Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.a (trivial) |
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: | yes |
Analytic conductor: | \(21.5545667584\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 466x^{4} + 540x^{3} + 48973x^{2} - 77282x - 1061812 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(18.9294\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −19.9294 | −1.76153 | −0.880764 | − | 0.473556i | \(-0.842970\pi\) | ||||
−0.880764 | + | 0.473556i | \(0.842970\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 269.181 | 2.10298 | ||||||||
\(5\) | 466.102 | 1.66758 | 0.833789 | − | 0.552083i | \(-0.186167\pi\) | ||||
0.833789 | + | 0.552083i | \(0.186167\pi\) | |||||||
\(6\) | −538.094 | −1.01702 | ||||||||
\(7\) | −1376.23 | −1.51652 | −0.758260 | − | 0.651953i | \(-0.773950\pi\) | ||||
−0.758260 | + | 0.651953i | \(0.773950\pi\) | |||||||
\(8\) | −2813.66 | −1.94293 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −9289.15 | −2.93749 | ||||||||
\(11\) | −6066.56 | −1.37426 | −0.687129 | − | 0.726535i | \(-0.741129\pi\) | ||||
−0.687129 | + | 0.726535i | \(0.741129\pi\) | |||||||
\(12\) | 7267.89 | 1.21416 | ||||||||
\(13\) | 9371.38 | 1.18305 | 0.591524 | − | 0.806288i | \(-0.298527\pi\) | ||||
0.591524 | + | 0.806288i | \(0.298527\pi\) | |||||||
\(14\) | 27427.5 | 2.67139 | ||||||||
\(15\) | 12584.8 | 0.962777 | ||||||||
\(16\) | 21619.3 | 1.31954 | ||||||||
\(17\) | −31738.9 | −1.56683 | −0.783414 | − | 0.621501i | \(-0.786523\pi\) | ||||
−0.783414 | + | 0.621501i | \(0.786523\pi\) | |||||||
\(18\) | −14528.5 | −0.587176 | ||||||||
\(19\) | −5025.16 | −0.168079 | −0.0840393 | − | 0.996462i | \(-0.526782\pi\) | ||||
−0.0840393 | + | 0.996462i | \(0.526782\pi\) | |||||||
\(20\) | 125466. | 3.50688 | ||||||||
\(21\) | −37158.2 | −0.875563 | ||||||||
\(22\) | 120903. | 2.42079 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | −75968.8 | −1.12175 | ||||||||
\(25\) | 139126. | 1.78082 | ||||||||
\(26\) | −186766. | −2.08397 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −370455. | −3.18921 | ||||||||
\(29\) | −124306. | −0.946449 | −0.473225 | − | 0.880942i | \(-0.656910\pi\) | ||||
−0.473225 | + | 0.880942i | \(0.656910\pi\) | |||||||
\(30\) | −250807. | −1.69596 | ||||||||
\(31\) | −16099.5 | −0.0970614 | −0.0485307 | − | 0.998822i | \(-0.515454\pi\) | ||||
−0.0485307 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(32\) | −70712.4 | −0.381479 | ||||||||
\(33\) | −163797. | −0.793428 | ||||||||
\(34\) | 632538. | 2.76001 | ||||||||
\(35\) | −641464. | −2.52892 | ||||||||
\(36\) | 196233. | 0.700993 | ||||||||
\(37\) | 101300. | 0.328778 | 0.164389 | − | 0.986396i | \(-0.447435\pi\) | ||||
0.164389 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(38\) | 100148. | 0.296075 | ||||||||
\(39\) | 253027. | 0.683033 | ||||||||
\(40\) | −1.31145e6 | −3.23998 | ||||||||
\(41\) | −598115. | −1.35532 | −0.677659 | − | 0.735377i | \(-0.737005\pi\) | ||||
−0.677659 | + | 0.735377i | \(0.737005\pi\) | |||||||
\(42\) | 740541. | 1.54233 | ||||||||
\(43\) | −118931. | −0.228115 | −0.114058 | − | 0.993474i | \(-0.536385\pi\) | ||||
−0.114058 | + | 0.993474i | \(0.536385\pi\) | |||||||
\(44\) | −1.63301e6 | −2.89004 | ||||||||
\(45\) | 339789. | 0.555860 | ||||||||
\(46\) | 242481. | 0.367304 | ||||||||
\(47\) | −255226. | −0.358577 | −0.179288 | − | 0.983797i | \(-0.557380\pi\) | ||||
−0.179288 | + | 0.983797i | \(0.557380\pi\) | |||||||
\(48\) | 583722. | 0.761837 | ||||||||
\(49\) | 1.07047e6 | 1.29983 | ||||||||
\(50\) | −2.77271e6 | −3.13696 | ||||||||
\(51\) | −856951. | −0.904608 | ||||||||
\(52\) | 2.52260e6 | 2.48792 | ||||||||
\(53\) | −109847. | −0.101349 | −0.0506747 | − | 0.998715i | \(-0.516137\pi\) | ||||
−0.0506747 | + | 0.998715i | \(0.516137\pi\) | |||||||
\(54\) | −392271. | −0.339006 | ||||||||
\(55\) | −2.82764e6 | −2.29168 | ||||||||
\(56\) | 3.87224e6 | 2.94649 | ||||||||
\(57\) | −135679. | −0.0970402 | ||||||||
\(58\) | 2.47734e6 | 1.66720 | ||||||||
\(59\) | 964886. | 0.611637 | 0.305819 | − | 0.952090i | \(-0.401070\pi\) | ||||
0.305819 | + | 0.952090i | \(0.401070\pi\) | |||||||
\(60\) | 3.38758e6 | 2.02470 | ||||||||
\(61\) | −1.44972e6 | −0.817767 | −0.408884 | − | 0.912587i | \(-0.634082\pi\) | ||||
−0.408884 | + | 0.912587i | \(0.634082\pi\) | |||||||
\(62\) | 320853. | 0.170976 | ||||||||
\(63\) | −1.00327e6 | −0.505506 | ||||||||
\(64\) | −1.35802e6 | −0.647554 | ||||||||
\(65\) | 4.36803e6 | 1.97282 | ||||||||
\(66\) | 3.26438e6 | 1.39765 | ||||||||
\(67\) | −4.27555e6 | −1.73672 | −0.868361 | − | 0.495932i | \(-0.834827\pi\) | ||||
−0.868361 | + | 0.495932i | \(0.834827\pi\) | |||||||
\(68\) | −8.54353e6 | −3.29500 | ||||||||
\(69\) | −328509. | −0.120386 | ||||||||
\(70\) | 1.27840e7 | 4.45475 | ||||||||
\(71\) | −814451. | −0.270060 | −0.135030 | − | 0.990841i | \(-0.543113\pi\) | ||||
−0.135030 | + | 0.990841i | \(0.543113\pi\) | |||||||
\(72\) | −2.05116e6 | −0.647642 | ||||||||
\(73\) | 6.40210e6 | 1.92616 | 0.963080 | − | 0.269214i | \(-0.0867639\pi\) | ||||
0.963080 | + | 0.269214i | \(0.0867639\pi\) | |||||||
\(74\) | −2.01884e6 | −0.579151 | ||||||||
\(75\) | 3.75642e6 | 1.02816 | ||||||||
\(76\) | −1.35268e6 | −0.353466 | ||||||||
\(77\) | 8.34899e6 | 2.08409 | ||||||||
\(78\) | −5.04269e6 | −1.20318 | ||||||||
\(79\) | −6.69183e6 | −1.52704 | −0.763519 | − | 0.645785i | \(-0.776530\pi\) | ||||
−0.763519 | + | 0.645785i | \(0.776530\pi\) | |||||||
\(80\) | 1.00768e7 | 2.20044 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.19201e7 | 2.38743 | ||||||||
\(83\) | −7.15533e6 | −1.37359 | −0.686793 | − | 0.726853i | \(-0.740982\pi\) | ||||
−0.686793 | + | 0.726853i | \(0.740982\pi\) | |||||||
\(84\) | −1.00023e7 | −1.84129 | ||||||||
\(85\) | −1.47936e7 | −2.61281 | ||||||||
\(86\) | 2.37022e6 | 0.401831 | ||||||||
\(87\) | −3.35625e6 | −0.546433 | ||||||||
\(88\) | 1.70692e7 | 2.67008 | ||||||||
\(89\) | −8.17909e6 | −1.22982 | −0.614908 | − | 0.788599i | \(-0.710807\pi\) | ||||
−0.614908 | + | 0.788599i | \(0.710807\pi\) | |||||||
\(90\) | −6.77179e6 | −0.979162 | ||||||||
\(91\) | −1.28972e7 | −1.79411 | ||||||||
\(92\) | −3.27513e6 | −0.438501 | ||||||||
\(93\) | −434686. | −0.0560384 | ||||||||
\(94\) | 5.08650e6 | 0.631643 | ||||||||
\(95\) | −2.34224e6 | −0.280284 | ||||||||
\(96\) | −1.90923e6 | −0.220247 | ||||||||
\(97\) | 1.53893e7 | 1.71205 | 0.856027 | − | 0.516931i | \(-0.172926\pi\) | ||||
0.856027 | + | 0.516931i | \(0.172926\pi\) | |||||||
\(98\) | −2.13338e7 | −2.28969 | ||||||||
\(99\) | −4.42252e6 | −0.458086 | ||||||||
\(100\) | 3.74502e7 | 3.74502 | ||||||||
\(101\) | −7.54010e6 | −0.728203 | −0.364101 | − | 0.931359i | \(-0.618624\pi\) | ||||
−0.364101 | + | 0.931359i | \(0.618624\pi\) | |||||||
\(102\) | 1.70785e7 | 1.59349 | ||||||||
\(103\) | −5.04980e6 | −0.455348 | −0.227674 | − | 0.973737i | \(-0.573112\pi\) | ||||
−0.227674 | + | 0.973737i | \(0.573112\pi\) | |||||||
\(104\) | −2.63679e7 | −2.29857 | ||||||||
\(105\) | −1.73195e7 | −1.46007 | ||||||||
\(106\) | 2.18918e6 | 0.178530 | ||||||||
\(107\) | 9.37807e6 | 0.740066 | 0.370033 | − | 0.929019i | \(-0.379346\pi\) | ||||
0.370033 | + | 0.929019i | \(0.379346\pi\) | |||||||
\(108\) | 5.29829e6 | 0.404718 | ||||||||
\(109\) | −2.92944e6 | −0.216667 | −0.108333 | − | 0.994115i | \(-0.534551\pi\) | ||||
−0.108333 | + | 0.994115i | \(0.534551\pi\) | |||||||
\(110\) | 5.63532e7 | 4.03686 | ||||||||
\(111\) | 2.73509e6 | 0.189820 | ||||||||
\(112\) | −2.97532e7 | −2.00111 | ||||||||
\(113\) | −2.03016e7 | −1.32360 | −0.661800 | − | 0.749681i | \(-0.730207\pi\) | ||||
−0.661800 | + | 0.749681i | \(0.730207\pi\) | |||||||
\(114\) | 2.70401e6 | 0.170939 | ||||||||
\(115\) | −5.67107e6 | −0.347714 | ||||||||
\(116\) | −3.34607e7 | −1.99036 | ||||||||
\(117\) | 6.83174e6 | 0.394349 | ||||||||
\(118\) | −1.92296e7 | −1.07742 | ||||||||
\(119\) | 4.36801e7 | 2.37612 | ||||||||
\(120\) | −3.54092e7 | −1.87061 | ||||||||
\(121\) | 1.73160e7 | 0.888586 | ||||||||
\(122\) | 2.88921e7 | 1.44052 | ||||||||
\(123\) | −1.61491e7 | −0.782493 | ||||||||
\(124\) | −4.33368e6 | −0.204118 | ||||||||
\(125\) | 2.84329e7 | 1.30208 | ||||||||
\(126\) | 1.99946e7 | 0.890463 | ||||||||
\(127\) | −1.35596e7 | −0.587400 | −0.293700 | − | 0.955898i | \(-0.594887\pi\) | ||||
−0.293700 | + | 0.955898i | \(0.594887\pi\) | |||||||
\(128\) | 3.61157e7 | 1.52216 | ||||||||
\(129\) | −3.21113e6 | −0.131702 | ||||||||
\(130\) | −8.70521e7 | −3.47518 | ||||||||
\(131\) | 411901. | 0.0160082 | 0.00800411 | − | 0.999968i | \(-0.497452\pi\) | ||||
0.00800411 | + | 0.999968i | \(0.497452\pi\) | |||||||
\(132\) | −4.40911e7 | −1.66856 | ||||||||
\(133\) | 6.91578e6 | 0.254894 | ||||||||
\(134\) | 8.52092e7 | 3.05928 | ||||||||
\(135\) | 9.17429e6 | 0.320926 | ||||||||
\(136\) | 8.93025e7 | 3.04423 | ||||||||
\(137\) | 5.98529e7 | 1.98867 | 0.994337 | − | 0.106274i | \(-0.0338921\pi\) | ||||
0.994337 | + | 0.106274i | \(0.0338921\pi\) | |||||||
\(138\) | 6.54699e6 | 0.212063 | ||||||||
\(139\) | 5.65384e7 | 1.78563 | 0.892815 | − | 0.450423i | \(-0.148727\pi\) | ||||
0.892815 | + | 0.450423i | \(0.148727\pi\) | |||||||
\(140\) | −1.72670e8 | −5.31825 | ||||||||
\(141\) | −6.89110e6 | −0.207024 | ||||||||
\(142\) | 1.62315e7 | 0.475719 | ||||||||
\(143\) | −5.68521e7 | −1.62581 | ||||||||
\(144\) | 1.57605e7 | 0.439847 | ||||||||
\(145\) | −5.79391e7 | −1.57828 | ||||||||
\(146\) | −1.27590e8 | −3.39298 | ||||||||
\(147\) | 2.89026e7 | 0.750458 | ||||||||
\(148\) | 2.72680e7 | 0.691412 | ||||||||
\(149\) | −3.55040e7 | −0.879275 | −0.439638 | − | 0.898175i | \(-0.644893\pi\) | ||||
−0.439638 | + | 0.898175i | \(0.644893\pi\) | |||||||
\(150\) | −7.48631e7 | −1.81113 | ||||||||
\(151\) | 1.69536e7 | 0.400721 | 0.200361 | − | 0.979722i | \(-0.435789\pi\) | ||||
0.200361 | + | 0.979722i | \(0.435789\pi\) | |||||||
\(152\) | 1.41391e7 | 0.326564 | ||||||||
\(153\) | −2.31377e7 | −0.522276 | ||||||||
\(154\) | −1.66390e8 | −3.67118 | ||||||||
\(155\) | −7.50401e6 | −0.161857 | ||||||||
\(156\) | 6.81102e7 | 1.43640 | ||||||||
\(157\) | 5.44237e7 | 1.12238 | 0.561189 | − | 0.827688i | \(-0.310344\pi\) | ||||
0.561189 | + | 0.827688i | \(0.310344\pi\) | |||||||
\(158\) | 1.33364e8 | 2.68992 | ||||||||
\(159\) | −2.96586e6 | −0.0585142 | ||||||||
\(160\) | −3.29592e7 | −0.636146 | ||||||||
\(161\) | 1.67446e7 | 0.316216 | ||||||||
\(162\) | −1.05913e7 | −0.195725 | ||||||||
\(163\) | −1.51739e7 | −0.274436 | −0.137218 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137218 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(164\) | −1.61001e8 | −2.85020 | ||||||||
\(165\) | −7.63463e7 | −1.32310 | ||||||||
\(166\) | 1.42601e8 | 2.41961 | ||||||||
\(167\) | −2.89893e7 | −0.481649 | −0.240824 | − | 0.970569i | \(-0.577418\pi\) | ||||
−0.240824 | + | 0.970569i | \(0.577418\pi\) | |||||||
\(168\) | 1.04551e8 | 1.70115 | ||||||||
\(169\) | 2.50743e7 | 0.399600 | ||||||||
\(170\) | 2.94828e8 | 4.60253 | ||||||||
\(171\) | −3.66334e6 | −0.0560262 | ||||||||
\(172\) | −3.20139e7 | −0.479721 | ||||||||
\(173\) | 1.52831e7 | 0.224413 | 0.112207 | − | 0.993685i | \(-0.464208\pi\) | ||||
0.112207 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(174\) | 6.68880e7 | 0.962556 | ||||||||
\(175\) | −1.91470e8 | −2.70065 | ||||||||
\(176\) | −1.31155e8 | −1.81339 | ||||||||
\(177\) | 2.60519e7 | 0.353129 | ||||||||
\(178\) | 1.63004e8 | 2.16635 | ||||||||
\(179\) | −1.01079e8 | −1.31727 | −0.658635 | − | 0.752463i | \(-0.728866\pi\) | ||||
−0.658635 | + | 0.752463i | \(0.728866\pi\) | |||||||
\(180\) | 9.14647e7 | 1.16896 | ||||||||
\(181\) | 4.91643e6 | 0.0616276 | 0.0308138 | − | 0.999525i | \(-0.490190\pi\) | ||||
0.0308138 | + | 0.999525i | \(0.490190\pi\) | |||||||
\(182\) | 2.57033e8 | 3.16038 | ||||||||
\(183\) | −3.91424e7 | −0.472138 | ||||||||
\(184\) | 3.42338e7 | 0.405128 | ||||||||
\(185\) | 4.72160e7 | 0.548263 | ||||||||
\(186\) | 8.66304e6 | 0.0987132 | ||||||||
\(187\) | 1.92546e8 | 2.15323 | ||||||||
\(188\) | −6.87020e7 | −0.754080 | ||||||||
\(189\) | −2.70883e7 | −0.291854 | ||||||||
\(190\) | 4.66794e7 | 0.493728 | ||||||||
\(191\) | −6.54949e7 | −0.680128 | −0.340064 | − | 0.940402i | \(-0.610449\pi\) | ||||
−0.340064 | + | 0.940402i | \(0.610449\pi\) | |||||||
\(192\) | −3.66665e7 | −0.373866 | ||||||||
\(193\) | 2.61850e7 | 0.262182 | 0.131091 | − | 0.991370i | \(-0.458152\pi\) | ||||
0.131091 | + | 0.991370i | \(0.458152\pi\) | |||||||
\(194\) | −3.06699e8 | −3.01583 | ||||||||
\(195\) | 1.17937e8 | 1.13901 | ||||||||
\(196\) | 2.88150e8 | 2.73352 | ||||||||
\(197\) | 4.80412e7 | 0.447695 | 0.223848 | − | 0.974624i | \(-0.428138\pi\) | ||||
0.223848 | + | 0.974624i | \(0.428138\pi\) | |||||||
\(198\) | 8.81383e7 | 0.806931 | ||||||||
\(199\) | 1.05462e7 | 0.0948664 | 0.0474332 | − | 0.998874i | \(-0.484896\pi\) | ||||
0.0474332 | + | 0.998874i | \(0.484896\pi\) | |||||||
\(200\) | −3.91454e8 | −3.46000 | ||||||||
\(201\) | −1.15440e8 | −1.00270 | ||||||||
\(202\) | 1.50270e8 | 1.28275 | ||||||||
\(203\) | 1.71073e8 | 1.43531 | ||||||||
\(204\) | −2.30675e8 | −1.90237 | ||||||||
\(205\) | −2.78783e8 | −2.26010 | ||||||||
\(206\) | 1.00639e8 | 0.802108 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | 2.02603e8 | 1.56108 | ||||||||
\(209\) | 3.04854e7 | 0.230983 | ||||||||
\(210\) | 3.45168e8 | 2.57195 | ||||||||
\(211\) | 9.30256e7 | 0.681733 | 0.340866 | − | 0.940112i | \(-0.389280\pi\) | ||||
0.340866 | + | 0.940112i | \(0.389280\pi\) | |||||||
\(212\) | −2.95687e7 | −0.213136 | ||||||||
\(213\) | −2.19902e7 | −0.155919 | ||||||||
\(214\) | −1.86899e8 | −1.30365 | ||||||||
\(215\) | −5.54339e7 | −0.380400 | ||||||||
\(216\) | −5.53812e7 | −0.373916 | ||||||||
\(217\) | 2.21566e7 | 0.147195 | ||||||||
\(218\) | 5.83821e7 | 0.381665 | ||||||||
\(219\) | 1.72857e8 | 1.11207 | ||||||||
\(220\) | −7.61148e8 | −4.81936 | ||||||||
\(221\) | −2.97438e8 | −1.85363 | ||||||||
\(222\) | −5.45088e7 | −0.334373 | ||||||||
\(223\) | −1.33339e8 | −0.805176 | −0.402588 | − | 0.915381i | \(-0.631889\pi\) | ||||
−0.402588 | + | 0.915381i | \(0.631889\pi\) | |||||||
\(224\) | 9.73165e7 | 0.578520 | ||||||||
\(225\) | 1.01423e8 | 0.593606 | ||||||||
\(226\) | 4.04600e8 | 2.33156 | ||||||||
\(227\) | 2.24477e8 | 1.27374 | 0.636872 | − | 0.770970i | \(-0.280228\pi\) | ||||
0.636872 | + | 0.770970i | \(0.280228\pi\) | |||||||
\(228\) | −3.65223e7 | −0.204073 | ||||||||
\(229\) | −2.59953e8 | −1.43045 | −0.715223 | − | 0.698897i | \(-0.753675\pi\) | ||||
−0.715223 | + | 0.698897i | \(0.753675\pi\) | |||||||
\(230\) | 1.13021e8 | 0.612508 | ||||||||
\(231\) | 2.25423e8 | 1.20325 | ||||||||
\(232\) | 3.49753e8 | 1.83888 | ||||||||
\(233\) | −5.23601e7 | −0.271178 | −0.135589 | − | 0.990765i | \(-0.543293\pi\) | ||||
−0.135589 | + | 0.990765i | \(0.543293\pi\) | |||||||
\(234\) | −1.36153e8 | −0.694657 | ||||||||
\(235\) | −1.18961e8 | −0.597955 | ||||||||
\(236\) | 2.59729e8 | 1.28626 | ||||||||
\(237\) | −1.80679e8 | −0.881636 | ||||||||
\(238\) | −8.70518e8 | −4.18561 | ||||||||
\(239\) | 3.85956e8 | 1.82871 | 0.914357 | − | 0.404910i | \(-0.132697\pi\) | ||||
0.914357 | + | 0.404910i | \(0.132697\pi\) | |||||||
\(240\) | 2.72074e8 | 1.27042 | ||||||||
\(241\) | 4.72252e7 | 0.217327 | 0.108664 | − | 0.994079i | \(-0.465343\pi\) | ||||
0.108664 | + | 0.994079i | \(0.465343\pi\) | |||||||
\(242\) | −3.45098e8 | −1.56527 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −3.90237e8 | −1.71975 | ||||||||
\(245\) | 4.98947e8 | 2.16757 | ||||||||
\(246\) | 3.21842e8 | 1.37838 | ||||||||
\(247\) | −4.70927e7 | −0.198845 | ||||||||
\(248\) | 4.52985e7 | 0.188583 | ||||||||
\(249\) | −1.93194e8 | −0.793041 | ||||||||
\(250\) | −5.66652e8 | −2.29364 | ||||||||
\(251\) | 4.32121e7 | 0.172484 | 0.0862418 | − | 0.996274i | \(-0.472514\pi\) | ||||
0.0862418 | + | 0.996274i | \(0.472514\pi\) | |||||||
\(252\) | −2.70062e8 | −1.06307 | ||||||||
\(253\) | 7.38119e7 | 0.286553 | ||||||||
\(254\) | 2.70235e8 | 1.03472 | ||||||||
\(255\) | −3.99427e8 | −1.50851 | ||||||||
\(256\) | −5.45938e8 | −2.03378 | ||||||||
\(257\) | −3.37491e8 | −1.24021 | −0.620106 | − | 0.784518i | \(-0.712911\pi\) | ||||
−0.620106 | + | 0.784518i | \(0.712911\pi\) | |||||||
\(258\) | 6.39959e7 | 0.231997 | ||||||||
\(259\) | −1.39412e8 | −0.498598 | ||||||||
\(260\) | 1.17579e9 | 4.14881 | ||||||||
\(261\) | −9.06187e7 | −0.315483 | ||||||||
\(262\) | −8.20894e6 | −0.0281989 | ||||||||
\(263\) | −1.49351e8 | −0.506249 | −0.253125 | − | 0.967434i | \(-0.581458\pi\) | ||||
−0.253125 | + | 0.967434i | \(0.581458\pi\) | |||||||
\(264\) | 4.60869e8 | 1.54157 | ||||||||
\(265\) | −5.11998e7 | −0.169008 | ||||||||
\(266\) | −1.37827e8 | −0.449003 | ||||||||
\(267\) | −2.20836e8 | −0.710035 | ||||||||
\(268\) | −1.15090e9 | −3.65229 | ||||||||
\(269\) | 3.20872e8 | 1.00508 | 0.502538 | − | 0.864555i | \(-0.332400\pi\) | ||||
0.502538 | + | 0.864555i | \(0.332400\pi\) | |||||||
\(270\) | −1.82838e8 | −0.565319 | ||||||||
\(271\) | 2.45542e7 | 0.0749433 | 0.0374716 | − | 0.999298i | \(-0.488070\pi\) | ||||
0.0374716 | + | 0.999298i | \(0.488070\pi\) | |||||||
\(272\) | −6.86175e8 | −2.06749 | ||||||||
\(273\) | −3.48224e8 | −1.03583 | ||||||||
\(274\) | −1.19283e9 | −3.50310 | ||||||||
\(275\) | −8.44020e8 | −2.44731 | ||||||||
\(276\) | −8.84285e7 | −0.253169 | ||||||||
\(277\) | 2.99640e8 | 0.847072 | 0.423536 | − | 0.905879i | \(-0.360789\pi\) | ||||
0.423536 | + | 0.905879i | \(0.360789\pi\) | |||||||
\(278\) | −1.12678e9 | −3.14544 | ||||||||
\(279\) | −1.17365e7 | −0.0323538 | ||||||||
\(280\) | 1.80486e9 | 4.91350 | ||||||||
\(281\) | 2.26970e8 | 0.610235 | 0.305117 | − | 0.952315i | \(-0.401304\pi\) | ||||
0.305117 | + | 0.952315i | \(0.401304\pi\) | |||||||
\(282\) | 1.37336e8 | 0.364679 | ||||||||
\(283\) | 7.55768e7 | 0.198215 | 0.0991073 | − | 0.995077i | \(-0.468401\pi\) | ||||
0.0991073 | + | 0.995077i | \(0.468401\pi\) | |||||||
\(284\) | −2.19235e8 | −0.567931 | ||||||||
\(285\) | −6.32405e7 | −0.161822 | ||||||||
\(286\) | 1.13303e9 | 2.86391 | ||||||||
\(287\) | 8.23144e8 | 2.05536 | ||||||||
\(288\) | −5.15493e7 | −0.127160 | ||||||||
\(289\) | 5.97021e8 | 1.45495 | ||||||||
\(290\) | 1.15469e9 | 2.78018 | ||||||||
\(291\) | 4.15511e8 | 0.988455 | ||||||||
\(292\) | 1.72333e9 | 4.05067 | ||||||||
\(293\) | 7.83295e8 | 1.81923 | 0.909617 | − | 0.415448i | \(-0.136375\pi\) | ||||
0.909617 | + | 0.415448i | \(0.136375\pi\) | |||||||
\(294\) | −5.76012e8 | −1.32195 | ||||||||
\(295\) | 4.49736e8 | 1.01995 | ||||||||
\(296\) | −2.85023e8 | −0.638791 | ||||||||
\(297\) | −1.19408e8 | −0.264476 | ||||||||
\(298\) | 7.07573e8 | 1.54887 | ||||||||
\(299\) | −1.14022e8 | −0.246682 | ||||||||
\(300\) | 1.01116e9 | 2.16219 | ||||||||
\(301\) | 1.63676e8 | 0.345941 | ||||||||
\(302\) | −3.37875e8 | −0.705881 | ||||||||
\(303\) | −2.03583e8 | −0.420428 | ||||||||
\(304\) | −1.08641e8 | −0.221786 | ||||||||
\(305\) | −6.75718e8 | −1.36369 | ||||||||
\(306\) | 4.61120e8 | 0.920003 | ||||||||
\(307\) | 4.64667e7 | 0.0916554 | 0.0458277 | − | 0.998949i | \(-0.485407\pi\) | ||||
0.0458277 | + | 0.998949i | \(0.485407\pi\) | |||||||
\(308\) | 2.24739e9 | 4.38279 | ||||||||
\(309\) | −1.36344e8 | −0.262895 | ||||||||
\(310\) | 1.49551e8 | 0.285116 | ||||||||
\(311\) | 9.79489e7 | 0.184645 | 0.0923227 | − | 0.995729i | \(-0.470571\pi\) | ||||
0.0923227 | + | 0.995729i | \(0.470571\pi\) | |||||||
\(312\) | −7.11933e8 | −1.32708 | ||||||||
\(313\) | −7.03146e8 | −1.29610 | −0.648052 | − | 0.761596i | \(-0.724416\pi\) | ||||
−0.648052 | + | 0.761596i | \(0.724416\pi\) | |||||||
\(314\) | −1.08463e9 | −1.97710 | ||||||||
\(315\) | −4.67627e8 | −0.842972 | ||||||||
\(316\) | −1.80131e9 | −3.21133 | ||||||||
\(317\) | 1.51468e8 | 0.267064 | 0.133532 | − | 0.991045i | \(-0.457368\pi\) | ||||
0.133532 | + | 0.991045i | \(0.457368\pi\) | |||||||
\(318\) | 5.91079e7 | 0.103074 | ||||||||
\(319\) | 7.54107e8 | 1.30067 | ||||||||
\(320\) | −6.32976e8 | −1.07985 | ||||||||
\(321\) | 2.53208e8 | 0.427277 | ||||||||
\(322\) | −3.33710e8 | −0.557023 | ||||||||
\(323\) | 1.59493e8 | 0.263350 | ||||||||
\(324\) | 1.43054e8 | 0.233664 | ||||||||
\(325\) | 1.30381e9 | 2.10679 | ||||||||
\(326\) | 3.02408e8 | 0.483427 | ||||||||
\(327\) | −7.90950e7 | −0.125093 | ||||||||
\(328\) | 1.68289e9 | 2.63328 | ||||||||
\(329\) | 3.51250e8 | 0.543789 | ||||||||
\(330\) | 1.52154e9 | 2.33068 | ||||||||
\(331\) | −3.67566e8 | −0.557105 | −0.278552 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278552 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(332\) | −1.92608e9 | −2.88862 | ||||||||
\(333\) | 7.38475e7 | 0.109593 | ||||||||
\(334\) | 5.77740e8 | 0.848438 | ||||||||
\(335\) | −1.99285e9 | −2.89612 | ||||||||
\(336\) | −8.03336e8 | −1.15534 | ||||||||
\(337\) | −3.50623e8 | −0.499041 | −0.249521 | − | 0.968370i | \(-0.580273\pi\) | ||||
−0.249521 | + | 0.968370i | \(0.580273\pi\) | |||||||
\(338\) | −4.99716e8 | −0.703907 | ||||||||
\(339\) | −5.48144e8 | −0.764180 | ||||||||
\(340\) | −3.98216e9 | −5.49468 | ||||||||
\(341\) | 9.76686e7 | 0.133387 | ||||||||
\(342\) | 7.30082e7 | 0.0986916 | ||||||||
\(343\) | −3.39824e8 | −0.454699 | ||||||||
\(344\) | 3.34630e8 | 0.443211 | ||||||||
\(345\) | −1.53119e8 | −0.200753 | ||||||||
\(346\) | −3.04582e8 | −0.395310 | ||||||||
\(347\) | 8.21515e7 | 0.105551 | 0.0527755 | − | 0.998606i | \(-0.483193\pi\) | ||||
0.0527755 | + | 0.998606i | \(0.483193\pi\) | |||||||
\(348\) | −9.03439e8 | −1.14914 | ||||||||
\(349\) | 5.47670e8 | 0.689652 | 0.344826 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344826 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(350\) | 3.81589e9 | 4.75726 | ||||||||
\(351\) | 1.84457e8 | 0.227678 | ||||||||
\(352\) | 4.28981e8 | 0.524251 | ||||||||
\(353\) | 7.05195e8 | 0.853292 | 0.426646 | − | 0.904419i | \(-0.359695\pi\) | ||||
0.426646 | + | 0.904419i | \(0.359695\pi\) | |||||||
\(354\) | −5.19199e8 | −0.622046 | ||||||||
\(355\) | −3.79618e8 | −0.450347 | ||||||||
\(356\) | −2.20166e9 | −2.58628 | ||||||||
\(357\) | 1.17936e9 | 1.37186 | ||||||||
\(358\) | 2.01444e9 | 2.32041 | ||||||||
\(359\) | −6.05279e8 | −0.690438 | −0.345219 | − | 0.938522i | \(-0.612195\pi\) | ||||
−0.345219 | + | 0.938522i | \(0.612195\pi\) | |||||||
\(360\) | −9.56049e8 | −1.07999 | ||||||||
\(361\) | −8.68620e8 | −0.971750 | ||||||||
\(362\) | −9.79816e7 | −0.108559 | ||||||||
\(363\) | 4.67533e8 | 0.513025 | ||||||||
\(364\) | −3.47168e9 | −3.77298 | ||||||||
\(365\) | 2.98404e9 | 3.21202 | ||||||||
\(366\) | 7.80086e8 | 0.831684 | ||||||||
\(367\) | −4.00347e8 | −0.422771 | −0.211386 | − | 0.977403i | \(-0.567798\pi\) | ||||
−0.211386 | + | 0.977403i | \(0.567798\pi\) | |||||||
\(368\) | −2.63043e8 | −0.275143 | ||||||||
\(369\) | −4.36026e8 | −0.451772 | ||||||||
\(370\) | −9.40988e8 | −0.965779 | ||||||||
\(371\) | 1.51174e8 | 0.153698 | ||||||||
\(372\) | −1.17009e8 | −0.117848 | ||||||||
\(373\) | 7.43740e8 | 0.742063 | 0.371031 | − | 0.928620i | \(-0.379004\pi\) | ||||
0.371031 | + | 0.928620i | \(0.379004\pi\) | |||||||
\(374\) | −3.83733e9 | −3.79297 | ||||||||
\(375\) | 7.67689e8 | 0.751755 | ||||||||
\(376\) | 7.18119e8 | 0.696689 | ||||||||
\(377\) | −1.16491e9 | −1.11969 | ||||||||
\(378\) | 5.39855e8 | 0.514109 | ||||||||
\(379\) | 1.08034e9 | 1.01935 | 0.509676 | − | 0.860366i | \(-0.329765\pi\) | ||||
0.509676 | + | 0.860366i | \(0.329765\pi\) | |||||||
\(380\) | −6.30487e8 | −0.589432 | ||||||||
\(381\) | −3.66109e8 | −0.339135 | ||||||||
\(382\) | 1.30528e9 | 1.19806 | ||||||||
\(383\) | 1.83043e9 | 1.66478 | 0.832389 | − | 0.554192i | \(-0.186973\pi\) | ||||
0.832389 | + | 0.554192i | \(0.186973\pi\) | |||||||
\(384\) | 9.75124e8 | 0.878822 | ||||||||
\(385\) | 3.89148e9 | 3.47538 | ||||||||
\(386\) | −5.21852e8 | −0.461840 | ||||||||
\(387\) | −8.67005e7 | −0.0760384 | ||||||||
\(388\) | 4.14251e9 | 3.60041 | ||||||||
\(389\) | −9.20484e8 | −0.792853 | −0.396426 | − | 0.918066i | \(-0.629750\pi\) | ||||
−0.396426 | + | 0.918066i | \(0.629750\pi\) | |||||||
\(390\) | −2.35041e9 | −2.00640 | ||||||||
\(391\) | 3.86168e8 | 0.326706 | ||||||||
\(392\) | −3.01193e9 | −2.52548 | ||||||||
\(393\) | 1.11213e7 | 0.00924235 | ||||||||
\(394\) | −9.57433e8 | −0.788627 | ||||||||
\(395\) | −3.11908e9 | −2.54646 | ||||||||
\(396\) | −1.19046e9 | −0.963345 | ||||||||
\(397\) | 1.68258e9 | 1.34961 | 0.674807 | − | 0.737995i | \(-0.264227\pi\) | ||||
0.674807 | + | 0.737995i | \(0.264227\pi\) | |||||||
\(398\) | −2.10180e8 | −0.167110 | ||||||||
\(399\) | 1.86726e8 | 0.147163 | ||||||||
\(400\) | 3.00782e9 | 2.34986 | ||||||||
\(401\) | 1.78289e9 | 1.38076 | 0.690381 | − | 0.723446i | \(-0.257443\pi\) | ||||
0.690381 | + | 0.723446i | \(0.257443\pi\) | |||||||
\(402\) | 2.30065e9 | 1.76628 | ||||||||
\(403\) | −1.50875e8 | −0.114828 | ||||||||
\(404\) | −2.02965e9 | −1.53139 | ||||||||
\(405\) | 2.47706e8 | 0.185287 | ||||||||
\(406\) | −3.40938e9 | −2.52834 | ||||||||
\(407\) | −6.14541e8 | −0.451825 | ||||||||
\(408\) | 2.41117e9 | 1.75759 | ||||||||
\(409\) | −1.62476e9 | −1.17425 | −0.587123 | − | 0.809498i | \(-0.699739\pi\) | ||||
−0.587123 | + | 0.809498i | \(0.699739\pi\) | |||||||
\(410\) | 5.55597e9 | 3.98123 | ||||||||
\(411\) | 1.61603e9 | 1.14816 | ||||||||
\(412\) | −1.35931e9 | −0.957587 | ||||||||
\(413\) | −1.32790e9 | −0.927559 | ||||||||
\(414\) | 1.76769e8 | 0.122435 | ||||||||
\(415\) | −3.33512e9 | −2.29056 | ||||||||
\(416\) | −6.62673e8 | −0.451308 | ||||||||
\(417\) | 1.52654e9 | 1.03093 | ||||||||
\(418\) | −6.07557e8 | −0.406883 | ||||||||
\(419\) | 2.24799e9 | 1.49295 | 0.746476 | − | 0.665412i | \(-0.231744\pi\) | ||||
0.746476 | + | 0.665412i | \(0.231744\pi\) | |||||||
\(420\) | −4.66209e9 | −3.07050 | ||||||||
\(421\) | 3.33475e8 | 0.217809 | 0.108904 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108904 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(422\) | −1.85395e9 | −1.20089 | ||||||||
\(423\) | −1.86060e8 | −0.119526 | ||||||||
\(424\) | 3.09071e8 | 0.196915 | ||||||||
\(425\) | −4.41573e9 | −2.79024 | ||||||||
\(426\) | 4.38251e8 | 0.274656 | ||||||||
\(427\) | 1.99515e9 | 1.24016 | ||||||||
\(428\) | 2.52440e9 | 1.55634 | ||||||||
\(429\) | −1.53501e9 | −0.938663 | ||||||||
\(430\) | 1.10476e9 | 0.670085 | ||||||||
\(431\) | −2.33004e9 | −1.40182 | −0.700910 | − | 0.713249i | \(-0.747223\pi\) | ||||
−0.700910 | + | 0.713249i | \(0.747223\pi\) | |||||||
\(432\) | 4.25534e8 | 0.253946 | ||||||||
\(433\) | 1.82844e8 | 0.108237 | 0.0541183 | − | 0.998535i | \(-0.482765\pi\) | ||||
0.0541183 | + | 0.998535i | \(0.482765\pi\) | |||||||
\(434\) | −4.41568e8 | −0.259289 | ||||||||
\(435\) | −1.56436e9 | −0.911220 | ||||||||
\(436\) | −7.88551e8 | −0.455646 | ||||||||
\(437\) | 6.11411e7 | 0.0350468 | ||||||||
\(438\) | −3.44493e9 | −1.95894 | ||||||||
\(439\) | −1.41207e9 | −0.796580 | −0.398290 | − | 0.917260i | \(-0.630396\pi\) | ||||
−0.398290 | + | 0.917260i | \(0.630396\pi\) | |||||||
\(440\) | 7.95601e9 | 4.45257 | ||||||||
\(441\) | 7.80370e8 | 0.433277 | ||||||||
\(442\) | 5.92776e9 | 3.26522 | ||||||||
\(443\) | 6.88910e8 | 0.376487 | 0.188243 | − | 0.982122i | \(-0.439721\pi\) | ||||
0.188243 | + | 0.982122i | \(0.439721\pi\) | |||||||
\(444\) | 7.36236e8 | 0.399187 | ||||||||
\(445\) | −3.81230e9 | −2.05082 | ||||||||
\(446\) | 2.65737e9 | 1.41834 | ||||||||
\(447\) | −9.58607e8 | −0.507650 | ||||||||
\(448\) | 1.86895e9 | 0.982029 | ||||||||
\(449\) | −6.50678e8 | −0.339238 | −0.169619 | − | 0.985510i | \(-0.554254\pi\) | ||||
−0.169619 | + | 0.985510i | \(0.554254\pi\) | |||||||
\(450\) | −2.02130e9 | −1.04565 | ||||||||
\(451\) | 3.62850e9 | 1.86256 | ||||||||
\(452\) | −5.46482e9 | −2.78350 | ||||||||
\(453\) | 4.57747e8 | 0.231356 | ||||||||
\(454\) | −4.47370e9 | −2.24373 | ||||||||
\(455\) | −6.01141e9 | −2.99183 | ||||||||
\(456\) | 3.81755e8 | 0.188542 | ||||||||
\(457\) | −1.61945e9 | −0.793708 | −0.396854 | − | 0.917882i | \(-0.629898\pi\) | ||||
−0.396854 | + | 0.917882i | \(0.629898\pi\) | |||||||
\(458\) | 5.18072e9 | 2.51977 | ||||||||
\(459\) | −6.24717e8 | −0.301536 | ||||||||
\(460\) | −1.52655e9 | −0.731236 | ||||||||
\(461\) | −6.21807e8 | −0.295599 | −0.147799 | − | 0.989017i | \(-0.547219\pi\) | ||||
−0.147799 | + | 0.989017i | \(0.547219\pi\) | |||||||
\(462\) | −4.49254e9 | −2.11956 | ||||||||
\(463\) | 2.85900e9 | 1.33869 | 0.669347 | − | 0.742950i | \(-0.266574\pi\) | ||||
0.669347 | + | 0.742950i | \(0.266574\pi\) | |||||||
\(464\) | −2.68740e9 | −1.24888 | ||||||||
\(465\) | −2.02608e8 | −0.0934484 | ||||||||
\(466\) | 1.04351e9 | 0.477688 | ||||||||
\(467\) | 1.28603e9 | 0.584309 | 0.292154 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292154 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(468\) | 1.83898e9 | 0.829307 | ||||||||
\(469\) | 5.88415e9 | 2.63377 | ||||||||
\(470\) | 2.37083e9 | 1.05331 | ||||||||
\(471\) | 1.46944e9 | 0.648005 | ||||||||
\(472\) | −2.71486e9 | −1.18837 | ||||||||
\(473\) | 7.21500e8 | 0.313489 | ||||||||
\(474\) | 3.60083e9 | 1.55303 | ||||||||
\(475\) | −6.99133e8 | −0.299317 | ||||||||
\(476\) | 1.17579e10 | 4.99694 | ||||||||
\(477\) | −8.00783e7 | −0.0337832 | ||||||||
\(478\) | −7.69188e9 | −3.22133 | ||||||||
\(479\) | −3.90154e9 | −1.62204 | −0.811021 | − | 0.585017i | \(-0.801088\pi\) | ||||
−0.811021 | + | 0.585017i | \(0.801088\pi\) | |||||||
\(480\) | −8.89899e8 | −0.367279 | ||||||||
\(481\) | 9.49319e8 | 0.388959 | ||||||||
\(482\) | −9.41170e8 | −0.382828 | ||||||||
\(483\) | 4.52104e8 | 0.182567 | ||||||||
\(484\) | 4.66115e9 | 1.86868 | ||||||||
\(485\) | 7.17299e9 | 2.85499 | ||||||||
\(486\) | −2.85965e8 | −0.113002 | ||||||||
\(487\) | −2.21345e9 | −0.868397 | −0.434199 | − | 0.900817i | \(-0.642968\pi\) | ||||
−0.434199 | + | 0.900817i | \(0.642968\pi\) | |||||||
\(488\) | 4.07902e9 | 1.58886 | ||||||||
\(489\) | −4.09696e8 | −0.158446 | ||||||||
\(490\) | −9.94372e9 | −3.81823 | ||||||||
\(491\) | −4.33060e9 | −1.65106 | −0.825530 | − | 0.564358i | \(-0.809124\pi\) | ||||
−0.825530 | + | 0.564358i | \(0.809124\pi\) | |||||||
\(492\) | −4.34703e9 | −1.64557 | ||||||||
\(493\) | 3.94532e9 | 1.48292 | ||||||||
\(494\) | 9.38530e8 | 0.350271 | ||||||||
\(495\) | −2.06135e9 | −0.763895 | ||||||||
\(496\) | −3.48061e8 | −0.128076 | ||||||||
\(497\) | 1.12087e9 | 0.409552 | ||||||||
\(498\) | 3.85024e9 | 1.39696 | ||||||||
\(499\) | −1.11601e9 | −0.402085 | −0.201042 | − | 0.979583i | \(-0.564433\pi\) | ||||
−0.201042 | + | 0.979583i | \(0.564433\pi\) | |||||||
\(500\) | 7.65362e9 | 2.73824 | ||||||||
\(501\) | −7.82712e8 | −0.278080 | ||||||||
\(502\) | −8.61192e8 | −0.303834 | ||||||||
\(503\) | −5.61394e9 | −1.96689 | −0.983444 | − | 0.181212i | \(-0.941998\pi\) | ||||
−0.983444 | + | 0.181212i | \(0.941998\pi\) | |||||||
\(504\) | 2.82286e9 | 0.982162 | ||||||||
\(505\) | −3.51446e9 | −1.21434 | ||||||||
\(506\) | −1.47103e9 | −0.504770 | ||||||||
\(507\) | 6.77007e8 | 0.230709 | ||||||||
\(508\) | −3.64999e9 | −1.23529 | ||||||||
\(509\) | 9.54298e8 | 0.320754 | 0.160377 | − | 0.987056i | \(-0.448729\pi\) | ||||
0.160377 | + | 0.987056i | \(0.448729\pi\) | |||||||
\(510\) | 7.96034e9 | 2.65727 | ||||||||
\(511\) | −8.81077e9 | −2.92106 | ||||||||
\(512\) | 6.25741e9 | 2.06039 | ||||||||
\(513\) | −9.89102e7 | −0.0323467 | ||||||||
\(514\) | 6.72600e9 | 2.18467 | ||||||||
\(515\) | −2.35372e9 | −0.759329 | ||||||||
\(516\) | −8.64375e8 | −0.276967 | ||||||||
\(517\) | 1.54834e9 | 0.492777 | ||||||||
\(518\) | 2.77839e9 | 0.878293 | ||||||||
\(519\) | 4.12642e8 | 0.129565 | ||||||||
\(520\) | −1.22901e10 | −3.83305 | ||||||||
\(521\) | −3.27349e9 | −1.01409 | −0.507047 | − | 0.861918i | \(-0.669263\pi\) | ||||
−0.507047 | + | 0.861918i | \(0.669263\pi\) | |||||||
\(522\) | 1.80598e9 | 0.555732 | ||||||||
\(523\) | 3.35615e9 | 1.02585 | 0.512927 | − | 0.858432i | \(-0.328561\pi\) | ||||
0.512927 | + | 0.858432i | \(0.328561\pi\) | |||||||
\(524\) | 1.10876e8 | 0.0336649 | ||||||||
\(525\) | −5.16969e9 | −1.55922 | ||||||||
\(526\) | 2.97649e9 | 0.891772 | ||||||||
\(527\) | 5.10981e8 | 0.152078 | ||||||||
\(528\) | −3.54119e9 | −1.04696 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 1.02038e9 | 0.297713 | ||||||||
\(531\) | 7.03402e8 | 0.203879 | ||||||||
\(532\) | 1.86160e9 | 0.536037 | ||||||||
\(533\) | −5.60516e9 | −1.60340 | ||||||||
\(534\) | 4.40112e9 | 1.25075 | ||||||||
\(535\) | 4.37114e9 | 1.23412 | ||||||||
\(536\) | 1.20299e10 | 3.37433 | ||||||||
\(537\) | −2.72913e9 | −0.760526 | ||||||||
\(538\) | −6.39479e9 | −1.77047 | ||||||||
\(539\) | −6.49405e9 | −1.78630 | ||||||||
\(540\) | 2.46955e9 | 0.674900 | ||||||||
\(541\) | −2.62460e9 | −0.712643 | −0.356321 | − | 0.934363i | \(-0.615969\pi\) | ||||
−0.356321 | + | 0.934363i | \(0.615969\pi\) | |||||||
\(542\) | −4.89350e8 | −0.132015 | ||||||||
\(543\) | 1.32744e8 | 0.0355807 | ||||||||
\(544\) | 2.24434e9 | 0.597712 | ||||||||
\(545\) | −1.36542e9 | −0.361309 | ||||||||
\(546\) | 6.93990e9 | 1.82465 | ||||||||
\(547\) | 1.01462e9 | 0.265063 | 0.132532 | − | 0.991179i | \(-0.457689\pi\) | ||||
0.132532 | + | 0.991179i | \(0.457689\pi\) | |||||||
\(548\) | 1.61113e10 | 4.18214 | ||||||||
\(549\) | −1.05685e9 | −0.272589 | ||||||||
\(550\) | 1.68208e10 | 4.31100 | ||||||||
\(551\) | 6.24655e8 | 0.159078 | ||||||||
\(552\) | 9.24312e8 | 0.233901 | ||||||||
\(553\) | 9.20949e9 | 2.31578 | ||||||||
\(554\) | −5.97164e9 | −1.49214 | ||||||||
\(555\) | 1.27483e9 | 0.316540 | ||||||||
\(556\) | 1.52191e10 | 3.75514 | ||||||||
\(557\) | 2.67923e9 | 0.656926 | 0.328463 | − | 0.944517i | \(-0.393469\pi\) | ||||
0.328463 | + | 0.944517i | \(0.393469\pi\) | |||||||
\(558\) | 2.33902e8 | 0.0569921 | ||||||||
\(559\) | −1.11454e9 | −0.269871 | ||||||||
\(560\) | −1.38680e10 | −3.33700 | ||||||||
\(561\) | 5.19875e9 | 1.24317 | ||||||||
\(562\) | −4.52338e9 | −1.07494 | ||||||||
\(563\) | 3.37265e9 | 0.796512 | 0.398256 | − | 0.917274i | \(-0.369616\pi\) | ||||
0.398256 | + | 0.917274i | \(0.369616\pi\) | |||||||
\(564\) | −1.85496e9 | −0.435368 | ||||||||
\(565\) | −9.46264e9 | −2.20721 | ||||||||
\(566\) | −1.50620e9 | −0.349161 | ||||||||
\(567\) | −7.31385e8 | −0.168502 | ||||||||
\(568\) | 2.29159e9 | 0.524707 | ||||||||
\(569\) | 5.59018e9 | 1.27213 | 0.636067 | − | 0.771634i | \(-0.280560\pi\) | ||||
0.636067 | + | 0.771634i | \(0.280560\pi\) | |||||||
\(570\) | 1.26034e9 | 0.285054 | ||||||||
\(571\) | −1.53052e9 | −0.344043 | −0.172022 | − | 0.985093i | \(-0.555030\pi\) | ||||
−0.172022 | + | 0.985093i | \(0.555030\pi\) | |||||||
\(572\) | −1.53035e10 | −3.41905 | ||||||||
\(573\) | −1.76836e9 | −0.392672 | ||||||||
\(574\) | −1.64048e10 | −3.62058 | ||||||||
\(575\) | −1.69275e9 | −0.371326 | ||||||||
\(576\) | −9.89996e8 | −0.215851 | ||||||||
\(577\) | −2.33744e9 | −0.506554 | −0.253277 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253277 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(578\) | −1.18983e10 | −2.56293 | ||||||||
\(579\) | 7.06995e8 | 0.151371 | ||||||||
\(580\) | −1.55961e10 | −3.31909 | ||||||||
\(581\) | 9.84738e9 | 2.08307 | ||||||||
\(582\) | −8.28088e9 | −1.74119 | ||||||||
\(583\) | 6.66392e8 | 0.139280 | ||||||||
\(584\) | −1.80133e10 | −3.74239 | ||||||||
\(585\) | 3.18429e9 | 0.657608 | ||||||||
\(586\) | −1.56106e10 | −3.20463 | ||||||||
\(587\) | −3.31061e9 | −0.675578 | −0.337789 | − | 0.941222i | \(-0.609679\pi\) | ||||
−0.337789 | + | 0.941222i | \(0.609679\pi\) | |||||||
\(588\) | 7.78004e9 | 1.57820 | ||||||||
\(589\) | 8.09025e7 | 0.0163139 | ||||||||
\(590\) | −8.96296e9 | −1.79668 | ||||||||
\(591\) | 1.29711e9 | 0.258477 | ||||||||
\(592\) | 2.19003e9 | 0.433835 | ||||||||
\(593\) | 8.44516e8 | 0.166309 | 0.0831546 | − | 0.996537i | \(-0.473500\pi\) | ||||
0.0831546 | + | 0.996537i | \(0.473500\pi\) | |||||||
\(594\) | 2.37973e9 | 0.465882 | ||||||||
\(595\) | 2.03594e10 | 3.96237 | ||||||||
\(596\) | −9.55700e9 | −1.84910 | ||||||||
\(597\) | 2.84749e8 | 0.0547711 | ||||||||
\(598\) | 2.27238e9 | 0.434538 | ||||||||
\(599\) | 5.48397e9 | 1.04256 | 0.521280 | − | 0.853386i | \(-0.325455\pi\) | ||||
0.521280 | + | 0.853386i | \(0.325455\pi\) | |||||||
\(600\) | −1.05693e10 | −1.99763 | ||||||||
\(601\) | −1.01235e10 | −1.90225 | −0.951127 | − | 0.308801i | \(-0.900072\pi\) | ||||
−0.951127 | + | 0.308801i | \(0.900072\pi\) | |||||||
\(602\) | −3.26196e9 | −0.609385 | ||||||||
\(603\) | −3.11688e9 | −0.578908 | ||||||||
\(604\) | 4.56359e9 | 0.842708 | ||||||||
\(605\) | 8.07104e9 | 1.48179 | ||||||||
\(606\) | 4.05728e9 | 0.740596 | ||||||||
\(607\) | −6.01963e9 | −1.09247 | −0.546235 | − | 0.837632i | \(-0.683939\pi\) | ||||
−0.546235 | + | 0.837632i | \(0.683939\pi\) | |||||||
\(608\) | 3.55341e8 | 0.0641184 | ||||||||
\(609\) | 4.61897e9 | 0.828676 | ||||||||
\(610\) | 1.34667e10 | 2.40218 | ||||||||
\(611\) | −2.39182e9 | −0.424213 | ||||||||
\(612\) | −6.22823e9 | −1.09833 | ||||||||
\(613\) | 1.95203e9 | 0.342274 | 0.171137 | − | 0.985247i | \(-0.445256\pi\) | ||||
0.171137 | + | 0.985247i | \(0.445256\pi\) | |||||||
\(614\) | −9.26055e8 | −0.161453 | ||||||||
\(615\) | −7.52713e9 | −1.30487 | ||||||||
\(616\) | −2.34912e10 | −4.04923 | ||||||||
\(617\) | 9.76165e8 | 0.167311 | 0.0836556 | − | 0.996495i | \(-0.473340\pi\) | ||||
0.0836556 | + | 0.996495i | \(0.473340\pi\) | |||||||
\(618\) | 2.71726e9 | 0.463097 | ||||||||
\(619\) | −2.48694e9 | −0.421452 | −0.210726 | − | 0.977545i | \(-0.567583\pi\) | ||||
−0.210726 | + | 0.977545i | \(0.567583\pi\) | |||||||
\(620\) | −2.01994e9 | −0.340383 | ||||||||
\(621\) | −2.39483e8 | −0.0401286 | ||||||||
\(622\) | −1.95206e9 | −0.325258 | ||||||||
\(623\) | 1.12563e10 | 1.86504 | ||||||||
\(624\) | 5.47029e9 | 0.901289 | ||||||||
\(625\) | 2.38341e9 | 0.390498 | ||||||||
\(626\) | 1.40133e10 | 2.28312 | ||||||||
\(627\) | 8.23107e8 | 0.133358 | ||||||||
\(628\) | 1.46498e10 | 2.36034 | ||||||||
\(629\) | −3.21515e9 | −0.515138 | ||||||||
\(630\) | 9.31954e9 | 1.48492 | ||||||||
\(631\) | 3.03958e9 | 0.481627 | 0.240813 | − | 0.970571i | \(-0.422586\pi\) | ||||
0.240813 | + | 0.970571i | \(0.422586\pi\) | |||||||
\(632\) | 1.88285e10 | 2.96692 | ||||||||
\(633\) | 2.51169e9 | 0.393598 | ||||||||
\(634\) | −3.01868e9 | −0.470440 | ||||||||
\(635\) | −6.32016e9 | −0.979536 | ||||||||
\(636\) | −7.98354e8 | −0.123054 | ||||||||
\(637\) | 1.00318e10 | 1.53776 | ||||||||
\(638\) | −1.50289e10 | −2.29116 | ||||||||
\(639\) | −5.93735e8 | −0.0900201 | ||||||||
\(640\) | 1.68336e10 | 2.53833 | ||||||||
\(641\) | −1.19765e10 | −1.79609 | −0.898046 | − | 0.439902i | \(-0.855013\pi\) | ||||
−0.898046 | + | 0.439902i | \(0.855013\pi\) | |||||||
\(642\) | −5.04628e9 | −0.752660 | ||||||||
\(643\) | 4.75355e9 | 0.705146 | 0.352573 | − | 0.935784i | \(-0.385307\pi\) | ||||
0.352573 | + | 0.935784i | \(0.385307\pi\) | |||||||
\(644\) | 4.50733e9 | 0.664996 | ||||||||
\(645\) | −1.49671e9 | −0.219624 | ||||||||
\(646\) | −3.17860e9 | −0.463898 | ||||||||
\(647\) | 2.68173e9 | 0.389269 | 0.194635 | − | 0.980876i | \(-0.437648\pi\) | ||||
0.194635 | + | 0.980876i | \(0.437648\pi\) | |||||||
\(648\) | −1.49529e9 | −0.215881 | ||||||||
\(649\) | −5.85354e9 | −0.840547 | ||||||||
\(650\) | −2.59841e10 | −3.71117 | ||||||||
\(651\) | 5.98229e8 | 0.0849833 | ||||||||
\(652\) | −4.08454e9 | −0.577134 | ||||||||
\(653\) | 2.10661e9 | 0.296065 | 0.148033 | − | 0.988982i | \(-0.452706\pi\) | ||||
0.148033 | + | 0.988982i | \(0.452706\pi\) | |||||||
\(654\) | 1.57632e9 | 0.220354 | ||||||||
\(655\) | 1.91988e8 | 0.0266950 | ||||||||
\(656\) | −1.29308e10 | −1.78840 | ||||||||
\(657\) | 4.66713e9 | 0.642054 | ||||||||
\(658\) | −7.00020e9 | −0.957899 | ||||||||
\(659\) | 1.10631e10 | 1.50583 | 0.752916 | − | 0.658117i | \(-0.228647\pi\) | ||||
0.752916 | + | 0.658117i | \(0.228647\pi\) | |||||||
\(660\) | −2.05510e10 | −2.78246 | ||||||||
\(661\) | −1.11027e10 | −1.49528 | −0.747641 | − | 0.664103i | \(-0.768814\pi\) | ||||
−0.747641 | + | 0.664103i | \(0.768814\pi\) | |||||||
\(662\) | 7.32537e9 | 0.981356 | ||||||||
\(663\) | −8.03082e9 | −1.07019 | ||||||||
\(664\) | 2.01326e10 | 2.66878 | ||||||||
\(665\) | 3.22346e9 | 0.425056 | ||||||||
\(666\) | −1.47174e9 | −0.193050 | ||||||||
\(667\) | 1.51243e9 | 0.197348 | ||||||||
\(668\) | −7.80338e9 | −1.01290 | ||||||||
\(669\) | −3.60016e9 | −0.464868 | ||||||||
\(670\) | 3.97162e10 | 5.10160 | ||||||||
\(671\) | 8.79482e9 | 1.12382 | ||||||||
\(672\) | 2.62755e9 | 0.334009 | ||||||||
\(673\) | 2.54772e9 | 0.322180 | 0.161090 | − | 0.986940i | \(-0.448499\pi\) | ||||
0.161090 | + | 0.986940i | \(0.448499\pi\) | |||||||
\(674\) | 6.98772e9 | 0.879074 | ||||||||
\(675\) | 2.73843e9 | 0.342719 | ||||||||
\(676\) | 6.74954e9 | 0.840351 | ||||||||
\(677\) | −1.21766e10 | −1.50822 | −0.754112 | − | 0.656745i | \(-0.771933\pi\) | ||||
−0.754112 | + | 0.656745i | \(0.771933\pi\) | |||||||
\(678\) | 1.09242e10 | 1.34612 | ||||||||
\(679\) | −2.11792e10 | −2.59636 | ||||||||
\(680\) | 4.16241e10 | 5.07649 | ||||||||
\(681\) | 6.06089e9 | 0.735396 | ||||||||
\(682\) | −1.94648e9 | −0.234965 | ||||||||
\(683\) | −9.17376e9 | −1.10173 | −0.550864 | − | 0.834595i | \(-0.685702\pi\) | ||||
−0.550864 | + | 0.834595i | \(0.685702\pi\) | |||||||
\(684\) | −9.86103e8 | −0.117822 | ||||||||
\(685\) | 2.78976e10 | 3.31627 | ||||||||
\(686\) | 6.77248e9 | 0.800965 | ||||||||
\(687\) | −7.01874e9 | −0.825868 | ||||||||
\(688\) | −2.57120e9 | −0.301007 | ||||||||
\(689\) | −1.02942e9 | −0.119901 | ||||||||
\(690\) | 3.05157e9 | 0.353632 | ||||||||
\(691\) | 2.31775e8 | 0.0267235 | 0.0133617 | − | 0.999911i | \(-0.495747\pi\) | ||||
0.0133617 | + | 0.999911i | \(0.495747\pi\) | |||||||
\(692\) | 4.11391e9 | 0.471936 | ||||||||
\(693\) | 6.08641e9 | 0.694696 | ||||||||
\(694\) | −1.63723e9 | −0.185931 | ||||||||
\(695\) | 2.63527e10 | 2.97768 | ||||||||
\(696\) | 9.44334e9 | 1.06168 | ||||||||
\(697\) | 1.89835e10 | 2.12355 | ||||||||
\(698\) | −1.09147e10 | −1.21484 | ||||||||
\(699\) | −1.41372e9 | −0.156565 | ||||||||
\(700\) | −5.15402e10 | −5.67940 | ||||||||
\(701\) | −5.45607e9 | −0.598228 | −0.299114 | − | 0.954217i | \(-0.596691\pi\) | ||||
−0.299114 | + | 0.954217i | \(0.596691\pi\) | |||||||
\(702\) | −3.67612e9 | −0.401060 | ||||||||
\(703\) | −5.09047e8 | −0.0552604 | ||||||||
\(704\) | 8.23851e9 | 0.889907 | ||||||||
\(705\) | −3.21196e9 | −0.345230 | ||||||||
\(706\) | −1.40541e10 | −1.50310 | ||||||||
\(707\) | 1.03769e10 | 1.10433 | ||||||||
\(708\) | 7.01269e9 | 0.742622 | ||||||||
\(709\) | −1.56400e9 | −0.164807 | −0.0824034 | − | 0.996599i | \(-0.526260\pi\) | ||||
−0.0824034 | + | 0.996599i | \(0.526260\pi\) | |||||||
\(710\) | 7.56556e9 | 0.793298 | ||||||||
\(711\) | −4.87834e9 | −0.509013 | ||||||||
\(712\) | 2.30132e10 | 2.38944 | ||||||||
\(713\) | 1.95883e8 | 0.0202387 | ||||||||
\(714\) | −2.35040e10 | −2.41656 | ||||||||
\(715\) | −2.64989e10 | −2.71117 | ||||||||
\(716\) | −2.72085e10 | −2.77019 | ||||||||
\(717\) | 1.04208e10 | 1.05581 | ||||||||
\(718\) | 1.20628e10 | 1.21623 | ||||||||
\(719\) | −1.01004e9 | −0.101341 | −0.0506706 | − | 0.998715i | \(-0.516136\pi\) | ||||
−0.0506706 | + | 0.998715i | \(0.516136\pi\) | |||||||
\(720\) | 7.34601e9 | 0.733479 | ||||||||
\(721\) | 6.94968e9 | 0.690544 | ||||||||
\(722\) | 1.73111e10 | 1.71176 | ||||||||
\(723\) | 1.27508e9 | 0.125474 | ||||||||
\(724\) | 1.32341e9 | 0.129601 | ||||||||
\(725\) | −1.72942e10 | −1.68546 | ||||||||
\(726\) | −9.31765e9 | −0.903708 | ||||||||
\(727\) | 2.06395e8 | 0.0199218 | 0.00996091 | − | 0.999950i | \(-0.496829\pi\) | ||||
0.00996091 | + | 0.999950i | \(0.496829\pi\) | |||||||
\(728\) | 3.62883e10 | 3.48583 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −5.94700e10 | −5.65807 | ||||||||
\(731\) | 3.77473e9 | 0.357417 | ||||||||
\(732\) | −1.05364e10 | −0.992896 | ||||||||
\(733\) | −1.37499e10 | −1.28954 | −0.644772 | − | 0.764375i | \(-0.723048\pi\) | ||||
−0.644772 | + | 0.764375i | \(0.723048\pi\) | |||||||
\(734\) | 7.97868e9 | 0.744723 | ||||||||
\(735\) | 1.34716e10 | 1.25145 | ||||||||
\(736\) | 8.60358e8 | 0.0795439 | ||||||||
\(737\) | 2.59379e10 | 2.38671 | ||||||||
\(738\) | 8.68973e9 | 0.795809 | ||||||||
\(739\) | −1.08060e10 | −0.984937 | −0.492469 | − | 0.870330i | \(-0.663905\pi\) | ||||
−0.492469 | + | 0.870330i | \(0.663905\pi\) | |||||||
\(740\) | 1.27097e10 | 1.15298 | ||||||||
\(741\) | −1.27150e9 | −0.114803 | ||||||||
\(742\) | −3.01282e9 | −0.270744 | ||||||||
\(743\) | −6.51922e9 | −0.583088 | −0.291544 | − | 0.956557i | \(-0.594169\pi\) | ||||
−0.291544 | + | 0.956557i | \(0.594169\pi\) | |||||||
\(744\) | 1.22306e9 | 0.108879 | ||||||||
\(745\) | −1.65485e10 | −1.46626 | ||||||||
\(746\) | −1.48223e10 | −1.30716 | ||||||||
\(747\) | −5.21623e9 | −0.457862 | ||||||||
\(748\) | 5.18298e10 | 4.52819 | ||||||||
\(749\) | −1.29064e10 | −1.12232 | ||||||||
\(750\) | −1.52996e10 | −1.32424 | ||||||||
\(751\) | −4.66797e9 | −0.402150 | −0.201075 | − | 0.979576i | \(-0.564443\pi\) | ||||
−0.201075 | + | 0.979576i | \(0.564443\pi\) | |||||||
\(752\) | −5.51782e9 | −0.473157 | ||||||||
\(753\) | 1.16673e9 | 0.0995834 | ||||||||
\(754\) | 2.32161e10 | 1.97237 | ||||||||
\(755\) | 7.90211e9 | 0.668234 | ||||||||
\(756\) | −7.29167e9 | −0.613763 | ||||||||
\(757\) | 1.84301e10 | 1.54416 | 0.772079 | − | 0.635526i | \(-0.219217\pi\) | ||||
0.772079 | + | 0.635526i | \(0.219217\pi\) | |||||||
\(758\) | −2.15306e10 | −1.79562 | ||||||||
\(759\) | 1.99292e9 | 0.165441 | ||||||||
\(760\) | 6.59026e9 | 0.544572 | ||||||||
\(761\) | 6.60838e9 | 0.543561 | 0.271781 | − | 0.962359i | \(-0.412387\pi\) | ||||
0.271781 | + | 0.962359i | \(0.412387\pi\) | |||||||
\(762\) | 7.29634e9 | 0.597396 | ||||||||
\(763\) | 4.03159e9 | 0.328579 | ||||||||
\(764\) | −1.76300e10 | −1.43030 | ||||||||
\(765\) | −1.07845e10 | −0.870936 | ||||||||
\(766\) | −3.64793e10 | −2.93255 | ||||||||
\(767\) | 9.04231e9 | 0.723595 | ||||||||
\(768\) | −1.47403e10 | −1.17420 | ||||||||
\(769\) | 1.51293e10 | 1.19971 | 0.599857 | − | 0.800107i | \(-0.295224\pi\) | ||||
0.599857 | + | 0.800107i | \(0.295224\pi\) | |||||||
\(770\) | −7.75550e10 | −6.12198 | ||||||||
\(771\) | −9.11226e9 | −0.716037 | ||||||||
\(772\) | 7.04851e9 | 0.551362 | ||||||||
\(773\) | −1.46251e10 | −1.13886 | −0.569432 | − | 0.822039i | \(-0.692837\pi\) | ||||
−0.569432 | + | 0.822039i | \(0.692837\pi\) | |||||||
\(774\) | 1.72789e9 | 0.133944 | ||||||||
\(775\) | −2.23987e9 | −0.172849 | ||||||||
\(776\) | −4.33002e10 | −3.32640 | ||||||||
\(777\) | −3.76412e9 | −0.287865 | ||||||||
\(778\) | 1.83447e10 | 1.39663 | ||||||||
\(779\) | 3.00562e9 | 0.227800 | ||||||||
\(780\) | 3.17463e10 | 2.39531 | ||||||||
\(781\) | 4.94092e9 | 0.371133 | ||||||||
\(782\) | −7.69609e9 | −0.575502 | ||||||||
\(783\) | −2.44671e9 | −0.182144 | ||||||||
\(784\) | 2.31428e10 | 1.71518 | ||||||||
\(785\) | 2.53670e10 | 1.87165 | ||||||||
\(786\) | −2.21641e8 | −0.0162807 | ||||||||
\(787\) | −7.19809e9 | −0.526387 | −0.263194 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263194 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(788\) | 1.29318e10 | 0.941493 | ||||||||
\(789\) | −4.03249e9 | −0.292283 | ||||||||
\(790\) | 6.21613e10 | 4.48565 | ||||||||
\(791\) | 2.79397e10 | 2.00726 | ||||||||
\(792\) | 1.24435e10 | 0.890028 | ||||||||
\(793\) | −1.35859e10 | −0.967457 | ||||||||
\(794\) | −3.35328e10 | −2.37738 | ||||||||
\(795\) | −1.38240e9 | −0.0975770 | ||||||||
\(796\) | 2.83885e9 | 0.199502 | ||||||||
\(797\) | −8.60373e9 | −0.601981 | −0.300990 | − | 0.953627i | \(-0.597317\pi\) | ||||
−0.300990 | + | 0.953627i | \(0.597317\pi\) | |||||||
\(798\) | −3.72134e9 | −0.259232 | ||||||||
\(799\) | 8.10060e9 | 0.561828 | ||||||||
\(800\) | −9.83797e9 | −0.679345 | ||||||||
\(801\) | −5.96256e9 | −0.409939 | ||||||||
\(802\) | −3.55319e10 | −2.43225 | ||||||||
\(803\) | −3.88388e10 | −2.64704 | ||||||||
\(804\) | −3.10743e10 | −2.10865 | ||||||||
\(805\) | 7.80470e9 | 0.527315 | ||||||||
\(806\) | 3.00684e9 | 0.202273 | ||||||||
\(807\) | 8.66354e9 | 0.580281 | ||||||||
\(808\) | 2.12153e10 | 1.41484 | ||||||||
\(809\) | 2.23111e10 | 1.48150 | 0.740748 | − | 0.671783i | \(-0.234471\pi\) | ||||
0.740748 | + | 0.671783i | \(0.234471\pi\) | |||||||
\(810\) | −4.93663e9 | −0.326387 | ||||||||
\(811\) | 6.50028e9 | 0.427917 | 0.213958 | − | 0.976843i | \(-0.431364\pi\) | ||||
0.213958 | + | 0.976843i | \(0.431364\pi\) | |||||||
\(812\) | 4.60496e10 | 3.01842 | ||||||||
\(813\) | 6.62963e8 | 0.0432685 | ||||||||
\(814\) | 1.22474e10 | 0.795903 | ||||||||
\(815\) | −7.07261e9 | −0.457644 | ||||||||
\(816\) | −1.85267e10 | −1.19367 | ||||||||
\(817\) | 5.97646e8 | 0.0383413 | ||||||||
\(818\) | 3.23806e10 | 2.06846 | ||||||||
\(819\) | −9.40205e9 | −0.598038 | ||||||||
\(820\) | −7.50431e10 | −4.75294 | ||||||||
\(821\) | 7.01294e9 | 0.442282 | 0.221141 | − | 0.975242i | \(-0.429022\pi\) | ||||
0.221141 | + | 0.975242i | \(0.429022\pi\) | |||||||
\(822\) | −3.22065e10 | −2.02252 | ||||||||
\(823\) | −1.67931e10 | −1.05010 | −0.525051 | − | 0.851071i | \(-0.675954\pi\) | ||||
−0.525051 | + | 0.851071i | \(0.675954\pi\) | |||||||
\(824\) | 1.42084e10 | 0.884708 | ||||||||
\(825\) | −2.27885e10 | −1.41295 | ||||||||
\(826\) | 2.64644e10 | 1.63392 | ||||||||
\(827\) | 5.65627e9 | 0.347745 | 0.173872 | − | 0.984768i | \(-0.444372\pi\) | ||||
0.173872 | + | 0.984768i | \(0.444372\pi\) | |||||||
\(828\) | −2.38757e9 | −0.146167 | ||||||||
\(829\) | 8.59914e9 | 0.524220 | 0.262110 | − | 0.965038i | \(-0.415582\pi\) | ||||
0.262110 | + | 0.965038i | \(0.415582\pi\) | |||||||
\(830\) | 6.64669e10 | 4.03489 | ||||||||
\(831\) | 8.09027e9 | 0.489057 | ||||||||
\(832\) | −1.27265e10 | −0.766087 | ||||||||
\(833\) | −3.39755e10 | −2.03661 | ||||||||
\(834\) | −3.04230e10 | −1.81602 | ||||||||
\(835\) | −1.35120e10 | −0.803187 | ||||||||
\(836\) | 8.20611e9 | 0.485753 | ||||||||
\(837\) | −3.16886e8 | −0.0186795 | ||||||||
\(838\) | −4.48012e10 | −2.62988 | ||||||||
\(839\) | −1.50648e10 | −0.880636 | −0.440318 | − | 0.897842i | \(-0.645134\pi\) | ||||
−0.440318 | + | 0.897842i | \(0.645134\pi\) | |||||||
\(840\) | 4.87313e10 | 2.83681 | ||||||||
\(841\) | −1.79802e9 | −0.104234 | ||||||||
\(842\) | −6.64595e9 | −0.383676 | ||||||||
\(843\) | 6.12820e9 | 0.352319 | ||||||||
\(844\) | 2.50408e10 | 1.43367 | ||||||||
\(845\) | 1.16872e10 | 0.666365 | ||||||||
\(846\) | 3.70806e9 | 0.210548 | ||||||||
\(847\) | −2.38308e10 | −1.34756 | ||||||||
\(848\) | −2.37481e9 | −0.133735 | ||||||||
\(849\) | 2.04057e9 | 0.114439 | ||||||||
\(850\) | 8.80028e10 | 4.91508 | ||||||||
\(851\) | −1.23251e9 | −0.0685549 | ||||||||
\(852\) | −5.91934e9 | −0.327895 | ||||||||
\(853\) | −1.71226e10 | −0.944598 | −0.472299 | − | 0.881438i | \(-0.656576\pi\) | ||||
−0.472299 | + | 0.881438i | \(0.656576\pi\) | |||||||
\(854\) | −3.97621e10 | −2.18458 | ||||||||
\(855\) | −1.70749e9 | −0.0934281 | ||||||||
\(856\) | −2.63867e10 | −1.43789 | ||||||||
\(857\) | −2.12967e10 | −1.15579 | −0.577897 | − | 0.816110i | \(-0.696126\pi\) | ||||
−0.577897 | + | 0.816110i | \(0.696126\pi\) | |||||||
\(858\) | 3.05918e10 | 1.65348 | ||||||||
\(859\) | −1.57530e10 | −0.847981 | −0.423990 | − | 0.905667i | \(-0.639371\pi\) | ||||
−0.423990 | + | 0.905667i | \(0.639371\pi\) | |||||||
\(860\) | −1.49218e10 | −0.799973 | ||||||||
\(861\) | 2.22249e10 | 1.18667 | ||||||||
\(862\) | 4.64363e10 | 2.46935 | ||||||||
\(863\) | 2.32739e10 | 1.23263 | 0.616313 | − | 0.787501i | \(-0.288626\pi\) | ||||
0.616313 | + | 0.787501i | \(0.288626\pi\) | |||||||
\(864\) | −1.39183e9 | −0.0734157 | ||||||||
\(865\) | 7.12347e9 | 0.374227 | ||||||||
\(866\) | −3.64398e9 | −0.190662 | ||||||||
\(867\) | 1.61196e10 | 0.840015 | ||||||||
\(868\) | 5.96414e9 | 0.309549 | ||||||||
\(869\) | 4.05964e10 | 2.09854 | ||||||||
\(870\) | 3.11767e10 | 1.60514 | ||||||||
\(871\) | −4.00679e10 | −2.05462 | ||||||||
\(872\) | 8.24245e9 | 0.420968 | ||||||||
\(873\) | 1.12188e10 | 0.570685 | ||||||||
\(874\) | −1.21851e9 | −0.0617359 | ||||||||
\(875\) | −3.91303e10 | −1.97463 | ||||||||
\(876\) | 4.65298e10 | 2.33866 | ||||||||
\(877\) | −9.84011e9 | −0.492608 | −0.246304 | − | 0.969193i | \(-0.579216\pi\) | ||||
−0.246304 | + | 0.969193i | \(0.579216\pi\) | |||||||
\(878\) | 2.81416e10 | 1.40320 | ||||||||
\(879\) | 2.11490e10 | 1.05034 | ||||||||
\(880\) | −6.11317e10 | −3.02397 | ||||||||
\(881\) | −2.40556e10 | −1.18522 | −0.592611 | − | 0.805489i | \(-0.701903\pi\) | ||||
−0.592611 | + | 0.805489i | \(0.701903\pi\) | |||||||
\(882\) | −1.55523e10 | −0.763229 | ||||||||
\(883\) | 4.99537e9 | 0.244177 | 0.122089 | − | 0.992519i | \(-0.461041\pi\) | ||||
0.122089 | + | 0.992519i | \(0.461041\pi\) | |||||||
\(884\) | −8.00647e10 | −3.89814 | ||||||||
\(885\) | 1.21429e10 | 0.588870 | ||||||||
\(886\) | −1.37296e10 | −0.663192 | ||||||||
\(887\) | −4.68695e9 | −0.225506 | −0.112753 | − | 0.993623i | \(-0.535967\pi\) | ||||
−0.112753 | + | 0.993623i | \(0.535967\pi\) | |||||||
\(888\) | −7.69562e9 | −0.368806 | ||||||||
\(889\) | 1.86611e10 | 0.890803 | ||||||||
\(890\) | 7.59768e10 | 3.61257 | ||||||||
\(891\) | −3.22402e9 | −0.152695 | ||||||||
\(892\) | −3.58924e10 | −1.69327 | ||||||||
\(893\) | 1.28255e9 | 0.0602691 | ||||||||
\(894\) | 1.91045e10 | 0.894239 | ||||||||
\(895\) | −4.71131e10 | −2.19665 | ||||||||
\(896\) | −4.97035e10 | −2.30839 | ||||||||
\(897\) | −3.07858e9 | −0.142422 | ||||||||
\(898\) | 1.29676e10 | 0.597577 | ||||||||
\(899\) | 2.00126e9 | 0.0918637 | ||||||||
\(900\) | 2.73012e10 | 1.24834 | ||||||||
\(901\) | 3.48642e9 | 0.158797 | ||||||||
\(902\) | −7.23139e10 | −3.28094 | ||||||||
\(903\) | 4.41925e9 | 0.199729 | ||||||||
\(904\) | 5.71219e10 | 2.57166 | ||||||||
\(905\) | 2.29156e9 | 0.102769 | ||||||||
\(906\) | −9.12262e9 | −0.407541 | ||||||||
\(907\) | 2.14893e10 | 0.956304 | 0.478152 | − | 0.878277i | \(-0.341307\pi\) | ||||
0.478152 | + | 0.878277i | \(0.341307\pi\) | |||||||
\(908\) | 6.04251e10 | 2.67865 | ||||||||
\(909\) | −5.49673e9 | −0.242734 | ||||||||
\(910\) | 1.19804e11 | 5.27018 | ||||||||
\(911\) | 3.15925e10 | 1.38443 | 0.692214 | − | 0.721693i | \(-0.256636\pi\) | ||||
0.692214 | + | 0.721693i | \(0.256636\pi\) | |||||||
\(912\) | −2.93330e9 | −0.128048 | ||||||||
\(913\) | 4.34082e10 | 1.88766 | ||||||||
\(914\) | 3.22747e10 | 1.39814 | ||||||||
\(915\) | −1.82444e10 | −0.787327 | ||||||||
\(916\) | −6.99746e10 | −3.00820 | ||||||||
\(917\) | −5.66870e8 | −0.0242768 | ||||||||
\(918\) | 1.24502e10 | 0.531164 | ||||||||
\(919\) | −1.58869e10 | −0.675205 | −0.337603 | − | 0.941289i | \(-0.609616\pi\) | ||||
−0.337603 | + | 0.941289i | \(0.609616\pi\) | |||||||
\(920\) | 1.59564e10 | 0.675583 | ||||||||
\(921\) | 1.25460e9 | 0.0529172 | ||||||||
\(922\) | 1.23922e10 | 0.520705 | ||||||||
\(923\) | −7.63254e9 | −0.319494 | ||||||||
\(924\) | 6.06796e10 | 2.53041 | ||||||||
\(925\) | 1.40935e10 | 0.585493 | ||||||||
\(926\) | −5.69782e10 | −2.35815 | ||||||||
\(927\) | −3.68130e9 | −0.151783 | ||||||||
\(928\) | 8.78994e9 | 0.361051 | ||||||||
\(929\) | −4.25155e10 | −1.73977 | −0.869886 | − | 0.493253i | \(-0.835808\pi\) | ||||
−0.869886 | + | 0.493253i | \(0.835808\pi\) | |||||||
\(930\) | 4.03786e9 | 0.164612 | ||||||||
\(931\) | −5.37927e9 | −0.218474 | ||||||||
\(932\) | −1.40944e10 | −0.570282 | ||||||||
\(933\) | 2.64462e9 | 0.106605 | ||||||||
\(934\) | −2.56298e10 | −1.02928 | ||||||||
\(935\) | 8.97463e10 | 3.59067 | ||||||||
\(936\) | −1.92222e10 | −0.766191 | ||||||||
\(937\) | −1.52382e9 | −0.0605126 | −0.0302563 | − | 0.999542i | \(-0.509632\pi\) | ||||
−0.0302563 | + | 0.999542i | \(0.509632\pi\) | |||||||
\(938\) | −1.17268e11 | −4.63946 | ||||||||
\(939\) | −1.89849e10 | −0.748306 | ||||||||
\(940\) | −3.20222e10 | −1.25749 | ||||||||
\(941\) | 3.98090e10 | 1.55746 | 0.778732 | − | 0.627357i | \(-0.215863\pi\) | ||||
0.778732 | + | 0.627357i | \(0.215863\pi\) | |||||||
\(942\) | −2.92850e10 | −1.14148 | ||||||||
\(943\) | 7.27726e9 | 0.282603 | ||||||||
\(944\) | 2.08602e10 | 0.807080 | ||||||||
\(945\) | −1.26259e10 | −0.486690 | ||||||||
\(946\) | −1.43791e10 | −0.552220 | ||||||||
\(947\) | 1.71695e9 | 0.0656949 | 0.0328475 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328475 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(948\) | −4.86355e10 | −1.85406 | ||||||||
\(949\) | 5.99966e10 | 2.27874 | ||||||||
\(950\) | 1.39333e10 | 0.527256 | ||||||||
\(951\) | 4.08965e9 | 0.154189 | ||||||||
\(952\) | −1.22901e11 | −4.61663 | ||||||||
\(953\) | −2.93461e10 | −1.09831 | −0.549155 | − | 0.835721i | \(-0.685050\pi\) | ||||
−0.549155 | + | 0.835721i | \(0.685050\pi\) | |||||||
\(954\) | 1.59591e9 | 0.0595100 | ||||||||
\(955\) | −3.05274e10 | −1.13417 | ||||||||
\(956\) | 1.03892e11 | 3.84574 | ||||||||
\(957\) | 2.03609e10 | 0.750940 | ||||||||
\(958\) | 7.77554e10 | 2.85727 | ||||||||
\(959\) | −8.23714e10 | −3.01586 | ||||||||
\(960\) | −1.70904e10 | −0.623450 | ||||||||
\(961\) | −2.72534e10 | −0.990579 | ||||||||
\(962\) | −1.89194e10 | −0.685163 | ||||||||
\(963\) | 6.83661e9 | 0.246689 | ||||||||
\(964\) | 1.27121e10 | 0.457034 | ||||||||
\(965\) | 1.22049e10 | 0.437209 | ||||||||
\(966\) | −9.01016e9 | −0.321598 | ||||||||
\(967\) | 1.69145e10 | 0.601543 | 0.300771 | − | 0.953696i | \(-0.402756\pi\) | ||||
0.300771 | + | 0.953696i | \(0.402756\pi\) | |||||||
\(968\) | −4.87214e10 | −1.72646 | ||||||||
\(969\) | 4.30632e9 | 0.152045 | ||||||||
\(970\) | −1.42953e11 | −5.02913 | ||||||||
\(971\) | −3.82953e9 | −0.134239 | −0.0671195 | − | 0.997745i | \(-0.521381\pi\) | ||||
−0.0671195 | + | 0.997745i | \(0.521381\pi\) | |||||||
\(972\) | 3.86246e9 | 0.134906 | ||||||||
\(973\) | −7.78098e10 | −2.70794 | ||||||||
\(974\) | 4.41127e10 | 1.52971 | ||||||||
\(975\) | 3.52028e10 | 1.21636 | ||||||||
\(976\) | −3.13420e10 | −1.07908 | ||||||||
\(977\) | −3.33271e10 | −1.14332 | −0.571658 | − | 0.820492i | \(-0.693700\pi\) | ||||
−0.571658 | + | 0.820492i | \(0.693700\pi\) | |||||||
\(978\) | 8.16500e9 | 0.279107 | ||||||||
\(979\) | 4.96190e10 | 1.69008 | ||||||||
\(980\) | 1.34307e11 | 4.55835 | ||||||||
\(981\) | −2.13556e9 | −0.0722223 | ||||||||
\(982\) | 8.63063e10 | 2.90839 | ||||||||
\(983\) | 1.71429e10 | 0.575634 | 0.287817 | − | 0.957685i | \(-0.407070\pi\) | ||||
0.287817 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(984\) | 4.54380e10 | 1.52033 | ||||||||
\(985\) | 2.23921e10 | 0.746567 | ||||||||
\(986\) | −7.86280e10 | −2.61221 | ||||||||
\(987\) | 9.48374e9 | 0.313957 | ||||||||
\(988\) | −1.26765e10 | −0.418166 | ||||||||
\(989\) | 1.44703e9 | 0.0475653 | ||||||||
\(990\) | 4.10815e10 | 1.34562 | ||||||||
\(991\) | 4.73510e10 | 1.54551 | 0.772755 | − | 0.634705i | \(-0.218878\pi\) | ||||
0.772755 | + | 0.634705i | \(0.218878\pi\) | |||||||
\(992\) | 1.13843e9 | 0.0370269 | ||||||||
\(993\) | −9.92427e9 | −0.321645 | ||||||||
\(994\) | −2.23383e10 | −0.721437 | ||||||||
\(995\) | 4.91563e9 | 0.158197 | ||||||||
\(996\) | −5.20042e10 | −1.66775 | ||||||||
\(997\) | −2.46977e10 | −0.789267 | −0.394634 | − | 0.918839i | \(-0.629128\pi\) | ||||
−0.394634 | + | 0.918839i | \(0.629128\pi\) | |||||||
\(998\) | 2.22415e10 | 0.708283 | ||||||||
\(999\) | 1.99388e9 | 0.0632733 |
(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 | 69.8.a.b.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 207.8.a.c.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.b.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
207.8.a.c.1.6 | 6 | 3.2 | odd | 2 |