Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,8,Mod(49,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("80.49");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(24.9908020387\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-29}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 29 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(5.38516i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.49 |
Dual form | 80.8.c.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 32.3110i | 0.690917i | 0.938434 | + | 0.345458i | \(0.112277\pi\) | ||||
−0.938434 | + | 0.345458i | \(0.887723\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 75.0000 | + | 269.258i | 0.268328 | + | 0.963328i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 420.043i | − | 0.462861i | −0.972851 | − | 0.231430i | \(-0.925659\pi\) | ||
0.972851 | − | 0.231430i | \(-0.0743406\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1143.00 | 0.522634 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6828.00 | 1.54675 | 0.773373 | − | 0.633951i | \(-0.218568\pi\) | ||||
0.773373 | + | 0.633951i | \(0.218568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10145.7i | 1.28079i | 0.768045 | + | 0.640395i | \(0.221229\pi\) | ||||
−0.768045 | + | 0.640395i | \(0.778771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8700.00 | + | 2423.32i | −0.665579 | + | 0.185392i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15681.6i | − | 0.774139i | −0.922050 | − | 0.387070i | \(-0.873487\pi\) | ||
0.922050 | − | 0.387070i | \(-0.126513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6860.00 | −0.229449 | −0.114725 | − | 0.993397i | \(-0.536599\pi\) | ||||
−0.114725 | + | 0.993397i | \(0.536599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13572.0 | 0.319798 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29219.9i | 0.500762i | 0.968147 | + | 0.250381i | \(0.0805559\pi\) | ||||
−0.968147 | + | 0.250381i | \(0.919444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −66875.0 | + | 40388.7i | −0.856000 | + | 0.516976i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 107596.i | 1.05201i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25590.0 | 0.194840 | 0.0974198 | − | 0.995243i | \(-0.468941\pi\) | ||||
0.0974198 | + | 0.995243i | \(0.468941\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −82112.0 | −0.495040 | −0.247520 | − | 0.968883i | \(-0.579616\pi\) | ||||
−0.247520 | + | 0.968883i | \(0.579616\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 220619.i | 1.06867i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 113100. | − | 31503.2i | 0.445887 | − | 0.124199i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 223527.i | 0.725479i | 0.931891 | + | 0.362739i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362739i | \(0.881842\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −327816. | −0.884920 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −533118. | −1.20804 | −0.604018 | − | 0.796971i | \(-0.706434\pi\) | ||||
−0.604018 | + | 0.796971i | \(0.706434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 708935.i | 1.35978i | 0.733316 | + | 0.679888i | \(0.237971\pi\) | ||||
−0.733316 | + | 0.679888i | \(0.762029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 85725.0 | + | 307762.i | 0.140237 | + | 0.503467i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5826.75i | 0.00818623i | 0.999992 | + | 0.00409311i | \(0.00130288\pi\) | ||||
−0.999992 | + | 0.00409311i | \(0.998697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 647107. | 0.785760 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 506688. | 0.534866 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 589374.i | 0.543783i | 0.962328 | + | 0.271891i | \(0.0876491\pi\) | ||||
−0.962328 | + | 0.271891i | \(0.912351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 512100. | + | 1.83850e6i | 0.415036 | + | 1.49002i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 221653.i | − | 0.158530i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.43898e6 | −0.912164 | −0.456082 | − | 0.889938i | \(-0.650748\pi\) | ||||
−0.456082 | + | 0.889938i | \(0.650748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.38102e6 | 0.779016 | 0.389508 | − | 0.921023i | \(-0.372645\pi\) | ||||
0.389508 | + | 0.921023i | \(0.372645\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 480109.i | − | 0.241907i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.73180e6 | + | 760924.i | −1.23382 | + | 0.343672i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.71487e6i | − | 1.10277i | −0.834250 | − | 0.551387i | \(-0.814099\pi\) | ||
0.834250 | − | 0.551387i | \(-0.185901\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −944124. | −0.345985 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 481608. | 0.159694 | 0.0798472 | − | 0.996807i | \(-0.474557\pi\) | ||||
0.0798472 | + | 0.996807i | \(0.474557\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.48618e6i | − | 0.447137i | −0.974688 | − | 0.223568i | \(-0.928229\pi\) | ||
0.974688 | − | 0.223568i | \(-0.0717706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.30500e6 | − | 2.16080e6i | −0.357187 | − | 0.591425i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.86805e6i | − | 0.715928i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.05976e6 | 0.241831 | 0.120916 | − | 0.992663i | \(-0.461417\pi\) | ||||
0.120916 | + | 0.992663i | \(0.461417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −976779. | −0.204220 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.60380e6i | − | 0.499844i | −0.968266 | − | 0.249922i | \(-0.919595\pi\) | ||
0.968266 | − | 0.249922i | \(-0.0804050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.22240e6 | − | 1.17612e6i | 0.745750 | − | 0.207723i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 826838.i | 0.134618i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.64417e6 | 0.848663 | 0.424331 | − | 0.905507i | \(-0.360509\pi\) | ||||
0.424331 | + | 0.905507i | \(0.360509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.26161e6 | 0.592828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.65312e6i | − | 0.342032i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −514500. | − | 1.84711e6i | −0.0615677 | − | 0.221035i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.20091e7i | − | 1.33601i | −0.744158 | − | 0.668004i | \(-0.767149\pi\) | ||
0.744158 | − | 0.668004i | \(-0.232851\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.80440e6 | 0.808382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.14270e6 | 0.496668 | 0.248334 | − | 0.968674i | \(-0.420117\pi\) | ||||
0.248334 | + | 0.968674i | \(0.420117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.48477e6i | 0.314227i | 0.987581 | + | 0.157114i | \(0.0502189\pi\) | ||||
−0.987581 | + | 0.157114i | \(0.949781\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.01790e6 | + | 3.65437e6i | 0.0858109 | + | 0.308071i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.48640e7i | − | 1.17299i | −0.809954 | − | 0.586493i | \(-0.800508\pi\) | ||
0.809954 | − | 0.586493i | \(-0.199492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.01124e7 | −1.48755 | −0.743773 | − | 0.668432i | \(-0.766966\pi\) | ||||
−0.743773 | + | 0.668432i | \(0.766966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.22239e6 | −0.501246 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.62633e6i | 0.366818i | 0.983037 | + | 0.183409i | \(0.0587133\pi\) | ||||
−0.983037 | + | 0.183409i | \(0.941287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.86770e6 | + | 2.19149e6i | −0.482398 | + | 0.134369i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.15965e7i | 0.669384i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.58694e6 | −0.358319 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71344e7 | 1.39242 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.72256e7i | − | 0.834653i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.58906e7 | − | 1.49775e7i | −0.727706 | − | 0.685889i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.85360e7i | 1.23618i | 0.786109 | + | 0.618088i | \(0.212092\pi\) | ||||
−0.786109 | + | 0.618088i | \(0.787908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.29064e7 | −0.939492 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.33132e7 | 1.29469 | 0.647346 | − | 0.762196i | \(-0.275879\pi\) | ||||
0.647346 | + | 0.762196i | \(0.275879\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.88149e6i | 0.106203i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.89710e7 | + | 8.06967e6i | −1.01343 | + | 0.282285i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.28099e7i | 1.42240i | 0.702988 | + | 0.711202i | \(0.251849\pi\) | ||||
−0.702988 | + | 0.711202i | \(0.748151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.13808e7 | −0.359436 | −0.179718 | − | 0.983718i | \(-0.557519\pi\) | ||||
−0.179718 | + | 0.983718i | \(0.557519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −188268. | −0.00565600 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.92745e7i | 1.98106i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.91925e6 | + | 6.89032e6i | 0.0522810 | + | 0.187694i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.09087e7i | 0.542895i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.00070e7 | 0.990794 | 0.495397 | − | 0.868667i | \(-0.335023\pi\) | ||||
0.495397 | + | 0.868667i | \(0.335023\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.86594e7 | 0.677405 | 0.338703 | − | 0.940893i | \(-0.390012\pi\) | ||||
0.338703 | + | 0.940893i | \(0.390012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.79241e7i | − | 0.404591i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.15840e6 | − | 2.21093e7i | −0.132833 | − | 0.476886i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.01958e7i | 0.622728i | 0.950291 | + | 0.311364i | \(0.100786\pi\) | ||||
−0.950291 | + | 0.311364i | \(0.899214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.90433e7 | −0.375709 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.22736e7 | 0.231783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.35416e7i | − | 1.69180i | −0.533345 | − | 0.845898i | \(-0.679065\pi\) | ||
0.533345 | − | 0.845898i | \(-0.320935\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.94036e7 | + | 1.65465e7i | −1.02948 | + | 0.286755i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.73507e7i | 0.952865i | 0.879211 | + | 0.476432i | \(0.158070\pi\) | ||||
−0.879211 | + | 0.476432i | \(0.841930\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.01857e7 | −0.640425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.84098e6 | −0.119918 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.87192e7i | 0.715383i | 0.933840 | + | 0.357691i | \(0.116436\pi\) | ||||
−0.933840 | + | 0.357691i | \(0.883564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.69650e7 | + | 2.80904e7i | 0.239288 | + | 0.396209i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 4.64949e7i | − | 0.630229i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.93505e7 | −0.252178 | −0.126089 | − | 0.992019i | \(-0.540243\pi\) | ||||
−0.126089 | + | 0.992019i | \(0.540243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.82617e7 | 0.981011 | 0.490506 | − | 0.871438i | \(-0.336812\pi\) | ||||
0.490506 | + | 0.871438i | \(0.336812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.46222e7i | 0.538235i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.01866e7 | + | 1.67646e7i | −0.698874 | + | 0.194666i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.07074e8i | − | 1.19740i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.51948e7 | 0.486936 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.19454e8 | 1.24046 | 0.620229 | − | 0.784420i | \(-0.287040\pi\) | ||||
0.620229 | + | 0.784420i | \(0.287040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.98469e7i | − | 0.599227i | −0.954061 | − | 0.299613i | \(-0.903142\pi\) | ||
0.954061 | − | 0.299613i | \(-0.0968577\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.45862e7 | − | 8.82672e7i | −0.237449 | − | 0.852468i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.22964e8i | − | 1.14590i | −0.819589 | − | 0.572952i | \(-0.805798\pi\) | ||
0.819589 | − | 0.572952i | \(-0.194202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.69053e8 | −1.52067 | −0.760337 | − | 0.649529i | \(-0.774966\pi\) | ||||
−0.760337 | + | 0.649529i | \(0.774966\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.77200e7 | 0.761925 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.07489e7i | − | 0.0901836i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.99838e7 | − | 1.43546e8i | −0.324150 | − | 1.16373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.33984e7i | 0.261715i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.68401e7 | −0.354900 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.67605e8 | 1.96113 | 0.980565 | − | 0.196195i | \(-0.0628586\pi\) | ||||
0.980565 | + | 0.196195i | \(0.0628586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.55612e7i | 0.110336i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.90887e8 | + | 5.31702e7i | −1.30991 | + | 0.364866i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.44906e7i | 0.229135i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.80198e7 | 0.308934 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.59100e8 | 0.991510 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.49333e8i | − | 0.901753i | −0.892586 | − | 0.450877i | \(-0.851111\pi\) | ||
0.892586 | − | 0.450877i | \(-0.148889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.64381e7 | + | 4.61643e7i | −0.447374 | + | 0.270189i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.34185e8i | − | 1.32883i | −0.747365 | − | 0.664414i | \(-0.768681\pi\) | ||
0.747365 | − | 0.664414i | \(-0.231319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.31882e8 | −0.725706 | −0.362853 | − | 0.931846i | \(-0.618197\pi\) | ||||
−0.362853 | + | 0.931846i | \(0.618197\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.26696e7 | 0.494647 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.83419e8i | − | 0.949948i | −0.880000 | − | 0.474974i | \(-0.842458\pi\) | ||
0.880000 | − | 0.474974i | \(-0.157542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.56890e6 | + | 437006.i | −0.00788602 | + | 0.00219660i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.42419e7i | 0.167085i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.05117e8 | 0.498058 | 0.249029 | − | 0.968496i | \(-0.419889\pi\) | ||||
0.249029 | + | 0.968496i | \(0.419889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.94216e8 | 0.893770 | 0.446885 | − | 0.894591i | \(-0.352533\pi\) | ||||
0.446885 | + | 0.894591i | \(0.352533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.03751e8i | 0.910914i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.85330e7 | + | 1.74239e8i | 0.210841 | + | 0.756944i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.95992e7i | − | 0.293876i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.41314e7 | 0.345351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.02689e8 | −0.809045 | −0.404523 | − | 0.914528i | \(-0.632562\pi\) | ||||
−0.404523 | + | 0.914528i | \(0.632562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.99514e8i | 0.774552i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.80016e7 | + | 1.36430e8i | 0.143520 | + | 0.515251i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.34593e7i | 0.0494603i | 0.999694 | + | 0.0247301i | \(0.00787265\pi\) | ||||
−0.999694 | + | 0.0247301i | \(0.992127\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.38911e7 | 0.335796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.92494e7 | 0.101830 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.42205e8i | 0.482026i | 0.970522 | + | 0.241013i | \(0.0774797\pi\) | ||||
−0.970522 | + | 0.241013i | \(0.922520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.58694e8 | + | 4.42030e7i | −0.523841 | + | 0.145912i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.82369e8i | 0.586355i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.07548e8 | −1.58981 | −0.794903 | − | 0.606737i | \(-0.792478\pi\) | ||||
−0.794903 | + | 0.606737i | \(0.792478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.12836e8 | −0.344393 | −0.172197 | − | 0.985063i | \(-0.555086\pi\) | ||||
−0.172197 | + | 0.985063i | \(0.555086\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.37697e8i | 0.409595i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.56622e8 | + | 2.75774e8i | −1.32401 | + | 0.799630i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.10728e8i | − | 1.44381i | −0.691991 | − | 0.721906i | \(-0.743266\pi\) | ||
0.691991 | − | 0.721906i | \(-0.256734\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.38540e7 | −0.258725 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.70459e8 | −0.458297 | −0.229148 | − | 0.973391i | \(-0.573594\pi\) | ||||
−0.229148 | + | 0.973391i | \(0.573594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.62144e8i | − | 0.425253i | −0.977134 | − | 0.212626i | \(-0.931798\pi\) | ||
0.977134 | − | 0.212626i | \(-0.0682017\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.96820e7 | − | 1.66240e7i | 0.152717 | − | 0.0425382i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.23932e8i | 0.559153i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64426e8 | 0.400708 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.88026e8 | 0.923071 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.85845e8i | 0.896141i | 0.893998 | + | 0.448070i | \(0.147889\pi\) | ||||
−0.893998 | + | 0.448070i | \(0.852111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.07924e8 | − | 3.87457e8i | −0.244759 | − | 0.878712i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.34663e8i | 1.62720i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.96455e8 | −0.641371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.97783e8 | 0.629387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.66166e8i | 0.343157i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.03577e8 | + | 3.71852e8i | 0.209032 | + | 0.750447i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.37817e8i | 1.25809i | 0.777369 | + | 0.629045i | \(0.216554\pi\) | ||||
−0.777369 | + | 0.629045i | \(0.783446\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.12596e8 | −0.217105 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.27817e8 | 1.37202 | 0.686010 | − | 0.727592i | \(-0.259360\pi\) | ||||
0.686010 | + | 0.727592i | \(0.259360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.46869e8i | − | 0.823711i | −0.911249 | − | 0.411855i | \(-0.864881\pi\) | ||
0.911249 | − | 0.411855i | \(-0.135119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.29273e8 | − | 3.60082e7i | 0.233035 | − | 0.0649104i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.91083e8i | 1.04218i | 0.853503 | + | 0.521088i | \(0.174474\pi\) | ||||
−0.853503 | + | 0.521088i | \(0.825526\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.74729e8 | 0.301367 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.80271e8 | 0.810436 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.07576e8i | 0.177626i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.09770e8 | − | 6.78490e8i | −0.662138 | − | 1.09636i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.49851e8i | − | 1.02777i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.44748e6 | 0.00378908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.84868e8 | −0.886462 | −0.443231 | − | 0.896407i | \(-0.646168\pi\) | ||||
−0.443231 | + | 0.896407i | \(0.646168\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.55492e8i | 0.379160i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.31000e8 | − | 2.03615e8i | 1.06233 | − | 0.295905i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.39373e8i | − | 1.05235i | −0.850377 | − | 0.526174i | \(-0.823626\pi\) | ||
0.850377 | − | 0.526174i | \(-0.176374\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.81792e8 | −0.253441 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.60661e8 | −0.765702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.17736e8i | − | 0.826558i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.08093e7 | − | 2.54213e8i | −0.0928375 | − | 0.333297i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.70870e8i | 0.476506i | 0.971203 | + | 0.238253i | \(0.0765747\pi\) | ||||
−0.971203 | + | 0.238253i | \(0.923425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.13274e9 | 1.42640 | 0.713199 | − | 0.700962i | \(-0.247246\pi\) | ||||
0.713199 | + | 0.700962i | \(0.247246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.09163e9 | −1.34741 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.32858e8i | − | 1.00777i | −0.863772 | − | 0.503883i | \(-0.831904\pi\) | ||
0.863772 | − | 0.503883i | \(-0.168096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.61206e7 | + | 1.29677e8i | 0.0428505 | + | 0.153838i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.12831e8i | − | 0.247569i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.75318e8 | −0.770332 | −0.385166 | − | 0.922847i | \(-0.625856\pi\) | ||||
−0.385166 | + | 0.922847i | \(0.625856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.46812e8 | −0.947353 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.76740e8i | 0.962050i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00165e8 | − | 1.11463e8i | 0.430739 | − | 0.119979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.80237e9i | − | 1.90333i | −0.307141 | − | 0.951664i | \(-0.599372\pi\) | ||
0.307141 | − | 0.951664i | \(-0.400628\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.09354e8 | −0.631360 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.47562e8 | 0.251696 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.29928e8i | − | 0.927830i | −0.885880 | − | 0.463915i | \(-0.846444\pi\) | ||
0.885880 | − | 0.463915i | \(-0.153556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.83938e8 | − | 5.13442e8i | 0.473893 | − | 0.502784i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.59627e8i | 0.249549i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.43545e9 | 1.35441 | 0.677206 | − | 0.735794i | \(-0.263191\pi\) | ||||
0.677206 | + | 0.735794i | \(0.263191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.22026e8 | −0.854094 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.57707e9i | − | 1.43435i | −0.696894 | − | 0.717174i | \(-0.745435\pi\) | ||
0.696894 | − | 0.717174i | \(-0.254565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.72247e8 | − | 2.15104e8i | 0.689674 | − | 0.192104i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.10313e8i | 0.710664i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.24425e9 | 1.93307 | 0.966537 | − | 0.256528i | \(-0.0825785\pi\) | ||||
0.966537 | + | 0.256528i | \(0.0825785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.58215e8 | 0.387660 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.07638e9i | 0.894525i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.94820e7 | + | 2.85349e8i | 0.0648902 | + | 0.232963i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.26641e8i | 0.181791i | 0.995860 | + | 0.0908956i | \(0.0289729\pi\) | ||||
−0.995860 | + | 0.0908956i | \(0.971027\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.31039e7 | −0.0733775 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.11721e8 | −0.706085 | −0.353042 | − | 0.935607i | \(-0.614853\pi\) | ||||
−0.353042 | + | 0.935607i | \(0.614853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.33080e8i | − | 0.634043i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.32584e7 | − | 2.63006e8i | −0.0547980 | − | 0.196731i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.52625e9i | 1.12213i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.55215e8 | −0.184449 | −0.0922243 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922243 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.38323e9 | −0.982763 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.04433e8i | 0.422205i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.01095e8 | − | 1.95285e8i | 0.481514 | − | 0.134122i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.67726e8i | − | 0.248341i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.96316e8 | −0.196791 | −0.0983957 | − | 0.995147i | \(-0.531371\pi\) | ||||
−0.0983957 | + | 0.995147i | \(0.531371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.06676e9 | 0.696754 | 0.348377 | − | 0.937354i | \(-0.386733\pi\) | ||||
0.348377 | + | 0.937354i | \(0.386733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.65997e6i | 0.00427840i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.33360e8 | + | 1.04871e9i | 0.400211 | + | 0.662663i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.80088e8i | − | 0.360576i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.23833e9 | −1.36875 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.53169e7 | −0.0573455 | −0.0286728 | − | 0.999589i | \(-0.509128\pi\) | ||||
−0.0286728 | + | 0.999589i | \(0.509128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.89973e9i | − | 1.12456i | −0.826946 | − | 0.562281i | \(-0.809924\pi\) | ||
0.826946 | − | 0.562281i | \(-0.190076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.22633e8 | + | 6.20129e7i | −0.129681 | + | 0.0361218i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.00449e8i | − | 0.114899i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.11226e9 | 0.627450 | 0.313725 | − | 0.949514i | \(-0.398423\pi\) | ||||
0.313725 | + | 0.949514i | \(0.398423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.39643e8 | 0.410665 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.22249e9i | 1.76108i | 0.473972 | + | 0.880540i | \(0.342820\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.23313e8 | + | 1.51974e9i | 0.227720 | + | 0.817540i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.29266e9i | 0.684557i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.29482e7 | −0.0380323 | −0.0190161 | − | 0.999819i | \(-0.506053\pi\) | ||||
−0.0190161 | + | 0.999819i | \(0.506053\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.64013e9 | −1.86853 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.26015e8i | 0.468031i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.19621e8 | + | 1.14747e9i | 0.159072 | + | 0.571087i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.45286e8i | − | 0.120217i | −0.998192 | − | 0.0601085i | \(-0.980855\pi\) | ||
0.998192 | − | 0.0601085i | \(-0.0191447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.68727e9 | 0.814405 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.25654e9 | −1.54812 | −0.774058 | − | 0.633115i | \(-0.781776\pi\) | ||||
−0.774058 | + | 0.633115i | \(0.781776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.48463e8i | 0.256811i | 0.991722 | + | 0.128406i | \(0.0409859\pi\) | ||||
−0.991722 | + | 0.128406i | \(0.959014\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.14374e8 | − | 1.98984e8i | 0.329489 | − | 0.0917768i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.31891e9i | − | 0.599245i | −0.954058 | − | 0.299623i | \(-0.903139\pi\) | ||
0.954058 | − | 0.299623i | \(-0.0968607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14036e9 | −0.510431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.75658e8 | −0.430253 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.84061e9i | 2.10323i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.58762e8 | − | 2.77067e8i | 0.196408 | − | 0.118620i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.73654e8i | 0.284199i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.59989e9 | −0.665144 | −0.332572 | − | 0.943078i | \(-0.607916\pi\) | ||||
−0.332572 | + | 0.943078i | \(0.607916\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.26783e9 | −0.929187 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.96573e8i | 0.160143i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.23355e9 | − | 9.00682e8i | 1.28701 | − | 0.358489i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.95948e9i | − | 0.768759i | −0.923175 | − | 0.384380i | \(-0.874415\pi\) | ||
0.923175 | − | 0.384380i | \(-0.125585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.02242e9 | 1.16889 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.38785e8 | −0.0910376 | −0.0455188 | − | 0.998963i | \(-0.514494\pi\) | ||||
−0.0455188 | + | 0.998963i | \(0.514494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.01292e8i | − | 0.150833i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.85330e8 | + | 2.10140e9i | 0.216912 | + | 0.778737i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.02296e8i | − | 0.0739163i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.06642e9 | 1.10479 | 0.552394 | − | 0.833583i | \(-0.313714\pi\) | ||||
0.552394 | + | 0.833583i | \(0.313714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.85306e9 | −0.658350 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.60348e9i | 0.561793i | 0.959738 | + | 0.280897i | \(0.0906318\pi\) | ||||
−0.959738 | + | 0.280897i | \(0.909368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.85703e8 | + | 1.38471e9i | 0.133270 | + | 0.478454i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.29844e9i | − | 0.442480i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.21742e9 | −0.409192 | −0.204596 | − | 0.978847i | \(-0.565588\pi\) | ||||
−0.204596 | + | 0.978847i | \(0.565588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.24258e8 | −0.206962 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.38106e8i | − | 0.241384i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.38304e8 | + | 2.61358e8i | −0.302704 | + | 0.0843161i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.97850e7i | 0.0126620i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.57416e9 | −0.494270 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.08635e9 | −0.646331 | −0.323166 | − | 0.946342i | \(-0.604747\pi\) | ||||
−0.323166 | + | 0.946342i | \(0.604747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.28922e9i | − | 1.31106i | −0.755169 | − | 0.655531i | \(-0.772445\pi\) | ||
0.755169 | − | 0.655531i | \(-0.227555\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.07628e8 | + | 5.48156e8i | −0.273747 | + | 0.165328i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.28765e9i | 0.383230i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.55102e9 | 0.749237 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.64475e9 | −0.476727 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.40883e9i | − | 1.54724i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00226e9 | − | 1.11480e9i | 1.12997 | − | 0.314745i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6.25235e8i | − | 0.174234i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.41845e9 | 1.21537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.91116e9 | 1.33350 | 0.666751 | − | 0.745280i | \(-0.267684\pi\) | ||||
0.666751 | + | 0.745280i | \(0.267684\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.52871e9i | 0.677797i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.50843e9 | − | 5.41542e9i | −0.399151 | − | 1.43299i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.76451e9i | 0.460965i | 0.973077 | + | 0.230482i | \(0.0740304\pi\) | ||||
−0.973077 | + | 0.230482i | \(0.925970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.57851e9 | 0.407140 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.75547e8 | −0.0447058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.45145e8i | − | 0.111934i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.41679e8 | − | 1.94469e9i | −0.134498 | − | 0.482864i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.13406e8i | 0.101364i | 0.998715 | + | 0.0506820i | \(0.0161395\pi\) | ||||
−0.998715 | + | 0.0506820i | \(0.983860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.19261e9 | −1.74159 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.45967e9 | 0.827302 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7.57073e9i | − | 1.78796i | −0.448104 | − | 0.893982i | \(-0.647900\pi\) | ||
0.448104 | − | 0.893982i | \(-0.352100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.51494e9 | + | 4.21975e8i | −0.353366 | + | 0.0984277i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.10289e8i | 0.0945255i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.90287e8 | −0.202599 | −0.101299 | − | 0.994856i | \(-0.532300\pi\) | ||||
−0.101299 | + | 0.994856i | \(0.532300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.96089e9 | 1.11515 | 0.557575 | − | 0.830126i | \(-0.311732\pi\) | ||||
0.557575 | + | 0.830126i | \(0.311732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.85966e9i | 0.857054i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.18016e9 | − | 1.95408e9i | −0.258882 | − | 0.428652i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.53066e9i | − | 0.331713i | −0.986150 | − | 0.165856i | \(-0.946961\pi\) | ||
0.986150 | − | 0.165856i | \(-0.0530388\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.93371e9 | 0.414016 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.09371e9 | −0.231358 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.02425e9i | 0.841094i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.12245e9 | + | 8.69736e8i | −0.644836 | + | 0.179615i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.39564e9i | − | 0.896992i | −0.893785 | − | 0.448496i | \(-0.851960\pi\) | ||
0.893785 | − | 0.448496i | \(-0.148040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.63288e8 | 0.113587 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.97310e9 | 0.791724 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.32990e9i | − | 0.655753i | −0.944721 | − | 0.327877i | \(-0.893667\pi\) | ||
0.944721 | − | 0.327877i | \(-0.106333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.94021e8 | − | 1.77359e9i | −0.0961470 | − | 0.345178i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 5.46226e9i | − | 1.05066i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.53030e9 | −0.861258 | −0.430629 | − | 0.902529i | \(-0.641708\pi\) | ||||
−0.430629 | + | 0.902529i | \(0.641708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.70479e9 | −0.884056 | −0.442028 | − | 0.897001i | \(-0.645741\pi\) | ||||
−0.442028 | + | 0.897001i | \(0.645741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3.10309e9i | − | 0.576347i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.03508e9 | + | 7.30616e9i | 0.373627 | + | 1.34136i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.24429e9i | 0.407303i | 0.979043 | + | 0.203652i | \(0.0652810\pi\) | ||||
−0.979043 | + | 0.203652i | \(0.934719\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.47307e8 | 0.0623094 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.91162e7 | −0.0104848 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.74415e9i | − | 1.53323i | −0.642109 | − | 0.766613i | \(-0.721941\pi\) | ||
0.642109 | − | 0.766613i | \(-0.278059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.63813e9 | − | 1.29192e9i | 0.804044 | − | 0.223961i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.49031e9i | 0.769623i | 0.922995 | + | 0.384812i | \(0.125734\pi\) | ||||
−0.922995 | + | 0.384812i | \(0.874266\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.74101e9 | −0.633974 | −0.316987 | − | 0.948430i | \(-0.602671\pi\) | ||||
−0.316987 | + | 0.948430i | \(0.602671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.14393e9 | −0.526808 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.37079e9i | − | 0.392813i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.84102e9 | − | 5.40199e9i | 0.465472 | − | 0.885063i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.51345e9i | − | 0.245206i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.50527e9 | 0.561622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.93545e9 | −0.306675 | −0.153337 | − | 0.988174i | \(-0.549002\pi\) | ||||
−0.153337 | + | 0.988174i | \(0.549002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.64660e9i | 1.35498i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.68355e9 | + | 2.14020e9i | −1.19084 | + | 0.331701i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.56532e9i | 1.00639i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.50478e8 | 0.0834616 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.89076e9 | 0.883422 | 0.441711 | − | 0.897157i | \(-0.354372\pi\) | ||||
0.441711 | + | 0.897157i | \(0.354372\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.16008e9i | 0.468770i | 0.972144 | + | 0.234385i | \(0.0753076\pi\) | ||||
−0.972144 | + | 0.234385i | \(0.924692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.71798e9 | − | 6.16774e9i | −0.252092 | − | 0.905038i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.27557e10i | 1.85157i | 0.378054 | + | 0.925783i | \(0.376593\pi\) | ||||
−0.378054 | + | 0.925783i | \(0.623407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.82536e9 | −1.41089 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11442e9 | −0.158313 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.43892e9i | 0.623852i | 0.950106 | + | 0.311926i | \(0.100974\pi\) | ||||
−0.950106 | + | 0.311926i | \(0.899026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.49849e9 | + | 8.96985e9i | 0.347402 | + | 1.24721i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.69870e9i | − | 0.233689i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.08526e10 | 1.47719 | 0.738595 | − | 0.674149i | \(-0.235489\pi\) | ||||
0.738595 | + | 0.674149i | \(0.235489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.49307e9 | 1.14382 | 0.571912 | − | 0.820315i | \(-0.306202\pi\) | ||||
0.571912 | + | 0.820315i | \(0.306202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.14068e9i | 0.685051i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.75866e8 | + | 2.16112e8i | −0.102308 | + | 0.0284973i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.47737e8i | 0.0975683i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.82509e9 | 0.623037 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.42962e9 | 1.20494 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.20188e9i | 0.531362i | 0.964061 | + | 0.265681i | \(0.0855969\pi\) | ||||
−0.964061 | + | 0.265681i | \(0.914403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.34565e9 | − | 7.19546e9i | −0.543866 | − | 0.900524i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.56755e9i | 0.813472i | 0.913546 | + | 0.406736i | \(0.133333\pi\) | ||||
−0.913546 | + | 0.406736i | \(0.866667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.04433e9 | −0.618386 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.56676e9 | 0.918110 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.31484e9i | 0.758386i | 0.925318 | + | 0.379193i | \(0.123798\pi\) | ||||
−0.925318 | + | 0.379193i | \(0.876202\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.15269e10 | + | 3.21075e9i | −1.37024 | + | 0.381671i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.26123e9i | − | 0.501403i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.97958e9 | −0.696472 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.76447e9 | −0.434041 | −0.217020 | − | 0.976167i | \(-0.569634\pi\) | ||||
−0.217020 | + | 0.976167i | \(0.569634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 3.27818e9i | − | 0.374168i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.53562e8 | − | 3.06438e9i | −0.0964468 | − | 0.346255i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.36014e9i | 0.935188i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.92646e9 | 0.656335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.97083e9 | 0.216090 | 0.108045 | − | 0.994146i | \(-0.465541\pi\) | ||||
0.108045 | + | 0.994146i | \(0.465541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.53340e9i | − | 0.166461i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.41201e7 | − | 5.06927e7i | −0.00151766 | − | 0.00544858i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.16016e9i | − | 0.229888i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.62853e9 | −1.01461 | −0.507304 | − | 0.861767i | \(-0.669358\pi\) | ||||
−0.507304 | + | 0.861767i | \(0.669358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.21131e9 | 0.126389 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.39930e9i | − | 0.247897i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.86527e10 | + | 5.19559e9i | −1.90841 | + | 0.531574i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.39643e9i | 0.344117i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.89490e10 | −1.90123 | −0.950614 | − | 0.310376i | \(-0.899545\pi\) | ||||
−0.950614 | + | 0.310376i | \(0.899545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.46375e9 | 0.145444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.27532e9i | 0.617521i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.71133e9 | + | 1.03355e9i | −0.166783 | + | 0.100727i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.44446e9i | − | 0.139423i | −0.997567 | − | 0.0697116i | \(-0.977792\pi\) | ||
0.997567 | − | 0.0697116i | \(-0.0222079\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.71961e9 | −0.833586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.11172e10 | 1.05266 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.38939e10i | 1.30305i | 0.758627 | + | 0.651525i | \(0.225871\pi\) | ||||
−0.758627 | + | 0.651525i | \(0.774129\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.62983e9 | + | 1.56815e9i | −0.522986 | + | 0.145674i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.85371e10i | − | 1.70571i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.19008e10 | 1.08473 | 0.542366 | − | 0.840142i | \(-0.317529\pi\) | ||||
0.542366 | + | 0.840142i | \(0.317529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.24882e9 | 0.203044 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.57512e10i | − | 1.40882i | −0.709796 | − | 0.704408i | \(-0.751213\pi\) | ||
0.709796 | − | 0.704408i | \(-0.248787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00052e9 | + | 1.07722e10i | 0.265858 | + | 0.954459i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 2.97615e9i | − | 0.261235i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.24352e9 | −0.542929 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.60645e10 | 1.38397 | 0.691984 | − | 0.721912i | \(-0.256737\pi\) | ||||
0.691984 | + | 0.721912i | \(0.256737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 6.54909e9i | − | 0.558983i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.14946e9 | + | 7.71679e9i | 0.181767 | + | 0.652563i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.88969e10i | − | 1.58327i | −0.610993 | − | 0.791636i | \(-0.709229\pi\) | ||
0.610993 | − | 0.791636i | \(-0.290771\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.44648e9 | −0.535151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.01100e10 | 0.831584 | 0.415792 | − | 0.909460i | \(-0.363504\pi\) | ||||
0.415792 | + | 0.909460i | \(0.363504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.44806e9i | 0.688527i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.82620e9 | − | 1.34431e9i | 0.389754 | − | 0.108563i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.45994e10i | − | 1.16829i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00677e10 | 1.59132 | 0.795658 | − | 0.605746i | \(-0.207125\pi\) | ||||
0.795658 | + | 0.605746i | \(0.207125\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.34883e8 | −0.0341729 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.15770e10i | − | 1.68020i | −0.542428 | − | 0.840102i | \(-0.682495\pi\) | ||
0.542428 | − | 0.840102i | \(-0.317505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.49124e9 | − | 3.31640e9i | 0.423755 | − | 0.255924i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.03371e9i | 0.232007i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.65719e9 | 0.277183 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.28842e9 | 0.247007 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.75337e9i | 0.204974i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.13048e9 | + | 2.26469e9i | −0.599891 | + | 0.167095i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.32055e10i | 1.69699i | 0.529205 | + | 0.848494i | \(0.322490\pi\) | ||||
−0.529205 | + | 0.848494i | \(0.677510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.59479e9 | −0.333040 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.36330e9 | 0.169786 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.40114e10i | 0.997756i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.42824e9 | − | 5.12755e9i | −0.100813 | − | 0.361931i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.77123e8i | 0.0473766i | 0.999719 | + | 0.0236883i | \(0.00754092\pi\) | ||||
−0.999719 | + | 0.0236883i | \(0.992459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.13727e7 | 0.00633728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.45129e9 | 0.443540 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.01476e10i | − | 0.691607i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.20521e8 | + | 3.30477e9i | 0.0621939 | + | 0.223283i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.63994e10i | − | 1.09842i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.84504e9 | 0.388122 | 0.194061 | − | 0.980990i | \(-0.437834\pi\) | ||||
0.194061 | + | 0.980990i | \(0.437834\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.91491e10 | −1.26060 | −0.630299 | − | 0.776353i | \(-0.717068\pi\) | ||||
−0.630299 | + | 0.776353i | \(0.717068\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.64584e9i | − | 0.237947i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.51868e10 | − | 7.01562e9i | 1.62975 | − | 0.453957i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.86330e9i | − | 0.311999i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.87102e9 | 0.309832 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.17006e9 | 0.389124 | 0.194562 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194562 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.25285e10i | − | 1.40875i | −0.709830 | − | 0.704373i | \(-0.751228\pi\) | ||
0.709830 | − | 0.704373i | \(-0.248772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.91054e9 | − | 1.47539e10i | −0.552478 | − | 0.914784i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.08545e9i | − | 0.374131i | −0.982347 | − | 0.187065i | \(-0.940102\pi\) | ||
0.982347 | − | 0.187065i | \(-0.0598976\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.81588e9 | −0.293586 | −0.146793 | − | 0.989167i | \(-0.546895\pi\) | ||||
−0.146793 | + | 0.989167i | \(0.546895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.65021e10 | 0.997554 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.01477e10i | − | 0.608288i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.54422e10 | + | 4.30130e9i | −0.917921 | + | 0.255680i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8.83489e9i | − | 0.520789i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.92635e10 | −1.71064 | −0.855320 | − | 0.518100i | \(-0.826640\pi\) | ||||
−0.855320 | + | 0.518100i | \(0.826640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65950e10 | −0.962038 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.50769e9i | − | 0.316645i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.01393e9 | − | 1.08203e10i | −0.171844 | − | 0.616939i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.13976e10i | − | 0.644499i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.23902e9 | 0.293814 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.53145e9 | −0.363292 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.17155e10i | 1.19797i | 0.800759 | + | 0.598987i | \(0.204430\pi\) | ||||
−0.800759 | + | 0.598987i | \(0.795570\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.88074e8 | − | 2.11125e9i | −0.0321773 | − | 0.115520i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.01757e9i | 0.218037i | 0.994040 | + | 0.109019i | \(0.0347708\pi\) | ||||
−0.994040 | + | 0.109019i | \(0.965229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.62487e10 | 0.874666 | 0.437333 | − | 0.899300i | \(-0.355923\pi\) | ||||
0.437333 | + | 0.899300i | \(0.355923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.23548e9 | −0.386328 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.95958e10i | 1.03783i | 0.854826 | + | 0.518914i | \(0.173664\pi\) | ||||
−0.854826 | + | 0.518914i | \(0.826336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.31180e10 | + | 3.65394e9i | −0.689148 | + | 0.191957i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.31277e9i | 0.276856i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.23604e9 | 0.374052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.75441e10 | 1.41242 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.37264e10i | − | 0.698243i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.29119e9 | + | 6.67474e9i | −0.317471 | + | 0.336827i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.67840e10i | 1.84145i | 0.390207 | + | 0.920727i | \(0.372403\pi\) | ||||
−0.390207 | + | 0.920727i | \(0.627597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.24670e10 | −0.619159 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.48378e9 | 0.0731062 | 0.0365531 | − | 0.999332i | \(-0.488362\pi\) | ||||
0.0365531 | + | 0.999332i | \(0.488362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.36597e10i | 1.15650i | 0.815859 | + | 0.578250i | \(0.196264\pi\) | ||||
−0.815859 | + | 0.578250i | \(0.803736\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.25191e10 | − | 3.48712e9i | 0.607117 | − | 0.169108i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.21269e9i | 0.202687i | 0.994851 | + | 0.101344i | \(0.0323142\pi\) | ||||
−0.994851 | + | 0.101344i | \(0.967686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.19863e10 | 0.572177 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.66945e9 | −0.315877 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.99715e7i | − | 0.00187832i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.45129e9 | − | 5.21029e9i | −0.0676665 | − | 0.242930i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 9.57875e9i | − | 0.443134i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.10125e9 | −0.0964535 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.24233e9 | 0.420964 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.62167e9i | 0.434854i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.86962e9 | + | 2.10726e10i | 0.263233 | + | 0.945035i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.32662e10i | 0.590367i | 0.955441 | + | 0.295184i | \(0.0953808\pi\) | ||||
−0.955441 | + | 0.295184i | \(0.904619\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.87811e9 | 0.259576 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.15727e9 | −0.313641 | −0.156821 | − | 0.987627i | \(-0.550124\pi\) | ||||
−0.156821 | + | 0.987627i | \(0.550124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.77788e10i | − | 0.773132i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.20149e10 | + | 3.34666e9i | −0.518497 | + | 0.144424i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.39930e10i | − | 0.599263i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.78152e9 | −0.415721 | −0.207860 | − | 0.978158i | \(-0.566650\pi\) | ||||
−0.207860 | + | 0.978158i | \(0.566650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.06085e10 | −0.869236 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.88623e9i | 0.204535i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.02799e9 | − | 1.49484e10i | −0.375055 | − | 0.621010i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.98309e9i | 0.164226i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.92073e10 | −1.19519 | −0.597594 | − | 0.801799i | \(-0.703876\pi\) | ||||
−0.597594 | + | 0.801799i | \(0.703876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.43915e9 | −0.180292 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.35165e10i | 0.947952i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.88305e10 | − | 8.03055e9i | 1.15349 | − | 0.321295i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.72053e10i | 1.47746i | 0.674000 | + | 0.738731i | \(0.264575\pi\) | ||||
−0.674000 | + | 0.738731i | \(0.735425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.44388e10 | 0.569116 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.20016e9 | 0.242571 | 0.121286 | − | 0.992618i | \(-0.461298\pi\) | ||||
0.121286 | + | 0.992618i | \(0.461298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.55777e10i | − | 0.604938i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.38961e9 | + | 1.21691e10i | 0.130659 | + | 0.469079i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.27543e10i | 0.488015i | 0.969773 | + | 0.244008i | \(0.0784622\pi\) | ||||
−0.969773 | + | 0.244008i | \(0.921538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50782e10 | 0.572689 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.90985e10 | −0.720057 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.08638e10i | 1.15511i | 0.816351 | + | 0.577556i | \(0.195994\pi\) | ||||
−0.816351 | + | 0.577556i | \(0.804006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.95902e9 | + | 3.21639e10i | 0.332850 | + | 1.19497i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.64565e9i | 0.208220i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.79820e10 | 0.658375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.07702e10 | −0.754935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.69896e10i | − | 0.613042i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.61143e10 | − | 4.48852e9i | 0.577252 | − | 0.160789i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.32539e10i | 1.18263i | 0.806439 | + | 0.591317i | \(0.201392\pi\) | ||||
−0.806439 | + | 0.591317i | \(0.798608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.47588e9 | −0.122725 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.45095e10 | −1.56022 | −0.780108 | − | 0.625644i | \(-0.784836\pi\) | ||||
−0.780108 | + | 0.625644i | \(0.784836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.78043e9i | 0.166369i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.19227e10 | − | 1.32401e10i | 0.757492 | − | 0.457482i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.80736e9i | 0.233533i | 0.993159 | + | 0.116766i | \(0.0372529\pi\) | ||||
−0.993159 | + | 0.116766i | \(0.962747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.85384e10 | 1.31267 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.29884e10 | −0.777442 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.37498e8i | 0.0214063i | 0.999943 | + | 0.0107031i | \(0.00340698\pi\) | ||||
−0.999943 | + | 0.0107031i | \(0.996593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.31092e10 | − | 9.22234e9i | 1.10388 | − | 0.307478i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.90806e7i | 0.00261794i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.07150e10 | −0.680924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.60147e10 | −1.82828 | −0.914142 | − | 0.405393i | \(-0.867135\pi\) | ||||
−0.914142 | + | 0.405393i | \(0.867135\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.88977e10i | − | 0.612472i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.26789e10 | − | 4.55188e10i | −0.408040 | − | 1.46491i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 8.97443e9i | − | 0.286796i | −0.989665 | − | 0.143398i | \(-0.954197\pi\) | ||
0.989665 | − | 0.143398i | \(-0.0458030\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.40506e10 | −0.763214 |
(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 | 80.8.c.a.49.2 | 2 | ||
4.3 | odd | 2 | 5.8.b.a.4.1 | ✓ | 2 | ||
5.2 | odd | 4 | 400.8.a.y.1.2 | 2 | |||
5.3 | odd | 4 | 400.8.a.y.1.1 | 2 | |||
5.4 | even | 2 | inner | 80.8.c.a.49.1 | 2 | ||
8.3 | odd | 2 | 320.8.c.d.129.2 | 2 | |||
8.5 | even | 2 | 320.8.c.c.129.1 | 2 | |||
12.11 | even | 2 | 45.8.b.a.19.2 | 2 | |||
20.3 | even | 4 | 25.8.a.d.1.1 | 2 | |||
20.7 | even | 4 | 25.8.a.d.1.2 | 2 | |||
20.19 | odd | 2 | 5.8.b.a.4.2 | yes | 2 | ||
40.19 | odd | 2 | 320.8.c.d.129.1 | 2 | |||
40.29 | even | 2 | 320.8.c.c.129.2 | 2 | |||
60.23 | odd | 4 | 225.8.a.n.1.2 | 2 | |||
60.47 | odd | 4 | 225.8.a.n.1.1 | 2 | |||
60.59 | even | 2 | 45.8.b.a.19.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.8.b.a.4.1 | ✓ | 2 | 4.3 | odd | 2 | ||
5.8.b.a.4.2 | yes | 2 | 20.19 | odd | 2 | ||
25.8.a.d.1.1 | 2 | 20.3 | even | 4 | |||
25.8.a.d.1.2 | 2 | 20.7 | even | 4 | |||
45.8.b.a.19.1 | 2 | 60.59 | even | 2 | |||
45.8.b.a.19.2 | 2 | 12.11 | even | 2 | |||
80.8.c.a.49.1 | 2 | 5.4 | even | 2 | inner | ||
80.8.c.a.49.2 | 2 | 1.1 | even | 1 | trivial | ||
225.8.a.n.1.1 | 2 | 60.47 | odd | 4 | |||
225.8.a.n.1.2 | 2 | 60.23 | odd | 4 | |||
320.8.c.c.129.1 | 2 | 8.5 | even | 2 | |||
320.8.c.c.129.2 | 2 | 40.29 | even | 2 | |||
320.8.c.d.129.1 | 2 | 40.19 | odd | 2 | |||
320.8.c.d.129.2 | 2 | 8.3 | odd | 2 | |||
400.8.a.y.1.1 | 2 | 5.3 | odd | 4 | |||
400.8.a.y.1.2 | 2 | 5.2 | odd | 4 |