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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(-41.5970 + 72.0480i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.9.z.d.145.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −1011.88 | + | 584.207i | −1.61900 | + | 0.934731i | −0.631822 | + | 0.775114i | \(0.717693\pi\) |
−0.987179 | + | 0.159617i | \(0.948974\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1829.74 | + | 1554.62i | −0.762075 | + | 0.647489i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13077.9 | − | 22651.7i | 0.893241 | − | 1.54714i | 0.0572739 | − | 0.998359i | \(-0.481759\pi\) |
0.835967 | − | 0.548780i | \(-0.184907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28593.8i | 1.00115i | 0.865694 | + | 0.500574i | \(0.166878\pi\) | ||||
−0.865694 | + | 0.500574i | \(0.833122\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18015.1 | + | 10401.0i | 0.215695 | + | 0.124532i | 0.603955 | − | 0.797018i | \(-0.293591\pi\) |
−0.388260 | + | 0.921550i | \(0.626924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 42991.6 | − | 24821.2i | 0.329890 | − | 0.190462i | −0.325902 | − | 0.945404i | \(-0.605668\pi\) |
0.655792 | + | 0.754941i | \(0.272335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −170925. | − | 296051.i | −0.610794 | − | 1.05793i | −0.991107 | − | 0.133068i | \(-0.957517\pi\) |
0.380313 | − | 0.924858i | \(-0.375816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 487282. | − | 843998.i | 1.24744 | − | 2.16063i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.12659e6 | 1.59284 | 0.796422 | − | 0.604741i | \(-0.206723\pi\) | ||||
0.796422 | + | 0.604741i | \(0.206723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.47519e6 | + | 851702.i | 1.59735 | + | 0.922233i | 0.991994 | + | 0.126282i | \(0.0403044\pi\) |
0.605360 | + | 0.795951i | \(0.293029\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 943251. | − | 2.64203e6i | 0.628572 | − | 1.76062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 320285. | + | 554750.i | 0.170895 | + | 0.295999i | 0.938733 | − | 0.344645i | \(-0.112001\pi\) |
−0.767838 | + | 0.640644i | \(0.778667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.34661e6i | − | 0.476549i | −0.971198 | − | 0.238275i | \(-0.923418\pi\) | ||
0.971198 | − | 0.238275i | \(-0.0765818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.80008e6 | −0.526524 | −0.263262 | − | 0.964724i | \(-0.584798\pi\) | ||||
−0.263262 | + | 0.964724i | \(0.584798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.88787e6 | + | 4.55406e6i | −1.61647 | + | 0.933270i | −0.628648 | + | 0.777690i | \(0.716392\pi\) |
−0.987823 | + | 0.155581i | \(0.950275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 931110. | − | 5.68911e6i | 0.161516 | − | 0.986870i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.82943e6 | − | 3.16867e6i | 0.231853 | − | 0.401582i | −0.726500 | − | 0.687166i | \(-0.758854\pi\) |
0.958354 | + | 0.285584i | \(0.0921877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.05609e7i | 3.33976i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.97907e6 | − | 5.76142e6i | −0.823535 | − | 0.475468i | 0.0280988 | − | 0.999605i | \(-0.491055\pi\) |
−0.851634 | + | 0.524137i | \(0.824388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.77419e6 | + | 5.06578e6i | −0.633706 | + | 0.365870i | −0.782186 | − | 0.623045i | \(-0.785895\pi\) |
0.148480 | + | 0.988915i | \(0.452562\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.67047e7 | − | 2.89334e7i | −0.935804 | − | 1.62086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.86768e6 | + | 1.53593e7i | −0.440059 | + | 0.762205i | −0.997693 | − | 0.0678821i | \(-0.978376\pi\) |
0.557634 | + | 0.830087i | \(0.311709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.79392e7 | 1.49298 | 0.746491 | − | 0.665396i | \(-0.231737\pi\) | ||||
0.746491 | + | 0.665396i | \(0.231737\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94841e7 | + | 1.70227e7i | 1.03824 | + | 0.599426i | 0.919333 | − | 0.393480i | \(-0.128729\pi\) |
0.118903 | + | 0.992906i | \(0.462062\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.12855e7 | + | 6.17779e7i | 0.321038 | + | 1.75740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.66395e6 | − | 1.67384e7i | −0.248111 | − | 0.429741i | 0.714891 | − | 0.699236i | \(-0.246476\pi\) |
−0.963002 | + | 0.269495i | \(0.913143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 960779.i | − | 0.0202447i | −0.999949 | − | 0.0101223i | \(-0.996778\pi\) | ||
0.999949 | − | 0.0101223i | \(-0.00322210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.43053e7 | −0.465614 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.62273e7 | + | 3.24629e7i | −0.896164 | + | 0.517400i | −0.875954 | − | 0.482395i | \(-0.839767\pi\) |
−0.0202100 | + | 0.999796i | \(0.506433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.44525e7 | − | 5.23193e7i | −0.648233 | − | 0.762950i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.90015e7 | + | 5.02320e7i | −0.356062 | + | 0.616717i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.66661e7i | − | 0.301213i | −0.988594 | − | 0.150606i | \(-0.951877\pi\) | ||
0.988594 | − | 0.150606i | \(-0.0481226\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.33466e6 | − | 3.65732e6i | −0.0608749 | − | 0.0351461i | 0.469254 | − | 0.883063i | \(-0.344523\pi\) |
−0.530129 | + | 0.847917i | \(0.677856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.35283e7 | − | 1.35841e7i | 0.209046 | − | 0.120693i | −0.391822 | − | 0.920041i | \(-0.628155\pi\) |
0.600868 | + | 0.799348i | \(0.294822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.81604e7 | + | 1.18057e8i | 0.519992 | + | 0.900653i | 0.999730 | + | 0.0232412i | \(0.00739857\pi\) |
−0.479737 | + | 0.877412i | \(0.659268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.81540e7 | − | 8.34051e7i | 0.341135 | − | 0.590863i | −0.643509 | − | 0.765439i | \(-0.722522\pi\) |
0.984644 | + | 0.174576i | \(0.0558554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.83287e7 | 0.541737 | 0.270868 | − | 0.962616i | \(-0.412689\pi\) | ||||
0.270868 | + | 0.962616i | \(0.412689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.45910e8 | + | 1.99711e8i | 1.97775 | + | 1.14185i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.91325e7 | + | 8.97544e6i | −0.245009 | + | 0.0447577i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.34885e8 | − | 4.06834e8i | −1.09576 | − | 1.89791i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.82283e8i | 2.79463i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.88706e7 | −0.149419 | −0.0747097 | − | 0.997205i | \(-0.523803\pi\) | ||||
−0.0747097 | + | 0.997205i | \(0.523803\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.31013e8 | + | 1.91111e8i | −1.12398 | + | 0.648933i | −0.942415 | − | 0.334445i | \(-0.891451\pi\) |
−0.181570 | + | 0.983378i | \(0.558118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00760e7 | + | 1.12252e8i | −0.128079 | + | 0.358747i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.14124e7 | − | 3.70873e7i | 0.0607831 | − | 0.105279i | −0.834033 | − | 0.551715i | \(-0.813974\pi\) |
0.894816 | + | 0.446436i | \(0.147307\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.51148e8i | 0.404896i | 0.979293 | + | 0.202448i | \(0.0648897\pi\) | ||||
−0.979293 | + | 0.202448i | \(0.935110\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.47697e8 | + | 3.73948e8i | 1.54892 | + | 0.894267i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.13997e9 | + | 6.58161e8i | −2.57882 | + | 1.48888i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.30228e8 | − | 2.25561e8i | −0.264215 | − | 0.457634i | 0.703143 | − | 0.711049i | \(-0.251780\pi\) |
−0.967358 | + | 0.253415i | \(0.918446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.43650e8 | + | 4.22014e8i | −0.468661 | + | 0.811744i | −0.999358 | − | 0.0358171i | \(-0.988597\pi\) |
0.530698 | + | 0.847561i | \(0.321930\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.99028e9 | −3.44816 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.17705e8 | + | 1.25692e8i | 0.358318 | + | 0.206875i | 0.668343 | − | 0.743853i | \(-0.267004\pi\) |
−0.310024 | + | 0.950729i | \(0.600337\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.72996e8 | + | 2.75973e8i | 1.15047 | + | 0.410736i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.84569e8 | + | 8.39298e8i | 0.686444 | + | 1.18896i | 0.972981 | + | 0.230887i | \(0.0741627\pi\) |
−0.286536 | + | 0.958069i | \(0.592504\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.87973e8i | 0.627378i | 0.949526 | + | 0.313689i | \(0.101565\pi\) | ||||
−0.949526 | + | 0.313689i | \(0.898435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.87509e6 | −0.00229867 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.43728e7 | − | 3.71657e7i | 0.0718651 | − | 0.0414914i | −0.463637 | − | 0.886025i | \(-0.653456\pi\) |
0.535502 | + | 0.844534i | \(0.320122\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.20496e8 | + | 2.30184e9i | 0.448342 | + | 2.45427i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.17987e8 | + | 3.77565e8i | −0.212334 | + | 0.367773i | −0.952444 | − | 0.304712i | \(-0.901440\pi\) |
0.740111 | + | 0.672485i | \(0.234773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.22472e9i | − | 1.14110i | −0.821264 | − | 0.570548i | \(-0.806731\pi\) | ||
0.821264 | − | 0.570548i | \(-0.193269\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.48177e8 | − | 3.74225e8i | −0.553359 | − | 0.319482i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.71200e8 | − | 2.72047e8i | 0.385335 | − | 0.222473i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.18497e8 | + | 5.51652e8i | 0.239316 | + | 0.414507i | 0.960518 | − | 0.278217i | \(-0.0897436\pi\) |
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.35413e8 | − | 1.44698e9i | 0.602105 | − | 1.04288i | −0.390397 | − | 0.920646i | \(-0.627662\pi\) |
0.992502 | − | 0.122229i | \(-0.0390043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.97108e8 | 0.330055 | 0.165027 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165027 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.42581e9 | + | 8.23189e8i | 0.909176 | + | 0.524913i | 0.880166 | − | 0.474666i | \(-0.157431\pi\) |
0.0290099 | + | 0.999579i | \(0.490765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.06137e9 | + | 1.75142e9i | −1.21387 | + | 1.03135i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.86701e8 | + | 1.36261e9i | 0.445445 | + | 0.771533i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.29844e9i | − | 0.680515i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.49413e9 | −1.76283 | −0.881413 | − | 0.472347i | \(-0.843407\pi\) | ||||
−0.881413 | + | 0.472347i | \(0.843407\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.82146e9 | − | 1.05162e9i | 0.852442 | − | 0.492158i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.02329e9 | + | 7.34968e8i | −1.81444 | + | 0.331459i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.97404e8 | + | 5.15119e8i | −0.124675 | + | 0.215943i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.69455e8i | − | 0.108960i | −0.998515 | − | 0.0544799i | \(-0.982650\pi\) | ||
0.998515 | − | 0.0544799i | \(-0.0173501\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.25301e9 | + | 7.23427e8i | 0.471902 | + | 0.272453i | 0.717036 | − | 0.697037i | \(-0.245499\pi\) |
−0.245134 | + | 0.969489i | \(0.578832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.59604e8 | − | 9.21477e7i | 0.0580367 | − | 0.0335075i | −0.470701 | − | 0.882293i | \(-0.655999\pi\) |
0.528738 | + | 0.848785i | \(0.322666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.09346e9 | + | 3.62598e9i | 0.710299 | + | 1.23027i | 0.964745 | + | 0.263186i | \(0.0847734\pi\) |
−0.254446 | + | 0.967087i | \(0.581893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.32103e9 | − | 9.21629e9i | 1.74471 | − | 3.02193i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.19326e9 | −0.672201 | −0.336101 | − | 0.941826i | \(-0.609108\pi\) | ||||
−0.336101 | + | 0.941826i | \(0.609108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.71562e9 | + | 2.72256e9i | 1.39788 | + | 0.807067i | 0.994171 | − | 0.107819i | \(-0.0343868\pi\) |
0.403711 | + | 0.914887i | \(0.367720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.38145e9 | + | 6.30063e9i | 0.660963 | + | 1.74872i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.09734e8 | + | 1.22929e9i | 0.190681 | + | 0.330269i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.90950e9i | − | 0.481089i | −0.970638 | − | 0.240544i | \(-0.922674\pi\) | ||
0.970638 | − | 0.240544i | \(-0.0773260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.94139e9 | −2.18234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.63082e9 | + | 2.09626e9i | −0.832286 | + | 0.480521i | −0.854635 | − | 0.519230i | \(-0.826219\pi\) |
0.0223487 | + | 0.999750i | \(0.492886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.44846e9 | − | 5.17127e8i | −0.321891 | − | 0.114921i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.08663e9 | + | 3.61415e9i | −0.436136 | + | 0.755410i | −0.997388 | − | 0.0722352i | \(-0.976987\pi\) |
0.561251 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.27507e9i | 0.866882i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.02865e9 | + | 3.48064e9i | 1.15136 | + | 0.664737i | 0.949218 | − | 0.314619i | \(-0.101877\pi\) |
0.202141 | + | 0.979356i | \(0.435210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.31995e9 | + | 3.07148e9i | −0.986349 | + | 0.569469i | −0.904181 | − | 0.427150i | \(-0.859518\pi\) |
−0.0821681 | + | 0.996618i | \(0.526184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.27453e10 | − | 2.20755e10i | −2.22853 | − | 3.85993i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.03712e8 | + | 3.52839e8i | −0.0346016 | + | 0.0599318i | −0.882808 | − | 0.469735i | \(-0.844350\pi\) |
0.848206 | + | 0.529666i | \(0.177683\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.61123e9 | 0.258423 | 0.129212 | − | 0.991617i | \(-0.458755\pi\) | ||||
0.129212 | + | 0.991617i | \(0.458755\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.30872e9 | − | 3.06499e9i | −0.827645 | − | 0.477841i | 0.0254009 | − | 0.999677i | \(-0.491914\pi\) |
−0.853046 | + | 0.521836i | \(0.825247\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.09347e9 | + | 2.46396e9i | 0.308560 | + | 0.363166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.27152e9 | − | 5.66643e9i | −0.468984 | − | 0.812304i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.04420e9i | 1.09147i | 0.837957 | + | 0.545736i | \(0.183750\pi\) | ||||
−0.837957 | + | 0.545736i | \(0.816250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.34634e10 | 1.77774 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.46522e9 | − | 4.88740e9i | 1.05914 | − | 0.611495i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.29368e9 | − | 2.79844e9i | 0.401250 | − | 0.340918i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.91893e9 | − | 1.02519e10i | 0.683981 | − | 1.18469i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.92170e9i | − | 0.666642i | −0.942813 | − | 0.333321i | \(-0.891831\pi\) | ||
0.942813 | − | 0.333321i | \(-0.108169\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70737e8 | − | 2.14045e8i | −0.0396300 | − | 0.0228804i | 0.480054 | − | 0.877239i | \(-0.340617\pi\) |
−0.519684 | + | 0.854358i | \(0.673950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.31975e9 | + | 4.22606e9i | −0.762639 | + | 0.440310i | −0.830242 | − | 0.557402i | \(-0.811798\pi\) |
0.0676034 | + | 0.997712i | \(0.478465\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.10216e9 | − | 5.37310e9i | −0.307204 | − | 0.532094i | 0.670545 | − | 0.741869i | \(-0.266060\pi\) |
−0.977750 | + | 0.209775i | \(0.932727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.47335e10 | − | 2.55191e10i | 1.42279 | − | 2.46435i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.03266e9 | 0.0948743 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41331e10 | + | 1.39333e10i | 2.16312 | + | 1.24888i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.35292e9 | − | 2.05954e10i | 0.627590 | − | 1.75787i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.74528e8 | + | 8.21906e8i | 0.0395321 | + | 0.0684716i | 0.885114 | − | 0.465373i | \(-0.154080\pi\) |
−0.845582 | + | 0.533845i | \(0.820747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.07222e10i | − | 1.64535i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.18629e10 | 0.919752 | 0.459876 | − | 0.887983i | \(-0.347894\pi\) | ||||
0.459876 | + | 0.887983i | \(0.347894\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.85849e10 | − | 2.22770e10i | 2.85364 | − | 1.64755i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.14072e9 | + | 1.18571e10i | 0.515900 | + | 0.856649i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.59847e9 | − | 2.76864e9i | 0.110252 | − | 0.190963i | −0.805620 | − | 0.592433i | \(-0.798167\pi\) |
0.915872 | + | 0.401471i | \(0.131501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.85896e10i | − | 1.25305i | −0.779401 | − | 0.626525i | \(-0.784477\pi\) | ||
0.779401 | − | 0.626525i | \(-0.215523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.29612e10 | − | 1.32566e10i | −1.47875 | − | 0.853758i | −0.479041 | − | 0.877793i | \(-0.659015\pi\) |
−0.999711 | + | 0.0240347i | \(0.992349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.83897e10 | + | 2.21643e10i | −2.41714 | + | 1.39554i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.13582e9 | − | 7.16345e9i | −0.248991 | − | 0.431265i | 0.714255 | − | 0.699886i | \(-0.246766\pi\) |
−0.963246 | + | 0.268620i | \(0.913432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.25959e9 | + | 1.25740e10i | −0.427448 | + | 0.740362i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.97790e10 | −2.24121 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.87269e9 | − | 5.70000e9i | −0.544216 | − | 0.314203i | 0.202570 | − | 0.979268i | \(-0.435071\pi\) |
−0.746786 | + | 0.665065i | \(0.768404\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.57869e9 | + | 8.64193e9i | 0.0833301 | + | 0.456158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.55738e10 | + | 2.69746e10i | 0.804562 | + | 1.39354i | 0.916587 | + | 0.399836i | \(0.130933\pi\) |
−0.112025 | + | 0.993705i | \(0.535734\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.22135e10i | 1.59467i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.55220e9 | 0.366030 | 0.183015 | − | 0.983110i | \(-0.441414\pi\) | ||||
0.183015 | + | 0.983110i | \(0.441414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.02966e9 | + | 3.48123e9i | −0.280219 | + | 0.161785i | −0.633523 | − | 0.773724i | \(-0.718392\pi\) |
0.353303 | + | 0.935509i | \(0.385058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.75106e10 | − | 5.59185e10i | −2.16246 | − | 2.54515i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.85548e9 | + | 1.53381e10i | −0.386735 | + | 0.669845i | −0.992008 | − | 0.126173i | \(-0.959731\pi\) |
0.605273 | + | 0.796018i | \(0.293064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.11117e9i | − | 0.304252i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.95574e10 | + | 1.12915e10i | 0.803384 | + | 0.463834i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.62194e10 | − | 1.51378e10i | 1.05551 | − | 0.609396i | 0.131320 | − | 0.991340i | \(-0.458078\pi\) |
0.924186 | + | 0.381944i | \(0.124745\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.80548e9 | + | 3.12718e9i | 0.0698257 | + | 0.120942i | 0.898824 | − | 0.438309i | \(-0.144422\pi\) |
−0.828999 | + | 0.559250i | \(0.811089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.43534e10 | + | 4.21813e10i | −0.923293 | + | 1.59919i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.67547e10 | 0.610602 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.41617e10 | − | 1.39498e10i | −0.863446 | − | 0.498511i | 0.00171879 | − | 0.999999i | \(-0.499453\pi\) |
−0.865165 | + | 0.501488i | \(0.832786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.72160e10 | − | 4.97176e9i | 0.935456 | − | 0.170887i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.61293e8 | + | 9.72188e8i | 0.0189233 | + | 0.0327762i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.41022e8i | − | 0.0175533i | −0.999961 | − | 0.00877665i | \(-0.997206\pi\) | ||
0.999961 | − | 0.00877665i | \(-0.00279373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.09569e10 | 0.985437 | 0.492718 | − | 0.870189i | \(-0.336003\pi\) | ||||
0.492718 | + | 0.870189i | \(0.336003\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.75568e10 | − | 1.01364e10i | 0.538134 | − | 0.310692i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.17914e9 | − | 2.29096e10i | 0.246035 | − | 0.689138i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.75045e10 | + | 4.76391e10i | −0.797066 | + | 1.38056i | 0.124453 | + | 0.992225i | \(0.460282\pi\) |
−0.921519 | + | 0.388333i | \(0.873051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.42119e9i | 0.268012i | 0.990981 | + | 0.134006i | \(0.0427842\pi\) | ||||
−0.990981 | + | 0.134006i | \(0.957216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.46967e10 | − | 8.48514e9i | −0.402990 | − | 0.232666i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.49773e10 | − | 1.44206e10i | 0.672492 | − | 0.388263i | −0.124529 | − | 0.992216i | \(-0.539742\pi\) |
0.797020 | + | 0.603953i | \(0.206408\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.66156e10 | − | 2.87791e10i | −0.431422 | − | 0.747245i | 0.565574 | − | 0.824697i | \(-0.308655\pi\) |
−0.996996 | + | 0.0774529i | \(0.975321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.79300e10 | − | 6.56967e10i | 0.967260 | − | 1.67534i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.22184e9 | 0.128481 | 0.0642404 | − | 0.997934i | \(-0.479538\pi\) | ||||
0.0642404 | + | 0.997934i | \(0.479538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.05030e10 | − | 1.76109e10i | −0.737287 | − | 0.425673i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.55457e10 | + | 2.69711e10i | 1.76264 | + | 0.629294i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.00779e10 | + | 6.94170e10i | 0.918841 | + | 1.59148i | 0.801178 | + | 0.598426i | \(0.204207\pi\) |
0.117664 | + | 0.993054i | \(0.462460\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.16689e9i | 0.114400i | 0.998363 | + | 0.0571999i | \(0.0182173\pi\) | ||||
−0.998363 | + | 0.0571999i | \(0.981783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.17425e10 | −0.255527 | −0.127764 | − | 0.991805i | \(-0.540780\pi\) | ||||
−0.127764 | + | 0.991805i | \(0.540780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.41407e7 | + | 3.70316e7i | −0.00134855 | + | 0.000778584i | −0.500674 | − | 0.865636i | \(-0.666914\pi\) |
0.499326 | + | 0.866414i | \(0.333581\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.65228e9 | − | 4.18894e10i | −0.158161 | − | 0.865790i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.35413e10 | + | 4.07748e10i | −0.470312 | + | 0.814605i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.83798e10i | − | 0.950363i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.21346e10 | − | 3.58735e10i | −1.18030 | − | 0.681445i | −0.224215 | − | 0.974540i | \(-0.571982\pi\) |
−0.956084 | + | 0.293094i | \(0.905315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.58624e10 | + | 9.15816e9i | −0.296339 | + | 0.171091i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.55785e10 | + | 2.69828e10i | 0.281553 | + | 0.487663i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.48075e10 | + | 4.29679e10i | −0.441029 | + | 0.763885i | −0.997766 | − | 0.0668039i | \(-0.978720\pi\) |
0.556737 | + | 0.830689i | \(0.312053\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.92296e10 | 0.502917 | 0.251458 | − | 0.967868i | \(-0.419090\pi\) | ||||
0.251458 | + | 0.967868i | \(0.419090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.02956e10 | + | 1.17177e10i | 0.343569 | + | 0.198359i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.94189e10 | + | 5.89810e10i | −1.13776 | + | 0.966689i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.45740e10 | + | 5.98840e10i | 0.557632 | + | 0.965847i | 0.997694 | + | 0.0678795i | \(0.0216233\pi\) |
−0.440061 | + | 0.897968i | \(0.645043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.21850e10i | 0.659001i | 0.944155 | + | 0.329501i | \(0.106880\pi\) | ||||
−0.944155 | + | 0.329501i | \(0.893120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.54652e9 | 0.131409 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.01952e10 | − | 1.74332e10i | 0.449849 | − | 0.259721i | −0.257917 | − | 0.966167i | \(-0.583036\pi\) |
0.707766 | + | 0.706446i | \(0.249703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.04120e10 | + | 1.46895e10i | −1.17934 | + | 0.215439i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.58718e10 | + | 2.74908e10i | −0.225630 | + | 0.390803i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.38231e11i | 3.33454i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.86868e10 | − | 3.96564e10i | −0.932229 | − | 0.538223i | −0.0447131 | − | 0.999000i | \(-0.514237\pi\) |
−0.887516 | + | 0.460777i | \(0.847571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.49357e10 | − | 8.62310e9i | 0.199626 | − | 0.115254i | −0.396855 | − | 0.917881i | \(-0.629898\pi\) |
0.596481 | + | 0.802627i | \(0.296565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.77171e10 | + | 3.06869e10i | 0.229694 | + | 0.397842i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.92753e10 | + | 3.33858e10i | −0.246138 | + | 0.426323i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.85048e10 | 0.477096 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.37940e11 | − | 7.96395e10i | −1.68374 | − | 0.972106i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.16691e11 | − | 9.54930e10i | −1.38255 | − | 1.13140i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.22880e10 | + | 1.42527e11i | 0.960611 | + | 1.66383i | 0.720970 | + | 0.692966i | \(0.243696\pi\) |
0.239641 | + | 0.970862i | \(0.422970\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.12527e11i | 1.27548i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.02743e10 | 0.226462 | 0.113231 | − | 0.993569i | \(-0.463880\pi\) | ||||
0.113231 | + | 0.993569i | \(0.463880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.84339e10 | − | 2.79633e10i | 0.525464 | − | 0.303377i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.37045e10 | + | 1.56033e10i | 0.467332 | + | 0.166846i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.16250e10 | + | 7.20966e10i | −0.432448 | + | 0.749021i | −0.997083 | − | 0.0763188i | \(-0.975683\pi\) |
0.564636 | + | 0.825340i | \(0.309017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.14711e10i | − | 0.527128i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.59377e10 | + | 9.20165e9i | 0.158633 | + | 0.0915867i | 0.577215 | − | 0.816592i | \(-0.304139\pi\) |
−0.418582 | + | 0.908179i | \(0.637473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.93777e10 | + | 5.16022e10i | −0.877072 | + | 0.506378i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.00051e10 | + | 6.92908e10i | 0.381651 | + | 0.661038i | 0.991298 | − | 0.131634i | \(-0.0420225\pi\) |
−0.609648 | + | 0.792672i | \(0.708689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.17409e10 | + | 1.58900e11i | −0.863015 | + | 1.49479i | 0.00598894 | + | 0.999982i | \(0.498094\pi\) |
−0.869004 | + | 0.494804i | \(0.835240\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.33155e11 | −3.04772 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.30693e10 | − | 1.33190e10i | −0.208128 | − | 0.120163i | 0.392313 | − | 0.919832i | \(-0.371675\pi\) |
−0.600441 | + | 0.799669i | \(0.705008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.49365e9 | + | 1.75798e9i | 0.0131082 | + | 0.0154280i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.78505e10 | − | 8.28794e10i | −0.414202 | − | 0.717419i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.04647e10i | 0.761950i | 0.924585 | + | 0.380975i | \(0.124412\pi\) | ||||
−0.924585 | + | 0.380975i | \(0.875588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.45612e10 | 0.702603 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.90780e10 | − | 1.67882e10i | 0.235151 | − | 0.135764i | −0.377795 | − | 0.925889i | \(-0.623318\pi\) |
0.612946 | + | 0.790125i | \(0.289984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.44725e10 | − | 3.77856e10i | 0.354833 | − | 0.301480i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.46968e10 | − | 1.29379e11i | 0.580223 | − | 1.00498i | −0.415230 | − | 0.909717i | \(-0.636299\pi\) |
0.995453 | − | 0.0952587i | \(-0.0303678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.12742e10i | − | 0.239711i | −0.992791 | − | 0.119856i | \(-0.961757\pi\) | ||
0.992791 | − | 0.119856i | \(-0.0382431\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.75350e11 | + | 2.74443e11i | 3.54807 | + | 2.04848i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.03866e11 | − | 5.99669e10i | 0.765099 | − | 0.441730i | −0.0660244 | − | 0.997818i | \(-0.521032\pi\) |
0.831124 | + | 0.556088i | \(0.187698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.30218e11 | − | 2.25544e11i | −0.934342 | − | 1.61833i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.95362e10 | − | 6.84787e10i | 0.279997 | − | 0.484968i | −0.691387 | − | 0.722485i | \(-0.743000\pi\) |
0.971384 | + | 0.237516i | \(0.0763333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.35075e10 | 0.507214 | 0.253607 | − | 0.967307i | \(-0.418383\pi\) | ||||
0.253607 | + | 0.967307i | \(0.418383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.19835e11 | + | 1.26922e11i | 1.49739 | + | 0.864517i | 0.999995 | − | 0.00300805i | \(-0.000957493\pi\) |
0.497393 | + | 0.867526i | \(0.334291\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.24140e10 | − | 1.46811e11i | 0.347933 | − | 0.974554i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.08250e11 | − | 3.60699e11i | −1.36478 | − | 2.36388i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.33251e10i | 0.0851273i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.11257e9 | 0.0385573 | 0.0192786 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192786 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.93322e10 | − | 2.27085e10i | 0.241910 | − | 0.139667i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.62673e11 | + | 2.66240e10i | 0.988004 | + | 0.161702i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.48169e10 | + | 1.64228e11i | −0.561634 | + | 0.972779i | 0.435720 | + | 0.900082i | \(0.356494\pi\) |
−0.997354 | + | 0.0726969i | \(0.976839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.50630e11i | − | 0.881188i | −0.897706 | − | 0.440594i | \(-0.854768\pi\) | ||
0.897706 | − | 0.440594i | \(-0.145232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.86275e11 | − | 1.07546e11i | −1.06301 | − | 0.613729i | −0.136747 | − | 0.990606i | \(-0.543665\pi\) |
−0.926264 | + | 0.376876i | \(0.876998\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.61011e11 | + | 1.50695e11i | −1.47123 | + | 0.849415i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.66655e11 | + | 2.88654e11i | 0.916567 | + | 1.58754i | 0.804590 | + | 0.593831i | \(0.202385\pi\) |
0.111977 | + | 0.993711i | \(0.464282\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.23296e11 | − | 3.86761e11i | 1.21316 | − | 2.10125i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.54805e10 | 0.347193 | 0.173596 | − | 0.984817i | \(-0.444461\pi\) | ||||
0.173596 | + | 0.984817i | \(0.444461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.46661e11 | + | 8.46750e10i | 0.768263 | + | 0.443557i | 0.832255 | − | 0.554394i | \(-0.187050\pi\) |
−0.0639915 | + | 0.997950i | \(0.520383\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50265e10 | − | 1.36998e11i | −0.127972 | − | 0.700531i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.92562e11 | − | 3.33528e11i | −0.972899 | − | 1.68511i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.65000e11i | 1.30724i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.23724e11 | −0.603105 | −0.301552 | − | 0.953450i | \(-0.597505\pi\) | ||||
−0.301552 | + | 0.953450i | \(0.597505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.80203e11 | + | 1.61775e11i | −1.33389 | + | 0.770119i | −0.985893 | − | 0.167378i | \(-0.946470\pi\) |
−0.347993 | + | 0.937497i | \(0.613137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.14557e10 | + | 4.87921e10i | 0.195032 | + | 0.229547i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.35871e10 | − | 1.62098e11i | 0.430064 | − | 0.744893i | −0.566814 | − | 0.823846i | \(-0.691824\pi\) |
0.996878 | + | 0.0789529i | \(0.0251577\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.00370e10i | 0.227263i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.06045e10 | + | 5.23105e10i | 0.402043 | + | 0.232120i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13839e11 | − | 6.57249e10i | 0.499319 | − | 0.288282i | −0.229113 | − | 0.973400i | \(-0.573583\pi\) |
0.728432 | + | 0.685118i | \(0.240249\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.83017e10 | − | 1.52943e11i | −0.378469 | − | 0.655527i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.40061e10 | − | 2.42593e10i | 0.0593454 | − | 0.102789i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.13631e10 | 0.0470569 | 0.0235285 | − | 0.999723i | \(-0.492510\pi\) | ||||
0.0235285 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.75391e10 | + | 1.58997e10i | 0.112753 | + | 0.0650981i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.72765e10 | − | 3.15605e9i | 0.0691479 | − | 0.0126318i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.67229e11 | + | 2.89649e11i | 0.661801 | + | 1.14627i | 0.980142 | + | 0.198296i | \(0.0635408\pi\) |
−0.318341 | + | 0.947976i | \(0.603126\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.82309e11i | − | 2.25318i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.73852e11 | −3.34359 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.41998e11 | + | 1.39717e11i | −0.905515 | + | 0.522800i | −0.878985 | − | 0.476849i | \(-0.841779\pi\) |
−0.0265298 | + | 0.999648i | \(0.508446\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.19326e10 | + | 6.14329e10i | −0.0811614 | + | 0.227332i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.48967e11 | − | 9.50839e11i | 1.98698 | − | 3.44156i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.98526e11i | 1.78464i | 0.451407 | + | 0.892318i | \(0.350922\pi\) | ||||
−0.451407 | + | 0.892318i | \(0.649078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.24286e10 | − | 1.87226e10i | −0.113569 | − | 0.0655688i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.34185e11 | − | 1.35207e11i | 0.811229 | − | 0.468363i | −0.0361535 | − | 0.999346i | \(-0.511511\pi\) |
0.847383 | + | 0.530983i | \(0.178177\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.31942e11 | + | 4.01735e11i | 0.786157 | + | 1.36166i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.38418e11 | + | 4.12953e11i | −0.799396 | + | 1.38459i | 0.120615 | + | 0.992699i | \(0.461513\pi\) |
−0.920010 | + | 0.391894i | \(0.871820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.19326e11 | −1.37593 | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687966 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.63548e11 | + | 1.52160e11i | 0.855529 | + | 0.493940i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.08250e11 | − | 1.10051e11i | −0.979436 | − | 0.349676i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.18803e10 | + | 2.05772e10i | 0.0373479 | + | 0.0646885i | 0.884095 | − | 0.467307i | \(-0.154776\pi\) |
−0.846747 | + | 0.531995i | \(0.821442\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.69368e11i | − | 1.75229i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.90289e11 | −1.49303 | −0.746516 | − | 0.665368i | \(-0.768275\pi\) | ||||
−0.746516 | + | 0.665368i | \(0.768275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.40688e11 | − | 1.38961e11i | 0.717656 | − | 0.414339i | −0.0962332 | − | 0.995359i | \(-0.530679\pi\) |
0.813889 | + | 0.581020i | \(0.197346\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.15540e10 | + | 2.27471e11i | 0.122607 | + | 0.671163i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.64741e11 | − | 2.85340e11i | 0.476014 | − | 0.824481i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.97929e11i | − | 0.565984i | −0.959122 | − | 0.282992i | \(-0.908673\pi\) | ||
0.959122 | − | 0.282992i | \(-0.0913270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.68415e11 | + | 2.70439e11i | 1.31194 | + | 0.757447i | 0.982417 | − | 0.186702i | \(-0.0597799\pi\) |
0.329520 | + | 0.944149i | \(0.393113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.43767e12 | − | 8.30038e11i | 3.98522 | − | 2.30087i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.34246e10 | − | 5.78931e10i | −0.0907646 | − | 0.157209i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.96166e11 | − | 8.59385e11i | 1.33359 | − | 2.30985i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.93720e11 | −0.773490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.58532e11 | + | 2.06999e11i | 0.934607 | + | 0.539596i | 0.888266 | − | 0.459330i | \(-0.151910\pi\) |
0.0463413 | + | 0.998926i | \(0.485244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.61619e11 | + | 1.37318e11i | −0.412844 | + | 0.350768i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.44850e11 | − | 2.50888e11i | −0.366291 | − | 0.634434i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.99422e11i | 0.742080i | 0.928617 | + | 0.371040i | \(0.120999\pi\) | ||||
−0.928617 | + | 0.371040i | \(0.879001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.89467e11 | −0.464887 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.71182e11 | − | 4.45242e11i | 1.85479 | − | 1.07086i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.43401e11 | + | 1.72339e11i | −2.24653 | + | 0.410393i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.92320e11 | − | 3.33107e11i | 0.448982 | − | 0.777660i | −0.549338 | − | 0.835601i | \(-0.685120\pi\) |
0.998320 | + | 0.0579400i | \(0.0184532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.67004e11i | 0.848374i | 0.905575 | + | 0.424187i | \(0.139440\pi\) | ||||
−0.905575 | + | 0.424187i | \(0.860560\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.80647e11 | − | 5.66177e11i | −2.22271 | − | 1.28328i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.73884e10 | + | 4.46802e10i | −0.173695 | + | 0.100283i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.74573e11 | − | 3.02370e11i | −0.384242 | − | 0.665527i | 0.607422 | − | 0.794380i | \(-0.292204\pi\) |
−0.991664 | + | 0.128853i | \(0.958870\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.55497e11 | + | 6.15739e11i | −0.774885 | + | 1.34214i | 0.159975 | + | 0.987121i | \(0.448859\pi\) |
−0.934859 | + | 0.355018i | \(0.884475\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.40466e11 | 0.941651 | 0.470825 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470825 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.98343e10 | − | 5.18659e10i | −0.190206 | − | 0.109815i | 0.401873 | − | 0.915695i | \(-0.368359\pi\) |
−0.592079 | + | 0.805880i | \(0.701693\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.59464e10 | − | 9.28052e10i | 0.157735 | − | 0.192749i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.85077e11 | − | 4.93768e11i | −0.586430 | − | 1.01573i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.98433e11i | 1.40954i | 0.709437 | + | 0.704769i | \(0.248949\pi\) | ||||
−0.709437 | + | 0.704769i | \(0.751051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.68956e11 | 1.53715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.89736e9 | − | 1.09544e9i | 0.00372155 | − | 0.00214864i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.06225e12 | + | 3.79243e11i | 2.06392 | + | 0.736857i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09489e11 | − | 1.89641e11i | 0.208763 | − | 0.361589i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.88287e11i | − | 1.11120i | −0.831449 | − | 0.555601i | \(-0.812488\pi\) | ||
0.831449 | − | 0.555601i | \(-0.187512\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.73418e11 | + | 2.73328e11i | 0.877650 | + | 0.506711i | 0.869883 | − | 0.493259i | \(-0.164194\pi\) |
0.00776698 | + | 0.999970i | \(0.497528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.67471e11 | + | 9.66896e10i | −0.307587 | + | 0.177585i | −0.645846 | − | 0.763468i | \(-0.723495\pi\) |
0.338259 | + | 0.941053i | \(0.390162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.49869e11 | + | 4.32786e11i | 0.450474 | + | 0.780244i | 0.998415 | − | 0.0562729i | \(-0.0179217\pi\) |
−0.547941 | + | 0.836517i | \(0.684588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.34249e10 | + | 7.52141e10i | −0.0775665 | + | 0.134349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.05538e11 | −0.886492 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.39180e11 | − | 2.53561e11i | −0.763080 | − | 0.440565i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.06069e12 | − | 1.24840e12i | −1.80949 | − | 2.12972i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06031e10 | + | 1.83651e10i | 0.0179239 | + | 0.0310452i | 0.874848 | − | 0.484397i | \(-0.160961\pi\) |
−0.856924 | + | 0.515442i | \(0.827628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.92261e11i | 1.48111i | 0.671994 | + | 0.740557i | \(0.265438\pi\) | ||||
−0.671994 | + | 0.740557i | \(0.734562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.55925e11 | −1.07898 | −0.539488 | − | 0.841994i | \(-0.681382\pi\) | ||||
−0.539488 | + | 0.841994i | \(0.681382\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.06329e11 | + | 4.07799e11i | −1.14107 | + | 0.658797i | −0.946696 | − | 0.322130i | \(-0.895601\pi\) |
−0.194375 | + | 0.980927i | \(0.562268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.11232e10 | − | 6.04291e10i | 0.113869 | − | 0.0967473i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.26075e11 | + | 3.91573e11i | −0.355506 | + | 0.615754i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.09399e11i | − | 0.793900i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.66193e12 | + | 9.59518e11i | 2.54434 | + | 1.46897i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.59148e10 | − | 3.80559e10i | 0.100019 | − | 0.0577461i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.15489e11 | + | 1.23926e12i | 1.06662 | + | 1.84744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.36544e10 | − | 1.27573e11i | 0.108835 | − | 0.188508i | −0.806463 | − | 0.591284i | \(-0.798621\pi\) |
0.915299 | + | 0.402776i | \(0.131955\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.13012e11 | −0.744824 | −0.372412 | − | 0.928067i | \(-0.621469\pi\) | ||||
−0.372412 | + | 0.928067i | \(0.621469\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.17632e10 | − | 1.25650e10i | −0.0313213 | − | 0.0180834i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.08565e11 | − | 8.64284e11i | 0.436384 | − | 1.22230i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.96143e11 | − | 8.59345e11i | −0.695577 | − | 1.20477i | −0.969986 | − | 0.243161i | \(-0.921816\pi\) |
0.274409 | − | 0.961613i | \(-0.411518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.08483e12i | 1.49470i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.24277e11 | 0.852727 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.54446e11 | + | 8.91694e10i | −0.207355 | + | 0.119716i | −0.600081 | − | 0.799939i | \(-0.704865\pi\) |
0.392727 | + | 0.919655i | \(0.371532\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.01181e11 | − | 2.67695e11i | −0.134679 | − | 0.356322i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.17864e11 | + | 5.50556e11i | −0.415905 | + | 0.720369i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.01978e12i | 1.32296i | 0.749961 | + | 0.661482i | \(0.230072\pi\) | ||||
−0.749961 | + | 0.661482i | \(0.769928\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.89803e11 | − | 5.13728e11i | −1.13484 | − | 0.655201i | −0.189694 | − | 0.981843i | \(-0.560750\pi\) |
−0.945148 | + | 0.326642i | \(0.894083\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.98666e11 | + | 2.30170e11i | −0.504153 | + | 0.291073i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.89538e10 | − | 1.19431e11i | −0.0857350 | − | 0.148497i | 0.819969 | − | 0.572408i | \(-0.193990\pi\) |
−0.905704 | + | 0.423910i | \(0.860657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.86742e11 | + | 8.43063e11i | −0.600115 | + | 1.03943i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.56628e11 | −0.432359 | −0.216179 | − | 0.976354i | \(-0.569360\pi\) | ||||
−0.216179 | + | 0.976354i | \(0.569360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.44558e11 | − | 3.72136e11i | −0.774905 | − | 0.447392i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.84776e10 | + | 1.01148e11i | 0.0218460 | + | 0.119587i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.02435e12 | + | 1.77422e12i | 1.20103 | + | 2.08024i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.95221e12i | 2.25122i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.50903e12 | −1.72581 | −0.862903 | − | 0.505370i | \(-0.831356\pi\) | ||||
−0.862903 | + | 0.505370i | \(0.831356\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.39050e12 | − | 8.02804e11i | 1.56420 | − | 0.903094i | 0.567380 | − | 0.823456i | \(-0.307957\pi\) |
0.996824 | − | 0.0796379i | \(-0.0253764\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.34978e11 | − | 2.76562e11i | −0.262166 | − | 0.308561i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.81046e11 | − | 6.59991e11i | 0.418215 | − | 0.724369i | −0.577545 | − | 0.816359i | \(-0.695989\pi\) |
0.995760 | + | 0.0919895i | \(0.0293226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.69819e12i | 1.84865i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.46472e12 | + | 8.45658e11i | 1.56870 | + | 0.905692i | 0.996320 | + | 0.0857061i | \(0.0273146\pi\) |
0.572384 | + | 0.819986i | \(0.306019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.03011e11 | + | 2.90414e11i | −0.534359 | + | 0.308512i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.07679e11 | + | 5.32915e11i | 0.321597 | + | 0.557023i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.67808e10 | − | 1.50309e11i | 0.0899764 | − | 0.155844i | −0.817524 | − | 0.575894i | \(-0.804654\pi\) |
0.907501 | + | 0.420050i | \(0.137987\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.92365e12 | −1.96261 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.36634e11 | − | 4.25296e11i | −0.745541 | − | 0.430438i | 0.0785396 | − | 0.996911i | \(-0.474974\pi\) |
−0.824080 | + | 0.566473i | \(0.808308\pi\) | |||||||
\(998\) | 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.d.73.1 | 12 | ||
3.2 | odd | 2 | 84.9.m.b.73.6 | yes | 12 | ||
7.5 | odd | 6 | inner | 252.9.z.d.145.1 | 12 | ||
21.5 | even | 6 | 84.9.m.b.61.6 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.6 | ✓ | 12 | 21.5 | even | 6 | ||
84.9.m.b.73.6 | yes | 12 | 3.2 | odd | 2 | ||
252.9.z.d.73.1 | 12 | 1.1 | even | 1 | trivial | ||
252.9.z.d.145.1 | 12 | 7.5 | odd | 6 | inner |