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: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + 130215 x^{8} - 239606 x^{7} + 378750 x^{6} - 477124 x^{5} + \cdots + 13417 \) |
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 | 439.5 | ||
Root | \(0.500000 + 3.19339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.439 |
Dual form | 462.2.p.b.241.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||
\(5\) | −2.01555 | − | 1.16368i | −0.901383 | − | 0.520414i | −0.0237343 | − | 0.999718i | \(-0.507556\pi\) |
−0.877649 | + | 0.479305i | \(0.840889\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.31629 | − | 2.29508i | 0.497509 | − | 0.867459i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.16368 | − | 2.01555i | −0.367988 | − | 0.637374i | ||||
\(11\) | 2.46679 | − | 2.21696i | 0.743767 | − | 0.668439i | ||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 1.44095 | 0.399647 | 0.199823 | − | 0.979832i | \(-0.435963\pi\) | ||||
0.199823 | + | 0.979832i | \(0.435963\pi\) | |||||||
\(14\) | 2.28748 | − | 1.32945i | 0.611354 | − | 0.355312i | ||||
\(15\) | −2.32736 | −0.600922 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.60782 | + | 2.78483i | 0.389954 | + | 0.675421i | 0.992443 | − | 0.122707i | \(-0.0391575\pi\) |
−0.602489 | + | 0.798127i | \(0.705824\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 3.07901 | − | 5.33301i | 0.706374 | − | 1.22348i | −0.259819 | − | 0.965657i | \(-0.583663\pi\) |
0.966193 | − | 0.257819i | \(-0.0830038\pi\) | |||||||
\(20\) | − | 2.32736i | − | 0.520414i | ||||||
\(21\) | −0.00760304 | − | 2.64574i | −0.00165912 | − | 0.577348i | ||||
\(22\) | 3.24479 | − | 0.686549i | 0.691791 | − | 0.146373i | ||||
\(23\) | −3.14645 | + | 5.44981i | −0.656080 | + | 1.13636i | 0.325542 | + | 0.945528i | \(0.394453\pi\) |
−0.981622 | + | 0.190836i | \(0.938880\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0.208304 | + | 0.360793i | 0.0416608 | + | 0.0721586i | ||||
\(26\) | 1.24790 | + | 0.720474i | 0.244733 | + | 0.141297i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.64574 | − | 0.00760304i | 0.499998 | − | 0.00143684i | ||||
\(29\) | 3.26833i | 0.606913i | 0.952845 | + | 0.303456i | \(0.0981407\pi\) | ||||
−0.952845 | + | 0.303456i | \(0.901859\pi\) | |||||||
\(30\) | −2.01555 | − | 1.16368i | −0.367988 | − | 0.212458i | ||||
\(31\) | 2.67692 | − | 1.54552i | 0.480789 | − | 0.277584i | −0.239956 | − | 0.970784i | \(-0.577133\pi\) |
0.720745 | + | 0.693200i | \(0.243800\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 1.02783 | − | 3.15334i | 0.178921 | − | 0.548927i | ||||
\(34\) | 3.21565i | 0.551479i | ||||||||
\(35\) | −5.32378 | + | 3.09412i | −0.899884 | + | 0.523002i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.57056 | + | 7.91644i | −0.751395 | + | 1.30145i | 0.195752 | + | 0.980653i | \(0.437285\pi\) |
−0.947147 | + | 0.320801i | \(0.896048\pi\) | |||||||
\(38\) | 5.33301 | − | 3.07901i | 0.865128 | − | 0.499482i | ||||
\(39\) | 1.24790 | − | 0.720474i | 0.199823 | − | 0.115368i | ||||
\(40\) | 1.16368 | − | 2.01555i | 0.183994 | − | 0.318687i | ||||
\(41\) | −3.41163 | −0.532808 | −0.266404 | − | 0.963861i | \(-0.585835\pi\) | ||||
−0.266404 | + | 0.963861i | \(0.585835\pi\) | |||||||
\(42\) | 1.31629 | − | 2.29508i | 0.203107 | − | 0.354139i | ||||
\(43\) | 1.89247i | 0.288599i | 0.989534 | + | 0.144300i | \(0.0460929\pi\) | ||||
−0.989534 | + | 0.144300i | \(0.953907\pi\) | |||||||
\(44\) | 3.15334 | + | 1.02783i | 0.475384 | + | 0.154951i | ||||
\(45\) | −2.01555 | + | 1.16368i | −0.300461 | + | 0.173471i | ||||
\(46\) | −5.44981 | + | 3.14645i | −0.803530 | + | 0.463919i | ||||
\(47\) | −9.22249 | − | 5.32461i | −1.34524 | − | 0.776674i | −0.357668 | − | 0.933849i | \(-0.616428\pi\) |
−0.987571 | + | 0.157175i | \(0.949761\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −3.53478 | − | 6.04196i | −0.504969 | − | 0.863137i | ||||
\(50\) | 0.416608i | 0.0589173i | ||||||||
\(51\) | 2.78483 | + | 1.60782i | 0.389954 | + | 0.225140i | ||||
\(52\) | 0.720474 | + | 1.24790i | 0.0999117 | + | 0.173052i | ||||
\(53\) | 4.60856 | + | 7.98226i | 0.633035 | + | 1.09645i | 0.986928 | + | 0.161162i | \(0.0515242\pi\) |
−0.353893 | + | 0.935286i | \(0.615142\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −7.55179 | + | 1.59785i | −1.01828 | + | 0.215454i | ||||
\(56\) | 2.29508 | + | 1.31629i | 0.306693 | + | 0.175896i | ||||
\(57\) | − | 6.15803i | − | 0.815651i | ||||||
\(58\) | −1.63416 | + | 2.83045i | −0.214576 | + | 0.371657i | ||||
\(59\) | −0.461345 | + | 0.266358i | −0.0600620 | + | 0.0346768i | −0.529730 | − | 0.848166i | \(-0.677707\pi\) |
0.469668 | + | 0.882843i | \(0.344374\pi\) | |||||||
\(60\) | −1.16368 | − | 2.01555i | −0.150230 | − | 0.260207i | ||||
\(61\) | 0.233713 | − | 0.404803i | 0.0299239 | − | 0.0518298i | −0.850676 | − | 0.525691i | \(-0.823807\pi\) |
0.880600 | + | 0.473861i | \(0.157140\pi\) | |||||||
\(62\) | 3.09104 | 0.392563 | ||||||||
\(63\) | −1.32945 | − | 2.28748i | −0.167496 | − | 0.288195i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.90431 | − | 1.67680i | −0.360235 | − | 0.207982i | ||||
\(66\) | 2.46679 | − | 2.21696i | 0.303641 | − | 0.272889i | ||||
\(67\) | 4.61347 | + | 7.99077i | 0.563625 | + | 0.976227i | 0.997176 | + | 0.0750984i | \(0.0239271\pi\) |
−0.433551 | + | 0.901129i | \(0.642740\pi\) | |||||||
\(68\) | −1.60782 | + | 2.78483i | −0.194977 | + | 0.337710i | ||||
\(69\) | 6.29290i | 0.757576i | ||||||||
\(70\) | −6.15759 | + | 0.0176950i | −0.735973 | + | 0.00211496i | ||||
\(71\) | −3.25253 | −0.386004 | −0.193002 | − | 0.981198i | \(-0.561822\pi\) | ||||
−0.193002 | + | 0.981198i | \(0.561822\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 2.50002 | + | 4.33016i | 0.292605 | + | 0.506807i | 0.974425 | − | 0.224713i | \(-0.0721446\pi\) |
−0.681820 | + | 0.731520i | \(0.738811\pi\) | |||||||
\(74\) | −7.91644 | + | 4.57056i | −0.920267 | + | 0.531316i | ||||
\(75\) | 0.360793 | + | 0.208304i | 0.0416608 | + | 0.0240529i | ||||
\(76\) | 6.15803 | 0.706374 | ||||||||
\(77\) | −1.84110 | − | 8.57965i | −0.209813 | − | 0.977742i | ||||
\(78\) | 1.44095 | 0.163155 | ||||||||
\(79\) | 7.21263 | + | 4.16421i | 0.811484 | + | 0.468510i | 0.847471 | − | 0.530842i | \(-0.178124\pi\) |
−0.0359870 | + | 0.999352i | \(0.511457\pi\) | |||||||
\(80\) | 2.01555 | − | 1.16368i | 0.225346 | − | 0.130103i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.95456 | − | 1.70582i | −0.326277 | − | 0.188376i | ||||
\(83\) | −4.56130 | −0.500668 | −0.250334 | − | 0.968160i | \(-0.580540\pi\) | ||||
−0.250334 | + | 0.968160i | \(0.580540\pi\) | |||||||
\(84\) | 2.28748 | − | 1.32945i | 0.249584 | − | 0.145055i | ||||
\(85\) | − | 7.48397i | − | 0.811750i | ||||||
\(86\) | −0.946236 | + | 1.63893i | −0.102035 | + | 0.176730i | ||||
\(87\) | 1.63416 | + | 2.83045i | 0.175201 | + | 0.303456i | ||||
\(88\) | 2.21696 | + | 2.46679i | 0.236329 | + | 0.262961i | ||||
\(89\) | −3.79409 | − | 2.19052i | −0.402173 | − | 0.232195i | 0.285248 | − | 0.958454i | \(-0.407924\pi\) |
−0.687421 | + | 0.726259i | \(0.741257\pi\) | |||||||
\(90\) | −2.32736 | −0.245325 | ||||||||
\(91\) | 1.89670 | − | 3.30709i | 0.198828 | − | 0.346677i | ||||
\(92\) | −6.29290 | −0.656080 | ||||||||
\(93\) | 1.54552 | − | 2.67692i | 0.160263 | − | 0.277584i | ||||
\(94\) | −5.32461 | − | 9.22249i | −0.549191 | − | 0.951227i | ||||
\(95\) | −12.4118 | + | 7.16598i | −1.27343 | + | 0.735214i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 17.8026i | − | 1.80758i | −0.427977 | − | 0.903790i | \(-0.640774\pi\) | ||
0.427977 | − | 0.903790i | \(-0.359226\pi\) | |||||||
\(98\) | −0.0402313 | − | 6.99988i | −0.00406398 | − | 0.707095i | ||||
\(99\) | −0.686549 | − | 3.24479i | −0.0690007 | − | 0.326113i | ||||
\(100\) | −0.208304 | + | 0.360793i | −0.0208304 | + | 0.0360793i | ||||
\(101\) | 5.34857 | + | 9.26399i | 0.532203 | + | 0.921802i | 0.999293 | + | 0.0375924i | \(0.0119688\pi\) |
−0.467091 | + | 0.884209i | \(0.654698\pi\) | |||||||
\(102\) | 1.60782 | + | 2.78483i | 0.159198 | + | 0.275739i | ||||
\(103\) | 11.7844 | + | 6.80370i | 1.16115 | + | 0.670388i | 0.951579 | − | 0.307406i | \(-0.0994609\pi\) |
0.209568 | + | 0.977794i | \(0.432794\pi\) | |||||||
\(104\) | 1.44095i | 0.141297i | ||||||||
\(105\) | −3.06347 | + | 5.34148i | −0.298964 | + | 0.521275i | ||||
\(106\) | 9.21712i | 0.895246i | ||||||||
\(107\) | 8.13694 | + | 4.69786i | 0.786627 | + | 0.454159i | 0.838774 | − | 0.544480i | \(-0.183273\pi\) |
−0.0521466 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −6.18076 | + | 3.56846i | −0.592009 | + | 0.341797i | −0.765892 | − | 0.642970i | \(-0.777702\pi\) |
0.173882 | + | 0.984766i | \(0.444369\pi\) | |||||||
\(110\) | −7.33897 | − | 2.39212i | −0.699743 | − | 0.228080i | ||||
\(111\) | 9.14111i | 0.867636i | ||||||||
\(112\) | 1.32945 | + | 2.28748i | 0.125622 | + | 0.216146i | ||||
\(113\) | −3.15100 | −0.296421 | −0.148210 | − | 0.988956i | \(-0.547351\pi\) | ||||
−0.148210 | + | 0.988956i | \(0.547351\pi\) | |||||||
\(114\) | 3.07901 | − | 5.33301i | 0.288376 | − | 0.499482i | ||||
\(115\) | 12.6837 | − | 7.32292i | 1.18276 | − | 0.682866i | ||||
\(116\) | −2.83045 | + | 1.63416i | −0.262801 | + | 0.151728i | ||||
\(117\) | 0.720474 | − | 1.24790i | 0.0666078 | − | 0.115368i | ||||
\(118\) | −0.532715 | −0.0490404 | ||||||||
\(119\) | 8.50776 | − | 0.0244487i | 0.779905 | − | 0.00224121i | ||||
\(120\) | − | 2.32736i | − | 0.212458i | ||||||
\(121\) | 1.17015 | − | 10.9376i | 0.106377 | − | 0.994326i | ||||
\(122\) | 0.404803 | − | 0.233713i | 0.0366492 | − | 0.0211594i | ||||
\(123\) | −2.95456 | + | 1.70582i | −0.266404 | + | 0.153808i | ||||
\(124\) | 2.67692 | + | 1.54552i | 0.240395 | + | 0.138792i | ||||
\(125\) | 10.6672i | 0.954104i | ||||||||
\(126\) | −0.00760304 | − | 2.64574i | −0.000677332 | − | 0.235701i | ||||
\(127\) | 10.8090i | 0.959143i | 0.877503 | + | 0.479571i | \(0.159208\pi\) | ||||
−0.877503 | + | 0.479571i | \(0.840792\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0.946236 | + | 1.63893i | 0.0833115 | + | 0.144300i | ||||
\(130\) | −1.67680 | − | 2.90431i | −0.147065 | − | 0.254725i | ||||
\(131\) | −5.48559 | + | 9.50131i | −0.479278 | + | 0.830134i | −0.999718 | − | 0.0237647i | \(-0.992435\pi\) |
0.520440 | + | 0.853898i | \(0.325768\pi\) | |||||||
\(132\) | 3.24479 | − | 0.686549i | 0.282423 | − | 0.0597564i | ||||
\(133\) | −8.18682 | − | 14.0863i | −0.709887 | − | 1.22144i | ||||
\(134\) | 9.22694i | 0.797086i | ||||||||
\(135\) | −1.16368 | + | 2.01555i | −0.100154 | + | 0.173471i | ||||
\(136\) | −2.78483 | + | 1.60782i | −0.238797 | + | 0.137870i | ||||
\(137\) | −4.83301 | − | 8.37102i | −0.412912 | − | 0.715185i | 0.582295 | − | 0.812978i | \(-0.302155\pi\) |
−0.995207 | + | 0.0977932i | \(0.968822\pi\) | |||||||
\(138\) | −3.14645 | + | 5.44981i | −0.267843 | + | 0.463919i | ||||
\(139\) | −23.3695 | −1.98218 | −0.991088 | − | 0.133208i | \(-0.957472\pi\) | ||||
−0.991088 | + | 0.133208i | \(0.957472\pi\) | |||||||
\(140\) | −5.34148 | − | 3.06347i | −0.451437 | − | 0.258911i | ||||
\(141\) | −10.6492 | −0.896826 | ||||||||
\(142\) | −2.81677 | − | 1.62627i | −0.236378 | − | 0.136473i | ||||
\(143\) | 3.55452 | − | 3.19453i | 0.297244 | − | 0.267140i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 3.80329 | − | 6.58749i | 0.315846 | − | 0.547061i | ||||
\(146\) | 5.00004i | 0.413806i | ||||||||
\(147\) | −6.08219 | − | 3.46510i | −0.501651 | − | 0.285797i | ||||
\(148\) | −9.14111 | −0.751395 | ||||||||
\(149\) | −13.0372 | − | 7.52705i | −1.06805 | − | 0.616640i | −0.140403 | − | 0.990094i | \(-0.544840\pi\) |
−0.927648 | + | 0.373455i | \(0.878173\pi\) | |||||||
\(150\) | 0.208304 | + | 0.360793i | 0.0170080 | + | 0.0294586i | ||||
\(151\) | 11.2506 | − | 6.49554i | 0.915561 | − | 0.528599i | 0.0333445 | − | 0.999444i | \(-0.489384\pi\) |
0.882216 | + | 0.470845i | \(0.156051\pi\) | |||||||
\(152\) | 5.33301 | + | 3.07901i | 0.432564 | + | 0.249741i | ||||
\(153\) | 3.21565 | 0.259970 | ||||||||
\(154\) | 2.69538 | − | 8.35074i | 0.217200 | − | 0.672922i | ||||
\(155\) | −7.19397 | −0.577833 | ||||||||
\(156\) | 1.24790 | + | 0.720474i | 0.0999117 | + | 0.0576841i | ||||
\(157\) | −9.98402 | + | 5.76428i | −0.796812 | + | 0.460039i | −0.842355 | − | 0.538923i | \(-0.818831\pi\) |
0.0455434 | + | 0.998962i | \(0.485498\pi\) | |||||||
\(158\) | 4.16421 | + | 7.21263i | 0.331287 | + | 0.573806i | ||||
\(159\) | 7.98226 | + | 4.60856i | 0.633035 | + | 0.365483i | ||||
\(160\) | 2.32736 | 0.183994 | ||||||||
\(161\) | 8.36612 | + | 14.3949i | 0.659343 | + | 1.13447i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 4.15686 | − | 7.19989i | 0.325590 | − | 0.563939i | −0.656041 | − | 0.754725i | \(-0.727770\pi\) |
0.981632 | + | 0.190786i | \(0.0611037\pi\) | |||||||
\(164\) | −1.70582 | − | 2.95456i | −0.133202 | − | 0.230713i | ||||
\(165\) | −5.74112 | + | 5.15967i | −0.446946 | + | 0.401680i | ||||
\(166\) | −3.95020 | − | 2.28065i | −0.306595 | − | 0.177013i | ||||
\(167\) | 15.5338 | 1.20204 | 0.601022 | − | 0.799232i | \(-0.294760\pi\) | ||||
0.601022 | + | 0.799232i | \(0.294760\pi\) | |||||||
\(168\) | 2.64574 | − | 0.00760304i | 0.204123 | − | 0.000586587i | ||||
\(169\) | −10.9237 | −0.840282 | ||||||||
\(170\) | 3.74198 | − | 6.48131i | 0.286997 | − | 0.497094i | ||||
\(171\) | −3.07901 | − | 5.33301i | −0.235458 | − | 0.407825i | ||||
\(172\) | −1.63893 | + | 0.946236i | −0.124967 | + | 0.0721499i | ||||
\(173\) | 6.60240 | − | 11.4357i | 0.501971 | − | 0.869439i | −0.498027 | − | 0.867162i | \(-0.665942\pi\) |
0.999997 | − | 0.00227722i | \(-0.000724861\pi\) | |||||||
\(174\) | 3.26833i | 0.247771i | ||||||||
\(175\) | 1.10224 | − | 0.00316749i | 0.0833213 | − | 0.000239439i | ||||
\(176\) | 0.686549 | + | 3.24479i | 0.0517506 | + | 0.244585i | ||||
\(177\) | −0.266358 | + | 0.461345i | −0.0200207 | + | 0.0346768i | ||||
\(178\) | −2.19052 | − | 3.79409i | −0.164186 | − | 0.284379i | ||||
\(179\) | 9.43539 | + | 16.3426i | 0.705234 | + | 1.22150i | 0.966607 | + | 0.256263i | \(0.0824913\pi\) |
−0.261373 | + | 0.965238i | \(0.584175\pi\) | |||||||
\(180\) | −2.01555 | − | 1.16368i | −0.150230 | − | 0.0867356i | ||||
\(181\) | 3.94448i | 0.293191i | 0.989197 | + | 0.146595i | \(0.0468316\pi\) | ||||
−0.989197 | + | 0.146595i | \(0.953168\pi\) | |||||||
\(182\) | 3.29613 | − | 1.91567i | 0.244326 | − | 0.141999i | ||||
\(183\) | − | 0.467427i | − | 0.0345532i | ||||||
\(184\) | −5.44981 | − | 3.14645i | −0.401765 | − | 0.231959i | ||||
\(185\) | 18.4244 | − | 10.6373i | 1.35459 | − | 0.782072i | ||||
\(186\) | 2.67692 | − | 1.54552i | 0.196281 | − | 0.113323i | ||||
\(187\) | 10.1400 | + | 3.30512i | 0.741513 | + | 0.241695i | ||||
\(188\) | − | 10.6492i | − | 0.776674i | ||||||
\(189\) | −2.29508 | − | 1.31629i | −0.166942 | − | 0.0957457i | ||||
\(190\) | −14.3320 | −1.03975 | ||||||||
\(191\) | −11.7619 | + | 20.3722i | −0.851062 | + | 1.47408i | 0.0291897 | + | 0.999574i | \(0.490707\pi\) |
−0.880251 | + | 0.474508i | \(0.842626\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 18.0103 | − | 10.3983i | 1.29641 | − | 0.748484i | 0.316629 | − | 0.948549i | \(-0.397449\pi\) |
0.979782 | + | 0.200066i | \(0.0641156\pi\) | |||||||
\(194\) | 8.90130 | − | 15.4175i | 0.639076 | − | 1.10691i | ||||
\(195\) | −3.35360 | −0.240157 | ||||||||
\(196\) | 3.46510 | − | 6.08219i | 0.247507 | − | 0.434442i | ||||
\(197\) | − | 21.3675i | − | 1.52237i | −0.648534 | − | 0.761186i | \(-0.724618\pi\) | ||
0.648534 | − | 0.761186i | \(-0.275382\pi\) | |||||||
\(198\) | 1.02783 | − | 3.15334i | 0.0730444 | − | 0.224098i | ||||
\(199\) | 17.3579 | − | 10.0216i | 1.23047 | − | 0.710410i | 0.263339 | − | 0.964703i | \(-0.415176\pi\) |
0.967127 | + | 0.254293i | \(0.0818429\pi\) | |||||||
\(200\) | −0.360793 | + | 0.208304i | −0.0255119 | + | 0.0147293i | ||||
\(201\) | 7.99077 | + | 4.61347i | 0.563625 | + | 0.325409i | ||||
\(202\) | 10.6971i | 0.752648i | ||||||||
\(203\) | 7.50107 | + | 4.30205i | 0.526472 | + | 0.301945i | ||||
\(204\) | 3.21565i | 0.225140i | ||||||||
\(205\) | 6.87633 | + | 3.97005i | 0.480264 | + | 0.277280i | ||||
\(206\) | 6.80370 | + | 11.7844i | 0.474036 | + | 0.821055i | ||||
\(207\) | 3.14645 | + | 5.44981i | 0.218693 | + | 0.378788i | ||||
\(208\) | −0.720474 | + | 1.24790i | −0.0499559 | + | 0.0865261i | ||||
\(209\) | −4.22779 | − | 19.9815i | −0.292442 | − | 1.38215i | ||||
\(210\) | −5.32378 | + | 3.09412i | −0.367376 | + | 0.213515i | ||||
\(211\) | − | 2.04651i | − | 0.140887i | −0.997516 | − | 0.0704437i | \(-0.977558\pi\) | ||
0.997516 | − | 0.0704437i | \(-0.0224415\pi\) | |||||||
\(212\) | −4.60856 | + | 7.98226i | −0.316517 | + | 0.548224i | ||||
\(213\) | −2.81677 | + | 1.62627i | −0.193002 | + | 0.111430i | ||||
\(214\) | 4.69786 | + | 8.13694i | 0.321139 | + | 0.556229i | ||||
\(215\) | 2.20223 | − | 3.81438i | 0.150191 | − | 0.260139i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.0235013 | − | 8.17809i | −0.00159537 | − | 0.555165i | ||||
\(218\) | −7.13693 | −0.483374 | ||||||||
\(219\) | 4.33016 | + | 2.50002i | 0.292605 | + | 0.168936i | ||||
\(220\) | −5.15967 | − | 5.74112i | −0.347865 | − | 0.387066i | ||||
\(221\) | 2.31679 | + | 4.01279i | 0.155844 | + | 0.269930i | ||||
\(222\) | −4.57056 | + | 7.91644i | −0.306756 | + | 0.531316i | ||||
\(223\) | 23.3804i | 1.56567i | 0.622230 | + | 0.782835i | \(0.286227\pi\) | ||||
−0.622230 | + | 0.782835i | \(0.713773\pi\) | |||||||
\(224\) | 0.00760304 | + | 2.64574i | 0.000507999 | + | 0.176776i | ||||
\(225\) | 0.416608 | 0.0277739 | ||||||||
\(226\) | −2.72884 | − | 1.57550i | −0.181520 | − | 0.104801i | ||||
\(227\) | −6.97413 | − | 12.0796i | −0.462890 | − | 0.801748i | 0.536214 | − | 0.844082i | \(-0.319854\pi\) |
−0.999104 | + | 0.0423338i | \(0.986521\pi\) | |||||||
\(228\) | 5.33301 | − | 3.07901i | 0.353187 | − | 0.203913i | ||||
\(229\) | −13.0033 | − | 7.50744i | −0.859281 | − | 0.496106i | 0.00449072 | − | 0.999990i | \(-0.498571\pi\) |
−0.863771 | + | 0.503884i | \(0.831904\pi\) | |||||||
\(230\) | 14.6458 | 0.965718 | ||||||||
\(231\) | −5.88426 | − | 6.50964i | −0.387156 | − | 0.428303i | ||||
\(232\) | −3.26833 | −0.214576 | ||||||||
\(233\) | 14.2393 | + | 8.22109i | 0.932850 | + | 0.538581i | 0.887712 | − | 0.460399i | \(-0.152294\pi\) |
0.0451385 | + | 0.998981i | \(0.485627\pi\) | |||||||
\(234\) | 1.24790 | − | 0.720474i | 0.0815776 | − | 0.0470988i | ||||
\(235\) | 12.3923 | + | 21.4641i | 0.808384 | + | 1.40016i | ||||
\(236\) | −0.461345 | − | 0.266358i | −0.0300310 | − | 0.0173384i | ||||
\(237\) | 8.32842 | 0.540989 | ||||||||
\(238\) | 7.38016 | + | 4.23271i | 0.478385 | + | 0.274366i | ||||
\(239\) | − | 24.7950i | − | 1.60386i | −0.597419 | − | 0.801929i | \(-0.703807\pi\) | ||
0.597419 | − | 0.801929i | \(-0.296193\pi\) | |||||||
\(240\) | 1.16368 | − | 2.01555i | 0.0751152 | − | 0.130103i | ||||
\(241\) | 11.1098 | + | 19.2427i | 0.715643 | + | 1.23953i | 0.962711 | + | 0.270532i | \(0.0871996\pi\) |
−0.247068 | + | 0.968998i | \(0.579467\pi\) | |||||||
\(242\) | 6.48217 | − | 8.88715i | 0.416690 | − | 0.571288i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0.467427 | 0.0299239 | ||||||||
\(245\) | 0.0936328 | + | 16.2913i | 0.00598198 | + | 1.04081i | ||||
\(246\) | −3.41163 | −0.217518 | ||||||||
\(247\) | 4.43670 | − | 7.68458i | 0.282300 | − | 0.488958i | ||||
\(248\) | 1.54552 | + | 2.67692i | 0.0981407 | + | 0.169985i | ||||
\(249\) | −3.95020 | + | 2.28065i | −0.250334 | + | 0.144530i | ||||
\(250\) | −5.33360 | + | 9.23807i | −0.337327 | + | 0.584267i | ||||
\(251\) | 4.73415i | 0.298817i | 0.988776 | + | 0.149409i | \(0.0477370\pi\) | ||||
−0.988776 | + | 0.149409i | \(0.952263\pi\) | |||||||
\(252\) | 1.31629 | − | 2.29508i | 0.0829182 | − | 0.144576i | ||||
\(253\) | 4.32038 | + | 20.4191i | 0.271620 | + | 1.28374i | ||||
\(254\) | −5.40449 | + | 9.36086i | −0.339108 | + | 0.587353i | ||||
\(255\) | −3.74198 | − | 6.48131i | −0.234332 | − | 0.405875i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.5961 | − | 6.11764i | −0.660965 | − | 0.381608i | 0.131680 | − | 0.991292i | \(-0.457963\pi\) |
−0.792644 | + | 0.609684i | \(0.791296\pi\) | |||||||
\(258\) | 1.89247i | 0.117820i | ||||||||
\(259\) | 12.1527 | + | 20.9101i | 0.755132 | + | 1.29929i | ||||
\(260\) | − | 3.35360i | − | 0.207982i | ||||||
\(261\) | 2.83045 | + | 1.63416i | 0.175201 | + | 0.101152i | ||||
\(262\) | −9.50131 | + | 5.48559i | −0.586993 | + | 0.338901i | ||||
\(263\) | 16.6883 | − | 9.63502i | 1.02905 | − | 0.594121i | 0.112336 | − | 0.993670i | \(-0.464167\pi\) |
0.916712 | + | 0.399550i | \(0.130833\pi\) | |||||||
\(264\) | 3.15334 | + | 1.02783i | 0.194075 | + | 0.0632583i | ||||
\(265\) | − | 21.4516i | − | 1.31776i | ||||||
\(266\) | −0.0468197 | − | 16.2925i | −0.00287070 | − | 0.998960i | ||||
\(267\) | −4.38104 | −0.268115 | ||||||||
\(268\) | −4.61347 | + | 7.99077i | −0.281813 | + | 0.488114i | ||||
\(269\) | 19.1299 | − | 11.0447i | 1.16637 | − | 0.673405i | 0.213549 | − | 0.976932i | \(-0.431498\pi\) |
0.952823 | + | 0.303527i | \(0.0981644\pi\) | |||||||
\(270\) | −2.01555 | + | 1.16368i | −0.122663 | + | 0.0708193i | ||||
\(271\) | −0.610555 | + | 1.05751i | −0.0370886 | + | 0.0642393i | −0.883974 | − | 0.467536i | \(-0.845142\pi\) |
0.846885 | + | 0.531776i | \(0.178475\pi\) | |||||||
\(272\) | −3.21565 | −0.194977 | ||||||||
\(273\) | −0.0109556 | − | 3.81237i | −0.000663062 | − | 0.230735i | ||||
\(274\) | − | 9.66602i | − | 0.583946i | ||||||
\(275\) | 1.31371 | + | 0.428200i | 0.0792196 | + | 0.0258215i | ||||
\(276\) | −5.44981 | + | 3.14645i | −0.328040 | + | 0.189394i | ||||
\(277\) | −10.8330 | + | 6.25443i | −0.650891 | + | 0.375792i | −0.788798 | − | 0.614653i | \(-0.789296\pi\) |
0.137906 | + | 0.990445i | \(0.455963\pi\) | |||||||
\(278\) | −20.2386 | − | 11.6848i | −1.21383 | − | 0.700805i | ||||
\(279\) | − | 3.09104i | − | 0.185056i | ||||||
\(280\) | −3.09412 | − | 5.32378i | −0.184909 | − | 0.318157i | ||||
\(281\) | − | 25.3495i | − | 1.51222i | −0.654443 | − | 0.756111i | \(-0.727097\pi\) | ||
0.654443 | − | 0.756111i | \(-0.272903\pi\) | |||||||
\(282\) | −9.22249 | − | 5.32461i | −0.549191 | − | 0.317076i | ||||
\(283\) | 1.38222 | + | 2.39408i | 0.0821646 | + | 0.142313i | 0.904179 | − | 0.427153i | \(-0.140483\pi\) |
−0.822015 | + | 0.569466i | \(0.807150\pi\) | |||||||
\(284\) | −1.62627 | − | 2.81677i | −0.0965011 | − | 0.167145i | ||||
\(285\) | −7.16598 | + | 12.4118i | −0.424476 | + | 0.735214i | ||||
\(286\) | 4.67557 | − | 0.989280i | 0.276472 | − | 0.0584974i | ||||
\(287\) | −4.49069 | + | 7.82997i | −0.265077 | + | 0.462189i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 3.32981 | − | 5.76740i | 0.195871 | − | 0.339259i | ||||
\(290\) | 6.58749 | − | 3.80329i | 0.386831 | − | 0.223337i | ||||
\(291\) | −8.90130 | − | 15.4175i | −0.521803 | − | 0.903790i | ||||
\(292\) | −2.50002 | + | 4.33016i | −0.146303 | + | 0.253403i | ||||
\(293\) | 9.03175 | 0.527640 | 0.263820 | − | 0.964572i | \(-0.415017\pi\) | ||||
0.263820 | + | 0.964572i | \(0.415017\pi\) | |||||||
\(294\) | −3.53478 | − | 6.04196i | −0.206153 | − | 0.352374i | ||||
\(295\) | 1.23982 | 0.0721851 | ||||||||
\(296\) | −7.91644 | − | 4.57056i | −0.460134 | − | 0.265658i | ||||
\(297\) | −2.21696 | − | 2.46679i | −0.128641 | − | 0.143138i | ||||
\(298\) | −7.52705 | − | 13.0372i | −0.436030 | − | 0.755226i | ||||
\(299\) | −4.53387 | + | 7.85289i | −0.262200 | + | 0.454144i | ||||
\(300\) | 0.416608i | 0.0240529i | ||||||||
\(301\) | 4.34338 | + | 2.49104i | 0.250348 | + | 0.143581i | ||||
\(302\) | 12.9911 | 0.747552 | ||||||||
\(303\) | 9.26399 | + | 5.34857i | 0.532203 | + | 0.307267i | ||||
\(304\) | 3.07901 | + | 5.33301i | 0.176594 | + | 0.305869i | ||||
\(305\) | −0.942123 | + | 0.543935i | −0.0539458 | + | 0.0311456i | ||||
\(306\) | 2.78483 | + | 1.60782i | 0.159198 | + | 0.0919131i | ||||
\(307\) | −3.52291 | −0.201063 | −0.100531 | − | 0.994934i | \(-0.532054\pi\) | ||||
−0.100531 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(308\) | 6.50964 | − | 5.88426i | 0.370921 | − | 0.335287i | ||||
\(309\) | 13.6074 | 0.774098 | ||||||||
\(310\) | −6.23016 | − | 3.59698i | −0.353849 | − | 0.204295i | ||||
\(311\) | 4.83852 | − | 2.79352i | 0.274367 | − | 0.158406i | −0.356503 | − | 0.934294i | \(-0.616031\pi\) |
0.630871 | + | 0.775888i | \(0.282698\pi\) | |||||||
\(312\) | 0.720474 | + | 1.24790i | 0.0407888 | + | 0.0706483i | ||||
\(313\) | 4.57178 | + | 2.63952i | 0.258412 | + | 0.149194i | 0.623610 | − | 0.781736i | \(-0.285665\pi\) |
−0.365198 | + | 0.930930i | \(0.618999\pi\) | |||||||
\(314\) | −11.5286 | −0.650594 | ||||||||
\(315\) | 0.0176950 | + | 6.15759i | 0.000997001 | + | 0.346941i | ||||
\(316\) | 8.32842i | 0.468510i | ||||||||
\(317\) | −15.8432 | + | 27.4412i | −0.889843 | + | 1.54125i | −0.0497829 | + | 0.998760i | \(0.515853\pi\) |
−0.840060 | + | 0.542493i | \(0.817480\pi\) | |||||||
\(318\) | 4.60856 | + | 7.98226i | 0.258435 | + | 0.447623i | ||||
\(319\) | 7.24576 | + | 8.06229i | 0.405685 | + | 0.451402i | ||||
\(320\) | 2.01555 | + | 1.16368i | 0.112673 | + | 0.0650517i | ||||
\(321\) | 9.39572 | 0.524418 | ||||||||
\(322\) | 0.0478451 | + | 16.6494i | 0.00266630 | + | 0.927833i | ||||
\(323\) | 19.8020 | 1.10181 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0.300155 | + | 0.519884i | 0.0166496 | + | 0.0288380i | ||||
\(326\) | 7.19989 | − | 4.15686i | 0.398765 | − | 0.230227i | ||||
\(327\) | −3.56846 | + | 6.18076i | −0.197336 | + | 0.341797i | ||||
\(328\) | − | 3.41163i | − | 0.188376i | ||||||
\(329\) | −24.3598 | + | 14.1577i | −1.34300 | + | 0.780537i | ||||
\(330\) | −7.55179 | + | 1.59785i | −0.415713 | + | 0.0879586i | ||||
\(331\) | 1.95793 | − | 3.39124i | 0.107618 | − | 0.186399i | −0.807187 | − | 0.590296i | \(-0.799011\pi\) |
0.914805 | + | 0.403896i | \(0.132344\pi\) | |||||||
\(332\) | −2.28065 | − | 3.95020i | −0.125167 | − | 0.216796i | ||||
\(333\) | 4.57056 | + | 7.91644i | 0.250465 | + | 0.433818i | ||||
\(334\) | 13.4527 | + | 7.76692i | 0.736099 | + | 0.424987i | ||||
\(335\) | − | 21.4744i | − | 1.17327i | ||||||
\(336\) | 2.29508 | + | 1.31629i | 0.125207 | + | 0.0718093i | ||||
\(337\) | − | 20.0534i | − | 1.09238i | −0.837662 | − | 0.546189i | \(-0.816078\pi\) | ||
0.837662 | − | 0.546189i | \(-0.183922\pi\) | |||||||
\(338\) | −9.46018 | − | 5.46184i | −0.514566 | − | 0.297085i | ||||
\(339\) | −2.72884 | + | 1.57550i | −0.148210 | + | 0.0855694i | ||||
\(340\) | 6.48131 | − | 3.74198i | 0.351498 | − | 0.202938i | ||||
\(341\) | 3.17705 | − | 9.74711i | 0.172047 | − | 0.527836i | ||||
\(342\) | − | 6.15803i | − | 0.332988i | ||||||
\(343\) | −18.5196 | + | 0.159662i | −0.999963 | + | 0.00862094i | ||||
\(344\) | −1.89247 | −0.102035 | ||||||||
\(345\) | 7.32292 | − | 12.6837i | 0.394253 | − | 0.682866i | ||||
\(346\) | 11.4357 | − | 6.60240i | 0.614786 | − | 0.354947i | ||||
\(347\) | 24.6999 | − | 14.2605i | 1.32596 | − | 0.765545i | 0.341290 | − | 0.939958i | \(-0.389136\pi\) |
0.984673 | + | 0.174413i | \(0.0558029\pi\) | |||||||
\(348\) | −1.63416 | + | 2.83045i | −0.0876003 | + | 0.151728i | ||||
\(349\) | −15.3941 | −0.824027 | −0.412014 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412014 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(350\) | 0.956149 | + | 0.548375i | 0.0511083 | + | 0.0293119i | ||||
\(351\) | − | 1.44095i | − | 0.0769121i | ||||||
\(352\) | −1.02783 | + | 3.15334i | −0.0547833 | + | 0.168074i | ||||
\(353\) | 4.80016 | − | 2.77137i | 0.255487 | − | 0.147505i | −0.366787 | − | 0.930305i | \(-0.619542\pi\) |
0.622274 | + | 0.782800i | \(0.286209\pi\) | |||||||
\(354\) | −0.461345 | + | 0.266358i | −0.0245202 | + | 0.0141567i | ||||
\(355\) | 6.55565 | + | 3.78491i | 0.347938 | + | 0.200882i | ||||
\(356\) | − | 4.38104i | − | 0.232195i | ||||||
\(357\) | 7.35572 | − | 4.27506i | 0.389306 | − | 0.226260i | ||||
\(358\) | 18.8708i | 0.997351i | ||||||||
\(359\) | −17.9527 | − | 10.3650i | −0.947508 | − | 0.547044i | −0.0552018 | − | 0.998475i | \(-0.517580\pi\) |
−0.892306 | + | 0.451431i | \(0.850914\pi\) | |||||||
\(360\) | −1.16368 | − | 2.01555i | −0.0613313 | − | 0.106229i | ||||
\(361\) | −9.46065 | − | 16.3863i | −0.497929 | − | 0.862439i | ||||
\(362\) | −1.97224 | + | 3.41602i | −0.103659 | + | 0.179542i | ||||
\(363\) | −4.45541 | − | 10.0573i | −0.233848 | − | 0.527871i | ||||
\(364\) | 3.81237 | − | 0.0109556i | 0.199823 | − | 0.000574228i | ||||
\(365\) | − | 11.6369i | − | 0.609103i | ||||||
\(366\) | 0.233713 | − | 0.404803i | 0.0122164 | − | 0.0211594i | ||||
\(367\) | −30.3880 | + | 17.5445i | −1.58624 | + | 0.915816i | −0.592320 | + | 0.805703i | \(0.701788\pi\) |
−0.993919 | + | 0.110113i | \(0.964879\pi\) | |||||||
\(368\) | −3.14645 | − | 5.44981i | −0.164020 | − | 0.284091i | ||||
\(369\) | −1.70582 | + | 2.95456i | −0.0888013 | + | 0.153808i | ||||
\(370\) | 21.2747 | 1.10602 | ||||||||
\(371\) | 24.3861 | − | 0.0700781i | 1.26606 | − | 0.00363827i | ||||
\(372\) | 3.09104 | 0.160263 | ||||||||
\(373\) | −21.2225 | − | 12.2528i | −1.09886 | − | 0.634427i | −0.162938 | − | 0.986636i | \(-0.552097\pi\) |
−0.935921 | + | 0.352210i | \(0.885430\pi\) | |||||||
\(374\) | 7.12897 | + | 7.93234i | 0.368630 | + | 0.410171i | ||||
\(375\) | 5.33360 | + | 9.23807i | 0.275426 | + | 0.477052i | ||||
\(376\) | 5.32461 | − | 9.22249i | 0.274596 | − | 0.475614i | ||||
\(377\) | 4.70949i | 0.242551i | ||||||||
\(378\) | −1.32945 | − | 2.28748i | −0.0683798 | − | 0.117655i | ||||
\(379\) | −3.42705 | −0.176036 | −0.0880179 | − | 0.996119i | \(-0.528053\pi\) | ||||
−0.0880179 | + | 0.996119i | \(0.528053\pi\) | |||||||
\(380\) | −12.4118 | − | 7.16598i | −0.636714 | − | 0.367607i | ||||
\(381\) | 5.40449 | + | 9.36086i | 0.276881 | + | 0.479571i | ||||
\(382\) | −20.3722 | + | 11.7619i | −1.04233 | + | 0.601791i | ||||
\(383\) | −28.2806 | − | 16.3278i | −1.44507 | − | 0.834312i | −0.446889 | − | 0.894590i | \(-0.647468\pi\) |
−0.998182 | + | 0.0602779i | \(0.980801\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −6.27313 | + | 19.4352i | −0.319708 | + | 0.990509i | ||||
\(386\) | 20.7965 | 1.05852 | ||||||||
\(387\) | 1.63893 | + | 0.946236i | 0.0833115 | + | 0.0480999i | ||||
\(388\) | 15.4175 | − | 8.90130i | 0.782705 | − | 0.451895i | ||||
\(389\) | −9.28386 | − | 16.0801i | −0.470711 | − | 0.815295i | 0.528728 | − | 0.848791i | \(-0.322669\pi\) |
−0.999439 | + | 0.0334965i | \(0.989336\pi\) | |||||||
\(390\) | −2.90431 | − | 1.67680i | −0.147065 | − | 0.0849082i | ||||
\(391\) | −20.2357 | −1.02336 | ||||||||
\(392\) | 6.04196 | − | 3.53478i | 0.305165 | − | 0.178534i | ||||
\(393\) | 10.9712i | 0.553422i | ||||||||
\(394\) | 10.6837 | − | 18.5048i | 0.538239 | − | 0.932258i | ||||
\(395\) | −9.69162 | − | 16.7864i | −0.487639 | − | 0.844615i | ||||
\(396\) | 2.46679 | − | 2.21696i | 0.123961 | − | 0.111407i | ||||
\(397\) | −4.84409 | − | 2.79674i | −0.243118 | − | 0.140364i | 0.373491 | − | 0.927634i | \(-0.378161\pi\) |
−0.616609 | + | 0.787270i | \(0.711494\pi\) | |||||||
\(398\) | 20.0431 | 1.00467 | ||||||||
\(399\) | −14.1332 | − | 8.10572i | −0.707543 | − | 0.405794i | ||||
\(400\) | −0.416608 | −0.0208304 | ||||||||
\(401\) | 5.17676 | − | 8.96641i | 0.258515 | − | 0.447761i | −0.707329 | − | 0.706884i | \(-0.750100\pi\) |
0.965844 | + | 0.259123i | \(0.0834335\pi\) | |||||||
\(402\) | 4.61347 | + | 7.99077i | 0.230099 | + | 0.398543i | ||||
\(403\) | 3.85730 | − | 2.22701i | 0.192146 | − | 0.110935i | ||||
\(404\) | −5.34857 | + | 9.26399i | −0.266101 | + | 0.460901i | ||||
\(405\) | 2.32736i | 0.115647i | ||||||||
\(406\) | 4.34509 | + | 7.47622i | 0.215643 | + | 0.371039i | ||||
\(407\) | 6.27582 | + | 29.6610i | 0.311081 | + | 1.47024i | ||||
\(408\) | −1.60782 | + | 2.78483i | −0.0795991 | + | 0.137870i | ||||
\(409\) | −10.4458 | − | 18.0927i | −0.516512 | − | 0.894625i | −0.999816 | − | 0.0191723i | \(-0.993897\pi\) |
0.483304 | − | 0.875452i | \(-0.339436\pi\) | |||||||
\(410\) | 3.97005 | + | 6.87633i | 0.196067 | + | 0.339598i | ||||
\(411\) | −8.37102 | − | 4.83301i | −0.412912 | − | 0.238395i | ||||
\(412\) | 13.6074i | 0.670388i | ||||||||
\(413\) | 0.00405025 | + | 1.40943i | 0.000199300 | + | 0.0693533i | ||||
\(414\) | 6.29290i | 0.309279i | ||||||||
\(415\) | 9.19355 | + | 5.30790i | 0.451293 | + | 0.260554i | ||||
\(416\) | −1.24790 | + | 0.720474i | −0.0611832 | + | 0.0353241i | ||||
\(417\) | −20.2386 | + | 11.6848i | −0.991088 | + | 0.572205i | ||||
\(418\) | 6.32938 | − | 19.4184i | 0.309580 | − | 0.949784i | ||||
\(419\) | − | 7.59471i | − | 0.371026i | −0.982642 | − | 0.185513i | \(-0.940605\pi\) | ||
0.982642 | − | 0.185513i | \(-0.0593946\pi\) | |||||||
\(420\) | −6.15759 | + | 0.0176950i | −0.300460 | + | 0.000863428i | ||||
\(421\) | −29.9360 | −1.45899 | −0.729496 | − | 0.683985i | \(-0.760246\pi\) | ||||
−0.729496 | + | 0.683985i | \(0.760246\pi\) | |||||||
\(422\) | 1.02325 | − | 1.77233i | 0.0498112 | − | 0.0862756i | ||||
\(423\) | −9.22249 | + | 5.32461i | −0.448413 | + | 0.258891i | ||||
\(424\) | −7.98226 | + | 4.60856i | −0.387653 | + | 0.223812i | ||||
\(425\) | −0.669832 | + | 1.16018i | −0.0324916 | + | 0.0562771i | ||||
\(426\) | −3.25253 | −0.157586 | ||||||||
\(427\) | −0.621422 | − | 1.06923i | −0.0300727 | − | 0.0517435i | ||||
\(428\) | 9.39572i | 0.454159i | ||||||||
\(429\) | 1.48104 | − | 4.54380i | 0.0715054 | − | 0.219377i | ||||
\(430\) | 3.81438 | − | 2.20223i | 0.183946 | − | 0.106201i | ||||
\(431\) | −28.8852 | + | 16.6769i | −1.39135 | + | 0.803297i | −0.993465 | − | 0.114138i | \(-0.963590\pi\) |
−0.397886 | + | 0.917435i | \(0.630256\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 27.7837i | 1.33520i | 0.744521 | + | 0.667599i | \(0.232678\pi\) | ||||
−0.744521 | + | 0.667599i | \(0.767322\pi\) | |||||||
\(434\) | 4.06869 | − | 7.09419i | 0.195304 | − | 0.340532i | ||||
\(435\) | − | 7.60657i | − | 0.364707i | ||||||
\(436\) | −6.18076 | − | 3.56846i | −0.296005 | − | 0.170898i | ||||
\(437\) | 19.3759 | + | 33.5601i | 0.926876 | + | 1.60540i | ||||
\(438\) | 2.50002 | + | 4.33016i | 0.119456 | + | 0.206903i | ||||
\(439\) | −15.5488 | + | 26.9314i | −0.742105 | + | 1.28536i | 0.209429 | + | 0.977824i | \(0.432839\pi\) |
−0.951535 | + | 0.307541i | \(0.900494\pi\) | |||||||
\(440\) | −1.59785 | − | 7.55179i | −0.0761743 | − | 0.360018i | ||||
\(441\) | −6.99988 | + | 0.0402313i | −0.333328 | + | 0.00191578i | ||||
\(442\) | 4.63358i | 0.220397i | ||||||||
\(443\) | 2.50430 | − | 4.33757i | 0.118983 | − | 0.206084i | −0.800382 | − | 0.599490i | \(-0.795370\pi\) |
0.919365 | + | 0.393406i | \(0.128703\pi\) | |||||||
\(444\) | −7.91644 | + | 4.57056i | −0.375697 | + | 0.216909i | ||||
\(445\) | 5.09813 | + | 8.83022i | 0.241675 | + | 0.418593i | ||||
\(446\) | −11.6902 | + | 20.2480i | −0.553548 | + | 0.958773i | ||||
\(447\) | −15.0541 | −0.712034 | ||||||||
\(448\) | −1.31629 | + | 2.29508i | −0.0621887 | + | 0.108432i | ||||
\(449\) | 24.8715 | 1.17376 | 0.586880 | − | 0.809674i | \(-0.300356\pi\) | ||||
0.586880 | + | 0.809674i | \(0.300356\pi\) | |||||||
\(450\) | 0.360793 | + | 0.208304i | 0.0170080 | + | 0.00981954i | ||||
\(451\) | −8.41580 | + | 7.56347i | −0.396285 | + | 0.356150i | ||||
\(452\) | −1.57550 | − | 2.72884i | −0.0741052 | − | 0.128354i | ||||
\(453\) | 6.49554 | − | 11.2506i | 0.305187 | − | 0.528599i | ||||
\(454\) | − | 13.9483i | − | 0.654625i | ||||||
\(455\) | −7.67129 | + | 4.45846i | −0.359636 | + | 0.209016i | ||||
\(456\) | 6.15803 | 0.288376 | ||||||||
\(457\) | 6.59453 | + | 3.80735i | 0.308479 | + | 0.178100i | 0.646246 | − | 0.763129i | \(-0.276338\pi\) |
−0.337767 | + | 0.941230i | \(0.609671\pi\) | |||||||
\(458\) | −7.50744 | − | 13.0033i | −0.350800 | − | 0.607603i | ||||
\(459\) | 2.78483 | − | 1.60782i | 0.129985 | − | 0.0750467i | ||||
\(460\) | 12.6837 | + | 7.32292i | 0.591379 | + | 0.341433i | ||||
\(461\) | −8.56061 | −0.398707 | −0.199354 | − | 0.979928i | \(-0.563884\pi\) | ||||
−0.199354 | + | 0.979928i | \(0.563884\pi\) | |||||||
\(462\) | −1.84110 | − | 8.57965i | −0.0856557 | − | 0.399161i | ||||
\(463\) | −2.87221 | −0.133483 | −0.0667415 | − | 0.997770i | \(-0.521260\pi\) | ||||
−0.0667415 | + | 0.997770i | \(0.521260\pi\) | |||||||
\(464\) | −2.83045 | − | 1.63416i | −0.131401 | − | 0.0758641i | ||||
\(465\) | −6.23016 | + | 3.59698i | −0.288917 | + | 0.166806i | ||||
\(466\) | 8.22109 | + | 14.2393i | 0.380835 | + | 0.659625i | ||||
\(467\) | −7.84052 | − | 4.52673i | −0.362816 | − | 0.209472i | 0.307499 | − | 0.951548i | \(-0.400508\pi\) |
−0.670315 | + | 0.742076i | \(0.733841\pi\) | |||||||
\(468\) | 1.44095 | 0.0666078 | ||||||||
\(469\) | 24.4121 | − | 0.0701528i | 1.12725 | − | 0.00323935i | ||||
\(470\) | 24.7846i | 1.14323i | ||||||||
\(471\) | −5.76428 | + | 9.98402i | −0.265604 | + | 0.460039i | ||||
\(472\) | −0.266358 | − | 0.461345i | −0.0122601 | − | 0.0212351i | ||||
\(473\) | 4.19554 | + | 4.66834i | 0.192911 | + | 0.214651i | ||||
\(474\) | 7.21263 | + | 4.16421i | 0.331287 | + | 0.191269i | ||||
\(475\) | 2.56548 | 0.117712 | ||||||||
\(476\) | 4.27506 | + | 7.35572i | 0.195947 | + | 0.337149i | ||||
\(477\) | 9.21712 | 0.422023 | ||||||||
\(478\) | 12.3975 | − | 21.4731i | 0.567050 | − | 0.982159i | ||||
\(479\) | −15.5977 | − | 27.0160i | −0.712677 | − | 1.23439i | −0.963849 | − | 0.266450i | \(-0.914149\pi\) |
0.251172 | − | 0.967943i | \(-0.419184\pi\) | |||||||
\(480\) | 2.01555 | − | 1.16368i | 0.0919970 | − | 0.0531145i | ||||
\(481\) | −6.58593 | + | 11.4072i | −0.300293 | + | 0.520122i | ||||
\(482\) | 22.2195i | 1.01207i | ||||||||
\(483\) | 14.4427 | + | 8.28325i | 0.657166 | + | 0.376901i | ||||
\(484\) | 10.0573 | − | 4.45541i | 0.457150 | − | 0.202519i | ||||
\(485\) | −20.7165 | + | 35.8821i | −0.940689 | + | 1.62932i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −18.0368 | − | 31.2407i | −0.817327 | − | 1.41565i | −0.907645 | − | 0.419738i | \(-0.862122\pi\) |
0.0903185 | − | 0.995913i | \(-0.471211\pi\) | |||||||
\(488\) | 0.404803 | + | 0.233713i | 0.0183246 | + | 0.0105797i | ||||
\(489\) | − | 8.31371i | − | 0.375959i | ||||||
\(490\) | −8.06454 | + | 14.1555i | −0.364319 | + | 0.639478i | ||||
\(491\) | 26.7561i | 1.20749i | 0.797179 | + | 0.603744i | \(0.206325\pi\) | ||||
−0.797179 | + | 0.603744i | \(0.793675\pi\) | |||||||
\(492\) | −2.95456 | − | 1.70582i | −0.133202 | − | 0.0769042i | ||||
\(493\) | −9.10174 | + | 5.25489i | −0.409922 | + | 0.236668i | ||||
\(494\) | 7.68458 | − | 4.43670i | 0.345746 | − | 0.199616i | ||||
\(495\) | −2.39212 | + | 7.33897i | −0.107518 | + | 0.329862i | ||||
\(496\) | 3.09104i | 0.138792i | ||||||||
\(497\) | −4.28126 | + | 7.46482i | −0.192041 | + | 0.334843i | ||||
\(498\) | −4.56130 | −0.204397 | ||||||||
\(499\) | −14.0487 | + | 24.3330i | −0.628906 | + | 1.08930i | 0.358866 | + | 0.933389i | \(0.383164\pi\) |
−0.987772 | + | 0.155907i | \(0.950170\pi\) | |||||||
\(500\) | −9.23807 | + | 5.33360i | −0.413139 | + | 0.238526i | ||||
\(501\) | 13.4527 | − | 7.76692i | 0.601022 | − | 0.347000i | ||||
\(502\) | −2.36708 | + | 4.09990i | −0.105648 | + | 0.182987i | ||||
\(503\) | 16.3197 | 0.727660 | 0.363830 | − | 0.931465i | \(-0.381469\pi\) | ||||
0.363830 | + | 0.931465i | \(0.381469\pi\) | |||||||
\(504\) | 2.28748 | − | 1.32945i | 0.101892 | − | 0.0592186i | ||||
\(505\) | − | 24.8961i | − | 1.10786i | ||||||
\(506\) | −6.46800 | + | 19.8437i | −0.287538 | + | 0.882159i | ||||
\(507\) | −9.46018 | + | 5.46184i | −0.420141 | + | 0.242569i | ||||
\(508\) | −9.36086 | + | 5.40449i | −0.415321 | + | 0.239786i | ||||
\(509\) | 3.92989 | + | 2.26892i | 0.174189 | + | 0.100568i | 0.584560 | − | 0.811351i | \(-0.301267\pi\) |
−0.410370 | + | 0.911919i | \(0.634601\pi\) | |||||||
\(510\) | − | 7.48397i | − | 0.331396i | ||||||
\(511\) | 13.2288 | − | 0.0380155i | 0.585208 | − | 0.00168171i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.33301 | − | 3.07901i | −0.235458 | − | 0.135942i | ||||
\(514\) | −6.11764 | − | 10.5961i | −0.269838 | − | 0.467373i | ||||
\(515\) | −15.8347 | − | 27.4264i | −0.697758 | − | 1.20855i | ||||
\(516\) | −0.946236 | + | 1.63893i | −0.0416557 | + | 0.0721499i | ||||
\(517\) | −34.5545 | + | 7.31121i | −1.51970 | + | 0.321546i | ||||
\(518\) | 0.0695002 | + | 24.1850i | 0.00305366 | + | 1.06263i | ||||
\(519\) | − | 13.2048i | − | 0.579626i | ||||||
\(520\) | 1.67680 | − | 2.90431i | 0.0735326 | − | 0.127362i | ||||
\(521\) | −0.675518 | + | 0.390011i | −0.0295950 | + | 0.0170867i | −0.514725 | − | 0.857356i | \(-0.672106\pi\) |
0.485130 | + | 0.874442i | \(0.338772\pi\) | |||||||
\(522\) | 1.63416 | + | 2.83045i | 0.0715254 | + | 0.123886i | ||||
\(523\) | −5.88383 | + | 10.1911i | −0.257282 | + | 0.445626i | −0.965513 | − | 0.260355i | \(-0.916160\pi\) |
0.708231 | + | 0.705981i | \(0.249494\pi\) | |||||||
\(524\) | −10.9712 | −0.479278 | ||||||||
\(525\) | 0.952981 | − | 0.553861i | 0.0415915 | − | 0.0241725i | ||||
\(526\) | 19.2700 | 0.840214 | ||||||||
\(527\) | 8.60803 | + | 4.96985i | 0.374972 | + | 0.216490i | ||||
\(528\) | 2.21696 | + | 2.46679i | 0.0964809 | + | 0.107353i | ||||
\(529\) | −8.30028 | − | 14.3765i | −0.360882 | − | 0.625065i | ||||
\(530\) | 10.7258 | − | 18.5776i | 0.465898 | − | 0.806959i | ||||
\(531\) | 0.532715i | 0.0231179i | ||||||||
\(532\) | 8.10572 | − | 14.1332i | 0.351428 | − | 0.612750i | ||||
\(533\) | −4.91598 | −0.212935 | ||||||||
\(534\) | −3.79409 | − | 2.19052i | −0.164186 | − | 0.0947931i | ||||
\(535\) | −10.9336 | − | 18.9376i | −0.472702 | − | 0.818743i | ||||
\(536\) | −7.99077 | + | 4.61347i | −0.345149 | + | 0.199272i | ||||
\(537\) | 16.3426 | + | 9.43539i | 0.705234 | + | 0.407167i | ||||
\(538\) | 22.0893 | 0.952338 | ||||||||
\(539\) | −22.1144 | − | 7.06780i | −0.952534 | − | 0.304432i | ||||
\(540\) | −2.32736 | −0.100154 | ||||||||
\(541\) | 9.27327 | + | 5.35393i | 0.398689 | + | 0.230183i | 0.685918 | − | 0.727679i | \(-0.259401\pi\) |
−0.287229 | + | 0.957862i | \(0.592734\pi\) | |||||||
\(542\) | −1.05751 | + | 0.610555i | −0.0454240 | + | 0.0262256i | ||||
\(543\) | 1.97224 | + | 3.41602i | 0.0846369 | + | 0.146595i | ||||
\(544\) | −2.78483 | − | 1.60782i | −0.119399 | − | 0.0689348i | ||||
\(545\) | 16.6102 | 0.711503 | ||||||||
\(546\) | 1.89670 | − | 3.30709i | 0.0811712 | − | 0.141530i | ||||
\(547\) | 19.5154i | 0.834419i | 0.908810 | + | 0.417210i | \(0.136992\pi\) | ||||
−0.908810 | + | 0.417210i | \(0.863008\pi\) | |||||||
\(548\) | 4.83301 | − | 8.37102i | 0.206456 | − | 0.357592i | ||||
\(549\) | −0.233713 | − | 0.404803i | −0.00997464 | − | 0.0172766i | ||||
\(550\) | 0.923604 | + | 1.02769i | 0.0393826 | + | 0.0438207i | ||||
\(551\) | 17.4300 | + | 10.0632i | 0.742544 | + | 0.428708i | ||||
\(552\) | −6.29290 | −0.267843 | ||||||||
\(553\) | 19.0511 | − | 11.0723i | 0.810134 | − | 0.470841i | ||||
\(554\) | −12.5089 | −0.531450 | ||||||||
\(555\) | 10.6373 | − | 18.4244i | 0.451530 | − | 0.782072i | ||||
\(556\) | −11.6848 | − | 20.2386i | −0.495544 | − | 0.858308i | ||||
\(557\) | 5.25260 | − | 3.03259i | 0.222560 | − | 0.128495i | −0.384575 | − | 0.923094i | \(-0.625652\pi\) |
0.607135 | + | 0.794599i | \(0.292319\pi\) | |||||||
\(558\) | 1.54552 | − | 2.67692i | 0.0654271 | − | 0.113323i | ||||
\(559\) | 2.72695i | 0.115338i | ||||||||
\(560\) | −0.0176950 | − | 6.15759i | −0.000747751 | − | 0.260206i | ||||
\(561\) | 10.4341 | − | 2.20770i | 0.440528 | − | 0.0932091i | ||||
\(562\) | 12.6747 | − | 21.9533i | 0.534651 | − | 0.926043i | ||||
\(563\) | 0.122186 | + | 0.211633i | 0.00514953 | + | 0.00891925i | 0.868589 | − | 0.495534i | \(-0.165028\pi\) |
−0.863439 | + | 0.504453i | \(0.831694\pi\) | |||||||
\(564\) | −5.32461 | − | 9.22249i | −0.224206 | − | 0.388337i | ||||
\(565\) | 6.35100 | + | 3.66675i | 0.267189 | + | 0.154262i | ||||
\(566\) | 2.76444i | 0.116198i | ||||||||
\(567\) | −2.64574 | + | 0.00760304i | −0.111111 | + | 0.000319298i | ||||
\(568\) | − | 3.25253i | − | 0.136473i | ||||||
\(569\) | −7.44979 | − | 4.30114i | −0.312311 | − | 0.180313i | 0.335649 | − | 0.941987i | \(-0.391044\pi\) |
−0.647960 | + | 0.761674i | \(0.724378\pi\) | |||||||
\(570\) | −12.4118 | + | 7.16598i | −0.519875 | + | 0.300150i | ||||
\(571\) | 26.9418 | − | 15.5548i | 1.12748 | − | 0.650950i | 0.184178 | − | 0.982893i | \(-0.441038\pi\) |
0.943299 | + | 0.331943i | \(0.107704\pi\) | |||||||
\(572\) | 4.54380 | + | 1.48104i | 0.189986 | + | 0.0619255i | ||||
\(573\) | 23.5238i | 0.982721i | ||||||||
\(574\) | −7.80403 | + | 4.53561i | −0.325734 | + | 0.189313i | ||||
\(575\) | −2.62167 | −0.109331 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −35.4669 | + | 20.4768i | −1.47651 | + | 0.852462i | −0.999648 | − | 0.0265176i | \(-0.991558\pi\) |
−0.476859 | + | 0.878980i | \(0.658225\pi\) | |||||||
\(578\) | 5.76740 | − | 3.32981i | 0.239892 | − | 0.138502i | ||||
\(579\) | 10.3983 | − | 18.0103i | 0.432137 | − | 0.748484i | ||||
\(580\) | 7.60657 | 0.315846 | ||||||||
\(581\) | −6.00398 | + | 10.4686i | −0.249087 | + | 0.434309i | ||||
\(582\) | − | 17.8026i | − | 0.737941i | ||||||
\(583\) | 29.0648 | + | 9.47359i | 1.20374 | + | 0.392356i | ||||
\(584\) | −4.33016 | + | 2.50002i | −0.179183 | + | 0.103451i | ||||
\(585\) | −2.90431 | + | 1.67680i | −0.120078 | + | 0.0693272i | ||||
\(586\) | 7.82172 | + | 4.51587i | 0.323112 | + | 0.186549i | ||||
\(587\) | − | 33.6048i | − | 1.38702i | −0.720449 | − | 0.693508i | \(-0.756064\pi\) | ||
0.720449 | − | 0.693508i | \(-0.243936\pi\) | |||||||
\(588\) | −0.0402313 | − | 6.99988i | −0.00165911 | − | 0.288670i | ||||
\(589\) | − | 19.0347i | − | 0.784312i | ||||||
\(590\) | 1.07372 | + | 0.619910i | 0.0442042 | + | 0.0255213i | ||||
\(591\) | −10.6837 | − | 18.5048i | −0.439471 | − | 0.761186i | ||||
\(592\) | −4.57056 | − | 7.91644i | −0.187849 | − | 0.325364i | ||||
\(593\) | −13.3626 | + | 23.1448i | −0.548738 | + | 0.950442i | 0.449624 | + | 0.893218i | \(0.351558\pi\) |
−0.998361 | + | 0.0572237i | \(0.981775\pi\) | |||||||
\(594\) | −0.686549 | − | 3.24479i | −0.0281694 | − | 0.133135i | ||||
\(595\) | −17.1763 | − | 9.85104i | −0.704160 | − | 0.403853i | ||||
\(596\) | − | 15.0541i | − | 0.616640i | ||||||
\(597\) | 10.0216 | − | 17.3579i | 0.410155 | − | 0.710410i | ||||
\(598\) | −7.85289 | + | 4.53387i | −0.321128 | + | 0.185404i | ||||
\(599\) | −12.4072 | − | 21.4899i | −0.506945 | − | 0.878055i | −0.999968 | − | 0.00803859i | \(-0.997441\pi\) |
0.493022 | − | 0.870017i | \(-0.335892\pi\) | |||||||
\(600\) | −0.208304 | + | 0.360793i | −0.00850398 | + | 0.0147293i | ||||
\(601\) | 17.8950 | 0.729952 | 0.364976 | − | 0.931017i | \(-0.381077\pi\) | ||||
0.364976 | + | 0.931017i | \(0.381077\pi\) | |||||||
\(602\) | 2.51596 | + | 4.32899i | 0.102543 | + | 0.176436i | ||||
\(603\) | 9.22694 | 0.375750 | ||||||||
\(604\) | 11.2506 | + | 6.49554i | 0.457780 | + | 0.264300i | ||||
\(605\) | −15.0864 | + | 20.6836i | −0.613348 | + | 0.840908i | ||||
\(606\) | 5.34857 | + | 9.26399i | 0.217271 | + | 0.376324i | ||||
\(607\) | 16.4712 | − | 28.5290i | 0.668546 | − | 1.15796i | −0.309765 | − | 0.950813i | \(-0.600250\pi\) |
0.978311 | − | 0.207142i | \(-0.0664162\pi\) | |||||||
\(608\) | 6.15803i | 0.249741i | ||||||||
\(609\) | 8.64714 | − | 0.0248492i | 0.350400 | − | 0.00100694i | ||||
\(610\) | −1.08787 | −0.0440466 | ||||||||
\(611\) | −13.2891 | − | 7.67248i | −0.537620 | − | 0.310395i | ||||
\(612\) | 1.60782 | + | 2.78483i | 0.0649924 | + | 0.112570i | ||||
\(613\) | 7.51244 | − | 4.33731i | 0.303425 | − | 0.175182i | −0.340556 | − | 0.940224i | \(-0.610615\pi\) |
0.643980 | + | 0.765042i | \(0.277282\pi\) | |||||||
\(614\) | −3.05093 | − | 1.76145i | −0.123125 | − | 0.0710865i | ||||
\(615\) | 7.94010 | 0.320176 | ||||||||
\(616\) | 8.57965 | − | 1.84110i | 0.345684 | − | 0.0741800i | ||||
\(617\) | 32.6421 | 1.31412 | 0.657061 | − | 0.753837i | \(-0.271799\pi\) | ||||
0.657061 | + | 0.753837i | \(0.271799\pi\) | |||||||
\(618\) | 11.7844 | + | 6.80370i | 0.474036 | + | 0.273685i | ||||
\(619\) | −13.6975 | + | 7.90825i | −0.550549 | + | 0.317859i | −0.749343 | − | 0.662182i | \(-0.769631\pi\) |
0.198795 | + | 0.980041i | \(0.436297\pi\) | |||||||
\(620\) | −3.59698 | − | 6.23016i | −0.144458 | − | 0.250209i | ||||
\(621\) | 5.44981 | + | 3.14645i | 0.218693 | + | 0.126263i | ||||
\(622\) | 5.58704 | 0.224020 | ||||||||
\(623\) | −10.0215 | + | 5.82439i | −0.401504 | + | 0.233349i | ||||
\(624\) | 1.44095i | 0.0576841i | ||||||||
\(625\) | 13.4547 | − | 23.3043i | 0.538190 | − | 0.932172i | ||||
\(626\) | 2.63952 | + | 4.57178i | 0.105496 | + | 0.182725i | ||||
\(627\) | −13.6521 | − | 15.1906i | −0.545213 | − | 0.606654i | ||||
\(628\) | −9.98402 | − | 5.76428i | −0.398406 | − | 0.230020i | ||||
\(629\) | −29.3946 | −1.17204 | ||||||||
\(630\) | −3.06347 | + | 5.34148i | −0.122052 | + | 0.212810i | ||||
\(631\) | 40.7984 | 1.62416 | 0.812080 | − | 0.583546i | \(-0.198335\pi\) | ||||
0.812080 | + | 0.583546i | \(0.198335\pi\) | |||||||
\(632\) | −4.16421 | + | 7.21263i | −0.165643 | + | 0.286903i | ||||
\(633\) | −1.02325 | − | 1.77233i | −0.0406707 | − | 0.0704437i | ||||
\(634\) | −27.4412 | + | 15.8432i | −1.08983 | + | 0.629214i | ||||
\(635\) | 12.5782 | − | 21.7861i | 0.499151 | − | 0.864555i | ||||
\(636\) | 9.21712i | 0.365483i | ||||||||
\(637\) | −5.09344 | − | 8.70615i | −0.201809 | − | 0.344950i | ||||
\(638\) | 2.24387 | + | 10.6050i | 0.0888355 | + | 0.419857i | ||||
\(639\) | −1.62627 | + | 2.81677i | −0.0643341 | + | 0.111430i | ||||
\(640\) | 1.16368 | + | 2.01555i | 0.0459985 | + | 0.0796717i | ||||
\(641\) | −11.9591 | − | 20.7137i | −0.472354 | − | 0.818142i | 0.527145 | − | 0.849775i | \(-0.323262\pi\) |
−0.999500 | + | 0.0316335i | \(0.989929\pi\) | |||||||
\(642\) | 8.13694 | + | 4.69786i | 0.321139 | + | 0.185410i | ||||
\(643\) | 19.6140i | 0.773502i | 0.922184 | + | 0.386751i | \(0.126403\pi\) | ||||
−0.922184 | + | 0.386751i | \(0.873597\pi\) | |||||||
\(644\) | −8.28325 | + | 14.4427i | −0.326406 | + | 0.569122i | ||||
\(645\) | − | 4.40447i | − | 0.173426i | ||||||
\(646\) | 17.1491 | + | 9.90102i | 0.674721 | + | 0.389550i | ||||
\(647\) | 22.5941 | − | 13.0447i | 0.888267 | − | 0.512841i | 0.0148918 | − | 0.999889i | \(-0.495260\pi\) |
0.873375 | + | 0.487048i | \(0.161926\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −0.547538 | + | 1.67983i | −0.0214928 | + | 0.0659392i | ||||
\(650\) | 0.600310i | 0.0235461i | ||||||||
\(651\) | −4.10940 | − | 7.07068i | −0.161060 | − | 0.277122i | ||||
\(652\) | 8.31371 | 0.325590 | ||||||||
\(653\) | 10.8589 | − | 18.8082i | 0.424942 | − | 0.736020i | −0.571473 | − | 0.820621i | \(-0.693628\pi\) |
0.996415 | + | 0.0846002i | \(0.0269613\pi\) | |||||||
\(654\) | −6.18076 | + | 3.56846i | −0.241687 | + | 0.139538i | ||||
\(655\) | 22.1130 | − | 12.7669i | 0.864026 | − | 0.498846i | ||||
\(656\) | 1.70582 | − | 2.95456i | 0.0666010 | − | 0.115356i | ||||
\(657\) | 5.00004 | 0.195070 | ||||||||
\(658\) | −28.1751 | + | 0.0809664i | −1.09838 | + | 0.00315640i | ||||
\(659\) | 12.7596i | 0.497044i | 0.968626 | + | 0.248522i | \(0.0799448\pi\) | ||||
−0.968626 | + | 0.248522i | \(0.920055\pi\) | |||||||
\(660\) | −7.33897 | − | 2.39212i | −0.285669 | − | 0.0931132i | ||||
\(661\) | −19.9646 | + | 11.5266i | −0.776533 | + | 0.448332i | −0.835200 | − | 0.549946i | \(-0.814648\pi\) |
0.0586670 | + | 0.998278i | \(0.481315\pi\) | |||||||
\(662\) | 3.39124 | − | 1.95793i | 0.131804 | − | 0.0760972i | ||||
\(663\) | 4.01279 | + | 2.31679i | 0.155844 | + | 0.0899766i | ||||
\(664\) | − | 4.56130i | − | 0.177013i | ||||||
\(665\) | 0.108966 | + | 37.9186i | 0.00422553 | + | 1.47042i | ||||
\(666\) | 9.14111i | 0.354211i | ||||||||
\(667\) | −17.8118 | − | 10.2836i | −0.689674 | − | 0.398183i | ||||
\(668\) | 7.76692 | + | 13.4527i | 0.300511 | + | 0.520500i | ||||
\(669\) | 11.6902 | + | 20.2480i | 0.451970 | + | 0.782835i | ||||
\(670\) | 10.7372 | − | 18.5974i | 0.414815 | − | 0.718480i | ||||
\(671\) | −0.320911 | − | 1.51670i | −0.0123886 | − | 0.0585516i | ||||
\(672\) | 1.32945 | + | 2.28748i | 0.0512848 | + | 0.0882413i | ||||
\(673\) | 10.4212i | 0.401709i | 0.979621 | + | 0.200854i | \(0.0643718\pi\) | ||||
−0.979621 | + | 0.200854i | \(0.935628\pi\) | |||||||
\(674\) | 10.0267 | − | 17.3668i | 0.386214 | − | 0.668942i | ||||
\(675\) | 0.360793 | − | 0.208304i | 0.0138869 | − | 0.00801762i | ||||
\(676\) | −5.46184 | − | 9.46018i | −0.210071 | − | 0.363853i | ||||
\(677\) | −7.14285 | + | 12.3718i | −0.274522 | + | 0.475486i | −0.970014 | − | 0.243047i | \(-0.921853\pi\) |
0.695492 | + | 0.718534i | \(0.255186\pi\) | |||||||
\(678\) | −3.15100 | −0.121013 | ||||||||
\(679\) | −40.8584 | − | 23.4333i | −1.56800 | − | 0.899287i | ||||
\(680\) | 7.48397 | 0.286997 | ||||||||
\(681\) | −12.0796 | − | 6.97413i | −0.462890 | − | 0.267249i | ||||
\(682\) | 7.62496 | − | 6.85272i | 0.291975 | − | 0.262404i | ||||
\(683\) | 17.3671 | + | 30.0806i | 0.664532 | + | 1.15100i | 0.979412 | + | 0.201872i | \(0.0647025\pi\) |
−0.314880 | + | 0.949132i | \(0.601964\pi\) | |||||||
\(684\) | 3.07901 | − | 5.33301i | 0.117729 | − | 0.203913i | ||||
\(685\) | 22.4963i | 0.859540i | ||||||||
\(686\) | −16.1182 | − | 9.12151i | −0.615398 | − | 0.348261i | ||||
\(687\) | −15.0149 | −0.572854 | ||||||||
\(688\) | −1.63893 | − | 0.946236i | −0.0624836 | − | 0.0360749i | ||||
\(689\) | 6.64069 | + | 11.5020i | 0.252990 | + | 0.438192i | ||||
\(690\) | 12.6837 | − | 7.32292i | 0.482859 | − | 0.278779i | ||||
\(691\) | 7.08434 | + | 4.09015i | 0.269501 | + | 0.155596i | 0.628661 | − | 0.777680i | \(-0.283603\pi\) |
−0.359160 | + | 0.933276i | \(0.616937\pi\) | |||||||
\(692\) | 13.2048 | 0.501971 | ||||||||
\(693\) | −8.35074 | − | 2.69538i | −0.317218 | − | 0.102389i | ||||
\(694\) | 28.5210 | 1.08264 | ||||||||
\(695\) | 47.1025 | + | 27.1946i | 1.78670 | + | 1.03155i | ||||
\(696\) | −2.83045 | + | 1.63416i | −0.107288 | + | 0.0619428i | ||||
\(697\) | −5.48530 | − | 9.50082i | −0.207771 | − | 0.359869i | ||||
\(698\) | −13.3317 | − | 7.69705i | −0.504612 | − | 0.291338i | ||||
\(699\) | 16.4422 | 0.621900 | ||||||||
\(700\) | 0.553861 | + | 0.952981i | 0.0209340 | + | 0.0360193i | ||||
\(701\) | − | 15.9970i | − | 0.604198i | −0.953277 | − | 0.302099i | \(-0.902313\pi\) | ||
0.953277 | − | 0.302099i | \(-0.0976874\pi\) | |||||||
\(702\) | 0.720474 | − | 1.24790i | 0.0271925 | − | 0.0470988i | ||||
\(703\) | 28.1456 | + | 48.7496i | 1.06153 | + | 1.83863i | ||||
\(704\) | −2.46679 | + | 2.21696i | −0.0929708 | + | 0.0835549i | ||||
\(705\) | 21.4641 | + | 12.3923i | 0.808384 | + | 0.466720i | ||||
\(706\) | 5.54275 | 0.208604 | ||||||||
\(707\) | 28.3019 | − | 0.0813307i | 1.06440 | − | 0.00305876i | ||||
\(708\) | −0.532715 | −0.0200207 | ||||||||
\(709\) | 4.39355 | − | 7.60985i | 0.165003 | − | 0.285794i | −0.771653 | − | 0.636043i | \(-0.780570\pi\) |
0.936656 | + | 0.350250i | \(0.113903\pi\) | |||||||
\(710\) | 3.78491 | + | 6.55565i | 0.142045 | + | 0.246029i | ||||
\(711\) | 7.21263 | − | 4.16421i | 0.270495 | − | 0.156170i | ||||
\(712\) | 2.19052 | − | 3.79409i | 0.0820932 | − | 0.142190i | ||||
\(713\) | 19.4516i | 0.728468i | ||||||||
\(714\) | 8.50776 | − | 0.0244487i | 0.318395 | − | 0.000914969i | ||||
\(715\) | −10.8817 | + | 2.30241i | −0.406954 | + | 0.0861053i | ||||
\(716\) | −9.43539 | + | 16.3426i | −0.352617 | + | 0.610750i | ||||
\(717\) | −12.3975 | − | 21.4731i | −0.462994 | − | 0.801929i | ||||
\(718\) | −10.3650 | − | 17.9527i | −0.386818 | − | 0.669989i | ||||
\(719\) | −27.2393 | − | 15.7266i | −1.01585 | − | 0.586503i | −0.102953 | − | 0.994686i | \(-0.532829\pi\) |
−0.912900 | + | 0.408183i | \(0.866163\pi\) | |||||||
\(720\) | − | 2.32736i | − | 0.0867356i | ||||||
\(721\) | 31.1266 | − | 18.0904i | 1.15922 | − | 0.673722i | ||||
\(722\) | − | 18.9213i | − | 0.704178i | ||||||
\(723\) | 19.2427 | + | 11.1098i | 0.715643 | + | 0.413177i | ||||
\(724\) | −3.41602 | + | 1.97224i | −0.126955 | + | 0.0732977i | ||||
\(725\) | −1.17919 | + | 0.680805i | −0.0437940 | + | 0.0252845i | ||||
\(726\) | 1.17015 | − | 10.9376i | 0.0434284 | − | 0.405932i | ||||
\(727\) | − | 50.7040i | − | 1.88051i | −0.340475 | − | 0.940254i | \(-0.610588\pi\) | ||
0.340475 | − | 0.940254i | \(-0.389412\pi\) | |||||||
\(728\) | 3.30709 | + | 1.89670i | 0.122569 | + | 0.0702963i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 5.81844 | − | 10.0778i | 0.215350 | − | 0.372998i | ||||
\(731\) | −5.27022 | + | 3.04276i | −0.194926 | + | 0.112541i | ||||
\(732\) | 0.404803 | − | 0.233713i | 0.0149620 | − | 0.00863829i | ||||
\(733\) | −3.99023 | + | 6.91128i | −0.147382 | + | 0.255274i | −0.930259 | − | 0.366903i | \(-0.880418\pi\) |
0.782877 | + | 0.622177i | \(0.213751\pi\) | |||||||
\(734\) | −35.0890 | −1.29516 | ||||||||
\(735\) | 8.22672 | + | 14.0618i | 0.303447 | + | 0.518678i | ||||
\(736\) | − | 6.29290i | − | 0.231959i | ||||||
\(737\) | 29.0957 | + | 9.48369i | 1.07175 | + | 0.349336i | ||||
\(738\) | −2.95456 | + | 1.70582i | −0.108759 | + | 0.0627920i | ||||
\(739\) | 38.2867 | − | 22.1048i | 1.40840 | − | 0.813140i | 0.413166 | − | 0.910656i | \(-0.364423\pi\) |
0.995234 | + | 0.0975161i | \(0.0310898\pi\) | |||||||
\(740\) | 18.4244 | + | 10.6373i | 0.677295 | + | 0.391036i | ||||
\(741\) | − | 8.87339i | − | 0.325972i | ||||||
\(742\) | 21.1540 | + | 12.1324i | 0.776589 | + | 0.445393i | ||||
\(743\) | 17.1346i | 0.628607i | 0.949323 | + | 0.314304i | \(0.101771\pi\) | ||||
−0.949323 | + | 0.314304i | \(0.898229\pi\) | |||||||
\(744\) | 2.67692 | + | 1.54552i | 0.0981407 | + | 0.0566615i | ||||
\(745\) | 17.5182 | + | 30.3423i | 0.641815 | + | 1.11166i | ||||
\(746\) | −12.2528 | − | 21.2225i | −0.448607 | − | 0.777011i | ||||
\(747\) | −2.28065 | + | 3.95020i | −0.0834446 | + | 0.144530i | ||||
\(748\) | 2.20770 | + | 10.4341i | 0.0807214 | + | 0.381508i | ||||
\(749\) | 21.4925 | − | 12.4912i | 0.785319 | − | 0.456418i | ||||
\(750\) | 10.6672i | 0.389511i | ||||||||
\(751\) | 20.4417 | − | 35.4061i | 0.745928 | − | 1.29199i | −0.203832 | − | 0.979006i | \(-0.565340\pi\) |
0.949760 | − | 0.312979i | \(-0.101327\pi\) | |||||||
\(752\) | 9.22249 | − | 5.32461i | 0.336310 | − | 0.194168i | ||||
\(753\) | 2.36708 | + | 4.09990i | 0.0862611 | + | 0.149409i | ||||
\(754\) | −2.35474 | + | 4.07853i | −0.0857547 | + | 0.148531i | ||||
\(755\) | −30.2349 | −1.10036 | ||||||||
\(756\) | −0.00760304 | − | 2.64574i | −0.000276520 | − | 0.0962246i | ||||
\(757\) | −20.2420 | −0.735709 | −0.367855 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367855 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(758\) | −2.96791 | − | 1.71353i | −0.107799 | − | 0.0622380i | ||||
\(759\) | 13.9511 | + | 15.5233i | 0.506394 | + | 0.563460i | ||||
\(760\) | −7.16598 | − | 12.4118i | −0.259937 | − | 0.450225i | ||||
\(761\) | 22.7554 | − | 39.4136i | 0.824884 | − | 1.42874i | −0.0771248 | − | 0.997021i | \(-0.524574\pi\) |
0.902008 | − | 0.431719i | \(-0.142093\pi\) | |||||||
\(762\) | 10.8090i | 0.391568i | ||||||||
\(763\) | 0.0542623 | + | 18.8825i | 0.00196443 | + | 0.683591i | ||||
\(764\) | −23.5238 | −0.851062 | ||||||||
\(765\) | −6.48131 | − | 3.74198i | −0.234332 | − | 0.135292i | ||||
\(766\) | −16.3278 | − | 28.2806i | −0.589947 | − | 1.02182i | ||||
\(767\) | −0.664773 | + | 0.383807i | −0.0240036 | + | 0.0138585i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | −2.76998 | −0.0998881 | −0.0499440 | − | 0.998752i | \(-0.515904\pi\) | ||||
−0.0499440 | + | 0.998752i | \(0.515904\pi\) | |||||||
\(770\) | −15.1503 | + | 13.6948i | −0.545978 | + | 0.493526i | ||||
\(771\) | −12.2353 | −0.440643 | ||||||||
\(772\) | 18.0103 | + | 10.3983i | 0.648206 | + | 0.374242i | ||||
\(773\) | −9.93494 | + | 5.73594i | −0.357335 | + | 0.206307i | −0.667911 | − | 0.744241i | \(-0.732811\pi\) |
0.310576 | + | 0.950548i | \(0.399478\pi\) | |||||||
\(774\) | 0.946236 | + | 1.63893i | 0.0340118 | + | 0.0589101i | ||||
\(775\) | 1.11523 | + | 0.643876i | 0.0400601 | + | 0.0231287i | ||||
\(776\) | 17.8026 | 0.639076 | ||||||||
\(777\) | 20.9796 | + | 12.0323i | 0.752639 | + | 0.431657i | ||||
\(778\) | − | 18.5677i | − | 0.665685i | ||||||
\(779\) | −10.5045 | + | 18.1943i | −0.376362 | + | 0.651877i | ||||
\(780\) | −1.67680 | − | 2.90431i | −0.0600391 | − | 0.103991i | ||||
\(781\) | −8.02332 | + | 7.21074i | −0.287097 | + | 0.258021i | ||||
\(782\) | −17.5247 | − | 10.1179i | −0.626680 | − | 0.361814i | ||||
\(783\) | 3.26833 | 0.116800 | ||||||||
\(784\) | 6.99988 | − | 0.0402313i | 0.249996 | − | 0.00143683i | ||||
\(785\) | 26.8311 | 0.957643 | ||||||||
\(786\) | −5.48559 | + | 9.50131i | −0.195664 | + | 0.338901i | ||||
\(787\) | −14.7757 | − | 25.5923i | −0.526698 | − | 0.912268i | −0.999516 | − | 0.0311080i | \(-0.990096\pi\) |
0.472818 | − | 0.881160i | \(-0.343237\pi\) | |||||||
\(788\) | 18.5048 | − | 10.6837i | 0.659206 | − | 0.380593i | ||||
\(789\) | 9.63502 | − | 16.6883i | 0.343016 | − | 0.594121i | ||||
\(790\) | − | 19.3832i | − | 0.689625i | ||||||
\(791\) | −4.14761 | + | 7.23179i | −0.147472 | + | 0.257133i | ||||
\(792\) | 3.24479 | − | 0.686549i | 0.115299 | − | 0.0243954i | ||||
\(793\) | 0.336769 | − | 0.583300i | 0.0119590 | − | 0.0207136i | ||||
\(794\) | −2.79674 | − | 4.84409i | −0.0992525 | − | 0.171910i | ||||
\(795\) | −10.7258 | − | 18.5776i | −0.380404 | − | 0.658880i | ||||
\(796\) | 17.3579 | + | 10.0216i | 0.615233 | + | 0.355205i | ||||
\(797\) | 3.17035i | 0.112300i | 0.998422 | + | 0.0561498i | \(0.0178824\pi\) | ||||
−0.998422 | + | 0.0561498i | \(0.982118\pi\) | |||||||
\(798\) | −8.18682 | − | 14.0863i | −0.289810 | − | 0.498651i | ||||
\(799\) | − | 34.2441i | − | 1.21147i | ||||||
\(800\) | −0.360793 | − | 0.208304i | −0.0127560 | − | 0.00736466i | ||||
\(801\) | −3.79409 | + | 2.19052i | −0.134058 | + | 0.0773982i | ||||
\(802\) | 8.96641 | − | 5.17676i | 0.316615 | − | 0.182798i | ||||
\(803\) | 15.7668 | + | 5.13917i | 0.556399 | + | 0.181357i | ||||
\(804\) | 9.22694i | 0.325409i | ||||||||
\(805\) | −0.111353 | − | 38.7491i | −0.00392467 | − | 1.36573i | ||||
\(806\) | 4.45403 | 0.156886 | ||||||||
\(807\) | 11.0447 | − | 19.1299i | 0.388791 | − | 0.673405i | ||||
\(808\) | −9.26399 | + | 5.34857i | −0.325906 | + | 0.188162i | ||||
\(809\) | −34.3262 | + | 19.8183i | −1.20685 | + | 0.696773i | −0.962069 | − | 0.272806i | \(-0.912048\pi\) |
−0.244777 | + | 0.969579i | \(0.578715\pi\) | |||||||
\(810\) | −1.16368 | + | 2.01555i | −0.0408876 | + | 0.0708193i | ||||
\(811\) | 24.9006 | 0.874377 | 0.437188 | − | 0.899370i | \(-0.355974\pi\) | ||||
0.437188 | + | 0.899370i | \(0.355974\pi\) | |||||||
\(812\) | 0.0248492 | + | 8.64714i | 0.000872036 | + | 0.303455i | ||||
\(813\) | 1.22111i | 0.0428262i | ||||||||
\(814\) | −9.39547 | + | 28.8251i | −0.329311 | + | 1.01032i | ||||
\(815\) | −16.7567 | + | 9.67451i | −0.586963 | + | 0.338883i | ||||
\(816\) | −2.78483 | + | 1.60782i | −0.0974886 | + | 0.0562851i | ||||
\(817\) | 10.0926 | + | 5.82695i | 0.353094 | + | 0.203859i | ||||
\(818\) | − | 20.8916i | − | 0.730458i | ||||||
\(819\) | −1.91567 | − | 3.29613i | −0.0669391 | − | 0.115176i | ||||
\(820\) | 7.94010i | 0.277280i | ||||||||
\(821\) | 11.6214 | + | 6.70962i | 0.405590 | + | 0.234167i | 0.688893 | − | 0.724863i | \(-0.258097\pi\) |
−0.283303 | + | 0.959030i | \(0.591430\pi\) | |||||||
\(822\) | −4.83301 | − | 8.37102i | −0.168571 | − | 0.291973i | ||||
\(823\) | 13.2288 | + | 22.9130i | 0.461127 | + | 0.798696i | 0.999017 | − | 0.0443189i | \(-0.0141118\pi\) |
−0.537890 | + | 0.843015i | \(0.680778\pi\) | |||||||
\(824\) | −6.80370 | + | 11.7844i | −0.237018 | + | 0.410527i | ||||
\(825\) | 1.35180 | − | 0.286022i | 0.0470638 | − | 0.00995800i | ||||
\(826\) | −0.701205 | + | 1.22262i | −0.0243981 | + | 0.0425405i | ||||
\(827\) | 43.1986i | 1.50216i | 0.660209 | + | 0.751081i | \(0.270467\pi\) | ||||
−0.660209 | + | 0.751081i | \(0.729533\pi\) | |||||||
\(828\) | −3.14645 | + | 5.44981i | −0.109347 | + | 0.189394i | ||||
\(829\) | −4.77405 | + | 2.75630i | −0.165810 | + | 0.0957303i | −0.580609 | − | 0.814183i | \(-0.697185\pi\) |
0.414799 | + | 0.909913i | \(0.363852\pi\) | |||||||
\(830\) | 5.30790 | + | 9.19355i | 0.184240 | + | 0.319113i | ||||
\(831\) | −6.25443 | + | 10.8330i | −0.216964 | + | 0.375792i | ||||
\(832\) | −1.44095 | −0.0499559 | ||||||||
\(833\) | 11.1425 | − | 19.5582i | 0.386066 | − | 0.677651i | ||||
\(834\) | −23.3695 | −0.809220 | ||||||||
\(835\) | −31.3093 | − | 18.0764i | −1.08350 | − | 0.625560i | ||||
\(836\) | 15.1906 | − | 13.6521i | 0.525378 | − | 0.472168i | ||||
\(837\) | −1.54552 | − | 2.67692i | −0.0534210 | − | 0.0925279i | ||||
\(838\) | 3.79735 | − | 6.57721i | 0.131177 | − | 0.227206i | ||||
\(839\) | 25.5783i | 0.883062i | 0.897246 | + | 0.441531i | \(0.145564\pi\) | ||||
−0.897246 | + | 0.441531i | \(0.854436\pi\) | |||||||
\(840\) | −5.34148 | − | 3.06347i | −0.184299 | − | 0.105700i | ||||
\(841\) | 18.3180 | 0.631657 | ||||||||
\(842\) | −25.9254 | − | 14.9680i | −0.893447 | − | 0.515832i | ||||
\(843\) | −12.6747 | − | 21.9533i | −0.436541 | − | 0.756111i | ||||
\(844\) | 1.77233 | − | 1.02325i | 0.0610060 | − | 0.0352219i | ||||
\(845\) | 22.0172 | + | 12.7117i | 0.757416 | + | 0.437294i | ||||
\(846\) | −10.6492 | −0.366128 | ||||||||
\(847\) | −23.5624 | − | 17.0826i | −0.809613 | − | 0.586964i | ||||
\(848\) | −9.21712 | −0.316517 | ||||||||
\(849\) | 2.39408 | + | 1.38222i | 0.0821646 | + | 0.0474378i | ||||
\(850\) | −1.16018 | + | 0.669832i | −0.0397939 | + | 0.0229750i | ||||
\(851\) | −28.7620 | − | 49.8173i | −0.985950 | − | 1.70772i | ||||
\(852\) | −2.81677 | − | 1.62627i | −0.0965011 | − | 0.0557149i | ||||
\(853\) | 26.6616 | 0.912877 | 0.456439 | − | 0.889755i | \(-0.349125\pi\) | ||||
0.456439 | + | 0.889755i | \(0.349125\pi\) | |||||||
\(854\) | −0.00355386 | − | 1.23669i | −0.000121611 | − | 0.0423186i | ||||
\(855\) | 14.3320i | 0.490142i | ||||||||
\(856\) | −4.69786 | + | 8.13694i | −0.160570 | + | 0.278115i | ||||
\(857\) | −16.9270 | − | 29.3183i | −0.578214 | − | 1.00150i | −0.995684 | − | 0.0928052i | \(-0.970417\pi\) |
0.417470 | − | 0.908690i | \(-0.362917\pi\) | |||||||
\(858\) | 3.55452 | − | 3.19453i | 0.121349 | − | 0.109059i | ||||
\(859\) | −9.66594 | − | 5.58063i | −0.329798 | − | 0.190409i | 0.325954 | − | 0.945386i | \(-0.394315\pi\) |
−0.655751 | + | 0.754977i | \(0.727648\pi\) | |||||||
\(860\) | 4.40447 | 0.150191 | ||||||||
\(861\) | 0.0259388 | + | 9.02630i | 0.000883991 | + | 0.307615i | ||||
\(862\) | −33.3538 | −1.13603 | ||||||||
\(863\) | −7.56384 | + | 13.1010i | −0.257476 | + | 0.445962i | −0.965565 | − | 0.260161i | \(-0.916224\pi\) |
0.708089 | + | 0.706123i | \(0.249558\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −26.6150 | + | 15.3662i | −0.904936 | + | 0.522465i | ||||
\(866\) | −13.8918 | + | 24.0614i | −0.472064 | + | 0.817639i | ||||
\(867\) | − | 6.65962i | − | 0.226173i | ||||||
\(868\) | 7.07068 | − | 4.10940i | 0.239995 | − | 0.139482i | ||||
\(869\) | 27.0240 | − | 5.71787i | 0.916726 | − | 0.193965i | ||||
\(870\) | 3.80329 | − | 6.58749i | 0.128944 | − | 0.223337i | ||||
\(871\) | 6.64777 | + | 11.5143i | 0.225251 | + | 0.390146i | ||||
\(872\) | −3.56846 | − | 6.18076i | −0.120843 | − | 0.209307i | ||||
\(873\) | −15.4175 | − | 8.90130i | −0.521803 | − | 0.301263i | ||||
\(874\) | 38.7518i | 1.31080i | ||||||||
\(875\) | 24.4821 | + | 14.0411i | 0.827646 | + | 0.474676i | ||||
\(876\) | 5.00004i | 0.168936i | ||||||||
\(877\) | 8.64012 | + | 4.98837i | 0.291756 | + | 0.168445i | 0.638733 | − | 0.769428i | \(-0.279459\pi\) |
−0.346977 | + | 0.937873i | \(0.612792\pi\) | |||||||
\(878\) | −26.9314 | + | 15.5488i | −0.908890 | + | 0.524748i | ||||
\(879\) | 7.82172 | − | 4.51587i | 0.263820 | − | 0.152317i | ||||
\(880\) | 2.39212 | − | 7.33897i | 0.0806384 | − | 0.247397i | ||||
\(881\) | − | 3.10955i | − | 0.104763i | −0.998627 | − | 0.0523816i | \(-0.983319\pi\) | ||
0.998627 | − | 0.0523816i | \(-0.0166812\pi\) | |||||||
\(882\) | −6.08219 | − | 3.46510i | −0.204798 | − | 0.116676i | ||||
\(883\) | 28.8971 | 0.972465 | 0.486233 | − | 0.873829i | \(-0.338371\pi\) | ||||
0.486233 | + | 0.873829i | \(0.338371\pi\) | |||||||
\(884\) | −2.31679 | + | 4.01279i | −0.0779220 | + | 0.134965i | ||||
\(885\) | 1.07372 | − | 0.619910i | 0.0360926 | − | 0.0208380i | ||||
\(886\) | 4.33757 | − | 2.50430i | 0.145723 | − | 0.0841335i | ||||
\(887\) | 6.85833 | − | 11.8790i | 0.230280 | − | 0.398857i | −0.727610 | − | 0.685991i | \(-0.759369\pi\) |
0.957890 | + | 0.287134i | \(0.0927024\pi\) | |||||||
\(888\) | −9.14111 | −0.306756 | ||||||||
\(889\) | 24.8075 | + | 14.2277i | 0.832017 | + | 0.477182i | ||||
\(890\) | 10.1963i | 0.341779i | ||||||||
\(891\) | −3.15334 | − | 1.02783i | −0.105641 | − | 0.0344334i | ||||
\(892\) | −20.2480 | + | 11.6902i | −0.677955 | + | 0.391417i | ||||
\(893\) | −56.7924 | + | 32.7891i | −1.90048 | + | 1.09724i | ||||
\(894\) | −13.0372 | − | 7.52705i | −0.436030 | − | 0.251742i | ||||
\(895\) | − | 43.9191i | − | 1.46805i | ||||||
\(896\) | −2.28748 | + | 1.32945i | −0.0764192 | + | 0.0444140i | ||||
\(897\) | 9.06773i | 0.302763i | ||||||||
\(898\) | 21.5394 | + | 12.4358i | 0.718778 | + | 0.414987i | ||||
\(899\) | 5.05127 | + | 8.74905i | 0.168469 | + | 0.291797i | ||||
\(900\) | 0.208304 | + | 0.360793i | 0.00694347 | + | 0.0120264i | ||||
\(901\) | −14.8195 | + | 25.6681i | −0.493709 | + | 0.855129i | ||||
\(902\) | −11.0700 | + | 2.34225i | −0.368592 | + | 0.0779885i | ||||
\(903\) | 5.00699 | − | 0.0143885i | 0.166622 | − | 0.000478821i | ||||
\(904\) | − | 3.15100i | − | 0.104801i | ||||||
\(905\) | 4.59012 | − | 7.95031i | 0.152581 | − | 0.264277i | ||||
\(906\) | 11.2506 | − | 6.49554i | 0.373776 | − | 0.215800i | ||||
\(907\) | 24.4939 | + | 42.4247i | 0.813307 | + | 1.40869i | 0.910537 | + | 0.413427i | \(0.135668\pi\) |
−0.0972300 | + | 0.995262i | \(0.530998\pi\) | |||||||
\(908\) | 6.97413 | − | 12.0796i | 0.231445 | − | 0.400874i | ||||
\(909\) | 10.6971 | 0.354802 | ||||||||
\(910\) | −8.87277 | + | 0.0254976i | −0.294129 | + | 0.000845236i | ||||
\(911\) | −26.6937 | −0.884401 | −0.442200 | − | 0.896916i | \(-0.645802\pi\) | ||||
−0.442200 | + | 0.896916i | \(0.645802\pi\) | |||||||
\(912\) | 5.33301 | + | 3.07901i | 0.176594 | + | 0.101956i | ||||
\(913\) | −11.2518 | + | 10.1122i | −0.372380 | + | 0.334666i | ||||
\(914\) | 3.80735 | + | 6.59453i | 0.125936 | + | 0.218128i | ||||
\(915\) | −0.543935 | + | 0.942123i | −0.0179819 | + | 0.0311456i | ||||
\(916\) | − | 15.0149i | − | 0.496106i | ||||||
\(917\) | 14.5857 | + | 25.0963i | 0.481661 | + | 0.828753i | ||||
\(918\) | 3.21565 | 0.106132 | ||||||||
\(919\) | −39.8952 | − | 23.0335i | −1.31602 | − | 0.759806i | −0.332936 | − | 0.942949i | \(-0.608039\pi\) |
−0.983086 | + | 0.183144i | \(0.941373\pi\) | |||||||
\(920\) | 7.32292 | + | 12.6837i | 0.241430 | + | 0.418168i | ||||
\(921\) | −3.05093 | + | 1.76145i | −0.100531 | + | 0.0580419i | ||||
\(922\) | −7.41371 | − | 4.28031i | −0.244157 | − | 0.140964i | ||||
\(923\) | −4.68672 | −0.154265 | ||||||||
\(924\) | 2.69538 | − | 8.35074i | 0.0886716 | − | 0.274719i | ||||
\(925\) | −3.80826 | −0.125215 | ||||||||
\(926\) | −2.48741 | − | 1.43611i | −0.0817413 | − | 0.0471933i | ||||
\(927\) | 11.7844 | − | 6.80370i | 0.387049 | − | 0.223463i | ||||
\(928\) | −1.63416 | − | 2.83045i | −0.0536440 | − | 0.0929142i | ||||
\(929\) | 10.5117 | + | 6.06892i | 0.344877 | + | 0.199115i | 0.662427 | − | 0.749127i | \(-0.269527\pi\) |
−0.317550 | + | 0.948242i | \(0.602860\pi\) | |||||||
\(930\) | −7.19397 | −0.235899 | ||||||||
\(931\) | −43.1055 | + | 0.247746i | −1.41273 | + | 0.00811953i | ||||
\(932\) | 16.4422i | 0.538581i | ||||||||
\(933\) | 2.79352 | − | 4.83852i | 0.0914557 | − | 0.158406i | ||||
\(934\) | −4.52673 | − | 7.84052i | −0.148119 | − | 0.256550i | ||||
\(935\) | −16.5917 | − | 18.4614i | −0.542606 | − | 0.603753i | ||||
\(936\) | 1.24790 | + | 0.720474i | 0.0407888 | + | 0.0235494i | ||||
\(937\) | −43.9719 | −1.43650 | −0.718250 | − | 0.695786i | \(-0.755056\pi\) | ||||
−0.718250 | + | 0.695786i | \(0.755056\pi\) | |||||||
\(938\) | 21.1766 | + | 12.1453i | 0.691439 | + | 0.396558i | ||||
\(939\) | 5.27903 | 0.172275 | ||||||||
\(940\) | −12.3923 | + | 21.4641i | −0.404192 | + | 0.700081i | ||||
\(941\) | 20.8247 | + | 36.0694i | 0.678866 | + | 1.17583i | 0.975323 | + | 0.220784i | \(0.0708615\pi\) |
−0.296457 | + | 0.955046i | \(0.595805\pi\) | |||||||
\(942\) | −9.98402 | + | 5.76428i | −0.325297 | + | 0.187810i | ||||
\(943\) | 10.7345 | − | 18.5928i | 0.349564 | − | 0.605463i | ||||
\(944\) | − | 0.532715i | − | 0.0173384i | ||||||
\(945\) | 3.09412 | + | 5.32378i | 0.100652 | + | 0.173183i | ||||
\(946\) | 1.29927 | + | 6.14067i | 0.0422431 | + | 0.199651i | ||||
\(947\) | 9.94370 | − | 17.2230i | 0.323127 | − | 0.559672i | −0.658005 | − | 0.753014i | \(-0.728599\pi\) |
0.981131 | + | 0.193342i | \(0.0619326\pi\) | |||||||
\(948\) | 4.16421 | + | 7.21263i | 0.135247 | + | 0.234255i | ||||
\(949\) | 3.60239 | + | 6.23953i | 0.116939 | + | 0.202544i | ||||
\(950\) | 2.22177 | + | 1.28274i | 0.0720839 | + | 0.0416176i | ||||
\(951\) | 31.6864i | 1.02750i | ||||||||
\(952\) | 0.0244487 | + | 8.50776i | 0.000792386 | + | 0.275738i | ||||
\(953\) | 42.1430i | 1.36514i | 0.730818 | + | 0.682572i | \(0.239139\pi\) | ||||
−0.730818 | + | 0.682572i | \(0.760861\pi\) | |||||||
\(954\) | 7.98226 | + | 4.60856i | 0.258435 | + | 0.149208i | ||||
\(955\) | 47.4135 | − | 27.3742i | 1.53426 | − | 0.885808i | ||||
\(956\) | 21.4731 | − | 12.3975i | 0.694491 | − | 0.400965i | ||||
\(957\) | 10.3062 | + | 3.35927i | 0.333151 | + | 0.108590i | ||||
\(958\) | − | 31.1954i | − | 1.00788i | ||||||
\(959\) | −25.5738 | + | 0.0734911i | −0.825821 | + | 0.00237315i | ||||
\(960\) | 2.32736 | 0.0751152 | ||||||||
\(961\) | −10.7227 | + | 18.5723i | −0.345895 | + | 0.599107i | ||||
\(962\) | −11.4072 | + | 6.58593i | −0.367782 | + | 0.212339i | ||||
\(963\) | 8.13694 | − | 4.69786i | 0.262209 | − | 0.151386i | ||||
\(964\) | −11.1098 | + | 19.2427i | −0.357822 | + | 0.619765i | ||||
\(965\) | −48.4010 | −1.55808 | ||||||||
\(966\) | 8.36612 | + | 14.3949i | 0.269176 | + | 0.463147i | ||||
\(967\) | 32.5204i | 1.04578i | 0.852399 | + | 0.522892i | \(0.175147\pi\) | ||||
−0.852399 | + | 0.522892i | \(0.824853\pi\) | |||||||
\(968\) | 10.9376 | + | 1.17015i | 0.351547 | + | 0.0376101i | ||||
\(969\) | 17.1491 | − | 9.90102i | 0.550907 | − | 0.318067i | ||||
\(970\) | −35.8821 | + | 20.7165i | −1.15210 | + | 0.665168i | ||||
\(971\) | −35.8435 | − | 20.6943i | −1.15027 | − | 0.664111i | −0.201319 | − | 0.979526i | \(-0.564523\pi\) |
−0.948954 | + | 0.315415i | \(0.897856\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −30.7610 | + | 53.6349i | −0.986151 | + | 1.71946i | ||||
\(974\) | − | 36.0737i | − | 1.15587i | ||||||
\(975\) | 0.519884 | + | 0.300155i | 0.0166496 | + | 0.00961266i | ||||
\(976\) | 0.233713 | + | 0.404803i | 0.00748098 | + | 0.0129574i | ||||
\(977\) | −7.05105 | − | 12.2128i | −0.225583 | − | 0.390721i | 0.730911 | − | 0.682473i | \(-0.239095\pi\) |
−0.956494 | + | 0.291751i | \(0.905762\pi\) | |||||||
\(978\) | 4.15686 | − | 7.19989i | 0.132922 | − | 0.230227i | ||||
\(979\) | −14.2155 | + | 3.00780i | −0.454331 | + | 0.0961296i | ||||
\(980\) | −14.0618 | + | 8.22672i | −0.449189 | + | 0.262793i | ||||
\(981\) | 7.13693i | 0.227865i | ||||||||
\(982\) | −13.3781 | + | 23.1715i | −0.426911 | + | 0.739432i | ||||
\(983\) | 38.2844 | − | 22.1035i | 1.22108 | − | 0.704992i | 0.255933 | − | 0.966695i | \(-0.417617\pi\) |
0.965149 | + | 0.261703i | \(0.0842840\pi\) | |||||||
\(984\) | −1.70582 | − | 2.95456i | −0.0543795 | − | 0.0941880i | ||||
\(985\) | −24.8649 | + | 43.0673i | −0.792263 | + | 1.37224i | ||||
\(986\) | −10.5098 | −0.334700 | ||||||||
\(987\) | −14.0174 | + | 24.4408i | −0.446179 | + | 0.777959i | ||||
\(988\) | 8.87339 | 0.282300 | ||||||||
\(989\) | −10.3136 | − | 5.95457i | −0.327954 | − | 0.189344i | ||||
\(990\) | −5.74112 | + | 5.15967i | −0.182465 | + | 0.163985i | ||||
\(991\) | −22.7546 | − | 39.4121i | −0.722824 | − | 1.25197i | −0.959863 | − | 0.280468i | \(-0.909510\pi\) |
0.237039 | − | 0.971500i | \(-0.423823\pi\) | |||||||
\(992\) | −1.54552 | + | 2.67692i | −0.0490703 | + | 0.0849923i | ||||
\(993\) | − | 3.91587i | − | 0.124266i | ||||||
\(994\) | −7.44009 | + | 4.32409i | −0.235985 | + | 0.137152i | ||||
\(995\) | −46.6476 | −1.47883 | ||||||||
\(996\) | −3.95020 | − | 2.28065i | −0.125167 | − | 0.0722652i | ||||
\(997\) | 24.1616 | + | 41.8491i | 0.765205 | + | 1.32537i | 0.940138 | + | 0.340793i | \(0.110696\pi\) |
−0.174934 | + | 0.984580i | \(0.555971\pi\) | |||||||
\(998\) | −24.3330 | + | 14.0487i | −0.770249 | + | 0.444703i | ||||
\(999\) | 7.91644 | + | 4.57056i | 0.250465 | + | 0.144606i |
(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.439.5 | yes | 16 | |
3.2 | odd | 2 | 1386.2.bk.b.901.4 | 16 | |||
7.2 | even | 3 | 3234.2.e.b.2155.7 | 16 | |||
7.3 | odd | 6 | 462.2.p.a.241.1 | ✓ | 16 | ||
7.5 | odd | 6 | 3234.2.e.a.2155.2 | 16 | |||
11.10 | odd | 2 | 462.2.p.a.439.1 | yes | 16 | ||
21.17 | even | 6 | 1386.2.bk.a.703.8 | 16 | |||
33.32 | even | 2 | 1386.2.bk.a.901.8 | 16 | |||
77.10 | even | 6 | inner | 462.2.p.b.241.5 | yes | 16 | |
77.54 | even | 6 | 3234.2.e.b.2155.10 | 16 | |||
77.65 | odd | 6 | 3234.2.e.a.2155.15 | 16 | |||
231.164 | odd | 6 | 1386.2.bk.b.703.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.1 | ✓ | 16 | 7.3 | odd | 6 | ||
462.2.p.a.439.1 | yes | 16 | 11.10 | odd | 2 | ||
462.2.p.b.241.5 | yes | 16 | 77.10 | even | 6 | inner | |
462.2.p.b.439.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1386.2.bk.a.703.8 | 16 | 21.17 | even | 6 | |||
1386.2.bk.a.901.8 | 16 | 33.32 | even | 2 | |||
1386.2.bk.b.703.4 | 16 | 231.164 | odd | 6 | |||
1386.2.bk.b.901.4 | 16 | 3.2 | odd | 2 | |||
3234.2.e.a.2155.2 | 16 | 7.5 | odd | 6 | |||
3234.2.e.a.2155.15 | 16 | 77.65 | odd | 6 | |||
3234.2.e.b.2155.7 | 16 | 7.2 | even | 3 | |||
3234.2.e.b.2155.10 | 16 | 77.54 | even | 6 |