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 | 143.9 | ||
Character | \(\chi\) | \(=\) | 750.143 |
Dual form | 750.2.l.b.257.9 |
$q$-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 | ||||
\(3\) | 1.06061 | + | 1.36935i | 0.612342 | + | 0.790593i | ||||
\(4\) | −0.587785 | − | 0.809017i | −0.293893 | − | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.70160 | − | 0.323338i | 0.694677 | − | 0.132002i | ||||
\(7\) | −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 | ||||
\(9\) | −0.750223 | + | 2.90468i | −0.250074 | + | 0.968227i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.57685 | − | 1.16219i | 1.07846 | − | 0.350413i | 0.284684 | − | 0.958622i | \(-0.408111\pi\) |
0.793778 | + | 0.608208i | \(0.208111\pi\) | |||||||
\(12\) | 0.484416 | − | 1.66293i | 0.139839 | − | 0.480047i | ||||
\(13\) | −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 | 0.994271 | − | 0.106893i | \(-0.0340902\pi\) |
−0.978639 | + | 0.205585i | \(0.934090\pi\) | |||||||
\(18\) | 2.24749 | + | 1.98715i | 0.529739 | + | 0.468376i | ||||
\(19\) | −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 | ||||||||
\(21\) | −7.62006 | − | 0.968173i | −1.66283 | − | 0.211273i | ||||
\(22\) | 0.588338 | − | 3.71462i | 0.125434 | − | 0.791960i | ||||
\(23\) | 4.48117 | + | 2.28327i | 0.934389 | + | 0.476095i | 0.853770 | − | 0.520650i | \(-0.174310\pi\) |
0.0806186 | + | 0.996745i | \(0.474310\pi\) | |||||||
\(24\) | −1.26176 | − | 1.18657i | −0.257556 | − | 0.242208i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.92451i | 0.769660i | ||||||||
\(27\) | −4.77321 | + | 2.05341i | −0.918604 | + | 0.395179i | ||||
\(28\) | 4.38021 | + | 0.693758i | 0.827783 | + | 0.131108i | ||||
\(29\) | −1.49299 | + | 1.08472i | −0.277241 | + | 0.201427i | −0.717713 | − | 0.696339i | \(-0.754811\pi\) |
0.440472 | + | 0.897766i | \(0.354811\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 5.38508 | + | 3.66532i | 0.937421 | + | 0.638051i | ||||
\(34\) | 0.391828 | + | 0.127313i | 0.0671980 | + | 0.0218340i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.79091 | − | 1.10038i | 0.465151 | − | 0.183397i | ||||
\(37\) | 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 | ||||
\(39\) | −6.14845 | − | 2.89861i | −0.984540 | − | 0.464149i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.24600 | − | 1.05469i | −0.506941 | − | 0.164715i | 0.0443698 | − | 0.999015i | \(-0.485872\pi\) |
−0.551310 | + | 0.834300i | \(0.685872\pi\) | |||||||
\(42\) | −4.32208 | + | 6.34998i | −0.666912 | + | 0.979824i | ||||
\(43\) | −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 | 0.517223 | − | 0.855851i | \(-0.326966\pi\) |
0.227436 | + | 0.973793i | \(0.426966\pi\) | |||||||
\(48\) | −1.63007 | + | 0.585546i | −0.235281 | + | 0.0845163i | ||||
\(49\) | − | 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 | \(-0.756735\pi\) |
0.900412 | − | 0.435037i | \(-0.143265\pi\) | |||||||
\(54\) | −0.337390 | + | 5.18519i | −0.0459130 | + | 0.705615i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.60672 | − | 3.58784i | 0.348337 | − | 0.479445i | ||||
\(57\) | −8.65677 | + | 0.265855i | −1.14662 | + | 0.0352134i | ||||
\(58\) | 0.288689 | + | 1.82271i | 0.0379068 | + | 0.239334i | ||||
\(59\) | 1.73564 | − | 5.34175i | 0.225961 | − | 0.695437i | −0.772231 | − | 0.635341i | \(-0.780859\pi\) |
0.998193 | − | 0.0600956i | \(-0.0191406\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | −6.75613 | − | 11.4614i | −0.851193 | − | 1.44400i | ||||
\(64\) | 0.951057 | − | 0.309017i | 0.118882 | − | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.71060 | − | 3.13412i | 0.702926 | − | 0.385783i | ||||
\(67\) | 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 | ||||
\(69\) | 1.62617 | + | 8.55793i | 0.195768 | + | 1.03025i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.992045 | + | 1.36543i | 0.117734 | + | 0.162047i | 0.863817 | − | 0.503806i | \(-0.168068\pi\) |
−0.746082 | + | 0.665854i | \(0.768068\pi\) | |||||||
\(72\) | 0.286595 | − | 2.98628i | 0.0337755 | − | 0.351936i | ||||
\(73\) | 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 | ||||
\(78\) | −5.37402 | + | 4.16237i | −0.608488 | + | 0.471295i | ||||
\(79\) | −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 | ||||||||
\(81\) | −7.87433 | − | 4.35832i | −0.874926 | − | 0.484258i | ||||
\(82\) | −2.41339 | + | 2.41339i | −0.266514 | + | 0.266514i | ||||
\(83\) | 7.00394 | − | 1.10932i | 0.768782 | − | 0.121763i | 0.240290 | − | 0.970701i | \(-0.422757\pi\) |
0.528493 | + | 0.848938i | \(0.322757\pi\) | |||||||
\(84\) | 3.69569 | + | 6.73384i | 0.403233 | + | 0.734722i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.99854 | + | 1.62412i | −0.539006 | + | 0.175134i | ||||
\(87\) | −3.06883 | − | 0.893957i | −0.329013 | − | 0.0958423i | ||||
\(88\) | −3.35101 | + | 1.70742i | −0.357219 | + | 0.182012i | ||||
\(89\) | −0.324819 | − | 0.999689i | −0.0344307 | − | 0.105967i | 0.932364 | − | 0.361521i | \(-0.117742\pi\) |
−0.966795 | + | 0.255554i | \(0.917742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.37828 | − | 16.5526i | 0.563797 | − | 1.73519i | ||||
\(92\) | −0.786761 | − | 4.96742i | −0.0820255 | − | 0.517889i | ||||
\(93\) | 0.177314 | + | 5.77369i | 0.0183866 | + | 0.598704i | ||||
\(94\) | 3.03812 | − | 4.18162i | 0.313358 | − | 0.431301i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.218312 | + | 1.71824i | −0.0222814 | + | 0.175367i | ||||
\(97\) | 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 | \(0.185939\pi\) | ||||
−0.834184 | + | 0.551487i | \(0.814061\pi\) | |||||||
\(102\) | 0.241241 | + | 0.671578i | 0.0238864 | + | 0.0664961i | ||||
\(103\) | −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 | 0.467590 | − | 0.883945i | \(-0.345122\pi\) |
−0.883945 | + | 0.467590i | \(0.845122\pi\) | |||||||
\(108\) | 4.46686 | + | 2.65464i | 0.429824 | + | 0.255443i | ||||
\(109\) | 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 | ||||||||
\(111\) | −3.89988 | + | 8.27231i | −0.370160 | + | 0.785173i | ||||
\(112\) | −2.01336 | − | 3.95145i | −0.190245 | − | 0.373377i | ||||
\(113\) | 7.76223 | + | 15.2342i | 0.730209 | + | 1.43312i | 0.894668 | + | 0.446732i | \(0.147412\pi\) |
−0.164459 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(114\) | −3.69321 | + | 7.83393i | −0.345901 | + | 0.733715i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.75511 | + | 0.570270i | 0.162958 | + | 0.0529483i | ||||
\(117\) | −2.55189 | − | 11.4937i | −0.235922 | − | 1.06259i | ||||
\(118\) | −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 | ||||
\(123\) | −1.99850 | − | 5.56352i | −0.180199 | − | 0.501646i | ||||
\(124\) | − | 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 | ||||
\(129\) | 1.14740 | − | 9.03067i | 0.101023 | − | 0.795106i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0644 | − | 16.6052i | 1.05407 | − | 1.45080i | 0.168841 | − | 0.985643i | \(-0.445998\pi\) |
0.885228 | − | 0.465158i | \(-0.154002\pi\) | |||||||
\(132\) | −0.199959 | − | 6.51104i | −0.0174042 | − | 0.566713i | ||||
\(133\) | −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 | −0.156675 | − | 0.987650i | \(-0.550078\pi\) |
0.706935 | + | 0.707279i | \(0.250078\pi\) | |||||||
\(138\) | 8.36344 | + | 2.43629i | 0.711943 | + | 0.207391i | ||||
\(139\) | 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 | ||||||||
\(141\) | 4.30732 | + | 7.84827i | 0.362742 | + | 0.660943i | ||||
\(142\) | 1.66699 | − | 0.264025i | 0.139891 | − | 0.0221565i | ||||
\(143\) | −10.4367 | + | 10.4367i | −0.872765 | + | 0.872765i | ||||
\(144\) | −2.53068 | − | 1.61110i | −0.210890 | − | 0.134258i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.10556 | − | 2.89805i | −0.174257 | − | 0.239845i | ||||
\(147\) | 17.3463 | − | 13.4353i | 1.43070 | − | 1.10813i | ||||
\(148\) | 2.39714 | − | 4.70465i | 0.197044 | − | 0.386720i | ||||
\(149\) | −4.14920 | −0.339915 | −0.169958 | − | 0.985451i | \(-0.554363\pi\) | ||||
−0.169958 | + | 0.985451i | \(0.554363\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | −1.23033 | − | 0.118075i | −0.0994659 | − | 0.00954580i | ||||
\(154\) | 9.80367 | + | 13.4936i | 0.790002 | + | 1.08734i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.26894 | + | 6.67796i | 0.101597 | + | 0.534665i | ||||
\(157\) | −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 | ||||
\(159\) | 12.6136 | − | 6.92265i | 1.00032 | − | 0.549002i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.2125 | + | 6.89237i | −1.67178 | + | 0.543195i | ||||
\(162\) | −7.45816 | + | 5.03744i | −0.585968 | + | 0.395779i | ||||
\(163\) | 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 | \(-0.867802\pi\) |
0.745527 | − | 0.666476i | \(-0.232198\pi\) | |||||||
\(168\) | 7.67770 | − | 0.235788i | 0.592348 | − | 0.0181914i | ||||
\(169\) | 1.41174 | − | 1.94309i | 0.108595 | − | 0.149469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.54548 | − | 11.5722i | −0.729961 | − | 0.884945i | ||||
\(172\) | −0.822184 | + | 5.19107i | −0.0626910 | + | 0.395815i | ||||
\(173\) | −6.24576 | − | 3.18237i | −0.474856 | − | 0.241951i | 0.200147 | − | 0.979766i | \(-0.435858\pi\) |
−0.675003 | + | 0.737815i | \(0.735858\pi\) | |||||||
\(174\) | −2.18974 | + | 2.32850i | −0.166004 | + | 0.176523i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.76092i | 0.283490i | ||||||||
\(177\) | 9.15555 | − | 3.28881i | 0.688173 | − | 0.247202i | ||||
\(178\) | −1.03819 | − | 0.164434i | −0.0778159 | − | 0.0123248i | ||||
\(179\) | −2.28996 | + | 1.66375i | −0.171159 | + | 0.124355i | −0.670067 | − | 0.742301i | \(-0.733735\pi\) |
0.498908 | + | 0.866655i | \(0.333735\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | −13.9975 | + | 20.5651i | −1.03473 | + | 1.52021i | ||||
\(184\) | −4.78318 | − | 1.55415i | −0.352621 | − | 0.114573i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.22490 | + | 2.46321i | 0.383108 | + | 0.180612i | ||||
\(187\) | 0.703446 | + | 1.38059i | 0.0514411 | + | 0.100959i | ||||
\(188\) | −2.34657 | − | 4.60540i | −0.171141 | − | 0.335883i | ||||
\(189\) | 8.52898 | − | 21.4075i | 0.620392 | − | 1.55717i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.07980 | + | 0.350849i | 0.0781318 | + | 0.0253866i | 0.347822 | − | 0.937561i | \(-0.386921\pi\) |
−0.269690 | + | 0.962947i | \(0.586921\pi\) | |||||||
\(192\) | 1.43185 | + | 0.974581i | 0.103335 | + | 0.0703343i | ||||
\(193\) | −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 | −0.562048 | − | 0.827105i | \(-0.689986\pi\) |
−0.790129 | + | 0.612941i | \(0.789986\pi\) | |||||||
\(198\) | 10.3484 | + | 4.49573i | 0.735429 | + | 0.319498i | ||||
\(199\) | 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 | ||||
\(204\) | 0.707901 | + | 0.0899429i | 0.0495630 | + | 0.00629726i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.44144 | + | 1.98397i | −0.100430 | + | 0.138230i | ||||
\(207\) | −9.99405 | + | 11.3034i | −0.694634 | + | 0.785641i | ||||
\(208\) | −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 | ||||
\(213\) | −0.817581 | + | 2.80664i | −0.0560198 | + | 0.192308i | ||||
\(214\) | −5.79265 | + | 1.88215i | −0.395977 | + | 0.128661i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.39322 | − | 2.77482i | 0.298921 | − | 0.188803i | ||||
\(217\) | −14.6081 | + | 2.31369i | −0.991661 | + | 0.157064i | ||||
\(218\) | 3.31779 | − | 3.31779i | 0.224709 | − | 0.224709i | ||||
\(219\) | 6.09547 | − | 1.15826i | 0.411893 | − | 0.0782677i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.950373 | − | 1.30808i | −0.0639290 | − | 0.0879907i | ||||
\(222\) | 5.60017 | + | 7.23036i | 0.375859 | + | 0.485270i | ||||
\(223\) | −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 | \(0.371380\pi\) |
−0.974962 | + | 0.222373i | \(0.928620\pi\) | |||||||
\(228\) | 5.30340 | + | 6.84721i | 0.351226 | + | 0.453467i | ||||
\(229\) | 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 | ||||||||
\(231\) | −28.3810 | + | 5.39295i | −1.86733 | + | 0.354830i | ||||
\(232\) | 1.30492 | − | 1.30492i | 0.0856721 | − | 0.0856721i | ||||
\(233\) | 0.601093 | − | 0.0952038i | 0.0393789 | − | 0.00623701i | −0.136714 | − | 0.990611i | \(-0.543654\pi\) |
0.176093 | + | 0.984374i | \(0.443654\pi\) | |||||||
\(234\) | −11.3995 | − | 2.94426i | −0.745205 | − | 0.192472i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.34175 | + | 1.73564i | −0.347718 | + | 0.112981i | ||||
\(237\) | 5.14955 | − | 17.6777i | 0.334499 | − | 1.14829i | ||||
\(238\) | −1.62797 | + | 0.829491i | −0.105525 | + | 0.0537679i | ||||
\(239\) | −2.47857 | − | 7.62825i | −0.160325 | − | 0.493430i | 0.838336 | − | 0.545154i | \(-0.183529\pi\) |
−0.998661 | + | 0.0517231i | \(0.983529\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | −2.38352 | − | 15.4052i | −0.152903 | − | 0.988241i | ||||
\(244\) | 8.44212 | − | 11.6196i | 0.540452 | − | 0.743868i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.86443 | − | 0.745110i | −0.373903 | − | 0.0475065i | ||||
\(247\) | 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 | \(0.151884\pi\) | ||||
−0.888304 | + | 0.459256i | \(0.848116\pi\) | |||||||
\(252\) | −5.30128 | + | 12.2026i | −0.333949 | + | 0.768694i | ||||
\(253\) | 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 | 0.673981 | − | 0.738749i | \(-0.264583\pi\) |
−0.738749 | + | 0.673981i | \(0.764583\pi\) | |||||||
\(258\) | −7.52548 | − | 5.12218i | −0.468516 | − | 0.318893i | ||||
\(259\) | −22.2704 | − | 7.23610i | −1.38382 | − | 0.449629i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.03069 | − | 5.15043i | −0.125696 | − | 0.318804i | ||||
\(262\) | −9.31821 | − | 18.2880i | −0.575681 | − | 1.12984i | ||||
\(263\) | −10.1330 | − | 19.8871i | −0.624825 | − | 1.22629i | −0.958901 | − | 0.283743i | \(-0.908424\pi\) |
0.334075 | − | 0.942546i | \(-0.391576\pi\) | |||||||
\(264\) | −5.89216 | − | 2.77779i | −0.362637 | − | 0.170961i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −21.0902 | − | 6.85264i | −1.29313 | − | 0.420162i | ||||
\(267\) | 1.02442 | − | 1.50507i | 0.0626933 | − | 0.0921086i | ||||
\(268\) | −4.37951 | − | 4.37951i | −0.267521 | − | 0.267521i | ||||
\(269\) | 20.2239 | + | 14.6936i | 1.23308 | + | 0.895882i | 0.997117 | − | 0.0758813i | \(-0.0241770\pi\) |
0.235959 | + | 0.971763i | \(0.424177\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 28.3706 | − | 10.1911i | 1.71706 | − | 0.616795i | ||||
\(274\) | − | 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 | ||||
\(279\) | −7.71813 | + | 6.36643i | −0.462072 | + | 0.381148i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3948 | − | 19.8128i | 0.858723 | − | 1.18193i | −0.123150 | − | 0.992388i | \(-0.539300\pi\) |
0.981873 | − | 0.189542i | \(-0.0607004\pi\) | |||||||
\(282\) | 8.94834 | − | 0.274810i | 0.532866 | − | 0.0163647i | ||||
\(283\) | 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 | ||||
\(288\) | −2.58441 | + | 1.52343i | −0.152288 | + | 0.0897690i | ||||
\(289\) | 16.0065 | − | 5.20084i | 0.941561 | − | 0.305932i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.7087 | − | 6.42603i | 0.686378 | − | 0.376701i | ||||
\(292\) | −3.53809 | + | 0.560378i | −0.207051 | + | 0.0327936i | ||||
\(293\) | −1.14628 | + | 1.14628i | −0.0669662 | + | 0.0669662i | −0.739797 | − | 0.672830i | \(-0.765078\pi\) |
0.672830 | + | 0.739797i | \(0.265078\pi\) | |||||||
\(294\) | −4.09590 | − | 21.5552i | −0.238878 | − | 1.25712i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.10360 | − | 4.27173i | −0.180393 | − | 0.248290i | ||||
\(297\) | −14.6866 | + | 12.8921i | −0.852203 | + | 0.748076i | ||||
\(298\) | −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 | ||||
\(303\) | −15.1789 | + | 11.7566i | −0.872003 | + | 0.675397i | ||||
\(304\) | −2.93913 | − | 4.04536i | −0.168571 | − | 0.232018i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.663762 | + | 1.04262i | −0.0379447 | + | 0.0596028i | ||||
\(307\) | 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 | ||||
\(309\) | −2.04361 | − | 3.72362i | −0.116257 | − | 0.211829i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.4637 | − | 10.2232i | 1.78414 | − | 0.579703i | 0.784937 | − | 0.619575i | \(-0.212695\pi\) |
0.999205 | + | 0.0398725i | \(0.0126952\pi\) | |||||||
\(312\) | 6.52620 | + | 1.90110i | 0.369473 | + | 0.107628i | ||||
\(313\) | −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 | \(0.238043\pi\) |
−0.487131 | + | 0.873329i | \(0.661957\pi\) | |||||||
\(318\) | −0.441669 | − | 14.3816i | −0.0247676 | − | 0.806481i | ||||
\(319\) | −4.07954 | + | 5.61501i | −0.228411 | + | 0.314380i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.32968 | − | 10.4654i | 0.0742157 | − | 0.584119i | ||||
\(322\) | −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 | ||||||
\(327\) | 2.74742 | + | 7.64841i | 0.151933 | + | 0.422958i | ||||
\(328\) | 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 | ||||
\(333\) | −15.4639 | + | 3.43338i | −0.847416 | + | 0.188148i | ||||
\(334\) | −13.3140 | − | 4.32598i | −0.728510 | − | 0.236707i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.27552 | − | 6.94793i | 0.178694 | − | 0.379041i | ||||
\(337\) | 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 | ||||
\(339\) | −12.6283 | + | 26.7867i | −0.685874 | + | 1.45485i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.9289 | + | 3.87592i | 0.645983 | + | 0.209893i | ||||
\(342\) | −14.6444 | + | 3.25144i | −0.791880 | + | 0.175818i | ||||
\(343\) | 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 | \(0.00737823\pi\) |
0.957963 | + | 0.286891i | \(0.0926218\pi\) | |||||||
\(348\) | 1.08059 | + | 3.00819i | 0.0579255 | + | 0.161256i | ||||
\(349\) | 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 | \(0.345792\pi\) |
−0.716392 | + | 0.697698i | \(0.754208\pi\) | |||||||
\(354\) | 1.22618 | − | 9.65074i | 0.0651708 | − | 0.512931i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.617842 | + | 0.850386i | −0.0327456 | + | 0.0450704i | ||||
\(357\) | −0.0971428 | − | 3.16316i | −0.00514134 | − | 0.167412i | ||||
\(358\) | 0.442795 | + | 2.79569i | 0.0234024 | + | 0.147757i | ||||
\(359\) | 1.07807 | − | 3.31797i | 0.0568986 | − | 0.175116i | −0.918568 | − | 0.395263i | \(-0.870654\pi\) |
0.975467 | + | 0.220147i | \(0.0706536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.85517 | − | 5.70961i | −0.0976403 | − | 0.300506i | ||||
\(362\) | −0.311866 | + | 0.158904i | −0.0163913 | + | 0.00835180i | ||||
\(363\) | 5.22917 | + | 1.52327i | 0.274460 | + | 0.0799508i | ||||
\(364\) | −16.5526 | + | 5.37828i | −0.867594 | + | 0.281898i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.9689 | + | 21.8082i | 0.625623 | + | 1.13993i | ||||
\(367\) | −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 | ||||
\(369\) | 5.49877 | − | 8.63735i | 0.286254 | − | 0.449642i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.6544 | + | 29.8047i | 1.12424 | + | 1.54738i | ||||
\(372\) | 4.56679 | − | 3.53714i | 0.236777 | − | 0.183392i | ||||
\(373\) | −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 | ||||
\(378\) | −15.2021 | − | 17.3182i | −0.781914 | − | 0.890751i | ||||
\(379\) | −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 | ||||||||
\(381\) | 6.34169 | + | 33.3739i | 0.324895 | + | 1.70980i | ||||
\(382\) | 0.802829 | − | 0.802829i | 0.0410763 | − | 0.0410763i | ||||
\(383\) | 29.5784 | − | 4.68475i | 1.51138 | − | 0.239380i | 0.654964 | − | 0.755660i | \(-0.272684\pi\) |
0.856420 | + | 0.516280i | \(0.172684\pi\) | |||||||
\(384\) | 1.51840 | − | 0.833337i | 0.0774857 | − | 0.0425260i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.59756 | + | 1.81876i | −0.284908 | + | 0.0925723i | ||||
\(387\) | 13.5831 | − | 8.00681i | 0.690466 | − | 0.407009i | ||||
\(388\) | −6.87074 | + | 3.50082i | −0.348809 | + | 0.177727i | ||||
\(389\) | 3.57268 | + | 10.9956i | 0.181142 | + | 0.557497i | 0.999861 | − | 0.0166975i | \(-0.00531522\pi\) |
−0.818719 | + | 0.574195i | \(0.805315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.640299 | + | 1.97064i | −0.0323813 | + | 0.0996594i | ||||
\(392\) | 1.98165 | + | 12.5116i | 0.100088 | + | 0.631932i | ||||
\(393\) | 35.5338 | − | 1.09127i | 1.79244 | − | 0.0550472i | ||||
\(394\) | −11.2945 | + | 15.5455i | −0.569007 | + | 0.783170i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.70380 | − | 7.17947i | 0.437382 | − | 0.360782i | ||||
\(397\) | 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 | \(-0.812119\pi\) | ||
0.830804 | − | 0.556565i | \(-0.187881\pi\) | |||||||
\(402\) | 10.0960 | − | 3.62662i | 0.503541 | − | 0.180879i | ||||
\(403\) | −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 | ||||
\(408\) | 0.401520 | − | 0.589911i | 0.0198782 | − | 0.0292050i | ||||
\(409\) | 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 | ||||||||
\(411\) | 11.3247 | + | 5.33889i | 0.558606 | + | 0.263348i | ||||
\(412\) | 1.11333 | + | 2.18504i | 0.0548499 | + | 0.107649i | ||||
\(413\) | 11.3084 | + | 22.1939i | 0.556448 | + | 1.09209i | ||||
\(414\) | 5.53420 | + | 14.0364i | 0.271991 | + | 0.689851i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.73243 | − | 1.21274i | −0.182998 | − | 0.0594595i | ||||
\(417\) | 13.8790 | + | 9.44670i | 0.679660 | + | 0.462607i | ||||
\(418\) | 13.2978 | + | 13.2978i | 0.650416 | + | 0.650416i | ||||
\(419\) | −4.58918 | − | 3.33423i | −0.224196 | − | 0.162888i | 0.470017 | − | 0.882657i | \(-0.344248\pi\) |
−0.694213 | + | 0.719769i | \(0.744248\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | −6.17863 | + | 14.2221i | −0.300415 | + | 0.691504i | ||||
\(424\) | 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 | ||||
\(429\) | −25.3608 | − | 3.22224i | −1.22443 | − | 0.155571i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.7415 | − | 16.1608i | 0.565568 | − | 0.778437i | −0.426453 | − | 0.904510i | \(-0.640237\pi\) |
0.992021 | + | 0.126072i | \(0.0402371\pi\) | |||||||
\(432\) | −0.477906 | − | 5.17413i | −0.0229932 | − | 0.248940i | ||||
\(433\) | 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 | ||||
\(438\) | 1.73527 | − | 5.95694i | 0.0829144 | − | 0.284633i | ||||
\(439\) | 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 | ||||||||
\(441\) | 36.7952 | + | 9.50351i | 1.75215 | + | 0.452548i | ||||
\(442\) | −1.59696 | + | 0.252934i | −0.0759598 | + | 0.0120309i | ||||
\(443\) | 5.43418 | − | 5.43418i | 0.258186 | − | 0.258186i | −0.566130 | − | 0.824316i | \(-0.691560\pi\) |
0.824316 | + | 0.566130i | \(0.191560\pi\) | |||||||
\(444\) | 8.98473 | − | 1.70727i | 0.426396 | − | 0.0810236i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.3051 | + | 18.3129i | 0.630015 | + | 0.867141i | ||||
\(447\) | −4.40067 | − | 5.68169i | −0.208144 | − | 0.268735i | ||||
\(448\) | −2.01336 | + | 3.95145i | −0.0951225 | + | 0.186688i | ||||
\(449\) | 26.9459 | 1.27165 | 0.635827 | − | 0.771831i | \(-0.280659\pi\) | ||||
0.635827 | + | 0.771831i | \(0.280659\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8362 | −0.604434 | ||||||||
\(452\) | 7.76223 | − | 15.2342i | 0.365104 | − | 0.716558i | ||||
\(453\) | −10.0765 | − | 13.0098i | −0.473436 | − | 0.611252i | ||||
\(454\) | 11.3490 | + | 15.6205i | 0.532634 | + | 0.733108i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.50860 | − | 1.61680i | 0.398452 | − | 0.0757136i | ||||
\(457\) | −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 | ||||
\(459\) | −1.14321 | − | 1.80997i | −0.0533603 | − | 0.0844823i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.3066 | + | 11.4718i | −1.64439 | + | 0.534295i | −0.977513 | − | 0.210873i | \(-0.932369\pi\) |
−0.666877 | + | 0.745168i | \(0.732369\pi\) | |||||||
\(462\) | −8.07957 | + | 27.7360i | −0.375896 | + | 1.29040i | ||||
\(463\) | −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 | \(-0.818884\pi\) |
0.634718 | − | 0.772744i | \(-0.281116\pi\) | |||||||
\(468\) | −7.79860 | + | 8.82032i | −0.360490 | + | 0.407719i | ||||
\(469\) | −16.1449 | + | 22.2215i | −0.745502 | + | 1.02609i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.24770 | − | 0.920861i | −0.333956 | − | 0.0424310i | ||||
\(472\) | −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 | ||||||||
\(477\) | 22.8576 | + | 9.93018i | 1.04658 | + | 0.454672i | ||||
\(478\) | −7.92207 | − | 1.25473i | −0.362347 | − | 0.0573901i | ||||
\(479\) | −10.3928 | + | 7.55082i | −0.474860 | + | 0.345006i | −0.799332 | − | 0.600889i | \(-0.794813\pi\) |
0.324473 | + | 0.945895i | \(0.394813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.7645 | − | 12.1801i | −0.764394 | − | 0.555365i | ||||
\(482\) | 5.12480 | + | 5.12480i | 0.233428 | + | 0.233428i | ||||
\(483\) | −31.9362 | − | 21.7372i | −1.45315 | − | 0.989077i | ||||
\(484\) | −2.99064 | − | 0.971718i | −0.135938 | − | 0.0441690i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.8082 | − | 4.87006i | −0.671713 | − | 0.220910i | ||||
\(487\) | −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 | ||||
\(489\) | 16.3277 | + | 7.69748i | 0.738363 | + | 0.348092i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.5707 | − | 8.63333i | −1.19912 | − | 0.389617i | −0.359681 | − | 0.933075i | \(-0.617114\pi\) |
−0.839436 | + | 0.543459i | \(0.817114\pi\) | |||||||
\(492\) | −3.32629 | + | 4.88697i | −0.149961 | + | 0.220322i | ||||
\(493\) | −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 | ||||
\(498\) | 11.5592 | − | 4.15225i | 0.517982 | − | 0.186067i | ||||
\(499\) | 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 | −0.957480 | − | 0.288498i | \(-0.906844\pi\) |
0.999769 | + | 0.0214995i | \(0.00684402\pi\) | |||||||
\(504\) | 8.46590 | + | 10.2634i | 0.377101 | + | 0.457167i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.1179 | − | 15.3025i | 0.494252 | − | 0.680280i | ||||
\(507\) | 4.15807 | − | 0.127697i | 0.184666 | − | 0.00567123i | ||||
\(508\) | −3.06818 | − | 19.3717i | −0.136129 | − | 0.859482i | ||||
\(509\) | 1.17675 | − | 3.62167i | 0.0521586 | − | 0.160528i | −0.921584 | − | 0.388178i | \(-0.873104\pi\) |
0.973743 | + | 0.227651i | \(0.0731044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.90915 | + | 15.1088i | 0.217168 | + | 0.668375i | ||||
\(512\) | −0.891007 | + | 0.453990i | −0.0393773 | + | 0.0200637i | ||||
\(513\) | 5.72229 | − | 25.3446i | 0.252645 | − | 1.11899i | ||||
\(514\) | −1.39651 | + | 0.453755i | −0.0615976 | + | 0.0200143i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.98039 | + | 4.37983i | −0.351317 | + | 0.192811i | ||||
\(517\) | 19.2000 | − | 3.04098i | 0.844414 | − | 0.133742i | ||||
\(518\) | −16.5580 | + | 16.5580i | −0.727515 | + | 0.727515i | ||||
\(519\) | −2.26652 | − | 11.9279i | −0.0994894 | − | 0.523575i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.70955 | − | 2.35299i | −0.0748966 | − | 0.103086i | 0.769925 | − | 0.638134i | \(-0.220294\pi\) |
−0.844822 | + | 0.535048i | \(0.820294\pi\) | |||||||
\(522\) | −5.51098 | − | 0.528892i | −0.241209 | − | 0.0231490i | ||||
\(523\) | −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 | ||||
\(528\) | −5.15001 | + | 3.98886i | −0.224125 | + | 0.173593i | ||||
\(529\) | 1.34851 | + | 1.85606i | 0.0586307 | + | 0.0806982i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2140 | + | 9.04899i | 0.616833 | + | 0.392693i | ||||
\(532\) | −15.6805 | + | 15.6805i | −0.679837 | + | 0.679837i | ||||
\(533\) | 13.2296 | − | 2.09537i | 0.573040 | − | 0.0907606i | ||||
\(534\) | −0.875950 | − | 1.59605i | −0.0379060 | − | 0.0690678i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.89043 | + | 1.91392i | −0.254428 | + | 0.0826686i | ||||
\(537\) | −4.70700 | − | 1.37116i | −0.203122 | − | 0.0591699i | ||||
\(538\) | 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 | ||||
\(543\) | −0.0186094 | − | 0.605959i | −0.000798607 | − | 0.0260042i | ||||
\(544\) | −0.242163 | + | 0.333309i | −0.0103827 | + | 0.0142905i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.79961 | − | 29.9050i | 0.162608 | − | 1.27982i | ||||
\(547\) | −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 | ||||||
\(552\) | −2.94491 | − | 8.19818i | −0.125344 | − | 0.348938i | ||||
\(553\) | 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 | 0.994279 | − | 0.106814i | \(-0.0340648\pi\) |
−0.106814 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(558\) | 2.16857 | + | 9.76720i | 0.0918029 | + | 0.413479i | ||||
\(559\) | 19.6168 | + | 6.37389i | 0.829703 | + | 0.269587i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14443 | + | 2.42753i | −0.0483178 | + | 0.102490i | ||||
\(562\) | −11.1182 | − | 21.8207i | −0.468993 | − | 0.920450i | ||||
\(563\) | 6.85128 | + | 13.4464i | 0.288747 | + | 0.566698i | 0.989126 | − | 0.147073i | \(-0.0469854\pi\) |
−0.700378 | + | 0.713772i | \(0.746985\pi\) | |||||||
\(564\) | 3.81760 | − | 8.09779i | 0.160750 | − | 0.340978i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.96420 | + | 2.26281i | 0.292727 | + | 0.0951128i | ||||
\(567\) | 38.3602 | − | 11.0258i | 1.61098 | − | 0.463041i | ||||
\(568\) | −1.19343 | − | 1.19343i | −0.0500753 | − | 0.0500753i | ||||
\(569\) | 7.06373 | + | 5.13210i | 0.296127 | + | 0.215149i | 0.725921 | − | 0.687778i | \(-0.241414\pi\) |
−0.429794 | + | 0.902927i | \(0.641414\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 0.664813 | + | 1.85074i | 0.0277730 | + | 0.0773157i | ||||
\(574\) | − | 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 | ||||
\(579\) | 1.28490 | − | 10.1129i | 0.0533987 | − | 0.420277i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.4849 | + | 25.4423i | −0.766882 | + | 1.05552i | ||||
\(582\) | −0.409985 | − | 13.3499i | −0.0169944 | − | 0.553372i | ||||
\(583\) | −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 | −0.650379 | − | 0.759609i | \(-0.725390\pi\) |
0.232254 | + | 0.972655i | \(0.425390\pi\) | |||||||
\(588\) | −21.0653 | − | 6.13637i | −0.868719 | − | 0.253060i | ||||
\(589\) | −15.8600 | + | 5.15324i | −0.653501 | + | 0.212335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0128 | − | 29.1766i | −0.658678 | − | 1.20016i | ||||
\(592\) | −5.21515 | + | 0.825998i | −0.214341 | + | 0.0339483i | ||||
\(593\) | −16.4362 | + | 16.4362i | −0.674952 | + | 0.674952i | −0.958854 | − | 0.283901i | \(-0.908371\pi\) |
0.283901 | + | 0.958854i | \(0.408371\pi\) | |||||||
\(594\) | 4.81937 | + | 18.9388i | 0.197741 | + | 0.777066i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.43884 | + | 3.35677i | 0.0998986 | + | 0.137499i | ||||
\(597\) | −17.4077 | + | 13.4829i | −0.712449 | + | 0.551817i | ||||
\(598\) | −8.96072 | + | 17.5864i | −0.366431 | + | 0.719162i | ||||
\(599\) | 16.9386 | 0.692094 | 0.346047 | − | 0.938217i | \(-0.387524\pi\) | ||||
0.346047 | + | 0.938217i | \(0.387524\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | −1.77504 | + | 18.4957i | −0.0722854 | + | 0.753204i | ||||
\(604\) | 5.58437 | + | 7.68623i | 0.227225 | + | 0.312748i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.58411 | + | 18.8618i | 0.145595 | + | 0.766210i | ||||
\(607\) | 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 | ||||
\(609\) | 12.4269 | − | 6.82016i | 0.503562 | − | 0.276367i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.2921 | + | 6.26837i | −0.780473 | + | 0.253591i | ||||
\(612\) | 0.627642 | + | 1.06476i | 0.0253709 | + | 0.0430402i | ||||
\(613\) | −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 | \(-0.795372\pi\) |
0.575960 | − | 0.817478i | \(-0.304628\pi\) | |||||||
\(618\) | −4.24555 | + | 0.130384i | −0.170781 | + | 0.00524480i | ||||
\(619\) | −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 | ||||||||
\(621\) | −26.0780 | − | 1.69685i | −1.04648 | − | 0.0680922i | ||||
\(622\) | 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 | ||||||||
\(627\) | −30.6550 | + | 11.0117i | −1.22424 | + | 0.439766i | ||||
\(628\) | 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 | ||||
\(633\) | 16.9929 | − | 24.9659i | 0.675407 | − | 0.992305i | ||||
\(634\) | 26.6314 | + | 8.65307i | 1.05767 | + | 0.343657i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.0146 | − | 6.13559i | −0.516063 | − | 0.243292i | ||||
\(637\) | 22.5697 | + | 44.2955i | 0.894244 | + | 1.75505i | ||||
\(638\) | 3.15094 | + | 6.18406i | 0.124747 | + | 0.244829i | ||||
\(639\) | −4.71040 | + | 1.85719i | −0.186341 | + | 0.0734695i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9664 | − | 4.21305i | −0.512144 | − | 0.166406i | 0.0415332 | − | 0.999137i | \(-0.486776\pi\) |
−0.553677 | + | 0.832732i | \(0.686776\pi\) | |||||||
\(642\) | −8.72104 | − | 5.93593i | −0.344192 | − | 0.234273i | ||||
\(643\) | 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 | −0.485263 | − | 0.874368i | \(-0.661276\pi\) |
−0.731707 | + | 0.681619i | \(0.761276\pi\) | |||||||
\(648\) | 8.45917 | + | 3.07284i | 0.332308 | + | 0.120713i | ||||
\(649\) | − | 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 | \(-0.680556\pi\) |
0.771626 | − | 0.636076i | \(-0.219444\pi\) | |||||||
\(654\) | 8.06209 | + | 1.02433i | 0.315253 | + | 0.0400546i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.00614 | − | 2.76122i | 0.0783266 | − | 0.107807i | ||||
\(657\) | 8.05095 | + | 7.11835i | 0.314098 | + | 0.277713i | ||||
\(658\) | 3.58587 | + | 22.6403i | 0.139792 | + | 0.882610i | ||||
\(659\) | 6.33270 | − | 19.4901i | 0.246687 | − | 0.759225i | −0.748667 | − | 0.662946i | \(-0.769306\pi\) |
0.995354 | − | 0.0962789i | \(-0.0306941\pi\) | |||||||
\(660\) | 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 | ||||
\(663\) | 0.783237 | − | 2.68874i | 0.0304184 | − | 0.104422i | ||||
\(664\) | −6.74418 | + | 2.19132i | −0.261725 | + | 0.0850395i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.96130 | + | 15.3372i | −0.153497 | + | 0.594303i | ||||
\(667\) | −9.16704 | + | 1.45192i | −0.354949 | + | 0.0562184i | ||||
\(668\) | −9.89891 | + | 9.89891i | −0.383000 | + | 0.383000i | ||||
\(669\) | −38.5175 | + | 7.31907i | −1.48917 | + | 0.282971i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.7502 | + | 43.7004i | 1.22570 | + | 1.68703i | ||||
\(672\) | −4.70360 | − | 6.07280i | −0.181445 | − | 0.234263i | ||||
\(673\) | 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 | \(-0.553670\pi\) |
0.896182 | − | 0.443686i | \(-0.146330\pi\) | |||||||
\(678\) | 18.1340 | + | 23.4128i | 0.696433 | + | 0.899163i | ||||
\(679\) | 20.1010 | + | 27.6666i | 0.771404 | + | 1.06175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.8546 | + | 6.24301i | −1.25899 | + | 0.239233i | ||||
\(682\) | 8.86905 | − | 8.86905i | 0.339614 | − | 0.339614i | ||||
\(683\) | −50.2616 | + | 7.96066i | −1.92321 | + | 0.304606i | −0.997318 | − | 0.0731865i | \(-0.976683\pi\) |
−0.925890 | + | 0.377793i | \(0.876683\pi\) | |||||||
\(684\) | −3.75138 | + | 14.5244i | −0.143437 | + | 0.555354i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.9045 | − | 7.76703i | 0.912677 | − | 0.296547i | ||||
\(687\) | −7.89565 | + | 27.1047i | −0.301238 | + | 1.03411i | ||||
\(688\) | 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 | ||||
\(693\) | −37.4860 | − | 33.1437i | −1.42397 | − | 1.25902i | ||||
\(694\) | 21.7024 | − | 29.8708i | 0.823813 | − | 1.13388i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.17089 | + | 0.402880i | 0.120192 | + | 0.0152711i | ||||
\(697\) | 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 | \(0.207900\pi\) | ||||
−0.794180 | + | 0.607682i | \(0.792100\pi\) | |||||||
\(702\) | −8.05863 | − | 18.7325i | −0.304153 | − | 0.707013i | ||||
\(703\) | −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 | ||||
\(708\) | −8.04220 | − | 5.47388i | −0.302244 | − | 0.205721i | ||||
\(709\) | −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 | ||||||||
\(711\) | 29.6686 | − | 11.6976i | 1.11266 | − | 0.438693i | ||||
\(712\) | 0.477205 | + | 0.936569i | 0.0178840 | + | 0.0350994i | ||||
\(713\) | 7.61474 | + | 14.9448i | 0.285174 | + | 0.559686i | ||||
\(714\) | −2.86250 | − | 1.34949i | −0.107126 | − | 0.0505033i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.69201 | + | 0.874686i | 0.100605 | + | 0.0326886i | ||||
\(717\) | 7.81693 | − | 11.4846i | 0.291929 | − | 0.428900i | ||||
\(718\) | −2.46690 | − | 2.46690i | −0.0920639 | − | 0.0920639i | ||||
\(719\) | −6.94235 | − | 5.04392i | −0.258906 | − | 0.188106i | 0.450759 | − | 0.892646i | \(-0.351154\pi\) |
−0.709665 | + | 0.704540i | \(0.751154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.79854 | − | 6.39251i | 0.327675 | − | 0.238070i | ||||
\(722\) | −5.92953 | − | 0.939145i | −0.220674 | − | 0.0349514i | ||||
\(723\) | −11.8140 | + | 4.24378i | −0.439369 | + | 0.157828i | ||||
\(724\) | 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 | ||||
\(729\) | 18.5670 | − | 19.6027i | 0.687668 | − | 0.726026i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.27276 | − | 1.75180i | 0.0470746 | − | 0.0647926i | ||||
\(732\) | 24.8650 | − | 0.763622i | 0.919038 | − | 0.0282243i | ||||
\(733\) | 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 | ||||
\(738\) | −5.19955 | − | 8.82071i | −0.191398 | − | 0.324695i | ||||
\(739\) | 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 | ||||||||
\(741\) | 29.7970 | − | 16.3533i | 1.09462 | − | 0.600754i | ||||
\(742\) | 36.3871 | − | 5.76314i | 1.33581 | − | 0.211572i | ||||
\(743\) | 25.7253 | − | 25.7253i | 0.943771 | − | 0.943771i | −0.0547306 | − | 0.998501i | \(-0.517430\pi\) |
0.998501 | + | 0.0547306i | \(0.0174300\pi\) | |||||||
\(744\) | −1.07834 | − | 5.67487i | −0.0395337 | − | 0.208051i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.74935 | + | 5.16053i | 0.137273 | + | 0.188940i | ||||
\(747\) | −2.03232 | + | 21.1764i | −0.0743585 | + | 0.774806i | ||||
\(748\) | 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 | ||||
\(753\) | −19.9267 | + | 15.4339i | −0.726169 | + | 0.562443i | ||||
\(754\) | −4.25699 | − | 5.85925i | −0.155031 | − | 0.213381i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −22.3322 | + | 5.68292i | −0.812216 | + | 0.206686i | ||||
\(757\) | 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 | ||||
\(759\) | 15.7625 | + | 28.7205i | 0.572143 | + | 1.04249i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.3818 | − | 11.8212i | 1.31884 | − | 0.428517i | 0.436744 | − | 0.899586i | \(-0.356132\pi\) |
0.882096 | + | 0.471069i | \(0.156132\pi\) | |||||||
\(762\) | 32.6154 | + | 9.50095i | 1.18153 | + | 0.344183i | ||||
\(763\) | −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 | ||||
\(768\) | −0.0531674 | − | 1.73123i | −0.00191851 | − | 0.0624705i | ||||
\(769\) | 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 | ||||||||
\(771\) | 0.320565 | − | 2.52303i | 0.0115449 | − | 0.0908646i | ||||
\(772\) | −0.920714 | + | 5.81316i | −0.0331372 | + | 0.209220i | ||||
\(773\) | −32.0052 | − | 16.3075i | −1.15115 | − | 0.586539i | −0.229019 | − | 0.973422i | \(-0.573552\pi\) |
−0.922129 | + | 0.386883i | \(0.873552\pi\) | |||||||
\(774\) | −0.967539 | − | 15.7376i | −0.0347775 | − | 0.565677i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.71121i | 0.276816i | ||||||||
\(777\) | −13.7114 | − | 38.1706i | −0.491895 | − | 1.36936i | ||||
\(778\) | 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 | ||||
\(783\) | 4.89897 | − | 8.24330i | 0.175075 | − | 0.294592i | ||||
\(784\) | 12.0476 | + | 3.91450i | 0.430271 | + | 0.139803i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.1597 | − | 32.1563i | 0.540728 | − | 1.14698i | ||||
\(787\) | 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 | ||||
\(789\) | 16.4852 | − | 34.9679i | 0.586889 | − | 1.24489i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.1143 | − | 23.4314i | −2.56409 | − | 0.833123i | ||||
\(792\) | −2.44551 | − | 11.0146i | −0.0868976 | − | 0.391385i | ||||
\(793\) | −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 | −0.0153481 | − | 0.999882i | \(-0.504886\pi\) |
−0.323578 | + | 0.946202i | \(0.604886\pi\) | |||||||
\(798\) | −12.9848 | − | 36.1478i | −0.459658 | − | 1.27962i | ||||
\(799\) | 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 | ||||
\(804\) | 1.35213 | − | 10.6420i | 0.0476859 | − | 0.375315i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.69311 | + | 10.5887i | −0.270978 | + | 0.372970i | ||||
\(807\) | 1.32909 | + | 43.2777i | 0.0467861 | + | 1.52345i | ||||
\(808\) | −1.73404 | − | 10.9483i | −0.0610032 | − | 0.385159i | ||||
\(809\) | 17.2607 | − | 53.1231i | 0.606855 | − | 1.86771i | 0.123359 | − | 0.992362i | \(-0.460633\pi\) |
0.483496 | − | 0.875346i | \(-0.339367\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | −27.0096 | − | 7.86795i | −0.947268 | − | 0.275941i | ||||
\(814\) | 18.8863 | − | 6.13654i | 0.661965 | − | 0.215086i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.343329 | − | 0.625571i | −0.0120189 | − | 0.0218994i | ||||
\(817\) | 25.9571 | − | 4.11120i | 0.908125 | − | 0.143833i | ||||
\(818\) | 9.95831 | − | 9.95831i | 0.348184 | − | 0.348184i | ||||
\(819\) | 44.0452 | + | 28.0404i | 1.53906 | + | 0.979810i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.0314 | − | 30.3236i | −0.768899 | − | 1.05830i | −0.996421 | − | 0.0845263i | \(-0.973062\pi\) |
0.227522 | − | 0.973773i | \(-0.426938\pi\) | |||||||
\(822\) | 9.89830 | − | 7.66658i | 0.345243 | − | 0.267403i | ||||
\(823\) | 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 | −0.601969 | − | 0.798519i | \(-0.705617\pi\) |
0.999844 | + | 0.0176456i | \(0.00561705\pi\) | |||||||
\(828\) | 15.0190 | + | 1.44138i | 0.521946 | + | 0.0500915i | ||||
\(829\) | −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 | ||||||||
\(831\) | 2.22656 | + | 11.7176i | 0.0772386 | + | 0.406478i | ||||
\(832\) | −2.77505 | + | 2.77505i | −0.0962075 | + | 0.0962075i | ||||
\(833\) | 5.15469 | − | 0.816423i | 0.178600 | − | 0.0282874i | ||||
\(834\) | 14.7180 | − | 8.07760i | 0.509643 | − | 0.279705i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.8855 | − | 5.81135i | 0.618582 | − | 0.200990i | ||||
\(837\) | −16.9038 | − | 3.81652i | −0.584279 | − | 0.131918i | ||||
\(838\) | −5.05427 | + | 2.57528i | −0.174597 | + | 0.0889615i | ||||
\(839\) | 1.11037 | + | 3.41736i | 0.0383342 | + | 0.117980i | 0.968392 | − | 0.249432i | \(-0.0802438\pi\) |
−0.930058 | + | 0.367412i | \(0.880244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.90910 | + | 24.3417i | −0.272727 | + | 0.839369i | ||||
\(842\) | −0.999080 | − | 6.30794i | −0.0344306 | − | 0.217386i | ||||
\(843\) | 42.3978 | − | 1.30207i | 1.46026 | − | 0.0448455i | ||||
\(844\) | −10.2487 | + | 14.1061i | −0.352774 | + | 0.485552i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.86698 | + | 11.9619i | 0.339234 | + | 0.411259i | ||||
\(847\) | −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 | ||||||||
\(852\) | 2.75118 | − | 0.988266i | 0.0942540 | − | 0.0338574i | ||||
\(853\) | −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 | 0.794639 | − | 0.607082i | \(-0.207660\pi\) |
−0.607082 | + | 0.794639i | \(0.707660\pi\) | |||||||
\(858\) | −14.3846 | + | 21.1338i | −0.491082 | + | 0.721496i | ||||
\(859\) | 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 | ||||||||
\(861\) | 23.7136 | + | 11.1795i | 0.808159 | + | 0.380996i | ||||
\(862\) | −9.06883 | − | 17.7986i | −0.308886 | − | 0.606222i | ||||
\(863\) | 5.28199 | + | 10.3665i | 0.179801 | + | 0.352880i | 0.963263 | − | 0.268560i | \(-0.0865479\pi\) |
−0.783462 | + | 0.621440i | \(0.786548\pi\) | |||||||
\(864\) | −4.82715 | − | 1.92319i | −0.164223 | − | 0.0654282i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.0640 | + | 7.16903i | 0.749765 | + | 0.243613i | ||||
\(867\) | 24.0984 | + | 16.4025i | 0.818424 | + | 0.557056i | ||||
\(868\) | 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 | ||||
\(873\) | 21.2178 | + | 9.21782i | 0.718115 | + | 0.311976i | ||||
\(874\) | 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 | ||||
\(879\) | −2.78540 | − | 0.353901i | −0.0939492 | − | 0.0119368i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.08613 | − | 9.75322i | 0.238738 | − | 0.328594i | −0.672790 | − | 0.739834i | \(-0.734904\pi\) |
0.911527 | + | 0.411240i | \(0.134904\pi\) | |||||||
\(882\) | 25.1724 | − | 28.4703i | 0.847598 | − | 0.958645i | ||||
\(883\) | −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 | −0.506410 | − | 0.862293i | \(-0.669028\pi\) |
0.399949 | + | 0.916537i | \(0.369028\pi\) | |||||||
\(888\) | 2.55779 | − | 8.78054i | 0.0858338 | − | 0.294655i | ||||
\(889\) | −82.7238 | + | 26.8786i | −2.77447 | + | 0.901479i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.2305 | − | 6.43759i | −1.11326 | − | 0.215667i | ||||
\(892\) | 22.3573 | − | 3.54105i | 0.748578 | − | 0.118563i | ||||
\(893\) | −18.2756 | + | 18.2756i | −0.611569 | + | 0.611569i | ||||
\(894\) | −7.06028 | + | 1.34159i | −0.236131 | + | 0.0448695i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.60672 | + | 3.58784i | 0.0870843 | + | 0.119861i | ||||
\(897\) | −20.9339 | − | 27.0277i | −0.698964 | − | 0.902430i | ||||
\(898\) | 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 | ||||
\(903\) | 24.7210 | + | 31.9173i | 0.822665 | + | 1.06214i | ||||
\(904\) | −10.0498 | − | 13.8324i | −0.334252 | − | 0.460058i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.1664 | + | 3.07193i | −0.537093 | + | 0.102058i | ||||
\(907\) | −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 | ||||
\(909\) | −32.1976 | − | 8.31603i | −1.06793 | − | 0.275825i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.38886 | − | 0.776187i | 0.0791464 | − | 0.0257162i | −0.269176 | − | 0.963091i | \(-0.586751\pi\) |
0.348323 | + | 0.937375i | \(0.386751\pi\) | |||||||
\(912\) | 2.42225 | − | 8.31523i | 0.0802086 | − | 0.275345i | ||||
\(913\) | 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 | ||||
\(918\) | −2.13170 | + | 0.196894i | −0.0703567 | + | 0.00649846i | ||||
\(919\) | −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 | ||||||||
\(921\) | 20.1506 | + | 2.56024i | 0.663983 | + | 0.0843629i | ||||
\(922\) | −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 | ||||||||
\(927\) | 2.93145 | − | 6.74771i | 0.0962816 | − | 0.221624i | ||||
\(928\) | −1.82271 | − | 0.288689i | −0.0598335 | − | 0.00947670i | ||||
\(929\) | 28.0139 | − | 20.3533i | 0.919106 | − | 0.667770i | −0.0241953 | − | 0.999707i | \(-0.507702\pi\) |
0.943301 | + | 0.331938i | \(0.107702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.2449 | + | 37.2316i | 1.67949 | + | 1.22022i | ||||
\(932\) | −0.430335 | − | 0.430335i | −0.0140961 | − | 0.0140961i | ||||
\(933\) | 47.3697 | + | 32.2419i | 1.55081 | + | 1.05555i | ||||
\(934\) | −27.2912 | − | 8.86745i | −0.892995 | − | 0.290152i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.31847 | + | 10.9529i | 0.141154 | + | 0.358008i | ||||
\(937\) | −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 | ||||
\(939\) | −6.86194 | − | 3.23498i | −0.223931 | − | 0.105570i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0255 | − | 8.78112i | −0.881006 | − | 0.286256i | −0.166631 | − | 0.986019i | \(-0.553289\pi\) |
−0.714375 | + | 0.699763i | \(0.753289\pi\) | |||||||
\(942\) | −4.11088 | + | 6.03968i | −0.133940 | + | 0.196783i | ||||
\(943\) | −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 | −0.479669 | − | 0.877450i | \(-0.659243\pi\) |
−0.727339 | + | 0.686279i | \(0.759243\pi\) | |||||||
\(948\) | −17.3284 | + | 6.22461i | −0.562800 | + | 0.202166i | ||||
\(949\) | 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 | \(-0.807992\pi\) |
0.958515 | − | 0.285042i | \(-0.0920076\pi\) | |||||||
\(954\) | 19.2250 | − | 15.8580i | 0.622432 | − | 0.513423i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.71452 | + | 6.48898i | −0.152478 | + | 0.209868i | ||||
\(957\) | −12.0157 | + | 0.369010i | −0.388412 | + | 0.0119284i | ||||
\(958\) | 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 | ||||
\(963\) | 15.7410 | − | 9.27884i | 0.507246 | − | 0.299006i | ||||
\(964\) | 6.89284 | − | 2.23962i | 0.222003 | − | 0.0721333i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −33.8667 | + | 18.5869i | −1.08964 | + | 0.598023i | ||||
\(967\) | −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 | ||||
\(969\) | −0.666109 | − | 3.50548i | −0.0213985 | − | 0.112612i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.52779 | − | 11.7375i | −0.273670 | − | 0.376674i | 0.649955 | − | 0.759973i | \(-0.274788\pi\) |
−0.923624 | + | 0.383299i | \(0.874788\pi\) | |||||||
\(972\) | −11.0620 | + | 10.9832i | −0.354815 | + | 0.352287i | ||||
\(973\) | −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 | −0.882121 | − | 0.471023i | \(-0.843885\pi\) |
0.899563 | + | 0.436791i | \(0.143885\pi\) | |||||||
\(978\) | 14.2711 | − | 11.0535i | 0.456340 | − | 0.353451i | ||||
\(979\) | −2.32366 | − | 3.19824i | −0.0742644 | − | 0.102216i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.55939 | + | 11.8741i | −0.241353 | + | 0.379112i | ||||
\(982\) | −19.7552 | + | 19.7552i | −0.630413 | + | 0.630413i | ||||
\(983\) | 17.7113 | − | 2.80520i | 0.564903 | − | 0.0894719i | 0.132550 | − | 0.991176i | \(-0.457683\pi\) |
0.432353 | + | 0.901704i | \(0.357683\pi\) | |||||||
\(984\) | 2.84422 | + | 5.18239i | 0.0906704 | + | 0.165209i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.723093 | + | 0.234947i | −0.0230280 | + | 0.00748224i | ||||
\(987\) | −38.1185 | − | 11.1040i | −1.21333 | − | 0.353445i | ||||
\(988\) | −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 | ||||
\(993\) | 0.509555 | + | 16.5921i | 0.0161702 | + | 0.526535i | ||||
\(994\) | −4.39954 | + | 6.05544i | −0.139545 | + | 0.192067i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.54810 | − | 12.1844i | 0.0490535 | − | 0.386079i | ||||
\(997\) | −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.143.9 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.143.5 | 80 | ||
5.2 | odd | 4 | 750.2.l.a.107.9 | 80 | |||
5.3 | odd | 4 | 750.2.l.c.107.2 | 80 | |||
5.4 | even | 2 | 150.2.l.a.83.2 | yes | 80 | ||
15.2 | even | 4 | 750.2.l.a.107.2 | 80 | |||
15.8 | even | 4 | 750.2.l.c.107.9 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.83.6 | yes | 80 | ||
25.3 | odd | 20 | 150.2.l.a.47.6 | yes | 80 | ||
25.4 | even | 10 | 750.2.l.c.743.9 | 80 | |||
25.21 | even | 5 | 750.2.l.a.743.2 | 80 | |||
25.22 | odd | 20 | inner | 750.2.l.b.257.5 | 80 | ||
75.29 | odd | 10 | 750.2.l.c.743.2 | 80 | |||
75.47 | even | 20 | inner | 750.2.l.b.257.9 | 80 | ||
75.53 | even | 20 | 150.2.l.a.47.2 | ✓ | 80 | ||
75.71 | odd | 10 | 750.2.l.a.743.9 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.2 | ✓ | 80 | 75.53 | even | 20 | ||
150.2.l.a.47.6 | yes | 80 | 25.3 | odd | 20 | ||
150.2.l.a.83.2 | yes | 80 | 5.4 | even | 2 | ||
150.2.l.a.83.6 | yes | 80 | 15.14 | odd | 2 | ||
750.2.l.a.107.2 | 80 | 15.2 | even | 4 | |||
750.2.l.a.107.9 | 80 | 5.2 | odd | 4 | |||
750.2.l.a.743.2 | 80 | 25.21 | even | 5 | |||
750.2.l.a.743.9 | 80 | 75.71 | odd | 10 | |||
750.2.l.b.143.5 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.143.9 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.b.257.5 | 80 | 25.22 | odd | 20 | inner | ||
750.2.l.b.257.9 | 80 | 75.47 | even | 20 | inner | ||
750.2.l.c.107.2 | 80 | 5.3 | odd | 4 | |||
750.2.l.c.107.9 | 80 | 15.8 | even | 4 | |||
750.2.l.c.743.2 | 80 | 75.29 | odd | 10 | |||
750.2.l.c.743.9 | 80 | 25.4 | even | 10 |