Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.415 |
Dual form | 966.2.i.h.277.2 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.62132 | − | 2.09077i | 0.612801 | − | 0.790237i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 1.00000 | + | 2.44949i | 0.267261 | + | 0.654654i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.707107 | + | 1.22474i | 0.171499 | + | 0.297044i | 0.938944 | − | 0.344070i | \(-0.111806\pi\) |
−0.767445 | + | 0.641114i | \(0.778472\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 1.70711 | − | 2.95680i | 0.391637 | − | 0.678335i | −0.601028 | − | 0.799228i | \(-0.705242\pi\) |
0.992666 | + | 0.120892i | \(0.0385755\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.62132 | − | 0.358719i | −0.572019 | − | 0.0782790i | ||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | −0.707107 | + | 1.22474i | −0.138675 | + | 0.240192i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.62132 | − | 0.358719i | −0.495383 | − | 0.0677916i | ||||
\(29\) | −0.757359 | −0.140638 | −0.0703190 | − | 0.997525i | \(-0.522402\pi\) | ||||
−0.0703190 | + | 0.997525i | \(0.522402\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | −2.32843 | − | 4.03295i | −0.418198 | − | 0.724340i | 0.577560 | − | 0.816348i | \(-0.304005\pi\) |
−0.995758 | + | 0.0920080i | \(0.970671\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | −1.41421 | −0.242536 | ||||||||
\(35\) | −1.00000 | − | 2.44949i | −0.169031 | − | 0.414039i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.53553 | − | 7.85578i | 0.745637 | − | 1.29148i | −0.204259 | − | 0.978917i | \(-0.565479\pi\) |
0.949896 | − | 0.312565i | \(-0.101188\pi\) | |||||||
\(38\) | 1.70711 | + | 2.95680i | 0.276929 | + | 0.479656i | ||||
\(39\) | −0.707107 | − | 1.22474i | −0.113228 | − | 0.196116i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 1.75736 | 0.274453 | 0.137227 | − | 0.990540i | \(-0.456181\pi\) | ||||
0.137227 | + | 0.990540i | \(0.456181\pi\) | |||||||
\(42\) | 1.62132 | − | 2.09077i | 0.250175 | − | 0.322613i | ||||
\(43\) | −7.65685 | −1.16766 | −0.583830 | − | 0.811876i | \(-0.698446\pi\) | ||||
−0.583830 | + | 0.811876i | \(0.698446\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | 4.65685 | − | 8.06591i | 0.679272 | − | 1.17653i | −0.295928 | − | 0.955210i | \(-0.595629\pi\) |
0.975200 | − | 0.221324i | \(-0.0710377\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | 0.707107 | − | 1.22474i | 0.0990148 | − | 0.171499i | ||||
\(52\) | −0.707107 | − | 1.22474i | −0.0980581 | − | 0.169842i | ||||
\(53\) | 1.08579 | + | 1.88064i | 0.149144 | + | 0.258325i | 0.930911 | − | 0.365245i | \(-0.119015\pi\) |
−0.781767 | + | 0.623570i | \(0.785681\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 1.62132 | − | 2.09077i | 0.216658 | − | 0.279391i | ||||
\(57\) | −3.41421 | −0.452224 | ||||||||
\(58\) | 0.378680 | − | 0.655892i | 0.0497231 | − | 0.0861229i | ||||
\(59\) | 0.378680 | + | 0.655892i | 0.0492999 | + | 0.0853899i | 0.889622 | − | 0.456697i | \(-0.150968\pi\) |
−0.840322 | + | 0.542087i | \(0.817634\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 4.65685 | 0.591421 | ||||||||
\(63\) | 1.00000 | + | 2.44949i | 0.125988 | + | 0.308607i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.707107 | − | 1.22474i | 0.0877058 | − | 0.151911i | ||||
\(66\) | 1.50000 | + | 2.59808i | 0.184637 | + | 0.319801i | ||||
\(67\) | 2.17157 | + | 3.76127i | 0.265300 | + | 0.459513i | 0.967642 | − | 0.252327i | \(-0.0811957\pi\) |
−0.702342 | + | 0.711839i | \(0.747862\pi\) | |||||||
\(68\) | 0.707107 | − | 1.22474i | 0.0857493 | − | 0.148522i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 2.62132 | + | 0.358719i | 0.313308 | + | 0.0428752i | ||||
\(71\) | 5.89949 | 0.700141 | 0.350071 | − | 0.936723i | \(-0.386158\pi\) | ||||
0.350071 | + | 0.936723i | \(0.386158\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −2.82843 | − | 4.89898i | −0.331042 | − | 0.573382i | 0.651674 | − | 0.758499i | \(-0.274067\pi\) |
−0.982717 | + | 0.185117i | \(0.940734\pi\) | |||||||
\(74\) | 4.53553 | + | 7.85578i | 0.527245 | + | 0.913215i | ||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | −3.41421 | −0.391637 | ||||||||
\(77\) | 7.86396 | + | 1.07616i | 0.896182 | + | 0.122640i | ||||
\(78\) | 1.41421 | 0.160128 | ||||||||
\(79\) | 0.207107 | − | 0.358719i | 0.0233013 | − | 0.0403591i | −0.854140 | − | 0.520044i | \(-0.825916\pi\) |
0.877441 | + | 0.479685i | \(0.159249\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.878680 | + | 1.52192i | −0.0970339 | + | 0.168068i | ||||
\(83\) | 12.3137 | 1.35161 | 0.675803 | − | 0.737083i | \(-0.263797\pi\) | ||||
0.675803 | + | 0.737083i | \(0.263797\pi\) | |||||||
\(84\) | 1.00000 | + | 2.44949i | 0.109109 | + | 0.267261i | ||||
\(85\) | 1.41421 | 0.153393 | ||||||||
\(86\) | 3.82843 | − | 6.63103i | 0.412830 | − | 0.715042i | ||||
\(87\) | 0.378680 | + | 0.655892i | 0.0405987 | + | 0.0703190i | ||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | −7.36396 | + | 12.7548i | −0.780578 | + | 1.35200i | 0.151027 | + | 0.988530i | \(0.451742\pi\) |
−0.931605 | + | 0.363472i | \(0.881591\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 2.29289 | − | 2.95680i | 0.240361 | − | 0.309956i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −2.32843 | + | 4.03295i | −0.241447 | + | 0.418198i | ||||
\(94\) | 4.65685 | + | 8.06591i | 0.480318 | + | 0.831935i | ||||
\(95\) | −1.70711 | − | 2.95680i | −0.175145 | − | 0.303361i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −3.58579 | −0.364081 | −0.182041 | − | 0.983291i | \(-0.558270\pi\) | ||||
−0.182041 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(98\) | 6.74264 | + | 1.88064i | 0.681110 | + | 0.189973i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | 2.24264 | + | 3.88437i | 0.223151 | + | 0.386509i | 0.955763 | − | 0.294137i | \(-0.0950323\pi\) |
−0.732612 | + | 0.680646i | \(0.761699\pi\) | |||||||
\(102\) | 0.707107 | + | 1.22474i | 0.0700140 | + | 0.121268i | ||||
\(103\) | 6.82843 | − | 11.8272i | 0.672825 | − | 1.16537i | −0.304275 | − | 0.952584i | \(-0.598414\pi\) |
0.977100 | − | 0.212783i | \(-0.0682526\pi\) | |||||||
\(104\) | 1.41421 | 0.138675 | ||||||||
\(105\) | −1.62132 | + | 2.09077i | −0.158225 | + | 0.204038i | ||||
\(106\) | −2.17157 | −0.210922 | ||||||||
\(107\) | 3.74264 | − | 6.48244i | 0.361815 | − | 0.626681i | −0.626445 | − | 0.779466i | \(-0.715491\pi\) |
0.988260 | + | 0.152784i | \(0.0488240\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −2.65685 | − | 4.60181i | −0.254480 | − | 0.440773i | 0.710274 | − | 0.703926i | \(-0.248571\pi\) |
−0.964754 | + | 0.263152i | \(0.915238\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | −9.07107 | −0.860988 | ||||||||
\(112\) | 1.00000 | + | 2.44949i | 0.0944911 | + | 0.231455i | ||||
\(113\) | −17.4142 | −1.63819 | −0.819096 | − | 0.573657i | \(-0.805524\pi\) | ||||
−0.819096 | + | 0.573657i | \(0.805524\pi\) | |||||||
\(114\) | 1.70711 | − | 2.95680i | 0.159885 | − | 0.276929i | ||||
\(115\) | −0.500000 | − | 0.866025i | −0.0466252 | − | 0.0807573i | ||||
\(116\) | 0.378680 | + | 0.655892i | 0.0351595 | + | 0.0608981i | ||||
\(117\) | −0.707107 | + | 1.22474i | −0.0653720 | + | 0.113228i | ||||
\(118\) | −0.757359 | −0.0697206 | ||||||||
\(119\) | 3.70711 | + | 0.507306i | 0.339830 | + | 0.0465047i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 3.00000 | + | 5.19615i | 0.271607 | + | 0.470438i | ||||
\(123\) | −0.878680 | − | 1.52192i | −0.0792279 | − | 0.137227i | ||||
\(124\) | −2.32843 | + | 4.03295i | −0.209099 | + | 0.362170i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | −2.62132 | − | 0.358719i | −0.233526 | − | 0.0319573i | ||||
\(127\) | −5.82843 | −0.517189 | −0.258595 | − | 0.965986i | \(-0.583259\pi\) | ||||
−0.258595 | + | 0.965986i | \(0.583259\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 3.82843 | + | 6.63103i | 0.337074 | + | 0.583830i | ||||
\(130\) | 0.707107 | + | 1.22474i | 0.0620174 | + | 0.107417i | ||||
\(131\) | 0.621320 | − | 1.07616i | 0.0542850 | − | 0.0940244i | −0.837606 | − | 0.546275i | \(-0.816045\pi\) |
0.891891 | + | 0.452251i | \(0.149379\pi\) | |||||||
\(132\) | −3.00000 | −0.261116 | ||||||||
\(133\) | −3.41421 | − | 8.36308i | −0.296050 | − | 0.725171i | ||||
\(134\) | −4.34315 | −0.375191 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0.707107 | + | 1.22474i | 0.0606339 | + | 0.105021i | ||||
\(137\) | 9.48528 | + | 16.4290i | 0.810382 | + | 1.40362i | 0.912597 | + | 0.408861i | \(0.134074\pi\) |
−0.102214 | + | 0.994762i | \(0.532593\pi\) | |||||||
\(138\) | 0.500000 | − | 0.866025i | 0.0425628 | − | 0.0737210i | ||||
\(139\) | −5.31371 | −0.450703 | −0.225351 | − | 0.974278i | \(-0.572353\pi\) | ||||
−0.225351 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(140\) | −1.62132 | + | 2.09077i | −0.137027 | + | 0.176702i | ||||
\(141\) | −9.31371 | −0.784356 | ||||||||
\(142\) | −2.94975 | + | 5.10911i | −0.247537 | + | 0.428747i | ||||
\(143\) | 2.12132 | + | 3.67423i | 0.177394 | + | 0.307255i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −0.378680 | + | 0.655892i | −0.0314476 | + | 0.0544689i | ||||
\(146\) | 5.65685 | 0.468165 | ||||||||
\(147\) | −5.00000 | + | 4.89898i | −0.412393 | + | 0.404061i | ||||
\(148\) | −9.07107 | −0.745637 | ||||||||
\(149\) | −6.82843 | + | 11.8272i | −0.559407 | + | 0.968921i | 0.438139 | + | 0.898907i | \(0.355638\pi\) |
−0.997546 | + | 0.0700136i | \(0.977696\pi\) | |||||||
\(150\) | 2.00000 | + | 3.46410i | 0.163299 | + | 0.282843i | ||||
\(151\) | 0.671573 | + | 1.16320i | 0.0546518 | + | 0.0946597i | 0.892057 | − | 0.451923i | \(-0.149262\pi\) |
−0.837405 | + | 0.546583i | \(0.815928\pi\) | |||||||
\(152\) | 1.70711 | − | 2.95680i | 0.138465 | − | 0.239828i | ||||
\(153\) | −1.41421 | −0.114332 | ||||||||
\(154\) | −4.86396 | + | 6.27231i | −0.391949 | + | 0.505437i | ||||
\(155\) | −4.65685 | −0.374048 | ||||||||
\(156\) | −0.707107 | + | 1.22474i | −0.0566139 | + | 0.0980581i | ||||
\(157\) | 1.94975 | + | 3.37706i | 0.155607 | + | 0.269519i | 0.933280 | − | 0.359150i | \(-0.116933\pi\) |
−0.777673 | + | 0.628669i | \(0.783600\pi\) | |||||||
\(158\) | 0.207107 | + | 0.358719i | 0.0164765 | + | 0.0285382i | ||||
\(159\) | 1.08579 | − | 1.88064i | 0.0861085 | − | 0.149144i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −1.00000 | − | 2.44949i | −0.0788110 | − | 0.193047i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 0.707107 | − | 1.22474i | 0.0553849 | − | 0.0959294i | −0.837004 | − | 0.547197i | \(-0.815695\pi\) |
0.892389 | + | 0.451268i | \(0.149028\pi\) | |||||||
\(164\) | −0.878680 | − | 1.52192i | −0.0686134 | − | 0.118842i | ||||
\(165\) | −1.50000 | − | 2.59808i | −0.116775 | − | 0.202260i | ||||
\(166\) | −6.15685 | + | 10.6640i | −0.477865 | + | 0.827686i | ||||
\(167\) | 18.4853 | 1.43043 | 0.715217 | − | 0.698902i | \(-0.246328\pi\) | ||||
0.715217 | + | 0.698902i | \(0.246328\pi\) | |||||||
\(168\) | −2.62132 | − | 0.358719i | −0.202239 | − | 0.0276758i | ||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | −0.707107 | + | 1.22474i | −0.0542326 | + | 0.0939336i | ||||
\(171\) | 1.70711 | + | 2.95680i | 0.130546 | + | 0.226112i | ||||
\(172\) | 3.82843 | + | 6.63103i | 0.291915 | + | 0.505611i | ||||
\(173\) | −2.41421 | + | 4.18154i | −0.183549 | + | 0.317917i | −0.943087 | − | 0.332547i | \(-0.892092\pi\) |
0.759537 | + | 0.650464i | \(0.225425\pi\) | |||||||
\(174\) | −0.757359 | −0.0574153 | ||||||||
\(175\) | 10.4853 | + | 1.43488i | 0.792613 | + | 0.108467i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0.378680 | − | 0.655892i | 0.0284633 | − | 0.0492999i | ||||
\(178\) | −7.36396 | − | 12.7548i | −0.551952 | − | 0.956009i | ||||
\(179\) | −8.00000 | − | 13.8564i | −0.597948 | − | 1.03568i | −0.993124 | − | 0.117071i | \(-0.962650\pi\) |
0.395175 | − | 0.918606i | \(-0.370684\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | −12.4853 | −0.928024 | −0.464012 | − | 0.885829i | \(-0.653590\pi\) | ||||
−0.464012 | + | 0.885829i | \(0.653590\pi\) | |||||||
\(182\) | 1.41421 | + | 3.46410i | 0.104828 | + | 0.256776i | ||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −4.53553 | − | 7.85578i | −0.333459 | − | 0.577568i | ||||
\(186\) | −2.32843 | − | 4.03295i | −0.170729 | − | 0.295711i | ||||
\(187\) | −2.12132 | + | 3.67423i | −0.155126 | + | 0.268687i | ||||
\(188\) | −9.31371 | −0.679272 | ||||||||
\(189\) | 1.62132 | − | 2.09077i | 0.117934 | − | 0.152081i | ||||
\(190\) | 3.41421 | 0.247693 | ||||||||
\(191\) | −0.707107 | + | 1.22474i | −0.0511645 | + | 0.0886194i | −0.890473 | − | 0.455035i | \(-0.849627\pi\) |
0.839309 | + | 0.543655i | \(0.182960\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 9.81371 | + | 16.9978i | 0.706406 | + | 1.22353i | 0.966182 | + | 0.257862i | \(0.0830181\pi\) |
−0.259775 | + | 0.965669i | \(0.583649\pi\) | |||||||
\(194\) | 1.79289 | − | 3.10538i | 0.128722 | − | 0.222953i | ||||
\(195\) | −1.41421 | −0.101274 | ||||||||
\(196\) | −5.00000 | + | 4.89898i | −0.357143 | + | 0.349927i | ||||
\(197\) | −3.17157 | −0.225965 | −0.112983 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112983 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(198\) | 1.50000 | − | 2.59808i | 0.106600 | − | 0.184637i | ||||
\(199\) | −2.65685 | − | 4.60181i | −0.188339 | − | 0.326213i | 0.756357 | − | 0.654159i | \(-0.226977\pi\) |
−0.944697 | + | 0.327945i | \(0.893644\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | 2.17157 | − | 3.76127i | 0.153171 | − | 0.265300i | ||||
\(202\) | −4.48528 | −0.315583 | ||||||||
\(203\) | −1.22792 | + | 1.58346i | −0.0861832 | + | 0.111137i | ||||
\(204\) | −1.41421 | −0.0990148 | ||||||||
\(205\) | 0.878680 | − | 1.52192i | 0.0613696 | − | 0.106295i | ||||
\(206\) | 6.82843 | + | 11.8272i | 0.475759 | + | 0.824039i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | −0.707107 | + | 1.22474i | −0.0490290 | + | 0.0849208i | ||||
\(209\) | 10.2426 | 0.708498 | ||||||||
\(210\) | −1.00000 | − | 2.44949i | −0.0690066 | − | 0.169031i | ||||
\(211\) | 4.82843 | 0.332403 | 0.166201 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166201 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(212\) | 1.08579 | − | 1.88064i | 0.0745721 | − | 0.129163i | ||||
\(213\) | −2.94975 | − | 5.10911i | −0.202113 | − | 0.350071i | ||||
\(214\) | 3.74264 | + | 6.48244i | 0.255842 | + | 0.443131i | ||||
\(215\) | −3.82843 | + | 6.63103i | −0.261097 | + | 0.452233i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −12.2071 | − | 1.67050i | −0.828672 | − | 0.113401i | ||||
\(218\) | 5.31371 | 0.359890 | ||||||||
\(219\) | −2.82843 | + | 4.89898i | −0.191127 | + | 0.331042i | ||||
\(220\) | −1.50000 | − | 2.59808i | −0.101130 | − | 0.175162i | ||||
\(221\) | 1.00000 | + | 1.73205i | 0.0672673 | + | 0.116510i | ||||
\(222\) | 4.53553 | − | 7.85578i | 0.304405 | − | 0.527245i | ||||
\(223\) | −10.1716 | −0.681139 | −0.340569 | − | 0.940219i | \(-0.610620\pi\) | ||||
−0.340569 | + | 0.940219i | \(0.610620\pi\) | |||||||
\(224\) | −2.62132 | − | 0.358719i | −0.175144 | − | 0.0239680i | ||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 8.70711 | − | 15.0812i | 0.579188 | − | 1.00318i | ||||
\(227\) | 3.91421 | + | 6.77962i | 0.259795 | + | 0.449979i | 0.966187 | − | 0.257842i | \(-0.0830115\pi\) |
−0.706392 | + | 0.707821i | \(0.749678\pi\) | |||||||
\(228\) | 1.70711 | + | 2.95680i | 0.113056 | + | 0.195819i | ||||
\(229\) | −11.3640 | + | 19.6830i | −0.750952 | + | 1.30069i | 0.196410 | + | 0.980522i | \(0.437072\pi\) |
−0.947362 | + | 0.320165i | \(0.896262\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −3.00000 | − | 7.34847i | −0.197386 | − | 0.483494i | ||||
\(232\) | −0.757359 | −0.0497231 | ||||||||
\(233\) | −7.60660 | + | 13.1750i | −0.498325 | + | 0.863124i | −0.999998 | − | 0.00193299i | \(-0.999385\pi\) |
0.501673 | + | 0.865057i | \(0.332718\pi\) | |||||||
\(234\) | −0.707107 | − | 1.22474i | −0.0462250 | − | 0.0800641i | ||||
\(235\) | −4.65685 | − | 8.06591i | −0.303780 | − | 0.526162i | ||||
\(236\) | 0.378680 | − | 0.655892i | 0.0246499 | − | 0.0426950i | ||||
\(237\) | −0.414214 | −0.0269061 | ||||||||
\(238\) | −2.29289 | + | 2.95680i | −0.148626 | + | 0.191661i | ||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | 4.96447 | + | 8.59871i | 0.319789 | + | 0.553891i | 0.980444 | − | 0.196799i | \(-0.0630545\pi\) |
−0.660655 | + | 0.750690i | \(0.729721\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | −6.74264 | − | 1.88064i | −0.430772 | − | 0.120150i | ||||
\(246\) | 1.75736 | 0.112045 | ||||||||
\(247\) | 2.41421 | − | 4.18154i | 0.153613 | − | 0.266065i | ||||
\(248\) | −2.32843 | − | 4.03295i | −0.147855 | − | 0.256093i | ||||
\(249\) | −6.15685 | − | 10.6640i | −0.390175 | − | 0.675803i | ||||
\(250\) | −4.50000 | + | 7.79423i | −0.284605 | + | 0.492950i | ||||
\(251\) | 25.8284 | 1.63028 | 0.815138 | − | 0.579267i | \(-0.196661\pi\) | ||||
0.815138 | + | 0.579267i | \(0.196661\pi\) | |||||||
\(252\) | 1.62132 | − | 2.09077i | 0.102134 | − | 0.131706i | ||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 2.91421 | − | 5.04757i | 0.182854 | − | 0.316712i | ||||
\(255\) | −0.707107 | − | 1.22474i | −0.0442807 | − | 0.0766965i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.707107 | − | 1.22474i | 0.0441081 | − | 0.0763975i | −0.843129 | − | 0.537712i | \(-0.819289\pi\) |
0.887237 | + | 0.461315i | \(0.152622\pi\) | |||||||
\(258\) | −7.65685 | −0.476695 | ||||||||
\(259\) | −9.07107 | − | 22.2195i | −0.563649 | − | 1.38065i | ||||
\(260\) | −1.41421 | −0.0877058 | ||||||||
\(261\) | 0.378680 | − | 0.655892i | 0.0234397 | − | 0.0405987i | ||||
\(262\) | 0.621320 | + | 1.07616i | 0.0383853 | + | 0.0664853i | ||||
\(263\) | −5.48528 | − | 9.50079i | −0.338237 | − | 0.585844i | 0.645864 | − | 0.763452i | \(-0.276497\pi\) |
−0.984101 | + | 0.177609i | \(0.943164\pi\) | |||||||
\(264\) | 1.50000 | − | 2.59808i | 0.0923186 | − | 0.159901i | ||||
\(265\) | 2.17157 | 0.133399 | ||||||||
\(266\) | 8.94975 | + | 1.22474i | 0.548744 | + | 0.0750939i | ||||
\(267\) | 14.7279 | 0.901334 | ||||||||
\(268\) | 2.17157 | − | 3.76127i | 0.132650 | − | 0.229756i | ||||
\(269\) | −0.792893 | − | 1.37333i | −0.0483436 | − | 0.0837335i | 0.840841 | − | 0.541282i | \(-0.182061\pi\) |
−0.889185 | + | 0.457549i | \(0.848728\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | 3.50000 | − | 6.06218i | 0.212610 | − | 0.368251i | −0.739921 | − | 0.672694i | \(-0.765137\pi\) |
0.952531 | + | 0.304443i | \(0.0984703\pi\) | |||||||
\(272\) | −1.41421 | −0.0857493 | ||||||||
\(273\) | −3.70711 | − | 0.507306i | −0.224364 | − | 0.0307036i | ||||
\(274\) | −18.9706 | −1.14605 | ||||||||
\(275\) | −6.00000 | + | 10.3923i | −0.361814 | + | 0.626680i | ||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | 1.41421 | + | 2.44949i | 0.0849719 | + | 0.147176i | 0.905379 | − | 0.424604i | \(-0.139587\pi\) |
−0.820407 | + | 0.571779i | \(0.806253\pi\) | |||||||
\(278\) | 2.65685 | − | 4.60181i | 0.159348 | − | 0.275998i | ||||
\(279\) | 4.65685 | 0.278799 | ||||||||
\(280\) | −1.00000 | − | 2.44949i | −0.0597614 | − | 0.146385i | ||||
\(281\) | −26.7279 | −1.59445 | −0.797227 | − | 0.603680i | \(-0.793701\pi\) | ||||
−0.797227 | + | 0.603680i | \(0.793701\pi\) | |||||||
\(282\) | 4.65685 | − | 8.06591i | 0.277312 | − | 0.480318i | ||||
\(283\) | 12.0711 | + | 20.9077i | 0.717551 | + | 1.24283i | 0.961968 | + | 0.273164i | \(0.0880701\pi\) |
−0.244417 | + | 0.969670i | \(0.578597\pi\) | |||||||
\(284\) | −2.94975 | − | 5.10911i | −0.175035 | − | 0.303170i | ||||
\(285\) | −1.70711 | + | 2.95680i | −0.101120 | + | 0.175145i | ||||
\(286\) | −4.24264 | −0.250873 | ||||||||
\(287\) | 2.84924 | − | 3.67423i | 0.168185 | − | 0.216883i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 7.50000 | − | 12.9904i | 0.441176 | − | 0.764140i | ||||
\(290\) | −0.378680 | − | 0.655892i | −0.0222368 | − | 0.0385153i | ||||
\(291\) | 1.79289 | + | 3.10538i | 0.105101 | + | 0.182041i | ||||
\(292\) | −2.82843 | + | 4.89898i | −0.165521 | + | 0.286691i | ||||
\(293\) | −21.6274 | −1.26349 | −0.631744 | − | 0.775177i | \(-0.717660\pi\) | ||||
−0.631744 | + | 0.775177i | \(0.717660\pi\) | |||||||
\(294\) | −1.74264 | − | 6.77962i | −0.101633 | − | 0.395395i | ||||
\(295\) | 0.757359 | 0.0440952 | ||||||||
\(296\) | 4.53553 | − | 7.85578i | 0.263623 | − | 0.456608i | ||||
\(297\) | 1.50000 | + | 2.59808i | 0.0870388 | + | 0.150756i | ||||
\(298\) | −6.82843 | − | 11.8272i | −0.395560 | − | 0.685130i | ||||
\(299\) | 0.707107 | − | 1.22474i | 0.0408930 | − | 0.0708288i | ||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | −12.4142 | + | 16.0087i | −0.715543 | + | 0.922727i | ||||
\(302\) | −1.34315 | −0.0772894 | ||||||||
\(303\) | 2.24264 | − | 3.88437i | 0.128836 | − | 0.223151i | ||||
\(304\) | 1.70711 | + | 2.95680i | 0.0979093 | + | 0.169584i | ||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | 0.707107 | − | 1.22474i | 0.0404226 | − | 0.0700140i | ||||
\(307\) | 25.8995 | 1.47816 | 0.739081 | − | 0.673616i | \(-0.235260\pi\) | ||||
0.739081 | + | 0.673616i | \(0.235260\pi\) | |||||||
\(308\) | −3.00000 | − | 7.34847i | −0.170941 | − | 0.418718i | ||||
\(309\) | −13.6569 | −0.776911 | ||||||||
\(310\) | 2.32843 | − | 4.03295i | 0.132246 | − | 0.229056i | ||||
\(311\) | −1.70711 | − | 2.95680i | −0.0968011 | − | 0.167665i | 0.813558 | − | 0.581484i | \(-0.197528\pi\) |
−0.910359 | + | 0.413820i | \(0.864194\pi\) | |||||||
\(312\) | −0.707107 | − | 1.22474i | −0.0400320 | − | 0.0693375i | ||||
\(313\) | −8.37868 | + | 14.5123i | −0.473591 | + | 0.820284i | −0.999543 | − | 0.0302306i | \(-0.990376\pi\) |
0.525952 | + | 0.850514i | \(0.323709\pi\) | |||||||
\(314\) | −3.89949 | −0.220061 | ||||||||
\(315\) | 2.62132 | + | 0.358719i | 0.147695 | + | 0.0202116i | ||||
\(316\) | −0.414214 | −0.0233013 | ||||||||
\(317\) | −4.96447 | + | 8.59871i | −0.278832 | + | 0.482952i | −0.971095 | − | 0.238694i | \(-0.923281\pi\) |
0.692263 | + | 0.721646i | \(0.256614\pi\) | |||||||
\(318\) | 1.08579 | + | 1.88064i | 0.0608879 | + | 0.105461i | ||||
\(319\) | −1.13604 | − | 1.96768i | −0.0636060 | − | 0.110169i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −7.48528 | −0.417788 | ||||||||
\(322\) | 2.62132 | + | 0.358719i | 0.146080 | + | 0.0199907i | ||||
\(323\) | 4.82843 | 0.268661 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 2.82843 | + | 4.89898i | 0.156893 | + | 0.271746i | ||||
\(326\) | 0.707107 | + | 1.22474i | 0.0391630 | + | 0.0678323i | ||||
\(327\) | −2.65685 | + | 4.60181i | −0.146924 | + | 0.254480i | ||||
\(328\) | 1.75736 | 0.0970339 | ||||||||
\(329\) | −9.31371 | − | 22.8138i | −0.513481 | − | 1.25777i | ||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | −12.9497 | + | 22.4296i | −0.711782 | + | 1.23284i | 0.252405 | + | 0.967622i | \(0.418778\pi\) |
−0.964187 | + | 0.265222i | \(0.914555\pi\) | |||||||
\(332\) | −6.15685 | − | 10.6640i | −0.337901 | − | 0.585262i | ||||
\(333\) | 4.53553 | + | 7.85578i | 0.248546 | + | 0.430494i | ||||
\(334\) | −9.24264 | + | 16.0087i | −0.505735 | + | 0.875958i | ||||
\(335\) | 4.34315 | 0.237291 | ||||||||
\(336\) | 1.62132 | − | 2.09077i | 0.0884503 | − | 0.114061i | ||||
\(337\) | −13.9289 | −0.758757 | −0.379379 | − | 0.925242i | \(-0.623862\pi\) | ||||
−0.379379 | + | 0.925242i | \(0.623862\pi\) | |||||||
\(338\) | 5.50000 | − | 9.52628i | 0.299161 | − | 0.518161i | ||||
\(339\) | 8.70711 | + | 15.0812i | 0.472905 | + | 0.819096i | ||||
\(340\) | −0.707107 | − | 1.22474i | −0.0383482 | − | 0.0664211i | ||||
\(341\) | 6.98528 | − | 12.0989i | 0.378274 | − | 0.655190i | ||||
\(342\) | −3.41421 | −0.184620 | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | −7.65685 | −0.412830 | ||||||||
\(345\) | −0.500000 | + | 0.866025i | −0.0269191 | + | 0.0466252i | ||||
\(346\) | −2.41421 | − | 4.18154i | −0.129789 | − | 0.224801i | ||||
\(347\) | 7.31371 | + | 12.6677i | 0.392620 | + | 0.680039i | 0.992794 | − | 0.119831i | \(-0.0382353\pi\) |
−0.600174 | + | 0.799870i | \(0.704902\pi\) | |||||||
\(348\) | 0.378680 | − | 0.655892i | 0.0202994 | − | 0.0351595i | ||||
\(349\) | 26.0416 | 1.39398 | 0.696988 | − | 0.717083i | \(-0.254523\pi\) | ||||
0.696988 | + | 0.717083i | \(0.254523\pi\) | |||||||
\(350\) | −6.48528 | + | 8.36308i | −0.346653 | + | 0.447025i | ||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | 1.50000 | − | 2.59808i | 0.0799503 | − | 0.138478i | ||||
\(353\) | 11.3640 | + | 19.6830i | 0.604843 | + | 1.04762i | 0.992076 | + | 0.125637i | \(0.0400973\pi\) |
−0.387234 | + | 0.921982i | \(0.626569\pi\) | |||||||
\(354\) | 0.378680 | + | 0.655892i | 0.0201266 | + | 0.0348603i | ||||
\(355\) | 2.94975 | − | 5.10911i | 0.156556 | − | 0.271164i | ||||
\(356\) | 14.7279 | 0.780578 | ||||||||
\(357\) | −1.41421 | − | 3.46410i | −0.0748481 | − | 0.183340i | ||||
\(358\) | 16.0000 | 0.845626 | ||||||||
\(359\) | −1.00000 | + | 1.73205i | −0.0527780 | + | 0.0914141i | −0.891207 | − | 0.453596i | \(-0.850141\pi\) |
0.838429 | + | 0.545010i | \(0.183474\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 3.67157 | + | 6.35935i | 0.193241 | + | 0.334703i | ||||
\(362\) | 6.24264 | − | 10.8126i | 0.328106 | − | 0.568296i | ||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | −3.70711 | − | 0.507306i | −0.194305 | − | 0.0265901i | ||||
\(365\) | −5.65685 | −0.296093 | ||||||||
\(366\) | 3.00000 | − | 5.19615i | 0.156813 | − | 0.271607i | ||||
\(367\) | 17.3492 | + | 30.0498i | 0.905623 | + | 1.56859i | 0.820079 | + | 0.572251i | \(0.193930\pi\) |
0.0855444 | + | 0.996334i | \(0.472737\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | −0.878680 | + | 1.52192i | −0.0457422 | + | 0.0792279i | ||||
\(370\) | 9.07107 | 0.471582 | ||||||||
\(371\) | 5.69239 | + | 0.778985i | 0.295534 | + | 0.0404429i | ||||
\(372\) | 4.65685 | 0.241447 | ||||||||
\(373\) | 7.17157 | − | 12.4215i | 0.371330 | − | 0.643162i | −0.618440 | − | 0.785832i | \(-0.712235\pi\) |
0.989770 | + | 0.142669i | \(0.0455685\pi\) | |||||||
\(374\) | −2.12132 | − | 3.67423i | −0.109691 | − | 0.189990i | ||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | 4.65685 | − | 8.06591i | 0.240159 | − | 0.415967i | ||||
\(377\) | −1.07107 | −0.0551628 | ||||||||
\(378\) | 1.00000 | + | 2.44949i | 0.0514344 | + | 0.125988i | ||||
\(379\) | 28.9706 | 1.48812 | 0.744059 | − | 0.668114i | \(-0.232898\pi\) | ||||
0.744059 | + | 0.668114i | \(0.232898\pi\) | |||||||
\(380\) | −1.70711 | + | 2.95680i | −0.0875727 | + | 0.151680i | ||||
\(381\) | 2.91421 | + | 5.04757i | 0.149300 | + | 0.258595i | ||||
\(382\) | −0.707107 | − | 1.22474i | −0.0361787 | − | 0.0626634i | ||||
\(383\) | 0.636039 | − | 1.10165i | 0.0325001 | − | 0.0562918i | −0.849318 | − | 0.527882i | \(-0.822986\pi\) |
0.881818 | + | 0.471590i | \(0.156320\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 4.86396 | − | 6.27231i | 0.247890 | − | 0.319667i | ||||
\(386\) | −19.6274 | −0.999009 | ||||||||
\(387\) | 3.82843 | − | 6.63103i | 0.194610 | − | 0.337074i | ||||
\(388\) | 1.79289 | + | 3.10538i | 0.0910204 | + | 0.157652i | ||||
\(389\) | 0.585786 | + | 1.01461i | 0.0297006 | + | 0.0514429i | 0.880494 | − | 0.474058i | \(-0.157211\pi\) |
−0.850793 | + | 0.525501i | \(0.823878\pi\) | |||||||
\(390\) | 0.707107 | − | 1.22474i | 0.0358057 | − | 0.0620174i | ||||
\(391\) | 1.41421 | 0.0715199 | ||||||||
\(392\) | −1.74264 | − | 6.77962i | −0.0880166 | − | 0.342422i | ||||
\(393\) | −1.24264 | −0.0626829 | ||||||||
\(394\) | 1.58579 | − | 2.74666i | 0.0798908 | − | 0.138375i | ||||
\(395\) | −0.207107 | − | 0.358719i | −0.0104207 | − | 0.0180491i | ||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | −0.221825 | + | 0.384213i | −0.0111331 | + | 0.0192831i | −0.871538 | − | 0.490327i | \(-0.836877\pi\) |
0.860405 | + | 0.509611i | \(0.170211\pi\) | |||||||
\(398\) | 5.31371 | 0.266352 | ||||||||
\(399\) | −5.53553 | + | 7.13834i | −0.277123 | + | 0.357364i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 0.242641 | − | 0.420266i | 0.0121169 | − | 0.0209871i | −0.859903 | − | 0.510457i | \(-0.829476\pi\) |
0.872020 | + | 0.489470i | \(0.162810\pi\) | |||||||
\(402\) | 2.17157 | + | 3.76127i | 0.108308 | + | 0.187595i | ||||
\(403\) | −3.29289 | − | 5.70346i | −0.164031 | − | 0.284109i | ||||
\(404\) | 2.24264 | − | 3.88437i | 0.111576 | − | 0.193255i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −0.757359 | − | 1.85514i | −0.0375871 | − | 0.0920692i | ||||
\(407\) | 27.2132 | 1.34891 | ||||||||
\(408\) | 0.707107 | − | 1.22474i | 0.0350070 | − | 0.0606339i | ||||
\(409\) | 6.67157 | + | 11.5555i | 0.329888 | + | 0.571383i | 0.982489 | − | 0.186319i | \(-0.0596557\pi\) |
−0.652601 | + | 0.757701i | \(0.726322\pi\) | |||||||
\(410\) | 0.878680 | + | 1.52192i | 0.0433949 | + | 0.0751622i | ||||
\(411\) | 9.48528 | − | 16.4290i | 0.467874 | − | 0.810382i | ||||
\(412\) | −13.6569 | −0.672825 | ||||||||
\(413\) | 1.98528 | + | 0.271680i | 0.0976893 | + | 0.0133685i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 6.15685 | − | 10.6640i | 0.302228 | − | 0.523474i | ||||
\(416\) | −0.707107 | − | 1.22474i | −0.0346688 | − | 0.0600481i | ||||
\(417\) | 2.65685 | + | 4.60181i | 0.130107 | + | 0.225351i | ||||
\(418\) | −5.12132 | + | 8.87039i | −0.250492 | + | 0.433865i | ||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 2.62132 | + | 0.358719i | 0.127907 | + | 0.0175037i | ||||
\(421\) | 31.4558 | 1.53306 | 0.766532 | − | 0.642206i | \(-0.221981\pi\) | ||||
0.766532 | + | 0.642206i | \(0.221981\pi\) | |||||||
\(422\) | −2.41421 | + | 4.18154i | −0.117522 | + | 0.203554i | ||||
\(423\) | 4.65685 | + | 8.06591i | 0.226424 | + | 0.392178i | ||||
\(424\) | 1.08579 | + | 1.88064i | 0.0527305 | + | 0.0913318i | ||||
\(425\) | −2.82843 | + | 4.89898i | −0.137199 | + | 0.237635i | ||||
\(426\) | 5.89949 | 0.285831 | ||||||||
\(427\) | −6.00000 | − | 14.6969i | −0.290360 | − | 0.711235i | ||||
\(428\) | −7.48528 | −0.361815 | ||||||||
\(429\) | 2.12132 | − | 3.67423i | 0.102418 | − | 0.177394i | ||||
\(430\) | −3.82843 | − | 6.63103i | −0.184623 | − | 0.319777i | ||||
\(431\) | −3.17157 | − | 5.49333i | −0.152769 | − | 0.264604i | 0.779475 | − | 0.626433i | \(-0.215486\pi\) |
−0.932245 | + | 0.361829i | \(0.882152\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 30.0000 | 1.44171 | 0.720854 | − | 0.693087i | \(-0.243750\pi\) | ||||
0.720854 | + | 0.693087i | \(0.243750\pi\) | |||||||
\(434\) | 7.55025 | − | 9.73641i | 0.362424 | − | 0.467363i | ||||
\(435\) | 0.757359 | 0.0363126 | ||||||||
\(436\) | −2.65685 | + | 4.60181i | −0.127240 | + | 0.220387i | ||||
\(437\) | −1.70711 | − | 2.95680i | −0.0816620 | − | 0.141443i | ||||
\(438\) | −2.82843 | − | 4.89898i | −0.135147 | − | 0.234082i | ||||
\(439\) | −5.57107 | + | 9.64937i | −0.265893 | + | 0.460539i | −0.967797 | − | 0.251732i | \(-0.919000\pi\) |
0.701905 | + | 0.712271i | \(0.252333\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | 6.74264 | + | 1.88064i | 0.321078 | + | 0.0895542i | ||||
\(442\) | −2.00000 | −0.0951303 | ||||||||
\(443\) | −5.13604 | + | 8.89588i | −0.244021 | + | 0.422656i | −0.961856 | − | 0.273557i | \(-0.911800\pi\) |
0.717835 | + | 0.696213i | \(0.245133\pi\) | |||||||
\(444\) | 4.53553 | + | 7.85578i | 0.215247 | + | 0.372819i | ||||
\(445\) | 7.36396 | + | 12.7548i | 0.349085 | + | 0.604633i | ||||
\(446\) | 5.08579 | − | 8.80884i | 0.240819 | − | 0.417111i | ||||
\(447\) | 13.6569 | 0.645947 | ||||||||
\(448\) | 1.62132 | − | 2.09077i | 0.0766002 | − | 0.0987796i | ||||
\(449\) | −1.75736 | −0.0829349 | −0.0414675 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414675 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(450\) | 2.00000 | − | 3.46410i | 0.0942809 | − | 0.163299i | ||||
\(451\) | 2.63604 | + | 4.56575i | 0.124126 | + | 0.214993i | ||||
\(452\) | 8.70711 | + | 15.0812i | 0.409548 | + | 0.709358i | ||||
\(453\) | 0.671573 | − | 1.16320i | 0.0315532 | − | 0.0546518i | ||||
\(454\) | −7.82843 | −0.367406 | ||||||||
\(455\) | −1.41421 | − | 3.46410i | −0.0662994 | − | 0.162400i | ||||
\(456\) | −3.41421 | −0.159885 | ||||||||
\(457\) | −10.1066 | + | 17.5051i | −0.472767 | + | 0.818856i | −0.999514 | − | 0.0311656i | \(-0.990078\pi\) |
0.526747 | + | 0.850022i | \(0.323411\pi\) | |||||||
\(458\) | −11.3640 | − | 19.6830i | −0.531003 | − | 0.919724i | ||||
\(459\) | 0.707107 | + | 1.22474i | 0.0330049 | + | 0.0571662i | ||||
\(460\) | −0.500000 | + | 0.866025i | −0.0233126 | + | 0.0403786i | ||||
\(461\) | 30.9706 | 1.44244 | 0.721221 | − | 0.692705i | \(-0.243581\pi\) | ||||
0.721221 | + | 0.692705i | \(0.243581\pi\) | |||||||
\(462\) | 7.86396 | + | 1.07616i | 0.365865 | + | 0.0500674i | ||||
\(463\) | −13.7990 | −0.641293 | −0.320647 | − | 0.947199i | \(-0.603900\pi\) | ||||
−0.320647 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(464\) | 0.378680 | − | 0.655892i | 0.0175798 | − | 0.0304490i | ||||
\(465\) | 2.32843 | + | 4.03295i | 0.107978 | + | 0.187024i | ||||
\(466\) | −7.60660 | − | 13.1750i | −0.352369 | − | 0.610321i | ||||
\(467\) | −14.4142 | + | 24.9662i | −0.667010 | + | 1.15530i | 0.311726 | + | 0.950172i | \(0.399093\pi\) |
−0.978736 | + | 0.205124i | \(0.934240\pi\) | |||||||
\(468\) | 1.41421 | 0.0653720 | ||||||||
\(469\) | 11.3848 | + | 1.55797i | 0.525700 | + | 0.0719404i | ||||
\(470\) | 9.31371 | 0.429609 | ||||||||
\(471\) | 1.94975 | − | 3.37706i | 0.0898396 | − | 0.155607i | ||||
\(472\) | 0.378680 | + | 0.655892i | 0.0174301 | + | 0.0301899i | ||||
\(473\) | −11.4853 | − | 19.8931i | −0.528094 | − | 0.914685i | ||||
\(474\) | 0.207107 | − | 0.358719i | 0.00951273 | − | 0.0164765i | ||||
\(475\) | 13.6569 | 0.626619 | ||||||||
\(476\) | −1.41421 | − | 3.46410i | −0.0648204 | − | 0.158777i | ||||
\(477\) | −2.17157 | −0.0994295 | ||||||||
\(478\) | 11.6569 | − | 20.1903i | 0.533172 | − | 0.923481i | ||||
\(479\) | −15.2635 | − | 26.4371i | −0.697405 | − | 1.20794i | −0.969363 | − | 0.245632i | \(-0.921005\pi\) |
0.271958 | − | 0.962309i | \(-0.412329\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | 6.41421 | − | 11.1097i | 0.292463 | − | 0.506561i | ||||
\(482\) | −9.92893 | −0.452250 | ||||||||
\(483\) | −1.62132 | + | 2.09077i | −0.0737726 | + | 0.0951333i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | −1.79289 | + | 3.10538i | −0.0814111 | + | 0.141008i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 14.7426 | + | 25.5350i | 0.668053 | + | 1.15710i | 0.978448 | + | 0.206494i | \(0.0662053\pi\) |
−0.310395 | + | 0.950608i | \(0.600461\pi\) | |||||||
\(488\) | 3.00000 | − | 5.19615i | 0.135804 | − | 0.235219i | ||||
\(489\) | −1.41421 | −0.0639529 | ||||||||
\(490\) | 5.00000 | − | 4.89898i | 0.225877 | − | 0.221313i | ||||
\(491\) | −9.10051 | −0.410700 | −0.205350 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205350 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(492\) | −0.878680 | + | 1.52192i | −0.0396139 | + | 0.0686134i | ||||
\(493\) | −0.535534 | − | 0.927572i | −0.0241192 | − | 0.0417757i | ||||
\(494\) | 2.41421 | + | 4.18154i | 0.108621 | + | 0.188136i | ||||
\(495\) | −1.50000 | + | 2.59808i | −0.0674200 | + | 0.116775i | ||||
\(496\) | 4.65685 | 0.209099 | ||||||||
\(497\) | 9.56497 | − | 12.3345i | 0.429048 | − | 0.553277i | ||||
\(498\) | 12.3137 | 0.551790 | ||||||||
\(499\) | 6.89949 | − | 11.9503i | 0.308864 | − | 0.534968i | −0.669250 | − | 0.743037i | \(-0.733385\pi\) |
0.978114 | + | 0.208069i | \(0.0667179\pi\) | |||||||
\(500\) | −4.50000 | − | 7.79423i | −0.201246 | − | 0.348569i | ||||
\(501\) | −9.24264 | − | 16.0087i | −0.412931 | − | 0.715217i | ||||
\(502\) | −12.9142 | + | 22.3681i | −0.576390 | + | 0.998336i | ||||
\(503\) | −6.82843 | −0.304465 | −0.152232 | − | 0.988345i | \(-0.548646\pi\) | ||||
−0.152232 | + | 0.988345i | \(0.548646\pi\) | |||||||
\(504\) | 1.00000 | + | 2.44949i | 0.0445435 | + | 0.109109i | ||||
\(505\) | 4.48528 | 0.199592 | ||||||||
\(506\) | −1.50000 | + | 2.59808i | −0.0666831 | + | 0.115499i | ||||
\(507\) | 5.50000 | + | 9.52628i | 0.244264 | + | 0.423077i | ||||
\(508\) | 2.91421 | + | 5.04757i | 0.129297 | + | 0.223950i | ||||
\(509\) | −20.8640 | + | 36.1374i | −0.924779 | + | 1.60176i | −0.132862 | + | 0.991135i | \(0.542417\pi\) |
−0.791917 | + | 0.610629i | \(0.790917\pi\) | |||||||
\(510\) | 1.41421 | 0.0626224 | ||||||||
\(511\) | −14.8284 | − | 2.02922i | −0.655971 | − | 0.0897676i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.70711 | − | 2.95680i | 0.0753706 | − | 0.130546i | ||||
\(514\) | 0.707107 | + | 1.22474i | 0.0311891 | + | 0.0540212i | ||||
\(515\) | −6.82843 | − | 11.8272i | −0.300896 | − | 0.521168i | ||||
\(516\) | 3.82843 | − | 6.63103i | 0.168537 | − | 0.291915i | ||||
\(517\) | 27.9411 | 1.22885 | ||||||||
\(518\) | 23.7782 | + | 3.25397i | 1.04475 | + | 0.142971i | ||||
\(519\) | 4.82843 | 0.211944 | ||||||||
\(520\) | 0.707107 | − | 1.22474i | 0.0310087 | − | 0.0537086i | ||||
\(521\) | −13.0000 | − | 22.5167i | −0.569540 | − | 0.986473i | −0.996611 | − | 0.0822547i | \(-0.973788\pi\) |
0.427071 | − | 0.904218i | \(-0.359545\pi\) | |||||||
\(522\) | 0.378680 | + | 0.655892i | 0.0165744 | + | 0.0287076i | ||||
\(523\) | 8.14214 | − | 14.1026i | 0.356031 | − | 0.616663i | −0.631263 | − | 0.775569i | \(-0.717463\pi\) |
0.987294 | + | 0.158905i | \(0.0507965\pi\) | |||||||
\(524\) | −1.24264 | −0.0542850 | ||||||||
\(525\) | −4.00000 | − | 9.79796i | −0.174574 | − | 0.427618i | ||||
\(526\) | 10.9706 | 0.478339 | ||||||||
\(527\) | 3.29289 | − | 5.70346i | 0.143441 | − | 0.248447i | ||||
\(528\) | 1.50000 | + | 2.59808i | 0.0652791 | + | 0.113067i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −1.08579 | + | 1.88064i | −0.0471635 | + | 0.0816897i | ||||
\(531\) | −0.757359 | −0.0328666 | ||||||||
\(532\) | −5.53553 | + | 7.13834i | −0.239996 | + | 0.309486i | ||||
\(533\) | 2.48528 | 0.107649 | ||||||||
\(534\) | −7.36396 | + | 12.7548i | −0.318670 | + | 0.551952i | ||||
\(535\) | −3.74264 | − | 6.48244i | −0.161808 | − | 0.280260i | ||||
\(536\) | 2.17157 | + | 3.76127i | 0.0937977 | + | 0.162462i | ||||
\(537\) | −8.00000 | + | 13.8564i | −0.345225 | + | 0.597948i | ||||
\(538\) | 1.58579 | 0.0683681 | ||||||||
\(539\) | 15.0000 | − | 14.6969i | 0.646096 | − | 0.633042i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 19.8492 | − | 34.3799i | 0.853386 | − | 1.47811i | −0.0247491 | − | 0.999694i | \(-0.507879\pi\) |
0.878135 | − | 0.478413i | \(-0.158788\pi\) | |||||||
\(542\) | 3.50000 | + | 6.06218i | 0.150338 | + | 0.260393i | ||||
\(543\) | 6.24264 | + | 10.8126i | 0.267897 | + | 0.464012i | ||||
\(544\) | 0.707107 | − | 1.22474i | 0.0303170 | − | 0.0525105i | ||||
\(545\) | −5.31371 | −0.227614 | ||||||||
\(546\) | 2.29289 | − | 2.95680i | 0.0981268 | − | 0.126539i | ||||
\(547\) | 24.2426 | 1.03654 | 0.518270 | − | 0.855217i | \(-0.326576\pi\) | ||||
0.518270 | + | 0.855217i | \(0.326576\pi\) | |||||||
\(548\) | 9.48528 | − | 16.4290i | 0.405191 | − | 0.701812i | ||||
\(549\) | 3.00000 | + | 5.19615i | 0.128037 | + | 0.221766i | ||||
\(550\) | −6.00000 | − | 10.3923i | −0.255841 | − | 0.443129i | ||||
\(551\) | −1.29289 | + | 2.23936i | −0.0550791 | + | 0.0953998i | ||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −0.414214 | − | 1.01461i | −0.0176142 | − | 0.0431457i | ||||
\(554\) | −2.82843 | −0.120168 | ||||||||
\(555\) | −4.53553 | + | 7.85578i | −0.192523 | + | 0.333459i | ||||
\(556\) | 2.65685 | + | 4.60181i | 0.112676 | + | 0.195160i | ||||
\(557\) | 20.1569 | + | 34.9127i | 0.854073 | + | 1.47930i | 0.877502 | + | 0.479573i | \(0.159208\pi\) |
−0.0234287 | + | 0.999726i | \(0.507458\pi\) | |||||||
\(558\) | −2.32843 | + | 4.03295i | −0.0985702 | + | 0.170729i | ||||
\(559\) | −10.8284 | −0.457994 | ||||||||
\(560\) | 2.62132 | + | 0.358719i | 0.110771 | + | 0.0151587i | ||||
\(561\) | 4.24264 | 0.179124 | ||||||||
\(562\) | 13.3640 | − | 23.1471i | 0.563725 | − | 0.976400i | ||||
\(563\) | 6.57107 | + | 11.3814i | 0.276937 | + | 0.479670i | 0.970622 | − | 0.240609i | \(-0.0773472\pi\) |
−0.693685 | + | 0.720279i | \(0.744014\pi\) | |||||||
\(564\) | 4.65685 | + | 8.06591i | 0.196089 | + | 0.339636i | ||||
\(565\) | −8.70711 | + | 15.0812i | −0.366311 | + | 0.634469i | ||||
\(566\) | −24.1421 | −1.01477 | ||||||||
\(567\) | −2.62132 | − | 0.358719i | −0.110085 | − | 0.0150648i | ||||
\(568\) | 5.89949 | 0.247537 | ||||||||
\(569\) | 2.92893 | − | 5.07306i | 0.122787 | − | 0.212674i | −0.798079 | − | 0.602553i | \(-0.794150\pi\) |
0.920866 | + | 0.389880i | \(0.127483\pi\) | |||||||
\(570\) | −1.70711 | − | 2.95680i | −0.0715028 | − | 0.123847i | ||||
\(571\) | −20.2635 | − | 35.0973i | −0.847999 | − | 1.46878i | −0.882991 | − | 0.469390i | \(-0.844474\pi\) |
0.0349916 | − | 0.999388i | \(-0.488860\pi\) | |||||||
\(572\) | 2.12132 | − | 3.67423i | 0.0886969 | − | 0.153627i | ||||
\(573\) | 1.41421 | 0.0590796 | ||||||||
\(574\) | 1.75736 | + | 4.30463i | 0.0733508 | + | 0.179672i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 3.81371 | + | 6.60554i | 0.158767 | + | 0.274992i | 0.934424 | − | 0.356162i | \(-0.115915\pi\) |
−0.775657 | + | 0.631154i | \(0.782582\pi\) | |||||||
\(578\) | 7.50000 | + | 12.9904i | 0.311959 | + | 0.540329i | ||||
\(579\) | 9.81371 | − | 16.9978i | 0.407844 | − | 0.706406i | ||||
\(580\) | 0.757359 | 0.0314476 | ||||||||
\(581\) | 19.9645 | − | 25.7451i | 0.828266 | − | 1.06809i | ||||
\(582\) | −3.58579 | −0.148636 | ||||||||
\(583\) | −3.25736 | + | 5.64191i | −0.134906 | + | 0.233664i | ||||
\(584\) | −2.82843 | − | 4.89898i | −0.117041 | − | 0.202721i | ||||
\(585\) | 0.707107 | + | 1.22474i | 0.0292353 | + | 0.0506370i | ||||
\(586\) | 10.8137 | − | 18.7299i | 0.446710 | − | 0.773725i | ||||
\(587\) | −2.41421 | −0.0996453 | −0.0498226 | − | 0.998758i | \(-0.515866\pi\) | ||||
−0.0498226 | + | 0.998758i | \(0.515866\pi\) | |||||||
\(588\) | 6.74264 | + | 1.88064i | 0.278062 | + | 0.0775562i | ||||
\(589\) | −15.8995 | −0.655127 | ||||||||
\(590\) | −0.378680 | + | 0.655892i | −0.0155900 | + | 0.0270027i | ||||
\(591\) | 1.58579 | + | 2.74666i | 0.0652305 | + | 0.112983i | ||||
\(592\) | 4.53553 | + | 7.85578i | 0.186409 | + | 0.322870i | ||||
\(593\) | −4.48528 | + | 7.76874i | −0.184188 | + | 0.319024i | −0.943303 | − | 0.331934i | \(-0.892299\pi\) |
0.759114 | + | 0.650957i | \(0.225632\pi\) | |||||||
\(594\) | −3.00000 | −0.123091 | ||||||||
\(595\) | 2.29289 | − | 2.95680i | 0.0939995 | − | 0.121217i | ||||
\(596\) | 13.6569 | 0.559407 | ||||||||
\(597\) | −2.65685 | + | 4.60181i | −0.108738 | + | 0.188339i | ||||
\(598\) | 0.707107 | + | 1.22474i | 0.0289157 | + | 0.0500835i | ||||
\(599\) | 0.464466 | + | 0.804479i | 0.0189776 | + | 0.0328701i | 0.875358 | − | 0.483475i | \(-0.160626\pi\) |
−0.856381 | + | 0.516345i | \(0.827292\pi\) | |||||||
\(600\) | 2.00000 | − | 3.46410i | 0.0816497 | − | 0.141421i | ||||
\(601\) | −40.9411 | −1.67002 | −0.835012 | − | 0.550232i | \(-0.814539\pi\) | ||||
−0.835012 | + | 0.550232i | \(0.814539\pi\) | |||||||
\(602\) | −7.65685 | − | 18.7554i | −0.312070 | − | 0.764412i | ||||
\(603\) | −4.34315 | −0.176867 | ||||||||
\(604\) | 0.671573 | − | 1.16320i | 0.0273259 | − | 0.0473299i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 2.24264 | + | 3.88437i | 0.0911011 | + | 0.157792i | ||||
\(607\) | −9.64214 | + | 16.7007i | −0.391362 | + | 0.677859i | −0.992629 | − | 0.121189i | \(-0.961329\pi\) |
0.601267 | + | 0.799048i | \(0.294663\pi\) | |||||||
\(608\) | −3.41421 | −0.138465 | ||||||||
\(609\) | 1.98528 | + | 0.271680i | 0.0804477 | + | 0.0110090i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 6.58579 | − | 11.4069i | 0.266432 | − | 0.461474i | ||||
\(612\) | 0.707107 | + | 1.22474i | 0.0285831 | + | 0.0495074i | ||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | −12.9497 | + | 22.4296i | −0.522609 | + | 0.905186i | ||||
\(615\) | −1.75736 | −0.0708636 | ||||||||
\(616\) | 7.86396 | + | 1.07616i | 0.316848 | + | 0.0433597i | ||||
\(617\) | −31.9411 | −1.28590 | −0.642951 | − | 0.765908i | \(-0.722290\pi\) | ||||
−0.642951 | + | 0.765908i | \(0.722290\pi\) | |||||||
\(618\) | 6.82843 | − | 11.8272i | 0.274680 | − | 0.475759i | ||||
\(619\) | −4.94975 | − | 8.57321i | −0.198947 | − | 0.344587i | 0.749240 | − | 0.662298i | \(-0.230419\pi\) |
−0.948187 | + | 0.317712i | \(0.897086\pi\) | |||||||
\(620\) | 2.32843 | + | 4.03295i | 0.0935119 | + | 0.161967i | ||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | 3.41421 | 0.136897 | ||||||||
\(623\) | 14.7279 | + | 36.0759i | 0.590062 | + | 1.44535i | ||||
\(624\) | 1.41421 | 0.0566139 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | −8.37868 | − | 14.5123i | −0.334879 | − | 0.580028i | ||||
\(627\) | −5.12132 | − | 8.87039i | −0.204526 | − | 0.354249i | ||||
\(628\) | 1.94975 | − | 3.37706i | 0.0778034 | − | 0.134759i | ||||
\(629\) | 12.8284 | 0.511503 | ||||||||
\(630\) | −1.62132 | + | 2.09077i | −0.0645949 | + | 0.0832983i | ||||
\(631\) | 2.41421 | 0.0961083 | 0.0480542 | − | 0.998845i | \(-0.484698\pi\) | ||||
0.0480542 | + | 0.998845i | \(0.484698\pi\) | |||||||
\(632\) | 0.207107 | − | 0.358719i | 0.00823827 | − | 0.0142691i | ||||
\(633\) | −2.41421 | − | 4.18154i | −0.0959564 | − | 0.166201i | ||||
\(634\) | −4.96447 | − | 8.59871i | −0.197164 | − | 0.341498i | ||||
\(635\) | −2.91421 | + | 5.04757i | −0.115647 | + | 0.200307i | ||||
\(636\) | −2.17157 | −0.0861085 | ||||||||
\(637\) | −2.46447 | − | 9.58783i | −0.0976457 | − | 0.379883i | ||||
\(638\) | 2.27208 | 0.0899524 | ||||||||
\(639\) | −2.94975 | + | 5.10911i | −0.116690 | + | 0.202113i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −19.8492 | − | 34.3799i | −0.783998 | − | 1.35792i | −0.929596 | − | 0.368580i | \(-0.879844\pi\) |
0.145598 | − | 0.989344i | \(-0.453489\pi\) | |||||||
\(642\) | 3.74264 | − | 6.48244i | 0.147710 | − | 0.255842i | ||||
\(643\) | −10.5858 | −0.417463 | −0.208731 | − | 0.977973i | \(-0.566933\pi\) | ||||
−0.208731 | + | 0.977973i | \(0.566933\pi\) | |||||||
\(644\) | −1.62132 | + | 2.09077i | −0.0638890 | + | 0.0823879i | ||||
\(645\) | 7.65685 | 0.301488 | ||||||||
\(646\) | −2.41421 | + | 4.18154i | −0.0949860 | + | 0.164521i | ||||
\(647\) | 0.414214 | + | 0.717439i | 0.0162844 | + | 0.0282054i | 0.874053 | − | 0.485831i | \(-0.161483\pi\) |
−0.857768 | + | 0.514036i | \(0.828150\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −1.13604 | + | 1.96768i | −0.0445934 | + | 0.0772381i | ||||
\(650\) | −5.65685 | −0.221880 | ||||||||
\(651\) | 4.65685 | + | 11.4069i | 0.182517 | + | 0.447072i | ||||
\(652\) | −1.41421 | −0.0553849 | ||||||||
\(653\) | −22.8640 | + | 39.6015i | −0.894736 | + | 1.54973i | −0.0606049 | + | 0.998162i | \(0.519303\pi\) |
−0.834131 | + | 0.551566i | \(0.814030\pi\) | |||||||
\(654\) | −2.65685 | − | 4.60181i | −0.103891 | − | 0.179945i | ||||
\(655\) | −0.621320 | − | 1.07616i | −0.0242770 | − | 0.0420490i | ||||
\(656\) | −0.878680 | + | 1.52192i | −0.0343067 | + | 0.0594209i | ||||
\(657\) | 5.65685 | 0.220695 | ||||||||
\(658\) | 24.4142 | + | 3.34101i | 0.951765 | + | 0.130246i | ||||
\(659\) | −43.9411 | −1.71170 | −0.855852 | − | 0.517221i | \(-0.826966\pi\) | ||||
−0.855852 | + | 0.517221i | \(0.826966\pi\) | |||||||
\(660\) | −1.50000 | + | 2.59808i | −0.0583874 | + | 0.101130i | ||||
\(661\) | −5.48528 | − | 9.50079i | −0.213353 | − | 0.369538i | 0.739409 | − | 0.673256i | \(-0.235105\pi\) |
−0.952762 | + | 0.303719i | \(0.901772\pi\) | |||||||
\(662\) | −12.9497 | − | 22.4296i | −0.503306 | − | 0.871752i | ||||
\(663\) | 1.00000 | − | 1.73205i | 0.0388368 | − | 0.0672673i | ||||
\(664\) | 12.3137 | 0.477865 | ||||||||
\(665\) | −8.94975 | − | 1.22474i | −0.347056 | − | 0.0474936i | ||||
\(666\) | −9.07107 | −0.351497 | ||||||||
\(667\) | −0.378680 | + | 0.655892i | −0.0146625 | + | 0.0253963i | ||||
\(668\) | −9.24264 | − | 16.0087i | −0.357609 | − | 0.619396i | ||||
\(669\) | 5.08579 | + | 8.80884i | 0.196628 | + | 0.340569i | ||||
\(670\) | −2.17157 | + | 3.76127i | −0.0838952 | + | 0.145311i | ||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 1.00000 | + | 2.44949i | 0.0385758 | + | 0.0944911i | ||||
\(673\) | 10.0294 | 0.386606 | 0.193303 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193303 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(674\) | 6.96447 | − | 12.0628i | 0.268261 | − | 0.464642i | ||||
\(675\) | 2.00000 | + | 3.46410i | 0.0769800 | + | 0.133333i | ||||
\(676\) | 5.50000 | + | 9.52628i | 0.211538 | + | 0.366395i | ||||
\(677\) | 21.3284 | − | 36.9419i | 0.819718 | − | 1.41979i | −0.0861720 | − | 0.996280i | \(-0.527463\pi\) |
0.905890 | − | 0.423513i | \(-0.139203\pi\) | |||||||
\(678\) | −17.4142 | −0.668789 | ||||||||
\(679\) | −5.81371 | + | 7.49706i | −0.223110 | + | 0.287711i | ||||
\(680\) | 1.41421 | 0.0542326 | ||||||||
\(681\) | 3.91421 | − | 6.77962i | 0.149993 | − | 0.259795i | ||||
\(682\) | 6.98528 | + | 12.0989i | 0.267480 | + | 0.463289i | ||||
\(683\) | 3.52082 | + | 6.09823i | 0.134720 | + | 0.233342i | 0.925491 | − | 0.378771i | \(-0.123653\pi\) |
−0.790770 | + | 0.612113i | \(0.790320\pi\) | |||||||
\(684\) | 1.70711 | − | 2.95680i | 0.0652729 | − | 0.113056i | ||||
\(685\) | 18.9706 | 0.724828 | ||||||||
\(686\) | 14.8640 | − | 11.0482i | 0.567509 | − | 0.421822i | ||||
\(687\) | 22.7279 | 0.867124 | ||||||||
\(688\) | 3.82843 | − | 6.63103i | 0.145957 | − | 0.252806i | ||||
\(689\) | 1.53553 | + | 2.65962i | 0.0584992 | + | 0.101324i | ||||
\(690\) | −0.500000 | − | 0.866025i | −0.0190347 | − | 0.0329690i | ||||
\(691\) | 23.2929 | − | 40.3445i | 0.886103 | − | 1.53478i | 0.0416597 | − | 0.999132i | \(-0.486735\pi\) |
0.844444 | − | 0.535644i | \(-0.179931\pi\) | |||||||
\(692\) | 4.82843 | 0.183549 | ||||||||
\(693\) | −4.86396 | + | 6.27231i | −0.184767 | + | 0.238265i | ||||
\(694\) | −14.6274 | −0.555249 | ||||||||
\(695\) | −2.65685 | + | 4.60181i | −0.100780 | + | 0.174556i | ||||
\(696\) | 0.378680 | + | 0.655892i | 0.0143538 | + | 0.0248615i | ||||
\(697\) | 1.24264 | + | 2.15232i | 0.0470684 | + | 0.0815248i | ||||
\(698\) | −13.0208 | + | 22.5527i | −0.492845 | + | 0.853633i | ||||
\(699\) | 15.2132 | 0.575416 | ||||||||
\(700\) | −4.00000 | − | 9.79796i | −0.151186 | − | 0.370328i | ||||
\(701\) | 0.514719 | 0.0194407 | 0.00972033 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972033 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(702\) | −0.707107 | + | 1.22474i | −0.0266880 | + | 0.0462250i | ||||
\(703\) | −15.4853 | − | 26.8213i | −0.584038 | − | 1.01158i | ||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | −4.65685 | + | 8.06591i | −0.175387 | + | 0.303780i | ||||
\(706\) | −22.7279 | −0.855377 | ||||||||
\(707\) | 11.7574 | + | 1.60896i | 0.442181 | + | 0.0605111i | ||||
\(708\) | −0.757359 | −0.0284633 | ||||||||
\(709\) | 3.29289 | − | 5.70346i | 0.123667 | − | 0.214198i | −0.797544 | − | 0.603261i | \(-0.793868\pi\) |
0.921211 | + | 0.389063i | \(0.127201\pi\) | |||||||
\(710\) | 2.94975 | + | 5.10911i | 0.110702 | + | 0.191742i | ||||
\(711\) | 0.207107 | + | 0.358719i | 0.00776711 | + | 0.0134530i | ||||
\(712\) | −7.36396 | + | 12.7548i | −0.275976 | + | 0.478005i | ||||
\(713\) | −4.65685 | −0.174401 | ||||||||
\(714\) | 3.70711 | + | 0.507306i | 0.138735 | + | 0.0189854i | ||||
\(715\) | 4.24264 | 0.158666 | ||||||||
\(716\) | −8.00000 | + | 13.8564i | −0.298974 | + | 0.517838i | ||||
\(717\) | 11.6569 | + | 20.1903i | 0.435333 | + | 0.754019i | ||||
\(718\) | −1.00000 | − | 1.73205i | −0.0373197 | − | 0.0646396i | ||||
\(719\) | 0.0710678 | − | 0.123093i | 0.00265038 | − | 0.00459060i | −0.864697 | − | 0.502294i | \(-0.832490\pi\) |
0.867348 | + | 0.497703i | \(0.165823\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −13.6569 | − | 33.4523i | −0.508608 | − | 1.24583i | ||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | 4.96447 | − | 8.59871i | 0.184630 | − | 0.319789i | ||||
\(724\) | 6.24264 | + | 10.8126i | 0.232006 | + | 0.401846i | ||||
\(725\) | −1.51472 | − | 2.62357i | −0.0562552 | − | 0.0974369i | ||||
\(726\) | 1.00000 | − | 1.73205i | 0.0371135 | − | 0.0642824i | ||||
\(727\) | −5.44365 | −0.201894 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(728\) | 2.29289 | − | 2.95680i | 0.0849803 | − | 0.109586i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.82843 | − | 4.89898i | 0.104685 | − | 0.181319i | ||||
\(731\) | −5.41421 | − | 9.37769i | −0.200252 | − | 0.346847i | ||||
\(732\) | 3.00000 | + | 5.19615i | 0.110883 | + | 0.192055i | ||||
\(733\) | −7.77817 | + | 13.4722i | −0.287293 | + | 0.497607i | −0.973163 | − | 0.230118i | \(-0.926089\pi\) |
0.685869 | + | 0.727725i | \(0.259422\pi\) | |||||||
\(734\) | −34.6985 | −1.28074 | ||||||||
\(735\) | 1.74264 | + | 6.77962i | 0.0642783 | + | 0.250070i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −6.51472 | + | 11.2838i | −0.239973 | + | 0.415645i | ||||
\(738\) | −0.878680 | − | 1.52192i | −0.0323446 | − | 0.0560226i | ||||
\(739\) | −10.4142 | − | 18.0379i | −0.383093 | − | 0.663537i | 0.608410 | − | 0.793623i | \(-0.291808\pi\) |
−0.991503 | + | 0.130087i | \(0.958474\pi\) | |||||||
\(740\) | −4.53553 | + | 7.85578i | −0.166730 | + | 0.288784i | ||||
\(741\) | −4.82843 | −0.177377 | ||||||||
\(742\) | −3.52082 | + | 4.54026i | −0.129253 | + | 0.166678i | ||||
\(743\) | −6.24264 | −0.229020 | −0.114510 | − | 0.993422i | \(-0.536530\pi\) | ||||
−0.114510 | + | 0.993422i | \(0.536530\pi\) | |||||||
\(744\) | −2.32843 | + | 4.03295i | −0.0853643 | + | 0.147855i | ||||
\(745\) | 6.82843 | + | 11.8272i | 0.250174 | + | 0.433314i | ||||
\(746\) | 7.17157 | + | 12.4215i | 0.262570 | + | 0.454784i | ||||
\(747\) | −6.15685 | + | 10.6640i | −0.225268 | + | 0.390175i | ||||
\(748\) | 4.24264 | 0.155126 | ||||||||
\(749\) | −7.48528 | − | 18.3351i | −0.273506 | − | 0.669951i | ||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | −17.7635 | + | 30.7672i | −0.648198 | + | 1.12271i | 0.335355 | + | 0.942092i | \(0.391144\pi\) |
−0.983553 | + | 0.180620i | \(0.942190\pi\) | |||||||
\(752\) | 4.65685 | + | 8.06591i | 0.169818 | + | 0.294133i | ||||
\(753\) | −12.9142 | − | 22.3681i | −0.470620 | − | 0.815138i | ||||
\(754\) | 0.535534 | − | 0.927572i | 0.0195030 | − | 0.0337802i | ||||
\(755\) | 1.34315 | 0.0488821 | ||||||||
\(756\) | −2.62132 | − | 0.358719i | −0.0953365 | − | 0.0130465i | ||||
\(757\) | 39.0711 | 1.42006 | 0.710031 | − | 0.704170i | \(-0.248681\pi\) | ||||
0.710031 | + | 0.704170i | \(0.248681\pi\) | |||||||
\(758\) | −14.4853 | + | 25.0892i | −0.526129 | + | 0.911282i | ||||
\(759\) | −1.50000 | − | 2.59808i | −0.0544466 | − | 0.0943042i | ||||
\(760\) | −1.70711 | − | 2.95680i | −0.0619233 | − | 0.107254i | ||||
\(761\) | −2.29289 | + | 3.97141i | −0.0831173 | + | 0.143963i | −0.904587 | − | 0.426288i | \(-0.859821\pi\) |
0.821470 | + | 0.570252i | \(0.193154\pi\) | |||||||
\(762\) | −5.82843 | −0.211142 | ||||||||
\(763\) | −13.9289 | − | 1.90613i | −0.504261 | − | 0.0690066i | ||||
\(764\) | 1.41421 | 0.0511645 | ||||||||
\(765\) | −0.707107 | + | 1.22474i | −0.0255655 | + | 0.0442807i | ||||
\(766\) | 0.636039 | + | 1.10165i | 0.0229810 | + | 0.0398043i | ||||
\(767\) | 0.535534 | + | 0.927572i | 0.0193370 | + | 0.0334927i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −42.0122 | −1.51500 | −0.757499 | − | 0.652836i | \(-0.773579\pi\) | ||||
−0.757499 | + | 0.652836i | \(0.773579\pi\) | |||||||
\(770\) | 3.00000 | + | 7.34847i | 0.108112 | + | 0.264820i | ||||
\(771\) | −1.41421 | −0.0509317 | ||||||||
\(772\) | 9.81371 | − | 16.9978i | 0.353203 | − | 0.611766i | ||||
\(773\) | −11.4142 | − | 19.7700i | −0.410541 | − | 0.711077i | 0.584408 | − | 0.811460i | \(-0.301327\pi\) |
−0.994949 | + | 0.100382i | \(0.967993\pi\) | |||||||
\(774\) | 3.82843 | + | 6.63103i | 0.137610 | + | 0.238347i | ||||
\(775\) | 9.31371 | − | 16.1318i | 0.334558 | − | 0.579472i | ||||
\(776\) | −3.58579 | −0.128722 | ||||||||
\(777\) | −14.7071 | + | 18.9655i | −0.527615 | + | 0.680384i | ||||
\(778\) | −1.17157 | −0.0420029 | ||||||||
\(779\) | 3.00000 | − | 5.19615i | 0.107486 | − | 0.186171i | ||||
\(780\) | 0.707107 | + | 1.22474i | 0.0253185 | + | 0.0438529i | ||||
\(781\) | 8.84924 | + | 15.3273i | 0.316651 | + | 0.548455i | ||||
\(782\) | −0.707107 | + | 1.22474i | −0.0252861 | + | 0.0437968i | ||||
\(783\) | −0.757359 | −0.0270658 | ||||||||
\(784\) | 6.74264 | + | 1.88064i | 0.240809 | + | 0.0671656i | ||||
\(785\) | 3.89949 | 0.139179 | ||||||||
\(786\) | 0.621320 | − | 1.07616i | 0.0221618 | − | 0.0383853i | ||||
\(787\) | −11.7279 | − | 20.3134i | −0.418055 | − | 0.724093i | 0.577689 | − | 0.816257i | \(-0.303955\pi\) |
−0.995744 | + | 0.0921643i | \(0.970621\pi\) | |||||||
\(788\) | 1.58579 | + | 2.74666i | 0.0564913 | + | 0.0978458i | ||||
\(789\) | −5.48528 | + | 9.50079i | −0.195281 | + | 0.338237i | ||||
\(790\) | 0.414214 | 0.0147371 | ||||||||
\(791\) | −28.2340 | + | 36.4091i | −1.00389 | + | 1.29456i | ||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | 4.24264 | − | 7.34847i | 0.150661 | − | 0.260952i | ||||
\(794\) | −0.221825 | − | 0.384213i | −0.00787229 | − | 0.0136352i | ||||
\(795\) | −1.08579 | − | 1.88064i | −0.0385089 | − | 0.0666993i | ||||
\(796\) | −2.65685 | + | 4.60181i | −0.0941697 | + | 0.163107i | ||||
\(797\) | −3.97056 | −0.140645 | −0.0703223 | − | 0.997524i | \(-0.522403\pi\) | ||||
−0.0703223 | + | 0.997524i | \(0.522403\pi\) | |||||||
\(798\) | −3.41421 | − | 8.36308i | −0.120862 | − | 0.296050i | ||||
\(799\) | 13.1716 | 0.465977 | ||||||||
\(800\) | 2.00000 | − | 3.46410i | 0.0707107 | − | 0.122474i | ||||
\(801\) | −7.36396 | − | 12.7548i | −0.260193 | − | 0.450667i | ||||
\(802\) | 0.242641 | + | 0.420266i | 0.00856794 | + | 0.0148401i | ||||
\(803\) | 8.48528 | − | 14.6969i | 0.299439 | − | 0.518644i | ||||
\(804\) | −4.34315 | −0.153171 | ||||||||
\(805\) | −2.62132 | − | 0.358719i | −0.0923894 | − | 0.0126432i | ||||
\(806\) | 6.58579 | 0.231974 | ||||||||
\(807\) | −0.792893 | + | 1.37333i | −0.0279112 | + | 0.0483436i | ||||
\(808\) | 2.24264 | + | 3.88437i | 0.0788958 | + | 0.136652i | ||||
\(809\) | −25.2635 | − | 43.7576i | −0.888216 | − | 1.53843i | −0.841983 | − | 0.539504i | \(-0.818612\pi\) |
−0.0462329 | − | 0.998931i | \(-0.514722\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | −42.2843 | −1.48480 | −0.742401 | − | 0.669956i | \(-0.766313\pi\) | ||||
−0.742401 | + | 0.669956i | \(0.766313\pi\) | |||||||
\(812\) | 1.98528 | + | 0.271680i | 0.0696697 | + | 0.00953408i | ||||
\(813\) | −7.00000 | −0.245501 | ||||||||
\(814\) | −13.6066 | + | 23.5673i | −0.476911 | + | 0.826034i | ||||
\(815\) | −0.707107 | − | 1.22474i | −0.0247689 | − | 0.0429009i | ||||
\(816\) | 0.707107 | + | 1.22474i | 0.0247537 | + | 0.0428746i | ||||
\(817\) | −13.0711 | + | 22.6398i | −0.457299 | + | 0.792065i | ||||
\(818\) | −13.3431 | −0.466532 | ||||||||
\(819\) | 1.41421 | + | 3.46410i | 0.0494166 | + | 0.121046i | ||||
\(820\) | −1.75736 | −0.0613696 | ||||||||
\(821\) | −7.37868 | + | 12.7802i | −0.257518 | + | 0.446034i | −0.965576 | − | 0.260120i | \(-0.916238\pi\) |
0.708059 | + | 0.706154i | \(0.249571\pi\) | |||||||
\(822\) | 9.48528 | + | 16.4290i | 0.330837 | + | 0.573027i | ||||
\(823\) | −23.3137 | − | 40.3805i | −0.812665 | − | 1.40758i | −0.910993 | − | 0.412423i | \(-0.864683\pi\) |
0.0983278 | − | 0.995154i | \(-0.468651\pi\) | |||||||
\(824\) | 6.82843 | − | 11.8272i | 0.237880 | − | 0.412019i | ||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | −1.22792 | + | 1.58346i | −0.0427249 | + | 0.0550958i | ||||
\(827\) | 20.7990 | 0.723252 | 0.361626 | − | 0.932323i | \(-0.382222\pi\) | ||||
0.361626 | + | 0.932323i | \(0.382222\pi\) | |||||||
\(828\) | 0.500000 | − | 0.866025i | 0.0173762 | − | 0.0300965i | ||||
\(829\) | 13.7574 | + | 23.8284i | 0.477813 | + | 0.827596i | 0.999677 | − | 0.0254328i | \(-0.00809638\pi\) |
−0.521864 | + | 0.853029i | \(0.674763\pi\) | |||||||
\(830\) | 6.15685 | + | 10.6640i | 0.213708 | + | 0.370152i | ||||
\(831\) | 1.41421 | − | 2.44949i | 0.0490585 | − | 0.0849719i | ||||
\(832\) | 1.41421 | 0.0490290 | ||||||||
\(833\) | 7.07107 | − | 6.92820i | 0.244998 | − | 0.240048i | ||||
\(834\) | −5.31371 | −0.183999 | ||||||||
\(835\) | 9.24264 | − | 16.0087i | 0.319855 | − | 0.554005i | ||||
\(836\) | −5.12132 | − | 8.87039i | −0.177125 | − | 0.306789i | ||||
\(837\) | −2.32843 | − | 4.03295i | −0.0804822 | − | 0.139399i | ||||
\(838\) | 3.00000 | − | 5.19615i | 0.103633 | − | 0.179498i | ||||
\(839\) | −17.6985 | −0.611020 | −0.305510 | − | 0.952189i | \(-0.598827\pi\) | ||||
−0.305510 | + | 0.952189i | \(0.598827\pi\) | |||||||
\(840\) | −1.62132 | + | 2.09077i | −0.0559409 | + | 0.0721384i | ||||
\(841\) | −28.4264 | −0.980221 | ||||||||
\(842\) | −15.7279 | + | 27.2416i | −0.542020 | + | 0.938806i | ||||
\(843\) | 13.3640 | + | 23.1471i | 0.460279 | + | 0.797227i | ||||
\(844\) | −2.41421 | − | 4.18154i | −0.0831007 | − | 0.143935i | ||||
\(845\) | −5.50000 | + | 9.52628i | −0.189206 | + | 0.327714i | ||||
\(846\) | −9.31371 | −0.320212 | ||||||||
\(847\) | −2.00000 | − | 4.89898i | −0.0687208 | − | 0.168331i | ||||
\(848\) | −2.17157 | −0.0745721 | ||||||||
\(849\) | 12.0711 | − | 20.9077i | 0.414278 | − | 0.717551i | ||||
\(850\) | −2.82843 | − | 4.89898i | −0.0970143 | − | 0.168034i | ||||
\(851\) | −4.53553 | − | 7.85578i | −0.155476 | − | 0.269293i | ||||
\(852\) | −2.94975 | + | 5.10911i | −0.101057 | + | 0.175035i | ||||
\(853\) | −28.1421 | −0.963568 | −0.481784 | − | 0.876290i | \(-0.660011\pi\) | ||||
−0.481784 | + | 0.876290i | \(0.660011\pi\) | |||||||
\(854\) | 15.7279 | + | 2.15232i | 0.538198 | + | 0.0736508i | ||||
\(855\) | 3.41421 | 0.116764 | ||||||||
\(856\) | 3.74264 | − | 6.48244i | 0.127921 | − | 0.221565i | ||||
\(857\) | −13.4350 | − | 23.2702i | −0.458932 | − | 0.794893i | 0.539973 | − | 0.841682i | \(-0.318434\pi\) |
−0.998905 | + | 0.0467891i | \(0.985101\pi\) | |||||||
\(858\) | 2.12132 | + | 3.67423i | 0.0724207 | + | 0.125436i | ||||
\(859\) | −9.70711 | + | 16.8132i | −0.331202 | + | 0.573659i | −0.982748 | − | 0.184950i | \(-0.940788\pi\) |
0.651546 | + | 0.758609i | \(0.274121\pi\) | |||||||
\(860\) | 7.65685 | 0.261097 | ||||||||
\(861\) | −4.60660 | − | 0.630399i | −0.156993 | − | 0.0214839i | ||||
\(862\) | 6.34315 | 0.216048 | ||||||||
\(863\) | −19.4350 | + | 33.6625i | −0.661576 | + | 1.14588i | 0.318625 | + | 0.947881i | \(0.396779\pi\) |
−0.980201 | + | 0.198003i | \(0.936555\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 2.41421 | + | 4.18154i | 0.0820857 | + | 0.142177i | ||||
\(866\) | −15.0000 | + | 25.9808i | −0.509721 | + | 0.882862i | ||||
\(867\) | −15.0000 | −0.509427 | ||||||||
\(868\) | 4.65685 | + | 11.4069i | 0.158064 | + | 0.387176i | ||||
\(869\) | 1.24264 | 0.0421537 | ||||||||
\(870\) | −0.378680 | + | 0.655892i | −0.0128384 | + | 0.0222368i | ||||
\(871\) | 3.07107 | + | 5.31925i | 0.104059 | + | 0.180236i | ||||
\(872\) | −2.65685 | − | 4.60181i | −0.0899724 | − | 0.155837i | ||||
\(873\) | 1.79289 | − | 3.10538i | 0.0606802 | − | 0.105101i | ||||
\(874\) | 3.41421 | 0.115487 | ||||||||
\(875\) | 14.5919 | − | 18.8169i | 0.493296 | − | 0.636128i | ||||
\(876\) | 5.65685 | 0.191127 | ||||||||
\(877\) | −18.9497 | + | 32.8219i | −0.639888 | + | 1.10832i | 0.345570 | + | 0.938393i | \(0.387686\pi\) |
−0.985457 | + | 0.169925i | \(0.945648\pi\) | |||||||
\(878\) | −5.57107 | − | 9.64937i | −0.188014 | − | 0.325651i | ||||
\(879\) | 10.8137 | + | 18.7299i | 0.364737 | + | 0.631744i | ||||
\(880\) | −1.50000 | + | 2.59808i | −0.0505650 | + | 0.0875811i | ||||
\(881\) | 8.14214 | 0.274316 | 0.137158 | − | 0.990549i | \(-0.456203\pi\) | ||||
0.137158 | + | 0.990549i | \(0.456203\pi\) | |||||||
\(882\) | −5.00000 | + | 4.89898i | −0.168359 | + | 0.164957i | ||||
\(883\) | 53.6985 | 1.80710 | 0.903549 | − | 0.428485i | \(-0.140952\pi\) | ||||
0.903549 | + | 0.428485i | \(0.140952\pi\) | |||||||
\(884\) | 1.00000 | − | 1.73205i | 0.0336336 | − | 0.0582552i | ||||
\(885\) | −0.378680 | − | 0.655892i | −0.0127292 | − | 0.0220476i | ||||
\(886\) | −5.13604 | − | 8.89588i | −0.172549 | − | 0.298863i | ||||
\(887\) | 22.8284 | − | 39.5400i | 0.766504 | − | 1.32762i | −0.172944 | − | 0.984932i | \(-0.555328\pi\) |
0.939448 | − | 0.342692i | \(-0.111339\pi\) | |||||||
\(888\) | −9.07107 | −0.304405 | ||||||||
\(889\) | −9.44975 | + | 12.1859i | −0.316934 | + | 0.408702i | ||||
\(890\) | −14.7279 | −0.493681 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | 5.08579 | + | 8.80884i | 0.170285 | + | 0.294942i | ||||
\(893\) | −15.8995 | − | 27.5387i | −0.532056 | − | 0.921549i | ||||
\(894\) | −6.82843 | + | 11.8272i | −0.228377 | + | 0.395560i | ||||
\(895\) | −16.0000 | −0.534821 | ||||||||
\(896\) | 1.00000 | + | 2.44949i | 0.0334077 | + | 0.0818317i | ||||
\(897\) | −1.41421 | −0.0472192 | ||||||||
\(898\) | 0.878680 | − | 1.52192i | 0.0293219 | − | 0.0507871i | ||||
\(899\) | 1.76346 | + | 3.05440i | 0.0588145 | + | 0.101870i | ||||
\(900\) | 2.00000 | + | 3.46410i | 0.0666667 | + | 0.115470i | ||||
\(901\) | −1.53553 | + | 2.65962i | −0.0511561 | + | 0.0886049i | ||||
\(902\) | −5.27208 | −0.175541 | ||||||||
\(903\) | 20.0711 | + | 2.74666i | 0.667923 | + | 0.0914032i | ||||
\(904\) | −17.4142 | −0.579188 | ||||||||
\(905\) | −6.24264 | + | 10.8126i | −0.207512 | + | 0.359422i | ||||
\(906\) | 0.671573 | + | 1.16320i | 0.0223115 | + | 0.0386447i | ||||
\(907\) | 12.5355 | + | 21.7122i | 0.416236 | + | 0.720941i | 0.995557 | − | 0.0941578i | \(-0.0300158\pi\) |
−0.579322 | + | 0.815099i | \(0.696682\pi\) | |||||||
\(908\) | 3.91421 | − | 6.77962i | 0.129898 | − | 0.224989i | ||||
\(909\) | −4.48528 | −0.148767 | ||||||||
\(910\) | 3.70711 | + | 0.507306i | 0.122889 | + | 0.0168170i | ||||
\(911\) | −4.34315 | −0.143895 | −0.0719474 | − | 0.997408i | \(-0.522921\pi\) | ||||
−0.0719474 | + | 0.997408i | \(0.522921\pi\) | |||||||
\(912\) | 1.70711 | − | 2.95680i | 0.0565280 | − | 0.0979093i | ||||
\(913\) | 18.4706 | + | 31.9920i | 0.611286 | + | 1.05878i | ||||
\(914\) | −10.1066 | − | 17.5051i | −0.334297 | − | 0.579019i | ||||
\(915\) | −3.00000 | + | 5.19615i | −0.0991769 | + | 0.171780i | ||||
\(916\) | 22.7279 | 0.750952 | ||||||||
\(917\) | −1.24264 | − | 3.04384i | −0.0410356 | − | 0.100516i | ||||
\(918\) | −1.41421 | −0.0466760 | ||||||||
\(919\) | −18.1421 | + | 31.4231i | −0.598454 | + | 1.03655i | 0.394596 | + | 0.918855i | \(0.370885\pi\) |
−0.993049 | + | 0.117698i | \(0.962449\pi\) | |||||||
\(920\) | −0.500000 | − | 0.866025i | −0.0164845 | − | 0.0285520i | ||||
\(921\) | −12.9497 | − | 22.4296i | −0.426709 | − | 0.739081i | ||||
\(922\) | −15.4853 | + | 26.8213i | −0.509981 | + | 0.883312i | ||||
\(923\) | 8.34315 | 0.274618 | ||||||||
\(924\) | −4.86396 | + | 6.27231i | −0.160013 | + | 0.206344i | ||||
\(925\) | 36.2843 | 1.19302 | ||||||||
\(926\) | 6.89949 | − | 11.9503i | 0.226731 | − | 0.392710i | ||||
\(927\) | 6.82843 | + | 11.8272i | 0.224275 | + | 0.388456i | ||||
\(928\) | 0.378680 | + | 0.655892i | 0.0124308 | + | 0.0215307i | ||||
\(929\) | −0.363961 | + | 0.630399i | −0.0119412 | + | 0.0206827i | −0.871934 | − | 0.489623i | \(-0.837134\pi\) |
0.859993 | + | 0.510306i | \(0.170468\pi\) | |||||||
\(930\) | −4.65685 | −0.152704 | ||||||||
\(931\) | −23.0208 | − | 6.42090i | −0.754477 | − | 0.210436i | ||||
\(932\) | 15.2132 | 0.498325 | ||||||||
\(933\) | −1.70711 | + | 2.95680i | −0.0558882 | + | 0.0968011i | ||||
\(934\) | −14.4142 | − | 24.9662i | −0.471647 | − | 0.816917i | ||||
\(935\) | 2.12132 | + | 3.67423i | 0.0693746 | + | 0.120160i | ||||
\(936\) | −0.707107 | + | 1.22474i | −0.0231125 | + | 0.0400320i | ||||
\(937\) | 47.1838 | 1.54143 | 0.770713 | − | 0.637182i | \(-0.219900\pi\) | ||||
0.770713 | + | 0.637182i | \(0.219900\pi\) | |||||||
\(938\) | −7.04163 | + | 9.08052i | −0.229917 | + | 0.296489i | ||||
\(939\) | 16.7574 | 0.546856 | ||||||||
\(940\) | −4.65685 | + | 8.06591i | −0.151890 | + | 0.263081i | ||||
\(941\) | −17.7426 | − | 30.7312i | −0.578394 | − | 1.00181i | −0.995664 | − | 0.0930246i | \(-0.970346\pi\) |
0.417270 | − | 0.908782i | \(-0.362987\pi\) | |||||||
\(942\) | 1.94975 | + | 3.37706i | 0.0635262 | + | 0.110031i | ||||
\(943\) | 0.878680 | − | 1.52192i | 0.0286137 | − | 0.0495605i | ||||
\(944\) | −0.757359 | −0.0246499 | ||||||||
\(945\) | −1.00000 | − | 2.44949i | −0.0325300 | − | 0.0796819i | ||||
\(946\) | 22.9706 | 0.746837 | ||||||||
\(947\) | 3.14214 | − | 5.44234i | 0.102106 | − | 0.176852i | −0.810446 | − | 0.585813i | \(-0.800775\pi\) |
0.912552 | + | 0.408961i | \(0.134109\pi\) | |||||||
\(948\) | 0.207107 | + | 0.358719i | 0.00672652 | + | 0.0116507i | ||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | −6.82843 | + | 11.8272i | −0.221543 | + | 0.383724i | ||||
\(951\) | 9.92893 | 0.321968 | ||||||||
\(952\) | 3.70711 | + | 0.507306i | 0.120148 | + | 0.0164419i | ||||
\(953\) | −37.7990 | −1.22443 | −0.612215 | − | 0.790692i | \(-0.709721\pi\) | ||||
−0.612215 | + | 0.790692i | \(0.709721\pi\) | |||||||
\(954\) | 1.08579 | − | 1.88064i | 0.0351536 | − | 0.0608879i | ||||
\(955\) | 0.707107 | + | 1.22474i | 0.0228814 | + | 0.0396318i | ||||
\(956\) | 11.6569 | + | 20.1903i | 0.377010 | + | 0.653000i | ||||
\(957\) | −1.13604 | + | 1.96768i | −0.0367229 | + | 0.0636060i | ||||
\(958\) | 30.5269 | 0.986280 | ||||||||
\(959\) | 49.7279 | + | 6.80511i | 1.60580 | + | 0.219748i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 4.65685 | − | 8.06591i | 0.150221 | − | 0.260191i | ||||
\(962\) | 6.41421 | + | 11.1097i | 0.206803 | + | 0.358193i | ||||
\(963\) | 3.74264 | + | 6.48244i | 0.120605 | + | 0.208894i | ||||
\(964\) | 4.96447 | − | 8.59871i | 0.159895 | − | 0.276946i | ||||
\(965\) | 19.6274 | 0.631829 | ||||||||
\(966\) | −1.00000 | − | 2.44949i | −0.0321745 | − | 0.0788110i | ||||
\(967\) | −35.9706 | −1.15674 | −0.578368 | − | 0.815776i | \(-0.696310\pi\) | ||||
−0.578368 | + | 0.815776i | \(0.696310\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | −2.41421 | − | 4.18154i | −0.0775557 | − | 0.134330i | ||||
\(970\) | −1.79289 | − | 3.10538i | −0.0575663 | − | 0.0997078i | ||||
\(971\) | −1.98528 | + | 3.43861i | −0.0637107 | + | 0.110350i | −0.896121 | − | 0.443809i | \(-0.853627\pi\) |
0.832411 | + | 0.554159i | \(0.186960\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −8.61522 | + | 11.1097i | −0.276191 | + | 0.356162i | ||||
\(974\) | −29.4853 | −0.944769 | ||||||||
\(975\) | 2.82843 | − | 4.89898i | 0.0905822 | − | 0.156893i | ||||
\(976\) | 3.00000 | + | 5.19615i | 0.0960277 | + | 0.166325i | ||||
\(977\) | −17.4853 | − | 30.2854i | −0.559404 | − | 0.968916i | −0.997546 | − | 0.0700102i | \(-0.977697\pi\) |
0.438143 | − | 0.898905i | \(-0.355637\pi\) | |||||||
\(978\) | 0.707107 | − | 1.22474i | 0.0226108 | − | 0.0391630i | ||||
\(979\) | −44.1838 | −1.41212 | ||||||||
\(980\) | 1.74264 | + | 6.77962i | 0.0556666 | + | 0.216567i | ||||
\(981\) | 5.31371 | 0.169654 | ||||||||
\(982\) | 4.55025 | − | 7.88127i | 0.145204 | − | 0.251501i | ||||
\(983\) | −3.29289 | − | 5.70346i | −0.105027 | − | 0.181912i | 0.808722 | − | 0.588191i | \(-0.200160\pi\) |
−0.913749 | + | 0.406279i | \(0.866826\pi\) | |||||||
\(984\) | −0.878680 | − | 1.52192i | −0.0280113 | − | 0.0485170i | ||||
\(985\) | −1.58579 | + | 2.74666i | −0.0505274 | + | 0.0875159i | ||||
\(986\) | 1.07107 | 0.0341097 | ||||||||
\(987\) | −15.1005 | + | 19.4728i | −0.480654 | + | 0.619827i | ||||
\(988\) | −4.82843 | −0.153613 | ||||||||
\(989\) | −3.82843 | + | 6.63103i | −0.121737 | + | 0.210854i | ||||
\(990\) | −1.50000 | − | 2.59808i | −0.0476731 | − | 0.0825723i | ||||
\(991\) | 17.8848 | + | 30.9773i | 0.568129 | + | 0.984028i | 0.996751 | + | 0.0805440i | \(0.0256657\pi\) |
−0.428622 | + | 0.903484i | \(0.641001\pi\) | |||||||
\(992\) | −2.32843 | + | 4.03295i | −0.0739276 | + | 0.128046i | ||||
\(993\) | 25.8995 | 0.821896 | ||||||||
\(994\) | 5.89949 | + | 14.4508i | 0.187121 | + | 0.458350i | ||||
\(995\) | −5.31371 | −0.168456 | ||||||||
\(996\) | −6.15685 | + | 10.6640i | −0.195087 | + | 0.337901i | ||||
\(997\) | 22.4350 | + | 38.8586i | 0.710524 | + | 1.23066i | 0.964660 | + | 0.263496i | \(0.0848756\pi\) |
−0.254136 | + | 0.967168i | \(0.581791\pi\) | |||||||
\(998\) | 6.89949 | + | 11.9503i | 0.218400 | + | 0.378279i | ||||
\(999\) | 4.53553 | − | 7.85578i | 0.143498 | − | 0.248546i |
(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 | 966.2.i.h.415.2 | yes | 4 | |
7.2 | even | 3 | 6762.2.a.cc.1.2 | 2 | |||
7.4 | even | 3 | inner | 966.2.i.h.277.2 | ✓ | 4 | |
7.5 | odd | 6 | 6762.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.h.277.2 | ✓ | 4 | 7.4 | even | 3 | inner | |
966.2.i.h.415.2 | yes | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.ca.1.1 | 2 | 7.5 | odd | 6 | |||
6762.2.a.cc.1.2 | 2 | 7.2 | even | 3 |