Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,36,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 36, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 36);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(193.987826584\) |
Analytic rank: | \(0\) |
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: | \( x^{6} + 24844388x^{4} + 154310903773636x^{2} + 6999547445919666225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.6 | ||
Root | \(-3626.53i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.36.b.a.24.1 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 331573.i | 1.78877i | 0.447298 | + | 0.894385i | \(0.352386\pi\) | ||||
−0.447298 | + | 0.894385i | \(0.647614\pi\) | |||||||
\(3\) | 1.54691e8i | 0.691580i | 0.938312 | + | 0.345790i | \(0.112389\pi\) | ||||
−0.938312 | + | 0.345790i | \(0.887611\pi\) | |||||||
\(4\) | −7.55810e10 | −2.19970 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.12913e13 | −1.23708 | ||||||||
\(7\) | 3.96640e14i | 0.644438i | 0.946665 | + | 0.322219i | \(0.104429\pi\) | ||||
−0.946665 | + | 0.322219i | \(0.895571\pi\) | |||||||
\(8\) | − 1.36679e16i | − 2.14598i | ||||||||
\(9\) | 2.61023e16 | 0.521717 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.82681e17 | −0.407236 | −0.203618 | − | 0.979050i | \(-0.565270\pi\) | ||||
−0.203618 | + | 0.979050i | \(0.565270\pi\) | |||||||
\(12\) | − 1.16917e19i | − 1.52127i | ||||||||
\(13\) | 1.17949e19i | 0.378169i | 0.981961 | + | 0.189085i | \(0.0605520\pi\) | ||||
−0.981961 | + | 0.189085i | \(0.939448\pi\) | |||||||
\(14\) | −1.31515e20 | −1.15275 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.93496e21 | 1.63897 | ||||||||
\(17\) | − 1.33083e21i | − 0.390181i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(18\) | 8.65483e21i | 0.933232i | ||||||||
\(19\) | 3.58945e22 | 1.50259 | 0.751294 | − | 0.659967i | \(-0.229430\pi\) | ||||
0.751294 | + | 0.659967i | \(0.229430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.13565e22 | −0.445680 | ||||||||
\(22\) | − 2.26359e23i | − 0.728451i | ||||||||
\(23\) | − 6.92195e23i | − 1.02327i | −0.859202 | − | 0.511636i | \(-0.829039\pi\) | ||||
0.859202 | − | 0.511636i | \(-0.170961\pi\) | |||||||
\(24\) | 2.11429e24 | 1.48412 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.91088e24 | −0.676457 | ||||||||
\(27\) | 1.17772e25i | 1.05239i | ||||||||
\(28\) | − 2.99785e25i | − 1.41757i | ||||||||
\(29\) | 5.67568e25 | 1.45229 | 0.726144 | − | 0.687542i | \(-0.241310\pi\) | ||||
0.726144 | + | 0.687542i | \(0.241310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.02960e26 | 0.820043 | 0.410022 | − | 0.912076i | \(-0.365521\pi\) | ||||
0.410022 | + | 0.912076i | \(0.365521\pi\) | |||||||
\(32\) | 1.71955e26i | 0.785760i | ||||||||
\(33\) | − 1.05604e26i | − 0.281636i | ||||||||
\(34\) | 4.41267e26 | 0.697943 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.97284e27 | −1.14762 | ||||||||
\(37\) | 4.50412e27i | 1.62211i | 0.584971 | + | 0.811054i | \(0.301106\pi\) | ||||
−0.584971 | + | 0.811054i | \(0.698894\pi\) | |||||||
\(38\) | 1.19017e28i | 2.68779i | ||||||||
\(39\) | −1.82456e27 | −0.261534 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.23104e27 | −0.372257 | −0.186129 | − | 0.982525i | \(-0.559594\pi\) | ||||
−0.186129 | + | 0.982525i | \(0.559594\pi\) | |||||||
\(42\) | − 2.03442e28i | − 0.797219i | ||||||||
\(43\) | 2.75822e27i | 0.0716029i | 0.999359 | + | 0.0358014i | \(0.0113984\pi\) | ||||
−0.999359 | + | 0.0358014i | \(0.988602\pi\) | |||||||
\(44\) | 5.15977e28 | 0.895795 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.29513e29 | 1.83040 | ||||||||
\(47\) | 1.41103e29i | 0.772365i | 0.922422 | + | 0.386182i | \(0.126207\pi\) | ||||
−0.922422 | + | 0.386182i | \(0.873793\pi\) | |||||||
\(48\) | 2.99320e29i | 1.13348i | ||||||||
\(49\) | 2.21495e29 | 0.584700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.05867e29 | 0.269841 | ||||||||
\(52\) | − 8.91472e29i | − 0.831858i | ||||||||
\(53\) | 2.48503e30i | 1.66151i | 0.556638 | + | 0.830755i | \(0.312091\pi\) | ||||
−0.556638 | + | 0.830755i | \(0.687909\pi\) | |||||||
\(54\) | −3.90500e30 | −1.88248 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.42123e30 | 1.38295 | ||||||||
\(57\) | 5.55255e30i | 1.03916i | ||||||||
\(58\) | 1.88190e31i | 2.59781i | ||||||||
\(59\) | −5.47495e30 | −0.560364 | −0.280182 | − | 0.959947i | \(-0.590395\pi\) | ||||
−0.280182 | + | 0.959947i | \(0.590395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.30979e31 | 1.31917 | 0.659585 | − | 0.751630i | \(-0.270732\pi\) | ||||
0.659585 | + | 0.751630i | \(0.270732\pi\) | |||||||
\(62\) | 3.41386e31i | 1.46687i | ||||||||
\(63\) | 1.03532e31i | 0.336214i | ||||||||
\(64\) | 9.46893e30 | 0.233427 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.50156e31 | 0.503782 | ||||||||
\(67\) | 1.55814e31i | 0.172304i | 0.996282 | + | 0.0861522i | \(0.0274571\pi\) | ||||
−0.996282 | + | 0.0861522i | \(0.972543\pi\) | |||||||
\(68\) | 1.00585e32i | 0.858279i | ||||||||
\(69\) | 1.07076e32 | 0.707675 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.13262e32 | −0.454008 | −0.227004 | − | 0.973894i | \(-0.572893\pi\) | ||||
−0.227004 | + | 0.973894i | \(0.572893\pi\) | |||||||
\(72\) | − 3.56763e32i | − 1.11960i | ||||||||
\(73\) | − 3.23524e32i | − 0.797548i | −0.917049 | − | 0.398774i | \(-0.869436\pi\) | ||||
0.917049 | − | 0.398774i | \(-0.130564\pi\) | |||||||
\(74\) | −1.49345e33 | −2.90158 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.71294e33 | −3.30524 | ||||||||
\(77\) | − 2.70778e32i | − 0.262438i | ||||||||
\(78\) | − 6.04976e32i | − 0.467824i | ||||||||
\(79\) | 1.44166e32 | 0.0892050 | 0.0446025 | − | 0.999005i | \(-0.485798\pi\) | ||||
0.0446025 | + | 0.999005i | \(0.485798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.15885e32 | −0.206094 | ||||||||
\(82\) | − 2.06605e33i | − 0.665882i | ||||||||
\(83\) | − 3.50421e33i | − 0.913532i | −0.889587 | − | 0.456766i | \(-0.849008\pi\) | ||||
0.889587 | − | 0.456766i | \(-0.150992\pi\) | |||||||
\(84\) | 4.63739e33 | 0.980361 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.14551e32 | −0.128081 | ||||||||
\(87\) | 8.77975e33i | 1.00437i | ||||||||
\(88\) | 9.33079e33i | 0.873920i | ||||||||
\(89\) | −9.37543e33 | −0.720553 | −0.360277 | − | 0.932846i | \(-0.617318\pi\) | ||||
−0.360277 | + | 0.932846i | \(0.617318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.67833e33 | −0.243706 | ||||||||
\(92\) | 5.23168e34i | 2.25089i | ||||||||
\(93\) | 1.59269e34i | 0.567126i | ||||||||
\(94\) | −4.67858e34 | −1.38158 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.65998e34 | −0.543416 | ||||||||
\(97\) | 3.59603e33i | 0.0612799i | 0.999530 | + | 0.0306399i | \(0.00975453\pi\) | ||||
−0.999530 | + | 0.0306399i | \(0.990245\pi\) | |||||||
\(98\) | 7.34419e34i | 1.04589i | ||||||||
\(99\) | −1.78195e34 | −0.212462 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.27571e34 | 0.611296 | 0.305648 | − | 0.952145i | \(-0.401127\pi\) | ||||
0.305648 | + | 0.952145i | \(0.401127\pi\) | |||||||
\(102\) | 6.82599e34i | 0.482683i | ||||||||
\(103\) | − 9.48038e34i | − 0.565164i | −0.959243 | − | 0.282582i | \(-0.908809\pi\) | ||||
0.959243 | − | 0.282582i | \(-0.0911909\pi\) | |||||||
\(104\) | 1.61211e35 | 0.811544 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.23968e35 | −2.97206 | ||||||||
\(107\) | 5.43957e35i | 1.66475i | 0.554214 | + | 0.832374i | \(0.313019\pi\) | ||||
−0.554214 | + | 0.832374i | \(0.686981\pi\) | |||||||
\(108\) | − 8.90133e35i | − 2.31494i | ||||||||
\(109\) | 2.19201e35 | 0.485153 | 0.242577 | − | 0.970132i | \(-0.422007\pi\) | ||||
0.242577 | + | 0.970132i | \(0.422007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.96746e35 | −1.12182 | ||||||||
\(112\) | 7.67481e35i | 1.05621i | ||||||||
\(113\) | 3.57083e35i | 0.420627i | 0.977634 | + | 0.210313i | \(0.0674484\pi\) | ||||
−0.977634 | + | 0.210313i | \(0.932552\pi\) | |||||||
\(114\) | −1.84108e36 | −1.85882 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.28974e36 | −3.19460 | ||||||||
\(117\) | 3.07875e35i | 0.197297i | ||||||||
\(118\) | − 1.81535e36i | − 1.00236i | ||||||||
\(119\) | 5.27859e35 | 0.251447 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.34419e36 | −0.834159 | ||||||||
\(122\) | 7.65865e36i | 2.35969i | ||||||||
\(123\) | − 9.63884e35i | − 0.257446i | ||||||||
\(124\) | −7.78179e36 | −1.80385 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.43285e36 | −0.601410 | ||||||||
\(127\) | − 2.98205e36i | − 0.454935i | −0.973786 | − | 0.227467i | \(-0.926955\pi\) | ||||
0.973786 | − | 0.227467i | \(-0.0730445\pi\) | |||||||
\(128\) | 9.04797e36i | 1.20331i | ||||||||
\(129\) | −4.26671e35 | −0.0495191 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.67513e37 | 1.48525 | 0.742627 | − | 0.669705i | \(-0.233579\pi\) | ||||
0.742627 | + | 0.669705i | \(0.233579\pi\) | |||||||
\(132\) | 7.98169e36i | 0.619514i | ||||||||
\(133\) | 1.42372e37i | 0.968325i | ||||||||
\(134\) | −5.16636e36 | −0.308213 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.81896e37 | −0.837321 | ||||||||
\(137\) | 7.05739e36i | 0.285782i | 0.989738 | + | 0.142891i | \(0.0456398\pi\) | ||||
−0.989738 | + | 0.142891i | \(0.954360\pi\) | |||||||
\(138\) | 3.55036e37i | 1.26587i | ||||||||
\(139\) | −5.54070e36 | −0.174103 | −0.0870514 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870514 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.18273e37 | −0.534152 | ||||||||
\(142\) | − 3.75546e37i | − 0.812115i | ||||||||
\(143\) | − 8.05216e36i | − 0.154004i | ||||||||
\(144\) | 5.05068e37 | 0.855080 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.07272e38 | 1.42663 | ||||||||
\(147\) | 3.42633e37i | 0.404367i | ||||||||
\(148\) | − 3.40426e38i | − 3.56815i | ||||||||
\(149\) | 1.26594e38 | 1.17938 | 0.589689 | − | 0.807631i | \(-0.299250\pi\) | ||||
0.589689 | + | 0.807631i | \(0.299250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.46030e38 | 1.07732 | 0.538661 | − | 0.842523i | \(-0.318930\pi\) | ||||
0.538661 | + | 0.842523i | \(0.318930\pi\) | |||||||
\(152\) | − 4.90602e38i | − 3.22453i | ||||||||
\(153\) | − 3.47377e37i | − 0.203564i | ||||||||
\(154\) | 8.97829e37 | 0.469441 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.37902e38 | 0.575296 | ||||||||
\(157\) | − 2.57702e38i | − 0.961332i | −0.876904 | − | 0.480666i | \(-0.840395\pi\) | ||||
0.876904 | − | 0.480666i | \(-0.159605\pi\) | |||||||
\(158\) | 4.78016e37i | 0.159567i | ||||||||
\(159\) | −3.84410e38 | −1.14907 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.74552e38 | 0.659436 | ||||||||
\(162\) | − 1.71054e38i | − 0.368655i | ||||||||
\(163\) | 1.00523e39i | 1.94529i | 0.232306 | + | 0.972643i | \(0.425373\pi\) | ||||
−0.232306 | + | 0.972643i | \(0.574627\pi\) | |||||||
\(164\) | 4.70948e38 | 0.818853 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.16190e39 | 1.63410 | ||||||||
\(167\) | 4.87583e38i | 0.617320i | 0.951172 | + | 0.308660i | \(0.0998805\pi\) | ||||
−0.951172 | + | 0.308660i | \(0.900119\pi\) | |||||||
\(168\) | 8.38614e38i | 0.956422i | ||||||||
\(169\) | 8.33666e38 | 0.856988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.36930e38 | 0.783926 | ||||||||
\(172\) | − 2.08469e38i | − 0.157505i | ||||||||
\(173\) | 3.15688e37i | 0.0215502i | 0.999942 | + | 0.0107751i | \(0.00342989\pi\) | ||||
−0.999942 | + | 0.0107751i | \(0.996570\pi\) | |||||||
\(174\) | −2.91113e39 | −1.79659 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.32096e39 | −0.667447 | ||||||||
\(177\) | − 8.46924e38i | − 0.387536i | ||||||||
\(178\) | − 3.10864e39i | − 1.28890i | ||||||||
\(179\) | 4.86041e38 | 0.182702 | 0.0913512 | − | 0.995819i | \(-0.470881\pi\) | ||||
0.0913512 | + | 0.995819i | \(0.470881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.89892e39 | −1.51609 | −0.758045 | − | 0.652202i | \(-0.773845\pi\) | ||||
−0.758045 | + | 0.652202i | \(0.773845\pi\) | |||||||
\(182\) | − 1.55121e39i | − 0.435935i | ||||||||
\(183\) | 3.57303e39i | 0.912311i | ||||||||
\(184\) | −9.46084e39 | −2.19593 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.28093e39 | −1.01446 | ||||||||
\(187\) | 9.08530e38i | 0.158895i | ||||||||
\(188\) | − 1.06647e40i | − 1.69897i | ||||||||
\(189\) | −4.67131e39 | −0.678199 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.79853e39 | −1.06249 | −0.531246 | − | 0.847217i | \(-0.678276\pi\) | ||||
−0.531246 | + | 0.847217i | \(0.678276\pi\) | |||||||
\(192\) | 1.46476e39i | 0.161434i | ||||||||
\(193\) | − 1.65403e40i | − 1.66452i | −0.554383 | − | 0.832262i | \(-0.687046\pi\) | ||||
0.554383 | − | 0.832262i | \(-0.312954\pi\) | |||||||
\(194\) | −1.19235e39 | −0.109616 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.67408e40 | −1.28616 | ||||||||
\(197\) | 3.96581e36i | 0 0.000278723i | 1.00000 | 0.000139362i | \(4.43602e-5\pi\) | |||||
−1.00000 | 0.000139362i | \(0.999956\pi\) | ||||||||
\(198\) | − 5.90848e39i | − 0.380045i | ||||||||
\(199\) | 1.61546e40 | 0.951409 | 0.475705 | − | 0.879605i | \(-0.342193\pi\) | ||||
0.475705 | + | 0.879605i | \(0.342193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.41029e39 | −0.119162 | ||||||||
\(202\) | 2.41243e40i | 1.09347i | ||||||||
\(203\) | 2.25120e40i | 0.935909i | ||||||||
\(204\) | −1.55596e40 | −0.593569 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.14344e40 | 1.01095 | ||||||||
\(207\) | − 1.80679e40i | − 0.533859i | ||||||||
\(208\) | 2.28226e40i | 0.619808i | ||||||||
\(209\) | −2.45045e40 | −0.611908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.70344e40 | 0.571444 | 0.285722 | − | 0.958313i | \(-0.407767\pi\) | ||||
0.285722 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(212\) | − 1.87821e41i | − 3.65482i | ||||||||
\(213\) | − 1.75206e40i | − 0.313983i | ||||||||
\(214\) | −1.80362e41 | −2.97785 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.60969e41 | 2.25841 | ||||||||
\(217\) | 4.08379e40i | 0.528467i | ||||||||
\(218\) | 7.26812e40i | 0.867827i | ||||||||
\(219\) | 5.00462e40 | 0.551569 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.56970e40 | 0.147554 | ||||||||
\(222\) | − 2.31022e41i | − 2.00667i | ||||||||
\(223\) | − 1.60448e41i | − 1.28825i | −0.764921 | − | 0.644124i | \(-0.777222\pi\) | ||||
0.764921 | − | 0.644124i | \(-0.222778\pi\) | |||||||
\(224\) | −6.82042e40 | −0.506374 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.18399e41 | −0.752405 | ||||||||
\(227\) | − 1.32023e41i | − 0.776597i | −0.921534 | − | 0.388299i | \(-0.873063\pi\) | ||||
0.921534 | − | 0.388299i | \(-0.126937\pi\) | |||||||
\(228\) | − 4.19667e41i | − 2.28584i | ||||||||
\(229\) | 1.27675e41 | 0.644147 | 0.322073 | − | 0.946715i | \(-0.395620\pi\) | ||||
0.322073 | + | 0.946715i | \(0.395620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.18869e40 | 0.181497 | ||||||||
\(232\) | − 7.75745e41i | − 3.11659i | ||||||||
\(233\) | 1.15249e41i | 0.429445i | 0.976675 | + | 0.214722i | \(0.0688847\pi\) | ||||
−0.976675 | + | 0.214722i | \(0.931115\pi\) | |||||||
\(234\) | −1.02083e41 | −0.352919 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.13802e41 | 1.23263 | ||||||||
\(237\) | 2.23012e40i | 0.0616924i | ||||||||
\(238\) | 1.75024e41i | 0.449781i | ||||||||
\(239\) | −1.42881e41 | −0.341201 | −0.170601 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170601 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.47367e41 | −0.304160 | −0.152080 | − | 0.988368i | \(-0.548597\pi\) | ||||
−0.152080 | + | 0.988368i | \(0.548597\pi\) | |||||||
\(242\) | − 7.77271e41i | − 1.49212i | ||||||||
\(243\) | 5.09429e41i | 0.909859i | ||||||||
\(244\) | −1.74576e42 | −2.90177 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.19598e41 | 0.460511 | ||||||||
\(247\) | 4.23373e41i | 0.568233i | ||||||||
\(248\) | − 1.40724e42i | − 1.75980i | ||||||||
\(249\) | 5.42069e41 | 0.631781 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.16925e42 | 1.18473 | 0.592363 | − | 0.805671i | \(-0.298195\pi\) | ||||
0.592363 | + | 0.805671i | \(0.298195\pi\) | |||||||
\(252\) | − 7.82507e41i | − 0.739569i | ||||||||
\(253\) | 4.72548e41i | 0.416713i | ||||||||
\(254\) | 9.88766e41 | 0.813773 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.67471e42 | −1.91901 | ||||||||
\(257\) | 6.14627e41i | 0.411890i | 0.978564 | + | 0.205945i | \(0.0660269\pi\) | ||||
−0.978564 | + | 0.205945i | \(0.933973\pi\) | |||||||
\(258\) | − 1.41473e41i | − 0.0885783i | ||||||||
\(259\) | −1.78651e42 | −1.04535 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.48148e42 | 0.757684 | ||||||||
\(262\) | 5.55428e42i | 2.65678i | ||||||||
\(263\) | − 5.29428e41i | − 0.236909i | −0.992959 | − | 0.118454i | \(-0.962206\pi\) | ||||
0.992959 | − | 0.118454i | \(-0.0377940\pi\) | |||||||
\(264\) | −1.44339e42 | −0.604386 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.72067e42 | −1.73211 | ||||||||
\(267\) | − 1.45029e42i | − 0.498320i | ||||||||
\(268\) | − 1.17766e42i | − 0.379018i | ||||||||
\(269\) | −2.61222e42 | −0.787670 | −0.393835 | − | 0.919181i | \(-0.628852\pi\) | ||||
−0.393835 | + | 0.919181i | \(0.628852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.35646e42 | −1.68365 | −0.841827 | − | 0.539748i | \(-0.818520\pi\) | ||||
−0.841827 | + | 0.539748i | \(0.818520\pi\) | |||||||
\(272\) | − 2.57509e42i | − 0.639495i | ||||||||
\(273\) | − 7.23695e41i | − 0.168542i | ||||||||
\(274\) | −2.34004e42 | −0.511197 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.09293e42 | −1.55667 | ||||||||
\(277\) | 1.32088e41i | 0.0238488i | 0.999929 | + | 0.0119244i | \(0.00379574\pi\) | ||||
−0.999929 | + | 0.0119244i | \(0.996204\pi\) | |||||||
\(278\) | − 1.83715e42i | − 0.311430i | ||||||||
\(279\) | 2.68748e42 | 0.427831 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21053e43 | 1.70065 | 0.850324 | − | 0.526260i | \(-0.176406\pi\) | ||||
0.850324 | + | 0.526260i | \(0.176406\pi\) | |||||||
\(282\) | − 7.23734e42i | − 0.955475i | ||||||||
\(283\) | − 1.08291e41i | − 0.0134378i | −0.999977 | − | 0.00671891i | \(-0.997861\pi\) | ||||
0.999977 | − | 0.00671891i | \(-0.00213871\pi\) | |||||||
\(284\) | 8.56046e42 | 0.998680 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.66988e42 | 0.275477 | ||||||||
\(287\) | − 2.47148e42i | − 0.239896i | ||||||||
\(288\) | 4.48842e42i | 0.409945i | ||||||||
\(289\) | 9.86245e42 | 0.847759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.56273e41 | −0.0423799 | ||||||||
\(292\) | 2.44523e43i | 1.75437i | ||||||||
\(293\) | 2.38381e42i | 0.161097i | 0.996751 | + | 0.0805486i | \(0.0256672\pi\) | ||||
−0.996751 | + | 0.0805486i | \(0.974333\pi\) | |||||||
\(294\) | −1.13608e43 | −0.723319 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.15617e43 | 3.48102 | ||||||||
\(297\) | − 8.04007e42i | − 0.428570i | ||||||||
\(298\) | 4.19751e43i | 2.10963i | ||||||||
\(299\) | 8.16438e42 | 0.386970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.09402e42 | −0.0461436 | ||||||||
\(302\) | 4.84196e43i | 1.92708i | ||||||||
\(303\) | 1.12548e43i | 0.422760i | ||||||||
\(304\) | 6.94543e43 | 2.46270 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.15181e43 | 0.364129 | ||||||||
\(307\) | − 4.84424e43i | − 1.44645i | −0.690611 | − | 0.723226i | \(-0.742658\pi\) | ||||
0.690611 | − | 0.723226i | \(-0.257342\pi\) | |||||||
\(308\) | 2.04657e43i | 0.577284i | ||||||||
\(309\) | 1.46653e43 | 0.390856 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.85715e43 | 0.442119 | 0.221060 | − | 0.975260i | \(-0.429048\pi\) | ||||
0.221060 | + | 0.975260i | \(0.429048\pi\) | |||||||
\(312\) | 2.49379e43i | 0.561248i | ||||||||
\(313\) | − 2.67734e43i | − 0.569740i | −0.958566 | − | 0.284870i | \(-0.908049\pi\) | ||||
0.958566 | − | 0.284870i | \(-0.0919505\pi\) | |||||||
\(314\) | 8.54470e43 | 1.71960 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.08962e43 | −0.196224 | ||||||||
\(317\) | − 2.42612e43i | − 0.413405i | −0.978404 | − | 0.206703i | \(-0.933727\pi\) | ||||
0.978404 | − | 0.206703i | \(-0.0662733\pi\) | |||||||
\(318\) | − 1.27460e44i | − 2.05542i | ||||||||
\(319\) | −3.87468e43 | −0.591423 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.41452e43 | −1.15131 | ||||||||
\(322\) | 9.10342e43i | 1.17958i | ||||||||
\(323\) | − 4.77694e43i | − 0.586281i | ||||||||
\(324\) | 3.89911e43 | 0.453344 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.33308e44 | −3.47967 | ||||||||
\(327\) | 3.39084e43i | 0.335522i | ||||||||
\(328\) | 8.51651e43i | 0.798857i | ||||||||
\(329\) | −5.59669e43 | −0.497741 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.83689e44 | 1.46924 | 0.734620 | − | 0.678479i | \(-0.237361\pi\) | ||||
0.734620 | + | 0.678479i | \(0.237361\pi\) | |||||||
\(332\) | 2.64852e44i | 2.00950i | ||||||||
\(333\) | 1.17568e44i | 0.846282i | ||||||||
\(334\) | −1.61669e44 | −1.10424 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.18722e44 | −0.730457 | ||||||||
\(337\) | 9.63203e42i | 0.0562593i | 0.999604 | + | 0.0281297i | \(0.00895513\pi\) | ||||
−0.999604 | + | 0.0281297i | \(0.991045\pi\) | |||||||
\(338\) | 2.76421e44i | 1.53295i | ||||||||
\(339\) | −5.52375e43 | −0.290897 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.02885e43 | −0.333951 | ||||||||
\(342\) | 3.10661e44i | 1.40226i | ||||||||
\(343\) | 2.38109e44i | 1.02124i | ||||||||
\(344\) | 3.76990e43 | 0.153659 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.04674e43 | −0.0385483 | ||||||||
\(347\) | 2.05198e44i | 0.718468i | 0.933247 | + | 0.359234i | \(0.116962\pi\) | ||||
−0.933247 | + | 0.359234i | \(0.883038\pi\) | |||||||
\(348\) | − 6.63583e44i | − 2.20932i | ||||||||
\(349\) | 1.00117e44 | 0.317003 | 0.158501 | − | 0.987359i | \(-0.449334\pi\) | ||||
0.158501 | + | 0.987359i | \(0.449334\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.38911e44 | −0.397981 | ||||||||
\(352\) | − 1.17390e44i | − 0.319990i | ||||||||
\(353\) | 2.71539e44i | 0.704328i | 0.935938 | + | 0.352164i | \(0.114554\pi\) | ||||
−0.935938 | + | 0.352164i | \(0.885446\pi\) | |||||||
\(354\) | 2.80817e44 | 0.693213 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.08605e44 | 1.58500 | ||||||||
\(357\) | 8.16550e43i | 0.173896i | ||||||||
\(358\) | 1.61158e44i | 0.326813i | ||||||||
\(359\) | −8.81356e44 | −1.70215 | −0.851076 | − | 0.525043i | \(-0.824049\pi\) | ||||
−0.851076 | + | 0.525043i | \(0.824049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.17758e44 | 1.25777 | ||||||||
\(362\) | − 1.62435e45i | − 2.71194i | ||||||||
\(363\) | − 3.62625e44i | − 0.576888i | ||||||||
\(364\) | 3.53593e44 | 0.536080 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.18472e45 | −1.63191 | ||||||||
\(367\) | − 1.11298e45i | − 1.46161i | −0.682585 | − | 0.730806i | \(-0.739144\pi\) | ||||
0.682585 | − | 0.730806i | \(-0.260856\pi\) | |||||||
\(368\) | − 1.33937e45i | − 1.67712i | ||||||||
\(369\) | −1.62645e44 | −0.194213 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.85661e44 | −1.07074 | ||||||||
\(372\) | − 1.20377e45i | − 1.24750i | ||||||||
\(373\) | 5.50495e44i | 0.544313i | 0.962253 | + | 0.272157i | \(0.0877368\pi\) | ||||
−0.962253 | + | 0.272157i | \(0.912263\pi\) | |||||||
\(374\) | −3.01244e44 | −0.284227 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.92857e45 | 1.65748 | ||||||||
\(377\) | 6.69441e44i | 0.549211i | ||||||||
\(378\) | − 1.54888e45i | − 1.21314i | ||||||||
\(379\) | 1.81534e45 | 1.35760 | 0.678799 | − | 0.734325i | \(-0.262501\pi\) | ||||
0.678799 | + | 0.734325i | \(0.262501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.61295e44 | 0.314624 | ||||||||
\(382\) | − 2.91736e45i | − 1.90056i | ||||||||
\(383\) | − 5.42819e44i | − 0.337813i | −0.985632 | − | 0.168907i | \(-0.945976\pi\) | ||||
0.985632 | − | 0.168907i | \(-0.0540236\pi\) | |||||||
\(384\) | −1.39964e45 | −0.832184 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.48431e45 | 2.97745 | ||||||||
\(387\) | 7.19958e43i | 0.0373564i | ||||||||
\(388\) | − 2.71792e44i | − 0.134797i | ||||||||
\(389\) | −2.27596e45 | −1.07906 | −0.539532 | − | 0.841965i | \(-0.681399\pi\) | ||||
−0.539532 | + | 0.841965i | \(0.681399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.21192e44 | −0.399261 | ||||||||
\(392\) | − 3.02737e45i | − 1.25476i | ||||||||
\(393\) | 2.59127e45i | 1.02717i | ||||||||
\(394\) | −1.31496e42 | −0.000498572 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.34682e45 | 0.467352 | ||||||||
\(397\) | 2.97575e45i | 0.988013i | 0.869458 | + | 0.494006i | \(0.164468\pi\) | ||||
−0.869458 | + | 0.494006i | \(0.835532\pi\) | |||||||
\(398\) | 5.35643e45i | 1.70185i | ||||||||
\(399\) | −2.20236e45 | −0.669674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.35408e45 | −0.934429 | −0.467215 | − | 0.884144i | \(-0.654742\pi\) | ||||
−0.467215 | + | 0.884144i | \(0.654742\pi\) | |||||||
\(402\) | − 7.99189e44i | − 0.213154i | ||||||||
\(403\) | 1.21440e45i | 0.310115i | ||||||||
\(404\) | −5.49906e45 | −1.34467 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.46438e45 | −1.67413 | ||||||||
\(407\) | − 3.07488e45i | − 0.660580i | ||||||||
\(408\) | − 2.81376e45i | − 0.579074i | ||||||||
\(409\) | −8.75180e45 | −1.72560 | −0.862799 | − | 0.505547i | \(-0.831291\pi\) | ||||
−0.862799 | + | 0.505547i | \(0.831291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.09171e45 | −0.197641 | ||||||||
\(412\) | 7.16537e45i | 1.24319i | ||||||||
\(413\) | − 2.17158e45i | − 0.361119i | ||||||||
\(414\) | 5.99083e45 | 0.954951 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.02819e45 | −0.297150 | ||||||||
\(417\) | − 8.57095e44i | − 0.120406i | ||||||||
\(418\) | − 8.12503e45i | − 1.09456i | ||||||||
\(419\) | −1.99625e45 | −0.257911 | −0.128955 | − | 0.991650i | \(-0.541162\pi\) | ||||
−0.128955 | + | 0.991650i | \(0.541162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.23389e46 | −1.46670 | −0.733348 | − | 0.679854i | \(-0.762043\pi\) | ||||
−0.733348 | + | 0.679854i | \(0.762043\pi\) | |||||||
\(422\) | 8.96388e45i | 1.02218i | ||||||||
\(423\) | 3.68311e45i | 0.402956i | ||||||||
\(424\) | 3.39650e46 | 3.56557 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.80936e45 | 0.561643 | ||||||||
\(427\) | 9.16156e45i | 0.850122i | ||||||||
\(428\) | − 4.11129e46i | − 3.66194i | ||||||||
\(429\) | 1.24559e45 | 0.106506 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.20357e46 | −0.948677 | −0.474339 | − | 0.880343i | \(-0.657313\pi\) | ||||
−0.474339 | + | 0.880343i | \(0.657313\pi\) | |||||||
\(432\) | 2.27884e46i | 1.72484i | ||||||||
\(433\) | 2.06332e46i | 1.49979i | 0.661559 | + | 0.749893i | \(0.269895\pi\) | ||||
−0.661559 | + | 0.749893i | \(0.730105\pi\) | |||||||
\(434\) | −1.35407e46 | −0.945305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.65674e46 | −1.06719 | ||||||||
\(437\) | − 2.48460e46i | − 1.53756i | ||||||||
\(438\) | 1.65940e46i | 0.986629i | ||||||||
\(439\) | −3.14998e46 | −1.79961 | −0.899805 | − | 0.436293i | \(-0.856291\pi\) | ||||
−0.899805 | + | 0.436293i | \(0.856291\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.78154e45 | 0.305048 | ||||||||
\(442\) | 5.20470e45i | 0.263941i | ||||||||
\(443\) | 2.49595e46i | 1.21667i | 0.793682 | + | 0.608333i | \(0.208161\pi\) | ||||
−0.793682 | + | 0.608333i | \(0.791839\pi\) | |||||||
\(444\) | 5.26608e46 | 2.46766 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.32003e46 | 2.30438 | ||||||||
\(447\) | 1.95829e46i | 0.815634i | ||||||||
\(448\) | 3.75576e45i | 0.150429i | ||||||||
\(449\) | −3.14792e46 | −1.21259 | −0.606294 | − | 0.795241i | \(-0.707344\pi\) | ||||
−0.606294 | + | 0.795241i | \(0.707344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.25381e45 | 0.151596 | ||||||||
\(452\) | − 2.69887e46i | − 0.925252i | ||||||||
\(453\) | 2.25895e46i | 0.745054i | ||||||||
\(454\) | 4.37752e46 | 1.38915 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.58916e46 | 2.23002 | ||||||||
\(457\) | 3.21994e46i | 0.910572i | 0.890345 | + | 0.455286i | \(0.150463\pi\) | ||||
−0.890345 | + | 0.455286i | \(0.849537\pi\) | |||||||
\(458\) | 4.23336e46i | 1.15223i | ||||||||
\(459\) | 1.56734e46 | 0.410622 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.96567e45 | 0.217679 | 0.108840 | − | 0.994059i | \(-0.465287\pi\) | ||||
0.108840 | + | 0.994059i | \(0.465287\pi\) | |||||||
\(462\) | 1.38886e46i | 0.324656i | ||||||||
\(463\) | 2.74379e46i | 0.617566i | 0.951133 | + | 0.308783i | \(0.0999216\pi\) | ||||
−0.951133 | + | 0.308783i | \(0.900078\pi\) | |||||||
\(464\) | 1.09822e47 | 2.38026 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.82134e46 | −0.768178 | ||||||||
\(467\) | − 8.40024e46i | − 1.62647i | −0.581935 | − | 0.813235i | \(-0.697704\pi\) | ||||
0.581935 | − | 0.813235i | \(-0.302296\pi\) | |||||||
\(468\) | − 2.32695e46i | − 0.433994i | ||||||||
\(469\) | −6.18019e45 | −0.111039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.98641e46 | 0.664838 | ||||||||
\(472\) | 7.48309e46i | 1.20253i | ||||||||
\(473\) | − 1.88298e45i | − 0.0291592i | ||||||||
\(474\) | −7.39447e45 | −0.110353 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.98962e46 | −0.553107 | ||||||||
\(477\) | 6.48649e46i | 0.866839i | ||||||||
\(478\) | − 4.73755e46i | − 0.610331i | ||||||||
\(479\) | −1.51913e47 | −1.88679 | −0.943395 | − | 0.331671i | \(-0.892388\pi\) | ||||
−0.943395 | + | 0.331671i | \(0.892388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.31257e46 | −0.613431 | ||||||||
\(482\) | − 4.88629e46i | − 0.544072i | ||||||||
\(483\) | 4.24707e46i | 0.456052i | ||||||||
\(484\) | 1.77176e47 | 1.83490 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.68913e47 | −1.62753 | ||||||||
\(487\) | − 9.57009e46i | − 0.889527i | −0.895648 | − | 0.444764i | \(-0.853288\pi\) | ||||
0.895648 | − | 0.444764i | \(-0.146712\pi\) | |||||||
\(488\) | − 3.15699e47i | − 2.83091i | ||||||||
\(489\) | −1.55500e47 | −1.34532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.00218e46 | −0.725139 | −0.362570 | − | 0.931957i | \(-0.618100\pi\) | ||||
−0.362570 | + | 0.931957i | \(0.618100\pi\) | |||||||
\(492\) | 7.28514e46i | 0.566302i | ||||||||
\(493\) | − 7.55335e46i | − 0.566655i | ||||||||
\(494\) | −1.40379e47 | −1.01644 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.99222e47 | 1.34403 | ||||||||
\(497\) | − 4.49242e46i | − 0.292580i | ||||||||
\(498\) | 1.79736e47i | 1.13011i | ||||||||
\(499\) | 1.31845e47 | 0.800394 | 0.400197 | − | 0.916429i | \(-0.368942\pi\) | ||||
0.400197 | + | 0.916429i | \(0.368942\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.54246e46 | −0.426926 | ||||||||
\(502\) | 3.87693e47i | 2.11920i | ||||||||
\(503\) | − 3.29261e46i | − 0.173820i | −0.996216 | − | 0.0869101i | \(-0.972301\pi\) | ||||
0.996216 | − | 0.0869101i | \(-0.0276993\pi\) | |||||||
\(504\) | 1.41507e47 | 0.721510 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.56684e47 | −0.745404 | ||||||||
\(507\) | 1.28960e47i | 0.592676i | ||||||||
\(508\) | 2.25386e47i | 1.00072i | ||||||||
\(509\) | −1.43449e47 | −0.615370 | −0.307685 | − | 0.951488i | \(-0.599554\pi\) | ||||
−0.307685 | + | 0.951488i | \(0.599554\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.28323e47 | 0.513970 | ||||||||
\(512\) | − 5.75978e47i | − 2.22937i | ||||||||
\(513\) | 4.22737e47i | 1.58131i | ||||||||
\(514\) | −2.03794e47 | −0.736777 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.22482e46 | 0.108927 | ||||||||
\(517\) | − 9.63280e46i | − 0.314534i | ||||||||
\(518\) | − 5.92360e47i | − 1.86989i | ||||||||
\(519\) | −4.88340e45 | −0.0149037 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.33055e47 | −0.664966 | −0.332483 | − | 0.943109i | \(-0.607886\pi\) | ||||
−0.332483 | + | 0.943109i | \(0.607886\pi\) | |||||||
\(522\) | 4.91220e47i | 1.35532i | ||||||||
\(523\) | 4.26380e47i | 1.13767i | 0.822451 | + | 0.568836i | \(0.192606\pi\) | ||||
−0.822451 | + | 0.568836i | \(0.807394\pi\) | |||||||
\(524\) | −1.26608e48 | −3.26711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.75544e47 | 0.423776 | ||||||||
\(527\) | − 1.37021e47i | − 0.319965i | ||||||||
\(528\) | − 2.04340e47i | − 0.461593i | ||||||||
\(529\) | −2.15467e46 | −0.0470875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.42909e47 | −0.292351 | ||||||||
\(532\) | − 1.07606e48i | − 2.13002i | ||||||||
\(533\) | − 7.34945e46i | − 0.140776i | ||||||||
\(534\) | 4.80878e47 | 0.891380 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.12964e47 | 0.369762 | ||||||||
\(537\) | 7.51860e46i | 0.126353i | ||||||||
\(538\) | − 8.66140e47i | − 1.40896i | ||||||||
\(539\) | −1.51211e47 | −0.238111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.43835e45 | −0.00802629 | −0.00401314 | − | 0.999992i | \(-0.501277\pi\) | ||||
−0.00401314 | + | 0.999992i | \(0.501277\pi\) | |||||||
\(542\) | − 2.10763e48i | − 3.01167i | ||||||||
\(543\) | − 7.57817e47i | − 1.04850i | ||||||||
\(544\) | 2.28842e47 | 0.306588 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.39958e47 | 0.301484 | ||||||||
\(547\) | − 4.15694e47i | − 0.505820i | −0.967490 | − | 0.252910i | \(-0.918612\pi\) | ||||
0.967490 | − | 0.252910i | \(-0.0813876\pi\) | |||||||
\(548\) | − 5.33405e47i | − 0.628633i | ||||||||
\(549\) | 6.02909e47 | 0.688233 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.03726e48 | 2.18219 | ||||||||
\(552\) | − 1.46350e48i | − 1.51866i | ||||||||
\(553\) | 5.71821e46i | 0.0574871i | ||||||||
\(554\) | −4.37967e46 | −0.0426600 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.18772e47 | 0.382973 | ||||||||
\(557\) | 1.81613e45i | 0.00160947i | 1.00000 | 0.000804733i | \(0.000256154\pi\) | |||||
−1.00000 | 0.000804733i | \(0.999744\pi\) | ||||||||
\(558\) | 8.91097e47i | 0.765291i | ||||||||
\(559\) | −3.25329e46 | −0.0270780 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.40541e47 | −0.109889 | ||||||||
\(562\) | 4.01379e48i | 3.04207i | ||||||||
\(563\) | 2.19502e48i | 1.61266i | 0.591468 | + | 0.806329i | \(0.298549\pi\) | ||||
−0.591468 | + | 0.806329i | \(0.701451\pi\) | |||||||
\(564\) | 1.64973e48 | 1.17497 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.59063e46 | 0.0240372 | ||||||||
\(567\) | − 2.04621e47i | − 0.132815i | ||||||||
\(568\) | 1.54805e48i | 0.974293i | ||||||||
\(569\) | −1.19614e48 | −0.729993 | −0.364996 | − | 0.931009i | \(-0.618930\pi\) | ||||
−0.364996 | + | 0.931009i | \(0.618930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.26426e48 | −0.725610 | −0.362805 | − | 0.931865i | \(-0.618181\pi\) | ||||
−0.362805 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(572\) | 6.08590e47i | 0.338762i | ||||||||
\(573\) | − 1.36105e48i | − 0.734799i | ||||||||
\(574\) | 8.19476e47 | 0.429120 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.47161e47 | 0.121783 | ||||||||
\(577\) | 2.42022e48i | 1.15686i | 0.815734 | + | 0.578428i | \(0.196333\pi\) | ||||
−0.815734 | + | 0.578428i | \(0.803667\pi\) | |||||||
\(578\) | 3.27012e48i | 1.51645i | ||||||||
\(579\) | 2.55863e48 | 1.15115 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.38991e48 | 0.588715 | ||||||||
\(582\) | − 1.84445e47i | − 0.0758080i | ||||||||
\(583\) | − 1.69648e48i | − 0.676626i | ||||||||
\(584\) | −4.42189e48 | −1.71153 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.90407e47 | −0.288166 | ||||||||
\(587\) | − 1.04500e48i | − 0.369787i | −0.982759 | − | 0.184893i | \(-0.940806\pi\) | ||||
0.982759 | − | 0.184893i | \(-0.0591940\pi\) | |||||||
\(588\) | − 2.58965e48i | − 0.889485i | ||||||||
\(589\) | 3.69568e48 | 1.23219 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.13475e44 | −0.000192760 0 | ||||||||
\(592\) | 8.71527e48i | 2.65859i | ||||||||
\(593\) | − 4.87793e48i | − 1.44470i | −0.691526 | − | 0.722351i | \(-0.743061\pi\) | ||||
0.691526 | − | 0.722351i | \(-0.256939\pi\) | |||||||
\(594\) | 2.66587e48 | 0.766613 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.56809e48 | −2.59427 | ||||||||
\(597\) | 2.49897e48i | 0.657976i | ||||||||
\(598\) | 2.70709e48i | 0.692201i | ||||||||
\(599\) | −8.48111e47 | −0.210612 | −0.105306 | − | 0.994440i | \(-0.533582\pi\) | ||||
−0.105306 | + | 0.994440i | \(0.533582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.23099e48 | −1.45967 | −0.729834 | − | 0.683624i | \(-0.760403\pi\) | ||||
−0.729834 | + | 0.683624i | \(0.760403\pi\) | |||||||
\(602\) | − 3.62747e47i | − 0.0825402i | ||||||||
\(603\) | 4.06710e47i | 0.0898942i | ||||||||
\(604\) | −1.10371e49 | −2.36978 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.73181e48 | −0.756220 | ||||||||
\(607\) | 2.65746e48i | 0.523197i | 0.965177 | + | 0.261598i | \(0.0842496\pi\) | ||||
−0.965177 | + | 0.261598i | \(0.915750\pi\) | |||||||
\(608\) | 6.17224e48i | 1.18067i | ||||||||
\(609\) | −3.48240e48 | −0.647256 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.66429e48 | −0.292085 | ||||||||
\(612\) | 2.62551e48i | 0.447779i | ||||||||
\(613\) | − 5.89105e48i | − 0.976415i | −0.872727 | − | 0.488208i | \(-0.837651\pi\) | ||||
0.872727 | − | 0.488208i | \(-0.162349\pi\) | |||||||
\(614\) | 1.60622e49 | 2.58737 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.70097e48 | −0.563187 | ||||||||
\(617\) | − 2.86204e48i | − 0.423337i | −0.977342 | − | 0.211668i | \(-0.932110\pi\) | ||||
0.977342 | − | 0.211668i | \(-0.0678897\pi\) | |||||||
\(618\) | 4.86261e48i | 0.699151i | ||||||||
\(619\) | 9.42149e48 | 1.31684 | 0.658420 | − | 0.752651i | \(-0.271225\pi\) | ||||
0.658420 | + | 0.752651i | \(0.271225\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.15212e48 | 1.07688 | ||||||||
\(622\) | 6.15780e48i | 0.790850i | ||||||||
\(623\) | − 3.71867e48i | − 0.464352i | ||||||||
\(624\) | −3.53045e48 | −0.428647 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.87733e48 | 1.01913 | ||||||||
\(627\) | − 3.79062e48i | − 0.423183i | ||||||||
\(628\) | 1.94774e49i | 2.11464i | ||||||||
\(629\) | 5.99421e48 | 0.632915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.74950e48 | 0.873915 | 0.436958 | − | 0.899482i | \(-0.356056\pi\) | ||||
0.436958 | + | 0.899482i | \(0.356056\pi\) | |||||||
\(632\) | − 1.97045e48i | − 0.191432i | ||||||||
\(633\) | 4.18197e48i | 0.395199i | ||||||||
\(634\) | 8.04438e48 | 0.739487 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.90541e49 | 2.52760 | ||||||||
\(637\) | 2.61252e48i | 0.221116i | ||||||||
\(638\) | − 1.28474e49i | − 1.05792i | ||||||||
\(639\) | −2.95640e48 | −0.236864 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.35983e48 | 0.406571 | 0.203285 | − | 0.979120i | \(-0.434838\pi\) | ||||
0.203285 | + | 0.979120i | \(0.434838\pi\) | |||||||
\(642\) | − 2.79003e49i | − 2.05942i | ||||||||
\(643\) | − 2.04799e49i | − 1.47108i | −0.677483 | − | 0.735538i | \(-0.736929\pi\) | ||||
0.677483 | − | 0.735538i | \(-0.263071\pi\) | |||||||
\(644\) | −2.07509e49 | −1.45056 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.58391e49 | 1.04872 | ||||||||
\(647\) | 2.13324e49i | 1.37472i | 0.726317 | + | 0.687360i | \(0.241231\pi\) | ||||
−0.726317 | + | 0.687360i | \(0.758769\pi\) | |||||||
\(648\) | 7.05105e48i | 0.442274i | ||||||||
\(649\) | 3.73764e48 | 0.228200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.31724e48 | −0.365477 | ||||||||
\(652\) | − 7.59765e49i | − 4.27904i | ||||||||
\(653\) | 2.78018e49i | 1.52438i | 0.647354 | + | 0.762189i | \(0.275876\pi\) | ||||
−0.647354 | + | 0.762189i | \(0.724124\pi\) | |||||||
\(654\) | −1.12431e49 | −0.600172 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.20568e49 | −0.610119 | ||||||||
\(657\) | − 8.44474e48i | − 0.416095i | ||||||||
\(658\) | − 1.85571e49i | − 0.890344i | ||||||||
\(659\) | 2.64746e49 | 1.23690 | 0.618450 | − | 0.785824i | \(-0.287761\pi\) | ||||
0.618450 | + | 0.785824i | \(0.287761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.31405e49 | 1.02529 | 0.512646 | − | 0.858600i | \(-0.328665\pi\) | ||||
0.512646 | + | 0.858600i | \(0.328665\pi\) | |||||||
\(662\) | 6.09062e49i | 2.62813i | ||||||||
\(663\) | 2.42818e48i | 0.102046i | ||||||||
\(664\) | −4.78952e49 | −1.96042 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.89824e49 | −1.51380 | ||||||||
\(667\) | − 3.92868e49i | − 1.48609i | ||||||||
\(668\) | − 3.68520e49i | − 1.35792i | ||||||||
\(669\) | 2.48198e49 | 0.890927 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.57685e49 | −0.537213 | ||||||||
\(672\) | − 1.05506e49i | − 0.350198i | ||||||||
\(673\) | − 3.41502e49i | − 1.10441i | −0.833709 | − | 0.552204i | \(-0.813787\pi\) | ||||
0.833709 | − | 0.552204i | \(-0.186213\pi\) | |||||||
\(674\) | −3.19372e48 | −0.100635 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.30093e49 | −1.88511 | ||||||||
\(677\) | 1.81760e49i | 0.529903i | 0.964262 | + | 0.264951i | \(0.0853559\pi\) | ||||
−0.964262 | + | 0.264951i | \(0.914644\pi\) | |||||||
\(678\) | − 1.83153e49i | − 0.520348i | ||||||||
\(679\) | −1.42633e48 | −0.0394911 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.04227e49 | 0.537079 | ||||||||
\(682\) | − 2.33058e49i | − 0.597361i | ||||||||
\(683\) | 1.52341e49i | 0.380587i | 0.981727 | + | 0.190294i | \(0.0609440\pi\) | ||||
−0.981727 | + | 0.190294i | \(0.939056\pi\) | |||||||
\(684\) | −7.08142e49 | −1.72440 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.89504e49 | −1.82676 | ||||||||
\(687\) | 1.97501e49i | 0.445479i | ||||||||
\(688\) | 5.33703e48i | 0.117355i | ||||||||
\(689\) | −2.93107e49 | −0.628332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.25243e49 | −0.255203 | −0.127602 | − | 0.991825i | \(-0.540728\pi\) | ||||
−0.127602 | + | 0.991825i | \(0.540728\pi\) | |||||||
\(692\) | − 2.38600e48i | − 0.0474039i | ||||||||
\(693\) | − 7.06795e48i | − 0.136918i | ||||||||
\(694\) | −6.80382e49 | −1.28517 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.20001e50 | 2.15537 | ||||||||
\(697\) | 8.29244e48i | 0.145247i | ||||||||
\(698\) | 3.31961e49i | 0.567045i | ||||||||
\(699\) | −1.78279e49 | −0.296995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.20207e49 | 0.665883 | 0.332942 | − | 0.942947i | \(-0.391959\pi\) | ||||
0.332942 | + | 0.942947i | \(0.391959\pi\) | |||||||
\(702\) | − 4.60592e49i | − 0.711896i | ||||||||
\(703\) | 1.61673e50i | 2.43736i | ||||||||
\(704\) | −6.46426e48 | −0.0950598 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00351e49 | −1.25988 | ||||||||
\(707\) | 2.88584e49i | 0.393942i | ||||||||
\(708\) | 6.40114e49i | 0.852463i | ||||||||
\(709\) | −9.39998e48 | −0.122129 | −0.0610644 | − | 0.998134i | \(-0.519449\pi\) | ||||
−0.0610644 | + | 0.998134i | \(0.519449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.76307e48 | 0.0465398 | ||||||||
\(712\) | 1.28142e50i | 1.54629i | ||||||||
\(713\) | − 7.12681e49i | − 0.839128i | ||||||||
\(714\) | −2.70746e49 | −0.311059 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.67354e49 | −0.401890 | ||||||||
\(717\) | − 2.21023e49i | − 0.235968i | ||||||||
\(718\) | − 2.92234e50i | − 3.04476i | ||||||||
\(719\) | 7.29315e49 | 0.741583 | 0.370792 | − | 0.928716i | \(-0.379086\pi\) | ||||
0.370792 | + | 0.928716i | \(0.379086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.76030e49 | 0.364213 | ||||||||
\(722\) | 2.37989e50i | 2.24987i | ||||||||
\(723\) | − 2.27963e49i | − 0.210351i | ||||||||
\(724\) | 3.70265e50 | 3.33494 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.20237e50 | 1.03192 | ||||||||
\(727\) | − 4.92620e49i | − 0.412724i | −0.978476 | − | 0.206362i | \(-0.933838\pi\) | ||||
0.978476 | − | 0.206362i | \(-0.0661624\pi\) | |||||||
\(728\) | 6.39429e49i | 0.522990i | ||||||||
\(729\) | −1.04614e50 | −0.835334 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.67071e48 | 0.0279380 | ||||||||
\(732\) | − 2.70054e50i | − 2.00681i | ||||||||
\(733\) | 1.28080e50i | 0.929310i | 0.885492 | + | 0.464655i | \(0.153822\pi\) | ||||
−0.885492 | + | 0.464655i | \(0.846178\pi\) | |||||||
\(734\) | 3.69035e50 | 2.61449 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.19026e50 | 0.804047 | ||||||||
\(737\) | − 1.06371e49i | − 0.0701685i | ||||||||
\(738\) | − 5.39286e49i | − 0.347402i | ||||||||
\(739\) | −1.99479e50 | −1.25493 | −0.627466 | − | 0.778644i | \(-0.715908\pi\) | ||||
−0.627466 | + | 0.778644i | \(0.715908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.54918e49 | −0.392978 | ||||||||
\(742\) | − 3.26819e50i | − 1.91531i | ||||||||
\(743\) | − 1.05855e50i | − 0.605907i | −0.953005 | − | 0.302954i | \(-0.902027\pi\) | ||||
0.953005 | − | 0.302954i | \(-0.0979728\pi\) | |||||||
\(744\) | 2.17687e50 | 1.21704 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.82529e50 | −0.973651 | ||||||||
\(747\) | − 9.14681e49i | − 0.476606i | ||||||||
\(748\) | − 6.86676e49i | − 0.349522i | ||||||||
\(749\) | −2.15755e50 | −1.07283 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.20549e50 | −0.572090 | −0.286045 | − | 0.958216i | \(-0.592341\pi\) | ||||
−0.286045 | + | 0.958216i | \(0.592341\pi\) | |||||||
\(752\) | 2.73027e50i | 1.26588i | ||||||||
\(753\) | 1.80872e50i | 0.819333i | ||||||||
\(754\) | −2.21969e50 | −0.982411 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.53062e50 | 1.49183 | ||||||||
\(757\) | 1.18495e50i | 0.489240i | 0.969619 | + | 0.244620i | \(0.0786633\pi\) | ||||
−0.969619 | + | 0.244620i | \(0.921337\pi\) | |||||||
\(758\) | 6.01917e50i | 2.42843i | ||||||||
\(759\) | −7.30989e49 | −0.288190 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.89900e50 | 1.09148 | 0.545741 | − | 0.837954i | \(-0.316248\pi\) | ||||
0.545741 | + | 0.837954i | \(0.316248\pi\) | |||||||
\(762\) | 1.52953e50i | 0.562789i | ||||||||
\(763\) | 8.69439e49i | 0.312651i | ||||||||
\(764\) | 6.65002e50 | 2.33716 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.79984e50 | 0.604270 | ||||||||
\(767\) | − 6.45766e49i | − 0.211912i | ||||||||
\(768\) | − 4.13754e50i | − 1.32715i | ||||||||
\(769\) | −6.18664e49 | −0.193974 | −0.0969870 | − | 0.995286i | \(-0.530921\pi\) | ||||
−0.0969870 | + | 0.995286i | \(0.530921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.50771e49 | −0.284855 | ||||||||
\(772\) | 1.25013e51i | 3.66145i | ||||||||
\(773\) | 6.37753e50i | 1.82604i | 0.407911 | + | 0.913022i | \(0.366257\pi\) | ||||
−0.407911 | + | 0.913022i | \(0.633743\pi\) | |||||||
\(774\) | −2.38719e49 | −0.0668221 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.91501e49 | 0.131506 | ||||||||
\(777\) | − 2.76357e50i | − 0.722941i | ||||||||
\(778\) | − 7.54649e50i | − 1.93020i | ||||||||
\(779\) | −2.23660e50 | −0.559349 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.73218e49 | 0.184888 | ||||||||
\(782\) | − 3.05443e50i | − 0.714186i | ||||||||
\(783\) | 6.68436e50i | 1.52837i | ||||||||
\(784\) | 4.28584e50 | 0.958307 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.59196e50 | −1.83737 | ||||||||
\(787\) | 6.23653e50i | 1.30432i | 0.758080 | + | 0.652161i | \(0.226138\pi\) | ||||
−0.758080 | + | 0.652161i | \(0.773862\pi\) | |||||||
\(788\) | − 2.99740e47i | 0 0.000613107i | ||||||||
\(789\) | 8.18976e49 | 0.163841 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.41634e50 | −0.271068 | ||||||||
\(792\) | 2.43555e50i | 0.455939i | ||||||||
\(793\) | 2.72438e50i | 0.498869i | ||||||||
\(794\) | −9.86679e50 | −1.76733 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.22098e51 | −2.09281 | ||||||||
\(797\) | 9.07097e50i | 1.52101i | 0.649329 | + | 0.760507i | \(0.275050\pi\) | ||||
−0.649329 | + | 0.760507i | \(0.724950\pi\) | |||||||
\(798\) | − 7.30245e50i | − 1.19789i | ||||||||
\(799\) | 1.87783e50 | 0.301362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.44720e50 | −0.375925 | ||||||||
\(802\) | − 1.11212e51i | − 1.67148i | ||||||||
\(803\) | 2.20864e50i | 0.324790i | ||||||||
\(804\) | 1.82172e50 | 0.262121 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.02662e50 | −0.554724 | ||||||||
\(807\) | − 4.04086e50i | − 0.544736i | ||||||||
\(808\) | − 9.94435e50i | − 1.31183i | ||||||||
\(809\) | −1.43609e51 | −1.85389 | −0.926943 | − | 0.375202i | \(-0.877573\pi\) | ||||
−0.926943 | + | 0.375202i | \(0.877573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.18627e50 | 0.764828 | 0.382414 | − | 0.923991i | \(-0.375093\pi\) | ||||
0.382414 | + | 0.923991i | \(0.375093\pi\) | |||||||
\(812\) | − 1.70148e51i | − 2.05872i | ||||||||
\(813\) | − 9.83286e50i | − 1.16438i | ||||||||
\(814\) | 1.01955e51 | 1.18163 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.98343e50 | 0.442262 | ||||||||
\(817\) | 9.90049e49i | 0.107590i | ||||||||
\(818\) | − 2.90186e51i | − 3.08670i | ||||||||
\(819\) | −1.22115e50 | −0.127146 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.87204e50 | −0.984922 | −0.492461 | − | 0.870335i | \(-0.663903\pi\) | ||||
−0.492461 | + | 0.870335i | \(0.663903\pi\) | |||||||
\(822\) | − 3.61983e50i | − 0.353534i | ||||||||
\(823\) | 1.56871e51i | 1.49985i | 0.661525 | + | 0.749923i | \(0.269909\pi\) | ||||
−0.661525 | + | 0.749923i | \(0.730091\pi\) | |||||||
\(824\) | −1.29577e51 | −1.21283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.20039e50 | 0.645960 | ||||||||
\(827\) | − 3.34712e49i | − 0.0293985i | −0.999892 | − | 0.0146992i | \(-0.995321\pi\) | ||||
0.999892 | − | 0.0146992i | \(-0.00467908\pi\) | |||||||
\(828\) | 1.36559e51i | 1.17433i | ||||||||
\(829\) | 1.24277e51 | 1.04638 | 0.523188 | − | 0.852217i | \(-0.324743\pi\) | ||||
0.523188 | + | 0.852217i | \(0.324743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.04327e49 | −0.0164933 | ||||||||
\(832\) | 1.11685e50i | 0.0882749i | ||||||||
\(833\) | − 2.94772e50i | − 0.228139i | ||||||||
\(834\) | 2.84190e50 | 0.215379 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.85208e51 | 1.34601 | ||||||||
\(837\) | 1.21258e51i | 0.863005i | ||||||||
\(838\) | − 6.61903e50i | − 0.461343i | ||||||||
\(839\) | −7.06560e50 | −0.482297 | −0.241149 | − | 0.970488i | \(-0.577524\pi\) | ||||
−0.241149 | + | 0.970488i | \(0.577524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.69401e51 | 1.10914 | ||||||||
\(842\) | − 4.09125e51i | − 2.62358i | ||||||||
\(843\) | 1.87258e51i | 1.17613i | ||||||||
\(844\) | −2.04329e51 | −1.25700 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.22122e51 | −0.720796 | ||||||||
\(847\) | − 9.29800e50i | − 0.537564i | ||||||||
\(848\) | 4.80842e51i | 2.72317i | ||||||||
\(849\) | 1.67516e49 | 0.00929333 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.11773e51 | 1.65986 | ||||||||
\(852\) | 1.32422e51i | 0.690667i | ||||||||
\(853\) | 4.40952e50i | 0.225311i | 0.993634 | + | 0.112656i | \(0.0359357\pi\) | ||||
−0.993634 | + | 0.112656i | \(0.964064\pi\) | |||||||
\(854\) | −3.03773e51 | −1.52067 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.43474e51 | 3.57252 | ||||||||
\(857\) | − 2.01998e51i | − 0.951004i | −0.879715 | − | 0.475502i | \(-0.842267\pi\) | ||||
0.879715 | − | 0.475502i | \(-0.157733\pi\) | |||||||
\(858\) | 4.13006e50i | 0.190515i | ||||||||
\(859\) | 2.47558e51 | 1.11891 | 0.559456 | − | 0.828860i | \(-0.311010\pi\) | ||||
0.559456 | + | 0.828860i | \(0.311010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.82315e50 | 0.165908 | ||||||||
\(862\) | − 3.99071e51i | − 1.69696i | ||||||||
\(863\) | − 1.15182e51i | − 0.479948i | −0.970779 | − | 0.239974i | \(-0.922861\pi\) | ||||
0.970779 | − | 0.239974i | \(-0.0771389\pi\) | |||||||
\(864\) | −2.02515e51 | −0.826926 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.84143e51 | −2.68277 | ||||||||
\(867\) | 1.52563e51i | 0.586293i | ||||||||
\(868\) | − 3.08657e51i | − 1.16247i | ||||||||
\(869\) | −9.84195e49 | −0.0363274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.83781e50 | −0.0651602 | ||||||||
\(872\) | − 2.99601e51i | − 1.04113i | ||||||||
\(873\) | 9.38647e49i | 0.0319708i | ||||||||
\(874\) | 8.23827e51 | 2.75034 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.78255e51 | −1.21328 | ||||||||
\(877\) | 1.21793e50i | 0.0382938i | 0.999817 | + | 0.0191469i | \(0.00609502\pi\) | ||||
−0.999817 | + | 0.0191469i | \(0.993905\pi\) | |||||||
\(878\) | − 1.04445e52i | − 3.21909i | ||||||||
\(879\) | −3.68753e50 | −0.111412 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.43159e51 | 0.415663 | 0.207832 | − | 0.978165i | \(-0.433359\pi\) | ||||
0.207832 | + | 0.978165i | \(0.433359\pi\) | |||||||
\(882\) | 1.91700e51i | 0.545661i | ||||||||
\(883\) | − 4.21625e51i | − 1.17656i | −0.808658 | − | 0.588280i | \(-0.799805\pi\) | ||||
0.808658 | − | 0.588280i | \(-0.200195\pi\) | |||||||
\(884\) | −1.18639e51 | −0.324575 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.27591e51 | −2.17634 | ||||||||
\(887\) | 1.06484e51i | 0.274549i | 0.990533 | + | 0.137274i | \(0.0438342\pi\) | ||||
−0.990533 | + | 0.137274i | \(0.956166\pi\) | |||||||
\(888\) | 9.52303e51i | 2.40740i | ||||||||
\(889\) | 1.18280e51 | 0.293177 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.52185e50 | 0.0839288 | ||||||||
\(892\) | 1.21268e52i | 2.83376i | ||||||||
\(893\) | 5.06481e51i | 1.16055i | ||||||||
\(894\) | −6.49316e51 | −1.45898 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.58879e51 | −0.775457 | ||||||||
\(897\) | 1.26295e51i | 0.267621i | ||||||||
\(898\) | − 1.04377e52i | − 2.16904i | ||||||||
\(899\) | 5.84365e51 | 1.19094 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.30714e51 | 0.648289 | ||||||||
\(902\) | 1.41045e51i | 0.271171i | ||||||||
\(903\) | − 1.69235e50i | − 0.0319120i | ||||||||
\(904\) | 4.88057e51 | 0.902658 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.49007e51 | −1.33273 | ||||||||
\(907\) | 5.18332e51i | 0.904649i | 0.891853 | + | 0.452325i | \(0.149405\pi\) | ||||
−0.891853 | + | 0.452325i | \(0.850595\pi\) | |||||||
\(908\) | 9.97841e51i | 1.70828i | ||||||||
\(909\) | 1.89913e51 | 0.318923 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.24676e51 | 1.49423 | 0.747116 | − | 0.664694i | \(-0.231438\pi\) | ||||
0.747116 | + | 0.664694i | \(0.231438\pi\) | |||||||
\(912\) | 1.07439e52i | 1.70315i | ||||||||
\(913\) | 2.39226e51i | 0.372023i | ||||||||
\(914\) | −1.06765e52 | −1.62880 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.64981e51 | −1.41693 | ||||||||
\(917\) | 6.64424e51i | 0.957154i | ||||||||
\(918\) | 5.19689e51i | 0.734508i | ||||||||
\(919\) | 4.29279e51 | 0.595275 | 0.297638 | − | 0.954679i | \(-0.403801\pi\) | ||||
0.297638 | + | 0.954679i | \(0.403801\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.49359e51 | 1.00034 | ||||||||
\(922\) | 2.97278e51i | 0.389378i | ||||||||
\(923\) | − 1.33592e51i | − 0.171692i | ||||||||
\(924\) | −3.16586e51 | −0.399238 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.09766e51 | −1.10468 | ||||||||
\(927\) | − 2.47460e51i | − 0.294856i | ||||||||
\(928\) | 9.75961e51i | 1.14115i | ||||||||
\(929\) | −4.47733e51 | −0.513740 | −0.256870 | − | 0.966446i | \(-0.582691\pi\) | ||||
−0.256870 | + | 0.966446i | \(0.582691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.95047e51 | 0.878564 | ||||||||
\(932\) | − 8.71061e51i | − 0.944649i | ||||||||
\(933\) | 2.87284e51i | 0.305761i | ||||||||
\(934\) | 2.78529e52 | 2.90938 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.20799e51 | 0.423397 | ||||||||
\(937\) | − 1.28073e50i | − 0.0126478i | −0.999980 | − | 0.00632388i | \(-0.997987\pi\) | ||||
0.999980 | − | 0.00632388i | \(-0.00201297\pi\) | |||||||
\(938\) | − 2.04919e51i | − 0.198624i | ||||||||
\(939\) | 4.14159e51 | 0.394021 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.26378e50 | 0.0299160 | 0.0149580 | − | 0.999888i | \(-0.495239\pi\) | ||||
0.0149580 | + | 0.999888i | \(0.495239\pi\) | |||||||
\(942\) | 1.32179e52i | 1.18924i | ||||||||
\(943\) | 4.31310e51i | 0.380921i | ||||||||
\(944\) | −1.05938e52 | −0.918420 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.24346e50 | 0.0521591 | ||||||||
\(947\) | − 1.57573e52i | − 1.29228i | −0.763219 | − | 0.646140i | \(-0.776382\pi\) | ||||
0.763219 | − | 0.646140i | \(-0.223618\pi\) | |||||||
\(948\) | − 1.68555e51i | − 0.135705i | ||||||||
\(949\) | 3.81594e51 | 0.301608 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.75299e51 | 0.285903 | ||||||||
\(952\) | − 7.21472e51i | − 0.539601i | ||||||||
\(953\) | 9.47096e51i | 0.695454i | 0.937596 | + | 0.347727i | \(0.113046\pi\) | ||||
−0.937596 | + | 0.347727i | \(0.886954\pi\) | |||||||
\(954\) | −2.15075e52 | −1.55057 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.07991e52 | 0.750540 | ||||||||
\(957\) | − 5.99377e51i | − 0.409017i | ||||||||
\(958\) | − 5.03703e52i | − 3.37503i | ||||||||
\(959\) | −2.79924e51 | −0.184168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.16308e51 | −0.327529 | ||||||||
\(962\) | − 1.76151e52i | − 1.09729i | ||||||||
\(963\) | 1.41985e52i | 0.868528i | ||||||||
\(964\) | 1.11381e52 | 0.669059 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.40821e52 | −0.815773 | ||||||||
\(967\) | 1.42806e52i | 0.812424i | 0.913779 | + | 0.406212i | \(0.133151\pi\) | ||||
−0.913779 | + | 0.406212i | \(0.866849\pi\) | |||||||
\(968\) | 3.20401e52i | 1.79009i | ||||||||
\(969\) | 7.38949e51 | 0.405460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.08920e51 | −0.216422 | −0.108211 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108211 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(972\) | − 3.85032e52i | − 2.00141i | ||||||||
\(973\) | − 2.19766e51i | − 0.112198i | ||||||||
\(974\) | 3.17319e52 | 1.59116 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.46934e52 | 2.16208 | ||||||||
\(977\) | 2.55940e52i | 1.21614i | 0.793883 | + | 0.608071i | \(0.208056\pi\) | ||||
−0.793883 | + | 0.608071i | \(0.791944\pi\) | |||||||
\(978\) | − 5.15597e52i | − 2.40647i | ||||||||
\(979\) | 6.40042e51 | 0.293435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.72166e51 | 0.253113 | ||||||||
\(982\) | − 2.98488e52i | − 1.29711i | ||||||||
\(983\) | − 1.82270e52i | − 0.778087i | −0.921219 | − | 0.389044i | \(-0.872806\pi\) | ||||
0.921219 | − | 0.389044i | \(-0.127194\pi\) | |||||||
\(984\) | −1.31742e52 | −0.552474 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.50449e52 | 1.01361 | ||||||||
\(987\) | − 8.65757e51i | − 0.344228i | ||||||||
\(988\) | − 3.19989e52i | − 1.24994i | ||||||||
\(989\) | 1.90922e51 | 0.0732693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.47738e51 | 0.314031 | 0.157015 | − | 0.987596i | \(-0.449813\pi\) | ||||
0.157015 | + | 0.987596i | \(0.449813\pi\) | |||||||
\(992\) | 1.77044e52i | 0.644358i | ||||||||
\(993\) | 2.84149e52i | 1.01610i | ||||||||
\(994\) | 1.48957e52 | 0.523358 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.09702e52 | −1.38973 | ||||||||
\(997\) | − 4.09490e52i | − 1.36483i | −0.730966 | − | 0.682414i | \(-0.760930\pi\) | ||||
0.730966 | − | 0.682414i | \(-0.239070\pi\) | |||||||
\(998\) | 4.37162e52i | 1.43172i | ||||||||
\(999\) | −5.30459e52 | −1.70709 |
(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 | 25.36.b.a.24.6 | 6 | ||
5.2 | odd | 4 | 25.36.a.a.1.1 | 3 | |||
5.3 | odd | 4 | 1.36.a.a.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 25.36.b.a.24.1 | 6 | ||
15.8 | even | 4 | 9.36.a.b.1.1 | 3 | |||
20.3 | even | 4 | 16.36.a.d.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.36.a.a.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
9.36.a.b.1.1 | 3 | 15.8 | even | 4 | |||
16.36.a.d.1.2 | 3 | 20.3 | even | 4 | |||
25.36.a.a.1.1 | 3 | 5.2 | odd | 4 | |||
25.36.b.a.24.1 | 6 | 5.4 | even | 2 | inner | ||
25.36.b.a.24.6 | 6 | 1.1 | even | 1 | trivial |