Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Character | \(\chi\) | \(=\) | 1148.113 |
Dual form | 1148.2.ba.a.701.20 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | ||||||||
\(3\) | − | 3.08866i | − | 1.78324i | −0.452787 | − | 0.891619i | \(-0.649570\pi\) | ||
0.452787 | − | 0.891619i | \(-0.350430\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.11364 | − | 3.42744i | −0.498036 | − | 1.53280i | −0.812172 | − | 0.583418i | \(-0.801715\pi\) |
0.314136 | − | 0.949378i | \(-0.398285\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | − | 0.809017i | −0.222162 | − | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.53981 | −2.17994 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.51230 | + | 1.79105i | 1.66202 | + | 0.540023i | 0.981294 | − | 0.192515i | \(-0.0616642\pi\) |
0.680726 | + | 0.732538i | \(0.261664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.99429 | + | 5.49767i | −1.10782 | + | 1.52478i | −0.283222 | + | 0.959054i | \(0.591403\pi\) |
−0.824594 | + | 0.565725i | \(0.808597\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.5862 | + | 3.43966i | −2.73334 | + | 0.888116i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.22070 | − | 1.69631i | −1.26621 | − | 0.411415i | −0.402504 | − | 0.915418i | \(-0.631860\pi\) |
−0.863702 | + | 0.504003i | \(0.831860\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80765 | − | 2.48802i | −0.414704 | − | 0.570791i | 0.549654 | − | 0.835392i | \(-0.314760\pi\) |
−0.964358 | + | 0.264601i | \(0.914760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.49878 | + | 1.81547i | −0.545278 | + | 0.396168i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.09184 | − | 0.793269i | −0.227665 | − | 0.165408i | 0.468105 | − | 0.883673i | \(-0.344937\pi\) |
−0.695770 | + | 0.718265i | \(0.744937\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.46203 | + | 4.69494i | −1.29241 | + | 0.938988i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.9333i | 2.10411i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.05917 | − | 2.94350i | 1.68225 | − | 0.546595i | 0.696901 | − | 0.717168i | \(-0.254562\pi\) |
0.985345 | + | 0.170573i | \(0.0545618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41863 | − | 4.36610i | 0.254794 | − | 0.784176i | −0.739076 | − | 0.673622i | \(-0.764738\pi\) |
0.993870 | − | 0.110554i | \(-0.0352624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.53195 | − | 17.0256i | 0.962990 | − | 2.96378i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.11827 | + | 2.91555i | −0.358053 | + | 0.492818i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00424 | − | 3.09074i | −0.165096 | − | 0.508115i | 0.833947 | − | 0.551845i | \(-0.186076\pi\) |
−0.999043 | + | 0.0437299i | \(0.986076\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.9804 | + | 12.3370i | 2.71904 | + | 1.97550i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.06447 | + | 2.05480i | −0.947111 | + | 0.320906i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.450967 | − | 0.327647i | −0.0687718 | − | 0.0499657i | 0.552868 | − | 0.833269i | \(-0.313533\pi\) |
−0.621640 | + | 0.783303i | \(0.713533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.28300 | + | 22.4148i | 1.08569 | + | 3.34140i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.526001 | + | 0.723978i | −0.0767251 | + | 0.105603i | −0.845655 | − | 0.533730i | \(-0.820790\pi\) |
0.768930 | + | 0.639334i | \(0.220790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | + | 0.951057i | −0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23932 | + | 16.1250i | −0.733651 | + | 2.25795i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.67195 | − | 1.84293i | 0.779103 | − | 0.253146i | 0.107646 | − | 0.994189i | \(-0.465669\pi\) |
0.671457 | + | 0.741043i | \(0.265669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 20.8876i | − | 2.81649i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.68464 | + | 5.58322i | −1.01786 | + | 0.739516i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.983245 | + | 0.714369i | 0.128008 | + | 0.0930029i | 0.649947 | − | 0.759980i | \(-0.274791\pi\) |
−0.521939 | + | 0.852983i | \(0.674791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.69686 | + | 1.23284i | −0.217261 | + | 0.157849i | −0.691093 | − | 0.722766i | \(-0.742870\pi\) |
0.473832 | + | 0.880615i | \(0.342870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.84400 | + | 5.29082i | 0.484299 | + | 0.666580i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.2911 | + | 7.56774i | 2.88891 | + | 0.938663i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.1189 | + | 4.58751i | −1.72490 | + | 0.560454i | −0.992697 | − | 0.120633i | \(-0.961508\pi\) |
−0.732203 | + | 0.681087i | \(0.761508\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.45014 | + | 3.37232i | −0.294962 | + | 0.405980i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.947422 | + | 0.307836i | 0.112438 | + | 0.0365334i | 0.364696 | − | 0.931127i | \(-0.381173\pi\) |
−0.252257 | + | 0.967660i | \(0.581173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.86712 | 0.803736 | 0.401868 | − | 0.915698i | \(-0.368361\pi\) | ||||
0.401868 | + | 0.915698i | \(0.368361\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.5011 | + | 19.9590i | 1.67444 | + | 2.30467i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.79105 | − | 5.51230i | −0.204110 | − | 0.628185i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.78933i | − | 0.876368i | −0.898885 | − | 0.438184i | \(-0.855622\pi\) | ||
0.898885 | − | 0.438184i | \(-0.144378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.1497 | 1.57219 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.588419 | 0.0645874 | 0.0322937 | − | 0.999478i | \(-0.489719\pi\) | ||||
0.0322937 | + | 0.999478i | \(0.489719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.7827i | 2.14573i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.09148 | − | 27.9807i | −0.974708 | − | 2.99984i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.21580 | − | 9.93170i | −0.764874 | − | 1.05276i | −0.996793 | − | 0.0800232i | \(-0.974501\pi\) |
0.231919 | − | 0.972735i | \(-0.425499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.79549 | 0.712361 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.4854 | − | 4.38167i | −1.39837 | − | 0.454358i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.51445 | + | 8.96638i | −0.668369 | + | 0.919931i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0390 | − | 4.23662i | 1.32391 | − | 0.430164i | 0.440073 | − | 0.897962i | \(-0.354953\pi\) |
0.883835 | + | 0.467798i | \(0.154953\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.0494 | − | 11.7132i | −3.62310 | − | 1.17722i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.80734 | − | 10.7459i | −0.776859 | − | 1.06926i | −0.995621 | − | 0.0934771i | \(-0.970202\pi\) |
0.218762 | − | 0.975778i | \(-0.429798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.74355 | + | 2.71985i | −0.368863 | + | 0.267994i | −0.756739 | − | 0.653717i | \(-0.773209\pi\) |
0.387877 | + | 0.921711i | \(0.373209\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.00514 | + | 6.54262i | 0.878812 | + | 0.638494i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.40007 | + | 3.92338i | −0.522044 | + | 0.379287i | −0.817373 | − | 0.576108i | \(-0.804571\pi\) |
0.295329 | + | 0.955396i | \(0.404571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.4780i | − | 1.38675i | −0.720579 | − | 0.693373i | \(-0.756124\pi\) | ||
0.720579 | − | 0.693373i | \(-0.243876\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.54624 | + | 3.10176i | −0.906089 | + | 0.294406i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.81046 | + | 5.57203i | −0.170314 | + | 0.524173i | −0.999389 | − | 0.0349655i | \(-0.988868\pi\) |
0.829074 | + | 0.559138i | \(0.188868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50296 | + | 4.62563i | −0.140152 | + | 0.431343i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.1219 | − | 35.9537i | 2.41497 | − | 3.32392i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.69631 | + | 5.22070i | 0.155500 | + | 0.478581i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.2784 | + | 13.2800i | 1.66167 | + | 1.20727i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.34657 | + | 18.7311i | 0.572251 | + | 1.68892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.71025 | + | 6.32836i | 0.779068 | + | 0.566026i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.64879 | − | 5.07444i | −0.146306 | − | 0.450284i | 0.850871 | − | 0.525375i | \(-0.176075\pi\) |
−0.997177 | + | 0.0750916i | \(0.976075\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.01199 | + | 1.39288i | −0.0891007 | + | 0.122637i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.23259 | + | 9.94890i | −0.282433 | + | 0.869240i | 0.704723 | + | 0.709482i | \(0.251071\pi\) |
−0.987156 | + | 0.159757i | \(0.948929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.950339 | + | 2.92484i | −0.0824049 | + | 0.253616i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 37.4731 | − | 12.1757i | 3.22517 | − | 1.04792i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7209i | 0.915945i | 0.888966 | + | 0.457972i | \(0.151424\pi\) | ||||
−0.888966 | + | 0.457972i | \(0.848576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.194030 | + | 0.140971i | −0.0164574 | + | 0.0119570i | −0.595984 | − | 0.802997i | \(-0.703238\pi\) |
0.579526 | + | 0.814954i | \(0.303238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.23612 | + | 1.62464i | 0.188315 | + | 0.136819i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.8643 | + | 23.1508i | −2.66463 | + | 1.93597i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.1773 | − | 27.7717i | −1.67564 | − | 2.30632i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.93749 | + | 0.954448i | 0.242280 | + | 0.0787215i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.51263 | − | 2.76592i | 0.697382 | − | 0.226593i | 0.0611923 | − | 0.998126i | \(-0.480510\pi\) |
0.636189 | + | 0.771533i | \(0.280510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.28301 | + | 8.64782i | −0.511304 | + | 0.703750i | −0.984139 | − | 0.177402i | \(-0.943231\pi\) |
0.472834 | + | 0.881151i | \(0.343231\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.1424 | + | 11.0935i | 2.76025 | + | 0.896859i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5444 | −1.32888 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.66886 | − | 7.80252i | −0.452424 | − | 0.622709i | 0.520492 | − | 0.853867i | \(-0.325749\pi\) |
−0.972916 | + | 0.231158i | \(0.925749\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.69218 | − | 17.5187i | −0.451419 | − | 1.38933i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.34959i | 0.106363i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.26336 | −0.490584 | −0.245292 | − | 0.969449i | \(-0.578884\pi\) | ||||
−0.245292 | + | 0.969449i | \(0.578884\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −64.5148 | −5.02247 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.0521509i | − | 0.00403556i | −0.999998 | − | 0.00201778i | \(-0.999358\pi\) | ||
0.999998 | − | 0.00201778i | \(-0.000642280\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2528 | − | 31.5548i | −0.788676 | − | 2.42729i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.8217 | + | 16.2712i | 0.904028 | + | 1.24429i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.63737 | 0.428601 | 0.214301 | − | 0.976768i | \(-0.431253\pi\) | ||||
0.214301 | + | 0.976768i | \(0.431253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.59658 | + | 2.46828i | 0.574247 | + | 0.186584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.20644 | − | 3.03691i | 0.165846 | − | 0.228268i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.1755 | + | 5.25574i | −1.20901 | + | 0.392832i | −0.843069 | − | 0.537805i | \(-0.819254\pi\) |
−0.365944 | + | 0.930637i | \(0.619254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.83006 | + | 2.86906i | 0.656333 | + | 0.213256i | 0.618205 | − | 0.786017i | \(-0.287860\pi\) |
0.0381286 | + | 0.999273i | \(0.487860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.80782 | + | 5.24102i | 0.281482 | + | 0.387427i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.47495 | + | 6.88396i | −0.696612 | + | 0.506118i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.7399 | − | 18.7011i | −1.88229 | − | 1.36756i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.84519 | − | 6.42641i | 0.643393 | − | 0.467453i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.62787i | 0.190146i | 0.995470 | + | 0.0950730i | \(0.0303084\pi\) | ||||
−0.995470 | + | 0.0950730i | \(0.969692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.1014 | + | 6.20643i | −1.37495 | + | 0.446749i | −0.901006 | − | 0.433806i | \(-0.857170\pi\) |
−0.473945 | + | 0.880555i | \(0.657170\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.3742 | − | 71.9383i | 1.67386 | − | 5.15161i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.44774 | + | 4.45569i | −0.103147 | + | 0.317455i | −0.989291 | − | 0.145955i | \(-0.953374\pi\) |
0.886144 | + | 0.463410i | \(0.153374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.61905 | − | 10.4867i | 0.540100 | − | 0.743384i | −0.448528 | − | 0.893769i | \(-0.648051\pi\) |
0.988627 | + | 0.150385i | \(0.0480514\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.1693 | + | 43.6085i | 0.999423 | + | 3.07591i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.70619 | − | 5.59888i | −0.540869 | − | 0.392964i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7963 | + | 18.4973i | 0.963578 | + | 1.29191i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.14043 | + | 5.18783i | 0.496294 | + | 0.360579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.50814 | − | 16.9523i | −0.381006 | − | 1.17262i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.17972 | − | 12.6348i | 0.631958 | − | 0.869816i | −0.366197 | − | 0.930538i | \(-0.619340\pi\) |
0.998155 | + | 0.0607217i | \(0.0193402\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.950800 | − | 2.92626i | 0.0651477 | − | 0.200504i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.620773 | + | 1.91054i | −0.0423363 | + | 0.130298i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.36610 | + | 1.41863i | −0.296390 | + | 0.0963031i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 21.2102i | − | 1.43325i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.1787 | − | 21.9261i | 2.03004 | − | 1.47491i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.61478 | − | 4.07938i | −0.375994 | − | 0.273175i | 0.383698 | − | 0.923459i | \(-0.374650\pi\) |
−0.759692 | + | 0.650283i | \(0.774650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 42.2605 | − | 30.7040i | 2.81736 | − | 2.04694i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.24608 | − | 8.59699i | −0.414567 | − | 0.570602i | 0.549758 | − | 0.835324i | \(-0.314720\pi\) |
−0.964325 | + | 0.264722i | \(0.914720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.60206 | − | 1.82022i | −0.370195 | − | 0.120284i | 0.118011 | − | 0.993012i | \(-0.462348\pi\) |
−0.488205 | + | 0.872729i | \(0.662348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.0256 | + | 5.53195i | −1.12020 | + | 0.363976i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1101 | − | 22.1737i | 1.05541 | − | 1.45265i | 0.171385 | − | 0.985204i | \(-0.445176\pi\) |
0.884024 | − | 0.467441i | \(-0.154824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.06717 | + | 0.996583i | 0.200080 | + | 0.0650099i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.0586 | −1.56277 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.49791 | + | 10.3200i | 0.484999 | + | 0.667544i | 0.979456 | − | 0.201658i | \(-0.0646329\pi\) |
−0.494457 | + | 0.869202i | \(0.664633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.29045 | + | 10.1270i | 0.211957 | + | 0.652336i | 0.999356 | + | 0.0358920i | \(0.0114272\pi\) |
−0.787399 | + | 0.616444i | \(0.788573\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 10.9037i | − | 0.699475i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.60382 | 0.230240 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.8986 | 1.32975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.81743i | − | 0.115175i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.03354 | + | 15.4916i | 0.317714 | + | 0.977823i | 0.974623 | + | 0.223853i | \(0.0718636\pi\) |
−0.656909 | + | 0.753970i | \(0.728136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.59777 | − | 6.32828i | −0.289059 | − | 0.397856i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 61.1020 | 3.82635 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.42559 | + | 1.76288i | 0.338439 | + | 0.109965i | 0.473306 | − | 0.880898i | \(-0.343061\pi\) |
−0.134867 | + | 0.990864i | \(0.543061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.91018 | + | 2.62914i | −0.118693 | + | 0.163367i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −59.2453 | + | 19.2499i | −3.66719 | + | 1.19154i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.07699 | − | 1.97453i | −0.374723 | − | 0.121755i | 0.115600 | − | 0.993296i | \(-0.463121\pi\) |
−0.490323 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.6330 | − | 17.3879i | −0.776042 | − | 1.06813i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.6756 | + | 22.2871i | −1.87732 | + | 1.36395i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.12042 | − | 4.44675i | −0.373169 | − | 0.271123i | 0.385355 | − | 0.922768i | \(-0.374079\pi\) |
−0.758524 | + | 0.651645i | \(0.774079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7073 | − | 18.6774i | 1.56161 | − | 1.13457i | 0.626929 | − | 0.779077i | \(-0.284312\pi\) |
0.934678 | − | 0.355497i | \(-0.115688\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 20.9890i | − | 1.27031i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −44.0296 | + | 14.3061i | −2.65508 | + | 0.862688i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.57383 | − | 4.84374i | 0.0945620 | − | 0.291032i | −0.892577 | − | 0.450894i | \(-0.851105\pi\) |
0.987139 | + | 0.159862i | \(0.0511051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.27759 | + | 28.5535i | −0.555435 | + | 1.70945i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.02831 | + | 8.29726i | −0.359619 | + | 0.494973i | −0.950043 | − | 0.312120i | \(-0.898961\pi\) |
0.590424 | + | 0.807094i | \(0.298961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.86290 | + | 14.9665i | 0.289069 | + | 0.889664i | 0.985149 | + | 0.171700i | \(0.0549259\pi\) |
−0.696080 | + | 0.717964i | \(0.745074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 27.6941 | + | 20.1209i | 1.64046 | + | 1.19186i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.22697 | + | 3.69848i | 0.308539 | + | 0.218314i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.6250 | + | 7.71948i | 0.624997 | + | 0.454087i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.0855 | − | 40.2730i | −0.767085 | − | 2.36084i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.17093 | − | 8.49355i | 0.360509 | − | 0.496199i | −0.589781 | − | 0.807563i | \(-0.700786\pi\) |
0.950291 | + | 0.311365i | \(0.100786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.35347 | − | 4.16556i | 0.0788022 | − | 0.242528i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.5821 | + | 60.2674i | −1.13627 | + | 3.49707i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.72226 | − | 2.83403i | 0.504421 | − | 0.163896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.557426i | 0.0321295i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.1904 | + | 24.1142i | −1.90674 | + | 1.38533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.11518 | + | 4.44294i | 0.350154 | + | 0.254402i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0682 | − | 8.04153i | 0.631697 | − | 0.458955i | −0.225291 | − | 0.974292i | \(-0.572333\pi\) |
0.856988 | + | 0.515337i | \(0.172333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.40067 | + | 11.5625i | 0.477898 | + | 0.657770i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0821 | + | 4.25063i | 0.741818 | + | 0.241031i | 0.655457 | − | 0.755233i | \(-0.272476\pi\) |
0.0863610 | + | 0.996264i | \(0.472476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8526 | + | 6.12558i | −1.06561 | + | 0.346238i | −0.788777 | − | 0.614679i | \(-0.789285\pi\) |
−0.276835 | + | 0.960918i | \(0.589285\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.8531 | − | 19.0671i | 0.780533 | − | 1.07431i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.4330 | − | 5.66433i | −0.979136 | − | 0.318140i | −0.224637 | − | 0.974442i | \(-0.572120\pi\) |
−0.754498 | + | 0.656302i | \(0.772120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 55.2088 | 3.09110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1180 | + | 16.6790i | 0.676359 | + | 0.930929i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.21676 | + | 16.0555i | 0.290268 | + | 0.893354i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 54.2791i | − | 3.01086i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −44.7177 | −2.47290 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.894886 | 0.0493367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.7100i | − | 0.588673i | −0.955702 | − | 0.294336i | \(-0.904901\pi\) | ||
0.955702 | − | 0.294336i | \(-0.0950986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.56756 | + | 20.2129i | 0.359900 | + | 1.10766i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.4468 | + | 43.2828i | 1.71812 | + | 2.36479i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.51109 | 0.191261 | 0.0956306 | − | 0.995417i | \(-0.469513\pi\) | ||||
0.0956306 | + | 0.995417i | \(0.469513\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.2101 | + | 5.59190i | 0.934724 | + | 0.303710i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.6399 | − | 21.5264i | 0.846946 | − | 1.16572i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | − | 0.309017i | 0.0513522 | − | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.2870 | + | 4.64213i | 0.769186 | + | 0.249924i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.7538 | − | 20.3069i | −0.792027 | − | 1.09013i | −0.993853 | − | 0.110710i | \(-0.964688\pi\) |
0.201826 | − | 0.979421i | \(-0.435312\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.63687 | − | 4.09543i | 0.301735 | − | 0.219223i | −0.426607 | − | 0.904437i | \(-0.640291\pi\) |
0.728342 | + | 0.685214i | \(0.240291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −60.1074 | − | 43.6706i | −3.20830 | − | 2.33096i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.4333 | + | 14.1191i | −1.03433 | + | 0.751484i | −0.969171 | − | 0.246391i | \(-0.920755\pi\) |
−0.0651587 | + | 0.997875i | \(0.520755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.59005i | − | 0.190540i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.1250 | − | 5.23932i | 0.853423 | − | 0.277294i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.99676 | − | 27.6892i | 0.474831 | − | 1.46138i | −0.371355 | − | 0.928491i | \(-0.621107\pi\) |
0.846186 | − | 0.532888i | \(-0.178893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.94869 | − | 9.07512i | 0.155194 | − | 0.477638i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 41.0174 | − | 56.4556i | 2.15286 | − | 2.96315i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.64751 | − | 23.5366i | −0.400289 | − | 1.23196i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.8398 | − | 18.7737i | −1.34882 | − | 0.979978i | −0.999069 | − | 0.0431371i | \(-0.986265\pi\) |
−0.349755 | − | 0.936841i | \(-0.613735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.6605 | − | 13.4380i | 2.06464 | − | 0.699554i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.82485 | − | 3.50546i | −0.250494 | − | 0.181994i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2834 | − | 31.6489i | −0.532452 | − | 1.63872i | −0.749090 | − | 0.662468i | \(-0.769509\pi\) |
0.216638 | − | 0.976252i | \(-0.430491\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.5462 | − | 26.9030i | 1.00936 | − | 1.38926i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0026 | + | 61.5615i | −1.03018 | + | 3.17058i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.48106 | − | 4.55822i | 0.0760767 | − | 0.234140i | −0.905785 | − | 0.423737i | \(-0.860718\pi\) |
0.981862 | + | 0.189597i | \(0.0607181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6732 | + | 5.09253i | −0.802963 | + | 0.260898i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9334i | 0.967453i | 0.875219 | + | 0.483727i | \(0.160717\pi\) | ||||
−0.875219 | + | 0.483727i | \(0.839283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.8985 | + | 12.2774i | −0.861225 | + | 0.625717i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.94924 | + | 2.14275i | 0.149918 | + | 0.108922i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.70335 | + | 7.04990i | −0.491979 | + | 0.357444i | −0.805945 | − | 0.591990i | \(-0.798342\pi\) |
0.313966 | + | 0.949434i | \(0.398342\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.35455 | + | 5.99352i | 0.220219 | + | 0.303105i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.7288 | + | 9.98438i | 1.55006 | + | 0.503645i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.6974 | + | 8.67452i | −1.34329 | + | 0.436463i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.57860 | + | 13.1838i | −0.480736 | + | 0.661677i | −0.978646 | − | 0.205552i | \(-0.934101\pi\) |
0.497910 | + | 0.867229i | \(0.334101\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.03384 | + | 2.93527i | 0.452258 | + | 0.146947i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.8536 | 0.941506 | 0.470753 | − | 0.882265i | \(-0.343982\pi\) | ||||
0.470753 | + | 0.882265i | \(0.343982\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.3370 | + | 25.2387i | 0.913429 | + | 1.25723i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.7577 | − | 48.4971i | −0.783005 | − | 2.40984i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.8357i | − | 0.933653i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.0194 | 1.87994 | 0.939969 | − | 0.341261i | \(-0.110854\pi\) | ||||
0.939969 | + | 0.341261i | \(0.110854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.1131 | 1.63335 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.21536i | − | 0.0598038i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.655288 | − | 2.01677i | −0.0321668 | − | 0.0989993i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.435411 | + | 0.599292i | 0.0213222 | + | 0.0293474i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.1308 | −1.47199 | −0.735994 | − | 0.676988i | \(-0.763285\pi\) | ||||
−0.735994 | + | 0.676988i | \(0.763285\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.7417 | + | 7.38921i | 1.10836 | + | 0.360128i | 0.805314 | − | 0.592848i | \(-0.201996\pi\) |
0.303046 | + | 0.952976i | \(0.401996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.43995 | − | 4.73468i | 0.167256 | − | 0.230208i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 41.7004 | − | 13.5493i | 2.02277 | − | 0.657237i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.99478 | + | 0.648143i | 0.0965341 | + | 0.0313658i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 71.5049 | + | 98.4181i | 3.45229 | + | 4.75167i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0717 | − | 15.3095i | 1.01499 | − | 0.737434i | 0.0497403 | − | 0.998762i | \(-0.484161\pi\) |
0.965250 | + | 0.261329i | \(0.0841606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.9391 | + | 9.40080i | 0.621813 | + | 0.451774i | 0.853554 | − | 0.521004i | \(-0.174442\pi\) |
−0.231741 | + | 0.972777i | \(0.574442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −85.7774 | + | 62.3209i | −4.11271 | + | 2.98806i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.15048i | 0.198544i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.7978 | + | 3.83335i | −0.563080 | + | 0.182956i | −0.576706 | − | 0.816951i | \(-0.695662\pi\) |
0.0136267 | + | 0.999907i | \(0.495662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.02091 | − | 6.21973i | 0.0962339 | − | 0.296178i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.2867 | − | 37.8147i | 0.583760 | − | 1.79663i | −0.0204335 | − | 0.999791i | \(-0.506505\pi\) |
0.604194 | − | 0.796838i | \(-0.293495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.0044 | + | 35.7921i | −1.23273 | + | 1.69671i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.54298 | − | 26.2926i | −0.404069 | − | 1.24360i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.38106 | − | 6.81574i | −0.442719 | − | 0.321654i | 0.343995 | − | 0.938971i | \(-0.388220\pi\) |
−0.786715 | + | 0.617317i | \(0.788220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.1094 | + | 0.464873i | −1.74741 | + | 0.0218900i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.7102 | + | 19.4061i | 1.25495 | + | 0.911777i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.56774 | − | 23.2911i | −0.354781 | − | 1.09190i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.0394 | − | 31.7110i | 1.07774 | − | 1.48338i | 0.215746 | − | 0.976450i | \(-0.430782\pi\) |
0.861989 | − | 0.506926i | \(-0.169218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.5462 | − | 57.0793i | 0.865662 | − | 2.66423i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1474 | + | 34.3081i | −0.519185 | + | 1.59789i | 0.256350 | + | 0.966584i | \(0.417480\pi\) |
−0.775536 | + | 0.631304i | \(0.782520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9673 | + | 6.16284i | −0.881484 | + | 0.286411i | −0.714573 | − | 0.699561i | \(-0.753379\pi\) |
−0.166911 | + | 0.985972i | \(0.553379\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 51.1000i | 2.36970i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2415 | − | 8.89400i | 0.566471 | − | 0.411565i | −0.267351 | − | 0.963599i | \(-0.586148\pi\) |
0.833821 | + | 0.552034i | \(0.186148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0103 | + | 8.72597i | 0.554583 | + | 0.402928i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.0993 | + | 17.5092i | −1.11044 | + | 0.806780i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.89903 | − | 2.61379i | −0.0873176 | − | 0.120182i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.3622 | + | 7.59085i | 1.07193 | + | 0.348292i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.0935 | + | 12.0524i | −1.69839 | + | 0.551842i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.1346 | − | 16.7019i | 0.554445 | − | 0.763128i | −0.436162 | − | 0.899868i | \(-0.643663\pi\) |
0.990607 | + | 0.136740i | \(0.0436626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.0031 | + | 6.82432i | 0.957659 | + | 0.311162i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.16842 | 0.189670 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.0415 | − | 39.9722i | −1.31871 | − | 1.81504i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.47164 | − | 10.6846i | −0.157315 | − | 0.484165i | 0.841073 | − | 0.540921i | \(-0.181924\pi\) |
−0.998388 | + | 0.0567560i | \(0.981924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.3454i | 0.874828i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.1870 | −1.58797 | −0.793984 | − | 0.607939i | \(-0.791997\pi\) | ||||
−0.793984 | + | 0.607939i | \(0.791997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −52.2883 | −2.35495 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 136.601i | 6.13977i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.307836 | − | 0.947422i | −0.0138083 | − | 0.0424977i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7594 | + | 18.9382i | 0.615957 | + | 0.847792i | 0.997051 | − | 0.0767445i | \(-0.0244526\pi\) |
−0.381094 | + | 0.924536i | \(0.624453\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.161076 | −0.00719636 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.2318 | + | 5.92387i | 0.812915 | + | 0.264132i | 0.685832 | − | 0.727760i | \(-0.259439\pi\) |
0.127083 | + | 0.991892i | \(0.459439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.1362 | + | 38.7262i | −1.25205 | + | 1.72329i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −97.4621 | + | 31.6673i | −4.32844 | + | 1.40640i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8817 | − | 6.45995i | −0.881240 | − | 0.286332i | −0.166768 | − | 0.985996i | \(-0.553333\pi\) |
−0.714472 | + | 0.699664i | \(0.753333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.03639 | − | 5.55562i | −0.178560 | − | 0.245766i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.2022 | − | 19.7635i | 1.20101 | − | 0.872582i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.4911 | + | 9.80183i | 0.594487 | + | 0.431920i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.19616 | + | 3.04869i | −0.184547 | + | 0.134081i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 17.4119i | − | 0.764297i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.190173 | + | 0.0617910i | −0.00833164 | + | 0.00270711i | −0.313180 | − | 0.949694i | \(-0.601394\pi\) |
0.304848 | + | 0.952401i | \(0.401394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.987891 | + | 3.04042i | −0.0431975 | + | 0.132948i | −0.970329 | − | 0.241787i | \(-0.922266\pi\) |
0.927132 | + | 0.374735i | \(0.122266\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.62366 | − | 23.4632i | 0.332724 | − | 1.02402i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.8125 | + | 20.3877i | −0.645243 | + | 0.888101i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.54455 | − | 20.1421i | −0.284546 | − | 0.875741i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.43023 | − | 4.67184i | −0.279048 | − | 0.202741i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.9266 | − | 41.5479i | 0.559915 | − | 1.79964i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.4609 | + | 14.1391i | 0.841366 | + | 0.611289i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.2332 | + | 49.9606i | 0.700513 | + | 2.15596i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.40679 | + | 4.68904i | −0.146741 | + | 0.201971i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.86917 | − | 18.0634i | 0.252335 | − | 0.776608i | −0.742008 | − | 0.670391i | \(-0.766126\pi\) |
0.994343 | − | 0.106217i | \(-0.0338738\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.86155 | − | 27.2730i | 0.380285 | − | 1.17040i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −49.6226 | + | 16.1234i | −2.12560 | + | 0.690649i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6830i | 0.798827i | 0.916771 | + | 0.399414i | \(0.130786\pi\) | ||||
−0.916771 | + | 0.399414i | \(0.869214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.0971 | − | 8.06254i | 0.473614 | − | 0.344101i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.6993 | − | 17.2186i | −1.00963 | − | 0.733536i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.30170 | + | 4.57845i | −0.267976 | + | 0.194696i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.2622 | + | 29.2649i | 0.902529 | + | 1.24223i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.0912 | + | 10.7520i | 1.40212 | + | 0.455576i | 0.909876 | − | 0.414881i | \(-0.136177\pi\) |
0.492244 | + | 0.870457i | \(0.336177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.60259 | − | 1.17055i | 0.152373 | − | 0.0495090i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.7613 | + | 79.5017i | −2.43869 | + | 3.35656i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.130119 | − | 0.0422783i | −0.00548387 | − | 0.00178182i | 0.306274 | − | 0.951943i | \(-0.400918\pi\) |
−0.311758 | + | 0.950162i | \(0.600918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.1140 | 0.888272 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.31697 | − | 11.4473i | −0.349280 | − | 0.480743i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.37158 | − | 19.6097i | −0.267110 | − | 0.822081i | −0.991200 | − | 0.132375i | \(-0.957740\pi\) |
0.724089 | − | 0.689706i | \(-0.242260\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.8896i | − | 0.539415i | −0.962942 | − | 0.269707i | \(-0.913073\pi\) | ||
0.962942 | − | 0.269707i | \(-0.0869269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.11659 | 0.339075 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.7799 | 0.449552 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 16.8202i | − | 0.700232i | −0.936706 | − | 0.350116i | \(-0.886142\pi\) | ||
0.936706 | − | 0.350116i | \(-0.113858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.1695 | + | 58.9978i | 0.796659 | + | 2.45186i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.345864 | − | 0.476041i | −0.0143489 | − | 0.0197495i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.5663 | 1.43159 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −152.319 | − | 49.4916i | −6.29763 | − | 2.04623i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.8657 | + | 16.3318i | −0.489751 | + | 0.674085i | −0.980342 | − | 0.197305i | \(-0.936781\pi\) |
0.490591 | + | 0.871390i | \(0.336781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4274 | + | 4.36281i | −0.553264 | + | 0.179767i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.7621 | + | 4.47158i | 0.566097 | + | 0.183936i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.64751 | + | 2.26760i | 0.0676550 | + | 0.0931192i | 0.841504 | − | 0.540251i | \(-0.181671\pi\) |
−0.773849 | + | 0.633371i | \(0.781671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0045 | − | 11.6280i | 0.656122 | − | 0.476700i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.3899 | − | 23.5326i | −1.32563 | − | 0.963126i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.9662 | − | 18.1390i | 1.02009 | − | 0.741139i | 0.0537894 | − | 0.998552i | \(-0.482870\pi\) |
0.966302 | + | 0.257413i | \(0.0828700\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.74140i | − | 0.315778i | −0.987457 | − | 0.157889i | \(-0.949531\pi\) | ||
0.987457 | − | 0.157889i | \(-0.0504689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 92.3350 | − | 30.0015i | 3.76017 | − | 1.22175i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.1608 | − | 77.4371i | 1.02293 | − | 3.14827i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.24158 | − | 13.0543i | 0.172161 | − | 0.529856i | −0.827332 | − | 0.561713i | \(-0.810142\pi\) |
0.999492 | + | 0.0318577i | \(0.0101423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.2930 | + | 23.8018i | −0.700748 | + | 0.964497i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.87919 | − | 5.78356i | −0.0760240 | − | 0.233978i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.5332 | − | 23.6368i | −1.31400 | − | 0.954679i | −0.999986 | − | 0.00526211i | \(-0.998325\pi\) |
−0.314017 | − | 0.949417i | \(-0.601675\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 57.1318 | − | 42.6122i | 2.30377 | − | 1.71829i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.3053 | + | 8.94035i | 0.495394 | + | 0.359925i | 0.807255 | − | 0.590203i | \(-0.200952\pi\) |
−0.311861 | + | 0.950128i | \(0.600952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.22364 | + | 3.76599i | 0.0491824 | + | 0.151368i | 0.972632 | − | 0.232353i | \(-0.0746424\pi\) |
−0.923449 | + | 0.383721i | \(0.874642\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.67302 | − | 11.9374i | 0.348036 | − | 0.479031i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.79357 | + | 11.6754i | −0.151986 | + | 0.467766i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.351415 | + | 1.08154i | −0.0140566 | + | 0.0432617i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −52.3599 | + | 17.0128i | −2.09105 | + | 0.679424i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.8393i | 0.711301i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.35000 | + | 3.16046i | −0.173171 | + | 0.125816i | −0.670995 | − | 0.741462i | \(-0.734133\pi\) |
0.497824 | + | 0.867278i | \(0.334133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.0246 | − | 28.3530i | −1.55109 | − | 1.12693i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.5562 | + | 11.3022i | −0.617327 | + | 0.448515i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.99429 | − | 5.49767i | −0.158260 | − | 0.217826i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.19596 | − | 2.01319i | −0.245108 | − | 0.0796405i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.838232 | − | 0.272358i | 0.0331082 | − | 0.0107575i | −0.292416 | − | 0.956291i | \(-0.594459\pi\) |
0.325524 | + | 0.945534i | \(0.394459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.28415 | + | 8.64939i | −0.247823 | + | 0.341099i | −0.914747 | − | 0.404027i | \(-0.867610\pi\) |
0.666925 | + | 0.745125i | \(0.267610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.90101 | + | 1.91735i | 0.232352 | + | 0.0754958i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.0227 | 1.88797 | 0.943984 | − | 0.329991i | \(-0.107046\pi\) | ||||
0.943984 | + | 0.329991i | \(0.107046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.14046 | + | 5.69886i | 0.162527 | + | 0.223700i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.38167 | + | 13.4854i | 0.171731 | + | 0.528535i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.12266i | − | 0.122199i | −0.998132 | − | 0.0610995i | \(-0.980539\pi\) | ||
0.998132 | − | 0.0610995i | \(-0.0194607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.6992 | 1.47303 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.9097 | −1.75209 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.1705i | 1.13632i | 0.822918 | + | 0.568161i | \(0.192345\pi\) | ||||
−0.822918 | + | 0.568161i | \(0.807655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.21650 | − | 6.82169i | −0.0862120 | − | 0.265333i | 0.898652 | − | 0.438662i | \(-0.144548\pi\) |
−0.984864 | + | 0.173329i | \(0.944548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −67.7223 | − | 93.2118i | −2.63012 | − | 3.62005i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.0831 | 0.429782 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.2262 | − | 3.97252i | −0.473399 | − | 0.153817i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.5998 | + | 17.3421i | −0.487137 | + | 0.670486i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.5617 | + | 3.75662i | −0.446334 | + | 0.145023i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.3011 | − | 11.7949i | −1.39931 | − | 0.454662i | −0.490339 | − | 0.871532i | \(-0.663127\pi\) |
−0.908966 | + | 0.416870i | \(0.863127\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −51.3310 | − | 70.6511i | −1.97573 | − | 2.71936i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.1359 | − | 25.5277i | 1.35038 | − | 0.981109i | 0.351389 | − | 0.936230i | \(-0.385709\pi\) |
0.998992 | − | 0.0448799i | \(-0.0142905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.0916 | − | 8.05854i | −0.425657 | − | 0.309258i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.5532 | + | 19.2920i | −1.01752 | + | 0.739271i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.0871i | 1.91653i | 0.285880 | + | 0.958265i | \(0.407714\pi\) | ||||
−0.285880 | + | 0.958265i | \(0.592286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.7451 | − | 11.9392i | 1.40396 | − | 0.456173i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.62204 | + | 17.3028i | −0.214494 | + | 0.660145i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.5236 | + | 38.5437i | −0.477112 | + | 1.46840i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3452 | + | 15.6153i | −0.431592 | + | 0.594036i | −0.968318 | − | 0.249721i | \(-0.919661\pi\) |
0.536726 | + | 0.843757i | \(0.319661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.7132 | + | 36.0494i | 0.444946 | + | 1.36940i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.699248 | + | 0.508034i | 0.0265240 | + | 0.0192708i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.1464 | − | 0.440281i | 1.33126 | − | 0.0166768i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −68.4869 | − | 49.7586i | −2.59041 | − | 1.88204i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.83745 | + | 24.1212i | 0.296016 | + | 0.911045i | 0.982878 | + | 0.184257i | \(0.0589878\pi\) |
−0.686862 | + | 0.726788i | \(0.741012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.87451 | + | 8.08556i | −0.221561 | + | 0.304953i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.07810 | − | 9.47343i | 0.115928 | − | 0.356790i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.10456 | + | 12.6325i | −0.154368 | + | 0.475096i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.05474 | − | 2.29223i | 0.264946 | − | 0.0860863i | −0.173531 | − | 0.984828i | \(-0.555518\pi\) |
0.438478 | + | 0.898742i | \(0.355518\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.9407i | 1.91043i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.01242 | + | 3.64174i | −0.187717 | + | 0.136384i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 114.833 | + | 83.4313i | 4.29452 | + | 3.12015i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.8749 | − | 23.1585i | 1.19039 | − | 0.864869i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5848 | + | 14.5687i | 0.394747 | + | 0.543323i | 0.959416 | − | 0.281995i | \(-0.0909961\pi\) |
−0.564669 | + | 0.825318i | \(0.690996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.40080 | + | 1.42991i | 0.163894 | + | 0.0532525i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.2788 | − | 10.1631i | 1.16327 | − | 0.377969i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −44.7211 | + | 61.5533i | −1.66090 | + | 2.28603i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.90835 | − | 3.21942i | −0.367480 | − | 0.119402i | 0.119455 | − | 0.992840i | \(-0.461885\pi\) |
−0.486935 | + | 0.873438i | \(0.661885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.77112 | 0.324856 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.79857 | + | 2.47552i | 0.0665227 | + | 0.0915606i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3805 | + | 31.9479i | 0.383413 | + | 1.18002i | 0.937625 | + | 0.347648i | \(0.113020\pi\) |
−0.554212 | + | 0.832375i | \(0.686980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 11.1310i | − | 0.410572i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −86.0442 | −3.16948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.7297 | −0.578626 | −0.289313 | − | 0.957234i | \(-0.593427\pi\) | ||||
−0.289313 | + | 0.957234i | \(0.593427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 64.5486i | − | 2.37125i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.37989 | + | 13.4799i | 0.160683 | + | 0.494531i | 0.998692 | − | 0.0511250i | \(-0.0162807\pi\) |
−0.838010 | + | 0.545656i | \(0.816281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9600 | − | 26.0962i | −0.694642 | − | 0.956092i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.84815 | −0.140796 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.34816 | + | 2.06264i | 0.231957 | + | 0.0753673i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.06974 | + | 11.1071i | −0.294469 | + | 0.405302i | −0.930459 | − | 0.366395i | \(-0.880592\pi\) |
0.635990 | + | 0.771697i | \(0.280592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 47.8483 | − | 15.5469i | 1.74369 | − | 0.566559i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.6369 | + | 11.9040i | 1.33335 | + | 0.433232i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.09793 | + | 11.1458i | 0.294324 | + | 0.405103i | 0.930413 | − | 0.366513i | \(-0.119449\pi\) |
−0.636088 | + | 0.771616i | \(0.719449\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.5459 | + | 14.2009i | −0.709471 | + | 0.515461i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.97524 | − | 5.79435i | −0.289102 | − | 0.210045i | 0.433776 | − | 0.901021i | \(-0.357181\pi\) |
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.7130 | + | 8.50998i | −0.424039 | + | 0.308082i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 129.375i | − | 4.67756i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.85473 | + | 2.55216i | −0.283618 | + | 0.0921530i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.42688 | − | 29.0130i | 0.339942 | − | 1.04623i | −0.624294 | − | 0.781189i | \(-0.714613\pi\) |
0.964236 | − | 0.265045i | \(-0.0853867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.44493 | − | 16.7578i | 0.196095 | − | 0.603517i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.9674 | − | 23.3537i | 0.610276 | − | 0.839973i | −0.386324 | − | 0.922363i | \(-0.626255\pi\) |
0.996600 | + | 0.0823902i | \(0.0262554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.3314 | + | 34.8743i | 0.407034 | + | 1.25272i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.12052 | + | 5.89990i | 0.291322 | + | 0.211658i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0748 | + | 11.3742i | 0.575941 | + | 0.407522i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.67112 | + | 3.39377i | 0.167146 | + | 0.121439i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.1821 | + | 99.0463i | 1.15009 | + | 3.53963i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4295 | + | 28.1189i | −0.729162 | + | 1.00361i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.10451 | − | 9.55471i | 0.110664 | − | 0.340589i | −0.880354 | − | 0.474317i | \(-0.842695\pi\) |
0.991018 | + | 0.133728i | \(0.0426950\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.09866 | + | 18.7697i | −0.217118 | + | 0.668220i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.57203 | − | 1.81046i | 0.198119 | − | 0.0643727i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 14.2531i | − | 0.506142i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −53.7053 | + | 39.0192i | −1.90473 | + | 1.38387i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.87960 | − | 4.99832i | −0.243688 | − | 0.177050i | 0.459237 | − | 0.888314i | \(-0.348123\pi\) |
−0.702925 | + | 0.711264i | \(0.748123\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.97418 | − | 2.88741i | 0.140597 | − | 0.102149i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.1900 | + | 64.9514i | 1.66738 | + | 2.29495i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.8536 | + | 12.2994i | 1.33583 | + | 0.434036i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.62563 | − | 1.50296i | 0.163032 | − | 0.0529724i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.7345 | + | 18.9039i | −0.483477 | + | 0.665448i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.49185 | + | 1.78441i | 0.193083 | + | 0.0627365i | 0.403962 | − | 0.914776i | \(-0.367633\pi\) |
−0.210879 | + | 0.977512i | \(0.567633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2439 | 1.13224 | 0.566118 | − | 0.824324i | \(-0.308445\pi\) | ||||
0.566118 | + | 0.824324i | \(0.308445\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.6882 | − | 79.4010i | −2.02321 | − | 2.78471i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.97514 | + | 21.4673i | 0.244328 | + | 0.751965i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.71429i | 0.0599753i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −44.4412 | −1.55290 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.96747 | 0.243166 | 0.121583 | − | 0.992581i | \(-0.461203\pi\) | ||||
0.121583 | + | 0.992581i | \(0.461203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 8.25033i | − | 0.287588i | −0.989608 | − | 0.143794i | \(-0.954070\pi\) | ||
0.989608 | − | 0.143794i | \(-0.0459303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 44.1866 | + | 135.992i | 1.53838 | + | 4.73464i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.6976 | + | 38.1225i | 0.963141 | + | 1.32565i | 0.945437 | + | 0.325806i | \(0.105636\pi\) |
0.0177044 | + | 0.999843i | \(0.494364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.56730 | −0.297555 | −0.148777 | − | 0.988871i | \(-0.547534\pi\) | ||||
−0.148777 | + | 0.988871i | \(0.547534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9607 | − | 4.86101i | −0.518979 | − | 0.168627i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.22657 | − | 4.44099i | 0.111794 | − | 0.153871i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.178744 | + | 0.0580774i | −0.00618569 | + | 0.00200985i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 47.7358 | + | 15.5103i | 1.64999 | + | 0.536114i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.7018 | − | 27.1172i | −0.680182 | − | 0.936190i | 0.319754 | − | 0.947500i | \(-0.396400\pi\) |
−0.999936 | + | 0.0113108i | \(0.996400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.9429 | − | 36.2856i | 1.72217 | − | 1.25123i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.6274 | + | 18.6194i | 0.882655 | + | 0.641286i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −96.7342 | + | 70.2815i | −3.32776 | + | 2.41776i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.5933i | − | 0.776315i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.2263 | − | 15.0198i | 1.58648 | − | 0.515479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.35532 | + | 4.17123i | −0.0464596 | + | 0.142988i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.07934 | − | 15.6326i | 0.173913 | − | 0.535250i | −0.825669 | − | 0.564155i | \(-0.809202\pi\) |
0.999582 | + | 0.0289048i | \(0.00920197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 42.6033 | − | 58.6384i | 1.45700 | − | 2.00539i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.36135 | + | 28.8113i | 0.319778 | + | 0.984174i | 0.973743 | + | 0.227650i | \(0.0731041\pi\) |
−0.653965 | + | 0.756524i | \(0.726896\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.73587 | + | 6.34698i | 0.298064 | + | 0.216556i | 0.726758 | − | 0.686893i | \(-0.241026\pi\) |
−0.428694 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4233 | − | 16.1443i | 0.389306 | − | 0.550197i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.9628 | + | 18.8631i | 0.883785 | + | 0.642108i | 0.934250 | − | 0.356618i | \(-0.116070\pi\) |
−0.0504648 | + | 0.998726i | \(0.516070\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.27800 | − | 19.3217i | −0.213459 | − | 0.656958i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.8428 | − | 32.8169i | 0.809745 | − | 1.11452i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9511 | − | 42.9371i | 0.473259 | − | 1.45654i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1744 | − | 95.9450i | 1.05630 | − | 3.25097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −85.2725 | + | 27.7067i | −2.88604 | + | 0.937730i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 10.7665i | − | 0.363973i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.2274 | − | 18.3288i | 0.851870 | − | 0.618920i | −0.0737910 | − | 0.997274i | \(-0.523510\pi\) |
0.925661 | + | 0.378354i | \(0.123510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.2337 | − | 19.0599i | −0.884840 | − | 0.642874i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.8844 | − | 12.2672i | 0.568849 | − | 0.413293i | −0.265838 | − | 0.964018i | \(-0.585649\pi\) |
0.834687 | + | 0.550725i | \(0.185649\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.86804 | + | 5.32390i | 0.130170 | + | 0.179163i | 0.869127 | − | 0.494589i | \(-0.164681\pi\) |
−0.738957 | + | 0.673752i | \(0.764681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.8660 | − | 4.18041i | −0.432486 | − | 0.140523i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.9929 | − | 6.17118i | 0.637721 | − | 0.207208i | 0.0277286 | − | 0.999615i | \(-0.491173\pi\) |
0.609992 | + | 0.792407i | \(0.291173\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.13618 | + | 4.31658i | −0.105184 | + | 0.144773i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 77.9973 | + | 25.3428i | 2.61301 | + | 0.849017i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.75210 | 0.0920955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0274 | + | 49.5875i | 1.20426 | + | 1.65753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.75336 | − | 26.9401i | −0.292266 | − | 0.899503i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 43.7290i | − | 1.45845i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.7377 | −1.09065 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.72170 | 0.0572945 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 33.4596i | − | 1.11223i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.79856 | − | 8.61308i | −0.0929246 | − | 0.285993i | 0.893783 | − | 0.448500i | \(-0.148042\pi\) |
−0.986707 | + | 0.162508i | \(0.948042\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 51.0585 | + | 70.2760i | 1.69350 | + | 2.33091i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.08614 | 0.0359855 | 0.0179928 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179928 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.24354 | + | 1.05389i | 0.107346 | + | 0.0348787i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.7227 | − | 18.8877i | 0.453659 | − | 0.624408i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.94890 | − | 3.23259i | 0.328542 | − | 0.106750i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.1185 | − | 15.3097i | −1.55430 | − | 0.505022i | −0.599020 | − | 0.800734i | \(-0.704443\pi\) |
−0.955277 | + | 0.295712i | \(0.904443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.8375 | − | 34.1860i | −0.818425 | − | 1.12647i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.47666 | + | 3.97902i | −0.180266 | + | 0.130971i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0003 | + | 15.2576i | 0.690486 | + | 0.501667i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.4821 | − | 17.7873i | 0.804097 | − | 0.584211i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29.7704i | − | 0.976735i | −0.872638 | − | 0.488367i | \(-0.837593\pi\) | ||
0.872638 | − | 0.488367i | \(-0.162407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.92484 | − | 0.950339i | 0.0958579 | − | 0.0311461i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.1287 | − | 40.4061i | 0.429816 | − | 1.32284i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.4319 | + | 109.048i | −1.15875 | + | 3.56625i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.4424 | − | 37.7712i | 0.896503 | − | 1.23393i | −0.0750674 | − | 0.997178i | \(-0.523917\pi\) |
0.971570 | − | 0.236752i | \(-0.0760828\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.9198 | + | 58.2292i | 0.617425 | + | 1.90024i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.7081 | + | 28.1231i | 1.26185 | + | 0.916786i | 0.998847 | − | 0.0480096i | \(-0.0152878\pi\) |
0.263001 | + | 0.964796i | \(0.415288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.25145 | + | 2.56724i | 0.268704 | + | 0.0836009i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31.8765 | − | 23.1596i | −1.03694 | − | 0.753382i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.60547 | + | 26.4849i | 0.279640 | + | 0.860644i | 0.987954 | + | 0.154746i | \(0.0494560\pi\) |
−0.708314 | + | 0.705897i | \(0.750544\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.4293 | + | 37.7532i | −0.890392 | + | 1.22552i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.4952 | + | 53.8446i | −0.567320 | + | 1.74603i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.94326 | + | 5.98075i | −0.0629485 | + | 0.193735i | −0.977585 | − | 0.210542i | \(-0.932477\pi\) |
0.914636 | + | 0.404278i | \(0.132477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.00685 | − | 2.92650i | 0.291455 | − | 0.0946994i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 170.521i | − | 5.51217i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.67336 | − | 6.30156i | 0.280077 | − | 0.203488i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.02918 | + | 5.83354i | 0.259006 | + | 0.188179i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.3154 | − | 25.6581i | 1.13802 | − | 0.826822i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42.5443 | + | 58.5572i | 1.36955 | + | 1.88502i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.2660 | − | 12.4334i | −1.23055 | − | 0.399830i | −0.379637 | − | 0.925136i | \(-0.623951\pi\) |
−0.850914 | + | 0.525306i | \(0.823951\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.5901 | − | 16.1128i | 1.59306 | − | 0.517618i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.1026 | − | 45.5618i | 1.06231 | − | 1.46215i | 0.184689 | − | 0.982797i | \(-0.440872\pi\) |
0.877624 | − | 0.479350i | \(-0.159128\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.228096 | + | 0.0741128i | 0.00731241 | + | 0.00237595i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −167.650 | −5.36908 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.55920 | − | 11.7807i | −0.273833 | − | 0.376899i | 0.649846 | − | 0.760066i | \(-0.274833\pi\) |
−0.923679 | + | 0.383167i | \(0.874833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.9874 | − | 67.6704i | −0.702722 | − | 2.16276i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 94.6837i | 3.02302i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.1894 | 0.420675 | 0.210338 | − | 0.977629i | \(-0.432544\pi\) | ||||
0.210338 | + | 0.977629i | \(0.432544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.8839 | 0.537964 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.76400i | − | 0.0879790i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.232472 | + | 0.715477i | 0.00739219 | + | 0.0227508i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6328 | + | 25.6459i | 0.591891 | + | 0.814669i | 0.994936 | − | 0.100512i | \(-0.0320480\pi\) |
−0.403045 | + | 0.915180i | \(0.632048\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.0794 | −1.04974 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −44.4274 | − | 14.4353i | −1.40844 | − | 0.457631i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.8276 | − | 31.4195i | 0.722957 | − | 0.995064i | −0.276464 | − | 0.961024i | \(-0.589163\pi\) |
0.999420 | − | 0.0340401i | \(-0.0108374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.7919 | − | 10.9796i | 1.06913 | − | 0.347381i |
(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 | 1148.2.ba.a.113.1 | ✓ | 80 | |
41.4 | even | 10 | inner | 1148.2.ba.a.701.20 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.1 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1148.2.ba.a.701.20 | yes | 80 | 41.4 | even | 10 | inner |