Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 643.9 | ||
Character | \(\chi\) | \(=\) | 690.643 |
Dual form | 690.2.j.b.367.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.643329 | + | 2.14152i | −0.287706 | + | 0.957719i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.01701 | − | 2.01701i | −0.762356 | − | 0.762356i | 0.214391 | − | 0.976748i | \(-0.431223\pi\) |
−0.976748 | + | 0.214391i | \(0.931223\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 1.05938 | + | 1.96919i | 0.335007 | + | 0.622712i | ||||
\(11\) | 5.11516i | 1.54228i | 0.636666 | + | 0.771139i | \(0.280313\pi\) | ||||
−0.636666 | + | 0.771139i | \(0.719687\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 4.36777 | + | 4.36777i | 1.21140 | + | 1.21140i | 0.970566 | + | 0.240836i | \(0.0774215\pi\) |
0.240836 | + | 0.970566i | \(0.422578\pi\) | |||||||
\(14\) | −2.85248 | −0.762356 | ||||||||
\(15\) | −1.96919 | + | 1.05938i | −0.508442 | + | 0.273532i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.390995 | + | 0.390995i | 0.0948301 | + | 0.0948301i | 0.752930 | − | 0.658100i | \(-0.228640\pi\) |
−0.658100 | + | 0.752930i | \(0.728640\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | 6.15278 | 1.41154 | 0.705772 | − | 0.708439i | \(-0.250600\pi\) | ||||
0.705772 | + | 0.708439i | \(0.250600\pi\) | |||||||
\(20\) | 2.14152 | + | 0.643329i | 0.478859 | + | 0.143853i | ||||
\(21\) | − | 2.85248i | − | 0.622461i | ||||||
\(22\) | 3.61696 | + | 3.61696i | 0.771139 | + | 0.771139i | ||||
\(23\) | 0.204508 | + | 4.79147i | 0.0426429 | + | 0.999090i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −4.17226 | − | 2.75541i | −0.834451 | − | 0.551082i | ||||
\(26\) | 6.17696 | 1.21140 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.01701 | + | 2.01701i | −0.381178 | + | 0.381178i | ||||
\(29\) | − | 5.15378i | − | 0.957032i | −0.878079 | − | 0.478516i | \(-0.841175\pi\) | ||
0.878079 | − | 0.478516i | \(-0.158825\pi\) | |||||||
\(30\) | −0.643329 | + | 2.14152i | −0.117455 | + | 0.390987i | ||||
\(31\) | 5.55456 | 0.997628 | 0.498814 | − | 0.866709i | \(-0.333769\pi\) | ||||
0.498814 | + | 0.866709i | \(0.333769\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.61696 | + | 3.61696i | −0.629633 | + | 0.629633i | ||||
\(34\) | 0.552950 | 0.0948301 | ||||||||
\(35\) | 5.61707 | − | 3.02187i | 0.949457 | − | 0.510789i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.66015 | − | 1.66015i | −0.272927 | − | 0.272927i | 0.557350 | − | 0.830277i | \(-0.311818\pi\) |
−0.830277 | + | 0.557350i | \(0.811818\pi\) | |||||||
\(38\) | 4.35067 | − | 4.35067i | 0.705772 | − | 0.705772i | ||||
\(39\) | 6.17696i | 0.989105i | ||||||||
\(40\) | 1.96919 | − | 1.05938i | 0.311356 | − | 0.167503i | ||||
\(41\) | −8.20789 | −1.28186 | −0.640928 | − | 0.767601i | \(-0.721450\pi\) | ||||
−0.640928 | + | 0.767601i | \(0.721450\pi\) | |||||||
\(42\) | −2.01701 | − | 2.01701i | −0.311231 | − | 0.311231i | ||||
\(43\) | −3.51520 | + | 3.51520i | −0.536063 | + | 0.536063i | −0.922370 | − | 0.386307i | \(-0.873751\pi\) |
0.386307 | + | 0.922370i | \(0.373751\pi\) | |||||||
\(44\) | 5.11516 | 0.771139 | ||||||||
\(45\) | −2.14152 | − | 0.643329i | −0.319240 | − | 0.0959018i | ||||
\(46\) | 3.53269 | + | 3.24347i | 0.520867 | + | 0.478224i | ||||
\(47\) | −3.69444 | + | 3.69444i | −0.538889 | + | 0.538889i | −0.923203 | − | 0.384314i | \(-0.874438\pi\) |
0.384314 | + | 0.923203i | \(0.374438\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 1.13662i | 0.162375i | ||||||||
\(50\) | −4.89860 | + | 1.00186i | −0.692767 | + | 0.141684i | ||||
\(51\) | 0.552950i | 0.0774285i | ||||||||
\(52\) | 4.36777 | − | 4.36777i | 0.605701 | − | 0.605701i | ||||
\(53\) | 3.27229 | − | 3.27229i | 0.449484 | − | 0.449484i | −0.445699 | − | 0.895183i | \(-0.647045\pi\) |
0.895183 | + | 0.445699i | \(0.147045\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −10.9542 | − | 3.29073i | −1.47707 | − | 0.443722i | ||||
\(56\) | 2.85248i | 0.381178i | ||||||||
\(57\) | 4.35067 | + | 4.35067i | 0.576261 | + | 0.576261i | ||||
\(58\) | −3.64427 | − | 3.64427i | −0.478516 | − | 0.478516i | ||||
\(59\) | 9.42889i | 1.22754i | 0.789486 | + | 0.613768i | \(0.210347\pi\) | ||||
−0.789486 | + | 0.613768i | \(0.789653\pi\) | |||||||
\(60\) | 1.05938 | + | 1.96919i | 0.136766 | + | 0.254221i | ||||
\(61\) | − | 6.90926i | − | 0.884639i | −0.896857 | − | 0.442320i | \(-0.854156\pi\) | ||
0.896857 | − | 0.442320i | \(-0.145844\pi\) | |||||||
\(62\) | 3.92767 | − | 3.92767i | 0.498814 | − | 0.498814i | ||||
\(63\) | 2.01701 | − | 2.01701i | 0.254119 | − | 0.254119i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −12.1636 | + | 6.54377i | −1.50871 | + | 0.811655i | ||||
\(66\) | 5.11516i | 0.629633i | ||||||||
\(67\) | −6.18692 | − | 6.18692i | −0.755853 | − | 0.755853i | 0.219712 | − | 0.975565i | \(-0.429488\pi\) |
−0.975565 | + | 0.219712i | \(0.929488\pi\) | |||||||
\(68\) | 0.390995 | − | 0.390995i | 0.0474151 | − | 0.0474151i | ||||
\(69\) | −3.24347 | + | 3.53269i | −0.390468 | + | 0.425286i | ||||
\(70\) | 1.83508 | − | 6.10865i | 0.219334 | − | 0.730123i | ||||
\(71\) | 10.0403 | 1.19157 | 0.595784 | − | 0.803144i | \(-0.296841\pi\) | ||||
0.595784 | + | 0.803144i | \(0.296841\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −9.69041 | − | 9.69041i | −1.13418 | − | 1.13418i | −0.989475 | − | 0.144702i | \(-0.953778\pi\) |
−0.144702 | − | 0.989475i | \(-0.546222\pi\) | |||||||
\(74\) | −2.34781 | −0.272927 | ||||||||
\(75\) | −1.00186 | − | 4.89860i | −0.115685 | − | 0.565642i | ||||
\(76\) | − | 6.15278i | − | 0.705772i | ||||||
\(77\) | 10.3173 | − | 10.3173i | 1.17577 | − | 1.17577i | ||||
\(78\) | 4.36777 | + | 4.36777i | 0.494553 | + | 0.494553i | ||||
\(79\) | 0.836863 | 0.0941545 | 0.0470772 | − | 0.998891i | \(-0.485009\pi\) | ||||
0.0470772 | + | 0.998891i | \(0.485009\pi\) | |||||||
\(80\) | 0.643329 | − | 2.14152i | 0.0719264 | − | 0.239430i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −5.80385 | + | 5.80385i | −0.640928 | + | 0.640928i | ||||
\(83\) | 7.68978 | − | 7.68978i | 0.844063 | − | 0.844063i | −0.145322 | − | 0.989384i | \(-0.546422\pi\) |
0.989384 | + | 0.145322i | \(0.0464217\pi\) | |||||||
\(84\) | −2.85248 | −0.311231 | ||||||||
\(85\) | −1.08886 | + | 0.585786i | −0.118104 | + | 0.0635375i | ||||
\(86\) | 4.97125i | 0.536063i | ||||||||
\(87\) | 3.64427 | − | 3.64427i | 0.390707 | − | 0.390707i | ||||
\(88\) | 3.61696 | − | 3.61696i | 0.385570 | − | 0.385570i | ||||
\(89\) | 8.61622 | 0.913317 | 0.456659 | − | 0.889642i | \(-0.349046\pi\) | ||||
0.456659 | + | 0.889642i | \(0.349046\pi\) | |||||||
\(90\) | −1.96919 | + | 1.05938i | −0.207571 | + | 0.111669i | ||||
\(91\) | − | 17.6196i | − | 1.84704i | ||||||
\(92\) | 4.79147 | − | 0.204508i | 0.499545 | − | 0.0213214i | ||||
\(93\) | 3.92767 | + | 3.92767i | 0.407280 | + | 0.407280i | ||||
\(94\) | 5.22472i | 0.538889i | ||||||||
\(95\) | −3.95826 | + | 13.1763i | −0.406109 | + | 1.35186i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 7.13357 | + | 7.13357i | 0.724304 | + | 0.724304i | 0.969479 | − | 0.245175i | \(-0.0788453\pi\) |
−0.245175 | + | 0.969479i | \(0.578845\pi\) | |||||||
\(98\) | 0.803714 | + | 0.803714i | 0.0811874 | + | 0.0811874i | ||||
\(99\) | −5.11516 | −0.514093 | ||||||||
\(100\) | −2.75541 | + | 4.17226i | −0.275541 | + | 0.417226i | ||||
\(101\) | 4.31730 | 0.429588 | 0.214794 | − | 0.976659i | \(-0.431092\pi\) | ||||
0.214794 | + | 0.976659i | \(0.431092\pi\) | |||||||
\(102\) | 0.390995 | + | 0.390995i | 0.0387142 | + | 0.0387142i | ||||
\(103\) | 12.0533 | − | 12.0533i | 1.18765 | − | 1.18765i | 0.209929 | − | 0.977717i | \(-0.432677\pi\) |
0.977717 | − | 0.209929i | \(-0.0673234\pi\) | |||||||
\(104\) | − | 6.17696i | − | 0.605701i | ||||||
\(105\) | 6.10865 | + | 1.83508i | 0.596143 | + | 0.179086i | ||||
\(106\) | − | 4.62772i | − | 0.449484i | ||||||
\(107\) | −5.43462 | − | 5.43462i | −0.525384 | − | 0.525384i | 0.393808 | − | 0.919193i | \(-0.371157\pi\) |
−0.919193 | + | 0.393808i | \(0.871157\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −1.98889 | −0.190501 | −0.0952507 | − | 0.995453i | \(-0.530365\pi\) | ||||
−0.0952507 | + | 0.995453i | \(0.530365\pi\) | |||||||
\(110\) | −10.0727 | + | 5.41892i | −0.960396 | + | 0.516674i | ||||
\(111\) | − | 2.34781i | − | 0.222844i | ||||||
\(112\) | 2.01701 | + | 2.01701i | 0.190589 | + | 0.190589i | ||||
\(113\) | −0.526241 | + | 0.526241i | −0.0495045 | + | 0.0495045i | −0.731426 | − | 0.681921i | \(-0.761145\pi\) |
0.681921 | + | 0.731426i | \(0.261145\pi\) | |||||||
\(114\) | 6.15278 | 0.576261 | ||||||||
\(115\) | −10.3926 | − | 2.64453i | −0.969116 | − | 0.246604i | ||||
\(116\) | −5.15378 | −0.478516 | ||||||||
\(117\) | −4.36777 | + | 4.36777i | −0.403801 | + | 0.403801i | ||||
\(118\) | 6.66723 | + | 6.66723i | 0.613768 | + | 0.613768i | ||||
\(119\) | − | 1.57728i | − | 0.144589i | ||||||
\(120\) | 2.14152 | + | 0.643329i | 0.195494 | + | 0.0587276i | ||||
\(121\) | −15.1649 | −1.37862 | ||||||||
\(122\) | −4.88558 | − | 4.88558i | −0.442320 | − | 0.442320i | ||||
\(123\) | −5.80385 | − | 5.80385i | −0.523316 | − | 0.523316i | ||||
\(124\) | − | 5.55456i | − | 0.498814i | ||||||
\(125\) | 8.58491 | − | 7.16235i | 0.767858 | − | 0.640620i | ||||
\(126\) | − | 2.85248i | − | 0.254119i | ||||||
\(127\) | −15.6798 | + | 15.6798i | −1.39136 | + | 1.39136i | −0.569068 | + | 0.822291i | \(0.692696\pi\) |
−0.822291 | + | 0.569068i | \(0.807304\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −4.97125 | −0.437694 | ||||||||
\(130\) | −3.97382 | + | 13.2281i | −0.348527 | + | 1.16018i | ||||
\(131\) | −3.31192 | −0.289364 | −0.144682 | − | 0.989478i | \(-0.546216\pi\) | ||||
−0.144682 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(132\) | 3.61696 | + | 3.61696i | 0.314816 | + | 0.314816i | ||||
\(133\) | −12.4102 | − | 12.4102i | −1.07610 | − | 1.07610i | ||||
\(134\) | −8.74963 | −0.755853 | ||||||||
\(135\) | −1.05938 | − | 1.96919i | −0.0911773 | − | 0.169481i | ||||
\(136\) | − | 0.552950i | − | 0.0474151i | ||||||
\(137\) | −2.13220 | − | 2.13220i | −0.182166 | − | 0.182166i | 0.610133 | − | 0.792299i | \(-0.291116\pi\) |
−0.792299 | + | 0.610133i | \(0.791116\pi\) | |||||||
\(138\) | 0.204508 | + | 4.79147i | 0.0174089 | + | 0.407877i | ||||
\(139\) | − | 8.40570i | − | 0.712963i | −0.934302 | − | 0.356481i | \(-0.883976\pi\) | ||
0.934302 | − | 0.356481i | \(-0.116024\pi\) | |||||||
\(140\) | −3.02187 | − | 5.61707i | −0.255395 | − | 0.474729i | ||||
\(141\) | −5.22472 | −0.440001 | ||||||||
\(142\) | 7.09959 | − | 7.09959i | 0.595784 | − | 0.595784i | ||||
\(143\) | −22.3418 | + | 22.3418i | −1.86832 | + | 1.86832i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 11.0369 | + | 3.31558i | 0.916568 | + | 0.275344i | ||||
\(146\) | −13.7043 | −1.13418 | ||||||||
\(147\) | −0.803714 | + | 0.803714i | −0.0662892 | + | 0.0662892i | ||||
\(148\) | −1.66015 | + | 1.66015i | −0.136464 | + | 0.136464i | ||||
\(149\) | 18.0134 | 1.47572 | 0.737859 | − | 0.674955i | \(-0.235837\pi\) | ||||
0.737859 | + | 0.674955i | \(0.235837\pi\) | |||||||
\(150\) | −4.17226 | − | 2.75541i | −0.340663 | − | 0.224978i | ||||
\(151\) | 12.3312 | 1.00350 | 0.501749 | − | 0.865013i | \(-0.332690\pi\) | ||||
0.501749 | + | 0.865013i | \(0.332690\pi\) | |||||||
\(152\) | −4.35067 | − | 4.35067i | −0.352886 | − | 0.352886i | ||||
\(153\) | −0.390995 | + | 0.390995i | −0.0316100 | + | 0.0316100i | ||||
\(154\) | − | 14.5909i | − | 1.17577i | ||||||
\(155\) | −3.57341 | + | 11.8952i | −0.287023 | + | 0.955447i | ||||
\(156\) | 6.17696 | 0.494553 | ||||||||
\(157\) | −1.55503 | − | 1.55503i | −0.124105 | − | 0.124105i | 0.642326 | − | 0.766431i | \(-0.277969\pi\) |
−0.766431 | + | 0.642326i | \(0.777969\pi\) | |||||||
\(158\) | 0.591752 | − | 0.591752i | 0.0470772 | − | 0.0470772i | ||||
\(159\) | 4.62772 | 0.367002 | ||||||||
\(160\) | −1.05938 | − | 1.96919i | −0.0837517 | − | 0.155678i | ||||
\(161\) | 9.25193 | − | 10.0769i | 0.729154 | − | 0.794172i | ||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 5.61838 | + | 5.61838i | 0.440065 | + | 0.440065i | 0.892034 | − | 0.451968i | \(-0.149278\pi\) |
−0.451968 | + | 0.892034i | \(0.649278\pi\) | |||||||
\(164\) | 8.20789i | 0.640928i | ||||||||
\(165\) | −5.41892 | − | 10.0727i | −0.421862 | − | 0.784160i | ||||
\(166\) | − | 10.8750i | − | 0.844063i | ||||||
\(167\) | 5.78732 | − | 5.78732i | 0.447836 | − | 0.447836i | −0.446798 | − | 0.894635i | \(-0.647436\pi\) |
0.894635 | + | 0.446798i | \(0.147436\pi\) | |||||||
\(168\) | −2.01701 | + | 2.01701i | −0.155615 | + | 0.155615i | ||||
\(169\) | 25.1548i | 1.93499i | ||||||||
\(170\) | −0.355729 | + | 1.18416i | −0.0272832 | + | 0.0908206i | ||||
\(171\) | 6.15278i | 0.470515i | ||||||||
\(172\) | 3.51520 | + | 3.51520i | 0.268032 | + | 0.268032i | ||||
\(173\) | −3.65117 | − | 3.65117i | −0.277593 | − | 0.277593i | 0.554554 | − | 0.832147i | \(-0.312889\pi\) |
−0.832147 | + | 0.554554i | \(0.812889\pi\) | |||||||
\(174\) | − | 5.15378i | − | 0.390707i | ||||||
\(175\) | 2.85778 | + | 13.9731i | 0.216028 | + | 1.05627i | ||||
\(176\) | − | 5.11516i | − | 0.385570i | ||||||
\(177\) | −6.66723 | + | 6.66723i | −0.501140 | + | 0.501140i | ||||
\(178\) | 6.09259 | − | 6.09259i | 0.456659 | − | 0.456659i | ||||
\(179\) | 18.7393i | 1.40064i | 0.713830 | + | 0.700319i | \(0.246959\pi\) | ||||
−0.713830 | + | 0.700319i | \(0.753041\pi\) | |||||||
\(180\) | −0.643329 | + | 2.14152i | −0.0479509 | + | 0.159620i | ||||
\(181\) | − | 20.7307i | − | 1.54090i | −0.637502 | − | 0.770449i | \(-0.720032\pi\) | ||
0.637502 | − | 0.770449i | \(-0.279968\pi\) | |||||||
\(182\) | −12.4590 | − | 12.4590i | −0.923520 | − | 0.923520i | ||||
\(183\) | 4.88558 | − | 4.88558i | 0.361153 | − | 0.361153i | ||||
\(184\) | 3.24347 | − | 3.53269i | 0.239112 | − | 0.260433i | ||||
\(185\) | 4.62328 | − | 2.48723i | 0.339910 | − | 0.182865i | ||||
\(186\) | 5.55456 | 0.407280 | ||||||||
\(187\) | −2.00000 | + | 2.00000i | −0.146254 | + | 0.146254i | ||||
\(188\) | 3.69444 | + | 3.69444i | 0.269444 | + | 0.269444i | ||||
\(189\) | 2.85248 | 0.207487 | ||||||||
\(190\) | 6.51816 | + | 12.1160i | 0.472877 | + | 0.878986i | ||||
\(191\) | 9.66249i | 0.699153i | 0.936908 | + | 0.349577i | \(0.113675\pi\) | ||||
−0.936908 | + | 0.349577i | \(0.886325\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −5.41019 | − | 5.41019i | −0.389434 | − | 0.389434i | 0.485052 | − | 0.874486i | \(-0.338801\pi\) |
−0.874486 | + | 0.485052i | \(0.838801\pi\) | |||||||
\(194\) | 10.0884 | 0.724304 | ||||||||
\(195\) | −13.2281 | − | 3.97382i | −0.947285 | − | 0.284571i | ||||
\(196\) | 1.13662 | 0.0811874 | ||||||||
\(197\) | 9.68778 | − | 9.68778i | 0.690226 | − | 0.690226i | −0.272056 | − | 0.962282i | \(-0.587703\pi\) |
0.962282 | + | 0.272056i | \(0.0877035\pi\) | |||||||
\(198\) | −3.61696 | + | 3.61696i | −0.257046 | + | 0.257046i | ||||
\(199\) | 1.92772 | 0.136652 | 0.0683262 | − | 0.997663i | \(-0.478234\pi\) | ||||
0.0683262 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(200\) | 1.00186 | + | 4.89860i | 0.0708422 | + | 0.346383i | ||||
\(201\) | − | 8.74963i | − | 0.617151i | ||||||
\(202\) | 3.05280 | − | 3.05280i | 0.214794 | − | 0.214794i | ||||
\(203\) | −10.3952 | + | 10.3952i | −0.729600 | + | 0.729600i | ||||
\(204\) | 0.552950 | 0.0387142 | ||||||||
\(205\) | 5.28037 | − | 17.5774i | 0.368797 | − | 1.22766i | ||||
\(206\) | − | 17.0459i | − | 1.18765i | ||||||
\(207\) | −4.79147 | + | 0.204508i | −0.333030 | + | 0.0142143i | ||||
\(208\) | −4.36777 | − | 4.36777i | −0.302850 | − | 0.302850i | ||||
\(209\) | 31.4724i | 2.17699i | ||||||||
\(210\) | 5.61707 | − | 3.02187i | 0.387614 | − | 0.208529i | ||||
\(211\) | 13.4119 | 0.923310 | 0.461655 | − | 0.887059i | \(-0.347256\pi\) | ||||
0.461655 | + | 0.887059i | \(0.347256\pi\) | |||||||
\(212\) | −3.27229 | − | 3.27229i | −0.224742 | − | 0.224742i | ||||
\(213\) | 7.09959 | + | 7.09959i | 0.486456 | + | 0.486456i | ||||
\(214\) | −7.68571 | −0.525384 | ||||||||
\(215\) | −5.26646 | − | 9.78932i | −0.359169 | − | 0.667626i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −11.2036 | − | 11.2036i | −0.760548 | − | 0.760548i | ||||
\(218\) | −1.40636 | + | 1.40636i | −0.0952507 | + | 0.0952507i | ||||
\(219\) | − | 13.7043i | − | 0.926052i | ||||||
\(220\) | −3.29073 | + | 10.9542i | −0.221861 | + | 0.738535i | ||||
\(221\) | 3.41555i | 0.229755i | ||||||||
\(222\) | −1.66015 | − | 1.66015i | −0.111422 | − | 0.111422i | ||||
\(223\) | −7.77131 | − | 7.77131i | −0.520405 | − | 0.520405i | 0.397289 | − | 0.917694i | \(-0.369951\pi\) |
−0.917694 | + | 0.397289i | \(0.869951\pi\) | |||||||
\(224\) | 2.85248 | 0.190589 | ||||||||
\(225\) | 2.75541 | − | 4.17226i | 0.183694 | − | 0.278150i | ||||
\(226\) | 0.744216i | 0.0495045i | ||||||||
\(227\) | −18.5374 | − | 18.5374i | −1.23037 | − | 1.23037i | −0.963821 | − | 0.266550i | \(-0.914116\pi\) |
−0.266550 | − | 0.963821i | \(-0.585884\pi\) | |||||||
\(228\) | 4.35067 | − | 4.35067i | 0.288130 | − | 0.288130i | ||||
\(229\) | 9.30733 | 0.615046 | 0.307523 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(230\) | −9.21866 | + | 5.47872i | −0.607860 | + | 0.361256i | ||||
\(231\) | 14.5909 | 0.960009 | ||||||||
\(232\) | −3.64427 | + | 3.64427i | −0.239258 | + | 0.239258i | ||||
\(233\) | −12.4073 | − | 12.4073i | −0.812826 | − | 0.812826i | 0.172230 | − | 0.985057i | \(-0.444903\pi\) |
−0.985057 | + | 0.172230i | \(0.944903\pi\) | |||||||
\(234\) | 6.17696i | 0.403801i | ||||||||
\(235\) | −5.53499 | − | 10.2885i | −0.361063 | − | 0.671145i | ||||
\(236\) | 9.42889 | 0.613768 | ||||||||
\(237\) | 0.591752 | + | 0.591752i | 0.0384384 | + | 0.0384384i | ||||
\(238\) | −1.11530 | − | 1.11530i | −0.0722944 | − | 0.0722944i | ||||
\(239\) | − | 12.7394i | − | 0.824041i | −0.911174 | − | 0.412021i | \(-0.864823\pi\) | ||
0.911174 | − | 0.412021i | \(-0.135177\pi\) | |||||||
\(240\) | 1.96919 | − | 1.05938i | 0.127111 | − | 0.0683830i | ||||
\(241\) | 5.57785i | 0.359301i | 0.983731 | + | 0.179650i | \(0.0574966\pi\) | ||||
−0.983731 | + | 0.179650i | \(0.942503\pi\) | |||||||
\(242\) | −10.7232 | + | 10.7232i | −0.689312 | + | 0.689312i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −6.90926 | −0.442320 | ||||||||
\(245\) | −2.43411 | − | 0.731223i | −0.155509 | − | 0.0467161i | ||||
\(246\) | −8.20789 | −0.523316 | ||||||||
\(247\) | 26.8739 | + | 26.8739i | 1.70995 | + | 1.70995i | ||||
\(248\) | −3.92767 | − | 3.92767i | −0.249407 | − | 0.249407i | ||||
\(249\) | 10.8750 | 0.689174 | ||||||||
\(250\) | 1.00590 | − | 11.1350i | 0.0636189 | − | 0.704239i | ||||
\(251\) | 28.1668i | 1.77787i | 0.458033 | + | 0.888935i | \(0.348554\pi\) | ||||
−0.458033 | + | 0.888935i | \(0.651446\pi\) | |||||||
\(252\) | −2.01701 | − | 2.01701i | −0.127059 | − | 0.127059i | ||||
\(253\) | −24.5091 | + | 1.04609i | −1.54088 | + | 0.0657672i | ||||
\(254\) | 22.1746i | 1.39136i | ||||||||
\(255\) | −1.18416 | − | 0.355729i | −0.0741547 | − | 0.0222766i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.11158 | + | 7.11158i | −0.443608 | + | 0.443608i | −0.893223 | − | 0.449614i | \(-0.851561\pi\) |
0.449614 | + | 0.893223i | \(0.351561\pi\) | |||||||
\(258\) | −3.51520 | + | 3.51520i | −0.218847 | + | 0.218847i | ||||
\(259\) | 6.69707i | 0.416135i | ||||||||
\(260\) | 6.54377 | + | 12.1636i | 0.405828 | + | 0.754355i | ||||
\(261\) | 5.15378 | 0.319011 | ||||||||
\(262\) | −2.34188 | + | 2.34188i | −0.144682 | + | 0.144682i | ||||
\(263\) | −9.62249 | + | 9.62249i | −0.593348 | + | 0.593348i | −0.938534 | − | 0.345186i | \(-0.887816\pi\) |
0.345186 | + | 0.938534i | \(0.387816\pi\) | |||||||
\(264\) | 5.11516 | 0.314816 | ||||||||
\(265\) | 4.90253 | + | 9.11286i | 0.301160 | + | 0.559798i | ||||
\(266\) | −17.5507 | −1.07610 | ||||||||
\(267\) | 6.09259 | + | 6.09259i | 0.372860 | + | 0.372860i | ||||
\(268\) | −6.18692 | + | 6.18692i | −0.377926 | + | 0.377926i | ||||
\(269\) | − | 6.89166i | − | 0.420192i | −0.977681 | − | 0.210096i | \(-0.932622\pi\) | ||
0.977681 | − | 0.210096i | \(-0.0673776\pi\) | |||||||
\(270\) | −2.14152 | − | 0.643329i | −0.130329 | − | 0.0391518i | ||||
\(271\) | 24.2167 | 1.47106 | 0.735530 | − | 0.677492i | \(-0.236933\pi\) | ||||
0.735530 | + | 0.677492i | \(0.236933\pi\) | |||||||
\(272\) | −0.390995 | − | 0.390995i | −0.0237075 | − | 0.0237075i | ||||
\(273\) | 12.4590 | − | 12.4590i | 0.754051 | − | 0.754051i | ||||
\(274\) | −3.01539 | −0.182166 | ||||||||
\(275\) | 14.0944 | − | 21.3418i | 0.849922 | − | 1.28696i | ||||
\(276\) | 3.53269 | + | 3.24347i | 0.212643 | + | 0.195234i | ||||
\(277\) | 19.0881 | − | 19.0881i | 1.14690 | − | 1.14690i | 0.159736 | − | 0.987160i | \(-0.448936\pi\) |
0.987160 | − | 0.159736i | \(-0.0510642\pi\) | |||||||
\(278\) | −5.94373 | − | 5.94373i | −0.356481 | − | 0.356481i | ||||
\(279\) | 5.55456i | 0.332543i | ||||||||
\(280\) | −6.10865 | − | 1.83508i | −0.365062 | − | 0.109667i | ||||
\(281\) | − | 20.3366i | − | 1.21318i | −0.795015 | − | 0.606590i | \(-0.792537\pi\) | ||
0.795015 | − | 0.606590i | \(-0.207463\pi\) | |||||||
\(282\) | −3.69444 | + | 3.69444i | −0.220000 | + | 0.220000i | ||||
\(283\) | −17.8450 | + | 17.8450i | −1.06078 | + | 1.06078i | −0.0627483 | + | 0.998029i | \(0.519987\pi\) |
−0.998029 | + | 0.0627483i | \(0.980013\pi\) | |||||||
\(284\) | − | 10.0403i | − | 0.595784i | ||||||
\(285\) | −12.1160 | + | 6.51816i | −0.717689 | + | 0.386102i | ||||
\(286\) | 31.5961i | 1.86832i | ||||||||
\(287\) | 16.5554 | + | 16.5554i | 0.977232 | + | 0.977232i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 16.6942i | − | 0.982014i | ||||||
\(290\) | 10.1488 | − | 5.45983i | 0.595956 | − | 0.320612i | ||||
\(291\) | 10.0884i | 0.591392i | ||||||||
\(292\) | −9.69041 | + | 9.69041i | −0.567088 | + | 0.567088i | ||||
\(293\) | −12.5889 | + | 12.5889i | −0.735454 | + | 0.735454i | −0.971695 | − | 0.236241i | \(-0.924085\pi\) |
0.236241 | + | 0.971695i | \(0.424085\pi\) | |||||||
\(294\) | 1.13662i | 0.0662892i | ||||||||
\(295\) | −20.1922 | − | 6.06588i | −1.17563 | − | 0.353169i | ||||
\(296\) | 2.34781i | 0.136464i | ||||||||
\(297\) | −3.61696 | − | 3.61696i | −0.209878 | − | 0.209878i | ||||
\(298\) | 12.7374 | − | 12.7374i | 0.737859 | − | 0.737859i | ||||
\(299\) | −20.0348 | + | 21.8213i | −1.15864 | + | 1.26196i | ||||
\(300\) | −4.89860 | + | 1.00186i | −0.282821 | + | 0.0578425i | ||||
\(301\) | 14.1804 | 0.817342 | ||||||||
\(302\) | 8.71948 | − | 8.71948i | 0.501749 | − | 0.501749i | ||||
\(303\) | 3.05280 | + | 3.05280i | 0.175379 | + | 0.175379i | ||||
\(304\) | −6.15278 | −0.352886 | ||||||||
\(305\) | 14.7963 | + | 4.44493i | 0.847236 | + | 0.254516i | ||||
\(306\) | 0.552950i | 0.0316100i | ||||||||
\(307\) | 4.59148 | − | 4.59148i | 0.262049 | − | 0.262049i | −0.563837 | − | 0.825886i | \(-0.690675\pi\) |
0.825886 | + | 0.563837i | \(0.190675\pi\) | |||||||
\(308\) | −10.3173 | − | 10.3173i | −0.587883 | − | 0.587883i | ||||
\(309\) | 17.0459 | 0.969709 | ||||||||
\(310\) | 5.88441 | + | 10.9380i | 0.334212 | + | 0.621235i | ||||
\(311\) | −16.9139 | −0.959097 | −0.479549 | − | 0.877515i | \(-0.659200\pi\) | ||||
−0.479549 | + | 0.877515i | \(0.659200\pi\) | |||||||
\(312\) | 4.36777 | − | 4.36777i | 0.247276 | − | 0.247276i | ||||
\(313\) | 8.92881 | − | 8.92881i | 0.504686 | − | 0.504686i | −0.408204 | − | 0.912891i | \(-0.633845\pi\) |
0.912891 | + | 0.408204i | \(0.133845\pi\) | |||||||
\(314\) | −2.19914 | −0.124105 | ||||||||
\(315\) | 3.02187 | + | 5.61707i | 0.170263 | + | 0.316486i | ||||
\(316\) | − | 0.836863i | − | 0.0470772i | ||||||
\(317\) | 2.16941 | − | 2.16941i | 0.121846 | − | 0.121846i | −0.643554 | − | 0.765400i | \(-0.722541\pi\) |
0.765400 | + | 0.643554i | \(0.222541\pi\) | |||||||
\(318\) | 3.27229 | − | 3.27229i | 0.183501 | − | 0.183501i | ||||
\(319\) | 26.3624 | 1.47601 | ||||||||
\(320\) | −2.14152 | − | 0.643329i | −0.119715 | − | 0.0359632i | ||||
\(321\) | − | 7.68571i | − | 0.428974i | ||||||
\(322\) | −0.583354 | − | 13.6676i | −0.0325091 | − | 0.761663i | ||||
\(323\) | 2.40570 | + | 2.40570i | 0.133857 | + | 0.133857i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −6.18845 | − | 30.2585i | −0.343274 | − | 1.67844i | ||||
\(326\) | 7.94559 | 0.440065 | ||||||||
\(327\) | −1.40636 | − | 1.40636i | −0.0777719 | − | 0.0777719i | ||||
\(328\) | 5.80385 | + | 5.80385i | 0.320464 | + | 0.320464i | ||||
\(329\) | 14.9034 | 0.821651 | ||||||||
\(330\) | −10.9542 | − | 3.29073i | −0.603011 | − | 0.181149i | ||||
\(331\) | −4.44874 | −0.244525 | −0.122262 | − | 0.992498i | \(-0.539015\pi\) | ||||
−0.122262 | + | 0.992498i | \(0.539015\pi\) | |||||||
\(332\) | −7.68978 | − | 7.68978i | −0.422031 | − | 0.422031i | ||||
\(333\) | 1.66015 | − | 1.66015i | 0.0909757 | − | 0.0909757i | ||||
\(334\) | − | 8.18451i | − | 0.447836i | ||||||
\(335\) | 17.2297 | − | 9.26921i | 0.941357 | − | 0.506431i | ||||
\(336\) | 2.85248i | 0.155615i | ||||||||
\(337\) | −0.387079 | − | 0.387079i | −0.0210856 | − | 0.0210856i | 0.696485 | − | 0.717571i | \(-0.254746\pi\) |
−0.717571 | + | 0.696485i | \(0.754746\pi\) | |||||||
\(338\) | 17.7872 | + | 17.7872i | 0.967494 | + | 0.967494i | ||||
\(339\) | −0.744216 | −0.0404203 | ||||||||
\(340\) | 0.585786 | + | 1.08886i | 0.0317687 | + | 0.0590519i | ||||
\(341\) | 28.4124i | 1.53862i | ||||||||
\(342\) | 4.35067 | + | 4.35067i | 0.235257 | + | 0.235257i | ||||
\(343\) | −11.8265 | + | 11.8265i | −0.638569 | + | 0.638569i | ||||
\(344\) | 4.97125 | 0.268032 | ||||||||
\(345\) | −5.47872 | − | 9.21866i | −0.294964 | − | 0.496316i | ||||
\(346\) | −5.16353 | −0.277593 | ||||||||
\(347\) | 21.9216 | − | 21.9216i | 1.17681 | − | 1.17681i | 0.196262 | − | 0.980551i | \(-0.437120\pi\) |
0.980551 | − | 0.196262i | \(-0.0628804\pi\) | |||||||
\(348\) | −3.64427 | − | 3.64427i | −0.195353 | − | 0.195353i | ||||
\(349\) | 29.6703i | 1.58821i | 0.607779 | + | 0.794106i | \(0.292061\pi\) | ||||
−0.607779 | + | 0.794106i | \(0.707939\pi\) | |||||||
\(350\) | 11.9013 | + | 7.85974i | 0.636149 | + | 0.420121i | ||||
\(351\) | −6.17696 | −0.329702 | ||||||||
\(352\) | −3.61696 | − | 3.61696i | −0.192785 | − | 0.192785i | ||||
\(353\) | −1.26153 | − | 1.26153i | −0.0671442 | − | 0.0671442i | 0.672737 | − | 0.739881i | \(-0.265118\pi\) |
−0.739881 | + | 0.672737i | \(0.765118\pi\) | |||||||
\(354\) | 9.42889i | 0.501140i | ||||||||
\(355\) | −6.45924 | + | 21.5016i | −0.342821 | + | 1.14119i | ||||
\(356\) | − | 8.61622i | − | 0.456659i | ||||||
\(357\) | 1.11530 | − | 1.11530i | 0.0590281 | − | 0.0590281i | ||||
\(358\) | 13.2507 | + | 13.2507i | 0.700319 | + | 0.700319i | ||||
\(359\) | 9.95032 | 0.525158 | 0.262579 | − | 0.964911i | \(-0.415427\pi\) | ||||
0.262579 | + | 0.964911i | \(0.415427\pi\) | |||||||
\(360\) | 1.05938 | + | 1.96919i | 0.0558344 | + | 0.103785i | ||||
\(361\) | 18.8567 | 0.992458 | ||||||||
\(362\) | −14.6588 | − | 14.6588i | −0.770449 | − | 0.770449i | ||||
\(363\) | −10.7232 | − | 10.7232i | −0.562821 | − | 0.562821i | ||||
\(364\) | −17.6196 | −0.923520 | ||||||||
\(365\) | 26.9864 | − | 14.5181i | 1.41253 | − | 0.759914i | ||||
\(366\) | − | 6.90926i | − | 0.361153i | ||||||
\(367\) | 22.7067 | + | 22.7067i | 1.18528 | + | 1.18528i | 0.978358 | + | 0.206922i | \(0.0663445\pi\) |
0.206922 | + | 0.978358i | \(0.433655\pi\) | |||||||
\(368\) | −0.204508 | − | 4.79147i | −0.0106607 | − | 0.249773i | ||||
\(369\) | − | 8.20789i | − | 0.427286i | ||||||
\(370\) | 1.51041 | − | 5.02789i | 0.0785226 | − | 0.261387i | ||||
\(371\) | −13.2005 | −0.685334 | ||||||||
\(372\) | 3.92767 | − | 3.92767i | 0.203640 | − | 0.203640i | ||||
\(373\) | −17.7101 | + | 17.7101i | −0.916992 | + | 0.916992i | −0.996809 | − | 0.0798177i | \(-0.974566\pi\) |
0.0798177 | + | 0.996809i | \(0.474566\pi\) | |||||||
\(374\) | 2.82843i | 0.146254i | ||||||||
\(375\) | 11.1350 | + | 1.00590i | 0.575009 | + | 0.0519446i | ||||
\(376\) | 5.22472 | 0.269444 | ||||||||
\(377\) | 22.5105 | − | 22.5105i | 1.15935 | − | 1.15935i | ||||
\(378\) | 2.01701 | − | 2.01701i | 0.103744 | − | 0.103744i | ||||
\(379\) | 11.5472 | 0.593142 | 0.296571 | − | 0.955011i | \(-0.404157\pi\) | ||||
0.296571 | + | 0.955011i | \(0.404157\pi\) | |||||||
\(380\) | 13.1763 | + | 3.95826i | 0.675931 | + | 0.203055i | ||||
\(381\) | −22.1746 | −1.13604 | ||||||||
\(382\) | 6.83241 | + | 6.83241i | 0.349577 | + | 0.349577i | ||||
\(383\) | 21.9574 | − | 21.9574i | 1.12197 | − | 1.12197i | 0.130527 | − | 0.991445i | \(-0.458333\pi\) |
0.991445 | − | 0.130527i | \(-0.0416668\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 15.4573 | + | 28.7322i | 0.787779 | + | 1.46433i | ||||
\(386\) | −7.65117 | −0.389434 | ||||||||
\(387\) | −3.51520 | − | 3.51520i | −0.178688 | − | 0.178688i | ||||
\(388\) | 7.13357 | − | 7.13357i | 0.362152 | − | 0.362152i | ||||
\(389\) | 20.6283 | 1.04589 | 0.522947 | − | 0.852365i | \(-0.324832\pi\) | ||||
0.522947 | + | 0.852365i | \(0.324832\pi\) | |||||||
\(390\) | −12.1636 | + | 6.54377i | −0.615928 | + | 0.331357i | ||||
\(391\) | −1.79348 | + | 1.95340i | −0.0907000 | + | 0.0987877i | ||||
\(392\) | 0.803714 | − | 0.803714i | 0.0405937 | − | 0.0405937i | ||||
\(393\) | −2.34188 | − | 2.34188i | −0.118132 | − | 0.118132i | ||||
\(394\) | − | 13.7006i | − | 0.690226i | ||||||
\(395\) | −0.538379 | + | 1.79216i | −0.0270888 | + | 0.0901735i | ||||
\(396\) | 5.11516i | 0.257046i | ||||||||
\(397\) | −1.70732 | + | 1.70732i | −0.0856879 | + | 0.0856879i | −0.748652 | − | 0.662964i | \(-0.769298\pi\) |
0.662964 | + | 0.748652i | \(0.269298\pi\) | |||||||
\(398\) | 1.36310 | − | 1.36310i | 0.0683262 | − | 0.0683262i | ||||
\(399\) | − | 17.5507i | − | 0.878632i | ||||||
\(400\) | 4.17226 | + | 2.75541i | 0.208613 | + | 0.137771i | ||||
\(401\) | 30.6848i | 1.53233i | 0.642646 | + | 0.766163i | \(0.277836\pi\) | ||||
−0.642646 | + | 0.766163i | \(0.722164\pi\) | |||||||
\(402\) | −6.18692 | − | 6.18692i | −0.308575 | − | 0.308575i | ||||
\(403\) | 24.2610 | + | 24.2610i | 1.20853 | + | 1.20853i | ||||
\(404\) | − | 4.31730i | − | 0.214794i | ||||||
\(405\) | 0.643329 | − | 2.14152i | 0.0319673 | − | 0.106413i | ||||
\(406\) | 14.7010i | 0.729600i | ||||||||
\(407\) | 8.49194 | − | 8.49194i | 0.420930 | − | 0.420930i | ||||
\(408\) | 0.390995 | − | 0.390995i | 0.0193571 | − | 0.0193571i | ||||
\(409\) | − | 9.11463i | − | 0.450689i | −0.974279 | − | 0.225345i | \(-0.927649\pi\) | ||
0.974279 | − | 0.225345i | \(-0.0723508\pi\) | |||||||
\(410\) | −8.69531 | − | 16.1629i | −0.429431 | − | 0.798228i | ||||
\(411\) | − | 3.01539i | − | 0.148738i | ||||||
\(412\) | −12.0533 | − | 12.0533i | −0.593823 | − | 0.593823i | ||||
\(413\) | 19.0181 | − | 19.0181i | 0.935820 | − | 0.935820i | ||||
\(414\) | −3.24347 | + | 3.53269i | −0.159408 | + | 0.173622i | ||||
\(415\) | 11.5208 | + | 21.4149i | 0.565533 | + | 1.05122i | ||||
\(416\) | −6.17696 | −0.302850 | ||||||||
\(417\) | 5.94373 | − | 5.94373i | 0.291066 | − | 0.291066i | ||||
\(418\) | 22.2544 | + | 22.2544i | 1.08850 | + | 1.08850i | ||||
\(419\) | −8.58413 | −0.419362 | −0.209681 | − | 0.977770i | \(-0.567243\pi\) | ||||
−0.209681 | + | 0.977770i | \(0.567243\pi\) | |||||||
\(420\) | 1.83508 | − | 6.10865i | 0.0895428 | − | 0.298072i | ||||
\(421\) | 7.06186i | 0.344174i | 0.985082 | + | 0.172087i | \(0.0550510\pi\) | ||||
−0.985082 | + | 0.172087i | \(0.944949\pi\) | |||||||
\(422\) | 9.48362 | − | 9.48362i | 0.461655 | − | 0.461655i | ||||
\(423\) | −3.69444 | − | 3.69444i | −0.179630 | − | 0.179630i | ||||
\(424\) | −4.62772 | −0.224742 | ||||||||
\(425\) | −0.553979 | − | 2.70868i | −0.0268719 | − | 0.131390i | ||||
\(426\) | 10.0403 | 0.486456 | ||||||||
\(427\) | −13.9360 | + | 13.9360i | −0.674411 | + | 0.674411i | ||||
\(428\) | −5.43462 | + | 5.43462i | −0.262692 | + | 0.262692i | ||||
\(429\) | −31.5961 | −1.52548 | ||||||||
\(430\) | −10.6460 | − | 3.19815i | −0.513398 | − | 0.154228i | ||||
\(431\) | − | 19.9570i | − | 0.961296i | −0.876914 | − | 0.480648i | \(-0.840401\pi\) | ||
0.876914 | − | 0.480648i | \(-0.159599\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −15.9071 | + | 15.9071i | −0.764447 | + | 0.764447i | −0.977123 | − | 0.212676i | \(-0.931782\pi\) |
0.212676 | + | 0.977123i | \(0.431782\pi\) | |||||||
\(434\) | −15.8442 | −0.760548 | ||||||||
\(435\) | 5.45983 | + | 10.1488i | 0.261779 | + | 0.486596i | ||||
\(436\) | 1.98889i | 0.0952507i | ||||||||
\(437\) | 1.25829 | + | 29.4809i | 0.0601923 | + | 1.41026i | ||||
\(438\) | −9.69041 | − | 9.69041i | −0.463026 | − | 0.463026i | ||||
\(439\) | − | 15.0024i | − | 0.716028i | −0.933716 | − | 0.358014i | \(-0.883454\pi\) | ||
0.933716 | − | 0.358014i | \(-0.116546\pi\) | |||||||
\(440\) | 5.41892 | + | 10.0727i | 0.258337 | + | 0.480198i | ||||
\(441\) | −1.13662 | −0.0541249 | ||||||||
\(442\) | 2.41516 | + | 2.41516i | 0.114877 | + | 0.114877i | ||||
\(443\) | 13.3100 | + | 13.3100i | 0.632377 | + | 0.632377i | 0.948664 | − | 0.316287i | \(-0.102436\pi\) |
−0.316287 | + | 0.948664i | \(0.602436\pi\) | |||||||
\(444\) | −2.34781 | −0.111422 | ||||||||
\(445\) | −5.54306 | + | 18.4518i | −0.262766 | + | 0.874701i | ||||
\(446\) | −10.9903 | −0.520405 | ||||||||
\(447\) | 12.7374 | + | 12.7374i | 0.602459 | + | 0.602459i | ||||
\(448\) | 2.01701 | − | 2.01701i | 0.0952946 | − | 0.0952946i | ||||
\(449\) | − | 29.8217i | − | 1.40737i | −0.710510 | − | 0.703687i | \(-0.751536\pi\) | ||
0.710510 | − | 0.703687i | \(-0.248464\pi\) | |||||||
\(450\) | −1.00186 | − | 4.89860i | −0.0472282 | − | 0.230922i | ||||
\(451\) | − | 41.9847i | − | 1.97698i | ||||||
\(452\) | 0.526241 | + | 0.526241i | 0.0247523 | + | 0.0247523i | ||||
\(453\) | 8.71948 | + | 8.71948i | 0.409677 | + | 0.409677i | ||||
\(454\) | −26.2159 | −1.23037 | ||||||||
\(455\) | 37.7329 | + | 11.3352i | 1.76894 | + | 0.531404i | ||||
\(456\) | − | 6.15278i | − | 0.288130i | ||||||
\(457\) | −28.1085 | − | 28.1085i | −1.31486 | − | 1.31486i | −0.917787 | − | 0.397074i | \(-0.870026\pi\) |
−0.397074 | − | 0.917787i | \(-0.629974\pi\) | |||||||
\(458\) | 6.58128 | − | 6.58128i | 0.307523 | − | 0.307523i | ||||
\(459\) | −0.552950 | −0.0258095 | ||||||||
\(460\) | −2.64453 | + | 10.3926i | −0.123302 | + | 0.484558i | ||||
\(461\) | −30.4481 | −1.41811 | −0.709054 | − | 0.705154i | \(-0.750878\pi\) | ||||
−0.709054 | + | 0.705154i | \(0.750878\pi\) | |||||||
\(462\) | 10.3173 | − | 10.3173i | 0.480004 | − | 0.480004i | ||||
\(463\) | 2.16221 | + | 2.16221i | 0.100486 | + | 0.100486i | 0.755563 | − | 0.655076i | \(-0.227364\pi\) |
−0.655076 | + | 0.755563i | \(0.727364\pi\) | |||||||
\(464\) | 5.15378i | 0.239258i | ||||||||
\(465\) | −10.9380 | + | 5.88441i | −0.507236 | + | 0.272883i | ||||
\(466\) | −17.5465 | −0.812826 | ||||||||
\(467\) | 10.3427 | + | 10.3427i | 0.478604 | + | 0.478604i | 0.904685 | − | 0.426081i | \(-0.140106\pi\) |
−0.426081 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(468\) | 4.36777 | + | 4.36777i | 0.201900 | + | 0.201900i | ||||
\(469\) | 24.9581i | 1.15246i | ||||||||
\(470\) | −11.1889 | − | 3.36121i | −0.516104 | − | 0.155041i | ||||
\(471\) | − | 2.19914i | − | 0.101331i | ||||||
\(472\) | 6.66723 | − | 6.66723i | 0.306884 | − | 0.306884i | ||||
\(473\) | −17.9808 | − | 17.9808i | −0.826759 | − | 0.826759i | ||||
\(474\) | 0.836863 | 0.0384384 | ||||||||
\(475\) | −25.6710 | − | 16.9534i | −1.17786 | − | 0.777877i | ||||
\(476\) | −1.57728 | −0.0722944 | ||||||||
\(477\) | 3.27229 | + | 3.27229i | 0.149828 | + | 0.149828i | ||||
\(478\) | −9.00810 | − | 9.00810i | −0.412021 | − | 0.412021i | ||||
\(479\) | −27.5688 | −1.25965 | −0.629826 | − | 0.776736i | \(-0.716874\pi\) | ||||
−0.629826 | + | 0.776736i | \(0.716874\pi\) | |||||||
\(480\) | 0.643329 | − | 2.14152i | 0.0293638 | − | 0.0977468i | ||||
\(481\) | − | 14.5023i | − | 0.661249i | ||||||
\(482\) | 3.94413 | + | 3.94413i | 0.179650 | + | 0.179650i | ||||
\(483\) | 13.6676 | − | 0.583354i | 0.621895 | − | 0.0265435i | ||||
\(484\) | 15.1649i | 0.689312i | ||||||||
\(485\) | −19.8659 | + | 10.6875i | −0.902066 | + | 0.485293i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −11.1321 | + | 11.1321i | −0.504442 | + | 0.504442i | −0.912815 | − | 0.408373i | \(-0.866096\pi\) |
0.408373 | + | 0.912815i | \(0.366096\pi\) | |||||||
\(488\) | −4.88558 | + | 4.88558i | −0.221160 | + | 0.221160i | ||||
\(489\) | 7.94559i | 0.359312i | ||||||||
\(490\) | −2.23823 | + | 1.20412i | −0.101113 | + | 0.0543966i | ||||
\(491\) | 12.2648 | 0.553501 | 0.276750 | − | 0.960942i | \(-0.410742\pi\) | ||||
0.276750 | + | 0.960942i | \(0.410742\pi\) | |||||||
\(492\) | −5.80385 | + | 5.80385i | −0.261658 | + | 0.261658i | ||||
\(493\) | 2.01510 | − | 2.01510i | 0.0907555 | − | 0.0907555i | ||||
\(494\) | 38.0055 | 1.70995 | ||||||||
\(495\) | 3.29073 | − | 10.9542i | 0.147907 | − | 0.492356i | ||||
\(496\) | −5.55456 | −0.249407 | ||||||||
\(497\) | −20.2514 | − | 20.2514i | −0.908400 | − | 0.908400i | ||||
\(498\) | 7.68978 | − | 7.68978i | 0.344587 | − | 0.344587i | ||||
\(499\) | − | 10.1093i | − | 0.452555i | −0.974063 | − | 0.226277i | \(-0.927344\pi\) | ||
0.974063 | − | 0.226277i | \(-0.0726556\pi\) | |||||||
\(500\) | −7.16235 | − | 8.58491i | −0.320310 | − | 0.383929i | ||||
\(501\) | 8.18451 | 0.365657 | ||||||||
\(502\) | 19.9169 | + | 19.9169i | 0.888935 | + | 0.888935i | ||||
\(503\) | −25.5661 | + | 25.5661i | −1.13994 | + | 1.13994i | −0.151476 | + | 0.988461i | \(0.548403\pi\) |
−0.988461 | + | 0.151476i | \(0.951597\pi\) | |||||||
\(504\) | −2.85248 | −0.127059 | ||||||||
\(505\) | −2.77745 | + | 9.24561i | −0.123595 | + | 0.411424i | ||||
\(506\) | −16.5909 | + | 18.0703i | −0.737554 | + | 0.803321i | ||||
\(507\) | −17.7872 | + | 17.7872i | −0.789955 | + | 0.789955i | ||||
\(508\) | 15.6798 | + | 15.6798i | 0.695679 | + | 0.695679i | ||||
\(509\) | − | 23.2951i | − | 1.03254i | −0.856427 | − | 0.516268i | \(-0.827321\pi\) | ||
0.856427 | − | 0.516268i | \(-0.172679\pi\) | |||||||
\(510\) | −1.08886 | + | 0.585786i | −0.0482157 | + | 0.0259391i | ||||
\(511\) | 39.0912i | 1.72929i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −4.35067 | + | 4.35067i | −0.192087 | + | 0.192087i | ||||
\(514\) | 10.0573i | 0.443608i | ||||||||
\(515\) | 18.0582 | + | 33.5666i | 0.795739 | + | 1.47912i | ||||
\(516\) | 4.97125i | 0.218847i | ||||||||
\(517\) | −18.8976 | − | 18.8976i | −0.831117 | − | 0.831117i | ||||
\(518\) | 4.73554 | + | 4.73554i | 0.208068 | + | 0.208068i | ||||
\(519\) | − | 5.16353i | − | 0.226654i | ||||||
\(520\) | 13.2281 | + | 3.97382i | 0.580091 | + | 0.174263i | ||||
\(521\) | 22.1829i | 0.971850i | 0.874001 | + | 0.485925i | \(0.161517\pi\) | ||||
−0.874001 | + | 0.485925i | \(0.838483\pi\) | |||||||
\(522\) | 3.64427 | − | 3.64427i | 0.159505 | − | 0.159505i | ||||
\(523\) | 14.7292 | − | 14.7292i | 0.644064 | − | 0.644064i | −0.307488 | − | 0.951552i | \(-0.599488\pi\) |
0.951552 | + | 0.307488i | \(0.0994883\pi\) | |||||||
\(524\) | 3.31192i | 0.144682i | ||||||||
\(525\) | −7.85974 | + | 11.9013i | −0.343027 | + | 0.519414i | ||||
\(526\) | 13.6083i | 0.593348i | ||||||||
\(527\) | 2.17180 | + | 2.17180i | 0.0946052 | + | 0.0946052i | ||||
\(528\) | 3.61696 | − | 3.61696i | 0.157408 | − | 0.157408i | ||||
\(529\) | −22.9164 | + | 1.95979i | −0.996363 | + | 0.0852082i | ||||
\(530\) | 9.91038 | + | 2.97715i | 0.430479 | + | 0.129319i | ||||
\(531\) | −9.42889 | −0.409179 | ||||||||
\(532\) | −12.4102 | + | 12.4102i | −0.538050 | + | 0.538050i | ||||
\(533\) | −35.8502 | − | 35.8502i | −1.55284 | − | 1.55284i | ||||
\(534\) | 8.61622 | 0.372860 | ||||||||
\(535\) | 15.1346 | − | 8.14212i | 0.654326 | − | 0.352014i | ||||
\(536\) | 8.74963i | 0.377926i | ||||||||
\(537\) | −13.2507 | + | 13.2507i | −0.571808 | + | 0.571808i | ||||
\(538\) | −4.87314 | − | 4.87314i | −0.210096 | − | 0.210096i | ||||
\(539\) | −5.81401 | −0.250427 | ||||||||
\(540\) | −1.96919 | + | 1.05938i | −0.0847404 | + | 0.0455886i | ||||
\(541\) | 25.8534 | 1.11152 | 0.555762 | − | 0.831341i | \(-0.312426\pi\) | ||||
0.555762 | + | 0.831341i | \(0.312426\pi\) | |||||||
\(542\) | 17.1238 | − | 17.1238i | 0.735530 | − | 0.735530i | ||||
\(543\) | 14.6588 | − | 14.6588i | 0.629069 | − | 0.629069i | ||||
\(544\) | −0.552950 | −0.0237075 | ||||||||
\(545\) | 1.27951 | − | 4.25926i | 0.0548083 | − | 0.182447i | ||||
\(546\) | − | 17.6196i | − | 0.754051i | ||||||
\(547\) | −9.64881 | + | 9.64881i | −0.412553 | + | 0.412553i | −0.882627 | − | 0.470074i | \(-0.844227\pi\) |
0.470074 | + | 0.882627i | \(0.344227\pi\) | |||||||
\(548\) | −2.13220 | + | 2.13220i | −0.0910831 | + | 0.0910831i | ||||
\(549\) | 6.90926 | 0.294880 | ||||||||
\(550\) | −5.12468 | − | 25.0571i | −0.218517 | − | 1.06844i | ||||
\(551\) | − | 31.7101i | − | 1.35089i | ||||||
\(552\) | 4.79147 | − | 0.204508i | 0.203938 | − | 0.00870444i | ||||
\(553\) | −1.68796 | − | 1.68796i | −0.0717793 | − | 0.0717793i | ||||
\(554\) | − | 26.9947i | − | 1.14690i | ||||||
\(555\) | 5.02789 | + | 1.51041i | 0.213422 | + | 0.0641135i | ||||
\(556\) | −8.40570 | −0.356481 | ||||||||
\(557\) | 2.29468 | + | 2.29468i | 0.0972289 | + | 0.0972289i | 0.754048 | − | 0.656819i | \(-0.228099\pi\) |
−0.656819 | + | 0.754048i | \(0.728099\pi\) | |||||||
\(558\) | 3.92767 | + | 3.92767i | 0.166271 | + | 0.166271i | ||||
\(559\) | −30.7072 | −1.29878 | ||||||||
\(560\) | −5.61707 | + | 3.02187i | −0.237364 | + | 0.127697i | ||||
\(561\) | −2.82843 | −0.119416 | ||||||||
\(562\) | −14.3801 | − | 14.3801i | −0.606590 | − | 0.606590i | ||||
\(563\) | 9.31814 | − | 9.31814i | 0.392713 | − | 0.392713i | −0.482941 | − | 0.875653i | \(-0.660431\pi\) |
0.875653 | + | 0.482941i | \(0.160431\pi\) | |||||||
\(564\) | 5.22472i | 0.220000i | ||||||||
\(565\) | −0.788411 | − | 1.46550i | −0.0331687 | − | 0.0616542i | ||||
\(566\) | 25.2367i | 1.06078i | ||||||||
\(567\) | 2.01701 | + | 2.01701i | 0.0847063 | + | 0.0847063i | ||||
\(568\) | −7.09959 | − | 7.09959i | −0.297892 | − | 0.297892i | ||||
\(569\) | 28.0086 | 1.17418 | 0.587090 | − | 0.809522i | \(-0.300273\pi\) | ||||
0.587090 | + | 0.809522i | \(0.300273\pi\) | |||||||
\(570\) | −3.95826 | + | 13.1763i | −0.165793 | + | 0.551896i | ||||
\(571\) | 36.3711i | 1.52208i | 0.648703 | + | 0.761042i | \(0.275312\pi\) | ||||
−0.648703 | + | 0.761042i | \(0.724688\pi\) | |||||||
\(572\) | 22.3418 | + | 22.3418i | 0.934159 | + | 0.934159i | ||||
\(573\) | −6.83241 | + | 6.83241i | −0.285428 | + | 0.285428i | ||||
\(574\) | 23.4128 | 0.977232 | ||||||||
\(575\) | 12.3492 | − | 20.5547i | 0.514997 | − | 0.857192i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −19.8564 | + | 19.8564i | −0.826634 | + | 0.826634i | −0.987050 | − | 0.160416i | \(-0.948716\pi\) |
0.160416 | + | 0.987050i | \(0.448716\pi\) | |||||||
\(578\) | −11.8046 | − | 11.8046i | −0.491007 | − | 0.491007i | ||||
\(579\) | − | 7.65117i | − | 0.317972i | ||||||
\(580\) | 3.31558 | − | 11.0369i | 0.137672 | − | 0.458284i | ||||
\(581\) | −31.0206 | −1.28695 | ||||||||
\(582\) | 7.13357 | + | 7.13357i | 0.295696 | + | 0.295696i | ||||
\(583\) | 16.7383 | + | 16.7383i | 0.693229 | + | 0.693229i | ||||
\(584\) | 13.7043i | 0.567088i | ||||||||
\(585\) | −6.54377 | − | 12.1636i | −0.270552 | − | 0.502903i | ||||
\(586\) | 17.8035i | 0.735454i | ||||||||
\(587\) | −26.7004 | + | 26.7004i | −1.10204 | + | 1.10204i | −0.107879 | + | 0.994164i | \(0.534406\pi\) |
−0.994164 | + | 0.107879i | \(0.965594\pi\) | |||||||
\(588\) | 0.803714 | + | 0.803714i | 0.0331446 | + | 0.0331446i | ||||
\(589\) | 34.1760 | 1.40820 | ||||||||
\(590\) | −18.5673 | + | 9.98881i | −0.764402 | + | 0.411233i | ||||
\(591\) | 13.7006 | 0.563567 | ||||||||
\(592\) | 1.66015 | + | 1.66015i | 0.0682318 | + | 0.0682318i | ||||
\(593\) | −3.37233 | − | 3.37233i | −0.138485 | − | 0.138485i | 0.634466 | − | 0.772951i | \(-0.281220\pi\) |
−0.772951 | + | 0.634466i | \(0.781220\pi\) | |||||||
\(594\) | −5.11516 | −0.209878 | ||||||||
\(595\) | 3.37778 | + | 1.01471i | 0.138475 | + | 0.0415990i | ||||
\(596\) | − | 18.0134i | − | 0.737859i | ||||||
\(597\) | 1.36310 | + | 1.36310i | 0.0557881 | + | 0.0557881i | ||||
\(598\) | 1.26324 | + | 29.5967i | 0.0516576 | + | 1.21030i | ||||
\(599\) | 16.1347i | 0.659248i | 0.944112 | + | 0.329624i | \(0.106922\pi\) | ||||
−0.944112 | + | 0.329624i | \(0.893078\pi\) | |||||||
\(600\) | −2.75541 | + | 4.17226i | −0.112489 | + | 0.170332i | ||||
\(601\) | 22.7683 | 0.928740 | 0.464370 | − | 0.885641i | \(-0.346281\pi\) | ||||
0.464370 | + | 0.885641i | \(0.346281\pi\) | |||||||
\(602\) | 10.0270 | − | 10.0270i | 0.408671 | − | 0.408671i | ||||
\(603\) | 6.18692 | − | 6.18692i | 0.251951 | − | 0.251951i | ||||
\(604\) | − | 12.3312i | − | 0.501749i | ||||||
\(605\) | 9.75599 | − | 32.4759i | 0.396638 | − | 1.32033i | ||||
\(606\) | 4.31730 | 0.175379 | ||||||||
\(607\) | 22.8209 | − | 22.8209i | 0.926273 | − | 0.926273i | −0.0711898 | − | 0.997463i | \(-0.522680\pi\) |
0.997463 | + | 0.0711898i | \(0.0226796\pi\) | |||||||
\(608\) | −4.35067 | + | 4.35067i | −0.176443 | + | 0.176443i | ||||
\(609\) | −14.7010 | −0.595716 | ||||||||
\(610\) | 13.6056 | − | 7.31956i | 0.550876 | − | 0.296360i | ||||
\(611\) | −32.2729 | −1.30562 | ||||||||
\(612\) | 0.390995 | + | 0.390995i | 0.0158050 | + | 0.0158050i | ||||
\(613\) | −15.0940 | + | 15.0940i | −0.609639 | + | 0.609639i | −0.942852 | − | 0.333213i | \(-0.891867\pi\) |
0.333213 | + | 0.942852i | \(0.391867\pi\) | |||||||
\(614\) | − | 6.49333i | − | 0.262049i | ||||||
\(615\) | 16.1629 | − | 8.69531i | 0.651750 | − | 0.350629i | ||||
\(616\) | −14.5909 | −0.587883 | ||||||||
\(617\) | −13.3305 | − | 13.3305i | −0.536665 | − | 0.536665i | 0.385883 | − | 0.922548i | \(-0.373897\pi\) |
−0.922548 | + | 0.385883i | \(0.873897\pi\) | |||||||
\(618\) | 12.0533 | − | 12.0533i | 0.484854 | − | 0.484854i | ||||
\(619\) | −31.9076 | −1.28247 | −0.641236 | − | 0.767343i | \(-0.721578\pi\) | ||||
−0.641236 | + | 0.767343i | \(0.721578\pi\) | |||||||
\(620\) | 11.8952 | + | 3.57341i | 0.477724 | + | 0.143512i | ||||
\(621\) | −3.53269 | − | 3.24347i | −0.141762 | − | 0.130156i | ||||
\(622\) | −11.9599 | + | 11.9599i | −0.479549 | + | 0.479549i | ||||
\(623\) | −17.3790 | − | 17.3790i | −0.696273 | − | 0.696273i | ||||
\(624\) | − | 6.17696i | − | 0.247276i | ||||||
\(625\) | 9.81543 | + | 22.9926i | 0.392617 | + | 0.919702i | ||||
\(626\) | − | 12.6272i | − | 0.504686i | ||||||
\(627\) | −22.2544 | + | 22.2544i | −0.888754 | + | 0.888754i | ||||
\(628\) | −1.55503 | + | 1.55503i | −0.0620523 | + | 0.0620523i | ||||
\(629\) | − | 1.29822i | − | 0.0517634i | ||||||
\(630\) | 6.10865 | + | 1.83508i | 0.243374 | + | 0.0731114i | ||||
\(631\) | − | 12.7919i | − | 0.509238i | −0.967041 | − | 0.254619i | \(-0.918050\pi\) | ||
0.967041 | − | 0.254619i | \(-0.0819500\pi\) | |||||||
\(632\) | −0.591752 | − | 0.591752i | −0.0235386 | − | 0.0235386i | ||||
\(633\) | 9.48362 | + | 9.48362i | 0.376940 | + | 0.376940i | ||||
\(634\) | − | 3.06801i | − | 0.121846i | ||||||
\(635\) | −23.4914 | − | 43.6660i | −0.932229 | − | 1.73283i | ||||
\(636\) | − | 4.62772i | − | 0.183501i | ||||||
\(637\) | −4.96451 | + | 4.96451i | −0.196701 | + | 0.196701i | ||||
\(638\) | 18.6410 | − | 18.6410i | 0.738005 | − | 0.738005i | ||||
\(639\) | 10.0403i | 0.397190i | ||||||||
\(640\) | −1.96919 | + | 1.05938i | −0.0778390 | + | 0.0418758i | ||||
\(641\) | − | 17.4191i | − | 0.688014i | −0.938967 | − | 0.344007i | \(-0.888216\pi\) | ||
0.938967 | − | 0.344007i | \(-0.111784\pi\) | |||||||
\(642\) | −5.43462 | − | 5.43462i | −0.214487 | − | 0.214487i | ||||
\(643\) | 27.1429 | − | 27.1429i | 1.07041 | − | 1.07041i | 0.0730859 | − | 0.997326i | \(-0.476715\pi\) |
0.997326 | − | 0.0730859i | \(-0.0232847\pi\) | |||||||
\(644\) | −10.0769 | − | 9.25193i | −0.397086 | − | 0.364577i | ||||
\(645\) | 3.19815 | − | 10.6460i | 0.125927 | − | 0.419188i | ||||
\(646\) | 3.40218 | 0.133857 | ||||||||
\(647\) | −26.3595 | + | 26.3595i | −1.03630 | + | 1.03630i | −0.0369830 | + | 0.999316i | \(0.511775\pi\) |
−0.999316 | + | 0.0369830i | \(0.988225\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | −48.2303 | −1.89320 | ||||||||
\(650\) | −25.7719 | − | 17.0201i | −1.01086 | − | 0.667582i | ||||
\(651\) | − | 15.8442i | − | 0.620985i | ||||||
\(652\) | 5.61838 | − | 5.61838i | 0.220033 | − | 0.220033i | ||||
\(653\) | 13.2363 | + | 13.2363i | 0.517978 | + | 0.517978i | 0.916959 | − | 0.398981i | \(-0.130636\pi\) |
−0.398981 | + | 0.916959i | \(0.630636\pi\) | |||||||
\(654\) | −1.98889 | −0.0777719 | ||||||||
\(655\) | 2.13065 | − | 7.09255i | 0.0832515 | − | 0.277129i | ||||
\(656\) | 8.20789 | 0.320464 | ||||||||
\(657\) | 9.69041 | − | 9.69041i | 0.378059 | − | 0.378059i | ||||
\(658\) | 10.5383 | − | 10.5383i | 0.410825 | − | 0.410825i | ||||
\(659\) | −26.8438 | −1.04569 | −0.522843 | − | 0.852429i | \(-0.675129\pi\) | ||||
−0.522843 | + | 0.852429i | \(0.675129\pi\) | |||||||
\(660\) | −10.0727 | + | 5.41892i | −0.392080 | + | 0.210931i | ||||
\(661\) | − | 29.5722i | − | 1.15023i | −0.818074 | − | 0.575113i | \(-0.804958\pi\) | ||
0.818074 | − | 0.575113i | \(-0.195042\pi\) | |||||||
\(662\) | −3.14573 | + | 3.14573i | −0.122262 | + | 0.122262i | ||||
\(663\) | −2.41516 | + | 2.41516i | −0.0937970 | + | 0.0937970i | ||||
\(664\) | −10.8750 | −0.422031 | ||||||||
\(665\) | 34.5606 | − | 18.5929i | 1.34020 | − | 0.721001i | ||||
\(666\) | − | 2.34781i | − | 0.0909757i | ||||||
\(667\) | 24.6942 | − | 1.05399i | 0.956162 | − | 0.0408106i | ||||
\(668\) | −5.78732 | − | 5.78732i | −0.223918 | − | 0.223918i | ||||
\(669\) | − | 10.9903i | − | 0.424909i | ||||||
\(670\) | 5.62889 | − | 18.7375i | 0.217463 | − | 0.723894i | ||||
\(671\) | 35.3419 | 1.36436 | ||||||||
\(672\) | 2.01701 | + | 2.01701i | 0.0778077 | + | 0.0778077i | ||||
\(673\) | −11.0151 | − | 11.0151i | −0.424602 | − | 0.424602i | 0.462182 | − | 0.886785i | \(-0.347067\pi\) |
−0.886785 | + | 0.462182i | \(0.847067\pi\) | |||||||
\(674\) | −0.547413 | −0.0210856 | ||||||||
\(675\) | 4.89860 | − | 1.00186i | 0.188547 | − | 0.0385616i | ||||
\(676\) | 25.1548 | 0.967494 | ||||||||
\(677\) | −5.28014 | − | 5.28014i | −0.202932 | − | 0.202932i | 0.598323 | − | 0.801255i | \(-0.295834\pi\) |
−0.801255 | + | 0.598323i | \(0.795834\pi\) | |||||||
\(678\) | −0.526241 | + | 0.526241i | −0.0202101 | + | 0.0202101i | ||||
\(679\) | − | 28.7769i | − | 1.10436i | ||||||
\(680\) | 1.18416 | + | 0.355729i | 0.0454103 | + | 0.0136416i | ||||
\(681\) | − | 26.2159i | − | 1.00459i | ||||||
\(682\) | 20.0906 | + | 20.0906i | 0.769310 | + | 0.769310i | ||||
\(683\) | −9.53627 | − | 9.53627i | −0.364895 | − | 0.364895i | 0.500716 | − | 0.865611i | \(-0.333070\pi\) |
−0.865611 | + | 0.500716i | \(0.833070\pi\) | |||||||
\(684\) | 6.15278 | 0.235257 | ||||||||
\(685\) | 5.93787 | − | 3.19445i | 0.226874 | − | 0.122054i | ||||
\(686\) | 16.7251i | 0.638569i | ||||||||
\(687\) | 6.58128 | + | 6.58128i | 0.251091 | + | 0.251091i | ||||
\(688\) | 3.51520 | − | 3.51520i | 0.134016 | − | 0.134016i | ||||
\(689\) | 28.5852 | 1.08901 | ||||||||
\(690\) | −10.3926 | − | 2.64453i | −0.395640 | − | 0.100676i | ||||
\(691\) | −40.3146 | −1.53364 | −0.766820 | − | 0.641862i | \(-0.778162\pi\) | ||||
−0.766820 | + | 0.641862i | \(0.778162\pi\) | |||||||
\(692\) | −3.65117 | + | 3.65117i | −0.138796 | + | 0.138796i | ||||
\(693\) | 10.3173 | + | 10.3173i | 0.391922 | + | 0.391922i | ||||
\(694\) | − | 31.0018i | − | 1.17681i | ||||||
\(695\) | 18.0010 | + | 5.40763i | 0.682818 | + | 0.205123i | ||||
\(696\) | −5.15378 | −0.195353 | ||||||||
\(697\) | −3.20924 | − | 3.20924i | −0.121559 | − | 0.121559i | ||||
\(698\) | 20.9800 | + | 20.9800i | 0.794106 | + | 0.794106i | ||||
\(699\) | − | 17.5465i | − | 0.663670i | ||||||
\(700\) | 13.9731 | − | 2.85778i | 0.528135 | − | 0.108014i | ||||
\(701\) | − | 10.9576i | − | 0.413862i | −0.978356 | − | 0.206931i | \(-0.933652\pi\) | ||
0.978356 | − | 0.206931i | \(-0.0663476\pi\) | |||||||
\(702\) | −4.36777 | + | 4.36777i | −0.164851 | + | 0.164851i | ||||
\(703\) | −10.2145 | − | 10.2145i | −0.385249 | − | 0.385249i | ||||
\(704\) | −5.11516 | −0.192785 | ||||||||
\(705\) | 3.36121 | − | 11.1889i | 0.126591 | − | 0.421397i | ||||
\(706\) | −1.78407 | −0.0671442 | ||||||||
\(707\) | −8.70803 | − | 8.70803i | −0.327499 | − | 0.327499i | ||||
\(708\) | 6.66723 | + | 6.66723i | 0.250570 | + | 0.250570i | ||||
\(709\) | 11.6600 | 0.437899 | 0.218950 | − | 0.975736i | \(-0.429737\pi\) | ||||
0.218950 | + | 0.975736i | \(0.429737\pi\) | |||||||
\(710\) | 10.6366 | + | 19.7713i | 0.399184 | + | 0.742004i | ||||
\(711\) | 0.836863i | 0.0313848i | ||||||||
\(712\) | −6.09259 | − | 6.09259i | −0.228329 | − | 0.228329i | ||||
\(713\) | 1.13595 | + | 26.6145i | 0.0425417 | + | 0.996721i | ||||
\(714\) | − | 1.57728i | − | 0.0590281i | ||||||
\(715\) | −33.4724 | − | 62.2188i | −1.25180 | − | 2.32685i | ||||
\(716\) | 18.7393 | 0.700319 | ||||||||
\(717\) | 9.00810 | − | 9.00810i | 0.336414 | − | 0.336414i | ||||
\(718\) | 7.03594 | − | 7.03594i | 0.262579 | − | 0.262579i | ||||
\(719\) | − | 17.1352i | − | 0.639036i | −0.947580 | − | 0.319518i | \(-0.896479\pi\) | ||
0.947580 | − | 0.319518i | \(-0.103521\pi\) | |||||||
\(720\) | 2.14152 | + | 0.643329i | 0.0798099 | + | 0.0239755i | ||||
\(721\) | −48.6231 | −1.81082 | ||||||||
\(722\) | 13.3337 | − | 13.3337i | 0.496229 | − | 0.496229i | ||||
\(723\) | −3.94413 | + | 3.94413i | −0.146684 | + | 0.146684i | ||||
\(724\) | −20.7307 | −0.770449 | ||||||||
\(725\) | −14.2008 | + | 21.5029i | −0.527403 | + | 0.798597i | ||||
\(726\) | −15.1649 | −0.562821 | ||||||||
\(727\) | −11.2875 | − | 11.2875i | −0.418630 | − | 0.418630i | 0.466101 | − | 0.884731i | \(-0.345658\pi\) |
−0.884731 | + | 0.466101i | \(0.845658\pi\) | |||||||
\(728\) | −12.4590 | + | 12.4590i | −0.461760 | + | 0.461760i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 8.81638 | − | 29.3481i | 0.326309 | − | 1.08622i | ||||
\(731\) | −2.74885 | −0.101670 | ||||||||
\(732\) | −4.88558 | − | 4.88558i | −0.180576 | − | 0.180576i | ||||
\(733\) | 26.0488 | − | 26.0488i | 0.962134 | − | 0.962134i | −0.0371743 | − | 0.999309i | \(-0.511836\pi\) |
0.999309 | + | 0.0371743i | \(0.0118357\pi\) | |||||||
\(734\) | 32.1121 | 1.18528 | ||||||||
\(735\) | −1.20412 | − | 2.23823i | −0.0444147 | − | 0.0825582i | ||||
\(736\) | −3.53269 | − | 3.24347i | −0.130217 | − | 0.119556i | ||||
\(737\) | 31.6471 | − | 31.6471i | 1.16574 | − | 1.16574i | ||||
\(738\) | −5.80385 | − | 5.80385i | −0.213643 | − | 0.213643i | ||||
\(739\) | 27.4713i | 1.01055i | 0.862959 | + | 0.505275i | \(0.168609\pi\) | ||||
−0.862959 | + | 0.505275i | \(0.831391\pi\) | |||||||
\(740\) | −2.48723 | − | 4.62328i | −0.0914324 | − | 0.169955i | ||||
\(741\) | 38.0055i | 1.39617i | ||||||||
\(742\) | −9.33414 | + | 9.33414i | −0.342667 | + | 0.342667i | ||||
\(743\) | −17.8846 | + | 17.8846i | −0.656122 | + | 0.656122i | −0.954460 | − | 0.298338i | \(-0.903568\pi\) |
0.298338 | + | 0.954460i | \(0.403568\pi\) | |||||||
\(744\) | − | 5.55456i | − | 0.203640i | ||||||
\(745\) | −11.5886 | + | 38.5762i | −0.424572 | + | 1.41332i | ||||
\(746\) | 25.0458i | 0.916992i | ||||||||
\(747\) | 7.68978 | + | 7.68978i | 0.281354 | + | 0.281354i | ||||
\(748\) | 2.00000 | + | 2.00000i | 0.0731272 | + | 0.0731272i | ||||
\(749\) | 21.9233i | 0.801060i | ||||||||
\(750\) | 8.58491 | − | 7.16235i | 0.313477 | − | 0.261532i | ||||
\(751\) | − | 9.57596i | − | 0.349432i | −0.984619 | − | 0.174716i | \(-0.944099\pi\) | ||
0.984619 | − | 0.174716i | \(-0.0559007\pi\) | |||||||
\(752\) | 3.69444 | − | 3.69444i | 0.134722 | − | 0.134722i | ||||
\(753\) | −19.9169 | + | 19.9169i | −0.725812 | + | 0.725812i | ||||
\(754\) | − | 31.8347i | − | 1.15935i | ||||||
\(755\) | −7.93302 | + | 26.4076i | −0.288712 | + | 0.961070i | ||||
\(756\) | − | 2.85248i | − | 0.103744i | ||||||
\(757\) | 34.4079 | + | 34.4079i | 1.25058 | + | 1.25058i | 0.955461 | + | 0.295116i | \(0.0953584\pi\) |
0.295116 | + | 0.955461i | \(0.404642\pi\) | |||||||
\(758\) | 8.16513 | − | 8.16513i | 0.296571 | − | 0.296571i | ||||
\(759\) | −18.0703 | − | 16.5909i | −0.655909 | − | 0.602211i | ||||
\(760\) | 12.1160 | − | 6.51816i | 0.439493 | − | 0.236438i | ||||
\(761\) | −26.3481 | −0.955116 | −0.477558 | − | 0.878600i | \(-0.658478\pi\) | ||||
−0.477558 | + | 0.878600i | \(0.658478\pi\) | |||||||
\(762\) | −15.6798 | + | 15.6798i | −0.568020 | + | 0.568020i | ||||
\(763\) | 4.01161 | + | 4.01161i | 0.145230 | + | 0.145230i | ||||
\(764\) | 9.66249 | 0.349577 | ||||||||
\(765\) | −0.585786 | − | 1.08886i | −0.0211792 | − | 0.0393679i | ||||
\(766\) | − | 31.0525i | − | 1.12197i | ||||||
\(767\) | −41.1832 | + | 41.1832i | −1.48704 | + | 1.48704i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −24.2043 | −0.872830 | −0.436415 | − | 0.899745i | \(-0.643752\pi\) | ||||
−0.436415 | + | 0.899745i | \(0.643752\pi\) | |||||||
\(770\) | 31.2467 | + | 9.38673i | 1.12605 | + | 0.338274i | ||||
\(771\) | −10.0573 | −0.362205 | ||||||||
\(772\) | −5.41019 | + | 5.41019i | −0.194717 | + | 0.194717i | ||||
\(773\) | 15.8801 | − | 15.8801i | 0.571168 | − | 0.571168i | −0.361286 | − | 0.932455i | \(-0.617662\pi\) |
0.932455 | + | 0.361286i | \(0.117662\pi\) | |||||||
\(774\) | −4.97125 | −0.178688 | ||||||||
\(775\) | −23.1750 | − | 15.3051i | −0.832472 | − | 0.549775i | ||||
\(776\) | − | 10.0884i | − | 0.362152i | ||||||
\(777\) | −4.73554 | + | 4.73554i | −0.169887 | + | 0.169887i | ||||
\(778\) | 14.5864 | − | 14.5864i | 0.522947 | − | 0.522947i | ||||
\(779\) | −50.5013 | −1.80940 | ||||||||
\(780\) | −3.97382 | + | 13.2281i | −0.142286 | + | 0.473642i | ||||
\(781\) | 51.3579i | 1.83773i | ||||||||
\(782\) | 0.113083 | + | 2.64944i | 0.00404383 | + | 0.0947439i | ||||
\(783\) | 3.64427 | + | 3.64427i | 0.130236 | + | 0.130236i | ||||
\(784\) | − | 1.13662i | − | 0.0405937i | ||||||
\(785\) | 4.33052 | − | 2.32973i | 0.154563 | − | 0.0831518i | ||||
\(786\) | −3.31192 | −0.118132 | ||||||||
\(787\) | −7.43774 | − | 7.43774i | −0.265127 | − | 0.265127i | 0.562006 | − | 0.827133i | \(-0.310030\pi\) |
−0.827133 | + | 0.562006i | \(0.810030\pi\) | |||||||
\(788\) | −9.68778 | − | 9.68778i | −0.345113 | − | 0.345113i | ||||
\(789\) | −13.6083 | −0.484467 | ||||||||
\(790\) | 0.886560 | + | 1.64794i | 0.0315424 | + | 0.0586311i | ||||
\(791\) | 2.12286 | 0.0754802 | ||||||||
\(792\) | 3.61696 | + | 3.61696i | 0.128523 | + | 0.128523i | ||||
\(793\) | 30.1780 | − | 30.1780i | 1.07165 | − | 1.07165i | ||||
\(794\) | 2.41452i | 0.0856879i | ||||||||
\(795\) | −2.97715 | + | 9.91038i | −0.105589 | + | 0.351485i | ||||
\(796\) | − | 1.92772i | − | 0.0683262i | ||||||
\(797\) | −34.2834 | − | 34.2834i | −1.21438 | − | 1.21438i | −0.969572 | − | 0.244807i | \(-0.921276\pi\) |
−0.244807 | − | 0.969572i | \(-0.578724\pi\) | |||||||
\(798\) | −12.4102 | − | 12.4102i | −0.439316 | − | 0.439316i | ||||
\(799\) | −2.88901 | −0.102206 | ||||||||
\(800\) | 4.89860 | − | 1.00186i | 0.173192 | − | 0.0354211i | ||||
\(801\) | 8.61622i | 0.304439i | ||||||||
\(802\) | 21.6974 | + | 21.6974i | 0.766163 | + | 0.766163i | ||||
\(803\) | 49.5680 | − | 49.5680i | 1.74922 | − | 1.74922i | ||||
\(804\) | −8.74963 | −0.308575 | ||||||||
\(805\) | 15.6279 | + | 26.2960i | 0.550812 | + | 0.926812i | ||||
\(806\) | 34.3103 | 1.20853 | ||||||||
\(807\) | 4.87314 | − | 4.87314i | 0.171543 | − | 0.171543i | ||||
\(808\) | −3.05280 | − | 3.05280i | −0.107397 | − | 0.107397i | ||||
\(809\) | − | 13.7935i | − | 0.484953i | −0.970157 | − | 0.242476i | \(-0.922040\pi\) | ||
0.970157 | − | 0.242476i | \(-0.0779597\pi\) | |||||||
\(810\) | −1.05938 | − | 1.96919i | −0.0372230 | − | 0.0691902i | ||||
\(811\) | −20.9214 | −0.734650 | −0.367325 | − | 0.930093i | \(-0.619726\pi\) | ||||
−0.367325 | + | 0.930093i | \(0.619726\pi\) | |||||||
\(812\) | 10.3952 | + | 10.3952i | 0.364800 | + | 0.364800i | ||||
\(813\) | 17.1238 | + | 17.1238i | 0.600558 | + | 0.600558i | ||||
\(814\) | − | 12.0094i | − | 0.420930i | ||||||
\(815\) | −15.6464 | + | 8.41743i | −0.548068 | + | 0.294850i | ||||
\(816\) | − | 0.552950i | − | 0.0193571i | ||||||
\(817\) | −21.6283 | + | 21.6283i | −0.756677 | + | 0.756677i | ||||
\(818\) | −6.44502 | − | 6.44502i | −0.225345 | − | 0.225345i | ||||
\(819\) | 17.6196 | 0.615680 | ||||||||
\(820\) | −17.5774 | − | 5.28037i | −0.613829 | − | 0.184399i | ||||
\(821\) | −6.90808 | −0.241094 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(822\) | −2.13220 | − | 2.13220i | −0.0743691 | − | 0.0743691i | ||||
\(823\) | −12.3135 | − | 12.3135i | −0.429223 | − | 0.429223i | 0.459141 | − | 0.888364i | \(-0.348157\pi\) |
−0.888364 | + | 0.459141i | \(0.848157\pi\) | |||||||
\(824\) | −17.0459 | −0.593823 | ||||||||
\(825\) | 25.0571 | − | 5.12468i | 0.872377 | − | 0.178418i | ||||
\(826\) | − | 26.8957i | − | 0.935820i | ||||||
\(827\) | −3.25744 | − | 3.25744i | −0.113272 | − | 0.113272i | 0.648199 | − | 0.761471i | \(-0.275523\pi\) |
−0.761471 | + | 0.648199i | \(0.775523\pi\) | |||||||
\(828\) | 0.204508 | + | 4.79147i | 0.00710714 | + | 0.166515i | ||||
\(829\) | 52.0135i | 1.80650i | 0.429111 | + | 0.903252i | \(0.358827\pi\) | ||||
−0.429111 | + | 0.903252i | \(0.641173\pi\) | |||||||
\(830\) | 23.2891 | + | 6.99620i | 0.808375 | + | 0.242841i | ||||
\(831\) | 26.9947 | 0.936436 | ||||||||
\(832\) | −4.36777 | + | 4.36777i | −0.151425 | + | 0.151425i | ||||
\(833\) | −0.444414 | + | 0.444414i | −0.0153980 | + | 0.0153980i | ||||
\(834\) | − | 8.40570i | − | 0.291066i | ||||||
\(835\) | 8.67054 | + | 16.1168i | 0.300056 | + | 0.557746i | ||||
\(836\) | 31.4724 | 1.08850 | ||||||||
\(837\) | −3.92767 | + | 3.92767i | −0.135760 | + | 0.135760i | ||||
\(838\) | −6.06990 | + | 6.06990i | −0.209681 | + | 0.209681i | ||||
\(839\) | −1.25549 | −0.0433444 | −0.0216722 | − | 0.999765i | \(-0.506899\pi\) | ||||
−0.0216722 | + | 0.999765i | \(0.506899\pi\) | |||||||
\(840\) | −3.02187 | − | 5.61707i | −0.104264 | − | 0.193807i | ||||
\(841\) | 2.43858 | 0.0840888 | ||||||||
\(842\) | 4.99349 | + | 4.99349i | 0.172087 | + | 0.172087i | ||||
\(843\) | 14.3801 | − | 14.3801i | 0.495278 | − | 0.495278i | ||||
\(844\) | − | 13.4119i | − | 0.461655i | ||||||
\(845\) | −53.8697 | − | 16.1828i | −1.85317 | − | 0.556707i | ||||
\(846\) | −5.22472 | −0.179630 | ||||||||
\(847\) | 30.5876 | + | 30.5876i | 1.05100 | + | 1.05100i | ||||
\(848\) | −3.27229 | + | 3.27229i | −0.112371 | + | 0.112371i | ||||
\(849\) | −25.2367 | −0.866121 | ||||||||
\(850\) | −2.30705 | − | 1.52360i | −0.0791311 | − | 0.0522592i | ||||
\(851\) | 7.61505 | − | 8.29408i | 0.261040 | − | 0.284317i | ||||
\(852\) | 7.09959 | − | 7.09959i | 0.243228 | − | 0.243228i | ||||
\(853\) | 30.5170 | + | 30.5170i | 1.04488 | + | 1.04488i | 0.998944 | + | 0.0459389i | \(0.0146279\pi\) |
0.0459389 | + | 0.998944i | \(0.485372\pi\) | |||||||
\(854\) | 19.7085i | 0.674411i | ||||||||
\(855\) | −13.1763 | − | 3.95826i | −0.450621 | − | 0.135370i | ||||
\(856\) | 7.68571i | 0.262692i | ||||||||
\(857\) | −14.6537 | + | 14.6537i | −0.500562 | + | 0.500562i | −0.911613 | − | 0.411051i | \(-0.865162\pi\) |
0.411051 | + | 0.911613i | \(0.365162\pi\) | |||||||
\(858\) | −22.3418 | + | 22.3418i | −0.762738 | + | 0.762738i | ||||
\(859\) | − | 43.2161i | − | 1.47451i | −0.675613 | − | 0.737256i | \(-0.736121\pi\) | ||
0.675613 | − | 0.737256i | \(-0.263879\pi\) | |||||||
\(860\) | −9.78932 | + | 5.26646i | −0.333813 | + | 0.179585i | ||||
\(861\) | 23.4128i | 0.797906i | ||||||||
\(862\) | −14.1117 | − | 14.1117i | −0.480648 | − | 0.480648i | ||||
\(863\) | 3.46294 | + | 3.46294i | 0.117880 | + | 0.117880i | 0.763586 | − | 0.645706i | \(-0.223437\pi\) |
−0.645706 | + | 0.763586i | \(0.723437\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 10.1680 | − | 5.47016i | 0.345721 | − | 0.185991i | ||||
\(866\) | 22.4960i | 0.764447i | ||||||||
\(867\) | 11.8046 | − | 11.8046i | 0.400906 | − | 0.400906i | ||||
\(868\) | −11.2036 | + | 11.2036i | −0.380274 | + | 0.380274i | ||||
\(869\) | 4.28069i | 0.145212i | ||||||||
\(870\) | 11.0369 | + | 3.31558i | 0.374187 | + | 0.112409i | ||||
\(871\) | − | 54.0461i | − | 1.83128i | ||||||
\(872\) | 1.40636 | + | 1.40636i | 0.0476253 | + | 0.0476253i | ||||
\(873\) | −7.13357 | + | 7.13357i | −0.241435 | + | 0.241435i | ||||
\(874\) | 21.7359 | + | 19.9564i | 0.735226 | + | 0.675034i | ||||
\(875\) | −31.7623 | − | 2.86931i | −1.07376 | − | 0.0970005i | ||||
\(876\) | −13.7043 | −0.463026 | ||||||||
\(877\) | −5.55079 | + | 5.55079i | −0.187437 | + | 0.187437i | −0.794587 | − | 0.607150i | \(-0.792313\pi\) |
0.607150 | + | 0.794587i | \(0.292313\pi\) | |||||||
\(878\) | −10.6083 | − | 10.6083i | −0.358014 | − | 0.358014i | ||||
\(879\) | −17.8035 | −0.600496 | ||||||||
\(880\) | 10.9542 | + | 3.29073i | 0.369267 | + | 0.110931i | ||||
\(881\) | 51.9461i | 1.75011i | 0.484024 | + | 0.875055i | \(0.339175\pi\) | ||||
−0.484024 | + | 0.875055i | \(0.660825\pi\) | |||||||
\(882\) | −0.803714 | + | 0.803714i | −0.0270625 | + | 0.0270625i | ||||
\(883\) | 13.6444 | + | 13.6444i | 0.459170 | + | 0.459170i | 0.898383 | − | 0.439213i | \(-0.144743\pi\) |
−0.439213 | + | 0.898383i | \(0.644743\pi\) | |||||||
\(884\) | 3.41555 | 0.114877 | ||||||||
\(885\) | −9.98881 | − | 18.5673i | −0.335770 | − | 0.624132i | ||||
\(886\) | 18.8232 | 0.632377 | ||||||||
\(887\) | −1.93479 | + | 1.93479i | −0.0649638 | + | 0.0649638i | −0.738842 | − | 0.673878i | \(-0.764627\pi\) |
0.673878 | + | 0.738842i | \(0.264627\pi\) | |||||||
\(888\) | −1.66015 | + | 1.66015i | −0.0557110 | + | 0.0557110i | ||||
\(889\) | 63.2525 | 2.12142 | ||||||||
\(890\) | 9.12789 | + | 16.9670i | 0.305967 | + | 0.568734i | ||||
\(891\) | − | 5.11516i | − | 0.171364i | ||||||
\(892\) | −7.77131 | + | 7.77131i | −0.260203 | + | 0.260203i | ||||
\(893\) | −22.7310 | + | 22.7310i | −0.760665 | + | 0.760665i | ||||
\(894\) | 18.0134 | 0.602459 | ||||||||
\(895\) | −40.1306 | − | 12.0555i | −1.34142 | − | 0.402971i | ||||
\(896\) | − | 2.85248i | − | 0.0952946i | ||||||
\(897\) | −29.5967 | + | 1.26324i | −0.988206 | + | 0.0421783i | ||||
\(898\) | −21.0871 | − | 21.0871i | −0.703687 | − | 0.703687i | ||||
\(899\) | − | 28.6270i | − | 0.954762i | ||||||
\(900\) | −4.17226 | − | 2.75541i | −0.139075 | − | 0.0918470i | ||||
\(901\) | 2.55890 | 0.0852492 | ||||||||
\(902\) | −29.6876 | − | 29.6876i | −0.988490 | − | 0.988490i | ||||
\(903\) | 10.0270 | + | 10.0270i | 0.333679 | + | 0.333679i | ||||
\(904\) | 0.744216 | 0.0247523 | ||||||||
\(905\) | 44.3952 | + | 13.3366i | 1.47575 | + | 0.443325i | ||||
\(906\) | 12.3312 | 0.409677 | ||||||||
\(907\) | −1.67221 | − | 1.67221i | −0.0555247 | − | 0.0555247i | 0.678799 | − | 0.734324i | \(-0.262501\pi\) |
−0.734324 | + | 0.678799i | \(0.762501\pi\) | |||||||
\(908\) | −18.5374 | + | 18.5374i | −0.615186 | + | 0.615186i | ||||
\(909\) | 4.31730i | 0.143196i | ||||||||
\(910\) | 34.6964 | − | 18.6660i | 1.15017 | − | 0.618771i | ||||
\(911\) | − | 8.95458i | − | 0.296678i | −0.988937 | − | 0.148339i | \(-0.952607\pi\) | ||
0.988937 | − | 0.148339i | \(-0.0473927\pi\) | |||||||
\(912\) | −4.35067 | − | 4.35067i | −0.144065 | − | 0.144065i | ||||
\(913\) | 39.3344 | + | 39.3344i | 1.30178 | + | 1.30178i | ||||
\(914\) | −39.7514 | −1.31486 | ||||||||
\(915\) | 7.31956 | + | 13.6056i | 0.241977 | + | 0.449788i | ||||
\(916\) | − | 9.30733i | − | 0.307523i | ||||||
\(917\) | 6.68016 | + | 6.68016i | 0.220598 | + | 0.220598i | ||||
\(918\) | −0.390995 | + | 0.390995i | −0.0129047 | + | 0.0129047i | ||||
\(919\) | 13.4943 | 0.445136 | 0.222568 | − | 0.974917i | \(-0.428556\pi\) | ||||
0.222568 | + | 0.974917i | \(0.428556\pi\) | |||||||
\(920\) | 5.47872 | + | 9.21866i | 0.180628 | + | 0.303930i | ||||
\(921\) | 6.49333 | 0.213962 | ||||||||
\(922\) | −21.5300 | + | 21.5300i | −0.709054 | + | 0.709054i | ||||
\(923\) | 43.8539 | + | 43.8539i | 1.44347 | + | 1.44347i | ||||
\(924\) | − | 14.5909i | − | 0.480004i | ||||||
\(925\) | 2.35218 | + | 11.5010i | 0.0773391 | + | 0.378150i | ||||
\(926\) | 3.05783 | 0.100486 | ||||||||
\(927\) | 12.0533 | + | 12.0533i | 0.395882 | + | 0.395882i | ||||
\(928\) | 3.64427 | + | 3.64427i | 0.119629 | + | 0.119629i | ||||
\(929\) | − | 23.6746i | − | 0.776740i | −0.921504 | − | 0.388370i | \(-0.873038\pi\) | ||
0.921504 | − | 0.388370i | \(-0.126962\pi\) | |||||||
\(930\) | −3.57341 | + | 11.8952i | −0.117177 | + | 0.390060i | ||||
\(931\) | 6.99339i | 0.229199i | ||||||||
\(932\) | −12.4073 | + | 12.4073i | −0.406413 | + | 0.406413i | ||||
\(933\) | −11.9599 | − | 11.9599i | −0.391550 | − | 0.391550i | ||||
\(934\) | 14.6268 | 0.478604 | ||||||||
\(935\) | −2.99639 | − | 5.56971i | −0.0979925 | − | 0.182149i | ||||
\(936\) | 6.17696 | 0.201900 | ||||||||
\(937\) | 32.6658 | + | 32.6658i | 1.06715 | + | 1.06715i | 0.997577 | + | 0.0695692i | \(0.0221625\pi\) |
0.0695692 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(938\) | 17.6480 | + | 17.6480i | 0.576229 | + | 0.576229i | ||||
\(939\) | 12.6272 | 0.412075 | ||||||||
\(940\) | −10.2885 | + | 5.53499i | −0.335573 | + | 0.180531i | ||||
\(941\) | 12.4003i | 0.404238i | 0.979361 | + | 0.202119i | \(0.0647827\pi\) | ||||
−0.979361 | + | 0.202119i | \(0.935217\pi\) | |||||||
\(942\) | −1.55503 | − | 1.55503i | −0.0506655 | − | 0.0506655i | ||||
\(943\) | −1.67858 | − | 39.3278i | −0.0546620 | − | 1.28069i | ||||
\(944\) | − | 9.42889i | − | 0.306884i | ||||||
\(945\) | −1.83508 | + | 6.10865i | −0.0596952 | + | 0.198714i | ||||
\(946\) | −25.4287 | −0.826759 | ||||||||
\(947\) | −25.3756 | + | 25.3756i | −0.824595 | + | 0.824595i | −0.986763 | − | 0.162168i | \(-0.948151\pi\) |
0.162168 | + | 0.986763i | \(0.448151\pi\) | |||||||
\(948\) | 0.591752 | − | 0.591752i | 0.0192192 | − | 0.0192192i | ||||
\(949\) | − | 84.6510i | − | 2.74789i | ||||||
\(950\) | −30.1400 | + | 6.16423i | −0.977871 | + | 0.199994i | ||||
\(951\) | 3.06801 | 0.0994869 | ||||||||
\(952\) | −1.11530 | + | 1.11530i | −0.0361472 | + | 0.0361472i | ||||
\(953\) | −2.72751 | + | 2.72751i | −0.0883527 | + | 0.0883527i | −0.749902 | − | 0.661549i | \(-0.769899\pi\) |
0.661549 | + | 0.749902i | \(0.269899\pi\) | |||||||
\(954\) | 4.62772 | 0.149828 | ||||||||
\(955\) | −20.6925 | − | 6.21616i | −0.669592 | − | 0.201150i | ||||
\(956\) | −12.7394 | −0.412021 | ||||||||
\(957\) | 18.6410 | + | 18.6410i | 0.602579 | + | 0.602579i | ||||
\(958\) | −19.4941 | + | 19.4941i | −0.629826 | + | 0.629826i | ||||
\(959\) | 8.60132i | 0.277751i | ||||||||
\(960\) | −1.05938 | − | 1.96919i | −0.0341915 | − | 0.0635553i | ||||
\(961\) | −0.146886 | −0.00473826 | ||||||||
\(962\) | −10.2547 | − | 10.2547i | −0.330624 | − | 0.330624i | ||||
\(963\) | 5.43462 | − | 5.43462i | 0.175128 | − | 0.175128i | ||||
\(964\) | 5.57785 | 0.179650 | ||||||||
\(965\) | 15.0666 | − | 8.10552i | 0.485011 | − | 0.260926i | ||||
\(966\) | 9.25193 | − | 10.0769i | 0.297676 | − | 0.324219i | ||||
\(967\) | 29.5079 | − | 29.5079i | 0.948911 | − | 0.948911i | −0.0498460 | − | 0.998757i | \(-0.515873\pi\) |
0.998757 | + | 0.0498460i | \(0.0158730\pi\) | |||||||
\(968\) | 10.7232 | + | 10.7232i | 0.344656 | + | 0.344656i | ||||
\(969\) | 3.40218i | 0.109294i | ||||||||
\(970\) | −6.49015 | + | 21.6045i | −0.208386 | + | 0.693680i | ||||
\(971\) | − | 18.8170i | − | 0.603868i | −0.953329 | − | 0.301934i | \(-0.902368\pi\) | ||
0.953329 | − | 0.301934i | \(-0.0976322\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −16.9544 | + | 16.9544i | −0.543532 | + | 0.543532i | ||||
\(974\) | 15.7431i | 0.504442i | ||||||||
\(975\) | 17.0201 | − | 25.7719i | 0.545078 | − | 0.825360i | ||||
\(976\) | 6.90926i | 0.221160i | ||||||||
\(977\) | 12.0016 | + | 12.0016i | 0.383966 | + | 0.383966i | 0.872529 | − | 0.488563i | \(-0.162479\pi\) |
−0.488563 | + | 0.872529i | \(0.662479\pi\) | |||||||
\(978\) | 5.61838 | + | 5.61838i | 0.179656 | + | 0.179656i | ||||
\(979\) | 44.0733i | 1.40859i | ||||||||
\(980\) | −0.731223 | + | 2.43411i | −0.0233581 | + | 0.0777547i | ||||
\(981\) | − | 1.98889i | − | 0.0635005i | ||||||
\(982\) | 8.67249 | − | 8.67249i | 0.276750 | − | 0.276750i | ||||
\(983\) | −25.4709 | + | 25.4709i | −0.812395 | + | 0.812395i | −0.984992 | − | 0.172597i | \(-0.944784\pi\) |
0.172597 | + | 0.984992i | \(0.444784\pi\) | |||||||
\(984\) | 8.20789i | 0.261658i | ||||||||
\(985\) | 14.5142 | + | 26.9791i | 0.462461 | + | 0.859624i | ||||
\(986\) | − | 2.84978i | − | 0.0907555i | ||||||
\(987\) | 10.5383 | + | 10.5383i | 0.335437 | + | 0.335437i | ||||
\(988\) | 26.8739 | − | 26.8739i | 0.854974 | − | 0.854974i | ||||
\(989\) | −17.5619 | − | 16.1241i | −0.558435 | − | 0.512716i | ||||
\(990\) | −5.41892 | − | 10.0727i | −0.172225 | − | 0.320132i | ||||
\(991\) | −24.2368 | −0.769909 | −0.384954 | − | 0.922936i | \(-0.625783\pi\) | ||||
−0.384954 | + | 0.922936i | \(0.625783\pi\) | |||||||
\(992\) | −3.92767 | + | 3.92767i | −0.124704 | + | 0.124704i | ||||
\(993\) | −3.14573 | − | 3.14573i | −0.0998268 | − | 0.0998268i | ||||
\(994\) | −28.6398 | −0.908400 | ||||||||
\(995\) | −1.24016 | + | 4.12826i | −0.0393157 | + | 0.130875i | ||||
\(996\) | − | 10.8750i | − | 0.344587i | ||||||
\(997\) | 31.0953 | − | 31.0953i | 0.984797 | − | 0.984797i | −0.0150892 | − | 0.999886i | \(-0.504803\pi\) |
0.999886 | + | 0.0150892i | \(0.00480322\pi\) | |||||||
\(998\) | −7.14836 | − | 7.14836i | −0.226277 | − | 0.226277i | ||||
\(999\) | 2.34781 | 0.0742813 |
(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 | 690.2.j.b.643.9 | yes | 24 | |
5.2 | odd | 4 | inner | 690.2.j.b.367.10 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.643.10 | yes | 24 | |
115.22 | even | 4 | inner | 690.2.j.b.367.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.9 | ✓ | 24 | 115.22 | even | 4 | inner | |
690.2.j.b.367.10 | yes | 24 | 5.2 | odd | 4 | inner | |
690.2.j.b.643.9 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.643.10 | yes | 24 | 23.22 | odd | 2 | inner |