Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(241,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 241.3 | ||
Root | \(0.500000 + 0.921602i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.241 |
Dual form | 462.2.p.b.439.3 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.54813 | − | 0.893814i | 0.692345 | − | 0.399726i | −0.112145 | − | 0.993692i | \(-0.535772\pi\) |
0.804490 | + | 0.593966i | \(0.202439\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.165362 | − | 2.64058i | −0.0625011 | − | 0.998045i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −0.893814 | + | 1.54813i | −0.282649 | + | 0.489562i | ||||
\(11\) | 2.46279 | − | 2.22141i | 0.742558 | − | 0.669782i | ||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | −6.37742 | −1.76878 | −0.884389 | − | 0.466751i | \(-0.845424\pi\) | ||||
−0.884389 | + | 0.466751i | \(0.845424\pi\) | |||||||
\(14\) | 1.46350 | + | 2.20413i | 0.391136 | + | 0.589078i | ||||
\(15\) | −1.78763 | −0.461563 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.0530476 | + | 0.0918811i | −0.0128659 | + | 0.0222844i | −0.872387 | − | 0.488816i | \(-0.837429\pi\) |
0.859521 | + | 0.511101i | \(0.170762\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | 2.07581 | + | 3.59541i | 0.476224 | + | 0.824844i | 0.999629 | − | 0.0272400i | \(-0.00867184\pi\) |
−0.523405 | + | 0.852084i | \(0.675339\pi\) | |||||||
\(20\) | − | 1.78763i | − | 0.399726i | ||||||
\(21\) | −1.17708 | + | 2.36949i | −0.256860 | + | 0.517065i | ||||
\(22\) | −1.02213 | + | 3.15519i | −0.217919 | + | 0.672690i | ||||
\(23\) | −3.97933 | − | 6.89240i | −0.829748 | − | 1.43717i | −0.898236 | − | 0.439514i | \(-0.855151\pi\) |
0.0684879 | − | 0.997652i | \(-0.478183\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.902194 | + | 1.56265i | −0.180439 | + | 0.312529i | ||||
\(26\) | 5.52301 | − | 3.18871i | 1.08315 | − | 0.625357i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.36949 | − | 1.17708i | −0.447791 | − | 0.222447i | ||||
\(29\) | − | 7.65230i | − | 1.42100i | −0.703699 | − | 0.710498i | \(-0.748470\pi\) | ||
0.703699 | − | 0.710498i | \(-0.251530\pi\) | |||||||
\(30\) | 1.54813 | − | 0.893814i | 0.282649 | − | 0.163187i | ||||
\(31\) | 1.10740 | + | 0.639360i | 0.198896 | + | 0.114833i | 0.596140 | − | 0.802880i | \(-0.296700\pi\) |
−0.397245 | + | 0.917713i | \(0.630034\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −3.24354 | + | 0.692408i | −0.564628 | + | 0.120533i | ||||
\(34\) | − | 0.106095i | − | 0.0181952i | ||||||
\(35\) | −2.61619 | − | 3.94016i | −0.442216 | − | 0.666008i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.26092 | − | 3.91603i | −0.371693 | − | 0.643792i | 0.618133 | − | 0.786074i | \(-0.287889\pi\) |
−0.989826 | + | 0.142282i | \(0.954556\pi\) | |||||||
\(38\) | −3.59541 | − | 2.07581i | −0.583253 | − | 0.336741i | ||||
\(39\) | 5.52301 | + | 3.18871i | 0.884389 | + | 0.510602i | ||||
\(40\) | 0.893814 | + | 1.54813i | 0.141324 | + | 0.244781i | ||||
\(41\) | −0.0321383 | −0.00501915 | −0.00250958 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00250958 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(42\) | −0.165362 | − | 2.64058i | −0.0255160 | − | 0.407450i | ||||
\(43\) | − | 6.87723i | − | 1.04877i | −0.851482 | − | 0.524384i | \(-0.824296\pi\) | ||
0.851482 | − | 0.524384i | \(-0.175704\pi\) | |||||||
\(44\) | −0.692408 | − | 3.24354i | −0.104384 | − | 0.488983i | ||||
\(45\) | 1.54813 | + | 0.893814i | 0.230782 | + | 0.133242i | ||||
\(46\) | 6.89240 | + | 3.97933i | 1.01623 | + | 0.586720i | ||||
\(47\) | 8.55805 | − | 4.94099i | 1.24832 | − | 0.720718i | 0.277545 | − | 0.960713i | \(-0.410479\pi\) |
0.970774 | + | 0.239995i | \(0.0771458\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −6.94531 | + | 0.873304i | −0.992187 | + | 0.124758i | ||||
\(50\) | − | 1.80439i | − | 0.255179i | ||||||
\(51\) | 0.0918811 | − | 0.0530476i | 0.0128659 | − | 0.00742815i | ||||
\(52\) | −3.18871 | + | 5.52301i | −0.442194 | + | 0.765903i | ||||
\(53\) | 0.313720 | − | 0.543380i | 0.0430928 | − | 0.0746389i | −0.843675 | − | 0.536855i | \(-0.819612\pi\) |
0.886767 | + | 0.462216i | \(0.152946\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 1.82718 | − | 5.64031i | 0.246378 | − | 0.760539i | ||||
\(56\) | 2.64058 | − | 0.165362i | 0.352862 | − | 0.0220975i | ||||
\(57\) | − | 4.15162i | − | 0.549896i | ||||||
\(58\) | 3.82615 | + | 6.62708i | 0.502398 | + | 0.870179i | ||||
\(59\) | 10.7863 | + | 6.22747i | 1.40426 | + | 0.810748i | 0.994826 | − | 0.101593i | \(-0.0323940\pi\) |
0.409431 | + | 0.912341i | \(0.365727\pi\) | |||||||
\(60\) | −0.893814 | + | 1.54813i | −0.115391 | + | 0.199863i | ||||
\(61\) | −4.97512 | − | 8.61716i | −0.636999 | − | 1.10331i | −0.986088 | − | 0.166224i | \(-0.946842\pi\) |
0.349089 | − | 0.937089i | \(-0.386491\pi\) | |||||||
\(62\) | −1.27872 | −0.162398 | ||||||||
\(63\) | 2.20413 | − | 1.46350i | 0.277694 | − | 0.184383i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −9.87308 | + | 5.70022i | −1.22460 | + | 0.707026i | ||||
\(66\) | 2.46279 | − | 2.22141i | 0.303148 | − | 0.273437i | ||||
\(67\) | −5.43609 | + | 9.41558i | −0.664124 | + | 1.15030i | 0.315398 | + | 0.948959i | \(0.397862\pi\) |
−0.979522 | + | 0.201337i | \(0.935471\pi\) | |||||||
\(68\) | 0.0530476 | + | 0.0918811i | 0.00643296 | + | 0.0111422i | ||||
\(69\) | 7.95866i | 0.958110i | ||||||||
\(70\) | 4.23576 | + | 2.10418i | 0.506271 | + | 0.251498i | ||||
\(71\) | −8.42785 | −1.00020 | −0.500101 | − | 0.865967i | \(-0.666704\pi\) | ||||
−0.500101 | + | 0.865967i | \(0.666704\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | −0.0625042 | + | 0.108260i | −0.00731556 | + | 0.0126709i | −0.869660 | − | 0.493651i | \(-0.835662\pi\) |
0.862344 | + | 0.506322i | \(0.168995\pi\) | |||||||
\(74\) | 3.91603 | + | 2.26092i | 0.455229 | + | 0.262827i | ||||
\(75\) | 1.56265 | − | 0.902194i | 0.180439 | − | 0.104176i | ||||
\(76\) | 4.15162 | 0.476224 | ||||||||
\(77\) | −6.27307 | − | 6.13584i | −0.714883 | − | 0.699244i | ||||
\(78\) | −6.37742 | −0.722100 | ||||||||
\(79\) | 8.80673 | − | 5.08457i | 0.990835 | − | 0.572059i | 0.0853112 | − | 0.996354i | \(-0.472812\pi\) |
0.905524 | + | 0.424295i | \(0.139478\pi\) | |||||||
\(80\) | −1.54813 | − | 0.893814i | −0.173086 | − | 0.0999314i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.0278326 | − | 0.0160691i | 0.00307359 | − | 0.00177454i | ||||
\(83\) | 12.0657 | 1.32438 | 0.662191 | − | 0.749335i | \(-0.269627\pi\) | ||||
0.662191 | + | 0.749335i | \(0.269627\pi\) | |||||||
\(84\) | 1.46350 | + | 2.20413i | 0.159681 | + | 0.240490i | ||||
\(85\) | 0.189659i | 0.0205714i | ||||||||
\(86\) | 3.43862 | + | 5.95586i | 0.370795 | + | 0.642237i | ||||
\(87\) | −3.82615 | + | 6.62708i | −0.410206 | + | 0.710498i | ||||
\(88\) | 2.22141 | + | 2.46279i | 0.236804 | + | 0.262534i | ||||
\(89\) | −4.64198 | + | 2.68005i | −0.492049 | + | 0.284084i | −0.725424 | − | 0.688302i | \(-0.758356\pi\) |
0.233375 | + | 0.972387i | \(0.425023\pi\) | |||||||
\(90\) | −1.78763 | −0.188432 | ||||||||
\(91\) | 1.05458 | + | 16.8401i | 0.110550 | + | 1.76532i | ||||
\(92\) | −7.95866 | −0.829748 | ||||||||
\(93\) | −0.639360 | − | 1.10740i | −0.0662986 | − | 0.114833i | ||||
\(94\) | −4.94099 | + | 8.55805i | −0.509624 | + | 0.882695i | ||||
\(95\) | 6.42726 | + | 3.71078i | 0.659423 | + | 0.380718i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 15.7498i | 1.59915i | 0.600569 | + | 0.799573i | \(0.294941\pi\) | ||||
−0.600569 | + | 0.799573i | \(0.705059\pi\) | |||||||
\(98\) | 5.57816 | − | 4.22896i | 0.563480 | − | 0.427189i | ||||
\(99\) | 3.15519 | + | 1.02213i | 0.317109 | + | 0.102728i | ||||
\(100\) | 0.902194 | + | 1.56265i | 0.0902194 | + | 0.156265i | ||||
\(101\) | −3.78650 | + | 6.55841i | −0.376771 | + | 0.652586i | −0.990590 | − | 0.136860i | \(-0.956299\pi\) |
0.613820 | + | 0.789446i | \(0.289632\pi\) | |||||||
\(102\) | −0.0530476 | + | 0.0918811i | −0.00525249 | + | 0.00909758i | ||||
\(103\) | −4.53550 | + | 2.61857i | −0.446896 | + | 0.258016i | −0.706519 | − | 0.707695i | \(-0.749735\pi\) |
0.259622 | + | 0.965710i | \(0.416402\pi\) | |||||||
\(104\) | − | 6.37742i | − | 0.625357i | ||||||
\(105\) | 0.295606 | + | 4.72037i | 0.0288482 | + | 0.460661i | ||||
\(106\) | 0.627441i | 0.0609424i | ||||||||
\(107\) | 4.12912 | − | 2.38395i | 0.399177 | − | 0.230465i | −0.286952 | − | 0.957945i | \(-0.592642\pi\) |
0.686129 | + | 0.727480i | \(0.259309\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 7.36585 | + | 4.25268i | 0.705521 | + | 0.407332i | 0.809400 | − | 0.587257i | \(-0.199792\pi\) |
−0.103880 | + | 0.994590i | \(0.533126\pi\) | |||||||
\(110\) | 1.23777 | + | 5.79825i | 0.118016 | + | 0.552841i | ||||
\(111\) | 4.52184i | 0.429194i | ||||||||
\(112\) | −2.20413 | + | 1.46350i | −0.208270 | + | 0.138287i | ||||
\(113\) | 10.3003 | 0.968969 | 0.484484 | − | 0.874800i | \(-0.339007\pi\) | ||||
0.484484 | + | 0.874800i | \(0.339007\pi\) | |||||||
\(114\) | 2.07581 | + | 3.59541i | 0.194418 | + | 0.336741i | ||||
\(115\) | −12.3210 | − | 7.11356i | −1.14894 | − | 0.663343i | ||||
\(116\) | −6.62708 | − | 3.82615i | −0.615309 | − | 0.355249i | ||||
\(117\) | −3.18871 | − | 5.52301i | −0.294796 | − | 0.510602i | ||||
\(118\) | −12.4549 | −1.14657 | ||||||||
\(119\) | 0.251391 | + | 0.124883i | 0.0230450 | + | 0.0114480i | ||||
\(120\) | − | 1.78763i | − | 0.163187i | ||||||
\(121\) | 1.13064 | − | 10.9417i | 0.102785 | − | 0.994704i | ||||
\(122\) | 8.61716 | + | 4.97512i | 0.780161 | + | 0.450426i | ||||
\(123\) | 0.0278326 | + | 0.0160691i | 0.00250958 | + | 0.00144891i | ||||
\(124\) | 1.10740 | − | 0.639360i | 0.0994479 | − | 0.0574163i | ||||
\(125\) | 12.1637i | 1.08796i | ||||||||
\(126\) | −1.17708 | + | 2.36949i | −0.104863 | + | 0.211091i | ||||
\(127\) | 3.18422i | 0.282553i | 0.989970 | + | 0.141277i | \(0.0451207\pi\) | ||||
−0.989970 | + | 0.141277i | \(0.954879\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −3.43862 | + | 5.95586i | −0.302753 | + | 0.524384i | ||||
\(130\) | 5.70022 | − | 9.87308i | 0.499943 | − | 0.865926i | ||||
\(131\) | −0.543099 | − | 0.940675i | −0.0474508 | − | 0.0821872i | 0.841324 | − | 0.540530i | \(-0.181776\pi\) |
−0.888775 | + | 0.458343i | \(0.848443\pi\) | |||||||
\(132\) | −1.02213 | + | 3.15519i | −0.0889649 | + | 0.274624i | ||||
\(133\) | 9.15071 | − | 6.07589i | 0.793467 | − | 0.526846i | ||||
\(134\) | − | 10.8722i | − | 0.939213i | ||||||
\(135\) | −0.893814 | − | 1.54813i | −0.0769272 | − | 0.133242i | ||||
\(136\) | −0.0918811 | − | 0.0530476i | −0.00787874 | − | 0.00454879i | ||||
\(137\) | 3.79098 | − | 6.56617i | 0.323885 | − | 0.560986i | −0.657401 | − | 0.753541i | \(-0.728344\pi\) |
0.981286 | + | 0.192555i | \(0.0616774\pi\) | |||||||
\(138\) | −3.97933 | − | 6.89240i | −0.338743 | − | 0.586720i | ||||
\(139\) | 1.34643 | 0.114203 | 0.0571013 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571013 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(140\) | −4.72037 | + | 0.295606i | −0.398944 | + | 0.0249833i | ||||
\(141\) | −9.88198 | −0.832213 | ||||||||
\(142\) | 7.29873 | − | 4.21392i | 0.612496 | − | 0.353625i | ||||
\(143\) | −15.7062 | + | 14.1669i | −1.31342 | + | 1.18469i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −6.83973 | − | 11.8468i | −0.568008 | − | 0.983819i | ||||
\(146\) | − | 0.125008i | − | 0.0103458i | ||||||
\(147\) | 6.45147 | + | 2.71635i | 0.532108 | + | 0.224041i | ||||
\(148\) | −4.52184 | −0.371693 | ||||||||
\(149\) | −0.424489 | + | 0.245079i | −0.0347755 | + | 0.0200776i | −0.517287 | − | 0.855812i | \(-0.673058\pi\) |
0.482511 | + | 0.875890i | \(0.339725\pi\) | |||||||
\(150\) | −0.902194 | + | 1.56265i | −0.0736639 | + | 0.127590i | ||||
\(151\) | 2.92130 | + | 1.68661i | 0.237732 | + | 0.137255i | 0.614134 | − | 0.789202i | \(-0.289505\pi\) |
−0.376402 | + | 0.926456i | \(0.622839\pi\) | |||||||
\(152\) | −3.59541 | + | 2.07581i | −0.291626 | + | 0.168371i | ||||
\(153\) | −0.106095 | −0.00857728 | ||||||||
\(154\) | 8.50056 | + | 2.17726i | 0.684995 | + | 0.175449i | ||||
\(155\) | 2.28588 | 0.183606 | ||||||||
\(156\) | 5.52301 | − | 3.18871i | 0.442194 | − | 0.255301i | ||||
\(157\) | 3.51865 | + | 2.03150i | 0.280819 | + | 0.162131i | 0.633794 | − | 0.773502i | \(-0.281497\pi\) |
−0.352975 | + | 0.935633i | \(0.614830\pi\) | |||||||
\(158\) | −5.08457 | + | 8.80673i | −0.404507 | + | 0.700626i | ||||
\(159\) | −0.543380 | + | 0.313720i | −0.0430928 | + | 0.0248796i | ||||
\(160\) | 1.78763 | 0.141324 | ||||||||
\(161\) | −17.5419 | + | 11.6475i | −1.38250 | + | 0.917950i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −10.3707 | − | 17.9626i | −0.812297 | − | 1.40694i | −0.911253 | − | 0.411848i | \(-0.864883\pi\) |
0.0989554 | − | 0.995092i | \(-0.468450\pi\) | |||||||
\(164\) | −0.0160691 | + | 0.0278326i | −0.00125479 | + | 0.00217336i | ||||
\(165\) | −4.40254 | + | 3.97106i | −0.342738 | + | 0.309147i | ||||
\(166\) | −10.4492 | + | 6.03285i | −0.811015 | + | 0.468240i | ||||
\(167\) | 3.42870 | 0.265321 | 0.132660 | − | 0.991162i | \(-0.457648\pi\) | ||||
0.132660 | + | 0.991162i | \(0.457648\pi\) | |||||||
\(168\) | −2.36949 | − | 1.17708i | −0.182810 | − | 0.0908138i | ||||
\(169\) | 27.6715 | 2.12857 | ||||||||
\(170\) | −0.0948293 | − | 0.164249i | −0.00727307 | − | 0.0125973i | ||||
\(171\) | −2.07581 | + | 3.59541i | −0.158741 | + | 0.274948i | ||||
\(172\) | −5.95586 | − | 3.43862i | −0.454130 | − | 0.262192i | ||||
\(173\) | 10.5762 | + | 18.3185i | 0.804094 | + | 1.39273i | 0.916901 | + | 0.399115i | \(0.130683\pi\) |
−0.112807 | + | 0.993617i | \(0.535984\pi\) | |||||||
\(174\) | − | 7.65230i | − | 0.580119i | ||||||
\(175\) | 4.27548 | + | 2.12391i | 0.323196 | + | 0.160553i | ||||
\(176\) | −3.15519 | − | 1.02213i | −0.237832 | − | 0.0770458i | ||||
\(177\) | −6.22747 | − | 10.7863i | −0.468086 | − | 0.810748i | ||||
\(178\) | 2.68005 | − | 4.64198i | 0.200878 | − | 0.347931i | ||||
\(179\) | 7.04330 | − | 12.1994i | 0.526441 | − | 0.911822i | −0.473085 | − | 0.881017i | \(-0.656860\pi\) |
0.999525 | − | 0.0308052i | \(-0.00980716\pi\) | |||||||
\(180\) | 1.54813 | − | 0.893814i | 0.115391 | − | 0.0666209i | ||||
\(181\) | − | 12.4579i | − | 0.925992i | −0.886360 | − | 0.462996i | \(-0.846775\pi\) | ||
0.886360 | − | 0.462996i | \(-0.153225\pi\) | |||||||
\(182\) | −9.33333 | − | 14.0566i | −0.691833 | − | 1.04195i | ||||
\(183\) | 9.95024i | 0.735543i | ||||||||
\(184\) | 6.89240 | − | 3.97933i | 0.508115 | − | 0.293360i | ||||
\(185\) | −7.00040 | − | 4.04169i | −0.514680 | − | 0.297151i | ||||
\(186\) | 1.10740 | + | 0.639360i | 0.0811988 | + | 0.0468802i | ||||
\(187\) | 0.0734611 | + | 0.344124i | 0.00537201 | + | 0.0251649i | ||||
\(188\) | − | 9.88198i | − | 0.720718i | ||||||
\(189\) | −2.64058 | + | 0.165362i | −0.192074 | + | 0.0120283i | ||||
\(190\) | −7.42156 | −0.538416 | ||||||||
\(191\) | 13.6147 | + | 23.5813i | 0.985122 | + | 1.70628i | 0.641391 | + | 0.767214i | \(0.278358\pi\) |
0.343731 | + | 0.939068i | \(0.388309\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 23.0692 | + | 13.3190i | 1.66056 | + | 0.958724i | 0.972448 | + | 0.233119i | \(0.0748933\pi\) |
0.688111 | + | 0.725605i | \(0.258440\pi\) | |||||||
\(194\) | −7.87488 | − | 13.6397i | −0.565384 | − | 0.979273i | ||||
\(195\) | 11.4004 | 0.816403 | ||||||||
\(196\) | −2.71635 | + | 6.45147i | −0.194025 | + | 0.460819i | ||||
\(197\) | − | 11.7764i | − | 0.839031i | −0.907748 | − | 0.419515i | \(-0.862200\pi\) | ||
0.907748 | − | 0.419515i | \(-0.137800\pi\) | |||||||
\(198\) | −3.24354 | + | 0.692408i | −0.230509 | + | 0.0492073i | ||||
\(199\) | 18.5336 | + | 10.7004i | 1.31381 | + | 0.758531i | 0.982726 | − | 0.185069i | \(-0.0592508\pi\) |
0.331089 | + | 0.943600i | \(0.392584\pi\) | |||||||
\(200\) | −1.56265 | − | 0.902194i | −0.110496 | − | 0.0637948i | ||||
\(201\) | 9.41558 | − | 5.43609i | 0.664124 | − | 0.383432i | ||||
\(202\) | − | 7.57300i | − | 0.532834i | ||||||
\(203\) | −20.2065 | + | 1.26540i | −1.41822 | + | 0.0888137i | ||||
\(204\) | − | 0.106095i | − | 0.00742815i | ||||||
\(205\) | −0.0497542 | + | 0.0287256i | −0.00347499 | + | 0.00200628i | ||||
\(206\) | 2.61857 | − | 4.53550i | 0.182445 | − | 0.316004i | ||||
\(207\) | 3.97933 | − | 6.89240i | 0.276583 | − | 0.479055i | ||||
\(208\) | 3.18871 | + | 5.52301i | 0.221097 | + | 0.382952i | ||||
\(209\) | 13.0992 | + | 4.24349i | 0.906089 | + | 0.293529i | ||||
\(210\) | −2.61619 | − | 3.94016i | −0.180534 | − | 0.271897i | ||||
\(211\) | − | 25.2654i | − | 1.73934i | −0.493630 | − | 0.869672i | \(-0.664330\pi\) | ||
0.493630 | − | 0.869672i | \(-0.335670\pi\) | |||||||
\(212\) | −0.313720 | − | 0.543380i | −0.0215464 | − | 0.0373195i | ||||
\(213\) | 7.29873 | + | 4.21392i | 0.500101 | + | 0.288733i | ||||
\(214\) | −2.38395 | + | 4.12912i | −0.162963 | + | 0.282261i | ||||
\(215\) | −6.14696 | − | 10.6469i | −0.419219 | − | 0.726109i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.50516 | − | 3.02992i | 0.102177 | − | 0.205684i | ||||
\(218\) | −8.50535 | −0.576055 | ||||||||
\(219\) | 0.108260 | − | 0.0625042i | 0.00731556 | − | 0.00422364i | ||||
\(220\) | −3.97106 | − | 4.40254i | −0.267729 | − | 0.296819i | ||||
\(221\) | 0.338307 | − | 0.585964i | 0.0227570 | − | 0.0394162i | ||||
\(222\) | −2.26092 | − | 3.91603i | −0.151743 | − | 0.262827i | ||||
\(223\) | − | 9.80133i | − | 0.656346i | −0.944618 | − | 0.328173i | \(-0.893567\pi\) | ||
0.944618 | − | 0.328173i | \(-0.106433\pi\) | |||||||
\(224\) | 1.17708 | − | 2.36949i | 0.0786471 | − | 0.158318i | ||||
\(225\) | −1.80439 | −0.120293 | ||||||||
\(226\) | −8.92030 | + | 5.15014i | −0.593370 | + | 0.342582i | ||||
\(227\) | 11.6454 | − | 20.1704i | 0.772931 | − | 1.33875i | −0.163020 | − | 0.986623i | \(-0.552123\pi\) |
0.935950 | − | 0.352132i | \(-0.114543\pi\) | |||||||
\(228\) | −3.59541 | − | 2.07581i | −0.238112 | − | 0.137474i | ||||
\(229\) | −5.65569 | + | 3.26531i | −0.373739 | + | 0.215778i | −0.675090 | − | 0.737735i | \(-0.735895\pi\) |
0.301352 | + | 0.953513i | \(0.402562\pi\) | |||||||
\(230\) | 14.2271 | 0.938109 | ||||||||
\(231\) | 2.36472 | + | 8.45033i | 0.155587 | + | 0.555991i | ||||
\(232\) | 7.65230 | 0.502398 | ||||||||
\(233\) | −9.41166 | + | 5.43383i | −0.616579 | + | 0.355982i | −0.775536 | − | 0.631304i | \(-0.782520\pi\) |
0.158957 | + | 0.987285i | \(0.449187\pi\) | |||||||
\(234\) | 5.52301 | + | 3.18871i | 0.361050 | + | 0.208452i | ||||
\(235\) | 8.83265 | − | 15.2986i | 0.576179 | − | 0.997971i | ||||
\(236\) | 10.7863 | − | 6.22747i | 0.702128 | − | 0.405374i | ||||
\(237\) | −10.1691 | −0.660557 | ||||||||
\(238\) | −0.280153 | + | 0.0175441i | −0.0181596 | + | 0.00113722i | ||||
\(239\) | 7.69148i | 0.497521i | 0.968565 | + | 0.248760i | \(0.0800231\pi\) | ||||
−0.968565 | + | 0.248760i | \(0.919977\pi\) | |||||||
\(240\) | 0.893814 | + | 1.54813i | 0.0576954 | + | 0.0999314i | ||||
\(241\) | −11.4067 | + | 19.7571i | −0.734773 | + | 1.27266i | 0.220050 | + | 0.975489i | \(0.429378\pi\) |
−0.954823 | + | 0.297176i | \(0.903955\pi\) | |||||||
\(242\) | 4.49171 | + | 10.0411i | 0.288738 | + | 0.645469i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −9.95024 | −0.636999 | ||||||||
\(245\) | −9.97168 | + | 7.55980i | −0.637067 | + | 0.482978i | ||||
\(246\) | −0.0321383 | −0.00204906 | ||||||||
\(247\) | −13.2383 | − | 22.9294i | −0.842334 | − | 1.45897i | ||||
\(248\) | −0.639360 | + | 1.10740i | −0.0405994 | + | 0.0703203i | ||||
\(249\) | −10.4492 | − | 6.03285i | −0.662191 | − | 0.382316i | ||||
\(250\) | −6.08186 | − | 10.5341i | −0.384650 | − | 0.666234i | ||||
\(251\) | − | 18.1111i | − | 1.14317i | −0.820544 | − | 0.571583i | \(-0.806330\pi\) | ||
0.820544 | − | 0.571583i | \(-0.193670\pi\) | |||||||
\(252\) | −0.165362 | − | 2.64058i | −0.0104168 | − | 0.166341i | ||||
\(253\) | −25.1111 | − | 8.13478i | −1.57872 | − | 0.511429i | ||||
\(254\) | −1.59211 | − | 2.75761i | −0.0998977 | − | 0.173028i | ||||
\(255\) | 0.0948293 | − | 0.164249i | 0.00593844 | − | 0.0102857i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.41428 | + | 1.97123i | −0.212977 | + | 0.122962i | −0.602694 | − | 0.797972i | \(-0.705906\pi\) |
0.389717 | + | 0.920935i | \(0.372573\pi\) | |||||||
\(258\) | − | 6.87723i | − | 0.428158i | ||||||
\(259\) | −9.96672 | + | 6.61771i | −0.619302 | + | 0.411204i | ||||
\(260\) | 11.4004i | 0.707026i | ||||||||
\(261\) | 6.62708 | − | 3.82615i | 0.410206 | − | 0.236833i | ||||
\(262\) | 0.940675 | + | 0.543099i | 0.0581151 | + | 0.0335528i | ||||
\(263\) | 1.79020 | + | 1.03357i | 0.110389 | + | 0.0637329i | 0.554178 | − | 0.832398i | \(-0.313033\pi\) |
−0.443789 | + | 0.896131i | \(0.646366\pi\) | |||||||
\(264\) | −0.692408 | − | 3.24354i | −0.0426148 | − | 0.199626i | ||||
\(265\) | − | 1.12163i | − | 0.0689012i | ||||||
\(266\) | −4.88680 | + | 9.83723i | −0.299629 | + | 0.603159i | ||||
\(267\) | 5.36009 | 0.328032 | ||||||||
\(268\) | 5.43609 | + | 9.41558i | 0.332062 | + | 0.575148i | ||||
\(269\) | 2.42902 | + | 1.40240i | 0.148100 | + | 0.0855057i | 0.572219 | − | 0.820101i | \(-0.306083\pi\) |
−0.424119 | + | 0.905607i | \(0.639416\pi\) | |||||||
\(270\) | 1.54813 | + | 0.893814i | 0.0942162 | + | 0.0543958i | ||||
\(271\) | −4.64046 | − | 8.03751i | −0.281888 | − | 0.488244i | 0.689962 | − | 0.723846i | \(-0.257627\pi\) |
−0.971850 | + | 0.235602i | \(0.924294\pi\) | |||||||
\(272\) | 0.106095 | 0.00643296 | ||||||||
\(273\) | 7.50674 | − | 15.1112i | 0.454329 | − | 0.914573i | ||||
\(274\) | 7.58196i | 0.458043i | ||||||||
\(275\) | 1.24937 | + | 5.85261i | 0.0753400 | + | 0.352926i | ||||
\(276\) | 6.89240 | + | 3.97933i | 0.414874 | + | 0.239528i | ||||
\(277\) | −4.53015 | − | 2.61548i | −0.272190 | − | 0.157149i | 0.357692 | − | 0.933839i | \(-0.383564\pi\) |
−0.629883 | + | 0.776690i | \(0.716897\pi\) | |||||||
\(278\) | −1.16604 | + | 0.673214i | −0.0699345 | + | 0.0403767i | ||||
\(279\) | 1.27872i | 0.0765550i | ||||||||
\(280\) | 3.94016 | − | 2.61619i | 0.235469 | − | 0.156347i | ||||
\(281\) | − | 6.87281i | − | 0.409998i | −0.978762 | − | 0.204999i | \(-0.934281\pi\) | ||
0.978762 | − | 0.204999i | \(-0.0657190\pi\) | |||||||
\(282\) | 8.55805 | − | 4.94099i | 0.509624 | − | 0.294232i | ||||
\(283\) | −6.00542 | + | 10.4017i | −0.356985 | + | 0.618316i | −0.987456 | − | 0.157897i | \(-0.949529\pi\) |
0.630471 | + | 0.776213i | \(0.282862\pi\) | |||||||
\(284\) | −4.21392 | + | 7.29873i | −0.250050 | + | 0.433100i | ||||
\(285\) | −3.71078 | − | 6.42726i | −0.219808 | − | 0.380718i | ||||
\(286\) | 6.51854 | − | 20.1220i | 0.385449 | − | 1.18984i | ||||
\(287\) | 0.00531446 | + | 0.0848636i | 0.000313703 | + | 0.00500934i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 8.49437 | + | 14.7127i | 0.499669 | + | 0.865452i | ||||
\(290\) | 11.8468 | + | 6.83973i | 0.695665 | + | 0.401643i | ||||
\(291\) | 7.87488 | − | 13.6397i | 0.461634 | − | 0.799573i | ||||
\(292\) | 0.0625042 | + | 0.108260i | 0.00365778 | + | 0.00633546i | ||||
\(293\) | 14.1147 | 0.824592 | 0.412296 | − | 0.911050i | \(-0.364727\pi\) | ||||
0.412296 | + | 0.911050i | \(0.364727\pi\) | |||||||
\(294\) | −6.94531 | + | 0.873304i | −0.405059 | + | 0.0509321i | ||||
\(295\) | 22.2648 | 1.29631 | ||||||||
\(296\) | 3.91603 | − | 2.26092i | 0.227615 | − | 0.131413i | ||||
\(297\) | −2.22141 | − | 2.46279i | −0.128900 | − | 0.142905i | ||||
\(298\) | 0.245079 | − | 0.424489i | 0.0141970 | − | 0.0245900i | ||||
\(299\) | 25.3779 | + | 43.9557i | 1.46764 | + | 2.54203i | ||||
\(300\) | − | 1.80439i | − | 0.104176i | ||||||
\(301\) | −18.1599 | + | 1.13723i | −1.04672 | + | 0.0655491i | ||||
\(302\) | −3.37323 | −0.194107 | ||||||||
\(303\) | 6.55841 | − | 3.78650i | 0.376771 | − | 0.217529i | ||||
\(304\) | 2.07581 | − | 3.59541i | 0.119056 | − | 0.206211i | ||||
\(305\) | −15.4043 | − | 8.89366i | −0.882046 | − | 0.509249i | ||||
\(306\) | 0.0918811 | − | 0.0530476i | 0.00525249 | − | 0.00303253i | ||||
\(307\) | −21.0753 | −1.20283 | −0.601417 | − | 0.798936i | \(-0.705397\pi\) | ||||
−0.601417 | + | 0.798936i | \(0.705397\pi\) | |||||||
\(308\) | −8.45033 | + | 2.36472i | −0.481502 | + | 0.134742i | ||||
\(309\) | 5.23715 | 0.297931 | ||||||||
\(310\) | −1.97963 | + | 1.14294i | −0.112435 | + | 0.0649145i | ||||
\(311\) | −12.0806 | − | 6.97475i | −0.685029 | − | 0.395502i | 0.116718 | − | 0.993165i | \(-0.462763\pi\) |
−0.801747 | + | 0.597663i | \(0.796096\pi\) | |||||||
\(312\) | −3.18871 | + | 5.52301i | −0.180525 | + | 0.312679i | ||||
\(313\) | 3.45030 | − | 1.99203i | 0.195023 | − | 0.112596i | −0.399309 | − | 0.916816i | \(-0.630750\pi\) |
0.594332 | + | 0.804220i | \(0.297417\pi\) | |||||||
\(314\) | −4.06299 | −0.229288 | ||||||||
\(315\) | 2.10418 | − | 4.23576i | 0.118557 | − | 0.238658i | ||||
\(316\) | − | 10.1691i | − | 0.572059i | ||||||
\(317\) | −6.14927 | − | 10.6509i | −0.345377 | − | 0.598211i | 0.640045 | − | 0.768338i | \(-0.278916\pi\) |
−0.985422 | + | 0.170126i | \(0.945582\pi\) | |||||||
\(318\) | 0.313720 | − | 0.543380i | 0.0175926 | − | 0.0304712i | ||||
\(319\) | −16.9989 | − | 18.8460i | −0.951757 | − | 1.05517i | ||||
\(320\) | −1.54813 | + | 0.893814i | −0.0865431 | + | 0.0499657i | ||||
\(321\) | −4.76790 | −0.266118 | ||||||||
\(322\) | 9.36799 | − | 18.8580i | 0.522058 | − | 1.05091i | ||||
\(323\) | −0.440467 | −0.0245082 | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 5.75367 | − | 9.96565i | 0.319156 | − | 0.552795i | ||||
\(326\) | 17.9626 | + | 10.3707i | 0.994857 | + | 0.574381i | ||||
\(327\) | −4.25268 | − | 7.36585i | −0.235174 | − | 0.407332i | ||||
\(328\) | − | 0.0321383i | − | 0.00177454i | ||||||
\(329\) | −14.4623 | − | 21.7811i | −0.797330 | − | 1.20083i | ||||
\(330\) | 1.82718 | − | 5.64031i | 0.100583 | − | 0.310489i | ||||
\(331\) | 15.5066 | + | 26.8582i | 0.852319 | + | 1.47626i | 0.879110 | + | 0.476619i | \(0.158138\pi\) |
−0.0267909 | + | 0.999641i | \(0.508529\pi\) | |||||||
\(332\) | 6.03285 | − | 10.4492i | 0.331096 | − | 0.573474i | ||||
\(333\) | 2.26092 | − | 3.91603i | 0.123898 | − | 0.214597i | ||||
\(334\) | −2.96934 | + | 1.71435i | −0.162475 | + | 0.0938051i | ||||
\(335\) | 19.4354i | 1.06187i | ||||||||
\(336\) | 2.64058 | − | 0.165362i | 0.144055 | − | 0.00902125i | ||||
\(337\) | 13.6161i | 0.741718i | 0.928689 | + | 0.370859i | \(0.120937\pi\) | ||||
−0.928689 | + | 0.370859i | \(0.879063\pi\) | |||||||
\(338\) | −23.9642 | + | 13.8357i | −1.30348 | + | 0.752565i | ||||
\(339\) | −8.92030 | − | 5.15014i | −0.484484 | − | 0.279717i | ||||
\(340\) | 0.164249 | + | 0.0948293i | 0.00890766 | + | 0.00514284i | ||||
\(341\) | 4.14759 | − | 0.885396i | 0.224604 | − | 0.0479469i | ||||
\(342\) | − | 4.15162i | − | 0.224494i | ||||||
\(343\) | 3.45452 | + | 18.1952i | 0.186527 | + | 0.982450i | ||||
\(344\) | 6.87723 | 0.370795 | ||||||||
\(345\) | 7.11356 | + | 12.3210i | 0.382981 | + | 0.663343i | ||||
\(346\) | −18.3185 | − | 10.5762i | −0.984810 | − | 0.568580i | ||||
\(347\) | 24.1708 | + | 13.9550i | 1.29756 | + | 0.749144i | 0.979981 | − | 0.199090i | \(-0.0637985\pi\) |
0.317574 | + | 0.948234i | \(0.397132\pi\) | |||||||
\(348\) | 3.82615 | + | 6.62708i | 0.205103 | + | 0.355249i | ||||
\(349\) | 27.8147 | 1.48888 | 0.744442 | − | 0.667687i | \(-0.232715\pi\) | ||||
0.744442 | + | 0.667687i | \(0.232715\pi\) | |||||||
\(350\) | −4.76463 | + | 0.298378i | −0.254680 | + | 0.0159490i | ||||
\(351\) | 6.37742i | 0.340401i | ||||||||
\(352\) | 3.24354 | − | 0.692408i | 0.172881 | − | 0.0369055i | ||||
\(353\) | −18.6325 | − | 10.7575i | −0.991706 | − | 0.572562i | −0.0859222 | − | 0.996302i | \(-0.527384\pi\) |
−0.905784 | + | 0.423740i | \(0.860717\pi\) | |||||||
\(354\) | 10.7863 | + | 6.22747i | 0.573285 | + | 0.330987i | ||||
\(355\) | −13.0474 | + | 7.53293i | −0.692485 | + | 0.399806i | ||||
\(356\) | 5.36009i | 0.284084i | ||||||||
\(357\) | −0.155270 | − | 0.233847i | −0.00821776 | − | 0.0123765i | ||||
\(358\) | 14.0866i | 0.744500i | ||||||||
\(359\) | −18.0949 | + | 10.4471i | −0.955015 | + | 0.551378i | −0.894635 | − | 0.446798i | \(-0.852564\pi\) |
−0.0603796 | + | 0.998175i | \(0.519231\pi\) | |||||||
\(360\) | −0.893814 | + | 1.54813i | −0.0471081 | + | 0.0815936i | ||||
\(361\) | 0.882009 | − | 1.52769i | 0.0464215 | − | 0.0804045i | ||||
\(362\) | 6.22897 | + | 10.7889i | 0.327387 | + | 0.567052i | ||||
\(363\) | −6.45003 | + | 8.91051i | −0.338539 | + | 0.467680i | ||||
\(364\) | 15.1112 | + | 7.50674i | 0.792043 | + | 0.393460i | ||||
\(365\) | 0.223468i | 0.0116969i | ||||||||
\(366\) | −4.97512 | − | 8.61716i | −0.260054 | − | 0.450426i | ||||
\(367\) | 4.62731 | + | 2.67158i | 0.241543 | + | 0.139455i | 0.615886 | − | 0.787835i | \(-0.288798\pi\) |
−0.374342 | + | 0.927291i | \(0.622132\pi\) | |||||||
\(368\) | −3.97933 | + | 6.89240i | −0.207437 | + | 0.359291i | ||||
\(369\) | −0.0160691 | − | 0.0278326i | −0.000836526 | − | 0.00144891i | ||||
\(370\) | 8.08337 | 0.420234 | ||||||||
\(371\) | −1.48671 | − | 0.738549i | −0.0771864 | − | 0.0383435i | ||||
\(372\) | −1.27872 | −0.0662986 | ||||||||
\(373\) | −21.9741 | + | 12.6868i | −1.13778 | + | 0.656895i | −0.945879 | − | 0.324520i | \(-0.894797\pi\) |
−0.191897 | + | 0.981415i | \(0.561464\pi\) | |||||||
\(374\) | −0.235681 | − | 0.261290i | −0.0121868 | − | 0.0135110i | ||||
\(375\) | 6.08186 | − | 10.5341i | 0.314066 | − | 0.543978i | ||||
\(376\) | 4.94099 | + | 8.55805i | 0.254812 | + | 0.441348i | ||||
\(377\) | 48.8019i | 2.51343i | ||||||||
\(378\) | 2.20413 | − | 1.46350i | 0.113368 | − | 0.0752742i | ||||
\(379\) | 22.7532 | 1.16875 | 0.584377 | − | 0.811483i | \(-0.301339\pi\) | ||||
0.584377 | + | 0.811483i | \(0.301339\pi\) | |||||||
\(380\) | 6.42726 | − | 3.71078i | 0.329711 | − | 0.190359i | ||||
\(381\) | 1.59211 | − | 2.75761i | 0.0815662 | − | 0.141277i | ||||
\(382\) | −23.5813 | − | 13.6147i | −1.20652 | − | 0.696587i | ||||
\(383\) | −14.3310 | + | 8.27402i | −0.732281 | + | 0.422783i | −0.819256 | − | 0.573428i | \(-0.805613\pi\) |
0.0869750 | + | 0.996210i | \(0.472280\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −15.1958 | − | 3.89213i | −0.774451 | − | 0.198361i | ||||
\(386\) | −26.6381 | −1.35584 | ||||||||
\(387\) | 5.95586 | − | 3.43862i | 0.302753 | − | 0.174795i | ||||
\(388\) | 13.6397 | + | 7.87488i | 0.692451 | + | 0.399787i | ||||
\(389\) | −3.69906 | + | 6.40696i | −0.187550 | + | 0.324846i | −0.944433 | − | 0.328705i | \(-0.893388\pi\) |
0.756883 | + | 0.653550i | \(0.226721\pi\) | |||||||
\(390\) | −9.87308 | + | 5.70022i | −0.499943 | + | 0.288642i | ||||
\(391\) | 0.844376 | 0.0427019 | ||||||||
\(392\) | −0.873304 | − | 6.94531i | −0.0441085 | − | 0.350791i | ||||
\(393\) | 1.08620i | 0.0547915i | ||||||||
\(394\) | 5.88818 | + | 10.1986i | 0.296642 | + | 0.513799i | ||||
\(395\) | 9.08932 | − | 15.7432i | 0.457333 | − | 0.792124i | ||||
\(396\) | 2.46279 | − | 2.22141i | 0.123760 | − | 0.111630i | ||||
\(397\) | 3.34925 | − | 1.93369i | 0.168094 | − | 0.0970492i | −0.413593 | − | 0.910462i | \(-0.635726\pi\) |
0.581687 | + | 0.813413i | \(0.302393\pi\) | |||||||
\(398\) | −21.4008 | −1.07272 | ||||||||
\(399\) | −10.9627 | + | 0.686522i | −0.548821 | + | 0.0343691i | ||||
\(400\) | 1.80439 | 0.0902194 | ||||||||
\(401\) | −1.56681 | − | 2.71379i | −0.0782426 | − | 0.135520i | 0.824249 | − | 0.566227i | \(-0.191598\pi\) |
−0.902492 | + | 0.430707i | \(0.858264\pi\) | |||||||
\(402\) | −5.43609 | + | 9.41558i | −0.271127 | + | 0.469606i | ||||
\(403\) | −7.06238 | − | 4.07747i | −0.351802 | − | 0.203113i | ||||
\(404\) | 3.78650 | + | 6.55841i | 0.188385 | + | 0.326293i | ||||
\(405\) | 1.78763i | 0.0888279i | ||||||||
\(406\) | 16.8666 | − | 11.1991i | 0.837077 | − | 0.555803i | ||||
\(407\) | −14.2673 | − | 4.62191i | −0.707204 | − | 0.229099i | ||||
\(408\) | 0.0530476 | + | 0.0918811i | 0.00262625 | + | 0.00454879i | ||||
\(409\) | −10.0511 | + | 17.4091i | −0.496996 | + | 0.860822i | −0.999994 | − | 0.00346526i | \(-0.998897\pi\) |
0.502998 | + | 0.864288i | \(0.332230\pi\) | |||||||
\(410\) | 0.0287256 | − | 0.0497542i | 0.00141866 | − | 0.00245719i | ||||
\(411\) | −6.56617 | + | 3.79098i | −0.323885 | + | 0.186995i | ||||
\(412\) | 5.23715i | 0.258016i | ||||||||
\(413\) | 14.6605 | − | 29.5119i | 0.721395 | − | 1.45218i | ||||
\(414\) | 7.95866i | 0.391147i | ||||||||
\(415\) | 18.6793 | − | 10.7845i | 0.916929 | − | 0.529389i | ||||
\(416\) | −5.52301 | − | 3.18871i | −0.270788 | − | 0.156339i | ||||
\(417\) | −1.16604 | − | 0.673214i | −0.0571013 | − | 0.0329674i | ||||
\(418\) | −13.4660 | + | 2.87462i | −0.658642 | + | 0.140602i | ||||
\(419\) | − | 2.63035i | − | 0.128501i | −0.997934 | − | 0.0642506i | \(-0.979534\pi\) | ||
0.997934 | − | 0.0642506i | \(-0.0204657\pi\) | |||||||
\(420\) | 4.23576 | + | 2.10418i | 0.206684 | + | 0.102674i | ||||
\(421\) | 24.9232 | 1.21468 | 0.607341 | − | 0.794441i | \(-0.292236\pi\) | ||||
0.607341 | + | 0.794441i | \(0.292236\pi\) | |||||||
\(422\) | 12.6327 | + | 21.8805i | 0.614951 | + | 1.06513i | ||||
\(423\) | 8.55805 | + | 4.94099i | 0.416107 | + | 0.240239i | ||||
\(424\) | 0.543380 | + | 0.313720i | 0.0263888 | + | 0.0152356i | ||||
\(425\) | −0.0957185 | − | 0.165789i | −0.00464303 | − | 0.00804196i | ||||
\(426\) | −8.42785 | −0.408331 | ||||||||
\(427\) | −21.9316 | + | 14.5621i | −1.06134 | + | 0.704712i | ||||
\(428\) | − | 4.76790i | − | 0.230465i | ||||||
\(429\) | 20.6854 | − | 4.41578i | 0.998702 | − | 0.213196i | ||||
\(430\) | 10.6469 | + | 6.14696i | 0.513437 | + | 0.296433i | ||||
\(431\) | 11.8175 | + | 6.82282i | 0.569227 | + | 0.328644i | 0.756841 | − | 0.653599i | \(-0.226742\pi\) |
−0.187613 | + | 0.982243i | \(0.560075\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 10.4001i | − | 0.499795i | −0.968272 | − | 0.249897i | \(-0.919603\pi\) | ||
0.968272 | − | 0.249897i | \(-0.0803969\pi\) | |||||||
\(434\) | 0.211452 | + | 3.37656i | 0.0101500 | + | 0.162080i | ||||
\(435\) | 13.6795i | 0.655879i | ||||||||
\(436\) | 7.36585 | − | 4.25268i | 0.352760 | − | 0.203666i | ||||
\(437\) | 16.5207 | − | 28.6147i | 0.790292 | − | 1.36883i | ||||
\(438\) | −0.0625042 | + | 0.108260i | −0.00298656 | + | 0.00517288i | ||||
\(439\) | −11.6619 | − | 20.1991i | −0.556594 | − | 0.964049i | −0.997778 | − | 0.0666324i | \(-0.978775\pi\) |
0.441183 | − | 0.897417i | \(-0.354559\pi\) | |||||||
\(440\) | 5.64031 | + | 1.82718i | 0.268891 | + | 0.0871076i | ||||
\(441\) | −4.22896 | − | 5.57816i | −0.201379 | − | 0.265627i | ||||
\(442\) | 0.676613i | 0.0321832i | ||||||||
\(443\) | −4.91726 | − | 8.51694i | −0.233626 | − | 0.404652i | 0.725247 | − | 0.688489i | \(-0.241726\pi\) |
−0.958872 | + | 0.283837i | \(0.908392\pi\) | |||||||
\(444\) | 3.91603 | + | 2.26092i | 0.185847 | + | 0.107299i | ||||
\(445\) | −4.79092 | + | 8.29813i | −0.227112 | + | 0.393369i | ||||
\(446\) | 4.90067 | + | 8.48820i | 0.232053 | + | 0.401928i | ||||
\(447\) | 0.490157 | 0.0231836 | ||||||||
\(448\) | 0.165362 | + | 2.64058i | 0.00781263 | + | 0.124756i | ||||
\(449\) | 9.26223 | 0.437112 | 0.218556 | − | 0.975824i | \(-0.429865\pi\) | ||||
0.218556 | + | 0.975824i | \(0.429865\pi\) | |||||||
\(450\) | 1.56265 | − | 0.902194i | 0.0736639 | − | 0.0425299i | ||||
\(451\) | −0.0791497 | + | 0.0713924i | −0.00372701 | + | 0.00336174i | ||||
\(452\) | 5.15014 | − | 8.92030i | 0.242242 | − | 0.419576i | ||||
\(453\) | −1.68661 | − | 2.92130i | −0.0792440 | − | 0.137255i | ||||
\(454\) | 23.2907i | 1.09309i | ||||||||
\(455\) | 16.6845 | + | 25.1280i | 0.782182 | + | 1.17802i | ||||
\(456\) | 4.15162 | 0.194418 | ||||||||
\(457\) | 2.21387 | − | 1.27818i | 0.103560 | − | 0.0597906i | −0.447325 | − | 0.894371i | \(-0.647623\pi\) |
0.550886 | + | 0.834581i | \(0.314290\pi\) | |||||||
\(458\) | 3.26531 | − | 5.65569i | 0.152578 | − | 0.264273i | ||||
\(459\) | 0.0918811 | + | 0.0530476i | 0.00428864 | + | 0.00247605i | ||||
\(460\) | −12.3210 | + | 7.11356i | −0.574472 | + | 0.331672i | ||||
\(461\) | −29.5798 | −1.37767 | −0.688834 | − | 0.724919i | \(-0.741877\pi\) | ||||
−0.688834 | + | 0.724919i | \(0.741877\pi\) | |||||||
\(462\) | −6.27307 | − | 6.13584i | −0.291850 | − | 0.285465i | ||||
\(463\) | −9.24447 | −0.429627 | −0.214813 | − | 0.976655i | \(-0.568914\pi\) | ||||
−0.214813 | + | 0.976655i | \(0.568914\pi\) | |||||||
\(464\) | −6.62708 | + | 3.82615i | −0.307655 | + | 0.177624i | ||||
\(465\) | −1.97963 | − | 1.14294i | −0.0918030 | − | 0.0530025i | ||||
\(466\) | 5.43383 | − | 9.41166i | 0.251717 | − | 0.435987i | ||||
\(467\) | −10.0889 | + | 5.82484i | −0.466859 | + | 0.269541i | −0.714924 | − | 0.699202i | \(-0.753539\pi\) |
0.248065 | + | 0.968743i | \(0.420205\pi\) | |||||||
\(468\) | −6.37742 | −0.294796 | ||||||||
\(469\) | 25.7615 | + | 12.7974i | 1.18956 | + | 0.590931i | ||||
\(470\) | 17.6653i | 0.814840i | ||||||||
\(471\) | −2.03150 | − | 3.51865i | −0.0936064 | − | 0.162131i | ||||
\(472\) | −6.22747 | + | 10.7863i | −0.286643 | + | 0.496480i | ||||
\(473\) | −15.2772 | − | 16.9372i | −0.702445 | − | 0.778771i | ||||
\(474\) | 8.80673 | − | 5.08457i | 0.404507 | − | 0.233542i | ||||
\(475\) | −7.49114 | −0.343717 | ||||||||
\(476\) | 0.233847 | − | 0.155270i | 0.0107184 | − | 0.00711679i | ||||
\(477\) | 0.627441 | 0.0287285 | ||||||||
\(478\) | −3.84574 | − | 6.66102i | −0.175900 | − | 0.304668i | ||||
\(479\) | 5.02758 | − | 8.70803i | 0.229716 | − | 0.397880i | −0.728008 | − | 0.685569i | \(-0.759554\pi\) |
0.957724 | + | 0.287689i | \(0.0928869\pi\) | |||||||
\(480\) | −1.54813 | − | 0.893814i | −0.0706622 | − | 0.0407968i | ||||
\(481\) | 14.4188 | + | 24.9742i | 0.657443 | + | 1.13872i | ||||
\(482\) | − | 22.8135i | − | 1.03913i | ||||||
\(483\) | 21.0155 | − | 1.31606i | 0.956237 | − | 0.0598829i | ||||
\(484\) | −8.91051 | − | 6.45003i | −0.405023 | − | 0.293183i | ||||
\(485\) | 14.0774 | + | 24.3827i | 0.639220 | + | 1.10716i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −8.65731 | + | 14.9949i | −0.392300 | + | 0.679484i | −0.992753 | − | 0.120176i | \(-0.961654\pi\) |
0.600452 | + | 0.799661i | \(0.294987\pi\) | |||||||
\(488\) | 8.61716 | − | 4.97512i | 0.390080 | − | 0.225213i | ||||
\(489\) | 20.7414i | 0.937960i | ||||||||
\(490\) | 4.85582 | − | 11.5328i | 0.219364 | − | 0.521000i | ||||
\(491\) | 8.44002i | 0.380893i | 0.981698 | + | 0.190446i | \(0.0609935\pi\) | ||||
−0.981698 | + | 0.190446i | \(0.939006\pi\) | |||||||
\(492\) | 0.0278326 | − | 0.0160691i | 0.00125479 | − | 0.000724453i | ||||
\(493\) | 0.703101 | + | 0.405936i | 0.0316661 | + | 0.0182824i | ||||
\(494\) | 22.9294 | + | 13.2383i | 1.03164 | + | 0.595620i | ||||
\(495\) | 5.79825 | − | 1.23777i | 0.260612 | − | 0.0556335i | ||||
\(496\) | − | 1.27872i | − | 0.0574163i | ||||||
\(497\) | 1.39365 | + | 22.2544i | 0.0625137 | + | 0.998246i | ||||
\(498\) | 12.0657 | 0.540677 | ||||||||
\(499\) | −9.53597 | − | 16.5168i | −0.426889 | − | 0.739393i | 0.569706 | − | 0.821849i | \(-0.307057\pi\) |
−0.996595 | + | 0.0824555i | \(0.973724\pi\) | |||||||
\(500\) | 10.5341 | + | 6.08186i | 0.471098 | + | 0.271989i | ||||
\(501\) | −2.96934 | − | 1.71435i | −0.132660 | − | 0.0765915i | ||||
\(502\) | 9.05557 | + | 15.6847i | 0.404170 | + | 0.700043i | ||||
\(503\) | −3.32018 | −0.148039 | −0.0740197 | − | 0.997257i | \(-0.523583\pi\) | ||||
−0.0740197 | + | 0.997257i | \(0.523583\pi\) | |||||||
\(504\) | 1.46350 | + | 2.20413i | 0.0651893 | + | 0.0981796i | ||||
\(505\) | 13.5377i | 0.602419i | ||||||||
\(506\) | 25.8143 | − | 5.51064i | 1.14758 | − | 0.244978i | ||||
\(507\) | −23.9642 | − | 13.8357i | −1.06429 | − | 0.614466i | ||||
\(508\) | 2.75761 | + | 1.59211i | 0.122349 | + | 0.0706384i | ||||
\(509\) | 3.91339 | − | 2.25939i | 0.173458 | − | 0.100146i | −0.410758 | − | 0.911745i | \(-0.634736\pi\) |
0.584215 | + | 0.811599i | \(0.301402\pi\) | |||||||
\(510\) | 0.189659i | 0.00839822i | ||||||||
\(511\) | 0.296206 | + | 0.147145i | 0.0131034 | + | 0.00650931i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 3.59541 | − | 2.07581i | 0.158741 | − | 0.0916493i | ||||
\(514\) | 1.97123 | − | 3.41428i | 0.0869474 | − | 0.150597i | ||||
\(515\) | −4.68103 | + | 8.10779i | −0.206271 | + | 0.357272i | ||||
\(516\) | 3.43862 | + | 5.95586i | 0.151377 | + | 0.262192i | ||||
\(517\) | 10.1007 | − | 31.1796i | 0.444226 | − | 1.37128i | ||||
\(518\) | 5.32258 | − | 10.7145i | 0.233861 | − | 0.470766i | ||||
\(519\) | − | 21.1524i | − | 0.928488i | ||||||
\(520\) | −5.70022 | − | 9.87308i | −0.249971 | − | 0.432963i | ||||
\(521\) | −8.10705 | − | 4.68061i | −0.355176 | − | 0.205061i | 0.311786 | − | 0.950152i | \(-0.399073\pi\) |
−0.666963 | + | 0.745091i | \(0.732406\pi\) | |||||||
\(522\) | −3.82615 | + | 6.62708i | −0.167466 | + | 0.290060i | ||||
\(523\) | −8.70477 | − | 15.0771i | −0.380633 | − | 0.659276i | 0.610520 | − | 0.792001i | \(-0.290961\pi\) |
−0.991153 | + | 0.132725i | \(0.957627\pi\) | |||||||
\(524\) | −1.08620 | −0.0474508 | ||||||||
\(525\) | −2.64072 | − | 3.97710i | −0.115250 | − | 0.173575i | ||||
\(526\) | −2.06715 | −0.0901320 | ||||||||
\(527\) | −0.117490 | + | 0.0678330i | −0.00511796 | + | 0.00295485i | ||||
\(528\) | 2.22141 | + | 2.46279i | 0.0966747 | + | 0.107179i | ||||
\(529\) | −20.1702 | + | 34.9357i | −0.876963 | + | 1.51895i | ||||
\(530\) | 0.560815 | + | 0.971360i | 0.0243603 | + | 0.0421932i | ||||
\(531\) | 12.4549i | 0.540499i | ||||||||
\(532\) | −0.686522 | − | 10.9627i | −0.0297645 | − | 0.475293i | ||||
\(533\) | 0.204959 | 0.00887777 | ||||||||
\(534\) | −4.64198 | + | 2.68005i | −0.200878 | + | 0.115977i | ||||
\(535\) | 4.26161 | − | 7.38132i | 0.184245 | − | 0.319122i | ||||
\(536\) | −9.41558 | − | 5.43609i | −0.406691 | − | 0.234803i | ||||
\(537\) | −12.1994 | + | 7.04330i | −0.526441 | + | 0.303941i | ||||
\(538\) | −2.80480 | −0.120923 | ||||||||
\(539\) | −15.1648 | + | 17.5792i | −0.653196 | + | 0.757189i | ||||
\(540\) | −1.78763 | −0.0769272 | ||||||||
\(541\) | 34.0973 | − | 19.6861i | 1.46596 | − | 0.846370i | 0.466681 | − | 0.884426i | \(-0.345450\pi\) |
0.999276 | + | 0.0380552i | \(0.0121163\pi\) | |||||||
\(542\) | 8.03751 | + | 4.64046i | 0.345241 | + | 0.199325i | ||||
\(543\) | −6.22897 | + | 10.7889i | −0.267311 | + | 0.462996i | ||||
\(544\) | −0.0918811 | + | 0.0530476i | −0.00393937 | + | 0.00227440i | ||||
\(545\) | 15.2044 | 0.651285 | ||||||||
\(546\) | 1.05458 | + | 16.8401i | 0.0451321 | + | 0.720689i | ||||
\(547\) | − | 20.3539i | − | 0.870271i | −0.900365 | − | 0.435135i | \(-0.856701\pi\) | ||
0.900365 | − | 0.435135i | \(-0.143299\pi\) | |||||||
\(548\) | −3.79098 | − | 6.56617i | −0.161943 | − | 0.280493i | ||||
\(549\) | 4.97512 | − | 8.61716i | 0.212333 | − | 0.367771i | ||||
\(550\) | −4.00830 | − | 4.44383i | −0.170914 | − | 0.189485i | ||||
\(551\) | 27.5132 | − | 15.8847i | 1.17210 | − | 0.676712i | ||||
\(552\) | −7.95866 | −0.338743 | ||||||||
\(553\) | −14.8825 | − | 22.4141i | −0.632869 | − | 0.953144i | ||||
\(554\) | 5.23096 | 0.222242 | ||||||||
\(555\) | 4.04169 | + | 7.00040i | 0.171560 | + | 0.297151i | ||||
\(556\) | 0.673214 | − | 1.16604i | 0.0285506 | − | 0.0494512i | ||||
\(557\) | −11.2830 | − | 6.51425i | −0.478076 | − | 0.276017i | 0.241538 | − | 0.970391i | \(-0.422348\pi\) |
−0.719614 | + | 0.694374i | \(0.755681\pi\) | |||||||
\(558\) | −0.639360 | − | 1.10740i | −0.0270663 | − | 0.0468802i | ||||
\(559\) | 43.8590i | 1.85504i | ||||||||
\(560\) | −2.10418 | + | 4.23576i | −0.0889179 | + | 0.178994i | ||||
\(561\) | 0.108443 | − | 0.334751i | 0.00457846 | − | 0.0141332i | ||||
\(562\) | 3.43641 | + | 5.95203i | 0.144956 | + | 0.251071i | ||||
\(563\) | 16.7817 | − | 29.0667i | 0.707262 | − | 1.22501i | −0.258607 | − | 0.965983i | \(-0.583263\pi\) |
0.965869 | − | 0.259032i | \(-0.0834034\pi\) | |||||||
\(564\) | −4.94099 | + | 8.55805i | −0.208053 | + | 0.360359i | ||||
\(565\) | 15.9462 | − | 9.20653i | 0.670861 | − | 0.387322i | ||||
\(566\) | − | 12.0108i | − | 0.504853i | ||||||
\(567\) | 2.36949 | + | 1.17708i | 0.0995092 | + | 0.0494328i | ||||
\(568\) | − | 8.42785i | − | 0.353625i | ||||||
\(569\) | −4.80366 | + | 2.77340i | −0.201380 | + | 0.116267i | −0.597299 | − | 0.802019i | \(-0.703759\pi\) |
0.395919 | + | 0.918285i | \(0.370426\pi\) | |||||||
\(570\) | 6.42726 | + | 3.71078i | 0.269208 | + | 0.155427i | ||||
\(571\) | −32.1228 | − | 18.5461i | −1.34430 | − | 0.776132i | −0.356864 | − | 0.934156i | \(-0.616154\pi\) |
−0.987435 | + | 0.158025i | \(0.949487\pi\) | |||||||
\(572\) | 4.41578 | + | 20.6854i | 0.184633 | + | 0.864901i | ||||
\(573\) | − | 27.2293i | − | 1.13752i | ||||||
\(574\) | −0.0470343 | − | 0.0708368i | −0.00196317 | − | 0.00295667i | ||||
\(575\) | 14.3605 | 0.598875 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 2.66926 | + | 1.54110i | 0.111123 | + | 0.0641567i | 0.554531 | − | 0.832163i | \(-0.312898\pi\) |
−0.443409 | + | 0.896320i | \(0.646231\pi\) | |||||||
\(578\) | −14.7127 | − | 8.49437i | −0.611967 | − | 0.353319i | ||||
\(579\) | −13.3190 | − | 23.0692i | −0.553520 | − | 0.958724i | ||||
\(580\) | −13.6795 | −0.568008 | ||||||||
\(581\) | −1.99521 | − | 31.8604i | −0.0827753 | − | 1.32179i | ||||
\(582\) | 15.7498i | 0.652849i | ||||||||
\(583\) | −0.434445 | − | 2.03513i | −0.0179929 | − | 0.0842865i | ||||
\(584\) | −0.108260 | − | 0.0625042i | −0.00447985 | − | 0.00258644i | ||||
\(585\) | −9.87308 | − | 5.70022i | −0.408201 | − | 0.235675i | ||||
\(586\) | −12.2237 | + | 7.05737i | −0.504957 | + | 0.291537i | ||||
\(587\) | − | 46.9255i | − | 1.93682i | −0.249356 | − | 0.968412i | \(-0.580219\pi\) | ||
0.249356 | − | 0.968412i | \(-0.419781\pi\) | |||||||
\(588\) | 5.57816 | − | 4.22896i | 0.230040 | − | 0.174399i | ||||
\(589\) | 5.30877i | 0.218744i | ||||||||
\(590\) | −19.2819 | + | 11.1324i | −0.793823 | + | 0.458314i | ||||
\(591\) | −5.88818 | + | 10.1986i | −0.242207 | + | 0.419515i | ||||
\(592\) | −2.26092 | + | 3.91603i | −0.0929233 | + | 0.160948i | ||||
\(593\) | −2.57479 | − | 4.45967i | −0.105734 | − | 0.183137i | 0.808304 | − | 0.588766i | \(-0.200386\pi\) |
−0.914038 | + | 0.405629i | \(0.867053\pi\) | |||||||
\(594\) | 3.15519 | + | 1.02213i | 0.129459 | + | 0.0419384i | ||||
\(595\) | 0.500808 | − | 0.0313624i | 0.0205311 | − | 0.00128573i | ||||
\(596\) | 0.490157i | 0.0200776i | ||||||||
\(597\) | −10.7004 | − | 18.5336i | −0.437938 | − | 0.758531i | ||||
\(598\) | −43.9557 | − | 25.3779i | −1.79748 | − | 1.03778i | ||||
\(599\) | 17.5731 | − | 30.4375i | 0.718017 | − | 1.24364i | −0.243768 | − | 0.969834i | \(-0.578384\pi\) |
0.961784 | − | 0.273808i | \(-0.0882832\pi\) | |||||||
\(600\) | 0.902194 | + | 1.56265i | 0.0368319 | + | 0.0637948i | ||||
\(601\) | −42.8385 | −1.74742 | −0.873710 | − | 0.486447i | \(-0.838293\pi\) | ||||
−0.873710 | + | 0.486447i | \(0.838293\pi\) | |||||||
\(602\) | 15.1583 | − | 10.0648i | 0.617806 | − | 0.410211i | ||||
\(603\) | −10.8722 | −0.442749 | ||||||||
\(604\) | 2.92130 | − | 1.68661i | 0.118866 | − | 0.0686273i | ||||
\(605\) | −8.02950 | − | 17.9498i | −0.326446 | − | 0.729764i | ||||
\(606\) | −3.78650 | + | 6.55841i | −0.153816 | + | 0.266417i | ||||
\(607\) | 8.33275 | + | 14.4328i | 0.338216 | + | 0.585807i | 0.984097 | − | 0.177631i | \(-0.0568432\pi\) |
−0.645881 | + | 0.763438i | \(0.723510\pi\) | |||||||
\(608\) | 4.15162i | 0.168371i | ||||||||
\(609\) | 18.1320 | + | 9.00737i | 0.734747 | + | 0.364997i | ||||
\(610\) | 17.7873 | 0.720187 | ||||||||
\(611\) | −54.5783 | + | 31.5108i | −2.20800 | + | 1.27479i | ||||
\(612\) | −0.0530476 | + | 0.0918811i | −0.00214432 | + | 0.00371407i | ||||
\(613\) | 10.3018 | + | 5.94776i | 0.416087 | + | 0.240228i | 0.693402 | − | 0.720551i | \(-0.256111\pi\) |
−0.277315 | + | 0.960779i | \(0.589445\pi\) | |||||||
\(614\) | 18.2518 | − | 10.5377i | 0.736582 | − | 0.425266i | ||||
\(615\) | 0.0574512 | 0.00231666 | ||||||||
\(616\) | 6.13584 | − | 6.27307i | 0.247220 | − | 0.252749i | ||||
\(617\) | −0.0716192 | −0.00288328 | −0.00144164 | − | 0.999999i | \(-0.500459\pi\) | ||||
−0.00144164 | + | 0.999999i | \(0.500459\pi\) | |||||||
\(618\) | −4.53550 | + | 2.61857i | −0.182445 | + | 0.105335i | ||||
\(619\) | 25.3042 | + | 14.6094i | 1.01706 | + | 0.587200i | 0.913251 | − | 0.407397i | \(-0.133563\pi\) |
0.103809 | + | 0.994597i | \(0.466897\pi\) | |||||||
\(620\) | 1.14294 | − | 1.97963i | 0.0459015 | − | 0.0795037i | ||||
\(621\) | −6.89240 | + | 3.97933i | −0.276583 | + | 0.159685i | ||||
\(622\) | 13.9495 | 0.559324 | ||||||||
\(623\) | 7.84448 | + | 11.8143i | 0.314283 | + | 0.473331i | ||||
\(624\) | − | 6.37742i | − | 0.255301i | ||||||
\(625\) | 6.36112 | + | 11.0178i | 0.254445 | + | 0.440711i | ||||
\(626\) | −1.99203 | + | 3.45030i | −0.0796177 | + | 0.137902i | ||||
\(627\) | −9.22248 | − | 10.2246i | −0.368310 | − | 0.408330i | ||||
\(628\) | 3.51865 | − | 2.03150i | 0.140410 | − | 0.0810655i | ||||
\(629\) | 0.479746 | 0.0191287 | ||||||||
\(630\) | 0.295606 | + | 4.72037i | 0.0117772 | + | 0.188064i | ||||
\(631\) | −43.3663 | −1.72638 | −0.863192 | − | 0.504876i | \(-0.831538\pi\) | ||||
−0.863192 | + | 0.504876i | \(0.831538\pi\) | |||||||
\(632\) | 5.08457 | + | 8.80673i | 0.202253 | + | 0.350313i | ||||
\(633\) | −12.6327 | + | 21.8805i | −0.502106 | + | 0.869672i | ||||
\(634\) | 10.6509 | + | 6.14927i | 0.422999 | + | 0.244219i | ||||
\(635\) | 2.84610 | + | 4.92958i | 0.112944 | + | 0.195624i | ||||
\(636\) | 0.627441i | 0.0248796i | ||||||||
\(637\) | 44.2932 | − | 5.56943i | 1.75496 | − | 0.220669i | ||||
\(638\) | 24.1445 | + | 7.82163i | 0.955889 | + | 0.309661i | ||||
\(639\) | −4.21392 | − | 7.29873i | −0.166700 | − | 0.288733i | ||||
\(640\) | 0.893814 | − | 1.54813i | 0.0353311 | − | 0.0611952i | ||||
\(641\) | 2.72745 | − | 4.72408i | 0.107728 | − | 0.186590i | −0.807122 | − | 0.590385i | \(-0.798976\pi\) |
0.914849 | + | 0.403795i | \(0.132309\pi\) | |||||||
\(642\) | 4.12912 | − | 2.38395i | 0.162963 | − | 0.0940869i | ||||
\(643\) | 4.26488i | 0.168190i | 0.996458 | + | 0.0840952i | \(0.0268000\pi\) | ||||
−0.996458 | + | 0.0840952i | \(0.973200\pi\) | |||||||
\(644\) | 1.31606 | + | 21.0155i | 0.0518601 | + | 0.828126i | ||||
\(645\) | 12.2939i | 0.484073i | ||||||||
\(646\) | 0.381456 | − | 0.220234i | 0.0150082 | − | 0.00866497i | ||||
\(647\) | 20.5525 | + | 11.8660i | 0.808004 | + | 0.466501i | 0.846262 | − | 0.532767i | \(-0.178848\pi\) |
−0.0382582 | + | 0.999268i | \(0.512181\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 40.3982 | − | 8.62390i | 1.58577 | − | 0.338518i | ||||
\(650\) | 11.5073i | 0.451355i | ||||||||
\(651\) | −2.81846 | + | 1.87140i | −0.110464 | + | 0.0733461i | ||||
\(652\) | −20.7414 | −0.812297 | ||||||||
\(653\) | −16.8093 | − | 29.1145i | −0.657797 | − | 1.13934i | −0.981185 | − | 0.193071i | \(-0.938155\pi\) |
0.323388 | − | 0.946266i | \(-0.395178\pi\) | |||||||
\(654\) | 7.36585 | + | 4.25268i | 0.288028 | + | 0.166293i | ||||
\(655\) | −1.68158 | − | 0.970859i | −0.0657047 | − | 0.0379346i | ||||
\(656\) | 0.0160691 | + | 0.0278326i | 0.000627394 | + | 0.00108668i | ||||
\(657\) | −0.125008 | −0.00487704 | ||||||||
\(658\) | 23.4153 | + | 11.6319i | 0.912822 | + | 0.453459i | ||||
\(659\) | − | 28.9405i | − | 1.12736i | −0.825993 | − | 0.563681i | \(-0.809385\pi\) | ||
0.825993 | − | 0.563681i | \(-0.190615\pi\) | |||||||
\(660\) | 1.23777 | + | 5.79825i | 0.0481800 | + | 0.225696i | ||||
\(661\) | −0.518650 | − | 0.299443i | −0.0201732 | − | 0.0116470i | 0.489880 | − | 0.871790i | \(-0.337041\pi\) |
−0.510053 | + | 0.860143i | \(0.670374\pi\) | |||||||
\(662\) | −26.8582 | − | 15.5066i | −1.04387 | − | 0.602681i | ||||
\(663\) | −0.585964 | + | 0.338307i | −0.0227570 | + | 0.0131387i | ||||
\(664\) | 12.0657i | 0.468240i | ||||||||
\(665\) | 8.73578 | − | 17.5853i | 0.338759 | − | 0.681929i | ||||
\(666\) | 4.52184i | 0.175218i | ||||||||
\(667\) | −52.7427 | + | 30.4510i | −2.04221 | + | 1.17907i | ||||
\(668\) | 1.71435 | − | 2.96934i | 0.0663302 | − | 0.114887i | ||||
\(669\) | −4.90067 | + | 8.48820i | −0.189471 | + | 0.328173i | ||||
\(670\) | −9.71770 | − | 16.8315i | −0.375427 | − | 0.650259i | ||||
\(671\) | −31.3949 | − | 10.1704i | −1.21199 | − | 0.392625i | ||||
\(672\) | −2.20413 | + | 1.46350i | −0.0850260 | + | 0.0564556i | ||||
\(673\) | 36.3353i | 1.40062i | 0.713837 | + | 0.700312i | \(0.246956\pi\) | ||||
−0.713837 | + | 0.700312i | \(0.753044\pi\) | |||||||
\(674\) | −6.80807 | − | 11.7919i | −0.262237 | − | 0.454208i | ||||
\(675\) | 1.56265 | + | 0.902194i | 0.0601463 | + | 0.0347255i | ||||
\(676\) | 13.8357 | − | 23.9642i | 0.532144 | − | 0.921700i | ||||
\(677\) | −9.99570 | − | 17.3131i | −0.384166 | − | 0.665395i | 0.607487 | − | 0.794329i | \(-0.292178\pi\) |
−0.991653 | + | 0.128935i | \(0.958844\pi\) | |||||||
\(678\) | 10.3003 | 0.395580 | ||||||||
\(679\) | 41.5885 | − | 2.60442i | 1.59602 | − | 0.0999484i | ||||
\(680\) | −0.189659 | −0.00727307 | ||||||||
\(681\) | −20.1704 | + | 11.6454i | −0.772931 | + | 0.446252i | ||||
\(682\) | −3.14922 | + | 2.84057i | −0.120590 | + | 0.108771i | ||||
\(683\) | 11.0162 | − | 19.0807i | 0.421524 | − | 0.730102i | −0.574564 | − | 0.818459i | \(-0.694829\pi\) |
0.996089 | + | 0.0883577i | \(0.0281619\pi\) | |||||||
\(684\) | 2.07581 | + | 3.59541i | 0.0793707 | + | 0.137474i | ||||
\(685\) | − | 13.5537i | − | 0.517861i | ||||||
\(686\) | −12.0893 | − | 14.0303i | −0.461572 | − | 0.535678i | ||||
\(687\) | 6.53063 | 0.249159 | ||||||||
\(688\) | −5.95586 | + | 3.43862i | −0.227065 | + | 0.131096i | ||||
\(689\) | −2.00073 | + | 3.46536i | −0.0762216 | + | 0.132020i | ||||
\(690\) | −12.3210 | − | 7.11356i | −0.469054 | − | 0.270809i | ||||
\(691\) | 9.88161 | − | 5.70515i | 0.375914 | − | 0.217034i | −0.300125 | − | 0.953900i | \(-0.597028\pi\) |
0.676039 | + | 0.736866i | \(0.263695\pi\) | |||||||
\(692\) | 21.1524 | 0.804094 | ||||||||
\(693\) | 2.17726 | − | 8.50056i | 0.0827073 | − | 0.322910i | ||||
\(694\) | −27.9100 | −1.05945 | ||||||||
\(695\) | 2.08445 | − | 1.20346i | 0.0790676 | − | 0.0456497i | ||||
\(696\) | −6.62708 | − | 3.82615i | −0.251199 | − | 0.145030i | ||||
\(697\) | 0.00170486 | − | 0.00295290i | 6.45761e−5 | − | 0.000111849i | ||||
\(698\) | −24.0882 | + | 13.9073i | −0.911752 | + | 0.526400i | ||||
\(699\) | 10.8677 | 0.411052 | ||||||||
\(700\) | 3.97710 | − | 2.64072i | 0.150320 | − | 0.0998098i | ||||
\(701\) | − | 1.92874i | − | 0.0728474i | −0.999336 | − | 0.0364237i | \(-0.988403\pi\) | ||
0.999336 | − | 0.0364237i | \(-0.0115966\pi\) | |||||||
\(702\) | −3.18871 | − | 5.52301i | −0.120350 | − | 0.208452i | ||||
\(703\) | 9.38650 | − | 16.2579i | 0.354018 | − | 0.613178i | ||||
\(704\) | −2.46279 | + | 2.22141i | −0.0928198 | + | 0.0837227i | ||||
\(705\) | −15.2986 | + | 8.83265i | −0.576179 | + | 0.332657i | ||||
\(706\) | 21.5149 | 0.809725 | ||||||||
\(707\) | 17.9441 | + | 8.91403i | 0.674859 | + | 0.335247i | ||||
\(708\) | −12.4549 | −0.468086 | ||||||||
\(709\) | −9.50162 | − | 16.4573i | −0.356841 | − | 0.618066i | 0.630590 | − | 0.776116i | \(-0.282813\pi\) |
−0.987431 | + | 0.158050i | \(0.949479\pi\) | |||||||
\(710\) | 7.53293 | − | 13.0474i | 0.282706 | − | 0.489661i | ||||
\(711\) | 8.80673 | + | 5.08457i | 0.330278 | + | 0.190686i | ||||
\(712\) | −2.68005 | − | 4.64198i | −0.100439 | − | 0.173965i | ||||
\(713\) | − | 10.1769i | − | 0.381128i | ||||||
\(714\) | 0.251391 | + | 0.124883i | 0.00940808 | + | 0.00467361i | ||||
\(715\) | −11.6527 | + | 35.9706i | −0.435787 | + | 1.34523i | ||||
\(716\) | −7.04330 | − | 12.1994i | −0.263220 | − | 0.455911i | ||||
\(717\) | 3.84574 | − | 6.66102i | 0.143622 | − | 0.248760i | ||||
\(718\) | 10.4471 | − | 18.0949i | 0.389883 | − | 0.675297i | ||||
\(719\) | 17.8998 | − | 10.3345i | 0.667551 | − | 0.385411i | −0.127597 | − | 0.991826i | \(-0.540726\pi\) |
0.795148 | + | 0.606415i | \(0.207393\pi\) | |||||||
\(720\) | − | 1.78763i | − | 0.0666209i | ||||||
\(721\) | 7.66455 | + | 11.5433i | 0.285443 | + | 0.429896i | ||||
\(722\) | 1.76402i | 0.0656500i | ||||||||
\(723\) | 19.7571 | − | 11.4067i | 0.734773 | − | 0.424221i | ||||
\(724\) | −10.7889 | − | 6.22897i | −0.400966 | − | 0.231498i | ||||
\(725\) | 11.9578 | + | 6.90386i | 0.444103 | + | 0.256403i | ||||
\(726\) | 1.13064 | − | 10.9417i | 0.0419619 | − | 0.406086i | ||||
\(727\) | 1.72185i | 0.0638600i | 0.999490 | + | 0.0319300i | \(0.0101654\pi\) | ||||
−0.999490 | + | 0.0319300i | \(0.989835\pi\) | |||||||
\(728\) | −16.8401 | + | 1.05458i | −0.624135 | + | 0.0390855i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.111734 | − | 0.193529i | −0.00413547 | − | 0.00716284i | ||||
\(731\) | 0.631887 | + | 0.364820i | 0.0233712 | + | 0.0134934i | ||||
\(732\) | 8.61716 | + | 4.97512i | 0.318499 | + | 0.183886i | ||||
\(733\) | −0.597125 | − | 1.03425i | −0.0220553 | − | 0.0382009i | 0.854787 | − | 0.518979i | \(-0.173688\pi\) |
−0.876842 | + | 0.480778i | \(0.840354\pi\) | |||||||
\(734\) | −5.34315 | −0.197219 | ||||||||
\(735\) | 12.4156 | − | 1.56114i | 0.457957 | − | 0.0575836i | ||||
\(736\) | − | 7.95866i | − | 0.293360i | ||||||
\(737\) | 7.52798 | + | 35.2644i | 0.277297 | + | 1.29898i | ||||
\(738\) | 0.0278326 | + | 0.0160691i | 0.00102453 | + | 0.000591513i | ||||
\(739\) | −10.7713 | − | 6.21881i | −0.396228 | − | 0.228763i | 0.288627 | − | 0.957442i | \(-0.406801\pi\) |
−0.684855 | + | 0.728679i | \(0.740135\pi\) | |||||||
\(740\) | −7.00040 | + | 4.04169i | −0.257340 | + | 0.148575i | ||||
\(741\) | 26.4766i | 0.972644i | ||||||||
\(742\) | 1.65681 | − | 0.103755i | 0.0608233 | − | 0.00380897i | ||||
\(743\) | 19.1754i | 0.703479i | 0.936098 | + | 0.351739i | \(0.114410\pi\) | ||||
−0.936098 | + | 0.351739i | \(0.885590\pi\) | |||||||
\(744\) | 1.10740 | − | 0.639360i | 0.0405994 | − | 0.0234401i | ||||
\(745\) | −0.438109 | + | 0.758827i | −0.0160511 | + | 0.0278013i | ||||
\(746\) | 12.6868 | − | 21.9741i | 0.464495 | − | 0.804529i | ||||
\(747\) | 6.03285 | + | 10.4492i | 0.220730 | + | 0.382316i | ||||
\(748\) | 0.334751 | + | 0.108443i | 0.0122397 | + | 0.00396506i | ||||
\(749\) | −6.97780 | − | 10.5090i | −0.254963 | − | 0.383992i | ||||
\(750\) | 12.1637i | 0.444156i | ||||||||
\(751\) | −22.9870 | − | 39.8146i | −0.838807 | − | 1.45286i | −0.890893 | − | 0.454213i | \(-0.849921\pi\) |
0.0520865 | − | 0.998643i | \(-0.483413\pi\) | |||||||
\(752\) | −8.55805 | − | 4.94099i | −0.312080 | − | 0.180179i | ||||
\(753\) | −9.05557 | + | 15.6847i | −0.330003 | + | 0.571583i | ||||
\(754\) | −24.4009 | − | 42.2637i | −0.888630 | − | 1.53915i | ||||
\(755\) | 6.03007 | 0.219457 | ||||||||
\(756\) | −1.17708 | + | 2.36949i | −0.0428100 | + | 0.0861775i | ||||
\(757\) | 32.1348 | 1.16796 | 0.583979 | − | 0.811768i | \(-0.301495\pi\) | ||||
0.583979 | + | 0.811768i | \(0.301495\pi\) | |||||||
\(758\) | −19.7048 | + | 11.3766i | −0.715712 | + | 0.413217i | ||||
\(759\) | 17.6795 | + | 19.6005i | 0.641725 | + | 0.711453i | ||||
\(760\) | −3.71078 | + | 6.42726i | −0.134604 | + | 0.233141i | ||||
\(761\) | 10.2499 | + | 17.7533i | 0.371558 | + | 0.643558i | 0.989805 | − | 0.142426i | \(-0.0454903\pi\) |
−0.618247 | + | 0.785984i | \(0.712157\pi\) | |||||||
\(762\) | 3.18422i | 0.115352i | ||||||||
\(763\) | 10.0115 | − | 20.1533i | 0.362440 | − | 0.729600i | ||||
\(764\) | 27.2293 | 0.985122 | ||||||||
\(765\) | −0.164249 | + | 0.0948293i | −0.00593844 | + | 0.00342856i | ||||
\(766\) | 8.27402 | − | 14.3310i | 0.298953 | − | 0.517801i | ||||
\(767\) | −68.7888 | − | 39.7152i | −2.48382 | − | 1.43403i | ||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 14.3312 | 0.516796 | 0.258398 | − | 0.966039i | \(-0.416805\pi\) | ||||
0.258398 | + | 0.966039i | \(0.416805\pi\) | |||||||
\(770\) | 15.1060 | − | 4.22723i | 0.544384 | − | 0.152339i | ||||
\(771\) | 3.94247 | 0.141984 | ||||||||
\(772\) | 23.0692 | − | 13.3190i | 0.830280 | − | 0.479362i | ||||
\(773\) | −25.6118 | − | 14.7870i | −0.921193 | − | 0.531851i | −0.0371778 | − | 0.999309i | \(-0.511837\pi\) |
−0.884016 | + | 0.467457i | \(0.845170\pi\) | |||||||
\(774\) | −3.43862 | + | 5.95586i | −0.123598 | + | 0.214079i | ||||
\(775\) | −1.99819 | + | 1.15365i | −0.0717771 | + | 0.0414405i | ||||
\(776\) | −15.7498 | −0.565384 | ||||||||
\(777\) | 11.9403 | − | 0.747742i | 0.428355 | − | 0.0268251i | ||||
\(778\) | − | 7.39812i | − | 0.265235i | ||||||
\(779\) | −0.0667130 | − | 0.115550i | −0.00239024 | − | 0.00414002i | ||||
\(780\) | 5.70022 | − | 9.87308i | 0.204101 | − | 0.353513i | ||||
\(781\) | −20.7560 | + | 18.7217i | −0.742708 | + | 0.669917i | ||||
\(782\) | −0.731251 | + | 0.422188i | −0.0261495 | + | 0.0150974i | ||||
\(783\) | −7.65230 | −0.273471 | ||||||||
\(784\) | 4.22896 | + | 5.57816i | 0.151034 | + | 0.199220i | ||||
\(785\) | 7.26311 | 0.259232 | ||||||||
\(786\) | −0.543099 | − | 0.940675i | −0.0193717 | − | 0.0335528i | ||||
\(787\) | −13.3487 | + | 23.1207i | −0.475831 | + | 0.824164i | −0.999617 | − | 0.0276865i | \(-0.991186\pi\) |
0.523786 | + | 0.851850i | \(0.324519\pi\) | |||||||
\(788\) | −10.1986 | − | 5.88818i | −0.363311 | − | 0.209758i | ||||
\(789\) | −1.03357 | − | 1.79020i | −0.0367962 | − | 0.0637329i | ||||
\(790\) | 18.1786i | 0.646767i | ||||||||
\(791\) | −1.70328 | − | 27.1987i | −0.0605616 | − | 0.967074i | ||||
\(792\) | −1.02213 | + | 3.15519i | −0.0363198 | + | 0.112115i | ||||
\(793\) | 31.7284 | + | 54.9552i | 1.12671 | + | 1.95152i | ||||
\(794\) | −1.93369 | + | 3.34925i | −0.0686241 | + | 0.118860i | ||||
\(795\) | −0.560815 | + | 0.971360i | −0.0198901 | + | 0.0344506i | ||||
\(796\) | 18.5336 | − | 10.7004i | 0.656907 | − | 0.379265i | ||||
\(797\) | 47.2556i | 1.67388i | 0.547294 | + | 0.836940i | \(0.315658\pi\) | ||||
−0.547294 | + | 0.836940i | \(0.684342\pi\) | |||||||
\(798\) | 9.15071 | − | 6.07589i | 0.323931 | − | 0.215084i | ||||
\(799\) | 1.04843i | 0.0370908i | ||||||||
\(800\) | −1.56265 | + | 0.902194i | −0.0552479 | + | 0.0318974i | ||||
\(801\) | −4.64198 | − | 2.68005i | −0.164016 | − | 0.0946948i | ||||
\(802\) | 2.71379 | + | 1.56681i | 0.0958272 | + | 0.0553259i | ||||
\(803\) | 0.0865568 | + | 0.405470i | 0.00305452 | + | 0.0143087i | ||||
\(804\) | − | 10.8722i | − | 0.383432i | ||||||
\(805\) | −16.7465 | + | 33.7110i | −0.590236 | + | 1.18816i | ||||
\(806\) | 8.15494 | 0.287245 | ||||||||
\(807\) | −1.40240 | − | 2.42902i | −0.0493667 | − | 0.0855057i | ||||
\(808\) | −6.55841 | − | 3.78650i | −0.230724 | − | 0.133209i | ||||
\(809\) | 18.2536 | + | 10.5387i | 0.641763 | + | 0.370522i | 0.785293 | − | 0.619124i | \(-0.212512\pi\) |
−0.143530 | + | 0.989646i | \(0.545845\pi\) | |||||||
\(810\) | −0.893814 | − | 1.54813i | −0.0314054 | − | 0.0543958i | ||||
\(811\) | −38.7457 | −1.36055 | −0.680273 | − | 0.732959i | \(-0.738139\pi\) | ||||
−0.680273 | + | 0.732959i | \(0.738139\pi\) | |||||||
\(812\) | −9.00737 | + | 18.1320i | −0.316097 | + | 0.636310i | ||||
\(813\) | 9.28092i | 0.325496i | ||||||||
\(814\) | 14.6668 | − | 3.13096i | 0.514071 | − | 0.109740i | ||||
\(815\) | −32.1104 | − | 18.5390i | −1.12478 | − | 0.649392i | ||||
\(816\) | −0.0918811 | − | 0.0530476i | −0.00321648 | − | 0.00185704i | ||||
\(817\) | 24.7265 | − | 14.2758i | 0.865070 | − | 0.499448i | ||||
\(818\) | − | 20.1022i | − | 0.702858i | ||||||
\(819\) | −14.0566 | + | 9.33333i | −0.491179 | + | 0.326133i | ||||
\(820\) | 0.0574512i | 0.00200628i | ||||||||
\(821\) | 37.0933 | − | 21.4158i | 1.29456 | − | 0.747417i | 0.315105 | − | 0.949057i | \(-0.397960\pi\) |
0.979460 | + | 0.201639i | \(0.0646269\pi\) | |||||||
\(822\) | 3.79098 | − | 6.56617i | 0.132226 | − | 0.229022i | ||||
\(823\) | −16.9309 | + | 29.3253i | −0.590176 | + | 1.02221i | 0.404033 | + | 0.914744i | \(0.367608\pi\) |
−0.994208 | + | 0.107469i | \(0.965725\pi\) | |||||||
\(824\) | −2.61857 | − | 4.53550i | −0.0912224 | − | 0.158002i | ||||
\(825\) | 1.84432 | − | 5.69320i | 0.0642109 | − | 0.198212i | ||||
\(826\) | 2.05958 | + | 32.8883i | 0.0716619 | + | 1.14433i | ||||
\(827\) | 15.2572i | 0.530544i | 0.964174 | + | 0.265272i | \(0.0854618\pi\) | ||||
−0.964174 | + | 0.265272i | \(0.914538\pi\) | |||||||
\(828\) | −3.97933 | − | 6.89240i | −0.138291 | − | 0.239528i | ||||
\(829\) | −14.9375 | − | 8.62414i | −0.518799 | − | 0.299529i | 0.217644 | − | 0.976028i | \(-0.430163\pi\) |
−0.736443 | + | 0.676499i | \(0.763496\pi\) | |||||||
\(830\) | −10.7845 | + | 18.6793i | −0.374335 | + | 0.648367i | ||||
\(831\) | 2.61548 | + | 4.53015i | 0.0907300 | + | 0.157149i | ||||
\(832\) | 6.37742 | 0.221097 | ||||||||
\(833\) | 0.288192 | − | 0.684469i | 0.00998525 | − | 0.0237155i | ||||
\(834\) | 1.34643 | 0.0466230 | ||||||||
\(835\) | 5.30808 | − | 3.06462i | 0.183694 | − | 0.106056i | ||||
\(836\) | 10.2246 | − | 9.22248i | 0.353624 | − | 0.318966i | ||||
\(837\) | 0.639360 | − | 1.10740i | 0.0220995 | − | 0.0382775i | ||||
\(838\) | 1.31518 | + | 2.27795i | 0.0454320 | + | 0.0786906i | ||||
\(839\) | − | 9.80607i | − | 0.338543i | −0.985569 | − | 0.169272i | \(-0.945859\pi\) | ||
0.985569 | − | 0.169272i | \(-0.0541415\pi\) | |||||||
\(840\) | −4.72037 | + | 0.295606i | −0.162868 | + | 0.0101994i | ||||
\(841\) | −29.5576 | −1.01923 | ||||||||
\(842\) | −21.5841 | + | 12.4616i | −0.743838 | + | 0.429455i | ||||
\(843\) | −3.43641 | + | 5.95203i | −0.118356 | + | 0.204999i | ||||
\(844\) | −21.8805 | − | 12.6327i | −0.753158 | − | 0.434836i | ||||
\(845\) | 42.8390 | − | 24.7331i | 1.47371 | − | 0.850846i | ||||
\(846\) | −9.88198 | −0.339750 | ||||||||
\(847\) | −29.0795 | − | 1.17618i | −0.999183 | − | 0.0404141i | ||||
\(848\) | −0.627441 | −0.0215464 | ||||||||
\(849\) | 10.4017 | − | 6.00542i | 0.356985 | − | 0.206105i | ||||
\(850\) | 0.165789 | + | 0.0957185i | 0.00568652 | + | 0.00328312i | ||||
\(851\) | −17.9939 | + | 31.1664i | −0.616823 | + | 1.06837i | ||||
\(852\) | 7.29873 | − | 4.21392i | 0.250050 | − | 0.144367i | ||||
\(853\) | 58.0237 | 1.98669 | 0.993346 | − | 0.115168i | \(-0.0367407\pi\) | ||||
0.993346 | + | 0.115168i | \(0.0367407\pi\) | |||||||
\(854\) | 11.7122 | − | 23.5770i | 0.400785 | − | 0.806788i | ||||
\(855\) | 7.42156i | 0.253812i | ||||||||
\(856\) | 2.38395 | + | 4.12912i | 0.0814817 | + | 0.141130i | ||||
\(857\) | −20.5434 | + | 35.5821i | −0.701748 | + | 1.21546i | 0.266105 | + | 0.963944i | \(0.414263\pi\) |
−0.967853 | + | 0.251518i | \(0.919070\pi\) | |||||||
\(858\) | −15.7062 | + | 14.1669i | −0.536202 | + | 0.483650i | ||||
\(859\) | −23.0028 | + | 13.2807i | −0.784845 | + | 0.453130i | −0.838144 | − | 0.545448i | \(-0.816359\pi\) |
0.0532999 | + | 0.998579i | \(0.483026\pi\) | |||||||
\(860\) | −12.2939 | −0.419219 | ||||||||
\(861\) | 0.0378294 | − | 0.0761513i | 0.00128922 | − | 0.00259523i | ||||
\(862\) | −13.6456 | −0.464772 | ||||||||
\(863\) | −4.54395 | − | 7.87036i | −0.154678 | − | 0.267910i | 0.778264 | − | 0.627938i | \(-0.216101\pi\) |
−0.932942 | + | 0.360027i | \(0.882767\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 32.7467 | + | 18.9063i | 1.11342 | + | 0.642834i | ||||
\(866\) | 5.20003 | + | 9.00671i | 0.176704 | + | 0.306061i | ||||
\(867\) | − | 16.9887i | − | 0.576968i | ||||||
\(868\) | −1.87140 | − | 2.81846i | −0.0635196 | − | 0.0956649i | ||||
\(869\) | 10.3942 | − | 32.0856i | 0.352598 | − | 1.08843i | ||||
\(870\) | −6.83973 | − | 11.8468i | −0.231888 | − | 0.401643i | ||||
\(871\) | 34.6682 | − | 60.0471i | 1.17469 | − | 2.03462i | ||||
\(872\) | −4.25268 | + | 7.36585i | −0.144014 | + | 0.249439i | ||||
\(873\) | −13.6397 | + | 7.87488i | −0.461634 | + | 0.266524i | ||||
\(874\) | 33.0414i | 1.11764i | ||||||||
\(875\) | 32.1192 | − | 2.01142i | 1.08583 | − | 0.0679984i | ||||
\(876\) | − | 0.125008i | − | 0.00422364i | ||||||
\(877\) | −3.95476 | + | 2.28328i | −0.133543 | + | 0.0771009i | −0.565283 | − | 0.824897i | \(-0.691233\pi\) |
0.431740 | + | 0.901998i | \(0.357900\pi\) | |||||||
\(878\) | 20.1991 | + | 11.6619i | 0.681686 | + | 0.393572i | ||||
\(879\) | −12.2237 | − | 7.05737i | −0.412296 | − | 0.238039i | ||||
\(880\) | −5.79825 | + | 1.23777i | −0.195459 | + | 0.0417251i | ||||
\(881\) | − | 35.4288i | − | 1.19363i | −0.802380 | − | 0.596813i | \(-0.796433\pi\) | ||
0.802380 | − | 0.596813i | \(-0.203567\pi\) | |||||||
\(882\) | 6.45147 | + | 2.71635i | 0.217232 | + | 0.0914643i | ||||
\(883\) | 25.2987 | 0.851368 | 0.425684 | − | 0.904872i | \(-0.360033\pi\) | ||||
0.425684 | + | 0.904872i | \(0.360033\pi\) | |||||||
\(884\) | −0.338307 | − | 0.585964i | −0.0113785 | − | 0.0197081i | ||||
\(885\) | −19.2819 | − | 11.1324i | −0.648153 | − | 0.374212i | ||||
\(886\) | 8.51694 | + | 4.91726i | 0.286132 | + | 0.165198i | ||||
\(887\) | 22.4831 | + | 38.9419i | 0.754909 | + | 1.30754i | 0.945420 | + | 0.325855i | \(0.105652\pi\) |
−0.190511 | + | 0.981685i | \(0.561014\pi\) | |||||||
\(888\) | −4.52184 | −0.151743 | ||||||||
\(889\) | 8.40817 | − | 0.526549i | 0.282001 | − | 0.0176599i | ||||
\(890\) | − | 9.58185i | − | 0.321184i | ||||||
\(891\) | 0.692408 | + | 3.24354i | 0.0231965 | + | 0.108663i | ||||
\(892\) | −8.48820 | − | 4.90067i | −0.284206 | − | 0.164086i | ||||
\(893\) | 35.5298 | + | 20.5131i | 1.18896 | + | 0.686446i | ||||
\(894\) | −0.424489 | + | 0.245079i | −0.0141970 | + | 0.00819666i | ||||
\(895\) | − | 25.1816i | − | 0.841727i | ||||||
\(896\) | −1.46350 | − | 2.20413i | −0.0488920 | − | 0.0736347i | ||||
\(897\) | − | 50.7557i | − | 1.69468i | ||||||
\(898\) | −8.02133 | + | 4.63112i | −0.267675 | + | 0.154542i | ||||
\(899\) | 4.89257 | − | 8.47419i | 0.163176 | − | 0.282630i | ||||
\(900\) | −0.902194 | + | 1.56265i | −0.0300731 | + | 0.0520882i | ||||
\(901\) | 0.0332842 | + | 0.0576499i | 0.00110886 | + | 0.00192060i | ||||
\(902\) | 0.0328494 | − | 0.101403i | 0.00109377 | − | 0.00337633i | ||||
\(903\) | 16.2955 | + | 8.09506i | 0.542281 | + | 0.269387i | ||||
\(904\) | 10.3003i | 0.342582i | ||||||||
\(905\) | −11.1351 | − | 19.2865i | −0.370143 | − | 0.641106i | ||||
\(906\) | 2.92130 | + | 1.68661i | 0.0970537 | + | 0.0560340i | ||||
\(907\) | 8.63064 | − | 14.9487i | 0.286576 | − | 0.496364i | −0.686414 | − | 0.727211i | \(-0.740816\pi\) |
0.972990 | + | 0.230847i | \(0.0741497\pi\) | |||||||
\(908\) | −11.6454 | − | 20.1704i | −0.386465 | − | 0.669377i | ||||
\(909\) | −7.57300 | −0.251180 | ||||||||
\(910\) | −27.0132 | − | 13.4193i | −0.895480 | − | 0.444844i | ||||
\(911\) | −18.9606 | −0.628194 | −0.314097 | − | 0.949391i | \(-0.601702\pi\) | ||||
−0.314097 | + | 0.949391i | \(0.601702\pi\) | |||||||
\(912\) | −3.59541 | + | 2.07581i | −0.119056 | + | 0.0687370i | ||||
\(913\) | 29.7152 | − | 26.8029i | 0.983431 | − | 0.887047i | ||||
\(914\) | −1.27818 | + | 2.21387i | −0.0422783 | + | 0.0732282i | ||||
\(915\) | 8.89366 | + | 15.4043i | 0.294015 | + | 0.509249i | ||||
\(916\) | 6.53063i | 0.215778i | ||||||||
\(917\) | −2.39412 | + | 1.58965i | −0.0790608 | + | 0.0524948i | ||||
\(918\) | −0.106095 | −0.00350166 | ||||||||
\(919\) | −30.9373 | + | 17.8617i | −1.02053 | + | 0.589203i | −0.914257 | − | 0.405134i | \(-0.867225\pi\) |
−0.106272 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(920\) | 7.11356 | − | 12.3210i | 0.234527 | − | 0.406213i | ||||
\(921\) | 18.2518 | + | 10.5377i | 0.601417 | + | 0.347228i | ||||
\(922\) | 25.6168 | − | 14.7899i | 0.843645 | − | 0.487079i | ||||
\(923\) | 53.7479 | 1.76913 | ||||||||
\(924\) | 8.50056 | + | 2.17726i | 0.279648 | + | 0.0716266i | ||||
\(925\) | 8.15916 | 0.268272 | ||||||||
\(926\) | 8.00595 | − | 4.62224i | 0.263092 | − | 0.151896i | ||||
\(927\) | −4.53550 | − | 2.61857i | −0.148965 | − | 0.0860053i | ||||
\(928\) | 3.82615 | − | 6.62708i | 0.125599 | − | 0.217545i | ||||
\(929\) | 35.0844 | − | 20.2560i | 1.15108 | − | 0.664577i | 0.201930 | − | 0.979400i | \(-0.435279\pi\) |
0.949150 | + | 0.314823i | \(0.101945\pi\) | |||||||
\(930\) | 2.28588 | 0.0749568 | ||||||||
\(931\) | −17.5570 | − | 23.1584i | −0.575409 | − | 0.758987i | ||||
\(932\) | 10.8677i | 0.355982i | ||||||||
\(933\) | 6.97475 | + | 12.0806i | 0.228343 | + | 0.395502i | ||||
\(934\) | 5.82484 | − | 10.0889i | 0.190595 | − | 0.330119i | ||||
\(935\) | 0.421310 | + | 0.467089i | 0.0137783 | + | 0.0152754i | ||||
\(936\) | 5.52301 | − | 3.18871i | 0.180525 | − | 0.104226i | ||||
\(937\) | −36.2513 | −1.18428 | −0.592140 | − | 0.805835i | \(-0.701717\pi\) | ||||
−0.592140 | + | 0.805835i | \(0.701717\pi\) | |||||||
\(938\) | −28.7088 | + | 1.79785i | −0.937376 | + | 0.0587018i | ||||
\(939\) | −3.98407 | −0.130015 | ||||||||
\(940\) | −8.83265 | − | 15.2986i | −0.288089 | − | 0.498985i | ||||
\(941\) | 22.3898 | − | 38.7803i | 0.729887 | − | 1.26420i | −0.227044 | − | 0.973884i | \(-0.572906\pi\) |
0.956931 | − | 0.290316i | \(-0.0937605\pi\) | |||||||
\(942\) | 3.51865 | + | 2.03150i | 0.114644 | + | 0.0661897i | ||||
\(943\) | 0.127889 | + | 0.221510i | 0.00416463 | + | 0.00721336i | ||||
\(944\) | − | 12.4549i | − | 0.405374i | ||||||
\(945\) | −3.94016 | + | 2.61619i | −0.128173 | + | 0.0851046i | ||||
\(946\) | 21.6990 | + | 7.02941i | 0.705495 | + | 0.228546i | ||||
\(947\) | 7.35348 | + | 12.7366i | 0.238956 | + | 0.413884i | 0.960415 | − | 0.278573i | \(-0.0898615\pi\) |
−0.721459 | + | 0.692457i | \(0.756528\pi\) | |||||||
\(948\) | −5.08457 | + | 8.80673i | −0.165139 | + | 0.286029i | ||||
\(949\) | 0.398615 | − | 0.690422i | 0.0129396 | − | 0.0224120i | ||||
\(950\) | 6.48752 | − | 3.74557i | 0.210483 | − | 0.121522i | ||||
\(951\) | 12.2985i | 0.398808i | ||||||||
\(952\) | −0.124883 | + | 0.251391i | −0.00404747 | + | 0.00814764i | ||||
\(953\) | 23.4615i | 0.759991i | 0.924988 | + | 0.379996i | \(0.124074\pi\) | ||||
−0.924988 | + | 0.379996i | \(0.875926\pi\) | |||||||
\(954\) | −0.543380 | + | 0.313720i | −0.0175926 | + | 0.0101571i | ||||
\(955\) | 42.1546 | + | 24.3379i | 1.36409 | + | 0.787557i | ||||
\(956\) | 6.66102 | + | 3.84574i | 0.215433 | + | 0.124380i | ||||
\(957\) | 5.29851 | + | 24.8205i | 0.171277 | + | 0.802334i | ||||
\(958\) | 10.0552i | 0.324868i | ||||||||
\(959\) | −17.9654 | − | 8.92459i | −0.580133 | − | 0.288190i | ||||
\(960\) | 1.78763 | 0.0576954 | ||||||||
\(961\) | −14.6824 | − | 25.4307i | −0.473627 | − | 0.820346i | ||||
\(962\) | −24.9742 | − | 14.4188i | −0.805200 | − | 0.464882i | ||||
\(963\) | 4.12912 | + | 2.38395i | 0.133059 | + | 0.0768216i | ||||
\(964\) | 11.4067 | + | 19.7571i | 0.367387 | + | 0.636332i | ||||
\(965\) | 47.6189 | 1.53291 | ||||||||
\(966\) | −17.5419 | + | 11.6475i | −0.564402 | + | 0.374752i | ||||
\(967\) | 57.3317i | 1.84366i | 0.387589 | + | 0.921832i | \(0.373308\pi\) | ||||
−0.387589 | + | 0.921832i | \(0.626692\pi\) | |||||||
\(968\) | 10.9417 | + | 1.13064i | 0.351681 | + | 0.0363400i | ||||
\(969\) | 0.381456 | + | 0.220234i | 0.0122541 | + | 0.00707492i | ||||
\(970\) | −24.3827 | − | 14.0774i | −0.782881 | − | 0.451997i | ||||
\(971\) | −42.1712 | + | 24.3476i | −1.35334 | + | 0.781351i | −0.988716 | − | 0.149805i | \(-0.952136\pi\) |
−0.364623 | + | 0.931155i | \(0.618802\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −0.222649 | − | 3.55535i | −0.00713778 | − | 0.113979i | ||||
\(974\) | − | 17.3146i | − | 0.554797i | ||||||
\(975\) | −9.96565 | + | 5.75367i | −0.319156 | + | 0.184265i | ||||
\(976\) | −4.97512 | + | 8.61716i | −0.159250 | + | 0.275828i | ||||
\(977\) | −21.1278 | + | 36.5945i | −0.675939 | + | 1.17076i | 0.300255 | + | 0.953859i | \(0.402928\pi\) |
−0.976193 | + | 0.216902i | \(0.930405\pi\) | |||||||
\(978\) | −10.3707 | − | 17.9626i | −0.331619 | − | 0.574381i | ||||
\(979\) | −5.47871 | + | 16.9121i | −0.175100 | + | 0.540514i | ||||
\(980\) | 1.56114 | + | 12.4156i | 0.0498689 | + | 0.396603i | ||||
\(981\) | 8.50535i | 0.271555i | ||||||||
\(982\) | −4.22001 | − | 7.30927i | −0.134666 | − | 0.233248i | ||||
\(983\) | 20.4533 | + | 11.8087i | 0.652359 | + | 0.376639i | 0.789359 | − | 0.613931i | \(-0.210413\pi\) |
−0.137001 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(984\) | −0.0160691 | + | 0.0278326i | −0.000512265 | + | 0.000887270i | ||||
\(985\) | −10.5259 | − | 18.2313i | −0.335382 | − | 0.580899i | ||||
\(986\) | −0.811871 | −0.0258553 | ||||||||
\(987\) | 1.63411 | + | 26.0942i | 0.0520142 | + | 0.830586i | ||||
\(988\) | −26.4766 | −0.842334 | ||||||||
\(989\) | −47.4007 | + | 27.3668i | −1.50725 | + | 0.870213i | ||||
\(990\) | −4.40254 | + | 3.97106i | −0.139922 | + | 0.126209i | ||||
\(991\) | −13.4870 | + | 23.3602i | −0.428429 | + | 0.742060i | −0.996734 | − | 0.0807577i | \(-0.974266\pi\) |
0.568305 | + | 0.822818i | \(0.307599\pi\) | |||||||
\(992\) | 0.639360 | + | 1.10740i | 0.0202997 | + | 0.0351601i | ||||
\(993\) | − | 31.0132i | − | 0.984173i | ||||||
\(994\) | −12.3341 | − | 18.5760i | −0.391215 | − | 0.589196i | ||||
\(995\) | 38.2566 | 1.21282 | ||||||||
\(996\) | −10.4492 | + | 6.03285i | −0.331096 | + | 0.191158i | ||||
\(997\) | 11.1707 | − | 19.3483i | 0.353781 | − | 0.612766i | −0.633128 | − | 0.774047i | \(-0.718229\pi\) |
0.986909 | + | 0.161281i | \(0.0515626\pi\) | |||||||
\(998\) | 16.5168 | + | 9.53597i | 0.522830 | + | 0.301856i | ||||
\(999\) | −3.91603 | + | 2.26092i | −0.123898 | + | 0.0715324i |
(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 | 462.2.p.b.241.3 | yes | 16 | |
3.2 | odd | 2 | 1386.2.bk.b.703.6 | 16 | |||
7.3 | odd | 6 | 3234.2.e.a.2155.3 | 16 | |||
7.4 | even | 3 | 3234.2.e.b.2155.6 | 16 | |||
7.5 | odd | 6 | 462.2.p.a.439.7 | yes | 16 | ||
11.10 | odd | 2 | 462.2.p.a.241.7 | ✓ | 16 | ||
21.5 | even | 6 | 1386.2.bk.a.901.2 | 16 | |||
33.32 | even | 2 | 1386.2.bk.a.703.2 | 16 | |||
77.10 | even | 6 | 3234.2.e.b.2155.11 | 16 | |||
77.32 | odd | 6 | 3234.2.e.a.2155.14 | 16 | |||
77.54 | even | 6 | inner | 462.2.p.b.439.3 | yes | 16 | |
231.131 | odd | 6 | 1386.2.bk.b.901.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.7 | ✓ | 16 | 11.10 | odd | 2 | ||
462.2.p.a.439.7 | yes | 16 | 7.5 | odd | 6 | ||
462.2.p.b.241.3 | yes | 16 | 1.1 | even | 1 | trivial | |
462.2.p.b.439.3 | yes | 16 | 77.54 | even | 6 | inner | |
1386.2.bk.a.703.2 | 16 | 33.32 | even | 2 | |||
1386.2.bk.a.901.2 | 16 | 21.5 | even | 6 | |||
1386.2.bk.b.703.6 | 16 | 3.2 | odd | 2 | |||
1386.2.bk.b.901.6 | 16 | 231.131 | odd | 6 | |||
3234.2.e.a.2155.3 | 16 | 7.3 | odd | 6 | |||
3234.2.e.a.2155.14 | 16 | 77.32 | odd | 6 | |||
3234.2.e.b.2155.6 | 16 | 7.4 | even | 3 | |||
3234.2.e.b.2155.11 | 16 | 77.10 | even | 6 |