Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,8,Mod(191,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.191");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.c (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: | \(59.9779248930\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(-0.866025 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.191 |
Dual form | 192.8.c.b.191.2 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −31.1769 | − | 34.8569i | −0.666667 | − | 0.745356i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 205.718i | − | 0.736000i | −0.929826 | − | 0.368000i | \(-0.880043\pi\) | ||
0.929826 | − | 0.368000i | \(-0.119957\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 999.230i | − | 1.10109i | −0.834806 | − | 0.550544i | \(-0.814420\pi\) | ||
0.834806 | − | 0.550544i | \(-0.185580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −243.000 | + | 2173.46i | −0.111111 | + | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1974.54 | 0.447292 | 0.223646 | − | 0.974670i | \(-0.428204\pi\) | ||||
0.223646 | + | 0.974670i | \(0.428204\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12730.0 | 1.60704 | 0.803520 | − | 0.595278i | \(-0.202958\pi\) | ||||
0.803520 | + | 0.595278i | \(0.202958\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7170.69 | + | 6413.66i | −0.548582 | + | 0.490667i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18854.5i | 0.930774i | 0.885107 | + | 0.465387i | \(0.154085\pi\) | ||||
−0.885107 | + | 0.465387i | \(0.845915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23911.8i | 0.799788i | 0.916561 | + | 0.399894i | \(0.130953\pi\) | ||||
−0.916561 | + | 0.399894i | \(0.869047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −34830.0 | + | 31152.9i | −0.820703 | + | 0.734059i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72372.0 | 1.24029 | 0.620145 | − | 0.784487i | \(-0.287074\pi\) | ||||
0.620145 | + | 0.784487i | \(0.287074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 35805.0 | 0.458304 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 83335.9 | − | 59291.5i | 0.814815 | − | 0.579721i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 106106.i | 0.807879i | 0.914786 | + | 0.403940i | \(0.132359\pi\) | ||||
−0.914786 | + | 0.403940i | \(0.867641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 90372.2i | 0.544840i | 0.962178 | + | 0.272420i | \(0.0878240\pi\) | ||||
−0.962178 | + | 0.272420i | \(0.912176\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −61560.0 | − | 68826.2i | −0.298195 | − | 0.333392i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −205560. | −0.810401 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −43310.0 | −0.140567 | −0.0702833 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702833 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −396882. | − | 443728.i | −1.07136 | − | 1.19782i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 785790.i | 1.78059i | 0.455388 | + | 0.890293i | \(0.349501\pi\) | ||||
−0.455388 | + | 0.890293i | \(0.650499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 70805.9i | − | 0.135809i | −0.997692 | − | 0.0679047i | \(-0.978369\pi\) | ||
0.997692 | − | 0.0679047i | \(-0.0216314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 447120. | + | 49989.5i | 0.731443 | + | 0.0817778i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 563762. | 0.792051 | 0.396025 | − | 0.918240i | \(-0.370389\pi\) | ||||
0.396025 | + | 0.918240i | \(0.370389\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −174917. | −0.212396 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 657209. | − | 587826.i | 0.693758 | − | 0.620516i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 348943.i | 0.321950i | 0.986958 | + | 0.160975i | \(0.0514639\pi\) | ||||
−0.986958 | + | 0.160975i | \(0.948536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 406198.i | − | 0.329207i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 833490. | − | 745496.i | 0.596126 | − | 0.533192i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 758119. | 0.480568 | 0.240284 | − | 0.970703i | \(-0.422759\pi\) | ||||
0.240284 | + | 0.970703i | \(0.422759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −314198. | −0.177235 | −0.0886174 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886174 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.17178e6 | + | 242813.i | 1.09427 | + | 0.122343i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.61879e6i | − | 1.18278i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 811351.i | − | 0.329570i | −0.986330 | − | 0.164785i | \(-0.947307\pi\) | ||
0.986330 | − | 0.164785i | \(-0.0526930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.25634e6 | − | 2.52266e6i | −0.826860 | − | 0.924458i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 265004. | 0.0878715 | 0.0439357 | − | 0.999034i | \(-0.486010\pi\) | ||||
0.0439357 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −259270. | −0.0780050 | −0.0390025 | − | 0.999239i | \(-0.512418\pi\) | ||||
−0.0390025 | + | 0.999239i | \(0.512418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.11629e6 | − | 1.24805e6i | −0.305536 | − | 0.341600i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.97302e6i | − | 0.492508i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.23482e6i | − | 1.19456i | −0.802033 | − | 0.597279i | \(-0.796248\pi\) | ||
0.802033 | − | 0.597279i | \(-0.203752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.66487e6 | − | 1.05630e6i | −0.975309 | − | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.01017e7 | 1.93919 | 0.969594 | − | 0.244718i | \(-0.0786955\pi\) | ||||
0.969594 | + | 0.244718i | \(0.0786955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.87872e6 | 0.685050 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.69852e6 | − | 3.30805e6i | 0.602158 | − | 0.538586i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.88455e6i | 0.584085i | 0.956405 | + | 0.292042i | \(0.0943348\pi\) | ||||
−0.956405 | + | 0.292042i | \(0.905665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.27202e7i | − | 1.76949i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.15009e6 | − | 2.81753e6i | 0.406100 | − | 0.363227i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.91909e6 | 0.588644 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.24301e6 | 0.805783 | 0.402891 | − | 0.915248i | \(-0.368005\pi\) | ||||
0.402891 | + | 0.915248i | \(0.368005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −479813. | + | 4.29158e6i | −0.0496991 | + | 0.444522i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.12157e7i | 1.08318i | 0.840642 | + | 0.541591i | \(0.182178\pi\) | ||||
−0.840642 | + | 0.541591i | \(0.817822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.15817e7i | − | 1.04434i | −0.852843 | − | 0.522168i | \(-0.825123\pi\) | ||
0.852843 | − | 0.522168i | \(-0.174877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.40872e6 | + | 7.16517e6i | 0.540267 | + | 0.604037i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −218675. | −0.0172566 | −0.00862831 | − | 0.999963i | \(-0.502747\pi\) | ||||
−0.00862831 | + | 0.999963i | \(0.502747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.80701e6 | −0.725344 | −0.362672 | − | 0.931917i | \(-0.618135\pi\) | ||||
−0.362672 | + | 0.931917i | \(0.618135\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.35027e6 | + | 1.50965e6i | 0.0937111 | + | 0.104772i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.41533e6i | − | 0.353061i | −0.984295 | − | 0.176531i | \(-0.943513\pi\) | ||
0.984295 | − | 0.176531i | \(-0.0564875\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.48882e7i | − | 0.912853i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.09339e6 | + | 2.76681e7i | −0.178560 | + | 1.59709i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.88400e7 | 1.02486 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.55884e7 | −0.799930 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.73902e7 | − | 2.44985e7i | 1.32717 | − | 1.18706i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.34375e7i | − | 1.07331i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.65498e7i | − | 0.716936i | −0.933542 | − | 0.358468i | \(-0.883299\pi\) | ||
0.933542 | − | 0.358468i | \(-0.116701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.46807e6 | + | 2.20751e6i | −0.101226 | + | 0.0905396i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.54476e6 | −0.0989004 | −0.0494502 | − | 0.998777i | \(-0.515747\pi\) | ||||
−0.0494502 | + | 0.998777i | \(0.515747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.38934e7 | 0.880637 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.21973e7 | − | 1.71437e7i | −0.426675 | − | 0.599704i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.54632e7i | 0.846040i | 0.906120 | + | 0.423020i | \(0.139030\pi\) | ||||
−0.906120 | + | 0.423020i | \(0.860970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.98426e7i | 1.25833i | 0.777270 | + | 0.629167i | \(0.216604\pi\) | ||||
−0.777270 | + | 0.629167i | \(0.783396\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.75764e7 | − | 1.96510e7i | −0.528034 | − | 0.590360i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.51359e7 | 0.718816 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.18279e7 | 0.594599 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.45337e6 | + | 6.09706e6i | 0.141597 | + | 0.158310i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.47666e6i | − | 0.0613359i | −0.999530 | − | 0.0306679i | \(-0.990237\pi\) | ||
0.999530 | − | 0.0306679i | \(-0.00976344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67175e7i | 1.34060i | 0.742092 | + | 0.670298i | \(0.233834\pi\) | ||||
−0.742092 | + | 0.670298i | \(0.766166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.09795e7 | − | 4.58165e6i | −0.925011 | − | 0.103419i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.85912e7 | 0.401002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.54237e7 | 0.524312 | 0.262156 | − | 0.965026i | \(-0.415566\pi\) | ||||
0.262156 | + | 0.965026i | \(0.415566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.21630e7 | − | 1.08790e7i | 0.239968 | − | 0.214634i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.23163e7i | − | 1.36567i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.04251e7i | − | 0.731130i | −0.930786 | − | 0.365565i | \(-0.880876\pi\) | ||
0.930786 | − | 0.365565i | \(-0.119124\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.41588e7 | + | 1.26640e7i | −0.245376 | + | 0.219471i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.30738e7 | −0.881805 | −0.440902 | − | 0.897555i | \(-0.645342\pi\) | ||||
−0.440902 | + | 0.897555i | \(0.645342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.93044e7 | 1.58258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.19713e7 | − | 5.81057e6i | −0.794835 | − | 0.0888653i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.80723e6i | 0.114640i | 0.998356 | + | 0.0573199i | \(0.0182555\pi\) | ||||
−0.998356 | + | 0.0573199i | \(0.981744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.57774e7i | − | 0.504633i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.36358e7 | − | 2.64256e7i | −0.320379 | − | 0.358194i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.52215e7 | −0.980294 | −0.490147 | − | 0.871640i | \(-0.663057\pi\) | ||||
−0.490147 | + | 0.871640i | \(0.663057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.63087e7 | −0.455130 | −0.227565 | − | 0.973763i | \(-0.573076\pi\) | ||||
−0.227565 | + | 0.973763i | \(0.573076\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.79572e6 | + | 1.09520e7i | 0.118157 | + | 0.132103i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.90966e6i | 0.103457i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.72290e7i | 0.416328i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.92458e7 | − | 8.32717e7i | −0.638324 | − | 0.897183i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.29538e8 | −1.34518 | −0.672590 | − | 0.740015i | \(-0.734818\pi\) | ||||
−0.672590 | + | 0.740015i | \(0.734818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.19989e8 | −1.20141 | −0.600703 | − | 0.799472i | \(-0.705112\pi\) | ||||
−0.600703 | + | 0.799472i | \(0.705112\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.12829e7 | + | 8.16459e7i | −0.881593 | + | 0.788521i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.80955e7i | − | 0.355011i | −0.984120 | − | 0.177506i | \(-0.943197\pi\) | ||
0.984120 | − | 0.177506i | \(-0.0568028\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.00917e8i | 0.907775i | 0.891059 | + | 0.453888i | \(0.149963\pi\) | ||||
−0.891059 | + | 0.453888i | \(0.850037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82812e7 | + | 2.52954e7i | −0.245647 | + | 0.219713i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.06024e8 | 0.889547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.61651e8 | 1.31051 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.75864e7 | + | 1.57298e8i | −0.137810 | + | 1.23261i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.72148e7i | 0.357739i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.02240e8i | 1.48210i | 0.671448 | + | 0.741052i | \(0.265673\pi\) | ||||
−0.671448 | + | 0.741052i | \(0.734327\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.26200e6 | − | 9.23720e6i | −0.0585810 | − | 0.0654955i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.45661e7 | −0.0999557 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.03026e7 | 0.599917 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.08324e6 | + | 9.03734e6i | 0.0520033 | + | 0.0581415i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.40018e8i | 1.49579i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.63341e7i | − | 0.279791i | −0.990166 | − | 0.139896i | \(-0.955323\pi\) | ||
0.990166 | − | 0.139896i | \(-0.0446767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.70062e6 | + | 7.78207e7i | −0.0509227 | + | 0.455466i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.52540e8 | −0.865554 | −0.432777 | − | 0.901501i | \(-0.642466\pi\) | ||||
−0.432777 | + | 0.901501i | \(0.642466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.39128e7 | 0.241639 | 0.120819 | − | 0.992675i | \(-0.461448\pi\) | ||||
0.120819 | + | 0.992675i | \(0.461448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.87732e7 | + | 6.15126e7i | −0.367094 | + | 0.328339i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.42578e8i | 1.25634i | 0.778077 | + | 0.628168i | \(0.216195\pi\) | ||||
−0.778077 | + | 0.628168i | \(0.783805\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.15976e8i | − | 0.582949i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.82470e8 | + | 1.63206e8i | −0.890371 | + | 0.796372i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.34211e8 | 0.635909 | 0.317954 | − | 0.948106i | \(-0.397004\pi\) | ||||
0.317954 | + | 0.948106i | \(0.397004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.19220e8 | 1.92922 | 0.964612 | − | 0.263674i | \(-0.0849343\pi\) | ||||
0.964612 | + | 0.263674i | \(0.0849343\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.08617e8 | + | 1.95535e8i | 0.485597 | + | 0.874183i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.59836e7i | 0.156323i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.04397e8i | 1.28529i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.14939e8 | − | 3.52113e8i | −1.29279 | − | 1.44539i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.44551e8 | −1.77445 | −0.887225 | − | 0.461337i | \(-0.847370\pi\) | ||||
−0.887225 | + | 0.461337i | \(0.847370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.42901e8 | 0.554772 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.20927e8 | − | 1.35200e8i | −0.456700 | − | 0.510606i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.24979e7i | − | 0.119423i | −0.998216 | − | 0.0597117i | \(-0.980982\pi\) | ||
0.998216 | − | 0.0597117i | \(-0.0190181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.32766e7i | 0.154776i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.30617e8 | − | 2.57837e7i | −0.802877 | − | 0.0897644i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.26351e8 | −1.44518 | −0.722590 | − | 0.691277i | \(-0.757048\pi\) | ||||
−0.722590 | + | 0.691277i | \(0.757048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.17839e7 | 0.236955 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.35403e8 | − | 1.21108e8i | 0.435351 | − | 0.389390i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.00361e8i | − | 0.940829i | −0.882445 | − | 0.470415i | \(-0.844104\pi\) | ||
0.882445 | − | 0.470415i | \(-0.155896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.68618e8i | − | 0.514648i | −0.966325 | − | 0.257324i | \(-0.917159\pi\) | ||
0.966325 | − | 0.257324i | \(-0.0828408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.43386e8 | + | 3.96576e8i | −1.31890 | + | 1.17966i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.06983e7 | 0.204996 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.20256e8 | 1.18805 | 0.594026 | − | 0.804446i | \(-0.297538\pi\) | ||||
0.594026 | + | 0.804446i | \(0.297538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.96420e8 | − | 2.19604e7i | −0.541466 | − | 0.0605378i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.09954e8i | − | 1.37107i | −0.728041 | − | 0.685533i | \(-0.759569\pi\) | ||
0.728041 | − | 0.685533i | \(-0.240431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.54638e7i | − | 0.0405567i | −0.999794 | − | 0.0202784i | \(-0.993545\pi\) | ||
0.999794 | − | 0.0202784i | \(-0.00645525\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.53362e8 | − | 1.71464e8i | −0.392429 | − | 0.438749i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.85185e8 | 1.96058 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.48456e7 | 0.133659 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.25815e8 | − | 2.52469e8i | −0.537189 | − | 0.600595i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.93186e8i | − | 1.84221i | −0.389318 | − | 0.921104i | \(-0.627289\pi\) | ||
0.389318 | − | 0.921104i | \(-0.372711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.55959e8i | − | 0.353698i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.64550e8 | − | 1.17073e8i | 0.364460 | − | 0.259305i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.21296e8 | 1.99320 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.07513e7 | −0.149538 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.90944e8 | − | 3.49671e8i | 0.807356 | − | 0.722121i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.46363e7i | 0.130445i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.07669e8i | 1.00137i | 0.865628 | + | 0.500687i | \(0.166919\pi\) | ||||
−0.865628 | + | 0.500687i | \(0.833081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.03700e8 | + | 3.61080e8i | −0.778402 | + | 0.696224i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.79184e8 | −0.526296 | −0.263148 | − | 0.964756i | \(-0.584761\pi\) | ||||
−0.263148 | + | 0.964756i | \(0.584761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.92840e7 | −0.127711 | −0.0638554 | − | 0.997959i | \(-0.520340\pi\) | ||||
−0.0638554 | + | 0.997959i | \(0.520340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.99510e7 | − | 4.46776e8i | 0.0900446 | − | 0.805383i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.97465e8i | 1.58238i | 0.611572 | + | 0.791189i | \(0.290537\pi\) | ||||
−0.611572 | + | 0.791189i | \(0.709463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.09510e8i | 0.361358i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.81761e6 | + | 7.62232e6i | 0.0115044 | + | 0.0128623i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.50846e8 | −0.744422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.55798e8 | 0.736513 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.05752e8 | + | 3.41842e8i | 0.483563 | + | 0.540640i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.63327e8i | − | 0.872118i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.19136e9i | − | 1.80570i | −0.429957 | − | 0.902849i | \(-0.641471\pi\) | ||
0.429957 | − | 0.902849i | \(-0.358529\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.05243e7 | − | 9.41325e7i | 0.0156185 | − | 0.139696i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.66910e8 | −0.242563 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.15595e9 | 1.64526 | 0.822630 | − | 0.568577i | \(-0.192506\pi\) | ||||
0.822630 | + | 0.568577i | \(0.192506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.88761e8 | + | 1.68833e8i | −0.263156 | + | 0.235374i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.78443e8i | 0.243702i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.48126e8i | − | 0.867222i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.18957e8 | + | 4.64170e8i | −0.680401 | + | 0.608569i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.31673e9 | 1.69178 | 0.845892 | − | 0.533355i | \(-0.179069\pi\) | ||||
0.845892 | + | 0.533355i | \(0.179069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.79115e8 | 0.351474 | 0.175737 | − | 0.984437i | \(-0.443769\pi\) | ||||
0.175737 | + | 0.984437i | \(0.443769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06087e9 | − | 7.54781e8i | 1.30944 | − | 0.931635i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.39614e8i | 0.773938i | 0.922093 | + | 0.386969i | \(0.126478\pi\) | ||||
−0.922093 | + | 0.386969i | \(0.873522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.45161e7i | − | 0.0646734i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.87373e8 | − | 6.56703e8i | −0.683243 | − | 0.763889i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.06233e8 | 0.805596 | 0.402798 | − | 0.915289i | \(-0.368038\pi\) | ||||
0.402798 | + | 0.915289i | \(0.368038\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.22098e8 | 0.360340 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.85997e8 | + | 5.43362e8i | 0.533287 | + | 0.596233i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.33366e7i | 0.0574117i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.52201e9i | − | 1.60726i | −0.595126 | − | 0.803632i | \(-0.702898\pi\) | ||
0.595126 | − | 0.803632i | \(-0.297102\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70788e9 | − | 1.90947e8i | −1.76956 | − | 0.197843i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.48674e8 | 0.354496 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.19200e8 | 0.418254 | 0.209127 | − | 0.977888i | \(-0.432938\pi\) | ||||
0.209127 | + | 0.977888i | \(0.432938\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.16957e8 | + | 7.30708e8i | −0.799999 | + | 0.715541i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.35073e9i | 1.29829i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.84045e9i | − | 1.73655i | −0.496082 | − | 0.868275i | \(-0.665229\pi\) | ||
0.496082 | − | 0.868275i | \(-0.334771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.76875e8 | + | 5.15972e8i | −0.534372 | + | 0.477957i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.87842e8 | 0.170843 | 0.0854216 | − | 0.996345i | \(-0.472776\pi\) | ||||
0.0854216 | + | 0.996345i | \(0.472776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.05886e8 | −0.362486 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.53894e8 | + | 1.72058e7i | 0.134968 | + | 0.0150899i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.22401e8i | 0.277698i | 0.990314 | + | 0.138849i | \(0.0443403\pi\) | ||||
−0.990314 | + | 0.138849i | \(0.955660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.36454e9i | 1.15443i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.93379e7 | + | 8.87024e7i | 0.0659336 | + | 0.0737160i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.07690e9 | −0.879195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.34603e9 | 1.07966 | 0.539832 | − | 0.841773i | \(-0.318488\pi\) | ||||
0.539832 | + | 0.841773i | \(0.318488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.44922e8 | − | 8.32848e8i | −0.587091 | − | 0.656388i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.73134e8i | − | 0.676201i | −0.941110 | − | 0.338100i | \(-0.890216\pi\) | ||
0.941110 | − | 0.338100i | \(-0.109784\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.15044e9i | 0.875579i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.17300e8 | + | 9.59649e8i | −0.162543 | + | 0.717827i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.55172e7 | −0.0628743 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.61913e9 | 1.17017 | 0.585086 | − | 0.810971i | \(-0.301061\pi\) | ||||
0.585086 | + | 0.810971i | \(0.301061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.87566e8 | − | 7.93863e8i | 0.630601 | − | 0.564026i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 7.57535e8i | − | 0.529148i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.07810e9i | − | 1.42724i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.38879e9 | − | 1.24217e9i | 0.937907 | − | 0.838889i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.83155e9 | −1.21638 | −0.608192 | − | 0.793790i | \(-0.708105\pi\) | ||||
−0.608192 | + | 0.793790i | \(0.708105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.29973e9 | −0.848918 | −0.424459 | − | 0.905447i | \(-0.639536\pi\) | ||||
−0.424459 | + | 0.905447i | \(0.639536\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.36994e8 | + | 1.22531e9i | −0.0880057 | + | 0.787147i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.75086e8i | 0.426578i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.13956e8i | 0.195151i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.83659e8 | − | 8.76157e8i | −0.479211 | − | 0.535774i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.25303e9 | 1.35549 | 0.677746 | − | 0.735296i | \(-0.262957\pi\) | ||||
0.677746 | + | 0.735296i | \(0.262957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.38794e8 | −0.200552 | −0.100276 | − | 0.994960i | \(-0.531973\pi\) | ||||
−0.100276 | + | 0.994960i | \(0.531973\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.80527e8 | − | 7.60853e8i | −0.396399 | − | 0.443188i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.73054e9i | 0.991968i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.72596e9i | 0.973657i | 0.873498 | + | 0.486828i | \(0.161846\pi\) | ||||
−0.873498 | + | 0.486828i | \(0.838154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.25048e7 | − | 3.80175e8i | 0.0235995 | − | 0.211081i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.73582e9 | 0.948616 | 0.474308 | − | 0.880359i | \(-0.342698\pi\) | ||||
0.474308 | + | 0.880359i | \(0.342698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.99123e8 | 0.429886 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.63286e7 | + | 7.72146e7i | −0.0457170 | + | 0.0408906i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.57315e8i | − | 0.499106i | −0.968361 | − | 0.249553i | \(-0.919716\pi\) | ||
0.968361 | − | 0.249553i | \(-0.0802836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.55157e9i | 0.796442i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.97699e9 | − | 1.76828e9i | 0.999221 | − | 0.893730i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.61678e9 | −1.30235 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.22751e9 | −1.09172 | −0.545862 | − | 0.837875i | \(-0.683798\pi\) | ||||
−0.545862 | + | 0.837875i | \(0.683798\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.11791e9 | + | 1.57126e9i | 0.539590 | + | 0.758409i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.47517e9i | − | 1.17666i | −0.808620 | − | 0.588331i | \(-0.799785\pi\) | ||
0.808620 | − | 0.588331i | \(-0.200215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.48039e9i | 1.16141i | 0.814113 | + | 0.580706i | \(0.197223\pi\) | ||||
−0.814113 | + | 0.580706i | \(0.802777\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.79617e8 | − | 6.48031e8i | −0.267335 | − | 0.298889i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.07555e9 | −0.488677 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.10726e8 | −0.362885 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.92632e8 | − | 8.86190e8i | −0.349541 | − | 0.390799i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.39809e8i | − | 0.0607464i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.56162e8i | 0.366546i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.58413e8 | − | 8.47931e7i | −0.319957 | − | 0.0357723i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.09105e8 | −0.128508 | −0.0642541 | − | 0.997934i | \(-0.520467\pi\) | ||||
−0.0642541 | + | 0.997934i | \(0.520467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.51336e8 | −0.225896 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.52072e9 | + | 2.25460e9i | −1.01791 | + | 0.910446i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.49002e9i | − | 0.593056i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.10568e9i | 0.826115i | 0.910705 | + | 0.413058i | \(0.135539\pi\) | ||||
−0.910705 | + | 0.413058i | \(0.864461\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.40909e9 | + | 1.26033e9i | −0.544952 | + | 0.487420i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.94413e8 | 0.226622 | 0.113311 | − | 0.993560i | \(-0.463854\pi\) | ||||
0.113311 | + | 0.993560i | \(0.463854\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00058e9 | −0.751953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.82855e8 | + | 9.87062e7i | 0.327168 | + | 0.0365785i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.64800e8i | − | 0.0967542i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.39922e9i | 1.22469i | 0.790590 | + | 0.612346i | \(0.209774\pi\) | ||||
−0.790590 | + | 0.612346i | \(0.790226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.65468e9 | + | 1.84999e9i | 0.587870 | + | 0.657259i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.02401e9 | −1.40985 | −0.704923 | − | 0.709284i | \(-0.749018\pi\) | ||||
−0.704923 | + | 0.709284i | \(0.749018\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.30727e9 | 0.797222 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.09600e9 | − | 3.46144e9i | −1.05505 | − | 1.17958i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.18155e9i | − | 0.397136i | −0.980087 | − | 0.198568i | \(-0.936371\pi\) | ||
0.980087 | − | 0.198568i | \(-0.0636291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.59070e8i | 0.0858904i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.41777e9 | + | 1.99271e9i | 0.463654 | + | 0.651679i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.38256e9 | −0.768631 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.11317e9 | 0.354278 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.72135e8 | − | 2.43405e8i | 0.0854475 | − | 0.0764266i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.54418e9i | − | 1.09795i | −0.835838 | − | 0.548976i | \(-0.815018\pi\) | ||
0.835838 | − | 0.548976i | \(-0.184982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.88980e9i | − | 0.883307i | −0.897186 | − | 0.441654i | \(-0.854392\pi\) | ||
0.897186 | − | 0.441654i | \(-0.145608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.24709e9 | + | 1.11543e9i | −0.376131 | + | 0.336422i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.70392e9 | −0.507123 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.83288e9 | 0.538319 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.84223e8 | + | 1.64774e9i | −0.0533965 | + | 0.477593i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.00031e10i | 2.86147i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.49854e7i | 0.0127009i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.34517e9 | + | 2.62198e9i | 0.653529 | + | 0.730668i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.45380e8 | −0.0950029 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.59048e8 | 0.124643 | 0.0623215 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623215 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.13199e9 | + | 1.26561e9i | 0.303420 | + | 0.339234i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.01748e9i | 0.533853i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.87269e7i | 0.0179544i | 0.999960 | + | 0.00897720i | \(0.00285757\pi\) | ||||
−0.999960 | + | 0.00897720i | \(0.997142\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.63501e7 | − | 6.82896e8i | 0.0196928 | − | 0.176137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.53718e9 | −0.646132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.23079e9 | −1.31531 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.10563e8 | − | 2.77776e8i | 0.0771123 | − | 0.0689713i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.71176e9i | − | 0.419710i | −0.977732 | − | 0.209855i | \(-0.932701\pi\) | ||
0.977732 | − | 0.209855i | \(-0.0672992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.01359e8i | − | 0.218251i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29768e9 | − | 1.16068e9i | 0.310312 | − | 0.277552i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.29253e9 | −0.305255 | −0.152627 | − | 0.988284i | \(-0.548773\pi\) | ||||
−0.152627 | + | 0.988284i | \(0.548773\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.11403e9 | −0.259853 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.05549e9 | + | 4.66128e9i | −0.243171 | + | 1.07390i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.52303e9i | 1.25685i | 0.777869 | + | 0.628426i | \(0.216301\pi\) | ||||
−0.777869 | + | 0.628426i | \(0.783699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.19314e9i | 1.39215i | 0.717971 | + | 0.696073i | \(0.245071\pi\) | ||||
−0.717971 | + | 0.696073i | \(0.754929\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.03860e9 | + | 4.51529e9i | 0.896787 | + | 1.00264i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.59128e9 | 0.568430 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.63098e9 | −0.570167 | −0.285083 | − | 0.958503i | \(-0.592021\pi\) | ||||
−0.285083 | + | 0.958503i | \(0.592021\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.74088e9 | + | 4.18243e9i | 0.800937 | + | 0.895475i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.00939e10i | − | 2.13522i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.89001e8i | 0.144006i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.69184e9 | + | 6.36367e8i | 1.17546 | + | 0.131420i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.81888e8 | −0.139149 | −0.0695744 | − | 0.997577i | \(-0.522164\pi\) | ||||
−0.0695744 | + | 0.997577i | \(0.522164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.16096e9 | −0.435756 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.32789e9 | + | 1.18770e9i | −0.264610 | + | 0.236674i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.90525e8i | 0.175370i | 0.996148 | + | 0.0876849i | \(0.0279468\pi\) | ||||
−0.996148 | + | 0.0876849i | \(0.972053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.87573e9i | − | 0.754300i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.51765e9 | − | 3.14628e9i | 0.676616 | − | 0.605183i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.68984e9 | 1.65203 | 0.826015 | − | 0.563648i | \(-0.190602\pi\) | ||||
0.826015 | + | 0.563648i | \(0.190602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.48769e9 | −1.21907 | −0.609536 | − | 0.792758i | \(-0.708644\pi\) | ||||
−0.609536 | + | 0.792758i | \(0.708644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.76344e9 | + | 1.97158e8i | 0.327529 | + | 0.0366188i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.20681e9i | 0.588748i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.67054e9i | − | 1.39209i | −0.718001 | − | 0.696043i | \(-0.754942\pi\) | ||
0.718001 | − | 0.696043i | \(-0.245058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.30551e9 | − | 3.69567e9i | −0.593031 | − | 0.663029i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.17669e9 | 1.27286 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.01986e10 | −1.78825 | −0.894123 | − | 0.447821i | \(-0.852200\pi\) | ||||
−0.894123 | + | 0.447821i | \(0.852200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.03979e9 | − | 5.63466e9i | −0.873674 | − | 0.976798i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.66633e9i | − | 1.31398i | −0.753898 | − | 0.656991i | \(-0.771829\pi\) | ||
0.753898 | − | 0.656991i | \(-0.228171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.72256e9i | − | 1.30871i | −0.756187 | − | 0.654356i | \(-0.772940\pi\) | ||
0.756187 | − | 0.654356i | \(-0.227060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.03119e9 | − | 4.29105e9i | 1.01061 | − | 0.719023i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.88156e9 | 0.643129 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.02425e9 | −0.331653 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.64576e9 | − | 1.47201e9i | 0.266643 | − | 0.238492i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8.16589e8i | − | 0.130836i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.86511e9i | 0.612433i | 0.951962 | + | 0.306217i | \(0.0990632\pi\) | ||||
−0.951962 | + | 0.306217i | \(0.900937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.04945e9 | − | 6.30522e9i | 1.10470 | − | 0.988069i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.40460e9 | −0.527665 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.22669e9 | −0.341328 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.43959e7 | + | 5.75975e8i | −0.00976350 | + | 0.0873274i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.14005e9i | 0.470905i | 0.971886 | + | 0.235453i | \(0.0756573\pi\) | ||||
−0.971886 | + | 0.235453i | \(0.924343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.73104e9i | − | 1.14683i | −0.819265 | − | 0.573416i | \(-0.805618\pi\) | ||
0.819265 | − | 0.573416i | \(-0.194382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.54125e8 | + | 5.07727e8i | 0.0666371 | + | 0.0745026i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.19275e9 | −0.318290 | −0.159145 | − | 0.987255i | \(-0.550874\pi\) | ||||
−0.159145 | + | 0.987255i | \(0.550874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.49693e9 | 0.214954 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.81536e9 | − | 3.14766e9i | −0.399945 | − | 0.447152i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.45493e9i | 0.907184i | 0.891209 | + | 0.453592i | \(0.149858\pi\) | ||||
−0.891209 | + | 0.453592i | \(0.850142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.23504e8i | 0.0727907i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.30026e7 | − | 5.63512e8i | 0.00866722 | − | 0.0775220i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.43719e9 | −1.01230 | −0.506151 | − | 0.862445i | \(-0.668932\pi\) | ||||
−0.506151 | + | 0.862445i | \(0.668932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.66092e9 | −0.358365 | −0.179183 | − | 0.983816i | \(-0.557345\pi\) | ||||
−0.179183 | + | 0.983816i | \(0.557345\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.36628e9 | − | 7.48302e9i | 1.11490 | − | 0.997194i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4.91530e9i | − | 0.648149i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.67910e9i | 1.00200i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.61506e9 | + | 1.44455e9i | −0.208544 | + | 0.186527i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.20396e8 | −0.0792757 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.42499e9 | 1.19187 | 0.595934 | − | 0.803033i | \(-0.296782\pi\) | ||||
0.595934 | + | 0.803033i | \(0.296782\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.98384e9 | − | 2.12293e9i | 0.373433 | − | 0.265689i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.08473e10i | − | 1.34357i | −0.740746 | − | 0.671785i | \(-0.765528\pi\) | ||
0.740746 | − | 0.671785i | \(-0.234472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 7.23743e9i | − | 0.887238i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.75574e9 | + | 5.31707e9i | 0.577036 | + | 0.645146i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.18751e10 | 1.42615 | 0.713075 | − | 0.701088i | \(-0.247302\pi\) | ||||
0.713075 | + | 0.701088i | \(0.247302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.23824e9 | 0.622685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.36907e9 | − | 1.53066e9i | −0.161093 | − | 0.180107i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.44204e9i | 0.517387i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.50025e8i | 0.109537i | 0.998499 | + | 0.0547686i | \(0.0174421\pi\) | ||||
−0.998499 | + | 0.0547686i | \(0.982558\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.28827e9 | + | 4.79443e8i | 0.489458 | + | 0.0547231i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.19635e9 | 0.926134 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48157e10 | −1.65732 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.45551e9 | − | 7.56284e9i | 0.936418 | − | 0.837558i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.66122e9i | 0.840011i | 0.907522 | + | 0.420006i | \(0.137972\pi\) | ||||
−0.907522 | + | 0.420006i | \(0.862028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.03562e9i | − | 0.112423i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.04256e9 | + | 3.61578e9i | −0.434505 | + | 0.388633i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.12071e10 | 1.19268 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.07576e9 | 0.640234 | 0.320117 | − | 0.947378i | \(-0.396278\pi\) | ||||
0.320117 | + | 0.947378i | \(0.396278\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.13777e10 | + | 1.27206e9i | 1.18716 | + | 0.132729i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.54042e9i | 0.675759i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.17091e9i | − | 0.529049i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.18428e9 | − | 4.67817e9i | −0.423939 | − | 0.473978i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50425e10 | −1.50928 | −0.754639 | − | 0.656140i | \(-0.772188\pi\) | ||||
−0.754639 | + | 0.656140i | \(0.772188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.15727e10 | −1.14991 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.30700e10 | − | 1.46127e10i | −1.28615 | − | 1.43796i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.79912e9i | 0.370254i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.39530e9i | − | 0.906860i | −0.891292 | − | 0.453430i | \(-0.850200\pi\) | ||
0.891292 | − | 0.453430i | \(-0.149800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.42939e9 | − | 9.88222e9i | 0.327846 | − | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.33501e9 | 0.126408 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.71856e9 | −0.723890 | −0.361945 | − | 0.932200i | \(-0.617887\pi\) | ||||
−0.361945 | + | 0.932200i | \(0.617887\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.25428e9 | − | 1.12186e9i | 0.116516 | − | 0.104215i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.60204e9i | − | 0.147414i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.96381e8i | − | 0.0361291i | −0.999837 | − | 0.0180646i | \(-0.994250\pi\) | ||
0.999837 | − | 0.0180646i | \(-0.00575044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.06103e10 | − | 9.49017e9i | 0.957999 | − | 0.856860i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.86457e9 | 0.435094 | 0.217547 | − | 0.976050i | \(-0.430194\pi\) | ||||
0.217547 | + | 0.976050i | \(0.430194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.09494e8 | −0.0451432 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.45471e9 | + | 2.19556e10i | −0.215465 | + | 1.92718i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.18506e8i | 0.0190011i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.71438e9i | 0.750753i | 0.926872 | + | 0.375376i | \(0.122487\pi\) | ||||
−0.926872 | + | 0.375376i | \(0.877513\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.38597e10 | + | 1.54957e10i | 1.18297 | + | 1.32260i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.16678e10 | 0.986678 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.67972e10 | −1.40735 | −0.703673 | − | 0.710524i | \(-0.748458\pi\) | ||||
−0.703673 | + | 0.710524i | \(0.748458\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.45522e9 | − | 4.98109e9i | −0.369848 | − | 0.413502i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.88336e8i | − | 0.0401673i | −0.999798 | − | 0.0200836i | \(-0.993607\pi\) | ||
0.999798 | − | 0.0200836i | \(-0.00639325\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.79946e9i | 0.798668i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.42529e8 | + | 8.43024e9i | −0.0761167 | + | 0.680808i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.65085e9 | 0.772292 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.73330e9 | 0.771824 | 0.385912 | − | 0.922536i | \(-0.373887\pi\) | ||||
0.385912 | + | 0.922536i | \(0.373887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.13277e9 | + | 1.01318e9i | −0.0890129 | + | 0.0796156i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.10035e10i | 1.63555i | 0.575540 | + | 0.817774i | \(0.304792\pi\) | ||||
−0.575540 | + | 0.817774i | \(0.695208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.23578e9i | 0.249702i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.50849e9 | − | 1.34923e9i | 0.115363 | − | 0.103184i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.87897e10 | −1.42409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.23260e8 | 0.0393042 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.29118e9 | + | 8.84243e9i | 0.468345 | + | 0.658272i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.23012e9i | − | 0.385894i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.27878e10i | − | 1.66644i | −0.552939 | − | 0.833222i | \(-0.686494\pi\) | ||
0.552939 | − | 0.833222i | \(-0.313506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.32923e10 | + | 1.48612e10i | 0.963453 | + | 1.07717i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.41116e9 | −0.388752 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.99974e9 | −0.284823 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.23800e9 | − | 2.50216e9i | −0.157970 | − | 0.176616i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.22577e10i | − | 0.857638i | −0.903391 | − | 0.428819i | \(-0.858930\pi\) | ||
0.903391 | − | 0.428819i | \(-0.141070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.06295e10i | 0.737221i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.44291e9 | − | 9.43946e8i | −0.580468 | − | 0.0648983i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.11938e8 | −0.0348910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.48768e10 | −1.00513 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.04696e10 | + | 9.36434e9i | −0.701253 | + | 0.627220i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.89938e9i | 0.258926i | 0.991584 | + | 0.129463i | \(0.0413253\pi\) | ||||
−0.991584 | + | 0.129463i | \(0.958675\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.83894e9i | 0.647702i | 0.946108 | + | 0.323851i | \(0.104978\pi\) | ||||
−0.946108 | + | 0.323851i | \(0.895022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.87748e9 | + | 5.25698e9i | −0.383596 | + | 0.343099i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.31618e9 | −0.538111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.69310e9 | 0.108619 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.76468e10 | + | 3.09101e9i | 1.75854 | + | 0.196610i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.76060e10i | − | 1.11035i | −0.831733 | − | 0.555176i | \(-0.812651\pi\) | ||
0.831733 | − | 0.555176i | \(-0.187349\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.59689e10i | − | 0.998564i | −0.866439 | − | 0.499282i | \(-0.833597\pi\) | ||
0.866439 | − | 0.499282i | \(-0.166403\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.20416e9 | − | 2.46432e9i | −0.136664 | − | 0.152795i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.38691e10 | −0.852666 | −0.426333 | − | 0.904566i | \(-0.640195\pi\) | ||||
−0.426333 | + | 0.904566i | \(0.640195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.03083e10 | 1.84766 | 0.923828 | − | 0.382808i | \(-0.125043\pi\) | ||||
0.923828 | + | 0.382808i | \(0.125043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.31023e10 | − | 1.46488e10i | −0.792034 | − | 0.885521i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.29798e9i | − | 0.197692i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.09182e10i | 0.649008i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.35830e9 | + | 7.53125e9i | 0.315855 | + | 0.443944i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.76156e10 | 1.02975 | 0.514873 | − | 0.857266i | \(-0.327839\pi\) | ||||
0.514873 | + | 0.857266i | \(0.327839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.99141e9 | 0.347331 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.77754e10 | + | 1.58988e10i | −1.02193 | + | 0.914044i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 2.04287e10i | − | 1.16478i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.55764e10i | 0.880794i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.39019e8 | + | 4.82113e8i | −0.0302292 | + | 0.0270378i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.13443e9 | −0.174343 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.77452e9 | 0.428896 | 0.214448 | − | 0.976735i | \(-0.431205\pi\) | ||||
0.214448 | + | 0.976735i | \(0.431205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.19534e9 | + | 1.06914e10i | −0.0654049 | + | 0.584999i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.40944e9i | 0.185033i | 0.995711 | + | 0.0925166i | \(0.0294911\pi\) | ||||
−0.995711 | + | 0.0925166i | \(0.970509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.01843e9i | − | 0.0548221i | −0.999624 | − | 0.0274111i | \(-0.991274\pi\) | ||
0.999624 | − | 0.0274111i | \(-0.00872631\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.44796e10 | − | 2.73691e10i | −1.30706 | − | 1.46133i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.23663e10 | −1.18456 | −0.592278 | − | 0.805734i | \(-0.701771\pi\) | ||||
−0.592278 | + | 0.805734i | \(0.701771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.60609e9 | 0.0843749 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.70992e9 | − | 1.91174e9i | −0.0891062 | − | 0.0996237i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.03364e10i | − | 0.534316i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.03285e10i | − | 0.529631i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.76005e9 | + | 1.57424e10i | −0.0895314 | + | 0.800793i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.34194e10 | −1.18181 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.42860e9 | 0.371885 | 0.185942 | − | 0.982561i | \(-0.440466\pi\) | ||||
0.185942 | + | 0.982561i | \(0.440466\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.76480e10 | + | 2.47291e10i | −1.37310 | + | 1.22814i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.83256e10i | − | 1.39561i | −0.716288 | − | 0.697804i | \(-0.754160\pi\) | ||
0.716288 | − | 0.697804i | \(-0.245840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.16342e10i | 1.05750i | 0.848779 | + | 0.528748i | \(0.177338\pi\) | ||||
−0.848779 | + | 0.528748i | \(0.822662\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.43623e9 | + | 4.86232e9i | −0.263631 | + | 0.235799i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.48940e9 | 0.119774 | 0.0598869 | − | 0.998205i | \(-0.480926\pi\) | ||||
0.0598869 | + | 0.998205i | \(0.480926\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.65371e10 | −0.789410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.21096e9 | − | 2.08571e9i | −0.436248 | − | 0.0987827i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.34806e10i | 0.633472i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.54744e10i | 0.721496i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.87232e10 | − | 3.21135e10i | −1.32880 | − | 1.48564i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.58902e9 | −0.440165 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.57915e9 | −0.299663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.20581e9 | + | 2.46617e9i | 0.0996921 | + | 0.111459i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.46936e9i | 0.334976i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.03196e8i | 0.0268431i | 0.999910 | + | 0.0134216i | \(0.00427234\pi\) | ||||
−0.999910 | + | 0.0134216i | \(0.995728\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.43768e10 | − | 2.72541e9i | −1.07647 | − | 0.120354i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.68931e10 | −1.17849 | −0.589246 | − | 0.807954i | \(-0.700575\pi\) | ||||
−0.589246 | + | 0.807954i | \(0.700575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.99461e10 | 0.867383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.25302e9 | − | 2.01516e9i | 0.0972278 | − | 0.0869632i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.54280e9i | 0.108898i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.44011e10i | − | 0.612056i | −0.952022 | − | 0.306028i | \(-0.901000\pi\) | ||
0.952022 | − | 0.306028i | \(-0.0990002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.76957e10 | − | 1.58276e10i | 0.746380 | − | 0.667583i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.37350e9 | 0.141213 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.55071e9 | −0.0644222 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.51722e10 | + | 2.81434e9i | 1.03787 | + | 0.116037i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.33324e9i | − | 0.341003i | −0.985357 | − | 0.170502i | \(-0.945461\pi\) | ||
0.985357 | − | 0.170502i | \(-0.0545388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.18258e9i | − | 0.169871i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.70411e9 | + | 9.73149e9i | 0.350864 | + | 0.392278i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.65868e9 | 0.306417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.24458e10 | 0.891346 | 0.445673 | − | 0.895196i | \(-0.352964\pi\) | ||||
0.445673 | + | 0.895196i | \(0.352964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.16006e9 | + | 2.41502e9i | 0.0851405 | + | 0.0951900i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.64833e10i | 1.03612i | 0.855345 | + | 0.518059i | \(0.173345\pi\) | ||||
−0.855345 | + | 0.518059i | \(0.826655\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.68692e10i | 2.20844i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.71305e10 | + | 1.21879e10i | −0.660327 | + | 0.469807i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.26400e10 | 0.866266 | 0.433133 | − | 0.901330i | \(-0.357408\pi\) | ||||
0.433133 | + | 0.901330i | \(0.357408\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.30051e9 | −0.125357 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.12828e10 | − | 2.79802e10i | 1.17943 | − | 1.05492i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.67746e10i | 1.75059i | 0.483586 | + | 0.875297i | \(0.339334\pi\) | ||||
−0.483586 | + | 0.875297i | \(0.660666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.66483e10i | 0.990052i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.30286e9 | − | 6.53188e9i | 0.269340 | − | 0.240905i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.54436e10 | 0.931564 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.93455e10 | 0.703149 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.31380e7 | − | 4.75281e8i | 0.00191740 | − | 0.0171498i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.46839e10i | 0.884235i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.66727e10i | 0.592942i | 0.955042 | + | 0.296471i | \(0.0958098\pi\) | ||||
−0.955042 | + | 0.296471i | \(0.904190\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.40560e10 | + | 1.57151e10i | 0.496281 | + | 0.554859i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.55445e9 | 0.0544889 | 0.0272445 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272445 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.98119e10 | 1.38554 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.42104e10 | − | 1.58877e10i | −0.491009 | − | 0.548964i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.71063e9i | 0.264520i | 0.991215 | + | 0.132260i | \(0.0422234\pi\) | ||||
−0.991215 | + | 0.132260i | \(0.957777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.67019e9i | 0.261256i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.38310e9 | − | 2.13151e10i | 0.0805938 | − | 0.720853i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.24036e10 | −1.75964 | −0.879820 | − | 0.475307i | \(-0.842337\pi\) | ||||
−0.879820 | + | 0.475307i | \(0.842337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.83694e9 | −0.261288 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.96358e10 | + | 1.75628e10i | −0.650038 | + | 0.581412i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.12436e9i | − | 0.168443i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6.02219e9i | − | 0.196561i | −0.995159 | − | 0.0982803i | \(-0.968666\pi\) | ||
0.995159 | − | 0.0982803i | \(-0.0313342\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.15271e10 | + | 3.71430e10i | −1.34589 | + | 1.20380i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.07605e10 | 0.668122 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.88566e9 | −0.315917 | −0.157958 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157958 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.60928e9 | + | 2.56791e9i | −0.114536 | + | 0.0814895i |
(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 | 192.8.c.b.191.1 | 4 | ||
3.2 | odd | 2 | inner | 192.8.c.b.191.3 | 4 | ||
4.3 | odd | 2 | inner | 192.8.c.b.191.4 | 4 | ||
8.3 | odd | 2 | 12.8.b.a.11.1 | ✓ | 4 | ||
8.5 | even | 2 | 12.8.b.a.11.3 | yes | 4 | ||
12.11 | even | 2 | inner | 192.8.c.b.191.2 | 4 | ||
24.5 | odd | 2 | 12.8.b.a.11.2 | yes | 4 | ||
24.11 | even | 2 | 12.8.b.a.11.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.8.b.a.11.1 | ✓ | 4 | 8.3 | odd | 2 | ||
12.8.b.a.11.2 | yes | 4 | 24.5 | odd | 2 | ||
12.8.b.a.11.3 | yes | 4 | 8.5 | even | 2 | ||
12.8.b.a.11.4 | yes | 4 | 24.11 | even | 2 | ||
192.8.c.b.191.1 | 4 | 1.1 | even | 1 | trivial | ||
192.8.c.b.191.2 | 4 | 12.11 | even | 2 | inner | ||
192.8.c.b.191.3 | 4 | 3.2 | odd | 2 | inner | ||
192.8.c.b.191.4 | 4 | 4.3 | odd | 2 | inner |