Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(101,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bk (of order \(6\), degree \(2\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.10 | ||
Character | \(\chi\) | \(=\) | 630.101 |
Dual form | 630.2.bk.c.131.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.61346 | + | 0.629881i | −0.931531 | + | 0.363662i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.629881 | − | 1.61346i | −0.257148 | − | 0.658692i | ||||
\(7\) | −0.166511 | + | 2.64051i | −0.0629353 | + | 0.998018i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.20650 | − | 2.03258i | 0.735500 | − | 0.677525i | ||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | 4.91769 | − | 2.83923i | 1.48274 | − | 0.856061i | 0.482932 | − | 0.875658i | \(-0.339572\pi\) |
0.999808 | + | 0.0195971i | \(0.00623836\pi\) | |||||||
\(12\) | 1.61346 | − | 0.629881i | 0.465765 | − | 0.181831i | ||||
\(13\) | 1.57532 | − | 0.909513i | 0.436916 | − | 0.252254i | −0.265373 | − | 0.964146i | \(-0.585495\pi\) |
0.702289 | + | 0.711892i | \(0.252162\pi\) | |||||||
\(14\) | −2.64051 | − | 0.166511i | −0.705705 | − | 0.0445020i | ||||
\(15\) | −0.261236 | + | 1.71224i | −0.0674509 | + | 0.442098i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.85981 | + | 4.95334i | −0.693606 | + | 1.20136i | 0.277042 | + | 0.960858i | \(0.410646\pi\) |
−0.970648 | + | 0.240503i | \(0.922688\pi\) | |||||||
\(18\) | 2.03258 | + | 2.20650i | 0.479083 | + | 0.520077i | ||||
\(19\) | 1.07373 | − | 0.619917i | 0.246330 | − | 0.142219i | −0.371753 | − | 0.928332i | \(-0.621243\pi\) |
0.618083 | + | 0.786113i | \(0.287910\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | −1.39455 | − | 4.36523i | −0.304315 | − | 0.952571i | ||||
\(22\) | 2.83923 | + | 4.91769i | 0.605326 | + | 1.04846i | ||||
\(23\) | 3.01902 | + | 1.74303i | 0.629510 | + | 0.363448i | 0.780562 | − | 0.625078i | \(-0.214933\pi\) |
−0.151052 | + | 0.988526i | \(0.548266\pi\) | |||||||
\(24\) | 0.629881 | + | 1.61346i | 0.128574 | + | 0.329346i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0.909513 | + | 1.57532i | 0.178370 | + | 0.308946i | ||||
\(27\) | −2.27981 | + | 4.66931i | −0.438751 | + | 0.898609i | ||||
\(28\) | 0.166511 | − | 2.64051i | 0.0314677 | − | 0.499009i | ||||
\(29\) | −2.25780 | − | 1.30354i | −0.419264 | − | 0.242062i | 0.275499 | − | 0.961301i | \(-0.411157\pi\) |
−0.694762 | + | 0.719240i | \(0.744490\pi\) | |||||||
\(30\) | −1.71224 | − | 0.261236i | −0.312610 | − | 0.0476950i | ||||
\(31\) | 8.91829i | 1.60177i | 0.598816 | + | 0.800886i | \(0.295638\pi\) | ||||
−0.598816 | + | 0.800886i | \(0.704362\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −6.14612 | + | 7.67855i | −1.06990 | + | 1.33666i | ||||
\(34\) | −4.95334 | − | 2.85981i | −0.849490 | − | 0.490454i | ||||
\(35\) | 2.20349 | + | 1.46446i | 0.372458 | + | 0.247538i | ||||
\(36\) | −2.20650 | + | 2.03258i | −0.367750 | + | 0.338763i | ||||
\(37\) | −2.02715 | − | 3.51113i | −0.333262 | − | 0.577226i | 0.649888 | − | 0.760030i | \(-0.274816\pi\) |
−0.983149 | + | 0.182804i | \(0.941483\pi\) | |||||||
\(38\) | 0.619917 | + | 1.07373i | 0.100564 | + | 0.174182i | ||||
\(39\) | −1.96883 | + | 2.45973i | −0.315266 | + | 0.393872i | ||||
\(40\) | −0.866025 | − | 0.500000i | −0.136931 | − | 0.0790569i | ||||
\(41\) | 6.21952 | + | 10.7725i | 0.971326 | + | 1.68239i | 0.691563 | + | 0.722316i | \(0.256923\pi\) |
0.279763 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(42\) | 4.36523 | − | 1.39455i | 0.673570 | − | 0.215183i | ||||
\(43\) | −2.45956 | + | 4.26008i | −0.375079 | + | 0.649656i | −0.990339 | − | 0.138669i | \(-0.955718\pi\) |
0.615260 | + | 0.788324i | \(0.289051\pi\) | |||||||
\(44\) | −4.91769 | + | 2.83923i | −0.741370 | + | 0.428030i | ||||
\(45\) | −0.657012 | − | 2.92717i | −0.0979416 | − | 0.436357i | ||||
\(46\) | −1.74303 | + | 3.01902i | −0.256996 | + | 0.445131i | ||||
\(47\) | 10.0448 | 1.46518 | 0.732590 | − | 0.680670i | \(-0.238311\pi\) | ||||
0.732590 | + | 0.680670i | \(0.238311\pi\) | |||||||
\(48\) | −1.61346 | + | 0.629881i | −0.232883 | + | 0.0909155i | ||||
\(49\) | −6.94455 | − | 0.879348i | −0.992078 | − | 0.125621i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | 1.49417 | − | 9.79335i | 0.209226 | − | 1.37134i | ||||
\(52\) | −1.57532 | + | 0.909513i | −0.218458 | + | 0.126127i | ||||
\(53\) | 0.844055 | + | 0.487315i | 0.115940 | + | 0.0669379i | 0.556848 | − | 0.830614i | \(-0.312010\pi\) |
−0.440909 | + | 0.897552i | \(0.645344\pi\) | |||||||
\(54\) | −4.66931 | − | 2.27981i | −0.635412 | − | 0.310244i | ||||
\(55\) | − | 5.67846i | − | 0.765684i | ||||||
\(56\) | 2.64051 | + | 0.166511i | 0.352853 | + | 0.0222510i | ||||
\(57\) | −1.34194 | + | 1.67653i | −0.177745 | + | 0.222062i | ||||
\(58\) | 1.30354 | − | 2.25780i | 0.171164 | − | 0.296464i | ||||
\(59\) | 11.3708 | 1.48035 | 0.740176 | − | 0.672413i | \(-0.234742\pi\) | ||||
0.740176 | + | 0.672413i | \(0.234742\pi\) | |||||||
\(60\) | 0.261236 | − | 1.71224i | 0.0337255 | − | 0.221049i | ||||
\(61\) | − | 7.44834i | − | 0.953662i | −0.878995 | − | 0.476831i | \(-0.841785\pi\) | ||
0.878995 | − | 0.476831i | \(-0.158215\pi\) | |||||||
\(62\) | −8.91829 | −1.13262 | ||||||||
\(63\) | 4.99962 | + | 6.16472i | 0.629893 | + | 0.776682i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 1.81903i | − | 0.225622i | ||||||
\(66\) | −7.67855 | − | 6.14612i | −0.945164 | − | 0.756535i | ||||
\(67\) | −0.0689019 | −0.00841770 | −0.00420885 | − | 0.999991i | \(-0.501340\pi\) | ||||
−0.00420885 | + | 0.999991i | \(0.501340\pi\) | |||||||
\(68\) | 2.85981 | − | 4.95334i | 0.346803 | − | 0.600680i | ||||
\(69\) | −5.96898 | − | 0.910688i | −0.718580 | − | 0.109634i | ||||
\(70\) | −1.46446 | + | 2.20349i | −0.175036 | + | 0.263367i | ||||
\(71\) | 6.62319i | 0.786028i | 0.919532 | + | 0.393014i | \(0.128568\pi\) | ||||
−0.919532 | + | 0.393014i | \(0.871432\pi\) | |||||||
\(72\) | −2.03258 | − | 2.20650i | −0.239541 | − | 0.260038i | ||||
\(73\) | −7.47035 | − | 4.31301i | −0.874339 | − | 0.504800i | −0.00555117 | − | 0.999985i | \(-0.501767\pi\) |
−0.868788 | + | 0.495185i | \(0.835100\pi\) | |||||||
\(74\) | 3.51113 | − | 2.02715i | 0.408160 | − | 0.235651i | ||||
\(75\) | 1.35222 | + | 1.08236i | 0.156141 | + | 0.124980i | ||||
\(76\) | −1.07373 | + | 0.619917i | −0.123165 | + | 0.0711094i | ||||
\(77\) | 6.67816 | + | 13.4580i | 0.761047 | + | 1.53368i | ||||
\(78\) | −2.45973 | − | 1.96883i | −0.278509 | − | 0.222927i | ||||
\(79\) | −1.36666 | −0.153761 | −0.0768806 | − | 0.997040i | \(-0.524496\pi\) | ||||
−0.0768806 | + | 0.997040i | \(0.524496\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 0.737278 | − | 8.96975i | 0.0819197 | − | 0.996639i | ||||
\(82\) | −10.7725 | + | 6.21952i | −1.18963 | + | 0.686831i | ||||
\(83\) | −6.04923 | + | 10.4776i | −0.663989 | + | 1.15006i | 0.315569 | + | 0.948903i | \(0.397805\pi\) |
−0.979558 | + | 0.201161i | \(0.935529\pi\) | |||||||
\(84\) | 1.39455 | + | 4.36523i | 0.152157 | + | 0.476286i | ||||
\(85\) | 2.85981 | + | 4.95334i | 0.310190 | + | 0.537265i | ||||
\(86\) | −4.26008 | − | 2.45956i | −0.459376 | − | 0.265221i | ||||
\(87\) | 4.46395 | + | 0.681066i | 0.478586 | + | 0.0730179i | ||||
\(88\) | −2.83923 | − | 4.91769i | −0.302663 | − | 0.524228i | ||||
\(89\) | −7.88750 | − | 13.6615i | −0.836073 | − | 1.44812i | −0.893154 | − | 0.449752i | \(-0.851513\pi\) |
0.0570806 | − | 0.998370i | \(-0.481821\pi\) | |||||||
\(90\) | 2.92717 | − | 0.657012i | 0.308551 | − | 0.0692551i | ||||
\(91\) | 2.13927 | + | 4.31109i | 0.224256 | + | 0.451926i | ||||
\(92\) | −3.01902 | − | 1.74303i | −0.314755 | − | 0.181724i | ||||
\(93\) | −5.61747 | − | 14.3893i | −0.582504 | − | 1.49210i | ||||
\(94\) | 10.0448i | 1.03604i | ||||||||
\(95\) | − | 1.23983i | − | 0.127204i | ||||||
\(96\) | −0.629881 | − | 1.61346i | −0.0642870 | − | 0.164673i | ||||
\(97\) | −1.67919 | − | 0.969482i | −0.170496 | − | 0.0984360i | 0.412324 | − | 0.911037i | \(-0.364717\pi\) |
−0.582820 | + | 0.812601i | \(0.698051\pi\) | |||||||
\(98\) | 0.879348 | − | 6.94455i | 0.0888276 | − | 0.701505i | ||||
\(99\) | 5.07994 | − | 16.2603i | 0.510553 | − | 1.63423i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 2.75742 | + | 4.77599i | 0.274373 | + | 0.475229i | 0.969977 | − | 0.243197i | \(-0.0781963\pi\) |
−0.695603 | + | 0.718426i | \(0.744863\pi\) | |||||||
\(102\) | 9.79335 | + | 1.49417i | 0.969686 | + | 0.147945i | ||||
\(103\) | 6.52554 | + | 3.76752i | 0.642980 | + | 0.371225i | 0.785762 | − | 0.618529i | \(-0.212271\pi\) |
−0.142781 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(104\) | −0.909513 | − | 1.57532i | −0.0891851 | − | 0.154473i | ||||
\(105\) | −4.47767 | − | 0.974903i | −0.436976 | − | 0.0951408i | ||||
\(106\) | −0.487315 | + | 0.844055i | −0.0473322 | + | 0.0819818i | ||||
\(107\) | 15.6906 | − | 9.05896i | 1.51686 | − | 0.875762i | 0.517061 | − | 0.855949i | \(-0.327026\pi\) |
0.999804 | − | 0.0198138i | \(-0.00630733\pi\) | |||||||
\(108\) | 2.27981 | − | 4.66931i | 0.219375 | − | 0.449304i | ||||
\(109\) | −1.76968 | + | 3.06518i | −0.169505 | + | 0.293591i | −0.938246 | − | 0.345969i | \(-0.887550\pi\) |
0.768741 | + | 0.639560i | \(0.220884\pi\) | |||||||
\(110\) | 5.67846 | 0.541420 | ||||||||
\(111\) | 5.48232 | + | 4.38820i | 0.520359 | + | 0.416509i | ||||
\(112\) | −0.166511 | + | 2.64051i | −0.0157338 | + | 0.249504i | ||||
\(113\) | 5.41190 | − | 3.12456i | 0.509109 | − | 0.293934i | −0.223358 | − | 0.974736i | \(-0.571702\pi\) |
0.732467 | + | 0.680802i | \(0.238369\pi\) | |||||||
\(114\) | −1.67653 | − | 1.34194i | −0.157022 | − | 0.125684i | ||||
\(115\) | 3.01902 | − | 1.74303i | 0.281526 | − | 0.162539i | ||||
\(116\) | 2.25780 | + | 1.30354i | 0.209632 | + | 0.121031i | ||||
\(117\) | 1.62730 | − | 5.20880i | 0.150444 | − | 0.481554i | ||||
\(118\) | 11.3708i | 1.04677i | ||||||||
\(119\) | −12.6031 | − | 8.37614i | −1.15533 | − | 0.767839i | ||||
\(120\) | 1.71224 | + | 0.261236i | 0.156305 | + | 0.0238475i | ||||
\(121\) | 10.6225 | − | 18.3987i | 0.965679 | − | 1.67261i | ||||
\(122\) | 7.44834 | 0.674341 | ||||||||
\(123\) | −16.8203 | − | 13.4635i | −1.51664 | − | 1.21396i | ||||
\(124\) | − | 8.91829i | − | 0.800886i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −6.16472 | + | 4.99962i | −0.549197 | + | 0.445402i | ||||
\(127\) | 19.0703 | 1.69222 | 0.846110 | − | 0.533009i | \(-0.178939\pi\) | ||||
0.846110 | + | 0.533009i | \(0.178939\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.28505 | − | 8.42269i | 0.113142 | − | 0.741576i | ||||
\(130\) | 1.81903 | 0.159539 | ||||||||
\(131\) | −0.0646409 | + | 0.111961i | −0.00564770 | + | 0.00978211i | −0.868835 | − | 0.495101i | \(-0.835131\pi\) |
0.863188 | + | 0.504883i | \(0.168464\pi\) | |||||||
\(132\) | 6.14612 | − | 7.67855i | 0.534951 | − | 0.668332i | ||||
\(133\) | 1.45811 | + | 2.93841i | 0.126434 | + | 0.254792i | ||||
\(134\) | − | 0.0689019i | − | 0.00595221i | ||||||
\(135\) | 2.90383 | + | 4.30903i | 0.249922 | + | 0.370862i | ||||
\(136\) | 4.95334 | + | 2.85981i | 0.424745 | + | 0.245227i | ||||
\(137\) | 6.91408 | − | 3.99184i | 0.590710 | − | 0.341046i | −0.174668 | − | 0.984627i | \(-0.555885\pi\) |
0.765378 | + | 0.643581i | \(0.222552\pi\) | |||||||
\(138\) | 0.910688 | − | 5.96898i | 0.0775229 | − | 0.508113i | ||||
\(139\) | −4.54379 | + | 2.62336i | −0.385400 | + | 0.222511i | −0.680165 | − | 0.733059i | \(-0.738092\pi\) |
0.294765 | + | 0.955570i | \(0.404759\pi\) | |||||||
\(140\) | −2.20349 | − | 1.46446i | −0.186229 | − | 0.123769i | ||||
\(141\) | −16.2068 | + | 6.32701i | −1.36486 | + | 0.532831i | ||||
\(142\) | −6.62319 | −0.555806 | ||||||||
\(143\) | 5.16464 | − | 8.94541i | 0.431889 | − | 0.748053i | ||||
\(144\) | 2.20650 | − | 2.03258i | 0.183875 | − | 0.169381i | ||||
\(145\) | −2.25780 | + | 1.30354i | −0.187500 | + | 0.108253i | ||||
\(146\) | 4.31301 | − | 7.47035i | 0.356947 | − | 0.618251i | ||||
\(147\) | 11.7586 | − | 2.95545i | 0.969835 | − | 0.243761i | ||||
\(148\) | 2.02715 | + | 3.51113i | 0.166631 | + | 0.288613i | ||||
\(149\) | 13.7747 | + | 7.95281i | 1.12847 | + | 0.651520i | 0.943549 | − | 0.331234i | \(-0.107465\pi\) |
0.184917 | + | 0.982754i | \(0.440798\pi\) | |||||||
\(150\) | −1.08236 | + | 1.35222i | −0.0883740 | + | 0.110409i | ||||
\(151\) | −9.79120 | − | 16.9589i | −0.796797 | − | 1.38009i | −0.921692 | − | 0.387923i | \(-0.873193\pi\) |
0.124895 | − | 0.992170i | \(-0.460141\pi\) | |||||||
\(152\) | −0.619917 | − | 1.07373i | −0.0502819 | − | 0.0870909i | ||||
\(153\) | 3.75786 | + | 16.7423i | 0.303805 | + | 1.35354i | ||||
\(154\) | −13.4580 | + | 6.67816i | −1.08447 | + | 0.538141i | ||||
\(155\) | 7.72347 | + | 4.45915i | 0.620364 | + | 0.358167i | ||||
\(156\) | 1.96883 | − | 2.45973i | 0.157633 | − | 0.196936i | ||||
\(157\) | 16.3621i | 1.30584i | 0.757426 | + | 0.652921i | \(0.226457\pi\) | ||||
−0.757426 | + | 0.652921i | \(0.773543\pi\) | |||||||
\(158\) | − | 1.36666i | − | 0.108726i | ||||||
\(159\) | −1.66880 | − | 0.254609i | −0.132344 | − | 0.0201918i | ||||
\(160\) | 0.866025 | + | 0.500000i | 0.0684653 | + | 0.0395285i | ||||
\(161\) | −5.10520 | + | 7.68152i | −0.402346 | + | 0.605389i | ||||
\(162\) | 8.96975 | + | 0.737278i | 0.704730 | + | 0.0579260i | ||||
\(163\) | −6.59007 | − | 11.4143i | −0.516174 | − | 0.894040i | −0.999824 | − | 0.0187781i | \(-0.994022\pi\) |
0.483650 | − | 0.875262i | \(-0.339311\pi\) | |||||||
\(164\) | −6.21952 | − | 10.7725i | −0.485663 | − | 0.841193i | ||||
\(165\) | 3.57676 | + | 9.16197i | 0.278450 | + | 0.713258i | ||||
\(166\) | −10.4776 | − | 6.04923i | −0.813217 | − | 0.469511i | ||||
\(167\) | −2.81257 | − | 4.87151i | −0.217643 | − | 0.376969i | 0.736444 | − | 0.676499i | \(-0.236503\pi\) |
−0.954087 | + | 0.299530i | \(0.903170\pi\) | |||||||
\(168\) | −4.36523 | + | 1.39455i | −0.336785 | + | 0.107592i | ||||
\(169\) | −4.84557 | + | 8.39278i | −0.372736 | + | 0.645598i | ||||
\(170\) | −4.95334 | + | 2.85981i | −0.379904 | + | 0.219337i | ||||
\(171\) | 1.10915 | − | 3.55028i | 0.0848190 | − | 0.271497i | ||||
\(172\) | 2.45956 | − | 4.26008i | 0.187539 | − | 0.324828i | ||||
\(173\) | −7.96037 | −0.605216 | −0.302608 | − | 0.953115i | \(-0.597857\pi\) | ||||
−0.302608 | + | 0.953115i | \(0.597857\pi\) | |||||||
\(174\) | −0.681066 | + | 4.46395i | −0.0516315 | + | 0.338411i | ||||
\(175\) | 2.37000 | − | 1.17605i | 0.179155 | − | 0.0889010i | ||||
\(176\) | 4.91769 | − | 2.83923i | 0.370685 | − | 0.214015i | ||||
\(177\) | −18.3463 | + | 7.16226i | −1.37899 | + | 0.538348i | ||||
\(178\) | 13.6615 | − | 7.88750i | 1.02398 | − | 0.591193i | ||||
\(179\) | 5.99647 | + | 3.46206i | 0.448197 | + | 0.258767i | 0.707068 | − | 0.707145i | \(-0.250017\pi\) |
−0.258871 | + | 0.965912i | \(0.583351\pi\) | |||||||
\(180\) | 0.657012 | + | 2.92717i | 0.0489708 | + | 0.218179i | ||||
\(181\) | − | 2.78183i | − | 0.206772i | −0.994641 | − | 0.103386i | \(-0.967032\pi\) | ||
0.994641 | − | 0.103386i | \(-0.0329676\pi\) | |||||||
\(182\) | −4.31109 | + | 2.13927i | −0.319560 | + | 0.158573i | ||||
\(183\) | 4.69157 | + | 12.0176i | 0.346811 | + | 0.888366i | ||||
\(184\) | 1.74303 | − | 3.01902i | 0.128498 | − | 0.222565i | ||||
\(185\) | −4.05430 | −0.298078 | ||||||||
\(186\) | 14.3893 | − | 5.61747i | 1.05507 | − | 0.411893i | ||||
\(187\) | 32.4787i | 2.37508i | ||||||||
\(188\) | −10.0448 | −0.732590 | ||||||||
\(189\) | −11.9497 | − | 6.79736i | −0.869215 | − | 0.494435i | ||||
\(190\) | 1.23983 | 0.0899471 | ||||||||
\(191\) | 3.02993i | 0.219238i | 0.993974 | + | 0.109619i | \(0.0349631\pi\) | ||||
−0.993974 | + | 0.109619i | \(0.965037\pi\) | |||||||
\(192\) | 1.61346 | − | 0.629881i | 0.116441 | − | 0.0454578i | ||||
\(193\) | −3.52611 | −0.253815 | −0.126907 | − | 0.991915i | \(-0.540505\pi\) | ||||
−0.126907 | + | 0.991915i | \(0.540505\pi\) | |||||||
\(194\) | 0.969482 | − | 1.67919i | 0.0696048 | − | 0.120559i | ||||
\(195\) | 1.14577 | + | 2.93492i | 0.0820503 | + | 0.210174i | ||||
\(196\) | 6.94455 | + | 0.879348i | 0.496039 | + | 0.0628106i | ||||
\(197\) | − | 9.09265i | − | 0.647825i | −0.946087 | − | 0.323912i | \(-0.895002\pi\) | ||
0.946087 | − | 0.323912i | \(-0.104998\pi\) | |||||||
\(198\) | 16.2603 | + | 5.07994i | 1.15557 | + | 0.361015i | ||||
\(199\) | −12.5241 | − | 7.23082i | −0.887813 | − | 0.512579i | −0.0145863 | − | 0.999894i | \(-0.504643\pi\) |
−0.873226 | + | 0.487315i | \(0.837976\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | 0.111170 | − | 0.0434000i | 0.00784135 | − | 0.00306120i | ||||
\(202\) | −4.77599 | + | 2.75742i | −0.336037 | + | 0.194011i | ||||
\(203\) | 3.81796 | − | 5.74469i | 0.267969 | − | 0.403198i | ||||
\(204\) | −1.49417 | + | 9.79335i | −0.104613 | + | 0.685672i | ||||
\(205\) | 12.4390 | 0.868780 | ||||||||
\(206\) | −3.76752 | + | 6.52554i | −0.262496 | + | 0.454656i | ||||
\(207\) | 10.2043 | − | 2.29039i | 0.709250 | − | 0.159193i | ||||
\(208\) | 1.57532 | − | 0.909513i | 0.109229 | − | 0.0630634i | ||||
\(209\) | 3.52018 | − | 6.09713i | 0.243496 | − | 0.421747i | ||||
\(210\) | 0.974903 | − | 4.47767i | 0.0672747 | − | 0.308989i | ||||
\(211\) | −6.72807 | − | 11.6534i | −0.463179 | − | 0.802250i | 0.535938 | − | 0.844257i | \(-0.319958\pi\) |
−0.999117 | + | 0.0420072i | \(0.986625\pi\) | |||||||
\(212\) | −0.844055 | − | 0.487315i | −0.0579699 | − | 0.0334689i | ||||
\(213\) | −4.17182 | − | 10.6862i | −0.285849 | − | 0.732210i | ||||
\(214\) | 9.05896 | + | 15.6906i | 0.619257 | + | 1.07259i | ||||
\(215\) | 2.45956 | + | 4.26008i | 0.167740 | + | 0.290535i | ||||
\(216\) | 4.66931 | + | 2.27981i | 0.317706 | + | 0.155122i | ||||
\(217\) | −23.5488 | − | 1.48500i | −1.59860 | − | 0.100808i | ||||
\(218\) | −3.06518 | − | 1.76968i | −0.207600 | − | 0.119858i | ||||
\(219\) | 14.7698 | + | 2.25343i | 0.998050 | + | 0.152273i | ||||
\(220\) | 5.67846i | 0.382842i | ||||||||
\(221\) | 10.4041i | 0.699858i | ||||||||
\(222\) | −4.38820 | + | 5.48232i | −0.294516 | + | 0.367949i | ||||
\(223\) | −9.11125 | − | 5.26038i | −0.610135 | − | 0.352261i | 0.162884 | − | 0.986645i | \(-0.447921\pi\) |
−0.773018 | + | 0.634384i | \(0.781254\pi\) | |||||||
\(224\) | −2.64051 | − | 0.166511i | −0.176426 | − | 0.0111255i | ||||
\(225\) | −2.86351 | − | 0.894597i | −0.190901 | − | 0.0596398i | ||||
\(226\) | 3.12456 | + | 5.41190i | 0.207843 | + | 0.359994i | ||||
\(227\) | −14.5390 | − | 25.1823i | −0.964987 | − | 1.67141i | −0.709651 | − | 0.704554i | \(-0.751147\pi\) |
−0.255336 | − | 0.966852i | \(-0.582186\pi\) | |||||||
\(228\) | 1.34194 | − | 1.67653i | 0.0888723 | − | 0.111031i | ||||
\(229\) | 7.36868 | + | 4.25431i | 0.486936 | + | 0.281133i | 0.723302 | − | 0.690531i | \(-0.242623\pi\) |
−0.236367 | + | 0.971664i | \(0.575957\pi\) | |||||||
\(230\) | 1.74303 | + | 3.01902i | 0.114932 | + | 0.199069i | ||||
\(231\) | −19.2519 | − | 17.5074i | −1.26668 | − | 1.15190i | ||||
\(232\) | −1.30354 | + | 2.25780i | −0.0855818 | + | 0.148232i | ||||
\(233\) | −22.5702 | + | 13.0309i | −1.47863 | + | 0.853685i | −0.999708 | − | 0.0241753i | \(-0.992304\pi\) |
−0.478917 | + | 0.877860i | \(0.658971\pi\) | |||||||
\(234\) | 5.20880 | + | 1.62730i | 0.340510 | + | 0.106380i | ||||
\(235\) | 5.02238 | − | 8.69903i | 0.327624 | − | 0.567462i | ||||
\(236\) | −11.3708 | −0.740176 | ||||||||
\(237\) | 2.20505 | − | 0.860833i | 0.143233 | − | 0.0559171i | ||||
\(238\) | 8.37614 | − | 12.6031i | 0.542944 | − | 0.816940i | ||||
\(239\) | −13.6870 | + | 7.90222i | −0.885341 | + | 0.511152i | −0.872416 | − | 0.488764i | \(-0.837448\pi\) |
−0.0129256 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(240\) | −0.261236 | + | 1.71224i | −0.0168627 | + | 0.110524i | ||||
\(241\) | −4.20612 | + | 2.42841i | −0.270940 | + | 0.156427i | −0.629315 | − | 0.777150i | \(-0.716664\pi\) |
0.358375 | + | 0.933578i | \(0.383331\pi\) | |||||||
\(242\) | 18.3987 | + | 10.6225i | 1.18271 | + | 0.682838i | ||||
\(243\) | 4.46031 | + | 14.9367i | 0.286129 | + | 0.958191i | ||||
\(244\) | 7.44834i | 0.476831i | ||||||||
\(245\) | −4.23381 | + | 5.57448i | −0.270488 | + | 0.356141i | ||||
\(246\) | 13.4635 | − | 16.8203i | 0.858399 | − | 1.07243i | ||||
\(247\) | 1.12765 | − | 1.95314i | 0.0717504 | − | 0.124275i | ||||
\(248\) | 8.91829 | 0.566312 | ||||||||
\(249\) | 3.16056 | − | 20.7154i | 0.200292 | − | 1.31279i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −21.6259 | −1.36502 | −0.682508 | − | 0.730879i | \(-0.739111\pi\) | ||||
−0.682508 | + | 0.730879i | \(0.739111\pi\) | |||||||
\(252\) | −4.99962 | − | 6.16472i | −0.314946 | − | 0.388341i | ||||
\(253\) | 19.7955 | 1.24453 | ||||||||
\(254\) | 19.0703i | 1.19658i | ||||||||
\(255\) | −7.73420 | − | 6.19067i | −0.484335 | − | 0.387675i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.44084 | − | 4.22766i | 0.152255 | − | 0.263714i | −0.779801 | − | 0.626028i | \(-0.784680\pi\) |
0.932056 | + | 0.362314i | \(0.118013\pi\) | |||||||
\(258\) | 8.42269 | + | 1.28505i | 0.524374 | + | 0.0800038i | ||||
\(259\) | 9.60870 | − | 4.76806i | 0.597056 | − | 0.296273i | ||||
\(260\) | 1.81903i | 0.112811i | ||||||||
\(261\) | −7.63139 | + | 1.71289i | −0.472371 | + | 0.106025i | ||||
\(262\) | −0.111961 | − | 0.0646409i | −0.00691699 | − | 0.00399353i | ||||
\(263\) | −12.3336 | + | 7.12083i | −0.760524 | + | 0.439089i | −0.829484 | − | 0.558530i | \(-0.811365\pi\) |
0.0689596 | + | 0.997619i | \(0.478032\pi\) | |||||||
\(264\) | 7.67855 | + | 6.14612i | 0.472582 | + | 0.378267i | ||||
\(265\) | 0.844055 | − | 0.487315i | 0.0518499 | − | 0.0299355i | ||||
\(266\) | −2.93841 | + | 1.45811i | −0.180165 | + | 0.0894023i | ||||
\(267\) | 21.3313 | + | 17.0742i | 1.30545 | + | 1.04492i | ||||
\(268\) | 0.0689019 | 0.00420885 | ||||||||
\(269\) | 11.3169 | − | 19.6014i | 0.690003 | − | 1.19512i | −0.281834 | − | 0.959463i | \(-0.590943\pi\) |
0.971836 | − | 0.235656i | \(-0.0757240\pi\) | |||||||
\(270\) | −4.30903 | + | 2.90383i | −0.262239 | + | 0.176722i | ||||
\(271\) | 6.61815 | − | 3.82099i | 0.402024 | − | 0.232109i | −0.285333 | − | 0.958428i | \(-0.592104\pi\) |
0.687357 | + | 0.726320i | \(0.258771\pi\) | |||||||
\(272\) | −2.85981 | + | 4.95334i | −0.173402 | + | 0.300340i | ||||
\(273\) | −6.16710 | − | 5.60829i | −0.373250 | − | 0.339429i | ||||
\(274\) | 3.99184 | + | 6.91408i | 0.241156 | + | 0.417695i | ||||
\(275\) | −4.91769 | − | 2.83923i | −0.296548 | − | 0.171212i | ||||
\(276\) | 5.96898 | + | 0.910688i | 0.359290 | + | 0.0548170i | ||||
\(277\) | 6.26276 | + | 10.8474i | 0.376293 | + | 0.651758i | 0.990520 | − | 0.137372i | \(-0.0438654\pi\) |
−0.614227 | + | 0.789129i | \(0.710532\pi\) | |||||||
\(278\) | −2.62336 | − | 4.54379i | −0.157339 | − | 0.272519i | ||||
\(279\) | 18.1271 | + | 19.6782i | 1.08524 | + | 1.17810i | ||||
\(280\) | 1.46446 | − | 2.20349i | 0.0875180 | − | 0.131684i | ||||
\(281\) | 18.6742 | + | 10.7815i | 1.11401 | + | 0.643172i | 0.939864 | − | 0.341548i | \(-0.110951\pi\) |
0.174143 | + | 0.984720i | \(0.444284\pi\) | |||||||
\(282\) | −6.32701 | − | 16.2068i | −0.376768 | − | 0.965102i | ||||
\(283\) | 27.4419i | 1.63125i | 0.578581 | + | 0.815625i | \(0.303607\pi\) | ||||
−0.578581 | + | 0.815625i | \(0.696393\pi\) | |||||||
\(284\) | − | 6.62319i | − | 0.393014i | ||||||
\(285\) | 0.780949 | + | 2.00042i | 0.0462594 | + | 0.118495i | ||||
\(286\) | 8.94541 | + | 5.16464i | 0.528953 | + | 0.305391i | ||||
\(287\) | −29.4805 | + | 14.6289i | −1.74018 | + | 0.863519i | ||||
\(288\) | 2.03258 | + | 2.20650i | 0.119771 | + | 0.130019i | ||||
\(289\) | −7.85704 | − | 13.6088i | −0.462179 | − | 0.800517i | ||||
\(290\) | −1.30354 | − | 2.25780i | −0.0765467 | − | 0.132583i | ||||
\(291\) | 3.31997 | + | 0.506528i | 0.194620 | + | 0.0296932i | ||||
\(292\) | 7.47035 | + | 4.31301i | 0.437169 | + | 0.252400i | ||||
\(293\) | −11.5161 | − | 19.9464i | −0.672776 | − | 1.16528i | −0.977114 | − | 0.212718i | \(-0.931768\pi\) |
0.304337 | − | 0.952564i | \(-0.401565\pi\) | |||||||
\(294\) | 2.95545 | + | 11.7586i | 0.172365 | + | 0.685777i | ||||
\(295\) | 5.68540 | − | 9.84741i | 0.331017 | − | 0.573338i | ||||
\(296\) | −3.51113 | + | 2.02715i | −0.204080 | + | 0.117826i | ||||
\(297\) | 2.04582 | + | 29.4352i | 0.118710 | + | 1.70800i | ||||
\(298\) | −7.95281 | + | 13.7747i | −0.460694 | + | 0.797946i | ||||
\(299\) | 6.34125 | 0.366724 | ||||||||
\(300\) | −1.35222 | − | 1.08236i | −0.0780706 | − | 0.0624898i | ||||
\(301\) | −10.8392 | − | 7.20383i | −0.624762 | − | 0.415222i | ||||
\(302\) | 16.9589 | − | 9.79120i | 0.975873 | − | 0.563421i | ||||
\(303\) | −7.45729 | − | 5.96902i | −0.428410 | − | 0.342911i | ||||
\(304\) | 1.07373 | − | 0.619917i | 0.0615825 | − | 0.0355547i | ||||
\(305\) | −6.45045 | − | 3.72417i | −0.369352 | − | 0.213245i | ||||
\(306\) | −16.7423 | + | 3.75786i | −0.957095 | + | 0.214823i | ||||
\(307\) | − | 14.6153i | − | 0.834137i | −0.908875 | − | 0.417069i | \(-0.863057\pi\) | ||
0.908875 | − | 0.417069i | \(-0.136943\pi\) | |||||||
\(308\) | −6.67816 | − | 13.4580i | −0.380523 | − | 0.766839i | ||||
\(309\) | −12.9018 | − | 1.96843i | −0.733957 | − | 0.111980i | ||||
\(310\) | −4.45915 | + | 7.72347i | −0.253262 | + | 0.438664i | ||||
\(311\) | 4.33309 | 0.245707 | 0.122853 | − | 0.992425i | \(-0.460796\pi\) | ||||
0.122853 | + | 0.992425i | \(0.460796\pi\) | |||||||
\(312\) | 2.45973 | + | 1.96883i | 0.139255 | + | 0.111463i | ||||
\(313\) | − | 9.03514i | − | 0.510697i | −0.966849 | − | 0.255348i | \(-0.917810\pi\) | ||
0.966849 | − | 0.255348i | \(-0.0821901\pi\) | |||||||
\(314\) | −16.3621 | −0.923370 | ||||||||
\(315\) | 7.83862 | − | 1.24744i | 0.441656 | − | 0.0702851i | ||||
\(316\) | 1.36666 | 0.0768806 | ||||||||
\(317\) | − | 19.3816i | − | 1.08858i | −0.838897 | − | 0.544289i | \(-0.816799\pi\) | ||
0.838897 | − | 0.544289i | \(-0.183201\pi\) | |||||||
\(318\) | 0.254609 | − | 1.66880i | 0.0142778 | − | 0.0935816i | ||||
\(319\) | −14.8042 | −0.828879 | ||||||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −19.6100 | + | 24.4994i | −1.09452 | + | 1.36743i | ||||
\(322\) | −7.68152 | − | 5.10520i | −0.428074 | − | 0.284501i | ||||
\(323\) | 7.09139i | 0.394575i | ||||||||
\(324\) | −0.737278 | + | 8.96975i | −0.0409599 | + | 0.498319i | ||||
\(325\) | −1.57532 | − | 0.909513i | −0.0873832 | − | 0.0504507i | ||||
\(326\) | 11.4143 | − | 6.59007i | 0.632182 | − | 0.364990i | ||||
\(327\) | 0.924611 | − | 6.06024i | 0.0511311 | − | 0.335132i | ||||
\(328\) | 10.7725 | − | 6.21952i | 0.594813 | − | 0.343416i | ||||
\(329\) | −1.67257 | + | 26.5233i | −0.0922116 | + | 1.46228i | ||||
\(330\) | −9.16197 | + | 3.57676i | −0.504350 | + | 0.196894i | ||||
\(331\) | 8.35472 | 0.459217 | 0.229608 | − | 0.973283i | \(-0.426255\pi\) | ||||
0.229608 | + | 0.973283i | \(0.426255\pi\) | |||||||
\(332\) | 6.04923 | − | 10.4776i | 0.331995 | − | 0.575032i | ||||
\(333\) | −11.6095 | − | 3.62697i | −0.636199 | − | 0.198756i | ||||
\(334\) | 4.87151 | − | 2.81257i | 0.266557 | − | 0.153897i | ||||
\(335\) | −0.0344509 | + | 0.0596708i | −0.00188226 | + | 0.00326016i | ||||
\(336\) | −1.39455 | − | 4.36523i | −0.0760787 | − | 0.238143i | ||||
\(337\) | −16.8897 | − | 29.2538i | −0.920039 | − | 1.59355i | −0.799351 | − | 0.600864i | \(-0.794823\pi\) |
−0.120688 | − | 0.992690i | \(-0.538510\pi\) | |||||||
\(338\) | −8.39278 | − | 4.84557i | −0.456507 | − | 0.263564i | ||||
\(339\) | −6.76378 | + | 8.45021i | −0.367358 | + | 0.458952i | ||||
\(340\) | −2.85981 | − | 4.95334i | −0.155095 | − | 0.268632i | ||||
\(341\) | 25.3211 | + | 43.8574i | 1.37121 | + | 2.37501i | ||||
\(342\) | 3.55028 | + | 1.10915i | 0.191977 | + | 0.0599761i | ||||
\(343\) | 3.47827 | − | 18.1907i | 0.187809 | − | 0.982206i | ||||
\(344\) | 4.26008 | + | 2.45956i | 0.229688 | + | 0.132610i | ||||
\(345\) | −3.77317 | + | 4.71394i | −0.203141 | + | 0.253790i | ||||
\(346\) | − | 7.96037i | − | 0.427952i | ||||||
\(347\) | 11.3240i | 0.607906i | 0.952687 | + | 0.303953i | \(0.0983066\pi\) | ||||
−0.952687 | + | 0.303953i | \(0.901693\pi\) | |||||||
\(348\) | −4.46395 | − | 0.681066i | −0.239293 | − | 0.0365090i | ||||
\(349\) | −3.37360 | − | 1.94775i | −0.180585 | − | 0.104261i | 0.406983 | − | 0.913436i | \(-0.366581\pi\) |
−0.587567 | + | 0.809175i | \(0.699914\pi\) | |||||||
\(350\) | 1.17605 | + | 2.37000i | 0.0628625 | + | 0.126682i | ||||
\(351\) | 0.655353 | + | 9.42919i | 0.0349802 | + | 0.503293i | ||||
\(352\) | 2.83923 | + | 4.91769i | 0.151332 | + | 0.262114i | ||||
\(353\) | −14.3522 | − | 24.8588i | −0.763892 | − | 1.32310i | −0.940830 | − | 0.338878i | \(-0.889953\pi\) |
0.176938 | − | 0.984222i | \(-0.443381\pi\) | |||||||
\(354\) | −7.16226 | − | 18.3463i | −0.380670 | − | 0.975096i | ||||
\(355\) | 5.73585 | + | 3.31160i | 0.304427 | + | 0.175761i | ||||
\(356\) | 7.88750 | + | 13.6615i | 0.418037 | + | 0.724061i | ||||
\(357\) | 25.6106 | + | 5.57608i | 1.35546 | + | 0.295117i | ||||
\(358\) | −3.46206 | + | 5.99647i | −0.182976 | + | 0.316923i | ||||
\(359\) | −2.00897 | + | 1.15988i | −0.106029 | + | 0.0612161i | −0.552077 | − | 0.833793i | \(-0.686165\pi\) |
0.446048 | + | 0.895009i | \(0.352831\pi\) | |||||||
\(360\) | −2.92717 | + | 0.657012i | −0.154276 | + | 0.0346276i | ||||
\(361\) | −8.73140 | + | 15.1232i | −0.459548 | + | 0.795960i | ||||
\(362\) | 2.78183 | 0.146210 | ||||||||
\(363\) | −5.54995 | + | 36.3764i | −0.291297 | + | 1.90926i | ||||
\(364\) | −2.13927 | − | 4.31109i | −0.112128 | − | 0.225963i | ||||
\(365\) | −7.47035 | + | 4.31301i | −0.391016 | + | 0.225753i | ||||
\(366\) | −12.0176 | + | 4.69157i | −0.628170 | + | 0.245232i | ||||
\(367\) | −11.4932 | + | 6.63561i | −0.599941 | + | 0.346376i | −0.769018 | − | 0.639227i | \(-0.779255\pi\) |
0.169077 | + | 0.985603i | \(0.445921\pi\) | |||||||
\(368\) | 3.01902 | + | 1.74303i | 0.157378 | + | 0.0908620i | ||||
\(369\) | 35.6193 | + | 11.1279i | 1.85427 | + | 0.579297i | ||||
\(370\) | − | 4.05430i | − | 0.210773i | ||||||
\(371\) | −1.42730 | + | 2.14759i | −0.0741019 | + | 0.111497i | ||||
\(372\) | 5.61747 | + | 14.3893i | 0.291252 | + | 0.746050i | ||||
\(373\) | 2.07132 | − | 3.58763i | 0.107249 | − | 0.185760i | −0.807406 | − | 0.589996i | \(-0.799129\pi\) |
0.914655 | + | 0.404236i | \(0.132463\pi\) | |||||||
\(374\) | −32.4787 | −1.67943 | ||||||||
\(375\) | 1.61346 | − | 0.629881i | 0.0833187 | − | 0.0325269i | ||||
\(376\) | − | 10.0448i | − | 0.518019i | ||||||
\(377\) | −4.74236 | −0.244244 | ||||||||
\(378\) | 6.79736 | − | 11.9497i | 0.349618 | − | 0.614628i | ||||
\(379\) | 6.21425 | 0.319204 | 0.159602 | − | 0.987181i | \(-0.448979\pi\) | ||||
0.159602 | + | 0.987181i | \(0.448979\pi\) | |||||||
\(380\) | 1.23983i | 0.0636022i | ||||||||
\(381\) | −30.7692 | + | 12.0121i | −1.57635 | + | 0.615396i | ||||
\(382\) | −3.02993 | −0.155025 | ||||||||
\(383\) | 6.81820 | − | 11.8095i | 0.348394 | − | 0.603435i | −0.637571 | − | 0.770392i | \(-0.720061\pi\) |
0.985964 | + | 0.166957i | \(0.0533940\pi\) | |||||||
\(384\) | 0.629881 | + | 1.61346i | 0.0321435 | + | 0.0823365i | ||||
\(385\) | 14.9940 | + | 0.945528i | 0.764166 | + | 0.0481886i | ||||
\(386\) | − | 3.52611i | − | 0.179474i | ||||||
\(387\) | 3.23192 | + | 14.3991i | 0.164288 | + | 0.731947i | ||||
\(388\) | 1.67919 | + | 0.969482i | 0.0852481 | + | 0.0492180i | ||||
\(389\) | 25.3739 | − | 14.6496i | 1.28651 | − | 0.742766i | 0.308479 | − | 0.951231i | \(-0.400180\pi\) |
0.978030 | + | 0.208465i | \(0.0668467\pi\) | |||||||
\(390\) | −2.93492 | + | 1.14577i | −0.148616 | + | 0.0580184i | ||||
\(391\) | −17.2677 | + | 9.96950i | −0.873264 | + | 0.504179i | ||||
\(392\) | −0.879348 | + | 6.94455i | −0.0444138 | + | 0.350753i | ||||
\(393\) | 0.0337731 | − | 0.221361i | 0.00170363 | − | 0.0111662i | ||||
\(394\) | 9.09265 | 0.458081 | ||||||||
\(395\) | −0.683330 | + | 1.18356i | −0.0343820 | + | 0.0595514i | ||||
\(396\) | −5.07994 | + | 16.2603i | −0.255276 | + | 0.817113i | ||||
\(397\) | 9.62007 | − | 5.55415i | 0.482817 | − | 0.278755i | −0.238772 | − | 0.971076i | \(-0.576745\pi\) |
0.721590 | + | 0.692321i | \(0.243412\pi\) | |||||||
\(398\) | 7.23082 | − | 12.5241i | 0.362448 | − | 0.627778i | ||||
\(399\) | −4.20345 | − | 3.82257i | −0.210436 | − | 0.191368i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −1.25249 | − | 0.723128i | −0.0625466 | − | 0.0361113i | 0.468401 | − | 0.883516i | \(-0.344830\pi\) |
−0.530947 | + | 0.847405i | \(0.678164\pi\) | |||||||
\(402\) | 0.0434000 | + | 0.111170i | 0.00216459 | + | 0.00554467i | ||||
\(403\) | 8.11131 | + | 14.0492i | 0.404053 | + | 0.699840i | ||||
\(404\) | −2.75742 | − | 4.77599i | −0.137187 | − | 0.237614i | ||||
\(405\) | −7.39939 | − | 5.12338i | −0.367679 | − | 0.254583i | ||||
\(406\) | 5.74469 | + | 3.81796i | 0.285104 | + | 0.189482i | ||||
\(407\) | −19.9378 | − | 11.5111i | −0.988281 | − | 0.570584i | ||||
\(408\) | −9.79335 | − | 1.49417i | −0.484843 | − | 0.0739726i | ||||
\(409\) | − | 16.2396i | − | 0.802996i | −0.915860 | − | 0.401498i | \(-0.868490\pi\) | ||
0.915860 | − | 0.401498i | \(-0.131510\pi\) | |||||||
\(410\) | 12.4390i | 0.614320i | ||||||||
\(411\) | −8.64119 | + | 10.7957i | −0.426239 | + | 0.532514i | ||||
\(412\) | −6.52554 | − | 3.76752i | −0.321490 | − | 0.185612i | ||||
\(413\) | −1.89337 | + | 30.0247i | −0.0931665 | + | 1.47742i | ||||
\(414\) | 2.29039 | + | 10.2043i | 0.112567 | + | 0.501515i | ||||
\(415\) | 6.04923 | + | 10.4776i | 0.296945 | + | 0.514324i | ||||
\(416\) | 0.909513 | + | 1.57532i | 0.0445926 | + | 0.0772366i | ||||
\(417\) | 5.67882 | − | 7.09474i | 0.278093 | − | 0.347431i | ||||
\(418\) | 6.09713 | + | 3.52018i | 0.298220 | + | 0.172178i | ||||
\(419\) | 4.24495 | + | 7.35247i | 0.207379 | + | 0.359192i | 0.950888 | − | 0.309534i | \(-0.100173\pi\) |
−0.743509 | + | 0.668726i | \(0.766840\pi\) | |||||||
\(420\) | 4.47767 | + | 0.974903i | 0.218488 | + | 0.0475704i | ||||
\(421\) | 0.808166 | − | 1.39979i | 0.0393876 | − | 0.0682214i | −0.845660 | − | 0.533723i | \(-0.820793\pi\) |
0.885047 | + | 0.465501i | \(0.154126\pi\) | |||||||
\(422\) | 11.6534 | − | 6.72807i | 0.567277 | − | 0.327517i | ||||
\(423\) | 22.1638 | − | 20.4167i | 1.07764 | − | 0.992696i | ||||
\(424\) | 0.487315 | − | 0.844055i | 0.0236661 | − | 0.0409909i | ||||
\(425\) | 5.71962 | 0.277442 | ||||||||
\(426\) | 10.6862 | − | 4.17182i | 0.517750 | − | 0.202126i | ||||
\(427\) | 19.6674 | + | 1.24023i | 0.951772 | + | 0.0600191i | ||||
\(428\) | −15.6906 | + | 9.05896i | −0.758432 | + | 0.437881i | ||||
\(429\) | −2.69838 | + | 17.6862i | −0.130279 | + | 0.853896i | ||||
\(430\) | −4.26008 | + | 2.45956i | −0.205439 | + | 0.118610i | ||||
\(431\) | 20.0356 | + | 11.5676i | 0.965081 | + | 0.557190i | 0.897733 | − | 0.440540i | \(-0.145213\pi\) |
0.0673476 | + | 0.997730i | \(0.478546\pi\) | |||||||
\(432\) | −2.27981 | + | 4.66931i | −0.109688 | + | 0.224652i | ||||
\(433\) | 2.88532i | 0.138660i | 0.997594 | + | 0.0693299i | \(0.0220861\pi\) | ||||
−0.997594 | + | 0.0693299i | \(0.977914\pi\) | |||||||
\(434\) | 1.48500 | − | 23.5488i | 0.0712821 | − | 1.13038i | ||||
\(435\) | 2.82180 | − | 3.52536i | 0.135295 | − | 0.169028i | ||||
\(436\) | 1.76968 | − | 3.06518i | 0.0847525 | − | 0.146796i | ||||
\(437\) | 4.32215 | 0.206756 | ||||||||
\(438\) | −2.25343 | + | 14.7698i | −0.107673 | + | 0.705728i | ||||
\(439\) | − | 5.18281i | − | 0.247362i | −0.992322 | − | 0.123681i | \(-0.960530\pi\) | ||
0.992322 | − | 0.123681i | \(-0.0394699\pi\) | |||||||
\(440\) | −5.67846 | −0.270710 | ||||||||
\(441\) | −17.1105 | + | 12.1750i | −0.814785 | + | 0.579764i | ||||
\(442\) | −10.4041 | −0.494875 | ||||||||
\(443\) | − | 18.7790i | − | 0.892215i | −0.894979 | − | 0.446108i | \(-0.852810\pi\) | ||
0.894979 | − | 0.446108i | \(-0.147190\pi\) | |||||||
\(444\) | −5.48232 | − | 4.38820i | −0.260179 | − | 0.208255i | ||||
\(445\) | −15.7750 | −0.747807 | ||||||||
\(446\) | 5.26038 | − | 9.11125i | 0.249086 | − | 0.431430i | ||||
\(447\) | −27.2342 | − | 4.15513i | −1.28813 | − | 0.196531i | ||||
\(448\) | 0.166511 | − | 2.64051i | 0.00786692 | − | 0.124752i | ||||
\(449\) | − | 23.1775i | − | 1.09381i | −0.837194 | − | 0.546907i | \(-0.815805\pi\) | ||
0.837194 | − | 0.546907i | \(-0.184195\pi\) | |||||||
\(450\) | 0.894597 | − | 2.86351i | 0.0421717 | − | 0.134987i | ||||
\(451\) | 61.1714 | + | 35.3173i | 2.88045 | + | 1.66303i | ||||
\(452\) | −5.41190 | + | 3.12456i | −0.254554 | + | 0.146967i | ||||
\(453\) | 26.4798 | + | 21.1951i | 1.24413 | + | 0.995834i | ||||
\(454\) | 25.1823 | − | 14.5390i | 1.18186 | − | 0.682349i | ||||
\(455\) | 4.80315 | + | 0.302888i | 0.225175 | + | 0.0141996i | ||||
\(456\) | 1.67653 | + | 1.34194i | 0.0785108 | + | 0.0628422i | ||||
\(457\) | 19.7423 | 0.923506 | 0.461753 | − | 0.887008i | \(-0.347221\pi\) | ||||
0.461753 | + | 0.887008i | \(0.347221\pi\) | |||||||
\(458\) | −4.25431 | + | 7.36868i | −0.198791 | + | 0.344316i | ||||
\(459\) | −16.6088 | − | 24.6460i | −0.775234 | − | 1.15038i | ||||
\(460\) | −3.01902 | + | 1.74303i | −0.140763 | + | 0.0812694i | ||||
\(461\) | 6.37073 | − | 11.0344i | 0.296714 | − | 0.513924i | −0.678668 | − | 0.734445i | \(-0.737442\pi\) |
0.975382 | + | 0.220521i | \(0.0707758\pi\) | |||||||
\(462\) | 17.5074 | − | 19.2519i | 0.814519 | − | 0.895677i | ||||
\(463\) | 6.41119 | + | 11.1045i | 0.297953 | + | 0.516070i | 0.975668 | − | 0.219255i | \(-0.0703627\pi\) |
−0.677714 | + | 0.735325i | \(0.737029\pi\) | |||||||
\(464\) | −2.25780 | − | 1.30354i | −0.104816 | − | 0.0605155i | ||||
\(465\) | −15.2702 | − | 2.32978i | −0.708140 | − | 0.108041i | ||||
\(466\) | −13.0309 | − | 22.5702i | −0.603646 | − | 1.04555i | ||||
\(467\) | −2.77900 | − | 4.81337i | −0.128597 | − | 0.222736i | 0.794536 | − | 0.607217i | \(-0.207714\pi\) |
−0.923133 | + | 0.384480i | \(0.874381\pi\) | |||||||
\(468\) | −1.62730 | + | 5.20880i | −0.0752218 | + | 0.240777i | ||||
\(469\) | 0.0114729 | − | 0.181936i | 0.000529771 | − | 0.00840101i | ||||
\(470\) | 8.69903 | + | 5.02238i | 0.401256 | + | 0.231665i | ||||
\(471\) | −10.3062 | − | 26.3997i | −0.474885 | − | 1.21643i | ||||
\(472\) | − | 11.3708i | − | 0.523384i | ||||||
\(473\) | 27.9330i | 1.28436i | ||||||||
\(474\) | 0.860833 | + | 2.20505i | 0.0395394 | + | 0.101281i | ||||
\(475\) | −1.07373 | − | 0.619917i | −0.0492660 | − | 0.0284438i | ||||
\(476\) | 12.6031 | + | 8.37614i | 0.577664 | + | 0.383920i | ||||
\(477\) | 2.85291 | − | 0.640344i | 0.130626 | − | 0.0293193i | ||||
\(478\) | −7.90222 | − | 13.6870i | −0.361439 | − | 0.626031i | ||||
\(479\) | 2.87590 | + | 4.98120i | 0.131403 | + | 0.227597i | 0.924218 | − | 0.381866i | \(-0.124718\pi\) |
−0.792815 | + | 0.609463i | \(0.791385\pi\) | |||||||
\(480\) | −1.71224 | − | 0.261236i | −0.0781526 | − | 0.0119238i | ||||
\(481\) | −6.38683 | − | 3.68744i | −0.291215 | − | 0.168133i | ||||
\(482\) | −2.42841 | − | 4.20612i | −0.110611 | − | 0.191584i | ||||
\(483\) | 3.39858 | − | 15.6095i | 0.154641 | − | 0.710256i | ||||
\(484\) | −10.6225 | + | 18.3987i | −0.482840 | + | 0.836303i | ||||
\(485\) | −1.67919 | + | 0.969482i | −0.0762482 | + | 0.0440219i | ||||
\(486\) | −14.9367 | + | 4.46031i | −0.677543 | + | 0.202324i | ||||
\(487\) | −15.3840 | + | 26.6459i | −0.697116 | + | 1.20744i | 0.272346 | + | 0.962199i | \(0.412200\pi\) |
−0.969462 | + | 0.245241i | \(0.921133\pi\) | |||||||
\(488\) | −7.44834 | −0.337171 | ||||||||
\(489\) | 17.8225 | + | 14.2656i | 0.805961 | + | 0.645113i | ||||
\(490\) | −5.57448 | − | 4.23381i | −0.251829 | − | 0.191264i | ||||
\(491\) | −12.6416 | + | 7.29865i | −0.570509 | + | 0.329383i | −0.757353 | − | 0.653006i | \(-0.773508\pi\) |
0.186844 | + | 0.982390i | \(0.440174\pi\) | |||||||
\(492\) | 16.8203 | + | 13.4635i | 0.758320 | + | 0.606980i | ||||
\(493\) | 12.9138 | − | 7.45578i | 0.581608 | − | 0.335791i | ||||
\(494\) | 1.95314 | + | 1.12765i | 0.0878759 | + | 0.0507352i | ||||
\(495\) | −11.5419 | − | 12.5295i | −0.518770 | − | 0.563160i | ||||
\(496\) | 8.91829i | 0.400443i | ||||||||
\(497\) | −17.4886 | − | 1.10284i | −0.784470 | − | 0.0494689i | ||||
\(498\) | 20.7154 | + | 3.16056i | 0.928281 | + | 0.141628i | ||||
\(499\) | 7.38881 | − | 12.7978i | 0.330768 | − | 0.572908i | −0.651894 | − | 0.758310i | \(-0.726025\pi\) |
0.982663 | + | 0.185402i | \(0.0593588\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 7.60643 | + | 6.08840i | 0.339830 | + | 0.272009i | ||||
\(502\) | − | 21.6259i | − | 0.965211i | ||||||
\(503\) | 12.4283 | 0.554152 | 0.277076 | − | 0.960848i | \(-0.410635\pi\) | ||||
0.277076 | + | 0.960848i | \(0.410635\pi\) | |||||||
\(504\) | 6.16472 | − | 4.99962i | 0.274599 | − | 0.222701i | ||||
\(505\) | 5.51484 | 0.245407 | ||||||||
\(506\) | 19.7955i | 0.880018i | ||||||||
\(507\) | 2.53168 | − | 16.5935i | 0.112436 | − | 0.736945i | ||||
\(508\) | −19.0703 | −0.846110 | ||||||||
\(509\) | 13.0624 | − | 22.6248i | 0.578982 | − | 1.00283i | −0.416614 | − | 0.909083i | \(-0.636783\pi\) |
0.995596 | − | 0.0937432i | \(-0.0298833\pi\) | |||||||
\(510\) | 6.19067 | − | 7.73420i | 0.274127 | − | 0.342476i | ||||
\(511\) | 12.6324 | − | 19.0074i | 0.558826 | − | 0.840836i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.446684 | + | 6.42687i | 0.0197216 | + | 0.283753i | ||||
\(514\) | 4.22766 | + | 2.44084i | 0.186474 | + | 0.107661i | ||||
\(515\) | 6.52554 | − | 3.76752i | 0.287550 | − | 0.166017i | ||||
\(516\) | −1.28505 | + | 8.42269i | −0.0565712 | + | 0.370788i | ||||
\(517\) | 49.3971 | − | 28.5194i | 2.17248 | − | 1.25428i | ||||
\(518\) | 4.76806 | + | 9.60870i | 0.209497 | + | 0.422182i | ||||
\(519\) | 12.8437 | − | 5.01409i | 0.563778 | − | 0.220094i | ||||
\(520\) | −1.81903 | −0.0797696 | ||||||||
\(521\) | −1.65977 | + | 2.87480i | −0.0727157 | + | 0.125947i | −0.900091 | − | 0.435703i | \(-0.856500\pi\) |
0.827375 | + | 0.561650i | \(0.189833\pi\) | |||||||
\(522\) | −1.71289 | − | 7.63139i | −0.0749710 | − | 0.334017i | ||||
\(523\) | −26.8169 | + | 15.4828i | −1.17262 | + | 0.677014i | −0.954296 | − | 0.298862i | \(-0.903393\pi\) |
−0.218326 | + | 0.975876i | \(0.570060\pi\) | |||||||
\(524\) | 0.0646409 | − | 0.111961i | 0.00282385 | − | 0.00489105i | ||||
\(525\) | −3.08313 | + | 3.39033i | −0.134559 | + | 0.147966i | ||||
\(526\) | −7.12083 | − | 12.3336i | −0.310483 | − | 0.537772i | ||||
\(527\) | −44.1753 | − | 25.5046i | −1.92431 | − | 1.11100i | ||||
\(528\) | −6.14612 | + | 7.67855i | −0.267475 | + | 0.334166i | ||||
\(529\) | −5.42366 | − | 9.39405i | −0.235811 | − | 0.408437i | ||||
\(530\) | 0.487315 | + | 0.844055i | 0.0211676 | + | 0.0366634i | ||||
\(531\) | 25.0897 | − | 23.1120i | 1.08880 | − | 1.00298i | ||||
\(532\) | −1.45811 | − | 2.93841i | −0.0632170 | − | 0.127396i | ||||
\(533\) | 19.5955 | + | 11.3135i | 0.848775 | + | 0.490041i | ||||
\(534\) | −17.0742 | + | 21.3313i | −0.738871 | + | 0.923096i | ||||
\(535\) | − | 18.1179i | − | 0.783306i | ||||||
\(536\) | 0.0689019i | 0.00297611i | ||||||||
\(537\) | −11.8557 | − | 1.80883i | −0.511613 | − | 0.0780569i | ||||
\(538\) | 19.6014 | + | 11.3169i | 0.845077 | + | 0.487906i | ||||
\(539\) | −36.6478 | + | 15.3928i | −1.57853 | + | 0.663016i | ||||
\(540\) | −2.90383 | − | 4.30903i | −0.124961 | − | 0.185431i | ||||
\(541\) | −16.6857 | − | 28.9005i | −0.717375 | − | 1.24253i | −0.962036 | − | 0.272921i | \(-0.912010\pi\) |
0.244662 | − | 0.969608i | \(-0.421323\pi\) | |||||||
\(542\) | 3.82099 | + | 6.61815i | 0.164126 | + | 0.284274i | ||||
\(543\) | 1.75222 | + | 4.48836i | 0.0751950 | + | 0.192614i | ||||
\(544\) | −4.95334 | − | 2.85981i | −0.212373 | − | 0.122613i | ||||
\(545\) | 1.76968 | + | 3.06518i | 0.0758049 | + | 0.131298i | ||||
\(546\) | 5.60829 | − | 6.16710i | 0.240013 | − | 0.263927i | ||||
\(547\) | 0.847928 | − | 1.46865i | 0.0362548 | − | 0.0627951i | −0.847329 | − | 0.531069i | \(-0.821791\pi\) |
0.883583 | + | 0.468274i | \(0.155124\pi\) | |||||||
\(548\) | −6.91408 | + | 3.99184i | −0.295355 | + | 0.170523i | ||||
\(549\) | −15.1393 | − | 16.4348i | −0.646130 | − | 0.701418i | ||||
\(550\) | 2.83923 | − | 4.91769i | 0.121065 | − | 0.209691i | ||||
\(551\) | −3.23236 | −0.137703 | ||||||||
\(552\) | −0.910688 | + | 5.96898i | −0.0387614 | + | 0.254057i | ||||
\(553\) | 0.227564 | − | 3.60867i | 0.00967701 | − | 0.153456i | ||||
\(554\) | −10.8474 | + | 6.26276i | −0.460862 | + | 0.266079i | ||||
\(555\) | 6.54145 | − | 2.55373i | 0.277669 | − | 0.108400i | ||||
\(556\) | 4.54379 | − | 2.62336i | 0.192700 | − | 0.111255i | ||||
\(557\) | −28.4998 | − | 16.4544i | −1.20757 | − | 0.697194i | −0.245346 | − | 0.969436i | \(-0.578902\pi\) |
−0.962229 | + | 0.272242i | \(0.912235\pi\) | |||||||
\(558\) | −19.6782 | + | 18.1271i | −0.833045 | + | 0.767381i | ||||
\(559\) | 8.94800i | 0.378460i | ||||||||
\(560\) | 2.20349 | + | 1.46446i | 0.0931144 | + | 0.0618846i | ||||
\(561\) | −20.4577 | − | 52.4030i | −0.863725 | − | 2.21246i | ||||
\(562\) | −10.7815 | + | 18.6742i | −0.454792 | + | 0.787722i | ||||
\(563\) | 31.7973 | 1.34010 | 0.670048 | − | 0.742318i | \(-0.266273\pi\) | ||||
0.670048 | + | 0.742318i | \(0.266273\pi\) | |||||||
\(564\) | 16.2068 | − | 6.32701i | 0.682430 | − | 0.266415i | ||||
\(565\) | − | 6.24913i | − | 0.262903i | ||||||
\(566\) | −27.4419 | −1.15347 | ||||||||
\(567\) | 23.5619 | + | 3.44035i | 0.989508 | + | 0.144481i | ||||
\(568\) | 6.62319 | 0.277903 | ||||||||
\(569\) | 38.0755i | 1.59621i | 0.602519 | + | 0.798105i | \(0.294164\pi\) | ||||
−0.602519 | + | 0.798105i | \(0.705836\pi\) | |||||||
\(570\) | −2.00042 | + | 0.780949i | −0.0837885 | + | 0.0327103i | ||||
\(571\) | −1.98160 | −0.0829274 | −0.0414637 | − | 0.999140i | \(-0.513202\pi\) | ||||
−0.0414637 | + | 0.999140i | \(0.513202\pi\) | |||||||
\(572\) | −5.16464 | + | 8.94541i | −0.215944 | + | 0.374027i | ||||
\(573\) | −1.90850 | − | 4.88867i | −0.0797286 | − | 0.204227i | ||||
\(574\) | −14.6289 | − | 29.4805i | −0.610600 | − | 1.23049i | ||||
\(575\) | − | 3.48607i | − | 0.145379i | ||||||
\(576\) | −2.20650 | + | 2.03258i | −0.0919375 | + | 0.0846906i | ||||
\(577\) | −5.04572 | − | 2.91315i | −0.210056 | − | 0.121276i | 0.391281 | − | 0.920271i | \(-0.372032\pi\) |
−0.601337 | + | 0.798995i | \(0.705365\pi\) | |||||||
\(578\) | 13.6088 | − | 7.85704i | 0.566051 | − | 0.326810i | ||||
\(579\) | 5.68923 | − | 2.22103i | 0.236436 | − | 0.0923028i | ||||
\(580\) | 2.25780 | − | 1.30354i | 0.0937502 | − | 0.0541267i | ||||
\(581\) | −26.6588 | − | 17.7177i | −1.10599 | − | 0.735053i | ||||
\(582\) | −0.506528 | + | 3.31997i | −0.0209963 | + | 0.137617i | ||||
\(583\) | 5.53440 | 0.229212 | ||||||||
\(584\) | −4.31301 | + | 7.47035i | −0.178474 | + | 0.309125i | ||||
\(585\) | −3.69731 | − | 4.01368i | −0.152865 | − | 0.165945i | ||||
\(586\) | 19.9464 | − | 11.5161i | 0.823979 | − | 0.475725i | ||||
\(587\) | −0.0736389 | + | 0.127546i | −0.00303940 | + | 0.00526440i | −0.867541 | − | 0.497365i | \(-0.834301\pi\) |
0.864502 | + | 0.502630i | \(0.167634\pi\) | |||||||
\(588\) | −11.7586 | + | 2.95545i | −0.484918 | + | 0.121881i | ||||
\(589\) | 5.52860 | + | 9.57582i | 0.227802 | + | 0.394565i | ||||
\(590\) | 9.84741 | + | 5.68540i | 0.405411 | + | 0.234064i | ||||
\(591\) | 5.72729 | + | 14.6706i | 0.235589 | + | 0.603469i | ||||
\(592\) | −2.02715 | − | 3.51113i | −0.0833154 | − | 0.144306i | ||||
\(593\) | −5.61919 | − | 9.73273i | −0.230753 | − | 0.399675i | 0.727277 | − | 0.686344i | \(-0.240785\pi\) |
−0.958030 | + | 0.286669i | \(0.907452\pi\) | |||||||
\(594\) | −29.4352 | + | 2.04582i | −1.20774 | + | 0.0839409i | ||||
\(595\) | −13.5555 | + | 6.72656i | −0.555722 | + | 0.275762i | ||||
\(596\) | −13.7747 | − | 7.95281i | −0.564233 | − | 0.325760i | ||||
\(597\) | 24.7617 | + | 3.77790i | 1.01343 | + | 0.154619i | ||||
\(598\) | 6.34125i | 0.259313i | ||||||||
\(599\) | 20.7903i | 0.849470i | 0.905318 | + | 0.424735i | \(0.139633\pi\) | ||||
−0.905318 | + | 0.424735i | \(0.860367\pi\) | |||||||
\(600\) | 1.08236 | − | 1.35222i | 0.0441870 | − | 0.0552043i | ||||
\(601\) | 8.15985 | + | 4.71109i | 0.332847 | + | 0.192169i | 0.657104 | − | 0.753800i | \(-0.271781\pi\) |
−0.324257 | + | 0.945969i | \(0.605114\pi\) | |||||||
\(602\) | 7.20383 | − | 10.8392i | 0.293606 | − | 0.441773i | ||||
\(603\) | −0.152032 | + | 0.140048i | −0.00619122 | + | 0.00570320i | ||||
\(604\) | 9.79120 | + | 16.9589i | 0.398398 | + | 0.690046i | ||||
\(605\) | −10.6225 | − | 18.3987i | −0.431865 | − | 0.748012i | ||||
\(606\) | 5.96902 | − | 7.45729i | 0.242475 | − | 0.302932i | ||||
\(607\) | −37.6028 | − | 21.7100i | −1.52625 | − | 0.881182i | −0.999515 | − | 0.0311539i | \(-0.990082\pi\) |
−0.526737 | − | 0.850028i | \(-0.676585\pi\) | |||||||
\(608\) | 0.619917 | + | 1.07373i | 0.0251410 | + | 0.0435454i | ||||
\(609\) | −2.54166 | + | 11.6737i | −0.102993 | + | 0.473042i | ||||
\(610\) | 3.72417 | − | 6.45045i | 0.150787 | − | 0.261171i | ||||
\(611\) | 15.8238 | − | 9.13585i | 0.640161 | − | 0.369597i | ||||
\(612\) | −3.75786 | − | 16.7423i | −0.151902 | − | 0.676768i | ||||
\(613\) | 4.95622 | − | 8.58442i | 0.200180 | − | 0.346722i | −0.748406 | − | 0.663240i | \(-0.769181\pi\) |
0.948586 | + | 0.316519i | \(0.102514\pi\) | |||||||
\(614\) | 14.6153 | 0.589824 | ||||||||
\(615\) | −20.0699 | + | 7.83512i | −0.809296 | + | 0.315942i | ||||
\(616\) | 13.4580 | − | 6.67816i | 0.542237 | − | 0.269071i | ||||
\(617\) | 32.9309 | − | 19.0126i | 1.32575 | − | 0.765420i | 0.341108 | − | 0.940024i | \(-0.389198\pi\) |
0.984639 | + | 0.174604i | \(0.0558645\pi\) | |||||||
\(618\) | 1.96843 | − | 12.9018i | 0.0791817 | − | 0.518986i | ||||
\(619\) | −35.4802 | + | 20.4845i | −1.42607 | + | 0.823341i | −0.996808 | − | 0.0798398i | \(-0.974559\pi\) |
−0.429261 | + | 0.903181i | \(0.641226\pi\) | |||||||
\(620\) | −7.72347 | − | 4.45915i | −0.310182 | − | 0.179084i | ||||
\(621\) | −15.0216 | + | 10.1230i | −0.602795 | + | 0.406220i | ||||
\(622\) | 4.33309i | 0.173741i | ||||||||
\(623\) | 37.3868 | − | 18.5522i | 1.49787 | − | 0.743278i | ||||
\(624\) | −1.96883 | + | 2.45973i | −0.0788164 | + | 0.0984679i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 9.03514 | 0.361117 | ||||||||
\(627\) | −1.83920 | + | 12.0548i | −0.0734504 | + | 0.481421i | ||||
\(628\) | − | 16.3621i | − | 0.652921i | ||||||
\(629\) | 23.1891 | 0.924609 | ||||||||
\(630\) | 1.24744 | + | 7.83862i | 0.0496991 | + | 0.312298i | ||||
\(631\) | 47.1379 | 1.87653 | 0.938265 | − | 0.345917i | \(-0.112432\pi\) | ||||
0.938265 | + | 0.345917i | \(0.112432\pi\) | |||||||
\(632\) | 1.36666i | 0.0543628i | ||||||||
\(633\) | 18.1957 | + | 14.5643i | 0.723214 | + | 0.578880i | ||||
\(634\) | 19.3816 | 0.769742 | ||||||||
\(635\) | 9.53517 | − | 16.5154i | 0.378392 | − | 0.655394i | ||||
\(636\) | 1.66880 | + | 0.254609i | 0.0661722 | + | 0.0100959i | ||||
\(637\) | −11.7397 | + | 4.93090i | −0.465143 | + | 0.195369i | ||||
\(638\) | − | 14.8042i | − | 0.586106i | ||||||
\(639\) | 13.4621 | + | 14.6141i | 0.532554 | + | 0.578123i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | −27.5136 | + | 15.8850i | −1.08672 | + | 0.627418i | −0.932701 | − | 0.360649i | \(-0.882555\pi\) |
−0.154019 | + | 0.988068i | \(0.549222\pi\) | |||||||
\(642\) | −24.4994 | − | 19.6100i | −0.966916 | − | 0.773946i | ||||
\(643\) | −22.8044 | + | 13.1661i | −0.899319 | + | 0.519222i | −0.876979 | − | 0.480528i | \(-0.840445\pi\) |
−0.0223397 | + | 0.999750i | \(0.507112\pi\) | |||||||
\(644\) | 5.10520 | − | 7.68152i | 0.201173 | − | 0.302694i | ||||
\(645\) | −6.65174 | − | 5.32423i | −0.261912 | − | 0.209641i | ||||
\(646\) | −7.09139 | −0.279007 | ||||||||
\(647\) | 14.6898 | − | 25.4435i | 0.577517 | − | 1.00029i | −0.418247 | − | 0.908333i | \(-0.637355\pi\) |
0.995763 | − | 0.0919545i | \(-0.0293114\pi\) | |||||||
\(648\) | −8.96975 | − | 0.737278i | −0.352365 | − | 0.0289630i | ||||
\(649\) | 55.9181 | − | 32.2843i | 2.19498 | − | 1.26727i | ||||
\(650\) | 0.909513 | − | 1.57532i | 0.0356740 | − | 0.0617893i | ||||
\(651\) | 38.9304 | − | 12.4370i | 1.52580 | − | 0.487443i | ||||
\(652\) | 6.59007 | + | 11.4143i | 0.258087 | + | 0.447020i | ||||
\(653\) | 16.0056 | + | 9.24086i | 0.626349 | + | 0.361623i | 0.779337 | − | 0.626605i | \(-0.215556\pi\) |
−0.152988 | + | 0.988228i | \(0.548889\pi\) | |||||||
\(654\) | 6.06024 | + | 0.924611i | 0.236974 | + | 0.0361552i | ||||
\(655\) | 0.0646409 | + | 0.111961i | 0.00252573 | + | 0.00437469i | ||||
\(656\) | 6.21952 | + | 10.7725i | 0.242831 | + | 0.420596i | ||||
\(657\) | −25.2498 | + | 5.66740i | −0.985090 | + | 0.221106i | ||||
\(658\) | −26.5233 | − | 1.67257i | −1.03399 | − | 0.0652034i | ||||
\(659\) | −26.9328 | − | 15.5497i | −1.04915 | − | 0.605729i | −0.126741 | − | 0.991936i | \(-0.540452\pi\) |
−0.922412 | + | 0.386207i | \(0.873785\pi\) | |||||||
\(660\) | −3.57676 | − | 9.16197i | −0.139225 | − | 0.356629i | ||||
\(661\) | − | 4.02105i | − | 0.156401i | −0.996938 | − | 0.0782003i | \(-0.975083\pi\) | ||
0.996938 | − | 0.0782003i | \(-0.0249174\pi\) | |||||||
\(662\) | 8.35472i | 0.324715i | ||||||||
\(663\) | −6.55337 | − | 16.7867i | −0.254512 | − | 0.651940i | ||||
\(664\) | 10.4776 | + | 6.04923i | 0.406609 | + | 0.234756i | ||||
\(665\) | 3.27379 | + | 0.206446i | 0.126952 | + | 0.00800565i | ||||
\(666\) | 3.62697 | − | 11.6095i | 0.140542 | − | 0.449860i | ||||
\(667\) | −4.54424 | − | 7.87086i | −0.175954 | − | 0.304761i | ||||
\(668\) | 2.81257 | + | 4.87151i | 0.108821 | + | 0.188484i | ||||
\(669\) | 18.0140 | + | 2.74841i | 0.696463 | + | 0.106260i | ||||
\(670\) | −0.0596708 | − | 0.0344509i | −0.00230528 | − | 0.00133096i | ||||
\(671\) | −21.1476 | − | 36.6287i | −0.816393 | − | 1.41403i | ||||
\(672\) | 4.36523 | − | 1.39455i | 0.168392 | − | 0.0537958i | ||||
\(673\) | 3.92719 | − | 6.80209i | 0.151382 | − | 0.262201i | −0.780354 | − | 0.625338i | \(-0.784961\pi\) |
0.931736 | + | 0.363137i | \(0.118294\pi\) | |||||||
\(674\) | 29.2538 | − | 16.8897i | 1.12681 | − | 0.650566i | ||||
\(675\) | 5.18365 | − | 0.360277i | 0.199519 | − | 0.0138671i | ||||
\(676\) | 4.84557 | − | 8.39278i | 0.186368 | − | 0.322799i | ||||
\(677\) | −33.9569 | −1.30507 | −0.652534 | − | 0.757760i | \(-0.726294\pi\) | ||||
−0.652534 | + | 0.757760i | \(0.726294\pi\) | |||||||
\(678\) | −8.45021 | − | 6.76378i | −0.324528 | − | 0.259761i | ||||
\(679\) | 2.83953 | − | 4.27249i | 0.108971 | − | 0.163963i | ||||
\(680\) | 4.95334 | − | 2.85981i | 0.189952 | − | 0.109669i | ||||
\(681\) | 39.3199 | + | 31.4727i | 1.50674 | + | 1.20604i | ||||
\(682\) | −43.8574 | + | 25.3211i | −1.67939 | + | 0.969595i | ||||
\(683\) | 5.22203 | + | 3.01494i | 0.199815 | + | 0.115363i | 0.596569 | − | 0.802562i | \(-0.296530\pi\) |
−0.396754 | + | 0.917925i | \(0.629863\pi\) | |||||||
\(684\) | −1.10915 | + | 3.55028i | −0.0424095 | + | 0.135748i | ||||
\(685\) | − | 7.98369i | − | 0.305041i | ||||||
\(686\) | 18.1907 | + | 3.47827i | 0.694524 | + | 0.132801i | ||||
\(687\) | −14.5688 | − | 2.22276i | −0.555833 | − | 0.0848035i | ||||
\(688\) | −2.45956 | + | 4.26008i | −0.0937697 | + | 0.162414i | ||||
\(689\) | 1.77288 | 0.0675413 | ||||||||
\(690\) | −4.71394 | − | 3.77317i | −0.179457 | − | 0.143642i | ||||
\(691\) | 17.6548i | 0.671621i | 0.941930 | + | 0.335811i | \(0.109010\pi\) | ||||
−0.941930 | + | 0.335811i | \(0.890990\pi\) | |||||||
\(692\) | 7.96037 | 0.302608 | ||||||||
\(693\) | 42.0897 | + | 16.1211i | 1.59885 | + | 0.612391i | ||||
\(694\) | −11.3240 | −0.429854 | ||||||||
\(695\) | 5.24672i | 0.199019i | ||||||||
\(696\) | 0.681066 | − | 4.46395i | 0.0258157 | − | 0.169206i | ||||
\(697\) | −71.1466 | −2.69487 | ||||||||
\(698\) | 1.94775 | − | 3.37360i | 0.0737234 | − | 0.127693i | ||||
\(699\) | 28.2082 | − | 35.2414i | 1.06693 | − | 1.33295i | ||||
\(700\) | −2.37000 | + | 1.17605i | −0.0895776 | + | 0.0444505i | ||||
\(701\) | 27.1258i | 1.02453i | 0.858828 | + | 0.512263i | \(0.171193\pi\) | ||||
−0.858828 | + | 0.512263i | \(0.828807\pi\) | |||||||
\(702\) | −9.42919 | + | 0.655353i | −0.355882 | + | 0.0247347i | ||||
\(703\) | −4.35322 | − | 2.51333i | −0.164185 | − | 0.0947921i | ||||
\(704\) | −4.91769 | + | 2.83923i | −0.185343 | + | 0.107008i | ||||
\(705\) | −2.62406 | + | 17.1990i | −0.0988277 | + | 0.647753i | ||||
\(706\) | 24.8588 | − | 14.3522i | 0.935573 | − | 0.540153i | ||||
\(707\) | −13.0702 | + | 6.48572i | −0.491554 | + | 0.243921i | ||||
\(708\) | 18.3463 | − | 7.16226i | 0.689497 | − | 0.269174i | ||||
\(709\) | 21.7165 | 0.815582 | 0.407791 | − | 0.913075i | \(-0.366299\pi\) | ||||
0.407791 | + | 0.913075i | \(0.366299\pi\) | |||||||
\(710\) | −3.31160 | + | 5.73585i | −0.124282 | + | 0.215263i | ||||
\(711\) | −3.01553 | + | 2.77784i | −0.113091 | + | 0.104177i | ||||
\(712\) | −13.6615 | + | 7.88750i | −0.511988 | + | 0.295596i | ||||
\(713\) | −15.5449 | + | 26.9245i | −0.582161 | + | 1.00833i | ||||
\(714\) | −5.57608 | + | 25.6106i | −0.208679 | + | 0.958453i | ||||
\(715\) | −5.16464 | − | 8.94541i | −0.193146 | − | 0.334540i | ||||
\(716\) | −5.99647 | − | 3.46206i | −0.224098 | − | 0.129383i | ||||
\(717\) | 17.1060 | − | 21.3711i | 0.638836 | − | 0.798119i | ||||
\(718\) | −1.15988 | − | 2.00897i | −0.0432863 | − | 0.0749741i | ||||
\(719\) | −13.2510 | − | 22.9514i | −0.494178 | − | 0.855941i | 0.505800 | − | 0.862651i | \(-0.331198\pi\) |
−0.999977 | + | 0.00670969i | \(0.997864\pi\) | |||||||
\(720\) | −0.657012 | − | 2.92717i | −0.0244854 | − | 0.109089i | ||||
\(721\) | −11.0347 | + | 16.6034i | −0.410955 | + | 0.618343i | ||||
\(722\) | −15.1232 | − | 8.73140i | −0.562829 | − | 0.324949i | ||||
\(723\) | 5.25680 | − | 6.56749i | 0.195503 | − | 0.244248i | ||||
\(724\) | 2.78183i | 0.103386i | ||||||||
\(725\) | 2.60709i | 0.0968248i | ||||||||
\(726\) | −36.3764 | − | 5.54995i | −1.35005 | − | 0.205978i | ||||
\(727\) | 6.52916 | + | 3.76961i | 0.242153 | + | 0.139807i | 0.616166 | − | 0.787616i | \(-0.288685\pi\) |
−0.374013 | + | 0.927424i | \(0.622018\pi\) | |||||||
\(728\) | 4.31109 | − | 2.13927i | 0.159780 | − | 0.0792865i | ||||
\(729\) | −16.6049 | − | 21.2903i | −0.614996 | − | 0.788530i | ||||
\(730\) | −4.31301 | − | 7.47035i | −0.159632 | − | 0.276490i | ||||
\(731\) | −14.0677 | − | 24.3660i | −0.520314 | − | 0.901210i | ||||
\(732\) | −4.69157 | − | 12.0176i | −0.173405 | − | 0.444183i | ||||
\(733\) | −18.3456 | − | 10.5918i | −0.677610 | − | 0.391218i | 0.121344 | − | 0.992611i | \(-0.461280\pi\) |
−0.798954 | + | 0.601392i | \(0.794613\pi\) | |||||||
\(734\) | −6.63561 | − | 11.4932i | −0.244925 | − | 0.424222i | ||||
\(735\) | 3.31982 | − | 11.6610i | 0.122453 | − | 0.430122i | ||||
\(736\) | −1.74303 | + | 3.01902i | −0.0642491 | + | 0.111283i | ||||
\(737\) | −0.338838 | + | 0.195628i | −0.0124813 | + | 0.00720606i | ||||
\(738\) | −11.1279 | + | 35.6193i | −0.409625 | + | 1.31117i | ||||
\(739\) | −23.0621 | + | 39.9448i | −0.848355 | + | 1.46939i | 0.0343210 | + | 0.999411i | \(0.489073\pi\) |
−0.882676 | + | 0.469983i | \(0.844260\pi\) | |||||||
\(740\) | 4.05430 | 0.149039 | ||||||||
\(741\) | −0.589164 | + | 3.86159i | −0.0216435 | + | 0.141859i | ||||
\(742\) | −2.14759 | − | 1.42730i | −0.0788405 | − | 0.0523980i | ||||
\(743\) | −33.6453 | + | 19.4252i | −1.23433 | + | 0.712640i | −0.967929 | − | 0.251223i | \(-0.919167\pi\) |
−0.266399 | + | 0.963863i | \(0.585834\pi\) | |||||||
\(744\) | −14.3893 | + | 5.61747i | −0.527537 | + | 0.205946i | ||||
\(745\) | 13.7747 | − | 7.95281i | 0.504665 | − | 0.291369i | ||||
\(746\) | 3.58763 | + | 2.07132i | 0.131352 | + | 0.0758364i | ||||
\(747\) | 7.94883 | + | 35.4143i | 0.290833 | + | 1.29574i | ||||
\(748\) | − | 32.4787i | − | 1.18754i | ||||||
\(749\) | 21.3076 | + | 42.9395i | 0.778562 | + | 1.56897i | ||||
\(750\) | 0.629881 | + | 1.61346i | 0.0230000 | + | 0.0589152i | ||||
\(751\) | 8.52796 | − | 14.7709i | 0.311190 | − | 0.538996i | −0.667431 | − | 0.744672i | \(-0.732606\pi\) |
0.978620 | + | 0.205676i | \(0.0659392\pi\) | |||||||
\(752\) | 10.0448 | 0.366295 | ||||||||
\(753\) | 34.8925 | − | 13.6218i | 1.27155 | − | 0.496404i | ||||
\(754\) | − | 4.74236i | − | 0.172707i | ||||||
\(755\) | −19.5824 | −0.712677 | ||||||||
\(756\) | 11.9497 | + | 6.79736i | 0.434607 | + | 0.247218i | ||||
\(757\) | 3.74105 | 0.135971 | 0.0679854 | − | 0.997686i | \(-0.478343\pi\) | ||||
0.0679854 | + | 0.997686i | \(0.478343\pi\) | |||||||
\(758\) | 6.21425i | 0.225712i | ||||||||
\(759\) | −31.9393 | + | 12.4688i | −1.15932 | + | 0.452590i | ||||
\(760\) | −1.23983 | −0.0449735 | ||||||||
\(761\) | 12.0610 | − | 20.8902i | 0.437210 | − | 0.757271i | −0.560263 | − | 0.828315i | \(-0.689300\pi\) |
0.997473 | + | 0.0710443i | \(0.0226332\pi\) | |||||||
\(762\) | −12.0121 | − | 30.7692i | −0.435151 | − | 1.11465i | ||||
\(763\) | −7.79896 | − | 5.18325i | −0.282341 | − | 0.187646i | ||||
\(764\) | − | 3.02993i | − | 0.109619i | ||||||
\(765\) | 16.3782 | + | 5.11676i | 0.592155 | + | 0.184997i | ||||
\(766\) | 11.8095 | + | 6.81820i | 0.426693 | + | 0.246351i | ||||
\(767\) | 17.9127 | − | 10.3419i | 0.646790 | − | 0.373424i | ||||
\(768\) | −1.61346 | + | 0.629881i | −0.0582207 | + | 0.0227289i | ||||
\(769\) | −11.7667 | + | 6.79354i | −0.424320 | + | 0.244981i | −0.696924 | − | 0.717145i | \(-0.745448\pi\) |
0.272604 | + | 0.962126i | \(0.412115\pi\) | |||||||
\(770\) | −0.945528 | + | 14.9940i | −0.0340745 | + | 0.540347i | ||||
\(771\) | −1.27527 | + | 8.35859i | −0.0459278 | + | 0.301027i | ||||
\(772\) | 3.52611 | 0.126907 | ||||||||
\(773\) | 9.03034 | − | 15.6410i | 0.324799 | − | 0.562568i | −0.656673 | − | 0.754175i | \(-0.728037\pi\) |
0.981472 | + | 0.191608i | \(0.0613701\pi\) | |||||||
\(774\) | −14.3991 | + | 3.23192i | −0.517565 | + | 0.116169i | ||||
\(775\) | 7.72347 | − | 4.45915i | 0.277435 | − | 0.160177i | ||||
\(776\) | −0.969482 | + | 1.67919i | −0.0348024 | + | 0.0602795i | ||||
\(777\) | −12.4999 | + | 13.7454i | −0.448432 | + | 0.493114i | ||||
\(778\) | 14.6496 | + | 25.3739i | 0.525215 | + | 0.909699i | ||||
\(779\) | 13.3561 | + | 7.71118i | 0.478534 | + | 0.276282i | ||||
\(780\) | −1.14577 | − | 2.93492i | −0.0410252 | − | 0.105087i | ||||
\(781\) | 18.8048 | + | 32.5708i | 0.672888 | + | 1.16548i | ||||
\(782\) | −9.96950 | − | 17.2677i | −0.356509 | − | 0.617491i | ||||
\(783\) | 11.2340 | − | 7.57054i | 0.401471 | − | 0.270549i | ||||
\(784\) | −6.94455 | − | 0.879348i | −0.248020 | − | 0.0314053i | ||||
\(785\) | 14.1700 | + | 8.18107i | 0.505750 | + | 0.291995i | ||||
\(786\) | 0.221361 | + | 0.0337731i | 0.00789569 | + | 0.00120465i | ||||
\(787\) | 33.3047i | 1.18718i | 0.804766 | + | 0.593592i | \(0.202291\pi\) | ||||
−0.804766 | + | 0.593592i | \(0.797709\pi\) | |||||||
\(788\) | 9.09265i | 0.323912i | ||||||||
\(789\) | 15.4145 | − | 19.2579i | 0.548772 | − | 0.685599i | ||||
\(790\) | −1.18356 | − | 0.683330i | −0.0421092 | − | 0.0243118i | ||||
\(791\) | 7.34929 | + | 14.8104i | 0.261311 | + | 0.526599i | ||||
\(792\) | −16.2603 | − | 5.07994i | −0.577786 | − | 0.180508i | ||||
\(793\) | −6.77436 | − | 11.7335i | −0.240565 | − | 0.416670i | ||||
\(794\) | 5.55415 | + | 9.62007i | 0.197109 | + | 0.341403i | ||||
\(795\) | −1.05490 | + | 1.31792i | −0.0374133 | + | 0.0467417i | ||||
\(796\) | 12.5241 | + | 7.23082i | 0.443906 | + | 0.256289i | ||||
\(797\) | −3.47393 | − | 6.01703i | −0.123053 | − | 0.213134i | 0.797917 | − | 0.602767i | \(-0.205935\pi\) |
−0.920970 | + | 0.389633i | \(0.872602\pi\) | |||||||
\(798\) | 3.82257 | − | 4.20345i | 0.135317 | − | 0.148800i | ||||
\(799\) | −28.7261 | + | 49.7551i | −1.01626 | + | 1.76021i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | −45.1719 | − | 14.1123i | −1.59607 | − | 0.498632i | ||||
\(802\) | 0.723128 | − | 1.25249i | 0.0255345 | − | 0.0442271i | ||||
\(803\) | −48.9825 | −1.72856 | ||||||||
\(804\) | −0.111170 | + | 0.0434000i | −0.00392067 | + | 0.00153060i | ||||
\(805\) | 4.09979 | + | 8.26199i | 0.144499 | + | 0.291197i | ||||
\(806\) | −14.0492 | + | 8.11131i | −0.494862 | + | 0.285709i | ||||
\(807\) | −5.91276 | + | 38.7544i | −0.208139 | + | 1.36422i | ||||
\(808\) | 4.77599 | − | 2.75742i | 0.168019 | − | 0.0970056i | ||||
\(809\) | 4.12744 | + | 2.38298i | 0.145113 | + | 0.0837810i | 0.570799 | − | 0.821090i | \(-0.306634\pi\) |
−0.425686 | + | 0.904871i | \(0.639967\pi\) | |||||||
\(810\) | 5.12338 | − | 7.39939i | 0.180017 | − | 0.259988i | ||||
\(811\) | − | 28.2422i | − | 0.991716i | −0.868404 | − | 0.495858i | \(-0.834854\pi\) | ||
0.868404 | − | 0.495858i | \(-0.165146\pi\) | |||||||
\(812\) | −3.81796 | + | 5.74469i | −0.133984 | + | 0.201599i | ||||
\(813\) | −8.27134 | + | 10.3337i | −0.290089 | + | 0.362417i | ||||
\(814\) | 11.5111 | − | 19.9378i | 0.403464 | − | 0.698820i | ||||
\(815\) | −13.1801 | −0.461680 | ||||||||
\(816\) | 1.49417 | − | 9.79335i | 0.0523065 | − | 0.342836i | ||||
\(817\) | 6.09889i | 0.213373i | ||||||||
\(818\) | 16.2396 | 0.567804 | ||||||||
\(819\) | 13.4829 | + | 5.16421i | 0.471131 | + | 0.180452i | ||||
\(820\) | −12.4390 | −0.434390 | ||||||||
\(821\) | 37.1488i | 1.29650i | 0.761427 | + | 0.648250i | \(0.224499\pi\) | ||||
−0.761427 | + | 0.648250i | \(0.775501\pi\) | |||||||
\(822\) | −10.7957 | − | 8.64119i | −0.376544 | − | 0.301396i | ||||
\(823\) | −4.24631 | −0.148017 | −0.0740086 | − | 0.997258i | \(-0.523579\pi\) | ||||
−0.0740086 | + | 0.997258i | \(0.523579\pi\) | |||||||
\(824\) | 3.76752 | − | 6.52554i | 0.131248 | − | 0.227328i | ||||
\(825\) | 9.72287 | + | 1.48342i | 0.338507 | + | 0.0516461i | ||||
\(826\) | −30.0247 | − | 1.89337i | −1.04469 | − | 0.0658787i | ||||
\(827\) | − | 25.2354i | − | 0.877519i | −0.898604 | − | 0.438760i | \(-0.855418\pi\) | ||
0.898604 | − | 0.438760i | \(-0.144582\pi\) | |||||||
\(828\) | −10.2043 | + | 2.29039i | −0.354625 | + | 0.0795965i | ||||
\(829\) | 3.50716 | + | 2.02486i | 0.121809 | + | 0.0703262i | 0.559666 | − | 0.828718i | \(-0.310929\pi\) |
−0.437858 | + | 0.899044i | \(0.644263\pi\) | |||||||
\(830\) | −10.4776 | + | 6.04923i | −0.363682 | + | 0.209972i | ||||
\(831\) | −16.9373 | − | 13.5571i | −0.587548 | − | 0.470289i | ||||
\(832\) | −1.57532 | + | 0.909513i | −0.0546145 | + | 0.0315317i | ||||
\(833\) | 24.2158 | − | 31.8839i | 0.839028 | − | 1.10471i | ||||
\(834\) | 7.09474 | + | 5.67882i | 0.245671 | + | 0.196641i | ||||
\(835\) | −5.62513 | −0.194666 | ||||||||
\(836\) | −3.52018 | + | 6.09713i | −0.121748 | + | 0.210874i | ||||
\(837\) | −41.6423 | − | 20.3321i | −1.43937 | − | 0.702779i | ||||
\(838\) | −7.35247 | + | 4.24495i | −0.253987 | + | 0.146639i | ||||
\(839\) | 23.7002 | − | 41.0500i | 0.818222 | − | 1.41720i | −0.0887683 | − | 0.996052i | \(-0.528293\pi\) |
0.906991 | − | 0.421151i | \(-0.138374\pi\) | |||||||
\(840\) | −0.974903 | + | 4.47767i | −0.0336373 | + | 0.154494i | ||||
\(841\) | −11.1015 | − | 19.2284i | −0.382812 | − | 0.663050i | ||||
\(842\) | 1.39979 | + | 0.808166i | 0.0482398 | + | 0.0278513i | ||||
\(843\) | −36.9211 | − | 5.63306i | −1.27163 | − | 0.194013i | ||||
\(844\) | 6.72807 | + | 11.6534i | 0.231590 | + | 0.401125i | ||||
\(845\) | 4.84557 | + | 8.39278i | 0.166693 | + | 0.288720i | ||||
\(846\) | 20.4167 | + | 22.1638i | 0.701942 | + | 0.762006i | ||||
\(847\) | 46.8130 | + | 31.1123i | 1.60851 | + | 1.06903i | ||||
\(848\) | 0.844055 | + | 0.487315i | 0.0289850 | + | 0.0167345i | ||||
\(849\) | −17.2851 | − | 44.2763i | −0.593224 | − | 1.51956i | ||||
\(850\) | 5.71962i | 0.196181i | ||||||||
\(851\) | − | 14.1336i | − | 0.484493i | ||||||
\(852\) | 4.17182 | + | 10.6862i | 0.142924 | + | 0.366105i | ||||
\(853\) | 15.0033 | + | 8.66216i | 0.513703 | + | 0.296587i | 0.734354 | − | 0.678766i | \(-0.237485\pi\) |
−0.220651 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(854\) | −1.24023 | + | 19.6674i | −0.0424399 | + | 0.673004i | ||||
\(855\) | −2.52006 | − | 2.73569i | −0.0861841 | − | 0.0935588i | ||||
\(856\) | −9.05896 | − | 15.6906i | −0.309629 | − | 0.536293i | ||||
\(857\) | 14.0937 | + | 24.4111i | 0.481433 | + | 0.833866i | 0.999773 | − | 0.0213087i | \(-0.00678329\pi\) |
−0.518340 | + | 0.855174i | \(0.673450\pi\) | |||||||
\(858\) | −17.6862 | − | 2.69838i | −0.603796 | − | 0.0921212i | ||||
\(859\) | 42.5542 | + | 24.5687i | 1.45193 | + | 0.838272i | 0.998591 | − | 0.0530671i | \(-0.0168997\pi\) |
0.453338 | + | 0.891339i | \(0.350233\pi\) | |||||||
\(860\) | −2.45956 | − | 4.26008i | −0.0838702 | − | 0.145267i | ||||
\(861\) | 38.3511 | − | 42.1724i | 1.30700 | − | 1.43723i | ||||
\(862\) | −11.5676 | + | 20.0356i | −0.393993 | + | 0.682415i | ||||
\(863\) | 20.4648 | − | 11.8154i | 0.696631 | − | 0.402200i | −0.109460 | − | 0.993991i | \(-0.534912\pi\) |
0.806092 | + | 0.591791i | \(0.201579\pi\) | |||||||
\(864\) | −4.66931 | − | 2.27981i | −0.158853 | − | 0.0775609i | ||||
\(865\) | −3.98019 | + | 6.89389i | −0.135330 | + | 0.234399i | ||||
\(866\) | −2.88532 | −0.0980473 | ||||||||
\(867\) | 21.2489 | + | 17.0082i | 0.721651 | + | 0.577629i | ||||
\(868\) | 23.5488 | + | 1.48500i | 0.799299 | + | 0.0504040i | ||||
\(869\) | −6.72081 | + | 3.88026i | −0.227988 | + | 0.131629i | ||||
\(870\) | 3.52536 | + | 2.82180i | 0.119521 | + | 0.0956678i | ||||
\(871\) | −0.108543 | + | 0.0626672i | −0.00367783 | + | 0.00212340i | ||||
\(872\) | 3.06518 | + | 1.76968i | 0.103800 | + | 0.0599291i | ||||
\(873\) | −5.67568 | + | 1.27392i | −0.192093 | + | 0.0431157i | ||||
\(874\) | 4.32215i | 0.146199i | ||||||||
\(875\) | 0.166511 | − | 2.64051i | 0.00562911 | − | 0.0892654i | ||||
\(876\) | −14.7698 | − | 2.25343i | −0.499025 | − | 0.0761363i | ||||
\(877\) | −9.45337 | + | 16.3737i | −0.319218 | + | 0.552901i | −0.980325 | − | 0.197390i | \(-0.936753\pi\) |
0.661107 | + | 0.750291i | \(0.270087\pi\) | |||||||
\(878\) | 5.18281 | 0.174911 | ||||||||
\(879\) | 31.1446 | + | 24.9290i | 1.05048 | + | 0.840833i | ||||
\(880\) | − | 5.67846i | − | 0.191421i | ||||||
\(881\) | −17.7505 | −0.598030 | −0.299015 | − | 0.954248i | \(-0.596658\pi\) | ||||
−0.299015 | + | 0.954248i | \(0.596658\pi\) | |||||||
\(882\) | −12.1750 | − | 17.1105i | −0.409955 | − | 0.576140i | ||||
\(883\) | −45.1444 | −1.51923 | −0.759614 | − | 0.650374i | \(-0.774612\pi\) | ||||
−0.759614 | + | 0.650374i | \(0.774612\pi\) | |||||||
\(884\) | − | 10.4041i | − | 0.349929i | ||||||
\(885\) | −2.97047 | + | 19.4695i | −0.0998512 | + | 0.654461i | ||||
\(886\) | 18.7790 | 0.630892 | ||||||||
\(887\) | −13.7214 | + | 23.7661i | −0.460718 | + | 0.797988i | −0.998997 | − | 0.0447794i | \(-0.985742\pi\) |
0.538279 | + | 0.842767i | \(0.319075\pi\) | |||||||
\(888\) | 4.38820 | − | 5.48232i | 0.147258 | − | 0.183975i | ||||
\(889\) | −3.17543 | + | 50.3554i | −0.106500 | + | 1.68886i | ||||
\(890\) | − | 15.7750i | − | 0.528779i | ||||||
\(891\) | −21.8415 | − | 46.2038i | −0.731718 | − | 1.54788i | ||||
\(892\) | 9.11125 | + | 5.26038i | 0.305067 | + | 0.176131i | ||||
\(893\) | 10.7854 | − | 6.22693i | 0.360918 | − | 0.208376i | ||||
\(894\) | 4.15513 | − | 27.2342i | 0.138968 | − | 0.910848i | ||||
\(895\) | 5.99647 | − | 3.46206i | 0.200440 | − | 0.115724i | ||||
\(896\) | 2.64051 | + | 0.166511i | 0.0882131 | + | 0.00556275i | ||||
\(897\) | −10.2314 | + | 3.99424i | −0.341615 | + | 0.133364i | ||||
\(898\) | 23.1775 | 0.773443 | ||||||||
\(899\) | 11.6254 | − | 20.1358i | 0.387728 | − | 0.671565i | ||||
\(900\) | 2.86351 | + | 0.894597i | 0.0954504 | + | 0.0298199i | ||||
\(901\) | −4.82767 | + | 2.78726i | −0.160833 | + | 0.0928571i | ||||
\(902\) | −35.3173 | + | 61.1714i | −1.17594 | + | 2.03678i | ||||
\(903\) | 22.0262 | + | 4.79566i | 0.732986 | + | 0.159589i | ||||
\(904\) | −3.12456 | − | 5.41190i | −0.103921 | − | 0.179997i | ||||
\(905\) | −2.40913 | − | 1.39091i | −0.0800823 | − | 0.0462355i | ||||
\(906\) | −21.1951 | + | 26.4798i | −0.704161 | + | 0.879732i | ||||
\(907\) | 17.0394 | + | 29.5132i | 0.565785 | + | 0.979969i | 0.996976 | + | 0.0777079i | \(0.0247602\pi\) |
−0.431191 | + | 0.902261i | \(0.641907\pi\) | |||||||
\(908\) | 14.5390 | + | 25.1823i | 0.482493 | + | 0.835703i | ||||
\(909\) | 15.7918 | + | 4.93356i | 0.523781 | + | 0.163636i | ||||
\(910\) | −0.302888 | + | 4.80315i | −0.0100407 | + | 0.159223i | ||||
\(911\) | 50.8899 | + | 29.3813i | 1.68606 | + | 0.973447i | 0.957487 | + | 0.288477i | \(0.0931490\pi\) |
0.728572 | + | 0.684969i | \(0.240184\pi\) | |||||||
\(912\) | −1.34194 | + | 1.67653i | −0.0444361 | + | 0.0555155i | ||||
\(913\) | 68.7007i | 2.27366i | ||||||||
\(914\) | 19.7423i | 0.653018i | ||||||||
\(915\) | 12.7533 | + | 1.94578i | 0.421612 | + | 0.0643254i | ||||
\(916\) | −7.36868 | − | 4.25431i | −0.243468 | − | 0.140566i | ||||
\(917\) | −0.284871 | − | 0.189328i | −0.00940728 | − | 0.00625215i | ||||
\(918\) | 24.6460 | − | 16.6088i | 0.813440 | − | 0.548173i | ||||
\(919\) | 25.0699 | + | 43.4223i | 0.826979 | + | 1.43237i | 0.900397 | + | 0.435068i | \(0.143276\pi\) |
−0.0734186 | + | 0.997301i | \(0.523391\pi\) | |||||||
\(920\) | −1.74303 | − | 3.01902i | −0.0574662 | − | 0.0995343i | ||||
\(921\) | 9.20588 | + | 23.5811i | 0.303344 | + | 0.777025i | ||||
\(922\) | 11.0344 | + | 6.37073i | 0.363399 | + | 0.209809i | ||||
\(923\) | 6.02388 | + | 10.4337i | 0.198278 | + | 0.343428i | ||||
\(924\) | 19.2519 | + | 17.5074i | 0.633339 | + | 0.575952i | ||||
\(925\) | −2.02715 | + | 3.51113i | −0.0666523 | + | 0.115445i | ||||
\(926\) | −11.1045 | + | 6.41119i | −0.364917 | + | 0.210685i | ||||
\(927\) | 22.0564 | − | 4.95061i | 0.724426 | − | 0.162599i | ||||
\(928\) | 1.30354 | − | 2.25780i | 0.0427909 | − | 0.0741160i | ||||
\(929\) | 9.13789 | 0.299804 | 0.149902 | − | 0.988701i | \(-0.452104\pi\) | ||||
0.149902 | + | 0.988701i | \(0.452104\pi\) | |||||||
\(930\) | 2.32978 | − | 15.2702i | 0.0763966 | − | 0.500731i | ||||
\(931\) | −8.00168 | + | 3.36087i | −0.262245 | + | 0.110148i | ||||
\(932\) | 22.5702 | − | 13.0309i | 0.739313 | − | 0.426842i | ||||
\(933\) | −6.99126 | + | 2.72933i | −0.228883 | + | 0.0893542i | ||||
\(934\) | 4.81337 | − | 2.77900i | 0.157498 | − | 0.0909316i | ||||
\(935\) | 28.1273 | + | 16.2393i | 0.919863 | + | 0.531083i | ||||
\(936\) | −5.20880 | − | 1.62730i | −0.170255 | − | 0.0531898i | ||||
\(937\) | − | 12.3801i | − | 0.404439i | −0.979340 | − | 0.202219i | \(-0.935185\pi\) | ||
0.979340 | − | 0.202219i | \(-0.0648154\pi\) | |||||||
\(938\) | 0.181936 | + | 0.0114729i | 0.00594041 | + | 0.000374605i | ||||
\(939\) | 5.69107 | + | 14.5778i | 0.185721 | + | 0.475730i | ||||
\(940\) | −5.02238 | + | 8.69903i | −0.163812 | + | 0.283731i | ||||
\(941\) | 28.2064 | 0.919502 | 0.459751 | − | 0.888048i | \(-0.347939\pi\) | ||||
0.459751 | + | 0.888048i | \(0.347939\pi\) | |||||||
\(942\) | 26.3997 | − | 10.3062i | 0.860147 | − | 0.335795i | ||||
\(943\) | 43.3634i | 1.41211i | ||||||||
\(944\) | 11.3708 | 0.370088 | ||||||||
\(945\) | −11.8615 | + | 6.95009i | −0.385856 | + | 0.226086i | ||||
\(946\) | −27.9330 | −0.908180 | ||||||||
\(947\) | − | 7.08925i | − | 0.230370i | −0.993344 | − | 0.115185i | \(-0.963254\pi\) | ||
0.993344 | − | 0.115185i | \(-0.0367460\pi\) | |||||||
\(948\) | −2.20505 | + | 0.860833i | −0.0716166 | + | 0.0279586i | ||||
\(949\) | −15.6910 | −0.509350 | ||||||||
\(950\) | 0.619917 | − | 1.07373i | 0.0201128 | − | 0.0348363i | ||||
\(951\) | 12.2081 | + | 31.2714i | 0.395875 | + | 1.01404i | ||||
\(952\) | −8.37614 | + | 12.6031i | −0.271472 | + | 0.408470i | ||||
\(953\) | − | 27.1147i | − | 0.878331i | −0.898406 | − | 0.439165i | \(-0.855274\pi\) | ||
0.898406 | − | 0.439165i | \(-0.144726\pi\) | |||||||
\(954\) | 0.640344 | + | 2.85291i | 0.0207319 | + | 0.0923664i | ||||
\(955\) | 2.62400 | + | 1.51497i | 0.0849105 | + | 0.0490231i | ||||
\(956\) | 13.6870 | − | 7.90222i | 0.442671 | − | 0.255576i | ||||
\(957\) | 23.8860 | − | 9.32492i | 0.772126 | − | 0.301432i | ||||
\(958\) | −4.98120 | + | 2.87590i | −0.160935 | + | 0.0929160i | ||||
\(959\) | 9.38922 | + | 18.9214i | 0.303194 | + | 0.611002i | ||||
\(960\) | 0.261236 | − | 1.71224i | 0.00843136 | − | 0.0552622i | ||||
\(961\) | −48.5359 | −1.56568 | ||||||||
\(962\) | 3.68744 | − | 6.38683i | 0.118888 | − | 0.205920i | ||||
\(963\) | 16.2082 | − | 51.8808i | 0.522303 | − | 1.67184i | ||||
\(964\) | 4.20612 | − | 2.42841i | 0.135470 | − | 0.0782137i | ||||
\(965\) | −1.76305 | + | 3.05370i | −0.0567547 | + | 0.0983020i | ||||
\(966\) | 15.6095 | + | 3.39858i | 0.502227 | + | 0.109347i | ||||
\(967\) | −12.5108 | − | 21.6694i | −0.402321 | − | 0.696840i | 0.591685 | − | 0.806170i | \(-0.298463\pi\) |
−0.994006 | + | 0.109329i | \(0.965130\pi\) | |||||||
\(968\) | −18.3987 | − | 10.6225i | −0.591355 | − | 0.341419i | ||||
\(969\) | −4.46673 | − | 11.4417i | −0.143492 | − | 0.367559i | ||||
\(970\) | −0.969482 | − | 1.67919i | −0.0311282 | − | 0.0539156i | ||||
\(971\) | −21.1676 | − | 36.6634i | −0.679302 | − | 1.17659i | −0.975191 | − | 0.221363i | \(-0.928949\pi\) |
0.295890 | − | 0.955222i | \(-0.404384\pi\) | |||||||
\(972\) | −4.46031 | − | 14.9367i | −0.143065 | − | 0.479096i | ||||
\(973\) | −6.17041 | − | 12.4347i | −0.197814 | − | 0.398639i | ||||
\(974\) | −26.6459 | − | 15.3840i | −0.853789 | − | 0.492935i | ||||
\(975\) | 3.11460 | + | 0.475196i | 0.0997472 | + | 0.0152184i | ||||
\(976\) | − | 7.44834i | − | 0.238416i | ||||||
\(977\) | − | 18.4350i | − | 0.589787i | −0.955530 | − | 0.294894i | \(-0.904716\pi\) | ||
0.955530 | − | 0.294894i | \(-0.0952842\pi\) | |||||||
\(978\) | −14.2656 | + | 17.8225i | −0.456164 | + | 0.569900i | ||||
\(979\) | −77.5766 | − | 44.7889i | −2.47936 | − | 1.43146i | ||||
\(980\) | 4.23381 | − | 5.57448i | 0.135244 | − | 0.178070i | ||||
\(981\) | 2.32541 | + | 10.3603i | 0.0742445 | + | 0.330780i | ||||
\(982\) | −7.29865 | − | 12.6416i | −0.232909 | − | 0.403411i | ||||
\(983\) | 28.4754 | + | 49.3208i | 0.908224 | + | 1.57309i | 0.816530 | + | 0.577302i | \(0.195895\pi\) |
0.0916934 | + | 0.995787i | \(0.470772\pi\) | |||||||
\(984\) | −13.4635 | + | 16.8203i | −0.429200 | + | 0.536213i | ||||
\(985\) | −7.87447 | − | 4.54633i | −0.250901 | − | 0.144858i | ||||
\(986\) | 7.45578 | + | 12.9138i | 0.237440 | + | 0.411259i | ||||
\(987\) | −14.0079 | − | 43.8477i | −0.445876 | − | 1.39569i | ||||
\(988\) | −1.12765 | + | 1.95314i | −0.0358752 | + | 0.0621377i | ||||
\(989\) | −14.8509 | + | 8.57419i | −0.472232 | + | 0.272643i | ||||
\(990\) | 12.5295 | − | 11.5419i | 0.398214 | − | 0.366826i | ||||
\(991\) | 20.5669 | − | 35.6229i | 0.653328 | − | 1.13160i | −0.328982 | − | 0.944336i | \(-0.606706\pi\) |
0.982310 | − | 0.187261i | \(-0.0599611\pi\) | |||||||
\(992\) | −8.91829 | −0.283156 | ||||||||
\(993\) | −13.4800 | + | 5.26248i | −0.427775 | + | 0.167000i | ||||
\(994\) | 1.10284 | − | 17.4886i | 0.0349798 | − | 0.554704i | ||||
\(995\) | −12.5241 | + | 7.23082i | −0.397042 | + | 0.229232i | ||||
\(996\) | −3.16056 | + | 20.7154i | −0.100146 | + | 0.656394i | ||||
\(997\) | −0.0787174 | + | 0.0454475i | −0.00249300 | + | 0.00143934i | −0.501246 | − | 0.865305i | \(-0.667125\pi\) |
0.498753 | + | 0.866744i | \(0.333791\pi\) | |||||||
\(998\) | 12.7978 | + | 7.38881i | 0.405107 | + | 0.233889i | ||||
\(999\) | 21.0161 | − | 1.46067i | 0.664919 | − | 0.0462136i |
(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 | 630.2.bk.c.101.10 | yes | 32 | |
3.2 | odd | 2 | 1890.2.bk.c.521.16 | 32 | |||
7.5 | odd | 6 | 630.2.t.c.551.12 | yes | 32 | ||
9.4 | even | 3 | 1890.2.t.c.1151.8 | 32 | |||
9.5 | odd | 6 | 630.2.t.c.311.12 | ✓ | 32 | ||
21.5 | even | 6 | 1890.2.t.c.1601.8 | 32 | |||
63.5 | even | 6 | inner | 630.2.bk.c.131.2 | yes | 32 | |
63.40 | odd | 6 | 1890.2.bk.c.341.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.c.311.12 | ✓ | 32 | 9.5 | odd | 6 | ||
630.2.t.c.551.12 | yes | 32 | 7.5 | odd | 6 | ||
630.2.bk.c.101.10 | yes | 32 | 1.1 | even | 1 | trivial | |
630.2.bk.c.131.2 | yes | 32 | 63.5 | even | 6 | inner | |
1890.2.t.c.1151.8 | 32 | 9.4 | even | 3 | |||
1890.2.t.c.1601.8 | 32 | 21.5 | even | 6 | |||
1890.2.bk.c.341.16 | 32 | 63.40 | odd | 6 | |||
1890.2.bk.c.521.16 | 32 | 3.2 | odd | 2 |