Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 38255 x^{8} + 1483053595 x^{6} - 139470625170 x^{5} + 5194605060018 x^{4} + \cdots + 15\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8}\cdot 7^{3} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(139.521 - 80.5522i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.145 |
Dual form | 252.9.z.b.73.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −111.592 | − | 64.4274i | −0.178546 | − | 0.103084i | 0.408063 | − | 0.912954i | \(-0.366204\pi\) |
−0.586610 | + | 0.809870i | \(0.699538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2392.99 | + | 195.963i | 0.996664 | + | 0.0816174i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14456.4 | + | 25039.2i | 0.987393 | + | 1.71021i | 0.630780 | + | 0.775962i | \(0.282735\pi\) |
0.356612 | + | 0.934252i | \(0.383932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39655.0i | 1.38843i | 0.719766 | + | 0.694216i | \(0.244249\pi\) | ||||
−0.719766 | + | 0.694216i | \(0.755751\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 68706.8 | − | 39667.9i | 0.822629 | − | 0.474945i | −0.0286935 | − | 0.999588i | \(-0.509135\pi\) |
0.851322 | + | 0.524643i | \(0.175801\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61517.2 | + | 35517.0i | 0.472044 | + | 0.272535i | 0.717095 | − | 0.696976i | \(-0.245471\pi\) |
−0.245051 | + | 0.969510i | \(0.578805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −182396. | + | 315919.i | −0.651784 | + | 1.12892i | 0.330905 | + | 0.943664i | \(0.392646\pi\) |
−0.982690 | + | 0.185259i | \(0.940687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −187011. | − | 323912.i | −0.478747 | − | 0.829215i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −765205. | −1.08190 | −0.540948 | − | 0.841056i | \(-0.681934\pi\) | ||||
−0.540948 | + | 0.841056i | \(0.681934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −499130. | + | 288173.i | −0.540464 | + | 0.312037i | −0.745267 | − | 0.666766i | \(-0.767678\pi\) |
0.204803 | + | 0.978803i | \(0.434345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −254412. | − | 176042.i | −0.169537 | − | 0.117312i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.57572e6 | − | 2.72923e6i | 0.840762 | − | 1.45624i | −0.0484895 | − | 0.998824i | \(-0.515441\pi\) |
0.889251 | − | 0.457419i | \(-0.151226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.40539e6i | 0.851235i | 0.904903 | + | 0.425617i | \(0.139943\pi\) | ||||
−0.904903 | + | 0.425617i | \(0.860057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.03645e6 | 1.18066 | 0.590332 | − | 0.807161i | \(-0.298997\pi\) | ||||
0.590332 | + | 0.807161i | \(0.298997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.04429e6 | − | 1.18027e6i | −0.418939 | − | 0.241874i | 0.275684 | − | 0.961248i | \(-0.411096\pi\) |
−0.694623 | + | 0.719374i | \(0.744429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.68800e6 | + | 937877.i | 0.986677 | + | 0.162690i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.86610e6 | + | 3.23217e6i | 0.236500 | + | 0.409629i | 0.959707 | − | 0.281001i | \(-0.0906665\pi\) |
−0.723208 | + | 0.690630i | \(0.757333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.72556e6i | − | 0.407137i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.79677e7 | + | 1.03737e7i | −1.48281 | + | 0.856100i | −0.999809 | − | 0.0195213i | \(-0.993786\pi\) |
−0.482999 | + | 0.875621i | \(0.660452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72341e7 | − | 9.95010e6i | −1.24471 | − | 0.718634i | −0.274662 | − | 0.961541i | \(-0.588566\pi\) |
−0.970050 | + | 0.242906i | \(0.921899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.55487e6 | − | 4.42517e6i | 0.143125 | − | 0.247900i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.98086e6 | + | 8.62710e6i | 0.247175 | + | 0.428120i | 0.962741 | − | 0.270425i | \(-0.0871643\pi\) |
−0.715566 | + | 0.698546i | \(0.753831\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.20838e7 | −0.869041 | −0.434520 | − | 0.900662i | \(-0.643082\pi\) | ||||
−0.434520 | + | 0.900662i | \(0.643082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.52062e7 | − | 2.60998e7i | 1.59187 | − | 0.919065i | 0.598880 | − | 0.800839i | \(-0.295613\pi\) |
0.992987 | − | 0.118226i | \(-0.0377207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.96873e7 | + | 6.27516e7i | 0.844515 | + | 1.78510i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.40366e7 | + | 2.43122e7i | −0.360375 | + | 0.624188i | −0.988023 | − | 0.154310i | \(-0.950685\pi\) |
0.627647 | + | 0.778498i | \(0.284018\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.12932e7i | 0.659382i | 0.944089 | + | 0.329691i | \(0.106945\pi\) | ||||
−0.944089 | + | 0.329691i | \(0.893055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.02228e7 | −0.195837 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.95320e7 | − | 3.43708e7i | −0.948834 | − | 0.547810i | −0.0561157 | − | 0.998424i | \(-0.517872\pi\) |
−0.892719 | + | 0.450615i | \(0.851205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.77093e6 | + | 9.48941e7i | −0.113320 | + | 1.38380i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.57653e6 | − | 7.92679e6i | −0.0561878 | − | 0.0973202i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.71832e7i | 1.09775i | 0.835904 | + | 0.548876i | \(0.184944\pi\) | ||||
−0.835904 | + | 0.548876i | \(0.815056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.77035e8 | − | 1.02211e8i | 1.70127 | − | 0.982229i | 0.756791 | − | 0.653657i | \(-0.226766\pi\) |
0.944479 | − | 0.328572i | \(-0.106567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.33010e7 | − | 4.80939e7i | −0.740119 | − | 0.427308i | 0.0819937 | − | 0.996633i | \(-0.473871\pi\) |
−0.822112 | + | 0.569325i | \(0.807205\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.45930e7 | + | 9.45579e7i | −0.416487 | + | 0.721377i | −0.995583 | − | 0.0938820i | \(-0.970072\pi\) |
0.579096 | + | 0.815259i | \(0.303406\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.19057e8 | − | 2.06214e8i | −0.843433 | − | 1.46087i | −0.886975 | − | 0.461818i | \(-0.847197\pi\) |
0.0435416 | − | 0.999052i | \(-0.486136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.73456e7 | −0.413043 | −0.206521 | − | 0.978442i | \(-0.566214\pi\) | ||||
−0.206521 | + | 0.978442i | \(0.566214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.07077e7 | − | 2.35026e7i | 0.232748 | − | 0.134377i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.72188e8 | − | 8.14608e7i | 0.858648 | − | 0.406219i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.10796e8 | + | 5.38315e8i | −1.44989 | + | 2.51128i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.85284e7i | 0.403572i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.24587e7 | 0.0478916 | 0.0239458 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239458 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.18661e6 | − | 685092.i | −0.00402925 | − | 0.00232629i | 0.497984 | − | 0.867186i | \(-0.334074\pi\) |
−0.502013 | + | 0.864860i | \(0.667407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.40250e8 | + | 9.70469e7i | 0.448225 | + | 0.310152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.28408e8 | + | 5.68819e8i | 0.932247 | + | 1.61470i | 0.779470 | + | 0.626439i | \(0.215488\pi\) |
0.152777 | + | 0.988261i | \(0.451178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.36252e8i | 0.364991i | 0.983207 | + | 0.182496i | \(0.0584175\pi\) | ||||
−0.983207 | + | 0.182496i | \(0.941582\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.92932e8 | + | 5.73269e8i | −2.37452 | + | 1.37093i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.53904e7 | + | 4.93001e7i | 0.193169 | + | 0.111526i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.27005e8 | + | 3.93184e8i | −0.460565 | + | 0.797721i | −0.998989 | − | 0.0449524i | \(-0.985686\pi\) |
0.538424 | + | 0.842674i | \(0.319020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.13822e8 | + | 5.43555e8i | 0.603636 | + | 1.04553i | 0.992265 | + | 0.124134i | \(0.0396152\pi\) |
−0.388630 | + | 0.921394i | \(0.627051\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.42649e7 | 0.128664 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.74432e8 | − | 1.00708e8i | 0.287095 | − | 0.165755i | −0.349536 | − | 0.936923i | \(-0.613661\pi\) |
0.636631 | + | 0.771168i | \(0.280327\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.98380e8 | + | 7.20248e8i | −0.741749 | + | 1.07196i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.33704e8 | − | 2.31582e8i | 0.189406 | − | 0.328061i | −0.755646 | − | 0.654980i | \(-0.772677\pi\) |
0.945052 | + | 0.326919i | \(0.106010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.34333e8i | 0.429846i | 0.976631 | + | 0.214923i | \(0.0689501\pi\) | ||||
−0.976631 | + | 0.214923i | \(0.931050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.56791e8 | −0.927746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.44134e7 | + | 8.32156e6i | 0.0160909 | + | 0.00929010i | 0.508024 | − | 0.861343i | \(-0.330376\pi\) |
−0.491933 | + | 0.870633i | \(0.663709\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.84040e8 | − | 8.11765e8i | −0.409472 | − | 0.865523i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.74376e8 | + | 4.75233e8i | 0.267260 | + | 0.462908i | 0.968153 | − | 0.250358i | \(-0.0805485\pi\) |
−0.700893 | + | 0.713266i | \(0.747215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.47149e8i | − | 0.602962i | −0.953472 | − | 0.301481i | \(-0.902519\pi\) | ||
0.953472 | − | 0.301481i | \(-0.0974810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.51675e8 | + | 2.03040e8i | −0.300230 | + | 0.173338i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.98651e9 | + | 1.14691e9i | 1.62451 | + | 0.937914i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.30628e8 | + | 1.26549e9i | −0.548988 | + | 0.950875i | 0.449356 | + | 0.893353i | \(0.351653\pi\) |
−0.998344 | + | 0.0575225i | \(0.981680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.13052e8 | − | 3.69017e8i | −0.153552 | − | 0.265961i | 0.778979 | − | 0.627051i | \(-0.215738\pi\) |
−0.932531 | + | 0.361090i | \(0.882405\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.63708e8 | −0.108694 | −0.0543469 | − | 0.998522i | \(-0.517308\pi\) | ||||
−0.0543469 | + | 0.998522i | \(0.517308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.59492e9 | + | 9.20826e8i | −1.01701 | + | 0.587172i | −0.913237 | − | 0.407429i | \(-0.866425\pi\) |
−0.103775 | + | 0.994601i | \(0.533092\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.83113e9 | − | 1.49952e8i | −1.07829 | − | 0.0883015i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.54973e8 | − | 2.68421e8i | 0.0877486 | − | 0.151985i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.05379e9i | 1.07639i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.46982e9 | 1.24605 | 0.623024 | − | 0.782203i | \(-0.285904\pi\) | ||||
0.623024 | + | 0.782203i | \(0.285904\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.50434e8 | − | 2.60058e8i | −0.210803 | − | 0.121707i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.25088e9 | + | 5.91784e8i | −0.564129 | + | 0.266885i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.57303e9 | + | 2.72457e9i | 0.659429 | + | 1.14216i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.01259e9i | 1.21821i | 0.793091 | + | 0.609103i | \(0.208470\pi\) | ||||
−0.793091 | + | 0.609103i | \(0.791530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.04253e7 | − | 2.91131e7i | 0.0189909 | − | 0.0109644i | −0.490474 | − | 0.871456i | \(-0.663177\pi\) |
0.509465 | + | 0.860491i | \(0.329843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.41882e8 | − | 3.12856e8i | −0.197044 | − | 0.113763i | 0.398232 | − | 0.917285i | \(-0.369624\pi\) |
−0.595276 | + | 0.803521i | \(0.702957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.06028e9 | − | 3.56850e9i | 0.699040 | − | 1.21077i | −0.269760 | − | 0.962928i | \(-0.586944\pi\) |
0.968800 | − | 0.247845i | \(-0.0797223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.52084e8 | + | 2.63416e8i | 0.0498667 | + | 0.0863717i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.56676e9 | 0.480186 | 0.240093 | − | 0.970750i | \(-0.422822\pi\) | ||||
0.240093 | + | 0.970750i | \(0.422822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00073e9 | + | 1.15512e9i | −0.593091 | + | 0.342421i | −0.766319 | − | 0.642461i | \(-0.777914\pi\) |
0.173228 | + | 0.984882i | \(0.444580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.74307e8 | − | 4.71122e8i | −0.159397 | − | 0.130758i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.40843e9 | + | 2.43947e9i | −0.378396 | + | 0.655401i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.63498e7i | − | 0.0167165i | −0.999965 | − | 0.00835823i | \(-0.997339\pi\) | ||
0.999965 | − | 0.00835823i | \(-0.00266054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.05472e10 | −2.57427 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.28769e9 | + | 7.43447e8i | 0.295174 | + | 0.170419i | 0.640273 | − | 0.768148i | \(-0.278821\pi\) |
−0.345099 | + | 0.938566i | \(0.612155\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.30552e9 | − | 6.22224e9i | 0.956812 | − | 1.38276i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.54599e9 | − | 4.40979e9i | −0.532151 | − | 0.921712i | −0.999295 | − | 0.0375311i | \(-0.988051\pi\) |
0.467145 | − | 0.884181i | \(-0.345283\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.80911e8i | − | 0.0975171i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.13647e9 | − | 4.12024e9i | 1.36293 | − | 0.786890i | 0.372920 | − | 0.927864i | \(-0.378357\pi\) |
0.990013 | + | 0.140974i | \(0.0450234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.02331e9 | + | 2.32286e9i | 0.745944 | + | 0.430671i | 0.824227 | − | 0.566260i | \(-0.191610\pi\) |
−0.0782825 | + | 0.996931i | \(0.524944\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.40701e9 | − | 9.36521e9i | 0.945423 | − | 1.63752i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.25437e9 | + | 2.17264e9i | 0.213063 | + | 0.369036i | 0.952672 | − | 0.304001i | \(-0.0983228\pi\) |
−0.739609 | + | 0.673037i | \(0.764989\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.18908e9 | −0.351104 | −0.175552 | − | 0.984470i | \(-0.556171\pi\) | ||||
−0.175552 | + | 0.984470i | \(0.556171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.54119e8 | − | 3.19921e8i | 0.0863887 | − | 0.0498766i | −0.456183 | − | 0.889886i | \(-0.650784\pi\) |
0.542572 | + | 0.840009i | \(0.317451\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.71368e8 | + | 5.75606e9i | −0.0694756 | + | 0.848395i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.40799e8 | + | 5.90282e8i | −0.0488548 | + | 0.0846191i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.48526e9i | 0.201527i | 0.994910 | + | 0.100763i | \(0.0321285\pi\) | ||||
−0.994910 | + | 0.100763i | \(0.967871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.67339e9 | 0.353000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.25278e10 | − | 7.23292e9i | −1.56743 | − | 0.904958i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.65919e9 | + | 7.90997e8i | 1.17672 | + | 0.0963627i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.28212e9 | + | 2.22069e9i | 0.148159 | + | 0.256619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.33187e10i | − | 1.49937i | −0.661793 | − | 0.749687i | \(-0.730204\pi\) | ||
0.661793 | − | 0.749687i | \(-0.269796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.31513e9 | − | 1.91399e9i | 0.354372 | − | 0.204597i | −0.312237 | − | 0.950004i | \(-0.601078\pi\) |
0.666609 | + | 0.745407i | \(0.267745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.91930e9 | + | 1.10811e9i | 0.199971 | + | 0.115453i | 0.596642 | − | 0.802508i | \(-0.296501\pi\) |
−0.396671 | + | 0.917961i | \(0.629835\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.52992e8 | − | 4.38195e8i | 0.0250536 | − | 0.0433940i | −0.853227 | − | 0.521540i | \(-0.825358\pi\) |
0.878280 | + | 0.478146i | \(0.158691\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.10621e10 | − | 1.91601e10i | −1.06826 | − | 1.85027i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.63553e9 | 0.517756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.28447e10 | − | 7.41592e9i | 1.15131 | − | 0.664709i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.66067e9 | − | 3.22498e9i | −0.397800 | − | 0.275260i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.85009e9 | + | 1.35968e10i | −0.653978 | + | 1.13272i | 0.328171 | + | 0.944618i | \(0.393568\pi\) |
−0.982149 | + | 0.188104i | \(0.939766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.28362e9i | − | 0.101919i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.56196e9 | 0.121101 | 0.0605507 | − | 0.998165i | \(-0.480714\pi\) | ||||
0.0605507 | + | 0.998165i | \(0.480714\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.44313e10 | − | 8.33189e9i | −1.06730 | − | 0.616206i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.34275e10 | + | 3.35897e9i | 0.970107 | + | 0.242677i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.09009e9 | + | 8.81629e9i | 0.351081 | + | 0.608090i | 0.986439 | − | 0.164127i | \(-0.0524808\pi\) |
−0.635358 | + | 0.772218i | \(0.719147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.88299e10i | − | 1.94331i | −0.236403 | − | 0.971655i | \(-0.575968\pi\) | ||
0.236403 | − | 0.971655i | \(-0.424032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.38733e9 | − | 4.26508e9i | 0.475761 | − | 0.274681i | −0.242887 | − | 0.970055i | \(-0.578095\pi\) |
0.718648 | + | 0.695374i | \(0.244761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.46436e9 | + | 1.42280e9i | 0.155164 | + | 0.0895840i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.99690e9 | − | 1.03869e10i | 0.361035 | − | 0.625330i | −0.627097 | − | 0.778941i | \(-0.715757\pi\) |
0.988131 | + | 0.153611i | \(0.0490903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.96887e9 | − | 1.03384e10i | −0.351450 | − | 0.608729i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.72618e9 | −0.378963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.66442e9 | − | 9.60953e8i | 0.0917484 | − | 0.0529710i | −0.453424 | − | 0.891295i | \(-0.649798\pi\) |
0.545172 | + | 0.838324i | \(0.316464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.83216e9 | + | 8.10024e9i | 0.202278 | + | 0.427565i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.22841e10 | + | 2.12767e10i | −0.634611 | + | 1.09918i | 0.351987 | + | 0.936005i | \(0.385506\pi\) |
−0.986597 | + | 0.163173i | \(0.947827\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.03442e10i | − | 1.50214i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.64148e10 | 0.795569 | 0.397785 | − | 0.917479i | \(-0.369779\pi\) | ||||
0.397785 | + | 0.917479i | \(0.369779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.04919e10 | − | 6.05749e9i | −0.487594 | − | 0.281512i | 0.235982 | − | 0.971757i | \(-0.424169\pi\) |
−0.723576 | + | 0.690245i | \(0.757503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.30073e8 | − | 8.91522e9i | 0.0332295 | − | 0.405779i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.60896e9 | + | 4.51886e9i | 0.113938 | + | 0.197347i | 0.917355 | − | 0.398070i | \(-0.130320\pi\) |
−0.803417 | + | 0.595417i | \(0.796987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.89410e10i | 1.23825i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.13274e9 | − | 1.80869e9i | 0.128687 | − | 0.0742977i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.21404e10 | + | 1.27828e10i | 0.891298 | + | 0.514591i | 0.874367 | − | 0.485265i | \(-0.161277\pi\) |
0.0169314 | + | 0.999857i | \(0.494610\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.85899e10 | − | 3.21987e10i | 0.718953 | − | 1.24526i | −0.242462 | − | 0.970161i | \(-0.577955\pi\) |
0.961415 | − | 0.275102i | \(-0.0887117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.14275e10 | − | 1.97930e10i | −0.433243 | − | 0.750398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.11172e10 | 3.32065 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.06294e10 | − | 6.13691e9i | 0.379854 | − | 0.219309i | −0.297901 | − | 0.954597i | \(-0.596286\pi\) |
0.677755 | + | 0.735288i | \(0.262953\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.50294e10 | + | 2.13031e10i | −1.54773 | + | 0.732221i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.01614e9 | − | 3.49205e9i | 0.0679717 | − | 0.117730i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.76170e10i | − | 0.571577i | −0.958293 | − | 0.285788i | \(-0.907745\pi\) | ||
0.958293 | − | 0.285788i | \(-0.0922555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.40629e10 | −1.72096 | −0.860480 | − | 0.509485i | \(-0.829836\pi\) | ||||
−0.860480 | + | 0.509485i | \(0.829836\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.56978e10 | − | 1.48366e10i | −0.787663 | − | 0.454757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.92911e10 | − | 2.71877e10i | −1.18191 | − | 0.817827i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.23020e9 | + | 1.42551e10i | 0.238507 | + | 0.413106i | 0.960286 | − | 0.279017i | \(-0.0900086\pi\) |
−0.721779 | + | 0.692124i | \(0.756675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.03523e10i | 0.578978i | 0.957181 | + | 0.289489i | \(0.0934853\pi\) | ||||
−0.957181 | + | 0.289489i | \(0.906515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.24410e10 | + | 1.29563e10i | −0.615341 | + | 0.355268i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.98300e10 | + | 1.14488e10i | 0.533905 | + | 0.308250i | 0.742605 | − | 0.669730i | \(-0.233590\pi\) |
−0.208700 | + | 0.977980i | \(0.566923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.69660e10 | − | 2.93860e10i | 0.440520 | − | 0.763003i | −0.557208 | − | 0.830373i | \(-0.688127\pi\) |
0.997728 | + | 0.0673700i | \(0.0214608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.42884e9 | + | 7.67098e9i | 0.112941 | + | 0.195619i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.99826e10 | −1.47584 | −0.737921 | − | 0.674887i | \(-0.764192\pi\) | ||||
−0.737921 | + | 0.674887i | \(0.764192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.02291e10 | + | 3.47733e10i | −1.45579 | + | 0.840503i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.98095e9 | − | 1.00887e10i | 0.162880 | − | 0.235391i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.57618e10 | + | 2.73002e10i | −0.361361 | + | 0.625895i | −0.988185 | − | 0.153266i | \(-0.951021\pi\) |
0.626824 | + | 0.779161i | \(0.284354\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.38684e10i | 1.19270i | 0.802725 | + | 0.596349i | \(0.203383\pi\) | ||||
−0.802725 | + | 0.596349i | \(0.796617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.39076e9 | 0.139068 | 0.0695342 | − | 0.997580i | \(-0.477849\pi\) | ||||
0.0695342 | + | 0.997580i | \(0.477849\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.01832e10 | + | 2.89733e10i | 1.05509 | + | 0.609158i | 0.924071 | − | 0.382222i | \(-0.124841\pi\) |
0.131022 | + | 0.991380i | \(0.458174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.02286e10 | + | 2.16206e10i | 0.211409 | + | 0.446866i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.83527e10 | + | 1.01070e11i | 1.16578 | + | 2.01919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.65682e10i | − | 0.521901i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.54905e10 | − | 1.47170e10i | 0.484214 | − | 0.279561i | −0.237957 | − | 0.971276i | \(-0.576478\pi\) |
0.722171 | + | 0.691715i | \(0.243144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.08228e11 | + | 6.24853e10i | 2.02189 | + | 1.16734i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.26126e9 | − | 1.08448e10i | 0.113161 | − | 0.196000i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.23988e8 | − | 9.07574e8i | −0.00931549 | − | 0.0161349i | 0.861330 | − | 0.508046i | \(-0.169632\pi\) |
−0.870646 | + | 0.491911i | \(0.836299\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.26283e10 | −1.42168 | −0.710842 | − | 0.703352i | \(-0.751686\pi\) | ||||
−0.710842 | + | 0.703352i | \(0.751686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.25747e10 | + | 3.03540e10i | −0.889999 | + | 0.513841i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.28463e10 | − | 4.32761e9i | −0.866141 | − | 0.0709288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.74791e10 | − | 3.02747e10i | 0.281914 | − | 0.488290i | −0.689942 | − | 0.723865i | \(-0.742364\pi\) |
0.971856 | + | 0.235575i | \(0.0756972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.71506e10i | 0.736573i | 0.929712 | + | 0.368286i | \(0.120055\pi\) | ||||
−0.929712 | + | 0.368286i | \(0.879945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.63408e10 | −0.405008 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.53536e10 | − | 8.86441e9i | −0.228739 | − | 0.132062i | 0.381251 | − | 0.924471i | \(-0.375493\pi\) |
−0.609990 | + | 0.792409i | \(0.708827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.13293e11 | − | 5.35978e10i | 1.66157 | − | 0.786074i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.19713e9 | + | 1.07337e10i | 0.0880971 | + | 0.152589i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.82499e10i | − | 0.955300i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.72635e10 | + | 5.61551e10i | −1.32008 | + | 0.762147i | −0.983741 | − | 0.179595i | \(-0.942521\pi\) |
−0.336336 | + | 0.941742i | \(0.609188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.21210e10 | − | 1.27716e10i | −0.295664 | − | 0.170702i | 0.344829 | − | 0.938665i | \(-0.387937\pi\) |
−0.640494 | + | 0.767964i | \(0.721270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.28624e10 | + | 3.95989e10i | −0.296401 | + | 0.513381i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.73811e10 | − | 4.74254e10i | −0.349645 | − | 0.605603i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.53857e10 | −1.18188 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21842e10 | − | 7.03457e9i | 0.148725 | − | 0.0858663i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.87443e10 | + | 1.55981e11i | 0.696003 | + | 1.84807i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.31041e9 | − | 1.43941e10i | 0.0970138 | − | 0.168033i | −0.813433 | − | 0.581658i | \(-0.802404\pi\) |
0.910447 | + | 0.413625i | \(0.135738\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.06823e10i | 0.347777i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.80622e10 | −0.313453 | −0.156727 | − | 0.987642i | \(-0.550094\pi\) | ||||
−0.156727 | + | 0.987642i | \(0.550094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.70733e10 | − | 2.71778e10i | −0.510702 | − | 0.294854i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.83538e10 | + | 5.54281e10i | −0.410117 | + | 0.592693i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.66577e10 | − | 1.32775e11i | −0.796407 | − | 1.37942i | −0.921942 | − | 0.387328i | \(-0.873398\pi\) |
0.125535 | − | 0.992089i | \(-0.459935\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.60066e11i | 1.63927i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.23010e10 | − | 1.86490e10i | 0.321501 | − | 0.185619i | −0.330560 | − | 0.943785i | \(-0.607238\pi\) |
0.652062 | + | 0.758166i | \(0.273904\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.51519e9 | + | 4.33890e9i | 0.0737473 | + | 0.0425781i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.60551e10 | + | 1.31731e11i | −0.725570 | + | 1.25672i | 0.233169 | + | 0.972436i | \(0.425090\pi\) |
−0.958739 | + | 0.284288i | \(0.908243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.27147e10 | + | 5.66635e10i | 0.307750 | + | 0.533039i | 0.977870 | − | 0.209214i | \(-0.0670906\pi\) |
−0.670120 | + | 0.742253i | \(0.733757\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.36440e11 | 1.24816 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.48040e10 | − | 5.47351e10i | 0.855310 | − | 0.493813i | −0.00712906 | − | 0.999975i | \(-0.502269\pi\) |
0.862439 | + | 0.506161i | \(0.168936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.13232e9 | + | 7.48842e10i | −0.0538171 | + | 0.657182i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.39541e10 | + | 9.34512e10i | −0.467036 | + | 0.808930i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.75131e11i | 1.47507i | 0.675311 | + | 0.737533i | \(0.264009\pi\) | ||||
−0.675311 | + | 0.737533i | \(0.735991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.09401e10 | −0.340164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.28936e11 | + | 7.44413e10i | 1.04269 | + | 0.601998i | 0.920595 | − | 0.390520i | \(-0.127705\pi\) |
0.122097 | + | 0.992518i | \(0.461038\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.44630e10 | − | 2.00329e9i | −0.195183 | − | 0.0159837i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.71938e10 | + | 4.71010e10i | 0.211233 | + | 0.365867i | 0.952101 | − | 0.305785i | \(-0.0989187\pi\) |
−0.740868 | + | 0.671651i | \(0.765585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.23469e10i | − | 0.477878i | −0.971035 | − | 0.238939i | \(-0.923200\pi\) | ||
0.971035 | − | 0.238939i | \(-0.0767996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.93645e10 | − | 4.00476e10i | 0.517745 | − | 0.298920i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.11628e9 | + | 4.68593e9i | 0.0597864 | + | 0.0345177i | 0.529595 | − | 0.848250i | \(-0.322344\pi\) |
−0.469809 | + | 0.882768i | \(0.655677\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.68037e10 | − | 8.10663e10i | 0.335826 | − | 0.581668i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.19383e10 | + | 7.26393e10i | 0.297009 | + | 0.514434i | 0.975450 | − | 0.220220i | \(-0.0706776\pi\) |
−0.678441 | + | 0.734654i | \(0.737344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.87511e10 | −0.198387 | −0.0991935 | − | 0.995068i | \(-0.531626\pi\) | ||||
−0.0991935 | + | 0.995068i | \(0.531626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.02776e10 | − | 1.74808e10i | 0.206233 | − | 0.119069i | −0.393327 | − | 0.919399i | \(-0.628676\pi\) |
0.599560 | + | 0.800330i | \(0.295342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.35724e11 | − | 9.39151e10i | −0.900958 | − | 0.623423i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.67031e10 | + | 1.15533e11i | −0.437146 | + | 0.757158i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.50022e11i | − | 1.59726i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.82364e10 | 0.241190 | 0.120595 | − | 0.992702i | \(-0.461520\pi\) | ||||
0.120595 | + | 0.992702i | \(0.461520\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.39029e9 | − | 8.02684e8i | −0.00855088 | − | 0.00493685i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.71915e10 | + | 2.25558e11i | −0.225884 | + | 1.36993i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.73930e10 | − | 8.20871e10i | −0.280726 | − | 0.486231i | 0.690838 | − | 0.723010i | \(-0.257242\pi\) |
−0.971564 | + | 0.236779i | \(0.923908\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.11036e11i | − | 1.23456i | −0.786743 | − | 0.617281i | \(-0.788234\pi\) | ||
0.786743 | − | 0.617281i | \(-0.211766\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.30606e11 | − | 1.33140e11i | 1.31599 | − | 0.759788i | 0.332910 | − | 0.942959i | \(-0.391969\pi\) |
0.983081 | + | 0.183171i | \(0.0586361\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.19498e11 | − | 2.99932e11i | −2.92823 | − | 1.69061i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.84667e9 | + | 6.66262e9i | −0.0211559 | + | 0.0366431i | −0.876410 | − | 0.481567i | \(-0.840068\pi\) |
0.855254 | + | 0.518210i | \(0.173401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.82774e7 | + | 1.52901e8i | 0.000479605 | + | 0.000830701i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.44191e11 | −0.764533 | −0.382267 | − | 0.924052i | \(-0.624856\pi\) | ||||
−0.382267 | + | 0.924052i | \(0.624856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.57512e10 | + | 4.95085e10i | −0.449195 | + | 0.259343i | −0.707490 | − | 0.706723i | \(-0.750173\pi\) |
0.258295 | + | 0.966066i | \(0.416839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.39824e9 | − | 1.98656e10i | −0.0480574 | − | 0.101581i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.39570e11 | − | 2.41743e11i | 0.705163 | − | 1.22138i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.75371e11i | − | 2.83830i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.97102e10 | 0.0960796 | 0.0480398 | − | 0.998845i | \(-0.484703\pi\) | ||||
0.0480398 | + | 0.998845i | \(0.484703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.24608e11 | + | 1.29677e11i | 1.06923 | + | 0.617319i | 0.927970 | − | 0.372654i | \(-0.121552\pi\) |
0.141257 | + | 0.989973i | \(0.454886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.90444e10 | + | 2.32558e11i | −0.0895957 | + | 1.09409i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.61231e10 | + | 7.98876e10i | 0.211951 | + | 0.367110i | 0.952325 | − | 0.305085i | \(-0.0986849\pi\) |
−0.740374 | + | 0.672195i | \(0.765352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.46339e10i | − | 0.384399i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.28172e11 | + | 7.40001e10i | −0.568743 | + | 0.328364i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.27987e11 | + | 1.89364e11i | 1.43862 | + | 0.830585i | 0.997754 | − | 0.0669894i | \(-0.0213394\pi\) |
0.440862 | + | 0.897575i | \(0.354673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.77834e9 | − | 1.52045e10i | 0.0376247 | − | 0.0651679i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.54165e10 | + | 1.65266e11i | 0.404290 | + | 0.700250i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.60282e10 | −0.190613 | −0.0953064 | − | 0.995448i | \(-0.530383\pi\) | ||||
−0.0953064 | + | 0.995448i | \(0.530383\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.93868e11 | − | 1.11930e11i | 0.793753 | − | 0.458273i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.43672e11 | − | 2.09898e11i | 1.77576 | − | 0.840099i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.64597e10 | − | 2.85091e10i | 0.0651385 | − | 0.112823i | −0.831617 | − | 0.555350i | \(-0.812584\pi\) |
0.896755 | + | 0.442527i | \(0.145918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.10246e11i | − | 0.813524i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.47737e11 | 0.565282 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.28200e11 | + | 7.40164e10i | 0.479704 | + | 0.276957i | 0.720293 | − | 0.693670i | \(-0.244007\pi\) |
−0.240589 | + | 0.970627i | \(0.577341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.89914e11 | − | 1.31412e11i | −0.702774 | − | 0.486289i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.43101e11 | + | 2.47859e11i | 0.517955 | + | 0.897124i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.87221e11i | − | 0.670218i | −0.942179 | − | 0.335109i | \(-0.891227\pi\) | ||
0.942179 | − | 0.335109i | \(-0.108773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.77332e11 | − | 1.60118e11i | 0.971248 | − | 0.560750i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.72527e11 | − | 1.57344e11i | −0.944047 | − | 0.545046i | −0.0528204 | − | 0.998604i | \(-0.516821\pi\) |
−0.891227 | + | 0.453558i | \(0.850154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.44011e11 | + | 2.49434e11i | −0.488118 | + | 0.845446i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.91103e11 | + | 3.31001e11i | 0.640753 | + | 1.10982i | 0.985265 | + | 0.171035i | \(0.0547111\pi\) |
−0.344512 | + | 0.938782i | \(0.611956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.66837e11 | −1.20370 | −0.601850 | − | 0.798609i | \(-0.705569\pi\) | ||||
−0.601850 | + | 0.798609i | \(0.705569\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.06637e10 | − | 2.92507e10i | 0.164464 | − | 0.0949536i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.49170e11 | + | 2.15578e11i | −0.473975 | + | 0.684978i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.58136e11 | − | 2.73899e11i | 0.497130 | − | 0.861054i | −0.502865 | − | 0.864365i | \(-0.667721\pi\) |
0.999995 | + | 0.00331119i | \(0.00105399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8.08748e10i | − | 0.248900i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.84918e10 | −0.117215 | −0.0586077 | − | 0.998281i | \(-0.518666\pi\) | ||||
−0.0586077 | + | 0.998281i | \(0.518666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.29914e11 | − | 1.32741e11i | −0.685532 | − | 0.395792i | 0.116404 | − | 0.993202i | \(-0.462863\pi\) |
−0.801936 | + | 0.597410i | \(0.796196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44493e11 | − | 5.16798e11i | −0.721387 | − | 1.52483i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.11368e11 | − | 7.12511e11i | −1.18864 | − | 2.05878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.74390e11i | 1.64248i | 0.570580 | + | 0.821242i | \(0.306719\pi\) | ||||
−0.570580 | + | 0.821242i | \(0.693281\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.81782e11 | + | 2.20422e11i | −1.06930 | + | 0.617358i | −0.927989 | − | 0.372608i | \(-0.878464\pi\) |
−0.141306 | + | 0.989966i | \(0.545130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.86685e11 | + | 1.07783e11i | 0.517492 | + | 0.298774i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.54321e10 | + | 1.47973e11i | −0.231991 | + | 0.401820i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.19252e11 | − | 5.52961e11i | −0.858084 | − | 1.48625i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.59534e10 | −0.0683465 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.86998e11 | − | 3.38904e11i | 1.53016 | − | 0.883441i | 0.530810 | − | 0.847491i | \(-0.321888\pi\) |
0.999354 | − | 0.0359500i | \(-0.0114457\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.61157e11 | − | 1.31973e10i | −0.411665 | − | 0.0337115i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.94571e11 | − | 6.83418e11i | 0.997776 | − | 1.72820i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.73315e11i | − | 1.17305i | −0.809931 | − | 0.586525i | \(-0.800495\pi\) | ||
0.809931 | − | 0.586525i | \(-0.199505\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.87275e11 | −0.459508 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.30704e12 | + | 7.54620e11i | 3.14359 | + | 1.81496i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.02019e11 | − | 4.82643e10i | 0.242939 | − | 0.114932i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.95659e11 | − | 5.12096e11i | −0.690235 | − | 1.19552i | −0.971761 | − | 0.235968i | \(-0.924174\pi\) |
0.281526 | − | 0.959554i | \(-0.409159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.08161e11i | − | 0.943513i | −0.881729 | − | 0.471756i | \(-0.843620\pi\) | ||
0.881729 | − | 0.471756i | \(-0.156380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.98404e10 | + | 1.72284e10i | −0.0676355 | + | 0.0390494i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.48311e11 | + | 1.43363e11i | 0.557325 | + | 0.321772i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.37680e11 | − | 4.11675e11i | 0.523144 | − | 0.906111i | −0.476494 | − | 0.879178i | \(-0.658092\pi\) |
0.999637 | − | 0.0269333i | \(-0.00857418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.56842e11 | + | 4.44863e11i | 0.559844 | + | 0.969678i | 0.997509 | + | 0.0705396i | \(0.0224721\pi\) |
−0.437665 | + | 0.899138i | \(0.644195\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.48614e11 | −1.60043 | −0.800214 | − | 0.599715i | \(-0.795281\pi\) | ||||
−0.800214 | + | 0.599715i | \(0.795281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.14063e10 | + | 3.54529e10i | −0.130015 | + | 0.0750644i | −0.563597 | − | 0.826050i | \(-0.690583\pi\) |
0.433582 | + | 0.901114i | \(0.357250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.28007e11 | − | 1.61192e11i | 0.888938 | − | 0.334784i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.15402e10 | − | 3.73087e10i | 0.0443102 | − | 0.0767476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.83142e11i | − | 0.773235i | −0.922240 | − | 0.386618i | \(-0.873643\pi\) | ||
0.922240 | − | 0.386618i | \(-0.126357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.52917e10 | 0.170499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.44514e10 | + | 4.87581e10i | 0.165646 | + | 0.0956356i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.49223e11 | + | 1.22728e12i | −1.65001 | + | 2.38457i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.74811e11 | + | 9.95602e11i | 1.09599 | + | 1.89831i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00261e11i | 0.378268i | 0.981951 | + | 0.189134i | \(0.0605680\pi\) | ||||
−0.981951 | + | 0.189134i | \(0.939432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.12447e11 | − | 2.95862e11i | 0.950005 | − | 0.548486i | 0.0569227 | − | 0.998379i | \(-0.481871\pi\) |
0.893083 | + | 0.449893i | \(0.148538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.34764e10 | − | 7.78060e9i | −0.0247515 | − | 0.0142903i | 0.487573 | − | 0.873082i | \(-0.337882\pi\) |
−0.512325 | + | 0.858792i | \(0.671216\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.22577e11 | − | 5.58719e11i | 0.581553 | − | 1.00728i | −0.413742 | − | 0.910394i | \(-0.635778\pi\) |
0.995295 | − | 0.0968860i | \(-0.0308882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.07227e9 | − | 1.85723e9i | −0.00191532 | − | 0.00331743i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.11678e11 | −1.42333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.42108e11 | + | 1.97516e11i | −0.594416 | + | 0.343186i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.93080e10 | + | 2.35777e11i | −0.0329385 | + | 0.402226i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.51275e11 | − | 6.08427e11i | 0.593812 | − | 1.02851i | −0.399901 | − | 0.916558i | \(-0.630955\pi\) |
0.993713 | − | 0.111955i | \(-0.0357112\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.60476e11i | 0.764369i | 0.924086 | + | 0.382185i | \(0.124828\pi\) | ||||
−0.924086 | + | 0.382185i | \(0.875172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.63870e11 | −0.927547 | −0.463774 | − | 0.885954i | \(-0.653505\pi\) | ||||
−0.463774 | + | 0.885954i | \(0.653505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.07767e11 | + | 1.77690e11i | 0.497197 | + | 0.287057i | 0.727555 | − | 0.686049i | \(-0.240657\pi\) |
−0.230358 | + | 0.973106i | \(0.573990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.98136e10 | + | 2.44146e9i | 0.0477318 | + | 0.00390879i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.38393e10 | − | 1.45214e11i | −0.131838 | − | 0.228351i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.07093e10i | − | 0.110201i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.81937e11 | − | 2.20511e11i | 0.584726 | − | 0.337592i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.56427e11 | + | 1.48048e11i | 0.389103 | + | 0.224648i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.16941e10 | + | 7.22164e10i | −0.0621557 | + | 0.107657i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.67768e11 | − | 2.90583e11i | −0.247902 | − | 0.429379i | 0.715041 | − | 0.699082i | \(-0.246408\pi\) |
−0.962944 | + | 0.269703i | \(0.913075\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.91134e11 | −1.29381 | −0.646904 | − | 0.762572i | \(-0.723936\pi\) | ||||
−0.646904 | + | 0.762572i | \(0.723936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.83557e11 | + | 4.52387e11i | −1.12768 | + | 0.651069i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.70530e9 | − | 1.87195e9i | −0.00382594 | − | 0.00264738i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.24743e11 | + | 2.16061e11i | −0.174885 | + | 0.302911i | −0.940122 | − | 0.340839i | \(-0.889289\pi\) |
0.765236 | + | 0.643750i | \(0.222622\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.75733e11i | − | 1.20660i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.17871e12 | −1.61005 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.86525e11 | + | 2.80895e11i | 0.653194 | + | 0.377122i | 0.789679 | − | 0.613521i | \(-0.210247\pi\) |
−0.136485 | + | 0.990642i | \(0.543581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.16599e11 | + | 2.59716e11i | 0.421416 | + | 0.345701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.47785e11 | − | 2.55971e11i | −0.193368 | − | 0.334922i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.30931e11i | 0.818510i | 0.912420 | + | 0.409255i | \(0.134211\pi\) | ||||
−0.912420 | + | 0.409255i | \(0.865789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.15139e11 | + | 5.28356e11i | −1.16716 | + | 0.673857i | −0.953008 | − | 0.302944i | \(-0.902030\pi\) |
−0.214147 | + | 0.976801i | \(0.568697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.59907e11 | − | 4.38733e11i | −0.960979 | − | 0.554821i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.00683e11 | + | 1.21362e12i | −0.871207 | + | 1.50898i | −0.0104586 | + | 0.999945i | \(0.503329\pi\) |
−0.860749 | + | 0.509030i | \(0.830004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.03499e12 | + | 1.79265e12i | 1.27606 | + | 2.21020i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.29698e11 | 0.763415 | 0.381707 | − | 0.924283i | \(-0.375336\pi\) | ||||
0.381707 | + | 0.924283i | \(0.375336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.63064e11 | − | 9.41450e10i | 0.196040 | − | 0.113184i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.74409e11 | + | 1.42553e12i | 0.797350 | + | 1.68540i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.60358e11 | + | 4.50954e11i | −0.305266 | + | 0.528736i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.49056e10i | 0.0633151i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.76815e11 | 1.00277 | 0.501386 | − | 0.865224i | \(-0.332824\pi\) | ||||
0.501386 | + | 0.865224i | \(0.332824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.84265e11 | + | 1.64121e11i | 0.319777 | + | 0.184623i | 0.651293 | − | 0.758826i | \(-0.274227\pi\) |
−0.331516 | + | 0.943449i | \(0.607560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.67003e10 | + | 3.26049e11i | −0.0297896 | + | 0.363774i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.77711e11 | + | 3.07804e11i | 0.195046 | + | 0.337829i | 0.946915 | − | 0.321483i | \(-0.104181\pi\) |
−0.751870 | + | 0.659311i | \(0.770848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.98751e12i | − | 2.16361i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.12439e12 | − | 6.49165e11i | 1.20421 | − | 0.695250i | 0.242720 | − | 0.970096i | \(-0.421960\pi\) |
0.961488 | + | 0.274846i | \(0.0886270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.82684e10 | + | 1.05473e10i | 0.0194069 | + | 0.0112046i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.36233e11 | + | 1.27519e12i | −0.769538 | + | 1.33288i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.60644e11 | + | 9.71063e11i | 0.581289 | + | 1.00682i | 0.995327 | + | 0.0965627i | \(0.0307848\pi\) |
−0.414038 | + | 0.910260i | \(0.635882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.37306e11 | 0.242112 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.13941e12 | − | 6.57840e11i | 1.15319 | − | 0.665794i | 0.203527 | − | 0.979069i | \(-0.434760\pi\) |
0.949662 | + | 0.313275i | \(0.101426\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.z.b.145.3 | 10 | ||
3.2 | odd | 2 | 84.9.m.a.61.3 | ✓ | 10 | ||
7.3 | odd | 6 | inner | 252.9.z.b.73.3 | 10 | ||
21.17 | even | 6 | 84.9.m.a.73.3 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.a.61.3 | ✓ | 10 | 3.2 | odd | 2 | ||
84.9.m.a.73.3 | yes | 10 | 21.17 | even | 6 | ||
252.9.z.b.73.3 | 10 | 7.3 | odd | 6 | inner | ||
252.9.z.b.145.3 | 10 | 1.1 | even | 1 | trivial |