
\(52\) | 0.0856157i | 0.0118728i | ||||||||
\(53\) | 5.09637 | − | 5.09637i | 0.700040 | − | 0.700040i | −0.264379 | − | 0.964419i | \(-0.585167\pi\) |
0.964419 | + | 0.264379i | \(0.0851670\pi\) | |||||||
\(54\) | −0.852091 | + | 0.352948i | −0.115955 | + | 0.0480301i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.88759 | − | 4.55706i | −0.252240 | − | 0.608962i | ||||
\(57\) | −0.119825 | + | 0.289282i | −0.0158712 | + | 0.0383164i | ||||
\(58\) | 6.68472 | + | 2.76890i | 0.877746 | + | 0.363574i | ||||
\(59\) | 1.54321 | − | 1.54321i | 0.200908 | − | 0.200908i | −0.599481 | − | 0.800389i | \(-0.704626\pi\) |
0.800389 | + | 0.599481i | \(0.204626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19586 | − | 5.30128i | 0.281152 | − | 0.678760i | −0.718712 | − | 0.695308i | \(-0.755268\pi\) |
0.999863 | + | 0.0165485i | \(0.00526780\pi\) | |||||||
\(62\) | −1.52235 | + | 3.67528i | −0.193339 | + | 0.466761i | ||||
\(63\) | −4.73635 | + | 1.96186i | −0.596724 | + | 0.247171i | ||||
\(64\) | 8.25411i | 1.03176i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.631803 | − | 0.631803i | −0.0777696 | − | 0.0777696i | ||||
\(67\) | 2.46660i | 0.301343i | 0.988584 | + | 0.150672i | \(0.0481436\pi\) | ||||
−0.988584 | + | 0.150672i | \(0.951856\pi\) | |||||||
\(68\) | 0.251551 | − | 0.126300i | 0.0305050 | − | 0.0153161i | ||||
\(69\) | −0.227460 | −0.0273829 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4522 | + | 5.15787i | −1.47780 | + | 0.612126i | −0.968623 | − | 0.248534i | \(-0.920051\pi\) |
−0.509180 | + | 0.860660i | \(0.670051\pi\) | |||||||
\(72\) | 8.58855 | 1.01217 | ||||||||
\(73\) | −5.39319 | + | 2.23393i | −0.631225 | + | 0.261462i | −0.675273 | − | 0.737567i | \(-0.735974\pi\) |
0.0440485 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(74\) | 8.10148 | + | 3.35574i | 0.941778 | + | 0.390097i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.136388 | − | 0.136388i | 0.0156447 | − | 0.0156447i | ||||
\(77\) | −7.03820 | − | 7.03820i | −0.802077 | − | 0.802077i | ||||
\(78\) | −0.178467 | − | 0.0739236i | −0.0202075 | − | 0.00837020i | ||||
\(79\) | 3.62361 | + | 1.50095i | 0.407688 | + | 0.168870i | 0.577096 | − | 0.816676i | \(-0.304186\pi\) |
−0.169408 | + | 0.985546i | \(0.554186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 8.88961i | − | 0.987735i | ||||||
\(82\) | 5.02698 | + | 12.1362i | 0.555137 | + | 1.34022i | ||||
\(83\) | −6.29967 | + | 6.29967i | −0.691478 | + | 0.691478i | −0.962557 | − | 0.271079i | \(-0.912620\pi\) |
0.271079 | + | 0.962557i | \(0.412620\pi\) | |||||||
\(84\) | −0.0129821 | −0.00141646 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3319 | −1.11411 | ||||||||
\(87\) | 0.407958 | − | 0.407958i | 0.0437376 | − | 0.0437376i | ||||
\(88\) | 6.38128 | + | 15.4058i | 0.680247 | + | 1.64226i | ||||
\(89\) | − | 14.3079i | − | 1.51664i | −0.651885 | − | 0.758318i | \(-0.726022\pi\) | ||
0.651885 | − | 0.758318i | \(-0.273978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.98810 | − | 0.823498i | −0.208410 | − | 0.0863261i | ||||
\(92\) | 0.129450 | + | 0.0536200i | 0.0134961 | + | 0.00559027i | ||||
\(93\) | 0.224296 | + | 0.224296i | 0.0232584 | + | 0.0232584i | ||||
\(94\) | −7.50348 | + | 7.50348i | −0.773925 | + | 0.773925i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0395233 | + | 0.0163711i | 0.00403383 | + | 0.00167087i | ||||
\(97\) | −7.84699 | + | 3.25033i | −0.796741 | + | 0.330021i | −0.743650 | − | 0.668569i | \(-0.766907\pi\) |
−0.0530907 | + | 0.998590i | \(0.516907\pi\) | |||||||
\(98\) | −5.63693 | −0.569416 | ||||||||
\(99\) | 16.0119 | − | 6.63234i | 1.60926 | − | 0.666576i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.53832 | 0.252572 | 0.126286 | − | 0.991994i | \(-0.459694\pi\) | ||||
0.126286 | + | 0.991994i | \(0.459694\pi\) | |||||||
\(102\) | 0.0460763 | + | 0.633414i | 0.00456224 | + | 0.0627173i | ||||
\(103\) | 16.6715i | 1.64269i | 0.570429 | + | 0.821347i | \(0.306777\pi\) | ||||
−0.570429 | + | 0.821347i | \(0.693223\pi\) | |||||||
\(104\) | 2.54918 | + | 2.54918i | 0.249967 | + | 0.249967i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 10.0173i | − | 0.972962i | ||||||
\(107\) | −8.40335 | + | 3.48078i | −0.812382 | + | 0.336500i | −0.749904 | − | 0.661546i | \(-0.769900\pi\) |
−0.0624783 | + | 0.998046i | \(0.519900\pi\) | |||||||
\(108\) | 0.0173363 | − | 0.0418535i | 0.00166818 | − | 0.00402735i | ||||
\(109\) | −0.284608 | + | 0.687106i | −0.0272605 | + | 0.0658128i | −0.936924 | − | 0.349534i | \(-0.886340\pi\) |
0.909663 | + | 0.415347i | \(0.136340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.494421 | − | 0.494421i | 0.0469283 | − | 0.0469283i | ||||
\(112\) | −6.11726 | − | 2.53385i | −0.578026 | − | 0.239426i | ||||
\(113\) | 3.45825 | − | 8.34896i | 0.325325 | − | 0.785404i | −0.673602 | − | 0.739094i | \(-0.735254\pi\) |
0.998927 | − | 0.0463099i | \(-0.0147462\pi\) | |||||||
\(114\) | 0.166540 | + | 0.402064i | 0.0155979 | + | 0.0376568i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.328344 | + | 0.136004i | −0.0304859 | + | 0.0126277i | ||||
\(117\) | 2.64947 | − | 2.64947i | 0.244944 | − | 0.244944i | ||||
\(118\) | − | 3.03328i | − | 0.279236i | ||||||
\(119\) | 0.513284 | + | 7.05614i | 0.0470526 | + | 0.646835i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0154 | + | 16.0154i | 1.45595 | + | 1.45595i | ||||
\(122\) | −3.05196 | − | 7.36808i | −0.276311 | − | 0.667075i | ||||
\(123\) | 1.04744 | 0.0944446 | ||||||||
\(124\) | −0.0747756 | − | 0.180524i | −0.00671505 | − | 0.0162116i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.72673 | + | 6.58290i | −0.242916 | + | 0.586451i | ||||
\(127\) | 10.2527 | + | 10.2527i | 0.909779 | + | 0.909779i | 0.996254 | − | 0.0864752i | \(-0.0275603\pi\) |
−0.0864752 | + | 0.996254i | \(0.527560\pi\) | |||||||
\(128\) | 7.56611 | + | 7.56611i | 0.668756 | + | 0.668756i | ||||
\(129\) | −0.315269 | + | 0.761126i | −0.0277579 | + | 0.0670134i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.44750 | − | 15.5656i | −0.563321 | − | 1.35998i | −0.907096 | − | 0.420924i | \(-0.861706\pi\) |
0.343775 | − | 0.939052i | \(-0.388294\pi\) | |||||||
\(132\) | 0.0438877 | 0.00381993 | ||||||||
\(133\) | 1.85524 | + | 4.47894i | 0.160869 | + | 0.388373i | ||||
\(134\) | 2.42414 | + | 2.42414i | 0.209414 | + | 0.209414i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.72930 | − | 11.2504i | 0.319785 | − | 0.964711i | ||||
\(137\) | − | 20.2283i | − | 1.72822i | −0.503300 | − | 0.864111i | \(-0.667881\pi\) | ||
0.503300 | − | 0.864111i | \(-0.332119\pi\) | |||||||
\(138\) | −0.223544 | + | 0.223544i | −0.0190293 | + | 0.0190293i | ||||
\(139\) | 3.93292 | − | 1.62907i | 0.333586 | − | 0.138176i | −0.209603 | − | 0.977787i | \(-0.567217\pi\) |
0.543188 | + | 0.839611i | \(0.317217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.323802 | + | 0.781727i | 0.0272690 | + | 0.0658333i | ||||
\(142\) | −7.16875 | + | 17.3069i | −0.601588 | + | 1.45236i | ||||
\(143\) | 6.72106 | + | 2.78395i | 0.562043 | + | 0.232806i | ||||
\(144\) | 8.15224 | − | 8.15224i | 0.679354 | − | 0.679354i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.10487 | + | 7.49582i | −0.256961 | + | 0.620358i | ||||
\(147\) | −0.172006 | + | 0.415260i | −0.0141868 | + | 0.0342501i | ||||
\(148\) | −0.397933 | + | 0.164829i | −0.0327099 | + | 0.0135489i | ||||
\(149\) | − | 4.32633i | − | 0.354427i | −0.984172 | − | 0.177213i | \(-0.943292\pi\) | ||
0.984172 | − | 0.177213i | \(-0.0567083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1854 | − | 14.1854i | −1.15439 | − | 1.15439i | −0.985663 | − | 0.168725i | \(-0.946035\pi\) |
−0.168725 | − | 0.985663i | \(-0.553965\pi\) | |||||||
\(152\) | − | 8.12178i | − | 0.658763i | ||||||
\(153\) | −11.6930 | − | 3.87603i | −0.945323 | − | 0.313358i | ||||
\(154\) | −13.8341 | −1.11478 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.00876606 | − | 0.00363102i | 0.000701846 | − | 0.000290714i | ||||
\(157\) | 21.7028 | 1.73207 | 0.866035 | − | 0.499983i | \(-0.166661\pi\) | ||||
0.866035 | + | 0.499983i | \(0.166661\pi\) | |||||||
\(158\) | 5.03634 | − | 2.08612i | 0.400669 | − | 0.165963i | ||||
\(159\) | −0.737950 | − | 0.305669i | −0.0585232 | − | 0.0242411i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.49025 | + | 2.49025i | −0.196259 | + | 0.196259i | ||||
\(162\) | −8.73658 | − | 8.73658i | −0.686410 | − | 0.686410i | ||||
\(163\) | −1.22517 | − | 0.507480i | −0.0959623 | − | 0.0397489i | 0.334186 | − | 0.942507i | \(-0.391539\pi\) |
−0.430148 | + | 0.902758i | \(0.641539\pi\) | |||||||
\(164\) | −0.596112 | − | 0.246918i | −0.0465486 | − | 0.0192810i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.3824i | 0.961063i | ||||||||
\(167\) | 9.56366 | + | 23.0887i | 0.740058 | + | 1.78666i | 0.605647 | + | 0.795733i | \(0.292914\pi\) |
0.134411 | + | 0.990926i | \(0.457086\pi\) | |||||||
\(168\) | −0.386536 | + | 0.386536i | −0.0298219 | + | 0.0298219i | ||||
\(169\) | −11.4272 | −0.879017 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.44132 | −0.645524 | ||||||||
\(172\) | 0.358847 | − | 0.358847i | 0.0273618 | − | 0.0273618i | ||||
\(173\) | −6.10776 | − | 14.7454i | −0.464364 | − | 1.12108i | −0.966587 | − | 0.256337i | \(-0.917484\pi\) |
0.502223 | − | 0.864738i | \(-0.332516\pi\) | |||||||
\(174\) | − | 0.801869i | − | 0.0607895i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.6802 | + | 8.56604i | 1.55883 | + | 0.645689i | ||||
\(177\) | −0.223455 | − | 0.0925582i | −0.0167959 | − | 0.00695710i | ||||
\(178\) | −14.0616 | − | 14.0616i | −1.05396 | − | 1.05396i | ||||
\(179\) | −10.5747 | + | 10.5747i | −0.790389 | + | 0.790389i | −0.981557 | − | 0.191168i | \(-0.938772\pi\) |
0.191168 | + | 0.981557i | \(0.438772\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6278 | + | 9.37275i | 1.68191 | + | 0.696671i | 0.999414 | − | 0.0342158i | \(-0.0108933\pi\) |
0.682499 | + | 0.730887i | \(0.260893\pi\) | |||||||
\(182\) | −2.76320 | + | 1.14455i | −0.204822 | + | 0.0848400i | ||||
\(183\) | −0.635918 | −0.0470084 | ||||||||
\(184\) | 5.45085 | − | 2.25782i | 0.401842 | − | 0.166448i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.440870 | 0.0323262 | ||||||||
\(187\) | −1.73523 | − | 23.8543i | −0.126892 | − | 1.74440i | ||||
\(188\) | − | 0.521222i | − | 0.0380140i | ||||||
\(189\) | 0.805139 | + | 0.805139i | 0.0585652 | + | 0.0585652i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.254656i | − | 0.0184263i | −0.999958 | − | 0.00921313i | \(-0.997067\pi\) | ||
0.999958 | − | 0.00921313i | \(-0.00293267\pi\) | |||||||
\(192\) | 0.845126 | − | 0.350063i | 0.0609917 | − | 0.0252636i | ||||
\(193\) | 1.13619 | − | 2.74301i | 0.0817848 | − | 0.197446i | −0.877697 | − | 0.479215i | \(-0.840921\pi\) |
0.959482 | + | 0.281769i | \(0.0909213\pi\) | |||||||
\(194\) | −4.51753 | + | 10.9063i | −0.324340 | + | 0.783025i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.195782 | − | 0.195782i | 0.0139844 | − | 0.0139844i | ||||
\(197\) | −5.61826 | − | 2.32716i | −0.400284 | − | 0.165803i | 0.173454 | − | 0.984842i | \(-0.444507\pi\) |
−0.573738 | + | 0.819039i | \(0.694507\pi\) | |||||||
\(198\) | 9.21808 | − | 22.2544i | 0.655100 | − | 1.58155i | ||||
\(199\) | −4.80772 | − | 11.6069i | −0.340810 | − | 0.822789i | −0.997634 | − | 0.0687451i | \(-0.978100\pi\) |
0.656824 | − | 0.754044i | \(-0.271900\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.252552 | − | 0.104610i | 0.0178136 | − | 0.00737864i | ||||
\(202\) | 2.49462 | − | 2.49462i | 0.175521 | − | 0.175521i | ||||
\(203\) | − | 8.93271i | − | 0.626953i | ||||||
\(204\) | −0.0236001 | − | 0.0203994i | −0.00165234 | − | 0.00142825i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.3845 | + | 16.3845i | 1.14156 | + | 1.14156i | ||||
\(207\) | −2.34665 | − | 5.66531i | −0.163103 | − | 0.393766i | ||||
\(208\) | 4.83935 | 0.335549 | ||||||||
\(209\) | −6.27189 | − | 15.1417i | −0.433836 | − | 1.04737i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.60978 | + | 11.1290i | −0.317351 | + | 0.766152i | 0.682042 | + | 0.731313i | \(0.261092\pi\) |
−0.999393 | + | 0.0348394i | \(0.988908\pi\) | |||||||
\(212\) | 0.347920 | + | 0.347920i | 0.0238953 | + | 0.0238953i | ||||
\(213\) | 1.05621 | + | 1.05621i | 0.0723705 | + | 0.0723705i | ||||
\(214\) | −4.83783 | + | 11.6795i | −0.330707 | + | 0.798397i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.729990 | − | 1.76235i | −0.0496695 | − | 0.119913i | ||||
\(217\) | 4.91123 | 0.333396 | ||||||||
\(218\) | 0.395568 | + | 0.954986i | 0.0267912 | + | 0.0646798i | ||||
\(219\) | 0.457458 | + | 0.457458i | 0.0309121 | + | 0.0309121i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.32016 | − | 4.62106i | −0.156071 | − | 0.310846i | ||||
\(222\) | − | 0.971818i | − | 0.0652242i | ||||||
\(223\) | 12.5656 | − | 12.5656i | 0.841453 | − | 0.841453i | −0.147595 | − | 0.989048i | \(-0.547153\pi\) |
0.989048 | + | 0.147595i | \(0.0471533\pi\) | |||||||
\(224\) | 0.611936 | − | 0.253472i | 0.0408867 | − | 0.0169358i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.80651 | − | 11.6039i | −0.319724 | − | 0.771883i | ||||
\(227\) | −4.27575 | + | 10.3226i | −0.283791 | + | 0.685133i | −0.999918 | − | 0.0128377i | \(-0.995914\pi\) |
0.716126 | + | 0.697971i | \(0.245914\pi\) | |||||||
\(228\) | −0.0197488 | − | 0.00818022i | −0.00130790 | − | 0.000541749i | ||||
\(229\) | −15.0941 | + | 15.0941i | −0.997445 | + | 0.997445i | −0.999997 | − | 0.00255174i | \(-0.999188\pi\) |
0.00255174 | + | 0.999997i | \(0.499188\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.422135 | + | 1.01913i | −0.0277745 | + | 0.0670535i | ||||
\(232\) | −5.72683 | + | 13.8258i | −0.375985 | + | 0.907708i | ||||
\(233\) | −7.67330 | + | 3.17839i | −0.502695 | + | 0.208223i | −0.619597 | − | 0.784920i | \(-0.712704\pi\) |
0.116902 | + | 0.993143i | \(0.462704\pi\) | |||||||
\(234\) | − | 5.20772i | − | 0.340439i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.105352 | + | 0.105352i | 0.00685784 | + | 0.00685784i | ||||
\(237\) | − | 0.434672i | − | 0.0282350i | ||||||
\(238\) | 7.43911 | + | 6.43022i | 0.482206 | + | 0.416809i | ||||
\(239\) | 3.42382 | 0.221468 | 0.110734 | − | 0.993850i | \(-0.464680\pi\) | ||||
0.110734 | + | 0.993850i | \(0.464680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.86504 | + | 2.42938i | −0.377800 | + | 0.156490i | −0.563499 | − | 0.826117i | \(-0.690545\pi\) |
0.185699 | + | 0.982607i | \(0.440545\pi\) | |||||||
\(242\) | 31.4795 | 2.02358 | ||||||||
\(243\) | −2.74941 | + | 1.13884i | −0.176375 | + | 0.0730569i | ||||
\(244\) | 0.361909 | + | 0.149908i | 0.0231689 | + | 0.00959686i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.02941 | − | 1.02941i | 0.0656327 | − | 0.0656327i | ||||
\(247\) | −2.50548 | − | 2.50548i | −0.159420 | − | 0.159420i | ||||
\(248\) | −7.60146 | − | 3.14863i | −0.482693 | − | 0.199938i | ||||
\(249\) | 0.912187 | + | 0.377840i | 0.0578075 | + | 0.0239446i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.06308i | − | 0.319579i | −0.987151 | − | 0.159789i | \(-0.948919\pi\) | ||
0.987151 | − | 0.159789i | \(-0.0510815\pi\) | |||||||
\(252\) | −0.133933 | − | 0.323342i | −0.00843697 | − | 0.0203687i | ||||
\(253\) | 8.41863 | − | 8.41863i | 0.529275 | − | 0.529275i | ||||
\(254\) | 20.1524 | 1.26447 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.63651 | −0.102282 | ||||||||
\(257\) | 12.6054 | − | 12.6054i | 0.786305 | − | 0.786305i | −0.194582 | − | 0.980886i | \(-0.562335\pi\) |
0.980886 | + | 0.194582i | \(0.0623349\pi\) | |||||||
\(258\) | 0.438182 | + | 1.05786i | 0.0272800 | + | 0.0658598i | ||||
\(259\) | − | 10.8259i | − | 0.672689i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.3698 | + | 5.95215i | 0.889465 | + | 0.368429i | ||||
\(262\) | −21.6342 | − | 8.96117i | −1.33656 | − | 0.553623i | ||||
\(263\) | 6.44016 | + | 6.44016i | 0.397117 | + | 0.397117i | 0.877215 | − | 0.480098i | \(-0.159399\pi\) |
−0.480098 | + | 0.877215i | \(0.659399\pi\) | |||||||
\(264\) | 1.30674 | − | 1.30674i | 0.0804242 | − | 0.0804242i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.22513 | + | 2.57853i | 0.381687 | + | 0.158100i | ||||
\(267\) | −1.46496 | + | 0.606808i | −0.0896544 | + | 0.0371361i | ||||
\(268\) | −0.168391 | −0.0102861 | ||||||||
\(269\) | 11.7926 | − | 4.88466i | 0.719008 | − | 0.297823i | 0.00698191 | − | 0.999976i | \(-0.497778\pi\) |
0.712027 | + | 0.702153i | \(0.247778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4128 | 0.997004 | 0.498502 | − | 0.866889i | \(-0.333884\pi\) | ||||
0.498502 | + | 0.866889i | \(0.333884\pi\) | |||||||
\(272\) | −7.13899 | − | 14.2187i | −0.432865 | − | 0.862134i | ||||
\(273\) | 0.238484i | 0.0144337i | ||||||||
\(274\) | −19.8801 | − | 19.8801i | −1.20100 | − | 1.20100i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 0.0155283i | − | 0.000934692i | ||||||
\(277\) | 17.0407 | − | 7.05850i | 1.02388 | − | 0.424104i | 0.193379 | − | 0.981124i | \(-0.438055\pi\) |
0.830499 | + | 0.557020i | \(0.188055\pi\) | |||||||
\(278\) | 2.26419 | − | 5.46623i | 0.135797 | − | 0.327843i | ||||
\(279\) | −3.27251 | + | 7.90053i | −0.195920 | + | 0.472992i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2557 | − | 13.2557i | 0.790767 | − | 0.790767i | −0.190852 | − | 0.981619i | \(-0.561125\pi\) |
0.981619 | + | 0.190852i | \(0.0611251\pi\) | |||||||
\(282\) | 1.08650 | + | 0.450042i | 0.0647000 | + | 0.0267996i | ||||
\(283\) | −7.57337 | + | 18.2837i | −0.450190 | + | 1.08686i | 0.522059 | + | 0.852909i | \(0.325164\pi\) |
−0.972250 | + | 0.233946i | \(0.924836\pi\) | |||||||
\(284\) | −0.352119 | − | 0.850090i | −0.0208944 | − | 0.0504435i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.34138 | − | 3.86933i | 0.552367 | − | 0.228798i | ||||
\(287\) | 11.4675 | − | 11.4675i | 0.676903 | − | 0.676903i | ||||
\(288\) | 1.15330i | 0.0679587i | ||||||||
\(289\) | −10.1546 | + | 13.6339i | −0.597330 | + | 0.801995i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.665592 | + | 0.665592i | 0.0390177 | + | 0.0390177i | ||||
\(292\) | −0.152507 | − | 0.368184i | −0.00892478 | − | 0.0215463i | ||||
\(293\) | −14.0051 | −0.818189 | −0.409094 | − | 0.912492i | \(-0.634155\pi\) | ||||
−0.409094 | + | 0.912492i | \(0.634155\pi\) | |||||||
\(294\) | 0.239066 | + | 0.577157i | 0.0139426 | + | 0.0336605i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.94058 | + | 16.7560i | −0.403413 | + | 0.973925i | ||||
\(297\) | −2.72189 | − | 2.72189i | −0.157940 | − | 0.157940i | ||||
\(298\) | −4.25185 | − | 4.25185i | −0.246303 | − | 0.246303i | ||||
\(299\) | 0.985014 | − | 2.37803i | 0.0569648 | − | 0.137525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.88128 | + | 11.7845i | 0.281352 | + | 0.679245i | ||||
\(302\) | −27.8823 | −1.60445 | ||||||||
\(303\) | −0.107652 | − | 0.259895i | −0.00618444 | − | 0.0149306i | ||||
\(304\) | −7.70919 | − | 7.70919i | −0.442152 | − | 0.442152i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.3010 | + | 7.68240i | −0.874700 | + | 0.439174i | ||||
\(307\) | 13.2813i | 0.758001i | 0.925396 | + | 0.379001i | \(0.123732\pi\) | ||||
−0.925396 | + | 0.379001i | \(0.876268\pi\) | |||||||
\(308\) | 0.480486 | − | 0.480486i | 0.0273782 | − | 0.0273782i | ||||
\(309\) | 1.70697 | − | 0.707051i | 0.0971062 | − | 0.0402227i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.01417 | − | 21.7621i | −0.511147 | − | 1.23402i | −0.943217 | − | 0.332178i | \(-0.892217\pi\) |
0.432070 | − | 0.901840i | \(-0.357783\pi\) | |||||||
\(312\) | 0.152894 | − | 0.369118i | 0.00865591 | − | 0.0208972i | ||||
\(313\) | 30.1714 | + | 12.4974i | 1.70539 | + | 0.706394i | 0.999997 | − | 0.00242660i | \(-0.000772411\pi\) |
0.705389 | + | 0.708821i | \(0.250772\pi\) | |||||||
\(314\) | 21.3292 | − | 21.3292i | 1.20367 | − | 1.20367i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.102467 | + | 0.247378i | −0.00576423 | + | 0.0139161i | ||||
\(317\) | −9.72053 | + | 23.4674i | −0.545960 | + | 1.31806i | 0.374501 | + | 0.927227i | \(0.377814\pi\) |
−0.920460 | + | 0.390836i | \(0.872186\pi\) | |||||||
\(318\) | −1.02565 | + | 0.424839i | −0.0575157 | + | 0.0238238i | ||||
\(319\) | 30.1983i | 1.69078i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.712784 | + | 0.712784i | 0.0397837 | + | 0.0397837i | ||||
\(322\) | 4.89475i | 0.272774i | ||||||||
\(323\) | −3.66537 | + | 11.0575i | −0.203947 | + | 0.615256i | ||||
\(324\) | 0.606878 | 0.0337155 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.70282 | + | 0.705330i | −0.0943103 | + | 0.0390646i | ||||
\(327\) | 0.0824221 | 0.00455795 | ||||||||
\(328\) | −25.1009 | + | 10.3971i | −1.38597 | + | 0.574086i | ||||
\(329\) | 12.1034 | + | 5.01340i | 0.667283 | + | 0.276398i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0376 | − | 13.0376i | 0.716613 | − | 0.716613i | −0.251297 | − | 0.967910i | \(-0.580857\pi\) |
0.967910 | + | 0.251297i | \(0.0808570\pi\) | |||||||
\(332\) | −0.430067 | − | 0.430067i | −0.0236030 | − | 0.0236030i | ||||
\(333\) | 17.4153 | + | 7.21365i | 0.954352 | + | 0.395306i | ||||
\(334\) | 32.0903 | + | 13.2922i | 1.75590 | + | 0.727318i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.733799i | 0.0400320i | ||||||||
\(337\) | 2.52852 | + | 6.10439i | 0.137737 | + | 0.332527i | 0.977664 | − | 0.210172i | \(-0.0674023\pi\) |
−0.839927 | + | 0.542699i | \(0.817402\pi\) | |||||||
\(338\) | −11.2305 | + | 11.2305i | −0.610858 | + | 0.610858i | ||||
\(339\) | −1.00150 | −0.0543942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.6031 | −0.899108 | ||||||||
\(342\) | −8.29600 | + | 8.29600i | −0.448596 | + | 0.448596i | ||||
\(343\) | 7.25965 | + | 17.5264i | 0.391984 | + | 0.946334i | ||||
\(344\) | − | 21.3691i | − | 1.15214i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.4942 | − | 8.48898i | −1.10178 | − | 0.456370i | ||||
\(347\) | −8.88319 | − | 3.67954i | −0.476875 | − | 0.197528i | 0.131282 | − | 0.991345i | \(-0.458091\pi\) |
−0.608157 | + | 0.793817i | \(0.708091\pi\) | |||||||
\(348\) | 0.0278506 | + | 0.0278506i | 0.00149295 | + | 0.00149295i | ||||
\(349\) | 0.486525 | − | 0.486525i | 0.0260431 | − | 0.0260431i | −0.693965 | − | 0.720008i | \(-0.744138\pi\) |
0.720008 | + | 0.693965i | \(0.244138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.768859 | − | 0.318472i | −0.0410387 | − | 0.0169988i | ||||
\(352\) | −2.06874 | + | 0.856898i | −0.110264 | + | 0.0456728i | ||||
\(353\) | 15.3590 | 0.817475 | 0.408737 | − | 0.912652i | \(-0.365969\pi\) | ||||
0.408737 | + | 0.912652i | \(0.365969\pi\) | |||||||
\(354\) | −0.310573 | + | 0.128644i | −0.0165068 | + | 0.00683733i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.976776 | 0.0517690 | ||||||||
\(357\) | 0.700699 | − | 0.351810i | 0.0370849 | − | 0.0186198i | ||||
\(358\) | 20.7853i | 1.09854i | ||||||||
\(359\) | 18.0696 | + | 18.0696i | 0.953676 | + | 0.953676i | 0.998974 | − | 0.0452975i | \(-0.0144236\pi\) |
−0.0452975 | + | 0.998974i | \(0.514424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.0174i | − | 0.579866i | ||||||
\(362\) | 31.4497 | − | 13.0269i | 1.65296 | − | 0.684678i | ||||
\(363\) | 0.960571 | − | 2.31902i | 0.0504169 | − | 0.121717i | ||||
\(364\) | 0.0562188 | − | 0.135724i | 0.00294667 | − | 0.00711388i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.624971 | + | 0.624971i | −0.0326678 | + | 0.0326678i | ||||
\(367\) | 1.06912 | + | 0.442844i | 0.0558076 | + | 0.0231163i | 0.410413 | − | 0.911900i | \(-0.365385\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(368\) | 3.03082 | − | 7.31706i | 0.157993 | − | 0.381428i | ||||
\(369\) | 10.8062 | + | 26.0885i | 0.562549 | + | 1.35811i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.4256 | + | 4.73265i | −0.593188 | + | 0.245707i | ||||
\(372\) | −0.0153123 | + | 0.0153123i | −0.000793907 | + | 0.000793907i | ||||
\(373\) | − | 15.1464i | − | 0.784251i | −0.919912 | − | 0.392126i | \(-0.871740\pi\) | ||
0.919912 | − | 0.392126i | \(-0.128260\pi\) | |||||||
\(374\) | −25.1490 | − | 21.7383i | −1.30042 | − | 1.12406i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.5192 | − | 15.5192i | −0.800342 | − | 0.800342i | ||||
\(377\) | 2.49844 | + | 6.03176i | 0.128676 | + | 0.310651i | ||||
\(378\) | 1.58256 | 0.0813979 | ||||||||
\(379\) | −5.98525 | − | 14.4497i | −0.307442 | − | 0.742230i | −0.999786 | − | 0.0206630i | \(-0.993422\pi\) |
0.692345 | − | 0.721567i | \(-0.256578\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.614933 | − | 1.48458i | 0.0315040 | − | 0.0760574i | ||||
\(382\) | −0.250272 | − | 0.250272i | −0.0128050 | − | 0.0128050i | ||||
\(383\) | −3.26890 | − | 3.26890i | −0.167033 | − | 0.167033i | 0.618641 | − | 0.785674i | \(-0.287684\pi\) |
−0.785674 | + | 0.618641i | \(0.787684\pi\) | |||||||
\(384\) | 0.453799 | − | 1.09557i | 0.0231578 | − | 0.0559079i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.57915 | − | 3.81242i | −0.0803769 | − | 0.194047i | ||||
\(387\) | −22.2098 | −1.12899 | ||||||||
\(388\) | −0.221894 | − | 0.535700i | −0.0112650 | − | 0.0271961i | ||||
\(389\) | −4.48189 | − | 4.48189i | −0.227241 | − | 0.227241i | 0.584298 | − | 0.811539i | \(-0.301370\pi\) |
−0.811539 | + | 0.584298i | \(0.801370\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.44009 | + | 0.613956i | −0.426834 | + | 0.0310491i | ||||
\(392\) | − | 11.6587i | − | 0.588852i | ||||||
\(393\) | −1.32030 | + | 1.32030i | −0.0666003 | + | 0.0666003i | ||||
\(394\) | −7.80864 | + | 3.23444i | −0.393393 | + | 0.162949i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.452779 | + | 1.09310i | 0.0227530 | + | 0.0549306i | ||||
\(397\) | −1.24201 | + | 2.99848i | −0.0623348 | + | 0.150490i | −0.951978 | − | 0.306167i | \(-0.900953\pi\) |
0.889643 | + | 0.456657i | \(0.150953\pi\) | |||||||
\(398\) | −16.1320 | − | 6.68210i | −0.808625 | − | 0.334943i | ||||
\(399\) | 0.379910 | − | 0.379910i | 0.0190193 | − | 0.0190193i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.78153 | − | 11.5436i | 0.238778 | − | 0.576462i | −0.758379 | − | 0.651814i | \(-0.774008\pi\) |
0.997157 | + | 0.0753522i | \(0.0240081\pi\) | |||||||
\(402\) | 0.145394 | − | 0.351013i | 0.00725161 | − | 0.0175069i | ||||
\(403\) | −3.31628 | + | 1.37365i | −0.165196 | + | 0.0684263i | ||||
\(404\) | 0.173287i | 0.00862133i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.77893 | − | 8.77893i | −0.435691 | − | 0.435691i | ||||
\(407\) | 36.5985i | 1.81412i | ||||||||
\(408\) | −1.31007 | + | 0.0952982i | −0.0648581 | + | 0.00471797i | ||||
\(409\) | −11.7076 | −0.578904 | −0.289452 | − | 0.957192i | \(-0.593473\pi\) | ||||
−0.289452 | + | 0.957192i | \(0.593473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.07115 | + | 0.857898i | −0.102162 | + | 0.0423170i | ||||
\(412\) | −1.13814 | −0.0560719 | ||||||||
\(413\) | −3.45974 | + | 1.43307i | −0.170243 | + | 0.0705168i | ||||
\(414\) | −7.87403 | − | 3.26153i | −0.386987 | − | 0.160295i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.342311 | + | 0.342311i | −0.0167832 | + | 0.0167832i | ||||
\(417\) | −0.333596 | − | 0.333596i | −0.0163362 | − | 0.0163362i | ||||
\(418\) | −21.0449 | − | 8.71709i | −1.02934 | − | 0.426367i | ||||
\(419\) | −0.503085 | − | 0.208385i | −0.0245773 | − | 0.0101803i | 0.370361 | − | 0.928888i | \(-0.379234\pi\) |
−0.394938 | + | 0.918708i | \(0.629234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3097i | 1.18478i | 0.805651 | + | 0.592391i | \(0.201816\pi\) | ||||
−0.805651 | + | 0.592391i | \(0.798184\pi\) | |||||||
\(422\) | 6.40699 | + | 15.4678i | 0.311887 | + | 0.752963i | ||||
\(423\) | −16.1298 | + | 16.1298i | −0.784257 | + | 0.784257i | ||||
\(424\) | 20.7184 | 1.00617 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.07606 | 0.100585 | ||||||||
\(427\) | −6.96209 | + | 6.96209i | −0.336919 | + | 0.336919i | ||||
\(428\) | −0.237627 | − | 0.573682i | −0.0114861 | − | 0.0277300i | ||||
\(429\) | − | 0.806228i | − | 0.0389251i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.92135 | − | 1.62428i | −0.188885 | − | 0.0782387i | 0.286236 | − | 0.958159i | \(-0.407596\pi\) |
−0.475121 | + | 0.879920i | \(0.657596\pi\) | |||||||
\(432\) | −2.36573 | − | 0.979917i | −0.113821 | − | 0.0471463i | ||||
\(433\) | 18.1756 | + | 18.1756i | 0.873464 | + | 0.873464i | 0.992848 | − | 0.119384i | \(-0.0380919\pi\) |
−0.119384 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(434\) | 4.82668 | − | 4.82668i | 0.231688 | − | 0.231688i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0469075 | − | 0.0194297i | −0.00224646 | − | 0.000930515i | ||||
\(437\) | −5.35741 | + | 2.21911i | −0.256280 | + | 0.106154i | ||||
\(438\) | 0.899165 | 0.0429638 | ||||||||
\(439\) | −2.86412 | + | 1.18636i | −0.136697 | + | 0.0566217i | −0.449983 | − | 0.893037i | \(-0.648570\pi\) |
0.313286 | + | 0.949659i | \(0.398570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.1174 | −0.577018 | ||||||||
\(442\) | −6.82172 | − | 2.26128i | −0.324476 | − | 0.107558i | ||||
\(443\) | − | 26.3141i | − | 1.25022i | −0.780537 | − | 0.625109i | \(-0.785054\pi\) | ||
0.780537 | − | 0.625109i | \(-0.214946\pi\) | |||||||
\(444\) | 0.0337532 | + | 0.0337532i | 0.00160186 | + | 0.00160186i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 24.6985i | − | 1.16951i | ||||||
\(447\) | −0.442967 | + | 0.183483i | −0.0209516 | + | 0.00867844i | ||||
\(448\) | 5.41999 | − | 13.0850i | 0.256071 | − | 0.618209i | ||||
\(449\) | −5.62744 | + | 13.5858i | −0.265575 | + | 0.641156i | −0.999265 | − | 0.0383289i | \(-0.987797\pi\) |
0.733690 | + | 0.679485i | \(0.237797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.7674 | + | 38.7674i | −1.82549 | + | 1.82549i | ||||
\(452\) | 0.569969 | + | 0.236089i | 0.0268091 | + | 0.0111047i | ||||
\(453\) | −0.850807 | + | 2.05403i | −0.0399744 | + | 0.0965067i | ||||
\(454\) | 5.94272 | + | 14.3470i | 0.278906 | + | 0.673338i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.831577 | + | 0.344450i | −0.0389421 | + | 0.0161304i | ||||
\(457\) | −7.48280 | + | 7.48280i | −0.350030 | + | 0.350030i | −0.860121 | − | 0.510090i | \(-0.829612\pi\) |
0.510090 | + | 0.860121i | \(0.329612\pi\) | |||||||
\(458\) | 29.6685i | 1.38632i | ||||||||
\(459\) | 0.198502 | + | 2.72882i | 0.00926530 | + | 0.127371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0851 | − | 13.0851i | −0.609433 | − | 0.609433i | 0.333365 | − | 0.942798i | \(-0.391816\pi\) |
−0.942798 | + | 0.333365i | \(0.891816\pi\) | |||||||
\(462\) | 0.586712 | + | 1.41645i | 0.0272963 | + | 0.0658992i | ||||
\(463\) | −37.7389 | −1.75387 | −0.876937 | − | 0.480605i | \(-0.840417\pi\) | ||||
−0.876937 | + | 0.480605i | \(0.840417\pi\) | |||||||
\(464\) | 7.68753 | + | 18.5593i | 0.356884 | + | 0.861595i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.41754 | + | 10.6649i | −0.204638 | + | 0.494041i | ||||
\(467\) | 21.3821 | + | 21.3821i | 0.989444 | + | 0.989444i | 0.999945 | − | 0.0105009i | \(-0.00334262\pi\) |
−0.0105009 | + | 0.999945i | \(0.503343\pi\) | |||||||
\(468\) | 0.180875 | + | 0.180875i | 0.00836094 | + | 0.00836094i | ||||
\(469\) | 1.61967 | − | 3.91024i | 0.0747895 | − | 0.180558i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.920430 | − | 2.22211i | −0.0424112 | − | 0.102390i | ||||
\(472\) | 6.27364 | 0.288768 | ||||||||
\(473\) | −16.5019 | − | 39.8390i | −0.758756 | − | 1.83180i | ||||
\(474\) | −0.427189 | − | 0.427189i | −0.0196214 | − | 0.0196214i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.481710 | + | 0.0350410i | −0.0220792 | + | 0.00160610i | ||||
\(477\) | − | 21.5335i | − | 0.985953i | ||||||
\(478\) | 3.36487 | − | 3.36487i | 0.153906 | − | 0.153906i | ||||
\(479\) | −24.9054 | + | 10.3162i | −1.13796 | + | 0.471358i | −0.870479 | − | 0.492206i | \(-0.836191\pi\) |
−0.267480 | + | 0.963563i | \(0.586191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.02796 | + | 7.31014i | 0.138063 | + | 0.333314i | ||||
\(482\) | −3.37651 | + | 8.15163i | −0.153796 | + | 0.371296i | ||||
\(483\) | 0.360585 | + | 0.149359i | 0.0164072 | + | 0.00679609i | ||||
\(484\) | −1.09335 | + | 1.09335i | −0.0496976 | + | 0.0496976i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.58284 | + | 3.82132i | −0.0717992 | + | 0.173339i | ||||
\(487\) | −1.46660 | + | 3.54069i | −0.0664581 | + | 0.160444i | −0.953619 | − | 0.301016i | \(-0.902674\pi\) |
0.887161 | + | 0.461460i | \(0.152674\pi\) | |||||||
\(488\) | 15.2392 | − | 6.31227i | 0.689845 | − | 0.285743i | ||||
\(489\) | 0.146965i | 0.00664600i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.17285 | − | 4.17285i | −0.188318 | − | 0.188318i | 0.606651 | − | 0.794969i | \(-0.292513\pi\) |
−0.794969 | + | 0.606651i | \(0.792513\pi\) | |||||||
\(492\) | 0.0715070i | 0.00322378i | ||||||||
\(493\) | 14.0365 | − | 16.2388i | 0.632171 | − | 0.731358i | ||||
\(494\) | −4.92469 | −0.221572 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.2040 | + | 4.22662i | −0.458172 | + | 0.189781i | ||||
\(497\) | 23.1270 | 1.03739 | ||||||||
\(498\) | 1.26782 | − | 0.525148i | 0.0568123 | − | 0.0235324i | ||||
\(499\) | 40.7345 | + | 16.8728i | 1.82352 | + | 0.755329i | 0.973538 | + | 0.228524i | \(0.0733899\pi\) |
0.849986 | + | 0.526805i | \(0.176610\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.95842 | − | 1.95842i | 0.0874956 | − | 0.0874956i | ||||
\(502\) | −4.97592 | − | 4.97592i | −0.222086 | − | 0.222086i | ||||
\(503\) | 32.8295 | + | 13.5984i | 1.46380 | + | 0.606324i | 0.965435 | − | 0.260645i | \(-0.0839352\pi\) |
0.498362 | + | 0.866969i | \(0.333935\pi\) | |||||||
\(504\) | −13.6152 | − | 5.63960i | −0.606469 | − | 0.251208i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 16.5474i | − | 0.735621i | ||||||
\(507\) | 0.484636 | + | 1.17002i | 0.0215235 | + | 0.0519622i | ||||
\(508\) | −0.699933 | + | 0.699933i | −0.0310545 | + | 0.0310545i | ||||
\(509\) | −32.9351 | −1.45982 | −0.729911 | − | 0.683542i | \(-0.760438\pi\) | ||||
−0.729911 | + | 0.683542i | \(0.760438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0166 | 0.443107 | ||||||||
\(512\) | −16.7406 | + | 16.7406i | −0.739835 | + | 0.739835i | ||||
\(513\) | 0.717476 | + | 1.73214i | 0.0316774 | + | 0.0764759i | ||||
\(514\) | − | 24.7768i | − | 1.09286i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.0519608 | − | 0.0215229i | −0.00228744 | − | 0.000947491i | ||||
\(517\) | −40.9173 | − | 16.9485i | −1.79954 | − | 0.745395i | ||||
\(518\) | −10.6395 | − | 10.6395i | −0.467475 | − | 0.467475i | ||||
\(519\) | −1.25073 | + | 1.25073i | −0.0549009 | + | 0.0549009i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.6197 | + | 9.36938i | 0.990986 | + | 0.410480i | 0.818484 | − | 0.574529i | \(-0.194815\pi\) |
0.172502 | + | 0.985009i | \(0.444815\pi\) | |||||||
\(522\) | 19.9721 | − | 8.27269i | 0.874153 | − | 0.362086i | ||||
\(523\) | 9.59229 | 0.419442 | 0.209721 | − | 0.977761i | \(-0.432744\pi\) | ||||
0.209721 | + | 0.977761i | \(0.432744\pi\) | |||||||
\(524\) | 1.06264 | − | 0.440160i | 0.0464216 | − | 0.0192285i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.6586 | 0.551940 | ||||||||
\(527\) | 8.92813 | + | 7.71729i | 0.388915 | + | 0.336171i | ||||
\(528\) | − | 2.48071i | − | 0.107959i | ||||||
\(529\) | 13.2848 | + | 13.2848i | 0.577600 | + | 0.577600i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.52047i | − | 0.282964i | ||||||
\(532\) | −0.305769 | + | 0.126654i | −0.0132568 | + | 0.00549114i | ||||
\(533\) | −4.53595 | + | 10.9507i | −0.196474 | + | 0.474329i | ||||
\(534\) | −0.843383 | + | 2.03611i | −0.0364968 | + | 0.0881110i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.01377 | + | 5.01377i | −0.216562 | + | 0.216562i | ||||
\(537\) | 1.53121 | + | 0.634246i | 0.0660764 | + | 0.0273697i | ||||
\(538\) | 6.78903 | − | 16.3902i | 0.292696 | − | 0.706631i | ||||
\(539\) | −9.00320 | − | 21.7356i | −0.387795 | − | 0.936220i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9482 | − | 14.4760i | 1.50254 | − | 0.622373i | 0.528539 | − | 0.848909i | \(-0.322740\pi\) |
0.974003 | + | 0.226536i | \(0.0727402\pi\) | |||||||
\(542\) | 16.1302 | − | 16.1302i | 0.692852 | − | 0.692852i | ||||
\(543\) | − | 2.71433i | − | 0.116483i | ||||||
\(544\) | 1.51073 | + | 0.500782i | 0.0647722 | + | 0.0214709i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.234378 | + | 0.234378i | 0.0100305 | + | 0.0100305i | ||||
\(547\) | −9.30496 | − | 22.4642i | −0.397851 | − | 0.960498i | −0.988175 | − | 0.153332i | \(-0.951000\pi\) |
0.590323 | − | 0.807167i | \(-0.299000\pi\) | |||||||
\(548\) | 1.38095 | 0.0589914 | ||||||||
\(549\) | −6.56062 | − | 15.8387i | −0.280000 | − | 0.675981i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.62866 | − | 13.5888i | 0.239789 | − | 0.578902i | ||||
\(552\) | −0.462349 | − | 0.462349i | −0.0196789 | − | 0.0196789i | ||||
\(553\) | −4.75882 | − | 4.75882i | −0.202366 | − | 0.202366i | ||||
\(554\) | 9.81038 | − | 23.6844i | 0.416803 | − | 1.00625i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.111214 | + | 0.268493i | 0.00471651 | + | 0.0113867i | ||||
\(557\) | 26.8276 | 1.13672 | 0.568360 | − | 0.822780i | \(-0.307578\pi\) | ||||
0.568360 | + | 0.822780i | \(0.307578\pi\) | |||||||
\(558\) | 4.54835 | + | 10.9807i | 0.192547 | + | 0.464850i | ||||
\(559\) | −6.59212 | − | 6.59212i | −0.278817 | − | 0.278817i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.36881 | + | 1.18934i | −0.100011 | + | 0.0502141i | ||||
\(562\) | − | 26.0549i | − | 1.09906i | ||||||
\(563\) | −27.7735 | + | 27.7735i | −1.17051 | + | 1.17051i | −0.188426 | + | 0.982087i | \(0.560338\pi\) |
−0.982087 | + | 0.188426i | \(0.939662\pi\) | |||||||
\(564\) | −0.0533672 | + | 0.0221054i | −0.00224716 | + | 0.000930805i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.5260 | + | 25.4120i | 0.442440 | + | 1.06814i | ||||
\(567\) | −5.83729 | + | 14.0925i | −0.245143 | + | 0.591828i | ||||
\(568\) | −35.7953 | − | 14.8269i | −1.50194 | − | 0.622123i | ||||
\(569\) | −7.03027 | + | 7.03027i | −0.294724 | + | 0.294724i | −0.838943 | − | 0.544219i | \(-0.816826\pi\) |
0.544219 | + | 0.838943i | \(0.316826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.173542 | − | 0.418968i | 0.00726251 | − | 0.0175333i | −0.920207 | − | 0.391433i | \(-0.871980\pi\) |
0.927469 | + | 0.373900i | \(0.121980\pi\) | |||||||
\(572\) | −0.190056 | + | 0.458835i | −0.00794662 | + | 0.0191848i | ||||
\(573\) | −0.0260738 | + | 0.0108001i | −0.00108925 | + | 0.000451182i | ||||
\(574\) | − | 22.5401i | − | 0.940806i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.4379 | + | 17.4379i | 0.726581 | + | 0.726581i | ||||
\(577\) | − | 28.8048i | − | 1.19916i | −0.800316 | − | 0.599579i | \(-0.795335\pi\) | ||
0.800316 | − | 0.599579i | \(-0.204665\pi\) | |||||||
\(578\) | 3.41941 | + | 23.3790i | 0.142229 | + | 0.972439i | ||||
\(579\) | −0.329039 | −0.0136744 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.1233 | − | 5.85007i | 0.585934 | − | 0.242702i | ||||
\(582\) | 1.30827 | 0.0542295 | ||||||||
\(583\) | 38.6259 | − | 15.9994i | 1.59972 | − | 0.662626i | ||||
\(584\) | −15.5034 | − | 6.42170i | −0.641534 | − | 0.265732i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.7640 | + | 13.7640i | −0.568587 | + | 0.568587i | ||||
\(587\) | −14.9214 | − | 14.9214i | −0.615871 | − | 0.615871i | 0.328599 | − | 0.944470i | \(-0.393424\pi\) |
−0.944470 | + | 0.328599i | \(0.893424\pi\) | |||||||
\(588\) | −0.0283491 | − | 0.0117426i | −0.00116910 | − | 0.000484256i | ||||
\(589\) | 7.47115 | + | 3.09465i | 0.307843 | + | 0.127513i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.673942i | 0.0277223i | ||||||||
\(592\) | 9.31683 | + | 22.4928i | 0.382919 | + | 0.924449i | ||||
\(593\) | 26.9570 | − | 26.9570i | 1.10699 | − | 1.10699i | 0.113445 | − | 0.993544i | \(-0.463811\pi\) |
0.993544 | − | 0.113445i | \(-0.0361886\pi\) | |||||||
\(594\) | −5.35005 | −0.219515 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.295351 | 0.0120981 | ||||||||
\(597\) | −0.984511 | + | 0.984511i | −0.0402933 | + | 0.0402933i | ||||
\(598\) | −1.36904 | − | 3.30515i | −0.0559842 | − | 0.135158i | ||||
\(599\) | 35.4595i | 1.44884i | 0.689360 | + | 0.724418i | \(0.257892\pi\) | ||||
−0.689360 | + | 0.724418i | \(0.742108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.4610 | + | 10.1321i | 0.997784 | + | 0.413296i | 0.820984 | − | 0.570951i | \(-0.193425\pi\) |
0.176800 | + | 0.984247i | \(0.443425\pi\) | |||||||
\(602\) | 16.3788 | + | 6.78433i | 0.667551 | + | 0.276509i | ||||
\(603\) | 5.21103 | + | 5.21103i | 0.212210 | + | 0.212210i | ||||
\(604\) | 0.968410 | − | 0.968410i | 0.0394041 | − | 0.0394041i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.361219 | − | 0.149622i | −0.0146735 | − | 0.00607797i | ||||
\(607\) | 22.6195 | − | 9.36932i | 0.918099 | − | 0.380289i | 0.126948 | − | 0.991909i | \(-0.459482\pi\) |
0.791151 | + | 0.611620i | \(0.209482\pi\) | |||||||
\(608\) | 1.09062 | 0.0442304 | ||||||||
\(609\) | −0.914606 | + | 0.378842i | −0.0370617 | + | 0.0153515i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.57499 | −0.387363 | ||||||||
\(612\) | 0.264610 | − | 0.798261i | 0.0106962 | − | 0.0322678i | ||||
\(613\) | 13.6998i | 0.553329i | 0.960967 | + | 0.276665i | \(0.0892291\pi\) | ||||
−0.960967 | + | 0.276665i | \(0.910771\pi\) | |||||||
\(614\) | 13.0526 | + | 13.0526i | 0.526761 | + | 0.526761i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 28.6126i | − | 1.15283i | ||||||
\(617\) | −7.11117 | + | 2.94554i | −0.286285 | + | 0.118583i | −0.521205 | − | 0.853432i | \(-0.674517\pi\) |
0.234920 | + | 0.972015i | \(0.424517\pi\) | |||||||
\(618\) | 0.982707 | − | 2.37247i | 0.0395303 | − | 0.0954345i | ||||
\(619\) | 16.5857 | − | 40.0413i | 0.666634 | − | 1.60940i | −0.120570 | − | 0.992705i | \(-0.538472\pi\) |
0.787204 | − | 0.616692i | \(-0.211528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.963054 | + | 0.963054i | −0.0386460 | + | 0.0386460i | ||||
\(622\) | −30.2465 | − | 12.5285i | −1.21277 | − | 0.502347i | ||||
\(623\) | −9.39517 | + | 22.6819i | −0.376409 | + | 0.908733i | ||||
\(624\) | −0.205240 | − | 0.495494i | −0.00821618 | − | 0.0198356i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 41.9342 | − | 17.3697i | 1.67603 | − | 0.694233i | ||||
\(627\) | −1.28434 | + | 1.28434i | −0.0512915 | + | 0.0512915i | ||||
\(628\) | 1.48161i | 0.0591227i | ||||||||
\(629\) | 17.0114 | − | 19.6804i | 0.678288 | − | 0.784711i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.518808 | + | 0.518808i | 0.0206534 | + | 0.0206534i | 0.717358 | − | 0.696705i | \(-0.245351\pi\) |
−0.696705 | + | 0.717358i | \(0.745351\pi\) | |||||||
\(632\) | 4.31465 | + | 10.4165i | 0.171628 | + | 0.414346i | ||||
\(633\) | 1.33499 | 0.0530609 | ||||||||
\(634\) | 13.5103 | + | 32.6166i | 0.536561 | + | 1.29537i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0208675 | − | 0.0503785i | 0.000827449 | − | 0.00199764i | ||||
\(637\) | −3.59657 | − | 3.59657i | −0.142501 | − | 0.142501i | ||||
\(638\) | 29.6784 | + | 29.6784i | 1.17498 | + | 1.17498i | ||||
\(639\) | −15.4103 | + | 37.2036i | −0.609620 | + | 1.47175i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7822 | + | 26.0306i | 0.425872 | + | 1.02815i | 0.980583 | + | 0.196103i | \(0.0628287\pi\) |
−0.554711 | + | 0.832043i | \(0.687171\pi\) | |||||||
\(642\) | 1.40103 | 0.0552941 | ||||||||
\(643\) | −3.62487 | − | 8.75122i | −0.142951 | − | 0.345114i | 0.836146 | − | 0.548506i | \(-0.184803\pi\) |
−0.979097 | + | 0.203392i | \(0.934803\pi\) | |||||||
\(644\) | −0.170005 | − | 0.170005i | −0.00669913 | − | 0.00669913i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.26488 | + | 14.4694i | 0.285833 | + | 0.569292i | ||||
\(647\) | − | 24.3690i | − | 0.958044i | −0.877803 | − | 0.479022i | \(-0.840991\pi\) | ||
0.877803 | − | 0.479022i | \(-0.159009\pi\) | |||||||
\(648\) | 18.0696 | − | 18.0696i | 0.709840 | − | 0.709840i | ||||
\(649\) | 11.6961 | − | 4.84470i | 0.459114 | − | 0.190171i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.208289 | − | 0.502853i | −0.00816347 | − | 0.0197084i | ||||
\(652\) | 0.0346448 | − | 0.0836399i | 0.00135679 | − | 0.00327559i | ||||
\(653\) | 4.66127 | + | 1.93076i | 0.182410 | + | 0.0755565i | 0.472019 | − | 0.881588i | \(-0.343525\pi\) |
−0.289609 | + | 0.957145i | \(0.593525\pi\) | |||||||
\(654\) | 0.0810032 | − | 0.0810032i | 0.00316748 | − | 0.00316748i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.9568 | + | 33.6947i | −0.544922 | + | 1.31556i | ||||
\(657\) | −6.67436 | + | 16.1133i | −0.260392 | + | 0.628641i | ||||
\(658\) | 16.8222 | − | 6.96796i | 0.655796 | − | 0.271640i | ||||
\(659\) | − | 8.17372i | − | 0.318403i | −0.987246 | − | 0.159201i | \(-0.949108\pi\) | ||
0.987246 | − | 0.159201i | \(-0.0508919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6693 | + | 21.6693i | 0.842839 | + | 0.842839i | 0.989227 | − | 0.146388i | \(-0.0467649\pi\) |
−0.146388 | + | 0.989227i | \(0.546765\pi\) | |||||||
\(662\) | − | 25.6264i | − | 0.995998i | ||||||
\(663\) | −0.374743 | + | 0.433540i | −0.0145538 | + | 0.0168373i | ||||
\(664\) | −25.6102 | −0.993869 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 24.2049 | − | 10.0260i | 0.937923 | − | 0.388500i | ||||
\(667\) | 10.6847 | 0.413714 | ||||||||
\(668\) | −1.57623 | + | 0.652895i | −0.0609861 | + | 0.0252613i | ||||
\(669\) | −1.81948 | − | 0.753655i | −0.0703453 | − | 0.0291380i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.5363 | − | 23.5363i | 0.908609 | − | 0.908609i | ||||
\(672\) | −0.0519053 | − | 0.0519053i | −0.00200229 | − | 0.00200229i | ||||
\(673\) | −6.11439 | − | 2.53266i | −0.235692 | − | 0.0976270i | 0.261711 | − | 0.965146i | \(-0.415713\pi\) |
−0.497404 | + | 0.867519i | \(0.665713\pi\) | |||||||
\(674\) | 8.48430 | + | 3.51431i | 0.326803 | + | 0.135366i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 0.780116i | − | 0.0300045i | ||||||
\(677\) | −15.7961 | − | 38.1352i | −0.607094 | − | 1.46565i | −0.866146 | − | 0.499791i | \(-0.833410\pi\) |
0.259052 | − | 0.965863i | \(-0.416590\pi\) | |||||||
\(678\) | −0.984263 | + | 0.984263i | −0.0378004 | + | 0.0378004i | ||||
\(679\) | 14.5739 | 0.559296 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.23825 | 0.0474498 | ||||||||
\(682\) | −16.3173 | + | 16.3173i | −0.624821 | + | 0.624821i | ||||
\(683\) | −5.06249 | − | 12.2219i | −0.193711 | − | 0.467659i | 0.796944 | − | 0.604054i | \(-0.206449\pi\) |
−0.990655 | + | 0.136394i | \(0.956449\pi\) | |||||||
\(684\) | − | 0.576275i | − | 0.0220344i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.3593 | + | 10.0900i | 0.930043 | + | 0.385236i | ||||
\(687\) | 2.18561 | + | 0.905310i | 0.0833862 | + | 0.0345397i | ||||
\(688\) | −20.2835 | − | 20.2835i | −0.773302 | − | 0.773302i | ||||
\(689\) | 6.39139 | − | 6.39139i | 0.243492 | − | 0.243492i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.9758 | − | 13.2448i | −1.21642 | − | 0.503856i | −0.320147 | − | 0.947368i | \(-0.603732\pi\) |
−0.896269 | + | 0.443512i | \(0.853732\pi\) | |||||||
\(692\) | 1.00665 | − | 0.416966i | 0.0382669 | − | 0.0158507i | ||||
\(693\) | −29.7383 | −1.12966 | ||||||||
\(694\) | −12.3465 | + | 5.11407i | −0.468665 | + | 0.194127i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.65848 | 0.0628645 | ||||||||
\(697\) | 38.8662 | − | 2.82724i | 1.47216 | − | 0.107089i | ||||
\(698\) | − | 0.956299i | − | 0.0361965i | ||||||
\(699\) | 0.650860 | + | 0.650860i | 0.0246178 | + | 0.0246178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6045i | 0.589373i | 0.955594 | + | 0.294687i | \(0.0952152\pi\) | ||||
−0.955594 | + | 0.294687i | \(0.904785\pi\) | |||||||
\(702\) | −1.06861 | + | 0.442634i | −0.0403322 | + | 0.0167061i | ||||
\(703\) | 6.82160 | − | 16.4688i | 0.257282 | − | 0.621133i | ||||
\(704\) | −18.3231 | + | 44.2358i | −0.690576 | + | 1.66720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0945 | − | 15.0945i | 0.568091 | − | 0.568091i | ||||
\(707\) | −4.02393 | − | 1.66677i | −0.151335 | − | 0.0626852i | ||||
\(708\) | 0.00631879 | − | 0.0152549i | 0.000237475 | − | 0.000573314i | ||||
\(709\) | −17.9860 | − | 43.4221i | −0.675480 | − | 1.63075i | −0.772153 | − | 0.635437i | \(-0.780820\pi\) |
0.0966730 | − | 0.995316i | \(-0.469180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8263 | − | 4.48441i | 0.406019 | − | 0.168179i | ||||
\(712\) | 29.0831 | − | 29.0831i | 1.08994 | − | 1.08994i | ||||
\(713\) | 5.87449i | 0.220001i | ||||||||
\(714\) | 0.342882 | − | 1.03439i | 0.0128320 | − | 0.0387111i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.721916 | − | 0.721916i | −0.0269793 | − | 0.0269793i | ||||
\(717\) | −0.145206 | − | 0.350559i | −0.00542283 | − | 0.0130919i | ||||
\(718\) | 35.5170 | 1.32548 | ||||||||
\(719\) | −14.5015 | − | 35.0097i | −0.540815 | − | 1.30564i | −0.924149 | − | 0.382033i | \(-0.875224\pi\) |
0.383334 | − | 0.923610i | \(-0.374776\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9472 | − | 26.4289i | 0.407696 | − | 0.984264i | ||||
\(722\) | −10.8278 | − | 10.8278i | −0.402968 | − | 0.402968i | ||||
\(723\) | 0.497481 | + | 0.497481i | 0.0185015 | + | 0.0185015i | ||||
\(724\) | −0.639862 | + | 1.54476i | −0.0237803 | + | 0.0574106i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.33507 | − | 3.22314i | −0.0495490 | − | 0.119622i | ||||
\(727\) | 20.6445 | 0.765664 | 0.382832 | − | 0.923818i | \(-0.374949\pi\) | ||||
0.382832 | + | 0.923818i | \(0.374949\pi\) | |||||||
\(728\) | −2.36724 | − | 5.71503i | −0.0877359 | − | 0.211813i | ||||
\(729\) | −18.6245 | − | 18.6245i | −0.689797 | − | 0.689797i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.64390 | + | 29.0932i | −0.356693 | + | 1.07605i | ||||
\(732\) | − | 0.0434131i | − | 0.00160459i | ||||||
\(733\) | −24.3066 | + | 24.3066i | −0.897786 | + | 0.897786i | −0.995240 | − | 0.0974544i | \(-0.968930\pi\) |
0.0974544 | + | 0.995240i | \(0.468930\pi\) | |||||||
\(734\) | 1.48594 | − | 0.615494i | 0.0548469 | − | 0.0227183i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.303187 | + | 0.731957i | 0.0111756 | + | 0.0269803i | ||||
\(737\) | −5.47553 | + | 13.2191i | −0.201694 | + | 0.486932i | ||||
\(738\) | 36.2595 | + | 15.0192i | 1.33473 | + | 0.552864i | ||||
\(739\) | 12.3512 | − | 12.3512i | 0.454347 | − | 0.454347i | −0.442448 | − | 0.896794i | \(-0.645890\pi\) |
0.896794 | + | 0.442448i | \(0.145890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.150273 | + | 0.362791i | −0.00552041 | + | 0.0133275i | ||||
\(742\) | −6.57775 | + | 15.8801i | −0.241477 | + | 0.582977i | ||||
\(743\) | 17.0027 | − | 7.04274i | 0.623768 | − | 0.258373i | −0.0483348 | − | 0.998831i | \(-0.515391\pi\) |
0.672102 | + | 0.740458i | \(0.265391\pi\) | |||||||
\(744\) | 0.911837i | 0.0334296i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.8857 | − | 14.8857i | −0.545003 | − | 0.545003i | ||||
\(747\) | 26.6178i | 0.973895i | ||||||||
\(748\) | 1.62849 | − | 0.118461i | 0.0595435 | − | 0.00433136i | ||||
\(749\) | 15.6072 | 0.570276 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.79602 | − | 1.15815i | 0.102028 | − | 0.0422615i | −0.331085 | − | 0.943601i | \(-0.607415\pi\) |
0.433114 | + | 0.901339i | \(0.357415\pi\) | |||||||
\(752\) | −29.4616 | −1.07436 | ||||||||
\(753\) | −0.518401 | + | 0.214729i | −0.0188916 | + | 0.00782515i | ||||
\(754\) | 8.38335 | + | 3.47250i | 0.305304 | + | 0.126461i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.0549654 | + | 0.0549654i | −0.00199907 | + | 0.00199907i | ||||
\(757\) | 8.25327 | + | 8.25327i | 0.299970 | + | 0.299970i | 0.841002 | − | 0.541032i | \(-0.181966\pi\) |
−0.541032 | + | 0.841002i | \(0.681966\pi\) | |||||||
\(758\) | −20.0831 | − | 8.31870i | −0.729452 | − | 0.302149i | ||||
\(759\) | −1.21901 | − | 0.504931i | −0.0442473 | − | 0.0183278i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.13354i | 0.0410908i | 0.999789 | + | 0.0205454i | \(0.00654027\pi\) | ||||
−0.999789 | + | 0.0205454i | \(0.993460\pi\) | |||||||
\(762\) | −0.854676 | − | 2.06337i | −0.0309616 | − | 0.0747480i | ||||
\(763\) | 0.902364 | − | 0.902364i | 0.0326678 | − | 0.0326678i | ||||
\(764\) | 0.0173849 | 0.000628964 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.42526 | −0.232154 | ||||||||
\(767\) | 1.93535 | − | 1.93535i | 0.0698813 | − | 0.0698813i | ||||
\(768\) | 0.0694054 | + | 0.167560i | 0.00250445 | + | 0.00604628i | ||||
\(769\) | − | 14.6207i | − | 0.527235i | −0.964627 | − | 0.263617i | \(-0.915084\pi\) | ||
0.964627 | − | 0.263617i | \(-0.0849156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.82526 | − | 0.756045i | −0.0657350 | − | 0.0272283i | ||||
\(772\) | 0.187260 | + | 0.0775658i | 0.00673965 | + | 0.00279165i | ||||
\(773\) | −17.5891 | − | 17.5891i | −0.632636 | − | 0.632636i | 0.316092 | − | 0.948729i | \(-0.397629\pi\) |
−0.948729 | + | 0.316092i | \(0.897629\pi\) | |||||||
\(774\) | −21.8275 | + | 21.8275i | −0.784572 | + | 0.784572i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −22.5571 | − | 9.34346i | −0.809753 | − | 0.335411i | ||||
\(777\) | −1.10845 | + | 0.459134i | −0.0397654 | + | 0.0164714i | ||||
\(778\) | −8.80946 | −0.315834 | ||||||||
\(779\) | 24.6706 | − | 10.2189i | 0.883917 | − | 0.366130i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −78.1841 | −2.79765 | ||||||||
\(782\) | −7.69140 | + | 8.89818i | −0.275044 | + | 0.318198i | ||||
\(783\) | − | 3.45455i | − | 0.123456i | ||||||
\(784\) | −11.0664 | − | 11.0664i | −0.395229 | − | 0.395229i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.59514i | 0.0925656i | ||||||||
\(787\) | −21.7614 | + | 9.01386i | −0.775709 | + | 0.321309i | −0.735183 | − | 0.677869i | \(-0.762904\pi\) |
−0.0405267 | + | 0.999178i | \(0.512904\pi\) | |||||||
\(788\) | 0.158871 | − | 0.383549i | 0.00565955 | − | 0.0136634i | ||||
\(789\) | 0.386267 | − | 0.932530i | 0.0137515 | − | 0.0331989i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9645 | + | 10.9645i | −0.389854 | + | 0.389854i | ||||
\(792\) | 46.0281 | + | 19.0655i | 1.63554 | + | 0.677462i | ||||
\(793\) | 2.75385 | − | 6.64837i | 0.0977920 | − | 0.236091i | ||||
\(794\) | 1.72623 | + | 4.16749i | 0.0612617 | + | 0.147899i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.792381 | − | 0.328215i | 0.0280852 | − | 0.0116333i | ||||
\(797\) | −22.4878 | + | 22.4878i | −0.796558 | + | 0.796558i | −0.982551 | − | 0.185993i | \(-0.940450\pi\) |
0.185993 | + | 0.982551i | \(0.440450\pi\) | |||||||
\(798\) | − | 0.746739i | − | 0.0264343i | ||||||
\(799\) | 14.1250 | + | 28.1327i | 0.499706 | + | 0.995262i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.2274 | − | 30.2274i | −1.06803 | − | 1.06803i | ||||
\(802\) | −6.64570 | − | 16.0441i | −0.234668 | − | 0.566538i | ||||
\(803\) | −33.8624 | −1.19498 | ||||||||
\(804\) | 0.00714156 | + | 0.0172413i | 0.000251863 | + | 0.000608052i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.90919 | + | 4.60919i | −0.0672483 | + | 0.162352i | ||||
\(807\) | −1.00027 | − | 1.00027i | −0.0352110 | − | 0.0352110i | ||||
\(808\) | 5.15954 | + | 5.15954i | 0.181512 | + | 0.181512i | ||||
\(809\) | −6.40172 | + | 15.4551i | −0.225072 | + | 0.543373i | −0.995565 | − | 0.0940762i | \(-0.970010\pi\) |
0.770493 | + | 0.637449i | \(0.220010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0514 | + | 45.9940i | 0.668983 | + | 1.61507i | 0.783314 | + | 0.621626i | \(0.213528\pi\) |
−0.114331 | + | 0.993443i | \(0.536472\pi\) | |||||||
\(812\) | 0.609820 | 0.0214005 | ||||||||
\(813\) | −0.696076 | − | 1.68048i | −0.0244125 | − | 0.0589369i | ||||
\(814\) | 35.9685 | + | 35.9685i | 1.26069 | + | 1.26069i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.15306 | + | 1.33397i | −0.0403652 | + | 0.0466984i | ||||
\(817\) | 21.0028i | 0.734794i | ||||||||
\(818\) | −11.5061 | + | 11.5061i | −0.402300 | + | 0.402300i | ||||
\(819\) | −5.93988 | + | 2.46038i | −0.207556 | + | 0.0859727i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.13317 | − | 14.8068i | −0.214049 | − | 0.516760i | 0.779989 | − | 0.625793i | \(-0.215225\pi\) |
−0.994038 | + | 0.109033i | \(0.965225\pi\) | |||||||
\(822\) | −1.19236 | + | 2.87862i | −0.0415885 | + | 0.100403i | ||||
\(823\) | −29.6365 | − | 12.2758i | −1.03306 | − | 0.427909i | −0.199247 | − | 0.979949i | \(-0.563849\pi\) |
−0.833817 | + | 0.552040i | \(0.813849\pi\) | |||||||
\(824\) | −33.8876 | + | 33.8876i | −1.18053 | + | 1.18053i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.99178 | + | 4.80858i | −0.0693028 | + | 0.167312i | ||||
\(827\) | 1.46488 | − | 3.53653i | 0.0509389 | − | 0.122977i | −0.896362 | − | 0.443324i | \(-0.853799\pi\) |
0.947301 | + | 0.320346i | \(0.103799\pi\) | |||||||
\(828\) | 0.386761 | − | 0.160202i | 0.0134409 | − | 0.00556739i | ||||
\(829\) | 4.09989i | 0.142395i | 0.997462 | + | 0.0711976i | \(0.0226821\pi\) | ||||
−0.997462 | + | 0.0711976i | \(0.977318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.44542 | − | 1.44542i | −0.0501410 | − | 0.0501410i | ||||
\(832\) | 10.3515i | 0.358875i | ||||||||
\(833\) | −5.26158 | + | 15.8729i | −0.182303 | + | 0.549962i | ||||
\(834\) | −0.655705 | −0.0227052 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.03370 | − | 0.428171i | 0.0357511 | − | 0.0148086i | ||||
\(837\) | 1.89932 | 0.0656501 | ||||||||
\(838\) | −0.699221 | + | 0.289627i | −0.0241542 | + | 0.0100050i | ||||
\(839\) | −43.0380 | − | 17.8269i | −1.48584 | − | 0.615453i | −0.515430 | − | 0.856932i | \(-0.672368\pi\) |
−0.970406 | + | 0.241479i | \(0.922368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.34265 | − | 1.34265i | 0.0462982 | − | 0.0462982i | ||||
\(842\) | 23.8912 | + | 23.8912i | 0.823345 | + | 0.823345i | ||||
\(843\) | −1.91941 | − | 0.795045i | −0.0661080 | − | 0.0273828i | ||||
\(844\) | −0.759758 | − | 0.314702i | −0.0261519 | − | 0.0108325i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 31.7042i | 1.09001i | ||||||||
\(847\) | −14.8724 | − | 35.9053i | −0.511023 | − | 1.23372i | ||||
\(848\) | 19.6659 | − | 19.6659i | 0.675329 | − | 0.675329i | ||||
\(849\) | 2.19324 | 0.0752717 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.9492 | 0.443894 | ||||||||
\(852\) | −0.0721058 | + | 0.0721058i | −0.00247030 | + | 0.00247030i | ||||
\(853\) | −13.5400 | − | 32.6885i | −0.463602 | − | 1.11923i | −0.966908 | − | 0.255125i | \(-0.917883\pi\) |
0.503306 | − | 0.864108i | \(-0.332117\pi\) | |||||||
\(854\) | 13.6845i | 0.468273i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.1564 | − | 10.0059i | −0.825650 | − | 0.341995i | ||||
\(857\) | −8.51086 | − | 3.52531i | −0.290725 | − | 0.120422i | 0.232554 | − | 0.972583i | \(-0.425292\pi\) |
−0.523280 | + | 0.852161i | \(0.675292\pi\) | |||||||
\(858\) | −0.792349 | − | 0.792349i | −0.0270503 | − | 0.0270503i | ||||
\(859\) | 11.8621 | − | 11.8621i | 0.404730 | − | 0.404730i | −0.475166 | − | 0.879896i | \(-0.657612\pi\) |
0.879896 | + | 0.475166i | \(0.157612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.66048 | − | 0.687793i | −0.0565890 | − | 0.0234399i | ||||
\(862\) | −5.45016 | + | 2.25753i | −0.185633 | + | 0.0768918i | ||||
\(863\) | 34.1729 | 1.16326 | 0.581630 | − | 0.813454i | \(-0.302415\pi\) | ||||
0.581630 | + | 0.813454i | \(0.302415\pi\) | |||||||
\(864\) | 0.236654 | − | 0.0980254i | 0.00805114 | − | 0.00333489i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.7254 | 1.21400 | ||||||||
\(867\) | 1.82662 | + | 0.461492i | 0.0620353 | + | 0.0156731i | ||||
\(868\) | 0.335281i | 0.0113802i | ||||||||
\(869\) | 16.0879 | + | 16.0879i | 0.545744 | + | 0.545744i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.09338i | 0.104815i | ||||||||
\(872\) | −1.97517 | + | 0.818141i | −0.0668876 | + | 0.0277057i | ||||
\(873\) | −9.71107 | + | 23.4446i | −0.328670 | + | 0.793479i | ||||
\(874\) | −3.08427 | + | 7.44609i | −0.104327 | + | 0.251868i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0312299 | + | 0.0312299i | −0.00105516 | + | 0.00105516i | ||||
\(877\) | 12.1834 | + | 5.04652i | 0.411404 | + | 0.170409i | 0.578779 | − | 0.815484i | \(-0.303529\pi\) |
−0.167376 | + | 0.985893i | \(0.553529\pi\) | |||||||
\(878\) | −1.64888 | + | 3.98075i | −0.0556470 | + | 0.134344i | ||||
\(879\) | 0.593968 | + | 1.43396i | 0.0200340 | + | 0.0483664i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.5578 | + | 12.2433i | −0.995829 | + | 0.412486i | −0.820266 | − | 0.571982i | \(-0.806175\pi\) |
−0.175563 | + | 0.984468i | \(0.556175\pi\) | |||||||
\(882\) | −11.9088 | + | 11.9088i | −0.400989 | + | 0.400989i | ||||
\(883\) | − | 48.1807i | − | 1.62141i | −0.585456 | − | 0.810704i | \(-0.699085\pi\) | ||
0.585456 | − | 0.810704i | \(-0.300915\pi\) | |||||||
\(884\) | 0.315472 | − | 0.158393i | 0.0106105 | − | 0.00532735i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.8611 | − | 25.8611i | −0.868819 | − | 0.868819i | ||||
\(887\) | −15.6909 | − | 37.8812i | −0.526850 | − | 1.27193i | −0.933577 | − | 0.358378i | \(-0.883330\pi\) |
0.406727 | − | 0.913550i | \(-0.366670\pi\) | |||||||
\(888\) | 2.00998 | 0.0674505 | ||||||||
\(889\) | −9.52097 | − | 22.9856i | −0.319323 | − | 0.770914i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.7338 | − | 47.6416i | 0.661106 | − | 1.59605i | ||||
\(892\) | 0.857830 | + | 0.857830i | 0.0287223 | + | 0.0287223i | ||||
\(893\) | 15.2532 | + | 15.2532i | 0.510428 | + | 0.510428i | ||||
\(894\) | −0.255017 | + | 0.615665i | −0.00852904 | + | 0.0205909i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.02613 | − | 16.9626i | −0.234726 | − | 0.566680i | ||||
\(897\) | −0.285259 | −0.00952450 | ||||||||
\(898\) | 7.82140 | + | 18.8825i | 0.261003 | + | 0.630118i | ||||
\(899\) | −10.5361 | − | 10.5361i | −0.351399 | − | 0.351399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.2073 | − | 9.35024i | −0.939722 | − | 0.311502i | ||||
\(902\) | 76.2000i | 2.53718i | ||||||||
\(903\) | 0.999574 | − | 0.999574i | 0.0332637 | − | 0.0332637i | ||||
\(904\) | 24.0001 | − | 9.94116i | 0.798231 | − | 0.330638i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.18251 | + | 2.85483i | 0.0392862 | + | 0.0948453i | ||||
\(907\) | 21.2985 | − | 51.4191i | 0.707205 | − | 1.70734i | 0.000335808 | − | 1.00000i | \(-0.499893\pi\) |
0.706869 | − | 0.707344i | \(-0.250107\pi\) | |||||||
\(908\) | −0.704704 | − | 0.291898i | −0.0233864 | − | 0.00968698i | ||||
\(909\) | 5.36254 | − | 5.36254i | 0.177864 | − | 0.177864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.61087 | − | 13.5458i | 0.185897 | − | 0.448794i | −0.803266 | − | 0.595621i | \(-0.796906\pi\) |
0.989162 | + | 0.146827i | \(0.0469061\pi\) | |||||||
\(912\) | −0.462380 | + | 1.11628i | −0.0153109 | + | 0.0369638i | ||||
\(913\) | −47.7459 | + | 19.7770i | −1.58016 | + | 0.654523i | ||||
\(914\) | 14.7080i | 0.486496i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.03045 | − | 1.03045i | −0.0340469 | − | 0.0340469i | ||||
\(917\) | 28.9095i | 0.954675i | ||||||||
\(918\) | 2.87693 | + | 2.48676i | 0.0949529 | + | 0.0820754i | ||||
\(919\) | −1.54175 | −0.0508578 | −0.0254289 | − | 0.999677i | \(-0.508095\pi\) | ||||
−0.0254289 | + | 0.999677i | \(0.508095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.35985 | − | 0.563267i | 0.0448085 | − | 0.0185603i | ||||
\(922\) | −25.7196 | −0.847031 | ||||||||
\(923\) | −15.6164 | + | 6.46851i | −0.514019 | + | 0.212914i | ||||
\(924\) | −0.0695739 | − | 0.0288185i | −0.00228881 | − | 0.000948058i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −37.0892 | + | 37.0892i | −1.21883 | + | 1.21883i | ||||
\(927\) | 35.2209 | + | 35.2209i | 1.15680 | + | 1.15680i | ||||
\(928\) | −1.85657 | − | 0.769017i | −0.0609449 | − | 0.0252442i | ||||
\(929\) | 12.5602 | + | 5.20262i | 0.412088 | + | 0.170692i | 0.579089 | − | 0.815264i | \(-0.303408\pi\) |
−0.167001 | + | 0.985957i | \(0.553408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4588i | 0.375548i | ||||||||
\(932\) | −0.216983 | − | 0.523843i | −0.00710751 | − | 0.0171591i | ||||
\(933\) | −1.84589 | + | 1.84589i | −0.0604319 | + | 0.0604319i | ||||
\(934\) | 42.0279 | 1.37520 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.7710 | 0.352060 | ||||||||
\(937\) | −11.1059 | + | 11.1059i | −0.362815 | + | 0.362815i | −0.864848 | − | 0.502033i | \(-0.832586\pi\) |
0.502033 | + | 0.864848i | \(0.332586\pi\) | |||||||
\(938\) | −2.25113 | − | 5.43471i | −0.0735020 | − | 0.177450i | ||||
\(939\) | − | 3.61922i | − | 0.118109i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.9824 | − | 16.5613i | −1.30339 | − | 0.539882i | −0.380441 | − | 0.924805i | \(-0.624228\pi\) |
−0.922948 | + | 0.384924i | \(0.874228\pi\) | |||||||
\(942\) | −3.08844 | − | 1.27928i | −0.100627 | − | 0.0416810i | ||||
\(943\) | 13.7166 | + | 13.7166i | 0.446675 | + | 0.446675i | ||||
\(944\) | 5.95493 | − | 5.95493i | 0.193817 | − | 0.193817i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.3710 | − | 22.9354i | −1.80027 | − | 0.745694i | ||||
\(947\) | −18.9459 | + | 7.84765i | −0.615659 | + | 0.255014i | −0.668646 | − | 0.743581i | \(-0.733126\pi\) |
0.0529869 | + | 0.998595i | \(0.483126\pi\) | |||||||
\(948\) | 0.0296743 | 0.000963777 | ||||||||
\(949\) | −6.76363 | + | 2.80159i | −0.219557 | + | 0.0909434i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.81505 | 0.0912843 | ||||||||
\(952\) | −13.2994 | + | 15.3861i | −0.431037 | + | 0.498666i | ||||
\(953\) | 5.27570i | 0.170897i | 0.996343 | + | 0.0854483i | \(0.0272322\pi\) | ||||
−0.996343 | + | 0.0854483i | \(0.972768\pi\) | |||||||
\(954\) | −21.1628 | − | 21.1628i | −0.685172 | − | 0.685172i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.233738i | 0.00755963i | ||||||||
\(957\) | 3.09196 | − | 1.28073i | 0.0999487 | − | 0.0414001i | ||||
\(958\) | −14.3381 | + | 34.6153i | −0.463243 | + | 1.11837i | ||||
\(959\) | −13.2828 | + | 32.0674i | −0.428923 | + | 1.03551i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.1275 | + | 16.1275i | −0.520243 | + | 0.520243i | ||||
\(962\) | 10.1601 | + | 4.20846i | 0.327575 | + | 0.135686i | ||||
\(963\) | −10.3996 | + | 25.1068i | −0.335122 | + | 0.809057i | ||||
\(964\) | −0.165849 | − | 0.400396i | −0.00534165 | − | 0.0128959i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.501166 | − | 0.207590i | 0.0161248 | − | 0.00667909i | ||||
\(967\) | 4.17382 | − | 4.17382i | 0.134221 | − | 0.134221i | −0.636804 | − | 0.771025i | \(-0.719744\pi\) |
0.771025 | + | 0.636804i | \(0.219744\pi\) | |||||||
\(968\) | 65.1080i | 2.09265i | ||||||||
\(969\) | 1.28761 | − | 0.0936646i | 0.0413641 | − | 0.00300894i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.27662 | + | 1.27662i | 0.0409687 | + | 0.0409687i | 0.727294 | − | 0.686326i | \(-0.240778\pi\) |
−0.686326 | + | 0.727294i | \(0.740778\pi\) | |||||||
\(972\) | −0.0777469 | − | 0.187698i | −0.00249373 | − | 0.00602041i | ||||
\(973\) | −7.30446 | −0.234170 | ||||||||
\(974\) | 2.03838 | + | 4.92109i | 0.0653140 | + | 0.157682i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.47341 | − | 20.4566i | 0.271227 | − | 0.654800i | ||||
\(977\) | −6.89768 | − | 6.89768i | −0.220676 | − | 0.220676i | 0.588107 | − | 0.808783i | \(-0.299873\pi\) |
−0.808783 | + | 0.588107i | \(0.799873\pi\) | |||||||
\(978\) | 0.144435 | + | 0.144435i | 0.00461853 | + | 0.00461853i | ||||
\(979\) | 31.7617 | − | 76.6795i | 1.01511 | − | 2.45069i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.850330 | + | 2.05288i | 0.0271489 | + | 0.0655433i | ||||
\(982\) | −8.20202 | −0.261737 | ||||||||
\(983\) | 1.53797 | + | 3.71298i | 0.0490535 | + | 0.118426i | 0.946507 | − | 0.322684i | \(-0.104585\pi\) |
−0.897453 | + | 0.441110i | \(0.854585\pi\) | |||||||
\(984\) | 2.12909 | + | 2.12909i | 0.0678731 | + | 0.0678731i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.16440 | − | 29.7541i | −0.0689284 | − | 0.947562i | ||||
\(987\) | − | 1.45187i | − | 0.0462136i | ||||||
\(988\) | 0.171045 | − | 0.171045i | 0.00544165 | − | 0.00544165i | ||||
\(989\) | −14.0958 | + | 5.83867i | −0.448220 | + | 0.185659i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.31652 | − | 12.8352i | −0.168885 | − | 0.407724i | 0.816665 | − | 0.577113i | \(-0.195821\pi\) |
−0.985549 | + | 0.169389i | \(0.945821\pi\) | |||||||
\(992\) | 0.422808 | − | 1.02075i | 0.0134242 | − | 0.0324088i | ||||
\(993\) | −1.88784 | − | 0.781969i | −0.0599088 | − | 0.0248150i | ||||
\(994\) | 22.7289 | − | 22.7289i | 0.720915 | − | 0.720915i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0257945 | + | 0.0622734i | −0.000817330 | + | 0.00197321i | ||||
\(997\) | 6.14934 | − | 14.8458i | 0.194751 | − | 0.470172i | −0.796094 | − | 0.605173i | \(-0.793104\pi\) |
0.990845 | + | 0.135001i | \(0.0431039\pi\) | |||||||
\(998\) | 56.6155 | − | 23.4509i | 1.79213 | − | 0.742325i | ||||
\(999\) | − | 4.18671i | − | 0.132462i |
(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 | 425.2.n.e.274.4 | 24 | ||
5.2 | odd | 4 | 425.2.m.d.376.4 | yes | 24 | ||
5.3 | odd | 4 | 425.2.m.c.376.3 | yes | 24 | ||
5.4 | even | 2 | 425.2.n.d.274.3 | 24 | |||
17.9 | even | 8 | 425.2.n.d.349.3 | 24 | |||
85.3 | even | 16 | 7225.2.a.bx.1.8 | 24 | |||
85.9 | even | 8 | inner | 425.2.n.e.349.4 | 24 | ||
85.37 | even | 16 | 7225.2.a.cb.1.17 | 24 | |||
85.43 | odd | 8 | 425.2.m.c.26.3 | ✓ | 24 | ||
85.48 | even | 16 | 7225.2.a.bx.1.7 | 24 | |||
85.77 | odd | 8 | 425.2.m.d.26.4 | yes | 24 | ||
85.82 | even | 16 | 7225.2.a.cb.1.18 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
425.2.m.c.26.3 | ✓ | 24 | 85.43 | odd | 8 | ||
425.2.m.c.376.3 | yes | 24 | 5.3 | odd | 4 | ||
425.2.m.d.26.4 | yes | 24 | 85.77 | odd | 8 | ||
425.2.m.d.376.4 | yes | 24 | 5.2 | odd | 4 | ||
425.2.n.d.274.3 | 24 | 5.4 | even | 2 | |||
425.2.n.d.349.3 | 24 | 17.9 | even | 8 | |||
425.2.n.e.274.4 | 24 | 1.1 | even | 1 | trivial | ||
425.2.n.e.349.4 | 24 | 85.9 | even | 8 | inner | ||
7225.2.a.bx.1.7 | 24 | 85.48 | even | 16 | |||
7225.2.a.bx.1.8 | 24 | 85.3 | even | 16 | |||
7225.2.a.cb.1.17 | 24 | 85.37 | even | 16 | |||
7225.2.a.cb.1.18 | 24 | 85.82 | even | 16 |