Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.796594176.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 275.4 | ||
Root | \(1.20711 + 0.0981308i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.275 |
Dual form | 392.3.k.j.67.4 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.97374 | + | 0.323042i | 0.986869 | + | 0.161521i | ||||
\(3\) | 0.292893 | + | 0.507306i | 0.0976311 | + | 0.169102i | 0.910704 | − | 0.413060i | \(-0.135540\pi\) |
−0.813073 | + | 0.582162i | \(0.802207\pi\) | |||||||
\(4\) | 3.79129 | + | 1.27520i | 0.947822 | + | 0.318800i | ||||
\(5\) | −7.82295 | − | 4.51658i | −1.56459 | − | 0.903316i | −0.996782 | − | 0.0801541i | \(-0.974459\pi\) |
−0.567807 | − | 0.823162i | \(-0.692208\pi\) | |||||||
\(6\) | 0.414214 | + | 1.09591i | 0.0690356 | + | 0.182651i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.07107 | + | 3.74166i | 0.883883 | + | 0.467707i | ||||
\(9\) | 4.32843 | − | 7.49706i | 0.480936 | − | 0.833006i | ||||
\(10\) | −13.9814 | − | 11.4417i | −1.39814 | − | 1.14417i | ||||
\(11\) | −6.24264 | − | 10.8126i | −0.567513 | − | 0.982961i | −0.996811 | − | 0.0797982i | \(-0.974572\pi\) |
0.429298 | − | 0.903163i | \(-0.358761\pi\) | |||||||
\(12\) | 0.463526 | + | 2.29684i | 0.0386271 | + | 0.191403i | ||||
\(13\) | − | 9.03316i | − | 0.694858i | −0.937706 | − | 0.347429i | \(-0.887055\pi\) | ||
0.937706 | − | 0.347429i | \(-0.112945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.29150i | − | 0.352767i | ||||||
\(16\) | 12.7477 | + | 9.66930i | 0.796733 | + | 0.604332i | ||||
\(17\) | 6.17157 | + | 10.6895i | 0.363034 | + | 0.628793i | 0.988459 | − | 0.151492i | \(-0.0484076\pi\) |
−0.625425 | + | 0.780284i | \(0.715074\pi\) | |||||||
\(18\) | 10.9650 | − | 13.3990i | 0.609169 | − | 0.744387i | ||||
\(19\) | 14.4350 | − | 25.0022i | 0.759738 | − | 1.31591i | −0.183246 | − | 0.983067i | \(-0.558660\pi\) |
0.942984 | − | 0.332838i | \(-0.108006\pi\) | |||||||
\(20\) | −23.8995 | − | 27.0995i | −1.19497 | − | 1.35497i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.82843 | − | 23.3578i | −0.401292 | − | 1.06172i | ||||
\(23\) | −21.3404 | − | 12.3209i | −0.927843 | − | 0.535690i | −0.0417142 | − | 0.999130i | \(-0.513282\pi\) |
−0.886129 | + | 0.463439i | \(0.846615\pi\) | |||||||
\(24\) | 0.172903 | + | 4.68310i | 0.00720428 | + | 0.195129i | ||||
\(25\) | 28.2990 | + | 49.0153i | 1.13196 | + | 1.96061i | ||||
\(26\) | 2.91809 | − | 17.8291i | 0.112234 | − | 0.685734i | ||||
\(27\) | 10.3431 | 0.383079 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 22.4499i | − | 0.774136i | −0.922051 | − | 0.387068i | \(-0.873488\pi\) | ||
0.922051 | − | 0.387068i | \(-0.126512\pi\) | |||||||
\(30\) | 1.70938 | − | 10.4440i | 0.0569792 | − | 0.348135i | ||||
\(31\) | −14.5340 | + | 8.39119i | −0.468838 | + | 0.270684i | −0.715753 | − | 0.698353i | \(-0.753916\pi\) |
0.246915 | + | 0.969037i | \(0.420583\pi\) | |||||||
\(32\) | 22.0371 | + | 23.2027i | 0.688659 | + | 0.725085i | ||||
\(33\) | 3.65685 | − | 6.33386i | 0.110814 | − | 0.191935i | ||||
\(34\) | 8.72792 | + | 23.0919i | 0.256704 | + | 0.679174i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.9706 | − | 22.9039i | 0.721405 | − | 0.636219i | ||||
\(37\) | 14.0734 | + | 8.12528i | 0.380362 | + | 0.219602i | 0.677976 | − | 0.735084i | \(-0.262857\pi\) |
−0.297614 | + | 0.954686i | \(0.596191\pi\) | |||||||
\(38\) | 36.5677 | − | 44.6847i | 0.962309 | − | 1.17591i | ||||
\(39\) | 4.58258 | − | 2.64575i | 0.117502 | − | 0.0678398i | ||||
\(40\) | −38.4171 | − | 61.2078i | −0.960427 | − | 1.53020i | ||||
\(41\) | −6.97056 | −0.170014 | −0.0850069 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850069 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.8284 | −0.530894 | −0.265447 | − | 0.964126i | \(-0.585519\pi\) | ||||
−0.265447 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(44\) | −9.87945 | − | 48.9542i | −0.224533 | − | 1.11260i | ||||
\(45\) | −67.7221 | + | 39.0994i | −1.50494 | + | 0.868875i | ||||
\(46\) | −38.1402 | − | 31.2120i | −0.829134 | − | 0.678522i | ||||
\(47\) | 5.36882 | + | 3.09969i | 0.114230 | + | 0.0659509i | 0.556027 | − | 0.831165i | \(-0.312325\pi\) |
−0.441796 | + | 0.897115i | \(0.645659\pi\) | |||||||
\(48\) | −1.17157 | + | 9.29907i | −0.0244078 | + | 0.193731i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 40.0208 | + | 105.885i | 0.800416 | + | 2.11770i | ||||
\(51\) | −3.61522 | + | 6.26175i | −0.0708867 | + | 0.122779i | ||||
\(52\) | 11.5191 | − | 34.2473i | 0.221521 | − | 0.658602i | ||||
\(53\) | −6.94131 | + | 4.00757i | −0.130968 | + | 0.0756145i | −0.564053 | − | 0.825739i | \(-0.690759\pi\) |
0.433084 | + | 0.901353i | \(0.357425\pi\) | |||||||
\(54\) | 20.4147 | + | 3.34127i | 0.378049 | + | 0.0618754i | ||||
\(55\) | 112.782i | 2.05057i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.9117 | 0.296696 | ||||||||
\(58\) | 7.25227 | − | 44.3103i | 0.125039 | − | 0.763971i | ||||
\(59\) | 15.2218 | + | 26.3650i | 0.257997 | + | 0.446864i | 0.965705 | − | 0.259641i | \(-0.0836042\pi\) |
−0.707708 | + | 0.706505i | \(0.750271\pi\) | |||||||
\(60\) | 6.74773 | − | 20.0616i | 0.112462 | − | 0.334360i | ||||
\(61\) | 13.1918 | + | 7.61627i | 0.216258 | + | 0.124857i | 0.604217 | − | 0.796820i | \(-0.293486\pi\) |
−0.387958 | + | 0.921677i | \(0.626819\pi\) | |||||||
\(62\) | −31.3970 | + | 11.8669i | −0.506403 | + | 0.191402i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.0000 | + | 52.9150i | 0.562500 | + | 0.826797i | ||||
\(65\) | −40.7990 | + | 70.6659i | −0.627677 | + | 1.08717i | ||||
\(66\) | 9.26378 | − | 11.3201i | 0.140360 | − | 0.171516i | ||||
\(67\) | 39.3137 | + | 68.0933i | 0.586772 | + | 1.01632i | 0.994652 | + | 0.103283i | \(0.0329348\pi\) |
−0.407880 | + | 0.913035i | \(0.633732\pi\) | |||||||
\(68\) | 9.76698 | + | 48.3969i | 0.143632 | + | 0.711719i | ||||
\(69\) | − | 14.4348i | − | 0.209200i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17.5345i | 0.246965i | 0.992347 | + | 0.123482i | \(0.0394062\pi\) | ||||
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(72\) | 58.6580 | − | 36.8167i | 0.814695 | − | 0.511343i | ||||
\(73\) | 23.3431 | + | 40.4315i | 0.319769 | + | 0.553856i | 0.980440 | − | 0.196820i | \(-0.0630613\pi\) |
−0.660671 | + | 0.750676i | \(0.729728\pi\) | |||||||
\(74\) | 25.1524 | + | 20.5835i | 0.339897 | + | 0.278155i | ||||
\(75\) | −16.5772 | + | 28.7125i | −0.221029 | + | 0.382833i | ||||
\(76\) | 86.6102 | − | 76.3830i | 1.13961 | − | 1.00504i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.89949 | − | 3.74166i | 0.126917 | − | 0.0479700i | ||||
\(79\) | −70.1762 | − | 40.5163i | −0.888307 | − | 0.512864i | −0.0149184 | − | 0.999889i | \(-0.504749\pi\) |
−0.873388 | + | 0.487025i | \(0.838082\pi\) | |||||||
\(80\) | −56.0526 | − | 133.219i | −0.700657 | − | 1.66523i | ||||
\(81\) | −35.9264 | − | 62.2264i | −0.443536 | − | 0.768227i | ||||
\(82\) | −13.7581 | − | 2.25178i | −0.167781 | − | 0.0274608i | ||||
\(83\) | −40.3848 | −0.486564 | −0.243282 | − | 0.969956i | \(-0.578224\pi\) | ||||
−0.243282 | + | 0.969956i | \(0.578224\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 111.498i | − | 1.31174i | ||||||
\(86\) | −45.0573 | − | 7.37454i | −0.523923 | − | 0.0857505i | ||||
\(87\) | 11.3890 | − | 6.57544i | 0.130908 | − | 0.0755797i | ||||
\(88\) | −3.68520 | − | 99.8142i | −0.0418773 | − | 1.13425i | ||||
\(89\) | 55.9706 | − | 96.9439i | 0.628883 | − | 1.08926i | −0.358894 | − | 0.933379i | \(-0.616846\pi\) |
0.987776 | − | 0.155878i | \(-0.0498208\pi\) | |||||||
\(90\) | −146.296 | + | 55.2949i | −1.62552 | + | 0.614387i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −65.1960 | − | 73.9253i | −0.708652 | − | 0.803536i | ||||
\(93\) | −8.51380 | − | 4.91545i | −0.0915463 | − | 0.0528543i | ||||
\(94\) | 9.59532 | + | 7.85233i | 0.102078 | + | 0.0835355i | ||||
\(95\) | −225.849 | + | 130.394i | −2.37736 | + | 1.37257i | ||||
\(96\) | −5.31637 | + | 17.9755i | −0.0553788 | + | 0.187244i | ||||
\(97\) | 164.108 | 1.69183 | 0.845916 | − | 0.533317i | \(-0.179055\pi\) | ||||
0.845916 | + | 0.533317i | \(0.179055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108.083 | −1.09175 | ||||||||
\(100\) | 44.7853 | + | 221.918i | 0.447853 | + | 2.21918i | ||||
\(101\) | 10.5074 | − | 6.06643i | 0.104033 | − | 0.0600636i | −0.447081 | − | 0.894494i | \(-0.647536\pi\) |
0.551114 | + | 0.834430i | \(0.314203\pi\) | |||||||
\(102\) | −9.15831 | + | 11.1912i | −0.0897874 | + | 0.109718i | ||||
\(103\) | 92.3029 | + | 53.2911i | 0.896144 | + | 0.517389i | 0.875947 | − | 0.482407i | \(-0.160237\pi\) |
0.0201970 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(104\) | 33.7990 | − | 63.8741i | 0.324990 | − | 0.614174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.9949 | + | 5.66756i | −0.141462 | + | 0.0534675i | ||||
\(107\) | 31.7990 | − | 55.0775i | 0.297187 | − | 0.514743i | −0.678304 | − | 0.734781i | \(-0.737285\pi\) |
0.975491 | + | 0.220038i | \(0.0706182\pi\) | |||||||
\(108\) | 39.2138 | + | 13.1896i | 0.363091 | + | 0.122126i | ||||
\(109\) | 113.318 | − | 65.4239i | 1.03961 | − | 0.600220i | 0.119888 | − | 0.992787i | \(-0.461747\pi\) |
0.919723 | + | 0.392568i | \(0.128413\pi\) | |||||||
\(110\) | −36.4332 | + | 222.601i | −0.331211 | + | 2.02365i | ||||
\(111\) | 9.51936i | 0.0857600i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −138.225 | −1.22323 | −0.611617 | − | 0.791154i | \(-0.709481\pi\) | ||||
−0.611617 | + | 0.791154i | \(0.709481\pi\) | |||||||
\(114\) | 33.3793 | + | 5.46318i | 0.292800 | + | 0.0479227i | ||||
\(115\) | 111.296 | + | 192.771i | 0.967795 | + | 1.67627i | ||||
\(116\) | 28.6282 | − | 85.1142i | 0.246795 | − | 0.733743i | ||||
\(117\) | −67.7221 | − | 39.0994i | −0.578821 | − | 0.334183i | ||||
\(118\) | 21.5269 | + | 56.9549i | 0.182431 | + | 0.482668i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 19.7990 | − | 37.4166i | 0.164992 | − | 0.311805i | ||||
\(121\) | −17.4411 | + | 30.2089i | −0.144142 | + | 0.249660i | ||||
\(122\) | 23.5767 | + | 19.2940i | 0.193252 | + | 0.158148i | ||||
\(123\) | −2.04163 | − | 3.53621i | −0.0165986 | − | 0.0287497i | ||||
\(124\) | −65.8029 | + | 13.2797i | −0.530669 | + | 0.107094i | ||||
\(125\) | − | 285.430i | − | 2.28344i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 114.442i | 0.901114i | 0.892748 | + | 0.450557i | \(0.148775\pi\) | ||||
−0.892748 | + | 0.450557i | \(0.851225\pi\) | |||||||
\(128\) | 53.9608 | + | 116.070i | 0.421569 | + | 0.906796i | ||||
\(129\) | −6.68629 | − | 11.5810i | −0.0518317 | − | 0.0897752i | ||||
\(130\) | −103.355 | + | 126.296i | −0.795035 | + | 0.971510i | ||||
\(131\) | −84.1751 | + | 145.796i | −0.642558 | + | 1.11294i | 0.342301 | + | 0.939590i | \(0.388794\pi\) |
−0.984860 | + | 0.173353i | \(0.944540\pi\) | |||||||
\(132\) | 21.9411 | − | 19.3503i | 0.166221 | − | 0.146593i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 55.5980 | + | 147.098i | 0.414910 | + | 1.09775i | ||||
\(135\) | −80.9139 | − | 46.7156i | −0.599362 | − | 0.346042i | ||||
\(136\) | 3.64325 | + | 98.6779i | 0.0267886 | + | 0.725573i | ||||
\(137\) | −17.3431 | − | 30.0392i | −0.126592 | − | 0.219264i | 0.795762 | − | 0.605610i | \(-0.207071\pi\) |
−0.922354 | + | 0.386345i | \(0.873737\pi\) | |||||||
\(138\) | 4.66305 | − | 28.4905i | 0.0337902 | − | 0.206453i | ||||
\(139\) | −107.664 | −0.774561 | −0.387281 | − | 0.921962i | \(-0.626586\pi\) | ||||
−0.387281 | + | 0.921962i | \(0.626586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.63151i | 0.0257554i | ||||||||
\(142\) | −5.66438 | + | 34.6085i | −0.0398900 | + | 0.243722i | ||||
\(143\) | −97.6717 | + | 56.3908i | −0.683019 | + | 0.394341i | ||||
\(144\) | 127.669 | − | 53.7175i | 0.886590 | − | 0.373038i | ||||
\(145\) | −101.397 | + | 175.625i | −0.699289 | + | 1.21120i | ||||
\(146\) | 33.0122 | + | 87.3421i | 0.226111 | + | 0.598233i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 42.9949 | + | 48.7517i | 0.290506 | + | 0.329403i | ||||
\(149\) | 218.391 | + | 126.088i | 1.46571 | + | 0.846229i | 0.999266 | − | 0.0383198i | \(-0.0122006\pi\) |
0.466447 | + | 0.884549i | \(0.345534\pi\) | |||||||
\(150\) | −41.9943 | + | 51.3158i | −0.279962 | + | 0.342106i | ||||
\(151\) | 203.071 | − | 117.243i | 1.34484 | − | 0.776444i | 0.357327 | − | 0.933979i | \(-0.383688\pi\) |
0.987513 | + | 0.157535i | \(0.0503548\pi\) | |||||||
\(152\) | 195.621 | − | 122.781i | 1.28698 | − | 0.807772i | ||||
\(153\) | 106.853 | 0.698384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 151.598 | 0.978051 | ||||||||
\(156\) | 20.7477 | − | 4.18710i | 0.132998 | − | 0.0268404i | ||||
\(157\) | −8.74409 | + | 5.04840i | −0.0556948 | + | 0.0321554i | −0.527589 | − | 0.849500i | \(-0.676904\pi\) |
0.471894 | + | 0.881655i | \(0.343570\pi\) | |||||||
\(158\) | −125.421 | − | 102.638i | −0.793804 | − | 0.649610i | ||||
\(159\) | −4.06613 | − | 2.34758i | −0.0255731 | − | 0.0147647i | ||||
\(160\) | −67.5980 | − | 281.046i | −0.422487 | − | 1.75654i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −50.8076 | − | 134.424i | −0.313627 | − | 0.829780i | ||||
\(163\) | −52.2670 | + | 90.5291i | −0.320657 | + | 0.555394i | −0.980624 | − | 0.195901i | \(-0.937237\pi\) |
0.659967 | + | 0.751295i | \(0.270570\pi\) | |||||||
\(164\) | −26.4274 | − | 8.88887i | −0.161143 | − | 0.0542004i | ||||
\(165\) | −57.2147 | + | 33.0329i | −0.346756 | + | 0.200200i | ||||
\(166\) | −79.7090 | − | 13.0460i | −0.480175 | − | 0.0785902i | ||||
\(167\) | 296.765i | 1.77703i | 0.458843 | + | 0.888517i | \(0.348264\pi\) | ||||
−0.458843 | + | 0.888517i | \(0.651736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.4020 | 0.517172 | ||||||||
\(170\) | 36.0184 | − | 220.067i | 0.211873 | − | 1.29451i | ||||
\(171\) | −124.962 | − | 216.440i | −0.730772 | − | 1.26573i | ||||
\(172\) | −86.5491 | − | 29.1108i | −0.503193 | − | 0.169249i | ||||
\(173\) | 34.6671 | + | 20.0150i | 0.200388 | + | 0.115694i | 0.596836 | − | 0.802363i | \(-0.296424\pi\) |
−0.396449 | + | 0.918057i | \(0.629758\pi\) | |||||||
\(174\) | 24.6030 | − | 9.29907i | 0.141397 | − | 0.0534429i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.9706 | − | 198.198i | 0.141878 | − | 1.12612i | ||||
\(177\) | −8.91674 | + | 15.4442i | −0.0503771 | + | 0.0872556i | ||||
\(178\) | 141.788 | − | 173.261i | 0.796563 | − | 0.973376i | ||||
\(179\) | −147.397 | − | 255.299i | −0.823447 | − | 1.42625i | −0.903101 | − | 0.429429i | \(-0.858715\pi\) |
0.0796538 | − | 0.996823i | \(-0.474619\pi\) | |||||||
\(180\) | −306.614 | + | 61.8777i | −1.70341 | + | 0.343765i | ||||
\(181\) | − | 40.4706i | − | 0.223595i | −0.993731 | − | 0.111797i | \(-0.964339\pi\) | ||
0.993731 | − | 0.111797i | \(-0.0356608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.92302i | 0.0487596i | ||||||||
\(184\) | −104.799 | − | 166.970i | −0.569559 | − | 0.907447i | ||||
\(185\) | −73.3970 | − | 127.127i | −0.396740 | − | 0.687174i | ||||
\(186\) | −15.2161 | − | 12.4521i | −0.0818071 | − | 0.0669469i | ||||
\(187\) | 77.0538 | − | 133.461i | 0.412053 | − | 0.713696i | ||||
\(188\) | 16.4020 | + | 18.5981i | 0.0872448 | + | 0.0989263i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −487.889 | + | 184.405i | −2.56784 | + | 0.970552i | ||||
\(191\) | 135.905 | + | 78.4647i | 0.711543 | + | 0.410810i | 0.811632 | − | 0.584169i | \(-0.198579\pi\) |
−0.100089 | + | 0.994979i | \(0.531913\pi\) | |||||||
\(192\) | −16.3000 | + | 33.7615i | −0.0848956 | + | 0.175841i | ||||
\(193\) | 130.652 | + | 226.296i | 0.676952 | + | 1.17252i | 0.975894 | + | 0.218245i | \(0.0700330\pi\) |
−0.298942 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(194\) | 323.906 | + | 53.0136i | 1.66962 | + | 0.273266i | ||||
\(195\) | −47.7990 | −0.245123 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 145.283i | − | 0.737475i | −0.929533 | − | 0.368738i | \(-0.879790\pi\) | ||
0.929533 | − | 0.368738i | \(-0.120210\pi\) | |||||||
\(198\) | −213.328 | − | 34.9154i | −1.07741 | − | 0.176341i | ||||
\(199\) | 338.189 | − | 195.254i | 1.69944 | − | 0.981175i | 0.753161 | − | 0.657836i | \(-0.228528\pi\) |
0.946283 | − | 0.323339i | \(-0.104805\pi\) | |||||||
\(200\) | 16.7057 | + | 452.476i | 0.0835283 | + | 2.26238i | ||||
\(201\) | −23.0294 | + | 39.8882i | −0.114574 | + | 0.198449i | ||||
\(202\) | 22.6985 | − | 8.57922i | 0.112369 | − | 0.0424714i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.6913 | + | 19.1300i | −0.106330 | + | 0.0937743i | ||||
\(205\) | 54.5303 | + | 31.4831i | 0.266002 | + | 0.153576i | ||||
\(206\) | 164.966 | + | 135.000i | 0.800808 | + | 0.655342i | ||||
\(207\) | −184.741 | + | 106.660i | −0.892467 | + | 0.515266i | ||||
\(208\) | 87.3444 | − | 115.152i | 0.419925 | − | 0.553617i | ||||
\(209\) | −360.451 | −1.72464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −164.049 | −0.777482 | −0.388741 | − | 0.921347i | \(-0.627090\pi\) | ||||
−0.388741 | + | 0.921347i | \(0.627090\pi\) | |||||||
\(212\) | −31.4270 | + | 6.34228i | −0.148240 | + | 0.0299164i | ||||
\(213\) | −8.89535 | + | 5.13574i | −0.0417622 | + | 0.0241114i | ||||
\(214\) | 80.5552 | − | 98.4361i | 0.376426 | − | 0.459982i | ||||
\(215\) | 178.586 | + | 103.106i | 0.830630 | + | 0.479565i | ||||
\(216\) | 73.1371 | + | 38.7005i | 0.338598 | + | 0.179169i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 244.794 | − | 92.5234i | 1.12291 | − | 0.424419i | ||||
\(219\) | −13.6741 | + | 23.6842i | −0.0624388 | + | 0.108147i | ||||
\(220\) | −143.819 | + | 427.587i | −0.653723 | + | 1.94358i | ||||
\(221\) | 96.5598 | − | 55.7488i | 0.436922 | − | 0.252257i | ||||
\(222\) | −3.07515 | + | 18.7887i | −0.0138520 | + | 0.0846339i | ||||
\(223\) | 10.5830i | 0.0474574i | 0.999718 | + | 0.0237287i | \(0.00755379\pi\) | ||||
−0.999718 | + | 0.0237287i | \(0.992446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 489.960 | 2.17760 | ||||||||
\(226\) | −272.821 | − | 44.6526i | −1.20717 | − | 0.197578i | ||||
\(227\) | −106.903 | − | 185.162i | −0.470939 | − | 0.815690i | 0.528509 | − | 0.848928i | \(-0.322751\pi\) |
−0.999447 | + | 0.0332382i | \(0.989418\pi\) | |||||||
\(228\) | 64.1171 | + | 21.5658i | 0.281215 | + | 0.0945868i | ||||
\(229\) | −200.942 | − | 116.014i | −0.877478 | − | 0.506612i | −0.00765200 | − | 0.999971i | \(-0.502436\pi\) |
−0.869826 | + | 0.493359i | \(0.835769\pi\) | |||||||
\(230\) | 157.397 | + | 416.433i | 0.684335 | + | 1.81058i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 84.0000 | − | 158.745i | 0.362069 | − | 0.684246i | ||||
\(233\) | 96.4315 | − | 167.024i | 0.413869 | − | 0.716842i | −0.581440 | − | 0.813589i | \(-0.697511\pi\) |
0.995309 | + | 0.0967472i | \(0.0308439\pi\) | |||||||
\(234\) | −121.035 | − | 99.0490i | −0.517244 | − | 0.423286i | ||||
\(235\) | −28.0000 | − | 48.4974i | −0.119149 | − | 0.206372i | ||||
\(236\) | 24.0897 | + | 119.368i | 0.102075 | + | 0.505797i | ||||
\(237\) | − | 47.4678i | − | 0.200286i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 327.917i | 1.37204i | 0.727583 | + | 0.686020i | \(0.240644\pi\) | ||||
−0.727583 | + | 0.686020i | \(0.759356\pi\) | |||||||
\(240\) | 51.1652 | − | 67.4546i | 0.213188 | − | 0.281061i | ||||
\(241\) | 35.9361 | + | 62.2431i | 0.149112 | + | 0.258270i | 0.930900 | − | 0.365275i | \(-0.119025\pi\) |
−0.781787 | + | 0.623545i | \(0.785692\pi\) | |||||||
\(242\) | −44.1830 | + | 53.9903i | −0.182574 | + | 0.223100i | ||||
\(243\) | 67.5894 | − | 117.068i | 0.278146 | − | 0.481762i | ||||
\(244\) | 40.3015 | + | 45.6976i | 0.165170 | + | 0.187285i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.88730 | − | 7.63908i | −0.0117370 | − | 0.0310532i | ||||
\(247\) | −225.849 | − | 130.394i | −0.914368 | − | 0.527911i | ||||
\(248\) | −134.168 | + | 4.95355i | −0.540999 | + | 0.0199740i | ||||
\(249\) | −11.8284 | − | 20.4874i | −0.0475037 | − | 0.0822789i | ||||
\(250\) | 92.2057 | − | 563.363i | 0.368823 | − | 2.25345i | ||||
\(251\) | 256.919 | 1.02358 | 0.511790 | − | 0.859110i | \(-0.328982\pi\) | ||||
0.511790 | + | 0.859110i | \(0.328982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 307.659i | 1.21604i | ||||||||
\(254\) | −36.9694 | + | 225.878i | −0.145549 | + | 0.889282i | ||||
\(255\) | 56.5634 | − | 32.6569i | 0.221817 | − | 0.128066i | ||||
\(256\) | 69.0091 | + | 246.523i | 0.269567 | + | 0.962982i | ||||
\(257\) | 159.676 | − | 276.567i | 0.621308 | − | 1.07614i | −0.367934 | − | 0.929852i | \(-0.619935\pi\) |
0.989242 | − | 0.146285i | \(-0.0467318\pi\) | |||||||
\(258\) | −9.45584 | − | 25.0178i | −0.0366506 | − | 0.0969683i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −244.794 | + | 215.888i | −0.941515 | + | 0.830338i | ||||
\(261\) | −168.308 | − | 97.1729i | −0.644860 | − | 0.372310i | ||||
\(262\) | −213.238 | + | 260.570i | −0.813885 | + | 0.994543i | ||||
\(263\) | 326.800 | − | 188.678i | 1.24259 | − | 0.717408i | 0.272967 | − | 0.962023i | \(-0.411995\pi\) |
0.969620 | + | 0.244615i | \(0.0786616\pi\) | |||||||
\(264\) | 49.5570 | − | 31.1044i | 0.187716 | − | 0.117820i | ||||
\(265\) | 72.4020 | 0.273215 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 65.5736 | 0.245594 | ||||||||
\(268\) | 62.2169 | + | 308.294i | 0.232153 | + | 1.15035i | ||||
\(269\) | 24.3900 | − | 14.0816i | 0.0906691 | − | 0.0523478i | −0.453980 | − | 0.891012i | \(-0.649996\pi\) |
0.544649 | + | 0.838664i | \(0.316663\pi\) | |||||||
\(270\) | −144.612 | − | 118.343i | −0.535599 | − | 0.438308i | ||||
\(271\) | −346.164 | − | 199.858i | −1.27736 | − | 0.737482i | −0.300995 | − | 0.953626i | \(-0.597319\pi\) |
−0.976362 | + | 0.216143i | \(0.930652\pi\) | |||||||
\(272\) | −24.6863 | + | 195.941i | −0.0907584 | + | 0.720373i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.5269 | − | 64.8921i | −0.0895143 | − | 0.236833i | ||||
\(275\) | 353.321 | − | 611.970i | 1.28480 | − | 2.22534i | ||||
\(276\) | 18.4073 | − | 54.7265i | 0.0666930 | − | 0.198284i | ||||
\(277\) | 89.1579 | − | 51.4753i | 0.321870 | − | 0.185831i | −0.330356 | − | 0.943856i | \(-0.607169\pi\) |
0.652226 | + | 0.758025i | \(0.273835\pi\) | |||||||
\(278\) | −212.501 | − | 34.7800i | −0.764391 | − | 0.125108i | ||||
\(279\) | 145.283i | 0.520726i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.235 | −0.534646 | −0.267323 | − | 0.963607i | \(-0.586139\pi\) | ||||
−0.267323 | + | 0.963607i | \(0.586139\pi\) | |||||||
\(282\) | −1.17313 | + | 7.16766i | −0.00416004 | + | 0.0254172i | ||||
\(283\) | −89.2807 | − | 154.639i | −0.315480 | − | 0.546427i | 0.664060 | − | 0.747679i | \(-0.268832\pi\) |
−0.979539 | + | 0.201253i | \(0.935499\pi\) | |||||||
\(284\) | −22.3600 | + | 66.4783i | −0.0787324 | + | 0.234079i | ||||
\(285\) | −132.299 | − | 76.3830i | −0.464208 | − | 0.268011i | ||||
\(286\) | −210.995 | + | 79.7486i | −0.737745 | + | 0.278841i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 269.338 | − | 64.7820i | 0.935202 | − | 0.224937i | ||||
\(289\) | 68.3234 | − | 118.340i | 0.236413 | − | 0.409479i | ||||
\(290\) | −256.865 | + | 313.882i | −0.885742 | + | 1.08235i | ||||
\(291\) | 48.0660 | + | 83.2528i | 0.165175 | + | 0.286092i | ||||
\(292\) | 36.9423 | + | 183.055i | 0.126515 | + | 0.626900i | ||||
\(293\) | − | 219.189i | − | 0.748085i | −0.927411 | − | 0.374043i | \(-0.877971\pi\) | ||
0.927411 | − | 0.374043i | \(-0.122029\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 275.002i | − | 0.932211i | ||||||
\(296\) | 69.1120 | + | 110.112i | 0.233486 | + | 0.372001i | ||||
\(297\) | −64.5685 | − | 111.836i | −0.217402 | − | 0.376552i | ||||
\(298\) | 390.315 | + | 319.415i | 1.30978 | + | 1.07186i | ||||
\(299\) | −111.296 | + | 192.771i | −0.372229 | + | 0.644720i | ||||
\(300\) | −99.4630 | + | 87.7181i | −0.331543 | + | 0.292394i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 438.683 | − | 165.807i | 1.45259 | − | 0.549029i | ||||
\(303\) | 6.15507 | + | 3.55363i | 0.0203138 | + | 0.0117282i | ||||
\(304\) | 425.768 | − | 179.145i | 1.40055 | − | 0.589291i | ||||
\(305\) | −68.7990 | − | 119.163i | −0.225570 | − | 0.390699i | ||||
\(306\) | 210.900 | + | 34.5179i | 0.689214 | + | 0.112804i | ||||
\(307\) | −316.669 | −1.03150 | −0.515748 | − | 0.856741i | \(-0.672486\pi\) | ||||
−0.515748 | + | 0.856741i | \(0.672486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 62.4344i | 0.202053i | ||||||||
\(310\) | 299.215 | + | 48.9725i | 0.965209 | + | 0.157976i | ||||
\(311\) | 62.5836 | − | 36.1326i | 0.201233 | − | 0.116182i | −0.395997 | − | 0.918252i | \(-0.629601\pi\) |
0.597231 | + | 0.802070i | \(0.296268\pi\) | |||||||
\(312\) | 42.3032 | − | 1.56186i | 0.135587 | − | 0.00500596i | ||||
\(313\) | 40.9756 | − | 70.9718i | 0.130913 | − | 0.226747i | −0.793116 | − | 0.609071i | \(-0.791543\pi\) |
0.924029 | + | 0.382323i | \(0.124876\pi\) | |||||||
\(314\) | −18.8894 | + | 7.13952i | −0.0601573 | + | 0.0227373i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −214.392 | − | 243.098i | −0.678455 | − | 0.769296i | ||||
\(317\) | −94.5267 | − | 54.5750i | −0.298191 | − | 0.172161i | 0.343439 | − | 0.939175i | \(-0.388408\pi\) |
−0.641630 | + | 0.767014i | \(0.721742\pi\) | |||||||
\(318\) | −7.26710 | − | 5.94704i | −0.0228525 | − | 0.0187014i | ||||
\(319\) | −242.742 | + | 140.147i | −0.760945 | + | 0.439332i | ||||
\(320\) | −42.6311 | − | 576.548i | −0.133222 | − | 1.80171i | ||||
\(321\) | 37.2548 | 0.116059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 356.347 | 1.10324 | ||||||||
\(324\) | −56.8563 | − | 281.731i | −0.175482 | − | 0.869541i | ||||
\(325\) | 442.763 | − | 255.629i | 1.36235 | − | 0.786552i | ||||
\(326\) | −132.406 | + | 161.796i | −0.406154 | + | 0.496308i | ||||
\(327\) | 66.3799 | + | 38.3245i | 0.202997 | + | 0.117200i | ||||
\(328\) | −49.2893 | − | 26.0815i | −0.150272 | − | 0.0795166i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −123.598 | + | 46.7156i | −0.374539 | + | 0.141563i | ||||
\(331\) | −160.870 | + | 278.635i | −0.486012 | + | 0.841798i | −0.999871 | − | 0.0160770i | \(-0.994882\pi\) |
0.513858 | + | 0.857875i | \(0.328216\pi\) | |||||||
\(332\) | −153.110 | − | 51.4987i | −0.461176 | − | 0.155117i | ||||
\(333\) | 121.831 | − | 70.3394i | 0.365860 | − | 0.211229i | ||||
\(334\) | −95.8674 | + | 585.736i | −0.287028 | + | 1.75370i | ||||
\(335\) | − | 710.254i | − | 2.12016i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −164.049 | −0.486792 | −0.243396 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243396 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(338\) | 172.509 | + | 28.2345i | 0.510381 | + | 0.0835341i | ||||
\(339\) | −40.4853 | − | 70.1226i | −0.119426 | − | 0.206851i | ||||
\(340\) | 142.182 | − | 422.720i | 0.418182 | − | 1.24329i | ||||
\(341\) | 181.461 | + | 104.766i | 0.532143 | + | 0.307233i | ||||
\(342\) | −176.723 | − | 467.565i | −0.516734 | − | 1.36715i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −161.421 | − | 85.4162i | −0.469248 | − | 0.248303i | ||||
\(345\) | −65.1960 | + | 112.923i | −0.188974 | + | 0.327312i | ||||
\(346\) | 61.9580 | + | 50.7034i | 0.179069 | + | 0.146541i | ||||
\(347\) | 165.154 | + | 286.056i | 0.475949 | + | 0.824368i | 0.999620 | − | 0.0275524i | \(-0.00877132\pi\) |
−0.523671 | + | 0.851920i | \(0.675438\pi\) | |||||||
\(348\) | 51.5639 | − | 10.4061i | 0.148172 | − | 0.0299027i | ||||
\(349\) | 262.402i | 0.751869i | 0.926646 | + | 0.375934i | \(0.122678\pi\) | ||||
−0.926646 | + | 0.375934i | \(0.877322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 93.4313i | − | 0.266186i | ||||||
\(352\) | 113.312 | − | 383.124i | 0.321908 | − | 1.08842i | ||||
\(353\) | −289.049 | − | 500.647i | −0.818835 | − | 1.41826i | −0.906541 | − | 0.422118i | \(-0.861287\pi\) |
0.0877061 | − | 0.996146i | \(-0.472046\pi\) | |||||||
\(354\) | −22.5884 | + | 27.6024i | −0.0638092 | + | 0.0779729i | ||||
\(355\) | 79.1960 | − | 137.171i | 0.223087 | − | 0.386398i | ||||
\(356\) | 335.823 | − | 296.168i | 0.943324 | − | 0.831934i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −208.451 | − | 551.509i | −0.582265 | − | 1.54053i | ||||
\(359\) | 316.198 | + | 182.557i | 0.880774 | + | 0.508515i | 0.870913 | − | 0.491437i | \(-0.163528\pi\) |
0.00986020 | + | 0.999951i | \(0.496861\pi\) | |||||||
\(360\) | −625.164 | + | 23.0814i | −1.73657 | + | 0.0641151i | ||||
\(361\) | −236.240 | − | 409.180i | −0.654405 | − | 1.13346i | ||||
\(362\) | 13.0737 | − | 79.8785i | 0.0361152 | − | 0.220659i | ||||
\(363\) | −20.4335 | −0.0562908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 421.725i | − | 1.15541i | ||||||
\(366\) | −2.88251 | + | 17.6117i | −0.00787571 | + | 0.0481194i | ||||
\(367\) | −450.395 | + | 260.036i | −1.22723 | + | 0.708544i | −0.966451 | − | 0.256853i | \(-0.917314\pi\) |
−0.260784 | + | 0.965397i | \(0.583981\pi\) | |||||||
\(368\) | −152.907 | − | 363.410i | −0.415508 | − | 0.987527i | ||||
\(369\) | −30.1716 | + | 52.2587i | −0.0817658 | + | 0.141622i | ||||
\(370\) | −103.799 | − | 274.626i | −0.280538 | − | 0.742233i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.0101 | − | 29.4927i | −0.0699196 | − | 0.0792814i | ||||
\(373\) | 456.145 | + | 263.356i | 1.22291 | + | 0.706048i | 0.965537 | − | 0.260265i | \(-0.0838098\pi\) |
0.257373 | + | 0.966312i | \(0.417143\pi\) | |||||||
\(374\) | 195.198 | − | 238.526i | 0.521919 | − | 0.637769i | ||||
\(375\) | 144.800 | − | 83.6004i | 0.386134 | − | 0.222934i | ||||
\(376\) | 26.3653 | + | 42.0064i | 0.0701205 | + | 0.111719i | ||||
\(377\) | −202.794 | −0.537915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 121.976 | 0.321835 | 0.160918 | − | 0.986968i | \(-0.448555\pi\) | ||||
0.160918 | + | 0.986968i | \(0.448555\pi\) | |||||||
\(380\) | −1022.54 | + | 206.358i | −2.69089 | + | 0.543048i | ||||
\(381\) | −58.0569 | + | 33.5191i | −0.152380 | + | 0.0879768i | ||||
\(382\) | 242.893 | + | 198.772i | 0.635846 | + | 0.520345i | ||||
\(383\) | −274.033 | − | 158.213i | −0.715492 | − | 0.413089i | 0.0975993 | − | 0.995226i | \(-0.468884\pi\) |
−0.813091 | + | 0.582136i | \(0.802217\pi\) | |||||||
\(384\) | −43.0782 | + | 61.3707i | −0.112183 | + | 0.159820i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 184.770 | + | 488.854i | 0.478678 | + | 1.26646i | ||||
\(387\) | −98.8112 | + | 171.146i | −0.255326 | + | 0.442238i | ||||
\(388\) | 622.179 | + | 209.270i | 1.60355 | + | 0.539356i | ||||
\(389\) | 79.8020 | − | 46.0737i | 0.205146 | − | 0.118441i | −0.393907 | − | 0.919150i | \(-0.628877\pi\) |
0.599054 | + | 0.800709i | \(0.295544\pi\) | |||||||
\(390\) | −94.3427 | − | 15.4411i | −0.241904 | − | 0.0395925i | ||||
\(391\) | − | 304.157i | − | 0.777895i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −98.6173 | −0.250935 | ||||||||
\(394\) | 46.9324 | − | 286.750i | 0.119118 | − | 0.727792i | ||||
\(395\) | 365.990 | + | 633.913i | 0.926557 | + | 1.60484i | ||||
\(396\) | −409.775 | − | 137.828i | −1.03478 | − | 0.348050i | ||||
\(397\) | 486.937 | + | 281.133i | 1.22654 | + | 0.708144i | 0.966305 | − | 0.257400i | \(-0.0828659\pi\) |
0.260237 | + | 0.965545i | \(0.416199\pi\) | |||||||
\(398\) | 730.573 | − | 276.131i | 1.83561 | − | 0.693795i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −113.196 | + | 898.465i | −0.282990 | + | 2.24616i | ||||
\(401\) | −40.6030 | + | 70.3265i | −0.101254 | + | 0.175378i | −0.912202 | − | 0.409741i | \(-0.865619\pi\) |
0.810947 | + | 0.585119i | \(0.198952\pi\) | |||||||
\(402\) | −58.3396 | + | 71.2893i | −0.145123 | + | 0.177337i | ||||
\(403\) | 75.7990 | + | 131.288i | 0.188087 | + | 0.325776i | ||||
\(404\) | 47.5723 | − | 9.60058i | 0.117753 | − | 0.0237638i | ||||
\(405\) | 649.058i | 1.60261i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 202.893i | − | 0.498508i | ||||||
\(408\) | −48.9928 | + | 30.7503i | −0.120080 | + | 0.0753685i | ||||
\(409\) | 225.368 | + | 390.348i | 0.551021 | + | 0.954396i | 0.998201 | + | 0.0599523i | \(0.0190949\pi\) |
−0.447180 | + | 0.894444i | \(0.647572\pi\) | |||||||
\(410\) | 97.4583 | + | 79.7550i | 0.237703 | + | 0.194524i | ||||
\(411\) | 10.1594 | − | 17.5966i | 0.0247187 | − | 0.0428140i | ||||
\(412\) | 281.990 | + | 319.746i | 0.684442 | + | 0.776084i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −399.085 | + | 150.840i | −0.963974 | + | 0.364348i | ||||
\(415\) | 315.928 | + | 182.401i | 0.761272 | + | 0.439521i | ||||
\(416\) | 209.594 | − | 199.065i | 0.503832 | − | 0.478521i | ||||
\(417\) | −31.5341 | − | 54.6186i | −0.0756212 | − | 0.130980i | ||||
\(418\) | −711.436 | − | 116.441i | −1.70200 | − | 0.278566i | ||||
\(419\) | −624.988 | −1.49162 | −0.745809 | − | 0.666160i | \(-0.767937\pi\) | ||||
−0.745809 | + | 0.666160i | \(0.767937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 566.476i | 1.34555i | 0.739848 | + | 0.672774i | \(0.234897\pi\) | ||||
−0.739848 | + | 0.672774i | \(0.765103\pi\) | |||||||
\(422\) | −323.789 | − | 52.9946i | −0.767273 | − | 0.125580i | ||||
\(423\) | 46.4771 | − | 26.8336i | 0.109875 | − | 0.0634363i | ||||
\(424\) | −64.0774 | + | 2.36578i | −0.151126 | + | 0.00557966i | ||||
\(425\) | −349.299 | + | 605.003i | −0.821879 | + | 1.42354i | ||||
\(426\) | −19.2162 | + | 7.26303i | −0.0451084 | + | 0.0170494i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 190.794 | − | 168.264i | 0.445780 | − | 0.393141i | ||||
\(429\) | −57.2147 | − | 33.0329i | −0.133368 | − | 0.0769999i | ||||
\(430\) | 319.174 | + | 261.196i | 0.742264 | + | 0.607432i | ||||
\(431\) | 250.739 | − | 144.764i | 0.581761 | − | 0.335880i | −0.180072 | − | 0.983653i | \(-0.557633\pi\) |
0.761833 | + | 0.647774i | \(0.224300\pi\) | |||||||
\(432\) | 131.852 | + | 100.011i | 0.305212 | + | 0.231507i | ||||
\(433\) | 597.696 | 1.38036 | 0.690180 | − | 0.723638i | \(-0.257532\pi\) | ||||
0.690180 | + | 0.723638i | \(0.257532\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −118.794 | −0.273090 | ||||||||
\(436\) | 513.048 | − | 103.538i | 1.17672 | − | 0.237473i | ||||
\(437\) | −616.098 | + | 355.704i | −1.40984 | + | 0.813969i | ||||
\(438\) | −34.6401 | + | 42.3292i | −0.0790870 | + | 0.0966420i | ||||
\(439\) | −33.2458 | − | 19.1945i | −0.0757308 | − | 0.0437232i | 0.461656 | − | 0.887059i | \(-0.347255\pi\) |
−0.537387 | + | 0.843336i | \(0.680589\pi\) | |||||||
\(440\) | −421.990 | + | 797.486i | −0.959068 | + | 1.81247i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 208.593 | − | 78.8407i | 0.471930 | − | 0.178373i | ||||
\(443\) | −299.529 | + | 518.799i | −0.676138 | + | 1.17110i | 0.299997 | + | 0.953940i | \(0.403014\pi\) |
−0.976135 | + | 0.217165i | \(0.930319\pi\) | |||||||
\(444\) | −12.1391 | + | 36.0906i | −0.0273403 | + | 0.0812852i | ||||
\(445\) | −875.709 | + | 505.591i | −1.96789 | + | 1.13616i | ||||
\(446\) | −3.41875 | + | 20.8881i | −0.00766537 | + | 0.0468343i | ||||
\(447\) | 147.721i | 0.330473i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −460.039 | −1.02459 | −0.512293 | − | 0.858811i | \(-0.671204\pi\) | ||||
−0.512293 | + | 0.858811i | \(0.671204\pi\) | |||||||
\(450\) | 967.054 | + | 158.278i | 2.14901 | + | 0.351728i | ||||
\(451\) | 43.5147 | + | 75.3697i | 0.0964850 | + | 0.167117i | ||||
\(452\) | −524.052 | − | 176.265i | −1.15941 | − | 0.389967i | ||||
\(453\) | 118.956 | + | 68.6794i | 0.262596 | + | 0.151610i | ||||
\(454\) | −151.184 | − | 399.995i | −0.333004 | − | 0.881045i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 119.584 | + | 63.2777i | 0.262245 | + | 0.138767i | ||||
\(457\) | −133.161 | + | 230.642i | −0.291382 | + | 0.504688i | −0.974137 | − | 0.225959i | \(-0.927448\pi\) |
0.682755 | + | 0.730647i | \(0.260782\pi\) | |||||||
\(458\) | −359.130 | − | 293.895i | −0.784128 | − | 0.641691i | ||||
\(459\) | 63.8335 | + | 110.563i | 0.139071 | + | 0.240878i | ||||
\(460\) | 176.135 | + | 872.776i | 0.382902 | + | 1.89734i | ||||
\(461\) | 763.123i | 1.65537i | 0.561196 | + | 0.827683i | \(0.310341\pi\) | ||||
−0.561196 | + | 0.827683i | \(0.689659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 123.988i | 0.267792i | 0.990995 | + | 0.133896i | \(0.0427488\pi\) | ||||
−0.990995 | + | 0.133896i | \(0.957251\pi\) | |||||||
\(464\) | 217.075 | − | 286.186i | 0.467835 | − | 0.616780i | ||||
\(465\) | 44.4020 | + | 76.9066i | 0.0954882 | + | 0.165390i | ||||
\(466\) | 244.286 | − | 298.511i | 0.524220 | − | 0.640581i | ||||
\(467\) | −384.359 | + | 665.729i | −0.823038 | + | 1.42554i | 0.0803710 | + | 0.996765i | \(0.474390\pi\) |
−0.903409 | + | 0.428779i | \(0.858944\pi\) | |||||||
\(468\) | −206.894 | − | 234.596i | −0.442082 | − | 0.501274i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −39.5980 | − | 104.766i | −0.0842510 | − | 0.222907i | ||||
\(471\) | −5.12217 | − | 2.95729i | −0.0108751 | − | 0.00627874i | ||||
\(472\) | 8.98586 | + | 243.383i | 0.0190378 | + | 0.515643i | ||||
\(473\) | 142.510 | + | 246.834i | 0.301289 | + | 0.521848i | ||||
\(474\) | 15.3341 | − | 93.6889i | 0.0323504 | − | 0.197656i | ||||
\(475\) | 1633.99 | 3.43997 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 69.3859i | 0.145463i | ||||||||
\(478\) | −105.931 | + | 647.223i | −0.221613 | + | 1.35402i | ||||
\(479\) | 103.041 | − | 59.4905i | 0.215116 | − | 0.124197i | −0.388571 | − | 0.921419i | \(-0.627031\pi\) |
0.603687 | + | 0.797222i | \(0.293698\pi\) | |||||||
\(480\) | 122.777 | − | 116.609i | 0.255786 | − | 0.242936i | ||||
\(481\) | 73.3970 | − | 127.127i | 0.152592 | − | 0.264298i | ||||
\(482\) | 50.8213 | + | 134.460i | 0.105438 | + | 0.278964i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −104.647 | + | 92.2898i | −0.216212 | + | 0.190681i | ||||
\(485\) | −1283.81 | − | 741.205i | −2.64702 | − | 1.52826i | ||||
\(486\) | 171.222 | − | 209.228i | 0.352308 | − | 0.430510i | ||||
\(487\) | −244.719 | + | 141.288i | −0.502503 | + | 0.290120i | −0.729746 | − | 0.683718i | \(-0.760362\pi\) |
0.227244 | + | 0.973838i | \(0.427029\pi\) | |||||||
\(488\) | 64.7824 | + | 103.214i | 0.132751 | + | 0.211505i | ||||
\(489\) | −61.2346 | −0.125224 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −388.049 | −0.790323 | −0.395162 | − | 0.918612i | \(-0.629311\pi\) | ||||
−0.395162 | + | 0.918612i | \(0.629311\pi\) | |||||||
\(492\) | −3.23103 | − | 16.0103i | −0.00656714 | − | 0.0325412i | ||||
\(493\) | 239.978 | − | 138.551i | 0.486771 | − | 0.281037i | ||||
\(494\) | −403.644 | − | 330.322i | −0.817093 | − | 0.668668i | ||||
\(495\) | 845.530 | + | 488.167i | 1.70814 | + | 0.986195i | ||||
\(496\) | −266.412 | − | 33.5648i | −0.537121 | − | 0.0676709i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.7279 | − | 44.2579i | −0.0335902 | − | 0.0888713i | ||||
\(499\) | 13.8579 | − | 24.0025i | 0.0277713 | − | 0.0481013i | −0.851806 | − | 0.523858i | \(-0.824492\pi\) |
0.879577 | + | 0.475757i | \(0.157826\pi\) | |||||||
\(500\) | 363.980 | − | 1082.15i | 0.727960 | − | 2.16429i | ||||
\(501\) | −150.551 | + | 86.9204i | −0.300500 | + | 0.173494i | ||||
\(502\) | 507.091 | + | 82.9956i | 1.01014 | + | 0.165330i | ||||
\(503\) | − | 727.477i | − | 1.44628i | −0.690703 | − | 0.723138i | \(-0.742699\pi\) | ||
0.690703 | − | 0.723138i | \(-0.257301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −109.598 | −0.217026 | ||||||||
\(506\) | −99.3868 | + | 607.239i | −0.196417 | + | 1.20008i | ||||
\(507\) | 25.5995 | + | 44.3396i | 0.0504920 | + | 0.0874548i | ||||
\(508\) | −145.936 | + | 433.881i | −0.287275 | + | 0.854096i | ||||
\(509\) | −549.218 | − | 317.091i | −1.07901 | − | 0.622969i | −0.148384 | − | 0.988930i | \(-0.547407\pi\) |
−0.930630 | + | 0.365961i | \(0.880740\pi\) | |||||||
\(510\) | 122.191 | − | 46.1838i | 0.239590 | − | 0.0905565i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 56.5685 | + | 508.865i | 0.110485 | + | 0.993878i | ||||
\(513\) | 149.304 | − | 258.601i | 0.291040 | − | 0.504096i | ||||
\(514\) | 404.502 | − | 494.289i | 0.786969 | − | 0.961653i | ||||
\(515\) | −481.387 | − | 833.787i | −0.934732 | − | 1.61900i | ||||
\(516\) | −10.5816 | − | 52.4333i | −0.0205069 | − | 0.101615i | ||||
\(517\) | − | 77.4010i | − | 0.149712i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4491i | 0.0451813i | ||||||||
\(520\) | −552.900 | + | 347.028i | −1.06327 | + | 0.667361i | ||||
\(521\) | 416.563 | + | 721.509i | 0.799546 | + | 1.38485i | 0.919912 | + | 0.392125i | \(0.128260\pi\) |
−0.120366 | + | 0.992730i | \(0.538407\pi\) | |||||||
\(522\) | −300.806 | − | 246.165i | −0.576257 | − | 0.471580i | ||||
\(523\) | 438.217 | − | 759.014i | 0.837891 | − | 1.45127i | −0.0537645 | − | 0.998554i | \(-0.517122\pi\) |
0.891655 | − | 0.452715i | \(-0.149545\pi\) | |||||||
\(524\) | −505.051 | + | 445.413i | −0.963838 | + | 0.850025i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 705.970 | − | 266.831i | 1.34215 | − | 0.507284i | ||||
\(527\) | −179.395 | − | 103.574i | −0.340408 | − | 0.196535i | ||||
\(528\) | 107.861 | − | 45.3830i | 0.204281 | − | 0.0859527i | ||||
\(529\) | 39.1081 | + | 67.7372i | 0.0739283 | + | 0.128048i | ||||
\(530\) | 142.903 | + | 23.3889i | 0.269628 | + | 0.0441300i | ||||
\(531\) | 263.546 | 0.496321 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 62.9662i | 0.118135i | ||||||||
\(534\) | 129.425 | + | 21.1830i | 0.242369 | + | 0.0396686i | ||||
\(535\) | −497.524 | + | 287.245i | −0.929951 | + | 0.536907i | ||||
\(536\) | 23.2079 | + | 628.591i | 0.0432984 | + | 1.17274i | ||||
\(537\) | 86.3431 | − | 149.551i | 0.160788 | − | 0.278493i | ||||
\(538\) | 52.6884 | − | 19.9143i | 0.0979338 | − | 0.0370155i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −247.196 | − | 280.294i | −0.457770 | − | 0.519063i | ||||
\(541\) | −351.532 | − | 202.957i | −0.649783 | − | 0.375152i | 0.138590 | − | 0.990350i | \(-0.455743\pi\) |
−0.788373 | + | 0.615198i | \(0.789076\pi\) | |||||||
\(542\) | −618.674 | − | 506.292i | −1.14147 | − | 0.934118i | ||||
\(543\) | 20.5310 | − | 11.8536i | 0.0378103 | − | 0.0218298i | ||||
\(544\) | −112.022 | + | 378.762i | −0.205922 | + | 0.696254i | ||||
\(545\) | −1181.97 | −2.16875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −606.024 | −1.10791 | −0.553953 | − | 0.832548i | \(-0.686881\pi\) | ||||
−0.553953 | + | 0.832548i | \(0.686881\pi\) | |||||||
\(548\) | −27.4468 | − | 136.003i | −0.0500855 | − | 0.248181i | ||||
\(549\) | 114.199 | − | 65.9329i | 0.208013 | − | 0.120096i | ||||
\(550\) | 895.055 | − | 1093.73i | 1.62737 | − | 1.98860i | ||||
\(551\) | −561.298 | − | 324.066i | −1.01869 | − | 0.588141i | ||||
\(552\) | 54.0101 | − | 102.069i | 0.0978444 | − | 0.184909i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 192.603 | − | 72.7971i | 0.347659 | − | 0.131403i | ||||
\(555\) | 42.9949 | − | 74.4694i | 0.0774684 | − | 0.134179i | ||||
\(556\) | −408.185 | − | 137.293i | −0.734146 | − | 0.246930i | ||||
\(557\) | −31.5616 | + | 18.2221i | −0.0566635 | + | 0.0327147i | −0.528064 | − | 0.849204i | \(-0.677082\pi\) |
0.471401 | + | 0.881919i | \(0.343749\pi\) | |||||||
\(558\) | −46.9324 | + | 286.750i | −0.0841082 | + | 0.513889i | ||||
\(559\) | 206.213i | 0.368896i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 90.2742 | 0.160917 | ||||||||
\(562\) | −296.526 | − | 48.5324i | −0.527626 | − | 0.0863565i | ||||
\(563\) | −93.1945 | − | 161.418i | −0.165532 | − | 0.286710i | 0.771312 | − | 0.636457i | \(-0.219601\pi\) |
−0.936844 | + | 0.349747i | \(0.886267\pi\) | |||||||
\(564\) | −4.63091 | + | 13.7681i | −0.00821083 | + | 0.0244115i | ||||
\(565\) | 1081.33 | + | 624.306i | 1.91386 | + | 1.10497i | ||||
\(566\) | −126.262 | − | 334.058i | −0.223078 | − | 0.590208i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −65.6081 | + | 123.988i | −0.115507 | + | 0.218288i | ||||
\(569\) | 335.446 | − | 581.009i | 0.589536 | − | 1.02111i | −0.404758 | − | 0.914424i | \(-0.632644\pi\) |
0.994293 | − | 0.106682i | \(-0.0340225\pi\) | |||||||
\(570\) | −236.449 | − | 193.498i | −0.414823 | − | 0.339471i | ||||
\(571\) | 338.541 | + | 586.371i | 0.592892 | + | 1.02692i | 0.993841 | + | 0.110818i | \(0.0353471\pi\) |
−0.400949 | + | 0.916100i | \(0.631320\pi\) | |||||||
\(572\) | −442.211 | + | 89.2427i | −0.773096 | + | 0.156019i | ||||
\(573\) | 91.9271i | 0.160431i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1394.67i | − | 2.42552i | ||||||
\(576\) | 552.530 | − | 40.8552i | 0.959254 | − | 0.0709291i | ||||
\(577\) | 463.950 | + | 803.586i | 0.804073 | + | 1.39270i | 0.916915 | + | 0.399083i | \(0.130671\pi\) |
−0.112841 | + | 0.993613i | \(0.535995\pi\) | |||||||
\(578\) | 173.081 | − | 211.500i | 0.299448 | − | 0.365917i | ||||
\(579\) | −76.5341 | + | 132.561i | −0.132183 | + | 0.228948i | ||||
\(580\) | −608.382 | + | 536.542i | −1.04893 | + | 0.925073i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 67.9756 | + | 179.847i | 0.116797 | + | 0.309015i | ||||
\(583\) | 86.6642 | + | 50.0356i | 0.148652 | + | 0.0858244i | ||||
\(584\) | 13.7801 | + | 373.236i | 0.0235960 | + | 0.639103i | ||||
\(585\) | 353.191 | + | 611.745i | 0.603745 | + | 1.04572i | ||||
\(586\) | 70.8072 | − | 432.622i | 0.120831 | − | 0.738263i | ||||
\(587\) | 321.120 | 0.547053 | 0.273526 | − | 0.961865i | \(-0.411810\pi\) | ||||
0.273526 | + | 0.961865i | \(0.411810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 484.508i | 0.822595i | ||||||||
\(590\) | 88.8373 | − | 542.783i | 0.150572 | − | 0.919971i | ||||
\(591\) | 73.7028 | − | 42.5523i | 0.124709 | − | 0.0720005i | ||||
\(592\) | 100.838 | + | 239.659i | 0.170335 | + | 0.404829i | ||||
\(593\) | −109.627 | + | 189.880i | −0.184869 | + | 0.320203i | −0.943532 | − | 0.331280i | \(-0.892519\pi\) |
0.758663 | + | 0.651483i | \(0.225853\pi\) | |||||||
\(594\) | −91.3137 | − | 241.593i | −0.153727 | − | 0.406723i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 667.196 | + | 756.529i | 1.11946 | + | 1.26934i | ||||
\(597\) | 198.107 | + | 114.377i | 0.331837 | + | 0.191586i | ||||
\(598\) | −281.943 | + | 344.526i | −0.471477 | + | 0.576131i | ||||
\(599\) | −134.062 | + | 77.4010i | −0.223811 | + | 0.129217i | −0.607713 | − | 0.794156i | \(-0.707913\pi\) |
0.383903 | + | 0.923373i | \(0.374580\pi\) | |||||||
\(600\) | −224.651 | + | 141.002i | −0.374418 | + | 0.235003i | ||||
\(601\) | −205.862 | −0.342533 | −0.171266 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171266 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 680.666 | 1.12880 | ||||||||
\(604\) | 919.409 | − | 185.546i | 1.52220 | − | 0.307195i | ||||
\(605\) | 272.882 | − | 157.548i | 0.451045 | − | 0.260411i | ||||
\(606\) | 11.0005 | + | 9.00228i | 0.0181527 | + | 0.0148552i | ||||
\(607\) | −684.735 | − | 395.332i | −1.12806 | − | 0.651288i | −0.184616 | − | 0.982811i | \(-0.559104\pi\) |
−0.943447 | + | 0.331523i | \(0.892438\pi\) | |||||||
\(608\) | 898.225 | − | 216.044i | 1.47734 | − | 0.355335i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −97.2965 | − | 257.422i | −0.159502 | − | 0.422004i | ||||
\(611\) | 28.0000 | − | 48.4974i | 0.0458265 | − | 0.0793739i | ||||
\(612\) | 405.110 | + | 136.259i | 0.661944 | + | 0.222645i | ||||
\(613\) | −642.133 | + | 370.736i | −1.04753 | + | 0.604789i | −0.921955 | − | 0.387296i | \(-0.873409\pi\) |
−0.125570 | + | 0.992085i | \(0.540076\pi\) | |||||||
\(614\) | −625.022 | − | 102.297i | −1.01795 | − | 0.166608i | ||||
\(615\) | 36.8848i | 0.0599752i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 171.578 | 0.278084 | 0.139042 | − | 0.990286i | \(-0.455598\pi\) | ||||
0.139042 | + | 0.990286i | \(0.455598\pi\) | |||||||
\(618\) | −20.1689 | + | 123.229i | −0.0326358 | + | 0.199400i | ||||
\(619\) | −270.099 | − | 467.825i | −0.436347 | − | 0.755776i | 0.561057 | − | 0.827777i | \(-0.310395\pi\) |
−0.997405 | + | 0.0720012i | \(0.977061\pi\) | |||||||
\(620\) | 574.752 | + | 193.318i | 0.927019 | + | 0.311803i | ||||
\(621\) | −220.727 | − | 127.437i | −0.355438 | − | 0.205212i | ||||
\(622\) | 135.196 | − | 51.0993i | 0.217357 | − | 0.0821532i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 84.0000 | + | 10.5830i | 0.134615 | + | 0.0169599i | ||||
\(625\) | −581.691 | + | 1007.52i | −0.930705 | + | 1.61203i | ||||
\(626\) | 103.802 | − | 126.843i | 0.165818 | − | 0.202625i | ||||
\(627\) | −105.574 | − | 182.859i | −0.168379 | − | 0.291641i | ||||
\(628\) | −39.5891 | + | 7.98948i | −0.0630400 | + | 0.0127221i | ||||
\(629\) | 200.583i | 0.318892i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 269.399i | − | 0.426940i | −0.976950 | − | 0.213470i | \(-0.931523\pi\) | ||
0.976950 | − | 0.213470i | \(-0.0684766\pi\) | |||||||
\(632\) | −344.623 | − | 549.069i | −0.545289 | − | 0.868780i | ||||
\(633\) | −48.0488 | − | 83.2229i | −0.0759064 | − | 0.131474i | ||||
\(634\) | −168.941 | − | 138.253i | −0.266468 | − | 0.218065i | ||||
\(635\) | 516.884 | − | 895.270i | 0.813991 | − | 1.40987i | ||||
\(636\) | −12.4222 | − | 14.0855i | −0.0195318 | − | 0.0221470i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −524.382 | + | 198.198i | −0.821915 | + | 0.310655i | ||||
\(639\) | 131.457 | + | 75.8968i | 0.205723 | + | 0.118774i | ||||
\(640\) | 102.107 | − | 1151.73i | 0.159542 | − | 1.79957i | ||||
\(641\) | −18.0934 | − | 31.3386i | −0.0282268 | − | 0.0488902i | 0.851567 | − | 0.524246i | \(-0.175653\pi\) |
−0.879794 | + | 0.475356i | \(0.842319\pi\) | |||||||
\(642\) | 73.5313 | + | 12.0349i | 0.114535 | + | 0.0187459i | ||||
\(643\) | −266.297 | −0.414148 | −0.207074 | − | 0.978325i | \(-0.566394\pi\) | ||||
−0.207074 | + | 0.978325i | \(0.566394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 120.797i | 0.187282i | ||||||||
\(646\) | 703.336 | + | 115.115i | 1.08876 | + | 0.178197i | ||||
\(647\) | −940.708 | + | 543.118i | −1.45395 | + | 0.839440i | −0.998703 | − | 0.0509233i | \(-0.983784\pi\) |
−0.455250 | + | 0.890363i | \(0.650450\pi\) | |||||||
\(648\) | −21.2083 | − | 574.431i | −0.0327289 | − | 0.886468i | ||||
\(649\) | 190.049 | − | 329.174i | 0.292833 | − | 0.507202i | ||||
\(650\) | 956.477 | − | 361.514i | 1.47150 | − | 0.556176i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −313.602 | + | 276.571i | −0.480985 | + | 0.424189i | ||||
\(653\) | 1035.20 | + | 597.674i | 1.58530 | + | 0.915274i | 0.994066 | + | 0.108774i | \(0.0346926\pi\) |
0.591234 | + | 0.806500i | \(0.298641\pi\) | |||||||
\(654\) | 118.636 | + | 97.0859i | 0.181401 | + | 0.148449i | ||||
\(655\) | 1317.00 | − | 760.368i | 2.01068 | − | 1.16087i | ||||
\(656\) | −88.8588 | − | 67.4005i | −0.135456 | − | 0.102745i | ||||
\(657\) | 404.156 | 0.615154 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −685.220 | −1.03979 | −0.519894 | − | 0.854231i | \(-0.674029\pi\) | ||||
−0.519894 | + | 0.854231i | \(0.674029\pi\) | |||||||
\(660\) | −259.041 | + | 52.2771i | −0.392487 | + | 0.0792078i | ||||
\(661\) | −860.294 | + | 496.691i | −1.30150 | + | 0.751423i | −0.980662 | − | 0.195710i | \(-0.937299\pi\) |
−0.320842 | + | 0.947133i | \(0.603966\pi\) | |||||||
\(662\) | −407.526 | + | 497.985i | −0.615599 | + | 0.752243i | ||||
\(663\) | 56.5634 | + | 32.6569i | 0.0853143 | + | 0.0492563i | ||||
\(664\) | −285.563 | − | 151.106i | −0.430065 | − | 0.227569i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 263.186 | − | 99.4749i | 0.395174 | − | 0.149362i | ||||
\(667\) | −276.603 | + | 479.091i | −0.414697 | + | 0.718277i | ||||
\(668\) | −378.435 | + | 1125.12i | −0.566519 | + | 1.68431i | ||||
\(669\) | −5.36882 | + | 3.09969i | −0.00802514 | + | 0.00463332i | ||||
\(670\) | 229.442 | − | 1401.86i | 0.342450 | − | 2.09232i | ||||
\(671\) | − | 190.183i | − | 0.283432i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 106.569 | 0.158349 | 0.0791743 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791743 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(674\) | −323.789 | − | 52.9946i | −0.480400 | − | 0.0786270i | ||||
\(675\) | 292.701 | + | 506.972i | 0.433630 | + | 0.751070i | ||||
\(676\) | 331.366 | + | 111.455i | 0.490187 | + | 0.164874i | ||||
\(677\) | −869.650 | − | 502.092i | −1.28456 | − | 0.741643i | −0.306885 | − | 0.951747i | \(-0.599287\pi\) |
−0.977679 | + | 0.210103i | \(0.932620\pi\) | |||||||
\(678\) | −57.2548 | − | 151.482i | −0.0844467 | − | 0.223425i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 417.186 | − | 788.407i | 0.613509 | − | 1.15942i | ||||
\(681\) | 62.6224 | − | 108.465i | 0.0919565 | − | 0.159273i | ||||
\(682\) | 324.312 | + | 265.401i | 0.475531 | + | 0.389151i | ||||
\(683\) | 339.113 | + | 587.360i | 0.496505 | + | 0.859971i | 0.999992 | − | 0.00403135i | \(-0.00128322\pi\) |
−0.503487 | + | 0.864003i | \(0.667950\pi\) | |||||||
\(684\) | −197.762 | − | 979.940i | −0.289125 | − | 1.43266i | ||||
\(685\) | 313.327i | 0.457411i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 135.919i | − | 0.197844i | ||||||
\(688\) | −291.011 | − | 220.735i | −0.422980 | − | 0.320836i | ||||
\(689\) | 36.2010 | + | 62.7020i | 0.0525414 | + | 0.0910043i | ||||
\(690\) | −165.159 | + | 201.819i | −0.239360 | + | 0.292491i | ||||
\(691\) | −182.587 | + | 316.250i | −0.264236 | + | 0.457671i | −0.967363 | − | 0.253394i | \(-0.918453\pi\) |
0.703127 | + | 0.711064i | \(0.251787\pi\) | |||||||
\(692\) | 105.910 | + | 120.090i | 0.153049 | + | 0.173541i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 233.563 | + | 617.951i | 0.336547 | + | 0.890419i | ||||
\(695\) | 842.250 | + | 486.273i | 1.21187 | + | 0.699673i | ||||
\(696\) | 105.135 | − | 3.88166i | 0.151057 | − | 0.00557710i | ||||
\(697\) | −43.0193 | − | 74.5117i | −0.0617207 | − | 0.106903i | ||||
\(698\) | −84.7669 | + | 517.913i | −0.121443 | + | 0.741996i | ||||
\(699\) | 112.976 | 0.161626 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 940.292i | − | 1.34136i | −0.741748 | − | 0.670679i | \(-0.766003\pi\) | ||
0.741748 | − | 0.670679i | \(-0.233997\pi\) | |||||||
\(702\) | 30.1822 | − | 184.409i | 0.0429946 | − | 0.262691i | ||||
\(703\) | 406.300 | − | 234.577i | 0.577951 | − | 0.333680i | ||||
\(704\) | 347.412 | − | 719.582i | 0.493484 | − | 1.02213i | ||||
\(705\) | 16.4020 | − | 28.4091i | 0.0232653 | − | 0.0402966i | ||||
\(706\) | −408.777 | − | 1081.52i | −0.579004 | − | 1.53190i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −53.5004 | + | 47.1829i | −0.0755656 | + | 0.0666426i | ||||
\(709\) | −915.785 | − | 528.729i | −1.29166 | − | 0.745738i | −0.312709 | − | 0.949849i | \(-0.601236\pi\) |
−0.978948 | + | 0.204110i | \(0.934570\pi\) | |||||||
\(710\) | 200.624 | − | 245.157i | 0.282569 | − | 0.345291i | ||||
\(711\) | −607.505 | + | 350.743i | −0.854438 | + | 0.493310i | ||||
\(712\) | 758.502 | − | 476.074i | 1.06531 | − | 0.668643i | ||||
\(713\) | 413.547 | 0.580010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1018.77 | 1.42486 | ||||||||
\(716\) | −233.267 | − | 1155.87i | −0.325792 | − | 1.61435i | ||||
\(717\) | −166.354 | + | 96.0448i | −0.232015 | + | 0.133954i | ||||
\(718\) | 565.118 | + | 462.465i | 0.787073 | + | 0.644101i | ||||
\(719\) | 896.185 | + | 517.412i | 1.24643 | + | 0.719628i | 0.970396 | − | 0.241520i | \(-0.0776458\pi\) |
0.276036 | + | 0.961147i | \(0.410979\pi\) | |||||||
\(720\) | −1241.37 | − | 156.397i | −1.72412 | − | 0.217219i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −334.094 | − | 883.930i | −0.462734 | − | 1.22428i | ||||
\(723\) | −21.0509 | + | 36.4612i | −0.0291160 | + | 0.0504304i | ||||
\(724\) | 51.6082 | − | 153.436i | 0.0712820 | − | 0.211928i | ||||
\(725\) | 1100.39 | − | 635.311i | 1.51778 | − | 0.876291i | ||||
\(726\) | −40.3305 | − | 6.60089i | −0.0555516 | − | 0.00909214i | ||||
\(727\) | − | 495.145i | − | 0.681080i | −0.940230 | − | 0.340540i | \(-0.889390\pi\) | ||
0.940230 | − | 0.340540i | \(-0.110610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −567.489 | −0.778449 | ||||||||
\(730\) | 136.235 | − | 832.374i | 0.186623 | − | 1.14024i | ||||
\(731\) | −140.887 | − | 244.024i | −0.192732 | − | 0.333822i | ||||
\(732\) | −11.3786 | + | 33.8297i | −0.0155446 | + | 0.0462155i | ||||
\(733\) | 491.464 | + | 283.747i | 0.670483 | + | 0.387103i | 0.796260 | − | 0.604955i | \(-0.206809\pi\) |
−0.125777 | + | 0.992059i | \(0.540142\pi\) | |||||||
\(734\) | −972.965 | + | 367.746i | −1.32556 | + | 0.501016i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −184.402 | − | 766.672i | −0.250546 | − | 1.04167i | ||||
\(737\) | 490.843 | − | 850.165i | 0.666001 | − | 1.15355i | ||||
\(738\) | −76.4325 | + | 93.3983i | −0.103567 | + | 0.126556i | ||||
\(739\) | 272.350 | + | 471.725i | 0.368539 | + | 0.638328i | 0.989337 | − | 0.145642i | \(-0.0465248\pi\) |
−0.620798 | + | 0.783970i | \(0.713191\pi\) | |||||||
\(740\) | −116.156 | − | 575.572i | −0.156968 | − | 0.777800i | ||||
\(741\) | − | 152.766i | − | 0.206162i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 731.264i | 0.984205i | 0.870537 | + | 0.492102i | \(0.163771\pi\) | ||||
−0.870537 | + | 0.492102i | \(0.836229\pi\) | |||||||
\(744\) | −41.8098 | − | 66.6132i | −0.0561959 | − | 0.0895339i | ||||
\(745\) | −1138.97 | − | 1972.76i | −1.52883 | − | 2.64800i | ||||
\(746\) | 815.237 | + | 667.149i | 1.09281 | + | 0.894302i | ||||
\(747\) | −174.803 | + | 302.767i | −0.234006 | + | 0.405310i | ||||
\(748\) | 462.323 | − | 407.731i | 0.618079 | − | 0.545094i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 312.804 | − | 118.229i | 0.417072 | − | 0.157638i | ||||
\(751\) | −577.000 | − | 333.131i | −0.768309 | − | 0.443583i | 0.0639622 | − | 0.997952i | \(-0.479626\pi\) |
−0.832271 | + | 0.554369i | \(0.812960\pi\) | |||||||
\(752\) | 38.4684 | + | 91.4268i | 0.0511548 | + | 0.121578i | ||||
\(753\) | 75.2498 | + | 130.336i | 0.0999333 | + | 0.173090i | ||||
\(754\) | −400.262 | − | 65.5109i | −0.530852 | − | 0.0868845i | ||||
\(755\) | −2118.15 | −2.80550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 238.623i | − | 0.315222i | −0.987501 | − | 0.157611i | \(-0.949621\pi\) | ||
0.987501 | − | 0.157611i | \(-0.0503791\pi\) | |||||||
\(758\) | 240.748 | + | 39.4032i | 0.317609 | + | 0.0519832i | ||||
\(759\) | −156.077 | + | 90.1113i | −0.205636 | + | 0.118724i | ||||
\(760\) | −2084.88 | + | 76.9751i | −2.74327 | + | 0.101283i | ||||
\(761\) | 307.465 | − | 532.545i | 0.404028 | − | 0.699797i | −0.590180 | − | 0.807272i | \(-0.700943\pi\) |
0.994208 | + | 0.107475i | \(0.0342766\pi\) | |||||||
\(762\) | −125.417 | + | 47.4032i | −0.164589 | + | 0.0622090i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 415.196 | + | 470.788i | 0.543450 | + | 0.616215i | ||||
\(765\) | −835.904 | − | 482.609i | −1.09268 | − | 0.630862i | ||||
\(766\) | −489.761 | − | 400.796i | −0.639374 | − | 0.523232i | ||||
\(767\) | 238.159 | − | 137.501i | 0.310507 | − | 0.179271i | ||||
\(768\) | −104.850 | + | 107.214i | −0.136524 | + | 0.139601i | ||||
\(769\) | −178.950 | −0.232705 | −0.116353 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116353 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 187.072 | 0.242636 | ||||||||
\(772\) | 206.766 | + | 1024.56i | 0.267832 | + | 1.32715i | ||||
\(773\) | 546.994 | − | 315.807i | 0.707625 | − | 0.408548i | −0.102556 | − | 0.994727i | \(-0.532702\pi\) |
0.810181 | + | 0.586180i | \(0.199369\pi\) | |||||||
\(774\) | −250.315 | + | 305.877i | −0.323404 | + | 0.395190i | ||||
\(775\) | −822.593 | − | 474.925i | −1.06141 | − | 0.612806i | ||||
\(776\) | 1160.42 | + | 614.035i | 1.49538 | + | 0.791282i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 172.392 | − | 65.1580i | 0.221583 | − | 0.0837507i | ||||
\(779\) | −100.620 | + | 174.279i | −0.129166 | + | 0.223722i | ||||
\(780\) | −181.220 | − | 60.9533i | −0.232333 | − | 0.0781453i | ||||
\(781\) | 189.593 | − | 109.462i | 0.242757 | − | 0.140156i | ||||
\(782\) | 98.2554 | − | 600.326i | 0.125646 | − | 0.767680i | ||||
\(783\) | − | 232.203i | − | 0.296556i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 91.2061 | 0.116186 | ||||||||
\(786\) | −194.645 | − | 31.8575i | −0.247640 | − | 0.0405312i | ||||
\(787\) | 228.327 | + | 395.475i | 0.290124 | + | 0.502509i | 0.973839 | − | 0.227240i | \(-0.0729702\pi\) |
−0.683715 | + | 0.729749i | \(0.739637\pi\) | |||||||
\(788\) | 185.265 | − | 550.808i | 0.235107 | − | 0.698995i | ||||
\(789\) | 191.435 | + | 110.525i | 0.242630 | + | 0.140083i | ||||
\(790\) | 517.588 | + | 1369.41i | 0.655175 | + | 1.73343i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −764.264 | − | 404.411i | −0.964980 | − | 0.510619i | ||||
\(793\) | 68.7990 | − | 119.163i | 0.0867579 | − | 0.150269i | ||||
\(794\) | 870.269 | + | 712.185i | 1.09606 | + | 0.896958i | ||||
\(795\) | 21.2061 | + | 36.7300i | 0.0266743 | + | 0.0462012i | ||||
\(796\) | 1531.16 | − | 309.004i | 1.92357 | − | 0.388196i | ||||
\(797\) | − | 218.566i | − | 0.274236i | −0.990555 | − | 0.137118i | \(-0.956216\pi\) | ||
0.990555 | − | 0.137118i | \(-0.0437839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.5199i | 0.0957695i | ||||||||
\(800\) | −513.661 | + | 1736.77i | −0.642076 | + | 2.17096i | ||||
\(801\) | −484.529 | − | 839.229i | −0.604905 | − | 1.04773i | ||||
\(802\) | −102.858 | + | 125.690i | −0.128252 | + | 0.156720i | ||||
\(803\) | 291.446 | − | 504.799i | 0.362946 | − | 0.628641i | ||||
\(804\) | −138.177 | + | 121.860i | −0.171861 | + | 0.151568i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 107.196 | + | 283.614i | 0.132997 | + | 0.351878i | ||||
\(807\) | 14.2873 | + | 8.24879i | 0.0177042 | + | 0.0102215i | ||||
\(808\) | 96.9967 | − | 3.58118i | 0.120045 | − | 0.00443215i | ||||
\(809\) | −673.730 | − | 1166.93i | −0.832794 | − | 1.44244i | −0.895814 | − | 0.444429i | \(-0.853407\pi\) |
0.0630207 | − | 0.998012i | \(-0.479927\pi\) | |||||||
\(810\) | −209.673 | + | 1281.07i | −0.258855 | + | 1.58157i | ||||
\(811\) | 672.620 | 0.829371 | 0.414686 | − | 0.909965i | \(-0.363892\pi\) | ||||
0.414686 | + | 0.909965i | \(0.363892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 234.148i | − | 0.288005i | ||||||
\(814\) | 65.5429 | − | 400.457i | 0.0805195 | − | 0.491962i | ||||
\(815\) | 817.764 | − | 472.136i | 1.00339 | − | 0.579308i | ||||
\(816\) | −106.633 | + | 44.8664i | −0.130677 | + | 0.0549833i | ||||
\(817\) | −329.529 | + | 570.761i | −0.403340 | + | 0.698606i | ||||
\(818\) | 318.718 | + | 843.248i | 0.389631 | + | 1.03087i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 166.593 | + | 188.899i | 0.203162 | + | 0.230364i | ||||
\(821\) | 1006.82 | + | 581.286i | 1.22633 | + | 0.708022i | 0.966260 | − | 0.257567i | \(-0.0829209\pi\) |
0.260070 | + | 0.965590i | \(0.416254\pi\) | |||||||
\(822\) | 25.7364 | − | 31.4491i | 0.0313095 | − | 0.0382593i | ||||
\(823\) | −902.093 | + | 520.824i | −1.09610 | + | 0.632835i | −0.935195 | − | 0.354134i | \(-0.884776\pi\) |
−0.160908 | + | 0.986969i | \(0.551442\pi\) | |||||||
\(824\) | 453.283 | + | 722.191i | 0.550101 | + | 0.876445i | ||||
\(825\) | 413.941 | 0.501747 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 278.432 | 0.336678 | 0.168339 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(828\) | −836.418 | + | 168.798i | −1.01017 | + | 0.203862i | ||||
\(829\) | 922.956 | − | 532.869i | 1.11334 | − | 0.642785i | 0.173645 | − | 0.984808i | \(-0.444445\pi\) |
0.939692 | + | 0.342023i | \(0.111112\pi\) | |||||||
\(830\) | 564.636 | + | 462.070i | 0.680284 | + | 0.556711i | ||||
\(831\) | 52.2275 | + | 30.1535i | 0.0628489 | + | 0.0362859i | ||||
\(832\) | 477.990 | − | 325.194i | 0.574507 | − | 0.390858i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −44.5959 | − | 117.990i | −0.0534723 | − | 0.141474i | ||||
\(835\) | 1340.36 | − | 2321.57i | 1.60522 | − | 2.78033i | ||||
\(836\) | −1366.57 | − | 459.647i | −1.63466 | − | 0.549817i | ||||
\(837\) | −150.327 | + | 86.7913i | −0.179602 | + | 0.103693i | ||||
\(838\) | −1233.56 | − | 201.897i | −1.47203 | − | 0.240928i | ||||
\(839\) | − | 305.844i | − | 0.364533i | −0.983249 | − | 0.182267i | \(-0.941657\pi\) | ||
0.983249 | − | 0.182267i | \(-0.0583434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 337.000 | 0.400713 | ||||||||
\(842\) | −182.995 | + | 1118.07i | −0.217334 | + | 1.32788i | ||||
\(843\) | −44.0030 | − | 76.2154i | −0.0521981 | − | 0.0904097i | ||||
\(844\) | −621.956 | − | 209.195i | −0.736915 | − | 0.247861i | ||||
\(845\) | −683.741 | − | 394.758i | −0.809161 | − | 0.467169i | ||||
\(846\) | 100.402 | − | 37.9484i | 0.118679 | − | 0.0448563i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −127.236 | − | 16.0303i | −0.150043 | − | 0.0189036i | ||||
\(849\) | 52.2994 | − | 90.5853i | 0.0616012 | − | 0.106696i | ||||
\(850\) | −884.865 | + | 1081.28i | −1.04102 | + | 1.27209i | ||||
\(851\) | −200.221 | − | 346.793i | −0.235278 | − | 0.407513i | ||||
\(852\) | −40.2739 | + | 8.12769i | −0.0472699 | + | 0.00953954i | ||||
\(853\) | 164.018i | 0.192283i | 0.995368 | + | 0.0961417i | \(0.0306502\pi\) | ||||
−0.995368 | + | 0.0961417i | \(0.969350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2257.60i | 2.64047i | ||||||||
\(856\) | 430.934 | − | 270.476i | 0.503427 | − | 0.315976i | ||||
\(857\) | 425.534 | + | 737.047i | 0.496539 | + | 0.860031i | 0.999992 | − | 0.00399164i | \(-0.00127058\pi\) |
−0.503453 | + | 0.864023i | \(0.667937\pi\) | |||||||
\(858\) | −102.256 | − | 83.6812i | −0.119179 | − | 0.0975305i | ||||
\(859\) | −589.846 | + | 1021.64i | −0.686666 | + | 1.18934i | 0.286244 | + | 0.958157i | \(0.407593\pi\) |
−0.972910 | + | 0.231184i | \(0.925740\pi\) | |||||||
\(860\) | 545.588 | + | 618.639i | 0.634405 | + | 0.719347i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 541.658 | − | 204.728i | 0.628374 | − | 0.237503i | ||||
\(863\) | −241.662 | − | 139.524i | −0.280026 | − | 0.161673i | 0.353409 | − | 0.935469i | \(-0.385022\pi\) |
−0.633435 | + | 0.773796i | \(0.718356\pi\) | |||||||
\(864\) | 227.933 | + | 239.989i | 0.263811 | + | 0.277765i | ||||
\(865\) | −180.799 | − | 313.153i | −0.209016 | − | 0.362027i | ||||
\(866\) | 1179.69 | + | 193.081i | 1.36223 | + | 0.222957i | ||||
\(867\) | 80.0458 | 0.0923250 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1011.71i | 1.16423i | ||||||||
\(870\) | −234.468 | − | 38.3754i | −0.269504 | − | 0.0441097i | ||||
\(871\) | 615.098 | − | 355.127i | 0.706198 | − | 0.407723i | ||||
\(872\) | 1046.07 | − | 38.6215i | 1.19962 | − | 0.0442907i | ||||
\(873\) | 710.328 | − | 1230.32i | 0.813663 | − | 1.40931i | ||||
\(874\) | −1330.92 | + | 503.042i | −1.52280 | + | 0.575563i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −82.0446 | + | 72.3565i | −0.0936582 | + | 0.0825988i | ||||
\(877\) | 583.839 | + | 337.080i | 0.665723 | + | 0.384355i | 0.794454 | − | 0.607324i | \(-0.207757\pi\) |
−0.128731 | + | 0.991680i | \(0.541090\pi\) | |||||||
\(878\) | −59.4179 | − | 48.6247i | −0.0676742 | − | 0.0553812i | ||||
\(879\) | 111.196 | − | 64.1990i | 0.126503 | − | 0.0730364i | ||||
\(880\) | −1090.52 | + | 1437.71i | −1.23923 | + | 1.63376i | ||||
\(881\) | 1001.29 | 1.13654 | 0.568271 | − | 0.822841i | \(-0.307613\pi\) | ||||
0.568271 | + | 0.822841i | \(0.307613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 882.010 | 0.998879 | 0.499439 | − | 0.866349i | \(-0.333539\pi\) | ||||
0.499439 | + | 0.866349i | \(0.333539\pi\) | |||||||
\(884\) | 437.177 | − | 88.2267i | 0.494544 | − | 0.0998040i | ||||
\(885\) | 139.510 | − | 80.5463i | 0.157639 | − | 0.0910128i | ||||
\(886\) | −758.786 | + | 927.214i | −0.856418 | + | 1.04652i | ||||
\(887\) | 6.13192 | + | 3.54027i | 0.00691310 | + | 0.00399128i | 0.503453 | − | 0.864023i | \(-0.332063\pi\) |
−0.496539 | + | 0.868014i | \(0.665396\pi\) | |||||||
\(888\) | −35.6182 | + | 67.3120i | −0.0401106 | + | 0.0758018i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1891.75 | + | 715.014i | −2.12556 | + | 0.803386i | ||||
\(891\) | −448.551 | + | 776.914i | −0.503425 | + | 0.871957i | ||||
\(892\) | −13.4955 | + | 40.1232i | −0.0151294 | + | 0.0449812i | ||||
\(893\) | 154.998 | − | 89.4882i | 0.173570 | − | 0.100211i | ||||
\(894\) | −47.7202 | + | 291.564i | −0.0533783 | + | 0.326134i | ||||
\(895\) | 2662.92i | 2.97533i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −130.392 | −0.145364 | ||||||||
\(898\) | −907.996 | − | 148.612i | −1.01113 | − | 0.165492i | ||||
\(899\) | 188.382 | + | 326.287i | 0.209546 | + | 0.362944i | ||||
\(900\) | 1857.58 | + | 624.798i | 2.06398 | + | 0.694220i | ||||
\(901\) | −85.6776 | − | 49.4660i | −0.0950917 | − | 0.0549012i | ||||
\(902\) | 61.5391 | + | 162.817i | 0.0682252 | + | 0.180507i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −977.401 | − | 517.192i | −1.08120 | − | 0.572115i | ||||
\(905\) | −182.789 | + | 316.600i | −0.201977 | + | 0.349834i | ||||
\(906\) | 212.602 | + | 173.983i | 0.234660 | + | 0.192034i | ||||
\(907\) | −225.186 | − | 390.033i | −0.248275 | − | 0.430026i | 0.714772 | − | 0.699358i | \(-0.246530\pi\) |
−0.963047 | + | 0.269332i | \(0.913197\pi\) | |||||||
\(908\) | −169.182 | − | 838.324i | −0.186324 | − | 0.923264i | ||||
\(909\) | − | 105.032i | − | 0.115547i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 202.426i | 0.222201i | 0.993809 | + | 0.111101i | \(0.0354376\pi\) | ||||
−0.993809 | + | 0.111101i | \(0.964562\pi\) | |||||||
\(912\) | 215.586 | + | 163.524i | 0.236388 | + | 0.179303i | ||||
\(913\) | 252.108 | + | 436.663i | 0.276131 | + | 0.478273i | ||||
\(914\) | −337.333 | + | 412.211i | −0.369073 | + | 0.450997i | ||||
\(915\) | 40.3015 | − | 69.8043i | 0.0440454 | − | 0.0762888i | ||||
\(916\) | −613.889 | − | 696.085i | −0.670185 | − | 0.759918i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 90.2742 | + | 238.843i | 0.0983379 | + | 0.260178i | ||||
\(919\) | −1380.21 | − | 796.863i | −1.50186 | − | 0.867098i | −0.999998 | − | 0.00214879i | \(-0.999316\pi\) |
−0.501860 | − | 0.864949i | \(-0.667351\pi\) | |||||||
\(920\) | 65.7013 | + | 1779.53i | 0.0714145 | + | 1.93427i | ||||
\(921\) | −92.7502 | − | 160.648i | −0.100706 | − | 0.174428i | ||||
\(922\) | −246.521 | + | 1506.21i | −0.267376 | + | 1.63363i | ||||
\(923\) | 158.392 | 0.171606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 919.749i | 0.994323i | ||||||||
\(926\) | −40.0532 | + | 244.719i | −0.0432540 | + | 0.264276i | ||||
\(927\) | 799.052 | − | 461.333i | 0.861977 | − | 0.497662i | ||||
\(928\) | 520.900 | − | 494.731i | 0.561315 | − | 0.533116i | ||||
\(929\) | −519.701 | + | 900.148i | −0.559419 | + | 0.968943i | 0.438126 | + | 0.898914i | \(0.355643\pi\) |
−0.997545 | + | 0.0700290i | \(0.977691\pi\) | |||||||
\(930\) | 62.7939 | + | 166.137i | 0.0675204 | + | 0.178642i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 578.589 | − | 510.267i | 0.620803 | − | 0.547497i | ||||
\(933\) | 36.6606 | + | 21.1660i | 0.0392933 | + | 0.0226860i | ||||
\(934\) | −973.682 | + | 1189.81i | −1.04249 | + | 1.27389i | ||||
\(935\) | −1205.58 | + | 696.040i | −1.28939 | + | 0.744427i | ||||
\(936\) | −332.571 | − | 529.867i | −0.355311 | − | 0.566097i | ||||
\(937\) | −881.765 | −0.941051 | −0.470525 | − | 0.882386i | \(-0.655936\pi\) | ||||
−0.470525 | + | 0.882386i | \(0.655936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.0059 | 0.0511245 | ||||||||
\(940\) | −44.3121 | − | 219.573i | −0.0471406 | − | 0.233589i | ||||
\(941\) | −825.620 | + | 476.672i | −0.877386 | + | 0.506559i | −0.869796 | − | 0.493412i | \(-0.835749\pi\) |
−0.00759016 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(942\) | −9.15450 | − | 7.49158i | −0.00971815 | − | 0.00795285i | ||||
\(943\) | 148.755 | + | 85.8835i | 0.157746 | + | 0.0910747i | ||||
\(944\) | −60.8873 | + | 483.278i | −0.0644993 | + | 0.511947i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 201.539 | + | 533.222i | 0.213043 | + | 0.563660i | ||||
\(947\) | −8.44783 | + | 14.6321i | −0.00892063 | + | 0.0154510i | −0.870451 | − | 0.492255i | \(-0.836173\pi\) |
0.861531 | + | 0.507706i | \(0.169506\pi\) | |||||||
\(948\) | 60.5309 | − | 179.964i | 0.0638512 | − | 0.189835i | ||||
\(949\) | 365.224 | − | 210.862i | 0.384852 | − | 0.222194i | ||||
\(950\) | 3225.06 | + | 527.846i | 3.39480 | + | 0.555628i | ||||
\(951\) | − | 63.9386i | − | 0.0672330i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1526.31 | 1.60159 | 0.800794 | − | 0.598940i | \(-0.204411\pi\) | ||||
0.800794 | + | 0.598940i | \(0.204411\pi\) | |||||||
\(954\) | −22.4145 | + | 136.950i | −0.0234953 | + | 0.143553i | ||||
\(955\) | −708.784 | − | 1227.65i | −0.742182 | − | 1.28550i | ||||
\(956\) | −418.160 | + | 1243.23i | −0.437406 | + | 1.30045i | ||||
\(957\) | −142.195 | − | 82.0962i | −0.148584 | − | 0.0857849i | ||||
\(958\) | 222.593 | − | 84.1322i | 0.232352 | − | 0.0878207i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 280.000 | − | 190.494i | 0.291667 | − | 0.198431i | ||||
\(961\) | −339.676 | + | 588.336i | −0.353461 | + | 0.612212i | ||||
\(962\) | 185.934 | − | 227.206i | 0.193278 | − | 0.236181i | ||||
\(963\) | −275.279 | − | 476.798i | −0.285856 | − | 0.495117i | ||||
\(964\) | 56.8716 | + | 281.807i | 0.0589954 | + | 0.292331i | ||||
\(965\) | − | 2360.40i | − | 2.44601i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1410.39i | − | 1.45852i | −0.684235 | − | 0.729262i | \(-0.739864\pi\) | ||
0.684235 | − | 0.729262i | \(-0.260136\pi\) | |||||||
\(968\) | −236.359 | + | 148.351i | −0.244172 | + | 0.153255i | ||||
\(969\) | 104.372 | + | 180.777i | 0.107711 | + | 0.186560i | ||||
\(970\) | −2294.46 | − | 1877.67i | −2.36542 | − | 1.93574i | ||||
\(971\) | −298.248 | + | 516.581i | −0.307156 | + | 0.532009i | −0.977739 | − | 0.209825i | \(-0.932711\pi\) |
0.670583 | + | 0.741834i | \(0.266044\pi\) | |||||||
\(972\) | 405.536 | − | 357.649i | 0.417218 | − | 0.367952i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −528.653 | + | 199.812i | −0.542765 | + | 0.205146i | ||||
\(975\) | 259.365 | + | 149.744i | 0.266015 | + | 0.153584i | ||||
\(976\) | 94.5210 | + | 224.645i | 0.0968453 | + | 0.230169i | ||||
\(977\) | −73.3431 | − | 127.034i | −0.0750698 | − | 0.130025i | 0.826047 | − | 0.563601i | \(-0.190585\pi\) |
−0.901117 | + | 0.433577i | \(0.857251\pi\) | |||||||
\(978\) | −120.861 | − | 19.7814i | −0.123580 | − | 0.0202263i | ||||
\(979\) | −1397.62 | −1.42760 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1132.73i | − | 1.15467i | ||||||
\(982\) | −765.907 | − | 125.356i | −0.779946 | − | 0.127654i | ||||
\(983\) | 146.754 | − | 84.7286i | 0.149292 | − | 0.0861939i | −0.423493 | − | 0.905899i | \(-0.639196\pi\) |
0.572785 | + | 0.819705i | \(0.305863\pi\) | |||||||
\(984\) | −1.20523 | − | 32.6438i | −0.00122483 | − | 0.0331746i | ||||
\(985\) | −656.181 | + | 1136.54i | −0.666173 | + | 1.15385i | ||||
\(986\) | 518.412 | − | 195.941i | 0.525773 | − | 0.198723i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −689.980 | − | 782.364i | −0.698360 | − | 0.791866i | ||||
\(989\) | 487.167 | + | 281.266i | 0.492586 | + | 0.284395i | ||||
\(990\) | 1511.16 | + | 1236.65i | 1.52642 | + | 1.24915i | ||||
\(991\) | 1460.90 | − | 843.449i | 1.47416 | − | 0.851109i | 0.474588 | − | 0.880208i | \(-0.342597\pi\) |
0.999577 | + | 0.0290984i | \(0.00926363\pi\) | |||||||
\(992\) | −514.985 | − | 152.310i | −0.519138 | − | 0.153539i | ||||
\(993\) | −188.471 | −0.189800 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3527.52 | −3.54524 | ||||||||
\(996\) | −18.7194 | − | 92.7574i | −0.0187946 | − | 0.0931299i | ||||
\(997\) | 1503.54 | − | 868.068i | 1.50806 | − | 0.870680i | 0.508107 | − | 0.861294i | \(-0.330345\pi\) |
0.999956 | − | 0.00938643i | \(-0.00298784\pi\) | |||||||
\(998\) | 35.1056 | − | 42.8980i | 0.0351760 | − | 0.0429840i | ||||
\(999\) | 145.563 | + | 84.0410i | 0.145709 | + | 0.0841251i |
(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 | 392.3.k.j.275.4 | 8 | ||
7.2 | even | 3 | 392.3.g.h.99.1 | 4 | |||
7.3 | odd | 6 | 392.3.k.i.67.2 | 8 | |||
7.4 | even | 3 | inner | 392.3.k.j.67.2 | 8 | ||
7.5 | odd | 6 | 56.3.g.a.43.1 | ✓ | 4 | ||
7.6 | odd | 2 | 392.3.k.i.275.4 | 8 | |||
8.3 | odd | 2 | inner | 392.3.k.j.275.2 | 8 | ||
21.5 | even | 6 | 504.3.g.a.379.4 | 4 | |||
28.19 | even | 6 | 224.3.g.a.15.3 | 4 | |||
28.23 | odd | 6 | 1568.3.g.h.687.2 | 4 | |||
56.3 | even | 6 | 392.3.k.i.67.4 | 8 | |||
56.5 | odd | 6 | 224.3.g.a.15.4 | 4 | |||
56.11 | odd | 6 | inner | 392.3.k.j.67.4 | 8 | ||
56.19 | even | 6 | 56.3.g.a.43.2 | yes | 4 | ||
56.27 | even | 2 | 392.3.k.i.275.2 | 8 | |||
56.37 | even | 6 | 1568.3.g.h.687.1 | 4 | |||
56.51 | odd | 6 | 392.3.g.h.99.2 | 4 | |||
84.47 | odd | 6 | 2016.3.g.a.1135.4 | 4 | |||
112.5 | odd | 12 | 1792.3.d.g.1023.4 | 8 | |||
112.19 | even | 12 | 1792.3.d.g.1023.3 | 8 | |||
112.61 | odd | 12 | 1792.3.d.g.1023.5 | 8 | |||
112.75 | even | 12 | 1792.3.d.g.1023.6 | 8 | |||
168.5 | even | 6 | 2016.3.g.a.1135.1 | 4 | |||
168.131 | odd | 6 | 504.3.g.a.379.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.1 | ✓ | 4 | 7.5 | odd | 6 | ||
56.3.g.a.43.2 | yes | 4 | 56.19 | even | 6 | ||
224.3.g.a.15.3 | 4 | 28.19 | even | 6 | |||
224.3.g.a.15.4 | 4 | 56.5 | odd | 6 | |||
392.3.g.h.99.1 | 4 | 7.2 | even | 3 | |||
392.3.g.h.99.2 | 4 | 56.51 | odd | 6 | |||
392.3.k.i.67.2 | 8 | 7.3 | odd | 6 | |||
392.3.k.i.67.4 | 8 | 56.3 | even | 6 | |||
392.3.k.i.275.2 | 8 | 56.27 | even | 2 | |||
392.3.k.i.275.4 | 8 | 7.6 | odd | 2 | |||
392.3.k.j.67.2 | 8 | 7.4 | even | 3 | inner | ||
392.3.k.j.67.4 | 8 | 56.11 | odd | 6 | inner | ||
392.3.k.j.275.2 | 8 | 8.3 | odd | 2 | inner | ||
392.3.k.j.275.4 | 8 | 1.1 | even | 1 | trivial | ||
504.3.g.a.379.3 | 4 | 168.131 | odd | 6 | |||
504.3.g.a.379.4 | 4 | 21.5 | even | 6 | |||
1568.3.g.h.687.1 | 4 | 56.37 | even | 6 | |||
1568.3.g.h.687.2 | 4 | 28.23 | odd | 6 | |||
1792.3.d.g.1023.3 | 8 | 112.19 | even | 12 | |||
1792.3.d.g.1023.4 | 8 | 112.5 | odd | 12 | |||
1792.3.d.g.1023.5 | 8 | 112.61 | odd | 12 | |||
1792.3.d.g.1023.6 | 8 | 112.75 | even | 12 | |||
2016.3.g.a.1135.1 | 4 | 168.5 | even | 6 | |||
2016.3.g.a.1135.4 | 4 | 84.47 | odd | 6 |