Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,2,Mod(74,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.74");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.k (of order \(6\), degree \(2\), 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: | \(1.39738203537\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 74.3 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.74 |
Dual form | 175.2.k.a.149.3 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.358719 | − | 0.207107i | 0.253653 | − | 0.146447i | −0.367783 | − | 0.929912i | \(-0.619883\pi\) |
0.621436 | + | 0.783465i | \(0.286550\pi\) | |||||||
\(3\) | −2.09077 | − | 1.20711i | −1.20711 | − | 0.696923i | −0.244981 | − | 0.969528i | \(-0.578782\pi\) |
−0.962126 | + | 0.272605i | \(0.912115\pi\) | |||||||
\(4\) | −0.914214 | + | 1.58346i | −0.457107 | + | 0.791732i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.09077 | + | 1.62132i | −0.790237 | + | 0.612801i | ||||
\(8\) | 1.58579i | 0.560660i | ||||||||
\(9\) | 1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41421 | + | 4.18154i | −0.727913 | + | 1.26078i | 0.229851 | + | 0.973226i | \(0.426176\pi\) |
−0.957764 | + | 0.287556i | \(0.907157\pi\) | |||||||
\(12\) | 3.82282 | − | 2.20711i | 1.10355 | − | 0.637137i | ||||
\(13\) | 0.828427i | 0.229764i | 0.993379 | + | 0.114882i | \(0.0366490\pi\) | ||||
−0.993379 | + | 0.114882i | \(0.963351\pi\) | |||||||
\(14\) | −0.414214 | + | 1.01461i | −0.110703 | + | 0.271166i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −0.717439 | − | 0.414214i | −0.174005 | − | 0.100462i | 0.410468 | − | 0.911875i | \(-0.365365\pi\) |
−0.584473 | + | 0.811413i | \(0.698699\pi\) | |||||||
\(18\) | 1.01461 | + | 0.585786i | 0.239146 | + | 0.138071i | ||||
\(19\) | −1.41421 | − | 2.44949i | −0.324443 | − | 0.561951i | 0.656957 | − | 0.753928i | \(-0.271843\pi\) |
−0.981399 | + | 0.191977i | \(0.938510\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.32843 | − | 0.866025i | 1.38098 | − | 0.188982i | ||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | −2.09077 | + | 1.20711i | −0.435956 | + | 0.251699i | −0.701881 | − | 0.712295i | \(-0.747656\pi\) |
0.265925 | + | 0.963994i | \(0.414323\pi\) | |||||||
\(24\) | 1.91421 | − | 3.31552i | 0.390737 | − | 0.676777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.171573 | + | 0.297173i | 0.0336482 | + | 0.0582804i | ||||
\(27\) | 0.414214i | 0.0797154i | ||||||||
\(28\) | −0.655892 | − | 4.79289i | −0.123952 | − | 0.905772i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | −3.82282 | − | 2.20711i | −0.675786 | − | 0.390165i | ||||
\(33\) | 10.0951 | − | 5.82843i | 1.75734 | − | 1.01460i | ||||
\(34\) | −0.343146 | −0.0588490 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.17157 | −0.861929 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | −1.01461 | − | 0.585786i | −0.164592 | − | 0.0950271i | ||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.17157 | −0.339143 | −0.169571 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169571 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(42\) | 2.09077 | − | 1.62132i | 0.322613 | − | 0.250175i | ||||
\(43\) | 6.41421i | 0.978158i | 0.872239 | + | 0.489079i | \(0.162667\pi\) | ||||
−0.872239 | + | 0.489079i | \(0.837333\pi\) | |||||||
\(44\) | −4.41421 | − | 7.64564i | −0.665468 | − | 1.15262i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | −1.73205 | + | 1.00000i | −0.252646 | + | 0.145865i | −0.620975 | − | 0.783830i | \(-0.713263\pi\) |
0.368329 | + | 0.929695i | \(0.379930\pi\) | |||||||
\(48\) | 7.24264i | 1.04539i | ||||||||
\(49\) | 1.74264 | − | 6.77962i | 0.248949 | − | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | −1.31178 | − | 0.757359i | −0.181912 | − | 0.105027i | ||||
\(53\) | 5.91359 | + | 3.41421i | 0.812294 | + | 0.468978i | 0.847752 | − | 0.530393i | \(-0.177956\pi\) |
−0.0354577 | + | 0.999371i | \(0.511289\pi\) | |||||||
\(54\) | 0.0857864 | + | 0.148586i | 0.0116741 | + | 0.0202201i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.57107 | − | 3.31552i | −0.343573 | − | 0.443054i | ||||
\(57\) | 6.82843i | 0.904447i | ||||||||
\(58\) | 0.358719 | − | 0.207107i | 0.0471022 | − | 0.0271945i | ||||
\(59\) | −6.24264 | + | 10.8126i | −0.812723 | + | 1.40768i | 0.0982291 | + | 0.995164i | \(0.468682\pi\) |
−0.910952 | + | 0.412513i | \(0.864651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.74264 | + | 9.94655i | 0.735270 | + | 1.27352i | 0.954605 | + | 0.297875i | \(0.0962779\pi\) |
−0.219335 | + | 0.975650i | \(0.570389\pi\) | |||||||
\(62\) | − | 2.48528i | − | 0.315631i | ||||||
\(63\) | −6.92820 | − | 2.82843i | −0.872872 | − | 0.356348i | ||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.41421 | − | 4.18154i | 0.297169 | − | 0.514712i | ||||
\(67\) | 10.7510 | + | 6.20711i | 1.31345 | + | 0.758319i | 0.982665 | − | 0.185389i | \(-0.0593544\pi\) |
0.330781 | + | 0.943707i | \(0.392688\pi\) | |||||||
\(68\) | 1.31178 | − | 0.757359i | 0.159077 | − | 0.0918433i | ||||
\(69\) | 5.82843 | 0.701660 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4853 | −1.48173 | −0.740865 | − | 0.671654i | \(-0.765584\pi\) | ||||
−0.740865 | + | 0.671654i | \(0.765584\pi\) | |||||||
\(72\) | −3.88437 | + | 2.24264i | −0.457777 | + | 0.264298i | ||||
\(73\) | −4.18154 | − | 2.41421i | −0.489412 | − | 0.282562i | 0.234918 | − | 0.972015i | \(-0.424518\pi\) |
−0.724331 | + | 0.689453i | \(0.757851\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | −1.73205 | − | 12.6569i | −0.197386 | − | 1.44238i | ||||
\(78\) | − | 0.828427i | − | 0.0938009i | ||||||
\(79\) | 4.58579 | + | 7.94282i | 0.515941 | + | 0.893637i | 0.999829 | + | 0.0185063i | \(0.00589107\pi\) |
−0.483887 | + | 0.875130i | \(0.660776\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | −0.778985 | + | 0.449747i | −0.0860246 | + | 0.0496663i | ||||
\(83\) | − | 11.7279i | − | 1.28731i | −0.765317 | − | 0.643653i | \(-0.777418\pi\) | ||
0.765317 | − | 0.643653i | \(-0.222582\pi\) | |||||||
\(84\) | −4.41421 | + | 10.8126i | −0.481630 | + | 1.17975i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.32843 | + | 2.30090i | 0.143248 | + | 0.248113i | ||||
\(87\) | −2.09077 | − | 1.20711i | −0.224154 | − | 0.129415i | ||||
\(88\) | −6.63103 | − | 3.82843i | −0.706870 | − | 0.408112i | ||||
\(89\) | 1.32843 | + | 2.30090i | 0.140813 | + | 0.243895i | 0.927803 | − | 0.373070i | \(-0.121695\pi\) |
−0.786990 | + | 0.616966i | \(0.788362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.34315 | − | 1.73205i | −0.140800 | − | 0.181568i | ||||
\(92\) | − | 4.41421i | − | 0.460214i | ||||||
\(93\) | −12.5446 | + | 7.24264i | −1.30082 | + | 0.751027i | ||||
\(94\) | −0.414214 | + | 0.717439i | −0.0427229 | + | 0.0739982i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.32843 | + | 9.22911i | 0.543830 | + | 0.941942i | ||||
\(97\) | − | 0.343146i | − | 0.0348412i | −0.999848 | − | 0.0174206i | \(-0.994455\pi\) | ||
0.999848 | − | 0.0174206i | \(-0.00554543\pi\) | |||||||
\(98\) | −0.778985 | − | 2.79289i | −0.0786894 | − | 0.282125i | ||||
\(99\) | −13.6569 | −1.37257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.15685 | + | 10.6640i | −0.612630 | + | 1.06111i | 0.378165 | + | 0.925738i | \(0.376555\pi\) |
−0.990795 | + | 0.135368i | \(0.956778\pi\) | |||||||
\(102\) | 0.717439 | + | 0.414214i | 0.0710370 | + | 0.0410133i | ||||
\(103\) | 0.358719 | − | 0.207107i | 0.0353457 | − | 0.0204068i | −0.482223 | − | 0.876048i | \(-0.660171\pi\) |
0.517569 | + | 0.855642i | \(0.326837\pi\) | |||||||
\(104\) | −1.31371 | −0.128820 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.82843 | 0.274721 | ||||||||
\(107\) | −2.38794 | + | 1.37868i | −0.230851 | + | 0.133282i | −0.610965 | − | 0.791658i | \(-0.709218\pi\) |
0.380113 | + | 0.924940i | \(0.375885\pi\) | |||||||
\(108\) | −0.655892 | − | 0.378680i | −0.0631133 | − | 0.0364385i | ||||
\(109\) | 1.74264 | − | 3.01834i | 0.166915 | − | 0.289105i | −0.770419 | − | 0.637538i | \(-0.779953\pi\) |
0.937334 | + | 0.348433i | \(0.113286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.34847 | + | 3.00000i | 0.694365 | + | 0.283473i | ||||
\(113\) | 12.4853i | 1.17452i | 0.809400 | + | 0.587258i | \(0.199793\pi\) | ||||
−0.809400 | + | 0.587258i | \(0.800207\pi\) | |||||||
\(114\) | 1.41421 | + | 2.44949i | 0.132453 | + | 0.229416i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.914214 | + | 1.58346i | −0.0848826 | + | 0.147021i | ||||
\(117\) | −2.02922 | + | 1.17157i | −0.187602 | + | 0.108312i | ||||
\(118\) | 5.17157i | 0.476082i | ||||||||
\(119\) | 2.17157 | − | 0.297173i | 0.199068 | − | 0.0272418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.15685 | − | 10.6640i | −0.559714 | − | 0.969453i | ||||
\(122\) | 4.11999 | + | 2.37868i | 0.373007 | + | 0.215356i | ||||
\(123\) | 4.54026 | + | 2.62132i | 0.409381 | + | 0.236356i | ||||
\(124\) | 5.48528 | + | 9.50079i | 0.492593 | + | 0.853196i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.07107 | + | 0.420266i | −0.273592 | + | 0.0374403i | ||||
\(127\) | − | 13.3137i | − | 1.18140i | −0.806891 | − | 0.590700i | \(-0.798852\pi\) | ||
0.806891 | − | 0.590700i | \(-0.201148\pi\) | |||||||
\(128\) | 9.14207 | − | 5.27817i | 0.808052 | − | 0.466529i | ||||
\(129\) | 7.74264 | − | 13.4106i | 0.681702 | − | 1.18074i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.65685 | − | 2.86976i | −0.144760 | − | 0.250732i | 0.784523 | − | 0.620099i | \(-0.212908\pi\) |
−0.929283 | + | 0.369368i | \(0.879574\pi\) | |||||||
\(132\) | 21.3137i | 1.85512i | ||||||||
\(133\) | 6.92820 | + | 2.82843i | 0.600751 | + | 0.245256i | ||||
\(134\) | 5.14214 | 0.444213 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.656854 | − | 1.13770i | 0.0563248 | − | 0.0975574i | ||||
\(137\) | 1.43488 | + | 0.828427i | 0.122590 | + | 0.0707773i | 0.560041 | − | 0.828465i | \(-0.310785\pi\) |
−0.437451 | + | 0.899242i | \(0.644119\pi\) | |||||||
\(138\) | 2.09077 | − | 1.20711i | 0.177978 | − | 0.102756i | ||||
\(139\) | −12.1421 | −1.02988 | −0.514941 | − | 0.857225i | \(-0.672186\pi\) | ||||
−0.514941 | + | 0.857225i | \(0.672186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | −4.47871 | + | 2.58579i | −0.375845 | + | 0.216994i | ||||
\(143\) | −3.46410 | − | 2.00000i | −0.289683 | − | 0.167248i | ||||
\(144\) | 4.24264 | − | 7.34847i | 0.353553 | − | 0.612372i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −11.8272 | + | 12.0711i | −0.975490 | + | 0.995605i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.91421 | − | 6.77962i | −0.320665 | − | 0.555408i | 0.659961 | − | 0.751300i | \(-0.270573\pi\) |
−0.980625 | + | 0.195892i | \(0.937240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.171573 | + | 0.297173i | −0.0139624 | + | 0.0241836i | −0.872922 | − | 0.487859i | \(-0.837778\pi\) |
0.858960 | + | 0.512043i | \(0.171111\pi\) | |||||||
\(152\) | 3.88437 | − | 2.24264i | 0.315064 | − | 0.181902i | ||||
\(153\) | − | 2.34315i | − | 0.189432i | ||||||
\(154\) | −3.24264 | − | 4.18154i | −0.261299 | − | 0.336958i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.82843 | + | 3.16693i | 0.146391 | + | 0.253557i | ||||
\(157\) | −4.60181 | − | 2.65685i | −0.367264 | − | 0.212040i | 0.304998 | − | 0.952353i | \(-0.401344\pi\) |
−0.672263 | + | 0.740313i | \(0.734677\pi\) | |||||||
\(158\) | 3.29002 | + | 1.89949i | 0.261740 | + | 0.151116i | ||||
\(159\) | −8.24264 | − | 14.2767i | −0.653684 | − | 1.13221i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.41421 | − | 5.91359i | 0.190267 | − | 0.466056i | ||||
\(162\) | − | 3.92893i | − | 0.308686i | ||||||
\(163\) | 20.4874 | − | 11.8284i | 1.60470 | − | 0.926474i | 0.614170 | − | 0.789173i | \(-0.289491\pi\) |
0.990529 | − | 0.137301i | \(-0.0438426\pi\) | |||||||
\(164\) | 1.98528 | − | 3.43861i | 0.155024 | − | 0.268510i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.42893 | − | 4.20703i | −0.188522 | − | 0.326529i | ||||
\(167\) | − | 19.5858i | − | 1.51559i | −0.652491 | − | 0.757797i | \(-0.726276\pi\) | ||
0.652491 | − | 0.757797i | \(-0.273724\pi\) | |||||||
\(168\) | 1.37333 | + | 10.0355i | 0.105955 | + | 0.774258i | ||||
\(169\) | 12.3137 | 0.947208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 6.92820i | 0.305888 | − | 0.529813i | ||||
\(172\) | −10.1567 | − | 5.86396i | −0.774439 | − | 0.447123i | ||||
\(173\) | −16.7262 | + | 9.65685i | −1.27167 | + | 0.734197i | −0.975302 | − | 0.220878i | \(-0.929108\pi\) |
−0.296365 | + | 0.955075i | \(0.595774\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.4853 | 1.09187 | ||||||||
\(177\) | 26.1039 | − | 15.0711i | 1.96209 | − | 1.13281i | ||||
\(178\) | 0.953065 | + | 0.550253i | 0.0714353 | + | 0.0412432i | ||||
\(179\) | −5.00000 | + | 8.66025i | −0.373718 | + | 0.647298i | −0.990134 | − | 0.140122i | \(-0.955250\pi\) |
0.616417 | + | 0.787420i | \(0.288584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.65685 | −0.643459 | −0.321729 | − | 0.946832i | \(-0.604264\pi\) | ||||
−0.321729 | + | 0.946832i | \(0.604264\pi\) | |||||||
\(182\) | −0.840532 | − | 0.343146i | −0.0623044 | − | 0.0254357i | ||||
\(183\) | − | 27.7279i | − | 2.04971i | ||||||
\(184\) | −1.91421 | − | 3.31552i | −0.141118 | − | 0.244423i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | + | 5.19615i | −0.219971 | + | 0.381000i | ||||
\(187\) | 3.46410 | − | 2.00000i | 0.253320 | − | 0.146254i | ||||
\(188\) | − | 3.65685i | − | 0.266704i | ||||||
\(189\) | −0.671573 | − | 0.866025i | −0.0488497 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.58579 | + | 6.21076i | 0.259458 | + | 0.449395i | 0.966097 | − | 0.258180i | \(-0.0831226\pi\) |
−0.706639 | + | 0.707575i | \(0.749789\pi\) | |||||||
\(192\) | −8.72180 | − | 5.03553i | −0.629442 | − | 0.363408i | ||||
\(193\) | 1.73205 | + | 1.00000i | 0.124676 | + | 0.0719816i | 0.561041 | − | 0.827788i | \(-0.310401\pi\) |
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(194\) | −0.0710678 | − | 0.123093i | −0.00510237 | − | 0.00883757i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.14214 | + | 8.95743i | 0.653010 | + | 0.639816i | ||||
\(197\) | 23.6569i | 1.68548i | 0.538320 | + | 0.842741i | \(0.319059\pi\) | ||||
−0.538320 | + | 0.842741i | \(0.680941\pi\) | |||||||
\(198\) | −4.89898 | + | 2.82843i | −0.348155 | + | 0.201008i | ||||
\(199\) | 0.828427 | − | 1.43488i | 0.0587256 | − | 0.101716i | −0.835168 | − | 0.549995i | \(-0.814630\pi\) |
0.893894 | + | 0.448279i | \(0.147963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.9853 | − | 25.9553i | −1.05698 | − | 1.83074i | ||||
\(202\) | 5.10051i | 0.358870i | ||||||||
\(203\) | −2.09077 | + | 1.62132i | −0.146743 | + | 0.113794i | ||||
\(204\) | −3.65685 | −0.256031 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.0857864 | − | 0.148586i | 0.00597702 | − | 0.0103525i | ||||
\(207\) | −5.91359 | − | 3.41421i | −0.411023 | − | 0.237304i | ||||
\(208\) | 2.15232 | − | 1.24264i | 0.149236 | − | 0.0861616i | ||||
\(209\) | 13.6569 | 0.944664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51472 | 0.241963 | 0.120982 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120982 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(212\) | −10.8126 | + | 6.24264i | −0.742610 | + | 0.428746i | ||||
\(213\) | 26.1039 | + | 15.0711i | 1.78861 | + | 1.03265i | ||||
\(214\) | −0.571068 | + | 0.989118i | −0.0390374 | + | 0.0676147i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.656854 | −0.0446933 | ||||||||
\(217\) | 2.15232 | + | 15.7279i | 0.146109 | + | 1.06768i | ||||
\(218\) | − | 1.44365i | − | 0.0977764i | ||||||
\(219\) | 5.82843 | + | 10.0951i | 0.393849 | + | 0.682166i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.343146 | − | 0.594346i | 0.0230825 | − | 0.0399800i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6569i | 0.780601i | 0.920688 | + | 0.390300i | \(0.127629\pi\) | ||||
−0.920688 | + | 0.390300i | \(0.872371\pi\) | |||||||
\(224\) | 11.5711 | − | 1.58346i | 0.773124 | − | 0.105800i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.58579 | + | 4.47871i | 0.172004 | + | 0.297920i | ||||
\(227\) | 23.3572 | + | 13.4853i | 1.55027 | + | 0.895050i | 0.998119 | + | 0.0613063i | \(0.0195266\pi\) |
0.552152 | + | 0.833743i | \(0.313807\pi\) | |||||||
\(228\) | −10.8126 | − | 6.24264i | −0.716080 | − | 0.413429i | ||||
\(229\) | −0.171573 | − | 0.297173i | −0.0113379 | − | 0.0196377i | 0.860301 | − | 0.509787i | \(-0.170276\pi\) |
−0.871639 | + | 0.490149i | \(0.836942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6569 | + | 28.5533i | −0.766965 | + | 1.87867i | ||||
\(232\) | 1.58579i | 0.104112i | ||||||||
\(233\) | −9.67487 | + | 5.58579i | −0.633822 | + | 0.365937i | −0.782231 | − | 0.622989i | \(-0.785918\pi\) |
0.148409 | + | 0.988926i | \(0.452585\pi\) | |||||||
\(234\) | −0.485281 | + | 0.840532i | −0.0317238 | + | 0.0549473i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.4142 | − | 19.7700i | −0.743002 | − | 1.28692i | ||||
\(237\) | − | 22.1421i | − | 1.43829i | ||||||
\(238\) | 0.717439 | − | 0.556349i | 0.0465047 | − | 0.0360628i | ||||
\(239\) | −1.31371 | −0.0849767 | −0.0424884 | − | 0.999097i | \(-0.513529\pi\) | ||||
−0.0424884 | + | 0.999097i | \(0.513529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.17157 | + | 14.1536i | −0.526377 | + | 0.911712i | 0.473150 | + | 0.880982i | \(0.343117\pi\) |
−0.999528 | + | 0.0307305i | \(0.990217\pi\) | |||||||
\(242\) | −4.41717 | − | 2.55025i | −0.283946 | − | 0.163936i | ||||
\(243\) | −18.7554 | + | 10.8284i | −1.20316 | + | 0.694644i | ||||
\(244\) | −21.0000 | −1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.17157 | 0.138454 | ||||||||
\(247\) | 2.02922 | − | 1.17157i | 0.129116 | − | 0.0745454i | ||||
\(248\) | 8.23999 | + | 4.75736i | 0.523240 | + | 0.302093i | ||||
\(249\) | −14.1569 | + | 24.5204i | −0.897154 | + | 1.55392i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3137 | 0.840354 | 0.420177 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420177 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(252\) | 10.8126 | − | 8.38478i | 0.681128 | − | 0.528191i | ||||
\(253\) | − | 11.6569i | − | 0.732860i | ||||||
\(254\) | −2.75736 | − | 4.77589i | −0.173012 | − | 0.299666i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | −15.2913 | + | 8.82843i | −0.953844 | + | 0.550702i | −0.894273 | − | 0.447522i | \(-0.852307\pi\) |
−0.0595711 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(258\) | − | 6.41421i | − | 0.399331i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41421 | + | 2.44949i | 0.0875376 | + | 0.151620i | ||||
\(262\) | −1.18869 | − | 0.686292i | −0.0734376 | − | 0.0423992i | ||||
\(263\) | −16.4905 | − | 9.52082i | −1.01685 | − | 0.587079i | −0.103660 | − | 0.994613i | \(-0.533055\pi\) |
−0.913190 | + | 0.407534i | \(0.866389\pi\) | |||||||
\(264\) | 9.24264 | + | 16.0087i | 0.568845 | + | 0.985269i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.07107 | − | 0.420266i | 0.188299 | − | 0.0257682i | ||||
\(267\) | − | 6.41421i | − | 0.392543i | ||||||
\(268\) | −19.6575 | + | 11.3492i | −1.20077 | + | 0.693265i | ||||
\(269\) | −15.2279 | + | 26.3755i | −0.928463 | + | 1.60814i | −0.142568 | + | 0.989785i | \(0.545536\pi\) |
−0.785895 | + | 0.618360i | \(0.787798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.242641 | + | 0.420266i | 0.0147394 | + | 0.0255293i | 0.873301 | − | 0.487181i | \(-0.161975\pi\) |
−0.858562 | + | 0.512710i | \(0.828641\pi\) | |||||||
\(272\) | 2.48528i | 0.150692i | ||||||||
\(273\) | 0.717439 | + | 5.24264i | 0.0434214 | + | 0.317299i | ||||
\(274\) | 0.686292 | 0.0414604 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.32843 | + | 9.22911i | −0.320734 | + | 0.555527i | ||||
\(277\) | −10.5154 | − | 6.07107i | −0.631809 | − | 0.364775i | 0.149643 | − | 0.988740i | \(-0.452187\pi\) |
−0.781452 | + | 0.623965i | \(0.785521\pi\) | |||||||
\(278\) | −4.35562 | + | 2.51472i | −0.261233 | + | 0.150823i | ||||
\(279\) | 16.9706 | 1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.2843 | 1.56799 | 0.783994 | − | 0.620768i | \(-0.213179\pi\) | ||||
0.783994 | + | 0.620768i | \(0.213179\pi\) | |||||||
\(282\) | 1.73205 | − | 1.00000i | 0.103142 | − | 0.0595491i | ||||
\(283\) | −12.1244 | − | 7.00000i | −0.720718 | − | 0.416107i | 0.0942988 | − | 0.995544i | \(-0.469939\pi\) |
−0.815017 | + | 0.579437i | \(0.803272\pi\) | |||||||
\(284\) | 11.4142 | − | 19.7700i | 0.677309 | − | 1.17313i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.65685 | −0.0979718 | ||||||||
\(287\) | 4.54026 | − | 3.52082i | 0.268003 | − | 0.207827i | ||||
\(288\) | − | 12.4853i | − | 0.735702i | ||||||
\(289\) | −8.15685 | − | 14.1281i | −0.479815 | − | 0.831064i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.414214 | + | 0.717439i | −0.0242816 | + | 0.0420570i | ||||
\(292\) | 7.64564 | − | 4.41421i | 0.447427 | − | 0.258322i | ||||
\(293\) | − | 16.0000i | − | 0.934730i | −0.884064 | − | 0.467365i | \(-0.845203\pi\) | ||
0.884064 | − | 0.467365i | \(-0.154797\pi\) | |||||||
\(294\) | −1.74264 | + | 6.77962i | −0.101633 | + | 0.395395i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.73205 | − | 1.00000i | −0.100504 | − | 0.0580259i | ||||
\(298\) | −2.80821 | − | 1.62132i | −0.162675 | − | 0.0939206i | ||||
\(299\) | −1.00000 | − | 1.73205i | −0.0578315 | − | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3995 | − | 13.4106i | −0.599417 | − | 0.772977i | ||||
\(302\) | 0.142136i | 0.00817899i | ||||||||
\(303\) | 25.7451 | − | 14.8640i | 1.47902 | − | 0.853912i | ||||
\(304\) | −4.24264 | + | 7.34847i | −0.243332 | + | 0.421464i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.485281 | − | 0.840532i | −0.0277417 | − | 0.0480500i | ||||
\(307\) | 13.2426i | 0.755797i | 0.925847 | + | 0.377899i | \(0.123353\pi\) | ||||
−0.925847 | + | 0.377899i | \(0.876647\pi\) | |||||||
\(308\) | 21.6251 | + | 8.82843i | 1.23221 | + | 0.503046i | ||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.41421 | − | 16.3059i | 0.533831 | − | 0.924623i | −0.465388 | − | 0.885107i | \(-0.654085\pi\) |
0.999219 | − | 0.0395157i | \(-0.0125815\pi\) | |||||||
\(312\) | 2.74666 | + | 1.58579i | 0.155499 | + | 0.0897775i | ||||
\(313\) | −15.2913 | + | 8.82843i | −0.864314 | + | 0.499012i | −0.865455 | − | 0.500987i | \(-0.832970\pi\) |
0.00114023 | + | 0.999999i | \(0.499637\pi\) | |||||||
\(314\) | −2.20101 | −0.124210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7696 | −0.943361 | ||||||||
\(317\) | −22.3426 | + | 12.8995i | −1.25488 | + | 0.724508i | −0.972075 | − | 0.234668i | \(-0.924600\pi\) |
−0.282809 | + | 0.959176i | \(0.591266\pi\) | |||||||
\(318\) | −5.91359 | − | 3.41421i | −0.331618 | − | 0.191460i | ||||
\(319\) | −2.41421 | + | 4.18154i | −0.135170 | + | 0.234121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.65685 | 0.371549 | ||||||||
\(322\) | −0.358719 | − | 2.62132i | −0.0199907 | − | 0.146080i | ||||
\(323\) | 2.34315i | 0.130376i | ||||||||
\(324\) | 8.67157 | + | 15.0196i | 0.481754 | + | 0.834422i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.89949 | − | 8.48617i | 0.271358 | − | 0.470006i | ||||
\(327\) | −7.28692 | + | 4.20711i | −0.402968 | + | 0.232654i | ||||
\(328\) | − | 3.44365i | − | 0.190144i | ||||||
\(329\) | 2.00000 | − | 4.89898i | 0.110264 | − | 0.270089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.48528 | + | 9.50079i | 0.301498 | + | 0.522210i | 0.976476 | − | 0.215628i | \(-0.0691799\pi\) |
−0.674977 | + | 0.737839i | \(0.735847\pi\) | |||||||
\(332\) | 18.5707 | + | 10.7218i | 1.01920 | + | 0.588437i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.05635 | − | 7.02580i | −0.221954 | − | 0.384435i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.7426 | − | 15.1427i | −0.640614 | − | 0.826102i | ||||
\(337\) | − | 14.8284i | − | 0.807756i | −0.914813 | − | 0.403878i | \(-0.867662\pi\) | ||
0.914813 | − | 0.403878i | \(-0.132338\pi\) | |||||||
\(338\) | 4.41717 | − | 2.55025i | 0.240262 | − | 0.138715i | ||||
\(339\) | 15.0711 | − | 26.1039i | 0.818548 | − | 1.41777i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.4853 | + | 25.0892i | 0.784422 | + | 1.35866i | ||||
\(342\) | − | 3.31371i | − | 0.179185i | ||||||
\(343\) | 7.34847 | + | 17.0000i | 0.396780 | + | 0.917914i | ||||
\(344\) | −10.1716 | −0.548414 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.00000 | + | 6.92820i | −0.215041 | + | 0.372463i | ||||
\(347\) | 19.1141 | + | 11.0355i | 1.02610 | + | 0.592418i | 0.915865 | − | 0.401487i | \(-0.131507\pi\) |
0.110234 | + | 0.993906i | \(0.464840\pi\) | |||||||
\(348\) | 3.82282 | − | 2.20711i | 0.204925 | − | 0.118313i | ||||
\(349\) | 26.6569 | 1.42691 | 0.713454 | − | 0.700702i | \(-0.247130\pi\) | ||||
0.713454 | + | 0.700702i | \(0.247130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.343146 | −0.0183158 | ||||||||
\(352\) | 18.4582 | − | 10.6569i | 0.983826 | − | 0.568012i | ||||
\(353\) | 18.3351 | + | 10.5858i | 0.975880 | + | 0.563425i | 0.901024 | − | 0.433770i | \(-0.142817\pi\) |
0.0748562 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(354\) | 6.24264 | − | 10.8126i | 0.331793 | − | 0.574682i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.85786 | −0.257466 | ||||||||
\(357\) | −4.89898 | − | 2.00000i | −0.259281 | − | 0.105851i | ||||
\(358\) | 4.14214i | 0.218919i | ||||||||
\(359\) | −5.00000 | − | 8.66025i | −0.263890 | − | 0.457071i | 0.703382 | − | 0.710812i | \(-0.251672\pi\) |
−0.967272 | + | 0.253741i | \(0.918339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | −3.10538 | + | 1.79289i | −0.163215 | + | 0.0942324i | ||||
\(363\) | 29.7279i | 1.56031i | ||||||||
\(364\) | 3.97056 | − | 0.543359i | 0.208114 | − | 0.0284798i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.74264 | − | 9.94655i | −0.300173 | − | 0.519914i | ||||
\(367\) | −9.73641 | − | 5.62132i | −0.508237 | − | 0.293431i | 0.223872 | − | 0.974619i | \(-0.428130\pi\) |
−0.732108 | + | 0.681188i | \(0.761464\pi\) | |||||||
\(368\) | 6.27231 | + | 3.62132i | 0.326967 | + | 0.188774i | ||||
\(369\) | −3.07107 | − | 5.31925i | −0.159873 | − | 0.276909i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.8995 | + | 2.44949i | −0.929295 | + | 0.127171i | ||||
\(372\) | − | 26.4853i | − | 1.37320i | ||||||
\(373\) | 11.2328 | − | 6.48528i | 0.581614 | − | 0.335795i | −0.180160 | − | 0.983637i | \(-0.557662\pi\) |
0.761775 | + | 0.647842i | \(0.224328\pi\) | |||||||
\(374\) | 0.828427 | − | 1.43488i | 0.0428369 | − | 0.0741958i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.58579 | − | 2.74666i | −0.0817807 | − | 0.141648i | ||||
\(377\) | 0.828427i | 0.0426662i | ||||||||
\(378\) | −0.420266 | − | 0.171573i | −0.0216162 | − | 0.00882476i | ||||
\(379\) | −21.1716 | −1.08751 | −0.543755 | − | 0.839244i | \(-0.682998\pi\) | ||||
−0.543755 | + | 0.839244i | \(0.682998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0711 | + | 27.8359i | −0.823346 | + | 1.42608i | ||||
\(382\) | 2.57258 | + | 1.48528i | 0.131625 | + | 0.0759936i | ||||
\(383\) | 14.6354 | − | 8.44975i | 0.747834 | − | 0.431762i | −0.0770770 | − | 0.997025i | \(-0.524559\pi\) |
0.824911 | + | 0.565263i | \(0.191225\pi\) | |||||||
\(384\) | −25.4853 | −1.30054 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.828427 | 0.0421658 | ||||||||
\(387\) | −15.7116 | + | 9.07107i | −0.798663 | + | 0.461108i | ||||
\(388\) | 0.543359 | + | 0.313708i | 0.0275849 | + | 0.0159261i | ||||
\(389\) | 6.17157 | − | 10.6895i | 0.312911 | − | 0.541978i | −0.666080 | − | 0.745880i | \(-0.732029\pi\) |
0.978991 | + | 0.203902i | \(0.0653625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 10.7510 | + | 2.76346i | 0.543009 | + | 0.139576i | ||||
\(393\) | 8.00000i | 0.403547i | ||||||||
\(394\) | 4.89949 | + | 8.48617i | 0.246833 | + | 0.427527i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.4853 | − | 21.6251i | 0.627409 | − | 1.08670i | ||||
\(397\) | −24.7921 | + | 14.3137i | −1.24428 | + | 0.718384i | −0.969962 | − | 0.243255i | \(-0.921785\pi\) |
−0.274316 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(398\) | − | 0.686292i | − | 0.0344007i | ||||||
\(399\) | −11.0711 | − | 14.2767i | −0.554247 | − | 0.714728i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.84315 | − | 6.65652i | −0.191918 | − | 0.332411i | 0.753968 | − | 0.656911i | \(-0.228137\pi\) |
−0.945886 | + | 0.324500i | \(0.894804\pi\) | |||||||
\(402\) | −10.7510 | − | 6.20711i | −0.536212 | − | 0.309582i | ||||
\(403\) | 4.30463 | + | 2.48528i | 0.214429 | + | 0.123801i | ||||
\(404\) | −11.2574 | − | 19.4983i | −0.560075 | − | 0.970078i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.414214 | + | 1.01461i | −0.0205571 | + | 0.0503543i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.74666 | + | 1.58579i | −0.135980 | + | 0.0785081i | ||||
\(409\) | 12.3995 | − | 21.4766i | 0.613116 | − | 1.06195i | −0.377596 | − | 0.925970i | \(-0.623249\pi\) |
0.990712 | − | 0.135977i | \(-0.0434173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | − | 3.46410i | −0.0986527 | − | 0.170872i | ||||
\(412\) | 0.757359i | 0.0373124i | ||||||||
\(413\) | −4.47871 | − | 32.7279i | −0.220383 | − | 1.61044i | ||||
\(414\) | −2.82843 | −0.139010 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.82843 | − | 3.16693i | 0.0896460 | − | 0.155271i | ||||
\(417\) | 25.3864 | + | 14.6569i | 1.24318 | + | 0.717749i | ||||
\(418\) | 4.89898 | − | 2.82843i | 0.239617 | − | 0.138343i | ||||
\(419\) | 23.3137 | 1.13895 | 0.569475 | − | 0.822009i | \(-0.307147\pi\) | ||||
0.569475 | + | 0.822009i | \(0.307147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.48528 | −0.169862 | −0.0849311 | − | 0.996387i | \(-0.527067\pi\) | ||||
−0.0849311 | + | 0.996387i | \(0.527067\pi\) | |||||||
\(422\) | 1.26080 | − | 0.727922i | 0.0613747 | − | 0.0354347i | ||||
\(423\) | −4.89898 | − | 2.82843i | −0.238197 | − | 0.137523i | ||||
\(424\) | −5.41421 | + | 9.37769i | −0.262937 | + | 0.455421i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.4853 | 0.604914 | ||||||||
\(427\) | −28.1331 | − | 11.4853i | −1.36146 | − | 0.555812i | ||||
\(428\) | − | 5.04163i | − | 0.243696i | ||||||
\(429\) | 4.82843 | + | 8.36308i | 0.233119 | + | 0.403773i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8995 | − | 18.8785i | 0.525010 | − | 0.909344i | −0.474566 | − | 0.880220i | \(-0.657395\pi\) |
0.999576 | − | 0.0291242i | \(-0.00927183\pi\) | |||||||
\(432\) | 1.07616 | − | 0.621320i | 0.0517767 | − | 0.0298933i | ||||
\(433\) | − | 31.7990i | − | 1.52816i | −0.645120 | − | 0.764081i | \(-0.723193\pi\) | ||
0.645120 | − | 0.764081i | \(-0.276807\pi\) | |||||||
\(434\) | 4.02944 | + | 5.19615i | 0.193419 | + | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.18629 | + | 5.51882i | 0.152596 | + | 0.264303i | ||||
\(437\) | 5.91359 | + | 3.41421i | 0.282885 | + | 0.163324i | ||||
\(438\) | 4.18154 | + | 2.41421i | 0.199802 | + | 0.115356i | ||||
\(439\) | 16.9706 | + | 29.3939i | 0.809961 | + | 1.40289i | 0.912890 | + | 0.408205i | \(0.133845\pi\) |
−0.102930 | + | 0.994689i | \(0.532822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0711 | − | 5.31925i | 0.908146 | − | 0.253297i | ||||
\(442\) | − | 0.284271i | − | 0.0135214i | ||||||
\(443\) | −10.5769 | + | 6.10660i | −0.502526 | + | 0.290133i | −0.729756 | − | 0.683708i | \(-0.760366\pi\) |
0.227230 | + | 0.973841i | \(0.427033\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.41421 | + | 4.18154i | 0.114316 | + | 0.198002i | ||||
\(447\) | 18.8995i | 0.893915i | ||||||||
\(448\) | −8.72180 | + | 6.76346i | −0.412066 | + | 0.319543i | ||||
\(449\) | 1.82843 | 0.0862888 | 0.0431444 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431444 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.24264 | − | 9.08052i | 0.246866 | − | 0.427585i | ||||
\(452\) | −19.7700 | − | 11.4142i | −0.929902 | − | 0.536879i | ||||
\(453\) | 0.717439 | − | 0.414214i | 0.0337082 | − | 0.0194615i | ||||
\(454\) | 11.1716 | 0.524308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.8284 | −0.507088 | ||||||||
\(457\) | 27.9590 | − | 16.1421i | 1.30787 | − | 0.755097i | 0.326127 | − | 0.945326i | \(-0.394256\pi\) |
0.981740 | + | 0.190229i | \(0.0609230\pi\) | |||||||
\(458\) | −0.123093 | − | 0.0710678i | −0.00575176 | − | 0.00332078i | ||||
\(459\) | 0.171573 | − | 0.297173i | 0.00800834 | − | 0.0138708i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.6863 | 0.870307 | 0.435154 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435154 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(462\) | 1.73205 | + | 12.6569i | 0.0805823 | + | 0.588850i | ||||
\(463\) | 11.0416i | 0.513148i | 0.966525 | + | 0.256574i | \(0.0825937\pi\) | ||||
−0.966525 | + | 0.256574i | \(0.917406\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.31371 | + | 4.00746i | −0.107180 | + | 0.185642i | ||||
\(467\) | 19.8315 | − | 11.4497i | 0.917694 | − | 0.529831i | 0.0347956 | − | 0.999394i | \(-0.488922\pi\) |
0.882899 | + | 0.469563i | \(0.155589\pi\) | |||||||
\(468\) | − | 4.28427i | − | 0.198041i | ||||||
\(469\) | −32.5416 | + | 4.45322i | −1.50263 | + | 0.205631i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.41421 | + | 11.1097i | 0.295551 | + | 0.511910i | ||||
\(472\) | −17.1464 | − | 9.89949i | −0.789228 | − | 0.455661i | ||||
\(473\) | −26.8213 | − | 15.4853i | −1.23324 | − | 0.712014i | ||||
\(474\) | −4.58579 | − | 7.94282i | −0.210632 | − | 0.364826i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.51472 | + | 3.71029i | −0.0694270 | + | 0.170061i | ||||
\(477\) | 19.3137i | 0.884314i | ||||||||
\(478\) | −0.471253 | + | 0.272078i | −0.0215546 | + | 0.0124446i | ||||
\(479\) | −12.1716 | + | 21.0818i | −0.556133 | + | 0.963251i | 0.441681 | + | 0.897172i | \(0.354382\pi\) |
−0.997814 | + | 0.0660791i | \(0.978951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.76955i | 0.308345i | ||||||||
\(483\) | −12.1859 | + | 9.44975i | −0.554478 | + | 0.429978i | ||||
\(484\) | 22.5147 | 1.02340 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.48528 | + | 7.76874i | −0.203456 | + | 0.352397i | ||||
\(487\) | 13.5592 | + | 7.82843i | 0.614428 | + | 0.354740i | 0.774696 | − | 0.632334i | \(-0.217903\pi\) |
−0.160269 | + | 0.987073i | \(0.551236\pi\) | |||||||
\(488\) | −15.7731 | + | 9.10660i | −0.714015 | + | 0.412236i | ||||
\(489\) | −57.1127 | −2.58273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3137 | −0.600839 | −0.300420 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300420 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(492\) | −8.30153 | + | 4.79289i | −0.374262 | + | 0.216080i | ||||
\(493\) | −0.717439 | − | 0.414214i | −0.0323118 | − | 0.0186552i | ||||
\(494\) | 0.485281 | − | 0.840532i | 0.0218338 | − | 0.0378173i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.0000 | −0.808224 | ||||||||
\(497\) | 26.1039 | − | 20.2426i | 1.17092 | − | 0.908007i | ||||
\(498\) | 11.7279i | 0.525541i | ||||||||
\(499\) | 2.41421 | + | 4.18154i | 0.108075 | + | 0.187191i | 0.914990 | − | 0.403476i | \(-0.132198\pi\) |
−0.806915 | + | 0.590667i | \(0.798865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.6421 | + | 40.9494i | −1.05625 | + | 1.82948i | ||||
\(502\) | 4.77589 | − | 2.75736i | 0.213158 | − | 0.123067i | ||||
\(503\) | 37.8701i | 1.68854i | 0.535916 | + | 0.844271i | \(0.319966\pi\) | ||||
−0.535916 | + | 0.844271i | \(0.680034\pi\) | |||||||
\(504\) | 4.48528 | − | 10.9867i | 0.199790 | − | 0.489384i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.41421 | − | 4.18154i | −0.107325 | − | 0.185892i | ||||
\(507\) | −25.7451 | − | 14.8640i | −1.14338 | − | 0.660132i | ||||
\(508\) | 21.0818 | + | 12.1716i | 0.935353 | + | 0.540026i | ||||
\(509\) | 12.3284 | + | 21.3535i | 0.546448 | + | 0.946476i | 0.998514 | + | 0.0544912i | \(0.0173537\pi\) |
−0.452066 | + | 0.891984i | \(0.649313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6569 | − | 1.73205i | 0.559906 | − | 0.0766214i | ||||
\(512\) | 22.7574i | 1.00574i | ||||||||
\(513\) | 1.01461 | − | 0.585786i | 0.0447962 | − | 0.0258631i | ||||
\(514\) | −3.65685 | + | 6.33386i | −0.161297 | + | 0.279374i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.1569 | + | 24.5204i | 0.623221 | + | 1.07945i | ||||
\(517\) | − | 9.65685i | − | 0.424708i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.6274 | 2.04672 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.48528 | − | 16.4290i | 0.415558 | − | 0.719767i | −0.579929 | − | 0.814667i | \(-0.696920\pi\) |
0.995487 | + | 0.0948999i | \(0.0302531\pi\) | |||||||
\(522\) | 1.01461 | + | 0.585786i | 0.0444084 | + | 0.0256392i | ||||
\(523\) | 21.0818 | − | 12.1716i | 0.921842 | − | 0.532226i | 0.0376197 | − | 0.999292i | \(-0.488022\pi\) |
0.884222 | + | 0.467066i | \(0.154689\pi\) | |||||||
\(524\) | 6.05887 | 0.264683 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.88730 | −0.343903 | ||||||||
\(527\) | −4.30463 | + | 2.48528i | −0.187513 | + | 0.108261i | ||||
\(528\) | −30.2854 | − | 17.4853i | −1.31800 | − | 0.760949i | ||||
\(529\) | −8.58579 | + | 14.8710i | −0.373295 | + | 0.646566i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.3137 | −1.53248 | ||||||||
\(532\) | −10.8126 | + | 8.38478i | −0.468784 | + | 0.363526i | ||||
\(533\) | − | 1.79899i | − | 0.0779229i | ||||||
\(534\) | −1.32843 | − | 2.30090i | −0.0574867 | − | 0.0995698i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.84315 | + | 17.0488i | −0.425159 | + | 0.736397i | ||||
\(537\) | 20.9077 | − | 12.0711i | 0.902234 | − | 0.520905i | ||||
\(538\) | 12.6152i | 0.543881i | ||||||||
\(539\) | 24.1421 | + | 23.6544i | 1.03988 | + | 1.01887i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.32843 | − | 16.1573i | −0.401060 | − | 0.694657i | 0.592794 | − | 0.805354i | \(-0.298025\pi\) |
−0.993854 | + | 0.110697i | \(0.964692\pi\) | |||||||
\(542\) | 0.174080 | + | 0.100505i | 0.00747737 | + | 0.00431706i | ||||
\(543\) | 18.0995 | + | 10.4497i | 0.776724 | + | 0.448442i | ||||
\(544\) | 1.82843 | + | 3.16693i | 0.0783932 | + | 0.135781i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.34315 | + | 1.73205i | 0.0574813 | + | 0.0741249i | ||||
\(547\) | − | 5.10051i | − | 0.218082i | −0.994037 | − | 0.109041i | \(-0.965222\pi\) | ||
0.994037 | − | 0.109041i | \(-0.0347780\pi\) | |||||||
\(548\) | −2.62357 | + | 1.51472i | −0.112073 | + | 0.0647056i | ||||
\(549\) | −16.2426 | + | 28.1331i | −0.693219 | + | 1.20069i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41421 | − | 2.44949i | −0.0602475 | − | 0.104352i | ||||
\(552\) | 9.24264i | 0.393393i | ||||||||
\(553\) | −22.4657 | − | 9.17157i | −0.955338 | − | 0.390015i | ||||
\(554\) | −5.02944 | −0.213680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.1005 | − | 19.2266i | 0.470766 | − | 0.815391i | ||||
\(557\) | −29.6910 | − | 17.1421i | −1.25805 | − | 0.726336i | −0.285355 | − | 0.958422i | \(-0.592111\pi\) |
−0.972695 | + | 0.232086i | \(0.925445\pi\) | |||||||
\(558\) | 6.08767 | − | 3.51472i | 0.257712 | − | 0.148790i | ||||
\(559\) | −5.31371 | −0.224746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.65685 | −0.407713 | ||||||||
\(562\) | 9.42868 | − | 5.44365i | 0.397725 | − | 0.229627i | ||||
\(563\) | −14.0920 | − | 8.13604i | −0.593908 | − | 0.342893i | 0.172733 | − | 0.984969i | \(-0.444740\pi\) |
−0.766641 | + | 0.642076i | \(0.778074\pi\) | |||||||
\(564\) | −4.41421 | + | 7.64564i | −0.185872 | + | 0.321940i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.79899 | −0.243750 | ||||||||
\(567\) | 3.40256 | + | 24.8640i | 0.142894 | + | 1.04419i | ||||
\(568\) | − | 19.7990i | − | 0.830747i | ||||||
\(569\) | −1.82843 | − | 3.16693i | −0.0766517 | − | 0.132765i | 0.825152 | − | 0.564911i | \(-0.191090\pi\) |
−0.901803 | + | 0.432147i | \(0.857756\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.41421 | + | 12.8418i | −0.310275 | + | 0.537412i | −0.978422 | − | 0.206617i | \(-0.933755\pi\) |
0.668147 | + | 0.744030i | \(0.267088\pi\) | |||||||
\(572\) | 6.33386 | − | 3.65685i | 0.264832 | − | 0.152901i | ||||
\(573\) | − | 17.3137i | − | 0.723291i | ||||||
\(574\) | 0.899495 | − | 2.20330i | 0.0375442 | − | 0.0919641i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.89949 | + | 10.2182i | 0.245812 | + | 0.425759i | ||||
\(577\) | 20.7336 | + | 11.9706i | 0.863152 | + | 0.498341i | 0.865067 | − | 0.501657i | \(-0.167276\pi\) |
−0.00191453 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(578\) | −5.85204 | − | 3.37868i | −0.243413 | − | 0.140535i | ||||
\(579\) | −2.41421 | − | 4.18154i | −0.100331 | − | 0.173779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.0147 | + | 24.5204i | 0.788863 | + | 1.01728i | ||||
\(582\) | 0.343146i | 0.0142238i | ||||||||
\(583\) | −28.5533 | + | 16.4853i | −1.18256 | + | 0.682751i | ||||
\(584\) | 3.82843 | − | 6.63103i | 0.158421 | − | 0.274394i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.31371 | − | 5.73951i | −0.136888 | − | 0.237097i | ||||
\(587\) | − | 22.2843i | − | 0.919770i | −0.887978 | − | 0.459885i | \(-0.847891\pi\) | ||
0.887978 | − | 0.459885i | \(-0.152109\pi\) | |||||||
\(588\) | −8.30153 | − | 29.7635i | −0.342350 | − | 1.22742i | ||||
\(589\) | −16.9706 | −0.699260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.5563 | − | 49.4610i | 1.17465 | − | 2.03456i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.9310 | − | 21.8995i | 1.55764 | − | 0.899304i | 0.560159 | − | 0.828385i | \(-0.310740\pi\) |
0.997482 | − | 0.0709193i | \(-0.0225933\pi\) | |||||||
\(594\) | −0.828427 | −0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.3137 | 0.586312 | ||||||||
\(597\) | −3.46410 | + | 2.00000i | −0.141776 | + | 0.0818546i | ||||
\(598\) | −0.717439 | − | 0.414214i | −0.0293383 | − | 0.0169385i | ||||
\(599\) | 8.82843 | − | 15.2913i | 0.360720 | − | 0.624785i | −0.627360 | − | 0.778730i | \(-0.715864\pi\) |
0.988079 | + | 0.153945i | \(0.0491977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.34315 | 0.340324 | 0.170162 | − | 0.985416i | \(-0.445571\pi\) | ||||
0.170162 | + | 0.985416i | \(0.445571\pi\) | |||||||
\(602\) | −6.50794 | − | 2.65685i | −0.265244 | − | 0.108285i | ||||
\(603\) | 35.1127i | 1.42990i | ||||||||
\(604\) | −0.313708 | − | 0.543359i | −0.0127646 | − | 0.0221090i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.15685 | − | 10.6640i | 0.250105 | − | 0.433195i | ||||
\(607\) | 3.64874 | − | 2.10660i | 0.148098 | − | 0.0855043i | −0.424120 | − | 0.905606i | \(-0.639417\pi\) |
0.572218 | + | 0.820102i | \(0.306083\pi\) | |||||||
\(608\) | 12.4853i | 0.506345i | ||||||||
\(609\) | 6.32843 | − | 0.866025i | 0.256441 | − | 0.0350931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.828427 | − | 1.43488i | −0.0335146 | − | 0.0580489i | ||||
\(612\) | 3.71029 | + | 2.14214i | 0.149979 | + | 0.0865907i | ||||
\(613\) | 13.3852 | + | 7.72792i | 0.540621 | + | 0.312128i | 0.745331 | − | 0.666695i | \(-0.232292\pi\) |
−0.204709 | + | 0.978823i | \(0.565625\pi\) | |||||||
\(614\) | 2.74264 | + | 4.75039i | 0.110684 | + | 0.191710i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.0711 | − | 2.74666i | 0.808686 | − | 0.110666i | ||||
\(617\) | 11.3137i | 0.455473i | 0.973723 | + | 0.227736i | \(0.0731324\pi\) | ||||
−0.973723 | + | 0.227736i | \(0.926868\pi\) | |||||||
\(618\) | −0.358719 | + | 0.207107i | −0.0144298 | + | 0.00833106i | ||||
\(619\) | 21.2426 | − | 36.7933i | 0.853814 | − | 1.47885i | −0.0239273 | − | 0.999714i | \(-0.507617\pi\) |
0.877741 | − | 0.479135i | \(-0.159050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | − | 7.79899i | − | 0.312711i | ||||||
\(623\) | −6.50794 | − | 2.65685i | −0.260735 | − | 0.106445i | ||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.65685 | + | 6.33386i | −0.146157 | + | 0.253152i | ||||
\(627\) | −28.5533 | − | 16.4853i | −1.14031 | − | 0.658359i | ||||
\(628\) | 8.41407 | − | 4.85786i | 0.335758 | − | 0.193850i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.14214 | 0.324133 | 0.162067 | − | 0.986780i | \(-0.448184\pi\) | ||||
0.162067 | + | 0.986780i | \(0.448184\pi\) | |||||||
\(632\) | −12.5956 | + | 7.27208i | −0.501026 | + | 0.289268i | ||||
\(633\) | −7.34847 | − | 4.24264i | −0.292075 | − | 0.168630i | ||||
\(634\) | −5.34315 | + | 9.25460i | −0.212203 | + | 0.367547i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 30.1421 | 1.19521 | ||||||||
\(637\) | 5.61642 | + | 1.44365i | 0.222531 | + | 0.0571995i | ||||
\(638\) | 2.00000i | 0.0791808i | ||||||||
\(639\) | −17.6569 | − | 30.5826i | −0.698494 | − | 1.20983i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.25736 | + | 12.5701i | −0.286648 | + | 0.496490i | −0.973008 | − | 0.230773i | \(-0.925875\pi\) |
0.686359 | + | 0.727263i | \(0.259208\pi\) | |||||||
\(642\) | 2.38794 | − | 1.37868i | 0.0942446 | − | 0.0544121i | ||||
\(643\) | − | 30.2843i | − | 1.19430i | −0.802131 | − | 0.597148i | \(-0.796301\pi\) | ||
0.802131 | − | 0.597148i | \(-0.203699\pi\) | |||||||
\(644\) | 7.15685 | + | 9.22911i | 0.282020 | + | 0.363678i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.485281 | + | 0.840532i | 0.0190931 | + | 0.0330703i | ||||
\(647\) | 14.7585 | + | 8.52082i | 0.580216 | + | 0.334988i | 0.761219 | − | 0.648495i | \(-0.224601\pi\) |
−0.181003 | + | 0.983482i | \(0.557934\pi\) | |||||||
\(648\) | 13.0264 | + | 7.52082i | 0.511727 | + | 0.295446i | ||||
\(649\) | −30.1421 | − | 52.2077i | −1.18318 | − | 2.04933i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.4853 | − | 35.4815i | 0.567723 | − | 1.39063i | ||||
\(652\) | 43.2548i | 1.69399i | ||||||||
\(653\) | −21.5020 | + | 12.4142i | −0.841440 | + | 0.485806i | −0.857754 | − | 0.514061i | \(-0.828140\pi\) |
0.0163133 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(654\) | −1.74264 | + | 3.01834i | −0.0681426 | + | 0.118027i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.25736 | + | 5.64191i | 0.127179 | + | 0.220280i | ||||
\(657\) | − | 13.6569i | − | 0.532805i | ||||||
\(658\) | −0.297173 | − | 2.17157i | −0.0115850 | − | 0.0846567i | ||||
\(659\) | −26.8284 | −1.04509 | −0.522544 | − | 0.852613i | \(-0.675017\pi\) | ||||
−0.522544 | + | 0.852613i | \(0.675017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0858 | + | 22.6652i | −0.508978 | + | 0.881576i | 0.490968 | + | 0.871178i | \(0.336643\pi\) |
−0.999946 | + | 0.0103982i | \(0.996690\pi\) | |||||||
\(662\) | 3.93535 | + | 2.27208i | 0.152952 | + | 0.0883068i | ||||
\(663\) | −1.43488 | + | 0.828427i | −0.0557260 | + | 0.0321734i | ||||
\(664\) | 18.5980 | 0.721742 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.09077 | + | 1.20711i | −0.0809549 | + | 0.0467394i | ||||
\(668\) | 31.0134 | + | 17.9056i | 1.19994 | + | 0.692788i | ||||
\(669\) | 14.0711 | − | 24.3718i | 0.544019 | − | 0.942268i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.4558 | −2.14085 | ||||||||
\(672\) | −26.1039 | − | 10.6569i | −1.00698 | − | 0.411097i | ||||
\(673\) | 18.3431i | 0.707076i | 0.935420 | + | 0.353538i | \(0.115022\pi\) | ||||
−0.935420 | + | 0.353538i | \(0.884978\pi\) | |||||||
\(674\) | −3.07107 | − | 5.31925i | −0.118293 | − | 0.204890i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.2574 | + | 19.4983i | −0.432975 | + | 0.749935i | ||||
\(677\) | −0.123093 | + | 0.0710678i | −0.00473085 | + | 0.00273136i | −0.502364 | − | 0.864656i | \(-0.667536\pi\) |
0.497633 | + | 0.867388i | \(0.334203\pi\) | |||||||
\(678\) | − | 12.4853i | − | 0.479494i | ||||||
\(679\) | 0.556349 | + | 0.717439i | 0.0213507 | + | 0.0275328i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.5563 | − | 56.3893i | −1.24756 | − | 2.16084i | ||||
\(682\) | 10.3923 | + | 6.00000i | 0.397942 | + | 0.229752i | ||||
\(683\) | 37.4492 | + | 21.6213i | 1.43295 | + | 0.827317i | 0.997345 | − | 0.0728189i | \(-0.0231995\pi\) |
0.435610 | + | 0.900136i | \(0.356533\pi\) | |||||||
\(684\) | 7.31371 | + | 12.6677i | 0.279647 | + | 0.484362i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.15685 | + | 4.57631i | 0.235070 | + | 0.174724i | ||||
\(687\) | 0.828427i | 0.0316065i | ||||||||
\(688\) | 16.6646 | − | 9.62132i | 0.635333 | − | 0.366809i | ||||
\(689\) | −2.82843 | + | 4.89898i | −0.107754 | + | 0.186636i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.41421 | + | 4.18154i | 0.0918410 | + | 0.159073i | 0.908286 | − | 0.418350i | \(-0.137392\pi\) |
−0.816445 | + | 0.577423i | \(0.804058\pi\) | |||||||
\(692\) | − | 35.3137i | − | 1.34243i | ||||||
\(693\) | 28.5533 | − | 22.1421i | 1.08465 | − | 0.841110i | ||||
\(694\) | 9.14214 | 0.347031 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.91421 | − | 3.31552i | 0.0725581 | − | 0.125674i | ||||
\(697\) | 1.55797 | + | 0.899495i | 0.0590124 | + | 0.0340708i | ||||
\(698\) | 9.56233 | − | 5.52082i | 0.361940 | − | 0.208966i | ||||
\(699\) | 26.9706 | 1.02012 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7990 | −1.61650 | −0.808248 | − | 0.588843i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588843i | \(0.799584\pi\) | |||||||
\(702\) | −0.123093 | + | 0.0710678i | −0.00464585 | + | 0.00268228i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −10.0711 | + | 17.4436i | −0.379568 | + | 0.657430i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.76955 | 0.330046 | ||||||||
\(707\) | −4.41717 | − | 32.2782i | −0.166125 | − | 1.21395i | ||||
\(708\) | 55.1127i | 2.07126i | ||||||||
\(709\) | 19.1569 | + | 33.1806i | 0.719451 | + | 1.24613i | 0.961218 | + | 0.275791i | \(0.0889397\pi\) |
−0.241767 | + | 0.970334i | \(0.577727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9706 | + | 22.4657i | −0.486434 | + | 0.842529i | ||||
\(712\) | −3.64874 | + | 2.10660i | −0.136742 | + | 0.0789482i | ||||
\(713\) | 14.4853i | 0.542478i | ||||||||
\(714\) | −2.17157 | + | 0.297173i | −0.0812691 | + | 0.0111214i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.14214 | − | 15.8346i | −0.341658 | − | 0.591768i | ||||
\(717\) | 2.74666 | + | 1.58579i | 0.102576 | + | 0.0592223i | ||||
\(718\) | −3.58719 | − | 2.07107i | −0.133873 | − | 0.0772916i | ||||
\(719\) | −20.5563 | − | 35.6046i | −0.766622 | − | 1.32783i | −0.939385 | − | 0.342865i | \(-0.888602\pi\) |
0.172762 | − | 0.984964i | \(-0.444731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.414214 | + | 1.01461i | −0.0154261 | + | 0.0377861i | ||||
\(722\) | − | 4.55635i | − | 0.169570i | ||||||
\(723\) | 34.1698 | − | 19.7279i | 1.27079 | − | 0.733689i | ||||
\(724\) | 7.91421 | − | 13.7078i | 0.294129 | − | 0.509447i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.15685 | + | 10.6640i | 0.228502 | + | 0.395778i | ||||
\(727\) | 40.4142i | 1.49888i | 0.662072 | + | 0.749440i | \(0.269677\pi\) | ||||
−0.662072 | + | 0.749440i | \(0.730323\pi\) | |||||||
\(728\) | 2.74666 | − | 2.12994i | 0.101798 | − | 0.0789409i | ||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.65685 | − | 4.60181i | 0.0982673 | − | 0.170204i | ||||
\(732\) | 43.9062 | + | 25.3492i | 1.62282 | + | 0.936935i | ||||
\(733\) | −19.0526 | + | 11.0000i | −0.703722 | + | 0.406294i | −0.808732 | − | 0.588177i | \(-0.799846\pi\) |
0.105010 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(734\) | −4.65685 | −0.171888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.6569 | 0.392817 | ||||||||
\(737\) | −51.9105 | + | 29.9706i | −1.91215 | + | 1.10398i | ||||
\(738\) | −2.20330 | − | 1.27208i | −0.0811047 | − | 0.0468258i | ||||
\(739\) | 20.5563 | − | 35.6046i | 0.756178 | − | 1.30974i | −0.188609 | − | 0.982052i | \(-0.560398\pi\) |
0.944787 | − | 0.327686i | \(-0.106269\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | −5.91359 | + | 4.58579i | −0.217095 | + | 0.168350i | ||||
\(743\) | − | 1.92893i | − | 0.0707657i | −0.999374 | − | 0.0353828i | \(-0.988735\pi\) | ||
0.999374 | − | 0.0353828i | \(-0.0112651\pi\) | |||||||
\(744\) | −11.4853 | − | 19.8931i | −0.421071 | − | 0.729316i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.68629 | − | 4.65279i | 0.0983521 | − | 0.170351i | ||||
\(747\) | 28.7274 | − | 16.5858i | 1.05108 | − | 0.606842i | ||||
\(748\) | 7.31371i | 0.267416i | ||||||||
\(749\) | 2.75736 | − | 6.75412i | 0.100752 | − | 0.246790i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.8284 | + | 36.0759i | 0.760040 | + | 1.31643i | 0.942829 | + | 0.333276i | \(0.108154\pi\) |
−0.182789 | + | 0.983152i | \(0.558513\pi\) | |||||||
\(752\) | 5.19615 | + | 3.00000i | 0.189484 | + | 0.109399i | ||||
\(753\) | −27.8359 | − | 16.0711i | −1.01440 | − | 0.585662i | ||||
\(754\) | 0.171573 | + | 0.297173i | 0.00624832 | + | 0.0108224i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.98528 | − | 0.271680i | 0.0722040 | − | 0.00988089i | ||||
\(757\) | − | 19.4558i | − | 0.707135i | −0.935409 | − | 0.353567i | \(-0.884969\pi\) | ||
0.935409 | − | 0.353567i | \(-0.115031\pi\) | |||||||
\(758\) | −7.59466 | + | 4.38478i | −0.275850 | + | 0.159262i | ||||
\(759\) | −14.0711 | + | 24.3718i | −0.510747 | + | 0.884640i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.65685 | + | 11.5300i | 0.241311 | + | 0.417963i | 0.961088 | − | 0.276243i | \(-0.0890894\pi\) |
−0.719777 | + | 0.694205i | \(0.755756\pi\) | |||||||
\(762\) | 13.3137i | 0.482305i | ||||||||
\(763\) | 1.25024 | + | 9.13604i | 0.0452617 | + | 0.330747i | ||||
\(764\) | −13.1127 | −0.474401 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.50000 | − | 6.06218i | 0.126460 | − | 0.219035i | ||||
\(767\) | −8.95743 | − | 5.17157i | −0.323434 | − | 0.186735i | ||||
\(768\) | 8.30153 | − | 4.79289i | 0.299556 | − | 0.172949i | ||||
\(769\) | −44.6274 | −1.60931 | −0.804653 | − | 0.593745i | \(-0.797649\pi\) | ||||
−0.804653 | + | 0.593745i | \(0.797649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.6274 | 1.53519 | ||||||||
\(772\) | −3.16693 | + | 1.82843i | −0.113980 | + | 0.0658065i | ||||
\(773\) | −21.7482 | − | 12.5563i | −0.782230 | − | 0.451620i | 0.0549903 | − | 0.998487i | \(-0.482487\pi\) |
−0.837220 | + | 0.546866i | \(0.815821\pi\) | |||||||
\(774\) | −3.75736 | + | 6.50794i | −0.135055 | + | 0.233923i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.544156 | 0.0195341 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 5.11270i | − | 0.183299i | ||||||
\(779\) | 3.07107 | + | 5.31925i | 0.110032 | + | 0.190582i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.1421 | − | 52.2077i | 1.07857 | − | 1.86814i | ||||
\(782\) | 0.717439 | − | 0.414214i | 0.0256556 | − | 0.0148122i | ||||
\(783\) | 0.414214i | 0.0148028i | ||||||||
\(784\) | −20.2279 | + | 5.64191i | −0.722426 | + | 0.201497i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.65685 | + | 2.86976i | 0.0590980 | + | 0.102361i | ||||
\(787\) | −24.7305 | − | 14.2782i | −0.881548 | − | 0.508962i | −0.0103795 | − | 0.999946i | \(-0.503304\pi\) |
−0.871168 | + | 0.490984i | \(0.836637\pi\) | |||||||
\(788\) | −37.4598 | − | 21.6274i | −1.33445 | − | 0.770445i | ||||
\(789\) | 22.9853 | + | 39.8117i | 0.818298 | + | 1.41733i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.2426 | − | 26.1039i | −0.719745 | − | 0.928146i | ||||
\(792\) | − | 21.6569i | − | 0.769543i | ||||||
\(793\) | −8.23999 | + | 4.75736i | −0.292611 | + | 0.168939i | ||||
\(794\) | −5.92893 | + | 10.2692i | −0.210410 | + | 0.364441i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.51472 | + | 2.62357i | 0.0536878 | + | 0.0929900i | ||||
\(797\) | 8.00000i | 0.283375i | 0.989911 | + | 0.141687i | \(0.0452527\pi\) | ||||
−0.989911 | + | 0.141687i | \(0.954747\pi\) | |||||||
\(798\) | −6.92820 | − | 2.82843i | −0.245256 | − | 0.100125i | ||||
\(799\) | 1.65685 | 0.0586153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.75736 | + | 6.50794i | −0.132760 | + | 0.229947i | ||||
\(802\) | −2.75722 | − | 1.59188i | −0.0973609 | − | 0.0562113i | ||||
\(803\) | 20.1903 | − | 11.6569i | 0.712499 | − | 0.411361i | ||||
\(804\) | 54.7990 | 1.93261 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.05887 | 0.0725208 | ||||||||
\(807\) | 63.6762 | − | 36.7635i | 2.24151 | − | 1.29413i | ||||
\(808\) | −16.9108 | − | 9.76346i | −0.594920 | − | 0.343477i | ||||
\(809\) | −4.81371 | + | 8.33759i | −0.169241 | + | 0.293134i | −0.938153 | − | 0.346220i | \(-0.887465\pi\) |
0.768912 | + | 0.639354i | \(0.220798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.6274 | 0.864786 | 0.432393 | − | 0.901685i | \(-0.357669\pi\) | ||||
0.432393 | + | 0.901685i | \(0.357669\pi\) | |||||||
\(812\) | −0.655892 | − | 4.79289i | −0.0230173 | − | 0.168198i | ||||
\(813\) | − | 1.17157i | − | 0.0410889i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | 15.7116 | − | 9.07107i | 0.549678 | − | 0.317356i | ||||
\(818\) | − | 10.2721i | − | 0.359155i | ||||||
\(819\) | 2.34315 | − | 5.73951i | 0.0818761 | − | 0.200555i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.97056 | + | 17.2695i | 0.347975 | + | 0.602710i | 0.985890 | − | 0.167397i | \(-0.0535361\pi\) |
−0.637915 | + | 0.770107i | \(0.720203\pi\) | |||||||
\(822\) | −1.43488 | − | 0.828427i | −0.0500471 | − | 0.0288947i | ||||
\(823\) | 10.4539 | + | 6.03553i | 0.364398 | + | 0.210385i | 0.671008 | − | 0.741450i | \(-0.265861\pi\) |
−0.306610 | + | 0.951835i | \(0.599195\pi\) | |||||||
\(824\) | 0.328427 | + | 0.568852i | 0.0114413 | + | 0.0198169i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.38478 | − | 10.8126i | −0.291744 | − | 0.376217i | ||||
\(827\) | − | 16.2132i | − | 0.563788i | −0.959446 | − | 0.281894i | \(-0.909037\pi\) | ||
0.959446 | − | 0.281894i | \(-0.0909627\pi\) | |||||||
\(828\) | 10.8126 | − | 6.24264i | 0.375763 | − | 0.216947i | ||||
\(829\) | 3.34315 | − | 5.79050i | 0.116112 | − | 0.201112i | −0.802112 | − | 0.597174i | \(-0.796290\pi\) |
0.918224 | + | 0.396062i | \(0.129623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.6569 | + | 25.3864i | 0.508441 | + | 0.880645i | ||||
\(832\) | 3.45584i | 0.119810i | ||||||||
\(833\) | −4.05845 | + | 4.14214i | −0.140617 | + | 0.143516i | ||||
\(834\) | 12.1421 | 0.420448 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.4853 | + | 21.6251i | −0.431812 | + | 0.747921i | ||||
\(837\) | 2.15232 | + | 1.24264i | 0.0743950 | + | 0.0429519i | ||||
\(838\) | 8.36308 | − | 4.82843i | 0.288898 | − | 0.166795i | ||||
\(839\) | −20.8284 | −0.719077 | −0.359539 | − | 0.933130i | \(-0.617066\pi\) | ||||
−0.359539 | + | 0.933130i | \(0.617066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −1.25024 | + | 0.721825i | −0.0430861 | + | 0.0248757i | ||||
\(843\) | −54.9544 | − | 31.7279i | −1.89273 | − | 1.09277i | ||||
\(844\) | −3.21320 | + | 5.56543i | −0.110603 | + | 0.191570i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.34315 | −0.0805590 | ||||||||
\(847\) | 30.1623 | + | 12.3137i | 1.03639 | + | 0.423104i | ||||
\(848\) | − | 20.4853i | − | 0.703467i | ||||||
\(849\) | 16.8995 | + | 29.2708i | 0.579989 | + | 1.00457i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −47.7290 | + | 27.5563i | −1.63517 | + | 0.944065i | ||||
\(853\) | 53.4558i | 1.83029i | 0.403121 | + | 0.915147i | \(0.367925\pi\) | ||||
−0.403121 | + | 0.915147i | \(0.632075\pi\) | |||||||
\(854\) | −12.4706 | + | 1.70656i | −0.426734 | + | 0.0583972i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.18629 | − | 3.78677i | −0.0747259 | − | 0.129429i | ||||
\(857\) | −19.2987 | − | 11.1421i | −0.659233 | − | 0.380608i | 0.132752 | − | 0.991149i | \(-0.457619\pi\) |
−0.791985 | + | 0.610541i | \(0.790952\pi\) | |||||||
\(858\) | 3.46410 | + | 2.00000i | 0.118262 | + | 0.0682789i | ||||
\(859\) | 23.3137 | + | 40.3805i | 0.795453 | + | 1.37777i | 0.922551 | + | 0.385876i | \(0.126101\pi\) |
−0.127097 | + | 0.991890i | \(0.540566\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.7426 | + | 1.88064i | −0.468348 | + | 0.0640919i | ||||
\(862\) | − | 9.02944i | − | 0.307544i | ||||||
\(863\) | −14.3382 | + | 8.27817i | −0.488079 | + | 0.281792i | −0.723777 | − | 0.690034i | \(-0.757596\pi\) |
0.235698 | + | 0.971826i | \(0.424262\pi\) | |||||||
\(864\) | 0.914214 | − | 1.58346i | 0.0311022 | − | 0.0538706i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.58579 | − | 11.4069i | −0.223794 | − | 0.387623i | ||||
\(867\) | 39.3848i | 1.33758i | ||||||||
\(868\) | −26.8723 | − | 10.9706i | −0.912105 | − | 0.372365i | ||||
\(869\) | −44.2843 | −1.50224 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.14214 | + | 8.90644i | −0.174235 | + | 0.301783i | ||||
\(872\) | 4.78645 | + | 2.76346i | 0.162090 | + | 0.0935824i | ||||
\(873\) | 0.840532 | − | 0.485281i | 0.0284477 | − | 0.0164243i | ||||
\(874\) | 2.82843 | 0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.3137 | −0.720123 | ||||||||
\(877\) | −26.6982 | + | 15.4142i | −0.901534 | + | 0.520501i | −0.877698 | − | 0.479215i | \(-0.840921\pi\) |
−0.0238366 | + | 0.999716i | \(0.507588\pi\) | |||||||
\(878\) | 12.1753 | + | 7.02944i | 0.410898 | + | 0.237232i | ||||
\(879\) | −19.3137 | + | 33.4523i | −0.651435 | + | 1.12832i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.82843 | −0.128983 | −0.0644915 | − | 0.997918i | \(-0.520543\pi\) | ||||
−0.0644915 | + | 0.997918i | \(0.520543\pi\) | |||||||
\(882\) | 5.73951 | − | 5.85786i | 0.193259 | − | 0.197245i | ||||
\(883\) | − | 38.2843i | − | 1.28837i | −0.764870 | − | 0.644184i | \(-0.777197\pi\) | ||
0.764870 | − | 0.644184i | \(-0.222803\pi\) | |||||||
\(884\) | 0.627417 | + | 1.08672i | 0.0211023 | + | 0.0365503i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.52944 | + | 4.38111i | −0.0849781 | + | 0.147186i | ||||
\(887\) | −38.1667 | + | 22.0355i | −1.28151 | + | 0.739881i | −0.977125 | − | 0.212668i | \(-0.931785\pi\) |
−0.304387 | + | 0.952549i | \(0.598451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.5858 | + | 27.8359i | 0.723964 | + | 0.933586i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.8995 | + | 39.6631i | 0.767162 | + | 1.32876i | ||||
\(892\) | −18.4582 | − | 10.6569i | −0.618027 | − | 0.356818i | ||||
\(893\) | 4.89898 | + | 2.82843i | 0.163938 | + | 0.0946497i | ||||
\(894\) | 3.91421 | + | 6.77962i | 0.130911 | + | 0.226744i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.5563 | + | 25.8577i | −0.352663 | + | 0.863844i | ||||
\(897\) | 4.82843i | 0.161216i | ||||||||
\(898\) | 0.655892 | − | 0.378680i | 0.0218874 | − | 0.0126367i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.82843 | − | 4.89898i | −0.0942286 | − | 0.163209i | ||||
\(902\) | − | 4.34315i | − | 0.144611i | ||||||
\(903\) | 5.55487 | + | 40.5919i | 0.184855 | + | 1.35081i | ||||
\(904\) | −19.7990 | −0.658505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.171573 | − | 0.297173i | 0.00570013 | − | 0.00987291i | ||||
\(907\) | 24.4334 | + | 14.1066i | 0.811296 | + | 0.468402i | 0.847406 | − | 0.530946i | \(-0.178163\pi\) |
−0.0361097 | + | 0.999348i | \(0.511497\pi\) | |||||||
\(908\) | −42.7069 | + | 24.6569i | −1.41728 | + | 0.818266i | ||||
\(909\) | −34.8284 | −1.15519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.7990 | −1.64991 | −0.824957 | − | 0.565195i | \(-0.808801\pi\) | ||||
−0.824957 | + | 0.565195i | \(0.808801\pi\) | |||||||
\(912\) | 17.7408 | − | 10.2426i | 0.587456 | − | 0.339168i | ||||
\(913\) | 49.0408 | + | 28.3137i | 1.62301 | + | 0.937047i | ||||
\(914\) | 6.68629 | − | 11.5810i | 0.221163 | − | 0.383065i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.627417 | 0.0207304 | ||||||||
\(917\) | 8.11689 | + | 3.31371i | 0.268043 | + | 0.109428i | ||||
\(918\) | − | 0.142136i | − | 0.00469117i | ||||||
\(919\) | 9.55635 | + | 16.5521i | 0.315235 | + | 0.546003i | 0.979487 | − | 0.201505i | \(-0.0645834\pi\) |
−0.664253 | + | 0.747508i | \(0.731250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9853 | − | 27.6873i | 0.526733 | − | 0.912328i | ||||
\(922\) | 6.70314 | − | 3.87006i | 0.220756 | − | 0.127454i | ||||
\(923\) | − | 10.3431i | − | 0.340449i | ||||||
\(924\) | −34.5563 | − | 44.5621i | −1.13682 | − | 1.46598i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.28680 | + | 3.96085i | 0.0751488 | + | 0.130162i | ||||
\(927\) | 1.01461 | + | 0.585786i | 0.0333242 | + | 0.0192398i | ||||
\(928\) | −3.82282 | − | 2.20711i | −0.125490 | − | 0.0724518i | ||||
\(929\) | −5.74264 | − | 9.94655i | −0.188410 | − | 0.326336i | 0.756310 | − | 0.654213i | \(-0.227000\pi\) |
−0.944720 | + | 0.327877i | \(0.893667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0711 | + | 5.31925i | −0.625029 | + | 0.174331i | ||||
\(932\) | − | 20.4264i | − | 0.669089i | ||||||
\(933\) | −39.3659 | + | 22.7279i | −1.28878 | + | 0.744079i | ||||
\(934\) | 4.74264 | − | 8.21449i | 0.155184 | − | 0.268786i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.85786 | − | 3.21792i | −0.0607262 | − | 0.105181i | ||||
\(937\) | 10.6274i | 0.347183i | 0.984818 | + | 0.173591i | \(0.0555372\pi\) | ||||
−0.984818 | + | 0.173591i | \(0.944463\pi\) | |||||||
\(938\) | −10.7510 | + | 8.33705i | −0.351033 | + | 0.272214i | ||||
\(939\) | 42.6274 | 1.39109 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.14214 | + | 8.90644i | −0.167629 | + | 0.290342i | −0.937586 | − | 0.347754i | \(-0.886944\pi\) |
0.769957 | + | 0.638096i | \(0.220278\pi\) | |||||||
\(942\) | 4.60181 | + | 2.65685i | 0.149935 | + | 0.0865650i | ||||
\(943\) | 4.54026 | − | 2.62132i | 0.147851 | − | 0.0853619i | ||||
\(944\) | 37.4558 | 1.21908 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.8284 | −0.417088 | ||||||||
\(947\) | 37.3982 | − | 21.5919i | 1.21528 | − | 0.701642i | 0.251375 | − | 0.967890i | \(-0.419117\pi\) |
0.963905 | + | 0.266248i | \(0.0857840\pi\) | |||||||
\(948\) | 35.0613 | + | 20.2426i | 1.13874 | + | 0.657450i | ||||
\(949\) | 2.00000 | − | 3.46410i | 0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 62.2843 | 2.01971 | ||||||||
\(952\) | 0.471253 | + | 3.44365i | 0.0152734 | + | 0.111609i | ||||
\(953\) | − | 2.34315i | − | 0.0759019i | −0.999280 | − | 0.0379510i | \(-0.987917\pi\) | ||
0.999280 | − | 0.0379510i | \(-0.0120831\pi\) | |||||||
\(954\) | 4.00000 | + | 6.92820i | 0.129505 | + | 0.224309i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.20101 | − | 2.08021i | 0.0388434 | − | 0.0672788i | ||||
\(957\) | 10.0951 | − | 5.82843i | 0.326329 | − | 0.188406i | ||||
\(958\) | 10.0833i | 0.325775i | ||||||||
\(959\) | −4.34315 | + | 0.594346i | −0.140247 | + | 0.0191924i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.75412 | − | 3.89949i | −0.217649 | − | 0.125659i | ||||
\(964\) | −14.9411 | − | 25.8788i | −0.481221 | − | 0.833500i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.41421 | + | 5.91359i | −0.0776760 | + | 0.190267i | ||||
\(967\) | 27.5269i | 0.885206i | 0.896718 | + | 0.442603i | \(0.145945\pi\) | ||||
−0.896718 | + | 0.442603i | \(0.854055\pi\) | |||||||
\(968\) | 16.9108 | − | 9.76346i | 0.543534 | − | 0.313809i | ||||
\(969\) | 2.82843 | − | 4.89898i | 0.0908622 | − | 0.157378i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | − | 39.5980i | − | 1.27011i | ||||||
\(973\) | 25.3864 | − | 19.6863i | 0.813851 | − | 0.631114i | ||||
\(974\) | 6.48528 | 0.207802 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.2279 | − | 29.8396i | 0.551452 | − | 0.955143i | ||||
\(977\) | 18.4582 | + | 10.6569i | 0.590531 | + | 0.340943i | 0.765307 | − | 0.643665i | \(-0.222587\pi\) |
−0.174777 | + | 0.984608i | \(0.555920\pi\) | |||||||
\(978\) | −20.4874 | + | 11.8284i | −0.655116 | + | 0.378231i | ||||
\(979\) | −12.8284 | −0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.85786 | 0.314737 | ||||||||
\(982\) | −4.77589 | + | 2.75736i | −0.152405 | + | 0.0879909i | ||||
\(983\) | 12.3090 | + | 7.10660i | 0.392596 | + | 0.226665i | 0.683284 | − | 0.730152i | \(-0.260551\pi\) |
−0.290688 | + | 0.956818i | \(0.593884\pi\) | |||||||
\(984\) | −4.15685 | + | 7.19988i | −0.132516 | + | 0.229524i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.343146 | −0.0109280 | ||||||||
\(987\) | −10.0951 | + | 7.82843i | −0.321332 | + | 0.249182i | ||||
\(988\) | 4.28427i | 0.136301i | ||||||||
\(989\) | −7.74264 | − | 13.4106i | −0.246202 | − | 0.426434i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.82843 | − | 13.5592i | 0.248678 | − | 0.430723i | −0.714481 | − | 0.699655i | \(-0.753337\pi\) |
0.963159 | + | 0.268931i | \(0.0866705\pi\) | |||||||
\(992\) | −22.9369 | + | 13.2426i | −0.728248 | + | 0.420454i | ||||
\(993\) | − | 26.4853i | − | 0.840485i | ||||||
\(994\) | 5.17157 | − | 12.6677i | 0.164032 | − | 0.401796i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.8848 | − | 44.8337i | −0.820191 | − | 1.42061i | ||||
\(997\) | −15.1172 | − | 8.72792i | −0.478767 | − | 0.276416i | 0.241136 | − | 0.970491i | \(-0.422480\pi\) |
−0.719902 | + | 0.694075i | \(0.755813\pi\) | |||||||
\(998\) | 1.73205 | + | 1.00000i | 0.0548271 | + | 0.0316544i | ||||
\(999\) | 0 | 0 |
(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 | 175.2.k.a.74.3 | 8 | ||
5.2 | odd | 4 | 35.2.e.a.11.2 | ✓ | 4 | ||
5.3 | odd | 4 | 175.2.e.c.151.1 | 4 | |||
5.4 | even | 2 | inner | 175.2.k.a.74.2 | 8 | ||
7.2 | even | 3 | inner | 175.2.k.a.149.2 | 8 | ||
7.3 | odd | 6 | 1225.2.b.h.99.3 | 4 | |||
7.4 | even | 3 | 1225.2.b.g.99.3 | 4 | |||
15.2 | even | 4 | 315.2.j.e.46.1 | 4 | |||
20.7 | even | 4 | 560.2.q.k.81.2 | 4 | |||
35.2 | odd | 12 | 35.2.e.a.16.2 | yes | 4 | ||
35.3 | even | 12 | 1225.2.a.m.1.2 | 2 | |||
35.4 | even | 6 | 1225.2.b.g.99.2 | 4 | |||
35.9 | even | 6 | inner | 175.2.k.a.149.3 | 8 | ||
35.12 | even | 12 | 245.2.e.e.226.2 | 4 | |||
35.17 | even | 12 | 245.2.a.g.1.1 | 2 | |||
35.18 | odd | 12 | 1225.2.a.k.1.2 | 2 | |||
35.23 | odd | 12 | 175.2.e.c.51.1 | 4 | |||
35.24 | odd | 6 | 1225.2.b.h.99.2 | 4 | |||
35.27 | even | 4 | 245.2.e.e.116.2 | 4 | |||
35.32 | odd | 12 | 245.2.a.h.1.1 | 2 | |||
105.2 | even | 12 | 315.2.j.e.226.1 | 4 | |||
105.17 | odd | 12 | 2205.2.a.q.1.2 | 2 | |||
105.32 | even | 12 | 2205.2.a.n.1.2 | 2 | |||
140.67 | even | 12 | 3920.2.a.bq.1.1 | 2 | |||
140.87 | odd | 12 | 3920.2.a.bv.1.2 | 2 | |||
140.107 | even | 12 | 560.2.q.k.401.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.2 | ✓ | 4 | 5.2 | odd | 4 | ||
35.2.e.a.16.2 | yes | 4 | 35.2 | odd | 12 | ||
175.2.e.c.51.1 | 4 | 35.23 | odd | 12 | |||
175.2.e.c.151.1 | 4 | 5.3 | odd | 4 | |||
175.2.k.a.74.2 | 8 | 5.4 | even | 2 | inner | ||
175.2.k.a.74.3 | 8 | 1.1 | even | 1 | trivial | ||
175.2.k.a.149.2 | 8 | 7.2 | even | 3 | inner | ||
175.2.k.a.149.3 | 8 | 35.9 | even | 6 | inner | ||
245.2.a.g.1.1 | 2 | 35.17 | even | 12 | |||
245.2.a.h.1.1 | 2 | 35.32 | odd | 12 | |||
245.2.e.e.116.2 | 4 | 35.27 | even | 4 | |||
245.2.e.e.226.2 | 4 | 35.12 | even | 12 | |||
315.2.j.e.46.1 | 4 | 15.2 | even | 4 | |||
315.2.j.e.226.1 | 4 | 105.2 | even | 12 | |||
560.2.q.k.81.2 | 4 | 20.7 | even | 4 | |||
560.2.q.k.401.2 | 4 | 140.107 | even | 12 | |||
1225.2.a.k.1.2 | 2 | 35.18 | odd | 12 | |||
1225.2.a.m.1.2 | 2 | 35.3 | even | 12 | |||
1225.2.b.g.99.2 | 4 | 35.4 | even | 6 | |||
1225.2.b.g.99.3 | 4 | 7.4 | even | 3 | |||
1225.2.b.h.99.2 | 4 | 35.24 | odd | 6 | |||
1225.2.b.h.99.3 | 4 | 7.3 | odd | 6 | |||
2205.2.a.n.1.2 | 2 | 105.32 | even | 12 | |||
2205.2.a.q.1.2 | 2 | 105.17 | odd | 12 | |||
3920.2.a.bq.1.1 | 2 | 140.67 | even | 12 | |||
3920.2.a.bv.1.2 | 2 | 140.87 | odd | 12 |