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 | \(1.20711 - 2.54762i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.275 |
Dual form | 392.3.k.i.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 | 0.813073 | − | 0.582162i | \(-0.197793\pi\) |
−0.910704 | + | 0.413060i | \(0.864460\pi\) | |||||||
\(4\) | 3.79129 | + | 1.27520i | 0.947822 | + | 0.318800i | ||||
\(5\) | 7.82295 | + | 4.51658i | 1.56459 | + | 0.903316i | 0.996782 | + | 0.0801541i | \(0.0255412\pi\) |
0.567807 | + | 0.823162i | \(0.307792\pi\) | |||||||
\(6\) | −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 | \(0.112945\pi\) | ||||
−0.937706 | + | 0.347429i | \(0.887055\pi\) | |||||||
\(14\) | 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 | 0.625425 | − | 0.780284i | \(-0.284926\pi\) |
−0.988459 | + | 0.151492i | \(0.951592\pi\) | |||||||
\(18\) | 10.9650 | − | 13.3990i | 0.609169 | − | 0.744387i | ||||
\(19\) | −14.4350 | + | 25.0022i | −0.759738 | + | 1.31591i | 0.183246 | + | 0.983067i | \(0.441340\pi\) |
−0.942984 | + | 0.332838i | \(0.891994\pi\) | |||||||
\(20\) | 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 | −0.246915 | − | 0.969037i | \(-0.579417\pi\) |
0.715753 | + | 0.698353i | \(0.246084\pi\) | |||||||
\(32\) | 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 | \(-0.472909\pi\) | ||||
0.0850069 | + | 0.996380i | \(0.472909\pi\) | |||||||
\(42\) | 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 | 0.441796 | − | 0.897115i | \(-0.354341\pi\) |
−0.556027 | + | 0.831165i | \(0.687675\pi\) | |||||||
\(48\) | 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 | 0.707708 | − | 0.706505i | \(-0.249729\pi\) |
−0.965705 | + | 0.259641i | \(0.916396\pi\) | |||||||
\(60\) | 6.74773 | − | 20.0616i | 0.112462 | − | 0.334360i | ||||
\(61\) | −13.1918 | − | 7.61627i | −0.216258 | − | 0.124857i | 0.387958 | − | 0.921677i | \(-0.373181\pi\) |
−0.604217 | + | 0.796820i | \(0.706514\pi\) | |||||||
\(62\) | 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 | 0.660671 | − | 0.750676i | \(-0.270272\pi\) |
−0.980440 | + | 0.196820i | \(0.936939\pi\) | |||||||
\(74\) | 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 | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(84\) | 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 | \(0.383154\pi\) |
−0.987776 | + | 0.155878i | \(0.950179\pi\) | |||||||
\(90\) | 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 | \(-0.820945\pi\) | ||||
−0.845916 | + | 0.533317i | \(0.820945\pi\) | |||||||
\(98\) | 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 | −0.551114 | − | 0.834430i | \(-0.685797\pi\) |
0.447081 | + | 0.894494i | \(0.352464\pi\) | |||||||
\(102\) | −9.15831 | + | 11.1912i | −0.0897874 | + | 0.109718i | ||||
\(103\) | −92.3029 | − | 53.2911i | −0.896144 | − | 0.517389i | −0.0201970 | − | 0.999796i | \(-0.506429\pi\) |
−0.875947 | + | 0.482407i | \(0.839763\pi\) | |||||||
\(104\) | −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 | \(-0.611206\pi\) |
0.984860 | − | 0.173353i | \(-0.0554603\pi\) | |||||||
\(132\) | −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 | \(-0.373414\pi\) | ||||
0.387281 | + | 0.921962i | \(0.373414\pi\) | |||||||
\(140\) | 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 | −0.471894 | − | 0.881655i | \(-0.656430\pi\) |
0.527589 | + | 0.849500i | \(0.323096\pi\) | |||||||
\(158\) | −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 | \(-0.651736\pi\) | ||
0.458843 | − | 0.888517i | \(-0.348264\pi\) | |||||||
\(168\) | 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 | 0.396449 | − | 0.918057i | \(-0.370242\pi\) |
−0.596836 | + | 0.802363i | \(0.703576\pi\) | |||||||
\(174\) | −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 | \(0.0356608\pi\) | ||||
−0.993731 | + | 0.111797i | \(0.964339\pi\) | |||||||
\(182\) | 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 | \(0.771472\pi\) |
−0.946283 | + | 0.323339i | \(0.895195\pi\) | |||||||
\(200\) | 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 | \(-0.992446\pi\) | ||
0.999718 | − | 0.0237287i | \(-0.00755379\pi\) | |||||||
\(224\) | 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 | 0.999447 | − | 0.0332382i | \(-0.0105820\pi\) |
−0.528509 | + | 0.848928i | \(0.677249\pi\) | |||||||
\(228\) | 64.1171 | + | 21.5658i | 0.281215 | + | 0.0945868i | ||||
\(229\) | 200.942 | + | 116.014i | 0.877478 | + | 0.506612i | 0.869826 | − | 0.493359i | \(-0.164231\pi\) |
0.00765200 | + | 0.999971i | \(0.497564\pi\) | |||||||
\(230\) | −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 | 0.781787 | − | 0.623545i | \(-0.214308\pi\) |
−0.930900 | + | 0.365275i | \(0.880975\pi\) | |||||||
\(242\) | −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 | \(-0.671018\pi\) | ||||
−0.511790 | + | 0.859110i | \(0.671018\pi\) | |||||||
\(252\) | 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 | \(0.380065\pi\) |
−0.989242 | + | 0.146285i | \(0.953268\pi\) | |||||||
\(258\) | 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 | −0.544649 | − | 0.838664i | \(-0.683337\pi\) |
0.453980 | + | 0.891012i | \(0.350004\pi\) | |||||||
\(270\) | −144.612 | − | 118.343i | −0.535599 | − | 0.438308i | ||||
\(271\) | 346.164 | + | 199.858i | 1.27736 | + | 0.737482i | 0.976362 | − | 0.216143i | \(-0.0693479\pi\) |
0.300995 | + | 0.953626i | \(0.402681\pi\) | |||||||
\(272\) | 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 | 0.979539 | − | 0.201253i | \(-0.0645013\pi\) |
−0.664060 | + | 0.747679i | \(0.731168\pi\) | |||||||
\(284\) | −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 | \(0.122029\pi\) | ||||
−0.927411 | + | 0.374043i | \(0.877971\pi\) | |||||||
\(294\) | 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 | \(-0.327514\pi\) | ||||
0.515748 | + | 0.856741i | \(0.327514\pi\) | |||||||
\(308\) | 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 | −0.597231 | − | 0.802070i | \(-0.703732\pi\) |
0.395997 | + | 0.918252i | \(0.370399\pi\) | |||||||
\(312\) | 42.3032 | − | 1.56186i | 0.135587 | − | 0.00500596i | ||||
\(313\) | −40.9756 | + | 70.9718i | −0.130913 | + | 0.226747i | −0.924029 | − | 0.382323i | \(-0.875124\pi\) |
0.793116 | + | 0.609071i | \(0.208457\pi\) | |||||||
\(314\) | 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 | \(-0.877322\pi\) | ||
0.926646 | − | 0.375934i | \(-0.122678\pi\) | |||||||
\(350\) | 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 | \(0.138713\pi\) |
−0.0877061 | + | 0.996146i | \(0.527954\pi\) | |||||||
\(354\) | −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 | 0.260784 | − | 0.965397i | \(-0.416019\pi\) |
0.966451 | + | 0.256853i | \(0.0826856\pi\) | |||||||
\(368\) | −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 | 0.813091 | − | 0.582136i | \(-0.197783\pi\) |
−0.0975993 | + | 0.995226i | \(0.531116\pi\) | |||||||
\(384\) | 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 | −0.260237 | − | 0.965545i | \(-0.583801\pi\) |
−0.966305 | + | 0.257400i | \(0.917134\pi\) | |||||||
\(398\) | −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 | \(-0.980905\pi\) |
0.447180 | − | 0.894444i | \(-0.352428\pi\) | |||||||
\(410\) | 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 | \(-0.232063\pi\) | ||||
0.745809 | + | 0.666160i | \(0.232063\pi\) | |||||||
\(420\) | 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 | \(-0.742468\pi\) | ||||
−0.690180 | + | 0.723638i | \(0.742468\pi\) | |||||||
\(434\) | 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 | 0.537387 | − | 0.843336i | \(-0.319411\pi\) |
−0.461656 | + | 0.887059i | \(0.652745\pi\) | |||||||
\(440\) | 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 | \(-0.689659\pi\) | ||
0.561196 | − | 0.827683i | \(-0.310341\pi\) | |||||||
\(462\) | 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 | \(-0.525610\pi\) |
0.903409 | − | 0.428779i | \(-0.141056\pi\) | |||||||
\(468\) | 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 | −0.603687 | − | 0.797222i | \(-0.706302\pi\) |
0.388571 | + | 0.921419i | \(0.372969\pi\) | |||||||
\(480\) | 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 | \(0.257301\pi\) | ||||
−0.690703 | + | 0.723138i | \(0.742699\pi\) | |||||||
\(504\) | 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 | 0.930630 | − | 0.365961i | \(-0.119260\pi\) |
0.148384 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(510\) | −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 | \(-0.871740\pi\) |
0.120366 | − | 0.992730i | \(-0.461593\pi\) | |||||||
\(522\) | −300.806 | − | 246.165i | −0.576257 | − | 0.471580i | ||||
\(523\) | −438.217 | + | 759.014i | −0.837891 | + | 1.45127i | 0.0537645 | + | 0.998554i | \(0.482878\pi\) |
−0.891655 | + | 0.452715i | \(0.850455\pi\) | |||||||
\(524\) | 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 | 0.936844 | − | 0.349747i | \(-0.113733\pi\) |
−0.771312 | + | 0.636457i | \(0.780399\pi\) | |||||||
\(564\) | −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 | \(-0.869329\pi\) |
0.112841 | − | 0.993613i | \(-0.464005\pi\) | |||||||
\(578\) | 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 | \(-0.588190\pi\) | ||||
−0.273526 | + | 0.961865i | \(0.588190\pi\) | |||||||
\(588\) | 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 | −0.758663 | − | 0.651483i | \(-0.774147\pi\) |
0.943532 | + | 0.331280i | \(0.107481\pi\) | |||||||
\(594\) | 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 | \(-0.445214\pi\) | ||||
0.171266 | + | 0.985225i | \(0.445214\pi\) | |||||||
\(602\) | 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 | 0.943447 | − | 0.331523i | \(-0.107562\pi\) |
0.184616 | + | 0.982811i | \(0.440896\pi\) | |||||||
\(608\) | −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 | 0.997405 | − | 0.0720012i | \(-0.0229386\pi\) |
−0.561057 | + | 0.827777i | \(0.689605\pi\) | |||||||
\(620\) | 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 | \(-0.433606\pi\) | ||||
0.207074 | + | 0.978325i | \(0.433606\pi\) | |||||||
\(644\) | 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 | 0.455250 | − | 0.890363i | \(-0.349550\pi\) |
0.998703 | + | 0.0509233i | \(0.0162164\pi\) | |||||||
\(648\) | −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 | 0.320842 | − | 0.947133i | \(-0.396034\pi\) |
0.980662 | + | 0.195710i | \(0.0627010\pi\) | |||||||
\(662\) | −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 | 0.977679 | − | 0.210103i | \(-0.0673801\pi\) |
0.306885 | + | 0.951747i | \(0.400713\pi\) | |||||||
\(678\) | 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 | −0.703127 | − | 0.711064i | \(-0.748213\pi\) |
0.967363 | + | 0.253394i | \(0.0815468\pi\) | |||||||
\(692\) | −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 | −0.276036 | − | 0.961147i | \(-0.589021\pi\) |
−0.970396 | + | 0.241520i | \(0.922354\pi\) | |||||||
\(720\) | 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 | \(0.110610\pi\) | ||||
−0.940230 | + | 0.340540i | \(0.889390\pi\) | |||||||
\(728\) | 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 | 0.125777 | − | 0.992059i | \(-0.459858\pi\) |
−0.796260 | + | 0.604955i | \(0.793191\pi\) | |||||||
\(734\) | 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 | −0.994208 | − | 0.107475i | \(-0.965723\pi\) |
0.590180 | + | 0.807272i | \(0.299057\pi\) | |||||||
\(762\) | 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 | \(-0.462880\pi\) | ||||
0.116353 | + | 0.993208i | \(0.462880\pi\) | |||||||
\(770\) | 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 | −0.810181 | − | 0.586180i | \(-0.800631\pi\) |
0.102556 | + | 0.994727i | \(0.467298\pi\) | |||||||
\(774\) | −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 | 0.683715 | − | 0.729749i | \(-0.260363\pi\) |
−0.973839 | + | 0.227240i | \(0.927030\pi\) | |||||||
\(788\) | 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 | \(0.0437839\pi\) | ||||
−0.990555 | + | 0.137118i | \(0.956216\pi\) | |||||||
\(798\) | 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 | \(-0.636108\pi\) | ||||
−0.414686 | + | 0.909965i | \(0.636108\pi\) | |||||||
\(812\) | 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 | −0.939692 | − | 0.342023i | \(-0.888888\pi\) |
−0.173645 | + | 0.984808i | \(0.555555\pi\) | |||||||
\(830\) | 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 | \(0.0583434\pi\) | ||||
−0.983249 | + | 0.182267i | \(0.941657\pi\) | |||||||
\(840\) | 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 | \(-0.969350\pi\) | ||
0.995368 | − | 0.0961417i | \(-0.0306502\pi\) | |||||||
\(854\) | 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 | 0.503453 | − | 0.864023i | \(-0.332063\pi\) |
−0.999992 | + | 0.00399164i | \(0.998729\pi\) | |||||||
\(858\) | −102.256 | − | 83.6812i | −0.119179 | − | 0.0975305i | ||||
\(859\) | 589.846 | − | 1021.64i | 0.686666 | − | 1.18934i | −0.286244 | − | 0.958157i | \(-0.592407\pi\) |
0.972910 | − | 0.231184i | \(-0.0742599\pi\) | |||||||
\(860\) | −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 | \(-0.692387\pi\) | ||||
−0.568271 | + | 0.822841i | \(0.692387\pi\) | |||||||
\(882\) | 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 | 0.496539 | − | 0.868014i | \(-0.334604\pi\) |
−0.503453 | + | 0.864023i | \(0.667937\pi\) | |||||||
\(888\) | 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 | \(-0.644357\pi\) |
0.997545 | − | 0.0700290i | \(-0.0223092\pi\) | |||||||
\(930\) | −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 | \(-0.344064\pi\) | ||||
0.470525 | + | 0.882386i | \(0.344064\pi\) | |||||||
\(938\) | 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 | 0.00759016 | − | 0.999971i | \(-0.497584\pi\) |
0.869796 | + | 0.493412i | \(0.164251\pi\) | |||||||
\(942\) | −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 | −0.670583 | − | 0.741834i | \(-0.733956\pi\) |
0.977739 | + | 0.209825i | \(0.0672894\pi\) | |||||||
\(972\) | −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 | −0.572785 | − | 0.819705i | \(-0.694137\pi\) |
0.423493 | + | 0.905899i | \(0.360804\pi\) | |||||||
\(984\) | −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 | \(0.669655\pi\) |
−0.999956 | + | 0.00938643i | \(0.997012\pi\) | |||||||
\(998\) | 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.i.275.4 | 8 | ||
7.2 | even | 3 | 56.3.g.a.43.1 | ✓ | 4 | ||
7.3 | odd | 6 | 392.3.k.j.67.2 | 8 | |||
7.4 | even | 3 | inner | 392.3.k.i.67.2 | 8 | ||
7.5 | odd | 6 | 392.3.g.h.99.1 | 4 | |||
7.6 | odd | 2 | 392.3.k.j.275.4 | 8 | |||
8.3 | odd | 2 | inner | 392.3.k.i.275.2 | 8 | ||
21.2 | odd | 6 | 504.3.g.a.379.4 | 4 | |||
28.19 | even | 6 | 1568.3.g.h.687.2 | 4 | |||
28.23 | odd | 6 | 224.3.g.a.15.3 | 4 | |||
56.3 | even | 6 | 392.3.k.j.67.4 | 8 | |||
56.5 | odd | 6 | 1568.3.g.h.687.1 | 4 | |||
56.11 | odd | 6 | inner | 392.3.k.i.67.4 | 8 | ||
56.19 | even | 6 | 392.3.g.h.99.2 | 4 | |||
56.27 | even | 2 | 392.3.k.j.275.2 | 8 | |||
56.37 | even | 6 | 224.3.g.a.15.4 | 4 | |||
56.51 | odd | 6 | 56.3.g.a.43.2 | yes | 4 | ||
84.23 | even | 6 | 2016.3.g.a.1135.4 | 4 | |||
112.37 | even | 12 | 1792.3.d.g.1023.4 | 8 | |||
112.51 | odd | 12 | 1792.3.d.g.1023.3 | 8 | |||
112.93 | even | 12 | 1792.3.d.g.1023.5 | 8 | |||
112.107 | odd | 12 | 1792.3.d.g.1023.6 | 8 | |||
168.107 | even | 6 | 504.3.g.a.379.3 | 4 | |||
168.149 | odd | 6 | 2016.3.g.a.1135.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.1 | ✓ | 4 | 7.2 | even | 3 | ||
56.3.g.a.43.2 | yes | 4 | 56.51 | odd | 6 | ||
224.3.g.a.15.3 | 4 | 28.23 | odd | 6 | |||
224.3.g.a.15.4 | 4 | 56.37 | even | 6 | |||
392.3.g.h.99.1 | 4 | 7.5 | odd | 6 | |||
392.3.g.h.99.2 | 4 | 56.19 | even | 6 | |||
392.3.k.i.67.2 | 8 | 7.4 | even | 3 | inner | ||
392.3.k.i.67.4 | 8 | 56.11 | odd | 6 | inner | ||
392.3.k.i.275.2 | 8 | 8.3 | odd | 2 | inner | ||
392.3.k.i.275.4 | 8 | 1.1 | even | 1 | trivial | ||
392.3.k.j.67.2 | 8 | 7.3 | odd | 6 | |||
392.3.k.j.67.4 | 8 | 56.3 | even | 6 | |||
392.3.k.j.275.2 | 8 | 56.27 | even | 2 | |||
392.3.k.j.275.4 | 8 | 7.6 | odd | 2 | |||
504.3.g.a.379.3 | 4 | 168.107 | even | 6 | |||
504.3.g.a.379.4 | 4 | 21.2 | odd | 6 | |||
1568.3.g.h.687.1 | 4 | 56.5 | odd | 6 | |||
1568.3.g.h.687.2 | 4 | 28.19 | even | 6 | |||
1792.3.d.g.1023.3 | 8 | 112.51 | odd | 12 | |||
1792.3.d.g.1023.4 | 8 | 112.37 | even | 12 | |||
1792.3.d.g.1023.5 | 8 | 112.93 | even | 12 | |||
1792.3.d.g.1023.6 | 8 | 112.107 | odd | 12 | |||
2016.3.g.a.1135.1 | 4 | 168.149 | odd | 6 | |||
2016.3.g.a.1135.4 | 4 | 84.23 | even | 6 |