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 | 367.10 | ||
Character | \(\chi\) | \(=\) | 690.367 |
Dual form | 690.2.j.b.643.10 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | \(-0.568777\pi\) |
0.976748 | + | 0.214391i | \(0.0687768\pi\) | |||||||
\(8\) | −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 | 0.240836 | − | 0.970566i | \(-0.422578\pi\) |
0.970566 | − | 0.240836i | \(-0.0774215\pi\) | |||||||
\(14\) | 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 | \(-0.771360\pi\) |
0.658100 | + | 0.752930i | \(0.271360\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | −6.15278 | −1.41154 | −0.705772 | − | 0.708439i | \(-0.749400\pi\) | ||||
−0.705772 | + | 0.708439i | \(0.749400\pi\) | |||||||
\(20\) | −2.14152 | + | 0.643329i | −0.478859 | + | 0.143853i | ||||
\(21\) | − | 2.85248i | − | 0.622461i | ||||||
\(22\) | −3.61696 | + | 3.61696i | −0.771139 | + | 0.771139i | ||||
\(23\) | 4.79147 | − | 0.204508i | 0.999090 | − | 0.0426429i | ||||
\(24\) | 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 | \(0.158825\pi\) | ||||
−0.878079 | + | 0.478516i | \(0.841175\pi\) | |||||||
\(30\) | 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 | \(-0.688182\pi\) |
0.830277 | + | 0.557350i | \(0.188182\pi\) | |||||||
\(38\) | −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 | \(-0.126249\pi\) |
−0.386307 | + | 0.922370i | \(0.626249\pi\) | |||||||
\(44\) | −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 | 0.384314 | − | 0.923203i | \(-0.374438\pi\) |
−0.923203 | + | 0.384314i | \(0.874438\pi\) | |||||||
\(48\) | −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 | \(-0.352955\pi\) |
−0.895183 | + | 0.445699i | \(0.852955\pi\) | |||||||
\(54\) | − | 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 | \(-0.789653\pi\) | ||
0.789486 | − | 0.613768i | \(-0.210347\pi\) | |||||||
\(60\) | −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 | \(-0.570512\pi\) |
0.975565 | + | 0.219712i | \(0.0705118\pi\) | |||||||
\(68\) | −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 | −0.144702 | + | 0.989475i | \(0.546222\pi\) |
−0.989475 | + | 0.144702i | \(0.953778\pi\) | |||||||
\(74\) | 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 | \(-0.514991\pi\) | ||||
−0.0470772 | + | 0.998891i | \(0.514991\pi\) | |||||||
\(80\) | −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 | \(-0.453578\pi\) |
−0.989384 | + | 0.145322i | \(0.953578\pi\) | |||||||
\(84\) | 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 | \(-0.650954\pi\) | ||||
−0.456659 | + | 0.889642i | \(0.650954\pi\) | |||||||
\(90\) | 1.96919 | + | 1.05938i | 0.207571 | + | 0.111669i | ||||
\(91\) | − | 17.6196i | − | 1.84704i | ||||||
\(92\) | 0.204508 | + | 4.79147i | 0.0213214 | + | 0.499545i | ||||
\(93\) | 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 | \(-0.921155\pi\) |
0.245175 | + | 0.969479i | \(0.421155\pi\) | |||||||
\(98\) | 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 | −0.977717 | − | 0.209929i | \(-0.932677\pi\) |
−0.209929 | − | 0.977717i | \(-0.567323\pi\) | |||||||
\(104\) | 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 | \(-0.628843\pi\) |
0.919193 | + | 0.393808i | \(0.128843\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 1.98889 | 0.190501 | 0.0952507 | − | 0.995453i | \(-0.469635\pi\) | ||||
0.0952507 | + | 0.995453i | \(0.469635\pi\) | |||||||
\(110\) | −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 | \(-0.238855\pi\) |
−0.681921 | + | 0.731426i | \(0.738855\pi\) | |||||||
\(114\) | −6.15278 | −0.576261 | ||||||||
\(115\) | 3.52045 | + | 10.1295i | 0.328284 | + | 0.944579i | ||||
\(116\) | −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 | −0.822291 | − | 0.569068i | \(-0.807304\pi\) |
−0.569068 | − | 0.822291i | \(-0.692696\pi\) | |||||||
\(128\) | 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 | \(-0.708884\pi\) |
0.792299 | + | 0.610133i | \(0.208884\pi\) | |||||||
\(138\) | 4.79147 | − | 0.204508i | 0.407877 | − | 0.0174089i | ||||
\(139\) | 8.40570i | 0.712963i | 0.934302 | + | 0.356481i | \(0.116024\pi\) | ||||
−0.934302 | + | 0.356481i | \(0.883976\pi\) | |||||||
\(140\) | −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 | \(-0.764163\pi\) | ||||
−0.737859 | + | 0.674955i | \(0.764163\pi\) | |||||||
\(150\) | −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 | \(-0.722031\pi\) |
0.766431 | + | 0.642326i | \(0.222031\pi\) | |||||||
\(158\) | −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 | −0.451968 | − | 0.892034i | \(-0.649278\pi\) |
0.892034 | + | 0.451968i | \(0.149278\pi\) | |||||||
\(164\) | − | 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 | 0.894635 | − | 0.446798i | \(-0.147436\pi\) |
−0.446798 | + | 0.894635i | \(0.647436\pi\) | |||||||
\(168\) | 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 | −0.832147 | − | 0.554554i | \(-0.812889\pi\) |
0.554554 | + | 0.832147i | \(0.312889\pi\) | |||||||
\(174\) | 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 | \(-0.753041\pi\) | ||
0.713830 | − | 0.700319i | \(-0.246959\pi\) | |||||||
\(180\) | 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 | −0.874486 | − | 0.485052i | \(-0.838801\pi\) |
0.485052 | + | 0.874486i | \(0.338801\pi\) | |||||||
\(194\) | −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 | 0.962282 | − | 0.272056i | \(-0.0877035\pi\) |
−0.272056 | + | 0.962282i | \(0.587703\pi\) | |||||||
\(198\) | 3.61696 | + | 3.61696i | 0.257046 | + | 0.257046i | ||||
\(199\) | −1.92772 | −0.136652 | −0.0683262 | − | 0.997663i | \(-0.521766\pi\) | ||||
−0.0683262 | + | 0.997663i | \(0.521766\pi\) | |||||||
\(200\) | 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 | ||||||
\(207\) | −0.204508 | − | 4.79147i | −0.0142143 | − | 0.333030i | ||||
\(208\) | −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 | −0.917694 | − | 0.397289i | \(-0.869951\pi\) |
0.397289 | + | 0.917694i | \(0.369951\pi\) | |||||||
\(224\) | −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 | 0.266550 | − | 0.963821i | \(-0.414116\pi\) |
0.963821 | − | 0.266550i | \(-0.0858837\pi\) | |||||||
\(228\) | −4.35067 | − | 4.35067i | −0.288130 | − | 0.288130i | ||||
\(229\) | −9.30733 | −0.615046 | −0.307523 | − | 0.951541i | \(-0.599500\pi\) | ||||
−0.307523 | + | 0.951541i | \(0.599500\pi\) | |||||||
\(230\) | −4.67329 | + | 9.65196i | −0.308148 | + | 0.636431i | ||||
\(231\) | 14.5909 | 0.960009 | ||||||||
\(232\) | −3.64427 | − | 3.64427i | −0.239258 | − | 0.239258i | ||||
\(233\) | −12.4073 | + | 12.4073i | −0.812826 | + | 0.812826i | −0.985057 | − | 0.172230i | \(-0.944903\pi\) |
0.172230 | + | 0.985057i | \(0.444903\pi\) | |||||||
\(234\) | − | 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 | \(0.135177\pi\) | ||||
−0.911174 | + | 0.412021i | \(0.864823\pi\) | |||||||
\(240\) | −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 | ||||
\(253\) | 1.04609 | + | 24.5091i | 0.0657672 | + | 1.54088i | ||||
\(254\) | − | 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 | 0.449614 | − | 0.893223i | \(-0.351561\pi\) |
−0.893223 | + | 0.449614i | \(0.851561\pi\) | |||||||
\(258\) | 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 | \(-0.112184\pi\) |
−0.345186 | + | 0.938534i | \(0.612184\pi\) | |||||||
\(264\) | −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 | \(0.0673776\pi\) | ||||
−0.977681 | + | 0.210096i | \(0.932622\pi\) | |||||||
\(270\) | 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 | 0.987160 | + | 0.159736i | \(0.0510642\pi\) |
0.159736 | + | 0.987160i | \(0.448936\pi\) | |||||||
\(278\) | −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 | 0.998029 | + | 0.0627483i | \(0.0199865\pi\) |
0.0627483 | + | 0.998029i | \(0.480013\pi\) | |||||||
\(284\) | 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 | \(-0.0759153\pi\) |
−0.236241 | + | 0.971695i | \(0.575915\pi\) | |||||||
\(294\) | − | 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 | 0.825886 | − | 0.563837i | \(-0.190675\pi\) |
−0.563837 | + | 0.825886i | \(0.690675\pi\) | |||||||
\(308\) | −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 | \(-0.366155\pi\) |
−0.912891 | + | 0.408204i | \(0.866155\pi\) | |||||||
\(314\) | 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 | 0.765400 | − | 0.643554i | \(-0.222541\pi\) |
−0.643554 | + | 0.765400i | \(0.722541\pi\) | |||||||
\(318\) | −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 | ||||||
\(322\) | 13.6676 | − | 0.583354i | 0.761663 | − | 0.0325091i | ||||
\(323\) | 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 | \(-0.745254\pi\) |
0.717571 | + | 0.696485i | \(0.245254\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 9.65196 | + | 4.67329i | 0.519644 | + | 0.251602i | ||||
\(346\) | −5.16353 | −0.277593 | ||||||||
\(347\) | 21.9216 | + | 21.9216i | 1.17681 | + | 1.17681i | 0.980551 | + | 0.196262i | \(0.0628804\pi\) |
0.196262 | + | 0.980551i | \(0.437120\pi\) | |||||||
\(348\) | −3.64427 | + | 3.64427i | −0.195353 | + | 0.195353i | ||||
\(349\) | − | 29.6703i | − | 1.58821i | −0.607779 | − | 0.794106i | \(-0.707939\pi\) | ||
0.607779 | − | 0.794106i | \(-0.292061\pi\) | |||||||
\(350\) | −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 | −0.739881 | − | 0.672737i | \(-0.765118\pi\) |
0.672737 | + | 0.739881i | \(0.265118\pi\) | |||||||
\(354\) | − | 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 | \(-0.584573\pi\) | ||||
−0.262579 | + | 0.964911i | \(0.584573\pi\) | |||||||
\(360\) | −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 | −0.206922 | + | 0.978358i | \(0.566345\pi\) |
−0.978358 | + | 0.206922i | \(0.933655\pi\) | |||||||
\(368\) | −4.79147 | + | 0.204508i | −0.249773 | + | 0.0106607i | ||||
\(369\) | 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 | \(-0.0254338\pi\) |
−0.0798177 | + | 0.996809i | \(0.525434\pi\) | |||||||
\(374\) | − | 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 | \(-0.595843\pi\) | ||||
−0.296571 | + | 0.955011i | \(0.595843\pi\) | |||||||
\(380\) | 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 | −0.991445 | − | 0.130527i | \(-0.958333\pi\) |
−0.130527 | − | 0.991445i | \(-0.541667\pi\) | |||||||
\(384\) | − | 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 | \(-0.675168\pi\) | ||||
−0.522947 | + | 0.852365i | \(0.675168\pi\) | |||||||
\(390\) | 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 | 0.662964 | − | 0.748652i | \(-0.269298\pi\) |
−0.748652 | + | 0.662964i | \(0.769298\pi\) | |||||||
\(398\) | −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 | \(0.0723508\pi\) | ||||
−0.974279 | + | 0.225345i | \(0.927649\pi\) | |||||||
\(410\) | 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 | \(-0.432757\pi\) | ||||
0.209681 | + | 0.977770i | \(0.432757\pi\) | |||||||
\(420\) | 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 | \(-0.0682179\pi\) |
−0.212676 | + | 0.977123i | \(0.568218\pi\) | |||||||
\(434\) | 15.8442 | 0.760548 | ||||||||
\(435\) | −5.45983 | + | 10.1488i | −0.261779 | + | 0.486596i | ||||
\(436\) | 1.98889i | 0.0952507i | ||||||||
\(437\) | −29.4809 | + | 1.25829i | −1.41026 | + | 0.0601923i | ||||
\(438\) | −9.69041 | + | 9.69041i | −0.463026 | + | 0.463026i | ||||
\(439\) | 15.0024i | 0.716028i | 0.933716 | + | 0.358014i | \(0.116546\pi\) | ||||
−0.933716 | + | 0.358014i | \(0.883454\pi\) | |||||||
\(440\) | 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 | −0.316287 | − | 0.948664i | \(-0.602436\pi\) |
0.948664 | + | 0.316287i | \(0.102436\pi\) | |||||||
\(444\) | 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 | \(0.248464\pi\) | ||||
−0.710510 | + | 0.703687i | \(0.751536\pi\) | |||||||
\(450\) | −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 | 0.397074 | − | 0.917787i | \(-0.370026\pi\) |
0.917787 | − | 0.397074i | \(-0.129974\pi\) | |||||||
\(458\) | −6.58128 | − | 6.58128i | −0.307523 | − | 0.307523i | ||||
\(459\) | 0.552950 | 0.0258095 | ||||||||
\(460\) | −10.1295 | + | 3.52045i | −0.472290 | + | 0.164142i | ||||
\(461\) | −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 | −0.655076 | − | 0.755563i | \(-0.727364\pi\) |
0.755563 | + | 0.655076i | \(0.227364\pi\) | |||||||
\(464\) | − | 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 | \(-0.859894\pi\) |
0.426081 | + | 0.904685i | \(0.359894\pi\) | |||||||
\(468\) | 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 | \(-0.283126\pi\) | ||||
0.629826 | + | 0.776736i | \(0.283126\pi\) | |||||||
\(480\) | −0.643329 | − | 2.14152i | −0.0293638 | − | 0.0977468i | ||||
\(481\) | − | 14.5023i | − | 0.661249i | ||||||
\(482\) | −3.94413 | + | 3.94413i | −0.179650 | + | 0.179650i | ||||
\(483\) | −0.583354 | − | 13.6676i | −0.0265435 | − | 0.621895i | ||||
\(484\) | − | 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 | 0.408373 | − | 0.912815i | \(-0.366096\pi\) |
−0.912815 | + | 0.408373i | \(0.866096\pi\) | |||||||
\(488\) | 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 | \(0.0726556\pi\) | ||||
−0.974063 | + | 0.226277i | \(0.927344\pi\) | |||||||
\(500\) | 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 | 0.988461 | + | 0.151476i | \(0.0484027\pi\) |
0.151476 | + | 0.988461i | \(0.451597\pi\) | |||||||
\(504\) | 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 | \(0.172679\pi\) | ||||
−0.856427 | + | 0.516268i | \(0.827321\pi\) | |||||||
\(510\) | −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 | \(-0.400512\pi\) |
−0.951552 | + | 0.307488i | \(0.900512\pi\) | |||||||
\(524\) | − | 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 | 0.470074 | − | 0.882627i | \(-0.344227\pi\) |
−0.882627 | + | 0.470074i | \(0.844227\pi\) | |||||||
\(548\) | 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 | ||||||
\(552\) | 0.204508 | + | 4.79147i | 0.00870444 | + | 0.203938i | ||||
\(553\) | −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 | \(-0.771901\pi\) |
0.656819 | + | 0.754048i | \(0.271901\pi\) | |||||||
\(558\) | 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 | \(-0.339569\pi\) |
−0.875653 | + | 0.482941i | \(0.839569\pi\) | |||||||
\(564\) | − | 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 | \(-0.699727\pi\) | ||||
−0.587090 | + | 0.809522i | \(0.699727\pi\) | |||||||
\(570\) | −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 | ||||||||
\(575\) | −19.4277 | + | 14.0557i | −0.810192 | + | 0.586164i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −19.8564 | − | 19.8564i | −0.826634 | − | 0.826634i | 0.160416 | − | 0.987050i | \(-0.448716\pi\) |
−0.987050 | + | 0.160416i | \(0.948716\pi\) | |||||||
\(578\) | −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 | −0.994164 | − | 0.107879i | \(-0.965594\pi\) |
−0.107879 | − | 0.994164i | \(-0.534406\pi\) | |||||||
\(588\) | 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 | −0.772951 | − | 0.634466i | \(-0.781220\pi\) |
0.634466 | + | 0.772951i | \(0.281220\pi\) | |||||||
\(594\) | 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 | ||||
\(598\) | 29.5967 | − | 1.26324i | 1.21030 | − | 0.0516576i | ||||
\(599\) | − | 16.1347i | − | 0.659248i | −0.944112 | − | 0.329624i | \(-0.893078\pi\) | ||
0.944112 | − | 0.329624i | \(-0.106922\pi\) | |||||||
\(600\) | −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 | 0.997463 | − | 0.0711898i | \(-0.0226796\pi\) |
−0.0711898 | + | 0.997463i | \(0.522680\pi\) | |||||||
\(608\) | 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 | \(-0.108133\pi\) |
−0.333213 | + | 0.942852i | \(0.608133\pi\) | |||||||
\(614\) | 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 | \(-0.626103\pi\) |
0.922548 | + | 0.385883i | \(0.126103\pi\) | |||||||
\(618\) | −12.0533 | − | 12.0533i | −0.484854 | − | 0.484854i | ||||
\(619\) | 31.9076 | 1.28247 | 0.641236 | − | 0.767343i | \(-0.278422\pi\) | ||||
0.641236 | + | 0.767343i | \(0.278422\pi\) | |||||||
\(620\) | −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 | −0.997326 | − | 0.0730859i | \(-0.976715\pi\) |
−0.0730859 | − | 0.997326i | \(-0.523285\pi\) | |||||||
\(644\) | 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 | −0.999316 | − | 0.0369830i | \(-0.988225\pi\) |
−0.0369830 | − | 0.999316i | \(-0.511775\pi\) | |||||||
\(648\) | 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 | −0.398981 | − | 0.916959i | \(-0.630636\pi\) |
0.916959 | + | 0.398981i | \(0.130636\pi\) | |||||||
\(654\) | 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 | \(-0.324871\pi\) | ||||
0.522843 | + | 0.852429i | \(0.324871\pi\) | |||||||
\(660\) | −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 | ||||||
\(667\) | 1.05399 | + | 24.6942i | 0.0408106 | + | 0.956162i | ||||
\(668\) | −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 | −0.886785 | − | 0.462182i | \(-0.847067\pi\) |
0.462182 | + | 0.886785i | \(0.347067\pi\) | |||||||
\(674\) | 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 | \(-0.704166\pi\) |
0.801255 | + | 0.598323i | \(0.204166\pi\) | |||||||
\(678\) | 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 | −0.865611 | − | 0.500716i | \(-0.833070\pi\) |
0.500716 | + | 0.865611i | \(0.333070\pi\) | |||||||
\(684\) | −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 | ||||||||
\(690\) | 3.52045 | + | 10.1295i | 0.134021 | + | 0.385623i | ||||
\(691\) | −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 | \(-0.570263\pi\) | ||||
−0.218950 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(710\) | −10.6366 | + | 19.7713i | −0.399184 | + | 0.742004i | ||||
\(711\) | 0.836863i | 0.0313848i | ||||||||
\(712\) | 6.09259 | − | 6.09259i | 0.228329 | − | 0.228329i | ||||
\(713\) | 26.6145 | − | 1.13595i | 0.996721 | − | 0.0425417i | ||||
\(714\) | 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 | \(0.103521\pi\) | ||||
−0.947580 | + | 0.319518i | \(0.896479\pi\) | |||||||
\(720\) | −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 | \(-0.654342\pi\) |
0.884731 | + | 0.466101i | \(0.154342\pi\) | |||||||
\(728\) | 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 | \(-0.488164\pi\) |
−0.999309 | + | 0.0371743i | \(0.988164\pi\) | |||||||
\(734\) | −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 | \(-0.831391\pi\) | ||
0.862959 | − | 0.505275i | \(-0.168609\pi\) | |||||||
\(740\) | −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 | \(-0.0964323\pi\) |
−0.298338 | + | 0.954460i | \(0.596432\pi\) | |||||||
\(744\) | 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 | −0.295116 | + | 0.955461i | \(0.595358\pi\) |
−0.955461 | + | 0.295116i | \(0.904642\pi\) | |||||||
\(758\) | −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 | \(-0.356248\pi\) | ||||
0.436415 | + | 0.899745i | \(0.356248\pi\) | |||||||
\(770\) | −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 | \(-0.382338\pi\) |
−0.932455 | + | 0.361286i | \(0.882338\pi\) | |||||||
\(774\) | 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 | ||||||||
\(782\) | −2.64944 | + | 0.113083i | −0.0947439 | + | 0.00404383i | ||||
\(783\) | 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 | \(-0.689970\pi\) |
0.827133 | + | 0.562006i | \(0.189970\pi\) | |||||||
\(788\) | −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 | 0.244807 | − | 0.969572i | \(-0.421276\pi\) |
0.969572 | − | 0.244807i | \(-0.0787245\pi\) | |||||||
\(798\) | −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 | ||||||||
\(805\) | 27.5320 | + | 13.3305i | 0.970375 | + | 0.469837i | ||||
\(806\) | 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 | \(0.0779597\pi\) | ||||
−0.970157 | + | 0.242476i | \(0.922040\pi\) | |||||||
\(810\) | 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 | −0.888364 | − | 0.459141i | \(-0.848157\pi\) |
0.459141 | + | 0.888364i | \(0.348157\pi\) | |||||||
\(824\) | 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 | \(-0.724477\pi\) |
0.761471 | + | 0.648199i | \(0.224477\pi\) | |||||||
\(828\) | 4.79147 | − | 0.204508i | 0.166515 | − | 0.00710714i | ||||
\(829\) | − | 52.0135i | − | 1.80650i | −0.429111 | − | 0.903252i | \(-0.641173\pi\) | ||
0.429111 | − | 0.903252i | \(-0.358827\pi\) | |||||||
\(830\) | 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 | \(-0.493101\pi\) | ||||
0.0216722 | + | 0.999765i | \(0.493101\pi\) | |||||||
\(840\) | −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 | 0.0459389 | − | 0.998944i | \(-0.485372\pi\) |
0.998944 | − | 0.0459389i | \(-0.0146279\pi\) | |||||||
\(854\) | − | 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 | 0.411051 | − | 0.911613i | \(-0.365162\pi\) |
−0.911613 | + | 0.411051i | \(0.865162\pi\) | |||||||
\(858\) | 22.3418 | + | 22.3418i | 0.762738 | + | 0.762738i | ||||
\(859\) | 43.2161i | 1.47451i | 0.675613 | + | 0.737256i | \(0.263879\pi\) | ||||
−0.675613 | + | 0.737256i | \(0.736121\pi\) | |||||||
\(860\) | −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 | −0.645706 | − | 0.763586i | \(-0.723437\pi\) |
0.763586 | + | 0.645706i | \(0.223437\pi\) | |||||||
\(864\) | 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 | 0.607150 | − | 0.794587i | \(-0.292313\pi\) |
−0.794587 | + | 0.607150i | \(0.792313\pi\) | |||||||
\(878\) | −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 | −0.439213 | − | 0.898383i | \(-0.644743\pi\) |
0.898383 | + | 0.439213i | \(0.144743\pi\) | |||||||
\(884\) | −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 | 0.673878 | − | 0.738842i | \(-0.264627\pi\) |
−0.738842 | + | 0.673878i | \(0.764627\pi\) | |||||||
\(888\) | 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 | ||||||
\(897\) | −1.26324 | − | 29.5967i | −0.0421783 | − | 0.988206i | ||||
\(898\) | −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 | \(-0.737499\pi\) |
0.734324 | + | 0.678799i | \(0.237499\pi\) | |||||||
\(908\) | 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 | \(-0.571444\pi\) | ||||
−0.222568 | + | 0.974917i | \(0.571444\pi\) | |||||||
\(920\) | −9.65196 | − | 4.67329i | −0.318216 | − | 0.154074i | ||||
\(921\) | 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 | \(0.126962\pi\) | ||||
−0.921504 | + | 0.388370i | \(0.873038\pi\) | |||||||
\(930\) | 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 | −0.0695692 | + | 0.997577i | \(0.522162\pi\) |
−0.997577 | + | 0.0695692i | \(0.977838\pi\) | |||||||
\(938\) | 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 | ||||
\(943\) | −39.3278 | + | 1.67858i | −1.28069 | + | 0.0546620i | ||||
\(944\) | 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 | 0.162168 | − | 0.986763i | \(-0.448151\pi\) |
−0.986763 | + | 0.162168i | \(0.948151\pi\) | |||||||
\(948\) | −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 | \(-0.230101\pi\) |
−0.661549 | + | 0.749902i | \(0.730101\pi\) | |||||||
\(954\) | −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 | 0.998757 | − | 0.0498460i | \(-0.0158730\pi\) |
−0.0498460 | + | 0.998757i | \(0.515873\pi\) | |||||||
\(968\) | 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 | \(-0.837521\pi\) |
0.488563 | + | 0.872529i | \(0.337521\pi\) | |||||||
\(978\) | 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 | \(-0.0552159\pi\) |
−0.172597 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(984\) | − | 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 | 0.999886 | − | 0.0150892i | \(-0.00480322\pi\) |
−0.0150892 | + | 0.999886i | \(0.504803\pi\) | |||||||
\(998\) | −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.367.10 | yes | 24 | |
5.3 | odd | 4 | inner | 690.2.j.b.643.9 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.367.9 | ✓ | 24 | |
115.68 | even | 4 | inner | 690.2.j.b.643.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.9 | ✓ | 24 | 23.22 | odd | 2 | inner | |
690.2.j.b.367.10 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.643.9 | yes | 24 | 5.3 | odd | 4 | inner | |
690.2.j.b.643.10 | yes | 24 | 115.68 | even | 4 | inner |