Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + \cdots + 33124 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.9 | ||
Root | \(1.20711 - 1.12945i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.e.601.13 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −6.73333 | − | 1.91369i | −0.961905 | − | 0.273384i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.5116 | 1.59196 | 0.795982 | − | 0.605321i | \(-0.206955\pi\) | ||||
0.795982 | + | 0.605321i | \(0.206955\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | − | 4.83531i | − | 0.371947i | −0.982555 | − | 0.185973i | \(-0.940456\pi\) | ||
0.982555 | − | 0.185973i | \(-0.0595438\pi\) | |||||||
\(14\) | −9.52237 | − | 2.70636i | −0.680170 | − | 0.193312i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 18.0284i | − | 1.06049i | −0.847843 | − | 0.530247i | \(-0.822099\pi\) | ||
0.847843 | − | 0.530247i | \(-0.177901\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 9.13350i | 0.480711i | 0.970685 | + | 0.240355i | \(0.0772640\pi\) | ||||
−0.970685 | + | 0.240355i | \(0.922736\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.31461 | + | 11.6625i | −0.157838 | + | 0.555356i | ||||
\(22\) | 24.7651 | 1.12569 | ||||||||
\(23\) | 3.72515 | 0.161963 | 0.0809816 | − | 0.996716i | \(-0.474194\pi\) | ||||
0.0809816 | + | 0.996716i | \(0.474194\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 6.83816i | − | 0.263006i | ||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −13.4667 | − | 3.82738i | −0.480952 | − | 0.136692i | ||||
\(29\) | −1.12582 | −0.0388213 | −0.0194107 | − | 0.999812i | \(-0.506179\pi\) | ||||
−0.0194107 | + | 0.999812i | \(0.506179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 57.0859i | − | 1.84148i | −0.390175 | − | 0.920741i | \(-0.627585\pi\) | ||
0.390175 | − | 0.920741i | \(-0.372415\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 30.3310i | − | 0.919120i | ||||||
\(34\) | − | 25.4960i | − | 0.749882i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −41.3624 | −1.11790 | −0.558952 | − | 0.829200i | \(-0.688796\pi\) | ||||
−0.558952 | + | 0.829200i | \(0.688796\pi\) | |||||||
\(38\) | 12.9167i | 0.339914i | ||||||||
\(39\) | −8.37500 | −0.214744 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.7156i | − | 0.285745i | −0.989741 | − | 0.142873i | \(-0.954366\pi\) | ||
0.989741 | − | 0.142873i | \(-0.0456340\pi\) | |||||||
\(42\) | −4.68756 | + | 16.4932i | −0.111609 | + | 0.392696i | ||||
\(43\) | −64.4171 | −1.49807 | −0.749036 | − | 0.662529i | \(-0.769483\pi\) | ||||
−0.749036 | + | 0.662529i | \(0.769483\pi\) | |||||||
\(44\) | 35.0232 | 0.795982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.26816 | 0.114525 | ||||||||
\(47\) | − | 77.6614i | − | 1.65237i | −0.563399 | − | 0.826185i | \(-0.690507\pi\) | ||
0.563399 | − | 0.826185i | \(-0.309493\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | 41.6756 | + | 25.7710i | 0.850522 | + | 0.525939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −31.2261 | −0.612276 | ||||||||
\(52\) | − | 9.67062i | − | 0.185973i | ||||||
\(53\) | 77.5383 | 1.46299 | 0.731493 | − | 0.681849i | \(-0.238824\pi\) | ||||
0.731493 | + | 0.681849i | \(0.238824\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.0447 | − | 5.41273i | −0.340085 | − | 0.0966559i | ||||
\(57\) | 15.8197 | 0.277539 | ||||||||
\(58\) | −1.59215 | −0.0274508 | ||||||||
\(59\) | − | 87.0651i | − | 1.47568i | −0.674976 | − | 0.737839i | \(-0.735846\pi\) | ||
0.674976 | − | 0.737839i | \(-0.264154\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.36957i | − | 0.0880258i | −0.999031 | − | 0.0440129i | \(-0.985986\pi\) | ||
0.999031 | − | 0.0440129i | \(-0.0140143\pi\) | |||||||
\(62\) | − | 80.7317i | − | 1.30212i | ||||||
\(63\) | 20.2000 | + | 5.74106i | 0.320635 | + | 0.0911280i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 42.8945i | − | 0.649916i | ||||||
\(67\) | −47.1879 | −0.704297 | −0.352149 | − | 0.935944i | \(-0.614549\pi\) | ||||
−0.352149 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(68\) | − | 36.0568i | − | 0.530247i | ||||||
\(69\) | − | 6.45216i | − | 0.0935095i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −58.3047 | −0.821193 | −0.410597 | − | 0.911817i | \(-0.634680\pi\) | ||||
−0.410597 | + | 0.911817i | \(0.634680\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | − | 53.4082i | − | 0.731619i | −0.930690 | − | 0.365810i | \(-0.880792\pi\) | ||
0.930690 | − | 0.365810i | \(-0.119208\pi\) | |||||||
\(74\) | −58.4953 | −0.790477 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 18.2670i | 0.240355i | ||||||||
\(77\) | −117.911 | − | 33.5117i | −1.53132 | − | 0.435217i | ||||
\(78\) | −11.8440 | −0.151847 | ||||||||
\(79\) | 74.9637 | 0.948907 | 0.474454 | − | 0.880280i | \(-0.342646\pi\) | ||||
0.474454 | + | 0.880280i | \(0.342646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 16.5683i | − | 0.202053i | ||||||
\(83\) | 28.7890i | 0.346855i | 0.984847 | + | 0.173428i | \(0.0554843\pi\) | ||||
−0.984847 | + | 0.173428i | \(0.944516\pi\) | |||||||
\(84\) | −6.62921 | + | 23.3250i | −0.0789192 | + | 0.277678i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −91.0996 | −1.05930 | ||||||||
\(87\) | 1.94997i | 0.0224135i | ||||||||
\(88\) | 49.5303 | 0.562844 | ||||||||
\(89\) | 101.499i | 1.14043i | 0.821494 | + | 0.570217i | \(0.193141\pi\) | ||||
−0.821494 | + | 0.570217i | \(0.806859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.25327 | + | 32.5578i | −0.101684 | + | 0.357778i | ||||
\(92\) | 7.45031 | 0.0809816 | ||||||||
\(93\) | −98.8757 | −1.06318 | ||||||||
\(94\) | − | 109.830i | − | 1.16840i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | − | 107.830i | − | 1.11165i | −0.831298 | − | 0.555827i | \(-0.812402\pi\) | ||
0.831298 | − | 0.555827i | \(-0.187598\pi\) | |||||||
\(98\) | 58.9382 | + | 36.4457i | 0.601410 | + | 0.371895i | ||||
\(99\) | −52.5348 | −0.530654 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52.6151i | 0.520941i | 0.965482 | + | 0.260471i | \(0.0838777\pi\) | ||||
−0.965482 | + | 0.260471i | \(0.916122\pi\) | |||||||
\(102\) | −44.1604 | −0.432945 | ||||||||
\(103\) | 72.4002i | 0.702915i | 0.936204 | + | 0.351457i | \(0.114314\pi\) | ||||
−0.936204 | + | 0.351457i | \(0.885686\pi\) | |||||||
\(104\) | − | 13.6763i | − | 0.131503i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 109.656 | 1.03449 | ||||||||
\(107\) | 173.562 | 1.62207 | 0.811037 | − | 0.584994i | \(-0.198903\pi\) | ||||
0.811037 | + | 0.584994i | \(0.198903\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −49.9966 | −0.458684 | −0.229342 | − | 0.973346i | \(-0.573658\pi\) | ||||
−0.229342 | + | 0.973346i | \(0.573658\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 71.6418i | 0.645422i | ||||||||
\(112\) | −26.9333 | − | 7.65475i | −0.240476 | − | 0.0683460i | ||||
\(113\) | −70.1536 | −0.620828 | −0.310414 | − | 0.950601i | \(-0.600468\pi\) | ||||
−0.310414 | + | 0.950601i | \(0.600468\pi\) | |||||||
\(114\) | 22.3724 | 0.196249 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.25164 | −0.0194107 | ||||||||
\(117\) | 14.5059i | 0.123982i | ||||||||
\(118\) | − | 123.129i | − | 1.04346i | ||||||
\(119\) | −34.5007 | + | 121.391i | −0.289922 | + | 1.02009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 185.656 | 1.53435 | ||||||||
\(122\) | − | 7.59373i | − | 0.0622436i | ||||||
\(123\) | −20.2919 | −0.164975 | ||||||||
\(124\) | − | 114.172i | − | 0.920741i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 28.5671 | + | 8.11909i | 0.226723 | + | 0.0644372i | ||||
\(127\) | 197.945 | 1.55863 | 0.779313 | − | 0.626635i | \(-0.215568\pi\) | ||||
0.779313 | + | 0.626635i | \(0.215568\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 111.574i | 0.864912i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 114.901i | 0.877105i | 0.898706 | + | 0.438552i | \(0.144509\pi\) | ||||
−0.898706 | + | 0.438552i | \(0.855491\pi\) | |||||||
\(132\) | − | 60.6619i | − | 0.459560i | ||||||
\(133\) | 17.4787 | − | 61.4989i | 0.131419 | − | 0.462398i | ||||
\(134\) | −66.7338 | −0.498013 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 50.9920i | − | 0.374941i | ||||||
\(137\) | −95.3358 | −0.695882 | −0.347941 | − | 0.937516i | \(-0.613119\pi\) | ||||
−0.347941 | + | 0.937516i | \(0.613119\pi\) | |||||||
\(138\) | − | 9.12473i | − | 0.0661212i | ||||||
\(139\) | 237.587i | 1.70926i | 0.519237 | + | 0.854630i | \(0.326216\pi\) | ||||
−0.519237 | + | 0.854630i | \(0.673784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −134.513 | −0.953996 | ||||||||
\(142\) | −82.4553 | −0.580671 | ||||||||
\(143\) | − | 84.6740i | − | 0.592126i | ||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 75.5306i | − | 0.517333i | ||||||
\(147\) | 44.6367 | − | 72.1842i | 0.303651 | − | 0.491049i | ||||
\(148\) | −82.7248 | −0.558952 | ||||||||
\(149\) | −133.844 | −0.898285 | −0.449142 | − | 0.893460i | \(-0.648270\pi\) | ||||
−0.449142 | + | 0.893460i | \(0.648270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155.064 | 1.02691 | 0.513456 | − | 0.858116i | \(-0.328365\pi\) | ||||
0.513456 | + | 0.858116i | \(0.328365\pi\) | |||||||
\(152\) | 25.8335i | 0.169957i | ||||||||
\(153\) | 54.0852i | 0.353498i | ||||||||
\(154\) | −166.752 | − | 47.3928i | −1.08280 | − | 0.307745i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −16.7500 | −0.107372 | ||||||||
\(157\) | − | 104.634i | − | 0.666459i | −0.942846 | − | 0.333230i | \(-0.891862\pi\) | ||
0.942846 | − | 0.333230i | \(-0.108138\pi\) | |||||||
\(158\) | 106.015 | 0.670979 | ||||||||
\(159\) | − | 134.300i | − | 0.844656i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.0827 | − | 7.12878i | −0.155793 | − | 0.0442782i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −130.909 | −0.803120 | −0.401560 | − | 0.915833i | \(-0.631532\pi\) | ||||
−0.401560 | + | 0.915833i | \(0.631532\pi\) | |||||||
\(164\) | − | 23.4311i | − | 0.142873i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 40.7138i | 0.245264i | ||||||||
\(167\) | − | 102.845i | − | 0.615838i | −0.951413 | − | 0.307919i | \(-0.900367\pi\) | ||
0.951413 | − | 0.307919i | \(-0.0996325\pi\) | |||||||
\(168\) | −9.37512 | + | 32.9865i | −0.0558043 | + | 0.196348i | ||||
\(169\) | 145.620 | 0.861656 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 27.4005i | − | 0.160237i | ||||||
\(172\) | −128.834 | −0.749036 | ||||||||
\(173\) | − | 197.432i | − | 1.14122i | −0.821220 | − | 0.570612i | \(-0.806706\pi\) | ||
0.821220 | − | 0.570612i | \(-0.193294\pi\) | |||||||
\(174\) | 2.75768i | 0.0158487i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 70.0464 | 0.397991 | ||||||||
\(177\) | −150.801 | −0.851984 | ||||||||
\(178\) | 143.541i | 0.806409i | ||||||||
\(179\) | 118.822 | 0.663809 | 0.331904 | − | 0.943313i | \(-0.392309\pi\) | ||||
0.331904 | + | 0.943313i | \(0.392309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.4148i | − | 0.0796399i | −0.999207 | − | 0.0398199i | \(-0.987322\pi\) | ||
0.999207 | − | 0.0398199i | \(-0.0126784\pi\) | |||||||
\(182\) | −13.0861 | + | 46.0436i | −0.0719017 | + | 0.252987i | ||||
\(183\) | −9.30038 | −0.0508217 | ||||||||
\(184\) | 10.5363 | 0.0572626 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −139.831 | −0.751782 | ||||||||
\(187\) | − | 315.706i | − | 1.68827i | ||||||
\(188\) | − | 155.323i | − | 0.826185i | ||||||
\(189\) | 9.94382 | − | 34.9874i | 0.0526128 | − | 0.185119i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 59.9375 | 0.313809 | 0.156904 | − | 0.987614i | \(-0.449849\pi\) | ||||
0.156904 | + | 0.987614i | \(0.449849\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | 245.948 | 1.27434 | 0.637171 | − | 0.770723i | \(-0.280105\pi\) | ||||
0.637171 | + | 0.770723i | \(0.280105\pi\) | |||||||
\(194\) | − | 152.495i | − | 0.786058i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 83.3512 | + | 51.5420i | 0.425261 | + | 0.262969i | ||||
\(197\) | −82.0594 | −0.416545 | −0.208273 | − | 0.978071i | \(-0.566784\pi\) | ||||
−0.208273 | + | 0.978071i | \(0.566784\pi\) | |||||||
\(198\) | −74.2954 | −0.375229 | ||||||||
\(199\) | 289.338i | 1.45396i | 0.686658 | + | 0.726981i | \(0.259077\pi\) | ||||
−0.686658 | + | 0.726981i | \(0.740923\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 81.7319i | 0.406626i | ||||||||
\(202\) | 74.4089i | 0.368361i | ||||||||
\(203\) | 7.58051 | + | 2.15447i | 0.0373424 | + | 0.0106131i | ||||
\(204\) | −62.4522 | −0.306138 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 102.389i | 0.497036i | ||||||||
\(207\) | −11.1755 | −0.0539877 | ||||||||
\(208\) | − | 19.3412i | − | 0.0929867i | ||||||
\(209\) | 159.942i | 0.765274i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 33.6995 | 0.159713 | 0.0798567 | − | 0.996806i | \(-0.474554\pi\) | ||||
0.0798567 | + | 0.996806i | \(0.474554\pi\) | |||||||
\(212\) | 155.077 | 0.731493 | ||||||||
\(213\) | 100.987i | 0.474116i | ||||||||
\(214\) | 245.454 | 1.14698 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −109.245 | + | 384.379i | −0.503432 | + | 1.77133i | ||||
\(218\) | −70.7059 | −0.324339 | ||||||||
\(219\) | −92.5057 | −0.422401 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −87.1728 | −0.394447 | ||||||||
\(222\) | 101.317i | 0.456382i | ||||||||
\(223\) | 10.7556i | 0.0482313i | 0.999709 | + | 0.0241156i | \(0.00767699\pi\) | ||||
−0.999709 | + | 0.0241156i | \(0.992323\pi\) | |||||||
\(224\) | −38.0895 | − | 10.8255i | −0.170042 | − | 0.0483279i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −99.2121 | −0.438992 | ||||||||
\(227\) | 416.450i | 1.83458i | 0.398219 | + | 0.917290i | \(0.369628\pi\) | ||||
−0.398219 | + | 0.917290i | \(0.630372\pi\) | |||||||
\(228\) | 31.6394 | 0.138769 | ||||||||
\(229\) | − | 388.469i | − | 1.69637i | −0.529700 | − | 0.848185i | \(-0.677695\pi\) | ||
0.529700 | − | 0.848185i | \(-0.322305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −58.0440 | + | 204.229i | −0.251273 | + | 0.884107i | ||||
\(232\) | −3.18429 | −0.0137254 | ||||||||
\(233\) | −70.4036 | −0.302162 | −0.151081 | − | 0.988521i | \(-0.548275\pi\) | ||||
−0.151081 | + | 0.988521i | \(0.548275\pi\) | |||||||
\(234\) | 20.5145i | 0.0876687i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 174.130i | − | 0.737839i | ||||||
\(237\) | − | 129.841i | − | 0.547852i | ||||||
\(238\) | −48.7914 | + | 171.673i | −0.205006 | + | 0.721315i | ||||
\(239\) | 313.133 | 1.31018 | 0.655091 | − | 0.755550i | \(-0.272630\pi\) | ||||
0.655091 | + | 0.755550i | \(0.272630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 198.727i | − | 0.824595i | −0.911049 | − | 0.412297i | \(-0.864726\pi\) | ||
0.911049 | − | 0.412297i | \(-0.135274\pi\) | |||||||
\(242\) | 262.557 | 1.08495 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 10.7391i | − | 0.0440129i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.6971 | −0.116655 | ||||||||
\(247\) | 44.1633 | 0.178799 | ||||||||
\(248\) | − | 161.463i | − | 0.651062i | ||||||
\(249\) | 49.8640 | 0.200257 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 300.878i | 1.19872i | 0.800480 | + | 0.599359i | \(0.204578\pi\) | ||||
−0.800480 | + | 0.599359i | \(0.795422\pi\) | |||||||
\(252\) | 40.4000 | + | 11.4821i | 0.160317 | + | 0.0455640i | ||||
\(253\) | 65.2334 | 0.257839 | ||||||||
\(254\) | 279.937 | 1.10211 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 306.052i | 1.19087i | 0.803405 | + | 0.595433i | \(0.203019\pi\) | ||||
−0.803405 | + | 0.595433i | \(0.796981\pi\) | |||||||
\(258\) | 157.789i | 0.611585i | ||||||||
\(259\) | 278.507 | + | 79.1548i | 1.07532 | + | 0.305617i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.37745 | 0.0129404 | ||||||||
\(262\) | 162.494i | 0.620207i | ||||||||
\(263\) | 286.135 | 1.08797 | 0.543984 | − | 0.839096i | \(-0.316915\pi\) | ||||
0.543984 | + | 0.839096i | \(0.316915\pi\) | |||||||
\(264\) | − | 85.7889i | − | 0.324958i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 24.7186 | − | 86.9726i | 0.0929270 | − | 0.326965i | ||||
\(267\) | 175.801 | 0.658430 | ||||||||
\(268\) | −94.3758 | −0.352149 | ||||||||
\(269\) | − | 188.412i | − | 0.700415i | −0.936672 | − | 0.350208i | \(-0.886111\pi\) | ||
0.936672 | − | 0.350208i | \(-0.113889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.59288i | − | 0.0353981i | −0.999843 | − | 0.0176990i | \(-0.994366\pi\) | ||
0.999843 | − | 0.0176990i | \(-0.00563408\pi\) | |||||||
\(272\) | − | 72.1136i | − | 0.265123i | ||||||
\(273\) | 56.3917 | + | 16.0271i | 0.206563 | + | 0.0587075i | ||||
\(274\) | −134.825 | −0.492063 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 12.9043i | − | 0.0467548i | ||||||
\(277\) | 161.066 | 0.581464 | 0.290732 | − | 0.956804i | \(-0.406101\pi\) | ||||
0.290732 | + | 0.956804i | \(0.406101\pi\) | |||||||
\(278\) | 335.999i | 1.20863i | ||||||||
\(279\) | 171.258i | 0.613827i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −343.107 | −1.22102 | −0.610510 | − | 0.792008i | \(-0.709036\pi\) | ||||
−0.610510 | + | 0.792008i | \(0.709036\pi\) | |||||||
\(282\) | −190.231 | −0.674577 | ||||||||
\(283\) | 324.748i | 1.14752i | 0.819024 | + | 0.573759i | \(0.194516\pi\) | ||||
−0.819024 | + | 0.573759i | \(0.805484\pi\) | |||||||
\(284\) | −116.609 | −0.410597 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 119.747i | − | 0.418696i | ||||||
\(287\) | −22.4199 | + | 78.8848i | −0.0781182 | + | 0.274860i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −36.0229 | −0.124647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −186.768 | −0.641813 | ||||||||
\(292\) | − | 106.816i | − | 0.365810i | ||||||
\(293\) | − | 100.918i | − | 0.344429i | −0.985059 | − | 0.172215i | \(-0.944908\pi\) | ||
0.985059 | − | 0.172215i | \(-0.0550923\pi\) | |||||||
\(294\) | 63.1258 | − | 102.084i | 0.214714 | − | 0.347224i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −116.991 | −0.395238 | ||||||||
\(297\) | 90.9929i | 0.306373i | ||||||||
\(298\) | −189.285 | −0.635183 | ||||||||
\(299\) | − | 18.0123i | − | 0.0602417i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 433.742 | + | 123.274i | 1.44100 | + | 0.409549i | ||||
\(302\) | 219.293 | 0.726136 | ||||||||
\(303\) | 91.1320 | 0.300766 | ||||||||
\(304\) | 36.5340i | 0.120178i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 76.4880i | 0.249961i | ||||||||
\(307\) | 41.3057i | 0.134546i | 0.997735 | + | 0.0672732i | \(0.0214299\pi\) | ||||
−0.997735 | + | 0.0672732i | \(0.978570\pi\) | |||||||
\(308\) | −235.823 | − | 67.0235i | −0.765659 | − | 0.217609i | ||||
\(309\) | 125.401 | 0.405828 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 470.341i | 1.51235i | 0.654369 | + | 0.756176i | \(0.272934\pi\) | ||||
−0.654369 | + | 0.756176i | \(0.727066\pi\) | |||||||
\(312\) | −23.6881 | −0.0759233 | ||||||||
\(313\) | 160.220i | 0.511884i | 0.966692 | + | 0.255942i | \(0.0823855\pi\) | ||||
−0.966692 | + | 0.255942i | \(0.917614\pi\) | |||||||
\(314\) | − | 147.975i | − | 0.471258i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 149.927 | 0.474454 | ||||||||
\(317\) | −268.766 | −0.847843 | −0.423922 | − | 0.905699i | \(-0.639347\pi\) | ||||
−0.423922 | + | 0.905699i | \(0.639347\pi\) | |||||||
\(318\) | − | 189.929i | − | 0.597262i | ||||||
\(319\) | −19.7149 | −0.0618021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 300.618i | − | 0.936505i | ||||||
\(322\) | −35.4723 | − | 10.0816i | −0.110162 | − | 0.0313094i | ||||
\(323\) | 164.662 | 0.509791 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −185.133 | −0.567891 | ||||||||
\(327\) | 86.5967i | 0.264822i | ||||||||
\(328\) | − | 33.1366i | − | 0.101026i | ||||||
\(329\) | −148.620 | + | 522.920i | −0.451732 | + | 1.58942i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 555.018 | 1.67679 | 0.838395 | − | 0.545063i | \(-0.183494\pi\) | ||||
0.838395 | + | 0.545063i | \(0.183494\pi\) | |||||||
\(332\) | 57.5780i | 0.173428i | ||||||||
\(333\) | 124.087 | 0.372634 | ||||||||
\(334\) | − | 145.445i | − | 0.435463i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13.2584 | + | 46.6499i | −0.0394596 | + | 0.138839i | ||||
\(337\) | −47.7972 | −0.141831 | −0.0709157 | − | 0.997482i | \(-0.522592\pi\) | ||||
−0.0709157 | + | 0.997482i | \(0.522592\pi\) | |||||||
\(338\) | 205.937 | 0.609282 | ||||||||
\(339\) | 121.510i | 0.358435i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 999.666i | − | 2.93157i | ||||||
\(342\) | − | 38.7502i | − | 0.113305i | ||||||
\(343\) | −231.298 | − | 253.279i | −0.674338 | − | 0.738422i | ||||
\(344\) | −182.199 | −0.529649 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 279.211i | − | 0.806967i | ||||||
\(347\) | 283.766 | 0.817771 | 0.408885 | − | 0.912586i | \(-0.365918\pi\) | ||||
0.408885 | + | 0.912586i | \(0.365918\pi\) | |||||||
\(348\) | 3.89995i | 0.0112067i | ||||||||
\(349\) | 20.0321i | 0.0573987i | 0.999588 | + | 0.0286993i | \(0.00913653\pi\) | ||||
−0.999588 | + | 0.0286993i | \(0.990863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.1250 | 0.0715812 | ||||||||
\(352\) | 99.0605 | 0.281422 | ||||||||
\(353\) | 595.015i | 1.68559i | 0.538231 | + | 0.842797i | \(0.319093\pi\) | ||||
−0.538231 | + | 0.842797i | \(0.680907\pi\) | |||||||
\(354\) | −213.265 | −0.602443 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 202.997i | 0.570217i | ||||||||
\(357\) | 210.256 | + | 59.7570i | 0.588952 | + | 0.167387i | ||||
\(358\) | 168.039 | 0.469384 | ||||||||
\(359\) | −588.390 | −1.63897 | −0.819485 | − | 0.573101i | \(-0.805740\pi\) | ||||
−0.819485 | + | 0.573101i | \(0.805740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 277.579 | 0.768917 | ||||||||
\(362\) | − | 20.3856i | − | 0.0563139i | ||||||
\(363\) | − | 321.566i | − | 0.885856i | ||||||
\(364\) | −18.5065 | + | 65.1155i | −0.0508422 | + | 0.178889i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.1527 | −0.0359364 | ||||||||
\(367\) | 662.601i | 1.80545i | 0.430215 | + | 0.902726i | \(0.358438\pi\) | ||||
−0.430215 | + | 0.902726i | \(0.641562\pi\) | |||||||
\(368\) | 14.9006 | 0.0404908 | ||||||||
\(369\) | 35.1467i | 0.0952485i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −522.091 | − | 148.384i | −1.40725 | − | 0.399957i | ||||
\(372\) | −197.751 | −0.531590 | ||||||||
\(373\) | 236.349 | 0.633644 | 0.316822 | − | 0.948485i | \(-0.397384\pi\) | ||||
0.316822 | + | 0.948485i | \(0.397384\pi\) | |||||||
\(374\) | − | 446.476i | − | 1.19378i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 219.660i | − | 0.584201i | ||||||
\(377\) | 5.44368i | 0.0144395i | ||||||||
\(378\) | 14.0627 | − | 49.4797i | 0.0372029 | − | 0.130899i | ||||
\(379\) | −344.235 | −0.908272 | −0.454136 | − | 0.890932i | \(-0.650052\pi\) | ||||
−0.454136 | + | 0.890932i | \(0.650052\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 342.852i | − | 0.899873i | ||||||
\(382\) | 84.7644 | 0.221896 | ||||||||
\(383\) | 65.7097i | 0.171566i | 0.996314 | + | 0.0857828i | \(0.0273391\pi\) | ||||
−0.996314 | + | 0.0857828i | \(0.972661\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 347.823 | 0.901095 | ||||||||
\(387\) | 193.251 | 0.499357 | ||||||||
\(388\) | − | 215.661i | − | 0.555827i | ||||||
\(389\) | −161.296 | −0.414642 | −0.207321 | − | 0.978273i | \(-0.566474\pi\) | ||||
−0.207321 | + | 0.978273i | \(0.566474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 67.1585i | − | 0.171761i | ||||||
\(392\) | 117.876 | + | 72.8914i | 0.300705 | + | 0.185947i | ||||
\(393\) | 199.014 | 0.506397 | ||||||||
\(394\) | −116.050 | −0.294542 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −105.070 | −0.265327 | ||||||||
\(397\) | 667.752i | 1.68200i | 0.541039 | + | 0.840998i | \(0.318031\pi\) | ||||
−0.541039 | + | 0.840998i | \(0.681969\pi\) | |||||||
\(398\) | 409.186i | 1.02811i | ||||||||
\(399\) | −106.519 | − | 30.2740i | −0.266966 | − | 0.0758746i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −593.826 | −1.48086 | −0.740431 | − | 0.672132i | \(-0.765379\pi\) | ||||
−0.740431 | + | 0.672132i | \(0.765379\pi\) | |||||||
\(402\) | 115.586i | 0.287528i | ||||||||
\(403\) | −276.028 | −0.684933 | ||||||||
\(404\) | 105.230i | 0.260471i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.7205 | + | 3.04687i | 0.0264051 | + | 0.00750461i | ||||
\(407\) | −724.322 | −1.77966 | ||||||||
\(408\) | −88.3207 | −0.216472 | ||||||||
\(409\) | − | 569.625i | − | 1.39273i | −0.717690 | − | 0.696363i | \(-0.754800\pi\) | ||
0.717690 | − | 0.696363i | \(-0.245200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 165.127i | 0.401768i | ||||||||
\(412\) | 144.800i | 0.351457i | ||||||||
\(413\) | −166.615 | + | 586.238i | −0.403427 | + | 1.41946i | ||||
\(414\) | −15.8045 | −0.0381751 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 27.3526i | − | 0.0657515i | ||||||
\(417\) | 411.513 | 0.986842 | ||||||||
\(418\) | 226.192i | 0.541130i | ||||||||
\(419\) | 209.456i | 0.499894i | 0.968260 | + | 0.249947i | \(0.0804132\pi\) | ||||
−0.968260 | + | 0.249947i | \(0.919587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −169.713 | −0.403119 | −0.201560 | − | 0.979476i | \(-0.564601\pi\) | ||||
−0.201560 | + | 0.979476i | \(0.564601\pi\) | |||||||
\(422\) | 47.6583 | 0.112934 | ||||||||
\(423\) | 232.984i | 0.550790i | ||||||||
\(424\) | 219.311 | 0.517244 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 142.817i | 0.335251i | ||||||||
\(427\) | −10.2757 | + | 36.1551i | −0.0240649 | + | 0.0846725i | ||||
\(428\) | 347.124 | 0.811037 | ||||||||
\(429\) | −146.660 | −0.341864 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 538.427 | 1.24925 | 0.624625 | − | 0.780925i | \(-0.285252\pi\) | ||||
0.624625 | + | 0.780925i | \(0.285252\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | − | 118.314i | − | 0.273243i | −0.990623 | − | 0.136622i | \(-0.956376\pi\) | ||
0.990623 | − | 0.136622i | \(-0.0436244\pi\) | |||||||
\(434\) | −154.495 | + | 543.593i | −0.355980 | + | 1.25252i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −99.9932 | −0.229342 | ||||||||
\(437\) | 34.0237i | 0.0778575i | ||||||||
\(438\) | −130.823 | −0.298682 | ||||||||
\(439\) | − | 434.834i | − | 0.990510i | −0.868748 | − | 0.495255i | \(-0.835075\pi\) | ||
0.868748 | − | 0.495255i | \(-0.164925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −125.027 | − | 77.3130i | −0.283507 | − | 0.175313i | ||||
\(442\) | −123.281 | −0.278916 | ||||||||
\(443\) | −555.005 | −1.25283 | −0.626417 | − | 0.779488i | \(-0.715479\pi\) | ||||
−0.626417 | + | 0.779488i | \(0.715479\pi\) | |||||||
\(444\) | 143.284i | 0.322711i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.2107i | 0.0341047i | ||||||||
\(447\) | 231.825i | 0.518625i | ||||||||
\(448\) | −53.8667 | − | 15.3095i | −0.120238 | − | 0.0341730i | ||||
\(449\) | 66.8926 | 0.148981 | 0.0744906 | − | 0.997222i | \(-0.476267\pi\) | ||||
0.0744906 | + | 0.997222i | \(0.476267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 205.158i | − | 0.454896i | ||||||
\(452\) | −140.307 | −0.310414 | ||||||||
\(453\) | − | 268.578i | − | 0.592888i | ||||||
\(454\) | 588.949i | 1.29724i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 44.7449 | 0.0981247 | ||||||||
\(457\) | 750.939 | 1.64319 | 0.821596 | − | 0.570070i | \(-0.193084\pi\) | ||||
0.821596 | + | 0.570070i | \(0.193084\pi\) | |||||||
\(458\) | − | 549.378i | − | 1.19951i | ||||||
\(459\) | 93.6783 | 0.204092 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 395.377i | 0.857651i | 0.903387 | + | 0.428826i | \(0.141072\pi\) | ||||
−0.903387 | + | 0.428826i | \(0.858928\pi\) | |||||||
\(462\) | −82.0867 | + | 288.823i | −0.177677 | + | 0.625158i | ||||
\(463\) | 423.981 | 0.915726 | 0.457863 | − | 0.889023i | \(-0.348615\pi\) | ||||
0.457863 | + | 0.889023i | \(0.348615\pi\) | |||||||
\(464\) | −4.50327 | −0.00970533 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −99.5658 | −0.213660 | ||||||||
\(467\) | − | 584.408i | − | 1.25141i | −0.780060 | − | 0.625705i | \(-0.784812\pi\) | ||
0.780060 | − | 0.625705i | \(-0.215188\pi\) | |||||||
\(468\) | 29.0119i | 0.0619911i | ||||||||
\(469\) | 317.732 | + | 90.3030i | 0.677467 | + | 0.192544i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −181.232 | −0.384780 | ||||||||
\(472\) | − | 246.257i | − | 0.521731i | ||||||
\(473\) | −1128.05 | −2.38488 | ||||||||
\(474\) | − | 183.623i | − | 0.387390i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −69.0014 | + | 242.782i | −0.144961 | + | 0.510047i | ||||
\(477\) | −232.615 | −0.487662 | ||||||||
\(478\) | 442.837 | 0.926438 | ||||||||
\(479\) | − | 734.511i | − | 1.53343i | −0.641990 | − | 0.766713i | \(-0.721891\pi\) | ||
0.641990 | − | 0.766713i | \(-0.278109\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 200.000i | 0.415801i | ||||||||
\(482\) | − | 281.043i | − | 0.583077i | ||||||
\(483\) | −12.3474 | + | 43.4445i | −0.0255640 | + | 0.0899473i | ||||
\(484\) | 371.312 | 0.767174 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | −91.6643 | −0.188222 | −0.0941111 | − | 0.995562i | \(-0.530001\pi\) | ||||
−0.0941111 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(488\) | − | 15.1875i | − | 0.0311218i | ||||||
\(489\) | 226.740i | 0.463681i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 460.086 | 0.937038 | 0.468519 | − | 0.883453i | \(-0.344788\pi\) | ||||
0.468519 | + | 0.883453i | \(0.344788\pi\) | |||||||
\(492\) | −40.5839 | −0.0824876 | ||||||||
\(493\) | 20.2967i | 0.0411698i | ||||||||
\(494\) | 62.4564 | 0.126430 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 228.344i | − | 0.460370i | ||||||
\(497\) | 392.585 | + | 111.577i | 0.789910 | + | 0.224501i | ||||
\(498\) | 70.5184 | 0.141603 | ||||||||
\(499\) | 487.126 | 0.976204 | 0.488102 | − | 0.872786i | \(-0.337689\pi\) | ||||
0.488102 | + | 0.872786i | \(0.337689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −178.133 | −0.355554 | ||||||||
\(502\) | 425.506i | 0.847622i | ||||||||
\(503\) | − | 305.145i | − | 0.606650i | −0.952887 | − | 0.303325i | \(-0.901903\pi\) | ||
0.952887 | − | 0.303325i | \(-0.0980967\pi\) | |||||||
\(504\) | 57.1342 | + | 16.2382i | 0.113362 | + | 0.0322186i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 92.2539 | 0.182320 | ||||||||
\(507\) | − | 252.221i | − | 0.497477i | ||||||
\(508\) | 395.891 | 0.779313 | ||||||||
\(509\) | − | 800.434i | − | 1.57256i | −0.617869 | − | 0.786281i | \(-0.712004\pi\) | ||
0.617869 | − | 0.786281i | \(-0.287996\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −102.207 | + | 359.615i | −0.200013 | + | 0.703748i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −47.4591 | −0.0925128 | ||||||||
\(514\) | 432.824i | 0.842069i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 223.147i | 0.432456i | ||||||||
\(517\) | − | 1359.97i | − | 2.63051i | ||||||
\(518\) | 393.868 | + | 111.942i | 0.760364 | + | 0.216104i | ||||
\(519\) | −341.962 | −0.658886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.4194i | − | 0.0411121i | −0.999789 | − | 0.0205560i | \(-0.993456\pi\) | ||
0.999789 | − | 0.0205560i | \(-0.00654365\pi\) | |||||||
\(522\) | 4.77644 | 0.00915027 | ||||||||
\(523\) | − | 842.290i | − | 1.61050i | −0.592937 | − | 0.805249i | \(-0.702032\pi\) | ||
0.592937 | − | 0.805249i | \(-0.297968\pi\) | |||||||
\(524\) | 229.801i | 0.438552i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 404.657 | 0.769309 | ||||||||
\(527\) | −1029.17 | −1.95288 | ||||||||
\(528\) | − | 121.324i | − | 0.229780i | ||||||
\(529\) | −515.123 | −0.973768 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 261.195i | 0.491893i | ||||||||
\(532\) | 34.9574 | − | 122.998i | 0.0657093 | − | 0.231199i | ||||
\(533\) | −56.6484 | −0.106282 | ||||||||
\(534\) | 248.620 | 0.465580 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −133.468 | −0.249007 | ||||||||
\(537\) | − | 205.805i | − | 0.383250i | ||||||
\(538\) | − | 266.454i | − | 0.495268i | ||||||
\(539\) | 729.806 | + | 451.291i | 1.35400 | + | 0.837275i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.6795 | −0.0289824 | −0.0144912 | − | 0.999895i | \(-0.504613\pi\) | ||||
−0.0144912 | + | 0.999895i | \(0.504613\pi\) | |||||||
\(542\) | − | 13.5664i | − | 0.0250302i | ||||||
\(543\) | −24.9672 | −0.0459801 | ||||||||
\(544\) | − | 101.984i | − | 0.187471i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 79.7499 | + | 22.6658i | 0.146062 | + | 0.0415125i | ||||
\(547\) | 315.792 | 0.577317 | 0.288659 | − | 0.957432i | \(-0.406791\pi\) | ||||
0.288659 | + | 0.957432i | \(0.406791\pi\) | |||||||
\(548\) | −190.672 | −0.347941 | ||||||||
\(549\) | 16.1087i | 0.0293419i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.2827i | − | 0.0186618i | ||||||
\(552\) | − | 18.2495i | − | 0.0330606i | ||||||
\(553\) | −504.756 | − | 143.457i | −0.912759 | − | 0.259416i | ||||
\(554\) | 227.781 | 0.411157 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 475.174i | 0.854630i | ||||||||
\(557\) | −358.421 | −0.643484 | −0.321742 | − | 0.946827i | \(-0.604268\pi\) | ||||
−0.321742 | + | 0.946827i | \(0.604268\pi\) | |||||||
\(558\) | 242.195i | 0.434041i | ||||||||
\(559\) | 311.477i | 0.557203i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −546.819 | −0.974721 | ||||||||
\(562\) | −485.226 | −0.863392 | ||||||||
\(563\) | 622.834i | 1.10628i | 0.833089 | + | 0.553138i | \(0.186570\pi\) | ||||
−0.833089 | + | 0.553138i | \(0.813430\pi\) | |||||||
\(564\) | −269.027 | −0.476998 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 459.263i | 0.811418i | ||||||||
\(567\) | −60.6000 | − | 17.2232i | −0.106878 | − | 0.0303760i | ||||
\(568\) | −164.911 | −0.290336 | ||||||||
\(569\) | 185.789 | 0.326518 | 0.163259 | − | 0.986583i | \(-0.447799\pi\) | ||||
0.163259 | + | 0.986583i | \(0.447799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −486.258 | −0.851589 | −0.425795 | − | 0.904820i | \(-0.640005\pi\) | ||||
−0.425795 | + | 0.904820i | \(0.640005\pi\) | |||||||
\(572\) | − | 169.348i | − | 0.296063i | ||||||
\(573\) | − | 103.815i | − | 0.181178i | ||||||
\(574\) | −31.7066 | + | 111.560i | −0.0552379 | + | 0.194355i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 270.057i | 0.468037i | 0.972232 | + | 0.234018i | \(0.0751876\pi\) | ||||
−0.972232 | + | 0.234018i | \(0.924812\pi\) | |||||||
\(578\) | −50.9440 | −0.0881385 | ||||||||
\(579\) | − | 425.994i | − | 0.735741i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 55.0932 | − | 193.846i | 0.0948247 | − | 0.333642i | ||||
\(582\) | −264.129 | −0.453831 | ||||||||
\(583\) | 1357.82 | 2.32902 | ||||||||
\(584\) | − | 151.061i | − | 0.258666i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 142.719i | − | 0.243548i | ||||||
\(587\) | 400.613i | 0.682476i | 0.939977 | + | 0.341238i | \(0.110846\pi\) | ||||
−0.939977 | + | 0.341238i | \(0.889154\pi\) | |||||||
\(588\) | 89.2734 | − | 144.368i | 0.151825 | − | 0.245525i | ||||
\(589\) | 521.395 | 0.885220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 142.131i | 0.240493i | ||||||||
\(592\) | −165.450 | −0.279476 | ||||||||
\(593\) | 157.686i | 0.265912i | 0.991122 | + | 0.132956i | \(0.0424469\pi\) | ||||
−0.991122 | + | 0.132956i | \(0.957553\pi\) | |||||||
\(594\) | 128.683i | 0.216639i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −267.689 | −0.449142 | ||||||||
\(597\) | 501.149 | 0.839445 | ||||||||
\(598\) | − | 25.4732i | − | 0.0425973i | ||||||
\(599\) | 468.940 | 0.782872 | 0.391436 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391436 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 255.932i | 0.425844i | 0.977069 | + | 0.212922i | \(0.0682980\pi\) | ||||
−0.977069 | + | 0.212922i | \(0.931702\pi\) | |||||||
\(602\) | 613.404 | + | 174.336i | 1.01894 | + | 0.289595i | ||||
\(603\) | 141.564 | 0.234766 | ||||||||
\(604\) | 310.127 | 0.513456 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 128.880 | 0.212673 | ||||||||
\(607\) | − | 773.553i | − | 1.27439i | −0.770704 | − | 0.637194i | \(-0.780095\pi\) | ||
0.770704 | − | 0.637194i | \(-0.219905\pi\) | |||||||
\(608\) | 51.6669i | 0.0849785i | ||||||||
\(609\) | 3.73164 | − | 13.1298i | 0.00612749 | − | 0.0215597i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −375.517 | −0.614594 | ||||||||
\(612\) | 108.170i | 0.176749i | ||||||||
\(613\) | −443.208 | −0.723015 | −0.361507 | − | 0.932369i | \(-0.617738\pi\) | ||||
−0.361507 | + | 0.932369i | \(0.617738\pi\) | |||||||
\(614\) | 58.4151i | 0.0951386i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −333.504 | − | 94.7855i | −0.541402 | − | 0.153873i | ||||
\(617\) | −363.298 | −0.588813 | −0.294407 | − | 0.955680i | \(-0.595122\pi\) | ||||
−0.294407 | + | 0.955680i | \(0.595122\pi\) | |||||||
\(618\) | 177.344 | 0.286964 | ||||||||
\(619\) | 292.211i | 0.472069i | 0.971745 | + | 0.236035i | \(0.0758479\pi\) | ||||
−0.971745 | + | 0.236035i | \(0.924152\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.3565i | 0.0311698i | ||||||||
\(622\) | 665.163i | 1.06939i | ||||||||
\(623\) | 194.237 | − | 683.425i | 0.311777 | − | 1.09699i | ||||
\(624\) | −33.5000 | −0.0536859 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 226.585i | 0.361956i | ||||||||
\(627\) | 277.028 | 0.441831 | ||||||||
\(628\) | − | 209.268i | − | 0.333230i | ||||||
\(629\) | 745.698i | 1.18553i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 189.221 | 0.299874 | 0.149937 | − | 0.988696i | \(-0.452093\pi\) | ||||
0.149937 | + | 0.988696i | \(0.452093\pi\) | |||||||
\(632\) | 212.029 | 0.335489 | ||||||||
\(633\) | − | 58.3693i | − | 0.0922106i | ||||||
\(634\) | −380.093 | −0.599516 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 268.600i | − | 0.422328i | ||||||
\(637\) | 124.611 | − | 201.514i | 0.195621 | − | 0.316349i | ||||
\(638\) | −27.8810 | −0.0437007 | ||||||||
\(639\) | 174.914 | 0.273731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1162.94 | 1.81425 | 0.907127 | − | 0.420857i | \(-0.138271\pi\) | ||||
0.907127 | + | 0.420857i | \(0.138271\pi\) | |||||||
\(642\) | − | 425.138i | − | 0.662209i | ||||||
\(643\) | 1096.08i | 1.70464i | 0.523021 | + | 0.852320i | \(0.324805\pi\) | ||||
−0.523021 | + | 0.852320i | \(0.675195\pi\) | |||||||
\(644\) | −50.1654 | − | 14.2576i | −0.0778966 | − | 0.0221391i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 232.868 | 0.360476 | ||||||||
\(647\) | 262.877i | 0.406302i | 0.979147 | + | 0.203151i | \(0.0651182\pi\) | ||||
−0.979147 | + | 0.203151i | \(0.934882\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | − | 1524.65i | − | 2.34923i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 665.763 | + | 189.217i | 1.02268 | + | 0.290656i | ||||
\(652\) | −261.817 | −0.401560 | ||||||||
\(653\) | −242.905 | −0.371983 | −0.185992 | − | 0.982551i | \(-0.559550\pi\) | ||||
−0.185992 | + | 0.982551i | \(0.559550\pi\) | |||||||
\(654\) | 122.466i | 0.187257i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 46.8622i | − | 0.0714364i | ||||||
\(657\) | 160.225i | 0.243873i | ||||||||
\(658\) | −210.180 | + | 739.521i | −0.319422 | + | 1.12389i | ||||
\(659\) | −1176.49 | −1.78527 | −0.892634 | − | 0.450783i | \(-0.851145\pi\) | ||||
−0.892634 | + | 0.450783i | \(0.851145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 246.444i | − | 0.372835i | −0.982471 | − | 0.186418i | \(-0.940312\pi\) | ||
0.982471 | − | 0.186418i | \(-0.0596877\pi\) | |||||||
\(662\) | 784.914 | 1.18567 | ||||||||
\(663\) | 150.988i | 0.227734i | ||||||||
\(664\) | 81.4276i | 0.122632i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 175.486 | 0.263492 | ||||||||
\(667\) | −4.19385 | −0.00628763 | ||||||||
\(668\) | − | 205.690i | − | 0.307919i | ||||||
\(669\) | 18.6292 | 0.0278464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 94.0298i | − | 0.140134i | ||||||
\(672\) | −18.7502 | + | 65.9729i | −0.0279021 | + | 0.0981740i | ||||
\(673\) | 76.3328 | 0.113422 | 0.0567109 | − | 0.998391i | \(-0.481939\pi\) | ||||
0.0567109 | + | 0.998391i | \(0.481939\pi\) | |||||||
\(674\) | −67.5954 | −0.100290 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 291.240 | 0.430828 | ||||||||
\(677\) | − | 310.277i | − | 0.458312i | −0.973390 | − | 0.229156i | \(-0.926403\pi\) | ||
0.973390 | − | 0.229156i | \(-0.0735965\pi\) | |||||||
\(678\) | 171.840i | 0.253452i | ||||||||
\(679\) | −206.354 | + | 726.058i | −0.303908 | + | 1.06930i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 721.312 | 1.05920 | ||||||||
\(682\) | − | 1413.74i | − | 2.07293i | ||||||
\(683\) | −157.333 | −0.230356 | −0.115178 | − | 0.993345i | \(-0.536744\pi\) | ||||
−0.115178 | + | 0.993345i | \(0.536744\pi\) | |||||||
\(684\) | − | 54.8010i | − | 0.0801185i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −327.105 | − | 358.190i | −0.476829 | − | 0.522144i | ||||
\(687\) | −672.848 | −0.979400 | ||||||||
\(688\) | −257.668 | −0.374518 | ||||||||
\(689\) | − | 374.921i | − | 0.544153i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 683.565i | − | 0.989240i | −0.869109 | − | 0.494620i | \(-0.835307\pi\) | ||
0.869109 | − | 0.494620i | \(-0.164693\pi\) | |||||||
\(692\) | − | 394.863i | − | 0.570612i | ||||||
\(693\) | 353.734 | + | 100.535i | 0.510439 | + | 0.145072i | ||||
\(694\) | 401.306 | 0.578251 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.51536i | 0.00792437i | ||||||||
\(697\) | −211.213 | −0.303031 | ||||||||
\(698\) | 28.3297i | 0.0405870i | ||||||||
\(699\) | 121.943i | 0.174453i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −306.153 | −0.436738 | −0.218369 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218369 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(702\) | 35.5321 | 0.0506156 | ||||||||
\(703\) | − | 377.784i | − | 0.537388i | ||||||
\(704\) | 140.093 | 0.198995 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 841.478i | 1.19190i | ||||||||
\(707\) | 100.689 | − | 354.275i | 0.142417 | − | 0.501096i | ||||
\(708\) | −301.602 | −0.425992 | ||||||||
\(709\) | −444.082 | −0.626350 | −0.313175 | − | 0.949695i | \(-0.601393\pi\) | ||||
−0.313175 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −224.891 | −0.316302 | ||||||||
\(712\) | 287.082i | 0.403205i | ||||||||
\(713\) | − | 212.654i | − | 0.298252i | ||||||
\(714\) | 297.346 | + | 84.5092i | 0.416452 | + | 0.118360i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 237.643 | 0.331904 | ||||||||
\(717\) | − | 542.363i | − | 0.756434i | ||||||
\(718\) | −832.109 | −1.15893 | ||||||||
\(719\) | − | 672.926i | − | 0.935919i | −0.883750 | − | 0.467960i | \(-0.844989\pi\) | ||
0.883750 | − | 0.467960i | \(-0.155011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 138.551 | − | 487.495i | 0.192166 | − | 0.676137i | ||||
\(722\) | 392.556 | 0.543707 | ||||||||
\(723\) | −344.206 | −0.476080 | ||||||||
\(724\) | − | 28.8296i | − | 0.0398199i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 454.762i | − | 0.626395i | ||||||
\(727\) | − | 675.927i | − | 0.929748i | −0.885377 | − | 0.464874i | \(-0.846100\pi\) | ||
0.885377 | − | 0.464874i | \(-0.153900\pi\) | |||||||
\(728\) | −26.1722 | + | 92.0872i | −0.0359508 | + | 0.126493i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1161.34i | 1.58870i | ||||||||
\(732\) | −18.6008 | −0.0254109 | ||||||||
\(733\) | − | 387.908i | − | 0.529206i | −0.964357 | − | 0.264603i | \(-0.914759\pi\) | ||
0.964357 | − | 0.264603i | \(-0.0852409\pi\) | |||||||
\(734\) | 937.059i | 1.27665i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.0727 | 0.0286313 | ||||||||
\(737\) | −826.336 | −1.12122 | ||||||||
\(738\) | 49.7049i | 0.0673508i | ||||||||
\(739\) | 394.643 | 0.534024 | 0.267012 | − | 0.963693i | \(-0.413964\pi\) | ||||
0.267012 | + | 0.963693i | \(0.413964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 76.4931i | − | 0.103230i | ||||||
\(742\) | −738.348 | − | 209.847i | −0.995079 | − | 0.282812i | ||||
\(743\) | −147.027 | −0.197883 | −0.0989414 | − | 0.995093i | \(-0.531546\pi\) | ||||
−0.0989414 | + | 0.995093i | \(0.531546\pi\) | |||||||
\(744\) | −279.663 | −0.375891 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 334.248 | 0.448054 | ||||||||
\(747\) | − | 86.3670i | − | 0.115618i | ||||||
\(748\) | − | 631.412i | − | 0.844133i | ||||||
\(749\) | −1168.65 | − | 332.144i | −1.56028 | − | 0.443449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 103.003 | 0.137154 | 0.0685771 | − | 0.997646i | \(-0.478154\pi\) | ||||
0.0685771 | + | 0.997646i | \(0.478154\pi\) | |||||||
\(752\) | − | 310.646i | − | 0.413092i | ||||||
\(753\) | 521.136 | 0.692080 | ||||||||
\(754\) | 7.69852i | 0.0102102i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.8876 | − | 69.9749i | 0.0263064 | − | 0.0925593i | ||||
\(757\) | 547.747 | 0.723575 | 0.361788 | − | 0.932261i | \(-0.382167\pi\) | ||||
0.361788 | + | 0.932261i | \(0.382167\pi\) | |||||||
\(758\) | −486.822 | −0.642246 | ||||||||
\(759\) | − | 112.988i | − | 0.148864i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1223.78i | − | 1.60813i | −0.594544 | − | 0.804063i | \(-0.702668\pi\) | ||
0.594544 | − | 0.804063i | \(-0.297332\pi\) | |||||||
\(762\) | − | 484.865i | − | 0.636306i | ||||||
\(763\) | 336.644 | + | 95.6779i | 0.441211 | + | 0.125397i | ||||
\(764\) | 119.875 | 0.156904 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 92.9275i | 0.121315i | ||||||||
\(767\) | −420.986 | −0.548874 | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | − | 194.874i | − | 0.253413i | −0.991940 | − | 0.126706i | \(-0.959559\pi\) | ||
0.991940 | − | 0.126706i | \(-0.0404406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 530.098 | 0.687547 | ||||||||
\(772\) | 491.896 | 0.637171 | ||||||||
\(773\) | − | 1017.59i | − | 1.31642i | −0.752835 | − | 0.658209i | \(-0.771314\pi\) | ||
0.752835 | − | 0.658209i | \(-0.228686\pi\) | |||||||
\(774\) | 273.299 | 0.353099 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 304.990i | − | 0.393029i | ||||||
\(777\) | 137.100 | − | 482.388i | 0.176448 | − | 0.620834i | ||||
\(778\) | −228.107 | −0.293196 | ||||||||
\(779\) | 107.004 | 0.137361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1021.01 | −1.30731 | ||||||||
\(782\) | − | 94.9765i | − | 0.121453i | ||||||
\(783\) | − | 5.84992i | − | 0.00747117i | ||||||
\(784\) | 166.702 | + | 103.084i | 0.212631 | + | 0.131485i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 281.448 | 0.358076 | ||||||||
\(787\) | 222.094i | 0.282203i | 0.989995 | + | 0.141101i | \(0.0450644\pi\) | ||||
−0.989995 | + | 0.141101i | \(0.954936\pi\) | |||||||
\(788\) | −164.119 | −0.208273 | ||||||||
\(789\) | − | 495.601i | − | 0.628138i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 472.367 | + | 134.252i | 0.597178 | + | 0.169724i | ||||
\(792\) | −148.591 | −0.187615 | ||||||||
\(793\) | −25.9636 | −0.0327409 | ||||||||
\(794\) | 944.344i | 1.18935i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 578.677i | 0.726981i | ||||||||
\(797\) | 340.349i | 0.427038i | 0.976939 | + | 0.213519i | \(0.0684926\pi\) | ||||
−0.976939 | + | 0.213519i | \(0.931507\pi\) | |||||||
\(798\) | −150.641 | − | 42.8139i | −0.188773 | − | 0.0536514i | ||||
\(799\) | −1400.11 | −1.75233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 304.496i | − | 0.380145i | ||||||
\(802\) | −839.796 | −1.04713 | ||||||||
\(803\) | − | 935.263i | − | 1.16471i | ||||||
\(804\) | 163.464i | 0.203313i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −390.363 | −0.484321 | ||||||||
\(807\) | −326.339 | −0.404385 | ||||||||
\(808\) | 148.818i | 0.184181i | ||||||||
\(809\) | 462.403 | 0.571573 | 0.285787 | − | 0.958293i | \(-0.407745\pi\) | ||||
0.285787 | + | 0.958293i | \(0.407745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1420.09i | 1.75103i | 0.483190 | + | 0.875516i | \(0.339478\pi\) | ||||
−0.483190 | + | 0.875516i | \(0.660522\pi\) | |||||||
\(812\) | 15.1610 | + | 4.30893i | 0.0186712 | + | 0.00530656i | ||||
\(813\) | −16.6154 | −0.0204371 | ||||||||
\(814\) | −1024.35 | −1.25841 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −124.904 | −0.153069 | ||||||||
\(817\) | − | 588.354i | − | 0.720140i | ||||||
\(818\) | − | 805.571i | − | 0.984806i | ||||||
\(819\) | 27.7598 | − | 97.6733i | 0.0338948 | − | 0.119259i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −651.695 | −0.793782 | −0.396891 | − | 0.917866i | \(-0.629911\pi\) | ||||
−0.396891 | + | 0.917866i | \(0.629911\pi\) | |||||||
\(822\) | 233.524i | 0.284093i | ||||||||
\(823\) | 604.705 | 0.734756 | 0.367378 | − | 0.930072i | \(-0.380255\pi\) | ||||
0.367378 | + | 0.930072i | \(0.380255\pi\) | |||||||
\(824\) | 204.779i | 0.248518i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −235.630 | + | 829.066i | −0.285266 | + | 1.00371i | ||||
\(827\) | 504.280 | 0.609771 | 0.304885 | − | 0.952389i | \(-0.401382\pi\) | ||||
0.304885 | + | 0.952389i | \(0.401382\pi\) | |||||||
\(828\) | −22.3509 | −0.0269939 | ||||||||
\(829\) | 814.575i | 0.982599i | 0.870991 | + | 0.491300i | \(0.163478\pi\) | ||||
−0.870991 | + | 0.491300i | \(0.836522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 278.974i | − | 0.335709i | ||||||
\(832\) | − | 38.6825i | − | 0.0464934i | ||||||
\(833\) | 464.610 | − | 751.344i | 0.557755 | − | 0.901973i | ||||
\(834\) | 581.967 | 0.697802 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 319.884i | 0.382637i | ||||||||
\(837\) | 296.627 | 0.354393 | ||||||||
\(838\) | 296.215i | 0.353478i | ||||||||
\(839\) | − | 128.459i | − | 0.153109i | −0.997065 | − | 0.0765547i | \(-0.975608\pi\) | ||
0.997065 | − | 0.0765547i | \(-0.0243920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −839.733 | −0.998493 | ||||||||
\(842\) | −240.011 | −0.285048 | ||||||||
\(843\) | 594.278i | 0.704956i | ||||||||
\(844\) | 67.3991 | 0.0798567 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 329.489i | 0.389467i | ||||||||
\(847\) | −1250.08 | − | 355.288i | −1.47590 | − | 0.419466i | ||||
\(848\) | 310.153 | 0.365747 | ||||||||
\(849\) | 562.480 | 0.662520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −154.081 | −0.181059 | ||||||||
\(852\) | 201.973i | 0.237058i | ||||||||
\(853\) | 636.175i | 0.745808i | 0.927870 | + | 0.372904i | \(0.121638\pi\) | ||||
−0.927870 | + | 0.372904i | \(0.878362\pi\) | |||||||
\(854\) | −14.5320 | + | 51.1311i | −0.0170164 | + | 0.0598725i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 490.907 | 0.573490 | ||||||||
\(857\) | − | 494.679i | − | 0.577221i | −0.957447 | − | 0.288611i | \(-0.906807\pi\) | ||
0.957447 | − | 0.288611i | \(-0.0931933\pi\) | |||||||
\(858\) | −207.408 | −0.241734 | ||||||||
\(859\) | − | 745.414i | − | 0.867770i | −0.900968 | − | 0.433885i | \(-0.857142\pi\) | ||
0.900968 | − | 0.433885i | \(-0.142858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 136.632 | + | 38.8325i | 0.158690 | + | 0.0451016i | ||||
\(862\) | 761.450 | 0.883353 | ||||||||
\(863\) | 593.451 | 0.687661 | 0.343830 | − | 0.939032i | \(-0.388275\pi\) | ||||
0.343830 | + | 0.939032i | \(0.388275\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 167.322i | − | 0.193212i | ||||||
\(867\) | 62.3935i | 0.0719648i | ||||||||
\(868\) | −218.489 | + | 768.757i | −0.251716 | + | 0.885665i | ||||
\(869\) | 1312.73 | 1.51063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 228.168i | 0.261961i | ||||||||
\(872\) | −141.412 | −0.162169 | ||||||||
\(873\) | 323.491i | 0.370551i | ||||||||
\(874\) | 48.1168i | 0.0550535i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −185.011 | −0.211200 | ||||||||
\(877\) | 291.879 | 0.332815 | 0.166407 | − | 0.986057i | \(-0.446783\pi\) | ||||
0.166407 | + | 0.986057i | \(0.446783\pi\) | |||||||
\(878\) | − | 614.948i | − | 0.700396i | ||||||
\(879\) | −174.795 | −0.198856 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1226.42i | − | 1.39208i | −0.718004 | − | 0.696039i | \(-0.754944\pi\) | ||
0.718004 | − | 0.696039i | \(-0.245056\pi\) | |||||||
\(882\) | −176.815 | − | 109.337i | −0.200470 | − | 0.123965i | ||||
\(883\) | −1132.03 | −1.28202 | −0.641012 | − | 0.767531i | \(-0.721485\pi\) | ||||
−0.641012 | + | 0.767531i | \(0.721485\pi\) | |||||||
\(884\) | −174.346 | −0.197224 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −784.896 | −0.885887 | ||||||||
\(887\) | 959.088i | 1.08127i | 0.841257 | + | 0.540636i | \(0.181816\pi\) | ||||
−0.841257 | + | 0.540636i | \(0.818184\pi\) | |||||||
\(888\) | 202.634i | 0.228191i | ||||||||
\(889\) | −1332.83 | − | 378.806i | −1.49925 | − | 0.426103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 157.604 | 0.176885 | ||||||||
\(892\) | 21.5112i | 0.0241156i | ||||||||
\(893\) | 709.321 | 0.794312 | ||||||||
\(894\) | 327.850i | 0.366723i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −76.1790 | − | 21.6509i | −0.0850212 | − | 0.0241640i | ||||
\(897\) | −31.1982 | −0.0347806 | ||||||||
\(898\) | 94.6004 | 0.105346 | ||||||||
\(899\) | 64.2684i | 0.0714887i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1397.89i | − | 1.55149i | ||||||
\(902\) | − | 290.137i | − | 0.321660i | ||||||
\(903\) | 213.517 | − | 751.263i | 0.236453 | − | 0.831964i | ||||
\(904\) | −198.424 | −0.219496 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 379.827i | − | 0.419235i | ||||||
\(907\) | −989.799 | −1.09129 | −0.545644 | − | 0.838017i | \(-0.683715\pi\) | ||||
−0.545644 | + | 0.838017i | \(0.683715\pi\) | |||||||
\(908\) | 832.900i | 0.917290i | ||||||||
\(909\) | − | 157.845i | − | 0.173647i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 994.781 | 1.09197 | 0.545983 | − | 0.837796i | \(-0.316156\pi\) | ||||
0.545983 | + | 0.837796i | \(0.316156\pi\) | |||||||
\(912\) | 63.2788 | 0.0693846 | ||||||||
\(913\) | 504.141i | 0.552181i | ||||||||
\(914\) | 1061.99 | 1.16191 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 776.938i | − | 0.848185i | ||||||
\(917\) | 219.884 | − | 773.665i | 0.239786 | − | 0.843691i | ||||
\(918\) | 132.481 | 0.144315 | ||||||||
\(919\) | 887.212 | 0.965410 | 0.482705 | − | 0.875783i | \(-0.339654\pi\) | ||||
0.482705 | + | 0.875783i | \(0.339654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 71.5436 | 0.0776804 | ||||||||
\(922\) | 559.148i | 0.606451i | ||||||||
\(923\) | 281.921i | 0.305440i | ||||||||
\(924\) | −116.088 | + | 408.457i | −0.125636 | + | 0.442053i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 599.600 | 0.647516 | ||||||||
\(927\) | − | 217.201i | − | 0.234305i | ||||||
\(928\) | −6.36859 | −0.00686270 | ||||||||
\(929\) | − | 1224.49i | − | 1.31808i | −0.752109 | − | 0.659039i | \(-0.770963\pi\) | ||
0.752109 | − | 0.659039i | \(-0.229037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −235.380 | + | 380.644i | −0.252825 | + | 0.408855i | ||||
\(932\) | −140.807 | −0.151081 | ||||||||
\(933\) | 814.655 | 0.873156 | ||||||||
\(934\) | − | 826.478i | − | 0.884880i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 41.0290i | 0.0438344i | ||||||||
\(937\) | 807.001i | 0.861260i | 0.902529 | + | 0.430630i | \(0.141709\pi\) | ||||
−0.902529 | + | 0.430630i | \(0.858291\pi\) | |||||||
\(938\) | 449.341 | + | 127.708i | 0.479042 | + | 0.136149i | ||||
\(939\) | 277.508 | 0.295536 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1246.48i | − | 1.32464i | −0.749223 | − | 0.662318i | \(-0.769573\pi\) | ||
0.749223 | − | 0.662318i | \(-0.230427\pi\) | |||||||
\(942\) | −256.300 | −0.272081 | ||||||||
\(943\) | − | 43.6423i | − | 0.0462802i | ||||||
\(944\) | − | 348.260i | − | 0.368920i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1595.30 | −1.68636 | ||||||||
\(947\) | 675.978 | 0.713810 | 0.356905 | − | 0.934141i | \(-0.383832\pi\) | ||||
0.356905 | + | 0.934141i | \(0.383832\pi\) | |||||||
\(948\) | − | 259.682i | − | 0.273926i | ||||||
\(949\) | −258.245 | −0.272123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 465.517i | 0.489502i | ||||||||
\(952\) | −97.5828 | + | 343.346i | −0.102503 | + | 0.360658i | ||||
\(953\) | −1098.24 | −1.15240 | −0.576201 | − | 0.817308i | \(-0.695466\pi\) | ||||
−0.576201 | + | 0.817308i | \(0.695466\pi\) | |||||||
\(954\) | −328.967 | −0.344829 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 626.267 | 0.655091 | ||||||||
\(957\) | 34.1472i | 0.0356815i | ||||||||
\(958\) | − | 1038.76i | − | 1.08430i | ||||||
\(959\) | 641.928 | + | 182.443i | 0.669372 | + | 0.190243i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2297.80 | −2.39105 | ||||||||
\(962\) | 282.843i | 0.294015i | ||||||||
\(963\) | −520.686 | −0.540692 | ||||||||
\(964\) | − | 397.455i | − | 0.412297i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.4619 | + | 61.4398i | −0.0180765 | + | 0.0636023i | ||||
\(967\) | 1345.41 | 1.39132 | 0.695661 | − | 0.718370i | \(-0.255111\pi\) | ||||
0.695661 | + | 0.718370i | \(0.255111\pi\) | |||||||
\(968\) | 525.114 | 0.542474 | ||||||||
\(969\) | − | 285.204i | − | 0.294328i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1230.36i | 1.26710i | 0.773701 | + | 0.633551i | \(0.218403\pi\) | ||||
−0.773701 | + | 0.633551i | \(0.781597\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | 454.668 | − | 1599.75i | 0.467284 | − | 1.64415i | ||||
\(974\) | −129.633 | −0.133093 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 21.4783i | − | 0.0220065i | ||||||
\(977\) | −228.116 | −0.233487 | −0.116743 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116743 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(978\) | 320.659i | 0.327872i | ||||||||
\(979\) | 1777.40i | 1.81553i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 149.990 | 0.152895 | ||||||||
\(982\) | 650.659 | 0.662586 | ||||||||
\(983\) | 1721.09i | 1.75085i | 0.483354 | + | 0.875425i | \(0.339418\pi\) | ||||
−0.483354 | + | 0.875425i | \(0.660582\pi\) | |||||||
\(984\) | −57.3943 | −0.0583275 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28.7039i | 0.0291114i | ||||||||
\(987\) | 905.724 | + | 257.417i | 0.917654 | + | 0.260807i | ||||
\(988\) | 88.3266 | 0.0893994 | ||||||||
\(989\) | −239.964 | −0.242633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1911.05 | −1.92841 | −0.964205 | − | 0.265159i | \(-0.914576\pi\) | ||||
−0.964205 | + | 0.265159i | \(0.914576\pi\) | |||||||
\(992\) | − | 322.927i | − | 0.325531i | ||||||
\(993\) | − | 961.319i | − | 0.968095i | ||||||
\(994\) | 555.199 | + | 157.794i | 0.558550 | + | 0.158746i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 99.7280 | 0.100129 | ||||||||
\(997\) | − | 31.3627i | − | 0.0314571i | −0.999876 | − | 0.0157285i | \(-0.994993\pi\) | ||
0.999876 | − | 0.0157285i | \(-0.00500676\pi\) | |||||||
\(998\) | 688.900 | 0.690281 | ||||||||
\(999\) | − | 214.925i | − | 0.215141i |
(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 | 1050.3.f.e.601.9 | 16 | ||
5.2 | odd | 4 | 210.3.h.a.139.9 | yes | 16 | ||
5.3 | odd | 4 | 210.3.h.a.139.8 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.3.f.e.601.8 | 16 | ||
7.6 | odd | 2 | inner | 1050.3.f.e.601.13 | 16 | ||
15.2 | even | 4 | 630.3.h.e.559.8 | 16 | |||
15.8 | even | 4 | 630.3.h.e.559.9 | 16 | |||
20.3 | even | 4 | 1680.3.bd.a.769.8 | 16 | |||
20.7 | even | 4 | 1680.3.bd.a.769.10 | 16 | |||
35.13 | even | 4 | 210.3.h.a.139.1 | ✓ | 16 | ||
35.27 | even | 4 | 210.3.h.a.139.16 | yes | 16 | ||
35.34 | odd | 2 | inner | 1050.3.f.e.601.4 | 16 | ||
105.62 | odd | 4 | 630.3.h.e.559.1 | 16 | |||
105.83 | odd | 4 | 630.3.h.e.559.16 | 16 | |||
140.27 | odd | 4 | 1680.3.bd.a.769.7 | 16 | |||
140.83 | odd | 4 | 1680.3.bd.a.769.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.1 | ✓ | 16 | 35.13 | even | 4 | ||
210.3.h.a.139.8 | yes | 16 | 5.3 | odd | 4 | ||
210.3.h.a.139.9 | yes | 16 | 5.2 | odd | 4 | ||
210.3.h.a.139.16 | yes | 16 | 35.27 | even | 4 | ||
630.3.h.e.559.1 | 16 | 105.62 | odd | 4 | |||
630.3.h.e.559.8 | 16 | 15.2 | even | 4 | |||
630.3.h.e.559.9 | 16 | 15.8 | even | 4 | |||
630.3.h.e.559.16 | 16 | 105.83 | odd | 4 | |||
1050.3.f.e.601.4 | 16 | 35.34 | odd | 2 | inner | ||
1050.3.f.e.601.8 | 16 | 5.4 | even | 2 | inner | ||
1050.3.f.e.601.9 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.f.e.601.13 | 16 | 7.6 | odd | 2 | inner | ||
1680.3.bd.a.769.7 | 16 | 140.27 | odd | 4 | |||
1680.3.bd.a.769.8 | 16 | 20.3 | even | 4 | |||
1680.3.bd.a.769.9 | 16 | 140.83 | odd | 4 | |||
1680.3.bd.a.769.10 | 16 | 20.7 | even | 4 |