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: | \(\Z[a_1, \ldots, a_{5}]\) |
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.j.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 | ||||
\(5\) | 1.20711 | − | 2.09077i | 0.539835 | − | 0.935021i | −0.459078 | − | 0.888396i | \(-0.651820\pi\) |
0.998912 | − | 0.0466249i | \(-0.0148465\pi\) | |||||||
\(6\) | −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 | ||||
\(10\) | −1.20711 | − | 2.09077i | −0.381721 | − | 0.661160i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 3.82843 | 1.06181 | 0.530907 | − | 0.847430i | \(-0.321851\pi\) | ||||
0.530907 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(14\) | 2.62132 | − | 0.358719i | 0.700577 | − | 0.0958718i | ||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.62132 | − | 4.54026i | −0.635764 | − | 1.10117i | −0.986353 | − | 0.164645i | \(-0.947352\pi\) |
0.350589 | − | 0.936529i | \(-0.385981\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 3.82843 | − | 6.63103i | 0.878301 | − | 1.52126i | 0.0250976 | − | 0.999685i | \(-0.492010\pi\) |
0.853204 | − | 0.521578i | \(-0.174656\pi\) | |||||||
\(20\) | −2.41421 | −0.539835 | ||||||||
\(21\) | 1.00000 | − | 2.44949i | 0.218218 | − | 0.534522i | ||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | ||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −0.414214 | − | 0.717439i | −0.0828427 | − | 0.143488i | ||||
\(26\) | 1.91421 | − | 3.31552i | 0.375408 | − | 0.650226i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | −1.20711 | + | 2.09077i | −0.220387 | + | 0.381721i | ||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | −5.24264 | −0.899105 | ||||||||
\(35\) | 6.32843 | − | 0.866025i | 1.06970 | − | 0.146385i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.41421 | − | 7.64564i | 0.725692 | − | 1.25694i | −0.232996 | − | 0.972478i | \(-0.574853\pi\) |
0.958688 | − | 0.284458i | \(-0.0918137\pi\) | |||||||
\(38\) | −3.82843 | − | 6.63103i | −0.621053 | − | 1.07570i | ||||
\(39\) | −1.91421 | − | 3.31552i | −0.306519 | − | 0.530907i | ||||
\(40\) | −1.20711 | + | 2.09077i | −0.190860 | + | 0.330580i | ||||
\(41\) | −5.17157 | −0.807664 | −0.403832 | − | 0.914833i | \(-0.632322\pi\) | ||||
−0.403832 | + | 0.914833i | \(0.632322\pi\) | |||||||
\(42\) | −1.62132 | − | 2.09077i | −0.250175 | − | 0.322613i | ||||
\(43\) | −0.343146 | −0.0523292 | −0.0261646 | − | 0.999658i | \(-0.508329\pi\) | ||||
−0.0261646 | + | 0.999658i | \(0.508329\pi\) | |||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | 1.20711 | + | 2.09077i | 0.179945 | + | 0.311674i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | −4.50000 | + | 7.79423i | −0.656392 | + | 1.13691i | 0.325150 | + | 0.945662i | \(0.394585\pi\) |
−0.981543 | + | 0.191243i | \(0.938748\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | −0.828427 | −0.117157 | ||||||||
\(51\) | −2.62132 | + | 4.54026i | −0.367058 | + | 0.635764i | ||||
\(52\) | −1.91421 | − | 3.31552i | −0.265454 | − | 0.459779i | ||||
\(53\) | −2.03553 | − | 3.52565i | −0.279602 | − | 0.484285i | 0.691684 | − | 0.722200i | \(-0.256869\pi\) |
−0.971286 | + | 0.237915i | \(0.923536\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −4.82843 | −0.651065 | ||||||||
\(56\) | −1.62132 | − | 2.09077i | −0.216658 | − | 0.279391i | ||||
\(57\) | −7.65685 | −1.01418 | ||||||||
\(58\) | −3.41421 | + | 5.91359i | −0.448308 | + | 0.776493i | ||||
\(59\) | 4.82843 | + | 8.36308i | 0.628608 | + | 1.08878i | 0.987831 | + | 0.155529i | \(0.0497082\pi\) |
−0.359224 | + | 0.933251i | \(0.616958\pi\) | |||||||
\(60\) | 1.20711 | + | 2.09077i | 0.155837 | + | 0.269917i | ||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | −2.62132 | + | 0.358719i | −0.330255 | + | 0.0451944i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.62132 | − | 8.00436i | 0.573204 | − | 0.992819i | ||||
\(66\) | 1.00000 | + | 1.73205i | 0.123091 | + | 0.213201i | ||||
\(67\) | 2.44975 | + | 4.24309i | 0.299284 | + | 0.518376i | 0.975972 | − | 0.217894i | \(-0.0699188\pi\) |
−0.676688 | + | 0.736270i | \(0.736585\pi\) | |||||||
\(68\) | −2.62132 | + | 4.54026i | −0.317882 | + | 0.550587i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 2.41421 | − | 5.91359i | 0.288554 | − | 0.706809i | ||||
\(71\) | −4.17157 | −0.495075 | −0.247537 | − | 0.968878i | \(-0.579621\pi\) | ||||
−0.247537 | + | 0.968878i | \(0.579621\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −0.328427 | − | 0.568852i | −0.0384395 | − | 0.0665791i | 0.846166 | − | 0.532920i | \(-0.178905\pi\) |
−0.884605 | + | 0.466341i | \(0.845572\pi\) | |||||||
\(74\) | −4.41421 | − | 7.64564i | −0.513142 | − | 0.888788i | ||||
\(75\) | −0.414214 | + | 0.717439i | −0.0478293 | + | 0.0828427i | ||||
\(76\) | −7.65685 | −0.878301 | ||||||||
\(77\) | 2.00000 | − | 4.89898i | 0.227921 | − | 0.558291i | ||||
\(78\) | −3.82843 | −0.433484 | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 1.20711 | + | 2.09077i | 0.134959 | + | 0.233755i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.58579 | + | 4.47871i | −0.285552 | + | 0.494591i | ||||
\(83\) | 7.17157 | 0.787182 | 0.393591 | − | 0.919286i | \(-0.371233\pi\) | ||||
0.393591 | + | 0.919286i | \(0.371233\pi\) | |||||||
\(84\) | −2.62132 | + | 0.358719i | −0.286009 | + | 0.0391395i | ||||
\(85\) | −12.6569 | −1.37283 | ||||||||
\(86\) | −0.171573 | + | 0.297173i | −0.0185012 | + | 0.0320450i | ||||
\(87\) | 3.41421 | + | 5.91359i | 0.366042 | + | 0.634004i | ||||
\(88\) | 1.00000 | + | 1.73205i | 0.106600 | + | 0.184637i | ||||
\(89\) | −3.41421 | + | 5.91359i | −0.361906 | + | 0.626839i | −0.988275 | − | 0.152688i | \(-0.951207\pi\) |
0.626369 | + | 0.779527i | \(0.284541\pi\) | |||||||
\(90\) | 2.41421 | 0.254480 | ||||||||
\(91\) | 6.20711 | + | 8.00436i | 0.650682 | + | 0.839085i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 1.00000 | − | 1.73205i | 0.103695 | − | 0.179605i | ||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | −9.24264 | − | 16.0087i | −0.948275 | − | 1.64246i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 1.65685 | 0.168228 | 0.0841140 | − | 0.996456i | \(-0.473194\pi\) | ||||
0.0841140 | + | 0.996456i | \(0.473194\pi\) | |||||||
\(98\) | 5.00000 | + | 4.89898i | 0.505076 | + | 0.494872i | ||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −0.414214 | + | 0.717439i | −0.0414214 | + | 0.0717439i | ||||
\(101\) | −4.41421 | − | 7.64564i | −0.439231 | − | 0.760770i | 0.558400 | − | 0.829572i | \(-0.311416\pi\) |
−0.997630 | + | 0.0688022i | \(0.978082\pi\) | |||||||
\(102\) | 2.62132 | + | 4.54026i | 0.259549 | + | 0.449553i | ||||
\(103\) | −5.44975 | + | 9.43924i | −0.536980 | + | 0.930076i | 0.462085 | + | 0.886836i | \(0.347101\pi\) |
−0.999065 | + | 0.0432403i | \(0.986232\pi\) | |||||||
\(104\) | −3.82843 | −0.375408 | ||||||||
\(105\) | −3.91421 | − | 5.04757i | −0.381988 | − | 0.492592i | ||||
\(106\) | −4.07107 | −0.395417 | ||||||||
\(107\) | 2.82843 | − | 4.89898i | 0.273434 | − | 0.473602i | −0.696305 | − | 0.717746i | \(-0.745174\pi\) |
0.969739 | + | 0.244144i | \(0.0785070\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −4.58579 | − | 7.94282i | −0.439239 | − | 0.760784i | 0.558392 | − | 0.829577i | \(-0.311418\pi\) |
−0.997631 | + | 0.0687933i | \(0.978085\pi\) | |||||||
\(110\) | −2.41421 | + | 4.18154i | −0.230186 | + | 0.398694i | ||||
\(111\) | −8.82843 | −0.837957 | ||||||||
\(112\) | −2.62132 | + | 0.358719i | −0.247691 | + | 0.0338958i | ||||
\(113\) | 11.7279 | 1.10327 | 0.551635 | − | 0.834086i | \(-0.314004\pi\) | ||||
0.551635 | + | 0.834086i | \(0.314004\pi\) | |||||||
\(114\) | −3.82843 | + | 6.63103i | −0.358565 | + | 0.621053i | ||||
\(115\) | 1.20711 | + | 2.09077i | 0.112563 | + | 0.194965i | ||||
\(116\) | 3.41421 | + | 5.91359i | 0.317002 | + | 0.549063i | ||||
\(117\) | −1.91421 | + | 3.31552i | −0.176969 | + | 0.306519i | ||||
\(118\) | 9.65685 | 0.888985 | ||||||||
\(119\) | 5.24264 | − | 12.8418i | 0.480592 | − | 1.17721i | ||||
\(120\) | 2.41421 | 0.220387 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | −1.00000 | − | 1.73205i | −0.0905357 | − | 0.156813i | ||||
\(123\) | 2.58579 | + | 4.47871i | 0.233153 | + | 0.403832i | ||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 10.0711 | 0.900784 | ||||||||
\(126\) | −1.00000 | + | 2.44949i | −0.0890871 | + | 0.218218i | ||||
\(127\) | −0.828427 | −0.0735110 | −0.0367555 | − | 0.999324i | \(-0.511702\pi\) | ||||
−0.0367555 | + | 0.999324i | \(0.511702\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0.171573 | + | 0.297173i | 0.0151061 | + | 0.0261646i | ||||
\(130\) | −4.62132 | − | 8.00436i | −0.405317 | − | 0.702029i | ||||
\(131\) | 4.57107 | − | 7.91732i | 0.399376 | − | 0.691740i | −0.594273 | − | 0.804263i | \(-0.702560\pi\) |
0.993649 | + | 0.112524i | \(0.0358935\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | 20.0711 | − | 2.74666i | 1.74038 | − | 0.238166i | ||||
\(134\) | 4.89949 | 0.423252 | ||||||||
\(135\) | 1.20711 | − | 2.09077i | 0.103891 | − | 0.179945i | ||||
\(136\) | 2.62132 | + | 4.54026i | 0.224776 | + | 0.389324i | ||||
\(137\) | 3.79289 | + | 6.56948i | 0.324049 | + | 0.561269i | 0.981319 | − | 0.192386i | \(-0.0616225\pi\) |
−0.657271 | + | 0.753655i | \(0.728289\pi\) | |||||||
\(138\) | 0.500000 | − | 0.866025i | 0.0425628 | − | 0.0737210i | ||||
\(139\) | 9.31371 | 0.789978 | 0.394989 | − | 0.918686i | \(-0.370748\pi\) | ||||
0.394989 | + | 0.918686i | \(0.370748\pi\) | |||||||
\(140\) | −3.91421 | − | 5.04757i | −0.330811 | − | 0.426597i | ||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | −2.08579 | + | 3.61269i | −0.175035 | + | 0.303170i | ||||
\(143\) | −3.82843 | − | 6.63103i | −0.320149 | − | 0.554515i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −8.24264 | + | 14.2767i | −0.684514 | + | 1.18561i | ||||
\(146\) | −0.656854 | −0.0543616 | ||||||||
\(147\) | 6.74264 | − | 1.88064i | 0.556124 | − | 0.155112i | ||||
\(148\) | −8.82843 | −0.725692 | ||||||||
\(149\) | −4.62132 | + | 8.00436i | −0.378593 | + | 0.655743i | −0.990858 | − | 0.134910i | \(-0.956925\pi\) |
0.612265 | + | 0.790653i | \(0.290259\pi\) | |||||||
\(150\) | 0.414214 | + | 0.717439i | 0.0338204 | + | 0.0585786i | ||||
\(151\) | 7.07107 | + | 12.2474i | 0.575435 | + | 0.996683i | 0.995994 | + | 0.0894180i | \(0.0285007\pi\) |
−0.420559 | + | 0.907265i | \(0.638166\pi\) | |||||||
\(152\) | −3.82843 | + | 6.63103i | −0.310526 | + | 0.537848i | ||||
\(153\) | 5.24264 | 0.423842 | ||||||||
\(154\) | −3.24264 | − | 4.18154i | −0.261299 | − | 0.336958i | ||||
\(155\) | 4.82843 | 0.387829 | ||||||||
\(156\) | −1.91421 | + | 3.31552i | −0.153260 | + | 0.265454i | ||||
\(157\) | 7.82843 | + | 13.5592i | 0.624777 | + | 1.08214i | 0.988584 | + | 0.150671i | \(0.0481433\pi\) |
−0.363808 | + | 0.931474i | \(0.618523\pi\) | |||||||
\(158\) | −5.00000 | − | 8.66025i | −0.397779 | − | 0.688973i | ||||
\(159\) | −2.03553 | + | 3.52565i | −0.161428 | + | 0.279602i | ||||
\(160\) | 2.41421 | 0.190860 | ||||||||
\(161\) | −2.62132 | + | 0.358719i | −0.206589 | + | 0.0282711i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.828427 | + | 1.43488i | −0.0648874 | + | 0.112388i | −0.896644 | − | 0.442752i | \(-0.854002\pi\) |
0.831757 | + | 0.555140i | \(0.187335\pi\) | |||||||
\(164\) | 2.58579 | + | 4.47871i | 0.201916 | + | 0.349729i | ||||
\(165\) | 2.41421 | + | 4.18154i | 0.187946 | + | 0.325532i | ||||
\(166\) | 3.58579 | − | 6.21076i | 0.278311 | − | 0.482049i | ||||
\(167\) | 24.7990 | 1.91900 | 0.959502 | − | 0.281703i | \(-0.0908992\pi\) | ||||
0.959502 | + | 0.281703i | \(0.0908992\pi\) | |||||||
\(168\) | −1.00000 | + | 2.44949i | −0.0771517 | + | 0.188982i | ||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | −6.32843 | + | 10.9612i | −0.485368 | + | 0.840682i | ||||
\(171\) | 3.82843 | + | 6.63103i | 0.292767 | + | 0.507088i | ||||
\(172\) | 0.171573 | + | 0.297173i | 0.0130823 | + | 0.0226592i | ||||
\(173\) | 3.65685 | − | 6.33386i | 0.278025 | − | 0.481554i | −0.692868 | − | 0.721064i | \(-0.743653\pi\) |
0.970894 | + | 0.239510i | \(0.0769867\pi\) | |||||||
\(174\) | 6.82843 | 0.517662 | ||||||||
\(175\) | 0.828427 | − | 2.02922i | 0.0626232 | − | 0.153395i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 4.82843 | − | 8.36308i | 0.362927 | − | 0.628608i | ||||
\(178\) | 3.41421 | + | 5.91359i | 0.255906 | + | 0.443242i | ||||
\(179\) | 10.9853 | + | 19.0271i | 0.821078 | + | 1.42215i | 0.904880 | + | 0.425667i | \(0.139961\pi\) |
−0.0838013 | + | 0.996482i | \(0.526706\pi\) | |||||||
\(180\) | 1.20711 | − | 2.09077i | 0.0899724 | − | 0.155837i | ||||
\(181\) | −9.31371 | −0.692283 | −0.346141 | − | 0.938182i | \(-0.612508\pi\) | ||||
−0.346141 | + | 0.938182i | \(0.612508\pi\) | |||||||
\(182\) | 10.0355 | − | 1.37333i | 0.743883 | − | 0.101798i | ||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −10.6569 | − | 18.4582i | −0.783508 | − | 1.35707i | ||||
\(186\) | −1.00000 | − | 1.73205i | −0.0733236 | − | 0.127000i | ||||
\(187\) | −5.24264 | + | 9.08052i | −0.383380 | + | 0.664033i | ||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | 1.62132 | + | 2.09077i | 0.117934 | + | 0.152081i | ||||
\(190\) | −18.4853 | −1.34106 | ||||||||
\(191\) | 2.58579 | − | 4.47871i | 0.187101 | − | 0.324068i | −0.757182 | − | 0.653205i | \(-0.773424\pi\) |
0.944282 | + | 0.329136i | \(0.106758\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.74264 | + | 4.75039i | 0.197420 | + | 0.341941i | 0.947691 | − | 0.319189i | \(-0.103411\pi\) |
−0.750271 | + | 0.661130i | \(0.770077\pi\) | |||||||
\(194\) | 0.828427 | − | 1.43488i | 0.0594776 | − | 0.103018i | ||||
\(195\) | −9.24264 | −0.661879 | ||||||||
\(196\) | 6.74264 | − | 1.88064i | 0.481617 | − | 0.134331i | ||||
\(197\) | −12.8284 | −0.913988 | −0.456994 | − | 0.889470i | \(-0.651074\pi\) | ||||
−0.456994 | + | 0.889470i | \(0.651074\pi\) | |||||||
\(198\) | 1.00000 | − | 1.73205i | 0.0710669 | − | 0.123091i | ||||
\(199\) | 13.8284 | + | 23.9515i | 0.980271 | + | 1.69788i | 0.661312 | + | 0.750111i | \(0.270000\pi\) |
0.318959 | + | 0.947768i | \(0.396667\pi\) | |||||||
\(200\) | 0.414214 | + | 0.717439i | 0.0292893 | + | 0.0507306i | ||||
\(201\) | 2.44975 | − | 4.24309i | 0.172792 | − | 0.299284i | ||||
\(202\) | −8.82843 | −0.621166 | ||||||||
\(203\) | −11.0711 | − | 14.2767i | −0.777037 | − | 1.00203i | ||||
\(204\) | 5.24264 | 0.367058 | ||||||||
\(205\) | −6.24264 | + | 10.8126i | −0.436005 | + | 0.755183i | ||||
\(206\) | 5.44975 | + | 9.43924i | 0.379702 | + | 0.657663i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.0347524 | − | 0.0601929i | ||||
\(208\) | −1.91421 | + | 3.31552i | −0.132727 | + | 0.229890i | ||||
\(209\) | −15.3137 | −1.05927 | ||||||||
\(210\) | −6.32843 | + | 0.866025i | −0.436703 | + | 0.0597614i | ||||
\(211\) | −11.1716 | −0.769083 | −0.384541 | − | 0.923108i | \(-0.625640\pi\) | ||||
−0.384541 | + | 0.923108i | \(0.625640\pi\) | |||||||
\(212\) | −2.03553 | + | 3.52565i | −0.139801 | + | 0.242143i | ||||
\(213\) | 2.08579 | + | 3.61269i | 0.142916 | + | 0.247537i | ||||
\(214\) | −2.82843 | − | 4.89898i | −0.193347 | − | 0.334887i | ||||
\(215\) | −0.414214 | + | 0.717439i | −0.0282491 | + | 0.0489289i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.00000 | + | 4.89898i | −0.135769 | + | 0.332564i | ||||
\(218\) | −9.17157 | −0.621177 | ||||||||
\(219\) | −0.328427 | + | 0.568852i | −0.0221930 | + | 0.0384395i | ||||
\(220\) | 2.41421 | + | 4.18154i | 0.162766 | + | 0.281919i | ||||
\(221\) | −10.0355 | − | 17.3821i | −0.675063 | − | 1.16924i | ||||
\(222\) | −4.41421 | + | 7.64564i | −0.296263 | + | 0.513142i | ||||
\(223\) | −12.4853 | −0.836076 | −0.418038 | − | 0.908429i | \(-0.637282\pi\) | ||||
−0.418038 | + | 0.908429i | \(0.637282\pi\) | |||||||
\(224\) | −1.00000 | + | 2.44949i | −0.0668153 | + | 0.163663i | ||||
\(225\) | 0.828427 | 0.0552285 | ||||||||
\(226\) | 5.86396 | − | 10.1567i | 0.390065 | − | 0.675612i | ||||
\(227\) | 5.48528 | + | 9.50079i | 0.364071 | + | 0.630589i | 0.988627 | − | 0.150391i | \(-0.0480532\pi\) |
−0.624556 | + | 0.780980i | \(0.714720\pi\) | |||||||
\(228\) | 3.82843 | + | 6.63103i | 0.253544 | + | 0.439151i | ||||
\(229\) | −1.07107 | + | 1.85514i | −0.0707782 | + | 0.122591i | −0.899243 | − | 0.437450i | \(-0.855882\pi\) |
0.828464 | + | 0.560042i | \(0.189215\pi\) | |||||||
\(230\) | 2.41421 | 0.159189 | ||||||||
\(231\) | −5.24264 | + | 0.717439i | −0.344940 | + | 0.0472040i | ||||
\(232\) | 6.82843 | 0.448308 | ||||||||
\(233\) | 4.00000 | − | 6.92820i | 0.262049 | − | 0.453882i | −0.704737 | − | 0.709468i | \(-0.748935\pi\) |
0.966786 | + | 0.255586i | \(0.0822686\pi\) | |||||||
\(234\) | 1.91421 | + | 3.31552i | 0.125136 | + | 0.216742i | ||||
\(235\) | 10.8640 | + | 18.8169i | 0.708687 | + | 1.22748i | ||||
\(236\) | 4.82843 | − | 8.36308i | 0.314304 | − | 0.544390i | ||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | −8.50000 | − | 10.9612i | −0.550973 | − | 0.710506i | ||||
\(239\) | 10.3431 | 0.669042 | 0.334521 | − | 0.942388i | \(-0.391425\pi\) | ||||
0.334521 | + | 0.942388i | \(0.391425\pi\) | |||||||
\(240\) | 1.20711 | − | 2.09077i | 0.0779184 | − | 0.134959i | ||||
\(241\) | 6.41421 | + | 11.1097i | 0.413176 | + | 0.715642i | 0.995235 | − | 0.0975049i | \(-0.0310862\pi\) |
−0.582059 | + | 0.813146i | \(0.697753\pi\) | |||||||
\(242\) | −3.50000 | − | 6.06218i | −0.224989 | − | 0.389692i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 12.0711 | + | 11.8272i | 0.771192 | + | 0.755611i | ||||
\(246\) | 5.17157 | 0.329727 | ||||||||
\(247\) | 14.6569 | − | 25.3864i | 0.932593 | − | 1.61530i | ||||
\(248\) | −1.00000 | − | 1.73205i | −0.0635001 | − | 0.109985i | ||||
\(249\) | −3.58579 | − | 6.21076i | −0.227240 | − | 0.393591i | ||||
\(250\) | 5.03553 | − | 8.72180i | 0.318475 | − | 0.551615i | ||||
\(251\) | 17.3137 | 1.09283 | 0.546416 | − | 0.837514i | \(-0.315992\pi\) | ||||
0.546416 | + | 0.837514i | \(0.315992\pi\) | |||||||
\(252\) | 1.62132 | + | 2.09077i | 0.102134 | + | 0.131706i | ||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | −0.414214 | + | 0.717439i | −0.0259901 | + | 0.0450161i | ||||
\(255\) | 6.32843 | + | 10.9612i | 0.396301 | + | 0.686414i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.75736 | + | 4.77589i | −0.171999 | + | 0.297912i | −0.939119 | − | 0.343593i | \(-0.888356\pi\) |
0.767119 | + | 0.641504i | \(0.221689\pi\) | |||||||
\(258\) | 0.343146 | 0.0213633 | ||||||||
\(259\) | 23.1421 | − | 3.16693i | 1.43798 | − | 0.196783i | ||||
\(260\) | −9.24264 | −0.573204 | ||||||||
\(261\) | 3.41421 | − | 5.91359i | 0.211335 | − | 0.366042i | ||||
\(262\) | −4.57107 | − | 7.91732i | −0.282402 | − | 0.489134i | ||||
\(263\) | −9.65685 | − | 16.7262i | −0.595467 | − | 1.03138i | −0.993481 | − | 0.114000i | \(-0.963634\pi\) |
0.398014 | − | 0.917380i | \(-0.369700\pi\) | |||||||
\(264\) | 1.00000 | − | 1.73205i | 0.0615457 | − | 0.106600i | ||||
\(265\) | −9.82843 | −0.603755 | ||||||||
\(266\) | 7.65685 | − | 18.7554i | 0.469472 | − | 1.14997i | ||||
\(267\) | 6.82843 | 0.417893 | ||||||||
\(268\) | 2.44975 | − | 4.24309i | 0.149642 | − | 0.259188i | ||||
\(269\) | 6.00000 | + | 10.3923i | 0.365826 | + | 0.633630i | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | −1.20711 | − | 2.09077i | −0.0734622 | − | 0.127240i | ||||
\(271\) | 15.1421 | − | 26.2269i | 0.919819 | − | 1.59317i | 0.120131 | − | 0.992758i | \(-0.461669\pi\) |
0.799688 | − | 0.600416i | \(-0.204998\pi\) | |||||||
\(272\) | 5.24264 | 0.317882 | ||||||||
\(273\) | 3.82843 | − | 9.37769i | 0.231707 | − | 0.567564i | ||||
\(274\) | 7.58579 | 0.458274 | ||||||||
\(275\) | −0.828427 | + | 1.43488i | −0.0499560 | + | 0.0865264i | ||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | −12.6421 | − | 21.8968i | −0.759592 | − | 1.31565i | −0.943059 | − | 0.332626i | \(-0.892065\pi\) |
0.183466 | − | 0.983026i | \(-0.441268\pi\) | |||||||
\(278\) | 4.65685 | − | 8.06591i | 0.279300 | − | 0.483761i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | −6.32843 | + | 0.866025i | −0.378196 | + | 0.0517549i | ||||
\(281\) | −13.5858 | −0.810460 | −0.405230 | − | 0.914215i | \(-0.632809\pi\) | ||||
−0.405230 | + | 0.914215i | \(0.632809\pi\) | |||||||
\(282\) | 4.50000 | − | 7.79423i | 0.267971 | − | 0.464140i | ||||
\(283\) | 14.6924 | + | 25.4480i | 0.873372 | + | 1.51272i | 0.858487 | + | 0.512835i | \(0.171405\pi\) |
0.0148847 | + | 0.999889i | \(0.495262\pi\) | |||||||
\(284\) | 2.08579 | + | 3.61269i | 0.123769 | + | 0.214374i | ||||
\(285\) | −9.24264 | + | 16.0087i | −0.547487 | + | 0.948275i | ||||
\(286\) | −7.65685 | −0.452759 | ||||||||
\(287\) | −8.38478 | − | 10.8126i | −0.494938 | − | 0.638246i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −5.24264 | + | 9.08052i | −0.308391 | + | 0.534148i | ||||
\(290\) | 8.24264 | + | 14.2767i | 0.484025 | + | 0.838355i | ||||
\(291\) | −0.828427 | − | 1.43488i | −0.0485633 | − | 0.0841140i | ||||
\(292\) | −0.328427 | + | 0.568852i | −0.0192197 | + | 0.0332896i | ||||
\(293\) | −3.58579 | −0.209484 | −0.104742 | − | 0.994499i | \(-0.533402\pi\) | ||||
−0.104742 | + | 0.994499i | \(0.533402\pi\) | |||||||
\(294\) | 1.74264 | − | 6.77962i | 0.101633 | − | 0.395395i | ||||
\(295\) | 23.3137 | 1.35738 | ||||||||
\(296\) | −4.41421 | + | 7.64564i | −0.256571 | + | 0.444394i | ||||
\(297\) | −1.00000 | − | 1.73205i | −0.0580259 | − | 0.100504i | ||||
\(298\) | 4.62132 | + | 8.00436i | 0.267706 | + | 0.463680i | ||||
\(299\) | −1.91421 | + | 3.31552i | −0.110702 | + | 0.191741i | ||||
\(300\) | 0.828427 | 0.0478293 | ||||||||
\(301\) | −0.556349 | − | 0.717439i | −0.0320674 | − | 0.0413525i | ||||
\(302\) | 14.1421 | 0.813788 | ||||||||
\(303\) | −4.41421 | + | 7.64564i | −0.253590 | + | 0.439231i | ||||
\(304\) | 3.82843 | + | 6.63103i | 0.219575 | + | 0.380316i | ||||
\(305\) | −2.41421 | − | 4.18154i | −0.138237 | − | 0.239434i | ||||
\(306\) | 2.62132 | − | 4.54026i | 0.149851 | − | 0.259549i | ||||
\(307\) | −14.1421 | −0.807134 | −0.403567 | − | 0.914950i | \(-0.632230\pi\) | ||||
−0.403567 | + | 0.914950i | \(0.632230\pi\) | |||||||
\(308\) | −5.24264 | + | 0.717439i | −0.298727 | + | 0.0408799i | ||||
\(309\) | 10.8995 | 0.620051 | ||||||||
\(310\) | 2.41421 | − | 4.18154i | 0.137118 | − | 0.237496i | ||||
\(311\) | 8.15685 | + | 14.1281i | 0.462533 | + | 0.801130i | 0.999086 | − | 0.0427360i | \(-0.0136074\pi\) |
−0.536554 | + | 0.843866i | \(0.680274\pi\) | |||||||
\(312\) | 1.91421 | + | 3.31552i | 0.108371 | + | 0.187704i | ||||
\(313\) | −16.4853 | + | 28.5533i | −0.931803 | + | 1.61393i | −0.151566 | + | 0.988447i | \(0.548431\pi\) |
−0.780238 | + | 0.625483i | \(0.784902\pi\) | |||||||
\(314\) | 15.6569 | 0.883567 | ||||||||
\(315\) | −2.41421 | + | 5.91359i | −0.136026 | + | 0.333193i | ||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 16.3137 | − | 28.2562i | 0.916269 | − | 1.58702i | 0.111237 | − | 0.993794i | \(-0.464519\pi\) |
0.805032 | − | 0.593231i | \(-0.202148\pi\) | |||||||
\(318\) | 2.03553 | + | 3.52565i | 0.114147 | + | 0.197709i | ||||
\(319\) | 6.82843 | + | 11.8272i | 0.382319 | + | 0.662195i | ||||
\(320\) | 1.20711 | − | 2.09077i | 0.0674793 | − | 0.116878i | ||||
\(321\) | −5.65685 | −0.315735 | ||||||||
\(322\) | −1.00000 | + | 2.44949i | −0.0557278 | + | 0.136505i | ||||
\(323\) | −40.1421 | −2.23357 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −1.58579 | − | 2.74666i | −0.0879636 | − | 0.152357i | ||||
\(326\) | 0.828427 | + | 1.43488i | 0.0458823 | + | 0.0794705i | ||||
\(327\) | −4.58579 | + | 7.94282i | −0.253595 | + | 0.439239i | ||||
\(328\) | 5.17157 | 0.285552 | ||||||||
\(329\) | −23.5919 | + | 3.22848i | −1.30066 | + | 0.177992i | ||||
\(330\) | 4.82843 | 0.265796 | ||||||||
\(331\) | 17.2426 | − | 29.8651i | 0.947741 | − | 1.64154i | 0.197574 | − | 0.980288i | \(-0.436694\pi\) |
0.750167 | − | 0.661248i | \(-0.229973\pi\) | |||||||
\(332\) | −3.58579 | − | 6.21076i | −0.196796 | − | 0.340860i | ||||
\(333\) | 4.41421 | + | 7.64564i | 0.241897 | + | 0.418979i | ||||
\(334\) | 12.3995 | − | 21.4766i | 0.678470 | − | 1.17514i | ||||
\(335\) | 11.8284 | 0.646256 | ||||||||
\(336\) | 1.62132 | + | 2.09077i | 0.0884503 | + | 0.114061i | ||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0.828427 | − | 1.43488i | 0.0450605 | − | 0.0780471i | ||||
\(339\) | −5.86396 | − | 10.1567i | −0.318487 | − | 0.551635i | ||||
\(340\) | 6.32843 | + | 10.9612i | 0.343207 | + | 0.594452i | ||||
\(341\) | 2.00000 | − | 3.46410i | 0.108306 | − | 0.187592i | ||||
\(342\) | 7.65685 | 0.414035 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0.343146 | 0.0185012 | ||||||||
\(345\) | 1.20711 | − | 2.09077i | 0.0649884 | − | 0.112563i | ||||
\(346\) | −3.65685 | − | 6.33386i | −0.196594 | − | 0.340510i | ||||
\(347\) | 16.3284 | + | 28.2817i | 0.876556 | + | 1.51824i | 0.855096 | + | 0.518470i | \(0.173498\pi\) |
0.0214599 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(348\) | 3.41421 | − | 5.91359i | 0.183021 | − | 0.317002i | ||||
\(349\) | −25.1421 | −1.34583 | −0.672914 | − | 0.739721i | \(-0.734958\pi\) | ||||
−0.672914 | + | 0.739721i | \(0.734958\pi\) | |||||||
\(350\) | −1.34315 | − | 1.73205i | −0.0717942 | − | 0.0925820i | ||||
\(351\) | 3.82843 | 0.204346 | ||||||||
\(352\) | 1.00000 | − | 1.73205i | 0.0533002 | − | 0.0923186i | ||||
\(353\) | −1.07107 | − | 1.85514i | −0.0570072 | − | 0.0987393i | 0.836113 | − | 0.548557i | \(-0.184822\pi\) |
−0.893121 | + | 0.449817i | \(0.851489\pi\) | |||||||
\(354\) | −4.82843 | − | 8.36308i | −0.256628 | − | 0.444493i | ||||
\(355\) | −5.03553 | + | 8.72180i | −0.267258 | + | 0.462905i | ||||
\(356\) | 6.82843 | 0.361906 | ||||||||
\(357\) | −13.7426 | + | 1.88064i | −0.727338 | + | 0.0995339i | ||||
\(358\) | 21.9706 | 1.16118 | ||||||||
\(359\) | −13.4853 | + | 23.3572i | −0.711726 | + | 1.23275i | 0.252483 | + | 0.967601i | \(0.418753\pi\) |
−0.964209 | + | 0.265144i | \(0.914580\pi\) | |||||||
\(360\) | −1.20711 | − | 2.09077i | −0.0636201 | − | 0.110193i | ||||
\(361\) | −19.8137 | − | 34.3183i | −1.04283 | − | 1.80623i | ||||
\(362\) | −4.65685 | + | 8.06591i | −0.244759 | + | 0.423935i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 3.82843 | − | 9.37769i | 0.200664 | − | 0.491525i | ||||
\(365\) | −1.58579 | −0.0830039 | ||||||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | −13.3492 | − | 23.1216i | −0.696825 | − | 1.20694i | −0.969562 | − | 0.244847i | \(-0.921262\pi\) |
0.272737 | − | 0.962089i | \(-0.412071\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | 2.58579 | − | 4.47871i | 0.134611 | − | 0.233153i | ||||
\(370\) | −21.3137 | −1.10805 | ||||||||
\(371\) | 4.07107 | − | 9.97204i | 0.211359 | − | 0.517722i | ||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | 0.171573 | − | 0.297173i | 0.00888371 | − | 0.0153870i | −0.861549 | − | 0.507674i | \(-0.830506\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(374\) | 5.24264 | + | 9.08052i | 0.271090 | + | 0.469543i | ||||
\(375\) | −5.03553 | − | 8.72180i | −0.260034 | − | 0.450392i | ||||
\(376\) | 4.50000 | − | 7.79423i | 0.232070 | − | 0.401957i | ||||
\(377\) | −26.1421 | −1.34639 | ||||||||
\(378\) | 2.62132 | − | 0.358719i | 0.134826 | − | 0.0184505i | ||||
\(379\) | −18.8995 | −0.970802 | −0.485401 | − | 0.874292i | \(-0.661326\pi\) | ||||
−0.485401 | + | 0.874292i | \(0.661326\pi\) | |||||||
\(380\) | −9.24264 | + | 16.0087i | −0.474137 | + | 0.821230i | ||||
\(381\) | 0.414214 | + | 0.717439i | 0.0212208 | + | 0.0367555i | ||||
\(382\) | −2.58579 | − | 4.47871i | −0.132300 | − | 0.229151i | ||||
\(383\) | −1.82843 | + | 3.16693i | −0.0934283 | + | 0.161822i | −0.908952 | − | 0.416902i | \(-0.863116\pi\) |
0.815523 | + | 0.578724i | \(0.196449\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −7.82843 | − | 10.0951i | −0.398974 | − | 0.514496i | ||||
\(386\) | 5.48528 | 0.279193 | ||||||||
\(387\) | 0.171573 | − | 0.297173i | 0.00872154 | − | 0.0151061i | ||||
\(388\) | −0.828427 | − | 1.43488i | −0.0420570 | − | 0.0728449i | ||||
\(389\) | 18.7279 | + | 32.4377i | 0.949543 | + | 1.64466i | 0.746388 | + | 0.665511i | \(0.231786\pi\) |
0.203155 | + | 0.979147i | \(0.434880\pi\) | |||||||
\(390\) | −4.62132 | + | 8.00436i | −0.234010 | + | 0.405317i | ||||
\(391\) | 5.24264 | 0.265132 | ||||||||
\(392\) | 1.74264 | − | 6.77962i | 0.0880166 | − | 0.342422i | ||||
\(393\) | −9.14214 | −0.461160 | ||||||||
\(394\) | −6.41421 | + | 11.1097i | −0.323143 | + | 0.559701i | ||||
\(395\) | −12.0711 | − | 20.9077i | −0.607361 | − | 1.05198i | ||||
\(396\) | −1.00000 | − | 1.73205i | −0.0502519 | − | 0.0870388i | ||||
\(397\) | 4.32843 | − | 7.49706i | 0.217238 | − | 0.376266i | −0.736725 | − | 0.676193i | \(-0.763629\pi\) |
0.953962 | + | 0.299926i | \(0.0969620\pi\) | |||||||
\(398\) | 27.6569 | 1.38631 | ||||||||
\(399\) | −12.4142 | − | 16.0087i | −0.621488 | − | 0.801439i | ||||
\(400\) | 0.828427 | 0.0414214 | ||||||||
\(401\) | 16.3492 | − | 28.3177i | 0.816442 | − | 1.41412i | −0.0918455 | − | 0.995773i | \(-0.529277\pi\) |
0.908288 | − | 0.418346i | \(-0.137390\pi\) | |||||||
\(402\) | −2.44975 | − | 4.24309i | −0.122182 | − | 0.211626i | ||||
\(403\) | 3.82843 | + | 6.63103i | 0.190708 | + | 0.330315i | ||||
\(404\) | −4.41421 | + | 7.64564i | −0.219615 | + | 0.380385i | ||||
\(405\) | −2.41421 | −0.119963 | ||||||||
\(406\) | −17.8995 | + | 2.44949i | −0.888337 | + | 0.121566i | ||||
\(407\) | −17.6569 | −0.875218 | ||||||||
\(408\) | 2.62132 | − | 4.54026i | 0.129775 | − | 0.224776i | ||||
\(409\) | 13.3995 | + | 23.2086i | 0.662562 | + | 1.14759i | 0.979940 | + | 0.199292i | \(0.0638644\pi\) |
−0.317378 | + | 0.948299i | \(0.602802\pi\) | |||||||
\(410\) | 6.24264 | + | 10.8126i | 0.308302 | + | 0.533995i | ||||
\(411\) | 3.79289 | − | 6.56948i | 0.187090 | − | 0.324049i | ||||
\(412\) | 10.8995 | 0.536980 | ||||||||
\(413\) | −9.65685 | + | 23.6544i | −0.475183 | + | 1.16396i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 8.65685 | − | 14.9941i | 0.424948 | − | 0.736032i | ||||
\(416\) | 1.91421 | + | 3.31552i | 0.0938520 | + | 0.162557i | ||||
\(417\) | −4.65685 | − | 8.06591i | −0.228047 | − | 0.394989i | ||||
\(418\) | −7.65685 | + | 13.2621i | −0.374509 | + | 0.648669i | ||||
\(419\) | 7.51472 | 0.367118 | 0.183559 | − | 0.983009i | \(-0.441238\pi\) | ||||
0.183559 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(420\) | −2.41421 | + | 5.91359i | −0.117802 | + | 0.288554i | ||||
\(421\) | −7.31371 | −0.356448 | −0.178224 | − | 0.983990i | \(-0.557035\pi\) | ||||
−0.178224 | + | 0.983990i | \(0.557035\pi\) | |||||||
\(422\) | −5.58579 | + | 9.67487i | −0.271912 | + | 0.470965i | ||||
\(423\) | −4.50000 | − | 7.79423i | −0.218797 | − | 0.378968i | ||||
\(424\) | 2.03553 | + | 3.52565i | 0.0988543 | + | 0.171221i | ||||
\(425\) | −2.17157 | + | 3.76127i | −0.105337 | + | 0.182449i | ||||
\(426\) | 4.17157 | 0.202113 | ||||||||
\(427\) | 5.24264 | − | 0.717439i | 0.253709 | − | 0.0347193i | ||||
\(428\) | −5.65685 | −0.273434 | ||||||||
\(429\) | −3.82843 | + | 6.63103i | −0.184838 | + | 0.320149i | ||||
\(430\) | 0.414214 | + | 0.717439i | 0.0199752 | + | 0.0345980i | ||||
\(431\) | 13.6569 | + | 23.6544i | 0.657828 | + | 1.13939i | 0.981177 | + | 0.193111i | \(0.0618578\pi\) |
−0.323349 | + | 0.946280i | \(0.604809\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 3.24264 | + | 4.18154i | 0.155652 | + | 0.200720i | ||||
\(435\) | 16.4853 | 0.790409 | ||||||||
\(436\) | −4.58579 | + | 7.94282i | −0.219619 | + | 0.380392i | ||||
\(437\) | 3.82843 | + | 6.63103i | 0.183139 | + | 0.317205i | ||||
\(438\) | 0.328427 | + | 0.568852i | 0.0156929 | + | 0.0271808i | ||||
\(439\) | −15.4853 | + | 26.8213i | −0.739072 | + | 1.28011i | 0.213841 | + | 0.976868i | \(0.431402\pi\) |
−0.952914 | + | 0.303242i | \(0.901931\pi\) | |||||||
\(440\) | 4.82843 | 0.230186 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | −20.0711 | −0.954683 | ||||||||
\(443\) | −5.57107 | + | 9.64937i | −0.264689 | + | 0.458456i | −0.967482 | − | 0.252939i | \(-0.918603\pi\) |
0.702793 | + | 0.711395i | \(0.251936\pi\) | |||||||
\(444\) | 4.41421 | + | 7.64564i | 0.209489 | + | 0.362846i | ||||
\(445\) | 8.24264 | + | 14.2767i | 0.390739 | + | 0.676779i | ||||
\(446\) | −6.24264 | + | 10.8126i | −0.295598 | + | 0.511990i | ||||
\(447\) | 9.24264 | 0.437162 | ||||||||
\(448\) | 1.62132 | + | 2.09077i | 0.0766002 | + | 0.0987796i | ||||
\(449\) | 9.51472 | 0.449027 | 0.224514 | − | 0.974471i | \(-0.427921\pi\) | ||||
0.224514 | + | 0.974471i | \(0.427921\pi\) | |||||||
\(450\) | 0.414214 | − | 0.717439i | 0.0195262 | − | 0.0338204i | ||||
\(451\) | 5.17157 | + | 8.95743i | 0.243520 | + | 0.421789i | ||||
\(452\) | −5.86396 | − | 10.1567i | −0.275818 | − | 0.477730i | ||||
\(453\) | 7.07107 | − | 12.2474i | 0.332228 | − | 0.575435i | ||||
\(454\) | 10.9706 | 0.514874 | ||||||||
\(455\) | 24.2279 | − | 3.31552i | 1.13582 | − | 0.155434i | ||||
\(456\) | 7.65685 | 0.358565 | ||||||||
\(457\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(458\) | 1.07107 | + | 1.85514i | 0.0500477 | + | 0.0866852i | ||||
\(459\) | −2.62132 | − | 4.54026i | −0.122353 | − | 0.211921i | ||||
\(460\) | 1.20711 | − | 2.09077i | 0.0562816 | − | 0.0974827i | ||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | −2.00000 | + | 4.89898i | −0.0930484 | + | 0.227921i | ||||
\(463\) | −34.6274 | −1.60927 | −0.804636 | − | 0.593768i | \(-0.797640\pi\) | ||||
−0.804636 | + | 0.593768i | \(0.797640\pi\) | |||||||
\(464\) | 3.41421 | − | 5.91359i | 0.158501 | − | 0.274532i | ||||
\(465\) | −2.41421 | − | 4.18154i | −0.111956 | − | 0.193914i | ||||
\(466\) | −4.00000 | − | 6.92820i | −0.185296 | − | 0.320943i | ||||
\(467\) | −10.8284 | + | 18.7554i | −0.501080 | + | 0.867896i | 0.498919 | + | 0.866648i | \(0.333730\pi\) |
−0.999999 | + | 0.00124735i | \(0.999603\pi\) | |||||||
\(468\) | 3.82843 | 0.176969 | ||||||||
\(469\) | −4.89949 | + | 12.0013i | −0.226238 | + | 0.554167i | ||||
\(470\) | 21.7279 | 1.00223 | ||||||||
\(471\) | 7.82843 | − | 13.5592i | 0.360715 | − | 0.624777i | ||||
\(472\) | −4.82843 | − | 8.36308i | −0.222246 | − | 0.384942i | ||||
\(473\) | 0.343146 | + | 0.594346i | 0.0157779 | + | 0.0273281i | ||||
\(474\) | −5.00000 | + | 8.66025i | −0.229658 | + | 0.397779i | ||||
\(475\) | −6.34315 | −0.291043 | ||||||||
\(476\) | −13.7426 | + | 1.88064i | −0.629893 | + | 0.0861989i | ||||
\(477\) | 4.07107 | 0.186401 | ||||||||
\(478\) | 5.17157 | − | 8.95743i | 0.236542 | − | 0.409703i | ||||
\(479\) | −2.92893 | − | 5.07306i | −0.133826 | − | 0.231794i | 0.791322 | − | 0.611399i | \(-0.209393\pi\) |
−0.925148 | + | 0.379605i | \(0.876060\pi\) | |||||||
\(480\) | −1.20711 | − | 2.09077i | −0.0550966 | − | 0.0954302i | ||||
\(481\) | 16.8995 | − | 29.2708i | 0.770551 | − | 1.33463i | ||||
\(482\) | 12.8284 | 0.584319 | ||||||||
\(483\) | 1.62132 | + | 2.09077i | 0.0737726 | + | 0.0951333i | ||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 2.00000 | − | 3.46410i | 0.0908153 | − | 0.157297i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −20.3848 | − | 35.3075i | −0.923722 | − | 1.59993i | −0.793603 | − | 0.608436i | \(-0.791797\pi\) |
−0.130119 | − | 0.991498i | \(-0.541536\pi\) | |||||||
\(488\) | −1.00000 | + | 1.73205i | −0.0452679 | + | 0.0784063i | ||||
\(489\) | 1.65685 | 0.0749255 | ||||||||
\(490\) | 16.2782 | − | 4.54026i | 0.735373 | − | 0.205108i | ||||
\(491\) | −22.6569 | −1.02249 | −0.511245 | − | 0.859435i | \(-0.670815\pi\) | ||||
−0.511245 | + | 0.859435i | \(0.670815\pi\) | |||||||
\(492\) | 2.58579 | − | 4.47871i | 0.116576 | − | 0.201916i | ||||
\(493\) | 17.8995 | + | 31.0028i | 0.806153 | + | 1.39630i | ||||
\(494\) | −14.6569 | − | 25.3864i | −0.659443 | − | 1.14219i | ||||
\(495\) | 2.41421 | − | 4.18154i | 0.108511 | − | 0.187946i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | −6.76346 | − | 8.72180i | −0.303382 | − | 0.391226i | ||||
\(498\) | −7.17157 | −0.321366 | ||||||||
\(499\) | −3.41421 | + | 5.91359i | −0.152841 | + | 0.264729i | −0.932271 | − | 0.361761i | \(-0.882176\pi\) |
0.779430 | + | 0.626490i | \(0.215509\pi\) | |||||||
\(500\) | −5.03553 | − | 8.72180i | −0.225196 | − | 0.390051i | ||||
\(501\) | −12.3995 | − | 21.4766i | −0.553969 | − | 0.959502i | ||||
\(502\) | 8.65685 | − | 14.9941i | 0.386374 | − | 0.669220i | ||||
\(503\) | 32.3431 | 1.44211 | 0.721055 | − | 0.692878i | \(-0.243658\pi\) | ||||
0.721055 | + | 0.692878i | \(0.243658\pi\) | |||||||
\(504\) | 2.62132 | − | 0.358719i | 0.116763 | − | 0.0159786i | ||||
\(505\) | −21.3137 | −0.948448 | ||||||||
\(506\) | 1.00000 | − | 1.73205i | 0.0444554 | − | 0.0769991i | ||||
\(507\) | −0.828427 | − | 1.43488i | −0.0367917 | − | 0.0637252i | ||||
\(508\) | 0.414214 | + | 0.717439i | 0.0183778 | + | 0.0318312i | ||||
\(509\) | −22.0711 | + | 38.2282i | −0.978283 | + | 1.69444i | −0.309637 | + | 0.950855i | \(0.600207\pi\) |
−0.668646 | + | 0.743581i | \(0.733126\pi\) | |||||||
\(510\) | 12.6569 | 0.560455 | ||||||||
\(511\) | 0.656854 | − | 1.60896i | 0.0290575 | − | 0.0711761i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.82843 | − | 6.63103i | 0.169029 | − | 0.292767i | ||||
\(514\) | 2.75736 | + | 4.77589i | 0.121622 | + | 0.210655i | ||||
\(515\) | 13.1569 | + | 22.7883i | 0.579760 | + | 1.00417i | ||||
\(516\) | 0.171573 | − | 0.297173i | 0.00755307 | − | 0.0130823i | ||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 8.82843 | − | 21.6251i | 0.387899 | − | 0.950154i | ||||
\(519\) | −7.31371 | −0.321036 | ||||||||
\(520\) | −4.62132 | + | 8.00436i | −0.202658 | + | 0.351014i | ||||
\(521\) | −14.2071 | − | 24.6074i | −0.622425 | − | 1.07807i | −0.989033 | − | 0.147696i | \(-0.952814\pi\) |
0.366608 | − | 0.930375i | \(-0.380519\pi\) | |||||||
\(522\) | −3.41421 | − | 5.91359i | −0.149436 | − | 0.258831i | ||||
\(523\) | −0.0355339 | + | 0.0615465i | −0.00155379 | + | 0.00269124i | −0.866801 | − | 0.498654i | \(-0.833828\pi\) |
0.865247 | + | 0.501345i | \(0.167161\pi\) | |||||||
\(524\) | −9.14214 | −0.399376 | ||||||||
\(525\) | −2.17157 | + | 0.297173i | −0.0947752 | + | 0.0129697i | ||||
\(526\) | −19.3137 | −0.842118 | ||||||||
\(527\) | 5.24264 | − | 9.08052i | 0.228373 | − | 0.395554i | ||||
\(528\) | −1.00000 | − | 1.73205i | −0.0435194 | − | 0.0753778i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −4.91421 | + | 8.51167i | −0.213460 | + | 0.369723i | ||||
\(531\) | −9.65685 | −0.419072 | ||||||||
\(532\) | −12.4142 | − | 16.0087i | −0.538224 | − | 0.694066i | ||||
\(533\) | −19.7990 | −0.857589 | ||||||||
\(534\) | 3.41421 | − | 5.91359i | 0.147747 | − | 0.255906i | ||||
\(535\) | −6.82843 | − | 11.8272i | −0.295219 | − | 0.511334i | ||||
\(536\) | −2.44975 | − | 4.24309i | −0.105813 | − | 0.183273i | ||||
\(537\) | 10.9853 | − | 19.0271i | 0.474050 | − | 0.821078i | ||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 13.4853 | − | 3.76127i | 0.580852 | − | 0.162010i | ||||
\(540\) | −2.41421 | −0.103891 | ||||||||
\(541\) | −20.5711 | + | 35.6301i | −0.884419 | + | 1.53186i | −0.0380415 | + | 0.999276i | \(0.512112\pi\) |
−0.846378 | + | 0.532583i | \(0.821221\pi\) | |||||||
\(542\) | −15.1421 | − | 26.2269i | −0.650410 | − | 1.12654i | ||||
\(543\) | 4.65685 | + | 8.06591i | 0.199845 | + | 0.346141i | ||||
\(544\) | 2.62132 | − | 4.54026i | 0.112388 | − | 0.194662i | ||||
\(545\) | −22.1421 | −0.948465 | ||||||||
\(546\) | −6.20711 | − | 8.00436i | −0.265640 | − | 0.342555i | ||||
\(547\) | 22.2843 | 0.952807 | 0.476403 | − | 0.879227i | \(-0.341940\pi\) | ||||
0.476403 | + | 0.879227i | \(0.341940\pi\) | |||||||
\(548\) | 3.79289 | − | 6.56948i | 0.162024 | − | 0.280634i | ||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | 0.828427 | + | 1.43488i | 0.0353243 | + | 0.0611834i | ||||
\(551\) | −26.1421 | + | 45.2795i | −1.11369 | + | 1.92897i | ||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 26.2132 | − | 3.58719i | 1.11470 | − | 0.152543i | ||||
\(554\) | −25.2843 | −1.07423 | ||||||||
\(555\) | −10.6569 | + | 18.4582i | −0.452358 | + | 0.783508i | ||||
\(556\) | −4.65685 | − | 8.06591i | −0.197495 | − | 0.342071i | ||||
\(557\) | −7.89949 | − | 13.6823i | −0.334712 | − | 0.579739i | 0.648717 | − | 0.761030i | \(-0.275306\pi\) |
−0.983430 | + | 0.181291i | \(0.941972\pi\) | |||||||
\(558\) | −1.00000 | + | 1.73205i | −0.0423334 | + | 0.0733236i | ||||
\(559\) | −1.31371 | −0.0555639 | ||||||||
\(560\) | −2.41421 | + | 5.91359i | −0.102019 | + | 0.249895i | ||||
\(561\) | 10.4853 | 0.442689 | ||||||||
\(562\) | −6.79289 | + | 11.7656i | −0.286541 | + | 0.496303i | ||||
\(563\) | −22.7279 | − | 39.3659i | −0.957868 | − | 1.65908i | −0.727665 | − | 0.685933i | \(-0.759394\pi\) |
−0.230203 | − | 0.973143i | \(-0.573939\pi\) | |||||||
\(564\) | −4.50000 | − | 7.79423i | −0.189484 | − | 0.328196i | ||||
\(565\) | 14.1569 | − | 24.5204i | 0.595583 | − | 1.03158i | ||||
\(566\) | 29.3848 | 1.23513 | ||||||||
\(567\) | 1.00000 | − | 2.44949i | 0.0419961 | − | 0.102869i | ||||
\(568\) | 4.17157 | 0.175035 | ||||||||
\(569\) | −3.79289 | + | 6.56948i | −0.159006 | + | 0.275407i | −0.934511 | − | 0.355935i | \(-0.884162\pi\) |
0.775504 | + | 0.631342i | \(0.217496\pi\) | |||||||
\(570\) | 9.24264 | + | 16.0087i | 0.387132 | + | 0.670532i | ||||
\(571\) | 0.550253 | + | 0.953065i | 0.0230274 | + | 0.0398845i | 0.877309 | − | 0.479925i | \(-0.159336\pi\) |
−0.854282 | + | 0.519810i | \(0.826003\pi\) | |||||||
\(572\) | −3.82843 | + | 6.63103i | −0.160075 | + | 0.277257i | ||||
\(573\) | −5.17157 | −0.216046 | ||||||||
\(574\) | −13.5563 | + | 1.85514i | −0.565831 | + | 0.0774322i | ||||
\(575\) | 0.828427 | 0.0345478 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −17.9706 | − | 31.1259i | −0.748124 | − | 1.29579i | −0.948721 | − | 0.316115i | \(-0.897621\pi\) |
0.200596 | − | 0.979674i | \(-0.435712\pi\) | |||||||
\(578\) | 5.24264 | + | 9.08052i | 0.218065 | + | 0.377700i | ||||
\(579\) | 2.74264 | − | 4.75039i | 0.113980 | − | 0.197420i | ||||
\(580\) | 16.4853 | 0.684514 | ||||||||
\(581\) | 11.6274 | + | 14.9941i | 0.482387 | + | 0.622061i | ||||
\(582\) | −1.65685 | −0.0686788 | ||||||||
\(583\) | −4.07107 | + | 7.05130i | −0.168606 | + | 0.292035i | ||||
\(584\) | 0.328427 | + | 0.568852i | 0.0135904 | + | 0.0235393i | ||||
\(585\) | 4.62132 | + | 8.00436i | 0.191068 | + | 0.330940i | ||||
\(586\) | −1.79289 | + | 3.10538i | −0.0740637 | + | 0.128282i | ||||
\(587\) | −27.1421 | −1.12028 | −0.560138 | − | 0.828399i | \(-0.689252\pi\) | ||||
−0.560138 | + | 0.828399i | \(0.689252\pi\) | |||||||
\(588\) | −5.00000 | − | 4.89898i | −0.206197 | − | 0.202031i | ||||
\(589\) | 15.3137 | 0.630990 | ||||||||
\(590\) | 11.6569 | − | 20.1903i | 0.479905 | − | 0.831220i | ||||
\(591\) | 6.41421 | + | 11.1097i | 0.263845 | + | 0.456994i | ||||
\(592\) | 4.41421 | + | 7.64564i | 0.181423 | + | 0.314234i | ||||
\(593\) | 16.0711 | − | 27.8359i | 0.659960 | − | 1.14308i | −0.320666 | − | 0.947192i | \(-0.603907\pi\) |
0.980626 | − | 0.195891i | \(-0.0627600\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | −20.5208 | − | 26.4626i | −0.841271 | − | 1.08486i | ||||
\(596\) | 9.24264 | 0.378593 | ||||||||
\(597\) | 13.8284 | − | 23.9515i | 0.565960 | − | 0.980271i | ||||
\(598\) | 1.91421 | + | 3.31552i | 0.0782780 | + | 0.135581i | ||||
\(599\) | 5.91421 | + | 10.2437i | 0.241648 | + | 0.418547i | 0.961184 | − | 0.275908i | \(-0.0889787\pi\) |
−0.719536 | + | 0.694455i | \(0.755645\pi\) | |||||||
\(600\) | 0.414214 | − | 0.717439i | 0.0169102 | − | 0.0292893i | ||||
\(601\) | 42.2843 | 1.72481 | 0.862406 | − | 0.506218i | \(-0.168957\pi\) | ||||
0.862406 | + | 0.506218i | \(0.168957\pi\) | |||||||
\(602\) | −0.899495 | + | 0.123093i | −0.0366607 | + | 0.00501690i | ||||
\(603\) | −4.89949 | −0.199523 | ||||||||
\(604\) | 7.07107 | − | 12.2474i | 0.287718 | − | 0.498342i | ||||
\(605\) | −8.44975 | − | 14.6354i | −0.343531 | − | 0.595013i | ||||
\(606\) | 4.41421 | + | 7.64564i | 0.179315 | + | 0.310583i | ||||
\(607\) | −3.92893 | + | 6.80511i | −0.159470 | + | 0.276211i | −0.934678 | − | 0.355496i | \(-0.884312\pi\) |
0.775207 | + | 0.631707i | \(0.217645\pi\) | |||||||
\(608\) | 7.65685 | 0.310526 | ||||||||
\(609\) | −6.82843 | + | 16.7262i | −0.276702 | + | 0.677778i | ||||
\(610\) | −4.82843 | −0.195497 | ||||||||
\(611\) | −17.2279 | + | 29.8396i | −0.696967 | + | 1.20718i | ||||
\(612\) | −2.62132 | − | 4.54026i | −0.105961 | − | 0.183529i | ||||
\(613\) | −10.8995 | − | 18.8785i | −0.440226 | − | 0.762495i | 0.557480 | − | 0.830191i | \(-0.311769\pi\) |
−0.997706 | + | 0.0676961i | \(0.978435\pi\) | |||||||
\(614\) | −7.07107 | + | 12.2474i | −0.285365 | + | 0.494267i | ||||
\(615\) | 12.4853 | 0.503455 | ||||||||
\(616\) | −2.00000 | + | 4.89898i | −0.0805823 | + | 0.197386i | ||||
\(617\) | −21.9289 | −0.882826 | −0.441413 | − | 0.897304i | \(-0.645523\pi\) | ||||
−0.441413 | + | 0.897304i | \(0.645523\pi\) | |||||||
\(618\) | 5.44975 | − | 9.43924i | 0.219221 | − | 0.379702i | ||||
\(619\) | −22.0355 | − | 38.1667i | −0.885683 | − | 1.53405i | −0.844929 | − | 0.534879i | \(-0.820357\pi\) |
−0.0407539 | − | 0.999169i | \(-0.512976\pi\) | |||||||
\(620\) | −2.41421 | − | 4.18154i | −0.0969571 | − | 0.167935i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 16.3137 | 0.654120 | ||||||||
\(623\) | −17.8995 | + | 2.44949i | −0.717128 | + | 0.0981367i | ||||
\(624\) | 3.82843 | 0.153260 | ||||||||
\(625\) | 14.2279 | − | 24.6435i | 0.569117 | − | 0.985739i | ||||
\(626\) | 16.4853 | + | 28.5533i | 0.658884 | + | 1.14122i | ||||
\(627\) | 7.65685 | + | 13.2621i | 0.305785 | + | 0.529636i | ||||
\(628\) | 7.82843 | − | 13.5592i | 0.312388 | − | 0.541072i | ||||
\(629\) | −46.2843 | −1.84547 | ||||||||
\(630\) | 3.91421 | + | 5.04757i | 0.155946 | + | 0.201100i | ||||
\(631\) | −15.4437 | −0.614802 | −0.307401 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307401 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(632\) | −5.00000 | + | 8.66025i | −0.198889 | + | 0.344486i | ||||
\(633\) | 5.58579 | + | 9.67487i | 0.222015 | + | 0.384541i | ||||
\(634\) | −16.3137 | − | 28.2562i | −0.647900 | − | 1.12220i | ||||
\(635\) | −1.00000 | + | 1.73205i | −0.0396838 | + | 0.0687343i | ||||
\(636\) | 4.07107 | 0.161428 | ||||||||
\(637\) | −6.67157 | + | 25.9553i | −0.264337 | + | 1.02839i | ||||
\(638\) | 13.6569 | 0.540680 | ||||||||
\(639\) | 2.08579 | − | 3.61269i | 0.0825124 | − | 0.142916i | ||||
\(640\) | −1.20711 | − | 2.09077i | −0.0477151 | − | 0.0826450i | ||||
\(641\) | 23.6924 | + | 41.0364i | 0.935793 | + | 1.62084i | 0.773214 | + | 0.634146i | \(0.218648\pi\) |
0.162579 | + | 0.986695i | \(0.448019\pi\) | |||||||
\(642\) | −2.82843 | + | 4.89898i | −0.111629 | + | 0.193347i | ||||
\(643\) | 29.3137 | 1.15602 | 0.578010 | − | 0.816030i | \(-0.303829\pi\) | ||||
0.578010 | + | 0.816030i | \(0.303829\pi\) | |||||||
\(644\) | 1.62132 | + | 2.09077i | 0.0638890 | + | 0.0823879i | ||||
\(645\) | 0.828427 | 0.0326193 | ||||||||
\(646\) | −20.0711 | + | 34.7641i | −0.789686 | + | 1.36778i | ||||
\(647\) | 5.17157 | + | 8.95743i | 0.203316 | + | 0.352153i | 0.949595 | − | 0.313480i | \(-0.101495\pi\) |
−0.746279 | + | 0.665633i | \(0.768162\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 9.65685 | − | 16.7262i | 0.379065 | − | 0.656559i | ||||
\(650\) | −3.17157 | −0.124399 | ||||||||
\(651\) | 5.24264 | − | 0.717439i | 0.205475 | − | 0.0281186i | ||||
\(652\) | 1.65685 | 0.0648874 | ||||||||
\(653\) | −17.9706 | + | 31.1259i | −0.703242 | + | 1.21805i | 0.264080 | + | 0.964501i | \(0.414932\pi\) |
−0.967322 | + | 0.253551i | \(0.918402\pi\) | |||||||
\(654\) | 4.58579 | + | 7.94282i | 0.179318 | + | 0.310589i | ||||
\(655\) | −11.0355 | − | 19.1141i | −0.431194 | − | 0.746850i | ||||
\(656\) | 2.58579 | − | 4.47871i | 0.100958 | − | 0.174864i | ||||
\(657\) | 0.656854 | 0.0256263 | ||||||||
\(658\) | −9.00000 | + | 22.0454i | −0.350857 | + | 0.859419i | ||||
\(659\) | −23.4558 | −0.913710 | −0.456855 | − | 0.889541i | \(-0.651024\pi\) | ||||
−0.456855 | + | 0.889541i | \(0.651024\pi\) | |||||||
\(660\) | 2.41421 | − | 4.18154i | 0.0939731 | − | 0.162766i | ||||
\(661\) | 16.7279 | + | 28.9736i | 0.650641 | + | 1.12694i | 0.982968 | + | 0.183779i | \(0.0588329\pi\) |
−0.332327 | + | 0.943164i | \(0.607834\pi\) | |||||||
\(662\) | −17.2426 | − | 29.8651i | −0.670154 | − | 1.16074i | ||||
\(663\) | −10.0355 | + | 17.3821i | −0.389748 | + | 0.675063i | ||||
\(664\) | −7.17157 | −0.278311 | ||||||||
\(665\) | 18.4853 | − | 45.2795i | 0.716828 | − | 1.75586i | ||||
\(666\) | 8.82843 | 0.342095 | ||||||||
\(667\) | 3.41421 | − | 5.91359i | 0.132199 | − | 0.228975i | ||||
\(668\) | −12.3995 | − | 21.4766i | −0.479751 | − | 0.830953i | ||||
\(669\) | 6.24264 | + | 10.8126i | 0.241354 | + | 0.418038i | ||||
\(670\) | 5.91421 | − | 10.2437i | 0.228486 | − | 0.395749i | ||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 2.62132 | − | 0.358719i | 0.101120 | − | 0.0138379i | ||||
\(673\) | −6.68629 | −0.257738 | −0.128869 | − | 0.991662i | \(-0.541135\pi\) | ||||
−0.128869 | + | 0.991662i | \(0.541135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.414214 | − | 0.717439i | −0.0159431 | − | 0.0276142i | ||||
\(676\) | −0.828427 | − | 1.43488i | −0.0318626 | − | 0.0551876i | ||||
\(677\) | 22.8640 | − | 39.6015i | 0.878733 | − | 1.52201i | 0.0260016 | − | 0.999662i | \(-0.491722\pi\) |
0.852732 | − | 0.522349i | \(-0.174944\pi\) | |||||||
\(678\) | −11.7279 | −0.450408 | ||||||||
\(679\) | 2.68629 | + | 3.46410i | 0.103090 | + | 0.132940i | ||||
\(680\) | 12.6569 | 0.485368 | ||||||||
\(681\) | 5.48528 | − | 9.50079i | 0.210196 | − | 0.364071i | ||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | 8.42893 | + | 14.5993i | 0.322524 | + | 0.558628i | 0.981008 | − | 0.193967i | \(-0.0621353\pi\) |
−0.658484 | + | 0.752595i | \(0.728802\pi\) | |||||||
\(684\) | 3.82843 | − | 6.63103i | 0.146384 | − | 0.253544i | ||||
\(685\) | 18.3137 | 0.699731 | ||||||||
\(686\) | −2.13604 | + | 18.3967i | −0.0815543 | + | 0.702388i | ||||
\(687\) | 2.14214 | 0.0817276 | ||||||||
\(688\) | 0.171573 | − | 0.297173i | 0.00654115 | − | 0.0113296i | ||||
\(689\) | −7.79289 | − | 13.4977i | −0.296886 | − | 0.514221i | ||||
\(690\) | −1.20711 | − | 2.09077i | −0.0459538 | − | 0.0795943i | ||||
\(691\) | 6.07107 | − | 10.5154i | 0.230954 | − | 0.400025i | −0.727135 | − | 0.686495i | \(-0.759149\pi\) |
0.958089 | + | 0.286470i | \(0.0924819\pi\) | |||||||
\(692\) | −7.31371 | −0.278025 | ||||||||
\(693\) | 3.24264 | + | 4.18154i | 0.123178 | + | 0.158844i | ||||
\(694\) | 32.6569 | 1.23964 | ||||||||
\(695\) | 11.2426 | − | 19.4728i | 0.426458 | − | 0.738646i | ||||
\(696\) | −3.41421 | − | 5.91359i | −0.129415 | − | 0.224154i | ||||
\(697\) | 13.5563 | + | 23.4803i | 0.513483 | + | 0.889379i | ||||
\(698\) | −12.5711 | + | 21.7737i | −0.475822 | + | 0.824148i | ||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | −2.17157 | + | 0.297173i | −0.0820777 | + | 0.0112321i | ||||
\(701\) | 8.61522 | 0.325393 | 0.162696 | − | 0.986676i | \(-0.447981\pi\) | ||||
0.162696 | + | 0.986676i | \(0.447981\pi\) | |||||||
\(702\) | 1.91421 | − | 3.31552i | 0.0722473 | − | 0.125136i | ||||
\(703\) | −33.7990 | − | 58.5416i | −1.27475 | − | 2.20794i | ||||
\(704\) | −1.00000 | − | 1.73205i | −0.0376889 | − | 0.0652791i | ||||
\(705\) | 10.8640 | − | 18.8169i | 0.409160 | − | 0.708687i | ||||
\(706\) | −2.14214 | −0.0806203 | ||||||||
\(707\) | 8.82843 | − | 21.6251i | 0.332027 | − | 0.813297i | ||||
\(708\) | −9.65685 | −0.362927 | ||||||||
\(709\) | 4.92893 | − | 8.53716i | 0.185110 | − | 0.320620i | −0.758504 | − | 0.651669i | \(-0.774069\pi\) |
0.943614 | + | 0.331049i | \(0.107403\pi\) | |||||||
\(710\) | 5.03553 | + | 8.72180i | 0.188980 | + | 0.327323i | ||||
\(711\) | 5.00000 | + | 8.66025i | 0.187515 | + | 0.324785i | ||||
\(712\) | 3.41421 | − | 5.91359i | 0.127953 | − | 0.221621i | ||||
\(713\) | −2.00000 | −0.0749006 | ||||||||
\(714\) | −5.24264 | + | 12.8418i | −0.196201 | + | 0.480592i | ||||
\(715\) | −18.4853 | −0.691310 | ||||||||
\(716\) | 10.9853 | − | 19.0271i | 0.410539 | − | 0.711075i | ||||
\(717\) | −5.17157 | − | 8.95743i | −0.193136 | − | 0.334521i | ||||
\(718\) | 13.4853 | + | 23.3572i | 0.503266 | + | 0.871683i | ||||
\(719\) | −7.32843 | + | 12.6932i | −0.273304 | + | 0.473377i | −0.969706 | − | 0.244275i | \(-0.921450\pi\) |
0.696402 | + | 0.717652i | \(0.254783\pi\) | |||||||
\(720\) | −2.41421 | −0.0899724 | ||||||||
\(721\) | −28.5711 | + | 3.90986i | −1.06404 | + | 0.145611i | ||||
\(722\) | −39.6274 | −1.47478 | ||||||||
\(723\) | 6.41421 | − | 11.1097i | 0.238547 | − | 0.413176i | ||||
\(724\) | 4.65685 | + | 8.06591i | 0.173071 | + | 0.299767i | ||||
\(725\) | 2.82843 | + | 4.89898i | 0.105045 | + | 0.181944i | ||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | −6.20711 | − | 8.00436i | −0.230051 | − | 0.296661i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.792893 | + | 1.37333i | −0.0293463 | + | 0.0508293i | ||||
\(731\) | 0.899495 | + | 1.55797i | 0.0332690 | + | 0.0576236i | ||||
\(732\) | 1.00000 | + | 1.73205i | 0.0369611 | + | 0.0640184i | ||||
\(733\) | 4.24264 | − | 7.34847i | 0.156706 | − | 0.271422i | −0.776973 | − | 0.629534i | \(-0.783246\pi\) |
0.933679 | + | 0.358112i | \(0.116579\pi\) | |||||||
\(734\) | −26.6985 | −0.985459 | ||||||||
\(735\) | 4.20711 | − | 16.3674i | 0.155181 | − | 0.603722i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 4.89949 | − | 8.48617i | 0.180475 | − | 0.312592i | ||||
\(738\) | −2.58579 | − | 4.47871i | −0.0951841 | − | 0.164864i | ||||
\(739\) | 22.6274 | + | 39.1918i | 0.832363 | + | 1.44169i | 0.896160 | + | 0.443732i | \(0.146346\pi\) |
−0.0637965 | + | 0.997963i | \(0.520321\pi\) | |||||||
\(740\) | −10.6569 | + | 18.4582i | −0.391754 | + | 0.678537i | ||||
\(741\) | −29.3137 | −1.07687 | ||||||||
\(742\) | −6.60051 | − | 8.51167i | −0.242312 | − | 0.312473i | ||||
\(743\) | 15.4558 | 0.567020 | 0.283510 | − | 0.958969i | \(-0.408501\pi\) | ||||
0.283510 | + | 0.958969i | \(0.408501\pi\) | |||||||
\(744\) | −1.00000 | + | 1.73205i | −0.0366618 | + | 0.0635001i | ||||
\(745\) | 11.1569 | + | 19.3242i | 0.408756 | + | 0.707985i | ||||
\(746\) | −0.171573 | − | 0.297173i | −0.00628173 | − | 0.0108803i | ||||
\(747\) | −3.58579 | + | 6.21076i | −0.131197 | + | 0.227240i | ||||
\(748\) | 10.4853 | 0.383380 | ||||||||
\(749\) | 14.8284 | − | 2.02922i | 0.541819 | − | 0.0741462i | ||||
\(750\) | −10.0711 | −0.367743 | ||||||||
\(751\) | −18.7990 | + | 32.5608i | −0.685985 | + | 1.18816i | 0.287141 | + | 0.957888i | \(0.407295\pi\) |
−0.973126 | + | 0.230272i | \(0.926038\pi\) | |||||||
\(752\) | −4.50000 | − | 7.79423i | −0.164098 | − | 0.284226i | ||||
\(753\) | −8.65685 | − | 14.9941i | −0.315473 | − | 0.546416i | ||||
\(754\) | −13.0711 | + | 22.6398i | −0.476020 | + | 0.824491i | ||||
\(755\) | 34.1421 | 1.24256 | ||||||||
\(756\) | 1.00000 | − | 2.44949i | 0.0363696 | − | 0.0890871i | ||||
\(757\) | 28.9706 | 1.05295 | 0.526477 | − | 0.850190i | \(-0.323513\pi\) | ||||
0.526477 | + | 0.850190i | \(0.323513\pi\) | |||||||
\(758\) | −9.44975 | + | 16.3674i | −0.343230 | + | 0.594492i | ||||
\(759\) | −1.00000 | − | 1.73205i | −0.0362977 | − | 0.0628695i | ||||
\(760\) | 9.24264 | + | 16.0087i | 0.335266 | + | 0.580697i | ||||
\(761\) | 10.8284 | − | 18.7554i | 0.392530 | − | 0.679882i | −0.600252 | − | 0.799811i | \(-0.704933\pi\) |
0.992783 | + | 0.119928i | \(0.0382665\pi\) | |||||||
\(762\) | 0.828427 | 0.0300107 | ||||||||
\(763\) | 9.17157 | − | 22.4657i | 0.332033 | − | 0.813312i | ||||
\(764\) | −5.17157 | −0.187101 | ||||||||
\(765\) | 6.32843 | − | 10.9612i | 0.228805 | − | 0.396301i | ||||
\(766\) | 1.82843 | + | 3.16693i | 0.0660638 | + | 0.114426i | ||||
\(767\) | 18.4853 | + | 32.0174i | 0.667465 | + | 1.15608i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 33.3137 | 1.20132 | 0.600662 | − | 0.799503i | \(-0.294904\pi\) | ||||
0.600662 | + | 0.799503i | \(0.294904\pi\) | |||||||
\(770\) | −12.6569 | + | 1.73205i | −0.456121 | + | 0.0624188i | ||||
\(771\) | 5.51472 | 0.198608 | ||||||||
\(772\) | 2.74264 | − | 4.75039i | 0.0987098 | − | 0.170970i | ||||
\(773\) | 0.378680 | + | 0.655892i | 0.0136202 | + | 0.0235908i | 0.872755 | − | 0.488158i | \(-0.162331\pi\) |
−0.859135 | + | 0.511749i | \(0.828998\pi\) | |||||||
\(774\) | −0.171573 | − | 0.297173i | −0.00616706 | − | 0.0106817i | ||||
\(775\) | 0.828427 | − | 1.43488i | 0.0297580 | − | 0.0515423i | ||||
\(776\) | −1.65685 | −0.0594776 | ||||||||
\(777\) | −14.3137 | − | 18.4582i | −0.513501 | − | 0.662185i | ||||
\(778\) | 37.4558 | 1.34286 | ||||||||
\(779\) | −19.7990 | + | 34.2929i | −0.709372 | + | 1.22867i | ||||
\(780\) | 4.62132 | + | 8.00436i | 0.165470 | + | 0.286602i | ||||
\(781\) | 4.17157 | + | 7.22538i | 0.149271 | + | 0.258544i | ||||
\(782\) | 2.62132 | − | 4.54026i | 0.0937382 | − | 0.162359i | ||||
\(783\) | −6.82843 | −0.244028 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | 37.7990 | 1.34910 | ||||||||
\(786\) | −4.57107 | + | 7.91732i | −0.163045 | + | 0.282402i | ||||
\(787\) | 18.5208 | + | 32.0790i | 0.660196 | + | 1.14349i | 0.980564 | + | 0.196200i | \(0.0628600\pi\) |
−0.320368 | + | 0.947293i | \(0.603807\pi\) | |||||||
\(788\) | 6.41421 | + | 11.1097i | 0.228497 | + | 0.395768i | ||||
\(789\) | −9.65685 | + | 16.7262i | −0.343793 | + | 0.595467i | ||||
\(790\) | −24.1421 | −0.858939 | ||||||||
\(791\) | 19.0147 | + | 24.5204i | 0.676086 | + | 0.871845i | ||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | 3.82843 | − | 6.63103i | 0.135951 | − | 0.235475i | ||||
\(794\) | −4.32843 | − | 7.49706i | −0.153610 | − | 0.266061i | ||||
\(795\) | 4.91421 | + | 8.51167i | 0.174289 | + | 0.301878i | ||||
\(796\) | 13.8284 | − | 23.9515i | 0.490136 | − | 0.848940i | ||||
\(797\) | −39.8701 | −1.41227 | −0.706135 | − | 0.708077i | \(-0.749563\pi\) | ||||
−0.706135 | + | 0.708077i | \(0.749563\pi\) | |||||||
\(798\) | −20.0711 | + | 2.74666i | −0.710508 | + | 0.0972308i | ||||
\(799\) | 47.1838 | 1.66924 | ||||||||
\(800\) | 0.414214 | − | 0.717439i | 0.0146447 | − | 0.0253653i | ||||
\(801\) | −3.41421 | − | 5.91359i | −0.120635 | − | 0.208946i | ||||
\(802\) | −16.3492 | − | 28.3177i | −0.577312 | − | 0.999933i | ||||
\(803\) | −0.656854 | + | 1.13770i | −0.0231799 | + | 0.0401487i | ||||
\(804\) | −4.89949 | −0.172792 | ||||||||
\(805\) | −2.41421 | + | 5.91359i | −0.0850898 | + | 0.208427i | ||||
\(806\) | 7.65685 | 0.269701 | ||||||||
\(807\) | 6.00000 | − | 10.3923i | 0.211210 | − | 0.365826i | ||||
\(808\) | 4.41421 | + | 7.64564i | 0.155291 | + | 0.268973i | ||||
\(809\) | 12.0711 | + | 20.9077i | 0.424396 | + | 0.735076i | 0.996364 | − | 0.0852005i | \(-0.0271531\pi\) |
−0.571968 | + | 0.820276i | \(0.693820\pi\) | |||||||
\(810\) | −1.20711 | + | 2.09077i | −0.0424134 | + | 0.0734622i | ||||
\(811\) | 21.1127 | 0.741367 | 0.370684 | − | 0.928759i | \(-0.379123\pi\) | ||||
0.370684 | + | 0.928759i | \(0.379123\pi\) | |||||||
\(812\) | −6.82843 | + | 16.7262i | −0.239631 | + | 0.586973i | ||||
\(813\) | −30.2843 | −1.06212 | ||||||||
\(814\) | −8.82843 | + | 15.2913i | −0.309436 | + | 0.535959i | ||||
\(815\) | 2.00000 | + | 3.46410i | 0.0700569 | + | 0.121342i | ||||
\(816\) | −2.62132 | − | 4.54026i | −0.0917646 | − | 0.158941i | ||||
\(817\) | −1.31371 | + | 2.27541i | −0.0459608 | + | 0.0796065i | ||||
\(818\) | 26.7990 | 0.937005 | ||||||||
\(819\) | −10.0355 | + | 1.37333i | −0.350670 | + | 0.0479881i | ||||
\(820\) | 12.4853 | 0.436005 | ||||||||
\(821\) | 1.14214 | − | 1.97824i | 0.0398608 | − | 0.0690409i | −0.845407 | − | 0.534123i | \(-0.820642\pi\) |
0.885268 | + | 0.465082i | \(0.153975\pi\) | |||||||
\(822\) | −3.79289 | − | 6.56948i | −0.132292 | − | 0.229137i | ||||
\(823\) | 6.89949 | + | 11.9503i | 0.240501 | + | 0.416560i | 0.960857 | − | 0.277044i | \(-0.0893548\pi\) |
−0.720356 | + | 0.693605i | \(0.756022\pi\) | |||||||
\(824\) | 5.44975 | − | 9.43924i | 0.189851 | − | 0.328831i | ||||
\(825\) | 1.65685 | 0.0576843 | ||||||||
\(826\) | 15.6569 | + | 20.1903i | 0.544772 | + | 0.702509i | ||||
\(827\) | −42.6274 | −1.48230 | −0.741150 | − | 0.671339i | \(-0.765719\pi\) | ||||
−0.741150 | + | 0.671339i | \(0.765719\pi\) | |||||||
\(828\) | −0.500000 | + | 0.866025i | −0.0173762 | + | 0.0300965i | ||||
\(829\) | −8.08579 | − | 14.0050i | −0.280831 | − | 0.486414i | 0.690759 | − | 0.723085i | \(-0.257277\pi\) |
−0.971590 | + | 0.236672i | \(0.923943\pi\) | |||||||
\(830\) | −8.65685 | − | 14.9941i | −0.300484 | − | 0.520453i | ||||
\(831\) | −12.6421 | + | 21.8968i | −0.438551 | + | 0.759592i | ||||
\(832\) | 3.82843 | 0.132727 | ||||||||
\(833\) | 35.3492 | − | 9.85951i | 1.22478 | − | 0.341612i | ||||
\(834\) | −9.31371 | −0.322507 | ||||||||
\(835\) | 29.9350 | − | 51.8490i | 1.03594 | − | 1.79431i | ||||
\(836\) | 7.65685 | + | 13.2621i | 0.264818 | + | 0.458678i | ||||
\(837\) | 1.00000 | + | 1.73205i | 0.0345651 | + | 0.0598684i | ||||
\(838\) | 3.75736 | − | 6.50794i | 0.129796 | − | 0.224813i | ||||
\(839\) | 24.9706 | 0.862080 | 0.431040 | − | 0.902333i | \(-0.358147\pi\) | ||||
0.431040 | + | 0.902333i | \(0.358147\pi\) | |||||||
\(840\) | 3.91421 | + | 5.04757i | 0.135053 | + | 0.174158i | ||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | −3.65685 | + | 6.33386i | −0.126024 | + | 0.218279i | ||||
\(843\) | 6.79289 | + | 11.7656i | 0.233960 | + | 0.405230i | ||||
\(844\) | 5.58579 | + | 9.67487i | 0.192271 | + | 0.333023i | ||||
\(845\) | 2.00000 | − | 3.46410i | 0.0688021 | − | 0.119169i | ||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 18.3492 | − | 2.51104i | 0.630487 | − | 0.0862802i | ||||
\(848\) | 4.07107 | 0.139801 | ||||||||
\(849\) | 14.6924 | − | 25.4480i | 0.504241 | − | 0.873372i | ||||
\(850\) | 2.17157 | + | 3.76127i | 0.0744843 | + | 0.129011i | ||||
\(851\) | 4.41421 | + | 7.64564i | 0.151317 | + | 0.262089i | ||||
\(852\) | 2.08579 | − | 3.61269i | 0.0714579 | − | 0.123769i | ||||
\(853\) | −52.9117 | −1.81166 | −0.905831 | − | 0.423640i | \(-0.860752\pi\) | ||||
−0.905831 | + | 0.423640i | \(0.860752\pi\) | |||||||
\(854\) | 2.00000 | − | 4.89898i | 0.0684386 | − | 0.167640i | ||||
\(855\) | 18.4853 | 0.632183 | ||||||||
\(856\) | −2.82843 | + | 4.89898i | −0.0966736 | + | 0.167444i | ||||
\(857\) | 0.313708 | + | 0.543359i | 0.0107161 | + | 0.0185608i | 0.871334 | − | 0.490691i | \(-0.163256\pi\) |
−0.860618 | + | 0.509252i | \(0.829922\pi\) | |||||||
\(858\) | 3.82843 | + | 6.63103i | 0.130700 | + | 0.226380i | ||||
\(859\) | 17.6569 | − | 30.5826i | 0.602444 | − | 1.04346i | −0.390006 | − | 0.920812i | \(-0.627527\pi\) |
0.992450 | − | 0.122651i | \(-0.0391397\pi\) | |||||||
\(860\) | 0.828427 | 0.0282491 | ||||||||
\(861\) | −5.17157 | + | 12.6677i | −0.176247 | + | 0.431715i | ||||
\(862\) | 27.3137 | 0.930309 | ||||||||
\(863\) | −21.3284 | + | 36.9419i | −0.726028 | + | 1.25752i | 0.232521 | + | 0.972591i | \(0.425302\pi\) |
−0.958549 | + | 0.284926i | \(0.908031\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −8.82843 | − | 15.2913i | −0.300176 | − | 0.519919i | ||||
\(866\) | −7.00000 | + | 12.1244i | −0.237870 | + | 0.412002i | ||||
\(867\) | 10.4853 | 0.356099 | ||||||||
\(868\) | 5.24264 | − | 0.717439i | 0.177947 | − | 0.0243515i | ||||
\(869\) | −20.0000 | −0.678454 | ||||||||
\(870\) | 8.24264 | − | 14.2767i | 0.279452 | − | 0.484025i | ||||
\(871\) | 9.37868 | + | 16.2443i | 0.317784 | + | 0.550419i | ||||
\(872\) | 4.58579 | + | 7.94282i | 0.155294 | + | 0.268978i | ||||
\(873\) | −0.828427 | + | 1.43488i | −0.0280380 | + | 0.0485633i | ||||
\(874\) | 7.65685 | 0.258997 | ||||||||
\(875\) | 16.3284 | + | 21.0563i | 0.552002 | + | 0.711832i | ||||
\(876\) | 0.656854 | 0.0221930 | ||||||||
\(877\) | 8.84315 | − | 15.3168i | 0.298612 | − | 0.517211i | −0.677207 | − | 0.735793i | \(-0.736810\pi\) |
0.975819 | + | 0.218582i | \(0.0701431\pi\) | |||||||
\(878\) | 15.4853 | + | 26.8213i | 0.522603 | + | 0.905175i | ||||
\(879\) | 1.79289 | + | 3.10538i | 0.0604728 | + | 0.104742i | ||||
\(880\) | 2.41421 | − | 4.18154i | 0.0813831 | − | 0.140960i | ||||
\(881\) | −6.27208 | −0.211312 | −0.105656 | − | 0.994403i | \(-0.533694\pi\) | ||||
−0.105656 | + | 0.994403i | \(0.533694\pi\) | |||||||
\(882\) | −6.74264 | + | 1.88064i | −0.227037 | + | 0.0633244i | ||||
\(883\) | −44.2843 | −1.49028 | −0.745142 | − | 0.666906i | \(-0.767618\pi\) | ||||
−0.745142 | + | 0.666906i | \(0.767618\pi\) | |||||||
\(884\) | −10.0355 | + | 17.3821i | −0.337532 | + | 0.584622i | ||||
\(885\) | −11.6569 | − | 20.1903i | −0.391841 | − | 0.678688i | ||||
\(886\) | 5.57107 | + | 9.64937i | 0.187164 | + | 0.324177i | ||||
\(887\) | −20.4853 | + | 35.4815i | −0.687828 | + | 1.19135i | 0.284711 | + | 0.958614i | \(0.408103\pi\) |
−0.972539 | + | 0.232740i | \(0.925231\pi\) | |||||||
\(888\) | 8.82843 | 0.296263 | ||||||||
\(889\) | −1.34315 | − | 1.73205i | −0.0450477 | − | 0.0580911i | ||||
\(890\) | 16.4853 | 0.552588 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 6.24264 | + | 10.8126i | 0.209019 | + | 0.362032i | ||||
\(893\) | 34.4558 | + | 59.6793i | 1.15302 | + | 1.99709i | ||||
\(894\) | 4.62132 | − | 8.00436i | 0.154560 | − | 0.267706i | ||||
\(895\) | 53.0416 | 1.77299 | ||||||||
\(896\) | 2.62132 | − | 0.358719i | 0.0875722 | − | 0.0119840i | ||||
\(897\) | 3.82843 | 0.127827 | ||||||||
\(898\) | 4.75736 | − | 8.23999i | 0.158755 | − | 0.274972i | ||||
\(899\) | −6.82843 | − | 11.8272i | −0.227741 | − | 0.394459i | ||||
\(900\) | −0.414214 | − | 0.717439i | −0.0138071 | − | 0.0239146i | ||||
\(901\) | −10.6716 | + | 18.4837i | −0.355522 | + | 0.615782i | ||||
\(902\) | 10.3431 | 0.344389 | ||||||||
\(903\) | −0.343146 | + | 0.840532i | −0.0114192 | + | 0.0279712i | ||||
\(904\) | −11.7279 | −0.390065 | ||||||||
\(905\) | −11.2426 | + | 19.4728i | −0.373718 | + | 0.647299i | ||||
\(906\) | −7.07107 | − | 12.2474i | −0.234920 | − | 0.406894i | ||||
\(907\) | −21.4497 | − | 37.1521i | −0.712227 | − | 1.23361i | −0.964019 | − | 0.265832i | \(-0.914353\pi\) |
0.251792 | − | 0.967781i | \(-0.418980\pi\) | |||||||
\(908\) | 5.48528 | − | 9.50079i | 0.182035 | − | 0.315295i | ||||
\(909\) | 8.82843 | 0.292820 | ||||||||
\(910\) | 9.24264 | − | 22.6398i | 0.306391 | − | 0.750501i | ||||
\(911\) | 8.48528 | 0.281130 | 0.140565 | − | 0.990071i | \(-0.455108\pi\) | ||||
0.140565 | + | 0.990071i | \(0.455108\pi\) | |||||||
\(912\) | 3.82843 | − | 6.63103i | 0.126772 | − | 0.219575i | ||||
\(913\) | −7.17157 | − | 12.4215i | −0.237344 | − | 0.411093i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.41421 | + | 4.18154i | −0.0798114 | + | 0.138237i | ||||
\(916\) | 2.14214 | 0.0707782 | ||||||||
\(917\) | 23.9645 | − | 3.27946i | 0.791376 | − | 0.108297i | ||||
\(918\) | −5.24264 | −0.173033 | ||||||||
\(919\) | 11.8640 | − | 20.5490i | 0.391356 | − | 0.677848i | −0.601273 | − | 0.799044i | \(-0.705339\pi\) |
0.992629 | + | 0.121195i | \(0.0386728\pi\) | |||||||
\(920\) | −1.20711 | − | 2.09077i | −0.0397971 | − | 0.0689307i | ||||
\(921\) | 7.07107 | + | 12.2474i | 0.233000 | + | 0.403567i | ||||
\(922\) | 7.00000 | − | 12.1244i | 0.230533 | − | 0.399294i | ||||
\(923\) | −15.9706 | −0.525677 | ||||||||
\(924\) | 3.24264 | + | 4.18154i | 0.106675 | + | 0.137563i | ||||
\(925\) | −7.31371 | −0.240473 | ||||||||
\(926\) | −17.3137 | + | 29.9882i | −0.568964 | + | 0.985474i | ||||
\(927\) | −5.44975 | − | 9.43924i | −0.178993 | − | 0.310025i | ||||
\(928\) | −3.41421 | − | 5.91359i | −0.112077 | − | 0.194123i | ||||
\(929\) | 2.68629 | − | 4.65279i | 0.0881344 | − | 0.152653i | −0.818588 | − | 0.574381i | \(-0.805243\pi\) |
0.906723 | + | 0.421728i | \(0.138576\pi\) | |||||||
\(930\) | −4.82843 | −0.158330 | ||||||||
\(931\) | 38.2843 | + | 37.5108i | 1.25472 | + | 1.22937i | ||||
\(932\) | −8.00000 | −0.262049 | ||||||||
\(933\) | 8.15685 | − | 14.1281i | 0.267043 | − | 0.462533i | ||||
\(934\) | 10.8284 | + | 18.7554i | 0.354317 | + | 0.613695i | ||||
\(935\) | 12.6569 | + | 21.9223i | 0.413923 | + | 0.716936i | ||||
\(936\) | 1.91421 | − | 3.31552i | 0.0625680 | − | 0.108371i | ||||
\(937\) | 4.48528 | 0.146528 | 0.0732639 | − | 0.997313i | \(-0.476658\pi\) | ||||
0.0732639 | + | 0.997313i | \(0.476658\pi\) | |||||||
\(938\) | 7.94365 | + | 10.2437i | 0.259369 | + | 0.334469i | ||||
\(939\) | 32.9706 | 1.07595 | ||||||||
\(940\) | 10.8640 | − | 18.8169i | 0.354343 | − | 0.613741i | ||||
\(941\) | −15.7574 | − | 27.2925i | −0.513675 | − | 0.889712i | −0.999874 | − | 0.0158634i | \(-0.994950\pi\) |
0.486199 | − | 0.873848i | \(-0.338383\pi\) | |||||||
\(942\) | −7.82843 | − | 13.5592i | −0.255064 | − | 0.441784i | ||||
\(943\) | 2.58579 | − | 4.47871i | 0.0842048 | − | 0.145847i | ||||
\(944\) | −9.65685 | −0.314304 | ||||||||
\(945\) | 6.32843 | − | 0.866025i | 0.205864 | − | 0.0281718i | ||||
\(946\) | 0.686292 | 0.0223133 | ||||||||
\(947\) | 5.84315 | − | 10.1206i | 0.189877 | − | 0.328876i | −0.755332 | − | 0.655342i | \(-0.772524\pi\) |
0.945209 | + | 0.326466i | \(0.105858\pi\) | |||||||
\(948\) | 5.00000 | + | 8.66025i | 0.162392 | + | 0.281272i | ||||
\(949\) | −1.25736 | − | 2.17781i | −0.0408156 | − | 0.0706947i | ||||
\(950\) | −3.17157 | + | 5.49333i | −0.102899 | + | 0.178227i | ||||
\(951\) | −32.6274 | −1.05802 | ||||||||
\(952\) | −5.24264 | + | 12.8418i | −0.169915 | + | 0.416205i | ||||
\(953\) | 11.7990 | 0.382207 | 0.191103 | − | 0.981570i | \(-0.438793\pi\) | ||||
0.191103 | + | 0.981570i | \(0.438793\pi\) | |||||||
\(954\) | 2.03553 | − | 3.52565i | 0.0659028 | − | 0.114147i | ||||
\(955\) | −6.24264 | − | 10.8126i | −0.202007 | − | 0.349887i | ||||
\(956\) | −5.17157 | − | 8.95743i | −0.167261 | − | 0.289704i | ||||
\(957\) | 6.82843 | − | 11.8272i | 0.220732 | − | 0.382319i | ||||
\(958\) | −5.85786 | −0.189259 | ||||||||
\(959\) | −7.58579 | + | 18.5813i | −0.244958 | + | 0.600022i | ||||
\(960\) | −2.41421 | −0.0779184 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | −16.8995 | − | 29.2708i | −0.544862 | − | 0.943728i | ||||
\(963\) | 2.82843 | + | 4.89898i | 0.0911448 | + | 0.157867i | ||||
\(964\) | 6.41421 | − | 11.1097i | 0.206588 | − | 0.357821i | ||||
\(965\) | 13.2426 | 0.426296 | ||||||||
\(966\) | 2.62132 | − | 0.358719i | 0.0843396 | − | 0.0115416i | ||||
\(967\) | −10.8284 | −0.348219 | −0.174109 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174109 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(968\) | −3.50000 | + | 6.06218i | −0.112494 | + | 0.194846i | ||||
\(969\) | 20.0711 | + | 34.7641i | 0.644776 | + | 1.11678i | ||||
\(970\) | −2.00000 | − | 3.46410i | −0.0642161 | − | 0.111226i | ||||
\(971\) | −6.82843 | + | 11.8272i | −0.219135 | + | 0.379552i | −0.954544 | − | 0.298071i | \(-0.903657\pi\) |
0.735409 | + | 0.677623i | \(0.236990\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 15.1005 | + | 19.4728i | 0.484100 | + | 0.624270i | ||||
\(974\) | −40.7696 | −1.30634 | ||||||||
\(975\) | −1.58579 | + | 2.74666i | −0.0507858 | + | 0.0879636i | ||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | −12.1777 | − | 21.0923i | −0.389598 | − | 0.674804i | 0.602797 | − | 0.797894i | \(-0.294053\pi\) |
−0.992395 | + | 0.123091i | \(0.960719\pi\) | |||||||
\(978\) | 0.828427 | − | 1.43488i | 0.0264902 | − | 0.0458823i | ||||
\(979\) | 13.6569 | 0.436475 | ||||||||
\(980\) | 4.20711 | − | 16.3674i | 0.134391 | − | 0.522839i | ||||
\(981\) | 9.17157 | 0.292826 | ||||||||
\(982\) | −11.3284 | + | 19.6214i | −0.361505 | + | 0.626144i | ||||
\(983\) | −0.272078 | − | 0.471253i | −0.00867794 | − | 0.0150306i | 0.861654 | − | 0.507496i | \(-0.169429\pi\) |
−0.870332 | + | 0.492466i | \(0.836096\pi\) | |||||||
\(984\) | −2.58579 | − | 4.47871i | −0.0824319 | − | 0.142776i | ||||
\(985\) | −15.4853 | + | 26.8213i | −0.493402 | + | 0.854597i | ||||
\(986\) | 35.7990 | 1.14007 | ||||||||
\(987\) | 14.5919 | + | 18.8169i | 0.464465 | + | 0.598950i | ||||
\(988\) | −29.3137 | −0.932593 | ||||||||
\(989\) | 0.171573 | − | 0.297173i | 0.00545570 | − | 0.00944955i | ||||
\(990\) | −2.41421 | − | 4.18154i | −0.0767287 | − | 0.132898i | ||||
\(991\) | −9.97056 | − | 17.2695i | −0.316725 | − | 0.548584i | 0.663077 | − | 0.748551i | \(-0.269250\pi\) |
−0.979803 | + | 0.199966i | \(0.935917\pi\) | |||||||
\(992\) | −1.00000 | + | 1.73205i | −0.0317500 | + | 0.0549927i | ||||
\(993\) | −34.4853 | −1.09436 | ||||||||
\(994\) | −10.9350 | + | 1.49642i | −0.346838 | + | 0.0474637i | ||||
\(995\) | 66.7696 | 2.11674 | ||||||||
\(996\) | −3.58579 | + | 6.21076i | −0.113620 | + | 0.196796i | ||||
\(997\) | 12.3137 | + | 21.3280i | 0.389979 | + | 0.675464i | 0.992446 | − | 0.122680i | \(-0.0391489\pi\) |
−0.602467 | + | 0.798144i | \(0.705816\pi\) | |||||||
\(998\) | 3.41421 | + | 5.91359i | 0.108075 | + | 0.187191i | ||||
\(999\) | 4.41421 | − | 7.64564i | 0.139660 | − | 0.241897i |
(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.j.415.2 | yes | 4 | |
7.2 | even | 3 | 6762.2.a.bv.1.1 | 2 | |||
7.4 | even | 3 | inner | 966.2.i.j.277.2 | ✓ | 4 | |
7.5 | odd | 6 | 6762.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.j.277.2 | ✓ | 4 | 7.4 | even | 3 | inner | |
966.2.i.j.415.2 | yes | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.bt.1.2 | 2 | 7.5 | odd | 6 | |||
6762.2.a.bv.1.1 | 2 | 7.2 | even | 3 |