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 | 601.4 | ||
Root | \(-0.207107 + 1.12945i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.e.601.8 |
$q$-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 | \(-0.922736\pi\) | ||
0.970685 | − | 0.240355i | \(-0.0772640\pi\) | |||||||
\(20\) | 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 | \(-0.525806\pi\) | ||||
−0.0809816 | + | 0.996716i | \(0.525806\pi\) | |||||||
\(24\) | 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 | \(0.372415\pi\) | ||||
−0.390175 | + | 0.920741i | \(0.627585\pi\) | |||||||
\(32\) | −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 | \(-0.311204\pi\) | ||||
0.558952 | + | 0.829200i | \(0.311204\pi\) | |||||||
\(38\) | 12.9167i | 0.339914i | ||||||||
\(39\) | −8.37500 | −0.214744 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7156i | 0.285745i | 0.989741 | + | 0.142873i | \(0.0456340\pi\) | ||||
−0.989741 | + | 0.142873i | \(0.954366\pi\) | |||||||
\(42\) | 4.68756 | + | 16.4932i | 0.111609 | + | 0.392696i | ||||
\(43\) | 64.4171 | 1.49807 | 0.749036 | − | 0.662529i | \(-0.230517\pi\) | ||||
0.749036 | + | 0.662529i | \(0.230517\pi\) | |||||||
\(44\) | 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 | \(-0.761176\pi\) | ||||
−0.731493 | + | 0.681849i | \(0.761176\pi\) | |||||||
\(54\) | − | 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 | \(0.264154\pi\) | ||||
−0.674976 | + | 0.737839i | \(0.735846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.36957i | 0.0880258i | 0.999031 | + | 0.0440129i | \(0.0140143\pi\) | ||||
−0.999031 | + | 0.0440129i | \(0.985986\pi\) | |||||||
\(62\) | − | 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 | \(-0.385451\pi\) | ||||
0.352149 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(68\) | − | 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 | \(-0.806859\pi\) | ||
0.821494 | − | 0.570217i | \(-0.193141\pi\) | |||||||
\(90\) | 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 | \(-0.916122\pi\) | ||
0.965482 | − | 0.260471i | \(-0.0838777\pi\) | |||||||
\(102\) | 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 | \(-0.801097\pi\) | ||||
−0.811037 | + | 0.584994i | \(0.801097\pi\) | |||||||
\(108\) | 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 | \(-0.399532\pi\) | ||||
0.310414 | + | 0.950601i | \(0.399532\pi\) | |||||||
\(114\) | 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 | \(-0.784432\pi\) | ||||
−0.779313 | + | 0.626635i | \(0.784432\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − | 111.574i | − | 0.864912i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 114.901i | − | 0.877105i | −0.898706 | − | 0.438552i | \(-0.855491\pi\) | ||
0.898706 | − | 0.438552i | \(-0.144509\pi\) | |||||||
\(132\) | − | 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 | \(-0.386881\pi\) | ||||
0.347941 | + | 0.937516i | \(0.386881\pi\) | |||||||
\(138\) | − | 9.12473i | − | 0.0661212i | ||||||
\(139\) | − | 237.587i | − | 1.70926i | −0.519237 | − | 0.854630i | \(-0.673784\pi\) | ||
0.519237 | − | 0.854630i | \(-0.326216\pi\) | |||||||
\(140\) | 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 | \(-0.368468\pi\) | ||||
0.401560 | + | 0.915833i | \(0.368468\pi\) | |||||||
\(164\) | 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 | \(0.0126784\pi\) | ||||
−0.999207 | + | 0.0398199i | \(0.987322\pi\) | |||||||
\(182\) | 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 | \(-0.719895\pi\) | ||||
−0.637171 | + | 0.770723i | \(0.719895\pi\) | |||||||
\(194\) | 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 | \(-0.433216\pi\) | ||||
0.208273 | + | 0.978071i | \(0.433216\pi\) | |||||||
\(198\) | 74.2954 | 0.375229 | ||||||||
\(199\) | − | 289.338i | − | 1.45396i | −0.686658 | − | 0.726981i | \(-0.740923\pi\) | ||
0.686658 | − | 0.726981i | \(-0.259077\pi\) | |||||||
\(200\) | 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 | \(0.322305\pi\) | ||||
−0.529700 | + | 0.848185i | \(0.677695\pi\) | |||||||
\(230\) | 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 | \(-0.451725\pi\) | ||||
0.151081 | + | 0.988521i | \(0.451725\pi\) | |||||||
\(234\) | − | 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 | \(0.135274\pi\) | ||||
−0.911049 | + | 0.412297i | \(0.864726\pi\) | |||||||
\(242\) | −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 | \(-0.795422\pi\) | ||
0.800480 | − | 0.599359i | \(-0.204578\pi\) | |||||||
\(252\) | −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 | \(-0.683085\pi\) | ||||
−0.543984 | + | 0.839096i | \(0.683085\pi\) | |||||||
\(264\) | 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 | \(0.113889\pi\) | ||||
−0.936672 | + | 0.350208i | \(0.886111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.59288i | 0.0353981i | 0.999843 | + | 0.0176990i | \(0.00563408\pi\) | ||||
−0.999843 | + | 0.0176990i | \(0.994366\pi\) | |||||||
\(272\) | − | 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 | \(-0.593899\pi\) | ||||
−0.290732 | + | 0.956804i | \(0.593899\pi\) | |||||||
\(278\) | 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 | \(-0.727066\pi\) | ||
0.654369 | − | 0.756176i | \(-0.272934\pi\) | |||||||
\(312\) | 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 | \(-0.360653\pi\) | ||||
0.423922 | + | 0.905699i | \(0.360653\pi\) | |||||||
\(318\) | − | 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 | \(-0.477408\pi\) | ||||
0.0709157 | + | 0.997482i | \(0.477408\pi\) | |||||||
\(338\) | −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 | \(-0.634082\pi\) | ||||
−0.408885 | + | 0.912586i | \(0.634082\pi\) | |||||||
\(348\) | 3.89995i | 0.0112067i | ||||||||
\(349\) | − | 20.0321i | − | 0.0573987i | −0.999588 | − | 0.0286993i | \(-0.990863\pi\) | ||
0.999588 | − | 0.0286993i | \(-0.00913653\pi\) | |||||||
\(350\) | 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 | \(-0.602616\pi\) | ||||
−0.316822 | + | 0.948485i | \(0.602616\pi\) | |||||||
\(374\) | 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 | \(0.245200\pi\) | ||||
−0.717690 | + | 0.696363i | \(0.754800\pi\) | |||||||
\(410\) | 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 | \(-0.919587\pi\) | ||
0.968260 | − | 0.249947i | \(-0.0804132\pi\) | |||||||
\(420\) | 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 | \(0.164925\pi\) | ||||
−0.868748 | + | 0.495255i | \(0.835075\pi\) | |||||||
\(440\) | 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 | \(-0.284521\pi\) | ||||
0.626417 | + | 0.779488i | \(0.284521\pi\) | |||||||
\(444\) | − | 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 | \(-0.806916\pi\) | ||||
−0.821596 | + | 0.570070i | \(0.806916\pi\) | |||||||
\(458\) | − | 549.378i | − | 1.19951i | ||||||
\(459\) | 93.6783 | 0.204092 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 395.377i | − | 0.857651i | −0.903387 | − | 0.428826i | \(-0.858928\pi\) | ||
0.903387 | − | 0.428826i | \(-0.141072\pi\) | |||||||
\(462\) | 82.0867 | + | 288.823i | 0.177677 | + | 0.625158i | ||||
\(463\) | −423.981 | −0.915726 | −0.457863 | − | 0.889023i | \(-0.651385\pi\) | ||||
−0.457863 | + | 0.889023i | \(0.651385\pi\) | |||||||
\(464\) | −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 | \(0.278109\pi\) | ||||
−0.641990 | + | 0.766713i | \(0.721891\pi\) | |||||||
\(480\) | 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 | \(-0.469999\pi\) | ||||
0.0941111 | + | 0.995562i | \(0.469999\pi\) | |||||||
\(488\) | − | 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 | \(0.287996\pi\) | ||||
−0.617869 | + | 0.786281i | \(0.712004\pi\) | |||||||
\(510\) | 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 | \(0.00654365\pi\) | ||||
−0.999789 | + | 0.0205560i | \(0.993456\pi\) | |||||||
\(522\) | −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 | \(-0.593209\pi\) | ||||
−0.288659 | + | 0.957432i | \(0.593209\pi\) | |||||||
\(548\) | 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 | \(-0.395732\pi\) | ||||
0.321742 | + | 0.946827i | \(0.395732\pi\) | |||||||
\(558\) | 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 | \(-0.931702\pi\) | ||
0.977069 | − | 0.212922i | \(-0.0682980\pi\) | |||||||
\(602\) | −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 | \(-0.382262\pi\) | ||||
0.361507 | + | 0.932369i | \(0.382262\pi\) | |||||||
\(614\) | − | 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 | \(-0.404878\pi\) | ||||
0.294407 | + | 0.955680i | \(0.404878\pi\) | |||||||
\(618\) | −177.344 | −0.286964 | ||||||||
\(619\) | − | 292.211i | − | 0.472069i | −0.971745 | − | 0.236035i | \(-0.924152\pi\) | ||
0.971745 | − | 0.236035i | \(-0.0758479\pi\) | |||||||
\(620\) | 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 | \(-0.440450\pi\) | ||||
0.185992 | + | 0.982551i | \(0.440450\pi\) | |||||||
\(654\) | − | 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 | \(0.0596877\pi\) | ||||
−0.982471 | + | 0.186418i | \(0.940312\pi\) | |||||||
\(662\) | −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 | \(-0.518061\pi\) | ||||
−0.0567109 | + | 0.998391i | \(0.518061\pi\) | |||||||
\(674\) | −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 | \(-0.463256\pi\) | ||||
0.115178 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(684\) | 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 | \(0.164693\pi\) | ||||
−0.869109 | + | 0.494620i | \(0.835307\pi\) | |||||||
\(692\) | − | 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 | \(0.155011\pi\) | ||||
−0.883750 | + | 0.467960i | \(0.844989\pi\) | |||||||
\(720\) | 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 | \(-0.468454\pi\) | ||||
0.0989414 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(744\) | −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 | \(-0.617833\pi\) | ||||
−0.361788 | + | 0.932261i | \(0.617833\pi\) | |||||||
\(758\) | 486.822 | 0.642246 | ||||||||
\(759\) | 112.988i | 0.148864i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1223.78i | 1.60813i | 0.594544 | + | 0.804063i | \(0.297332\pi\) | ||||
−0.594544 | + | 0.804063i | \(0.702668\pi\) | |||||||
\(762\) | − | 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 | \(0.0404406\pi\) | ||||
−0.991940 | + | 0.126706i | \(0.959559\pi\) | |||||||
\(770\) | 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 | \(-0.660522\pi\) | ||
0.483190 | − | 0.875516i | \(-0.339478\pi\) | |||||||
\(812\) | −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 | \(-0.619745\pi\) | ||||
−0.367378 | + | 0.930072i | \(0.619745\pi\) | |||||||
\(824\) | − | 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 | \(-0.598618\pi\) | ||||
−0.304885 | + | 0.952389i | \(0.598618\pi\) | |||||||
\(828\) | 22.3509 | 0.0269939 | ||||||||
\(829\) | − | 814.575i | − | 0.982599i | −0.870991 | − | 0.491300i | \(-0.836522\pi\) | ||
0.870991 | − | 0.491300i | \(-0.163478\pi\) | |||||||
\(830\) | 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 | \(0.0243920\pi\) | ||||
−0.997065 | + | 0.0765547i | \(0.975608\pi\) | |||||||
\(840\) | 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 | \(0.142858\pi\) | ||||
−0.900968 | + | 0.433885i | \(0.857142\pi\) | |||||||
\(860\) | 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 | \(-0.611725\pi\) | ||||
−0.343830 | + | 0.939032i | \(0.611725\pi\) | |||||||
\(864\) | − | 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 | \(-0.553217\pi\) | ||||
−0.166407 | + | 0.986057i | \(0.553217\pi\) | |||||||
\(878\) | − | 614.948i | − | 0.700396i | ||||||
\(879\) | −174.795 | −0.198856 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1226.42i | 1.39208i | 0.718004 | + | 0.696039i | \(0.245056\pi\) | ||||
−0.718004 | + | 0.696039i | \(0.754944\pi\) | |||||||
\(882\) | 176.815 | − | 109.337i | 0.200470 | − | 0.123965i | ||||
\(883\) | 1132.03 | 1.28202 | 0.641012 | − | 0.767531i | \(-0.278515\pi\) | ||||
0.641012 | + | 0.767531i | \(0.278515\pi\) | |||||||
\(884\) | −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 | \(-0.316285\pi\) | ||||
0.545644 | + | 0.838017i | \(0.316285\pi\) | |||||||
\(908\) | 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 | \(0.229037\pi\) | ||||
−0.752109 | + | 0.659039i | \(0.770963\pi\) | |||||||
\(930\) | 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 | \(0.230427\pi\) | ||||
−0.749223 | + | 0.662318i | \(0.769573\pi\) | |||||||
\(942\) | 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 | \(-0.616168\pi\) | ||||
−0.356905 | + | 0.934141i | \(0.616168\pi\) | |||||||
\(948\) | − | 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 | \(-0.304534\pi\) | ||||
0.576201 | + | 0.817308i | \(0.304534\pi\) | |||||||
\(954\) | −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 | \(-0.744889\pi\) | ||||
−0.695661 | + | 0.718370i | \(0.744889\pi\) | |||||||
\(968\) | −525.114 | −0.542474 | ||||||||
\(969\) | 285.204i | 0.294328i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1230.36i | − | 1.26710i | −0.773701 | − | 0.633551i | \(-0.781597\pi\) | ||
0.773701 | − | 0.633551i | \(-0.218403\pi\) | |||||||
\(972\) | − | 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 | \(-0.462755\pi\) | ||||
0.116743 | + | 0.993162i | \(0.462755\pi\) | |||||||
\(978\) | 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.601.4 | 16 | ||
5.2 | odd | 4 | 210.3.h.a.139.1 | ✓ | 16 | ||
5.3 | odd | 4 | 210.3.h.a.139.16 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.3.f.e.601.13 | 16 | ||
7.6 | odd | 2 | inner | 1050.3.f.e.601.8 | 16 | ||
15.2 | even | 4 | 630.3.h.e.559.16 | 16 | |||
15.8 | even | 4 | 630.3.h.e.559.1 | 16 | |||
20.3 | even | 4 | 1680.3.bd.a.769.7 | 16 | |||
20.7 | even | 4 | 1680.3.bd.a.769.9 | 16 | |||
35.13 | even | 4 | 210.3.h.a.139.9 | yes | 16 | ||
35.27 | even | 4 | 210.3.h.a.139.8 | yes | 16 | ||
35.34 | odd | 2 | inner | 1050.3.f.e.601.9 | 16 | ||
105.62 | odd | 4 | 630.3.h.e.559.9 | 16 | |||
105.83 | odd | 4 | 630.3.h.e.559.8 | 16 | |||
140.27 | odd | 4 | 1680.3.bd.a.769.8 | 16 | |||
140.83 | odd | 4 | 1680.3.bd.a.769.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.1 | ✓ | 16 | 5.2 | odd | 4 | ||
210.3.h.a.139.8 | yes | 16 | 35.27 | even | 4 | ||
210.3.h.a.139.9 | yes | 16 | 35.13 | even | 4 | ||
210.3.h.a.139.16 | yes | 16 | 5.3 | odd | 4 | ||
630.3.h.e.559.1 | 16 | 15.8 | even | 4 | |||
630.3.h.e.559.8 | 16 | 105.83 | odd | 4 | |||
630.3.h.e.559.9 | 16 | 105.62 | odd | 4 | |||
630.3.h.e.559.16 | 16 | 15.2 | even | 4 | |||
1050.3.f.e.601.4 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.f.e.601.8 | 16 | 7.6 | odd | 2 | inner | ||
1050.3.f.e.601.9 | 16 | 35.34 | odd | 2 | inner | ||
1050.3.f.e.601.13 | 16 | 5.4 | even | 2 | inner | ||
1680.3.bd.a.769.7 | 16 | 20.3 | even | 4 | |||
1680.3.bd.a.769.8 | 16 | 140.27 | odd | 4 | |||
1680.3.bd.a.769.9 | 16 | 20.7 | even | 4 | |||
1680.3.bd.a.769.10 | 16 | 140.83 | odd | 4 |