Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,2,Mod(11,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.279476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.16 |
Dual form | 35.2.e.a.11.2 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.207107 | − | 0.358719i | 0.146447 | − | 0.253653i | −0.783465 | − | 0.621436i | \(-0.786550\pi\) |
0.929912 | + | 0.367783i | \(0.119883\pi\) | |||||||
\(3\) | −1.20711 | − | 2.09077i | −0.696923 | − | 1.20711i | −0.969528 | − | 0.244981i | \(-0.921218\pi\) |
0.272605 | − | 0.962126i | \(-0.412115\pi\) | |||||||
\(4\) | 0.914214 | + | 1.58346i | 0.457107 | + | 0.791732i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.62132 | + | 2.09077i | −0.612801 | + | 0.790237i | ||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | −1.41421 | + | 2.44949i | −0.471405 | + | 0.816497i | ||||
\(10\) | 0.207107 | + | 0.358719i | 0.0654929 | + | 0.113437i | ||||
\(11\) | −2.41421 | − | 4.18154i | −0.727913 | − | 1.26078i | −0.957764 | − | 0.287556i | \(-0.907157\pi\) |
0.229851 | − | 0.973226i | \(-0.426176\pi\) | |||||||
\(12\) | 2.20711 | − | 3.82282i | 0.637137 | − | 1.10355i | ||||
\(13\) | 0.828427 | 0.229764 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(14\) | 0.414214 | + | 1.01461i | 0.110703 | + | 0.271166i | ||||
\(15\) | 2.41421 | 0.623347 | ||||||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | 0.414214 | + | 0.717439i | 0.100462 | + | 0.174005i | 0.911875 | − | 0.410468i | \(-0.134635\pi\) |
−0.811413 | + | 0.584473i | \(0.801301\pi\) | |||||||
\(18\) | 0.585786 | + | 1.01461i | 0.138071 | + | 0.239146i | ||||
\(19\) | 1.41421 | − | 2.44949i | 0.324443 | − | 0.561951i | −0.656957 | − | 0.753928i | \(-0.728157\pi\) |
0.981399 | + | 0.191977i | \(0.0614899\pi\) | |||||||
\(20\) | −1.82843 | −0.408849 | ||||||||
\(21\) | 6.32843 | + | 0.866025i | 1.38098 | + | 0.188982i | ||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 1.20711 | − | 2.09077i | 0.251699 | − | 0.435956i | −0.712295 | − | 0.701881i | \(-0.752344\pi\) |
0.963994 | + | 0.265925i | \(0.0856773\pi\) | |||||||
\(24\) | −1.91421 | − | 3.31552i | −0.390737 | − | 0.676777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0.171573 | − | 0.297173i | 0.0336482 | − | 0.0582804i | ||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | −4.79289 | − | 0.655892i | −0.905772 | − | 0.123952i | ||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | 2.20711 | + | 3.82282i | 0.390165 | + | 0.675786i | ||||
\(33\) | −5.82843 | + | 10.0951i | −1.01460 | + | 1.75734i | ||||
\(34\) | 0.343146 | 0.0588490 | ||||||||
\(35\) | −1.00000 | − | 2.44949i | −0.169031 | − | 0.414039i | ||||
\(36\) | −5.17157 | −0.861929 | ||||||||
\(37\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(38\) | −0.585786 | − | 1.01461i | −0.0950271 | − | 0.164592i | ||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | −0.792893 | + | 1.37333i | −0.125367 | + | 0.217143i | ||||
\(41\) | −2.17157 | −0.339143 | −0.169571 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169571 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(42\) | 1.62132 | − | 2.09077i | 0.250175 | − | 0.322613i | ||||
\(43\) | 6.41421 | 0.978158 | 0.489079 | − | 0.872239i | \(-0.337333\pi\) | ||||
0.489079 | + | 0.872239i | \(0.337333\pi\) | |||||||
\(44\) | 4.41421 | − | 7.64564i | 0.665468 | − | 1.15262i | ||||
\(45\) | −1.41421 | − | 2.44949i | −0.210819 | − | 0.365148i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | −1.00000 | + | 1.73205i | −0.145865 | + | 0.252646i | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 7.24264 | 1.04539 | ||||||||
\(49\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(50\) | −0.414214 | −0.0585786 | ||||||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | 0.757359 | + | 1.31178i | 0.105027 | + | 0.181912i | ||||
\(53\) | 3.41421 | + | 5.91359i | 0.468978 | + | 0.812294i | 0.999371 | − | 0.0354577i | \(-0.0112889\pi\) |
−0.530393 | + | 0.847752i | \(0.677956\pi\) | |||||||
\(54\) | −0.0857864 | + | 0.148586i | −0.0116741 | + | 0.0202201i | ||||
\(55\) | 4.82843 | 0.651065 | ||||||||
\(56\) | −2.57107 | + | 3.31552i | −0.343573 | + | 0.443054i | ||||
\(57\) | −6.82843 | −0.904447 | ||||||||
\(58\) | −0.207107 | + | 0.358719i | −0.0271945 | + | 0.0471022i | ||||
\(59\) | 6.24264 | + | 10.8126i | 0.812723 | + | 1.40768i | 0.910952 | + | 0.412513i | \(0.135349\pi\) |
−0.0982291 | + | 0.995164i | \(0.531318\pi\) | |||||||
\(60\) | 2.20711 | + | 3.82282i | 0.284936 | + | 0.493524i | ||||
\(61\) | 5.74264 | − | 9.94655i | 0.735270 | − | 1.27352i | −0.219335 | − | 0.975650i | \(-0.570389\pi\) |
0.954605 | − | 0.297875i | \(-0.0962779\pi\) | |||||||
\(62\) | 2.48528 | 0.315631 | ||||||||
\(63\) | −2.82843 | − | 6.92820i | −0.356348 | − | 0.872872i | ||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −0.414214 | + | 0.717439i | −0.0513769 | + | 0.0889873i | ||||
\(66\) | 2.41421 | + | 4.18154i | 0.297169 | + | 0.514712i | ||||
\(67\) | −6.20711 | − | 10.7510i | −0.758319 | − | 1.31345i | −0.943707 | − | 0.330781i | \(-0.892688\pi\) |
0.185389 | − | 0.982665i | \(-0.440646\pi\) | |||||||
\(68\) | −0.757359 | + | 1.31178i | −0.0918433 | + | 0.159077i | ||||
\(69\) | −5.82843 | −0.701660 | ||||||||
\(70\) | −1.08579 | − | 0.148586i | −0.129776 | − | 0.0177595i | ||||
\(71\) | −12.4853 | −1.48173 | −0.740865 | − | 0.671654i | \(-0.765584\pi\) | ||||
−0.740865 | + | 0.671654i | \(0.765584\pi\) | |||||||
\(72\) | −2.24264 | + | 3.88437i | −0.264298 | + | 0.457777i | ||||
\(73\) | −2.41421 | − | 4.18154i | −0.282562 | − | 0.489412i | 0.689453 | − | 0.724331i | \(-0.257851\pi\) |
−0.972015 | + | 0.234918i | \(0.924518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.20711 | + | 2.09077i | −0.139385 | + | 0.241421i | ||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 12.6569 | + | 1.73205i | 1.44238 | + | 0.197386i | ||||
\(78\) | −0.828427 | −0.0938009 | ||||||||
\(79\) | −4.58579 | + | 7.94282i | −0.515941 | + | 0.893637i | 0.483887 | + | 0.875130i | \(0.339224\pi\) |
−0.999829 | + | 0.0185063i | \(0.994109\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 4.74264 | + | 8.21449i | 0.526960 | + | 0.912722i | ||||
\(82\) | −0.449747 | + | 0.778985i | −0.0496663 | + | 0.0860246i | ||||
\(83\) | −11.7279 | −1.28731 | −0.643653 | − | 0.765317i | \(-0.722582\pi\) | ||||
−0.643653 | + | 0.765317i | \(0.722582\pi\) | |||||||
\(84\) | 4.41421 | + | 10.8126i | 0.481630 | + | 1.17975i | ||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | 1.32843 | − | 2.30090i | 0.143248 | − | 0.248113i | ||||
\(87\) | 1.20711 | + | 2.09077i | 0.129415 | + | 0.224154i | ||||
\(88\) | −3.82843 | − | 6.63103i | −0.408112 | − | 0.706870i | ||||
\(89\) | −1.32843 | + | 2.30090i | −0.140813 | + | 0.243895i | −0.927803 | − | 0.373070i | \(-0.878305\pi\) |
0.786990 | + | 0.616966i | \(0.211638\pi\) | |||||||
\(90\) | −1.17157 | −0.123495 | ||||||||
\(91\) | −1.34315 | + | 1.73205i | −0.140800 | + | 0.181568i | ||||
\(92\) | 4.41421 | 0.460214 | ||||||||
\(93\) | 7.24264 | − | 12.5446i | 0.751027 | − | 1.30082i | ||||
\(94\) | 0.414214 | + | 0.717439i | 0.0427229 | + | 0.0739982i | ||||
\(95\) | 1.41421 | + | 2.44949i | 0.145095 | + | 0.251312i | ||||
\(96\) | 5.32843 | − | 9.22911i | 0.543830 | − | 0.941942i | ||||
\(97\) | 0.343146 | 0.0348412 | 0.0174206 | − | 0.999848i | \(-0.494455\pi\) | ||||
0.0174206 | + | 0.999848i | \(0.494455\pi\) | |||||||
\(98\) | −2.79289 | − | 0.778985i | −0.282125 | − | 0.0786894i | ||||
\(99\) | 13.6569 | 1.37257 | ||||||||
\(100\) | 0.914214 | − | 1.58346i | 0.0914214 | − | 0.158346i | ||||
\(101\) | −6.15685 | − | 10.6640i | −0.612630 | − | 1.06111i | −0.990795 | − | 0.135368i | \(-0.956778\pi\) |
0.378165 | − | 0.925738i | \(-0.376555\pi\) | |||||||
\(102\) | −0.414214 | − | 0.717439i | −0.0410133 | − | 0.0710370i | ||||
\(103\) | −0.207107 | + | 0.358719i | −0.0204068 | + | 0.0353457i | −0.876048 | − | 0.482223i | \(-0.839829\pi\) |
0.855642 | + | 0.517569i | \(0.173163\pi\) | |||||||
\(104\) | 1.31371 | 0.128820 | ||||||||
\(105\) | −3.91421 | + | 5.04757i | −0.381988 | + | 0.492592i | ||||
\(106\) | 2.82843 | 0.274721 | ||||||||
\(107\) | −1.37868 | + | 2.38794i | −0.133282 | + | 0.230851i | −0.924940 | − | 0.380113i | \(-0.875885\pi\) |
0.791658 | + | 0.610965i | \(0.209218\pi\) | |||||||
\(108\) | −0.378680 | − | 0.655892i | −0.0364385 | − | 0.0631133i | ||||
\(109\) | −1.74264 | − | 3.01834i | −0.166915 | − | 0.289105i | 0.770419 | − | 0.637538i | \(-0.220047\pi\) |
−0.937334 | + | 0.348433i | \(0.886714\pi\) | |||||||
\(110\) | 1.00000 | − | 1.73205i | 0.0953463 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.00000 | − | 7.34847i | −0.283473 | − | 0.694365i | ||||
\(113\) | 12.4853 | 1.17452 | 0.587258 | − | 0.809400i | \(-0.300207\pi\) | ||||
0.587258 | + | 0.809400i | \(0.300207\pi\) | |||||||
\(114\) | −1.41421 | + | 2.44949i | −0.132453 | + | 0.229416i | ||||
\(115\) | 1.20711 | + | 2.09077i | 0.112563 | + | 0.194965i | ||||
\(116\) | −0.914214 | − | 1.58346i | −0.0848826 | − | 0.147021i | ||||
\(117\) | −1.17157 | + | 2.02922i | −0.108312 | + | 0.187602i | ||||
\(118\) | 5.17157 | 0.476082 | ||||||||
\(119\) | −2.17157 | − | 0.297173i | −0.199068 | − | 0.0272418i | ||||
\(120\) | 3.82843 | 0.349486 | ||||||||
\(121\) | −6.15685 | + | 10.6640i | −0.559714 | + | 0.969453i | ||||
\(122\) | −2.37868 | − | 4.11999i | −0.215356 | − | 0.373007i | ||||
\(123\) | 2.62132 | + | 4.54026i | 0.236356 | + | 0.409381i | ||||
\(124\) | −5.48528 | + | 9.50079i | −0.492593 | + | 0.853196i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.07107 | − | 0.420266i | −0.273592 | − | 0.0374403i | ||||
\(127\) | 13.3137 | 1.18140 | 0.590700 | − | 0.806891i | \(-0.298852\pi\) | ||||
0.590700 | + | 0.806891i | \(0.298852\pi\) | |||||||
\(128\) | −5.27817 | + | 9.14207i | −0.466529 | + | 0.808052i | ||||
\(129\) | −7.74264 | − | 13.4106i | −0.681702 | − | 1.18074i | ||||
\(130\) | 0.171573 | + | 0.297173i | 0.0150479 | + | 0.0260638i | ||||
\(131\) | −1.65685 | + | 2.86976i | −0.144760 | + | 0.250732i | −0.929283 | − | 0.369368i | \(-0.879574\pi\) |
0.784523 | + | 0.620099i | \(0.212908\pi\) | |||||||
\(132\) | −21.3137 | −1.85512 | ||||||||
\(133\) | 2.82843 | + | 6.92820i | 0.245256 | + | 0.600751i | ||||
\(134\) | −5.14214 | −0.444213 | ||||||||
\(135\) | 0.207107 | − | 0.358719i | 0.0178249 | − | 0.0308737i | ||||
\(136\) | 0.656854 | + | 1.13770i | 0.0563248 | + | 0.0975574i | ||||
\(137\) | −0.828427 | − | 1.43488i | −0.0707773 | − | 0.122590i | 0.828465 | − | 0.560041i | \(-0.189215\pi\) |
−0.899242 | + | 0.437451i | \(0.855881\pi\) | |||||||
\(138\) | −1.20711 | + | 2.09077i | −0.102756 | + | 0.177978i | ||||
\(139\) | 12.1421 | 1.02988 | 0.514941 | − | 0.857225i | \(-0.327814\pi\) | ||||
0.514941 | + | 0.857225i | \(0.327814\pi\) | |||||||
\(140\) | 2.96447 | − | 3.82282i | 0.250543 | − | 0.323087i | ||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | −2.58579 | + | 4.47871i | −0.216994 | + | 0.375845i | ||||
\(143\) | −2.00000 | − | 3.46410i | −0.167248 | − | 0.289683i | ||||
\(144\) | −4.24264 | − | 7.34847i | −0.353553 | − | 0.612372i | ||||
\(145\) | 0.500000 | − | 0.866025i | 0.0415227 | − | 0.0719195i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −12.0711 | + | 11.8272i | −0.995605 | + | 0.975490i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.91421 | − | 6.77962i | 0.320665 | − | 0.555408i | −0.659961 | − | 0.751300i | \(-0.729427\pi\) |
0.980625 | + | 0.195892i | \(0.0627603\pi\) | |||||||
\(150\) | 0.500000 | + | 0.866025i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | −0.171573 | − | 0.297173i | −0.0139624 | − | 0.0241836i | 0.858960 | − | 0.512043i | \(-0.171111\pi\) |
−0.872922 | + | 0.487859i | \(0.837778\pi\) | |||||||
\(152\) | 2.24264 | − | 3.88437i | 0.181902 | − | 0.315064i | ||||
\(153\) | −2.34315 | −0.189432 | ||||||||
\(154\) | 3.24264 | − | 4.18154i | 0.261299 | − | 0.336958i | ||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 1.82843 | − | 3.16693i | 0.146391 | − | 0.253557i | ||||
\(157\) | 2.65685 | + | 4.60181i | 0.212040 | + | 0.367264i | 0.952353 | − | 0.304998i | \(-0.0986559\pi\) |
−0.740313 | + | 0.672263i | \(0.765323\pi\) | |||||||
\(158\) | 1.89949 | + | 3.29002i | 0.151116 | + | 0.261740i | ||||
\(159\) | 8.24264 | − | 14.2767i | 0.653684 | − | 1.13221i | ||||
\(160\) | −4.41421 | −0.348974 | ||||||||
\(161\) | 2.41421 | + | 5.91359i | 0.190267 | + | 0.466056i | ||||
\(162\) | 3.92893 | 0.308686 | ||||||||
\(163\) | −11.8284 | + | 20.4874i | −0.926474 | + | 1.60470i | −0.137301 | + | 0.990529i | \(0.543843\pi\) |
−0.789173 | + | 0.614170i | \(0.789491\pi\) | |||||||
\(164\) | −1.98528 | − | 3.43861i | −0.155024 | − | 0.268510i | ||||
\(165\) | −5.82843 | − | 10.0951i | −0.453742 | − | 0.785905i | ||||
\(166\) | −2.42893 | + | 4.20703i | −0.188522 | + | 0.326529i | ||||
\(167\) | 19.5858 | 1.51559 | 0.757797 | − | 0.652491i | \(-0.226276\pi\) | ||||
0.757797 | + | 0.652491i | \(0.226276\pi\) | |||||||
\(168\) | 10.0355 | + | 1.37333i | 0.774258 | + | 0.105955i | ||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | −0.171573 | + | 0.297173i | −0.0131590 | + | 0.0227921i | ||||
\(171\) | 4.00000 | + | 6.92820i | 0.305888 | + | 0.529813i | ||||
\(172\) | 5.86396 | + | 10.1567i | 0.447123 | + | 0.774439i | ||||
\(173\) | 9.65685 | − | 16.7262i | 0.734197 | − | 1.27167i | −0.220878 | − | 0.975302i | \(-0.570892\pi\) |
0.955075 | − | 0.296365i | \(-0.0957745\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 2.62132 | + | 0.358719i | 0.198153 | + | 0.0271166i | ||||
\(176\) | 14.4853 | 1.09187 | ||||||||
\(177\) | 15.0711 | − | 26.1039i | 1.13281 | − | 1.96209i | ||||
\(178\) | 0.550253 | + | 0.953065i | 0.0412432 | + | 0.0714353i | ||||
\(179\) | 5.00000 | + | 8.66025i | 0.373718 | + | 0.647298i | 0.990134 | − | 0.140122i | \(-0.0447496\pi\) |
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(180\) | 2.58579 | − | 4.47871i | 0.192733 | − | 0.333824i | ||||
\(181\) | −8.65685 | −0.643459 | −0.321729 | − | 0.946832i | \(-0.604264\pi\) | ||||
−0.321729 | + | 0.946832i | \(0.604264\pi\) | |||||||
\(182\) | 0.343146 | + | 0.840532i | 0.0254357 | + | 0.0623044i | ||||
\(183\) | −27.7279 | −2.04971 | ||||||||
\(184\) | 1.91421 | − | 3.31552i | 0.141118 | − | 0.244423i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | − | 5.19615i | −0.219971 | − | 0.381000i | ||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | −3.65685 | −0.266704 | ||||||||
\(189\) | 0.671573 | − | 0.866025i | 0.0488497 | − | 0.0629941i | ||||
\(190\) | 1.17157 | 0.0849948 | ||||||||
\(191\) | 3.58579 | − | 6.21076i | 0.259458 | − | 0.449395i | −0.706639 | − | 0.707575i | \(-0.749789\pi\) |
0.966097 | + | 0.258180i | \(0.0831226\pi\) | |||||||
\(192\) | 5.03553 | + | 8.72180i | 0.363408 | + | 0.629442i | ||||
\(193\) | 1.00000 | + | 1.73205i | 0.0719816 | + | 0.124676i | 0.899770 | − | 0.436365i | \(-0.143734\pi\) |
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 0.0710678 | − | 0.123093i | 0.00510237 | − | 0.00883757i | ||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 9.14214 | − | 8.95743i | 0.653010 | − | 0.639816i | ||||
\(197\) | −23.6569 | −1.68548 | −0.842741 | − | 0.538320i | \(-0.819059\pi\) | ||||
−0.842741 | + | 0.538320i | \(0.819059\pi\) | |||||||
\(198\) | 2.82843 | − | 4.89898i | 0.201008 | − | 0.348155i | ||||
\(199\) | −0.828427 | − | 1.43488i | −0.0587256 | − | 0.101716i | 0.835168 | − | 0.549995i | \(-0.185370\pi\) |
−0.893894 | + | 0.448279i | \(0.852037\pi\) | |||||||
\(200\) | −0.792893 | − | 1.37333i | −0.0560660 | − | 0.0971092i | ||||
\(201\) | −14.9853 | + | 25.9553i | −1.05698 | + | 1.83074i | ||||
\(202\) | −5.10051 | −0.358870 | ||||||||
\(203\) | 1.62132 | − | 2.09077i | 0.113794 | − | 0.146743i | ||||
\(204\) | 3.65685 | 0.256031 | ||||||||
\(205\) | 1.08579 | − | 1.88064i | 0.0758346 | − | 0.131349i | ||||
\(206\) | 0.0857864 | + | 0.148586i | 0.00597702 | + | 0.0103525i | ||||
\(207\) | 3.41421 | + | 5.91359i | 0.237304 | + | 0.411023i | ||||
\(208\) | −1.24264 | + | 2.15232i | −0.0861616 | + | 0.149236i | ||||
\(209\) | −13.6569 | −0.944664 | ||||||||
\(210\) | 1.00000 | + | 2.44949i | 0.0690066 | + | 0.169031i | ||||
\(211\) | 3.51472 | 0.241963 | 0.120982 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120982 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(212\) | −6.24264 | + | 10.8126i | −0.428746 | + | 0.742610i | ||||
\(213\) | 15.0711 | + | 26.1039i | 1.03265 | + | 1.78861i | ||||
\(214\) | 0.571068 | + | 0.989118i | 0.0390374 | + | 0.0676147i | ||||
\(215\) | −3.20711 | + | 5.55487i | −0.218723 | + | 0.378839i | ||||
\(216\) | −0.656854 | −0.0446933 | ||||||||
\(217\) | −15.7279 | − | 2.15232i | −1.06768 | − | 0.146109i | ||||
\(218\) | −1.44365 | −0.0977764 | ||||||||
\(219\) | −5.82843 | + | 10.0951i | −0.393849 | + | 0.682166i | ||||
\(220\) | 4.41421 | + | 7.64564i | 0.297606 | + | 0.515469i | ||||
\(221\) | 0.343146 | + | 0.594346i | 0.0230825 | + | 0.0399800i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6569 | 0.780601 | 0.390300 | − | 0.920688i | \(-0.372371\pi\) | ||||
0.390300 | + | 0.920688i | \(0.372371\pi\) | |||||||
\(224\) | −11.5711 | − | 1.58346i | −0.773124 | − | 0.105800i | ||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 2.58579 | − | 4.47871i | 0.172004 | − | 0.297920i | ||||
\(227\) | −13.4853 | − | 23.3572i | −0.895050 | − | 1.55027i | −0.833743 | − | 0.552152i | \(-0.813807\pi\) |
−0.0613063 | − | 0.998119i | \(-0.519527\pi\) | |||||||
\(228\) | −6.24264 | − | 10.8126i | −0.413429 | − | 0.716080i | ||||
\(229\) | 0.171573 | − | 0.297173i | 0.0113379 | − | 0.0196377i | −0.860301 | − | 0.509787i | \(-0.829724\pi\) |
0.871639 | + | 0.490149i | \(0.163058\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −11.6569 | − | 28.5533i | −0.766965 | − | 1.87867i | ||||
\(232\) | −1.58579 | −0.104112 | ||||||||
\(233\) | 5.58579 | − | 9.67487i | 0.365937 | − | 0.633822i | −0.622989 | − | 0.782231i | \(-0.714082\pi\) |
0.988926 | + | 0.148409i | \(0.0474152\pi\) | |||||||
\(234\) | 0.485281 | + | 0.840532i | 0.0317238 | + | 0.0549473i | ||||
\(235\) | −1.00000 | − | 1.73205i | −0.0652328 | − | 0.112987i | ||||
\(236\) | −11.4142 | + | 19.7700i | −0.743002 | + | 1.28692i | ||||
\(237\) | 22.1421 | 1.43829 | ||||||||
\(238\) | −0.556349 | + | 0.717439i | −0.0360628 | + | 0.0465047i | ||||
\(239\) | 1.31371 | 0.0849767 | 0.0424884 | − | 0.999097i | \(-0.486471\pi\) | ||||
0.0424884 | + | 0.999097i | \(0.486471\pi\) | |||||||
\(240\) | −3.62132 | + | 6.27231i | −0.233755 | + | 0.404876i | ||||
\(241\) | −8.17157 | − | 14.1536i | −0.526377 | − | 0.911712i | −0.999528 | − | 0.0307305i | \(-0.990217\pi\) |
0.473150 | − | 0.880982i | \(-0.343117\pi\) | |||||||
\(242\) | 2.55025 | + | 4.41717i | 0.163936 | + | 0.283946i | ||||
\(243\) | 10.8284 | − | 18.7554i | 0.694644 | − | 1.20316i | ||||
\(244\) | 21.0000 | 1.34439 | ||||||||
\(245\) | 6.74264 | + | 1.88064i | 0.430772 | + | 0.120150i | ||||
\(246\) | 2.17157 | 0.138454 | ||||||||
\(247\) | 1.17157 | − | 2.02922i | 0.0745454 | − | 0.129116i | ||||
\(248\) | 4.75736 | + | 8.23999i | 0.302093 | + | 0.523240i | ||||
\(249\) | 14.1569 | + | 24.5204i | 0.897154 | + | 1.55392i | ||||
\(250\) | 0.207107 | − | 0.358719i | 0.0130986 | − | 0.0226874i | ||||
\(251\) | 13.3137 | 0.840354 | 0.420177 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420177 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(252\) | 8.38478 | − | 10.8126i | 0.528191 | − | 0.681128i | ||||
\(253\) | −11.6569 | −0.732860 | ||||||||
\(254\) | 2.75736 | − | 4.77589i | 0.173012 | − | 0.299666i | ||||
\(255\) | 1.00000 | + | 1.73205i | 0.0626224 | + | 0.108465i | ||||
\(256\) | −1.98528 | − | 3.43861i | −0.124080 | − | 0.214913i | ||||
\(257\) | −8.82843 | + | 15.2913i | −0.550702 | + | 0.953844i | 0.447522 | + | 0.894273i | \(0.352307\pi\) |
−0.998224 | + | 0.0595711i | \(0.981027\pi\) | |||||||
\(258\) | −6.41421 | −0.399331 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.51472 | −0.0939389 | ||||||||
\(261\) | 1.41421 | − | 2.44949i | 0.0875376 | − | 0.151620i | ||||
\(262\) | 0.686292 | + | 1.18869i | 0.0423992 | + | 0.0734376i | ||||
\(263\) | −9.52082 | − | 16.4905i | −0.587079 | − | 1.01685i | −0.994613 | − | 0.103660i | \(-0.966945\pi\) |
0.407534 | − | 0.913190i | \(-0.366389\pi\) | |||||||
\(264\) | −9.24264 | + | 16.0087i | −0.568845 | + | 0.985269i | ||||
\(265\) | −6.82843 | −0.419467 | ||||||||
\(266\) | 3.07107 | + | 0.420266i | 0.188299 | + | 0.0257682i | ||||
\(267\) | 6.41421 | 0.392543 | ||||||||
\(268\) | 11.3492 | − | 19.6575i | 0.693265 | − | 1.20077i | ||||
\(269\) | 15.2279 | + | 26.3755i | 0.928463 | + | 1.60814i | 0.785895 | + | 0.618360i | \(0.212202\pi\) |
0.142568 | + | 0.989785i | \(0.454464\pi\) | |||||||
\(270\) | −0.0857864 | − | 0.148586i | −0.00522080 | − | 0.00904268i | ||||
\(271\) | 0.242641 | − | 0.420266i | 0.0147394 | − | 0.0255293i | −0.858562 | − | 0.512710i | \(-0.828641\pi\) |
0.873301 | + | 0.487181i | \(0.161975\pi\) | |||||||
\(272\) | −2.48528 | −0.150692 | ||||||||
\(273\) | 5.24264 | + | 0.717439i | 0.317299 | + | 0.0434214i | ||||
\(274\) | −0.686292 | −0.0414604 | ||||||||
\(275\) | −2.41421 | + | 4.18154i | −0.145583 | + | 0.252156i | ||||
\(276\) | −5.32843 | − | 9.22911i | −0.320734 | − | 0.555527i | ||||
\(277\) | 6.07107 | + | 10.5154i | 0.364775 | + | 0.631809i | 0.988740 | − | 0.149643i | \(-0.0478125\pi\) |
−0.623965 | + | 0.781452i | \(0.714479\pi\) | |||||||
\(278\) | 2.51472 | − | 4.35562i | 0.150823 | − | 0.261233i | ||||
\(279\) | −16.9706 | −1.01600 | ||||||||
\(280\) | −1.58579 | − | 3.88437i | −0.0947689 | − | 0.232135i | ||||
\(281\) | 26.2843 | 1.56799 | 0.783994 | − | 0.620768i | \(-0.213179\pi\) | ||||
0.783994 | + | 0.620768i | \(0.213179\pi\) | |||||||
\(282\) | 1.00000 | − | 1.73205i | 0.0595491 | − | 0.103142i | ||||
\(283\) | −7.00000 | − | 12.1244i | −0.416107 | − | 0.720718i | 0.579437 | − | 0.815017i | \(-0.303272\pi\) |
−0.995544 | + | 0.0942988i | \(0.969939\pi\) | |||||||
\(284\) | −11.4142 | − | 19.7700i | −0.677309 | − | 1.17313i | ||||
\(285\) | 3.41421 | − | 5.91359i | 0.202241 | − | 0.350291i | ||||
\(286\) | −1.65685 | −0.0979718 | ||||||||
\(287\) | 3.52082 | − | 4.54026i | 0.207827 | − | 0.268003i | ||||
\(288\) | −12.4853 | −0.735702 | ||||||||
\(289\) | 8.15685 | − | 14.1281i | 0.479815 | − | 0.831064i | ||||
\(290\) | −0.207107 | − | 0.358719i | −0.0121617 | − | 0.0210647i | ||||
\(291\) | −0.414214 | − | 0.717439i | −0.0242816 | − | 0.0420570i | ||||
\(292\) | 4.41421 | − | 7.64564i | 0.258322 | − | 0.447427i | ||||
\(293\) | −16.0000 | −0.934730 | −0.467365 | − | 0.884064i | \(-0.654797\pi\) | ||||
−0.467365 | + | 0.884064i | \(0.654797\pi\) | |||||||
\(294\) | 1.74264 | + | 6.77962i | 0.101633 | + | 0.395395i | ||||
\(295\) | −12.4853 | −0.726921 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | + | 1.73205i | 0.0580259 | + | 0.100504i | ||||
\(298\) | −1.62132 | − | 2.80821i | −0.0939206 | − | 0.162675i | ||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | −4.41421 | −0.254855 | ||||||||
\(301\) | −10.3995 | + | 13.4106i | −0.599417 | + | 0.772977i | ||||
\(302\) | −0.142136 | −0.00817899 | ||||||||
\(303\) | −14.8640 | + | 25.7451i | −0.853912 | + | 1.47902i | ||||
\(304\) | 4.24264 | + | 7.34847i | 0.243332 | + | 0.421464i | ||||
\(305\) | 5.74264 | + | 9.94655i | 0.328823 | + | 0.569538i | ||||
\(306\) | −0.485281 | + | 0.840532i | −0.0277417 | + | 0.0480500i | ||||
\(307\) | −13.2426 | −0.755797 | −0.377899 | − | 0.925847i | \(-0.623353\pi\) | ||||
−0.377899 | + | 0.925847i | \(0.623353\pi\) | |||||||
\(308\) | 8.82843 | + | 21.6251i | 0.503046 | + | 1.23221i | ||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −1.24264 | + | 2.15232i | −0.0705772 | + | 0.122243i | ||||
\(311\) | 9.41421 | + | 16.3059i | 0.533831 | + | 0.924623i | 0.999219 | + | 0.0395157i | \(0.0125815\pi\) |
−0.465388 | + | 0.885107i | \(0.654085\pi\) | |||||||
\(312\) | −1.58579 | − | 2.74666i | −0.0897775 | − | 0.155499i | ||||
\(313\) | 8.82843 | − | 15.2913i | 0.499012 | − | 0.864314i | −0.500987 | − | 0.865455i | \(-0.667030\pi\) |
0.999999 | + | 0.00114023i | \(0.000362947\pi\) | |||||||
\(314\) | 2.20101 | 0.124210 | ||||||||
\(315\) | 7.41421 | + | 1.01461i | 0.417744 | + | 0.0571669i | ||||
\(316\) | −16.7696 | −0.943361 | ||||||||
\(317\) | −12.8995 | + | 22.3426i | −0.724508 | + | 1.25488i | 0.234668 | + | 0.972075i | \(0.424600\pi\) |
−0.959176 | + | 0.282809i | \(0.908734\pi\) | |||||||
\(318\) | −3.41421 | − | 5.91359i | −0.191460 | − | 0.331618i | ||||
\(319\) | 2.41421 | + | 4.18154i | 0.135170 | + | 0.234121i | ||||
\(320\) | 2.08579 | − | 3.61269i | 0.116599 | − | 0.201955i | ||||
\(321\) | 6.65685 | 0.371549 | ||||||||
\(322\) | 2.62132 | + | 0.358719i | 0.146080 | + | 0.0199907i | ||||
\(323\) | 2.34315 | 0.130376 | ||||||||
\(324\) | −8.67157 | + | 15.0196i | −0.481754 | + | 0.834422i | ||||
\(325\) | −0.414214 | − | 0.717439i | −0.0229764 | − | 0.0397964i | ||||
\(326\) | 4.89949 | + | 8.48617i | 0.271358 | + | 0.470006i | ||||
\(327\) | −4.20711 | + | 7.28692i | −0.232654 | + | 0.402968i | ||||
\(328\) | −3.44365 | −0.190144 | ||||||||
\(329\) | −2.00000 | − | 4.89898i | −0.110264 | − | 0.270089i | ||||
\(330\) | −4.82843 | −0.265796 | ||||||||
\(331\) | 5.48528 | − | 9.50079i | 0.301498 | − | 0.522210i | −0.674977 | − | 0.737839i | \(-0.735847\pi\) |
0.976476 | + | 0.215628i | \(0.0691799\pi\) | |||||||
\(332\) | −10.7218 | − | 18.5707i | −0.588437 | − | 1.01920i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.05635 | − | 7.02580i | 0.221954 | − | 0.384435i | ||||
\(335\) | 12.4142 | 0.678261 | ||||||||
\(336\) | −11.7426 | + | 15.1427i | −0.640614 | + | 0.826102i | ||||
\(337\) | 14.8284 | 0.807756 | 0.403878 | − | 0.914813i | \(-0.367662\pi\) | ||||
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(338\) | −2.55025 | + | 4.41717i | −0.138715 | + | 0.240262i | ||||
\(339\) | −15.0711 | − | 26.1039i | −0.818548 | − | 1.41777i | ||||
\(340\) | −0.757359 | − | 1.31178i | −0.0410736 | − | 0.0711415i | ||||
\(341\) | 14.4853 | − | 25.0892i | 0.784422 | − | 1.35866i | ||||
\(342\) | 3.31371 | 0.179185 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 10.1716 | 0.548414 | ||||||||
\(345\) | 2.91421 | − | 5.04757i | 0.156896 | − | 0.271752i | ||||
\(346\) | −4.00000 | − | 6.92820i | −0.215041 | − | 0.372463i | ||||
\(347\) | −11.0355 | − | 19.1141i | −0.592418 | − | 1.02610i | −0.993906 | − | 0.110234i | \(-0.964840\pi\) |
0.401487 | − | 0.915865i | \(-0.368493\pi\) | |||||||
\(348\) | −2.20711 | + | 3.82282i | −0.118313 | + | 0.204925i | ||||
\(349\) | −26.6569 | −1.42691 | −0.713454 | − | 0.700702i | \(-0.752870\pi\) | ||||
−0.713454 | + | 0.700702i | \(0.752870\pi\) | |||||||
\(350\) | 0.671573 | − | 0.866025i | 0.0358971 | − | 0.0462910i | ||||
\(351\) | −0.343146 | −0.0183158 | ||||||||
\(352\) | 10.6569 | − | 18.4582i | 0.568012 | − | 0.983826i | ||||
\(353\) | 10.5858 | + | 18.3351i | 0.563425 | + | 0.975880i | 0.997194 | + | 0.0748562i | \(0.0238498\pi\) |
−0.433770 | + | 0.901024i | \(0.642817\pi\) | |||||||
\(354\) | −6.24264 | − | 10.8126i | −0.331793 | − | 0.574682i | ||||
\(355\) | 6.24264 | − | 10.8126i | 0.331325 | − | 0.573872i | ||||
\(356\) | −4.85786 | −0.257466 | ||||||||
\(357\) | 2.00000 | + | 4.89898i | 0.105851 | + | 0.259281i | ||||
\(358\) | 4.14214 | 0.218919 | ||||||||
\(359\) | 5.00000 | − | 8.66025i | 0.263890 | − | 0.457071i | −0.703382 | − | 0.710812i | \(-0.748328\pi\) |
0.967272 | + | 0.253741i | \(0.0816611\pi\) | |||||||
\(360\) | −2.24264 | − | 3.88437i | −0.118198 | − | 0.204724i | ||||
\(361\) | 5.50000 | + | 9.52628i | 0.289474 | + | 0.501383i | ||||
\(362\) | −1.79289 | + | 3.10538i | −0.0942324 | + | 0.163215i | ||||
\(363\) | 29.7279 | 1.56031 | ||||||||
\(364\) | −3.97056 | − | 0.543359i | −0.208114 | − | 0.0284798i | ||||
\(365\) | 4.82843 | 0.252731 | ||||||||
\(366\) | −5.74264 | + | 9.94655i | −0.300173 | + | 0.519914i | ||||
\(367\) | 5.62132 | + | 9.73641i | 0.293431 | + | 0.508237i | 0.974619 | − | 0.223872i | \(-0.0718697\pi\) |
−0.681188 | + | 0.732108i | \(0.738536\pi\) | |||||||
\(368\) | 3.62132 | + | 6.27231i | 0.188774 | + | 0.326967i | ||||
\(369\) | 3.07107 | − | 5.31925i | 0.159873 | − | 0.276909i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.8995 | − | 2.44949i | −0.929295 | − | 0.127171i | ||||
\(372\) | 26.4853 | 1.37320 | ||||||||
\(373\) | −6.48528 | + | 11.2328i | −0.335795 | + | 0.581614i | −0.983637 | − | 0.180160i | \(-0.942338\pi\) |
0.647842 | + | 0.761775i | \(0.275672\pi\) | |||||||
\(374\) | −0.828427 | − | 1.43488i | −0.0428369 | − | 0.0741958i | ||||
\(375\) | −1.20711 | − | 2.09077i | −0.0623347 | − | 0.107967i | ||||
\(376\) | −1.58579 | + | 2.74666i | −0.0817807 | + | 0.141648i | ||||
\(377\) | −0.828427 | −0.0426662 | ||||||||
\(378\) | −0.171573 | − | 0.420266i | −0.00882476 | − | 0.0216162i | ||||
\(379\) | 21.1716 | 1.08751 | 0.543755 | − | 0.839244i | \(-0.317002\pi\) | ||||
0.543755 | + | 0.839244i | \(0.317002\pi\) | |||||||
\(380\) | −2.58579 | + | 4.47871i | −0.132648 | + | 0.229753i | ||||
\(381\) | −16.0711 | − | 27.8359i | −0.823346 | − | 1.42608i | ||||
\(382\) | −1.48528 | − | 2.57258i | −0.0759936 | − | 0.131625i | ||||
\(383\) | −8.44975 | + | 14.6354i | −0.431762 | + | 0.747834i | −0.997025 | − | 0.0770770i | \(-0.975441\pi\) |
0.565263 | + | 0.824911i | \(0.308775\pi\) | |||||||
\(384\) | 25.4853 | 1.30054 | ||||||||
\(385\) | −7.82843 | + | 10.0951i | −0.398974 | + | 0.514496i | ||||
\(386\) | 0.828427 | 0.0421658 | ||||||||
\(387\) | −9.07107 | + | 15.7116i | −0.461108 | + | 0.798663i | ||||
\(388\) | 0.313708 | + | 0.543359i | 0.0159261 | + | 0.0275849i | ||||
\(389\) | −6.17157 | − | 10.6895i | −0.312911 | − | 0.541978i | 0.666080 | − | 0.745880i | \(-0.267971\pi\) |
−0.978991 | + | 0.203902i | \(0.934638\pi\) | |||||||
\(390\) | 0.414214 | − | 0.717439i | 0.0209745 | − | 0.0363289i | ||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | −2.76346 | − | 10.7510i | −0.139576 | − | 0.543009i | ||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | −4.89949 | + | 8.48617i | −0.246833 | + | 0.427527i | ||||
\(395\) | −4.58579 | − | 7.94282i | −0.230736 | − | 0.399646i | ||||
\(396\) | 12.4853 | + | 21.6251i | 0.627409 | + | 1.08670i | ||||
\(397\) | −14.3137 | + | 24.7921i | −0.718384 | + | 1.24428i | 0.243255 | + | 0.969962i | \(0.421785\pi\) |
−0.961640 | + | 0.274316i | \(0.911549\pi\) | |||||||
\(398\) | −0.686292 | −0.0344007 | ||||||||
\(399\) | 11.0711 | − | 14.2767i | 0.554247 | − | 0.714728i | ||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −3.84315 | + | 6.65652i | −0.191918 | + | 0.332411i | −0.945886 | − | 0.324500i | \(-0.894804\pi\) |
0.753968 | + | 0.656911i | \(0.228137\pi\) | |||||||
\(402\) | 6.20711 | + | 10.7510i | 0.309582 | + | 0.536212i | ||||
\(403\) | 2.48528 | + | 4.30463i | 0.123801 | + | 0.214429i | ||||
\(404\) | 11.2574 | − | 19.4983i | 0.560075 | − | 0.970078i | ||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | −0.414214 | − | 1.01461i | −0.0205571 | − | 0.0503543i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.58579 | − | 2.74666i | 0.0785081 | − | 0.135980i | ||||
\(409\) | −12.3995 | − | 21.4766i | −0.613116 | − | 1.06195i | −0.990712 | − | 0.135977i | \(-0.956583\pi\) |
0.377596 | − | 0.925970i | \(-0.376751\pi\) | |||||||
\(410\) | −0.449747 | − | 0.778985i | −0.0222114 | − | 0.0384713i | ||||
\(411\) | −2.00000 | + | 3.46410i | −0.0986527 | + | 0.170872i | ||||
\(412\) | −0.757359 | −0.0373124 | ||||||||
\(413\) | −32.7279 | − | 4.47871i | −1.61044 | − | 0.220383i | ||||
\(414\) | 2.82843 | 0.139010 | ||||||||
\(415\) | 5.86396 | − | 10.1567i | 0.287851 | − | 0.498572i | ||||
\(416\) | 1.82843 | + | 3.16693i | 0.0896460 | + | 0.155271i | ||||
\(417\) | −14.6569 | − | 25.3864i | −0.717749 | − | 1.24318i | ||||
\(418\) | −2.82843 | + | 4.89898i | −0.138343 | + | 0.239617i | ||||
\(419\) | −23.3137 | −1.13895 | −0.569475 | − | 0.822009i | \(-0.692853\pi\) | ||||
−0.569475 | + | 0.822009i | \(0.692853\pi\) | |||||||
\(420\) | −11.5711 | − | 1.58346i | −0.564610 | − | 0.0772651i | ||||
\(421\) | −3.48528 | −0.169862 | −0.0849311 | − | 0.996387i | \(-0.527067\pi\) | ||||
−0.0849311 | + | 0.996387i | \(0.527067\pi\) | |||||||
\(422\) | 0.727922 | − | 1.26080i | 0.0354347 | − | 0.0613747i | ||||
\(423\) | −2.82843 | − | 4.89898i | −0.137523 | − | 0.238197i | ||||
\(424\) | 5.41421 | + | 9.37769i | 0.262937 | + | 0.455421i | ||||
\(425\) | 0.414214 | − | 0.717439i | 0.0200923 | − | 0.0348009i | ||||
\(426\) | 12.4853 | 0.604914 | ||||||||
\(427\) | 11.4853 | + | 28.1331i | 0.555812 | + | 1.36146i | ||||
\(428\) | −5.04163 | −0.243696 | ||||||||
\(429\) | −4.82843 | + | 8.36308i | −0.233119 | + | 0.403773i | ||||
\(430\) | 1.32843 | + | 2.30090i | 0.0640624 | + | 0.110959i | ||||
\(431\) | 10.8995 | + | 18.8785i | 0.525010 | + | 0.909344i | 0.999576 | + | 0.0291242i | \(0.00927183\pi\) |
−0.474566 | + | 0.880220i | \(0.657395\pi\) | |||||||
\(432\) | 0.621320 | − | 1.07616i | 0.0298933 | − | 0.0517767i | ||||
\(433\) | −31.7990 | −1.52816 | −0.764081 | − | 0.645120i | \(-0.776807\pi\) | ||||
−0.764081 | + | 0.645120i | \(0.776807\pi\) | |||||||
\(434\) | −4.02944 | + | 5.19615i | −0.193419 | + | 0.249423i | ||||
\(435\) | −2.41421 | −0.115753 | ||||||||
\(436\) | 3.18629 | − | 5.51882i | 0.152596 | − | 0.264303i | ||||
\(437\) | −3.41421 | − | 5.91359i | −0.163324 | − | 0.282885i | ||||
\(438\) | 2.41421 | + | 4.18154i | 0.115356 | + | 0.199802i | ||||
\(439\) | −16.9706 | + | 29.3939i | −0.809961 | + | 1.40289i | 0.102930 | + | 0.994689i | \(0.467178\pi\) |
−0.912890 | + | 0.408205i | \(0.866155\pi\) | |||||||
\(440\) | 7.65685 | 0.365026 | ||||||||
\(441\) | 19.0711 | + | 5.31925i | 0.908146 | + | 0.253297i | ||||
\(442\) | 0.284271 | 0.0135214 | ||||||||
\(443\) | 6.10660 | − | 10.5769i | 0.290133 | − | 0.502526i | −0.683708 | − | 0.729756i | \(-0.739634\pi\) |
0.973841 | + | 0.227230i | \(0.0729670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.32843 | − | 2.30090i | −0.0629735 | − | 0.109073i | ||||
\(446\) | 2.41421 | − | 4.18154i | 0.114316 | − | 0.198002i | ||||
\(447\) | −18.8995 | −0.893915 | ||||||||
\(448\) | 6.76346 | − | 8.72180i | 0.319543 | − | 0.412066i | ||||
\(449\) | −1.82843 | −0.0862888 | −0.0431444 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431444 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(450\) | 0.585786 | − | 1.01461i | 0.0276142 | − | 0.0478293i | ||||
\(451\) | 5.24264 | + | 9.08052i | 0.246866 | + | 0.427585i | ||||
\(452\) | 11.4142 | + | 19.7700i | 0.536879 | + | 0.929902i | ||||
\(453\) | −0.414214 | + | 0.717439i | −0.0194615 | + | 0.0337082i | ||||
\(454\) | −11.1716 | −0.524308 | ||||||||
\(455\) | −0.828427 | − | 2.02922i | −0.0388373 | − | 0.0951315i | ||||
\(456\) | −10.8284 | −0.507088 | ||||||||
\(457\) | 16.1421 | − | 27.9590i | 0.755097 | − | 1.30787i | −0.190229 | − | 0.981740i | \(-0.560923\pi\) |
0.945326 | − | 0.326127i | \(-0.105744\pi\) | |||||||
\(458\) | −0.0710678 | − | 0.123093i | −0.00332078 | − | 0.00575176i | ||||
\(459\) | −0.171573 | − | 0.297173i | −0.00800834 | − | 0.0138708i | ||||
\(460\) | −2.20711 | + | 3.82282i | −0.102907 | + | 0.178240i | ||||
\(461\) | 18.6863 | 0.870307 | 0.435154 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435154 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(462\) | −12.6569 | − | 1.73205i | −0.588850 | − | 0.0805823i | ||||
\(463\) | 11.0416 | 0.513148 | 0.256574 | − | 0.966525i | \(-0.417406\pi\) | ||||
0.256574 | + | 0.966525i | \(0.417406\pi\) | |||||||
\(464\) | 1.50000 | − | 2.59808i | 0.0696358 | − | 0.120613i | ||||
\(465\) | 7.24264 | + | 12.5446i | 0.335869 | + | 0.581743i | ||||
\(466\) | −2.31371 | − | 4.00746i | −0.107180 | − | 0.185642i | ||||
\(467\) | 11.4497 | − | 19.8315i | 0.529831 | − | 0.917694i | −0.469563 | − | 0.882899i | \(-0.655589\pi\) |
0.999394 | − | 0.0347956i | \(-0.0110780\pi\) | |||||||
\(468\) | −4.28427 | −0.198041 | ||||||||
\(469\) | 32.5416 | + | 4.45322i | 1.50263 | + | 0.205631i | ||||
\(470\) | −0.828427 | −0.0382125 | ||||||||
\(471\) | 6.41421 | − | 11.1097i | 0.295551 | − | 0.511910i | ||||
\(472\) | 9.89949 | + | 17.1464i | 0.455661 | + | 0.789228i | ||||
\(473\) | −15.4853 | − | 26.8213i | −0.712014 | − | 1.23324i | ||||
\(474\) | 4.58579 | − | 7.94282i | 0.210632 | − | 0.364826i | ||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | −1.51472 | − | 3.71029i | −0.0694270 | − | 0.170061i | ||||
\(477\) | −19.3137 | −0.884314 | ||||||||
\(478\) | 0.272078 | − | 0.471253i | 0.0124446 | − | 0.0215546i | ||||
\(479\) | 12.1716 | + | 21.0818i | 0.556133 | + | 0.963251i | 0.997814 | + | 0.0660791i | \(0.0210490\pi\) |
−0.441681 | + | 0.897172i | \(0.645618\pi\) | |||||||
\(480\) | 5.32843 | + | 9.22911i | 0.243208 | + | 0.421249i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6.76955 | −0.308345 | ||||||||
\(483\) | 9.44975 | − | 12.1859i | 0.429978 | − | 0.554478i | ||||
\(484\) | −22.5147 | −1.02340 | ||||||||
\(485\) | −0.171573 | + | 0.297173i | −0.00779072 | + | 0.0134939i | ||||
\(486\) | −4.48528 | − | 7.76874i | −0.203456 | − | 0.352397i | ||||
\(487\) | −7.82843 | − | 13.5592i | −0.354740 | − | 0.614428i | 0.632334 | − | 0.774696i | \(-0.282097\pi\) |
−0.987073 | + | 0.160269i | \(0.948764\pi\) | |||||||
\(488\) | 9.10660 | − | 15.7731i | 0.412236 | − | 0.714015i | ||||
\(489\) | 57.1127 | 2.58273 | ||||||||
\(490\) | 2.07107 | − | 2.02922i | 0.0935613 | − | 0.0916710i | ||||
\(491\) | −13.3137 | −0.600839 | −0.300420 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300420 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(492\) | −4.79289 | + | 8.30153i | −0.216080 | + | 0.374262i | ||||
\(493\) | −0.414214 | − | 0.717439i | −0.0186552 | − | 0.0323118i | ||||
\(494\) | −0.485281 | − | 0.840532i | −0.0218338 | − | 0.0378173i | ||||
\(495\) | −6.82843 | + | 11.8272i | −0.306915 | + | 0.531592i | ||||
\(496\) | −18.0000 | −0.808224 | ||||||||
\(497\) | 20.2426 | − | 26.1039i | 0.908007 | − | 1.17092i | ||||
\(498\) | 11.7279 | 0.525541 | ||||||||
\(499\) | −2.41421 | + | 4.18154i | −0.108075 | + | 0.187191i | −0.914990 | − | 0.403476i | \(-0.867802\pi\) |
0.806915 | + | 0.590667i | \(0.201135\pi\) | |||||||
\(500\) | 0.914214 | + | 1.58346i | 0.0408849 | + | 0.0708147i | ||||
\(501\) | −23.6421 | − | 40.9494i | −1.05625 | − | 1.82948i | ||||
\(502\) | 2.75736 | − | 4.77589i | 0.123067 | − | 0.213158i | ||||
\(503\) | 37.8701 | 1.68854 | 0.844271 | − | 0.535916i | \(-0.180034\pi\) | ||||
0.844271 | + | 0.535916i | \(0.180034\pi\) | |||||||
\(504\) | −4.48528 | − | 10.9867i | −0.199790 | − | 0.489384i | ||||
\(505\) | 12.3137 | 0.547953 | ||||||||
\(506\) | −2.41421 | + | 4.18154i | −0.107325 | + | 0.185892i | ||||
\(507\) | 14.8640 | + | 25.7451i | 0.660132 | + | 1.14338i | ||||
\(508\) | 12.1716 | + | 21.0818i | 0.540026 | + | 0.935353i | ||||
\(509\) | −12.3284 | + | 21.3535i | −0.546448 | + | 0.946476i | 0.452066 | + | 0.891984i | \(0.350687\pi\) |
−0.998514 | + | 0.0544912i | \(0.982646\pi\) | |||||||
\(510\) | 0.828427 | 0.0366834 | ||||||||
\(511\) | 12.6569 | + | 1.73205i | 0.559906 | + | 0.0766214i | ||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | −0.585786 | + | 1.01461i | −0.0258631 | + | 0.0447962i | ||||
\(514\) | 3.65685 | + | 6.33386i | 0.161297 | + | 0.279374i | ||||
\(515\) | −0.207107 | − | 0.358719i | −0.00912622 | − | 0.0158071i | ||||
\(516\) | 14.1569 | − | 24.5204i | 0.623221 | − | 1.07945i | ||||
\(517\) | 9.65685 | 0.424708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.6274 | −2.04672 | ||||||||
\(520\) | −0.656854 | + | 1.13770i | −0.0288050 | + | 0.0498917i | ||||
\(521\) | 9.48528 | + | 16.4290i | 0.415558 | + | 0.719767i | 0.995487 | − | 0.0948999i | \(-0.0302531\pi\) |
−0.579929 | + | 0.814667i | \(0.696920\pi\) | |||||||
\(522\) | −0.585786 | − | 1.01461i | −0.0256392 | − | 0.0444084i | ||||
\(523\) | −12.1716 | + | 21.0818i | −0.532226 | + | 0.921842i | 0.467066 | + | 0.884222i | \(0.345311\pi\) |
−0.999292 | + | 0.0376197i | \(0.988022\pi\) | |||||||
\(524\) | −6.05887 | −0.264683 | ||||||||
\(525\) | −2.41421 | − | 5.91359i | −0.105365 | − | 0.258090i | ||||
\(526\) | −7.88730 | −0.343903 | ||||||||
\(527\) | −2.48528 | + | 4.30463i | −0.108261 | + | 0.187513i | ||||
\(528\) | −17.4853 | − | 30.2854i | −0.760949 | − | 1.31800i | ||||
\(529\) | 8.58579 | + | 14.8710i | 0.373295 | + | 0.646566i | ||||
\(530\) | −1.41421 | + | 2.44949i | −0.0614295 | + | 0.106399i | ||||
\(531\) | −35.3137 | −1.53248 | ||||||||
\(532\) | −8.38478 | + | 10.8126i | −0.363526 | + | 0.468784i | ||||
\(533\) | −1.79899 | −0.0779229 | ||||||||
\(534\) | 1.32843 | − | 2.30090i | 0.0574867 | − | 0.0995698i | ||||
\(535\) | −1.37868 | − | 2.38794i | −0.0596055 | − | 0.103240i | ||||
\(536\) | −9.84315 | − | 17.0488i | −0.425159 | − | 0.736397i | ||||
\(537\) | 12.0711 | − | 20.9077i | 0.520905 | − | 0.902234i | ||||
\(538\) | 12.6152 | 0.543881 | ||||||||
\(539\) | −24.1421 | + | 23.6544i | −1.03988 | + | 1.01887i | ||||
\(540\) | 0.757359 | 0.0325916 | ||||||||
\(541\) | −9.32843 | + | 16.1573i | −0.401060 | + | 0.694657i | −0.993854 | − | 0.110697i | \(-0.964692\pi\) |
0.592794 | + | 0.805354i | \(0.298025\pi\) | |||||||
\(542\) | −0.100505 | − | 0.174080i | −0.00431706 | − | 0.00747737i | ||||
\(543\) | 10.4497 | + | 18.0995i | 0.448442 | + | 0.776724i | ||||
\(544\) | −1.82843 | + | 3.16693i | −0.0783932 | + | 0.135781i | ||||
\(545\) | 3.48528 | 0.149293 | ||||||||
\(546\) | 1.34315 | − | 1.73205i | 0.0574813 | − | 0.0741249i | ||||
\(547\) | 5.10051 | 0.218082 | 0.109041 | − | 0.994037i | \(-0.465222\pi\) | ||||
0.109041 | + | 0.994037i | \(0.465222\pi\) | |||||||
\(548\) | 1.51472 | − | 2.62357i | 0.0647056 | − | 0.112073i | ||||
\(549\) | 16.2426 | + | 28.1331i | 0.693219 | + | 1.20069i | ||||
\(550\) | 1.00000 | + | 1.73205i | 0.0426401 | + | 0.0738549i | ||||
\(551\) | −1.41421 | + | 2.44949i | −0.0602475 | + | 0.104352i | ||||
\(552\) | −9.24264 | −0.393393 | ||||||||
\(553\) | −9.17157 | − | 22.4657i | −0.390015 | − | 0.955338i | ||||
\(554\) | 5.02944 | 0.213680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.1005 | + | 19.2266i | 0.470766 | + | 0.815391i | ||||
\(557\) | 17.1421 | + | 29.6910i | 0.726336 | + | 1.25805i | 0.958422 | + | 0.285355i | \(0.0921115\pi\) |
−0.232086 | + | 0.972695i | \(0.574555\pi\) | |||||||
\(558\) | −3.51472 | + | 6.08767i | −0.148790 | + | 0.257712i | ||||
\(559\) | 5.31371 | 0.224746 | ||||||||
\(560\) | 7.86396 | + | 1.07616i | 0.332313 | + | 0.0454760i | ||||
\(561\) | −9.65685 | −0.407713 | ||||||||
\(562\) | 5.44365 | − | 9.42868i | 0.229627 | − | 0.397725i | ||||
\(563\) | −8.13604 | − | 14.0920i | −0.342893 | − | 0.593908i | 0.642076 | − | 0.766641i | \(-0.278074\pi\) |
−0.984969 | + | 0.172733i | \(0.944740\pi\) | |||||||
\(564\) | 4.41421 | + | 7.64564i | 0.185872 | + | 0.321940i | ||||
\(565\) | −6.24264 | + | 10.8126i | −0.262630 | + | 0.454888i | ||||
\(566\) | −5.79899 | −0.243750 | ||||||||
\(567\) | −24.8640 | − | 3.40256i | −1.04419 | − | 0.142894i | ||||
\(568\) | −19.7990 | −0.830747 | ||||||||
\(569\) | 1.82843 | − | 3.16693i | 0.0766517 | − | 0.132765i | −0.825152 | − | 0.564911i | \(-0.808910\pi\) |
0.901803 | + | 0.432147i | \(0.142244\pi\) | |||||||
\(570\) | −1.41421 | − | 2.44949i | −0.0592349 | − | 0.102598i | ||||
\(571\) | −7.41421 | − | 12.8418i | −0.310275 | − | 0.537412i | 0.668147 | − | 0.744030i | \(-0.267088\pi\) |
−0.978422 | + | 0.206617i | \(0.933755\pi\) | |||||||
\(572\) | 3.65685 | − | 6.33386i | 0.152901 | − | 0.264832i | ||||
\(573\) | −17.3137 | −0.723291 | ||||||||
\(574\) | −0.899495 | − | 2.20330i | −0.0375442 | − | 0.0919641i | ||||
\(575\) | −2.41421 | −0.100680 | ||||||||
\(576\) | 5.89949 | − | 10.2182i | 0.245812 | − | 0.425759i | ||||
\(577\) | −11.9706 | − | 20.7336i | −0.498341 | − | 0.863152i | 0.501657 | − | 0.865067i | \(-0.332724\pi\) |
−0.999998 | + | 0.00191453i | \(0.999391\pi\) | |||||||
\(578\) | −3.37868 | − | 5.85204i | −0.140535 | − | 0.243413i | ||||
\(579\) | 2.41421 | − | 4.18154i | 0.100331 | − | 0.173779i | ||||
\(580\) | 1.82843 | 0.0759213 | ||||||||
\(581\) | 19.0147 | − | 24.5204i | 0.788863 | − | 1.01728i | ||||
\(582\) | −0.343146 | −0.0142238 | ||||||||
\(583\) | 16.4853 | − | 28.5533i | 0.682751 | − | 1.18256i | ||||
\(584\) | −3.82843 | − | 6.63103i | −0.158421 | − | 0.274394i | ||||
\(585\) | −1.17157 | − | 2.02922i | −0.0484386 | − | 0.0838981i | ||||
\(586\) | −3.31371 | + | 5.73951i | −0.136888 | + | 0.237097i | ||||
\(587\) | 22.2843 | 0.919770 | 0.459885 | − | 0.887978i | \(-0.347891\pi\) | ||||
0.459885 | + | 0.887978i | \(0.347891\pi\) | |||||||
\(588\) | −29.7635 | − | 8.30153i | −1.22742 | − | 0.342350i | ||||
\(589\) | 16.9706 | 0.699260 | ||||||||
\(590\) | −2.58579 | + | 4.47871i | −0.106455 | + | 0.184386i | ||||
\(591\) | 28.5563 | + | 49.4610i | 1.17465 | + | 2.03456i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.8995 | + | 37.9310i | −0.899304 | + | 1.55764i | −0.0709193 | + | 0.997482i | \(0.522593\pi\) |
−0.828385 | + | 0.560159i | \(0.810740\pi\) | |||||||
\(594\) | 0.828427 | 0.0339908 | ||||||||
\(595\) | 1.34315 | − | 1.73205i | 0.0550636 | − | 0.0710072i | ||||
\(596\) | 14.3137 | 0.586312 | ||||||||
\(597\) | −2.00000 | + | 3.46410i | −0.0818546 | + | 0.141776i | ||||
\(598\) | −0.414214 | − | 0.717439i | −0.0169385 | − | 0.0293383i | ||||
\(599\) | −8.82843 | − | 15.2913i | −0.360720 | − | 0.624785i | 0.627360 | − | 0.778730i | \(-0.284136\pi\) |
−0.988079 | + | 0.153945i | \(0.950802\pi\) | |||||||
\(600\) | −1.91421 | + | 3.31552i | −0.0781474 | + | 0.135355i | ||||
\(601\) | 8.34315 | 0.340324 | 0.170162 | − | 0.985416i | \(-0.445571\pi\) | ||||
0.170162 | + | 0.985416i | \(0.445571\pi\) | |||||||
\(602\) | 2.65685 | + | 6.50794i | 0.108285 | + | 0.265244i | ||||
\(603\) | 35.1127 | 1.42990 | ||||||||
\(604\) | 0.313708 | − | 0.543359i | 0.0127646 | − | 0.0221090i | ||||
\(605\) | −6.15685 | − | 10.6640i | −0.250312 | − | 0.433553i | ||||
\(606\) | 6.15685 | + | 10.6640i | 0.250105 | + | 0.433195i | ||||
\(607\) | 2.10660 | − | 3.64874i | 0.0855043 | − | 0.148098i | −0.820102 | − | 0.572218i | \(-0.806083\pi\) |
0.905606 | + | 0.424120i | \(0.139417\pi\) | |||||||
\(608\) | 12.4853 | 0.506345 | ||||||||
\(609\) | −6.32843 | − | 0.866025i | −0.256441 | − | 0.0350931i | ||||
\(610\) | 4.75736 | 0.192620 | ||||||||
\(611\) | −0.828427 | + | 1.43488i | −0.0335146 | + | 0.0580489i | ||||
\(612\) | −2.14214 | − | 3.71029i | −0.0865907 | − | 0.149979i | ||||
\(613\) | 7.72792 | + | 13.3852i | 0.312128 | + | 0.540621i | 0.978823 | − | 0.204709i | \(-0.0656249\pi\) |
−0.666695 | + | 0.745331i | \(0.732292\pi\) | |||||||
\(614\) | −2.74264 | + | 4.75039i | −0.110684 | + | 0.191710i | ||||
\(615\) | −5.24264 | −0.211404 | ||||||||
\(616\) | 20.0711 | + | 2.74666i | 0.808686 | + | 0.110666i | ||||
\(617\) | −11.3137 | −0.455473 | −0.227736 | − | 0.973723i | \(-0.573132\pi\) | ||||
−0.227736 | + | 0.973723i | \(0.573132\pi\) | |||||||
\(618\) | 0.207107 | − | 0.358719i | 0.00833106 | − | 0.0144298i | ||||
\(619\) | −21.2426 | − | 36.7933i | −0.853814 | − | 1.47885i | −0.877741 | − | 0.479135i | \(-0.840950\pi\) |
0.0239273 | − | 0.999714i | \(-0.492383\pi\) | |||||||
\(620\) | −5.48528 | − | 9.50079i | −0.220294 | − | 0.381561i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 7.79899 | 0.312711 | ||||||||
\(623\) | −2.65685 | − | 6.50794i | −0.106445 | − | 0.260735i | ||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −3.65685 | − | 6.33386i | −0.146157 | − | 0.253152i | ||||
\(627\) | 16.4853 | + | 28.5533i | 0.658359 | + | 1.14031i | ||||
\(628\) | −4.85786 | + | 8.41407i | −0.193850 | + | 0.335758i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.89949 | − | 2.44949i | 0.0756777 | − | 0.0975900i | ||||
\(631\) | 8.14214 | 0.324133 | 0.162067 | − | 0.986780i | \(-0.448184\pi\) | ||||
0.162067 | + | 0.986780i | \(0.448184\pi\) | |||||||
\(632\) | −7.27208 | + | 12.5956i | −0.289268 | + | 0.501026i | ||||
\(633\) | −4.24264 | − | 7.34847i | −0.168630 | − | 0.292075i | ||||
\(634\) | 5.34315 | + | 9.25460i | 0.212203 | + | 0.367547i | ||||
\(635\) | −6.65685 | + | 11.5300i | −0.264169 | + | 0.457554i | ||||
\(636\) | 30.1421 | 1.19521 | ||||||||
\(637\) | −1.44365 | − | 5.61642i | −0.0571995 | − | 0.222531i | ||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 17.6569 | − | 30.5826i | 0.698494 | − | 1.20983i | ||||
\(640\) | −5.27817 | − | 9.14207i | −0.208638 | − | 0.361372i | ||||
\(641\) | −7.25736 | − | 12.5701i | −0.286648 | − | 0.496490i | 0.686359 | − | 0.727263i | \(-0.259208\pi\) |
−0.973008 | + | 0.230773i | \(0.925875\pi\) | |||||||
\(642\) | 1.37868 | − | 2.38794i | 0.0544121 | − | 0.0942446i | ||||
\(643\) | −30.2843 | −1.19430 | −0.597148 | − | 0.802131i | \(-0.703699\pi\) | ||||
−0.597148 | + | 0.802131i | \(0.703699\pi\) | |||||||
\(644\) | −7.15685 | + | 9.22911i | −0.282020 | + | 0.363678i | ||||
\(645\) | 15.4853 | 0.609732 | ||||||||
\(646\) | 0.485281 | − | 0.840532i | 0.0190931 | − | 0.0330703i | ||||
\(647\) | −8.52082 | − | 14.7585i | −0.334988 | − | 0.580216i | 0.648495 | − | 0.761219i | \(-0.275399\pi\) |
−0.983482 | + | 0.181003i | \(0.942066\pi\) | |||||||
\(648\) | 7.52082 | + | 13.0264i | 0.295446 | + | 0.511727i | ||||
\(649\) | 30.1421 | − | 52.2077i | 1.18318 | − | 2.04933i | ||||
\(650\) | −0.343146 | −0.0134593 | ||||||||
\(651\) | 14.4853 | + | 35.4815i | 0.567723 | + | 1.39063i | ||||
\(652\) | −43.2548 | −1.69399 | ||||||||
\(653\) | 12.4142 | − | 21.5020i | 0.485806 | − | 0.841440i | −0.514061 | − | 0.857754i | \(-0.671860\pi\) |
0.999867 | + | 0.0163133i | \(0.00519292\pi\) | |||||||
\(654\) | 1.74264 | + | 3.01834i | 0.0681426 | + | 0.118027i | ||||
\(655\) | −1.65685 | − | 2.86976i | −0.0647387 | − | 0.112131i | ||||
\(656\) | 3.25736 | − | 5.64191i | 0.127179 | − | 0.220280i | ||||
\(657\) | 13.6569 | 0.532805 | ||||||||
\(658\) | −2.17157 | − | 0.297173i | −0.0846567 | − | 0.0115850i | ||||
\(659\) | 26.8284 | 1.04509 | 0.522544 | − | 0.852613i | \(-0.324983\pi\) | ||||
0.522544 | + | 0.852613i | \(0.324983\pi\) | |||||||
\(660\) | 10.6569 | − | 18.4582i | 0.414817 | − | 0.718485i | ||||
\(661\) | −13.0858 | − | 22.6652i | −0.508978 | − | 0.881576i | −0.999946 | − | 0.0103982i | \(-0.996690\pi\) |
0.490968 | − | 0.871178i | \(-0.336643\pi\) | |||||||
\(662\) | −2.27208 | − | 3.93535i | −0.0883068 | − | 0.152952i | ||||
\(663\) | 0.828427 | − | 1.43488i | 0.0321734 | − | 0.0557260i | ||||
\(664\) | −18.5980 | −0.721742 | ||||||||
\(665\) | −7.41421 | − | 1.01461i | −0.287511 | − | 0.0393450i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.20711 | + | 2.09077i | −0.0467394 | + | 0.0809549i | ||||
\(668\) | 17.9056 | + | 31.0134i | 0.692788 | + | 1.19994i | ||||
\(669\) | −14.0711 | − | 24.3718i | −0.544019 | − | 0.942268i | ||||
\(670\) | 2.57107 | − | 4.45322i | 0.0993290 | − | 0.172043i | ||||
\(671\) | −55.4558 | −2.14085 | ||||||||
\(672\) | 10.6569 | + | 26.1039i | 0.411097 | + | 1.00698i | ||||
\(673\) | 18.3431 | 0.707076 | 0.353538 | − | 0.935420i | \(-0.384978\pi\) | ||||
0.353538 | + | 0.935420i | \(0.384978\pi\) | |||||||
\(674\) | 3.07107 | − | 5.31925i | 0.118293 | − | 0.204890i | ||||
\(675\) | 0.207107 | + | 0.358719i | 0.00797154 | + | 0.0138071i | ||||
\(676\) | −11.2574 | − | 19.4983i | −0.432975 | − | 0.749935i | ||||
\(677\) | −0.0710678 | + | 0.123093i | −0.00273136 | + | 0.00473085i | −0.867388 | − | 0.497633i | \(-0.834203\pi\) |
0.864656 | + | 0.502364i | \(0.167536\pi\) | |||||||
\(678\) | −12.4853 | −0.479494 | ||||||||
\(679\) | −0.556349 | + | 0.717439i | −0.0213507 | + | 0.0275328i | ||||
\(680\) | −1.31371 | −0.0503784 | ||||||||
\(681\) | −32.5563 | + | 56.3893i | −1.24756 | + | 2.16084i | ||||
\(682\) | −6.00000 | − | 10.3923i | −0.229752 | − | 0.397942i | ||||
\(683\) | 21.6213 | + | 37.4492i | 0.827317 | + | 1.43295i | 0.900136 | + | 0.435610i | \(0.143467\pi\) |
−0.0728189 | + | 0.997345i | \(0.523199\pi\) | |||||||
\(684\) | −7.31371 | + | 12.6677i | −0.279647 | + | 0.484362i | ||||
\(685\) | 1.65685 | 0.0633051 | ||||||||
\(686\) | 6.15685 | − | 4.57631i | 0.235070 | − | 0.174724i | ||||
\(687\) | −0.828427 | −0.0316065 | ||||||||
\(688\) | −9.62132 | + | 16.6646i | −0.366809 | + | 0.635333i | ||||
\(689\) | 2.82843 | + | 4.89898i | 0.107754 | + | 0.186636i | ||||
\(690\) | −1.20711 | − | 2.09077i | −0.0459538 | − | 0.0795943i | ||||
\(691\) | 2.41421 | − | 4.18154i | 0.0918410 | − | 0.159073i | −0.816445 | − | 0.577423i | \(-0.804058\pi\) |
0.908286 | + | 0.418350i | \(0.137392\pi\) | |||||||
\(692\) | 35.3137 | 1.34243 | ||||||||
\(693\) | −22.1421 | + | 28.5533i | −0.841110 | + | 1.08465i | ||||
\(694\) | −9.14214 | −0.347031 | ||||||||
\(695\) | −6.07107 | + | 10.5154i | −0.230289 | + | 0.398872i | ||||
\(696\) | 1.91421 | + | 3.31552i | 0.0725581 | + | 0.125674i | ||||
\(697\) | −0.899495 | − | 1.55797i | −0.0340708 | − | 0.0590124i | ||||
\(698\) | −5.52082 | + | 9.56233i | −0.208966 | + | 0.361940i | ||||
\(699\) | −26.9706 | −1.02012 | ||||||||
\(700\) | 1.82843 | + | 4.47871i | 0.0691080 | + | 0.169279i | ||||
\(701\) | −42.7990 | −1.61650 | −0.808248 | − | 0.588843i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588843i | \(0.799584\pi\) | |||||||
\(702\) | −0.0710678 | + | 0.123093i | −0.00268228 | + | 0.00464585i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 10.0711 | + | 17.4436i | 0.379568 | + | 0.657430i | ||||
\(705\) | −2.41421 | + | 4.18154i | −0.0909245 | + | 0.157486i | ||||
\(706\) | 8.76955 | 0.330046 | ||||||||
\(707\) | 32.2782 | + | 4.41717i | 1.21395 | + | 0.166125i | ||||
\(708\) | 55.1127 | 2.07126 | ||||||||
\(709\) | −19.1569 | + | 33.1806i | −0.719451 | + | 1.24613i | 0.241767 | + | 0.970334i | \(0.422273\pi\) |
−0.961218 | + | 0.275791i | \(0.911060\pi\) | |||||||
\(710\) | −2.58579 | − | 4.47871i | −0.0970428 | − | 0.168083i | ||||
\(711\) | −12.9706 | − | 22.4657i | −0.486434 | − | 0.842529i | ||||
\(712\) | −2.10660 | + | 3.64874i | −0.0789482 | + | 0.136742i | ||||
\(713\) | 14.4853 | 0.542478 | ||||||||
\(714\) | 2.17157 | + | 0.297173i | 0.0812691 | + | 0.0111214i | ||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | −9.14214 | + | 15.8346i | −0.341658 | + | 0.591768i | ||||
\(717\) | −1.58579 | − | 2.74666i | −0.0592223 | − | 0.102576i | ||||
\(718\) | −2.07107 | − | 3.58719i | −0.0772916 | − | 0.133873i | ||||
\(719\) | 20.5563 | − | 35.6046i | 0.766622 | − | 1.32783i | −0.172762 | − | 0.984964i | \(-0.555269\pi\) |
0.939385 | − | 0.342865i | \(-0.111398\pi\) | |||||||
\(720\) | 8.48528 | 0.316228 | ||||||||
\(721\) | −0.414214 | − | 1.01461i | −0.0154261 | − | 0.0377861i | ||||
\(722\) | 4.55635 | 0.169570 | ||||||||
\(723\) | −19.7279 | + | 34.1698i | −0.733689 | + | 1.27079i | ||||
\(724\) | −7.91421 | − | 13.7078i | −0.294129 | − | 0.509447i | ||||
\(725\) | 0.500000 | + | 0.866025i | 0.0185695 | + | 0.0321634i | ||||
\(726\) | 6.15685 | − | 10.6640i | 0.228502 | − | 0.395778i | ||||
\(727\) | −40.4142 | −1.49888 | −0.749440 | − | 0.662072i | \(-0.769677\pi\) | ||||
−0.749440 | + | 0.662072i | \(0.769677\pi\) | |||||||
\(728\) | −2.12994 | + | 2.74666i | −0.0789409 | + | 0.101798i | ||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 1.00000 | − | 1.73205i | 0.0370117 | − | 0.0641061i | ||||
\(731\) | 2.65685 | + | 4.60181i | 0.0982673 | + | 0.170204i | ||||
\(732\) | −25.3492 | − | 43.9062i | −0.936935 | − | 1.62282i | ||||
\(733\) | 11.0000 | − | 19.0526i | 0.406294 | − | 0.703722i | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | 4.65685 | 0.171888 | ||||||||
\(735\) | −4.20711 | − | 16.3674i | −0.155181 | − | 0.603722i | ||||
\(736\) | 10.6569 | 0.392817 | ||||||||
\(737\) | −29.9706 | + | 51.9105i | −1.10398 | + | 1.91215i | ||||
\(738\) | −1.27208 | − | 2.20330i | −0.0468258 | − | 0.0811047i | ||||
\(739\) | −20.5563 | − | 35.6046i | −0.756178 | − | 1.30974i | −0.944787 | − | 0.327686i | \(-0.893731\pi\) |
0.188609 | − | 0.982052i | \(-0.439602\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | −4.58579 | + | 5.91359i | −0.168350 | + | 0.217095i | ||||
\(743\) | −1.92893 | −0.0707657 | −0.0353828 | − | 0.999374i | \(-0.511265\pi\) | ||||
−0.0353828 | + | 0.999374i | \(0.511265\pi\) | |||||||
\(744\) | 11.4853 | − | 19.8931i | 0.421071 | − | 0.729316i | ||||
\(745\) | 3.91421 | + | 6.77962i | 0.143406 | + | 0.248386i | ||||
\(746\) | 2.68629 | + | 4.65279i | 0.0983521 | + | 0.170351i | ||||
\(747\) | 16.5858 | − | 28.7274i | 0.606842 | − | 1.05108i | ||||
\(748\) | 7.31371 | 0.267416 | ||||||||
\(749\) | −2.75736 | − | 6.75412i | −0.100752 | − | 0.246790i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 20.8284 | − | 36.0759i | 0.760040 | − | 1.31643i | −0.182789 | − | 0.983152i | \(-0.558513\pi\) |
0.942829 | − | 0.333276i | \(-0.108154\pi\) | |||||||
\(752\) | −3.00000 | − | 5.19615i | −0.109399 | − | 0.189484i | ||||
\(753\) | −16.0711 | − | 27.8359i | −0.585662 | − | 1.01440i | ||||
\(754\) | −0.171573 | + | 0.297173i | −0.00624832 | + | 0.0108224i | ||||
\(755\) | 0.343146 | 0.0124884 | ||||||||
\(756\) | 1.98528 | + | 0.271680i | 0.0722040 | + | 0.00988089i | ||||
\(757\) | 19.4558 | 0.707135 | 0.353567 | − | 0.935409i | \(-0.384969\pi\) | ||||
0.353567 | + | 0.935409i | \(0.384969\pi\) | |||||||
\(758\) | 4.38478 | − | 7.59466i | 0.159262 | − | 0.275850i | ||||
\(759\) | 14.0711 | + | 24.3718i | 0.510747 | + | 0.884640i | ||||
\(760\) | 2.24264 | + | 3.88437i | 0.0813491 | + | 0.140901i | ||||
\(761\) | 6.65685 | − | 11.5300i | 0.241311 | − | 0.417963i | −0.719777 | − | 0.694205i | \(-0.755756\pi\) |
0.961088 | + | 0.276243i | \(0.0890894\pi\) | |||||||
\(762\) | −13.3137 | −0.482305 | ||||||||
\(763\) | 9.13604 | + | 1.25024i | 0.330747 | + | 0.0452617i | ||||
\(764\) | 13.1127 | 0.474401 | ||||||||
\(765\) | 1.17157 | − | 2.02922i | 0.0423583 | − | 0.0733667i | ||||
\(766\) | 3.50000 | + | 6.06218i | 0.126460 | + | 0.219035i | ||||
\(767\) | 5.17157 | + | 8.95743i | 0.186735 | + | 0.323434i | ||||
\(768\) | −4.79289 | + | 8.30153i | −0.172949 | + | 0.299556i | ||||
\(769\) | 44.6274 | 1.60931 | 0.804653 | − | 0.593745i | \(-0.202351\pi\) | ||||
0.804653 | + | 0.593745i | \(0.202351\pi\) | |||||||
\(770\) | 2.00000 | + | 4.89898i | 0.0720750 | + | 0.176547i | ||||
\(771\) | 42.6274 | 1.53519 | ||||||||
\(772\) | −1.82843 | + | 3.16693i | −0.0658065 | + | 0.113980i | ||||
\(773\) | −12.5563 | − | 21.7482i | −0.451620 | − | 0.782230i | 0.546866 | − | 0.837220i | \(-0.315821\pi\) |
−0.998487 | + | 0.0549903i | \(0.982487\pi\) | |||||||
\(774\) | 3.75736 | + | 6.50794i | 0.135055 | + | 0.233923i | ||||
\(775\) | 3.00000 | − | 5.19615i | 0.107763 | − | 0.186651i | ||||
\(776\) | 0.544156 | 0.0195341 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.11270 | −0.183299 | ||||||||
\(779\) | −3.07107 | + | 5.31925i | −0.110032 | + | 0.190582i | ||||
\(780\) | 1.82843 | + | 3.16693i | 0.0654682 | + | 0.113394i | ||||
\(781\) | 30.1421 | + | 52.2077i | 1.07857 | + | 1.86814i | ||||
\(782\) | 0.414214 | − | 0.717439i | 0.0148122 | − | 0.0256556i | ||||
\(783\) | 0.414214 | 0.0148028 | ||||||||
\(784\) | 20.2279 | + | 5.64191i | 0.722426 | + | 0.201497i | ||||
\(785\) | −5.31371 | −0.189654 | ||||||||
\(786\) | 1.65685 | − | 2.86976i | 0.0590980 | − | 0.102361i | ||||
\(787\) | 14.2782 | + | 24.7305i | 0.508962 | + | 0.881548i | 0.999946 | + | 0.0103795i | \(0.00330395\pi\) |
−0.490984 | + | 0.871168i | \(0.663363\pi\) | |||||||
\(788\) | −21.6274 | − | 37.4598i | −0.770445 | − | 1.33445i | ||||
\(789\) | −22.9853 | + | 39.8117i | −0.818298 | + | 1.41733i | ||||
\(790\) | −3.79899 | −0.135162 | ||||||||
\(791\) | −20.2426 | + | 26.1039i | −0.719745 | + | 0.928146i | ||||
\(792\) | 21.6569 | 0.769543 | ||||||||
\(793\) | 4.75736 | − | 8.23999i | 0.168939 | − | 0.292611i | ||||
\(794\) | 5.92893 | + | 10.2692i | 0.210410 | + | 0.364441i | ||||
\(795\) | 8.24264 | + | 14.2767i | 0.292336 | + | 0.506341i | ||||
\(796\) | 1.51472 | − | 2.62357i | 0.0536878 | − | 0.0929900i | ||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | −2.82843 | − | 6.92820i | −0.100125 | − | 0.245256i | ||||
\(799\) | −1.65685 | −0.0586153 | ||||||||
\(800\) | 2.20711 | − | 3.82282i | 0.0780330 | − | 0.135157i | ||||
\(801\) | −3.75736 | − | 6.50794i | −0.132760 | − | 0.229947i | ||||
\(802\) | 1.59188 | + | 2.75722i | 0.0562113 | + | 0.0973609i | ||||
\(803\) | −11.6569 | + | 20.1903i | −0.411361 | + | 0.712499i | ||||
\(804\) | −54.7990 | −1.93261 | ||||||||
\(805\) | −6.32843 | − | 0.866025i | −0.223048 | − | 0.0305234i | ||||
\(806\) | 2.05887 | 0.0725208 | ||||||||
\(807\) | 36.7635 | − | 63.6762i | 1.29413 | − | 2.24151i | ||||
\(808\) | −9.76346 | − | 16.9108i | −0.343477 | − | 0.594920i | ||||
\(809\) | 4.81371 | + | 8.33759i | 0.169241 | + | 0.293134i | 0.938153 | − | 0.346220i | \(-0.112535\pi\) |
−0.768912 | + | 0.639354i | \(0.779202\pi\) | |||||||
\(810\) | −1.96447 | + | 3.40256i | −0.0690243 | + | 0.119554i | ||||
\(811\) | 24.6274 | 0.864786 | 0.432393 | − | 0.901685i | \(-0.357669\pi\) | ||||
0.432393 | + | 0.901685i | \(0.357669\pi\) | |||||||
\(812\) | 4.79289 | + | 0.655892i | 0.168198 | + | 0.0230173i | ||||
\(813\) | −1.17157 | −0.0410889 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8284 | − | 20.4874i | −0.414332 | − | 0.717644i | ||||
\(816\) | 3.00000 | + | 5.19615i | 0.105021 | + | 0.181902i | ||||
\(817\) | 9.07107 | − | 15.7116i | 0.317356 | − | 0.549678i | ||||
\(818\) | −10.2721 | −0.359155 | ||||||||
\(819\) | −2.34315 | − | 5.73951i | −0.0818761 | − | 0.200555i | ||||
\(820\) | 3.97056 | 0.138658 | ||||||||
\(821\) | 9.97056 | − | 17.2695i | 0.347975 | − | 0.602710i | −0.637915 | − | 0.770107i | \(-0.720203\pi\) |
0.985890 | + | 0.167397i | \(0.0535361\pi\) | |||||||
\(822\) | 0.828427 | + | 1.43488i | 0.0288947 | + | 0.0500471i | ||||
\(823\) | 6.03553 | + | 10.4539i | 0.210385 | + | 0.364398i | 0.951835 | − | 0.306610i | \(-0.0991948\pi\) |
−0.741450 | + | 0.671008i | \(0.765861\pi\) | |||||||
\(824\) | −0.328427 | + | 0.568852i | −0.0114413 | + | 0.0198169i | ||||
\(825\) | 11.6569 | 0.405840 | ||||||||
\(826\) | −8.38478 | + | 10.8126i | −0.291744 | + | 0.376217i | ||||
\(827\) | 16.2132 | 0.563788 | 0.281894 | − | 0.959446i | \(-0.409037\pi\) | ||||
0.281894 | + | 0.959446i | \(0.409037\pi\) | |||||||
\(828\) | −6.24264 | + | 10.8126i | −0.216947 | + | 0.375763i | ||||
\(829\) | −3.34315 | − | 5.79050i | −0.116112 | − | 0.201112i | 0.802112 | − | 0.597174i | \(-0.203710\pi\) |
−0.918224 | + | 0.396062i | \(0.870377\pi\) | |||||||
\(830\) | −2.42893 | − | 4.20703i | −0.0843095 | − | 0.146028i | ||||
\(831\) | 14.6569 | − | 25.3864i | 0.508441 | − | 0.880645i | ||||
\(832\) | −3.45584 | −0.119810 | ||||||||
\(833\) | 4.14214 | − | 4.05845i | 0.143516 | − | 0.140617i | ||||
\(834\) | −12.1421 | −0.420448 | ||||||||
\(835\) | −9.79289 | + | 16.9618i | −0.338897 | + | 0.586987i | ||||
\(836\) | −12.4853 | − | 21.6251i | −0.431812 | − | 0.747921i | ||||
\(837\) | −1.24264 | − | 2.15232i | −0.0429519 | − | 0.0743950i | ||||
\(838\) | −4.82843 | + | 8.36308i | −0.166795 | + | 0.288898i | ||||
\(839\) | 20.8284 | 0.719077 | 0.359539 | − | 0.933130i | \(-0.382934\pi\) | ||||
0.359539 | + | 0.933130i | \(0.382934\pi\) | |||||||
\(840\) | −6.20711 | + | 8.00436i | −0.214166 | + | 0.276177i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −0.721825 | + | 1.25024i | −0.0248757 | + | 0.0430861i | ||||
\(843\) | −31.7279 | − | 54.9544i | −1.09277 | − | 1.89273i | ||||
\(844\) | 3.21320 | + | 5.56543i | 0.110603 | + | 0.191570i | ||||
\(845\) | 6.15685 | − | 10.6640i | 0.211802 | − | 0.366852i | ||||
\(846\) | −2.34315 | −0.0805590 | ||||||||
\(847\) | −12.3137 | − | 30.1623i | −0.423104 | − | 1.03639i | ||||
\(848\) | −20.4853 | −0.703467 | ||||||||
\(849\) | −16.8995 | + | 29.2708i | −0.579989 | + | 1.00457i | ||||
\(850\) | −0.171573 | − | 0.297173i | −0.00588490 | − | 0.0101929i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −27.5563 | + | 47.7290i | −0.944065 | + | 1.63517i | ||||
\(853\) | 53.4558 | 1.83029 | 0.915147 | − | 0.403121i | \(-0.132075\pi\) | ||||
0.915147 | + | 0.403121i | \(0.132075\pi\) | |||||||
\(854\) | 12.4706 | + | 1.70656i | 0.426734 | + | 0.0583972i | ||||
\(855\) | −8.00000 | −0.273594 | ||||||||
\(856\) | −2.18629 | + | 3.78677i | −0.0747259 | + | 0.129429i | ||||
\(857\) | 11.1421 | + | 19.2987i | 0.380608 | + | 0.659233i | 0.991149 | − | 0.132752i | \(-0.0423814\pi\) |
−0.610541 | + | 0.791985i | \(0.709048\pi\) | |||||||
\(858\) | 2.00000 | + | 3.46410i | 0.0682789 | + | 0.118262i | ||||
\(859\) | −23.3137 | + | 40.3805i | −0.795453 | + | 1.37777i | 0.127097 | + | 0.991890i | \(0.459434\pi\) |
−0.922551 | + | 0.385876i | \(0.873899\pi\) | |||||||
\(860\) | −11.7279 | −0.399919 | ||||||||
\(861\) | −13.7426 | − | 1.88064i | −0.468348 | − | 0.0640919i | ||||
\(862\) | 9.02944 | 0.307544 | ||||||||
\(863\) | 8.27817 | − | 14.3382i | 0.281792 | − | 0.488079i | −0.690034 | − | 0.723777i | \(-0.742404\pi\) |
0.971826 | + | 0.235698i | \(0.0757377\pi\) | |||||||
\(864\) | −0.914214 | − | 1.58346i | −0.0311022 | − | 0.0538706i | ||||
\(865\) | 9.65685 | + | 16.7262i | 0.328343 | + | 0.568707i | ||||
\(866\) | −6.58579 | + | 11.4069i | −0.223794 | + | 0.387623i | ||||
\(867\) | −39.3848 | −1.33758 | ||||||||
\(868\) | −10.9706 | − | 26.8723i | −0.372365 | − | 0.912105i | ||||
\(869\) | 44.2843 | 1.50224 | ||||||||
\(870\) | −0.500000 | + | 0.866025i | −0.0169516 | + | 0.0293610i | ||||
\(871\) | −5.14214 | − | 8.90644i | −0.174235 | − | 0.301783i | ||||
\(872\) | −2.76346 | − | 4.78645i | −0.0935824 | − | 0.162090i | ||||
\(873\) | −0.485281 | + | 0.840532i | −0.0164243 | + | 0.0284477i | ||||
\(874\) | −2.82843 | −0.0956730 | ||||||||
\(875\) | −1.62132 | + | 2.09077i | −0.0548106 | + | 0.0706809i | ||||
\(876\) | −21.3137 | −0.720123 | ||||||||
\(877\) | −15.4142 | + | 26.6982i | −0.520501 | + | 0.901534i | 0.479215 | + | 0.877698i | \(0.340921\pi\) |
−0.999716 | + | 0.0238366i | \(0.992412\pi\) | |||||||
\(878\) | 7.02944 | + | 12.1753i | 0.237232 | + | 0.410898i | ||||
\(879\) | 19.3137 | + | 33.4523i | 0.651435 | + | 1.12832i | ||||
\(880\) | −7.24264 | + | 12.5446i | −0.244149 | + | 0.422879i | ||||
\(881\) | −3.82843 | −0.128983 | −0.0644915 | − | 0.997918i | \(-0.520543\pi\) | ||||
−0.0644915 | + | 0.997918i | \(0.520543\pi\) | |||||||
\(882\) | 5.85786 | − | 5.73951i | 0.197245 | − | 0.193259i | ||||
\(883\) | −38.2843 | −1.28837 | −0.644184 | − | 0.764870i | \(-0.722803\pi\) | ||||
−0.644184 | + | 0.764870i | \(0.722803\pi\) | |||||||
\(884\) | −0.627417 | + | 1.08672i | −0.0211023 | + | 0.0365503i | ||||
\(885\) | 15.0711 | + | 26.1039i | 0.506608 | + | 0.877471i | ||||
\(886\) | −2.52944 | − | 4.38111i | −0.0849781 | − | 0.147186i | ||||
\(887\) | −22.0355 | + | 38.1667i | −0.739881 | + | 1.28151i | 0.212668 | + | 0.977125i | \(0.431785\pi\) |
−0.952549 | + | 0.304387i | \(0.901549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.5858 | + | 27.8359i | −0.723964 | + | 0.933586i | ||||
\(890\) | −1.10051 | −0.0368890 | ||||||||
\(891\) | 22.8995 | − | 39.6631i | 0.767162 | − | 1.32876i | ||||
\(892\) | 10.6569 | + | 18.4582i | 0.356818 | + | 0.618027i | ||||
\(893\) | 2.82843 | + | 4.89898i | 0.0946497 | + | 0.163938i | ||||
\(894\) | −3.91421 | + | 6.77962i | −0.130911 | + | 0.226744i | ||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | −10.5563 | − | 25.8577i | −0.352663 | − | 0.863844i | ||||
\(897\) | −4.82843 | −0.161216 | ||||||||
\(898\) | −0.378680 | + | 0.655892i | −0.0126367 | + | 0.0218874i | ||||
\(899\) | −3.00000 | − | 5.19615i | −0.100056 | − | 0.173301i | ||||
\(900\) | 2.58579 | + | 4.47871i | 0.0861929 | + | 0.149290i | ||||
\(901\) | −2.82843 | + | 4.89898i | −0.0942286 | + | 0.163209i | ||||
\(902\) | 4.34315 | 0.144611 | ||||||||
\(903\) | 40.5919 | + | 5.55487i | 1.35081 | + | 0.184855i | ||||
\(904\) | 19.7990 | 0.658505 | ||||||||
\(905\) | 4.32843 | − | 7.49706i | 0.143882 | − | 0.249211i | ||||
\(906\) | 0.171573 | + | 0.297173i | 0.00570013 | + | 0.00987291i | ||||
\(907\) | −14.1066 | − | 24.4334i | −0.468402 | − | 0.811296i | 0.530946 | − | 0.847406i | \(-0.321837\pi\) |
−0.999348 | + | 0.0361097i | \(0.988503\pi\) | |||||||
\(908\) | 24.6569 | − | 42.7069i | 0.818266 | − | 1.41728i | ||||
\(909\) | 34.8284 | 1.15519 | ||||||||
\(910\) | −0.899495 | − | 0.123093i | −0.0298180 | − | 0.00408050i | ||||
\(911\) | −49.7990 | −1.64991 | −0.824957 | − | 0.565195i | \(-0.808801\pi\) | ||||
−0.824957 | + | 0.565195i | \(0.808801\pi\) | |||||||
\(912\) | 10.2426 | − | 17.7408i | 0.339168 | − | 0.587456i | ||||
\(913\) | 28.3137 | + | 49.0408i | 0.937047 | + | 1.62301i | ||||
\(914\) | −6.68629 | − | 11.5810i | −0.221163 | − | 0.383065i | ||||
\(915\) | 13.8640 | − | 24.0131i | 0.458328 | − | 0.793848i | ||||
\(916\) | 0.627417 | 0.0207304 | ||||||||
\(917\) | −3.31371 | − | 8.11689i | −0.109428 | − | 0.268043i | ||||
\(918\) | −0.142136 | −0.00469117 | ||||||||
\(919\) | −9.55635 | + | 16.5521i | −0.315235 | + | 0.546003i | −0.979487 | − | 0.201505i | \(-0.935417\pi\) |
0.664253 | + | 0.747508i | \(0.268750\pi\) | |||||||
\(920\) | 1.91421 | + | 3.31552i | 0.0631098 | + | 0.109309i | ||||
\(921\) | 15.9853 | + | 27.6873i | 0.526733 | + | 0.912328i | ||||
\(922\) | 3.87006 | − | 6.70314i | 0.127454 | − | 0.220756i | ||||
\(923\) | −10.3431 | −0.340449 | ||||||||
\(924\) | 34.5563 | − | 44.5621i | 1.13682 | − | 1.46598i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.28680 | − | 3.96085i | 0.0751488 | − | 0.130162i | ||||
\(927\) | −0.585786 | − | 1.01461i | −0.0192398 | − | 0.0333242i | ||||
\(928\) | −2.20711 | − | 3.82282i | −0.0724518 | − | 0.125490i | ||||
\(929\) | 5.74264 | − | 9.94655i | 0.188410 | − | 0.326336i | −0.756310 | − | 0.654213i | \(-0.773000\pi\) |
0.944720 | + | 0.327877i | \(0.106333\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | −19.0711 | − | 5.31925i | −0.625029 | − | 0.174331i | ||||
\(932\) | 20.4264 | 0.669089 | ||||||||
\(933\) | 22.7279 | − | 39.3659i | 0.744079 | − | 1.28878i | ||||
\(934\) | −4.74264 | − | 8.21449i | −0.155184 | − | 0.268786i | ||||
\(935\) | 2.00000 | + | 3.46410i | 0.0654070 | + | 0.113288i | ||||
\(936\) | −1.85786 | + | 3.21792i | −0.0607262 | + | 0.105181i | ||||
\(937\) | −10.6274 | −0.347183 | −0.173591 | − | 0.984818i | \(-0.555537\pi\) | ||||
−0.173591 | + | 0.984818i | \(0.555537\pi\) | |||||||
\(938\) | 8.33705 | − | 10.7510i | 0.272214 | − | 0.351033i | ||||
\(939\) | −42.6274 | −1.39109 | ||||||||
\(940\) | 1.82843 | − | 3.16693i | 0.0596367 | − | 0.103294i | ||||
\(941\) | −5.14214 | − | 8.90644i | −0.167629 | − | 0.290342i | 0.769957 | − | 0.638096i | \(-0.220278\pi\) |
−0.937586 | + | 0.347754i | \(0.886944\pi\) | |||||||
\(942\) | −2.65685 | − | 4.60181i | −0.0865650 | − | 0.149935i | ||||
\(943\) | −2.62132 | + | 4.54026i | −0.0853619 | + | 0.147851i | ||||
\(944\) | −37.4558 | −1.21908 | ||||||||
\(945\) | 0.414214 | + | 1.01461i | 0.0134744 | + | 0.0330053i | ||||
\(946\) | −12.8284 | −0.417088 | ||||||||
\(947\) | 21.5919 | − | 37.3982i | 0.701642 | − | 1.21528i | −0.266248 | − | 0.963905i | \(-0.585784\pi\) |
0.967890 | − | 0.251375i | \(-0.0808827\pi\) | |||||||
\(948\) | 20.2426 | + | 35.0613i | 0.657450 | + | 1.13874i | ||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | −0.585786 | + | 1.01461i | −0.0190054 | + | 0.0329184i | ||||
\(951\) | 62.2843 | 2.01971 | ||||||||
\(952\) | −3.44365 | − | 0.471253i | −0.111609 | − | 0.0152734i | ||||
\(953\) | −2.34315 | −0.0759019 | −0.0379510 | − | 0.999280i | \(-0.512083\pi\) | ||||
−0.0379510 | + | 0.999280i | \(0.512083\pi\) | |||||||
\(954\) | −4.00000 | + | 6.92820i | −0.129505 | + | 0.224309i | ||||
\(955\) | 3.58579 | + | 6.21076i | 0.116033 | + | 0.200976i | ||||
\(956\) | 1.20101 | + | 2.08021i | 0.0388434 | + | 0.0672788i | ||||
\(957\) | 5.82843 | − | 10.0951i | 0.188406 | − | 0.326329i | ||||
\(958\) | 10.0833 | 0.325775 | ||||||||
\(959\) | 4.34315 | + | 0.594346i | 0.140247 | + | 0.0191924i | ||||
\(960\) | −10.0711 | −0.325042 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.89949 | − | 6.75412i | −0.125659 | − | 0.217649i | ||||
\(964\) | 14.9411 | − | 25.8788i | 0.481221 | − | 0.833500i | ||||
\(965\) | −2.00000 | −0.0643823 | ||||||||
\(966\) | −2.41421 | − | 5.91359i | −0.0776760 | − | 0.190267i | ||||
\(967\) | −27.5269 | −0.885206 | −0.442603 | − | 0.896718i | \(-0.645945\pi\) | ||||
−0.442603 | + | 0.896718i | \(0.645945\pi\) | |||||||
\(968\) | −9.76346 | + | 16.9108i | −0.313809 | + | 0.543534i | ||||
\(969\) | −2.82843 | − | 4.89898i | −0.0908622 | − | 0.157378i | ||||
\(970\) | 0.0710678 | + | 0.123093i | 0.00228185 | + | 0.00395228i | ||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | 39.5980 | 1.27011 | ||||||||
\(973\) | −19.6863 | + | 25.3864i | −0.631114 | + | 0.813851i | ||||
\(974\) | −6.48528 | −0.207802 | ||||||||
\(975\) | −1.00000 | + | 1.73205i | −0.0320256 | + | 0.0554700i | ||||
\(976\) | 17.2279 | + | 29.8396i | 0.551452 | + | 0.955143i | ||||
\(977\) | −10.6569 | − | 18.4582i | −0.340943 | − | 0.590531i | 0.643665 | − | 0.765307i | \(-0.277413\pi\) |
−0.984608 | + | 0.174777i | \(0.944080\pi\) | |||||||
\(978\) | 11.8284 | − | 20.4874i | 0.378231 | − | 0.655116i | ||||
\(979\) | 12.8284 | 0.409998 | ||||||||
\(980\) | 3.18629 | + | 12.3960i | 0.101782 | + | 0.395977i | ||||
\(981\) | 9.85786 | 0.314737 | ||||||||
\(982\) | −2.75736 | + | 4.77589i | −0.0879909 | + | 0.152405i | ||||
\(983\) | 7.10660 | + | 12.3090i | 0.226665 | + | 0.392596i | 0.956818 | − | 0.290688i | \(-0.0938843\pi\) |
−0.730152 | + | 0.683284i | \(0.760551\pi\) | |||||||
\(984\) | 4.15685 | + | 7.19988i | 0.132516 | + | 0.229524i | ||||
\(985\) | 11.8284 | − | 20.4874i | 0.376885 | − | 0.652784i | ||||
\(986\) | −0.343146 | −0.0109280 | ||||||||
\(987\) | −7.82843 | + | 10.0951i | −0.249182 | + | 0.321332i | ||||
\(988\) | 4.28427 | 0.136301 | ||||||||
\(989\) | 7.74264 | − | 13.4106i | 0.246202 | − | 0.426434i | ||||
\(990\) | 2.82843 | + | 4.89898i | 0.0898933 | + | 0.155700i | ||||
\(991\) | 7.82843 | + | 13.5592i | 0.248678 | + | 0.430723i | 0.963159 | − | 0.268931i | \(-0.0866705\pi\) |
−0.714481 | + | 0.699655i | \(0.753337\pi\) | |||||||
\(992\) | −13.2426 | + | 22.9369i | −0.420454 | + | 0.728248i | ||||
\(993\) | −26.4853 | −0.840485 | ||||||||
\(994\) | −5.17157 | − | 12.6677i | −0.164032 | − | 0.401796i | ||||
\(995\) | 1.65685 | 0.0525258 | ||||||||
\(996\) | −25.8848 | + | 44.8337i | −0.820191 | + | 1.42061i | ||||
\(997\) | 8.72792 | + | 15.1172i | 0.276416 | + | 0.478767i | 0.970491 | − | 0.241136i | \(-0.0775199\pi\) |
−0.694075 | + | 0.719902i | \(0.744187\pi\) | |||||||
\(998\) | 1.00000 | + | 1.73205i | 0.0316544 | + | 0.0548271i | ||||
\(999\) | 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 | 35.2.e.a.16.2 | yes | 4 | |
3.2 | odd | 2 | 315.2.j.e.226.1 | 4 | |||
4.3 | odd | 2 | 560.2.q.k.401.2 | 4 | |||
5.2 | odd | 4 | 175.2.k.a.149.3 | 8 | |||
5.3 | odd | 4 | 175.2.k.a.149.2 | 8 | |||
5.4 | even | 2 | 175.2.e.c.51.1 | 4 | |||
7.2 | even | 3 | 245.2.a.h.1.1 | 2 | |||
7.3 | odd | 6 | 245.2.e.e.116.2 | 4 | |||
7.4 | even | 3 | inner | 35.2.e.a.11.2 | ✓ | 4 | |
7.5 | odd | 6 | 245.2.a.g.1.1 | 2 | |||
7.6 | odd | 2 | 245.2.e.e.226.2 | 4 | |||
21.2 | odd | 6 | 2205.2.a.n.1.2 | 2 | |||
21.5 | even | 6 | 2205.2.a.q.1.2 | 2 | |||
21.11 | odd | 6 | 315.2.j.e.46.1 | 4 | |||
28.11 | odd | 6 | 560.2.q.k.81.2 | 4 | |||
28.19 | even | 6 | 3920.2.a.bv.1.2 | 2 | |||
28.23 | odd | 6 | 3920.2.a.bq.1.1 | 2 | |||
35.2 | odd | 12 | 1225.2.b.g.99.2 | 4 | |||
35.4 | even | 6 | 175.2.e.c.151.1 | 4 | |||
35.9 | even | 6 | 1225.2.a.k.1.2 | 2 | |||
35.12 | even | 12 | 1225.2.b.h.99.2 | 4 | |||
35.18 | odd | 12 | 175.2.k.a.74.3 | 8 | |||
35.19 | odd | 6 | 1225.2.a.m.1.2 | 2 | |||
35.23 | odd | 12 | 1225.2.b.g.99.3 | 4 | |||
35.32 | odd | 12 | 175.2.k.a.74.2 | 8 | |||
35.33 | even | 12 | 1225.2.b.h.99.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.2 | ✓ | 4 | 7.4 | even | 3 | inner | |
35.2.e.a.16.2 | yes | 4 | 1.1 | even | 1 | trivial | |
175.2.e.c.51.1 | 4 | 5.4 | even | 2 | |||
175.2.e.c.151.1 | 4 | 35.4 | even | 6 | |||
175.2.k.a.74.2 | 8 | 35.32 | odd | 12 | |||
175.2.k.a.74.3 | 8 | 35.18 | odd | 12 | |||
175.2.k.a.149.2 | 8 | 5.3 | odd | 4 | |||
175.2.k.a.149.3 | 8 | 5.2 | odd | 4 | |||
245.2.a.g.1.1 | 2 | 7.5 | odd | 6 | |||
245.2.a.h.1.1 | 2 | 7.2 | even | 3 | |||
245.2.e.e.116.2 | 4 | 7.3 | odd | 6 | |||
245.2.e.e.226.2 | 4 | 7.6 | odd | 2 | |||
315.2.j.e.46.1 | 4 | 21.11 | odd | 6 | |||
315.2.j.e.226.1 | 4 | 3.2 | odd | 2 | |||
560.2.q.k.81.2 | 4 | 28.11 | odd | 6 | |||
560.2.q.k.401.2 | 4 | 4.3 | odd | 2 | |||
1225.2.a.k.1.2 | 2 | 35.9 | even | 6 | |||
1225.2.a.m.1.2 | 2 | 35.19 | odd | 6 | |||
1225.2.b.g.99.2 | 4 | 35.2 | odd | 12 | |||
1225.2.b.g.99.3 | 4 | 35.23 | odd | 12 | |||
1225.2.b.h.99.2 | 4 | 35.12 | even | 12 | |||
1225.2.b.h.99.3 | 4 | 35.33 | even | 12 | |||
2205.2.a.n.1.2 | 2 | 21.2 | odd | 6 | |||
2205.2.a.q.1.2 | 2 | 21.5 | even | 6 | |||
3920.2.a.bq.1.1 | 2 | 28.23 | odd | 6 | |||
3920.2.a.bv.1.2 | 2 | 28.19 | even | 6 |