Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.19269881856.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(1.91950 + 3.32468i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.449 |
Dual form | 1728.3.q.i.1601.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.80902 | + | 1.04444i | 0.361805 | + | 0.208888i | 0.669872 | − | 0.742476i | \(-0.266349\pi\) |
−0.308067 | + | 0.951365i | \(0.599682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.781452 | + | 1.35351i | 0.111636 | + | 0.193359i | 0.916430 | − | 0.400195i | \(-0.131058\pi\) |
−0.804794 | + | 0.593554i | \(0.797724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.8302 | − | 6.25280i | 0.984560 | − | 0.568436i | 0.0809165 | − | 0.996721i | \(-0.474215\pi\) |
0.903644 | + | 0.428285i | \(0.140882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.0441 | + | 19.1289i | −0.849545 | + | 1.47145i | 0.0320708 | + | 0.999486i | \(0.489790\pi\) |
−0.881615 | + | 0.471969i | \(0.843544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 12.6991i | − | 0.747005i | −0.927629 | − | 0.373503i | \(-0.878157\pi\) | ||
0.927629 | − | 0.373503i | \(-0.121843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.7686 | −1.14572 | −0.572859 | − | 0.819654i | \(-0.694166\pi\) | ||||
−0.572859 | + | 0.819654i | \(0.694166\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.7989 | − | 16.6271i | −1.25213 | − | 0.722916i | −0.280596 | − | 0.959826i | \(-0.590532\pi\) |
−0.971532 | + | 0.236909i | \(0.923866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3183 | − | 17.8718i | −0.412732 | − | 0.714872i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.7787 | + | 14.8833i | −0.888920 | + | 0.513218i | −0.873589 | − | 0.486665i | \(-0.838213\pi\) |
−0.0153306 | + | 0.999882i | \(0.504880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.91549 | + | 11.9780i | −0.223080 | + | 0.386386i | −0.955742 | − | 0.294207i | \(-0.904945\pi\) |
0.732662 | + | 0.680593i | \(0.238278\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.26472i | 0.0932777i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.26807 | 0.223461 | 0.111731 | − | 0.993739i | \(-0.464361\pi\) | ||||
0.111731 | + | 0.993739i | \(0.464361\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.8453 | − | 25.3141i | −1.06940 | − | 0.617418i | −0.141382 | − | 0.989955i | \(-0.545154\pi\) |
−0.928017 | + | 0.372538i | \(0.878488\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 35.5364 | + | 61.5508i | 0.826427 | + | 1.43141i | 0.900824 | + | 0.434185i | \(0.142964\pi\) |
−0.0743965 | + | 0.997229i | \(0.523703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 57.2470 | − | 33.0516i | 1.21802 | − | 0.703225i | 0.253527 | − | 0.967328i | \(-0.418409\pi\) |
0.964495 | + | 0.264103i | \(0.0850759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.2787 | − | 40.3198i | 0.475075 | − | 0.822854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.04384i | − | 0.114035i | −0.998373 | − | 0.0570174i | \(-0.981841\pi\) | ||
0.998373 | − | 0.0570174i | \(-0.0181590\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.1227 | 0.474958 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.01575 | + | 4.62789i | 0.135860 | + | 0.0784389i | 0.566390 | − | 0.824138i | \(-0.308340\pi\) |
−0.430529 | + | 0.902577i | \(0.641673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −51.9009 | − | 89.8950i | −0.850834 | − | 1.47369i | −0.880457 | − | 0.474127i | \(-0.842764\pi\) |
0.0296226 | − | 0.999561i | \(-0.490569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −39.9580 | + | 23.0698i | −0.614738 | + | 0.354919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −19.8853 | + | 34.4424i | −0.296796 | + | 0.514065i | −0.975401 | − | 0.220438i | \(-0.929251\pi\) |
0.678605 | + | 0.734503i | \(0.262585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 18.3599i | − | 0.258590i | −0.991606 | − | 0.129295i | \(-0.958729\pi\) | ||
0.991606 | − | 0.129295i | \(-0.0412714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68.5777 | −0.939421 | −0.469711 | − | 0.882820i | \(-0.655642\pi\) | ||||
−0.469711 | + | 0.882820i | \(0.655642\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.9265 | + | 9.77252i | 0.219825 | + | 0.126916i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.3130 | − | 23.0587i | −0.168518 | − | 0.291883i | 0.769381 | − | 0.638791i | \(-0.220565\pi\) |
−0.937899 | + | 0.346908i | \(0.887232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −21.0376 | + | 12.1461i | −0.253465 | + | 0.146338i | −0.621350 | − | 0.783533i | \(-0.713415\pi\) |
0.367885 | + | 0.929871i | \(0.380082\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.2634 | − | 22.9729i | 0.156040 | − | 0.270270i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 111.730i | 1.25539i | 0.778459 | + | 0.627695i | \(0.216001\pi\) | ||||
−0.778459 | + | 0.627695i | \(0.783999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34.5217 | −0.379359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −39.3800 | − | 22.7360i | −0.414526 | − | 0.239327i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.51182 | − | 4.35061i | −0.0258951 | − | 0.0448516i | 0.852787 | − | 0.522258i | \(-0.174910\pi\) |
−0.878683 | + | 0.477407i | \(0.841577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −86.1052 | + | 49.7129i | −0.852527 | + | 0.492207i | −0.861503 | − | 0.507753i | \(-0.830476\pi\) |
0.00897555 | + | 0.999960i | \(0.497143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6160 | + | 23.5836i | −0.132194 | + | 0.228967i | −0.924522 | − | 0.381128i | \(-0.875536\pi\) |
0.792328 | + | 0.610096i | \(0.208869\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 127.242i | − | 1.18918i | −0.804030 | − | 0.594588i | \(-0.797315\pi\) | ||
0.804030 | − | 0.594588i | \(-0.202685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −55.3100 | −0.507431 | −0.253716 | − | 0.967279i | \(-0.581653\pi\) | ||||
−0.253716 | + | 0.967279i | \(0.581653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −102.845 | − | 59.3775i | −0.910131 | − | 0.525464i | −0.0296577 | − | 0.999560i | \(-0.509442\pi\) |
−0.880473 | + | 0.474096i | \(0.842775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.7320 | − | 60.1576i | −0.302017 | − | 0.523109i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.1884 | − | 9.92372i | 0.144440 | − | 0.0833926i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6950 | − | 30.6486i | 0.146239 | − | 0.253294i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 95.3294i | − | 0.762635i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −74.4516 | −0.586233 | −0.293116 | − | 0.956077i | \(-0.594692\pi\) | ||||
−0.293116 | + | 0.956077i | \(0.594692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.08499 | + | 4.09052i | 0.0540839 | + | 0.0312254i | 0.526798 | − | 0.849990i | \(-0.323392\pi\) |
−0.472714 | + | 0.881216i | \(0.656726\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.0111 | − | 29.4642i | −0.127903 | − | 0.221535i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 41.7273 | − | 24.0913i | 0.304579 | − | 0.175849i | −0.339919 | − | 0.940455i | \(-0.610400\pi\) |
0.644498 | + | 0.764606i | \(0.277066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 119.023 | − | 206.155i | 0.856284 | − | 1.48313i | −0.0191645 | − | 0.999816i | \(-0.506101\pi\) |
0.875449 | − | 0.483311i | \(-0.160566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 276.226i | 1.93165i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −62.1789 | −0.428820 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −246.854 | − | 142.521i | −1.65674 | − | 0.956517i | −0.974207 | − | 0.225658i | \(-0.927547\pi\) |
−0.682529 | − | 0.730859i | \(-0.739120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 77.2434 | + | 133.790i | 0.511546 | + | 0.886024i | 0.999910 | + | 0.0133838i | \(0.00426032\pi\) |
−0.488365 | + | 0.872640i | \(0.662406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.0206 | + | 14.4456i | −0.161423 | + | 0.0931976i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 119.947 | − | 207.754i | 0.763993 | − | 1.32328i | −0.176784 | − | 0.984250i | \(-0.556569\pi\) |
0.940777 | − | 0.339026i | \(-0.110097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 51.9730i | − | 0.322814i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 111.245 | 0.682483 | 0.341241 | − | 0.939976i | \(-0.389153\pi\) | ||||
0.341241 | + | 0.939976i | \(0.389153\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 37.9116 | + | 21.8883i | 0.227016 | + | 0.131068i | 0.609195 | − | 0.793021i | \(-0.291493\pi\) |
−0.382179 | + | 0.924088i | \(0.624826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −159.443 | − | 276.164i | −0.943452 | − | 1.63411i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −253.383 | + | 146.291i | −1.46464 | + | 0.845611i | −0.999220 | − | 0.0394795i | \(-0.987430\pi\) |
−0.465420 | + | 0.885090i | \(0.654097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.1265 | − | 27.9319i | 0.0921514 | − | 0.159611i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 194.612i | 1.08722i | 0.839338 | + | 0.543610i | \(0.182943\pi\) | ||||
−0.839338 | + | 0.543610i | \(0.817057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −89.3906 | −0.493871 | −0.246935 | − | 0.969032i | \(-0.579424\pi\) | ||||
−0.246935 | + | 0.969032i | \(0.579424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.9571 | + | 8.63550i | 0.0808494 | + | 0.0466784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −79.4048 | − | 137.533i | −0.424625 | − | 0.735472i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −44.9085 | + | 25.9279i | −0.235123 | + | 0.135748i | −0.612933 | − | 0.790135i | \(-0.710011\pi\) |
0.377810 | + | 0.925883i | \(0.376677\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −29.7763 | + | 51.5741i | −0.154281 | + | 0.267223i | −0.932797 | − | 0.360402i | \(-0.882640\pi\) |
0.778516 | + | 0.627625i | \(0.215973\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 47.4968i | − | 0.241100i | −0.992707 | − | 0.120550i | \(-0.961534\pi\) | ||
0.992707 | − | 0.120550i | \(-0.0384659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −29.5239 | −0.148361 | −0.0741805 | − | 0.997245i | \(-0.523634\pi\) | ||||
−0.0741805 | + | 0.997245i | \(0.523634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −40.2896 | − | 23.2612i | −0.198471 | − | 0.114587i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −52.8782 | − | 91.5877i | −0.257942 | − | 0.446769i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −235.758 | + | 136.115i | −1.12803 | + | 0.651268i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −81.0561 | + | 140.393i | −0.384152 | + | 0.665371i | −0.991651 | − | 0.128949i | \(-0.958840\pi\) |
0.607499 | + | 0.794320i | \(0.292173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 148.462i | 0.690523i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.6165 | −0.0996151 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 242.920 | + | 140.250i | 1.09918 | + | 0.634614i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −102.706 | − | 177.891i | −0.460564 | − | 0.797719i | 0.538426 | − | 0.842673i | \(-0.319019\pi\) |
−0.998989 | + | 0.0449536i | \(0.985686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −54.0416 | + | 31.2009i | −0.238069 | + | 0.137449i | −0.614289 | − | 0.789081i | \(-0.710557\pi\) |
0.376220 | + | 0.926530i | \(0.377224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.73790 | − | 9.93834i | 0.0250563 | − | 0.0433989i | −0.853225 | − | 0.521542i | \(-0.825357\pi\) |
0.878282 | + | 0.478144i | \(0.158690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 177.096i | 0.760069i | 0.924972 | + | 0.380035i | \(0.124088\pi\) | ||||
−0.924972 | + | 0.380035i | \(0.875912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 138.082 | 0.587581 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −231.234 | − | 133.503i | −0.967505 | − | 0.558589i | −0.0690305 | − | 0.997615i | \(-0.521991\pi\) |
−0.898475 | + | 0.439025i | \(0.855324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 40.7178 | + | 70.5252i | 0.168953 | + | 0.292636i | 0.938052 | − | 0.346494i | \(-0.112628\pi\) |
−0.769099 | + | 0.639130i | \(0.779295\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 84.2233 | − | 48.6263i | 0.343769 | − | 0.198475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 240.415 | − | 416.410i | 0.973338 | − | 1.68587i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 311.819i | 1.24231i | 0.783689 | + | 0.621153i | \(0.213336\pi\) | ||||
−0.783689 | + | 0.621153i | \(0.786664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −415.863 | −1.64373 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −335.121 | − | 193.482i | −1.30397 | − | 0.752849i | −0.322889 | − | 0.946437i | \(-0.604654\pi\) |
−0.981083 | + | 0.193588i | \(0.937988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.46110 | + | 11.1909i | 0.0249463 | + | 0.0432083i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 417.095 | − | 240.810i | 1.58591 | − | 0.915627i | 0.591942 | − | 0.805981i | \(-0.298362\pi\) |
0.993971 | − | 0.109646i | \(-0.0349718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.31243 | − | 10.9334i | 0.0238205 | − | 0.0412583i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 225.818i | 0.839474i | 0.907646 | + | 0.419737i | \(0.137878\pi\) | ||||
−0.907646 | + | 0.419737i | \(0.862122\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.6619 | 0.0873135 | 0.0436567 | − | 0.999047i | \(-0.486099\pi\) | ||||
0.0436567 | + | 0.999047i | \(0.486099\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −223.498 | − | 129.036i | −0.812718 | − | 0.469223i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.9969 | + | 48.4920i | 0.101072 | + | 0.175061i | 0.912126 | − | 0.409909i | \(-0.134440\pi\) |
−0.811055 | + | 0.584970i | \(0.801106\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −122.023 | + | 70.4498i | −0.434244 | + | 0.250711i | −0.701153 | − | 0.713011i | \(-0.747331\pi\) |
0.266909 | + | 0.963722i | \(0.413998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −155.690 | + | 269.663i | −0.550141 | + | 0.952872i | 0.448123 | + | 0.893972i | \(0.352093\pi\) |
−0.998264 | + | 0.0589002i | \(0.981241\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 79.1271i | − | 0.275704i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 127.733 | 0.441983 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −273.621 | − | 157.975i | −0.933859 | − | 0.539164i | −0.0458290 | − | 0.998949i | \(-0.514593\pi\) |
−0.888030 | + | 0.459786i | \(0.847926\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.66712 | + | 16.7439i | 0.0327699 | + | 0.0567591i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 636.116 | − | 367.262i | 2.12748 | − | 1.22830i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −55.5399 | + | 96.1980i | −0.184518 | + | 0.319595i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 216.829i | − | 0.710916i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −379.819 | −1.23720 | −0.618598 | − | 0.785707i | \(-0.712299\pi\) | ||||
−0.618598 | + | 0.785707i | \(0.712299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −335.497 | − | 193.699i | −1.07877 | − | 0.622827i | −0.148204 | − | 0.988957i | \(-0.547349\pi\) |
−0.930564 | + | 0.366130i | \(0.880683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −100.742 | − | 174.491i | −0.321860 | − | 0.557479i | 0.659011 | − | 0.752133i | \(-0.270975\pi\) |
−0.980872 | + | 0.194654i | \(0.937642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 319.046 | − | 184.201i | 1.00645 | − | 0.581077i | 0.0963027 | − | 0.995352i | \(-0.469298\pi\) |
0.910152 | + | 0.414275i | \(0.135965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −186.125 | + | 322.378i | −0.583463 | + | 1.01059i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 276.442i | 0.855857i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 455.824 | 1.40254 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 89.4716 | + | 51.6564i | 0.271950 | + | 0.157010i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 150.832 | + | 261.248i | 0.455684 | + | 0.789268i | 0.998727 | − | 0.0504365i | \(-0.0160613\pi\) |
−0.543043 | + | 0.839705i | \(0.682728\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −71.9460 | + | 41.5380i | −0.214764 | + | 0.123994i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 85.5075 | − | 148.103i | 0.253732 | − | 0.439476i | −0.710819 | − | 0.703375i | \(-0.751675\pi\) |
0.964550 | + | 0.263899i | \(0.0850087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 172.965i | 0.507227i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 149.347 | 0.435414 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −264.744 | − | 152.850i | −0.762950 | − | 0.440489i | 0.0674041 | − | 0.997726i | \(-0.478528\pi\) |
−0.830354 | + | 0.557237i | \(0.811862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1944 | + | 19.3893i | 0.0320756 | + | 0.0555566i | 0.881618 | − | 0.471964i | \(-0.156455\pi\) |
−0.849542 | + | 0.527521i | \(0.823122\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 462.657 | − | 267.115i | 1.31064 | − | 0.756700i | 0.328440 | − | 0.944525i | \(-0.393477\pi\) |
0.982203 | + | 0.187825i | \(0.0601437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1758 | − | 33.2134i | 0.0540163 | − | 0.0935590i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 217.172i | − | 0.604936i | −0.953159 | − | 0.302468i | \(-0.902189\pi\) | ||
0.953159 | − | 0.302468i | \(-0.0978106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 112.874 | 0.312669 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −124.059 | − | 71.6253i | −0.339887 | − | 0.196234i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 51.1847 | + | 88.6546i | 0.139468 | + | 0.241566i | 0.927295 | − | 0.374330i | \(-0.122127\pi\) |
−0.787827 | + | 0.615896i | \(0.788794\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.18042 | − | 4.72297i | 0.0220497 | − | 0.0127304i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −243.458 | + | 421.682i | −0.652702 | + | 1.13051i | 0.329762 | + | 0.944064i | \(0.393031\pi\) |
−0.982464 | + | 0.186450i | \(0.940302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 657.490i | − | 1.74401i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 553.727 | 1.46102 | 0.730510 | − | 0.682901i | \(-0.239282\pi\) | ||||
0.730510 | + | 0.682901i | \(0.239282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 184.612 | + | 106.586i | 0.482016 | + | 0.278292i | 0.721256 | − | 0.692668i | \(-0.243565\pi\) |
−0.239240 | + | 0.970960i | \(0.576898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.4136 | + | 35.3574i | 0.0530224 | + | 0.0918375i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −82.4958 | + | 47.6290i | −0.212071 | + | 0.122439i | −0.602274 | − | 0.798290i | \(-0.705738\pi\) |
0.390202 | + | 0.920729i | \(0.372405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −211.149 | + | 365.720i | −0.540022 | + | 0.935346i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 55.6184i | − | 0.140806i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 481.407 | 1.21261 | 0.606306 | − | 0.795231i | \(-0.292651\pi\) | ||||
0.606306 | + | 0.795231i | \(0.292651\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 517.354 | + | 298.694i | 1.29016 | + | 0.744874i | 0.978682 | − | 0.205380i | \(-0.0658430\pi\) |
0.311477 | + | 0.950254i | \(0.399176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −152.750 | − | 264.571i | −0.379033 | − | 0.656505i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 89.5446 | − | 51.6986i | 0.220011 | − | 0.127024i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −53.7260 | + | 93.0562i | −0.131359 | + | 0.227521i | −0.924201 | − | 0.381907i | \(-0.875268\pi\) |
0.792841 | + | 0.609428i | \(0.208601\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.4659i | 0.0350264i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.7433 | −0.122273 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.6993 | − | 22.9204i | −0.0947477 | − | 0.0547026i | 0.451878 | − | 0.892080i | \(-0.350754\pi\) |
−0.546625 | + | 0.837377i | \(0.684088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.53062 | + | 9.57932i | 0.0131369 | + | 0.0227537i | 0.872519 | − | 0.488580i | \(-0.162485\pi\) |
−0.859382 | + | 0.511334i | \(0.829152\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −226.956 | + | 131.033i | −0.534013 | + | 0.308313i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 81.1161 | − | 140.497i | 0.189967 | − | 0.329033i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 590.788i | 1.37074i | 0.728196 | + | 0.685369i | \(0.240359\pi\) | ||||
−0.728196 | + | 0.685369i | \(0.759641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9683 | −0.0322594 | −0.0161297 | − | 0.999870i | \(-0.505134\pi\) | ||||
−0.0161297 | + | 0.999870i | \(0.505134\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 626.914 | + | 361.949i | 1.43459 | + | 0.828258i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.9051 | − | 62.1894i | −0.0817883 | − | 0.141662i | 0.822230 | − | 0.569156i | \(-0.192730\pi\) |
−0.904018 | + | 0.427494i | \(0.859396\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 581.028 | − | 335.457i | 1.31158 | − | 0.757239i | 0.329219 | − | 0.944254i | \(-0.393214\pi\) |
0.982357 | + | 0.187015i | \(0.0598812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −116.695 | + | 202.122i | −0.262236 | + | 0.454206i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 830.401i | 1.84945i | 0.380642 | + | 0.924723i | \(0.375703\pi\) | ||||
−0.380642 | + | 0.924723i | \(0.624297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −633.136 | −1.40385 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −62.4505 | − | 36.0558i | −0.137254 | − | 0.0792435i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 423.113 | + | 732.854i | 0.925850 | + | 1.60362i | 0.790188 | + | 0.612864i | \(0.209983\pi\) |
0.135661 | + | 0.990755i | \(0.456684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 109.019 | − | 62.9423i | 0.236484 | − | 0.136534i | −0.377076 | − | 0.926182i | \(-0.623070\pi\) |
0.613560 | + | 0.789648i | \(0.289737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −307.121 | + | 531.950i | −0.663329 | + | 1.14892i | 0.316407 | + | 0.948624i | \(0.397524\pi\) |
−0.979735 | + | 0.200296i | \(0.935810\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 172.270i | 0.368887i | 0.982843 | + | 0.184444i | \(0.0590484\pi\) | ||||
−0.982843 | + | 0.184444i | \(0.940952\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −62.1576 | −0.132532 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 769.729 | + | 444.403i | 1.62733 | + | 0.939542i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 224.615 | + | 389.045i | 0.472874 | + | 0.819042i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −174.532 | + | 100.766i | −0.364367 | + | 0.210367i | −0.670995 | − | 0.741462i | \(-0.734133\pi\) |
0.306628 | + | 0.951829i | \(0.400799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −91.3132 | + | 158.159i | −0.189840 | + | 0.328813i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 10.4938i | − | 0.0216367i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 801.178 | 1.64513 | 0.822565 | − | 0.568671i | \(-0.192542\pi\) | ||||
0.822565 | + | 0.568671i | \(0.192542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −625.711 | − | 361.255i | −1.27436 | − | 0.735753i | −0.298555 | − | 0.954392i | \(-0.596505\pi\) |
−0.975806 | + | 0.218640i | \(0.929838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 189.005 | + | 327.366i | 0.383376 | + | 0.664028i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.8503 | − | 14.3474i | 0.0500007 | − | 0.0288679i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −69.4409 | + | 120.275i | −0.139160 | + | 0.241032i | −0.927179 | − | 0.374619i | \(-0.877774\pi\) |
0.788019 | + | 0.615651i | \(0.211107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 794.533i | − | 1.57959i | −0.613372 | − | 0.789794i | \(-0.710187\pi\) | ||
0.613372 | − | 0.789794i | \(-0.289813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −207.689 | −0.411264 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −179.929 | − | 103.882i | −0.353495 | − | 0.204090i | 0.312729 | − | 0.949843i | \(-0.398757\pi\) |
−0.666224 | + | 0.745752i | \(0.732090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.5902 | − | 92.8209i | −0.104873 | − | 0.181646i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −49.2634 | + | 28.4422i | −0.0956571 | + | 0.0552276i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 413.330 | − | 715.908i | 0.799477 | − | 1.38474i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 248.275i | − | 0.476535i | −0.971200 | − | 0.238267i | \(-0.923421\pi\) | ||
0.971200 | − | 0.238267i | \(-0.0765795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −108.678 | −0.207797 | −0.103898 | − | 0.994588i | \(-0.533132\pi\) | ||||
−0.103898 | + | 0.994588i | \(0.533132\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 152.109 | + | 87.8204i | 0.288633 | + | 0.166642i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 288.420 | + | 499.557i | 0.545216 | + | 0.944343i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 968.463 | − | 559.142i | 1.81700 | − | 1.04905i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 132.896 | − | 230.183i | 0.248405 | − | 0.430249i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 582.227i | − | 1.08020i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0646 | 0.0370880 | 0.0185440 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185440 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −100.057 | − | 57.7680i | −0.183591 | − | 0.105996i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 86.6937 | + | 150.158i | 0.158489 | + | 0.274512i | 0.934324 | − | 0.356424i | \(-0.116004\pi\) |
−0.775835 | + | 0.630936i | \(0.782671\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 561.167 | − | 323.990i | 1.01845 | − | 0.588003i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.8069 | − | 36.0386i | 0.0376254 | − | 0.0651692i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 434.666i | − | 0.780370i | −0.920737 | − | 0.390185i | \(-0.872411\pi\) | ||
0.920737 | − | 0.390185i | \(-0.127589\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1569.87 | −2.80835 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −86.8277 | − | 50.1300i | −0.154223 | − | 0.0890409i | 0.420902 | − | 0.907106i | \(-0.361714\pi\) |
−0.575126 | + | 0.818065i | \(0.695047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −124.032 | − | 214.830i | −0.219526 | − | 0.380231i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −44.1556 | + | 25.4932i | −0.0776020 | + | 0.0448036i | −0.538299 | − | 0.842754i | \(-0.680933\pi\) |
0.460697 | + | 0.887558i | \(0.347600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 430.481 | − | 745.615i | 0.753907 | − | 1.30581i | −0.192009 | − | 0.981393i | \(-0.561500\pi\) |
0.945916 | − | 0.324412i | \(-0.105166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 686.252i | 1.19348i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 59.3431 | 0.102848 | 0.0514239 | − | 0.998677i | \(-0.483624\pi\) | ||||
0.0514239 | + | 0.998677i | \(0.483624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.8797 | − | 18.9831i | −0.0565916 | − | 0.0326732i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.7909 | − | 65.4558i | −0.0648215 | − | 0.112274i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −534.777 | + | 308.754i | −0.911034 | + | 0.525986i | −0.880764 | − | 0.473556i | \(-0.842970\pi\) |
−0.0302706 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 150.541 | − | 260.744i | 0.255587 | − | 0.442690i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 342.310i | − | 0.577251i | −0.957442 | − | 0.288626i | \(-0.906802\pi\) | ||
0.957442 | − | 0.288626i | \(-0.0931983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.4589 | 0.0696789 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 379.292 | + | 218.984i | 0.633209 | + | 0.365583i | 0.781994 | − | 0.623286i | \(-0.214203\pi\) |
−0.148785 | + | 0.988870i | \(0.547536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 304.452 | + | 527.327i | 0.506576 | + | 0.877416i | 0.999971 | + | 0.00761053i | \(0.00242253\pi\) |
−0.493395 | + | 0.869806i | \(0.664244\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 64.0212 | − | 36.9627i | 0.105820 | − | 0.0610953i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 540.751 | − | 936.608i | 0.890858 | − | 1.54301i | 0.0520102 | − | 0.998647i | \(-0.483437\pi\) |
0.838848 | − | 0.544365i | \(-0.183230\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1460.10i | 2.38968i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 222.279 | 0.362609 | 0.181304 | − | 0.983427i | \(-0.441968\pi\) | ||||
0.181304 | + | 0.983427i | \(0.441968\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.0310 | + | 17.9158i | 0.0502934 | + | 0.0290369i | 0.524936 | − | 0.851142i | \(-0.324089\pi\) |
−0.474642 | + | 0.880179i | \(0.657423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −161.494 | − | 279.717i | −0.260896 | − | 0.451885i | 0.705584 | − | 0.708626i | \(-0.250685\pi\) |
−0.966480 | + | 0.256741i | \(0.917351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −151.228 | + | 87.3114i | −0.242741 | + | 0.140147i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −158.391 | + | 274.342i | −0.253426 | + | 0.438947i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 104.997i | − | 0.166927i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 794.037 | 1.25838 | 0.629189 | − | 0.777252i | \(-0.283387\pi\) | ||||
0.629189 | + | 0.777252i | \(0.283387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −134.685 | − | 77.7602i | −0.212102 | − | 0.122457i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 514.183 | + | 890.591i | 0.807194 | + | 1.39810i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 753.063 | − | 434.781i | 1.17483 | − | 0.678286i | 0.220013 | − | 0.975497i | \(-0.429390\pi\) |
0.954812 | + | 0.297211i | \(0.0960566\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.2519 | − | 54.1299i | 0.0486033 | − | 0.0841834i | −0.840700 | − | 0.541501i | \(-0.817856\pi\) |
0.889304 | + | 0.457317i | \(0.151190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 761.439i | 1.17688i | 0.808542 | + | 0.588438i | \(0.200257\pi\) | ||||
−0.808542 | + | 0.588438i | \(0.799743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 115.749 | 0.178350 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 129.622 | + | 74.8371i | 0.198502 | + | 0.114605i | 0.595956 | − | 0.803017i | \(-0.296773\pi\) |
−0.397455 | + | 0.917622i | \(0.630106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.54461 | + | 14.7997i | 0.0130452 | + | 0.0225950i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 564.273 | − | 325.783i | 0.856256 | − | 0.494360i | −0.00650063 | − | 0.999979i | \(-0.502069\pi\) |
0.862757 | + | 0.505619i | \(0.168736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −596.672 | + | 1033.47i | −0.902681 | + | 1.56349i | −0.0786818 | + | 0.996900i | \(0.525071\pi\) |
−0.824000 | + | 0.566590i | \(0.808262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 71.0685i | − | 0.106870i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 989.865 | 1.48405 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1124.19 | − | 649.051i | −1.67539 | − | 0.967290i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −74.7771 | − | 129.518i | −0.111110 | − | 0.192448i | 0.805108 | − | 0.593128i | \(-0.202107\pi\) |
−0.916218 | + | 0.400680i | \(0.868774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −607.487 | + | 350.733i | −0.897322 | + | 0.518069i | −0.876331 | − | 0.481710i | \(-0.840016\pi\) |
−0.0209919 | + | 0.999780i | \(0.506682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.92574 | − | 6.79958i | 0.00578165 | − | 0.0100141i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 503.096i | 0.736597i | 0.929708 | + | 0.368299i | \(0.120060\pi\) | ||||
−0.929708 | + | 0.368299i | \(0.879940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 100.648 | 0.146931 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 115.612 | + | 66.7487i | 0.167797 | + | 0.0968776i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −329.413 | − | 570.561i | −0.476720 | − | 0.825703i | 0.522924 | − | 0.852379i | \(-0.324841\pi\) |
−0.999644 | + | 0.0266761i | \(0.991508\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 430.633 | − | 248.626i | 0.619615 | − | 0.357735i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −321.466 | + | 556.796i | −0.461214 | + | 0.798846i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 172.963i | 0.246738i | 0.992361 | + | 0.123369i | \(0.0393698\pi\) | ||||
−0.992361 | + | 0.123369i | \(0.960630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −179.985 | −0.256024 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −134.574 | − | 77.6964i | −0.190345 | − | 0.109896i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 527.267 | + | 913.254i | 0.743677 | + | 1.28809i | 0.950810 | + | 0.309774i | \(0.100253\pi\) |
−0.207133 | + | 0.978313i | \(0.566413\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 398.317 | − | 229.969i | 0.558650 | − | 0.322537i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −288.501 | + | 499.699i | −0.403498 | + | 0.698879i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1164.78i | 1.62000i | 0.586432 | + | 0.809998i | \(0.300532\pi\) | ||||
−0.586432 | + | 0.809998i | \(0.699468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.5611 | −0.0590306 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 531.983 | + | 307.141i | 0.733770 | + | 0.423642i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 492.209 | + | 852.530i | 0.677041 | + | 1.17267i | 0.975868 | + | 0.218362i | \(0.0700712\pi\) |
−0.298827 | + | 0.954307i | \(0.596595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 781.639 | − | 451.280i | 1.06927 | − | 0.617345i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −246.459 | + | 426.879i | −0.336233 | + | 0.582372i | −0.983721 | − | 0.179703i | \(-0.942486\pi\) |
0.647488 | + | 0.762076i | \(0.275820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 497.355i | 0.674837i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −571.150 | −0.772869 | −0.386435 | − | 0.922317i | \(-0.626293\pi\) | ||||
−0.386435 | + | 0.922317i | \(0.626293\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −910.255 | − | 525.536i | −1.22511 | − | 0.707316i | −0.259105 | − | 0.965849i | \(-0.583427\pi\) |
−0.966002 | + | 0.258533i | \(0.916761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −297.709 | − | 515.648i | −0.399610 | − | 0.692144i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 172.224 | − | 99.4334i | 0.229938 | − | 0.132755i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.3053 | − | 73.2749i | 0.0563319 | − | 0.0975698i | −0.836484 | − | 0.547991i | \(-0.815393\pi\) |
0.892816 | + | 0.450421i | \(0.148726\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 322.705i | 0.427423i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1007.63 | −1.33109 | −0.665543 | − | 0.746360i | \(-0.731800\pi\) | ||||
−0.665543 | + | 0.746360i | \(0.731800\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −393.981 | − | 227.465i | −0.517715 | − | 0.298903i | 0.218285 | − | 0.975885i | \(-0.429954\pi\) |
−0.735999 | + | 0.676983i | \(0.763287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.2221 | − | 74.8629i | −0.0566476 | − | 0.0981165i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −177.053 | + | 102.222i | −0.230838 | + | 0.133275i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 352.232 | − | 610.084i | 0.458039 | − | 0.793347i | −0.540818 | − | 0.841139i | \(-0.681885\pi\) |
0.998857 | + | 0.0477927i | \(0.0152187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1021.43i | 1.32138i | 0.750658 | + | 0.660691i | \(0.229737\pi\) | ||||
−0.750658 | + | 0.660691i | \(0.770263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 285.424 | 0.368289 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 954.453 | + | 551.054i | 1.22523 | + | 0.707386i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −114.801 | − | 198.840i | −0.146992 | − | 0.254597i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 433.974 | − | 250.555i | 0.552833 | − | 0.319178i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −202.007 | + | 349.886i | −0.256680 | + | 0.444582i | −0.965350 | − | 0.260957i | \(-0.915962\pi\) |
0.708671 | + | 0.705539i | \(0.249295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 185.603i | − | 0.234643i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2292.79 | 2.89129 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 765.042 | + | 441.697i | 0.959902 | + | 0.554200i | 0.896143 | − | 0.443766i | \(-0.146358\pi\) |
0.0637592 | + | 0.997965i | \(0.479691\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −419.725 | − | 726.985i | −0.525313 | − | 0.909869i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −742.708 | + | 428.803i | −0.924917 | + | 0.534001i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.2827 | − | 94.0204i | 0.0674320 | − | 0.116796i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 372.575i | − | 0.460537i | −0.973127 | − | 0.230269i | \(-0.926040\pi\) | ||
0.973127 | − | 0.230269i | \(-0.0739605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 267.519 | 0.329863 | 0.164932 | − | 0.986305i | \(-0.447260\pi\) | ||||
0.164932 | + | 0.986305i | \(0.447260\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 201.244 | + | 116.188i | 0.246925 | + | 0.142562i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −773.578 | − | 1339.88i | −0.946852 | − | 1.64000i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 574.911 | − | 331.925i | 0.700257 | − | 0.404293i | −0.107186 | − | 0.994239i | \(-0.534184\pi\) |
0.807443 | + | 0.589946i | \(0.200851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 468.171 | − | 810.896i | 0.568859 | − | 0.985292i | −0.427820 | − | 0.903864i | \(-0.640718\pi\) |
0.996679 | − | 0.0814286i | \(-0.0259483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 499.832i | − | 0.604392i | −0.953246 | − | 0.302196i | \(-0.902280\pi\) | ||
0.953246 | − | 0.302196i | \(-0.0977196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 667.578 | 0.805280 | 0.402640 | − | 0.915358i | \(-0.368093\pi\) | ||||
0.402640 | + | 0.915358i | \(0.368093\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −512.025 | − | 295.618i | −0.614676 | − | 0.354883i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.7220 | + | 79.1929i | 0.0547569 | + | 0.0948418i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 64.1295 | − | 37.0252i | 0.0764356 | − | 0.0441301i | −0.461295 | − | 0.887247i | \(-0.652615\pi\) |
0.537731 | + | 0.843117i | \(0.319282\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.5264 | − | 39.0169i | 0.0267853 | − | 0.0463935i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 666.116i | − | 0.788303i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 55.3110 | 0.0653023 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −238.112 | − | 137.474i | −0.279802 | − | 0.161544i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −553.775 | − | 959.167i | −0.649209 | − | 1.12446i | −0.983312 | − | 0.181927i | \(-0.941767\pi\) |
0.334103 | − | 0.942537i | \(-0.391567\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −687.370 | + | 396.854i | −0.802066 | + | 0.463073i | −0.844193 | − | 0.536039i | \(-0.819920\pi\) |
0.0421271 | + | 0.999112i | \(0.486587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 121.830 | − | 211.016i | 0.141828 | − | 0.245653i | −0.786357 | − | 0.617772i | \(-0.788035\pi\) |
0.928185 | + | 0.372119i | \(0.121369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 841.279i | − | 0.974830i | −0.873170 | − | 0.487415i | \(-0.837940\pi\) | ||
0.873170 | − | 0.487415i | \(-0.162060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −611.167 | −0.706552 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −288.363 | − | 166.486i | −0.331833 | − | 0.191584i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −439.230 | − | 760.768i | −0.504282 | − | 0.873442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 129.030 | − | 74.4953i | 0.147462 | − | 0.0851375i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 302.656 | − | 524.216i | 0.345104 | − | 0.597738i | −0.640269 | − | 0.768151i | \(-0.721177\pi\) |
0.985373 | + | 0.170413i | \(0.0545103\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 820.188i | 0.930974i | 0.885055 | + | 0.465487i | \(0.154121\pi\) | ||||
−0.885055 | + | 0.465487i | \(0.845879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −623.820 | −0.706478 | −0.353239 | − | 0.935533i | \(-0.614920\pi\) | ||||
−0.353239 | + | 0.935533i | \(0.614920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −212.242 | − | 122.538i | −0.239281 | − | 0.138149i | 0.375565 | − | 0.926796i | \(-0.377449\pi\) |
−0.614846 | + | 0.788647i | \(0.710782\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.1803 | − | 100.771i | −0.0654447 | − | 0.113353i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1246.19 | + | 719.488i | −1.39551 | + | 0.805698i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −203.261 | + | 352.058i | −0.227107 | + | 0.393361i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 411.702i | − | 0.457955i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −76.7513 | −0.0851845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −161.710 | − | 93.3632i | −0.178685 | − | 0.103164i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −109.071 | − | 188.917i | −0.120255 | − | 0.208287i | 0.799613 | − | 0.600515i | \(-0.205038\pi\) |
−0.919868 | + | 0.392228i | \(0.871704\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 558.980 | − | 322.727i | 0.613589 | − | 0.354256i | −0.160780 | − | 0.986990i | \(-0.551401\pi\) |
0.774369 | + | 0.632735i | \(0.218068\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −151.894 | + | 263.088i | −0.166368 | + | 0.288157i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.7862i | 0.0139435i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1567.66 | −1.70583 | −0.852917 | − | 0.522047i | \(-0.825169\pi\) | ||||
−0.852917 | + | 0.522047i | \(0.825169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 351.204 | + | 202.768i | 0.380503 | + | 0.219684i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −85.3123 | − | 147.765i | −0.0922296 | − | 0.159746i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −78.1550 | + | 45.1228i | −0.0841281 | + | 0.0485714i | −0.541474 | − | 0.840718i | \(-0.682133\pi\) |
0.457346 | + | 0.889289i | \(0.348800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −506.745 | + | 877.708i | −0.544302 | + | 0.942758i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 331.734i | − | 0.354796i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −593.849 | −0.633777 | −0.316889 | − | 0.948463i | \(-0.602638\pi\) | ||||
−0.316889 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.2459 | + | 23.2360i | 0.0427693 | + | 0.0246928i | 0.521232 | − | 0.853415i | \(-0.325473\pi\) |
−0.478463 | + | 0.878108i | \(0.658806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 841.800 | + | 1458.04i | 0.892683 | + | 1.54617i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1614.20 | + | 931.957i | −1.70454 | + | 0.984115i | −0.763502 | + | 0.645806i | \(0.776522\pi\) |
−0.941035 | + | 0.338309i | \(0.890145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 757.378 | − | 1311.82i | 0.798080 | − | 1.38232i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 293.678i | − | 0.308162i | −0.988058 | − | 0.154081i | \(-0.950758\pi\) | ||
0.988058 | − | 0.154081i | \(-0.0492416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −108.321 | −0.113425 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 65.2158 | + | 37.6523i | 0.0680039 | + | 0.0392621i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 384.852 | + | 666.583i | 0.400470 | + | 0.693635i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −107.732 | + | 62.1991i | −0.111639 | + | 0.0644550i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.1241 | − | 97.2098i | 0.0580394 | − | 0.100527i | −0.835546 | − | 0.549421i | \(-0.814848\pi\) |
0.893585 | + | 0.448894i | \(0.148182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1539.13i | − | 1.58510i | −0.609807 | − | 0.792550i | \(-0.708753\pi\) | ||
0.609807 | − | 0.792550i | \(-0.291247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 372.044 | 0.382368 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −294.065 | − | 169.778i | −0.300987 | − | 0.173775i | 0.341899 | − | 0.939737i | \(-0.388930\pi\) |
−0.642886 | + | 0.765962i | \(0.722263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 698.623 | + | 1210.05i | 0.713609 | + | 1.23601i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 892.130 | − | 515.072i | 0.907559 | − | 0.523979i | 0.0279139 | − | 0.999610i | \(-0.491114\pi\) |
0.879645 | + | 0.475631i | \(0.157780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.6075 | − | 85.9228i | 0.0503630 | − | 0.0872312i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2363.46i | − | 2.38975i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 439.103 | 0.443091 | 0.221546 | − | 0.975150i | \(-0.428890\pi\) | ||||
0.221546 | + | 0.975150i | \(0.428890\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.4094 | − | 30.8359i | −0.0536777 | − | 0.0309909i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −381.047 | − | 659.993i | −0.382194 | − | 0.661979i | 0.609182 | − | 0.793031i | \(-0.291498\pi\) |
−0.991376 | + | 0.131051i | \(0.958165\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.q.i.449.3 | 8 | ||
3.2 | odd | 2 | 576.3.q.j.257.4 | 8 | |||
4.3 | odd | 2 | 1728.3.q.j.449.3 | 8 | |||
8.3 | odd | 2 | 216.3.m.b.17.2 | 8 | |||
8.5 | even | 2 | 432.3.q.e.17.2 | 8 | |||
9.2 | odd | 6 | inner | 1728.3.q.i.1601.3 | 8 | ||
9.7 | even | 3 | 576.3.q.j.65.4 | 8 | |||
12.11 | even | 2 | 576.3.q.i.257.1 | 8 | |||
24.5 | odd | 2 | 144.3.q.e.113.1 | 8 | |||
24.11 | even | 2 | 72.3.m.b.41.4 | ✓ | 8 | ||
36.7 | odd | 6 | 576.3.q.i.65.1 | 8 | |||
36.11 | even | 6 | 1728.3.q.j.1601.3 | 8 | |||
72.5 | odd | 6 | 1296.3.e.i.161.3 | 8 | |||
72.11 | even | 6 | 216.3.m.b.89.2 | 8 | |||
72.13 | even | 6 | 1296.3.e.i.161.6 | 8 | |||
72.29 | odd | 6 | 432.3.q.e.305.2 | 8 | |||
72.43 | odd | 6 | 72.3.m.b.65.4 | yes | 8 | ||
72.59 | even | 6 | 648.3.e.c.161.3 | 8 | |||
72.61 | even | 6 | 144.3.q.e.65.1 | 8 | |||
72.67 | odd | 6 | 648.3.e.c.161.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.b.41.4 | ✓ | 8 | 24.11 | even | 2 | ||
72.3.m.b.65.4 | yes | 8 | 72.43 | odd | 6 | ||
144.3.q.e.65.1 | 8 | 72.61 | even | 6 | |||
144.3.q.e.113.1 | 8 | 24.5 | odd | 2 | |||
216.3.m.b.17.2 | 8 | 8.3 | odd | 2 | |||
216.3.m.b.89.2 | 8 | 72.11 | even | 6 | |||
432.3.q.e.17.2 | 8 | 8.5 | even | 2 | |||
432.3.q.e.305.2 | 8 | 72.29 | odd | 6 | |||
576.3.q.i.65.1 | 8 | 36.7 | odd | 6 | |||
576.3.q.i.257.1 | 8 | 12.11 | even | 2 | |||
576.3.q.j.65.4 | 8 | 9.7 | even | 3 | |||
576.3.q.j.257.4 | 8 | 3.2 | odd | 2 | |||
648.3.e.c.161.3 | 8 | 72.59 | even | 6 | |||
648.3.e.c.161.6 | 8 | 72.67 | odd | 6 | |||
1296.3.e.i.161.3 | 8 | 72.5 | odd | 6 | |||
1296.3.e.i.161.6 | 8 | 72.13 | even | 6 | |||
1728.3.q.i.449.3 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.q.i.1601.3 | 8 | 9.2 | odd | 6 | inner | ||
1728.3.q.j.449.3 | 8 | 4.3 | odd | 2 | |||
1728.3.q.j.1601.3 | 8 | 36.11 | even | 6 |