Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [816,2,Mod(239,816)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(816, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("816.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 816 = 2^{4} \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 816.e (of order \(2\), degree \(1\), 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: | \(6.51579280494\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + 11 x^{16} - 28 x^{15} + 36 x^{14} - 38 x^{13} + 61 x^{12} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.17 | ||
Root | \(0.689587 + 1.23469i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 816.239 |
Dual form | 816.2.e.c.239.18 |
$q$-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 \(\left(\mathbb{Z}/816\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(511\) | \(545\) | \(613\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.39392 | − | 1.02809i | 0.804782 | − | 0.593571i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.10097i | − | 1.38680i | −0.720554 | − | 0.693398i | \(-0.756113\pi\) | ||
0.720554 | − | 0.693398i | \(-0.243887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.09021i | 0.412062i | 0.978545 | + | 0.206031i | \(0.0660548\pi\) | ||||
−0.978545 | + | 0.206031i | \(0.933945\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.886042 | − | 2.86617i | 0.295347 | − | 0.955390i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.168447 | −0.0507886 | −0.0253943 | − | 0.999678i | \(-0.508084\pi\) | ||||
−0.0253943 | + | 0.999678i | \(0.508084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.08110 | −1.13189 | −0.565947 | − | 0.824442i | \(-0.691489\pi\) | ||||
−0.565947 | + | 0.824442i | \(0.691489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.18809 | − | 4.32252i | −0.823162 | − | 1.11607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.00000i | − | 0.242536i | ||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.15205i | − | 1.64079i | −0.571795 | − | 0.820396i | \(-0.693753\pi\) | ||
0.571795 | − | 0.820396i | \(-0.306247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.12084 | + | 1.51967i | 0.244588 | + | 0.331620i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.51061 | 1.56607 | 0.783035 | − | 0.621978i | \(-0.213671\pi\) | ||||
0.783035 | + | 0.621978i | \(0.213671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61603 | −0.923205 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.71162 | − | 4.90615i | −0.329402 | − | 0.944190i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.05922i | 0.753778i | 0.926258 | + | 0.376889i | \(0.123006\pi\) | ||||
−0.926258 | + | 0.376889i | \(0.876994\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.53949i | 0.994921i | 0.867487 | + | 0.497461i | \(0.165734\pi\) | ||||
−0.867487 | + | 0.497461i | \(0.834266\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.234802 | + | 0.173179i | −0.0408737 | + | 0.0301466i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.38072 | 0.571447 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4493 | −1.71786 | −0.858930 | − | 0.512093i | \(-0.828870\pi\) | ||||
−0.858930 | + | 0.512093i | \(0.828870\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.68874 | + | 4.19576i | −0.910927 | + | 0.671859i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.08110i | − | 0.325013i | −0.986707 | − | 0.162507i | \(-0.948042\pi\) | ||
0.986707 | − | 0.162507i | \(-0.0519579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.33573i | − | 0.203696i | −0.994800 | − | 0.101848i | \(-0.967524\pi\) | ||
0.994800 | − | 0.101848i | \(-0.0324756\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.88791 | − | 2.74759i | −1.32493 | − | 0.409587i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.73245 | 0.398568 | 0.199284 | − | 0.979942i | \(-0.436138\pi\) | ||||
0.199284 | + | 0.979942i | \(0.436138\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.81143 | 0.830205 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.02809 | − | 1.39392i | −0.143962 | − | 0.195188i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.96479i | − | 0.819326i | −0.912237 | − | 0.409663i | \(-0.865646\pi\) | ||
0.912237 | − | 0.409663i | \(-0.134354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.522349i | 0.0704335i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.35299 | − | 9.96941i | −0.973927 | − | 1.32048i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.28367 | 0.167120 | 0.0835600 | − | 0.996503i | \(-0.473371\pi\) | ||||
0.0835600 | + | 0.996503i | \(0.473371\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.71247 | −1.11552 | −0.557759 | − | 0.830003i | \(-0.688339\pi\) | ||||
−0.557759 | + | 0.830003i | \(0.688339\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.12474 | + | 0.965975i | 0.393680 | + | 0.121701i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.6554i | 1.56971i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.24977i | 0.641361i | 0.947187 | + | 0.320681i | \(0.103912\pi\) | ||||
−0.947187 | + | 0.320681i | \(0.896088\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.4692 | − | 7.72162i | 1.26034 | − | 0.929574i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1023 | 1.31760 | 0.658800 | − | 0.752318i | \(-0.271064\pi\) | ||||
0.658800 | + | 0.752318i | \(0.271064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.69752 | 0.315721 | 0.157860 | − | 0.987461i | \(-0.449540\pi\) | ||||
0.157860 | + | 0.987461i | \(0.449540\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.43438 | + | 4.74571i | −0.742979 | + | 0.547988i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.183643i | − | 0.0209281i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.09021i | − | 0.122659i | −0.998118 | − | 0.0613293i | \(-0.980466\pi\) | ||
0.998118 | − | 0.0613293i | \(-0.0195340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.42986 | − | 5.07909i | −0.825540 | − | 0.564344i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6611 | 1.38974 | 0.694871 | − | 0.719135i | \(-0.255462\pi\) | ||||
0.694871 | + | 0.719135i | \(0.255462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.10097 | −0.336348 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.17326 | + | 5.65824i | 0.447421 | + | 0.606627i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.18817i | 0.867945i | 0.900926 | + | 0.433972i | \(0.142888\pi\) | ||||
−0.900926 | + | 0.433972i | \(0.857112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.44927i | − | 0.466411i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.69512 | + | 7.72162i | 0.590556 | + | 0.800694i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22.1783 | −2.27545 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.4432 | 1.97416 | 0.987081 | − | 0.160224i | \(-0.0512215\pi\) | ||||
0.987081 | + | 0.160224i | \(0.0512215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.149251 | + | 0.482797i | −0.0150003 | + | 0.0485229i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.92544i | 0.291092i | 0.989352 | + | 0.145546i | \(0.0464938\pi\) | ||||
−0.989352 | + | 0.145546i | \(0.953506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.46343i | 0.735394i | 0.929946 | + | 0.367697i | \(0.119854\pi\) | ||||
−0.929946 | + | 0.367697i | \(0.880146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.71247 | − | 3.47570i | 0.459890 | − | 0.339194i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.64168 | 0.835423 | 0.417712 | − | 0.908580i | \(-0.362832\pi\) | ||||
0.417712 | + | 0.908580i | \(0.362832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3702 | 1.08907 | 0.544536 | − | 0.838738i | \(-0.316706\pi\) | ||||
0.544536 | + | 0.838738i | \(0.316706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.5656 | + | 10.7429i | −1.38250 | + | 1.01967i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19.8569i | − | 1.86798i | −0.357296 | − | 0.933991i | \(-0.616301\pi\) | ||
0.357296 | − | 0.933991i | \(-0.383699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 23.2902i | − | 2.17182i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.61603 | + | 11.6971i | −0.334302 | + | 1.08140i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.09021 | 0.0999398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9716 | −0.997421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.13957 | − | 2.90089i | −0.192918 | − | 0.261565i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.19069i | − | 0.106499i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.7825i | − | 1.40047i | −0.713910 | − | 0.700237i | \(-0.753078\pi\) | ||
0.713910 | − | 0.700237i | \(-0.246922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.37325 | − | 1.86190i | −0.120908 | − | 0.163931i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.31148 | 0.726178 | 0.363089 | − | 0.931755i | \(-0.381722\pi\) | ||||
0.363089 | + | 0.931755i | \(0.381722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.79727 | 0.676109 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.2138 | + | 5.30769i | −1.30940 | + | 0.456813i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.9740i | 1.19388i | 0.802285 | + | 0.596941i | \(0.203617\pi\) | ||||
−0.802285 | + | 0.596941i | \(0.796383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.08390i | 0.0919353i | 0.998943 | + | 0.0459676i | \(0.0146371\pi\) | ||||
−0.998943 | + | 0.0459676i | \(0.985363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.80882 | − | 2.80921i | 0.320760 | − | 0.236578i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.687448 | 0.0574873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.5875 | 1.04534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.10069 | − | 5.97470i | 0.668134 | − | 0.492785i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.5519i | 1.60176i | 0.598828 | + | 0.800878i | \(0.295633\pi\) | ||||
−0.598828 | + | 0.800878i | \(0.704367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8830i | 0.967028i | 0.875337 | + | 0.483514i | \(0.160640\pi\) | ||||
−0.875337 | + | 0.483514i | \(0.839360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.86617 | − | 0.886042i | −0.231716 | − | 0.0716322i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.1778 | 1.37975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.19954 | 0.494777 | 0.247389 | − | 0.968916i | \(-0.420428\pi\) | ||||
0.247389 | + | 0.968916i | \(0.420428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.13236 | − | 8.31445i | −0.486328 | − | 0.659379i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.18817i | 0.645318i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4740i | 0.977039i | 0.872553 | + | 0.488520i | \(0.162463\pi\) | ||||
−0.872553 | + | 0.488520i | \(0.837537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.537024 | + | 0.728114i | 0.0418073 | + | 0.0566836i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.4915 | −1.81783 | −0.908913 | − | 0.416986i | \(-0.863086\pi\) | ||||
−0.908913 | + | 0.416986i | \(0.863086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.65537 | 0.281183 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.4990 | − | 6.33702i | −1.56760 | − | 0.484604i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.28501i | 0.173726i | 0.996220 | + | 0.0868630i | \(0.0276843\pi\) | ||||
−0.996220 | + | 0.0868630i | \(0.972316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.03246i | − | 0.380418i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.78934 | − | 1.31974i | 0.134495 | − | 0.0991976i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.61732 | −0.718832 | −0.359416 | − | 0.933177i | \(-0.617024\pi\) | ||||
−0.359416 | + | 0.933177i | \(0.617024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0678 | 1.19431 | 0.597154 | − | 0.802127i | \(-0.296298\pi\) | ||||
0.597154 | + | 0.802127i | \(0.296298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1445 | + | 8.95724i | −0.897748 | + | 0.662138i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 32.4031i | 2.38232i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.168447i | 0.0123180i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.34876 | − | 1.86603i | 0.389065 | − | 0.135734i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0609939 | 0.00441337 | 0.00220668 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220668 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3601 | −1.03366 | −0.516832 | − | 0.856087i | \(-0.672889\pi\) | ||||
−0.516832 | + | 0.856087i | \(0.672889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.0109 | + | 17.6406i | 0.931732 | + | 1.26327i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.1500i | − | 0.936896i | −0.883491 | − | 0.468448i | \(-0.844813\pi\) | ||
0.883491 | − | 0.468448i | \(-0.155187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.33736i | 0.661908i | 0.943647 | + | 0.330954i | \(0.107370\pi\) | ||||
−0.943647 | + | 0.330954i | \(0.892630\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.39726 | + | 7.31777i | 0.380693 | + | 0.516156i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.42542 | −0.310604 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.45343 | −0.450727 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.65471 | − | 21.5267i | 0.462535 | − | 1.49621i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.20474i | 0.0833336i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7706i | 0.948004i | 0.880524 | + | 0.474002i | \(0.157191\pi\) | ||||
−0.880524 | + | 0.474002i | \(0.842809\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.4757 | − | 11.4142i | 1.06038 | − | 0.782089i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.14205 | −0.282485 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.03923 | −0.409970 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.76013 | − | 2.77331i | 0.254086 | − | 0.187403i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.08110i | 0.274524i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.5000i | 1.64064i | 0.571905 | + | 0.820320i | \(0.306205\pi\) | ||||
−0.571905 | + | 0.820320i | \(0.693795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.08999 | + | 13.2303i | −0.272666 | + | 0.882021i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.9511 | 1.45695 | 0.728473 | − | 0.685074i | \(-0.240230\pi\) | ||||
0.728473 | + | 0.685074i | \(0.240230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.22299 | 0.477309 | 0.238654 | − | 0.971105i | \(-0.423294\pi\) | ||||
0.238654 | + | 0.971105i | \(0.423294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.188802 | − | 0.255984i | −0.0124223 | − | 0.0168425i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.92814i | 0.388366i | 0.980965 | + | 0.194183i | \(0.0622055\pi\) | ||||
−0.980965 | + | 0.194183i | \(0.937795\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.47324i | − | 0.552733i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.12084 | − | 1.51967i | −0.0728066 | − | 0.0987135i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.6065 | 1.85040 | 0.925202 | − | 0.379476i | \(-0.123896\pi\) | ||||
0.925202 | + | 0.379476i | \(0.123896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4737 | 0.867920 | 0.433960 | − | 0.900932i | \(-0.357116\pi\) | ||||
0.433960 | + | 0.900932i | \(0.357116\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5784 | + | 0.558736i | −0.999357 | + | 0.0358430i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 18.0211i | − | 1.15133i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.1882i | 1.85720i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6487 | − | 13.0169i | 1.11844 | − | 0.824910i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.43830 | −0.280143 | −0.140072 | − | 0.990141i | \(-0.544733\pi\) | ||||
−0.140072 | + | 0.990141i | \(0.544733\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.26514 | −0.0795385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.32252 | + | 3.18809i | −0.270686 | + | 0.199646i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 27.2101i | − | 1.69732i | −0.528940 | − | 0.848659i | \(-0.677410\pi\) | ||
0.528940 | − | 0.848659i | \(-0.322590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.3920i | − | 0.707865i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.6344 | + | 3.59664i | 0.720152 | + | 0.222626i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.324267 | −0.0199952 | −0.00999758 | − | 0.999950i | \(-0.503182\pi\) | ||||
−0.00999758 | + | 0.999950i | \(0.503182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.4966 | −1.13624 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.41822 | + | 11.4137i | 0.515187 | + | 0.698506i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.0267i | − | 0.794253i | −0.917764 | − | 0.397126i | \(-0.870007\pi\) | ||
0.917764 | − | 0.397126i | \(-0.129993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.43249i | − | 0.269254i | −0.990896 | − | 0.134627i | \(-0.957016\pi\) | ||
0.990896 | − | 0.134627i | \(-0.0429837\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.57427 | − | 6.20194i | −0.276848 | − | 0.375359i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.777554 | 0.0468883 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.4279 | −0.746720 | −0.373360 | − | 0.927687i | \(-0.621794\pi\) | ||||
−0.373360 | + | 0.927687i | \(0.621794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.8771 | + | 4.90822i | 0.950538 | + | 0.293847i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.39425i | − | 0.321794i | −0.986971 | − | 0.160897i | \(-0.948561\pi\) | ||
0.986971 | − | 0.160897i | \(-0.0514387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4863i | 1.33667i | 0.743859 | + | 0.668337i | \(0.232994\pi\) | ||||
−0.743859 | + | 0.668337i | \(0.767006\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −30.9148 | + | 22.8014i | −1.83124 | + | 1.35064i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.26884 | 0.133926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.1024 | − | 19.9895i | 1.58877 | − | 1.17180i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.08724i | 0.472462i | 0.971697 | + | 0.236231i | \(0.0759121\pi\) | ||||
−0.971697 | + | 0.236231i | \(0.924088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.98063i | − | 0.231761i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.288317 | + | 0.826426i | 0.0167298 | + | 0.0479541i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −30.6515 | −1.77262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.45623 | 0.0839355 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.00763 | + | 4.07783i | 0.172784 | + | 0.234265i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.0171i | 1.54700i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.68628i | − | 0.0962411i | −0.998842 | − | 0.0481206i | \(-0.984677\pi\) | ||
0.998842 | − | 0.0481206i | \(-0.0153232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.67312 | + | 10.4035i | 0.436508 | + | 0.591832i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.9998 | −0.793858 | −0.396929 | − | 0.917849i | \(-0.629924\pi\) | ||||
−0.396929 | + | 0.917849i | \(0.629924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.40428 | 0.418515 | 0.209257 | − | 0.977861i | \(-0.432895\pi\) | ||||
0.209257 | + | 0.977861i | \(0.432895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.99546 | − | 9.68973i | 0.168775 | − | 0.545954i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 21.5807i | − | 1.21209i | −0.795429 | − | 0.606047i | \(-0.792754\pi\) | ||
0.795429 | − | 0.606047i | \(-0.207246\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.683763i | − | 0.0382834i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0458 | − | 8.88447i | 0.672333 | − | 0.495883i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.15205 | −0.397951 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8385 | 1.04497 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.8492 | − | 11.6897i | 0.876465 | − | 0.646441i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.97895i | 0.164235i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.42414i | 0.0782779i | 0.999234 | + | 0.0391390i | \(0.0124615\pi\) | ||||
−0.999234 | + | 0.0391390i | \(0.987538\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.25855 | + | 29.9496i | −0.507365 | + | 1.64123i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.2794 | 0.889438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0119 | −1.79827 | −0.899136 | − | 0.437669i | \(-0.855804\pi\) | ||||
−0.899136 | + | 0.437669i | \(0.855804\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.4148 | − | 27.6790i | −1.10878 | − | 1.50332i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.933109i | − | 0.0505307i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9672i | 0.754158i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.9445 | − | 32.4647i | −1.28913 | − | 1.74784i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.1438 | −1.45715 | −0.728577 | − | 0.684963i | \(-0.759818\pi\) | ||||
−0.728577 | + | 0.684963i | \(0.759818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.07627 | 0.0576112 | 0.0288056 | − | 0.999585i | \(-0.490830\pi\) | ||||
0.0288056 | + | 0.999585i | \(0.490830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.98529 | + | 20.0225i | 0.372847 | + | 1.06872i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.7706i | 1.15873i | 0.815068 | + | 0.579366i | \(0.196700\pi\) | ||||
−0.815068 | + | 0.579366i | \(0.803300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 34.4279i | − | 1.82724i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.51967 | − | 1.12084i | 0.0804297 | − | 0.0593213i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.5060 | −1.61005 | −0.805023 | − | 0.593243i | \(-0.797847\pi\) | ||||
−0.805023 | + | 0.593243i | \(0.797847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −32.1518 | −1.69220 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.2936 | + | 11.2799i | −0.802706 | + | 0.592040i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.36493i | − | 0.437841i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.1445i | − | 1.20813i | −0.796934 | − | 0.604067i | \(-0.793546\pi\) | ||
0.796934 | − | 0.604067i | \(-0.206454\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.96479 | − | 1.84394i | −0.310514 | − | 0.0959918i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.50289 | 0.337613 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1832 | −0.889715 | −0.444857 | − | 0.895601i | \(-0.646746\pi\) | ||||
−0.444857 | + | 0.895601i | \(0.646746\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.22415 | − | 1.65974i | −0.0632147 | − | 0.0857084i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.5661i | − | 0.853197i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.3573i | − | 0.634750i | −0.948300 | − | 0.317375i | \(-0.897199\pi\) | ||
0.948300 | − | 0.317375i | \(-0.102801\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.2259 | − | 21.9996i | −0.831281 | − | 1.12708i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.9596 | 1.07098 | 0.535492 | − | 0.844540i | \(-0.320126\pi\) | ||||
0.535492 | + | 0.844540i | \(0.320126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.569472 | −0.0290230 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.82842 | − | 1.18351i | −0.194609 | − | 0.0601611i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1.27730i | − | 0.0647615i | −0.999476 | − | 0.0323808i | \(-0.989691\pi\) | ||
0.999476 | − | 0.0323808i | \(-0.0103089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.51061i | − | 0.379828i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5856 | − | 8.54499i | 0.584415 | − | 0.431038i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.38072 | −0.170103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.84094 | 0.142583 | 0.0712914 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712914 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.8688 | − | 8.01633i | 0.544120 | − | 0.401318i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8477i | 0.591645i | 0.955243 | + | 0.295822i | \(0.0955937\pi\) | ||||
−0.955243 | + | 0.295822i | \(0.904406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 22.6072i | − | 1.12614i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.7501 | + | 23.0398i | −0.782630 | + | 1.14486i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.76016 | 0.0872477 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.67682 | 0.330147 | 0.165074 | − | 0.986281i | \(-0.447214\pi\) | ||||
0.165074 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.3666 | + | 19.4787i | 0.708653 | + | 0.960814i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.39948i | 0.0688638i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 39.2619i | − | 1.92729i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.11435 | + | 1.51087i | 0.0545701 | + | 0.0739878i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.1181 | 0.592007 | 0.296003 | − | 0.955187i | \(-0.404346\pi\) | ||||
0.296003 | + | 0.955187i | \(0.404346\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.29607 | 0.160640 | 0.0803202 | − | 0.996769i | \(-0.474406\pi\) | ||||
0.0803202 | + | 0.996769i | \(0.474406\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.42106 | − | 7.83165i | 0.117716 | − | 0.380788i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.61603i | 0.223910i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.49846i | − | 0.459663i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.958249 | − | 0.706762i | 0.0462647 | − | 0.0341228i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.6357 | 0.897650 | 0.448825 | − | 0.893620i | \(-0.351843\pi\) | ||||
0.448825 | + | 0.893620i | \(0.351843\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.76044 | 0.276829 | 0.138415 | − | 0.990374i | \(-0.455799\pi\) | ||||
0.138415 | + | 0.990374i | \(0.455799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.5460 | − | 12.9412i | 0.841268 | − | 0.620482i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 53.7162i | − | 2.56960i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.7061i | − | 1.08370i | −0.840474 | − | 0.541852i | \(-0.817723\pi\) | ||
0.840474 | − | 0.541852i | \(-0.182277\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.14917 | − | 16.6566i | 0.245199 | − | 0.793169i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.5258 | 1.21277 | 0.606383 | − | 0.795172i | \(-0.292620\pi\) | ||||
0.606383 | + | 0.795172i | \(0.292620\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.3913 | 1.20366 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.1012 | + | 27.2539i | 0.950755 | + | 1.28906i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.5958i | − | 1.44390i | −0.691943 | − | 0.721952i | \(-0.743245\pi\) | ||
0.691943 | − | 0.721952i | \(-0.256755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.350554i | 0.0165070i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.2169 | + | 16.5640i | 0.574000 | + | 0.778246i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.7971 | −0.646817 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.1068 | −1.82934 | −0.914668 | − | 0.404205i | \(-0.867548\pi\) | ||||
−0.914668 | + | 0.404205i | \(0.867548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.90615 | + | 1.71162i | −0.229000 | + | 0.0798916i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.35639i | 0.296047i | 0.988984 | + | 0.148023i | \(0.0472911\pi\) | ||||
−0.988984 | + | 0.148023i | \(0.952709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.75421i | 0.360369i | 0.983633 | + | 0.180184i | \(0.0576694\pi\) | ||||
−0.983633 | + | 0.180184i | \(0.942331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.9445 | − | 17.6604i | 1.11040 | − | 0.818981i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.6447 | −1.69572 | −0.847858 | − | 0.530224i | \(-0.822108\pi\) | ||||
−0.847858 | + | 0.530224i | \(0.822108\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.72337 | −0.264281 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.64168 | − | 6.37372i | 0.398188 | − | 0.293685i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.224999i | 0.0103455i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.0140i | 1.51479i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.0961 | − | 5.28505i | −0.782776 | − | 0.241986i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.90526 | −0.178436 | −0.0892179 | − | 0.996012i | \(-0.528437\pi\) | ||||
−0.0892179 | + | 0.996012i | \(0.528437\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.6448 | 1.94443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.41822 | + | 11.4137i | 0.383042 | + | 0.519340i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 60.2929i | − | 2.73776i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.9757i | − | 0.678614i | −0.940676 | − | 0.339307i | \(-0.889807\pi\) | ||
0.940676 | − | 0.339307i | \(-0.110193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.8245 | + | 17.3878i | 0.579942 | + | 0.786303i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0949 | −0.906871 | −0.453435 | − | 0.891289i | \(-0.649802\pi\) | ||||
−0.453435 | + | 0.891289i | \(0.649802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.05922 | 0.182818 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.49714 | + | 0.462823i | 0.0672914 | + | 0.0208023i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1039i | 0.542933i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.7294i | 1.10704i | 0.832836 | + | 0.553520i | \(0.186716\pi\) | ||||
−0.832836 | + | 0.553520i | \(0.813284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.7453 | + | 24.1515i | −1.46295 | + | 1.07901i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.2379 | −1.61577 | −0.807885 | − | 0.589341i | \(-0.799388\pi\) | ||||
−0.807885 | + | 0.589341i | \(0.799388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.07169 | 0.403685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.09531 | − | 3.75807i | 0.226291 | − | 0.166902i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 35.7061i | − | 1.58264i | −0.611399 | − | 0.791322i | \(-0.709393\pi\) | ||
0.611399 | − | 0.791322i | \(-0.290607\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.94087i | 0.130097i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.0891 | + | 12.2416i | −1.54922 | + | 0.540480i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.1439 | 1.01984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.460272 | −0.0202427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.34921 | + | 3.18513i | 0.103119 | + | 0.139812i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.1237i | − | 0.837823i | −0.908027 | − | 0.418912i | \(-0.862412\pi\) | ||
0.908027 | − | 0.418912i | \(-0.137588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.4324i | − | 0.805992i | −0.915202 | − | 0.402996i | \(-0.867969\pi\) | ||
0.915202 | − | 0.402996i | \(-0.132031\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.17384 | − | 7.01486i | −0.225805 | − | 0.306153i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.53949 | 0.241304 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.4092 | 1.45258 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.13739 | − | 3.67923i | 0.0493584 | − | 0.159665i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.49318i | 0.367880i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.7976i | − | 1.15856i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.4058 | + | 9.88752i | −0.578503 | + | 0.426678i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.978917 | −0.0421649 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.6597 | −1.83409 | −0.917043 | − | 0.398789i | \(-0.869430\pi\) | ||||
−0.917043 | + | 0.398789i | \(0.869430\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.3972 | − | 16.5192i | 0.961157 | − | 0.708906i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 35.2588i | − | 1.51032i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3482i | 0.784512i | 0.919856 | + | 0.392256i | \(0.128305\pi\) | ||||
−0.919856 | + | 0.392256i | \(0.871695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.71961 | + | 24.9714i | −0.329465 | + | 1.06575i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.0318 | 1.23679 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.18857 | 0.0505430 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.3135 | + | 45.1674i | 1.41408 | + | 1.91725i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.5598i | 1.63383i | 0.576757 | + | 0.816915i | \(0.304318\pi\) | ||||
−0.576757 | + | 0.816915i | \(0.695682\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.45123i | 0.230562i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.173179 | + | 0.234802i | 0.00731163 | + | 0.00991334i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.40731 | −0.185746 | −0.0928730 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928730 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −61.5758 | −2.59051 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.53730 | − | 8.10014i | 0.232545 | − | 0.340174i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.8686i | 1.00062i | 0.865846 | + | 0.500311i | \(0.166781\pi\) | ||||
−0.865846 | + | 0.500311i | \(0.833219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.0015i | 1.79956i | 0.436346 | + | 0.899779i | \(0.356272\pi\) | ||||
−0.436346 | + | 0.899779i | \(0.643728\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0850208 | − | 0.0627076i | 0.00355180 | − | 0.00261965i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.6692 | −1.44580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.8354 | −1.53348 | −0.766738 | − | 0.641960i | \(-0.778121\pi\) | ||||
−0.766738 | + | 0.641960i | \(0.778121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.0169 | + | 14.7636i | −0.831875 | + | 0.613553i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8034i | 0.572660i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00475i | 0.0416124i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.2725 | + | 11.2132i | 1.49968 | + | 0.463608i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.2245 | 1.33005 | 0.665024 | − | 0.746822i | \(-0.268421\pi\) | ||||
0.665024 | + | 0.746822i | \(0.268421\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.6187 | 1.63246 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.5194 | − | 18.3300i | −0.556114 | − | 0.753997i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.7104i | 0.563018i | 0.959559 | + | 0.281509i | \(0.0908349\pi\) | ||||
−0.959559 | + | 0.281509i | \(0.909165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.38072i | − | 0.138596i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.59969 | + | 13.0156i | 0.392889 | + | 0.532691i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.7552 | −1.42006 | −0.710029 | − | 0.704172i | \(-0.751318\pi\) | ||||
−0.710029 | + | 0.704172i | \(0.751318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9814 | 1.10059 | 0.550297 | − | 0.834969i | \(-0.314515\pi\) | ||||
0.550297 | + | 0.834969i | \(0.314515\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.0467 | + | 4.65151i | 0.612750 | + | 0.189424i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.0227i | 1.38322i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 30.2488i | − | 1.22776i | −0.789399 | − | 0.613880i | \(-0.789608\pi\) | ||
0.789399 | − | 0.613880i | \(-0.210392\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.16870 | + | 4.54975i | −0.249968 | + | 0.184365i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1514 | −0.451137 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.3561 | 1.10490 | 0.552452 | − | 0.833545i | \(-0.313692\pi\) | ||||
0.552452 | + | 0.833545i | \(0.313692\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.99559 | + | 6.63474i | −0.362737 | + | 0.267539i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.50883i | − | 0.262036i | −0.991380 | − | 0.131018i | \(-0.958175\pi\) | ||
0.991380 | − | 0.131018i | \(-0.0418245\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.0376i | 1.81021i | 0.425185 | + | 0.905107i | \(0.360209\pi\) | ||||
−0.425185 | + | 0.905107i | \(0.639791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.8553 | − | 36.8482i | −0.515866 | − | 1.47867i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.92686 | −0.357647 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.7724 | −1.07090 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.23859 | + | 1.67931i | 0.0494644 | + | 0.0670653i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.4493i | 0.416642i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7130i | 1.34209i | 0.741414 | + | 0.671047i | \(0.234155\pi\) | ||||
−0.741414 | + | 0.671047i | \(0.765845\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.1574 | + | 19.1951i | 0.562708 | + | 0.762937i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −48.9412 | −1.94217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.7170 | −0.939703 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.83710 | − | 31.8211i | 0.389150 | − | 1.25882i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.5942i | − | 0.576436i | −0.957565 | − | 0.288218i | \(-0.906937\pi\) | ||
0.957565 | − | 0.288218i | \(-0.0930627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.9445i | − | 1.25977i | −0.776689 | − | 0.629884i | \(-0.783102\pi\) | ||
0.776689 | − | 0.629884i | \(-0.216898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.77370 | + | 4.25842i | −0.227339 | + | 0.167675i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1484 | 0.752801 | 0.376400 | − | 0.926457i | \(-0.377162\pi\) | ||||
0.376400 | + | 0.926457i | \(0.377162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.216231 | −0.00848779 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.41822 | + | 6.20890i | −0.329936 | + | 0.243346i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.6937i | 0.457611i | 0.973472 | + | 0.228806i | \(0.0734820\pi\) | ||||
−0.973472 | + | 0.228806i | \(0.926518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 25.7737i | − | 1.00706i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.39012 | − | 7.73155i | 0.0932473 | − | 0.301636i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5948 | −1.03599 | −0.517993 | − | 0.855385i | \(-0.673321\pi\) | ||||
−0.517993 | + | 0.855385i | \(0.673321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2489 | −0.670905 | −0.335453 | − | 0.942057i | \(-0.608889\pi\) | ||||
−0.335453 | + | 0.942057i | \(0.608889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.19576 | + | 5.68874i | 0.162950 | + | 0.220932i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 24.1791i | − | 0.937625i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.4872i | 1.18047i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.1883 | + | 34.1511i | 0.973836 | + | 1.32036i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.46759 | 0.0566556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.9908 | −0.539304 | −0.269652 | − | 0.962958i | \(-0.586909\pi\) | ||||
−0.269652 | + | 0.962958i | \(0.586909\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.90088 | + | 22.6469i | 0.304105 | + | 0.871681i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.10176i | − | 0.0423441i | −0.999776 | − | 0.0211721i | \(-0.993260\pi\) | ||
0.999776 | − | 0.0211721i | \(-0.00673978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.1973i | 0.813477i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.5982 | − | 22.5678i | 1.17252 | − | 0.864801i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.3480 | −1.12297 | −0.561484 | − | 0.827488i | \(-0.689769\pi\) | ||||
−0.561484 | + | 0.827488i | \(0.689769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.3331 | 1.65567 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0683 | − | 7.42592i | 0.384129 | − | 0.283317i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.3429i | 0.927390i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.1447i | − | 0.956548i | −0.878211 | − | 0.478274i | \(-0.841263\pi\) | ||
0.878211 | − | 0.478274i | \(-0.158737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.526352 | − | 0.162715i | −0.0199945 | − | 0.00618105i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.36115 | 0.127496 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.08110 | −0.0788273 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.09469 | + | 8.26337i | 0.230522 | + | 0.312549i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.6537i | 0.893389i | 0.894687 | + | 0.446694i | \(0.147399\pi\) | ||||
−0.894687 | + | 0.446694i | \(0.852601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 74.7342i | 2.81865i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.71129 | − | 11.8110i | −0.328086 | − | 0.444829i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.18935 | −0.119948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.61489 | 0.210872 | 0.105436 | − | 0.994426i | \(-0.466376\pi\) | ||||
0.105436 | + | 0.994426i | \(0.466376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.12474 | − | 0.965975i | −0.117187 | − | 0.0362269i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.6049i | 1.55812i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.13176i | − | 0.0797232i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.8753 | − | 29.4102i | 1.48917 | − | 1.09835i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.6326 | 1.21699 | 0.608495 | − | 0.793558i | \(-0.291774\pi\) | ||||
0.608495 | + | 0.793558i | \(0.291774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.13674 | −0.303028 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7814 | − | 13.8523i | 0.698486 | − | 0.515172i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 18.7375i | − | 0.695892i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.33041i | 0.160606i | 0.996770 | + | 0.0803030i | \(0.0255888\pi\) | ||||
−0.996770 | + | 0.0803030i | \(0.974411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.1407 | + | 16.7950i | −0.782989 | + | 0.622035i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.33573 | −0.0494036 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7413 | 0.396738 | 0.198369 | − | 0.980127i | \(-0.436436\pi\) | ||||
0.198369 | + | 0.980127i | \(0.436436\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.5274 | − | 25.1200i | −0.683393 | − | 0.926565i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.884306i | − | 0.0325738i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.8147i | 1.17032i | 0.810917 | + | 0.585161i | \(0.198969\pi\) | ||||
−0.810917 | + | 0.585161i | \(0.801031\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.0083 | + | 40.6861i | 1.10238 | + | 1.49464i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.5017 | −1.04563 | −0.522813 | − | 0.852447i | \(-0.675118\pi\) | ||||
−0.522813 | + | 0.852447i | \(0.675118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 60.6299 | 2.22131 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2183 | − | 36.2890i | 0.410456 | − | 1.32775i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.42129i | 0.344246i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 41.6427i | − | 1.51956i | −0.650178 | − | 0.759782i | \(-0.725306\pi\) | ||
0.650178 | − | 0.759782i | \(-0.274694\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.18665 | + | 4.56300i | −0.225454 | + | 0.166285i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.8490 | 1.34107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.4316 | −0.706253 | −0.353127 | − | 0.935576i | \(-0.614882\pi\) | ||||
−0.353127 | + | 0.935576i | \(0.614882\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.76350 | + | 1.30068i | −0.0640111 | + | 0.0472117i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0473i | 0.509215i | 0.967045 | + | 0.254607i | \(0.0819462\pi\) | ||||
−0.967045 | + | 0.254607i | \(0.918054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3960i | 0.448765i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.74759 | + | 8.88791i | −0.0993394 | + | 0.321343i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.23880 | −0.189162 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.2339 | 1.45087 | 0.725435 | − | 0.688291i | \(-0.241639\pi\) | ||||
0.725435 | + | 0.688291i | \(0.241639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.9746 | − | 37.9288i | −1.00748 | − | 1.36597i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 44.6057i | − | 1.60436i | −0.597084 | − | 0.802178i | \(-0.703674\pi\) | ||
0.597084 | − | 0.802178i | \(-0.296326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 25.5704i | − | 0.918516i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.7121 | − | 15.8796i | −0.420168 | − | 0.569677i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.8841 | −0.533279 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.87015 | −0.0669191 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.9152 | − | 6.94785i | 0.711710 | − | 0.248296i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 19.2246i | − | 0.686156i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.5848i | − | 1.16152i | −0.814074 | − | 0.580762i | \(-0.802755\pi\) | ||
0.814074 | − | 0.580762i | \(-0.197245\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.452003 | + | 0.333377i | −0.0160917 | + | 0.0118685i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.6483 | 0.769725 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.5564 | 1.26265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.7829 | + | 19.0163i | −0.914424 | + | 0.674438i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.2015i | − | 1.17606i | −0.808841 | − | 0.588028i | \(-0.799904\pi\) | ||
0.808841 | − | 0.588028i | \(-0.200096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.73245i | − | 0.0966670i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.4687 | + | 7.25506i | 0.829225 | + | 0.256345i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.454388 | −0.0160350 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.3913 | 0.894925 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.3927 | − | 18.1582i | −0.471445 | − | 0.639200i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 51.6323i | 1.81530i | 0.419733 | + | 0.907648i | \(0.362124\pi\) | ||||
−0.419733 | + | 0.907648i | \(0.637876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.7697i | 1.71254i | 0.516531 | + | 0.856269i | \(0.327223\pi\) | ||||
−0.516531 | + | 0.856269i | \(0.672777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.55702 | − | 6.17855i | −0.159822 | − | 0.216691i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.6815 | 1.35495 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.55318 | −0.334223 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.7524 | − | 3.94224i | −0.445604 | − | 0.137753i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.8502i | 0.518276i | 0.965840 | + | 0.259138i | \(0.0834385\pi\) | ||||
−0.965840 | + | 0.259138i | \(0.916561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3.59778i | − | 0.125411i | −0.998032 | − | 0.0627053i | \(-0.980027\pi\) | ||
0.998032 | − | 0.0627053i | \(-0.0199728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.08385 | − | 0.799400i | 0.0377348 | − | 0.0278315i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.66698 | −0.162287 | −0.0811434 | − | 0.996702i | \(-0.525857\pi\) | ||||
−0.0811434 | + | 0.996702i | \(0.525857\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.73560 | 0.0950115 | 0.0475057 | − | 0.998871i | \(-0.484873\pi\) | ||||
0.0475057 | + | 0.998871i | \(0.484873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.3235 | + | 12.7771i | −0.600946 | + | 0.443231i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.81143i | − | 0.201354i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 72.8464i | 2.52095i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.1776 | − | 9.48150i | 0.939395 | − | 0.327729i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.7235 | 1.12974 | 0.564871 | − | 0.825179i | \(-0.308926\pi\) | ||||
0.564871 | + | 0.825179i | \(0.308926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5227 | 0.431818 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.54580 | − | 7.51917i | −0.191008 | − | 0.258974i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 11.3352i | − | 0.389943i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.9614i | − | 0.410999i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.1181 | + | 31.3442i | 0.793411 | + | 1.07573i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −78.4809 | −2.69029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.45976 | −0.323896 | −0.161948 | − | 0.986799i | \(-0.551778\pi\) | ||||
−0.161948 | + | 0.986799i | \(0.551778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.6509 | + | 63.5668i | −0.672047 | + | 2.17394i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.27266i | − | 0.248429i | −0.992255 | − | 0.124215i | \(-0.960359\pi\) | ||
0.992255 | − | 0.124215i | \(-0.0396412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.35729i | − | 0.148669i | −0.997233 | − | 0.0743344i | \(-0.976317\pi\) | ||
0.997233 | − | 0.0743344i | \(-0.0236832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.16259 | − | 2.33259i | 0.107781 | − | 0.0794944i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.3967 | −0.932596 | −0.466298 | − | 0.884628i | \(-0.654413\pi\) | ||||
−0.466298 | + | 0.884628i | \(0.654413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.08575 | 0.240923 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.39392 | + | 1.02809i | −0.0473401 | + | 0.0349159i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.183643i | 0.00622966i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 21.4248i | − | 0.725952i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.2275 | − | 55.7276i | 0.583063 | − | 1.88609i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.29811 | 0.0438842 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.3046 | −0.516800 | −0.258400 | − | 0.966038i | \(-0.583195\pi\) | ||||
−0.258400 | + | 0.966038i | \(0.583195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.31445 | + | 11.2730i | 0.280439 | + | 0.380228i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.8324i | 1.77997i | 0.455990 | + | 0.889985i | \(0.349285\pi\) | ||||
−0.455990 | + | 0.889985i | \(0.650715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.6903i | − | 1.30203i | −0.759065 | − | 0.651015i | \(-0.774343\pi\) | ||
0.759065 | − | 0.651015i | \(-0.225657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.09247 | − | 5.54870i | −0.137567 | − | 0.186517i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.58730 | −0.154026 | −0.0770132 | − | 0.997030i | \(-0.524538\pi\) | ||||
−0.0770132 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.2064 | 0.577082 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.25154 | + | 0.855557i | 0.0419280 | + | 0.0286622i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 19.5426i | − | 0.653968i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.8230i | 0.996874i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.7259 | + | 31.5127i | −1.42658 | + | 1.05218i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.4860 | −0.749950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.96479 | −0.198716 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.02987 | − | 1.49714i | 0.0675498 | − | 0.0498217i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 49.8257i | − | 1.65626i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 4.05385i | − | 0.134606i | −0.997733 | − | 0.0673030i | \(-0.978561\pi\) | ||
0.997733 | − | 0.0673030i | \(-0.0214394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.38480 | + | 2.59206i | 0.278106 | + | 0.0859732i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.2276 | 1.63098 | 0.815491 | − | 0.578769i | \(-0.196467\pi\) | ||||
0.815491 | + | 0.578769i | \(0.196467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.13273 | −0.0705830 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.7762 | + | 37.6598i | 0.918251 | + | 1.24499i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.06130i | 0.299230i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.6754i | 0.780981i | 0.920607 | + | 0.390490i | \(0.127695\pi\) | ||||
−0.920607 | + | 0.390490i | \(0.872305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.73366 | − | 2.35054i | −0.0571259 | − | 0.0774531i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.3096 | −1.49138 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.2344 | 1.58594 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.3915 | + | 6.61292i | 0.702588 | + | 0.217197i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.29926i | − | 0.272290i | −0.990689 | − | 0.136145i | \(-0.956529\pi\) | ||
0.990689 | − | 0.136145i | \(-0.0434713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 41.5637i | − | 1.36219i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.5147 | + | 14.3932i | −0.638883 | + | 0.471211i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.522349 | 0.0170826 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2859 | −0.597373 | −0.298687 | − | 0.954351i | \(-0.596549\pi\) | ||||
−0.298687 | + | 0.954351i | \(0.596549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.3210 | − | 7.61230i | 0.336813 | − | 0.248418i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.3824i | 0.892639i | 0.894874 | + | 0.446320i | \(0.147266\pi\) | ||||
−0.894874 | + | 0.446320i | \(0.852734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.6303i | − | 0.508993i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.78652 | − | 16.5864i | −0.188235 | − | 0.539554i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.16508 | −0.0703556 | −0.0351778 | − | 0.999381i | \(-0.511200\pi\) | ||||
−0.0351778 | + | 0.999381i | \(0.511200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0088 | −0.357362 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.1870 | − | 30.0819i | −0.719464 | − | 0.975472i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2985i | 1.46736i | 0.679495 | + | 0.733680i | \(0.262199\pi\) | ||||
−0.679495 | + | 0.733680i | \(0.737801\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.189140i | − | 0.00612044i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.702973 | − | 0.953112i | −0.0227239 | − | 0.0308097i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.2347 | −0.491954 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.314081 | 0.0101317 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.65689 | − | 24.7685i | 0.246740 | − | 0.798155i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.5304i | 1.43348i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.6736i | − | 0.761291i | −0.924721 | − | 0.380645i | \(-0.875702\pi\) | ||
0.924721 | − | 0.380645i | \(-0.124298\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.96941 | + | 7.35299i | −0.320263 | + | 0.236212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.8717 | 1.92137 | 0.960686 | − | 0.277636i | \(-0.0895508\pi\) | ||||
0.960686 | + | 0.277636i | \(0.0895508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.18168 | −0.0378831 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.2594 | − | 19.3677i | 0.840973 | − | 0.620264i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 11.2749i | − | 0.360717i | −0.983601 | − | 0.180359i | \(-0.942274\pi\) | ||
0.983601 | − | 0.180359i | \(-0.0577258\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.37927i | − | 0.0440817i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0745 | − | 32.5890i | 0.321654 | − | 1.04049i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.9095 | 1.30481 | 0.652405 | − | 0.757871i | \(-0.273760\pi\) | ||||
0.652405 | + | 0.757871i | \(0.273760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.7776 | −1.29928 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.06264 | + | 4.15243i | 0.0974850 | + | 0.132173i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.0321i | − | 0.319003i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.1635i | − | 1.33937i | −0.742647 | − | 0.669683i | \(-0.766430\pi\) | ||
0.742647 | − | 0.669683i | \(-0.233570\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.46415 | + | 1.98514i | 0.0464635 | + | 0.0629966i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.9549 | 0.917931 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2484 | 0.324569 | 0.162285 | − | 0.986744i | \(-0.448114\pi\) | ||||
0.162285 | + | 0.986744i | \(0.448114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.8853 | + | 51.2661i | 0.565866 | + | 1.62199i |
(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 | 816.2.e.c.239.17 | yes | 20 | |
3.2 | odd | 2 | inner | 816.2.e.c.239.3 | ✓ | 20 | |
4.3 | odd | 2 | inner | 816.2.e.c.239.4 | yes | 20 | |
12.11 | even | 2 | inner | 816.2.e.c.239.18 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
816.2.e.c.239.3 | ✓ | 20 | 3.2 | odd | 2 | inner | |
816.2.e.c.239.4 | yes | 20 | 4.3 | odd | 2 | inner | |
816.2.e.c.239.17 | yes | 20 | 1.1 | even | 1 | trivial | |
816.2.e.c.239.18 | yes | 20 | 12.11 | even | 2 | inner |