Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,3,Mod(769,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.769");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bd (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(45.7766844125\) |
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: | \( x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.8 | ||
Root | \(0.500000 - 0.422343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.769 |
Dual form | 1680.3.bd.a.769.7 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.91728 | + | 0.905717i | 0.983457 | + | 0.181143i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.91369 | − | 6.73333i | 0.273384 | − | 0.961905i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.5116 | −1.59196 | −0.795982 | − | 0.605321i | \(-0.793045\pi\) | ||||
−0.795982 | + | 0.605321i | \(0.793045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.83531 | 0.371947 | 0.185973 | − | 0.982555i | \(-0.440456\pi\) | ||||
0.185973 | + | 0.982555i | \(0.440456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.51698 | − | 1.56875i | −0.567799 | − | 0.104583i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.0284 | −1.06049 | −0.530247 | − | 0.847843i | \(-0.677901\pi\) | ||||
−0.530247 | + | 0.847843i | \(0.677901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.72515i | − | 0.161963i | −0.996716 | − | 0.0809816i | \(-0.974194\pi\) | ||
0.996716 | − | 0.0809816i | \(-0.0258055\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.3594 | + | 8.90734i | 0.934374 | + | 0.356294i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.12582 | 0.0388213 | 0.0194107 | − | 0.999812i | \(-0.493821\pi\) | ||||
0.0194107 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.0859i | 1.84148i | 0.390175 | + | 0.920741i | \(0.372415\pi\) | ||||
−0.390175 | + | 0.920741i | \(0.627585\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 30.3310 | 0.919120 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.5086 | − | 31.3765i | 0.443104 | − | 0.896470i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.3624i | 1.11790i | 0.829200 | + | 0.558952i | \(0.188796\pi\) | ||||
−0.829200 | + | 0.558952i | \(0.811204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.37500 | −0.214744 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.7156i | − | 0.285745i | −0.989741 | − | 0.142873i | \(-0.954366\pi\) | ||
0.989741 | − | 0.142873i | \(-0.0456340\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.4171i | 1.49807i | 0.662529 | + | 0.749036i | \(0.269483\pi\) | ||||
−0.662529 | + | 0.749036i | \(0.730517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.7519 | + | 2.71715i | 0.327819 | + | 0.0603812i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 77.6614 | 1.65237 | 0.826185 | − | 0.563399i | \(-0.190507\pi\) | ||||
0.826185 | + | 0.563399i | \(0.190507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.6756 | − | 25.7710i | −0.850522 | − | 0.525939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 31.2261 | 0.612276 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 77.5383i | 1.46299i | 0.681849 | + | 0.731493i | \(0.261176\pi\) | ||||
−0.681849 | + | 0.731493i | \(0.738824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −86.1095 | − | 15.8606i | −1.56563 | − | 0.288374i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15.8197i | − | 0.277539i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 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 | \(-0.0140143\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.74106 | − | 20.2000i | 0.0911280 | − | 0.320635i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.7766 | + | 4.37942i | 0.365794 | + | 0.0673757i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 47.1879i | − | 0.704297i | −0.935944 | − | 0.352149i | \(-0.885451\pi\) | ||
0.935944 | − | 0.352149i | \(-0.114549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.45216i | 0.0935095i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58.3047 | 0.821193 | 0.410597 | − | 0.911817i | \(-0.365320\pi\) | ||||
0.410597 | + | 0.911817i | \(0.365320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 53.4082 | 0.731619 | 0.365810 | − | 0.930690i | \(-0.380792\pi\) | ||||
0.365810 | + | 0.930690i | \(0.380792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −40.4596 | − | 15.4280i | −0.539461 | − | 0.205706i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −33.5117 | + | 117.911i | −0.435217 | + | 1.53132i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28.7890 | 0.346855 | 0.173428 | − | 0.984847i | \(-0.444516\pi\) | ||||
0.173428 | + | 0.984847i | \(0.444516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −88.6507 | − | 16.3286i | −1.04295 | − | 0.192101i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.94997 | −0.0224135 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 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 | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 98.8757i | − | 1.06318i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.27237 | + | 44.9120i | −0.0870776 | + | 0.472758i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −107.830 | −1.11165 | −0.555827 | − | 0.831298i | \(-0.687598\pi\) | ||||
−0.555827 | + | 0.831298i | \(0.687598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −52.5348 | −0.530654 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52.6151i | 0.520941i | 0.965482 | + | 0.260471i | \(0.0838777\pi\) | ||||
−0.965482 | + | 0.260471i | \(0.916122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 72.4002 | 0.702915 | 0.351457 | − | 0.936204i | \(-0.385686\pi\) | ||||
0.351457 | + | 0.936204i | \(0.385686\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −26.8618 | + | 54.3456i | −0.255826 | + | 0.517577i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 173.562i | 1.62207i | 0.584994 | + | 0.811037i | \(0.301097\pi\) | ||||
−0.584994 | + | 0.811037i | \(0.698903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 49.9966 | 0.458684 | 0.229342 | − | 0.973346i | \(-0.426342\pi\) | ||||
0.229342 | + | 0.973346i | \(0.426342\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 71.6418i | − | 0.645422i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 70.1536i | − | 0.620828i | −0.950601 | − | 0.310414i | \(-0.899532\pi\) | ||
0.950601 | − | 0.310414i | \(-0.100468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.37394 | − | 18.3176i | 0.0293386 | − | 0.159284i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5059 | 0.123982 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −34.5007 | + | 121.391i | −0.289922 | + | 1.02009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 185.656 | 1.53435 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.2919i | 0.164975i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 106.797 | + | 64.9569i | 0.854376 | + | 0.519655i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 197.945i | 1.55863i | 0.626635 | + | 0.779313i | \(0.284432\pi\) | ||||
−0.626635 | + | 0.779313i | \(0.715568\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 111.574i | − | 0.864912i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 114.901i | − | 0.877105i | −0.898706 | − | 0.438552i | \(-0.855491\pi\) | ||
0.898706 | − | 0.438552i | \(-0.144509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 61.4989 | + | 17.4787i | 0.462398 | + | 0.131419i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −25.5510 | − | 4.70625i | −0.189266 | − | 0.0348611i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 95.3358i | 0.695882i | 0.937516 | + | 0.347941i | \(0.113119\pi\) | ||||
−0.937516 | + | 0.347941i | \(0.886881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −84.6740 | −0.592126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.53597 | + | 1.01967i | 0.0381791 | + | 0.00703223i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 72.1842 | + | 44.6367i | 0.491049 | + | 0.303651i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 133.844 | 0.898285 | 0.449142 | − | 0.893460i | \(-0.351730\pi\) | ||||
0.449142 | + | 0.893460i | \(0.351730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −155.064 | −1.02691 | −0.513456 | − | 0.858116i | \(-0.671635\pi\) | ||||
−0.513456 | + | 0.858116i | \(0.671635\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −54.0852 | −0.353498 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −51.7037 | + | 280.708i | −0.333572 | + | 1.81102i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −104.634 | −0.666459 | −0.333230 | − | 0.942846i | \(-0.608138\pi\) | ||||
−0.333230 | + | 0.942846i | \(0.608138\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 134.300i | − | 0.844656i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.0827 | − | 7.12878i | −0.155793 | − | 0.0442782i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 130.909i | 0.803120i | 0.915833 | + | 0.401560i | \(0.131532\pi\) | ||||
−0.915833 | + | 0.401560i | \(0.868468\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 149.146 | + | 27.4713i | 0.903915 | + | 0.166493i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 102.845 | 0.615838 | 0.307919 | − | 0.951413i | \(-0.400367\pi\) | ||||
0.307919 | + | 0.951413i | \(0.400367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −145.620 | −0.861656 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.4005i | 0.160237i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 197.432 | 1.14122 | 0.570612 | − | 0.821220i | \(-0.306706\pi\) | ||||
0.570612 | + | 0.821220i | \(0.306706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 104.679 | − | 140.240i | 0.598163 | − | 0.801374i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 150.801i | 0.851984i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(-0.0126784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.30038i | 0.0508217i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −37.4627 | + | 203.391i | −0.202501 | + | 1.09941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 315.706 | 1.68827 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.94382 | + | 34.9874i | −0.0526128 | + | 0.185119i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −59.9375 | −0.313809 | −0.156904 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156904 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 245.948i | 1.27434i | 0.770723 | + | 0.637171i | \(0.219895\pi\) | ||||
−0.770723 | + | 0.637171i | \(0.780105\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −41.1823 | − | 7.58538i | −0.211191 | − | 0.0388994i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 82.0594i | 0.416545i | 0.978071 | + | 0.208273i | \(0.0667842\pi\) | ||||
−0.978071 | + | 0.208273i | \(0.933216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 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 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.15447 | − | 7.58051i | 0.0106131 | − | 0.0373424i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6110 | − | 57.6087i | 0.0517609 | − | 0.281018i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 11.1755i | − | 0.0539877i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 159.942i | − | 0.765274i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −33.6995 | −0.159713 | −0.0798567 | − | 0.996806i | \(-0.525446\pi\) | ||||
−0.0798567 | + | 0.996806i | \(0.525446\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −100.987 | −0.474116 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −58.3437 | + | 316.757i | −0.271366 | + | 1.47329i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 384.379 | + | 109.245i | 1.77133 | + | 0.503432i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −92.5057 | −0.422401 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −87.1728 | −0.394447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.7556 | 0.0482313 | 0.0241156 | − | 0.999709i | \(-0.492323\pi\) | ||||
0.0241156 | + | 0.999709i | \(0.492323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 70.0781 | + | 26.7220i | 0.311458 | + | 0.118765i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −416.450 | −1.83458 | −0.917290 | − | 0.398219i | \(-0.869628\pi\) | ||||
−0.917290 | + | 0.398219i | \(0.869628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 70.4036i | − | 0.302162i | −0.988521 | − | 0.151081i | \(-0.951725\pi\) | ||
0.988521 | − | 0.151081i | \(-0.0482754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 381.883 | + | 70.3393i | 1.62503 | + | 0.299316i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −129.841 | −0.547852 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(-0.135274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −181.589 | − | 164.470i | −0.741181 | − | 0.671305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.1633i | 0.178799i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −49.8640 | −0.200257 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 300.878i | − | 1.19872i | −0.800480 | − | 0.599359i | \(-0.795422\pi\) | ||
0.800480 | − | 0.599359i | \(-0.204578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 65.2334i | 0.257839i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 153.548 | + | 28.2820i | 0.602147 | + | 0.110910i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 306.052 | 1.19087 | 0.595433 | − | 0.803405i | \(-0.296981\pi\) | ||||
0.595433 | + | 0.803405i | \(0.296981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 278.507 | + | 79.1548i | 1.07532 | + | 0.305617i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.37745 | 0.0129404 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 286.135i | − | 1.08797i | −0.839096 | − | 0.543984i | \(-0.816915\pi\) | ||
0.839096 | − | 0.543984i | \(-0.183085\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −70.2278 | + | 381.278i | −0.265010 | + | 1.43878i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 175.801i | 0.658430i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 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 | \(0.994366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.0271 | + | 56.3917i | −0.0587075 | + | 0.206563i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −409.060 | − | 155.982i | −1.48749 | − | 0.567206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 161.066i | − | 0.581464i | −0.956804 | − | 0.290732i | \(-0.906101\pi\) | ||
0.956804 | − | 0.290732i | \(-0.0938989\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 171.258i | 0.613827i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −343.107 | −1.22102 | −0.610510 | − | 0.792008i | \(-0.709036\pi\) | ||||
−0.610510 | + | 0.792008i | \(0.709036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 324.748 | 1.14752 | 0.573759 | − | 0.819024i | \(-0.305484\pi\) | ||||
0.573759 | + | 0.819024i | \(0.305484\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.3282 | − | 77.7899i | 0.0502743 | − | 0.272947i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −78.8848 | − | 22.4199i | −0.274860 | − | 0.0781182i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.0229 | 0.124647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 186.768 | 0.641813 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 100.918 | 0.344429 | 0.172215 | − | 0.985059i | \(-0.444908\pi\) | ||||
0.172215 | + | 0.985059i | \(0.444908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 78.8563 | − | 428.124i | 0.267310 | − | 1.45127i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 90.9929 | 0.306373 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 18.0123i | − | 0.0602417i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 433.742 | + | 123.274i | 1.44100 | + | 0.409549i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 91.1320i | − | 0.300766i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.86332 | − | 26.4037i | 0.0159453 | − | 0.0865696i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −41.3057 | −0.134546 | −0.0672732 | − | 0.997735i | \(-0.521430\pi\) | ||||
−0.0672732 | + | 0.997735i | \(0.521430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −125.401 | −0.405828 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 470.341i | − | 1.51235i | −0.654369 | − | 0.756176i | \(-0.727066\pi\) | ||
0.654369 | − | 0.756176i | \(-0.272934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −160.220 | −0.511884 | −0.255942 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255942 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 46.5259 | − | 94.1294i | 0.147701 | − | 0.298823i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 268.766i | 0.847843i | 0.905699 | + | 0.423922i | \(0.139347\pi\) | ||||
−0.905699 | + | 0.423922i | \(0.860653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.7149 | −0.0618021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 300.618i | − | 0.936505i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 164.662i | − | 0.509791i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 112.950 | + | 43.0697i | 0.347537 | + | 0.132522i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −86.5967 | −0.264822 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 148.620 | − | 522.920i | 0.451732 | − | 1.58942i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −555.018 | −1.67679 | −0.838395 | − | 0.545063i | \(-0.816506\pi\) | ||||
−0.838395 | + | 0.545063i | \(0.816506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 124.087i | 0.372634i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42.7389 | − | 232.036i | 0.127579 | − | 0.692646i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 47.7972i | 0.141831i | 0.997482 | + | 0.0709157i | \(0.0225921\pi\) | ||||
−0.997482 | + | 0.0709157i | \(0.977408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 121.510i | 0.358435i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 999.666i | − | 2.93157i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −253.279 | + | 231.298i | −0.738422 | + | 0.674338i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.84383 | + | 31.7271i | −0.0169386 | + | 0.0919625i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 283.766i | 0.817771i | 0.912586 | + | 0.408885i | \(0.134082\pi\) | ||||
−0.912586 | + | 0.408885i | \(0.865918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 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 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −595.015 | −1.68559 | −0.842797 | − | 0.538231i | \(-0.819093\pi\) | ||||
−0.842797 | + | 0.538231i | \(0.819093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 286.701 | + | 52.8076i | 0.807608 | + | 0.148754i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 59.7570 | − | 210.256i | 0.167387 | − | 0.588952i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −321.566 | −0.885856 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 262.623 | + | 48.3727i | 0.719516 | + | 0.132528i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −662.601 | −1.80545 | −0.902726 | − | 0.430215i | \(-0.858438\pi\) | ||||
−0.902726 | + | 0.430215i | \(0.858438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 35.1467i | − | 0.0952485i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 522.091 | + | 148.384i | 1.40725 | + | 0.399957i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 236.349i | 0.633644i | 0.948485 | + | 0.316822i | \(0.102616\pi\) | ||||
−0.948485 | + | 0.316822i | \(0.897384\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −184.978 | − | 112.509i | −0.493274 | − | 0.300023i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.44368 | 0.0144395 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 65.7097 | 0.171566 | 0.0857828 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857828 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −271.581 | + | 549.452i | −0.705406 | + | 1.42715i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 193.251i | 0.499357i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 161.296 | 0.414642 | 0.207321 | − | 0.978273i | \(-0.433526\pi\) | ||||
0.207321 | + | 0.978273i | \(0.433526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 67.1585i | 0.171761i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 199.014i | 0.506397i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 368.618 | + | 67.8959i | 0.933209 | + | 0.171888i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 667.752 | 1.68200 | 0.840998 | − | 0.541039i | \(-0.181969\pi\) | ||||
0.840998 | + | 0.541039i | \(0.181969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −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 | \(0.765379\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 276.028i | 0.684933i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 44.2556 | + | 8.15146i | 0.109273 | + | 0.0201271i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 724.322i | − | 1.77966i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 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 | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −586.238 | − | 166.615i | −1.41946 | − | 0.403427i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 141.564 | + | 26.0747i | 0.341117 | + | 0.0628306i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 411.513i | − | 0.986842i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.564601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 232.984 | 0.550790 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −421.132 | − | 160.585i | −0.990898 | − | 0.377847i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.1551 | − | 10.2757i | −0.0846725 | − | 0.0240649i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 146.660 | 0.341864 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −538.427 | −1.24925 | −0.624625 | − | 0.780925i | \(-0.714748\pi\) | ||||
−0.624625 | + | 0.780925i | \(0.714748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 118.314 | 0.273243 | 0.136622 | − | 0.990623i | \(-0.456376\pi\) | ||||
0.136622 | + | 0.990623i | \(0.456376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.58858 | − | 1.76613i | −0.0220427 | − | 0.00406006i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.0237 | 0.0778575 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 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 | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 555.005i | 1.25283i | 0.779488 | + | 0.626417i | \(0.215479\pi\) | ||||
−0.779488 | + | 0.626417i | \(0.784521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 91.9291 | − | 499.098i | 0.206582 | − | 1.12157i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −231.825 | −0.518625 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −66.8926 | −0.148981 | −0.0744906 | − | 0.997222i | \(-0.523733\pi\) | ||||
−0.0744906 | + | 0.997222i | \(0.523733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 205.158i | 0.454896i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 268.578 | 0.592888 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 74.9891 | − | 151.715i | 0.164811 | − | 0.333439i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 750.939i | − | 1.64319i | −0.570070 | − | 0.821596i | \(-0.693084\pi\) | ||
0.570070 | − | 0.821596i | \(-0.306916\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 93.6783 | 0.204092 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 395.377i | 0.857651i | 0.903387 | + | 0.428826i | \(0.141072\pi\) | ||||
−0.903387 | + | 0.428826i | \(0.858928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 423.981i | − | 0.915726i | −0.889023 | − | 0.457863i | \(-0.848615\pi\) | ||
0.889023 | − | 0.457863i | \(-0.151385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 89.5535 | − | 486.200i | 0.192588 | − | 1.04559i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 584.408 | 1.25141 | 0.625705 | − | 0.780060i | \(-0.284812\pi\) | ||||
0.625705 | + | 0.780060i | \(0.284812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −317.732 | − | 90.3030i | −0.677467 | − | 0.192544i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 181.232 | 0.384780 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1128.05i | − | 2.38488i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −81.3552 | + | 213.353i | −0.171274 | + | 0.449164i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 232.615i | 0.487662i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 43.4445 | + | 12.3474i | 0.0899473 | + | 0.0255640i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −530.232 | − | 97.6638i | −1.09326 | − | 0.201369i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 91.6643i | − | 0.188222i | −0.995562 | − | 0.0941111i | \(-0.969999\pi\) | ||
0.995562 | − | 0.0941111i | \(-0.0300009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 226.740i | − | 0.463681i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −460.086 | −0.937038 | −0.468519 | − | 0.883453i | \(-0.655212\pi\) | ||||
−0.468519 | + | 0.883453i | \(0.655212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.2967 | −0.0411698 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −258.328 | − | 47.5817i | −0.521876 | − | 0.0961246i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 111.577 | − | 392.585i | 0.224501 | − | 0.789910i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −305.145 | −0.606650 | −0.303325 | − | 0.952887i | \(-0.598097\pi\) | ||||
−0.303325 | + | 0.952887i | \(0.598097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.6544 | + | 258.723i | −0.0943651 | + | 0.512323i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 252.221 | 0.497477 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 47.4591i | − | 0.0925128i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 356.012 | + | 65.5741i | 0.691286 | + | 0.127328i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1359.97 | −2.63051 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −341.962 | −0.658886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.4194i | − | 0.0411121i | −0.999789 | − | 0.0205560i | \(-0.993456\pi\) | ||
0.999789 | − | 0.0205560i | \(-0.00654365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −842.290 | −1.61050 | −0.805249 | − | 0.592937i | \(-0.797968\pi\) | ||||
−0.805249 | + | 0.592937i | \(0.797968\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −181.309 | + | 242.904i | −0.345350 | + | 0.462674i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1029.17i | − | 1.95288i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 515.123 | 0.973768 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 261.195i | − | 0.491893i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 56.6484i | − | 0.106282i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −157.198 | + | 853.453i | −0.293828 | + | 1.59524i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −205.805 | −0.383250 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 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 | \(0.504613\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.9672i | 0.0459801i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 245.847 | + | 45.2828i | 0.451096 | + | 0.0830877i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 315.792i | 0.577317i | 0.957432 | + | 0.288659i | \(0.0932092\pi\) | ||||
−0.957432 | + | 0.288659i | \(0.906791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 16.1087i | − | 0.0293419i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2827i | 0.0186618i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 143.457 | − | 504.756i | 0.259416 | − | 0.912759i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 64.8872 | − | 352.283i | 0.116914 | − | 0.634744i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 358.421i | 0.643484i | 0.946827 | + | 0.321742i | \(0.104268\pi\) | ||||
−0.946827 | + | 0.321742i | \(0.895732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 311.477i | 0.557203i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −546.819 | −0.974721 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 622.834 | 1.10628 | 0.553138 | − | 0.833089i | \(-0.313430\pi\) | ||||
0.553138 | + | 0.833089i | \(0.313430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 63.5393 | − | 344.965i | 0.112459 | − | 0.610557i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.2232 | − | 60.6000i | 0.0303760 | − | 0.106878i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −185.789 | −0.326518 | −0.163259 | − | 0.986583i | \(-0.552201\pi\) | ||||
−0.163259 | + | 0.986583i | \(0.552201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 486.258 | 0.851589 | 0.425795 | − | 0.904820i | \(-0.359995\pi\) | ||||
0.425795 | + | 0.904820i | \(0.359995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 103.815 | 0.181178 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.1812 | − | 87.0172i | 0.0577064 | − | 0.151334i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 270.057 | 0.468037 | 0.234018 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 425.994i | − | 0.735741i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 55.0932 | − | 193.846i | 0.0948247 | − | 0.333642i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1357.82i | − | 2.32902i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 71.3298 | + | 13.1383i | 0.121931 | + | 0.0224586i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −400.613 | −0.682476 | −0.341238 | − | 0.939977i | \(-0.610846\pi\) | ||||
−0.341238 | + | 0.939977i | \(0.610846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −521.395 | −0.885220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 142.131i | − | 0.240493i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −157.686 | −0.265912 | −0.132956 | − | 0.991122i | \(-0.542447\pi\) | ||||
−0.132956 | + | 0.991122i | \(0.542447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −279.596 | + | 565.667i | −0.469909 | + | 0.950701i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 501.149i | − | 0.839445i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | \(0.931702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 141.564i | − | 0.234766i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 912.923 | + | 168.152i | 1.50896 | + | 0.277937i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 773.553 | 1.27439 | 0.637194 | − | 0.770704i | \(-0.280095\pi\) | ||||
0.637194 | + | 0.770704i | \(0.280095\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.73164 | + | 13.1298i | −0.00612749 | + | 0.0215597i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 375.517 | 0.614594 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 443.208i | − | 0.723015i | −0.932369 | − | 0.361507i | \(-0.882262\pi\) | ||
0.932369 | − | 0.361507i | \(-0.117738\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.3788 | + | 99.7813i | −0.0298842 | + | 0.162246i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 363.298i | 0.588813i | 0.955680 | + | 0.294407i | \(0.0951220\pi\) | ||||
−0.955680 | + | 0.294407i | \(0.904878\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 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 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −683.425 | − | 194.237i | −1.09699 | − | 0.311777i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 466.319 | + | 416.139i | 0.746110 | + | 0.665823i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 277.028i | 0.441831i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 745.698i | − | 1.18553i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −189.221 | −0.299874 | −0.149937 | − | 0.988696i | \(-0.547907\pi\) | ||||
−0.149937 | + | 0.988696i | \(0.547907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58.3693 | 0.0922106 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −179.283 | + | 973.354i | −0.282335 | + | 1.53284i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −201.514 | − | 124.611i | −0.316349 | − | 0.195621i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 174.914 | 0.273731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1162.94 | 1.81425 | 0.907127 | − | 0.420857i | \(-0.138271\pi\) | ||||
0.907127 | + | 0.420857i | \(0.138271\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1096.08 | 1.70464 | 0.852320 | − | 0.523021i | \(-0.175195\pi\) | ||||
0.852320 | + | 0.523021i | \(0.175195\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 101.054 | − | 548.640i | 0.156673 | − | 0.850604i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −262.877 | −0.406302 | −0.203151 | − | 0.979147i | \(-0.565118\pi\) | ||||
−0.203151 | + | 0.979147i | \(0.565118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1524.65i | 2.34923i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −665.763 | − | 189.217i | −1.02268 | − | 0.290656i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 242.905i | − | 0.371983i | −0.982551 | − | 0.185992i | \(-0.940450\pi\) | ||
0.982551 | − | 0.185992i | \(-0.0595498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 104.068 | − | 564.999i | 0.158882 | − | 0.862594i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 160.225 | 0.243873 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(-0.0596877\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 150.988 | 0.227734 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 286.577 | + | 141.648i | 0.430943 | + | 0.213005i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.19385i | − | 0.00628763i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.6292 | −0.0278464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 94.0298i | 0.140134i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 76.3328i | 0.113422i | 0.998391 | + | 0.0567109i | \(0.0180613\pi\) | ||||
−0.998391 | + | 0.0567109i | \(0.981939\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −121.379 | − | 46.2839i | −0.179820 | − | 0.0685687i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −310.277 | −0.458312 | −0.229156 | − | 0.973390i | \(-0.573597\pi\) | ||||
−0.229156 | + | 0.973390i | \(0.573597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −206.354 | + | 726.058i | −0.303908 | + | 1.06930i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 721.312 | 1.05920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 157.333i | 0.230356i | 0.993345 | + | 0.115178i | \(0.0367438\pi\) | ||||
−0.993345 | + | 0.115178i | \(0.963256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −86.3473 | + | 468.793i | −0.126054 | + | 0.684370i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 672.848i | − | 0.979400i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 374.921i | 0.544153i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 683.565i | 0.989240i | 0.869109 | + | 0.494620i | \(0.164693\pi\) | ||||
−0.869109 | + | 0.494620i | \(0.835307\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −100.535 | + | 353.734i | −0.145072 | + | 0.510439i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −215.187 | + | 1168.28i | −0.309621 | + | 1.68098i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 211.213i | 0.303031i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 121.943i | 0.174453i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −306.153 | −0.436738 | −0.218369 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218369 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −377.784 | −0.537388 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −661.441 | − | 121.831i | −0.938214 | − | 0.172810i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 354.275 | + | 100.689i | 0.501096 | + | 0.142417i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 444.082 | 0.626350 | 0.313175 | − | 0.949695i | \(-0.398607\pi\) | ||||
0.313175 | + | 0.949695i | \(0.398607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 224.891 | 0.316302 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 212.654 | 0.298252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −416.366 | − | 76.6907i | −0.582330 | − | 0.107260i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −542.363 | −0.756434 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 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 | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 344.206i | 0.476080i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.2984 | + | 10.0280i | 0.0362736 | + | 0.0138318i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 675.927 | 0.929748 | 0.464874 | − | 0.885377i | \(-0.346100\pi\) | ||||
0.464874 | + | 0.885377i | \(0.346100\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1161.34i | − | 1.58870i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 387.908 | 0.529206 | 0.264603 | − | 0.964357i | \(-0.414759\pi\) | ||||
0.264603 | + | 0.964357i | \(0.414759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 314.522 | + | 284.870i | 0.427921 | + | 0.387578i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 826.336i | 1.12122i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 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 | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 147.027i | 0.197883i | 0.995093 | + | 0.0989414i | \(0.0315456\pi\) | ||||
−0.995093 | + | 0.0989414i | \(0.968454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 658.151 | + | 121.225i | 0.883424 | + | 0.162718i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 86.3670 | 0.115618 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1168.65 | + | 332.144i | 1.56028 | + | 0.443449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −103.003 | −0.137154 | −0.0685771 | − | 0.997646i | \(-0.521846\pi\) | ||||
−0.0685771 | + | 0.997646i | \(0.521846\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 521.136i | 0.692080i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −762.492 | − | 140.444i | −1.00992 | − | 0.186018i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 547.747i | − | 0.723575i | −0.932261 | − | 0.361788i | \(-0.882167\pi\) | ||
0.932261 | − | 0.361788i | \(-0.117833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 112.988i | − | 0.148864i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1223.78i | − | 1.60813i | −0.594544 | − | 0.804063i | \(-0.702668\pi\) | ||
0.594544 | − | 0.804063i | \(-0.297332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 95.6779 | − | 336.644i | 0.125397 | − | 0.441211i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −265.952 | − | 48.9859i | −0.347650 | − | 0.0640338i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 420.986i | − | 0.548874i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1017.59 | 1.31642 | 0.658209 | − | 0.752835i | \(-0.271314\pi\) | ||||
0.658209 | + | 0.752835i | \(0.271314\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −508.484 | + | 1333.49i | −0.656108 | + | 1.72063i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −482.388 | − | 137.100i | −0.620834 | − | 0.176448i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 107.004 | 0.137361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1021.01 | −1.30731 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.84992 | −0.00747117 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −514.515 | − | 94.7689i | −0.655434 | − | 0.120725i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −222.094 | −0.282203 | −0.141101 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141101 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 495.601i | 0.628138i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −472.367 | − | 134.252i | −0.597178 | − | 0.169724i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.9636i | − | 0.0327409i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 121.638 | − | 660.392i | 0.153004 | − | 0.830682i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 340.349 | 0.427038 | 0.213519 | − | 0.976939i | \(-0.431507\pi\) | ||||
0.213519 | + | 0.976939i | \(0.431507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1400.11 | −1.75233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 304.496i | − | 0.380145i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −935.263 | −1.16471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −116.882 | − | 57.7721i | −0.145195 | − | 0.0717666i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 326.339i | − | 0.404385i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −462.403 | −0.571573 | −0.285787 | − | 0.958293i | \(-0.592255\pi\) | ||||
−0.285787 | + | 0.958293i | \(0.592255\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1420.09i | − | 1.75103i | −0.483190 | − | 0.875516i | \(-0.660522\pi\) | ||
0.483190 | − | 0.875516i | \(-0.339478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.6154i | − | 0.0204371i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −118.566 | + | 643.714i | −0.145480 | + | 0.789833i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −588.354 | −0.720140 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 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 | \(0.629911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 604.705i | − | 0.734756i | −0.930072 | − | 0.367378i | \(-0.880255\pi\) | ||
0.930072 | − | 0.367378i | \(-0.119745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 708.512 | + | 270.168i | 0.858802 | + | 0.327477i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 504.280i | 0.609771i | 0.952389 | + | 0.304885i | \(0.0986181\pi\) | ||||
−0.952389 | + | 0.304885i | \(0.901382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 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 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 751.344 | + | 464.610i | 0.901973 | + | 0.557755i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 505.718 | + | 93.1484i | 0.605650 | + | 0.111555i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 296.627i | − | 0.354393i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 594.278 | 0.704956 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −716.054 | − | 131.890i | −0.847401 | − | 0.156083i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 355.288 | − | 1250.08i | 0.419466 | − | 1.47590i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −562.480 | −0.662520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 154.081 | 0.181059 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −636.175 | −0.745808 | −0.372904 | − | 0.927870i | \(-0.621638\pi\) | ||||
−0.372904 | + | 0.927870i | \(0.621638\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.8171 | + | 134.736i | −0.0290259 | + | 0.157586i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −494.679 | −0.577221 | −0.288611 | − | 0.957447i | \(-0.593193\pi\) | ||||
−0.288611 | + | 0.957447i | \(0.593193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 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 | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 593.451i | − | 0.687661i | −0.939032 | − | 0.343830i | \(-0.888275\pi\) | ||
0.939032 | − | 0.343830i | \(-0.111725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 970.828 | + | 178.817i | 1.12234 | + | 0.206725i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −62.3935 | −0.0719648 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1312.73 | −1.51063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 228.168i | − | 0.261961i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −323.491 | −0.370551 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 641.753 | − | 594.793i | 0.733432 | − | 0.679763i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 291.879i | − | 0.332815i | −0.986057 | − | 0.166407i | \(-0.946783\pi\) | ||
0.986057 | − | 0.166407i | \(-0.0532167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −174.795 | −0.198856 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1226.42i | − | 1.39208i | −0.718004 | − | 0.696039i | \(-0.754944\pi\) | ||
0.718004 | − | 0.696039i | \(-0.245056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1132.03i | 1.28202i | 0.767531 | + | 0.641012i | \(0.221485\pi\) | ||||
−0.767531 | + | 0.641012i | \(0.778515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −136.583 | + | 741.532i | −0.154331 | + | 0.837889i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −959.088 | −1.08127 | −0.540636 | − | 0.841257i | \(-0.681816\pi\) | ||||
−0.540636 | + | 0.841257i | \(0.681816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1332.83 | + | 378.806i | 1.49925 | + | 0.426103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −157.604 | −0.176885 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 709.321i | 0.794312i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 584.280 | + | 107.619i | 0.652827 | + | 0.120245i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.1982i | 0.0347806i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.2684i | 0.0714887i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1397.89i | − | 1.55149i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −751.263 | − | 213.517i | −0.831964 | − | 0.236453i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.0558 | − | 70.8817i | 0.0144262 | − | 0.0783224i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 989.799i | − | 1.09129i | −0.838017 | − | 0.545644i | \(-0.816285\pi\) | ||
0.838017 | − | 0.545644i | \(-0.183715\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 157.845i | 0.173647i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −994.781 | −1.09197 | −0.545983 | − | 0.837796i | \(-0.683844\pi\) | ||||
−0.545983 | + | 0.837796i | \(0.683844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −504.141 | −0.552181 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.42351 | + | 45.7326i | −0.00920602 | + | 0.0499810i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −773.665 | − | 219.884i | −0.843691 | − | 0.239786i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 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 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 281.921 | 0.305440 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −368.429 | + | 966.199i | −0.398302 | + | 1.04454i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 217.201 | 0.234305 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 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 | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 814.655i | 0.873156i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1552.42 | + | 285.940i | 1.66034 | + | 0.305819i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 807.001 | 0.861260 | 0.430630 | − | 0.902529i | \(-0.358291\pi\) | ||||
0.430630 | + | 0.902529i | \(0.358291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 277.508 | 0.295536 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1246.48i | − | 1.32464i | −0.749223 | − | 0.662318i | \(-0.769573\pi\) | ||
0.749223 | − | 0.662318i | \(-0.230427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.6423 | −0.0462802 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −80.5853 | + | 163.037i | −0.0852754 | + | 0.172526i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 675.978i | 0.713810i | 0.934141 | + | 0.356905i | \(0.116168\pi\) | ||||
−0.934141 | + | 0.356905i | \(0.883832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 258.245 | 0.272123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 465.517i | − | 0.489502i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1098.24i | − | 1.15240i | −0.817308 | − | 0.576201i | \(-0.804534\pi\) | ||
0.817308 | − | 0.576201i | \(-0.195466\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −294.730 | − | 54.2864i | −0.308618 | − | 0.0568444i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.1472 | 0.0356815 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 641.928 | + | 182.443i | 0.669372 | + | 0.190243i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2297.80 | −2.39105 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 520.686i | 0.540692i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −222.759 | + | 1209.40i | −0.230839 | + | 1.25326i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1345.41i | 1.39132i | 0.718370 | + | 0.695661i | \(0.244889\pi\) | ||||
−0.718370 | + | 0.695661i | \(0.755111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 285.204i | 0.294328i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1230.36i | − | 1.26710i | −0.773701 | − | 0.633551i | \(-0.781597\pi\) | ||
0.773701 | − | 0.633551i | \(-0.218403\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1599.75 | + | 454.668i | 1.64415 | + | 0.467284i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −195.635 | − | 74.5990i | −0.200651 | − | 0.0765118i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 228.116i | 0.233487i | 0.993162 | + | 0.116743i | \(0.0372455\pi\) | ||||
−0.993162 | + | 0.116743i | \(0.962755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1777.40i | 1.81553i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 149.990 | 0.152895 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1721.09 | 1.75085 | 0.875425 | − | 0.483354i | \(-0.160582\pi\) | ||||
0.875425 | + | 0.483354i | \(0.160582\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −74.3227 | + | 403.510i | −0.0754545 | + | 0.409654i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −257.417 | + | 905.724i | −0.260807 | + | 0.917654i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 239.964 | 0.242633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1911.05 | 1.92841 | 0.964205 | − | 0.265159i | \(-0.0854244\pi\) | ||||
0.964205 | + | 0.265159i | \(0.0854244\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 961.319 | 0.968095 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −262.059 | + | 1422.76i | −0.263376 | + | 1.42991i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.3627 | −0.0314571 | −0.0157285 | − | 0.999876i | \(-0.505007\pi\) | ||||
−0.0157285 | + | 0.999876i | \(0.505007\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 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 | 1680.3.bd.a.769.8 | 16 | ||
4.3 | odd | 2 | 210.3.h.a.139.8 | yes | 16 | ||
5.4 | even | 2 | inner | 1680.3.bd.a.769.10 | 16 | ||
7.6 | odd | 2 | inner | 1680.3.bd.a.769.9 | 16 | ||
12.11 | even | 2 | 630.3.h.e.559.9 | 16 | |||
20.3 | even | 4 | 1050.3.f.e.601.8 | 16 | |||
20.7 | even | 4 | 1050.3.f.e.601.9 | 16 | |||
20.19 | odd | 2 | 210.3.h.a.139.9 | yes | 16 | ||
28.27 | even | 2 | 210.3.h.a.139.1 | ✓ | 16 | ||
35.34 | odd | 2 | inner | 1680.3.bd.a.769.7 | 16 | ||
60.59 | even | 2 | 630.3.h.e.559.8 | 16 | |||
84.83 | odd | 2 | 630.3.h.e.559.16 | 16 | |||
140.27 | odd | 4 | 1050.3.f.e.601.13 | 16 | |||
140.83 | odd | 4 | 1050.3.f.e.601.4 | 16 | |||
140.139 | even | 2 | 210.3.h.a.139.16 | yes | 16 | ||
420.419 | odd | 2 | 630.3.h.e.559.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.1 | ✓ | 16 | 28.27 | even | 2 | ||
210.3.h.a.139.8 | yes | 16 | 4.3 | odd | 2 | ||
210.3.h.a.139.9 | yes | 16 | 20.19 | odd | 2 | ||
210.3.h.a.139.16 | yes | 16 | 140.139 | even | 2 | ||
630.3.h.e.559.1 | 16 | 420.419 | odd | 2 | |||
630.3.h.e.559.8 | 16 | 60.59 | even | 2 | |||
630.3.h.e.559.9 | 16 | 12.11 | even | 2 | |||
630.3.h.e.559.16 | 16 | 84.83 | odd | 2 | |||
1050.3.f.e.601.4 | 16 | 140.83 | odd | 4 | |||
1050.3.f.e.601.8 | 16 | 20.3 | even | 4 | |||
1050.3.f.e.601.9 | 16 | 20.7 | even | 4 | |||
1050.3.f.e.601.13 | 16 | 140.27 | odd | 4 | |||
1680.3.bd.a.769.7 | 16 | 35.34 | odd | 2 | inner | ||
1680.3.bd.a.769.8 | 16 | 1.1 | even | 1 | trivial | ||
1680.3.bd.a.769.9 | 16 | 7.6 | odd | 2 | inner | ||
1680.3.bd.a.769.10 | 16 | 5.4 | even | 2 | inner |