Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.3 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.b.769.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52930 | −1.78849 | −0.894244 | − | 0.447581i | \(-0.852286\pi\) | ||||
−0.894244 | + | 0.447581i | \(0.852286\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.39737 | 2.19869 | ||||||||
\(5\) | −1.63381 | − | 1.52665i | −0.730662 | − | 0.682739i | ||||
\(6\) | −2.52930 | −1.03258 | ||||||||
\(7\) | −2.48590 | − | 0.905718i | −0.939580 | − | 0.342329i | ||||
\(8\) | −6.06368 | −2.14384 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.13240 | + | 3.86136i | 1.30678 | + | 1.22107i | ||||
\(11\) | −2.13976 | − | 2.53405i | −0.645163 | − | 0.764045i | ||||
\(12\) | 4.39737 | 1.26941 | ||||||||
\(13\) | 5.27466i | 1.46293i | 0.681880 | + | 0.731464i | \(0.261163\pi\) | ||||
−0.681880 | + | 0.731464i | \(0.738837\pi\) | |||||||
\(14\) | 6.28758 | + | 2.29084i | 1.68043 | + | 0.612251i | ||||
\(15\) | −1.63381 | − | 1.52665i | −0.421848 | − | 0.394180i | ||||
\(16\) | 6.54214 | 1.63554 | ||||||||
\(17\) | − | 5.11968i | − | 1.24171i | −0.783927 | − | 0.620853i | \(-0.786787\pi\) | ||
0.783927 | − | 0.620853i | \(-0.213213\pi\) | |||||||
\(18\) | −2.52930 | −0.596162 | ||||||||
\(19\) | −4.28158 | −0.982263 | −0.491131 | − | 0.871085i | \(-0.663417\pi\) | ||||
−0.491131 | + | 0.871085i | \(0.663417\pi\) | |||||||
\(20\) | −7.18448 | − | 6.71325i | −1.60650 | − | 1.50113i | ||||
\(21\) | −2.48590 | − | 0.905718i | −0.542467 | − | 0.197644i | ||||
\(22\) | 5.41211 | + | 6.40938i | 1.15387 | + | 1.36648i | ||||
\(23\) | − | 1.22635i | − | 0.255711i | −0.991793 | − | 0.127855i | \(-0.959191\pi\) | ||
0.991793 | − | 0.127855i | \(-0.0408093\pi\) | |||||||
\(24\) | −6.06368 | −1.23774 | ||||||||
\(25\) | 0.338675 | + | 4.98852i | 0.0677351 | + | 0.997703i | ||||
\(26\) | − | 13.3412i | − | 2.61643i | ||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −10.9314 | − | 3.98278i | −2.06584 | − | 0.752675i | ||||
\(29\) | 8.66218i | 1.60853i | 0.594274 | + | 0.804263i | \(0.297440\pi\) | ||||
−0.594274 | + | 0.804263i | \(0.702560\pi\) | |||||||
\(30\) | 4.13240 | + | 3.86136i | 0.754470 | + | 0.704985i | ||||
\(31\) | 3.16260i | 0.568020i | 0.958821 | + | 0.284010i | \(0.0916649\pi\) | ||||
−0.958821 | + | 0.284010i | \(0.908335\pi\) | |||||||
\(32\) | −4.41970 | −0.781300 | ||||||||
\(33\) | −2.13976 | − | 2.53405i | −0.372485 | − | 0.441122i | ||||
\(34\) | 12.9492i | 2.22077i | ||||||||
\(35\) | 2.67877 | + | 5.27487i | 0.452794 | + | 0.891615i | ||||
\(36\) | 4.39737 | 0.732896 | ||||||||
\(37\) | − | 3.79008i | − | 0.623085i | −0.950232 | − | 0.311543i | \(-0.899154\pi\) | ||
0.950232 | − | 0.311543i | \(-0.100846\pi\) | |||||||
\(38\) | 10.8294 | 1.75676 | ||||||||
\(39\) | 5.27466i | 0.844622i | ||||||||
\(40\) | 9.90691 | + | 9.25713i | 1.56642 | + | 1.46368i | ||||
\(41\) | 5.95804 | 0.930489 | 0.465245 | − | 0.885182i | \(-0.345966\pi\) | ||||
0.465245 | + | 0.885182i | \(0.345966\pi\) | |||||||
\(42\) | 6.28758 | + | 2.29084i | 0.970195 | + | 0.353484i | ||||
\(43\) | 7.87280 | 1.20059 | 0.600296 | − | 0.799778i | \(-0.295050\pi\) | ||||
0.600296 | + | 0.799778i | \(0.295050\pi\) | |||||||
\(44\) | −9.40934 | − | 11.1432i | −1.41851 | − | 1.67990i | ||||
\(45\) | −1.63381 | − | 1.52665i | −0.243554 | − | 0.227580i | ||||
\(46\) | 3.10180i | 0.457335i | ||||||||
\(47\) | −6.85157 | −0.999404 | −0.499702 | − | 0.866198i | \(-0.666557\pi\) | ||||
−0.499702 | + | 0.866198i | \(0.666557\pi\) | |||||||
\(48\) | 6.54214 | 0.944277 | ||||||||
\(49\) | 5.35935 | + | 4.50304i | 0.765621 | + | 0.643291i | ||||
\(50\) | −0.856613 | − | 12.6175i | −0.121143 | − | 1.78438i | ||||
\(51\) | − | 5.11968i | − | 0.716899i | ||||||
\(52\) | 23.1947i | 3.21652i | ||||||||
\(53\) | 12.4608i | 1.71162i | 0.517289 | + | 0.855811i | \(0.326941\pi\) | ||||
−0.517289 | + | 0.855811i | \(0.673059\pi\) | |||||||
\(54\) | −2.52930 | −0.344195 | ||||||||
\(55\) | −0.372642 | + | 7.40683i | −0.0502470 | + | 0.998737i | ||||
\(56\) | 15.0737 | + | 5.49199i | 2.01431 | + | 0.733898i | ||||
\(57\) | −4.28158 | −0.567110 | ||||||||
\(58\) | − | 21.9093i | − | 2.87683i | ||||||
\(59\) | − | 1.69675i | − | 0.220898i | −0.993882 | − | 0.110449i | \(-0.964771\pi\) | ||
0.993882 | − | 0.110449i | \(-0.0352289\pi\) | |||||||
\(60\) | −7.18448 | − | 6.71325i | −0.927512 | − | 0.866677i | ||||
\(61\) | 7.32231 | 0.937525 | 0.468763 | − | 0.883324i | \(-0.344700\pi\) | ||||
0.468763 | + | 0.883324i | \(0.344700\pi\) | |||||||
\(62\) | − | 7.99918i | − | 1.01590i | ||||||
\(63\) | −2.48590 | − | 0.905718i | −0.313193 | − | 0.114110i | ||||
\(64\) | −1.90553 | −0.238191 | ||||||||
\(65\) | 8.05257 | − | 8.61780i | 0.998798 | − | 1.06891i | ||||
\(66\) | 5.41211 | + | 6.40938i | 0.666185 | + | 0.788940i | ||||
\(67\) | − | 1.64438i | − | 0.200893i | −0.994942 | − | 0.100446i | \(-0.967973\pi\) | ||
0.994942 | − | 0.100446i | \(-0.0320271\pi\) | |||||||
\(68\) | − | 22.5131i | − | 2.73012i | ||||||
\(69\) | − | 1.22635i | − | 0.147635i | ||||||
\(70\) | −6.77541 | − | 13.3417i | −0.809817 | − | 1.59464i | ||||
\(71\) | −4.95049 | −0.587515 | −0.293758 | − | 0.955880i | \(-0.594906\pi\) | ||||
−0.293758 | + | 0.955880i | \(0.594906\pi\) | |||||||
\(72\) | −6.06368 | −0.714612 | ||||||||
\(73\) | − | 13.6548i | − | 1.59817i | −0.601218 | − | 0.799085i | \(-0.705318\pi\) | ||
0.601218 | − | 0.799085i | \(-0.294682\pi\) | |||||||
\(74\) | 9.58626i | 1.11438i | ||||||||
\(75\) | 0.338675 | + | 4.98852i | 0.0391069 | + | 0.576024i | ||||
\(76\) | −18.8277 | −2.15969 | ||||||||
\(77\) | 3.02409 | + | 8.23741i | 0.344627 | + | 0.938740i | ||||
\(78\) | − | 13.3412i | − | 1.51060i | ||||||
\(79\) | 2.01901i | 0.227157i | 0.993529 | + | 0.113578i | \(0.0362313\pi\) | ||||
−0.993529 | + | 0.113578i | \(0.963769\pi\) | |||||||
\(80\) | −10.6886 | − | 9.98757i | −1.19502 | − | 1.11664i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.0697 | −1.66417 | ||||||||
\(83\) | 3.14880i | 0.345626i | 0.984955 | + | 0.172813i | \(0.0552856\pi\) | ||||
−0.984955 | + | 0.172813i | \(0.944714\pi\) | |||||||
\(84\) | −10.9314 | − | 3.98278i | −1.19271 | − | 0.434557i | ||||
\(85\) | −7.81596 | + | 8.36459i | −0.847760 | + | 0.907267i | ||||
\(86\) | −19.9127 | −2.14724 | ||||||||
\(87\) | 8.66218i | 0.928683i | ||||||||
\(88\) | 12.9748 | + | 15.3657i | 1.38312 | + | 1.63799i | ||||
\(89\) | 4.88199i | 0.517489i | 0.965946 | + | 0.258745i | \(0.0833088\pi\) | ||||
−0.965946 | + | 0.258745i | \(0.916691\pi\) | |||||||
\(90\) | 4.13240 | + | 3.86136i | 0.435593 | + | 0.407023i | ||||
\(91\) | 4.77736 | − | 13.1123i | 0.500803 | − | 1.37454i | ||||
\(92\) | − | 5.39270i | − | 0.562228i | ||||||
\(93\) | 3.16260i | 0.327947i | ||||||||
\(94\) | 17.3297 | 1.78742 | ||||||||
\(95\) | 6.99530 | + | 6.53648i | 0.717703 | + | 0.670629i | ||||
\(96\) | −4.41970 | −0.451084 | ||||||||
\(97\) | 15.6959 | 1.59368 | 0.796838 | − | 0.604193i | \(-0.206505\pi\) | ||||
0.796838 | + | 0.604193i | \(0.206505\pi\) | |||||||
\(98\) | −13.5554 | − | 11.3896i | −1.36930 | − | 1.15052i | ||||
\(99\) | −2.13976 | − | 2.53405i | −0.215054 | − | 0.254682i | ||||
\(100\) | 1.48928 | + | 21.9364i | 0.148928 | + | 2.19364i | ||||
\(101\) | 3.17273 | 0.315699 | 0.157849 | − | 0.987463i | \(-0.449544\pi\) | ||||
0.157849 | + | 0.987463i | \(0.449544\pi\) | |||||||
\(102\) | 12.9492i | 1.28216i | ||||||||
\(103\) | 8.09081 | 0.797211 | 0.398605 | − | 0.917123i | \(-0.369494\pi\) | ||||
0.398605 | + | 0.917123i | \(0.369494\pi\) | |||||||
\(104\) | − | 31.9839i | − | 3.13628i | ||||||
\(105\) | 2.67877 | + | 5.27487i | 0.261421 | + | 0.514774i | ||||
\(106\) | − | 31.5171i | − | 3.06121i | ||||||
\(107\) | −11.5492 | −1.11650 | −0.558250 | − | 0.829673i | \(-0.688527\pi\) | ||||
−0.558250 | + | 0.829673i | \(0.688527\pi\) | |||||||
\(108\) | 4.39737 | 0.423137 | ||||||||
\(109\) | 12.2689i | 1.17515i | 0.809171 | + | 0.587573i | \(0.199917\pi\) | ||||
−0.809171 | + | 0.587573i | \(0.800083\pi\) | |||||||
\(110\) | 0.942524 | − | 18.7341i | 0.0898661 | − | 1.78623i | ||||
\(111\) | − | 3.79008i | − | 0.359738i | ||||||
\(112\) | −16.2631 | − | 5.92534i | −1.53672 | − | 0.559892i | ||||
\(113\) | 5.43099i | 0.510904i | 0.966822 | + | 0.255452i | \(0.0822243\pi\) | ||||
−0.966822 | + | 0.255452i | \(0.917776\pi\) | |||||||
\(114\) | 10.8294 | 1.01427 | ||||||||
\(115\) | −1.87220 | + | 2.00362i | −0.174584 | + | 0.186838i | ||||
\(116\) | 38.0908i | 3.53664i | ||||||||
\(117\) | 5.27466i | 0.487643i | ||||||||
\(118\) | 4.29160i | 0.395073i | ||||||||
\(119\) | −4.63699 | + | 12.7270i | −0.425072 | + | 1.16668i | ||||
\(120\) | 9.90691 | + | 9.25713i | 0.904373 | + | 0.845056i | ||||
\(121\) | −1.84283 | + | 10.8445i | −0.167530 | + | 0.985867i | ||||
\(122\) | −18.5203 | −1.67675 | ||||||||
\(123\) | 5.95804 | 0.537218 | ||||||||
\(124\) | 13.9071i | 1.24890i | ||||||||
\(125\) | 7.06239 | − | 8.66733i | 0.631679 | − | 0.775230i | ||||
\(126\) | 6.28758 | + | 2.29084i | 0.560142 | + | 0.204084i | ||||
\(127\) | 14.9817 | 1.32941 | 0.664707 | − | 0.747104i | \(-0.268556\pi\) | ||||
0.664707 | + | 0.747104i | \(0.268556\pi\) | |||||||
\(128\) | 13.6591 | 1.20730 | ||||||||
\(129\) | 7.87280 | 0.693162 | ||||||||
\(130\) | −20.3674 | + | 21.7970i | −1.78634 | + | 1.91173i | ||||
\(131\) | −0.877747 | −0.0766891 | −0.0383446 | − | 0.999265i | \(-0.512208\pi\) | ||||
−0.0383446 | + | 0.999265i | \(0.512208\pi\) | |||||||
\(132\) | −9.40934 | − | 11.1432i | −0.818978 | − | 0.969888i | ||||
\(133\) | 10.6436 | + | 3.87791i | 0.922915 | + | 0.336257i | ||||
\(134\) | 4.15913i | 0.359294i | ||||||||
\(135\) | −1.63381 | − | 1.52665i | −0.140616 | − | 0.131393i | ||||
\(136\) | 31.0441i | 2.66201i | ||||||||
\(137\) | 19.7845i | 1.69030i | 0.534529 | + | 0.845150i | \(0.320489\pi\) | ||||
−0.534529 | + | 0.845150i | \(0.679511\pi\) | |||||||
\(138\) | 3.10180i | 0.264043i | ||||||||
\(139\) | −11.5988 | −0.983800 | −0.491900 | − | 0.870652i | \(-0.663697\pi\) | ||||
−0.491900 | + | 0.870652i | \(0.663697\pi\) | |||||||
\(140\) | 11.7795 | + | 23.1956i | 0.995553 | + | 1.96038i | ||||
\(141\) | −6.85157 | −0.577006 | ||||||||
\(142\) | 12.5213 | 1.05076 | ||||||||
\(143\) | 13.3663 | − | 11.2865i | 1.11774 | − | 0.943827i | ||||
\(144\) | 6.54214 | 0.545179 | ||||||||
\(145\) | 13.2241 | − | 14.1524i | 1.09820 | − | 1.17529i | ||||
\(146\) | 34.5371i | 2.85831i | ||||||||
\(147\) | 5.35935 | + | 4.50304i | 0.442032 | + | 0.371404i | ||||
\(148\) | − | 16.6664i | − | 1.36997i | ||||||
\(149\) | 6.43246i | 0.526967i | 0.964664 | + | 0.263484i | \(0.0848715\pi\) | ||||
−0.964664 | + | 0.263484i | \(0.915128\pi\) | |||||||
\(150\) | −0.856613 | − | 12.6175i | −0.0699421 | − | 1.03021i | ||||
\(151\) | 20.2373i | 1.64689i | 0.567396 | + | 0.823445i | \(0.307951\pi\) | ||||
−0.567396 | + | 0.823445i | \(0.692049\pi\) | |||||||
\(152\) | 25.9622 | 2.10581 | ||||||||
\(153\) | − | 5.11968i | − | 0.413902i | ||||||
\(154\) | −7.64884 | − | 20.8349i | −0.616361 | − | 1.67892i | ||||
\(155\) | 4.82819 | − | 5.16709i | 0.387809 | − | 0.415031i | ||||
\(156\) | 23.1947i | 1.85706i | ||||||||
\(157\) | −19.2805 | −1.53876 | −0.769378 | − | 0.638794i | \(-0.779434\pi\) | ||||
−0.769378 | + | 0.638794i | \(0.779434\pi\) | |||||||
\(158\) | − | 5.10670i | − | 0.406267i | ||||||
\(159\) | 12.4608i | 0.988205i | ||||||||
\(160\) | 7.22095 | + | 6.74734i | 0.570866 | + | 0.533424i | ||||
\(161\) | −1.11072 | + | 3.04857i | −0.0875373 | + | 0.240261i | ||||
\(162\) | −2.52930 | −0.198721 | ||||||||
\(163\) | 17.2041i | 1.34753i | 0.738946 | + | 0.673765i | \(0.235324\pi\) | ||||
−0.738946 | + | 0.673765i | \(0.764676\pi\) | |||||||
\(164\) | 26.1997 | 2.04585 | ||||||||
\(165\) | −0.372642 | + | 7.40683i | −0.0290101 | + | 0.576621i | ||||
\(166\) | − | 7.96427i | − | 0.618147i | ||||||
\(167\) | 5.88119i | 0.455100i | 0.973766 | + | 0.227550i | \(0.0730716\pi\) | ||||
−0.973766 | + | 0.227550i | \(0.926928\pi\) | |||||||
\(168\) | 15.0737 | + | 5.49199i | 1.16296 | + | 0.423716i | ||||
\(169\) | −14.8221 | −1.14016 | ||||||||
\(170\) | 19.7689 | − | 21.1566i | 1.51621 | − | 1.62264i | ||||
\(171\) | −4.28158 | −0.327421 | ||||||||
\(172\) | 34.6197 | 2.63972 | ||||||||
\(173\) | 1.71236i | 0.130188i | 0.997879 | + | 0.0650941i | \(0.0207348\pi\) | ||||
−0.997879 | + | 0.0650941i | \(0.979265\pi\) | |||||||
\(174\) | − | 21.9093i | − | 1.66094i | ||||||
\(175\) | 3.67628 | − | 12.7077i | 0.277901 | − | 0.960610i | ||||
\(176\) | −13.9986 | − | 16.5781i | −1.05519 | − | 1.24962i | ||||
\(177\) | − | 1.69675i | − | 0.127536i | ||||||
\(178\) | − | 12.3480i | − | 0.925523i | ||||||
\(179\) | −7.42437 | −0.554924 | −0.277462 | − | 0.960737i | \(-0.589493\pi\) | ||||
−0.277462 | + | 0.960737i | \(0.589493\pi\) | |||||||
\(180\) | −7.18448 | − | 6.71325i | −0.535499 | − | 0.500376i | ||||
\(181\) | 7.98549i | 0.593556i | 0.954946 | + | 0.296778i | \(0.0959122\pi\) | ||||
−0.954946 | + | 0.296778i | \(0.904088\pi\) | |||||||
\(182\) | −12.0834 | + | 33.1649i | −0.895680 | + | 2.45834i | ||||
\(183\) | 7.32231 | 0.541281 | ||||||||
\(184\) | 7.43617i | 0.548202i | ||||||||
\(185\) | −5.78613 | + | 6.19227i | −0.425405 | + | 0.455265i | ||||
\(186\) | − | 7.99918i | − | 0.586528i | ||||||
\(187\) | −12.9735 | + | 10.9549i | −0.948719 | + | 0.801102i | ||||
\(188\) | −30.1289 | −2.19738 | ||||||||
\(189\) | −2.48590 | − | 0.905718i | −0.180822 | − | 0.0658813i | ||||
\(190\) | −17.6932 | − | 16.5327i | −1.28360 | − | 1.19941i | ||||
\(191\) | 1.11911 | 0.0809760 | 0.0404880 | − | 0.999180i | \(-0.487109\pi\) | ||||
0.0404880 | + | 0.999180i | \(0.487109\pi\) | |||||||
\(192\) | −1.90553 | −0.137520 | ||||||||
\(193\) | −25.2805 | −1.81973 | −0.909865 | − | 0.414904i | \(-0.863815\pi\) | ||||
−0.909865 | + | 0.414904i | \(0.863815\pi\) | |||||||
\(194\) | −39.6996 | −2.85027 | ||||||||
\(195\) | 8.05257 | − | 8.61780i | 0.576656 | − | 0.617134i | ||||
\(196\) | 23.5671 | + | 19.8015i | 1.68336 | + | 1.41440i | ||||
\(197\) | 17.1708 | 1.22337 | 0.611683 | − | 0.791103i | \(-0.290493\pi\) | ||||
0.611683 | + | 0.791103i | \(0.290493\pi\) | |||||||
\(198\) | 5.41211 | + | 6.40938i | 0.384622 | + | 0.455495i | ||||
\(199\) | − | 23.6135i | − | 1.67392i | −0.547267 | − | 0.836958i | \(-0.684332\pi\) | ||
0.547267 | − | 0.836958i | \(-0.315668\pi\) | |||||||
\(200\) | −2.05362 | − | 30.2488i | −0.145213 | − | 2.13891i | ||||
\(201\) | − | 1.64438i | − | 0.115986i | ||||||
\(202\) | −8.02481 | −0.564623 | ||||||||
\(203\) | 7.84549 | − | 21.5333i | 0.550645 | − | 1.51134i | ||||
\(204\) | − | 22.5131i | − | 1.57624i | ||||||
\(205\) | −9.73430 | − | 9.09584i | −0.679873 | − | 0.635281i | ||||
\(206\) | −20.4641 | −1.42580 | ||||||||
\(207\) | − | 1.22635i | − | 0.0852369i | ||||||
\(208\) | 34.5076i | 2.39267i | ||||||||
\(209\) | 9.16158 | + | 10.8498i | 0.633720 | + | 0.750493i | ||||
\(210\) | −6.77541 | − | 13.3417i | −0.467548 | − | 0.920667i | ||||
\(211\) | 6.53077i | 0.449597i | 0.974405 | + | 0.224798i | \(0.0721724\pi\) | ||||
−0.974405 | + | 0.224798i | \(0.927828\pi\) | |||||||
\(212\) | 54.7948i | 3.76332i | ||||||||
\(213\) | −4.95049 | −0.339202 | ||||||||
\(214\) | 29.2113 | 1.99685 | ||||||||
\(215\) | −12.8627 | − | 12.0190i | −0.877227 | − | 0.819690i | ||||
\(216\) | −6.06368 | −0.412581 | ||||||||
\(217\) | 2.86443 | − | 7.86190i | 0.194450 | − | 0.533700i | ||||
\(218\) | − | 31.0317i | − | 2.10173i | ||||||
\(219\) | − | 13.6548i | − | 0.922704i | ||||||
\(220\) | −1.63865 | + | 32.5706i | −0.110477 | + | 2.19591i | ||||
\(221\) | 27.0046 | 1.81653 | ||||||||
\(222\) | 9.58626i | 0.643388i | ||||||||
\(223\) | 18.7020 | 1.25238 | 0.626189 | − | 0.779671i | \(-0.284614\pi\) | ||||
0.626189 | + | 0.779671i | \(0.284614\pi\) | |||||||
\(224\) | 10.9869 | + | 4.00300i | 0.734094 | + | 0.267462i | ||||
\(225\) | 0.338675 | + | 4.98852i | 0.0225784 | + | 0.332568i | ||||
\(226\) | − | 13.7366i | − | 0.913746i | ||||||
\(227\) | 20.9094i | 1.38780i | 0.720070 | + | 0.693902i | \(0.244110\pi\) | ||||
−0.720070 | + | 0.693902i | \(0.755890\pi\) | |||||||
\(228\) | −18.8277 | −1.24690 | ||||||||
\(229\) | − | 8.20518i | − | 0.542214i | −0.962549 | − | 0.271107i | \(-0.912610\pi\) | ||
0.962549 | − | 0.271107i | \(-0.0873896\pi\) | |||||||
\(230\) | 4.73536 | − | 5.06775i | 0.312241 | − | 0.334158i | ||||
\(231\) | 3.02409 | + | 8.23741i | 0.198971 | + | 0.541982i | ||||
\(232\) | − | 52.5247i | − | 3.44842i | ||||||
\(233\) | −12.1849 | −0.798261 | −0.399131 | − | 0.916894i | \(-0.630688\pi\) | ||||
−0.399131 | + | 0.916894i | \(0.630688\pi\) | |||||||
\(234\) | − | 13.3412i | − | 0.872143i | ||||||
\(235\) | 11.1942 | + | 10.4599i | 0.730227 | + | 0.682332i | ||||
\(236\) | − | 7.46125i | − | 0.485686i | ||||||
\(237\) | 2.01901i | 0.131149i | ||||||||
\(238\) | 11.7283 | − | 32.1904i | 0.760236 | − | 2.08659i | ||||
\(239\) | 5.67839i | 0.367304i | 0.982991 | + | 0.183652i | \(0.0587920\pi\) | ||||
−0.982991 | + | 0.183652i | \(0.941208\pi\) | |||||||
\(240\) | −10.6886 | − | 9.98757i | −0.689948 | − | 0.644695i | ||||
\(241\) | −18.7726 | −1.20925 | −0.604624 | − | 0.796511i | \(-0.706677\pi\) | ||||
−0.604624 | + | 0.796511i | \(0.706677\pi\) | |||||||
\(242\) | 4.66106 | − | 27.4291i | 0.299625 | − | 1.76321i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 32.1989 | 2.06132 | ||||||||
\(245\) | −1.88159 | − | 15.5390i | −0.120211 | − | 0.992748i | ||||
\(246\) | −15.0697 | −0.960808 | ||||||||
\(247\) | − | 22.5839i | − | 1.43698i | ||||||
\(248\) | − | 19.1770i | − | 1.21774i | ||||||
\(249\) | 3.14880i | 0.199547i | ||||||||
\(250\) | −17.8629 | + | 21.9223i | −1.12975 | + | 1.38649i | ||||
\(251\) | − | 2.11549i | − | 0.133528i | −0.997769 | − | 0.0667642i | \(-0.978732\pi\) | ||
0.997769 | − | 0.0667642i | \(-0.0212675\pi\) | |||||||
\(252\) | −10.9314 | − | 3.98278i | −0.688614 | − | 0.250892i | ||||
\(253\) | −3.10762 | + | 2.62409i | −0.195375 | + | 0.164975i | ||||
\(254\) | −37.8934 | −2.37764 | ||||||||
\(255\) | −7.81596 | + | 8.36459i | −0.489455 | + | 0.523811i | ||||
\(256\) | −30.7368 | −1.92105 | ||||||||
\(257\) | 14.8176 | 0.924296 | 0.462148 | − | 0.886803i | \(-0.347079\pi\) | ||||
0.462148 | + | 0.886803i | \(0.347079\pi\) | |||||||
\(258\) | −19.9127 | −1.23971 | ||||||||
\(259\) | −3.43274 | + | 9.42174i | −0.213300 | + | 0.585438i | ||||
\(260\) | 35.4102 | − | 37.8957i | 2.19604 | − | 2.35019i | ||||
\(261\) | 8.66218i | 0.536175i | ||||||||
\(262\) | 2.22009 | 0.137157 | ||||||||
\(263\) | −13.1506 | −0.810903 | −0.405452 | − | 0.914117i | \(-0.632886\pi\) | ||||
−0.405452 | + | 0.914117i | \(0.632886\pi\) | |||||||
\(264\) | 12.9748 | + | 15.3657i | 0.798547 | + | 0.945692i | ||||
\(265\) | 19.0233 | − | 20.3586i | 1.16859 | − | 1.25062i | ||||
\(266\) | −26.9208 | − | 9.80840i | −1.65062 | − | 0.601392i | ||||
\(267\) | 4.88199i | 0.298773i | ||||||||
\(268\) | − | 7.23095i | − | 0.441700i | ||||||
\(269\) | − | 19.7999i | − | 1.20722i | −0.797280 | − | 0.603610i | \(-0.793729\pi\) | ||
0.797280 | − | 0.603610i | \(-0.206271\pi\) | |||||||
\(270\) | 4.13240 | + | 3.86136i | 0.251490 | + | 0.234995i | ||||
\(271\) | 11.6788 | 0.709435 | 0.354718 | − | 0.934973i | \(-0.384577\pi\) | ||||
0.354718 | + | 0.934973i | \(0.384577\pi\) | |||||||
\(272\) | − | 33.4937i | − | 2.03085i | ||||||
\(273\) | 4.77736 | − | 13.1123i | 0.289139 | − | 0.793590i | ||||
\(274\) | − | 50.0409i | − | 3.02308i | ||||||
\(275\) | 11.9165 | − | 11.5325i | 0.718590 | − | 0.695434i | ||||
\(276\) | − | 5.39270i | − | 0.324602i | ||||||
\(277\) | 3.48113 | 0.209161 | 0.104580 | − | 0.994516i | \(-0.466650\pi\) | ||||
0.104580 | + | 0.994516i | \(0.466650\pi\) | |||||||
\(278\) | 29.3369 | 1.75951 | ||||||||
\(279\) | 3.16260i | 0.189340i | ||||||||
\(280\) | −16.2432 | − | 31.9851i | −0.970717 | − | 1.91148i | ||||
\(281\) | − | 22.0902i | − | 1.31779i | −0.752234 | − | 0.658896i | \(-0.771024\pi\) | ||
0.752234 | − | 0.658896i | \(-0.228976\pi\) | |||||||
\(282\) | 17.3297 | 1.03197 | ||||||||
\(283\) | 3.35901i | 0.199672i | 0.995004 | + | 0.0998361i | \(0.0318318\pi\) | ||||
−0.995004 | + | 0.0998361i | \(0.968168\pi\) | |||||||
\(284\) | −21.7692 | −1.29176 | ||||||||
\(285\) | 6.99530 | + | 6.53648i | 0.414366 | + | 0.387188i | ||||
\(286\) | −33.8073 | + | 28.5471i | −1.99907 | + | 1.68802i | ||||
\(287\) | −14.8111 | − | 5.39630i | −0.874269 | − | 0.318534i | ||||
\(288\) | −4.41970 | −0.260433 | ||||||||
\(289\) | −9.21113 | −0.541831 | ||||||||
\(290\) | −33.4478 | + | 35.7956i | −1.96412 | + | 2.10199i | ||||
\(291\) | 15.6959 | 0.920109 | ||||||||
\(292\) | − | 60.0451i | − | 3.51388i | ||||||
\(293\) | 13.6906i | 0.799812i | 0.916556 | + | 0.399906i | \(0.130957\pi\) | ||||
−0.916556 | + | 0.399906i | \(0.869043\pi\) | |||||||
\(294\) | −13.5554 | − | 11.3896i | −0.790568 | − | 0.664252i | ||||
\(295\) | −2.59035 | + | 2.77217i | −0.150816 | + | 0.161402i | ||||
\(296\) | 22.9818i | 1.33579i | ||||||||
\(297\) | −2.13976 | − | 2.53405i | −0.124162 | − | 0.147041i | ||||
\(298\) | − | 16.2696i | − | 0.942475i | ||||||
\(299\) | 6.46856 | 0.374087 | ||||||||
\(300\) | 1.48928 | + | 21.9364i | 0.0859837 | + | 1.26650i | ||||
\(301\) | −19.5710 | − | 7.13054i | −1.12805 | − | 0.410997i | ||||
\(302\) | − | 51.1863i | − | 2.94544i | ||||||
\(303\) | 3.17273 | 0.182269 | ||||||||
\(304\) | −28.0107 | −1.60653 | ||||||||
\(305\) | −11.9633 | − | 11.1786i | −0.685015 | − | 0.640085i | ||||
\(306\) | 12.9492i | 0.740258i | ||||||||
\(307\) | − | 3.58318i | − | 0.204503i | −0.994759 | − | 0.102251i | \(-0.967395\pi\) | ||
0.994759 | − | 0.102251i | \(-0.0326046\pi\) | |||||||
\(308\) | 13.2981 | + | 36.2230i | 0.757727 | + | 2.06399i | ||||
\(309\) | 8.09081 | 0.460270 | ||||||||
\(310\) | −12.2120 | + | 13.0691i | −0.693592 | + | 0.742277i | ||||
\(311\) | − | 4.38304i | − | 0.248540i | −0.992248 | − | 0.124270i | \(-0.960341\pi\) | ||
0.992248 | − | 0.124270i | \(-0.0396588\pi\) | |||||||
\(312\) | − | 31.9839i | − | 1.81073i | ||||||
\(313\) | −15.3099 | −0.865367 | −0.432683 | − | 0.901546i | \(-0.642433\pi\) | ||||
−0.432683 | + | 0.901546i | \(0.642433\pi\) | |||||||
\(314\) | 48.7663 | 2.75204 | ||||||||
\(315\) | 2.67877 | + | 5.27487i | 0.150931 | + | 0.297205i | ||||
\(316\) | 8.87836i | 0.499447i | ||||||||
\(317\) | 22.3499i | 1.25529i | 0.778499 | + | 0.627646i | \(0.215982\pi\) | ||||
−0.778499 | + | 0.627646i | \(0.784018\pi\) | |||||||
\(318\) | − | 31.5171i | − | 1.76739i | ||||||
\(319\) | 21.9504 | − | 18.5350i | 1.22899 | − | 1.03776i | ||||
\(320\) | 3.11328 | + | 2.90908i | 0.174037 | + | 0.162623i | ||||
\(321\) | −11.5492 | −0.644612 | ||||||||
\(322\) | 2.80936 | − | 7.71075i | 0.156559 | − | 0.429703i | ||||
\(323\) | 21.9203i | 1.21968i | ||||||||
\(324\) | 4.39737 | 0.244299 | ||||||||
\(325\) | −26.3128 | + | 1.78640i | −1.45957 | + | 0.0990916i | ||||
\(326\) | − | 43.5144i | − | 2.41004i | ||||||
\(327\) | 12.2689i | 0.678471i | ||||||||
\(328\) | −36.1276 | −1.99482 | ||||||||
\(329\) | 17.0323 | + | 6.20559i | 0.939020 | + | 0.342125i | ||||
\(330\) | 0.942524 | − | 18.7341i | 0.0518842 | − | 1.03128i | ||||
\(331\) | −17.0600 | −0.937702 | −0.468851 | − | 0.883277i | \(-0.655332\pi\) | ||||
−0.468851 | + | 0.883277i | \(0.655332\pi\) | |||||||
\(332\) | 13.8464i | 0.759922i | ||||||||
\(333\) | − | 3.79008i | − | 0.207695i | ||||||
\(334\) | − | 14.8753i | − | 0.813941i | ||||||
\(335\) | −2.51039 | + | 2.68660i | −0.137157 | + | 0.146785i | ||||
\(336\) | −16.2631 | − | 5.92534i | −0.887224 | − | 0.323254i | ||||
\(337\) | −11.7119 | −0.637989 | −0.318994 | − | 0.947757i | \(-0.603345\pi\) | ||||
−0.318994 | + | 0.947757i | \(0.603345\pi\) | |||||||
\(338\) | 37.4895 | 2.03916 | ||||||||
\(339\) | 5.43099i | 0.294971i | ||||||||
\(340\) | −34.3697 | + | 36.7822i | −1.86396 | + | 1.99480i | ||||
\(341\) | 8.01419 | − | 6.76722i | 0.433993 | − | 0.366465i | ||||
\(342\) | 10.8294 | 0.585588 | ||||||||
\(343\) | −9.24430 | − | 16.0481i | −0.499145 | − | 0.866518i | ||||
\(344\) | −47.7382 | −2.57387 | ||||||||
\(345\) | −1.87220 | + | 2.00362i | −0.100796 | + | 0.107871i | ||||
\(346\) | − | 4.33107i | − | 0.232840i | ||||||
\(347\) | −22.2943 | −1.19682 | −0.598411 | − | 0.801189i | \(-0.704201\pi\) | ||||
−0.598411 | + | 0.801189i | \(0.704201\pi\) | |||||||
\(348\) | 38.0908i | 2.04188i | ||||||||
\(349\) | −18.3957 | −0.984701 | −0.492351 | − | 0.870397i | \(-0.663862\pi\) | ||||
−0.492351 | + | 0.870397i | \(0.663862\pi\) | |||||||
\(350\) | −9.29842 | + | 32.1416i | −0.497022 | + | 1.71804i | ||||
\(351\) | 5.27466i | 0.281541i | ||||||||
\(352\) | 9.45711 | + | 11.1997i | 0.504066 | + | 0.596948i | ||||
\(353\) | −20.2639 | −1.07854 | −0.539270 | − | 0.842133i | \(-0.681300\pi\) | ||||
−0.539270 | + | 0.842133i | \(0.681300\pi\) | |||||||
\(354\) | 4.29160i | 0.228096i | ||||||||
\(355\) | 8.08817 | + | 7.55767i | 0.429275 | + | 0.401120i | ||||
\(356\) | 21.4679i | 1.13780i | ||||||||
\(357\) | −4.63699 | + | 12.7270i | −0.245415 | + | 0.673584i | ||||
\(358\) | 18.7785 | 0.992474 | ||||||||
\(359\) | 9.69378i | 0.511618i | 0.966727 | + | 0.255809i | \(0.0823418\pi\) | ||||
−0.966727 | + | 0.255809i | \(0.917658\pi\) | |||||||
\(360\) | 9.90691 | + | 9.25713i | 0.522140 | + | 0.487893i | ||||
\(361\) | −0.668034 | −0.0351597 | ||||||||
\(362\) | − | 20.1977i | − | 1.06157i | ||||||
\(363\) | −1.84283 | + | 10.8445i | −0.0967233 | + | 0.569191i | ||||
\(364\) | 21.0078 | − | 57.6595i | 1.10111 | − | 3.02218i | ||||
\(365\) | −20.8461 | + | 22.3093i | −1.09113 | + | 1.16772i | ||||
\(366\) | −18.5203 | −0.968073 | ||||||||
\(367\) | 35.0965 | 1.83202 | 0.916012 | − | 0.401152i | \(-0.131390\pi\) | ||||
0.916012 | + | 0.401152i | \(0.131390\pi\) | |||||||
\(368\) | − | 8.02293i | − | 0.418224i | ||||||
\(369\) | 5.95804 | 0.310163 | ||||||||
\(370\) | 14.6349 | − | 15.6621i | 0.760831 | − | 0.814236i | ||||
\(371\) | 11.2860 | − | 30.9762i | 0.585938 | − | 1.60821i | ||||
\(372\) | 13.9071i | 0.721052i | ||||||||
\(373\) | −1.01774 | −0.0526964 | −0.0263482 | − | 0.999653i | \(-0.508388\pi\) | ||||
−0.0263482 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(374\) | 32.8140 | − | 27.7083i | 1.69677 | − | 1.43276i | ||||
\(375\) | 7.06239 | − | 8.66733i | 0.364700 | − | 0.447579i | ||||
\(376\) | 41.5457 | 2.14256 | ||||||||
\(377\) | −45.6901 | −2.35316 | ||||||||
\(378\) | 6.28758 | + | 2.29084i | 0.323398 | + | 0.117828i | ||||
\(379\) | 24.1247 | 1.23920 | 0.619601 | − | 0.784917i | \(-0.287294\pi\) | ||||
0.619601 | + | 0.784917i | \(0.287294\pi\) | |||||||
\(380\) | 30.7609 | + | 28.7434i | 1.57800 | + | 1.47450i | ||||
\(381\) | 14.9817 | 0.767538 | ||||||||
\(382\) | −2.83057 | −0.144825 | ||||||||
\(383\) | −15.1817 | −0.775749 | −0.387875 | − | 0.921712i | \(-0.626791\pi\) | ||||
−0.387875 | + | 0.921712i | \(0.626791\pi\) | |||||||
\(384\) | 13.6591 | 0.697036 | ||||||||
\(385\) | 7.63485 | − | 18.0751i | 0.389108 | − | 0.921192i | ||||
\(386\) | 63.9421 | 3.25456 | ||||||||
\(387\) | 7.87280 | 0.400197 | ||||||||
\(388\) | 69.0207 | 3.50399 | ||||||||
\(389\) | −1.96963 | −0.0998644 | −0.0499322 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499322 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(390\) | −20.3674 | + | 21.7970i | −1.03134 | + | 1.10374i | ||||
\(391\) | −6.27850 | −0.317517 | ||||||||
\(392\) | −32.4974 | − | 27.3050i | −1.64137 | − | 1.37911i | ||||
\(393\) | −0.877747 | −0.0442765 | ||||||||
\(394\) | −43.4301 | −2.18798 | ||||||||
\(395\) | 3.08233 | − | 3.29869i | 0.155089 | − | 0.165975i | ||||
\(396\) | −9.40934 | − | 11.1432i | −0.472837 | − | 0.559965i | ||||
\(397\) | −2.33578 | −0.117229 | −0.0586146 | − | 0.998281i | \(-0.518668\pi\) | ||||
−0.0586146 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(398\) | 59.7257i | 2.99378i | ||||||||
\(399\) | 10.6436 | + | 3.87791i | 0.532845 | + | 0.194138i | ||||
\(400\) | 2.21566 | + | 32.6356i | 0.110783 | + | 1.63178i | ||||
\(401\) | 30.6222 | 1.52920 | 0.764600 | − | 0.644505i | \(-0.222936\pi\) | ||||
0.764600 | + | 0.644505i | \(0.222936\pi\) | |||||||
\(402\) | 4.15913i | 0.207439i | ||||||||
\(403\) | −16.6817 | −0.830973 | ||||||||
\(404\) | 13.9517 | 0.694123 | ||||||||
\(405\) | −1.63381 | − | 1.52665i | −0.0811847 | − | 0.0758599i | ||||
\(406\) | −19.8436 | + | 54.4641i | −0.984822 | + | 2.70301i | ||||
\(407\) | −9.60425 | + | 8.10987i | −0.476065 | + | 0.401992i | ||||
\(408\) | 31.0441i | 1.53691i | ||||||||
\(409\) | 1.89620 | 0.0937609 | 0.0468804 | − | 0.998901i | \(-0.485072\pi\) | ||||
0.0468804 | + | 0.998901i | \(0.485072\pi\) | |||||||
\(410\) | 24.6210 | + | 23.0061i | 1.21594 | + | 1.13619i | ||||
\(411\) | 19.7845i | 0.975895i | ||||||||
\(412\) | 35.5783 | 1.75282 | ||||||||
\(413\) | −1.53678 | + | 4.21794i | −0.0756199 | + | 0.207551i | ||||
\(414\) | 3.10180i | 0.152445i | ||||||||
\(415\) | 4.80712 | − | 5.14454i | 0.235972 | − | 0.252536i | ||||
\(416\) | − | 23.3124i | − | 1.14299i | ||||||
\(417\) | −11.5988 | −0.567997 | ||||||||
\(418\) | −23.1724 | − | 27.4423i | −1.13340 | − | 1.34225i | ||||
\(419\) | − | 2.90534i | − | 0.141935i | −0.997479 | − | 0.0709677i | \(-0.977391\pi\) | ||
0.997479 | − | 0.0709677i | \(-0.0226087\pi\) | |||||||
\(420\) | 11.7795 | + | 23.1956i | 0.574783 | + | 1.13183i | ||||
\(421\) | 30.0571 | 1.46489 | 0.732446 | − | 0.680825i | \(-0.238379\pi\) | ||||
0.732446 | + | 0.680825i | \(0.238379\pi\) | |||||||
\(422\) | − | 16.5183i | − | 0.804098i | ||||||
\(423\) | −6.85157 | −0.333135 | ||||||||
\(424\) | − | 75.5583i | − | 3.66944i | ||||||
\(425\) | 25.5396 | − | 1.73391i | 1.23885 | − | 0.0841070i | ||||
\(426\) | 12.5213 | 0.606659 | ||||||||
\(427\) | −18.2025 | − | 6.63195i | −0.880880 | − | 0.320942i | ||||
\(428\) | −50.7860 | −2.45483 | ||||||||
\(429\) | 13.3663 | − | 11.2865i | 0.645329 | − | 0.544919i | ||||
\(430\) | 32.5336 | + | 30.3997i | 1.56891 | + | 1.46601i | ||||
\(431\) | − | 20.5074i | − | 0.987807i | −0.869517 | − | 0.493904i | \(-0.835570\pi\) | ||
0.869517 | − | 0.493904i | \(-0.164430\pi\) | |||||||
\(432\) | 6.54214 | 0.314759 | ||||||||
\(433\) | −30.0295 | −1.44313 | −0.721563 | − | 0.692349i | \(-0.756576\pi\) | ||||
−0.721563 | + | 0.692349i | \(0.756576\pi\) | |||||||
\(434\) | −7.24500 | + | 19.8851i | −0.347771 | + | 0.954516i | ||||
\(435\) | 13.2241 | − | 14.1524i | 0.634048 | − | 0.678554i | ||||
\(436\) | 53.9509i | 2.58378i | ||||||||
\(437\) | 5.25070i | 0.251175i | ||||||||
\(438\) | 34.5371i | 1.65024i | ||||||||
\(439\) | −25.5270 | −1.21834 | −0.609169 | − | 0.793041i | \(-0.708497\pi\) | ||||
−0.609169 | + | 0.793041i | \(0.708497\pi\) | |||||||
\(440\) | 2.25958 | − | 44.9127i | 0.107721 | − | 2.14113i | ||||
\(441\) | 5.35935 | + | 4.50304i | 0.255207 | + | 0.214430i | ||||
\(442\) | −68.3028 | −3.24883 | ||||||||
\(443\) | − | 14.5242i | − | 0.690065i | −0.938591 | − | 0.345032i | \(-0.887868\pi\) | ||
0.938591 | − | 0.345032i | \(-0.112132\pi\) | |||||||
\(444\) | − | 16.6664i | − | 0.790952i | ||||||
\(445\) | 7.45309 | − | 7.97624i | 0.353310 | − | 0.378110i | ||||
\(446\) | −47.3030 | −2.23986 | ||||||||
\(447\) | 6.43246i | 0.304245i | ||||||||
\(448\) | 4.73695 | + | 1.72587i | 0.223800 | + | 0.0815399i | ||||
\(449\) | 4.91667 | 0.232032 | 0.116016 | − | 0.993247i | \(-0.462988\pi\) | ||||
0.116016 | + | 0.993247i | \(0.462988\pi\) | |||||||
\(450\) | −0.856613 | − | 12.6175i | −0.0403811 | − | 0.594793i | ||||
\(451\) | −12.7488 | − | 15.0980i | −0.600317 | − | 0.710936i | ||||
\(452\) | 23.8821i | 1.12332i | ||||||||
\(453\) | 20.2373i | 0.950833i | ||||||||
\(454\) | − | 52.8861i | − | 2.48207i | ||||||
\(455\) | −27.8231 | + | 14.1296i | −1.30437 | + | 0.662406i | ||||
\(456\) | 25.9622 | 1.21579 | ||||||||
\(457\) | 30.2232 | 1.41378 | 0.706891 | − | 0.707323i | \(-0.250097\pi\) | ||||
0.706891 | + | 0.707323i | \(0.250097\pi\) | |||||||
\(458\) | 20.7534i | 0.969742i | ||||||||
\(459\) | − | 5.11968i | − | 0.238966i | ||||||
\(460\) | −8.23277 | + | 8.81065i | −0.383855 | + | 0.410799i | ||||
\(461\) | −21.0017 | −0.978146 | −0.489073 | − | 0.872243i | \(-0.662665\pi\) | ||||
−0.489073 | + | 0.872243i | \(0.662665\pi\) | |||||||
\(462\) | −7.64884 | − | 20.8349i | −0.355856 | − | 0.969327i | ||||
\(463\) | − | 15.0004i | − | 0.697126i | −0.937285 | − | 0.348563i | \(-0.886670\pi\) | ||
0.937285 | − | 0.348563i | \(-0.113330\pi\) | |||||||
\(464\) | 56.6692i | 2.63080i | ||||||||
\(465\) | 4.82819 | − | 5.16709i | 0.223902 | − | 0.239618i | ||||
\(466\) | 30.8194 | 1.42768 | ||||||||
\(467\) | 10.5444 | 0.487936 | 0.243968 | − | 0.969783i | \(-0.421551\pi\) | ||||
0.243968 | + | 0.969783i | \(0.421551\pi\) | |||||||
\(468\) | 23.1947i | 1.07217i | ||||||||
\(469\) | −1.48934 | + | 4.08775i | −0.0687715 | + | 0.188755i | ||||
\(470\) | −28.3134 | − | 26.4564i | −1.30600 | − | 1.22034i | ||||
\(471\) | −19.2805 | −0.888401 | ||||||||
\(472\) | 10.2886i | 0.473569i | ||||||||
\(473\) | −16.8459 | − | 19.9501i | −0.774577 | − | 0.917306i | ||||
\(474\) | − | 5.10670i | − | 0.234559i | ||||||
\(475\) | −1.45007 | − | 21.3588i | −0.0665336 | − | 0.980007i | ||||
\(476\) | −20.3906 | + | 55.9653i | −0.934600 | + | 2.56517i | ||||
\(477\) | 12.4608i | 0.570541i | ||||||||
\(478\) | − | 14.3624i | − | 0.656919i | ||||||
\(479\) | 29.2808 | 1.33787 | 0.668936 | − | 0.743320i | \(-0.266750\pi\) | ||||
0.668936 | + | 0.743320i | \(0.266750\pi\) | |||||||
\(480\) | 7.22095 | + | 6.74734i | 0.329590 | + | 0.307972i | ||||
\(481\) | 19.9914 | 0.911529 | ||||||||
\(482\) | 47.4815 | 2.16272 | ||||||||
\(483\) | −1.11072 | + | 3.04857i | −0.0505397 | + | 0.138715i | ||||
\(484\) | −8.10359 | + | 47.6875i | −0.368345 | + | 2.16761i | ||||
\(485\) | −25.6441 | − | 23.9621i | −1.16444 | − | 1.08806i | ||||
\(486\) | −2.52930 | −0.114732 | ||||||||
\(487\) | 8.75333i | 0.396651i | 0.980136 | + | 0.198326i | \(0.0635504\pi\) | ||||
−0.980136 | + | 0.198326i | \(0.936450\pi\) | |||||||
\(488\) | −44.4002 | −2.00990 | ||||||||
\(489\) | 17.2041i | 0.777997i | ||||||||
\(490\) | 4.75912 | + | 39.3028i | 0.214995 | + | 1.77552i | ||||
\(491\) | 8.44903i | 0.381299i | 0.981658 | + | 0.190650i | \(0.0610595\pi\) | ||||
−0.981658 | + | 0.190650i | \(0.938941\pi\) | |||||||
\(492\) | 26.1997 | 1.18117 | ||||||||
\(493\) | 44.3476 | 1.99731 | ||||||||
\(494\) | 57.1216i | 2.57002i | ||||||||
\(495\) | −0.372642 | + | 7.40683i | −0.0167490 | + | 0.332912i | ||||
\(496\) | 20.6902i | 0.929017i | ||||||||
\(497\) | 12.3064 | + | 4.48375i | 0.552018 | + | 0.201124i | ||||
\(498\) | − | 7.96427i | − | 0.356887i | ||||||
\(499\) | 0.908981 | 0.0406916 | 0.0203458 | − | 0.999793i | \(-0.493523\pi\) | ||||
0.0203458 | + | 0.999793i | \(0.493523\pi\) | |||||||
\(500\) | 31.0560 | − | 38.1135i | 1.38887 | − | 1.70449i | ||||
\(501\) | 5.88119i | 0.262752i | ||||||||
\(502\) | 5.35071i | 0.238814i | ||||||||
\(503\) | − | 17.3007i | − | 0.771402i | −0.922624 | − | 0.385701i | \(-0.873960\pi\) | ||
0.922624 | − | 0.385701i | \(-0.126040\pi\) | |||||||
\(504\) | 15.0737 | + | 5.49199i | 0.671435 | + | 0.244633i | ||||
\(505\) | −5.18365 | − | 4.84366i | −0.230669 | − | 0.215540i | ||||
\(506\) | 7.86012 | − | 6.63712i | 0.349425 | − | 0.295056i | ||||
\(507\) | −14.8221 | −0.658272 | ||||||||
\(508\) | 65.8803 | 2.92297 | ||||||||
\(509\) | 9.56749i | 0.424072i | 0.977262 | + | 0.212036i | \(0.0680093\pi\) | ||||
−0.977262 | + | 0.212036i | \(0.931991\pi\) | |||||||
\(510\) | 19.7689 | − | 21.1566i | 0.875383 | − | 0.936829i | ||||
\(511\) | −12.3674 | + | 33.9443i | −0.547100 | + | 1.50161i | ||||
\(512\) | 50.4247 | 2.22848 | ||||||||
\(513\) | −4.28158 | −0.189037 | ||||||||
\(514\) | −37.4782 | −1.65309 | ||||||||
\(515\) | −13.2188 | − | 12.3518i | −0.582492 | − | 0.544287i | ||||
\(516\) | 34.6197 | 1.52405 | ||||||||
\(517\) | 14.6607 | + | 17.3622i | 0.644778 | + | 0.763589i | ||||
\(518\) | 8.68245 | − | 23.8304i | 0.381485 | − | 1.04705i | ||||
\(519\) | 1.71236i | 0.0751642i | ||||||||
\(520\) | −48.8282 | + | 52.2556i | −2.14126 | + | 2.29156i | ||||
\(521\) | 0.937460i | 0.0410709i | 0.999789 | + | 0.0205354i | \(0.00653709\pi\) | ||||
−0.999789 | + | 0.0205354i | \(0.993463\pi\) | |||||||
\(522\) | − | 21.9093i | − | 0.958943i | ||||||
\(523\) | − | 10.0718i | − | 0.440409i | −0.975454 | − | 0.220205i | \(-0.929328\pi\) | ||
0.975454 | − | 0.220205i | \(-0.0706725\pi\) | |||||||
\(524\) | −3.85978 | −0.168615 | ||||||||
\(525\) | 3.67628 | − | 12.7077i | 0.160446 | − | 0.554608i | ||||
\(526\) | 33.2619 | 1.45029 | ||||||||
\(527\) | 16.1915 | 0.705313 | ||||||||
\(528\) | −13.9986 | − | 16.5781i | −0.609213 | − | 0.721470i | ||||
\(529\) | 21.4961 | 0.934612 | ||||||||
\(530\) | −48.1156 | + | 51.4930i | −2.09001 | + | 2.23671i | ||||
\(531\) | − | 1.69675i | − | 0.0736327i | ||||||
\(532\) | 46.8038 | + | 17.0526i | 2.02920 | + | 0.739324i | ||||
\(533\) | 31.4266i | 1.36124i | ||||||||
\(534\) | − | 12.3480i | − | 0.534351i | ||||||
\(535\) | 18.8692 | + | 17.6315i | 0.815785 | + | 0.762278i | ||||
\(536\) | 9.97099i | 0.430681i | ||||||||
\(537\) | −7.42437 | −0.320385 | ||||||||
\(538\) | 50.0799i | 2.15910i | ||||||||
\(539\) | −0.0568077 | − | 23.2163i | −0.00244688 | − | 0.999997i | ||||
\(540\) | −7.18448 | − | 6.71325i | −0.309171 | − | 0.288892i | ||||
\(541\) | − | 23.4799i | − | 1.00948i | −0.863272 | − | 0.504740i | \(-0.831589\pi\) | ||
0.863272 | − | 0.504740i | \(-0.168411\pi\) | |||||||
\(542\) | −29.5392 | −1.26882 | ||||||||
\(543\) | 7.98549i | 0.342690i | ||||||||
\(544\) | 22.6275i | 0.970144i | ||||||||
\(545\) | 18.7303 | − | 20.0450i | 0.802318 | − | 0.858636i | ||||
\(546\) | −12.0834 | + | 33.1649i | −0.517121 | + | 1.41933i | ||||
\(547\) | −0.147356 | −0.00630050 | −0.00315025 | − | 0.999995i | \(-0.501003\pi\) | ||||
−0.00315025 | + | 0.999995i | \(0.501003\pi\) | |||||||
\(548\) | 86.9996i | 3.71644i | ||||||||
\(549\) | 7.32231 | 0.312508 | ||||||||
\(550\) | −30.1404 | + | 29.1691i | −1.28519 | + | 1.24377i | ||||
\(551\) | − | 37.0878i | − | 1.58000i | ||||||
\(552\) | 7.43617i | 0.316504i | ||||||||
\(553\) | 1.82866 | − | 5.01906i | 0.0777625 | − | 0.213432i | ||||
\(554\) | −8.80483 | −0.374081 | ||||||||
\(555\) | −5.78613 | + | 6.19227i | −0.245607 | + | 0.262847i | ||||
\(556\) | −51.0044 | −2.16307 | ||||||||
\(557\) | −15.6424 | −0.662790 | −0.331395 | − | 0.943492i | \(-0.607519\pi\) | ||||
−0.331395 | + | 0.943492i | \(0.607519\pi\) | |||||||
\(558\) | − | 7.99918i | − | 0.338632i | ||||||
\(559\) | 41.5264i | 1.75638i | ||||||||
\(560\) | 17.5249 | + | 34.5089i | 0.740561 | + | 1.45827i | ||||
\(561\) | −12.9735 | + | 10.9549i | −0.547743 | + | 0.462516i | ||||
\(562\) | 55.8728i | 2.35685i | ||||||||
\(563\) | − | 41.6902i | − | 1.75703i | −0.477714 | − | 0.878515i | \(-0.658534\pi\) | ||
0.477714 | − | 0.878515i | \(-0.341466\pi\) | |||||||
\(564\) | −30.1289 | −1.26866 | ||||||||
\(565\) | 8.29122 | − | 8.87320i | 0.348814 | − | 0.373299i | ||||
\(566\) | − | 8.49594i | − | 0.357111i | ||||||
\(567\) | −2.48590 | − | 0.905718i | −0.104398 | − | 0.0380366i | ||||
\(568\) | 30.0182 | 1.25954 | ||||||||
\(569\) | 8.89030i | 0.372701i | 0.982483 | + | 0.186350i | \(0.0596660\pi\) | ||||
−0.982483 | + | 0.186350i | \(0.940334\pi\) | |||||||
\(570\) | −17.6932 | − | 16.5327i | −0.741088 | − | 0.692481i | ||||
\(571\) | 20.5378i | 0.859478i | 0.902953 | + | 0.429739i | \(0.141394\pi\) | ||||
−0.902953 | + | 0.429739i | \(0.858606\pi\) | |||||||
\(572\) | 58.7765 | − | 49.6311i | 2.45757 | − | 2.07518i | ||||
\(573\) | 1.11911 | 0.0467515 | ||||||||
\(574\) | 37.4616 | + | 13.6489i | 1.56362 | + | 0.569693i | ||||
\(575\) | 6.11765 | − | 0.415333i | 0.255123 | − | 0.0173206i | ||||
\(576\) | −1.90553 | −0.0793971 | ||||||||
\(577\) | −20.0840 | −0.836107 | −0.418054 | − | 0.908422i | \(-0.637288\pi\) | ||||
−0.418054 | + | 0.908422i | \(0.637288\pi\) | |||||||
\(578\) | 23.2977 | 0.969059 | ||||||||
\(579\) | −25.2805 | −1.05062 | ||||||||
\(580\) | 58.1514 | − | 62.2332i | 2.41460 | − | 2.58409i | ||||
\(581\) | 2.85192 | − | 7.82758i | 0.118318 | − | 0.324743i | ||||
\(582\) | −39.6996 | −1.64560 | ||||||||
\(583\) | 31.5763 | − | 26.6632i | 1.30776 | − | 1.10427i | ||||
\(584\) | 82.7982i | 3.42621i | ||||||||
\(585\) | 8.05257 | − | 8.61780i | 0.332933 | − | 0.356302i | ||||
\(586\) | − | 34.6276i | − | 1.43045i | ||||||
\(587\) | −27.5953 | −1.13898 | −0.569490 | − | 0.821998i | \(-0.692859\pi\) | ||||
−0.569490 | + | 0.821998i | \(0.692859\pi\) | |||||||
\(588\) | 23.5671 | + | 19.8015i | 0.971889 | + | 0.816602i | ||||
\(589\) | − | 13.5409i | − | 0.557945i | ||||||
\(590\) | 6.55177 | − | 7.01166i | 0.269732 | − | 0.288665i | ||||
\(591\) | 17.1708 | 0.706311 | ||||||||
\(592\) | − | 24.7952i | − | 1.01908i | ||||||
\(593\) | 40.9519i | 1.68169i | 0.541275 | + | 0.840846i | \(0.317942\pi\) | ||||
−0.541275 | + | 0.840846i | \(0.682058\pi\) | |||||||
\(594\) | 5.41211 | + | 6.40938i | 0.222062 | + | 0.262980i | ||||
\(595\) | 27.0056 | − | 13.7144i | 1.10712 | − | 0.562237i | ||||
\(596\) | 28.2859i | 1.15864i | ||||||||
\(597\) | − | 23.6135i | − | 0.966436i | ||||||
\(598\) | −16.3610 | −0.669049 | ||||||||
\(599\) | −16.4285 | −0.671251 | −0.335625 | − | 0.941996i | \(-0.608948\pi\) | ||||
−0.335625 | + | 0.941996i | \(0.608948\pi\) | |||||||
\(600\) | −2.05362 | − | 30.2488i | −0.0838387 | − | 1.23490i | ||||
\(601\) | 2.68019 | 0.109327 | 0.0546636 | − | 0.998505i | \(-0.482591\pi\) | ||||
0.0546636 | + | 0.998505i | \(0.482591\pi\) | |||||||
\(602\) | 49.5009 | + | 18.0353i | 2.01751 | + | 0.735064i | ||||
\(603\) | − | 1.64438i | − | 0.0669643i | ||||||
\(604\) | 88.9911i | 3.62100i | ||||||||
\(605\) | 19.5666 | − | 14.9046i | 0.795497 | − | 0.605957i | ||||
\(606\) | −8.02481 | −0.325985 | ||||||||
\(607\) | − | 26.9310i | − | 1.09309i | −0.837428 | − | 0.546547i | \(-0.815942\pi\) | ||
0.837428 | − | 0.546547i | \(-0.184058\pi\) | |||||||
\(608\) | 18.9233 | 0.767442 | ||||||||
\(609\) | 7.84549 | − | 21.5333i | 0.317915 | − | 0.872572i | ||||
\(610\) | 30.2587 | + | 28.2741i | 1.22514 | + | 1.14478i | ||||
\(611\) | − | 36.1397i | − | 1.46206i | ||||||
\(612\) | − | 22.5131i | − | 0.910040i | ||||||
\(613\) | −17.3037 | −0.698891 | −0.349445 | − | 0.936957i | \(-0.613630\pi\) | ||||
−0.349445 | + | 0.936957i | \(0.613630\pi\) | |||||||
\(614\) | 9.06295i | 0.365751i | ||||||||
\(615\) | −9.73430 | − | 9.09584i | −0.392525 | − | 0.366780i | ||||
\(616\) | −18.3371 | − | 49.9490i | −0.738824 | − | 2.01250i | ||||
\(617\) | − | 32.5802i | − | 1.31163i | −0.754923 | − | 0.655814i | \(-0.772326\pi\) | ||
0.754923 | − | 0.655814i | \(-0.227674\pi\) | |||||||
\(618\) | −20.4641 | −0.823187 | ||||||||
\(619\) | 30.1512i | 1.21188i | 0.795511 | + | 0.605940i | \(0.207203\pi\) | ||||
−0.795511 | + | 0.605940i | \(0.792797\pi\) | |||||||
\(620\) | 21.2313 | − | 22.7216i | 0.852671 | − | 0.912523i | ||||
\(621\) | − | 1.22635i | − | 0.0492116i | ||||||
\(622\) | 11.0860i | 0.444510i | ||||||||
\(623\) | 4.42170 | − | 12.1361i | 0.177152 | − | 0.486223i | ||||
\(624\) | 34.5076i | 1.38141i | ||||||||
\(625\) | −24.7706 | + | 3.37898i | −0.990824 | + | 0.135159i | ||||
\(626\) | 38.7234 | 1.54770 | ||||||||
\(627\) | 9.16158 | + | 10.8498i | 0.365878 | + | 0.433297i | ||||
\(628\) | −84.7838 | −3.38324 | ||||||||
\(629\) | −19.4040 | −0.773688 | ||||||||
\(630\) | −6.77541 | − | 13.3417i | −0.269939 | − | 0.531547i | ||||
\(631\) | −46.9350 | −1.86845 | −0.934227 | − | 0.356680i | \(-0.883909\pi\) | ||||
−0.934227 | + | 0.356680i | \(0.883909\pi\) | |||||||
\(632\) | − | 12.2427i | − | 0.486987i | ||||||
\(633\) | 6.53077i | 0.259575i | ||||||||
\(634\) | − | 56.5295i | − | 2.24508i | ||||||
\(635\) | −24.4773 | − | 22.8719i | −0.971353 | − | 0.907643i | ||||
\(636\) | 54.7948i | 2.17275i | ||||||||
\(637\) | −23.7520 | + | 28.2688i | −0.941089 | + | 1.12005i | ||||
\(638\) | −55.5192 | + | 46.8807i | −2.19803 | + | 1.85602i | ||||
\(639\) | −4.95049 | −0.195838 | ||||||||
\(640\) | −22.3163 | − | 20.8526i | −0.882130 | − | 0.824272i | ||||
\(641\) | 27.4786 | 1.08534 | 0.542670 | − | 0.839946i | \(-0.317413\pi\) | ||||
0.542670 | + | 0.839946i | \(0.317413\pi\) | |||||||
\(642\) | 29.2113 | 1.15288 | ||||||||
\(643\) | −4.30470 | −0.169761 | −0.0848805 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848805 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(644\) | −4.88426 | + | 13.4057i | −0.192467 | + | 0.528258i | ||||
\(645\) | −12.8627 | − | 12.0190i | −0.506467 | − | 0.473248i | ||||
\(646\) | − | 55.4432i | − | 2.18138i | ||||||
\(647\) | −11.8230 | −0.464808 | −0.232404 | − | 0.972619i | \(-0.574659\pi\) | ||||
−0.232404 | + | 0.972619i | \(0.574659\pi\) | |||||||
\(648\) | −6.06368 | −0.238204 | ||||||||
\(649\) | −4.29965 | + | 3.63064i | −0.168776 | + | 0.142515i | ||||
\(650\) | 66.5529 | − | 4.51834i | 2.61042 | − | 0.177224i | ||||
\(651\) | 2.86443 | − | 7.86190i | 0.112266 | − | 0.308132i | ||||
\(652\) | 75.6529i | 2.96280i | ||||||||
\(653\) | 10.1480i | 0.397121i | 0.980089 | + | 0.198561i | \(0.0636267\pi\) | ||||
−0.980089 | + | 0.198561i | \(0.936373\pi\) | |||||||
\(654\) | − | 31.0317i | − | 1.21344i | ||||||
\(655\) | 1.43407 | + | 1.34001i | 0.0560338 | + | 0.0523586i | ||||
\(656\) | 38.9783 | 1.52185 | ||||||||
\(657\) | − | 13.6548i | − | 0.532723i | ||||||
\(658\) | −43.0798 | − | 15.6958i | −1.67942 | − | 0.611886i | ||||
\(659\) | 25.3086i | 0.985882i | 0.870063 | + | 0.492941i | \(0.164078\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(660\) | −1.63865 | + | 32.5706i | −0.0637842 | + | 1.26781i | ||||
\(661\) | 38.8425i | 1.51080i | 0.655265 | + | 0.755399i | \(0.272557\pi\) | ||||
−0.655265 | + | 0.755399i | \(0.727443\pi\) | |||||||
\(662\) | 43.1499 | 1.67707 | ||||||||
\(663\) | 27.0046 | 1.04877 | ||||||||
\(664\) | − | 19.0933i | − | 0.740965i | ||||||
\(665\) | −11.4694 | − | 22.5848i | −0.444763 | − | 0.875800i | ||||
\(666\) | 9.58626i | 0.371460i | ||||||||
\(667\) | 10.6228 | 0.411317 | ||||||||
\(668\) | 25.8618i | 1.00062i | ||||||||
\(669\) | 18.7020 | 0.723061 | ||||||||
\(670\) | 6.34954 | − | 6.79523i | 0.245304 | − | 0.262523i | ||||
\(671\) | −15.6680 | − | 18.5551i | −0.604857 | − | 0.716312i | ||||
\(672\) | 10.9869 | + | 4.00300i | 0.423829 | + | 0.154419i | ||||
\(673\) | −3.24113 | −0.124936 | −0.0624681 | − | 0.998047i | \(-0.519897\pi\) | ||||
−0.0624681 | + | 0.998047i | \(0.519897\pi\) | |||||||
\(674\) | 29.6230 | 1.14103 | ||||||||
\(675\) | 0.338675 | + | 4.98852i | 0.0130356 | + | 0.192008i | ||||
\(676\) | −65.1782 | −2.50685 | ||||||||
\(677\) | 14.4950i | 0.557089i | 0.960423 | + | 0.278544i | \(0.0898520\pi\) | ||||
−0.960423 | + | 0.278544i | \(0.910148\pi\) | |||||||
\(678\) | − | 13.7366i | − | 0.527551i | ||||||
\(679\) | −39.0183 | − | 14.2160i | −1.49739 | − | 0.545562i | ||||
\(680\) | 47.3935 | − | 50.7202i | 1.81746 | − | 1.94503i | ||||
\(681\) | 20.9094i | 0.801249i | ||||||||
\(682\) | −20.2703 | + | 17.1163i | −0.776191 | + | 0.655419i | ||||
\(683\) | 17.8839i | 0.684309i | 0.939644 | + | 0.342154i | \(0.111157\pi\) | ||||
−0.939644 | + | 0.342154i | \(0.888843\pi\) | |||||||
\(684\) | −18.8277 | −0.719896 | ||||||||
\(685\) | 30.2040 | − | 32.3241i | 1.15403 | − | 1.23504i | ||||
\(686\) | 23.3816 | + | 40.5906i | 0.892715 | + | 1.54976i | ||||
\(687\) | − | 8.20518i | − | 0.313047i | ||||||
\(688\) | 51.5050 | 1.96361 | ||||||||
\(689\) | −65.7265 | −2.50398 | ||||||||
\(690\) | 4.73536 | − | 5.06775i | 0.180272 | − | 0.192926i | ||||
\(691\) | − | 49.9283i | − | 1.89936i | −0.313219 | − | 0.949681i | \(-0.601407\pi\) | ||
0.313219 | − | 0.949681i | \(-0.398593\pi\) | |||||||
\(692\) | 7.52988i | 0.286243i | ||||||||
\(693\) | 3.02409 | + | 8.23741i | 0.114876 | + | 0.312913i | ||||
\(694\) | 56.3891 | 2.14050 | ||||||||
\(695\) | 18.9503 | + | 17.7074i | 0.718825 | + | 0.671678i | ||||
\(696\) | − | 52.5247i | − | 1.99094i | ||||||
\(697\) | − | 30.5032i | − | 1.15539i | ||||||
\(698\) | 46.5284 | 1.76113 | ||||||||
\(699\) | −12.1849 | −0.460876 | ||||||||
\(700\) | 16.1660 | − | 55.8804i | 0.611016 | − | 2.11208i | ||||
\(701\) | 6.73723i | 0.254462i | 0.991873 | + | 0.127231i | \(0.0406089\pi\) | ||||
−0.991873 | + | 0.127231i | \(0.959391\pi\) | |||||||
\(702\) | − | 13.3412i | − | 0.503532i | ||||||
\(703\) | 16.2275i | 0.612034i | ||||||||
\(704\) | 4.07739 | + | 4.82871i | 0.153672 | + | 0.181989i | ||||
\(705\) | 11.1942 | + | 10.4599i | 0.421597 | + | 0.393944i | ||||
\(706\) | 51.2536 | 1.92896 | ||||||||
\(707\) | −7.88708 | − | 2.87360i | −0.296624 | − | 0.108073i | ||||
\(708\) | − | 7.46125i | − | 0.280411i | ||||||
\(709\) | −10.5335 | −0.395592 | −0.197796 | − | 0.980243i | \(-0.563378\pi\) | ||||
−0.197796 | + | 0.980243i | \(0.563378\pi\) | |||||||
\(710\) | −20.4574 | − | 19.1156i | −0.767754 | − | 0.717397i | ||||
\(711\) | 2.01901i | 0.0757190i | ||||||||
\(712\) | − | 29.6028i | − | 1.10941i | ||||||
\(713\) | 3.87844 | 0.145249 | ||||||||
\(714\) | 11.7283 | − | 32.1904i | 0.438922 | − | 1.20470i | ||||
\(715\) | −39.0685 | − | 1.96556i | −1.46108 | − | 0.0735078i | ||||
\(716\) | −32.6477 | −1.22010 | ||||||||
\(717\) | 5.67839i | 0.212063i | ||||||||
\(718\) | − | 24.5185i | − | 0.915022i | ||||||
\(719\) | 53.0463i | 1.97830i | 0.146926 | + | 0.989148i | \(0.453062\pi\) | ||||
−0.146926 | + | 0.989148i | \(0.546938\pi\) | |||||||
\(720\) | −10.6886 | − | 9.98757i | −0.398342 | − | 0.372215i | ||||
\(721\) | −20.1129 | − | 7.32799i | −0.749043 | − | 0.272909i | ||||
\(722\) | 1.68966 | 0.0628827 | ||||||||
\(723\) | −18.7726 | −0.698160 | ||||||||
\(724\) | 35.1152i | 1.30504i | ||||||||
\(725\) | −43.2114 | + | 2.93367i | −1.60483 | + | 0.108954i | ||||
\(726\) | 4.66106 | − | 27.4291i | 0.172988 | − | 1.01799i | ||||
\(727\) | −38.0980 | −1.41298 | −0.706488 | − | 0.707725i | \(-0.749722\pi\) | ||||
−0.706488 | + | 0.707725i | \(0.749722\pi\) | |||||||
\(728\) | −28.9684 | + | 79.5086i | −1.07364 | + | 2.94678i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 52.7260 | − | 56.4270i | 1.95148 | − | 2.08846i | ||||
\(731\) | − | 40.3062i | − | 1.49078i | ||||||
\(732\) | 32.1989 | 1.19011 | ||||||||
\(733\) | 23.1051i | 0.853408i | 0.904391 | + | 0.426704i | \(0.140325\pi\) | ||||
−0.904391 | + | 0.426704i | \(0.859675\pi\) | |||||||
\(734\) | −88.7697 | −3.27655 | ||||||||
\(735\) | −1.88159 | − | 15.5390i | −0.0694036 | − | 0.573164i | ||||
\(736\) | 5.42008i | 0.199787i | ||||||||
\(737\) | −4.16694 | + | 3.51858i | −0.153491 | + | 0.129609i | ||||
\(738\) | −15.0697 | −0.554723 | ||||||||
\(739\) | − | 49.3616i | − | 1.81579i | −0.419193 | − | 0.907897i | \(-0.637687\pi\) | ||
0.419193 | − | 0.907897i | \(-0.362313\pi\) | |||||||
\(740\) | −25.4438 | + | 27.2297i | −0.935331 | + | 1.00098i | ||||
\(741\) | − | 22.5839i | − | 0.829641i | ||||||
\(742\) | −28.5456 | + | 78.3483i | −1.04794 | + | 2.87626i | ||||
\(743\) | 23.1357 | 0.848767 | 0.424384 | − | 0.905483i | \(-0.360491\pi\) | ||||
0.424384 | + | 0.905483i | \(0.360491\pi\) | |||||||
\(744\) | − | 19.1770i | − | 0.703063i | ||||||
\(745\) | 9.82012 | − | 10.5094i | 0.359781 | − | 0.385035i | ||||
\(746\) | 2.57416 | 0.0942468 | ||||||||
\(747\) | 3.14880i | 0.115209i | ||||||||
\(748\) | −57.0495 | + | 48.1728i | −2.08593 | + | 1.76137i | ||||
\(749\) | 28.7100 | + | 10.4603i | 1.04904 | + | 0.382211i | ||||
\(750\) | −17.8629 | + | 21.9223i | −0.652262 | + | 0.800489i | ||||
\(751\) | 19.0911 | 0.696643 | 0.348322 | − | 0.937375i | \(-0.386752\pi\) | ||||
0.348322 | + | 0.937375i | \(0.386752\pi\) | |||||||
\(752\) | −44.8239 | −1.63456 | ||||||||
\(753\) | − | 2.11549i | − | 0.0770927i | ||||||
\(754\) | 115.564 | 4.20859 | ||||||||
\(755\) | 30.8953 | − | 33.0640i | 1.12440 | − | 1.20332i | ||||
\(756\) | −10.9314 | − | 3.98278i | −0.397571 | − | 0.144852i | ||||
\(757\) | 50.0487i | 1.81905i | 0.415650 | + | 0.909525i | \(0.363554\pi\) | ||||
−0.415650 | + | 0.909525i | \(0.636446\pi\) | |||||||
\(758\) | −61.0187 | −2.21630 | ||||||||
\(759\) | −3.10762 | + | 2.62409i | −0.112800 | + | 0.0952484i | ||||
\(760\) | −42.4173 | − | 39.6352i | −1.53864 | − | 1.43772i | ||||
\(761\) | 2.79970 | 0.101489 | 0.0507444 | − | 0.998712i | \(-0.483841\pi\) | ||||
0.0507444 | + | 0.998712i | \(0.483841\pi\) | |||||||
\(762\) | −37.8934 | −1.37273 | ||||||||
\(763\) | 11.1122 | − | 30.4992i | 0.402287 | − | 1.10414i | ||||
\(764\) | 4.92115 | 0.178041 | ||||||||
\(765\) | −7.81596 | + | 8.36459i | −0.282587 | + | 0.302422i | ||||
\(766\) | 38.3991 | 1.38742 | ||||||||
\(767\) | 8.94979 | 0.323158 | ||||||||
\(768\) | −30.7368 | −1.10912 | ||||||||
\(769\) | −17.6150 | −0.635212 | −0.317606 | − | 0.948223i | \(-0.602879\pi\) | ||||
−0.317606 | + | 0.948223i | \(0.602879\pi\) | |||||||
\(770\) | −19.3108 | + | 45.7174i | −0.695915 | + | 1.64754i | ||||
\(771\) | 14.8176 | 0.533642 | ||||||||
\(772\) | −111.168 | −4.00102 | ||||||||
\(773\) | 19.1967 | 0.690457 | 0.345228 | − | 0.938519i | \(-0.387801\pi\) | ||||
0.345228 | + | 0.938519i | \(0.387801\pi\) | |||||||
\(774\) | −19.9127 | −0.715747 | ||||||||
\(775\) | −15.7767 | + | 1.07110i | −0.566716 | + | 0.0384749i | ||||
\(776\) | −95.1749 | −3.41658 | ||||||||
\(777\) | −3.43274 | + | 9.42174i | −0.123149 | + | 0.338003i | ||||
\(778\) | 4.98180 | 0.178606 | ||||||||
\(779\) | −25.5098 | −0.913985 | ||||||||
\(780\) | 35.4102 | − | 37.8957i | 1.26789 | − | 1.35688i | ||||
\(781\) | 10.5929 | + | 12.5448i | 0.379043 | + | 0.448888i | ||||
\(782\) | 15.8802 | 0.567876 | ||||||||
\(783\) | 8.66218i | 0.309561i | ||||||||
\(784\) | 35.0616 | + | 29.4595i | 1.25220 | + | 1.05213i | ||||
\(785\) | 31.5008 | + | 29.4347i | 1.12431 | + | 1.05057i | ||||
\(786\) | 2.22009 | 0.0791879 | ||||||||
\(787\) | 49.9063i | 1.77897i | 0.456966 | + | 0.889484i | \(0.348936\pi\) | ||||
−0.456966 | + | 0.889484i | \(0.651064\pi\) | |||||||
\(788\) | 75.5063 | 2.68980 | ||||||||
\(789\) | −13.1506 | −0.468175 | ||||||||
\(790\) | −7.79615 | + | 8.34338i | −0.277374 | + | 0.296844i | ||||
\(791\) | 4.91894 | − | 13.5009i | 0.174897 | − | 0.480035i | ||||
\(792\) | 12.9748 | + | 15.3657i | 0.461041 | + | 0.545996i | ||||
\(793\) | 38.6227i | 1.37153i | ||||||||
\(794\) | 5.90788 | 0.209663 | ||||||||
\(795\) | 19.0233 | − | 20.3586i | 0.674686 | − | 0.722044i | ||||
\(796\) | − | 103.837i | − | 3.68042i | ||||||
\(797\) | 50.0048 | 1.77126 | 0.885631 | − | 0.464390i | \(-0.153726\pi\) | ||||
0.885631 | + | 0.464390i | \(0.153726\pi\) | |||||||
\(798\) | −26.9208 | − | 9.80840i | −0.952986 | − | 0.347214i | ||||
\(799\) | 35.0778i | 1.24096i | ||||||||
\(800\) | −1.49684 | − | 22.0477i | −0.0529214 | − | 0.779505i | ||||
\(801\) | 4.88199i | 0.172496i | ||||||||
\(802\) | −77.4529 | −2.73496 | ||||||||
\(803\) | −34.6019 | + | 29.2180i | −1.22107 | + | 1.03108i | ||||
\(804\) | − | 7.23095i | − | 0.255016i | ||||||
\(805\) | 6.46881 | − | 3.28509i | 0.227996 | − | 0.115784i | ||||
\(806\) | 42.1930 | 1.48618 | ||||||||
\(807\) | − | 19.7999i | − | 0.696988i | ||||||
\(808\) | −19.2385 | −0.676806 | ||||||||
\(809\) | 3.95612i | 0.139090i | 0.997579 | + | 0.0695449i | \(0.0221547\pi\) | ||||
−0.997579 | + | 0.0695449i | \(0.977845\pi\) | |||||||
\(810\) | 4.13240 | + | 3.86136i | 0.145198 | + | 0.135674i | ||||
\(811\) | 15.5581 | 0.546318 | 0.273159 | − | 0.961969i | \(-0.411932\pi\) | ||||
0.273159 | + | 0.961969i | \(0.411932\pi\) | |||||||
\(812\) | 34.4995 | − | 94.6898i | 1.21070 | − | 3.32296i | ||||
\(813\) | 11.6788 | 0.409593 | ||||||||
\(814\) | 24.2921 | − | 20.5123i | 0.851437 | − | 0.718957i | ||||
\(815\) | 26.2647 | − | 28.1083i | 0.920011 | − | 0.984590i | ||||
\(816\) | − | 33.4937i | − | 1.17251i | ||||||
\(817\) | −33.7081 | −1.17930 | ||||||||
\(818\) | −4.79606 | −0.167690 | ||||||||
\(819\) | 4.77736 | − | 13.1123i | 0.166934 | − | 0.458180i | ||||
\(820\) | −42.8054 | − | 39.9978i | −1.49483 | − | 1.39678i | ||||
\(821\) | 12.6375i | 0.441052i | 0.975381 | + | 0.220526i | \(0.0707774\pi\) | ||||
−0.975381 | + | 0.220526i | \(0.929223\pi\) | |||||||
\(822\) | − | 50.0409i | − | 1.74538i | ||||||
\(823\) | 51.2750i | 1.78733i | 0.448730 | + | 0.893667i | \(0.351876\pi\) | ||||
−0.448730 | + | 0.893667i | \(0.648124\pi\) | |||||||
\(824\) | −49.0601 | −1.70909 | ||||||||
\(825\) | 11.9165 | − | 11.5325i | 0.414878 | − | 0.401509i | ||||
\(826\) | 3.88698 | − | 10.6685i | 0.135245 | − | 0.371203i | ||||
\(827\) | 40.9493 | 1.42395 | 0.711974 | − | 0.702206i | \(-0.247802\pi\) | ||||
0.711974 | + | 0.702206i | \(0.247802\pi\) | |||||||
\(828\) | − | 5.39270i | − | 0.187409i | ||||||
\(829\) | 5.57913i | 0.193771i | 0.995296 | + | 0.0968856i | \(0.0308881\pi\) | ||||
−0.995296 | + | 0.0968856i | \(0.969112\pi\) | |||||||
\(830\) | −12.1587 | + | 13.0121i | −0.422033 | + | 0.451657i | ||||
\(831\) | 3.48113 | 0.120759 | ||||||||
\(832\) | − | 10.0510i | − | 0.348457i | ||||||
\(833\) | 23.0541 | − | 27.4382i | 0.798778 | − | 0.950676i | ||||
\(834\) | 29.3369 | 1.01586 | ||||||||
\(835\) | 8.97853 | − | 9.60875i | 0.310715 | − | 0.332525i | ||||
\(836\) | 40.2869 | + | 47.7104i | 1.39335 | + | 1.65010i | ||||
\(837\) | 3.16260i | 0.109316i | ||||||||
\(838\) | 7.34850i | 0.253850i | ||||||||
\(839\) | 21.3749i | 0.737942i | 0.929441 | + | 0.368971i | \(0.120290\pi\) | ||||
−0.929441 | + | 0.368971i | \(0.879710\pi\) | |||||||
\(840\) | −16.2432 | − | 31.9851i | −0.560443 | − | 1.10359i | ||||
\(841\) | −46.0333 | −1.58736 | ||||||||
\(842\) | −76.0234 | −2.61994 | ||||||||
\(843\) | − | 22.0902i | − | 0.760827i | ||||||
\(844\) | 28.7182i | 0.988523i | ||||||||
\(845\) | 24.2165 | + | 22.6281i | 0.833072 | + | 0.778432i | ||||
\(846\) | 17.3297 | 0.595807 | ||||||||
\(847\) | 14.4032 | − | 25.2893i | 0.494899 | − | 0.868951i | ||||
\(848\) | 81.5203i | 2.79942i | ||||||||
\(849\) | 3.35901i | 0.115281i | ||||||||
\(850\) | −64.5974 | + | 4.38558i | −2.21567 | + | 0.150424i | ||||
\(851\) | −4.64795 | −0.159330 | ||||||||
\(852\) | −21.7692 | −0.745799 | ||||||||
\(853\) | − | 24.9537i | − | 0.854398i | −0.904158 | − | 0.427199i | \(-0.859500\pi\) | ||
0.904158 | − | 0.427199i | \(-0.140500\pi\) | |||||||
\(854\) | 46.0396 | + | 16.7742i | 1.57544 | + | 0.574001i | ||||
\(855\) | 6.99530 | + | 6.53648i | 0.239234 | + | 0.223543i | ||||
\(856\) | 70.0305 | 2.39359 | ||||||||
\(857\) | 26.2752i | 0.897543i | 0.893647 | + | 0.448771i | \(0.148138\pi\) | ||||
−0.893647 | + | 0.448771i | \(0.851862\pi\) | |||||||
\(858\) | −33.8073 | + | 28.5471i | −1.15416 | + | 0.974581i | ||||
\(859\) | − | 4.31760i | − | 0.147315i | −0.997284 | − | 0.0736573i | \(-0.976533\pi\) | ||
0.997284 | − | 0.0736573i | \(-0.0234671\pi\) | |||||||
\(860\) | −56.5620 | − | 52.8521i | −1.92875 | − | 1.80224i | ||||
\(861\) | −14.8111 | − | 5.39630i | −0.504759 | − | 0.183905i | ||||
\(862\) | 51.8695i | 1.76668i | ||||||||
\(863\) | − | 34.2800i | − | 1.16690i | −0.812147 | − | 0.583452i | \(-0.801702\pi\) | ||
0.812147 | − | 0.583452i | \(-0.198298\pi\) | |||||||
\(864\) | −4.41970 | −0.150361 | ||||||||
\(865\) | 2.61417 | − | 2.79767i | 0.0888846 | − | 0.0951237i | ||||
\(866\) | 75.9537 | 2.58101 | ||||||||
\(867\) | −9.21113 | −0.312826 | ||||||||
\(868\) | 12.5959 | − | 34.5717i | 0.427534 | − | 1.17344i | ||||
\(869\) | 5.11629 | − | 4.32021i | 0.173558 | − | 0.146553i | ||||
\(870\) | −33.4478 | + | 35.7956i | −1.13399 | + | 1.21358i | ||||
\(871\) | 8.67354 | 0.293892 | ||||||||
\(872\) | − | 74.3947i | − | 2.51932i | ||||||
\(873\) | 15.6959 | 0.531225 | ||||||||
\(874\) | − | 13.2806i | − | 0.449224i | ||||||
\(875\) | −25.4065 | + | 15.1495i | −0.858897 | + | 0.512148i | ||||
\(876\) | − | 60.0451i | − | 2.02874i | ||||||
\(877\) | 16.9574 | 0.572610 | 0.286305 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286305 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(878\) | 64.5655 | 2.17898 | ||||||||
\(879\) | 13.6906i | 0.461772i | ||||||||
\(880\) | −2.43788 | + | 48.4566i | −0.0821808 | + | 1.63347i | ||||
\(881\) | − | 24.9230i | − | 0.839678i | −0.907599 | − | 0.419839i | \(-0.862086\pi\) | ||
0.907599 | − | 0.419839i | \(-0.137914\pi\) | |||||||
\(882\) | −13.5554 | − | 11.3896i | −0.456435 | − | 0.383506i | ||||
\(883\) | − | 50.6335i | − | 1.70395i | −0.523579 | − | 0.851977i | \(-0.675403\pi\) | ||
0.523579 | − | 0.851977i | \(-0.324597\pi\) | |||||||
\(884\) | 118.749 | 3.99397 | ||||||||
\(885\) | −2.59035 | + | 2.77217i | −0.0870735 | + | 0.0931855i | ||||
\(886\) | 36.7361i | 1.23417i | ||||||||
\(887\) | 49.0775i | 1.64786i | 0.566691 | + | 0.823930i | \(0.308223\pi\) | ||||
−0.566691 | + | 0.823930i | \(0.691777\pi\) | |||||||
\(888\) | 22.9818i | 0.771220i | ||||||||
\(889\) | −37.2430 | − | 13.5692i | −1.24909 | − | 0.455097i | ||||
\(890\) | −18.8511 | + | 20.1743i | −0.631891 | + | 0.676245i | ||||
\(891\) | −2.13976 | − | 2.53405i | −0.0716848 | − | 0.0848939i | ||||
\(892\) | 82.2396 | 2.75359 | ||||||||
\(893\) | 29.3356 | 0.981677 | ||||||||
\(894\) | − | 16.2696i | − | 0.544138i | ||||||
\(895\) | 12.1300 | + | 11.3344i | 0.405462 | + | 0.378868i | ||||
\(896\) | −33.9550 | − | 12.3713i | −1.13436 | − | 0.413295i | ||||
\(897\) | 6.46856 | 0.215979 | ||||||||
\(898\) | −12.4357 | −0.414986 | ||||||||
\(899\) | −27.3950 | −0.913675 | ||||||||
\(900\) | 1.48928 | + | 21.9364i | 0.0496427 | + | 0.731212i | ||||
\(901\) | 63.7953 | 2.12533 | ||||||||
\(902\) | 32.2455 | + | 38.1873i | 1.07366 | + | 1.27150i | ||||
\(903\) | −19.5710 | − | 7.13054i | −0.651281 | − | 0.237290i | ||||
\(904\) | − | 32.9318i | − | 1.09529i | ||||||
\(905\) | 12.1910 | − | 13.0468i | 0.405244 | − | 0.433689i | ||||
\(906\) | − | 51.1863i | − | 1.70055i | ||||||
\(907\) | 14.0049i | 0.465025i | 0.972593 | + | 0.232512i | \(0.0746946\pi\) | ||||
−0.972593 | + | 0.232512i | \(0.925305\pi\) | |||||||
\(908\) | 91.9463i | 3.05135i | ||||||||
\(909\) | 3.17273 | 0.105233 | ||||||||
\(910\) | 70.3732 | − | 35.7380i | 2.33285 | − | 1.18470i | ||||
\(911\) | −14.3142 | −0.474252 | −0.237126 | − | 0.971479i | \(-0.576205\pi\) | ||||
−0.237126 | + | 0.971479i | \(0.576205\pi\) | |||||||
\(912\) | −28.0107 | −0.927528 | ||||||||
\(913\) | 7.97922 | − | 6.73769i | 0.264074 | − | 0.222985i | ||||
\(914\) | −76.4436 | −2.52853 | ||||||||
\(915\) | −11.9633 | − | 11.1786i | −0.395493 | − | 0.369553i | ||||
\(916\) | − | 36.0812i | − | 1.19216i | ||||||
\(917\) | 2.18199 | + | 0.794991i | 0.0720556 | + | 0.0262529i | ||||
\(918\) | 12.9492i | 0.427388i | ||||||||
\(919\) | 0.700370i | 0.0231031i | 0.999933 | + | 0.0115515i | \(0.00367705\pi\) | ||||
−0.999933 | + | 0.0115515i | \(0.996323\pi\) | |||||||
\(920\) | 11.3524 | − | 12.1493i | 0.374279 | − | 0.400550i | ||||
\(921\) | − | 3.58318i | − | 0.118070i | ||||||
\(922\) | 53.1196 | 1.74940 | ||||||||
\(923\) | − | 26.1122i | − | 0.859493i | ||||||
\(924\) | 13.2981 | + | 36.2230i | 0.437474 | + | 1.19165i | ||||
\(925\) | 18.9069 | − | 1.28361i | 0.621654 | − | 0.0422047i | ||||
\(926\) | 37.9405i | 1.24680i | ||||||||
\(927\) | 8.09081 | 0.265737 | ||||||||
\(928\) | − | 38.2842i | − | 1.25674i | ||||||
\(929\) | 10.7090i | 0.351351i | 0.984448 | + | 0.175675i | \(0.0562109\pi\) | ||||
−0.984448 | + | 0.175675i | \(0.943789\pi\) | |||||||
\(930\) | −12.2120 | + | 13.0691i | −0.400446 | + | 0.428554i | ||||
\(931\) | −22.9465 | − | 19.2801i | −0.752041 | − | 0.631881i | ||||
\(932\) | −53.5817 | −1.75513 | ||||||||
\(933\) | − | 4.38304i | − | 0.143494i | ||||||
\(934\) | −26.6699 | −0.872667 | ||||||||
\(935\) | 37.9206 | + | 1.90781i | 1.24014 | + | 0.0623920i | ||||
\(936\) | − | 31.9839i | − | 1.04543i | ||||||
\(937\) | 52.3296i | 1.70953i | 0.519013 | + | 0.854767i | \(0.326300\pi\) | ||||
−0.519013 | + | 0.854767i | \(0.673700\pi\) | |||||||
\(938\) | 3.76700 | − | 10.3392i | 0.122997 | − | 0.337586i | ||||
\(939\) | −15.3099 | −0.499620 | ||||||||
\(940\) | 49.2249 | + | 45.9963i | 1.60554 | + | 1.50023i | ||||
\(941\) | 18.6624 | 0.608375 | 0.304188 | − | 0.952612i | \(-0.401615\pi\) | ||||
0.304188 | + | 0.952612i | \(0.401615\pi\) | |||||||
\(942\) | 48.7663 | 1.58889 | ||||||||
\(943\) | − | 7.30661i | − | 0.237936i | ||||||
\(944\) | − | 11.1004i | − | 0.361287i | ||||||
\(945\) | 2.67877 | + | 5.27487i | 0.0871403 | + | 0.171591i | ||||
\(946\) | 42.6085 | + | 50.4598i | 1.38532 | + | 1.64059i | ||||
\(947\) | 9.59885i | 0.311921i | 0.987763 | + | 0.155960i | \(0.0498472\pi\) | ||||
−0.987763 | + | 0.155960i | \(0.950153\pi\) | |||||||
\(948\) | 8.87836i | 0.288356i | ||||||||
\(949\) | 72.0243 | 2.33801 | ||||||||
\(950\) | 3.66766 | + | 54.0228i | 0.118995 | + | 1.75273i | ||||
\(951\) | 22.3499i | 0.724744i | ||||||||
\(952\) | 28.1172 | − | 77.1724i | 0.911284 | − | 2.50117i | ||||
\(953\) | −14.5092 | −0.469999 | −0.235000 | − | 0.971995i | \(-0.575509\pi\) | ||||
−0.235000 | + | 0.971995i | \(0.575509\pi\) | |||||||
\(954\) | − | 31.5171i | − | 1.02040i | ||||||
\(955\) | −1.82841 | − | 1.70849i | −0.0591661 | − | 0.0552855i | ||||
\(956\) | 24.9700i | 0.807587i | ||||||||
\(957\) | 21.9504 | − | 18.5350i | 0.709556 | − | 0.599152i | ||||
\(958\) | −74.0599 | −2.39277 | ||||||||
\(959\) | 17.9191 | − | 49.1821i | 0.578639 | − | 1.58817i | ||||
\(960\) | 3.11328 | + | 2.90908i | 0.100481 | + | 0.0938902i | ||||
\(961\) | 20.9979 | 0.677353 | ||||||||
\(962\) | −50.5643 | −1.63026 | ||||||||
\(963\) | −11.5492 | −0.372167 | ||||||||
\(964\) | −82.5500 | −2.65876 | ||||||||
\(965\) | 41.3036 | + | 38.5945i | 1.32961 | + | 1.24240i | ||||
\(966\) | 2.80936 | − | 7.71075i | 0.0903895 | − | 0.248089i | ||||
\(967\) | −28.9914 | −0.932302 | −0.466151 | − | 0.884705i | \(-0.654360\pi\) | ||||
−0.466151 | + | 0.884705i | \(0.654360\pi\) | |||||||
\(968\) | 11.1743 | − | 65.7578i | 0.359156 | − | 2.11354i | ||||
\(969\) | 21.9203i | 0.704183i | ||||||||
\(970\) | 64.8617 | + | 60.6075i | 2.08258 | + | 1.94599i | ||||
\(971\) | 19.0976i | 0.612870i | 0.951892 | + | 0.306435i | \(0.0991362\pi\) | ||||
−0.951892 | + | 0.306435i | \(0.900864\pi\) | |||||||
\(972\) | 4.39737 | 0.141046 | ||||||||
\(973\) | 28.8335 | + | 10.5053i | 0.924359 | + | 0.336783i | ||||
\(974\) | − | 22.1398i | − | 0.709406i | ||||||
\(975\) | −26.3128 | + | 1.78640i | −0.842682 | + | 0.0572105i | ||||
\(976\) | 47.9036 | 1.53336 | ||||||||
\(977\) | 26.7156i | 0.854708i | 0.904084 | + | 0.427354i | \(0.140554\pi\) | ||||
−0.904084 | + | 0.427354i | \(0.859446\pi\) | |||||||
\(978\) | − | 43.5144i | − | 1.39144i | ||||||
\(979\) | 12.3712 | − | 10.4463i | 0.395385 | − | 0.333865i | ||||
\(980\) | −8.27407 | − | 68.3307i | −0.264305 | − | 2.18274i | ||||
\(981\) | 12.2689i | 0.391716i | ||||||||
\(982\) | − | 21.3702i | − | 0.681949i | ||||||
\(983\) | −53.8774 | −1.71842 | −0.859211 | − | 0.511621i | \(-0.829045\pi\) | ||||
−0.859211 | + | 0.511621i | \(0.829045\pi\) | |||||||
\(984\) | −36.1276 | −1.15171 | ||||||||
\(985\) | −28.0538 | − | 26.2138i | −0.893868 | − | 0.835240i | ||||
\(986\) | −112.168 | −3.57217 | ||||||||
\(987\) | 17.0323 | + | 6.20559i | 0.542143 | + | 0.197526i | ||||
\(988\) | − | 99.3099i | − | 3.15947i | ||||||
\(989\) | − | 9.65478i | − | 0.307004i | ||||||
\(990\) | 0.942524 | − | 18.7341i | 0.0299554 | − | 0.595409i | ||||
\(991\) | −53.8681 | −1.71118 | −0.855588 | − | 0.517657i | \(-0.826804\pi\) | ||||
−0.855588 | + | 0.517657i | \(0.826804\pi\) | |||||||
\(992\) | − | 13.9777i | − | 0.443794i | ||||||
\(993\) | −17.0600 | −0.541383 | ||||||||
\(994\) | −31.1266 | − | 11.3408i | −0.987277 | − | 0.359707i | ||||
\(995\) | −36.0496 | + | 38.5800i | −1.14285 | + | 1.22307i | ||||
\(996\) | 13.8464i | 0.438741i | ||||||||
\(997\) | − | 52.7933i | − | 1.67198i | −0.548745 | − | 0.835990i | \(-0.684894\pi\) | ||
0.548745 | − | 0.835990i | \(-0.315106\pi\) | |||||||
\(998\) | −2.29909 | −0.0727763 | ||||||||
\(999\) | − | 3.79008i | − | 0.119913i |
(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 | 1155.2.k.b.769.3 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.a.769.46 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.a.769.4 | yes | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.b.769.46 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.b.769.45 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.a.769.3 | ✓ | 48 | ||
77.76 | even | 2 | 1155.2.k.a.769.45 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.b.769.4 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.3 | ✓ | 48 | 55.54 | odd | 2 | ||
1155.2.k.a.769.4 | yes | 48 | 7.6 | odd | 2 | ||
1155.2.k.a.769.45 | yes | 48 | 77.76 | even | 2 | ||
1155.2.k.a.769.46 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.b.769.3 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.b.769.4 | yes | 48 | 385.384 | even | 2 | inner | |
1155.2.k.b.769.45 | yes | 48 | 35.34 | odd | 2 | inner | |
1155.2.k.b.769.46 | yes | 48 | 11.10 | odd | 2 | inner |