Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 143.5 | ||
Character | \(\chi\) | \(=\) | 750.143 |
Dual form | 750.2.l.b.257.5 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.453990 | + | 0.891007i | −0.321020 | + | 0.630037i | ||||
\(3\) | 1.43185 | − | 0.974581i | 0.826679 | − | 0.562674i | ||||
\(4\) | −0.587785 | − | 0.809017i | −0.293893 | − | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.218312 | + | 1.71824i | 0.0891255 | + | 0.701467i | ||||
\(7\) | −3.13589 | + | 3.13589i | −1.18525 | + | 1.18525i | −0.206890 | + | 0.978364i | \(0.566334\pi\) |
−0.978364 | + | 0.206890i | \(0.933666\pi\) | |||||||
\(8\) | 0.987688 | − | 0.156434i | 0.349201 | − | 0.0553079i | ||||
\(9\) | 1.10038 | − | 2.79091i | 0.366795 | − | 0.930302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.57685 | + | 1.16219i | −1.07846 | + | 0.350413i | −0.793778 | − | 0.608208i | \(-0.791889\pi\) |
−0.284684 | + | 0.958622i | \(0.591889\pi\) | |||||||
\(12\) | −1.63007 | − | 0.585546i | −0.470561 | − | 0.169033i | ||||
\(13\) | −3.49677 | + | 1.78169i | −0.969828 | + | 0.494152i | −0.865783 | − | 0.500420i | \(-0.833179\pi\) |
−0.104046 | + | 0.994573i | \(0.533179\pi\) | |||||||
\(14\) | −1.37043 | − | 4.21776i | −0.366264 | − | 1.12724i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −0.0644499 | − | 0.406920i | −0.0156314 | − | 0.0986927i | 0.978639 | − | 0.205585i | \(-0.0659098\pi\) |
−0.994271 | + | 0.106893i | \(0.965910\pi\) | |||||||
\(18\) | 1.98715 | + | 2.24749i | 0.468376 | + | 0.529739i | ||||
\(19\) | −2.93913 | + | 4.04536i | −0.674282 | + | 0.928070i | −0.999848 | − | 0.0174495i | \(-0.994445\pi\) |
0.325565 | + | 0.945520i | \(0.394445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.43394 | + | 7.54629i | −0.312912 | + | 1.64674i | ||||
\(22\) | 0.588338 | − | 3.71462i | 0.125434 | − | 0.791960i | ||||
\(23\) | −4.48117 | − | 2.28327i | −0.934389 | − | 0.476095i | −0.0806186 | − | 0.996745i | \(-0.525690\pi\) |
−0.853770 | + | 0.520650i | \(0.825690\pi\) | |||||||
\(24\) | 1.26176 | − | 1.18657i | 0.257556 | − | 0.242208i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.92451i | − | 0.769660i | ||||||
\(27\) | −1.14438 | − | 5.06857i | −0.220236 | − | 0.975447i | ||||
\(28\) | 4.38021 | + | 0.693758i | 0.827783 | + | 0.131108i | ||||
\(29\) | 1.49299 | − | 1.08472i | 0.277241 | − | 0.201427i | −0.440472 | − | 0.897766i | \(-0.645189\pi\) |
0.717713 | + | 0.696339i | \(0.245189\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.69808 | + | 1.96027i | 0.484590 | + | 0.352075i | 0.803100 | − | 0.595844i | \(-0.203182\pi\) |
−0.318510 | + | 0.947920i | \(0.603182\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −3.98886 | + | 5.15001i | −0.694372 | + | 0.896502i | ||||
\(34\) | 0.391828 | + | 0.127313i | 0.0671980 | + | 0.0218340i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.90468 | + | 0.750223i | −0.484113 | + | 0.125037i | ||||
\(37\) | 2.39714 | + | 4.70465i | 0.394087 | + | 0.773440i | 0.999752 | − | 0.0222802i | \(-0.00709259\pi\) |
−0.605664 | + | 0.795720i | \(0.707093\pi\) | |||||||
\(38\) | −2.27011 | − | 4.45534i | −0.368260 | − | 0.722751i | ||||
\(39\) | −3.27044 | + | 5.95899i | −0.523689 | + | 0.954203i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.24600 | + | 1.05469i | 0.506941 | + | 0.164715i | 0.551310 | − | 0.834300i | \(-0.314128\pi\) |
−0.0443698 | + | 0.999015i | \(0.514128\pi\) | |||||||
\(42\) | −6.07280 | − | 4.70360i | −0.937053 | − | 0.725781i | ||||
\(43\) | −3.71639 | − | 3.71639i | −0.566745 | − | 0.566745i | 0.364470 | − | 0.931215i | \(-0.381250\pi\) |
−0.931215 | + | 0.364470i | \(0.881250\pi\) | |||||||
\(44\) | 3.04265 | + | 2.21062i | 0.458697 | + | 0.333263i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.06882 | − | 2.95617i | 0.599914 | − | 0.435863i | ||||
\(47\) | −5.10512 | − | 0.808572i | −0.744659 | − | 0.117942i | −0.227436 | − | 0.973793i | \(-0.573034\pi\) |
−0.517223 | + | 0.855851i | \(0.673034\pi\) | |||||||
\(48\) | 0.484416 | + | 1.66293i | 0.0699194 | + | 0.240023i | ||||
\(49\) | − | 12.6676i | − | 1.80965i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.488859 | − | 0.519837i | −0.0684540 | − | 0.0727917i | ||||
\(52\) | 3.49677 | + | 1.78169i | 0.484914 | + | 0.247076i | ||||
\(53\) | −1.29952 | + | 8.20487i | −0.178503 | + | 1.12703i | 0.721909 | + | 0.691988i | \(0.243265\pi\) |
−0.900412 | + | 0.435037i | \(0.856735\pi\) | |||||||
\(54\) | 5.03567 | + | 1.28143i | 0.685267 | + | 0.174381i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.60672 | + | 3.58784i | −0.348337 | + | 0.479445i | ||||
\(57\) | −0.265855 | + | 8.65677i | −0.0352134 | + | 1.14662i | ||||
\(58\) | 0.288689 | + | 1.82271i | 0.0379068 | + | 0.239334i | ||||
\(59\) | −1.73564 | + | 5.34175i | −0.225961 | + | 0.695437i | 0.772231 | + | 0.635341i | \(0.219141\pi\) |
−0.998193 | + | 0.0600956i | \(0.980859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.43829 | + | 13.6596i | 0.568264 | + | 1.74894i | 0.658047 | + | 0.752977i | \(0.271383\pi\) |
−0.0897825 | + | 0.995961i | \(0.528617\pi\) | |||||||
\(62\) | −2.97152 | + | 1.51406i | −0.377383 | + | 0.192286i | ||||
\(63\) | 5.30128 | + | 12.2026i | 0.667899 | + | 1.53739i | ||||
\(64\) | 0.951057 | − | 0.309017i | 0.118882 | − | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.77779 | − | 5.89216i | −0.341922 | − | 0.725275i | ||||
\(67\) | 6.11731 | − | 0.968887i | 0.747349 | − | 0.118368i | 0.228868 | − | 0.973458i | \(-0.426498\pi\) |
0.518481 | + | 0.855089i | \(0.326498\pi\) | |||||||
\(68\) | −0.291323 | + | 0.291323i | −0.0353281 | + | 0.0353281i | ||||
\(69\) | −8.64159 | + | 1.09796i | −1.04033 | + | 0.132179i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.992045 | − | 1.36543i | −0.117734 | − | 0.162047i | 0.746082 | − | 0.665854i | \(-0.231932\pi\) |
−0.863817 | + | 0.503806i | \(0.831932\pi\) | |||||||
\(72\) | 0.650243 | − | 2.92868i | 0.0766319 | − | 0.345149i | ||||
\(73\) | 1.62628 | − | 3.19175i | 0.190342 | − | 0.373567i | −0.776038 | − | 0.630686i | \(-0.782773\pi\) |
0.966380 | + | 0.257120i | \(0.0827735\pi\) | |||||||
\(74\) | −5.28015 | −0.613805 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00034 | 0.573579 | ||||||||
\(77\) | 7.57211 | − | 14.8611i | 0.862922 | − | 1.69358i | ||||
\(78\) | −3.82475 | − | 5.61931i | −0.433068 | − | 0.636262i | ||||
\(79\) | −6.24842 | − | 8.60021i | −0.703002 | − | 0.967599i | −0.999919 | − | 0.0126959i | \(-0.995959\pi\) |
0.296918 | − | 0.954903i | \(-0.404041\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.57831 | − | 6.14214i | −0.730923 | − | 0.682460i | ||||
\(82\) | −2.41339 | + | 2.41339i | −0.266514 | + | 0.266514i | ||||
\(83\) | −7.00394 | + | 1.10932i | −0.768782 | + | 0.121763i | −0.528493 | − | 0.848938i | \(-0.677243\pi\) |
−0.240290 | + | 0.970701i | \(0.577243\pi\) | |||||||
\(84\) | 6.94793 | − | 3.27552i | 0.758081 | − | 0.357388i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.99854 | − | 1.62412i | 0.539006 | − | 0.175134i | ||||
\(87\) | 1.08059 | − | 3.00819i | 0.115851 | − | 0.322512i | ||||
\(88\) | −3.35101 | + | 1.70742i | −0.357219 | + | 0.182012i | ||||
\(89\) | 0.324819 | + | 0.999689i | 0.0344307 | + | 0.105967i | 0.966795 | − | 0.255554i | \(-0.0822577\pi\) |
−0.932364 | + | 0.361521i | \(0.882258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.37828 | − | 16.5526i | 0.563797 | − | 1.73519i | ||||
\(92\) | 0.786761 | + | 4.96742i | 0.0820255 | + | 0.517889i | ||||
\(93\) | 5.77369 | + | 0.177314i | 0.598704 | + | 0.0183866i | ||||
\(94\) | 3.03812 | − | 4.18162i | 0.313358 | − | 0.431301i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.70160 | − | 0.323338i | −0.173669 | − | 0.0330005i | ||||
\(97\) | 1.20630 | − | 7.61627i | 0.122481 | − | 0.773315i | −0.847618 | − | 0.530607i | \(-0.821964\pi\) |
0.970099 | − | 0.242709i | \(-0.0780359\pi\) | |||||||
\(98\) | 11.2869 | + | 5.75096i | 1.14015 | + | 0.580935i | ||||
\(99\) | −0.692350 | + | 11.2615i | −0.0695838 | + | 1.13182i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 11.0847i | − | 1.10297i | −0.834184 | − | 0.551487i | \(-0.814061\pi\) | ||
0.834184 | − | 0.551487i | \(-0.185939\pi\) | |||||||
\(102\) | 0.685116 | − | 0.199576i | 0.0678366 | − | 0.0197609i | ||||
\(103\) | −2.42213 | − | 0.383628i | −0.238660 | − | 0.0378000i | 0.0359588 | − | 0.999353i | \(-0.488552\pi\) |
−0.274618 | + | 0.961553i | \(0.588552\pi\) | |||||||
\(104\) | −3.17500 | + | 2.30677i | −0.311334 | + | 0.226197i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.72062 | − | 4.88282i | −0.652764 | − | 0.474261i | ||||
\(107\) | 4.30681 | + | 4.30681i | 0.416355 | + | 0.416355i | 0.883945 | − | 0.467590i | \(-0.154878\pi\) |
−0.467590 | + | 0.883945i | \(0.654878\pi\) | |||||||
\(108\) | −3.42791 | + | 3.90505i | −0.329851 | + | 0.375764i | ||||
\(109\) | 4.46242 | + | 1.44993i | 0.427422 | + | 0.138878i | 0.514825 | − | 0.857295i | \(-0.327857\pi\) |
−0.0874029 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.01741 | + | 4.40015i | 0.760979 | + | 0.417643i | ||||
\(112\) | −2.01336 | − | 3.95145i | −0.190245 | − | 0.373377i | ||||
\(113\) | −7.76223 | − | 15.2342i | −0.730209 | − | 1.43312i | −0.894668 | − | 0.446732i | \(-0.852588\pi\) |
0.164459 | − | 0.986384i | \(-0.447412\pi\) | |||||||
\(114\) | −7.59254 | − | 4.16697i | −0.711107 | − | 0.390272i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.75511 | − | 0.570270i | −0.162958 | − | 0.0529483i | ||||
\(117\) | 1.12475 | + | 11.7197i | 0.103983 | + | 1.08349i | ||||
\(118\) | −3.97157 | − | 3.97157i | −0.365613 | − | 0.365613i | ||||
\(119\) | 1.47816 | + | 1.07395i | 0.135503 | + | 0.0984487i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.54399 | − | 1.84832i | 0.231272 | − | 0.168029i | ||||
\(122\) | −14.1858 | − | 2.24681i | −1.28432 | − | 0.203416i | ||||
\(123\) | 5.67567 | − | 1.65334i | 0.511758 | − | 0.149076i | ||||
\(124\) | − | 3.33501i | − | 0.299493i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.2794 | − | 0.816407i | −1.18302 | − | 0.0727313i | ||||
\(127\) | 17.4755 | + | 8.90421i | 1.55070 | + | 0.790121i | 0.999034 | − | 0.0439442i | \(-0.0139924\pi\) |
0.551666 | + | 0.834065i | \(0.313992\pi\) | |||||||
\(128\) | −0.156434 | + | 0.987688i | −0.0138270 | + | 0.0873001i | ||||
\(129\) | −8.94324 | − | 1.69939i | −0.787409 | − | 0.149623i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0644 | + | 16.6052i | −1.05407 | + | 1.45080i | −0.168841 | + | 0.985643i | \(0.554002\pi\) |
−0.885228 | + | 0.465158i | \(0.845998\pi\) | |||||||
\(132\) | 6.51104 | + | 0.199959i | 0.566713 | + | 0.0174042i | ||||
\(133\) | −3.46903 | − | 21.9026i | −0.300803 | − | 1.89919i | ||||
\(134\) | −1.91392 | + | 5.89043i | −0.165337 | + | 0.508856i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.127313 | − | 0.391828i | −0.0109170 | − | 0.0335990i | ||||
\(137\) | −6.44062 | + | 3.28166i | −0.550259 | + | 0.280371i | −0.706935 | − | 0.707279i | \(-0.749922\pi\) |
0.156675 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(138\) | 2.94491 | − | 8.19818i | 0.250687 | − | 0.697875i | ||||
\(139\) | 9.21867 | − | 2.99533i | 0.781918 | − | 0.254060i | 0.109259 | − | 0.994013i | \(-0.465152\pi\) |
0.672659 | + | 0.739953i | \(0.265152\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.09779 | + | 3.81760i | −0.681957 | + | 0.321500i | ||||
\(142\) | 1.66699 | − | 0.264025i | 0.139891 | − | 0.0221565i | ||||
\(143\) | 10.4367 | − | 10.4367i | 0.872765 | − | 0.872765i | ||||
\(144\) | 2.31427 | + | 1.90897i | 0.192856 | + | 0.159080i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.10556 | + | 2.89805i | 0.174257 | + | 0.239845i | ||||
\(147\) | −12.3456 | − | 18.1381i | −1.01825 | − | 1.49600i | ||||
\(148\) | 2.39714 | − | 4.70465i | 0.197044 | − | 0.386720i | ||||
\(149\) | 4.14920 | 0.339915 | 0.169958 | − | 0.985451i | \(-0.445637\pi\) | ||||
0.169958 | + | 0.985451i | \(0.445637\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50070 | −0.773156 | −0.386578 | − | 0.922257i | \(-0.626343\pi\) | ||||
−0.386578 | + | 0.922257i | \(0.626343\pi\) | |||||||
\(152\) | −2.27011 | + | 4.45534i | −0.184130 | + | 0.361376i | ||||
\(153\) | −1.20660 | − | 0.267895i | −0.0975475 | − | 0.0216581i | ||||
\(154\) | 9.80367 | + | 13.4936i | 0.790002 | + | 1.08734i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.74324 | − | 0.856768i | 0.539892 | − | 0.0685963i | ||||
\(157\) | −2.98265 | + | 2.98265i | −0.238041 | + | 0.238041i | −0.816039 | − | 0.577997i | \(-0.803834\pi\) |
0.577997 | + | 0.816039i | \(0.303834\pi\) | |||||||
\(158\) | 10.4996 | − | 1.66297i | 0.835300 | − | 0.132299i | ||||
\(159\) | 6.13559 | + | 13.0146i | 0.486584 | + | 1.03213i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.2125 | − | 6.89237i | 1.67178 | − | 0.543195i | ||||
\(162\) | 8.45917 | − | 3.07284i | 0.664616 | − | 0.241425i | ||||
\(163\) | 9.28593 | − | 4.73142i | 0.727330 | − | 0.370593i | −0.0507896 | − | 0.998709i | \(-0.516174\pi\) |
0.778119 | + | 0.628116i | \(0.216174\pi\) | |||||||
\(164\) | −1.05469 | − | 3.24600i | −0.0823575 | − | 0.253470i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.19132 | − | 6.74418i | 0.170079 | − | 0.523450i | ||||
\(167\) | 2.18995 | + | 13.8268i | 0.169464 | + | 1.06995i | 0.914990 | + | 0.403476i | \(0.132198\pi\) |
−0.745527 | + | 0.666476i | \(0.767802\pi\) | |||||||
\(168\) | −0.235788 | + | 7.67770i | −0.0181914 | + | 0.592348i | ||||
\(169\) | 1.41174 | − | 1.94309i | 0.108595 | − | 0.149469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.05606 | + | 12.6543i | 0.616062 | + | 0.967697i | ||||
\(172\) | −0.822184 | + | 5.19107i | −0.0626910 | + | 0.395815i | ||||
\(173\) | 6.24576 | + | 3.18237i | 0.474856 | + | 0.241951i | 0.675003 | − | 0.737815i | \(-0.264142\pi\) |
−0.200147 | + | 0.979766i | \(0.564142\pi\) | |||||||
\(174\) | 2.18974 | + | 2.32850i | 0.166004 | + | 0.176523i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.76092i | − | 0.283490i | ||||||
\(177\) | 2.72079 | + | 9.34011i | 0.204507 | + | 0.702045i | ||||
\(178\) | −1.03819 | − | 0.164434i | −0.0778159 | − | 0.0123248i | ||||
\(179\) | 2.28996 | − | 1.66375i | 0.171159 | − | 0.124355i | −0.498908 | − | 0.866655i | \(-0.666265\pi\) |
0.670067 | + | 0.742301i | \(0.266265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.283169 | − | 0.205734i | −0.0210478 | − | 0.0152921i | 0.577212 | − | 0.816595i | \(-0.304141\pi\) |
−0.598259 | + | 0.801302i | \(0.704141\pi\) | |||||||
\(182\) | 12.3068 | + | 12.3068i | 0.912243 | + | 0.912243i | ||||
\(183\) | 19.6674 | + | 15.2331i | 1.45386 | + | 1.12606i | ||||
\(184\) | −4.78318 | − | 1.55415i | −0.352621 | − | 0.114573i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.77919 | + | 5.06390i | −0.203780 | + | 0.371303i | ||||
\(187\) | 0.703446 | + | 1.38059i | 0.0514411 | + | 0.100959i | ||||
\(188\) | 2.34657 | + | 4.60540i | 0.171141 | + | 0.335883i | ||||
\(189\) | 19.4831 | + | 12.3058i | 1.41719 | + | 0.895117i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.07980 | − | 0.350849i | −0.0781318 | − | 0.0253866i | 0.269690 | − | 0.962947i | \(-0.413079\pi\) |
−0.347822 | + | 0.937561i | \(0.613079\pi\) | |||||||
\(192\) | 1.06061 | − | 1.36935i | 0.0765428 | − | 0.0988241i | ||||
\(193\) | −4.16176 | − | 4.16176i | −0.299570 | − | 0.299570i | 0.541275 | − | 0.840845i | \(-0.317942\pi\) |
−0.840845 | + | 0.541275i | \(0.817942\pi\) | |||||||
\(194\) | 6.23850 | + | 4.53254i | 0.447898 | + | 0.325417i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.2483 | + | 7.44581i | −0.732020 | + | 0.531844i | ||||
\(197\) | 18.9787 | + | 3.00593i | 1.35218 | + | 0.214164i | 0.790129 | − | 0.612941i | \(-0.210014\pi\) |
0.562048 | + | 0.827105i | \(0.310014\pi\) | |||||||
\(198\) | −9.71976 | − | 5.72951i | −0.690753 | − | 0.407178i | ||||
\(199\) | 12.7124i | 0.901157i | 0.892737 | + | 0.450579i | \(0.148782\pi\) | ||||
−0.892737 | + | 0.450579i | \(0.851218\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.81481 | − | 7.34912i | 0.551214 | − | 0.518367i | ||||
\(202\) | 9.87658 | + | 5.03237i | 0.694914 | + | 0.354076i | ||||
\(203\) | −1.28028 | + | 8.08340i | −0.0898583 | + | 0.567343i | ||||
\(204\) | −0.133213 | + | 0.701048i | −0.00932676 | + | 0.0490832i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.44144 | − | 1.98397i | 0.100430 | − | 0.138230i | ||||
\(207\) | −11.3034 | + | 9.99405i | −0.785641 | + | 0.694634i | ||||
\(208\) | −0.613929 | − | 3.87619i | −0.0425683 | − | 0.268766i | ||||
\(209\) | 5.81135 | − | 17.8855i | 0.401979 | − | 1.23716i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.38805 | − | 16.5827i | −0.370929 | − | 1.14160i | −0.946184 | − | 0.323628i | \(-0.895097\pi\) |
0.575255 | − | 0.817974i | \(-0.304903\pi\) | |||||||
\(212\) | 7.40172 | − | 3.77136i | 0.508352 | − | 0.259018i | ||||
\(213\) | −2.75118 | − | 0.988266i | −0.188508 | − | 0.0677149i | ||||
\(214\) | −5.79265 | + | 1.88215i | −0.395977 | + | 0.128661i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.92319 | − | 4.82715i | −0.130856 | − | 0.328446i | ||||
\(217\) | −14.6081 | + | 2.31369i | −0.991661 | + | 0.157064i | ||||
\(218\) | −3.31779 | + | 3.31779i | −0.224709 | + | 0.224709i | ||||
\(219\) | −0.782035 | − | 6.15505i | −0.0528450 | − | 0.415920i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.950373 | + | 1.30808i | 0.0639290 | + | 0.0879907i | ||||
\(222\) | −7.56039 | + | 5.14594i | −0.507420 | + | 0.345373i | ||||
\(223\) | −10.2765 | + | 20.1688i | −0.688167 | + | 1.35060i | 0.237174 | + | 0.971467i | \(0.423779\pi\) |
−0.925341 | + | 0.379136i | \(0.876221\pi\) | |||||||
\(224\) | 4.43481 | 0.296313 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0978 | 1.13733 | ||||||||
\(227\) | 8.76566 | − | 17.2036i | 0.581797 | − | 1.14184i | −0.393164 | − | 0.919468i | \(-0.628620\pi\) |
0.974962 | − | 0.222373i | \(-0.0713804\pi\) | |||||||
\(228\) | 7.15974 | − | 4.87324i | 0.474165 | − | 0.322738i | ||||
\(229\) | 9.58051 | + | 13.1864i | 0.633098 | + | 0.871384i | 0.998224 | − | 0.0595738i | \(-0.0189742\pi\) |
−0.365126 | + | 0.930958i | \(0.618974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.64122 | − | 28.6585i | −0.239575 | − | 1.88559i | ||||
\(232\) | 1.30492 | − | 1.30492i | 0.0856721 | − | 0.0856721i | ||||
\(233\) | −0.601093 | + | 0.0952038i | −0.0393789 | + | 0.00623701i | −0.176093 | − | 0.984374i | \(-0.556346\pi\) |
0.136714 | + | 0.990611i | \(0.456346\pi\) | |||||||
\(234\) | −10.9529 | − | 4.31847i | −0.716016 | − | 0.282307i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.34175 | − | 1.73564i | 0.347718 | − | 0.112981i | ||||
\(237\) | −17.3284 | − | 6.22461i | −1.12560 | − | 0.404332i | ||||
\(238\) | −1.62797 | + | 0.829491i | −0.105525 | + | 0.0537679i | ||||
\(239\) | 2.47857 | + | 7.62825i | 0.160325 | + | 0.493430i | 0.998661 | − | 0.0517231i | \(-0.0164713\pi\) |
−0.838336 | + | 0.545154i | \(0.816471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.23962 | + | 6.89284i | −0.144267 | + | 0.444007i | −0.996916 | − | 0.0784767i | \(-0.974994\pi\) |
0.852649 | + | 0.522484i | \(0.174994\pi\) | |||||||
\(242\) | 0.491916 | + | 3.10583i | 0.0316215 | + | 0.199650i | ||||
\(243\) | −15.4052 | − | 2.38352i | −0.988241 | − | 0.152903i | ||||
\(244\) | 8.44212 | − | 11.6196i | 0.540452 | − | 0.743868i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.10357 | + | 5.80766i | −0.0703609 | + | 0.370283i | ||||
\(247\) | 3.06986 | − | 19.3823i | 0.195330 | − | 1.23327i | ||||
\(248\) | 2.97152 | + | 1.51406i | 0.188692 | + | 0.0961432i | ||||
\(249\) | −8.94747 | + | 8.41428i | −0.567023 | + | 0.533233i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.5520i | − | 0.918511i | −0.888304 | − | 0.459256i | \(-0.848116\pi\) | ||
0.888304 | − | 0.459256i | \(-0.151884\pi\) | |||||||
\(252\) | 6.75613 | − | 11.4614i | 0.425596 | − | 0.721998i | ||||
\(253\) | 18.6821 | + | 2.95895i | 1.17453 | + | 0.186028i | ||||
\(254\) | −15.8674 | + | 11.5284i | −0.995611 | + | 0.723353i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 1.03830 | + | 1.03830i | 0.0647675 | + | 0.0647675i | 0.738749 | − | 0.673981i | \(-0.235417\pi\) |
−0.673981 | + | 0.738749i | \(0.735417\pi\) | |||||||
\(258\) | 5.57431 | − | 7.19698i | 0.347042 | − | 0.448064i | ||||
\(259\) | −22.2704 | − | 7.23610i | −1.38382 | − | 0.449629i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.38449 | − | 5.36039i | −0.0856976 | − | 0.331800i | ||||
\(262\) | −9.31821 | − | 18.2880i | −0.575681 | − | 1.12984i | ||||
\(263\) | 10.1330 | + | 19.8871i | 0.624825 | + | 1.22629i | 0.958901 | + | 0.283743i | \(0.0915761\pi\) |
−0.334075 | + | 0.942546i | \(0.608424\pi\) | |||||||
\(264\) | −3.13412 | + | 5.71060i | −0.192891 | + | 0.351463i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.0902 | + | 6.85264i | 1.29313 | + | 0.420162i | ||||
\(267\) | 1.43937 | + | 1.11484i | 0.0880880 | + | 0.0682272i | ||||
\(268\) | −4.37951 | − | 4.37951i | −0.267521 | − | 0.267521i | ||||
\(269\) | −20.2239 | − | 14.6936i | −1.23308 | − | 0.895882i | −0.235959 | − | 0.971763i | \(-0.575823\pi\) |
−0.997117 | + | 0.0758813i | \(0.975823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1402 | + | 9.54690i | −0.798209 | + | 0.579933i | −0.910388 | − | 0.413755i | \(-0.864217\pi\) |
0.112179 | + | 0.993688i | \(0.464217\pi\) | |||||||
\(272\) | 0.406920 | + | 0.0644499i | 0.0246732 | + | 0.00390785i | ||||
\(273\) | −8.43100 | − | 28.9425i | −0.510268 | − | 1.75168i | ||||
\(274\) | − | 7.22848i | − | 0.436688i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.96767 | + | 6.34583i | 0.359212 | + | 0.381974i | ||||
\(277\) | 6.13564 | + | 3.12626i | 0.368655 | + | 0.187839i | 0.628497 | − | 0.777812i | \(-0.283670\pi\) |
−0.259842 | + | 0.965651i | \(0.583670\pi\) | |||||||
\(278\) | −1.51633 | + | 9.57375i | −0.0909436 | + | 0.574195i | ||||
\(279\) | 8.43986 | − | 5.37304i | 0.505281 | − | 0.321676i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3948 | + | 19.8128i | −0.858723 | + | 1.18193i | 0.123150 | + | 0.992388i | \(0.460700\pi\) |
−0.981873 | + | 0.189542i | \(0.939300\pi\) | |||||||
\(282\) | 0.274810 | − | 8.94834i | 0.0163647 | − | 0.532866i | ||||
\(283\) | 1.14551 | + | 7.23244i | 0.0680933 | + | 0.429924i | 0.998059 | + | 0.0622774i | \(0.0198363\pi\) |
−0.929966 | + | 0.367646i | \(0.880164\pi\) | |||||||
\(284\) | −0.521549 | + | 1.60516i | −0.0309482 | + | 0.0952489i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.56103 | + | 14.0374i | 0.269699 | + | 0.830049i | ||||
\(287\) | −13.4865 | + | 6.87171i | −0.796083 | + | 0.405624i | ||||
\(288\) | −2.75156 | + | 1.19538i | −0.162137 | + | 0.0704384i | ||||
\(289\) | 16.0065 | − | 5.20084i | 0.941561 | − | 0.305932i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.69543 | − | 12.0810i | −0.333872 | − | 0.708200i | ||||
\(292\) | −3.53809 | + | 0.560378i | −0.207051 | + | 0.0327936i | ||||
\(293\) | 1.14628 | − | 1.14628i | 0.0669662 | − | 0.0669662i | −0.672830 | − | 0.739797i | \(-0.734922\pi\) |
0.739797 | + | 0.672830i | \(0.234922\pi\) | |||||||
\(294\) | 21.7659 | − | 2.76548i | 1.26941 | − | 0.161286i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.10360 | + | 4.27173i | 0.180393 | + | 0.248290i | ||||
\(297\) | 9.98391 | + | 16.7995i | 0.579325 | + | 0.974808i | ||||
\(298\) | −1.88370 | + | 3.69696i | −0.109120 | + | 0.214159i | ||||
\(299\) | 19.7377 | 1.14146 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3084 | 1.34347 | ||||||||
\(302\) | 4.31323 | − | 8.46519i | 0.248198 | − | 0.487117i | ||||
\(303\) | −10.8030 | − | 15.8717i | −0.620615 | − | 0.911804i | ||||
\(304\) | −2.93913 | − | 4.04536i | −0.168571 | − | 0.232018i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.786480 | − | 0.953463i | 0.0449600 | − | 0.0545058i | ||||
\(307\) | 8.29257 | − | 8.29257i | 0.473282 | − | 0.473282i | −0.429693 | − | 0.902975i | \(-0.641378\pi\) |
0.902975 | + | 0.429693i | \(0.141378\pi\) | |||||||
\(308\) | −16.4737 | + | 2.60917i | −0.938673 | + | 0.148671i | ||||
\(309\) | −3.84200 | + | 1.81126i | −0.218564 | + | 0.103039i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.4637 | + | 10.2232i | −1.78414 | + | 0.579703i | −0.999205 | − | 0.0398725i | \(-0.987305\pi\) |
−0.784937 | + | 0.619575i | \(0.787305\pi\) | |||||||
\(312\) | −2.29798 | + | 6.39724i | −0.130098 | + | 0.362172i | ||||
\(313\) | −3.90255 | + | 1.98845i | −0.220585 | + | 0.112394i | −0.560791 | − | 0.827957i | \(-0.689503\pi\) |
0.340206 | + | 0.940351i | \(0.389503\pi\) | |||||||
\(314\) | −1.30346 | − | 4.01165i | −0.0735587 | − | 0.226391i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.28499 | + | 10.1102i | −0.184795 | + | 0.568740i | ||||
\(317\) | −4.38047 | − | 27.6572i | −0.246032 | − | 1.55338i | −0.733163 | − | 0.680053i | \(-0.761957\pi\) |
0.487131 | − | 0.873329i | \(-0.338043\pi\) | |||||||
\(318\) | −14.3816 | − | 0.441669i | −0.806481 | − | 0.0247676i | ||||
\(319\) | −4.07954 | + | 5.61501i | −0.228411 | + | 0.314380i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3640 | + | 1.96937i | 0.578464 | + | 0.109919i | ||||
\(322\) | −3.48914 | + | 22.0296i | −0.194442 | + | 1.22766i | ||||
\(323\) | 1.83557 | + | 0.935268i | 0.102134 | + | 0.0520397i | ||||
\(324\) | −1.10246 | + | 8.93222i | −0.0612479 | + | 0.496235i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.4218i | 0.577212i | ||||||||
\(327\) | 7.80259 | − | 2.27291i | 0.431484 | − | 0.125692i | ||||
\(328\) | 3.37103 | + | 0.533919i | 0.186134 | + | 0.0294807i | ||||
\(329\) | 18.5447 | − | 13.4735i | 1.02240 | − | 0.742818i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.75360 | + | 5.63332i | 0.426176 | + | 0.309635i | 0.780118 | − | 0.625632i | \(-0.215159\pi\) |
−0.353942 | + | 0.935267i | \(0.615159\pi\) | |||||||
\(332\) | 5.01427 | + | 5.01427i | 0.275194 | + | 0.275194i | ||||
\(333\) | 15.7680 | − | 1.51327i | 0.864082 | − | 0.0829264i | ||||
\(334\) | −13.3140 | − | 4.32598i | −0.728510 | − | 0.236707i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.73384 | − | 3.69569i | −0.367361 | − | 0.201617i | ||||
\(337\) | 7.11185 | + | 13.9578i | 0.387407 | + | 0.760329i | 0.999537 | − | 0.0304279i | \(-0.00968701\pi\) |
−0.612130 | + | 0.790757i | \(0.709687\pi\) | |||||||
\(338\) | 1.09039 | + | 2.14002i | 0.0593095 | + | 0.116401i | ||||
\(339\) | −25.9613 | − | 14.2482i | −1.41003 | − | 0.773856i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.9289 | − | 3.87592i | −0.645983 | − | 0.209893i | ||||
\(342\) | −14.9324 | + | 1.43307i | −0.807453 | + | 0.0774917i | ||||
\(343\) | 17.7729 | + | 17.7729i | 0.959645 | + | 0.959645i | ||||
\(344\) | −4.25201 | − | 3.08927i | −0.229253 | − | 0.166562i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.67103 | + | 4.12024i | −0.304876 | + | 0.221506i | ||||
\(347\) | −36.4678 | − | 5.77593i | −1.95769 | − | 0.310068i | −0.999731 | − | 0.0231773i | \(-0.992622\pi\) |
−0.957963 | − | 0.286891i | \(-0.907378\pi\) | |||||||
\(348\) | −3.06883 | + | 0.893957i | −0.164507 | + | 0.0479211i | ||||
\(349\) | 15.0145i | 0.803705i | 0.915704 | + | 0.401853i | \(0.131634\pi\) | ||||
−0.915704 | + | 0.401853i | \(0.868366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.0322 | + | 15.6847i | 0.695610 | + | 0.837186i | ||||
\(352\) | 3.35101 | + | 1.70742i | 0.178609 | + | 0.0910060i | ||||
\(353\) | 4.70953 | − | 29.7348i | 0.250663 | − | 1.58263i | −0.465729 | − | 0.884927i | \(-0.654208\pi\) |
0.716392 | − | 0.697698i | \(-0.245792\pi\) | |||||||
\(354\) | −9.55731 | − | 1.81607i | −0.507965 | − | 0.0965233i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.617842 | − | 0.850386i | 0.0327456 | − | 0.0450704i | ||||
\(357\) | 3.16316 | + | 0.0971428i | 0.167412 | + | 0.00514134i | ||||
\(358\) | 0.442795 | + | 2.79569i | 0.0234024 | + | 0.147757i | ||||
\(359\) | −1.07807 | + | 3.31797i | −0.0568986 | + | 0.175116i | −0.975467 | − | 0.220147i | \(-0.929346\pi\) |
0.918568 | + | 0.395263i | \(0.129346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.85517 | − | 5.70961i | −0.0976403 | − | 0.300506i | ||||
\(362\) | 0.311866 | − | 0.158904i | 0.0163913 | − | 0.00835180i | ||||
\(363\) | 1.84128 | − | 5.12584i | 0.0966420 | − | 0.269037i | ||||
\(364\) | −16.5526 | + | 5.37828i | −0.867594 | + | 0.281898i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −22.5016 | + | 10.6081i | −1.17618 | + | 0.554494i | ||||
\(367\) | −15.4679 | + | 2.44988i | −0.807418 | + | 0.127882i | −0.546479 | − | 0.837473i | \(-0.684032\pi\) |
−0.260939 | + | 0.965355i | \(0.584032\pi\) | |||||||
\(368\) | 3.55628 | − | 3.55628i | 0.185384 | − | 0.185384i | ||||
\(369\) | 6.51539 | − | 7.89873i | 0.339178 | − | 0.411191i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.6544 | − | 29.8047i | −1.12424 | − | 1.54738i | ||||
\(372\) | −3.25024 | − | 4.77524i | −0.168517 | − | 0.247585i | ||||
\(373\) | −2.89590 | + | 5.68352i | −0.149944 | + | 0.294282i | −0.953745 | − | 0.300616i | \(-0.902808\pi\) |
0.803801 | + | 0.594898i | \(0.202808\pi\) | |||||||
\(374\) | −1.54947 | −0.0801213 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.16876 | −0.266558 | ||||||||
\(377\) | −3.28799 | + | 6.45305i | −0.169340 | + | 0.332349i | ||||
\(378\) | −19.8097 | + | 11.7728i | −1.01890 | + | 0.605530i | ||||
\(379\) | −15.8374 | − | 21.7983i | −0.813510 | − | 1.11970i | −0.990772 | − | 0.135537i | \(-0.956724\pi\) |
0.177262 | − | 0.984164i | \(-0.443276\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.7002 | − | 4.28180i | 1.72651 | − | 0.219363i | ||||
\(382\) | 0.802829 | − | 0.802829i | 0.0410763 | − | 0.0410763i | ||||
\(383\) | −29.5784 | + | 4.68475i | −1.51138 | + | 0.239380i | −0.856420 | − | 0.516280i | \(-0.827316\pi\) |
−0.654964 | + | 0.755660i | \(0.727316\pi\) | |||||||
\(384\) | 0.738592 | + | 1.56668i | 0.0376911 | + | 0.0799492i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.59756 | − | 1.81876i | 0.284908 | − | 0.0925723i | ||||
\(387\) | −14.4616 | + | 6.28264i | −0.735123 | + | 0.319365i | ||||
\(388\) | −6.87074 | + | 3.50082i | −0.348809 | + | 0.177727i | ||||
\(389\) | −3.57268 | − | 10.9956i | −0.181142 | − | 0.557497i | 0.818719 | − | 0.574195i | \(-0.194685\pi\) |
−0.999861 | + | 0.0166975i | \(0.994685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.640299 | + | 1.97064i | −0.0323813 | + | 0.0996594i | ||||
\(392\) | −1.98165 | − | 12.5116i | −0.100088 | − | 0.631932i | ||||
\(393\) | −1.09127 | + | 35.5338i | −0.0550472 | + | 1.79244i | ||||
\(394\) | −11.2945 | + | 15.5455i | −0.569007 | + | 0.783170i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.51771 | − | 6.05923i | 0.478283 | − | 0.304488i | ||||
\(397\) | 2.09608 | − | 13.2341i | 0.105199 | − | 0.664203i | −0.877581 | − | 0.479427i | \(-0.840844\pi\) |
0.982781 | − | 0.184775i | \(-0.0591557\pi\) | |||||||
\(398\) | −11.3268 | − | 5.77130i | −0.567762 | − | 0.289289i | ||||
\(399\) | −26.3130 | − | 27.9803i | −1.31730 | − | 1.40077i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.2904i | 1.11313i | 0.830804 | + | 0.556565i | \(0.187881\pi\) | ||||
−0.830804 | + | 0.556565i | \(0.812119\pi\) | |||||||
\(402\) | 3.00026 | + | 10.2995i | 0.149639 | + | 0.513691i | ||||
\(403\) | −12.9272 | − | 2.04746i | −0.643948 | − | 0.101991i | ||||
\(404\) | −8.96775 | + | 6.51545i | −0.446162 | + | 0.324156i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.62112 | − | 4.81053i | −0.328601 | − | 0.238742i | ||||
\(407\) | −14.0419 | − | 14.0419i | −0.696032 | − | 0.696032i | ||||
\(408\) | −0.564161 | − | 0.436963i | −0.0279301 | − | 0.0216329i | ||||
\(409\) | 13.3939 | + | 4.35194i | 0.662285 | + | 0.215190i | 0.620823 | − | 0.783951i | \(-0.286798\pi\) |
0.0414620 | + | 0.999140i | \(0.486798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.02376 | + | 10.9757i | −0.297130 | + | 0.541394i | ||||
\(412\) | 1.11333 | + | 2.18504i | 0.0548499 | + | 0.107649i | ||||
\(413\) | −11.3084 | − | 22.1939i | −0.556448 | − | 1.09209i | ||||
\(414\) | −3.77313 | − | 14.6086i | −0.185439 | − | 0.717974i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.73243 | + | 1.21274i | 0.182998 | + | 0.0594595i | ||||
\(417\) | 10.2806 | − | 13.2732i | 0.503441 | − | 0.649992i | ||||
\(418\) | 13.2978 | + | 13.2978i | 0.650416 | + | 0.650416i | ||||
\(419\) | 4.58918 | + | 3.33423i | 0.224196 | + | 0.162888i | 0.694213 | − | 0.719769i | \(-0.255752\pi\) |
−0.470017 | + | 0.882657i | \(0.655752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.16685 | − | 3.75393i | 0.251817 | − | 0.182956i | −0.454715 | − | 0.890637i | \(-0.650259\pi\) |
0.706532 | + | 0.707682i | \(0.250259\pi\) | |||||||
\(422\) | 17.2214 | + | 2.72761i | 0.838327 | + | 0.132778i | ||||
\(423\) | −7.87425 | + | 13.3582i | −0.382859 | + | 0.649497i | ||||
\(424\) | 8.30714i | 0.403431i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.12956 | − | 2.00266i | 0.103178 | − | 0.0970292i | ||||
\(427\) | −56.7531 | − | 28.9171i | −2.74647 | − | 1.39940i | ||||
\(428\) | 0.952804 | − | 6.01577i | 0.0460555 | − | 0.290783i | ||||
\(429\) | 4.77240 | − | 25.1153i | 0.230413 | − | 1.21258i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.7415 | + | 16.1608i | −0.565568 | + | 0.778437i | −0.992021 | − | 0.126072i | \(-0.959763\pi\) |
0.426453 | + | 0.904510i | \(0.359763\pi\) | |||||||
\(432\) | 5.17413 | + | 0.477906i | 0.248940 | + | 0.0229932i | ||||
\(433\) | 3.62919 | + | 22.9138i | 0.174408 | + | 1.10117i | 0.907195 | + | 0.420710i | \(0.138219\pi\) |
−0.732787 | + | 0.680458i | \(0.761781\pi\) | |||||||
\(434\) | 4.57041 | − | 14.0663i | 0.219387 | − | 0.675203i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.44993 | − | 4.46242i | −0.0694390 | − | 0.213711i | ||||
\(437\) | 22.4074 | − | 11.4171i | 1.07189 | − | 0.546156i | ||||
\(438\) | 5.83923 | + | 2.09754i | 0.279009 | + | 0.100224i | ||||
\(439\) | 10.7777 | − | 3.50189i | 0.514393 | − | 0.167136i | −0.0403065 | − | 0.999187i | \(-0.512833\pi\) |
0.554699 | + | 0.832051i | \(0.312833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.3540 | − | 13.9392i | −1.68352 | − | 0.663772i | ||||
\(442\) | −1.59696 | + | 0.252934i | −0.0759598 | + | 0.0120309i | ||||
\(443\) | −5.43418 | + | 5.43418i | −0.258186 | + | 0.258186i | −0.824316 | − | 0.566130i | \(-0.808440\pi\) |
0.566130 | + | 0.824316i | \(0.308440\pi\) | |||||||
\(444\) | −1.15272 | − | 9.07256i | −0.0547057 | − | 0.430565i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.3051 | − | 18.3129i | −0.630015 | − | 0.867141i | ||||
\(447\) | 5.94102 | − | 4.04373i | 0.281001 | − | 0.191262i | ||||
\(448\) | −2.01336 | + | 3.95145i | −0.0951225 | + | 0.186688i | ||||
\(449\) | −26.9459 | −1.27165 | −0.635827 | − | 0.771831i | \(-0.719341\pi\) | ||||
−0.635827 | + | 0.771831i | \(0.719341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8362 | −0.604434 | ||||||||
\(452\) | −7.76223 | + | 15.2342i | −0.365104 | + | 0.716558i | ||||
\(453\) | −13.6036 | + | 9.25920i | −0.639152 | + | 0.435035i | ||||
\(454\) | 11.3490 | + | 15.6205i | 0.532634 | + | 0.733108i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.09163 | + | 8.59178i | 0.0511205 | + | 0.402347i | ||||
\(457\) | −24.1951 | + | 24.1951i | −1.13180 | + | 1.13180i | −0.141919 | + | 0.989878i | \(0.545327\pi\) |
−0.989878 | + | 0.141919i | \(0.954673\pi\) | |||||||
\(458\) | −16.0987 | + | 2.54978i | −0.752241 | + | 0.119143i | ||||
\(459\) | −1.98875 | + | 0.792339i | −0.0928269 | + | 0.0369832i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.3066 | − | 11.4718i | 1.64439 | − | 0.534295i | 0.666877 | − | 0.745168i | \(-0.267631\pi\) |
0.977513 | + | 0.210873i | \(0.0676307\pi\) | |||||||
\(462\) | 27.1880 | + | 9.76632i | 1.26490 | + | 0.454370i | ||||
\(463\) | −6.25735 | + | 3.18828i | −0.290804 | + | 0.148172i | −0.593307 | − | 0.804977i | \(-0.702178\pi\) |
0.302503 | + | 0.953149i | \(0.402178\pi\) | |||||||
\(464\) | 0.570270 | + | 1.75511i | 0.0264741 | + | 0.0814790i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.188063 | − | 0.578799i | 0.00871187 | − | 0.0268124i | ||||
\(467\) | 4.48899 | + | 28.3424i | 0.207726 | + | 1.31153i | 0.842444 | + | 0.538785i | \(0.181116\pi\) |
−0.634718 | + | 0.772744i | \(0.718884\pi\) | |||||||
\(468\) | 8.82032 | − | 7.79860i | 0.407719 | − | 0.360490i | ||||
\(469\) | −16.1449 | + | 22.2215i | −0.745502 | + | 1.02609i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.36387 | + | 7.17753i | −0.0628438 | + | 0.330723i | ||||
\(472\) | −0.878638 | + | 5.54750i | −0.0404426 | + | 0.255344i | ||||
\(473\) | 17.6121 | + | 8.97383i | 0.809807 | + | 0.412617i | ||||
\(474\) | 13.4131 | − | 12.6138i | 0.616084 | − | 0.579371i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1.82711i | − | 0.0837455i | ||||||
\(477\) | 21.4690 | + | 12.6554i | 0.983000 | + | 0.579449i | ||||
\(478\) | −7.92207 | − | 1.25473i | −0.362347 | − | 0.0573901i | ||||
\(479\) | 10.3928 | − | 7.55082i | 0.474860 | − | 0.345006i | −0.324473 | − | 0.945895i | \(-0.605187\pi\) |
0.799332 | + | 0.600889i | \(0.205187\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.7645 | − | 12.1801i | −0.764394 | − | 0.555365i | ||||
\(482\) | −5.12480 | − | 5.12480i | −0.233428 | − | 0.233428i | ||||
\(483\) | 23.6560 | − | 30.5421i | 1.07638 | − | 1.38972i | ||||
\(484\) | −2.99064 | − | 0.971718i | −0.135938 | − | 0.0441690i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.11753 | − | 12.6440i | 0.413580 | − | 0.573543i | ||||
\(487\) | −9.39682 | − | 18.4423i | −0.425810 | − | 0.835700i | −0.999858 | − | 0.0168777i | \(-0.994627\pi\) |
0.574047 | − | 0.818822i | \(-0.305373\pi\) | |||||||
\(488\) | 6.52048 | + | 12.7972i | 0.295168 | + | 0.579301i | ||||
\(489\) | 8.68490 | − | 15.8246i | 0.392745 | − | 0.715611i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.5707 | + | 8.63333i | 1.19912 | + | 0.389617i | 0.839436 | − | 0.543459i | \(-0.182886\pi\) |
0.359681 | + | 0.933075i | \(0.382886\pi\) | |||||||
\(492\) | −4.67365 | − | 3.61991i | −0.210704 | − | 0.163198i | ||||
\(493\) | −0.537617 | − | 0.537617i | −0.0242131 | − | 0.0242131i | ||||
\(494\) | 15.8761 | + | 11.5346i | 0.714298 | + | 0.518968i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.69808 | + | 1.96027i | −0.121148 | + | 0.0880188i | ||||
\(497\) | 7.39279 | + | 1.17090i | 0.331612 | + | 0.0525221i | ||||
\(498\) | −3.43511 | − | 11.7923i | −0.153931 | − | 0.528424i | ||||
\(499\) | 0.405848i | 0.0181683i | 0.999959 | + | 0.00908413i | \(0.00289161\pi\) | ||||
−0.999959 | + | 0.00908413i | \(0.997108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.6110 | + | 17.6636i | 0.742126 | + | 0.789153i | ||||
\(502\) | 12.9659 | + | 6.60645i | 0.578696 | + | 0.294860i | ||||
\(503\) | −0.948431 | + | 5.98816i | −0.0422885 | + | 0.266999i | −0.999769 | − | 0.0214995i | \(-0.993156\pi\) |
0.957480 | + | 0.288498i | \(0.0931560\pi\) | |||||||
\(504\) | 7.14493 | + | 11.2231i | 0.318260 | + | 0.499917i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.1179 | + | 15.3025i | −0.494252 | + | 0.680280i | ||||
\(507\) | 0.127697 | − | 4.15807i | 0.00567123 | − | 0.184666i | ||||
\(508\) | −3.06818 | − | 19.3717i | −0.136129 | − | 0.859482i | ||||
\(509\) | −1.17675 | + | 3.62167i | −0.0521586 | + | 0.160528i | −0.973743 | − | 0.227651i | \(-0.926896\pi\) |
0.921584 | + | 0.388178i | \(0.126896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.90915 | + | 15.1088i | 0.217168 | + | 0.668375i | ||||
\(512\) | 0.891007 | − | 0.453990i | 0.0393773 | − | 0.0200637i | ||||
\(513\) | 23.8677 | + | 10.2678i | 1.05378 | + | 0.453332i | ||||
\(514\) | −1.39651 | + | 0.453755i | −0.0615976 | + | 0.0200143i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.88187 | + | 8.23411i | 0.170890 | + | 0.362487i | ||||
\(517\) | 19.2000 | − | 3.04098i | 0.844414 | − | 0.133742i | ||||
\(518\) | 16.5580 | − | 16.5580i | 0.727515 | − | 0.727515i | ||||
\(519\) | 12.0445 | − | 1.53032i | 0.528693 | − | 0.0671735i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.70955 | + | 2.35299i | 0.0748966 | + | 0.103086i | 0.844822 | − | 0.535048i | \(-0.179706\pi\) |
−0.769925 | + | 0.638134i | \(0.779706\pi\) | |||||||
\(522\) | 5.40469 | + | 1.19998i | 0.236557 | + | 0.0525217i | ||||
\(523\) | −4.02250 | + | 7.89460i | −0.175892 | + | 0.345207i | −0.962074 | − | 0.272787i | \(-0.912054\pi\) |
0.786183 | + | 0.617994i | \(0.212054\pi\) | |||||||
\(524\) | 20.5251 | 0.896645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.3198 | −0.973188 | ||||||||
\(527\) | 0.623784 | − | 1.22424i | 0.0271724 | − | 0.0533289i | ||||
\(528\) | −3.66532 | − | 5.38508i | −0.159513 | − | 0.234355i | ||||
\(529\) | 1.34851 | + | 1.85606i | 0.0586307 | + | 0.0806982i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.9985 | + | 10.7220i | 0.564085 | + | 0.465295i | ||||
\(532\) | −15.6805 | + | 15.6805i | −0.679837 | + | 0.679837i | ||||
\(533\) | −13.2296 | + | 2.09537i | −0.573040 | + | 0.0907606i | ||||
\(534\) | −1.64679 | + | 0.776360i | −0.0712636 | + | 0.0335964i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.89043 | − | 1.91392i | 0.254428 | − | 0.0826686i | ||||
\(537\) | 1.65741 | − | 4.61399i | 0.0715227 | − | 0.199108i | ||||
\(538\) | 22.2735 | − | 11.3489i | 0.960280 | − | 0.489287i | ||||
\(539\) | 14.7221 | + | 45.3100i | 0.634127 | + | 1.95164i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3923 | + | 35.0618i | −0.489792 | + | 1.50742i | 0.335128 | + | 0.942173i | \(0.391221\pi\) |
−0.824919 | + | 0.565251i | \(0.808779\pi\) | |||||||
\(542\) | −2.54083 | − | 16.0422i | −0.109138 | − | 0.689071i | ||||
\(543\) | −0.605959 | − | 0.0186094i | −0.0260042 | − | 0.000798607i | ||||
\(544\) | −0.242163 | + | 0.333309i | −0.0103827 | + | 0.0142905i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 29.6155 | + | 5.62752i | 1.26743 | + | 0.240836i | ||||
\(547\) | −4.14971 | + | 26.2003i | −0.177429 | + | 1.12024i | 0.724792 | + | 0.688968i | \(0.241936\pi\) |
−0.902221 | + | 0.431274i | \(0.858064\pi\) | |||||||
\(548\) | 6.44062 | + | 3.28166i | 0.275130 | + | 0.140186i | ||||
\(549\) | 43.0066 | + | 2.64402i | 1.83548 | + | 0.112844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.22780i | 0.393118i | ||||||||
\(552\) | −8.36344 | + | 2.43629i | −0.355972 | + | 0.103695i | ||||
\(553\) | 46.5636 | + | 7.37495i | 1.98009 | + | 0.313615i | ||||
\(554\) | −5.57104 | + | 4.04760i | −0.236691 | + | 0.171966i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.84187 | − | 5.69745i | −0.332569 | − | 0.241626i | ||||
\(557\) | −20.9449 | − | 20.9449i | −0.887465 | − | 0.887465i | 0.106814 | − | 0.994279i | \(-0.465935\pi\) |
−0.994279 | + | 0.106814i | \(0.965935\pi\) | |||||||
\(558\) | 0.955798 | + | 9.95928i | 0.0404622 | + | 0.421610i | ||||
\(559\) | 19.6168 | + | 6.37389i | 0.829703 | + | 0.269587i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.35273 | + | 1.29123i | 0.0993322 | + | 0.0545159i | ||||
\(562\) | −11.1182 | − | 21.8207i | −0.468993 | − | 0.920450i | ||||
\(563\) | −6.85128 | − | 13.4464i | −0.288747 | − | 0.566698i | 0.700378 | − | 0.713772i | \(-0.253015\pi\) |
−0.989126 | + | 0.147073i | \(0.953015\pi\) | |||||||
\(564\) | 7.84827 | + | 4.30732i | 0.330472 | + | 0.181371i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.96420 | − | 2.26281i | −0.292727 | − | 0.0951128i | ||||
\(567\) | 39.8899 | − | 1.36778i | 1.67522 | − | 0.0574413i | ||||
\(568\) | −1.19343 | − | 1.19343i | −0.0500753 | − | 0.0500753i | ||||
\(569\) | −7.06373 | − | 5.13210i | −0.296127 | − | 0.215149i | 0.429794 | − | 0.902927i | \(-0.358586\pi\) |
−0.725921 | + | 0.687778i | \(0.758586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6305 | − | 14.2624i | 0.821513 | − | 0.596864i | −0.0956328 | − | 0.995417i | \(-0.530487\pi\) |
0.917145 | + | 0.398553i | \(0.130487\pi\) | |||||||
\(572\) | −14.5781 | − | 2.30894i | −0.609540 | − | 0.0965416i | ||||
\(573\) | −1.88805 | + | 0.549992i | −0.0788743 | + | 0.0229762i | ||||
\(574\) | − | 15.1362i | − | 0.631775i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.184091 | − | 2.99435i | 0.00767044 | − | 0.124764i | ||||
\(577\) | −32.6160 | − | 16.6187i | −1.35782 | − | 0.691845i | −0.384896 | − | 0.922960i | \(-0.625763\pi\) |
−0.972927 | + | 0.231114i | \(0.925763\pi\) | |||||||
\(578\) | −2.63283 | + | 16.6231i | −0.109511 | + | 0.691428i | ||||
\(579\) | −10.0150 | − | 1.90304i | −0.416209 | − | 0.0790877i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.4849 | − | 25.4423i | 0.766882 | − | 1.05552i | ||||
\(582\) | 13.3499 | + | 0.409985i | 0.553372 | + | 0.0169944i | ||||
\(583\) | −4.88741 | − | 30.8579i | −0.202416 | − | 1.27800i | ||||
\(584\) | 1.10696 | − | 3.40687i | 0.0458062 | − | 0.140977i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.500941 | + | 1.54174i | 0.0206937 | + | 0.0636887i | ||||
\(587\) | 10.1304 | − | 5.16169i | 0.418126 | − | 0.213046i | −0.232254 | − | 0.972655i | \(-0.574610\pi\) |
0.650379 | + | 0.759609i | \(0.274610\pi\) | |||||||
\(588\) | −7.41745 | + | 20.6491i | −0.305890 | + | 0.851553i | ||||
\(589\) | −15.8600 | + | 5.15324i | −0.653501 | + | 0.212335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.1042 | − | 14.1922i | 1.23832 | − | 0.583791i | ||||
\(592\) | −5.21515 | + | 0.825998i | −0.214341 | + | 0.0339483i | ||||
\(593\) | 16.4362 | − | 16.4362i | 0.674952 | − | 0.674952i | −0.283901 | − | 0.958854i | \(-0.591629\pi\) |
0.958854 | + | 0.283901i | \(0.0916288\pi\) | |||||||
\(594\) | −19.5011 | + | 1.26890i | −0.800140 | + | 0.0520636i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.43884 | − | 3.35677i | −0.0998986 | − | 0.137499i | ||||
\(597\) | 12.3893 | + | 18.2022i | 0.507058 | + | 0.744968i | ||||
\(598\) | −8.96072 | + | 17.5864i | −0.366431 | + | 0.719162i | ||||
\(599\) | −16.9386 | −0.692094 | −0.346047 | − | 0.938217i | \(-0.612476\pi\) | ||||
−0.346047 | + | 0.938217i | \(0.612476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0220 | −1.06146 | −0.530730 | − | 0.847541i | \(-0.678082\pi\) | ||||
−0.530730 | + | 0.847541i | \(0.678082\pi\) | |||||||
\(602\) | −10.5818 | + | 20.7679i | −0.431281 | + | 0.846437i | ||||
\(603\) | 4.02732 | − | 18.1390i | 0.164005 | − | 0.738677i | ||||
\(604\) | 5.58437 | + | 7.68623i | 0.227225 | + | 0.312748i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 19.0462 | − | 2.41993i | 0.773700 | − | 0.0983030i | ||||
\(607\) | 29.4219 | − | 29.4219i | 1.19420 | − | 1.19420i | 0.218322 | − | 0.975877i | \(-0.429942\pi\) |
0.975877 | − | 0.218322i | \(-0.0700583\pi\) | |||||||
\(608\) | 4.93878 | − | 0.782226i | 0.200294 | − | 0.0317235i | ||||
\(609\) | 6.04475 | + | 12.8219i | 0.244946 | + | 0.519571i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.2921 | − | 6.26837i | 0.780473 | − | 0.253591i | ||||
\(612\) | 0.492487 | + | 1.13362i | 0.0199076 | + | 0.0458239i | ||||
\(613\) | −5.01575 | + | 2.55565i | −0.202584 | + | 0.103222i | −0.552339 | − | 0.833619i | \(-0.686265\pi\) |
0.349755 | + | 0.936841i | \(0.386265\pi\) | |||||||
\(614\) | 3.62398 | + | 11.1535i | 0.146252 | + | 0.450118i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.15409 | − | 15.8627i | 0.207664 | − | 0.639125i | ||||
\(617\) | 5.57460 | + | 35.1967i | 0.224425 | + | 1.41696i | 0.800385 | + | 0.599486i | \(0.204628\pi\) |
−0.575960 | + | 0.817478i | \(0.695372\pi\) | |||||||
\(618\) | 0.130384 | − | 4.24555i | 0.00524480 | − | 0.170781i | ||||
\(619\) | −20.2991 | + | 27.9393i | −0.815889 | + | 1.12297i | 0.174499 | + | 0.984657i | \(0.444169\pi\) |
−0.990388 | + | 0.138317i | \(0.955831\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.44476 | + | 25.3261i | −0.258619 | + | 1.01630i | ||||
\(622\) | 5.17530 | − | 32.6756i | 0.207511 | − | 1.31017i | ||||
\(623\) | −4.15351 | − | 2.11632i | −0.166407 | − | 0.0847885i | ||||
\(624\) | −4.65672 | − | 4.95180i | −0.186418 | − | 0.198231i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 4.37993i | − | 0.175057i | ||||||
\(627\) | −9.10988 | − | 31.2729i | −0.363814 | − | 1.24892i | ||||
\(628\) | 4.16617 | + | 0.659856i | 0.166248 | + | 0.0263311i | ||||
\(629\) | 1.75992 | − | 1.27866i | 0.0701727 | − | 0.0509835i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.95722 | − | 5.05472i | −0.276963 | − | 0.201225i | 0.440629 | − | 0.897689i | \(-0.354755\pi\) |
−0.717591 | + | 0.696464i | \(0.754755\pi\) | |||||||
\(632\) | −7.51686 | − | 7.51686i | −0.299005 | − | 0.299005i | ||||
\(633\) | −23.8761 | − | 18.4929i | −0.948989 | − | 0.735026i | ||||
\(634\) | 26.6314 | + | 8.65307i | 1.05767 | + | 0.343657i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.92265 | − | 12.6136i | 0.274501 | − | 0.500162i | ||||
\(637\) | 22.5697 | + | 44.2955i | 0.894244 | + | 1.75505i | ||||
\(638\) | −3.15094 | − | 6.18406i | −0.124747 | − | 0.244829i | ||||
\(639\) | −4.90243 | + | 1.26620i | −0.193937 | + | 0.0500902i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9664 | + | 4.21305i | 0.512144 | + | 0.166406i | 0.553677 | − | 0.832732i | \(-0.313224\pi\) |
−0.0415332 | + | 0.999137i | \(0.513224\pi\) | |||||||
\(642\) | −6.45990 | + | 8.34036i | −0.254952 | + | 0.329168i | ||||
\(643\) | 11.4059 | + | 11.4059i | 0.449806 | + | 0.449806i | 0.895290 | − | 0.445484i | \(-0.146968\pi\) |
−0.445484 | + | 0.895290i | \(0.646968\pi\) | |||||||
\(644\) | −18.0445 | − | 13.1101i | −0.711051 | − | 0.516609i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.66666 | + | 1.21090i | −0.0655739 | + | 0.0476422i | ||||
\(647\) | 30.9551 | + | 4.90280i | 1.21697 | + | 0.192749i | 0.731707 | − | 0.681619i | \(-0.238724\pi\) |
0.485263 | + | 0.874368i | \(0.338724\pi\) | |||||||
\(648\) | −7.45816 | − | 5.03744i | −0.292984 | − | 0.197889i | ||||
\(649\) | − | 21.1238i | − | 0.829181i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.6617 | + | 17.5496i | −0.731409 | + | 0.687823i | ||||
\(652\) | −9.28593 | − | 4.73142i | −0.363665 | − | 0.185297i | ||||
\(653\) | −5.98789 | + | 37.8061i | −0.234324 | + | 1.47947i | 0.537302 | + | 0.843390i | \(0.319444\pi\) |
−0.771626 | + | 0.636076i | \(0.780556\pi\) | |||||||
\(654\) | −1.51712 | + | 7.98404i | −0.0593242 | + | 0.312201i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00614 | + | 2.76122i | −0.0783266 | + | 0.107807i | ||||
\(657\) | −7.11835 | − | 8.05095i | −0.277713 | − | 0.314098i | ||||
\(658\) | 3.58587 | + | 22.6403i | 0.139792 | + | 0.882610i | ||||
\(659\) | −6.33270 | + | 19.4901i | −0.246687 | + | 0.759225i | 0.748667 | + | 0.662946i | \(0.230694\pi\) |
−0.995354 | + | 0.0962789i | \(0.969306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4948 | − | 41.5327i | −0.524887 | − | 1.61544i | −0.764539 | − | 0.644577i | \(-0.777033\pi\) |
0.239652 | − | 0.970859i | \(-0.422967\pi\) | |||||||
\(662\) | −8.53939 | + | 4.35103i | −0.331893 | + | 0.169108i | ||||
\(663\) | 2.63562 | + | 0.946752i | 0.102359 | + | 0.0367688i | ||||
\(664\) | −6.74418 | + | 2.19132i | −0.261725 | + | 0.0850395i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.81020 | + | 14.7364i | −0.225141 | + | 0.571024i | ||||
\(667\) | −9.16704 | + | 1.45192i | −0.354949 | + | 0.0562184i | ||||
\(668\) | 9.89891 | − | 9.89891i | 0.383000 | − | 0.383000i | ||||
\(669\) | 4.94171 | + | 38.8940i | 0.191057 | + | 1.50373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.7502 | − | 43.7004i | −1.22570 | − | 1.68703i | ||||
\(672\) | 6.34998 | − | 4.32208i | 0.244956 | − | 0.166728i | ||||
\(673\) | 16.8283 | − | 33.0273i | 0.648681 | − | 1.27311i | −0.299110 | − | 0.954219i | \(-0.596690\pi\) |
0.947792 | − | 0.318890i | \(-0.103310\pi\) | |||||||
\(674\) | −15.6652 | −0.603401 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.40180 | −0.0923767 | ||||||||
\(677\) | −18.9516 | + | 37.1946i | −0.728369 | + | 1.42951i | 0.167813 | + | 0.985819i | \(0.446330\pi\) |
−0.896182 | + | 0.443686i | \(0.853670\pi\) | |||||||
\(678\) | 24.4814 | − | 16.6632i | 0.940204 | − | 0.639945i | ||||
\(679\) | 20.1010 | + | 27.6666i | 0.771404 | + | 1.06175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.21517 | − | 33.1758i | −0.161526 | − | 1.27130i | ||||
\(682\) | 8.86905 | − | 8.86905i | 0.339614 | − | 0.339614i | ||||
\(683\) | 50.2616 | − | 7.96066i | 1.92321 | − | 0.304606i | 0.925890 | − | 0.377793i | \(-0.123317\pi\) |
0.997318 | + | 0.0731865i | \(0.0233168\pi\) | |||||||
\(684\) | 5.50230 | − | 13.9555i | 0.210386 | − | 0.533601i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −23.9045 | + | 7.76703i | −0.912677 | + | 0.296547i | ||||
\(687\) | 26.5691 | + | 9.54401i | 1.01367 | + | 0.364127i | ||||
\(688\) | 4.68293 | − | 2.38607i | 0.178535 | − | 0.0909681i | ||||
\(689\) | −10.0744 | − | 31.0059i | −0.383805 | − | 1.18123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.91187 | + | 30.5056i | −0.377065 | + | 1.16049i | 0.565010 | + | 0.825084i | \(0.308872\pi\) |
−0.942075 | + | 0.335403i | \(0.891128\pi\) | |||||||
\(692\) | −1.09657 | − | 6.92347i | −0.0416854 | − | 0.263191i | ||||
\(693\) | −33.1437 | − | 37.4860i | −1.25902 | − | 1.42397i | ||||
\(694\) | 21.7024 | − | 29.8708i | 0.823813 | − | 1.13388i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.596698 | − | 3.14020i | 0.0226178 | − | 0.119029i | ||||
\(697\) | 0.219971 | − | 1.38884i | 0.00833198 | − | 0.0526061i | ||||
\(698\) | −13.3780 | − | 6.81642i | −0.506364 | − | 0.258005i | ||||
\(699\) | −0.767891 | + | 0.722131i | −0.0290443 | + | 0.0273135i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.1785i | − | 1.21536i | −0.794180 | − | 0.607682i | \(-0.792100\pi\) | ||
0.794180 | − | 0.607682i | \(-0.207900\pi\) | |||||||
\(702\) | −19.8917 | + | 4.49113i | −0.750762 | + | 0.169507i | ||||
\(703\) | −26.0775 | − | 4.13027i | −0.983533 | − | 0.155776i | ||||
\(704\) | −3.04265 | + | 2.21062i | −0.114674 | + | 0.0833157i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.3558 | + | 17.6956i | 0.916644 | + | 0.665981i | ||||
\(707\) | 34.7605 | + | 34.7605i | 1.30730 | + | 1.30730i | ||||
\(708\) | 5.95706 | − | 7.69114i | 0.223880 | − | 0.289051i | ||||
\(709\) | −2.62130 | − | 0.851713i | −0.0984451 | − | 0.0319867i | 0.259380 | − | 0.965775i | \(-0.416482\pi\) |
−0.357825 | + | 0.933789i | \(0.616482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.8780 | + | 7.97521i | −1.15802 | + | 0.299094i | ||||
\(712\) | 0.477205 | + | 0.936569i | 0.0178840 | + | 0.0350994i | ||||
\(713\) | −7.61474 | − | 14.9448i | −0.285174 | − | 0.559686i | ||||
\(714\) | −1.52260 | + | 2.77429i | −0.0569818 | + | 0.103825i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.69201 | − | 0.874686i | −0.100605 | − | 0.0326886i | ||||
\(717\) | 10.9833 | + | 8.50694i | 0.410178 | + | 0.317697i | ||||
\(718\) | −2.46690 | − | 2.46690i | −0.0920639 | − | 0.0920639i | ||||
\(719\) | 6.94235 | + | 5.04392i | 0.258906 | + | 0.188106i | 0.709665 | − | 0.704540i | \(-0.248846\pi\) |
−0.450759 | + | 0.892646i | \(0.648846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.79854 | − | 6.39251i | 0.327675 | − | 0.238070i | ||||
\(722\) | 5.92953 | + | 0.939145i | 0.220674 | + | 0.0349514i | ||||
\(723\) | 3.51083 | + | 12.0522i | 0.130569 | + | 0.448226i | ||||
\(724\) | 0.350016i | 0.0130082i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.73123 | + | 3.96767i | 0.138479 | + | 0.147254i | ||||
\(727\) | 30.4942 | + | 15.5376i | 1.13097 | + | 0.576257i | 0.916325 | − | 0.400435i | \(-0.131141\pi\) |
0.214644 | + | 0.976692i | \(0.431141\pi\) | |||||||
\(728\) | 2.72266 | − | 17.1902i | 0.100909 | − | 0.637111i | ||||
\(729\) | −24.3808 | + | 11.6007i | −0.902992 | + | 0.429656i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.27276 | + | 1.75180i | −0.0470746 | + | 0.0647926i | ||||
\(732\) | 0.763622 | − | 24.8650i | 0.0282243 | − | 0.919038i | ||||
\(733\) | 6.22770 | + | 39.3201i | 0.230025 | + | 1.45232i | 0.784504 | + | 0.620124i | \(0.212918\pi\) |
−0.554478 | + | 0.832198i | \(0.687082\pi\) | |||||||
\(734\) | 4.83943 | − | 14.8942i | 0.178627 | − | 0.549756i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.55415 | + | 4.78318i | 0.0572867 | + | 0.176310i | ||||
\(737\) | −20.7547 | + | 10.5750i | −0.764509 | + | 0.389537i | ||||
\(738\) | 4.07989 | + | 9.39121i | 0.150183 | + | 0.345695i | ||||
\(739\) | 19.6010 | − | 6.36874i | 0.721033 | − | 0.234278i | 0.0745620 | − | 0.997216i | \(-0.476244\pi\) |
0.646471 | + | 0.762939i | \(0.276244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.4941 | − | 30.7444i | −0.532452 | − | 1.12942i | ||||
\(742\) | 36.3871 | − | 5.76314i | 1.33581 | − | 0.211572i | ||||
\(743\) | −25.7253 | + | 25.7253i | −0.943771 | + | 0.943771i | −0.998501 | − | 0.0547306i | \(-0.982570\pi\) |
0.0547306 | + | 0.998501i | \(0.482570\pi\) | |||||||
\(744\) | 5.73035 | − | 0.728073i | 0.210085 | − | 0.0266925i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.74935 | − | 5.16053i | −0.137273 | − | 0.188940i | ||||
\(747\) | −4.61103 | + | 20.7680i | −0.168709 | + | 0.759862i | ||||
\(748\) | 0.703446 | − | 1.38059i | 0.0257205 | − | 0.0504794i | ||||
\(749\) | −27.0114 | −0.986973 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8571 | −0.505654 | −0.252827 | − | 0.967511i | \(-0.581360\pi\) | ||||
−0.252827 | + | 0.967511i | \(0.581360\pi\) | |||||||
\(752\) | 2.34657 | − | 4.60540i | 0.0855705 | − | 0.167942i | ||||
\(753\) | −14.1821 | − | 20.8362i | −0.516823 | − | 0.759314i | ||||
\(754\) | −4.25699 | − | 5.85925i | −0.155031 | − | 0.213381i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.49626 | − | 22.9953i | −0.0544186 | − | 0.836332i | ||||
\(757\) | 28.7075 | − | 28.7075i | 1.04339 | − | 1.04339i | 0.0443764 | − | 0.999015i | \(-0.485870\pi\) |
0.999015 | − | 0.0443764i | \(-0.0141301\pi\) | |||||||
\(758\) | 26.6124 | − | 4.21499i | 0.966606 | − | 0.153095i | ||||
\(759\) | 29.6336 | − | 13.9704i | 1.07563 | − | 0.507094i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.3818 | + | 11.8212i | −1.31884 | + | 0.428517i | −0.882096 | − | 0.471069i | \(-0.843868\pi\) |
−0.436744 | + | 0.899586i | \(0.643868\pi\) | |||||||
\(762\) | −11.4844 | + | 31.9710i | −0.416037 | + | 1.15819i | ||||
\(763\) | −18.5405 | + | 9.44684i | −0.671210 | + | 0.341998i | ||||
\(764\) | 0.350849 | + | 1.07980i | 0.0126933 | + | 0.0390659i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.25415 | − | 28.4814i | 0.334366 | − | 1.02907i | ||||
\(767\) | −3.44822 | − | 21.7712i | −0.124508 | − | 0.786114i | ||||
\(768\) | −1.73123 | − | 0.0531674i | −0.0624705 | − | 0.00191851i | ||||
\(769\) | 23.2438 | − | 31.9924i | 0.838194 | − | 1.15368i | −0.148148 | − | 0.988965i | \(-0.547331\pi\) |
0.986342 | − | 0.164710i | \(-0.0526688\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.49860 | + | 0.474783i | 0.0899850 | + | 0.0170989i | ||||
\(772\) | −0.920714 | + | 5.81316i | −0.0331372 | + | 0.209220i | ||||
\(773\) | 32.0052 | + | 16.3075i | 1.15115 | + | 0.586539i | 0.922129 | − | 0.386883i | \(-0.126448\pi\) |
0.229019 | + | 0.973422i | \(0.426448\pi\) | |||||||
\(774\) | 0.967539 | − | 15.7376i | 0.0347775 | − | 0.565677i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 7.71121i | − | 0.276816i | ||||||
\(777\) | −38.9400 | + | 11.3433i | −1.39697 | + | 0.406939i | ||||
\(778\) | 11.4191 | + | 1.80860i | 0.409394 | + | 0.0648416i | ||||
\(779\) | −13.8070 | + | 10.0314i | −0.494688 | + | 0.359412i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.13529 | + | 3.73101i | 0.183755 | + | 0.133506i | ||||
\(782\) | −1.46516 | − | 1.46516i | −0.0523940 | − | 0.0523940i | ||||
\(783\) | −7.20652 | − | 6.32598i | −0.257540 | − | 0.226072i | ||||
\(784\) | 12.0476 | + | 3.91450i | 0.430271 | + | 0.139803i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.1654 | − | 17.1043i | −1.11163 | − | 0.610092i | ||||
\(787\) | 13.0206 | + | 25.5543i | 0.464133 | + | 0.910913i | 0.997868 | + | 0.0652610i | \(0.0207880\pi\) |
−0.533735 | + | 0.845652i | \(0.679212\pi\) | |||||||
\(788\) | −8.72355 | − | 17.1209i | −0.310764 | − | 0.609908i | ||||
\(789\) | 33.8904 | + | 18.5999i | 1.20653 | + | 0.662173i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 72.1143 | + | 23.4314i | 2.56409 | + | 0.833123i | ||||
\(792\) | 1.07786 | + | 11.2312i | 0.0383001 | + | 0.399082i | ||||
\(793\) | −39.8569 | − | 39.8569i | −1.41536 | − | 1.41536i | ||||
\(794\) | 10.8401 | + | 7.87580i | 0.384701 | + | 0.279502i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2845 | − | 7.47216i | 0.364526 | − | 0.264844i | ||||
\(797\) | 9.56827 | + | 1.51547i | 0.338926 | + | 0.0536805i | 0.323578 | − | 0.946202i | \(-0.395114\pi\) |
0.0153481 | + | 0.999882i | \(0.495114\pi\) | |||||||
\(798\) | 36.8765 | − | 10.7422i | 1.30541 | − | 0.380270i | ||||
\(799\) | 2.12949i | 0.0753360i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.14746 | + | 0.193504i | 0.111210 | + | 0.00683713i | ||||
\(802\) | −19.8609 | − | 10.1196i | −0.701313 | − | 0.357337i | ||||
\(803\) | −2.10754 | + | 13.3065i | −0.0743734 | + | 0.469575i | ||||
\(804\) | −10.5390 | − | 2.00261i | −0.371682 | − | 0.0706267i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.69311 | − | 10.5887i | 0.270978 | − | 0.372970i | ||||
\(807\) | −43.2777 | − | 1.32909i | −1.52345 | − | 0.0467861i | ||||
\(808\) | −1.73404 | − | 10.9483i | −0.0610032 | − | 0.385159i | ||||
\(809\) | −17.2607 | + | 53.1231i | −0.606855 | + | 1.86771i | −0.123359 | + | 0.992362i | \(0.539367\pi\) |
−0.483496 | + | 0.875346i | \(0.660633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.13462 | − | 18.8804i | −0.215416 | − | 0.662981i | −0.999124 | − | 0.0418519i | \(-0.986674\pi\) |
0.783708 | − | 0.621129i | \(-0.213326\pi\) | |||||||
\(812\) | 7.29214 | − | 3.71553i | 0.255904 | − | 0.130390i | ||||
\(813\) | −9.51053 | + | 26.4759i | −0.333549 | + | 0.928550i | ||||
\(814\) | 18.8863 | − | 6.13654i | 0.661965 | − | 0.215086i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.645460 | − | 0.304294i | 0.0225956 | − | 0.0106524i | ||||
\(817\) | 25.9571 | − | 4.11120i | 0.908125 | − | 0.143833i | ||||
\(818\) | −9.95831 | + | 9.95831i | −0.348184 | + | 0.348184i | ||||
\(819\) | −40.2787 | − | 33.2245i | −1.40745 | − | 1.16096i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0314 | + | 30.3236i | 0.768899 | + | 1.05830i | 0.996421 | + | 0.0845263i | \(0.0269377\pi\) |
−0.227522 | + | 0.973773i | \(0.573062\pi\) | |||||||
\(822\) | −7.04474 | − | 10.3501i | −0.245713 | − | 0.361001i | ||||
\(823\) | 17.9173 | − | 35.1647i | 0.624559 | − | 1.22577i | −0.334456 | − | 0.942411i | \(-0.608553\pi\) |
0.959015 | − | 0.283355i | \(-0.0914474\pi\) | |||||||
\(824\) | −2.45232 | −0.0854307 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.9088 | 0.866688 | ||||||||
\(827\) | −11.4419 | + | 22.4561i | −0.397875 | + | 0.780874i | −0.999844 | − | 0.0176456i | \(-0.994383\pi\) |
0.601969 | + | 0.798519i | \(0.294383\pi\) | |||||||
\(828\) | 14.7293 | + | 3.27029i | 0.511880 | + | 0.113650i | ||||
\(829\) | −22.7111 | − | 31.2592i | −0.788791 | − | 1.08568i | −0.994258 | − | 0.107013i | \(-0.965871\pi\) |
0.205467 | − | 0.978664i | \(-0.434129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.8321 | − | 1.50334i | 0.410451 | − | 0.0521502i | ||||
\(832\) | −2.77505 | + | 2.77505i | −0.0962075 | + | 0.0962075i | ||||
\(833\) | −5.15469 | + | 0.816423i | −0.178600 | + | 0.0282874i | ||||
\(834\) | 7.15923 | + | 15.1860i | 0.247904 | + | 0.525847i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.8855 | + | 5.81135i | −0.618582 | + | 0.200990i | ||||
\(837\) | 6.84815 | − | 15.9187i | 0.236707 | − | 0.550231i | ||||
\(838\) | −5.05427 | + | 2.57528i | −0.174597 | + | 0.0889615i | ||||
\(839\) | −1.11037 | − | 3.41736i | −0.0383342 | − | 0.117980i | 0.930058 | − | 0.367412i | \(-0.119756\pi\) |
−0.968392 | + | 0.249432i | \(0.919756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.90910 | + | 24.3417i | −0.272727 | + | 0.839369i | ||||
\(842\) | 0.999080 | + | 6.30794i | 0.0344306 | + | 0.217386i | ||||
\(843\) | −1.30207 | + | 42.3978i | −0.0448455 | + | 1.46026i | ||||
\(844\) | −10.2487 | + | 14.1061i | −0.352774 | + | 0.485552i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.32739 | − | 13.0805i | −0.286302 | − | 0.449717i | ||||
\(847\) | −2.18155 | + | 13.7738i | −0.0749591 | + | 0.473273i | ||||
\(848\) | −7.40172 | − | 3.77136i | −0.254176 | − | 0.129509i | ||||
\(849\) | 8.68879 | + | 9.23937i | 0.298198 | + | 0.317095i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 26.5557i | − | 0.910317i | ||||||
\(852\) | 0.817581 | + | 2.80664i | 0.0280099 | + | 0.0961540i | ||||
\(853\) | −44.8288 | − | 7.10018i | −1.53491 | − | 0.243106i | −0.668983 | − | 0.743278i | \(-0.733270\pi\) |
−0.865926 | + | 0.500172i | \(0.833270\pi\) | |||||||
\(854\) | 51.5307 | − | 37.4393i | 1.76334 | − | 1.28114i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.92752 | + | 3.58005i | 0.168419 | + | 0.122364i | ||||
\(857\) | −5.49063 | − | 5.49063i | −0.187556 | − | 0.187556i | 0.607082 | − | 0.794639i | \(-0.292340\pi\) |
−0.794639 | + | 0.607082i | \(0.792340\pi\) | |||||||
\(858\) | 20.2113 | + | 15.6543i | 0.690002 | + | 0.534431i | ||||
\(859\) | 10.7387 | + | 3.48922i | 0.366400 | + | 0.119051i | 0.486430 | − | 0.873720i | \(-0.338299\pi\) |
−0.120030 | + | 0.992770i | \(0.538299\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.6136 | + | 22.9829i | −0.429870 | + | 0.783256i | ||||
\(862\) | −9.06883 | − | 17.7986i | −0.308886 | − | 0.606222i | ||||
\(863\) | −5.28199 | − | 10.3665i | −0.179801 | − | 0.352880i | 0.783462 | − | 0.621440i | \(-0.213452\pi\) |
−0.963263 | + | 0.268560i | \(0.913452\pi\) | |||||||
\(864\) | −2.77482 | + | 4.39322i | −0.0944014 | + | 0.149460i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22.0640 | − | 7.16903i | −0.749765 | − | 0.243613i | ||||
\(867\) | 17.8503 | − | 23.0465i | 0.606228 | − | 0.782699i | ||||
\(868\) | 10.4582 | + | 10.4582i | 0.354975 | + | 0.354975i | ||||
\(869\) | 32.3447 | + | 23.4998i | 1.09722 | + | 0.797177i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.6646 | + | 14.2871i | −0.666308 | + | 0.484101i | ||||
\(872\) | 4.63430 | + | 0.734001i | 0.156937 | + | 0.0248564i | ||||
\(873\) | −19.9289 | − | 11.7475i | −0.674491 | − | 0.397592i | ||||
\(874\) | 25.1484i | 0.850658i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.51987 | + | 4.25053i | −0.152712 | + | 0.143612i | ||||
\(877\) | −22.0344 | − | 11.2271i | −0.744049 | − | 0.379112i | 0.0404992 | − | 0.999180i | \(-0.487105\pi\) |
−0.784548 | + | 0.620068i | \(0.787105\pi\) | |||||||
\(878\) | −1.77277 | + | 11.1928i | −0.0598282 | + | 0.377740i | ||||
\(879\) | 0.524156 | − | 2.75844i | 0.0176794 | − | 0.0930397i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.08613 | + | 9.75322i | −0.238738 | + | 0.328594i | −0.911527 | − | 0.411240i | \(-0.865096\pi\) |
0.672790 | + | 0.739834i | \(0.265096\pi\) | |||||||
\(882\) | 28.4703 | − | 25.1724i | 0.958645 | − | 0.847598i | ||||
\(883\) | −1.11758 | − | 7.05614i | −0.0376097 | − | 0.237458i | 0.961721 | − | 0.274029i | \(-0.0883565\pi\) |
−0.999331 | + | 0.0365710i | \(0.988356\pi\) | |||||||
\(884\) | 0.499640 | − | 1.53774i | 0.0168047 | − | 0.0517196i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.37482 | − | 7.30895i | −0.0797837 | − | 0.245549i | ||||
\(887\) | 3.17069 | − | 1.61555i | 0.106461 | − | 0.0542448i | −0.399949 | − | 0.916537i | \(-0.630972\pi\) |
0.506410 | + | 0.862293i | \(0.330972\pi\) | |||||||
\(888\) | 8.60703 | + | 3.09177i | 0.288833 | + | 0.103753i | ||||
\(889\) | −82.7238 | + | 26.8786i | −2.77447 | + | 0.901479i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.6680 | + | 14.3243i | 1.02742 | + | 0.479881i | ||||
\(892\) | 22.3573 | − | 3.54105i | 0.748578 | − | 0.118563i | ||||
\(893\) | 18.2756 | − | 18.2756i | 0.611569 | − | 0.611569i | ||||
\(894\) | 0.905819 | + | 7.12930i | 0.0302951 | + | 0.238440i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.60672 | − | 3.58784i | −0.0870843 | − | 0.119861i | ||||
\(897\) | 28.2614 | − | 19.2360i | 0.943620 | − | 0.642270i | ||||
\(898\) | 12.2332 | − | 24.0090i | 0.408226 | − | 0.801189i | ||||
\(899\) | 6.15455 | 0.205266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.42248 | 0.114019 | ||||||||
\(902\) | 5.82752 | − | 11.4372i | 0.194035 | − | 0.380816i | ||||
\(903\) | 33.3741 | − | 22.7159i | 1.11062 | − | 0.755938i | ||||
\(904\) | −10.0498 | − | 13.8324i | −0.334252 | − | 0.460058i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.07412 | − | 16.3245i | −0.0689079 | − | 0.542344i | ||||
\(907\) | −1.89862 | + | 1.89862i | −0.0630427 | + | 0.0630427i | −0.737925 | − | 0.674883i | \(-0.764194\pi\) |
0.674883 | + | 0.737925i | \(0.264194\pi\) | |||||||
\(908\) | −19.0703 | + | 3.02044i | −0.632871 | + | 0.100237i | ||||
\(909\) | −30.9365 | − | 12.1975i | −1.02610 | − | 0.404565i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.38886 | + | 0.776187i | −0.0791464 | + | 0.0257162i | −0.348323 | − | 0.937375i | \(-0.613249\pi\) |
0.269176 | + | 0.963091i | \(0.413249\pi\) | |||||||
\(912\) | −8.15092 | − | 2.92793i | −0.269904 | − | 0.0969535i | ||||
\(913\) | 23.7628 | − | 12.1078i | 0.786435 | − | 0.400708i | ||||
\(914\) | −10.5736 | − | 32.5423i | −0.349744 | − | 1.07640i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.03677 | − | 15.5016i | 0.166420 | − | 0.512187i | ||||
\(917\) | −14.2395 | − | 89.9045i | −0.470229 | − | 2.96891i | ||||
\(918\) | 0.196894 | − | 2.13170i | 0.00649846 | − | 0.0703567i | ||||
\(919\) | −5.62589 | + | 7.74338i | −0.185581 | + | 0.255430i | −0.891663 | − | 0.452700i | \(-0.850461\pi\) |
0.706082 | + | 0.708130i | \(0.250461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.79193 | − | 19.9555i | 0.124948 | − | 0.657555i | ||||
\(922\) | −5.80740 | + | 36.6665i | −0.191256 | + | 1.20755i | ||||
\(923\) | 5.90173 | + | 3.00708i | 0.194258 | + | 0.0989793i | ||||
\(924\) | −21.0449 | + | 19.7908i | −0.692328 | + | 0.651071i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 7.02279i | − | 0.230783i | ||||||
\(927\) | −3.73594 | + | 6.33780i | −0.122704 | + | 0.208161i | ||||
\(928\) | −1.82271 | − | 0.288689i | −0.0598335 | − | 0.00947670i | ||||
\(929\) | −28.0139 | + | 20.3533i | −0.919106 | + | 0.667770i | −0.943301 | − | 0.331938i | \(-0.892298\pi\) |
0.0241953 | + | 0.999707i | \(0.492298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.2449 | + | 37.2316i | 1.67949 | + | 1.22022i | ||||
\(932\) | 0.430335 | + | 0.430335i | 0.0140961 | + | 0.0140961i | ||||
\(933\) | −35.0879 | + | 45.3019i | −1.14873 | + | 1.48312i | ||||
\(934\) | −27.2912 | − | 8.86745i | −0.892995 | − | 0.290152i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.94426 | + | 11.3995i | 0.0962362 | + | 0.372603i | ||||
\(937\) | −6.94494 | − | 13.6302i | −0.226881 | − | 0.445280i | 0.749302 | − | 0.662229i | \(-0.230389\pi\) |
−0.976183 | + | 0.216949i | \(0.930389\pi\) | |||||||
\(938\) | −12.4699 | − | 24.4736i | −0.407157 | − | 0.799090i | ||||
\(939\) | −3.64996 | + | 6.65050i | −0.119112 | + | 0.217031i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0255 | + | 8.78112i | 0.881006 | + | 0.286256i | 0.714375 | − | 0.699763i | \(-0.246711\pi\) |
0.166631 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(942\) | −5.77604 | − | 4.47375i | −0.188194 | − | 0.145763i | ||||
\(943\) | −12.1378 | − | 12.1378i | −0.395260 | − | 0.395260i | ||||
\(944\) | −4.54397 | − | 3.30138i | −0.147893 | − | 0.107451i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.9915 | + | 11.6185i | −0.519928 | + | 0.377750i | ||||
\(947\) | 37.1437 | + | 5.88298i | 1.20701 | + | 0.191171i | 0.727339 | − | 0.686279i | \(-0.240757\pi\) |
0.479669 | + | 0.877450i | \(0.340757\pi\) | |||||||
\(948\) | 5.14955 | + | 17.6777i | 0.167250 | + | 0.574145i | ||||
\(949\) | 14.0583i | 0.456353i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.2263 | − | 35.3318i | −1.07744 | − | 1.14571i | ||||
\(952\) | 1.62797 | + | 0.829491i | 0.0527627 | + | 0.0268840i | ||||
\(953\) | −4.16742 | + | 26.3120i | −0.134996 | + | 0.852331i | 0.823519 | + | 0.567289i | \(0.192008\pi\) |
−0.958515 | + | 0.285042i | \(0.907992\pi\) | |||||||
\(954\) | −21.0227 | + | 13.3836i | −0.680636 | + | 0.433311i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.71452 | − | 6.48898i | 0.152478 | − | 0.209868i | ||||
\(957\) | −0.369010 | + | 12.0157i | −0.0119284 | + | 0.388412i | ||||
\(958\) | 2.00959 | + | 12.6881i | 0.0649269 | + | 0.409933i | ||||
\(959\) | 9.90614 | − | 30.4880i | 0.319886 | − | 0.984508i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.14254 | − | 18.9048i | −0.198146 | − | 0.609832i | ||||
\(962\) | 18.4635 | − | 9.40760i | 0.595286 | − | 0.303313i | ||||
\(963\) | 16.7591 | − | 7.28076i | 0.540053 | − | 0.234619i | ||||
\(964\) | 6.89284 | − | 2.23962i | 0.222003 | − | 0.0721333i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.4737 | + | 34.9435i | 0.530032 | + | 1.12429i | ||||
\(967\) | −41.4802 | + | 6.56982i | −1.33391 | + | 0.211271i | −0.782339 | − | 0.622853i | \(-0.785973\pi\) |
−0.551576 | + | 0.834125i | \(0.685973\pi\) | |||||||
\(968\) | 2.22353 | − | 2.22353i | 0.0714670 | − | 0.0714670i | ||||
\(969\) | 3.53975 | − | 0.449746i | 0.113713 | − | 0.0144479i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.52779 | + | 11.7375i | 0.273670 | + | 0.376674i | 0.923624 | − | 0.383299i | \(-0.125212\pi\) |
−0.649955 | + | 0.759973i | \(0.725212\pi\) | |||||||
\(972\) | 7.12661 | + | 13.8640i | 0.228586 | + | 0.444689i | ||||
\(973\) | −19.5157 | + | 38.3017i | −0.625645 | + | 1.22790i | ||||
\(974\) | 20.6983 | 0.663215 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.3626 | −0.459736 | ||||||||
\(977\) | −0.545186 | + | 1.06999i | −0.0174420 | + | 0.0342319i | −0.899563 | − | 0.436791i | \(-0.856115\pi\) |
0.882121 | + | 0.471023i | \(0.156115\pi\) | |||||||
\(978\) | 10.1569 | + | 14.9225i | 0.324783 | + | 0.477169i | ||||
\(979\) | −2.32366 | − | 3.19824i | −0.0742644 | − | 0.102216i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.95699 | − | 10.8587i | 0.285975 | − | 0.346692i | ||||
\(982\) | −19.7552 | + | 19.7552i | −0.630413 | + | 0.630413i | ||||
\(983\) | −17.7113 | + | 2.80520i | −0.564903 | + | 0.0894719i | −0.432353 | − | 0.901704i | \(-0.642317\pi\) |
−0.132550 | + | 0.991176i | \(0.542317\pi\) | |||||||
\(984\) | 5.34715 | − | 2.52085i | 0.170461 | − | 0.0803618i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.723093 | − | 0.234947i | 0.0230280 | − | 0.00748224i | ||||
\(987\) | 13.4222 | − | 37.3653i | 0.427233 | − | 1.18935i | ||||
\(988\) | −17.4850 | + | 8.90907i | −0.556273 | + | 0.283435i | ||||
\(989\) | 8.16826 | + | 25.1393i | 0.259736 | + | 0.799384i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9087 | − | 45.8841i | 0.473589 | − | 1.45756i | −0.374262 | − | 0.927323i | \(-0.622104\pi\) |
0.847851 | − | 0.530234i | \(-0.177896\pi\) | |||||||
\(992\) | −0.521711 | − | 3.29395i | −0.0165643 | − | 0.104583i | ||||
\(993\) | 16.5921 | + | 0.509555i | 0.526535 | + | 0.0161702i | ||||
\(994\) | −4.39954 | + | 6.05544i | −0.139545 | + | 0.192067i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.0665 | + | 2.29287i | 0.382341 | + | 0.0726523i | ||||
\(997\) | −3.38611 | + | 21.3791i | −0.107239 | + | 0.677082i | 0.874237 | + | 0.485499i | \(0.161362\pi\) |
−0.981476 | + | 0.191583i | \(0.938638\pi\) | |||||||
\(998\) | −0.361613 | − | 0.184251i | −0.0114467 | − | 0.00583237i | ||||
\(999\) | 21.1026 | − | 17.5340i | 0.667657 | − | 0.554750i |
(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 | 750.2.l.b.143.5 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.143.9 | 80 | ||
5.2 | odd | 4 | 750.2.l.a.107.2 | 80 | |||
5.3 | odd | 4 | 750.2.l.c.107.9 | 80 | |||
5.4 | even | 2 | 150.2.l.a.83.6 | yes | 80 | ||
15.2 | even | 4 | 750.2.l.a.107.9 | 80 | |||
15.8 | even | 4 | 750.2.l.c.107.2 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.83.2 | yes | 80 | ||
25.3 | odd | 20 | 150.2.l.a.47.2 | ✓ | 80 | ||
25.4 | even | 10 | 750.2.l.c.743.2 | 80 | |||
25.21 | even | 5 | 750.2.l.a.743.9 | 80 | |||
25.22 | odd | 20 | inner | 750.2.l.b.257.9 | 80 | ||
75.29 | odd | 10 | 750.2.l.c.743.9 | 80 | |||
75.47 | even | 20 | inner | 750.2.l.b.257.5 | 80 | ||
75.53 | even | 20 | 150.2.l.a.47.6 | yes | 80 | ||
75.71 | odd | 10 | 750.2.l.a.743.2 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.2 | ✓ | 80 | 25.3 | odd | 20 | ||
150.2.l.a.47.6 | yes | 80 | 75.53 | even | 20 | ||
150.2.l.a.83.2 | yes | 80 | 15.14 | odd | 2 | ||
150.2.l.a.83.6 | yes | 80 | 5.4 | even | 2 | ||
750.2.l.a.107.2 | 80 | 5.2 | odd | 4 | |||
750.2.l.a.107.9 | 80 | 15.2 | even | 4 | |||
750.2.l.a.743.2 | 80 | 75.71 | odd | 10 | |||
750.2.l.a.743.9 | 80 | 25.21 | even | 5 | |||
750.2.l.b.143.5 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.b.143.9 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.257.5 | 80 | 75.47 | even | 20 | inner | ||
750.2.l.b.257.9 | 80 | 25.22 | odd | 20 | inner | ||
750.2.l.c.107.2 | 80 | 15.8 | even | 4 | |||
750.2.l.c.107.9 | 80 | 5.3 | odd | 4 | |||
750.2.l.c.743.2 | 80 | 25.4 | even | 10 | |||
750.2.l.c.743.9 | 80 | 75.29 | odd | 10 |