Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.24 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.24 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.962094 | − | 2.84154i | 0.320698 | − | 0.947181i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.17611 | − | 7.23323i | −0.835221 | − | 1.44665i | −0.893850 | − | 0.448365i | \(-0.852006\pi\) |
0.0586293 | − | 0.998280i | \(-0.481327\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.352343 | + | 0.610277i | 0.0503348 | + | 0.0871824i | 0.890095 | − | 0.455775i | \(-0.150638\pi\) |
−0.839760 | + | 0.542957i | \(0.817305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.14875 | − | 5.46767i | −0.794305 | − | 0.607519i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.3266 | − | 17.8862i | −0.938780 | − | 1.62601i | −0.767751 | − | 0.640749i | \(-0.778624\pi\) |
−0.171029 | − | 0.985266i | \(-0.554709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.59104i | 0.660849i | 0.943832 | + | 0.330425i | \(0.107192\pi\) | ||||
−0.943832 | + | 0.330425i | \(0.892808\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.5713 | + | 4.90754i | −1.63809 | + | 0.327169i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.72428 | − | 4.71858i | 0.160251 | − | 0.277564i | −0.774707 | − | 0.632320i | \(-0.782103\pi\) |
0.934959 | + | 0.354756i | \(0.115436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.849123 | + | 18.9810i | 0.0446907 | + | 0.999001i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.07312 | − | 0.414056i | 0.0987198 | − | 0.0197169i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.7392 | 1.03214 | 0.516069 | − | 0.856547i | \(-0.327395\pi\) | ||||
0.516069 | + | 0.856547i | \(0.327395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22.3797 | + | 38.7628i | −0.895188 | + | 1.55051i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −22.4144 | + | 15.0531i | −0.830163 | + | 0.557521i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.06106 | − | 1.18995i | −0.0710711 | − | 0.0410329i | 0.464043 | − | 0.885812i | \(-0.346398\pi\) |
−0.535114 | + | 0.844780i | \(0.679732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.32115 | − | 1.34012i | −0.0748757 | − | 0.0432295i | 0.462095 | − | 0.886831i | \(-0.347098\pi\) |
−0.536970 | + | 0.843601i | \(0.680431\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −60.7595 | + | 12.1353i | −1.84120 | + | 0.367735i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.94285 | − | 5.09716i | 0.0840813 | − | 0.145633i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 19.8089i | − | 0.535376i | −0.963506 | − | 0.267688i | \(-0.913740\pi\) | ||
0.963506 | − | 0.267688i | \(-0.0862596\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.4118 | + | 8.26539i | 0.625944 | + | 0.211933i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 65.3355 | − | 37.7215i | 1.59355 | − | 0.920036i | 0.600857 | − | 0.799356i | \(-0.294826\pi\) |
0.992692 | − | 0.120679i | \(-0.0385073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8967 | 0.253412 | 0.126706 | − | 0.991940i | \(-0.459559\pi\) | ||||
0.126706 | + | 0.991940i | \(0.459559\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.69495 | + | 74.5421i | −0.215443 | + | 1.65649i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −15.4130 | + | 26.6960i | −0.327936 | + | 0.568001i | −0.982102 | − | 0.188350i | \(-0.939686\pi\) |
0.654167 | + | 0.756351i | \(0.273020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 24.2517 | − | 42.0052i | 0.494933 | − | 0.857249i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.7871 | − | 12.2809i | −0.211511 | − | 0.240801i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −76.8522 | + | 44.3706i | −1.45004 | + | 0.837182i | −0.998483 | − | 0.0550603i | \(-0.982465\pi\) |
−0.451558 | + | 0.892242i | \(0.649132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −86.2498 | + | 149.389i | −1.56818 | + | 2.71616i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 54.7523 | + | 15.8487i | 0.960567 | + | 0.278047i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −79.2807 | + | 45.7727i | −1.34374 | + | 0.775809i | −0.987354 | − | 0.158529i | \(-0.949325\pi\) |
−0.356387 | + | 0.934339i | \(0.615991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.04264 | − | 8.73410i | 0.0826662 | − | 0.143182i | −0.821728 | − | 0.569880i | \(-0.806990\pi\) |
0.904394 | + | 0.426698i | \(0.140323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.817975 | − | 6.28921i | 0.0129837 | − | 0.0998287i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 62.1410 | − | 35.8771i | 0.956015 | − | 0.551955i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 16.0987i | − | 0.240280i | −0.992757 | − | 0.120140i | \(-0.961666\pi\) | ||
0.992757 | − | 0.120140i | \(-0.0383343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.8393 | − | 67.4559i | 0.331004 | − | 0.977621i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 67.0947 | + | 38.7371i | 0.944995 | + | 0.545593i | 0.891523 | − | 0.452976i | \(-0.149638\pi\) |
0.0534727 | + | 0.998569i | \(0.482971\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.6851 | + | 68.7366i | −0.543631 | + | 0.941597i | 0.455061 | + | 0.890460i | \(0.349618\pi\) |
−0.998692 | + | 0.0511363i | \(0.983716\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 88.6148 | + | 100.886i | 1.18153 | + | 1.34515i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.27700 | − | 12.6041i | 0.0945065 | − | 0.163690i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 90.4947i | − | 1.14550i | −0.819729 | − | 0.572751i | \(-0.805876\pi\) | ||
0.819729 | − | 0.572751i | \(-0.194124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 21.2092 | + | 78.1740i | 0.261842 | + | 0.965111i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −31.5302 | − | 54.6119i | −0.379882 | − | 0.657975i | 0.611163 | − | 0.791505i | \(-0.290702\pi\) |
−0.991045 | + | 0.133530i | \(0.957369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −45.5074 | −0.535382 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.36424 | + | 4.71175i | −0.0616580 | + | 0.0541580i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −65.0621 | + | 37.5636i | −0.731035 | + | 0.422063i | −0.818801 | − | 0.574078i | \(-0.805361\pi\) |
0.0877659 | + | 0.996141i | \(0.472027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.24291 | + | 3.02700i | −0.0576144 | + | 0.0332637i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.04116 | + | 5.30633i | −0.0649587 | + | 0.0570573i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 133.748 | − | 85.4086i | 1.40787 | − | 0.899038i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 75.6045i | − | 0.779428i | −0.920936 | − | 0.389714i | \(-0.872574\pi\) | ||
0.920936 | − | 0.389714i | \(-0.127426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.9734 | + | 184.326i | −0.242156 | + | 1.86188i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −42.4567 | + | 73.5371i | −0.420363 | + | 0.728090i | −0.995975 | − | 0.0896329i | \(-0.971431\pi\) |
0.575612 | + | 0.817723i | \(0.304764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −24.5788 | − | 14.1906i | −0.238629 | − | 0.137772i | 0.375918 | − | 0.926653i | \(-0.377328\pi\) |
−0.614546 | + | 0.788881i | \(0.710661\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.6525 | − | 13.2662i | −0.110976 | − | 0.126345i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 148.821i | − | 1.39085i | −0.718600 | − | 0.695423i | \(-0.755217\pi\) | ||
0.718600 | − | 0.695423i | \(-0.244783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.6931 | − | 28.6903i | −0.455900 | − | 0.263214i | 0.254419 | − | 0.967094i | \(-0.418116\pi\) |
−0.710319 | + | 0.703880i | \(0.751449\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −56.2879 | − | 19.0580i | −0.507098 | − | 0.171694i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −59.1471 | − | 34.1486i | −0.523426 | − | 0.302200i | 0.214909 | − | 0.976634i | \(-0.431054\pi\) |
−0.738335 | + | 0.674434i | \(0.764388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −99.1372 | − | 171.711i | −0.862063 | − | 1.49314i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 46.9730 | − | 61.4152i | 0.401478 | − | 0.524916i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.83952 | 0.0322649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152.776 | + | 264.617i | −1.26262 | + | 2.18691i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −44.3283 | − | 221.945i | −0.360393 | − | 1.80443i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 165.035 | 1.32028 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −45.0028 | + | 25.9824i | −0.354353 | + | 0.204586i | −0.666601 | − | 0.745415i | \(-0.732251\pi\) |
0.312248 | + | 0.950001i | \(0.398918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4837 | − | 30.9635i | 0.0812689 | − | 0.240027i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −45.3935 | − | 78.6238i | −0.346515 | − | 0.600181i | 0.639113 | − | 0.769113i | \(-0.279302\pi\) |
−0.985628 | + | 0.168932i | \(0.945968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.2845 | + | 7.20604i | −0.0848458 | + | 0.0541807i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 202.487 | + | 99.2651i | 1.49990 | + | 0.735297i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −116.094 | + | 201.081i | −0.847403 | + | 1.46774i | 0.0361153 | + | 0.999348i | \(0.488502\pi\) |
−0.883518 | + | 0.468397i | \(0.844832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −26.3828 | −0.189804 | −0.0949022 | − | 0.995487i | \(-0.530254\pi\) | ||||
−0.0949022 | + | 0.995487i | \(0.530254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 61.0293 | + | 69.4808i | 0.432832 | + | 0.492771i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 153.661 | − | 88.7161i | 1.07455 | − | 0.620392i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.8775i | 0.137086i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −96.0272 | − | 109.325i | −0.653246 | − | 0.743709i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −50.4334 | − | 87.3533i | −0.338479 | − | 0.586264i | 0.645668 | − | 0.763619i | \(-0.276579\pi\) |
−0.984147 | + | 0.177355i | \(0.943246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 201.351 | − | 116.250i | 1.33345 | − | 0.769868i | 0.347624 | − | 0.937634i | \(-0.386988\pi\) |
0.985827 | + | 0.167765i | \(0.0536551\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −45.2748 | + | 18.8365i | −0.295914 | + | 0.123115i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.3859i | 0.144425i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.6975 | − | 170.949i | −0.628647 | − | 1.08885i | −0.987824 | − | 0.155578i | \(-0.950276\pi\) |
0.359177 | − | 0.933269i | \(-0.383057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 52.1421 | + | 261.068i | 0.327937 | + | 1.64193i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.36433 | + | 14.4875i | 0.0519524 | + | 0.0899842i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −238.025 | −1.46027 | −0.730137 | − | 0.683301i | \(-0.760544\pi\) | ||||
−0.730137 | + | 0.683301i | \(0.760544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 341.515 | + | 388.809i | 2.06979 | + | 2.35642i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 251.379i | − | 1.50526i | −0.658443 | − | 0.752631i | \(-0.728784\pi\) | ||
0.658443 | − | 0.752631i | \(-0.271216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 95.1940 | 0.563278 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 97.7117 | − | 140.333i | 0.571414 | − | 0.820662i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 274.857i | 1.58877i | 0.607416 | + | 0.794384i | \(0.292206\pi\) | ||||
−0.607416 | + | 0.794384i | \(0.707794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −31.5414 | −0.180236 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 53.7898 | + | 269.317i | 0.303897 | + | 1.52157i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 106.008i | − | 0.592221i | −0.955154 | − | 0.296111i | \(-0.904310\pi\) | ||
0.955154 | − | 0.296111i | \(-0.0956897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 155.686 | − | 89.8854i | 0.860144 | − | 0.496604i | −0.00391638 | − | 0.999992i | \(-0.501247\pi\) |
0.864061 | + | 0.503388i | \(0.167913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.9668 | − | 22.7319i | −0.109108 | − | 0.124218i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −143.282 | + | 82.7240i | −0.774499 | + | 0.447157i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −112.530 | −0.601763 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.0841 | − | 8.37513i | −0.0903921 | − | 0.0443128i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −60.2220 | − | 104.308i | −0.315298 | − | 0.546113i | 0.664203 | − | 0.747553i | \(-0.268771\pi\) |
−0.979501 | + | 0.201440i | \(0.935438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −101.549 | + | 58.6291i | −0.526158 | + | 0.303778i | −0.739451 | − | 0.673211i | \(-0.764915\pi\) |
0.213292 | + | 0.976988i | \(0.431581\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −42.1609 | − | 211.093i | −0.216210 | − | 1.08253i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 216.141 | 1.09716 | 0.548581 | − | 0.836098i | \(-0.315168\pi\) | ||||
0.548581 | + | 0.836098i | \(0.315168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 129.858 | + | 224.920i | 0.652551 | + | 1.13025i | 0.982502 | + | 0.186254i | \(0.0596347\pi\) |
−0.329950 | + | 0.943998i | \(0.607032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −45.7453 | − | 15.4885i | −0.227589 | − | 0.0770573i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.67709i | − | 0.00826153i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −545.696 | − | 315.058i | −2.66193 | − | 1.53687i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −169.705 | − | 129.798i | −0.819832 | − | 0.627042i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 330.729 | − | 211.197i | 1.58244 | − | 1.01051i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −36.2971 | + | 20.9561i | −0.172024 | + | 0.0993182i | −0.583540 | − | 0.812084i | \(-0.698333\pi\) |
0.411516 | + | 0.911403i | \(0.365000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 174.625 | − | 153.384i | 0.819834 | − | 0.720111i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −45.5059 | − | 78.8185i | −0.211655 | − | 0.366598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.88872i | − | 0.00870379i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 157.137 | + | 178.898i | 0.717522 | + | 0.816886i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.5375 | + | 23.4044i | 0.183428 | + | 0.105902i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 105.577i | − | 0.473439i | −0.971578 | − | 0.236720i | \(-0.923928\pi\) | ||
0.971578 | − | 0.236720i | \(-0.0760723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 371.929 | − | 154.741i | 1.65302 | − | 0.687736i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 384.737 | − | 222.128i | 1.69488 | − | 0.978537i | 0.744403 | − | 0.667730i | \(-0.232734\pi\) |
0.950473 | − | 0.310807i | \(-0.100599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 118.302 | − | 204.906i | 0.516604 | − | 0.894784i | −0.483210 | − | 0.875504i | \(-0.660529\pi\) |
0.999814 | − | 0.0192797i | \(-0.00613729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.8141 | − | 32.8043i | −0.124736 | − | 0.142010i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −85.0481 | + | 147.308i | −0.365013 | + | 0.632222i | −0.988778 | − | 0.149390i | \(-0.952269\pi\) |
0.623765 | + | 0.781612i | \(0.285602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 257.465 | 1.09559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −257.145 | − | 87.0644i | −1.08500 | − | 0.367360i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 221.528 | − | 383.698i | 0.926896 | − | 1.60543i | 0.138413 | − | 0.990375i | \(-0.455800\pi\) |
0.788483 | − | 0.615057i | \(-0.210867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −133.094 | − | 76.8417i | −0.552256 | − | 0.318845i | 0.197775 | − | 0.980247i | \(-0.436628\pi\) |
−0.750031 | + | 0.661402i | \(0.769962\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 242.540 | + | 14.9438i | 0.998107 | + | 0.0614969i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −405.111 | −1.65351 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −163.067 | + | 7.29485i | −0.660189 | + | 0.0295338i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −185.517 | + | 37.0527i | −0.745049 | + | 0.148806i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −84.3664 | − | 146.127i | −0.336121 | − | 0.582179i | 0.647578 | − | 0.761999i | \(-0.275782\pi\) |
−0.983700 | + | 0.179820i | \(0.942449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −245.144 | − | 424.602i | −0.968950 | − | 1.67827i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −43.7824 | + | 129.311i | −0.171696 | + | 0.507104i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 323.090i | − | 1.25716i | −0.777744 | − | 0.628581i | \(-0.783636\pi\) | ||
0.777744 | − | 0.628581i | \(-0.216364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0889 | − | 6.97953i | 0.0466753 | − | 0.0269480i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.22773 | + | 19.7759i | 0.0315239 | + | 0.0757696i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 214.364 | 0.815074 | 0.407537 | − | 0.913189i | \(-0.366388\pi\) | ||||
0.407537 | + | 0.913189i | \(0.366388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 641.885 | + | 370.593i | 2.42221 | + | 1.39846i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 44.1428 | + | 221.017i | 0.165329 | + | 0.827777i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −339.682 | − | 196.116i | −1.26276 | − | 0.729054i | −0.289152 | − | 0.957283i | \(-0.593373\pi\) |
−0.973608 | + | 0.228229i | \(0.926707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −89.8653 | + | 155.651i | −0.331606 | + | 0.574359i | −0.982827 | − | 0.184529i | \(-0.940924\pi\) |
0.651221 | + | 0.758888i | \(0.274257\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.55717 | + | 17.8102i | 0.0130299 | + | 0.0652389i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 924.423 | 3.36154 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 112.854 | + | 195.468i | 0.407414 | + | 0.705662i | 0.994599 | − | 0.103791i | \(-0.0330973\pi\) |
−0.587185 | + | 0.809453i | \(0.699764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.26600 | + | 22.2714i | 0.0332115 | + | 0.0798259i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 120.212 | + | 69.4045i | 0.427801 | + | 0.246991i | 0.698409 | − | 0.715699i | \(-0.253892\pi\) |
−0.270608 | + | 0.962689i | \(0.587225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.9508 | − | 39.7520i | −0.0810984 | − | 0.140466i | 0.822624 | − | 0.568586i | \(-0.192509\pi\) |
−0.903722 | + | 0.428120i | \(0.859176\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −114.014 | − | 462.222i | −0.400050 | − | 1.62183i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 46.0411 | + | 26.5818i | 0.160422 | + | 0.0926196i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 129.657 | + | 224.572i | 0.448639 | + | 0.777065i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −214.834 | − | 72.7386i | −0.738259 | − | 0.249961i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −357.501 | − | 206.404i | −1.22014 | − | 0.704449i | −0.255193 | − | 0.966890i | \(-0.582139\pi\) |
−0.964948 | + | 0.262441i | \(0.915472\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 662.169 | + | 382.304i | 2.24464 | + | 1.29594i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 500.706 | + | 245.461i | 1.68588 | + | 0.826467i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 203.944i | 0.682087i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.83939 | + | 6.65002i | 0.0127555 | + | 0.0220931i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 168.112 | + | 191.392i | 0.554824 | + | 0.631657i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −84.2343 | −0.276178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 48.2502 | + | 27.8573i | 0.157167 | + | 0.0907403i | 0.576521 | − | 0.817083i | \(-0.304410\pi\) |
−0.419354 | + | 0.907823i | \(0.637743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −63.9702 | + | 56.1890i | −0.207023 | + | 0.181841i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 143.848 | − | 249.152i | 0.462534 | − | 0.801133i | −0.536552 | − | 0.843867i | \(-0.680274\pi\) |
0.999086 | + | 0.0427343i | \(0.0136069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −253.663 | + | 439.358i | −0.810426 | + | 1.40370i | 0.102141 | + | 0.994770i | \(0.467431\pi\) |
−0.912566 | + | 0.408929i | \(0.865903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −48.9072 | + | 20.3478i | −0.155261 | + | 0.0645962i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −43.3887 | − | 25.0505i | −0.136873 | − | 0.0790235i | 0.430000 | − | 0.902829i | \(-0.358514\pi\) |
−0.566873 | + | 0.823805i | \(0.691847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 49.1526i | 0.154083i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −422.880 | − | 143.179i | −1.31738 | − | 0.446042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 91.8767 | + | 47.7029i | 0.284448 | + | 0.147687i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −333.013 | − | 192.265i | −1.02465 | − | 0.591585i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −129.334 | + | 113.602i | −0.395518 | + | 0.347408i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.7226 | −0.0660262 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −269.005 | + | 155.310i | −0.812705 | + | 0.469215i | −0.847894 | − | 0.530165i | \(-0.822130\pi\) |
0.0351896 | + | 0.999381i | \(0.488796\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −108.308 | + | 141.609i | −0.325251 | + | 0.425252i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −116.446 | + | 67.2301i | −0.347600 | + | 0.200687i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0500 | + | 15.6173i | −0.0802671 | + | 0.0463423i | −0.539596 | − | 0.841924i | \(-0.681423\pi\) |
0.459329 | + | 0.888266i | \(0.348090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −153.940 | + | 135.215i | −0.454100 | + | 0.398864i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.3552i | 0.162332i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 68.7094 | 0.200319 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −583.303 | + | 116.501i | −1.69073 | + | 0.337684i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −184.556 | − | 319.660i | −0.531861 | − | 0.921210i | −0.999308 | − | 0.0371889i | \(-0.988160\pi\) |
0.467448 | − | 0.884021i | \(-0.345174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 182.826 | + | 316.663i | 0.523856 | + | 0.907345i | 0.999614 | + | 0.0277692i | \(0.00884035\pi\) |
−0.475758 | + | 0.879576i | \(0.657826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −129.322 | − | 192.563i | −0.368438 | − | 0.548612i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 289.028 | + | 500.611i | 0.818776 | + | 1.41816i | 0.906584 | + | 0.422025i | \(0.138681\pi\) |
−0.0878078 | + | 0.996137i | \(0.527986\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 647.081i | − | 1.82276i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.69398 | − | 10.9102i | 0.0103473 | − | 0.0305607i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 311.123 | − | 538.882i | 0.866639 | − | 1.50106i | 0.00122868 | − | 0.999999i | \(-0.499609\pi\) |
0.865410 | − | 0.501064i | \(-0.167058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −359.558 | + | 32.2344i | −0.996005 | + | 0.0892921i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 604.934 | + | 688.707i | 1.66649 | + | 1.89727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 662.916 | 1.81621 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −121.099 | + | 209.750i | −0.329970 | + | 0.571525i | −0.982506 | − | 0.186233i | \(-0.940372\pi\) |
0.652536 | + | 0.757758i | \(0.273705\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −673.315 | − | 87.5715i | −1.82470 | − | 0.237321i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54.1567 | − | 31.2674i | −0.145975 | − | 0.0842787i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 290.835 | + | 167.914i | 0.779718 | + | 0.450170i | 0.836330 | − | 0.548226i | \(-0.184697\pi\) |
−0.0566124 | + | 0.998396i | \(0.518030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 158.779 | − | 468.954i | 0.423411 | − | 1.25054i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2229 | − | 17.7067i | 0.0271166 | − | 0.0469673i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 83.3649i | − | 0.219960i | −0.993934 | − | 0.109980i | \(-0.964921\pi\) | ||
0.993934 | − | 0.109980i | \(-0.0350787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.5331 | + | 152.875i | 0.0801395 | + | 0.401246i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2753 | − | 16.3247i | 0.0738258 | − | 0.0426234i | −0.462633 | − | 0.886550i | \(-0.653095\pi\) |
0.536459 | + | 0.843927i | \(0.319762\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −121.558 | −0.315735 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −77.8980 | − | 59.5797i | −0.201287 | − | 0.153953i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 126.631 | − | 219.331i | 0.325529 | − | 0.563833i | −0.656090 | − | 0.754682i | \(-0.727791\pi\) |
0.981619 | + | 0.190850i | \(0.0611243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.6720 | − | 112.015i | 0.165402 | − | 0.286484i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −267.086 | + | 53.3440i | −0.679607 | + | 0.135735i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −654.568 | + | 377.915i | −1.65714 | + | 0.956747i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 131.950 | − | 228.543i | 0.332367 | − | 0.575676i | −0.650609 | − | 0.759413i | \(-0.725486\pi\) |
0.982975 | + | 0.183737i | \(0.0588195\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.61953 | + | 38.9983i | 0.0241091 | + | 0.0977400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −644.581 | + | 372.149i | −1.60743 | + | 0.928052i | −0.617492 | + | 0.786577i | \(0.711851\pi\) |
−0.989942 | + | 0.141475i | \(0.954815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5130 | − | 19.9411i | 0.0285682 | − | 0.0494816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 476.878 | − | 479.874i | 1.17748 | − | 1.18487i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −354.305 | + | 204.558i | −0.870529 | + | 0.502600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 46.9946i | 0.114901i | 0.998348 | + | 0.0574506i | \(0.0182972\pi\) | ||||
−0.998348 | + | 0.0574506i | \(0.981703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 459.687 | + | 523.346i | 1.11846 | + | 1.27335i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −55.8681 | − | 32.2555i | −0.135274 | − | 0.0781004i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −263.347 | + | 456.130i | −0.634571 | + | 1.09911i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.3827 | + | 74.9679i | −0.0608699 | + | 0.179779i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.3570 | + | 61.2401i | −0.0843842 | + | 0.146158i | −0.905129 | − | 0.425138i | \(-0.860226\pi\) |
0.820744 | + | 0.571295i | \(0.193559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 127.574i | 0.303027i | 0.988455 | + | 0.151513i | \(0.0484147\pi\) | ||||
−0.988455 | + | 0.151513i | \(0.951585\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 256.149 | − | 106.570i | 0.605552 | − | 0.251939i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 121.937 | + | 211.201i | 0.286911 | + | 0.496944i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.10696 | 0.0166439 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −104.255 | − | 521.987i | −0.243018 | − | 1.21675i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −541.149 | + | 312.432i | −1.25557 | + | 0.724901i | −0.972209 | − | 0.234113i | \(-0.924781\pi\) |
−0.283357 | + | 0.959015i | \(0.591448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 78.5687 | − | 45.3617i | 0.181452 | − | 0.104761i | −0.406523 | − | 0.913641i | \(-0.633259\pi\) |
0.587975 | + | 0.808879i | \(0.299925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 56.4828 | + | 19.1240i | 0.129845 | + | 0.0439633i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.1575 | + | 450.593i | 0.0461269 | + | 1.03111i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 151.104i | − | 0.344201i | −0.985079 | − | 0.172101i | \(-0.944945\pi\) | ||
0.985079 | − | 0.172101i | \(-0.0550554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −403.040 | + | 167.684i | −0.913922 | + | 0.380237i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −435.614 | + | 754.506i | −0.983328 | + | 1.70317i | −0.334184 | + | 0.942508i | \(0.608461\pi\) |
−0.649144 | + | 0.760666i | \(0.724873\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 543.412 | + | 313.739i | 1.22115 | + | 0.705032i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −296.740 | + | 59.2668i | −0.663848 | + | 0.132588i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 174.763i | − | 0.389228i | −0.980880 | − | 0.194614i | \(-0.937655\pi\) | ||
0.980880 | − | 0.194614i | \(-0.0623454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1349.38 | − | 779.067i | −2.99198 | − | 1.72742i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −136.611 | − | 683.992i | −0.301570 | − | 1.50992i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.7899 | + | 25.2821i | 0.0962416 | + | 0.0555651i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −370.554 | − | 641.818i | −0.810840 | − | 1.40442i | −0.912277 | − | 0.409574i | \(-0.865677\pi\) |
0.101437 | − | 0.994842i | \(-0.467656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.96623 | + | 146.773i | 0.0217129 | + | 0.319767i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −565.944 | −1.22764 | −0.613822 | − | 0.789444i | \(-0.710369\pi\) | ||||
−0.613822 | + | 0.789444i | \(0.710369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 178.485 | − | 309.146i | 0.385497 | − | 0.667701i | −0.606341 | − | 0.795205i | \(-0.707363\pi\) |
0.991838 | + | 0.127504i | \(0.0406965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 63.6104 | + | 21.5373i | 0.136797 | + | 0.0463168i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −427.161 | −0.914691 | −0.457345 | − | 0.889289i | \(-0.651200\pi\) | ||||
−0.457345 | + | 0.889289i | \(0.651200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.82469 | − | 5.67229i | 0.0209482 | − | 0.0120944i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −580.716 | + | 115.984i | −1.23294 | + | 0.246251i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −112.526 | − | 194.901i | −0.237898 | − | 0.412052i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −754.760 | − | 391.875i | −1.58897 | − | 0.825000i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 792.001 | + | 103.008i | 1.66038 | + | 0.215949i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 164.600 | − | 285.096i | 0.343633 | − | 0.595190i | −0.641471 | − | 0.767147i | \(-0.721676\pi\) |
0.985104 | + | 0.171957i | \(0.0550091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 170.179 | 0.353803 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 49.2140 | − | 9.82933i | 0.101892 | − | 0.0203506i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −546.864 | + | 315.732i | −1.12756 | + | 0.650994i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 788.052i | − | 1.61818i | −0.587687 | − | 0.809088i | \(-0.699961\pi\) | ||
0.587687 | − | 0.809088i | \(-0.300039\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −229.002 | + | 676.357i | −0.468307 | + | 1.38314i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 390.588 | + | 676.518i | 0.795495 | + | 1.37784i | 0.922525 | + | 0.385938i | \(0.126122\pi\) |
−0.127030 | + | 0.991899i | \(0.540544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.2298 | + | 6.48352i | −0.0227785 | + | 0.0131512i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1433.39 | − | 596.359i | 2.89573 | − | 1.20477i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 54.5951i | 0.109849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −116.750 | − | 202.218i | −0.233969 | − | 0.405246i | 0.725004 | − | 0.688745i | \(-0.241838\pi\) |
−0.958973 | + | 0.283499i | \(0.908505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −714.304 | − | 241.850i | −1.42576 | − | 0.482735i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 402.390 | + | 696.960i | 0.799980 | + | 1.38561i | 0.919628 | + | 0.392789i | \(0.128490\pi\) |
−0.119649 | + | 0.992816i | \(0.538177\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 709.214 | 1.40438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 91.5856 | − | 270.498i | 0.180642 | − | 0.533527i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 114.097i | 0.224160i | 0.993699 | + | 0.112080i | \(0.0357513\pi\) | ||||
−0.993699 | + | 0.112080i | \(0.964249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.9311 | −0.109454 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −304.755 | − | 412.666i | −0.594065 | − | 0.804417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 237.045i | 0.460282i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 636.653 | 1.23144 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 781.018 | + | 264.438i | 1.50485 | + | 0.509515i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 330.381i | − | 0.634130i | −0.948404 | − | 0.317065i | \(-0.897303\pi\) | ||
0.948404 | − | 0.317065i | \(-0.102697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 223.871 | − | 129.252i | 0.428052 | − | 0.247136i | −0.270464 | − | 0.962730i | \(-0.587177\pi\) |
0.698517 | + | 0.715594i | \(0.253844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −30.3458 | + | 89.6262i | −0.0578015 | + | 0.170717i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.6469 | + | 7.30169i | −0.0239979 | + | 0.0138552i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.5474 | 0.0653070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 817.028 | + | 106.263i | 1.53866 | + | 0.200118i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 324.067 | + | 561.300i | 0.608005 | + | 1.05310i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1076.45 | + | 621.490i | −2.01206 | + | 1.16166i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −301.225 | − | 101.989i | −0.560941 | − | 0.189924i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1001.75 | −1.85853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 307.180 | + | 532.051i | 0.567800 | + | 0.983458i | 0.996783 | + | 0.0801456i | \(0.0255385\pi\) |
−0.428983 | + | 0.903312i | \(0.641128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −105.629 | − | 528.867i | −0.194528 | − | 0.973973i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 479.255i | 0.879367i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 278.732 | + | 160.926i | 0.509564 | + | 0.294197i | 0.732654 | − | 0.680601i | \(-0.238281\pi\) |
−0.223090 | + | 0.974798i | \(0.571614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −83.8037 | + | 34.8664i | −0.152648 | + | 0.0635090i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.8364 | − | 40.1314i | 0.0378157 | − | 0.0728338i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.2268 | − | 31.8852i | 0.0998676 | − | 0.0576586i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 97.2130 | + | 486.731i | 0.175159 | + | 0.876993i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −257.207 | − | 445.496i | −0.461772 | − | 0.799813i | 0.537277 | − | 0.843406i | \(-0.319453\pi\) |
−0.999049 | + | 0.0435927i | \(0.986120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 93.6143i | 0.167467i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −108.264 | + | 319.758i | −0.192984 | + | 0.569979i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −378.199 | − | 218.353i | −0.671756 | − | 0.387839i | 0.124986 | − | 0.992159i | \(-0.460112\pi\) |
−0.796742 | + | 0.604320i | \(0.793445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 570.433i | 1.00962i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −40.2348 | + | 40.4876i | −0.0709609 | + | 0.0714067i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −734.219 | + | 423.901i | −1.29037 | + | 0.744994i | −0.978719 | − | 0.205204i | \(-0.934214\pi\) |
−0.311648 | + | 0.950198i | \(0.600881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −393.820 | + | 682.116i | −0.689702 | + | 1.19460i | 0.282232 | + | 0.959346i | \(0.408925\pi\) |
−0.971934 | + | 0.235253i | \(0.924408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −354.334 | + | 70.7698i | −0.618383 | + | 0.123507i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −531.275 | + | 920.196i | −0.923957 | + | 1.60034i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 291.421 | 0.505062 | 0.252531 | − | 0.967589i | \(-0.418737\pi\) | ||||
0.252531 | + | 0.967589i | \(0.418737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 68.8979 | + | 344.961i | 0.118995 | + | 0.595788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.2189 | − | 38.4843i | 0.0382425 | − | 0.0662380i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1587.24 | + | 916.393i | 2.72254 | + | 1.57186i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −640.394 | − | 83.2897i | −1.09469 | − | 0.142376i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 899.053 | 1.53161 | 0.765803 | − | 0.643075i | \(-0.222342\pi\) | ||||
0.765803 | + | 0.643075i | \(0.222342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.4658 | − | 45.1957i | 0.0398401 | − | 0.0767329i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 207.948 | − | 614.174i | 0.351858 | − | 1.03921i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 272.320 | + | 471.672i | 0.459224 | + | 0.795400i | 0.998920 | − | 0.0464601i | \(-0.0147941\pi\) |
−0.539696 | + | 0.841860i | \(0.681461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0342 | − | 27.7721i | −0.0269483 | − | 0.0466758i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 764.056 | − | 152.602i | 1.27983 | − | 0.255615i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 430.405i | − | 0.718540i | −0.933234 | − | 0.359270i | \(-0.883026\pi\) | ||
0.933234 | − | 0.359270i | \(-0.116974\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 640.942 | − | 370.048i | 1.06646 | − | 0.615721i | 0.139247 | − | 0.990258i | \(-0.455532\pi\) |
0.927212 | + | 0.374537i | \(0.122198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −88.0226 | + | 115.086i | −0.145974 | + | 0.190856i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2552.04 | 4.21825 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 452.418 | + | 261.204i | 0.745334 | + | 0.430319i | 0.824006 | − | 0.566582i | \(-0.191734\pi\) |
−0.0786715 | + | 0.996901i | \(0.525068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.76552 | − | 1.61352i | −0.00782516 | − | 0.00264946i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −229.347 | − | 132.413i | −0.375363 | − | 0.216716i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −129.627 | + | 224.520i | −0.211463 | + | 0.366264i | −0.952172 | − | 0.305561i | \(-0.901156\pi\) |
0.740710 | + | 0.671825i | \(0.234489\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1420.26 | + | 1247.50i | −2.30937 | + | 2.02846i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 51.2846 | 0.0831193 | 0.0415596 | − | 0.999136i | \(-0.486767\pi\) | ||||
0.0415596 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −338.509 | − | 586.315i | −0.546865 | − | 0.947197i | −0.998487 | − | 0.0549882i | \(-0.982488\pi\) |
0.451622 | − | 0.892209i | \(-0.350845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −532.099 | + | 357.347i | −0.856842 | + | 0.575438i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.8484 | − | 26.4706i | −0.0735929 | − | 0.0424889i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −129.710 | − | 224.664i | −0.207536 | − | 0.359463i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −281.932 | − | 1142.97i | −0.449652 | − | 1.82292i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −93.4699 | − | 53.9649i | −0.148601 | − | 0.0857947i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −174.679 | − | 302.553i | −0.276829 | − | 0.479481i | 0.693766 | − | 0.720200i | \(-0.255950\pi\) |
−0.970595 | + | 0.240719i | \(0.922617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.6266 | + | 123.302i | 0.0389045 | + | 0.194789i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 375.873 | + | 217.010i | 0.591926 | + | 0.341748i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 360.868 | + | 208.347i | 0.566512 | + | 0.327076i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −267.841 | − | 643.773i | −0.419157 | − | 1.00747i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 334.673i | − | 0.522111i | −0.965324 | − | 0.261056i | \(-0.915929\pi\) | ||
0.965324 | − | 0.261056i | \(-0.0840706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.5540 | + | 51.1890i | 0.0459626 | + | 0.0796096i | 0.888091 | − | 0.459667i | \(-0.152031\pi\) |
−0.842129 | + | 0.539276i | \(0.818698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −267.747 | + | 53.4762i | −0.415112 | + | 0.0829088i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 157.684 | 0.243716 | 0.121858 | − | 0.992548i | \(-0.461115\pi\) | ||||
0.121858 | + | 0.992548i | \(0.461115\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1637.40 | + | 945.352i | 2.52295 | + | 1.45663i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.36689 | − | 1.81713i | −0.00824407 | − | 0.00279129i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 199.103 | − | 344.856i | 0.304905 | − | 0.528111i | −0.672335 | − | 0.740247i | \(-0.734709\pi\) |
0.977240 | + | 0.212136i | \(0.0680420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −379.136 | + | 656.682i | −0.578833 | + | 1.00257i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 659.527 | − | 274.396i | 1.00385 | − | 0.417649i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −919.880 | − | 531.093i | −1.39587 | − | 0.805908i | −0.401916 | − | 0.915677i | \(-0.631656\pi\) |
−0.993957 | + | 0.109769i | \(0.964989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 406.874i | 0.615543i | 0.951460 | + | 0.307772i | \(0.0995832\pi\) | ||||
−0.951460 | + | 0.307772i | \(0.900417\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 105.505 | − | 92.6720i | 0.159133 | − | 0.139777i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 99.2481 | + | 51.5301i | 0.149245 | + | 0.0774889i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.9278 | − | 28.2485i | −0.0733551 | − | 0.0423516i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −300.001 | − | 101.575i | −0.448433 | − | 0.151831i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −208.293 | −0.310421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −376.962 | + | 217.639i | −0.560122 | + | 0.323387i | −0.753195 | − | 0.657798i | \(-0.771488\pi\) |
0.193072 | + | 0.981185i | \(0.438155\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −81.8718 | − | 1205.73i | −0.121292 | − | 1.78626i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −396.408 | + | 228.866i | −0.585536 | + | 0.338059i | −0.763330 | − | 0.646008i | \(-0.776437\pi\) |
0.177794 | + | 0.984068i | \(0.443104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 46.1397 | − | 26.6387i | 0.0679524 | − | 0.0392323i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −261.033 | − | 1306.96i | −0.383309 | − | 1.91917i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 332.751i | − | 0.487190i | −0.969877 | − | 0.243595i | \(-0.921673\pi\) | ||
0.969877 | − | 0.243595i | \(-0.0783267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1939.29 | 2.83107 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −468.430 | − | 533.300i | −0.681849 | − | 0.776273i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −381.190 | − | 660.240i | −0.553251 | − | 0.958259i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.6760 | + | 73.9170i | 0.0617598 | + | 0.106971i | 0.895252 | − | 0.445560i | \(-0.146995\pi\) |
−0.833492 | + | 0.552531i | \(0.813662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −120.937 | + | 50.3156i | −0.174512 | + | 0.0726055i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 110.177 | + | 190.833i | 0.158529 | + | 0.274580i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 411.055i | − | 0.589748i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 336.757 | + | 383.392i | 0.481770 | + | 0.548486i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −264.113 | + | 457.458i | −0.376766 | + | 0.652579i | −0.990590 | − | 0.136865i | \(-0.956297\pi\) |
0.613823 | + | 0.789443i | \(0.289631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 375.993 | − | 16.8202i | 0.534841 | − | 0.0239263i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 247.705 | − | 731.597i | 0.351355 | − | 1.03773i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −59.8373 | −0.0846355 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 601.129 | − | 1041.19i | 0.847854 | − | 1.46853i | −0.0352651 | − | 0.999378i | \(-0.511228\pi\) |
0.883119 | − | 0.469149i | \(-0.155439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −494.795 | + | 646.924i | −0.695914 | + | 0.909879i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −55.1021 | − | 31.8132i | −0.0772820 | − | 0.0446188i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1283.41 | − | 740.975i | −1.79497 | − | 1.03633i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −877.164 | − | 998.636i | −1.22338 | − | 1.39280i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 346.447 | − | 600.064i | 0.481846 | − | 0.834581i | −0.517937 | − | 0.855419i | \(-0.673300\pi\) |
0.999783 | + | 0.0208376i | \(0.00663328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 19.9998i | − | 0.0277390i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −346.398 | + | 304.263i | −0.479112 | + | 0.420834i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 92.2519 | − | 53.2616i | 0.127244 | − | 0.0734643i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1308.09 | 1.79929 | 0.899646 | − | 0.436620i | \(-0.143824\pi\) | ||||
0.899646 | + | 0.436620i | \(0.143824\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 275.810 | − | 674.811i | 0.378340 | − | 0.925667i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.6857 | − | 51.4171i | 0.0406097 | − | 0.0703381i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −216.509 | + | 375.004i | −0.295374 | + | 0.511602i | −0.975072 | − | 0.221890i | \(-0.928777\pi\) |
0.679698 | + | 0.733492i | \(0.262111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −389.755 | + | 1151.14i | −0.530279 | + | 1.56618i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −287.945 | + | 166.245i | −0.390698 | + | 0.225570i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 617.926 | − | 1070.28i | 0.836165 | − | 1.44828i | −0.0569131 | − | 0.998379i | \(-0.518126\pi\) |
0.893078 | − | 0.449901i | \(-0.148541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −136.157 | + | 470.380i | −0.183748 | + | 0.634790i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 820.310 | − | 473.606i | 1.10405 | − | 0.637424i | 0.166769 | − | 0.985996i | \(-0.446667\pi\) |
0.937282 | + | 0.348572i | \(0.113333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −421.231 | + | 729.593i | −0.565410 | + | 0.979319i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −73.1983 | + | 562.804i | −0.0979896 | + | 0.753418i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 90.8217 | − | 52.4359i | 0.121257 | − | 0.0700079i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1407.77i | − | 1.87453i | −0.348623 | − | 0.937263i | \(-0.613351\pi\) | ||
0.348623 | − | 0.937263i | \(-0.386649\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −496.395 | + | 99.1431i | −0.659223 | + | 0.131664i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1681.73 | − | 970.946i | −2.22745 | − | 1.28602i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −325.685 | + | 564.102i | −0.430231 | + | 0.745182i | −0.996893 | − | 0.0787687i | \(-0.974901\pi\) |
0.566662 | + | 0.823950i | \(0.308234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1442.38 | + | 288.081i | −1.90037 | + | 0.379553i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 261.899 | − | 453.622i | 0.344151 | − | 0.596087i | −0.641048 | − | 0.767501i | \(-0.721500\pi\) |
0.985199 | + | 0.171414i | \(0.0548335\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 40.4354i | − | 0.0529953i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 325.321 | + | 248.820i | 0.425257 | + | 0.325254i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −393.236 | − | 681.104i | −0.512693 | − | 0.888010i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −184.489 | −0.239907 | −0.119954 | − | 0.992779i | \(-0.538275\pi\) | ||||
−0.119954 | + | 0.992779i | \(0.538275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −918.076 | − | 310.843i | −1.19076 | − | 0.403169i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 152.283 | − | 87.9206i | 0.197002 | − | 0.113739i | −0.398254 | − | 0.917275i | \(-0.630384\pi\) |
0.595257 | + | 0.803536i | \(0.297050\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 103.893 | − | 59.9828i | 0.134056 | − | 0.0773971i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.20199 | − | 41.0661i | −0.0105560 | − | 0.0528522i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 771.470 | + | 1208.10i | 0.990333 | + | 1.55084i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1600.09i | − | 2.04877i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 64.1099 | − | 4.35321i | 0.0818773 | − | 0.00555966i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −824.342 | + | 1427.80i | −1.05012 | + | 1.81886i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 80.0272 | + | 46.2037i | 0.101686 | + | 0.0587087i | 0.549981 | − | 0.835177i | \(-0.314635\pi\) |
−0.448294 | + | 0.893886i | \(0.647968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 206.239 | − | 609.126i | 0.261393 | − | 0.772023i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 48.1281i | − | 0.0608447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 75.0350 | + | 43.3215i | 0.0946217 | + | 0.0546299i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1670.61 | − | 1467.40i | 2.10140 | − | 1.84579i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 769.440 | + | 444.236i | 0.965420 | + | 0.557385i | 0.897837 | − | 0.440328i | \(-0.145138\pi\) |
0.0675830 | + | 0.997714i | \(0.478471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 83.9783 | + | 145.455i | 0.105104 | + | 0.182046i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 670.498 | + | 87.2050i | 0.837076 | + | 0.108870i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1639.24 | 2.04140 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69.8607 | − | 121.002i | 0.0867834 | − | 0.150313i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −884.078 | + | 776.540i | −1.09551 | + | 0.962256i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −939.940 | −1.16185 | −0.580927 | − | 0.813956i | \(-0.697310\pi\) | ||||
−0.580927 | + | 0.813956i | \(0.697310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 361.756 | − | 208.860i | 0.446062 | − | 0.257534i | −0.260104 | − | 0.965581i | \(-0.583757\pi\) |
0.706166 | + | 0.708047i | \(0.250423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 355.831 | + | 405.108i | 0.437677 | + | 0.498287i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 994.016 | + | 1721.69i | 1.21965 | + | 2.11250i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.25267 | + | 206.831i | 0.0113252 | + | 0.253159i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 54.0309 | + | 7.02726i | 0.0659718 | + | 0.00858029i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 280.068 | − | 485.091i | 0.341130 | − | 0.590854i | −0.643513 | − | 0.765435i | \(-0.722524\pi\) |
0.984643 | + | 0.174581i | \(0.0558571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1247.92 | −1.51631 | −0.758154 | − | 0.652076i | \(-0.773898\pi\) | ||||
−0.758154 | + | 0.652076i | \(0.773898\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 889.382 | − | 2626.79i | 1.07804 | − | 3.18399i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 496.644 | − | 286.737i | 0.600537 | − | 0.346720i | −0.168716 | − | 0.985665i | \(-0.553962\pi\) |
0.769253 | + | 0.638945i | \(0.220629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 921.847i | 1.11200i | 0.831183 | + | 0.555999i | \(0.187664\pi\) | ||||
−0.831183 | + | 0.555999i | \(0.812336\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 664.008 | − | 132.620i | 0.799047 | − | 0.159591i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −132.137 | − | 228.867i | −0.158627 | − | 0.274751i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1818.28 | + | 1049.78i | −2.17758 | + | 1.25723i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 72.2000 | − | 4.90255i | 0.0862604 | − | 0.00585729i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 498.538i | − | 0.594205i | −0.954846 | − | 0.297102i | \(-0.903980\pi\) | ||
0.954846 | − | 0.297102i | \(-0.0960203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −417.668 | − | 723.422i | −0.496633 | − | 0.860193i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 312.871 | − | 274.814i | 0.371140 | − | 0.325996i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −397.540 | − | 688.560i | −0.470462 | − | 0.814864i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −215.319 | −0.254214 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −135.038 | + | 26.9706i | −0.159055 | + | 0.0317675i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 470.246i | − | 0.552581i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1363.70 | 1.59872 | 0.799358 | − | 0.600855i | \(-0.205173\pi\) | ||||
0.799358 | + | 0.600855i | \(0.205173\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1423.12 | − | 120.725i | −1.66446 | − | 0.141198i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1338.69i | 1.56207i | 0.624487 | + | 0.781036i | \(0.285308\pi\) | ||||
−0.624487 | + | 0.781036i | \(0.714692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 632.570 | 0.736403 | 0.368202 | − | 0.929746i | \(-0.379974\pi\) | ||||
0.368202 | + | 0.929746i | \(0.379974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 119.829 | − | 105.253i | 0.139175 | − | 0.122246i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 731.113i | − | 0.847176i | −0.905855 | − | 0.423588i | \(-0.860770\pi\) | ||
0.905855 | − | 0.423588i | \(-0.139230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1988.10 | − | 1147.83i | 2.29838 | − | 1.32697i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 762.873 | − | 152.366i | 0.879900 | − | 0.175739i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1618.60 | + | 934.500i | −1.86260 | + | 1.07537i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 138.305 | 0.158789 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −413.380 | + | 540.478i | −0.473517 | + | 0.619104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 58.1489 | + | 100.717i | 0.0664559 | + | 0.115105i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1002.62 | − | 578.861i | 1.14323 | − | 0.660047i | 0.196005 | − | 0.980603i | \(-0.437203\pi\) |
0.947230 | + | 0.320556i | \(0.103870\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −930.455 | + | 817.277i | −1.05854 | + | 0.929780i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0365 | 0.0204728 | 0.0102364 | − | 0.999948i | \(-0.496742\pi\) | ||||
0.0102364 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 494.516 | + | 856.527i | 0.560041 | + | 0.970019i | 0.997492 | + | 0.0707772i | \(0.0225479\pi\) |
−0.437451 | + | 0.899242i | \(0.644119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1723.40 | − | 1513.77i | 1.94735 | − | 1.71048i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1210.81i | − | 1.36506i | −0.730859 | − | 0.682528i | \(-0.760880\pi\) | ||
0.730859 | − | 0.682528i | \(-0.239120\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.7129 | − | 18.3094i | −0.0356725 | − | 0.0205955i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1179.21 | − | 1186.62i | 1.32347 | − | 1.33179i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −519.806 | − | 269.886i | −0.582089 | − | 0.302224i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −766.777 | + | 442.699i | −0.856734 | + | 0.494636i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 579.516 | + | 196.213i | 0.646060 | + | 0.218744i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.18935 | + | 5.52412i | 0.00354767 | + | 0.00614474i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 483.511i | 0.536638i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.5902 | − | 4.51185i | 0.0250168 | − | 0.00499652i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1300.32 | − | 750.742i | −1.43682 | − | 0.829549i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 322.748i | 0.355842i | 0.984045 | + | 0.177921i | \(0.0569371\pi\) | ||||
−0.984045 | + | 0.177921i | \(0.943063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 705.589 | − | 293.559i | 0.776225 | − | 0.322948i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −567.038 | + | 327.380i | −0.622435 | + | 0.359363i | −0.777816 | − | 0.628492i | \(-0.783673\pi\) |
0.155382 | + | 0.987855i | \(0.450339\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −651.198 | + | 1127.91i | −0.713251 | + | 1.23539i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −81.0414 | + | 239.356i | −0.0885698 | + | 0.261591i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.9882 | − | 55.4051i | 0.0348835 | − | 0.0604200i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1299.09 | −1.41359 | −0.706796 | − | 0.707417i | \(-0.749860\pi\) | ||||
−0.706796 | + | 0.707417i | \(0.749860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 125.579 | − | 110.304i | 0.136351 | − | 0.119765i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −332.792 | + | 576.413i | −0.360555 | + | 0.624500i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 767.848 | + | 443.317i | 0.830106 | + | 0.479262i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 98.1182 | + | 235.833i | 0.105845 | + | 0.254405i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 521.542 | 0.561401 | 0.280701 | − | 0.959795i | \(-0.409433\pi\) | ||||
0.280701 | + | 0.959795i | \(0.409433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 817.894 | + | 424.655i | 0.878511 | + | 0.456127i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −569.582 | − | 648.459i | −0.610484 | − | 0.695026i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 469.936 | + | 813.953i | 0.502606 | + | 0.870538i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −625.318 | − | 1083.08i | −0.667362 | − | 1.15590i | −0.978639 | − | 0.205586i | \(-0.934090\pi\) |
0.311277 | − | 0.950319i | \(-0.399243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1004.41 | + | 1143.50i | 1.06966 | + | 1.21778i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 191.045i | − | 0.203023i | −0.994834 | − | 0.101512i | \(-0.967632\pi\) | ||
0.994834 | − | 0.101512i | \(-0.0323679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1551.01 | − | 895.476i | 1.64476 | − | 0.949603i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.7658 | + | 158.549i | 0.0113924 | + | 0.167776i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −584.486 | −0.617198 | −0.308599 | − | 0.951192i | \(-0.599860\pi\) | ||||
−0.308599 | + | 0.951192i | \(0.599860\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −590.519 | − | 340.936i | −0.622254 | − | 0.359258i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −112.926 | + | 99.1899i | −0.118744 | + | 0.104301i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 221.454 | + | 127.856i | 0.232375 | + | 0.134162i | 0.611667 | − | 0.791115i | \(-0.290499\pi\) |
−0.379292 | + | 0.925277i | \(0.623832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −502.987 | + | 871.198i | −0.526688 | + | 0.912250i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 139.669 | + | 47.2895i | 0.145945 | + | 0.0494143i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −163.620 | −0.170615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −476.908 | − | 826.029i | −0.496262 | − | 0.859552i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −813.701 | + | 1063.88i | −0.844965 | + | 1.10476i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 848.155 | + | 489.682i | 0.878917 | + | 0.507443i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 387.929 | + | 671.912i | 0.401167 | + | 0.694842i | 0.993867 | − | 0.110582i | \(-0.0352713\pi\) |
−0.592700 | + | 0.805423i | \(0.701938\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 223.944 | − | 215.177i | 0.231108 | − | 0.222061i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 618.028 | + | 356.819i | 0.636486 | + | 0.367476i | 0.783260 | − | 0.621695i | \(-0.213555\pi\) |
−0.146773 | + | 0.989170i | \(0.546889\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.29581 | − | 16.1008i | −0.00955376 | − | 0.0165476i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −866.719 | + | 761.293i | −0.888943 | + | 0.780814i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 749.812 | + | 432.904i | 0.767463 | + | 0.443095i | 0.831969 | − | 0.554822i | \(-0.187214\pi\) |
−0.0645057 | + | 0.997917i | \(0.520547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1343.74 | + | 775.807i | 1.37256 | + | 0.792449i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 198.374 | + | 476.805i | 0.202216 | + | 0.486040i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1579.12i | 1.60642i | 0.595693 | + | 0.803212i | \(0.296878\pi\) | ||||
−0.595693 | + | 0.803212i | \(0.703122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −902.627 | − | 1563.40i | −0.916372 | − | 1.58720i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.8992 | + | 61.7258i | −0.0211745 | + | 0.0625388i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 258.679 | 0.261556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 208.038 | + | 120.111i | 0.209927 | + | 0.121202i | 0.601278 | − | 0.799040i | \(-0.294659\pi\) |
−0.391350 | + | 0.920242i | \(0.627992\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 182.513 | + | 913.813i | 0.183799 | + | 0.920255i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1084.60 | − | 1878.58i | 1.09005 | − | 1.88802i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 227.311 | − | 393.715i | 0.227995 | − | 0.394900i | −0.729218 | − | 0.684281i | \(-0.760116\pi\) |
0.957214 | + | 0.289381i | \(0.0934495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 298.185 | + | 444.004i | 0.298483 | + | 0.444449i |
(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 | 684.3.s.a.445.24 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.38 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.3 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.11 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.11 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.3 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.24 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.38 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.24 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.24 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.11 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.11 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.38 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.38 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.3 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.3 | 80 | 9.2 | odd | 6 |