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 | 277.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.j.415.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | −0.207107 | − | 0.358719i | −0.0926210 | − | 0.160424i | 0.815992 | − | 0.578063i | \(-0.196191\pi\) |
−0.908613 | + | 0.417639i | \(0.862858\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.62132 | + | 0.358719i | −0.990766 | + | 0.135583i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.207107 | − | 0.358719i | 0.0654929 | − | 0.113437i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | −1.62132 | − | 2.09077i | −0.433316 | − | 0.558782i | ||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.62132 | − | 2.80821i | 0.393228 | − | 0.681091i | −0.599645 | − | 0.800266i | \(-0.704692\pi\) |
0.992873 | + | 0.119175i | \(0.0380250\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −1.82843 | − | 3.16693i | −0.419470 | − | 0.726543i | 0.576416 | − | 0.817156i | \(-0.304451\pi\) |
−0.995886 | + | 0.0906130i | \(0.971117\pi\) | |||||||
\(20\) | 0.414214 | 0.0926210 | ||||||||
\(21\) | 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 | ||||
\(25\) | 2.41421 | − | 4.18154i | 0.482843 | − | 0.836308i | ||||
\(26\) | −0.914214 | − | 1.58346i | −0.179292 | − | 0.310543i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | 0.207107 | + | 0.358719i | 0.0378124 | + | 0.0654929i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 3.24264 | 0.556108 | ||||||||
\(35\) | 0.671573 | + | 0.866025i | 0.113517 | + | 0.146385i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.58579 | + | 2.74666i | 0.260702 | + | 0.451549i | 0.966429 | − | 0.256935i | \(-0.0827128\pi\) |
−0.705727 | + | 0.708484i | \(0.749379\pi\) | |||||||
\(38\) | 1.82843 | − | 3.16693i | 0.296610 | − | 0.513744i | ||||
\(39\) | 0.914214 | − | 1.58346i | 0.146391 | − | 0.253557i | ||||
\(40\) | 0.207107 | + | 0.358719i | 0.0327465 | + | 0.0567185i | ||||
\(41\) | −10.8284 | −1.69112 | −0.845558 | − | 0.533883i | \(-0.820732\pi\) | ||||
−0.845558 | + | 0.533883i | \(0.820732\pi\) | |||||||
\(42\) | 2.62132 | − | 0.358719i | 0.404479 | − | 0.0553516i | ||||
\(43\) | −11.6569 | −1.77765 | −0.888827 | − | 0.458243i | \(-0.848479\pi\) | ||||
−0.888827 | + | 0.458243i | \(0.848479\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | −0.207107 | + | 0.358719i | −0.0308737 | + | 0.0534747i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 4.82843 | 0.682843 | ||||||||
\(51\) | 1.62132 | + | 2.80821i | 0.227030 | + | 0.393228i | ||||
\(52\) | 0.914214 | − | 1.58346i | 0.126779 | − | 0.219587i | ||||
\(53\) | 5.03553 | − | 8.72180i | 0.691684 | − | 1.19803i | −0.279602 | − | 0.960116i | \(-0.590203\pi\) |
0.971286 | − | 0.237915i | \(-0.0764641\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0.828427 | 0.111705 | ||||||||
\(56\) | 2.62132 | − | 0.358719i | 0.350289 | − | 0.0479359i | ||||
\(57\) | 3.65685 | 0.484362 | ||||||||
\(58\) | −0.585786 | − | 1.01461i | −0.0769175 | − | 0.133225i | ||||
\(59\) | −0.828427 | + | 1.43488i | −0.107852 | + | 0.186805i | −0.914900 | − | 0.403681i | \(-0.867731\pi\) |
0.807048 | + | 0.590486i | \(0.201064\pi\) | |||||||
\(60\) | −0.207107 | + | 0.358719i | −0.0267374 | + | 0.0463105i | ||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 1.62132 | + | 2.09077i | 0.204267 | + | 0.263412i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.378680 | + | 0.655892i | 0.0469694 | + | 0.0813534i | ||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | −7.44975 | + | 12.9033i | −0.910132 | + | 1.57639i | −0.0962546 | + | 0.995357i | \(0.530686\pi\) |
−0.813877 | + | 0.581037i | \(0.802647\pi\) | |||||||
\(68\) | 1.62132 | + | 2.80821i | 0.196614 | + | 0.340545i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −0.414214 | + | 1.01461i | −0.0495080 | + | 0.121269i | ||||
\(71\) | −9.82843 | −1.16642 | −0.583210 | − | 0.812322i | \(-0.698203\pi\) | ||||
−0.583210 | + | 0.812322i | \(0.698203\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 5.32843 | − | 9.22911i | 0.623645 | − | 1.08019i | −0.365156 | − | 0.930946i | \(-0.618984\pi\) |
0.988801 | − | 0.149239i | \(-0.0476823\pi\) | |||||||
\(74\) | −1.58579 | + | 2.74666i | −0.184344 | + | 0.319293i | ||||
\(75\) | 2.41421 | + | 4.18154i | 0.278769 | + | 0.482843i | ||||
\(76\) | 3.65685 | 0.419470 | ||||||||
\(77\) | 2.00000 | − | 4.89898i | 0.227921 | − | 0.558291i | ||||
\(78\) | 1.82843 | 0.207029 | ||||||||
\(79\) | 5.00000 | + | 8.66025i | 0.562544 | + | 0.974355i | 0.997274 | + | 0.0737937i | \(0.0235106\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | −0.207107 | + | 0.358719i | −0.0231552 | + | 0.0401061i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −5.41421 | − | 9.37769i | −0.597900 | − | 1.03559i | ||||
\(83\) | 12.8284 | 1.40810 | 0.704051 | − | 0.710149i | \(-0.251372\pi\) | ||||
0.704051 | + | 0.710149i | \(0.251372\pi\) | |||||||
\(84\) | 1.62132 | + | 2.09077i | 0.176901 | + | 0.228122i | ||||
\(85\) | −1.34315 | −0.145685 | ||||||||
\(86\) | −5.82843 | − | 10.0951i | −0.628495 | − | 1.08859i | ||||
\(87\) | 0.585786 | − | 1.01461i | 0.0628029 | − | 0.108778i | ||||
\(88\) | 1.00000 | − | 1.73205i | 0.106600 | − | 0.184637i | ||||
\(89\) | −0.585786 | − | 1.01461i | −0.0620932 | − | 0.107549i | 0.833308 | − | 0.552809i | \(-0.186444\pi\) |
−0.895401 | + | 0.445261i | \(0.853111\pi\) | |||||||
\(90\) | −0.414214 | −0.0436619 | ||||||||
\(91\) | 4.79289 | − | 0.655892i | 0.502432 | − | 0.0687562i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | 4.50000 | − | 7.79423i | 0.464140 | − | 0.803913i | ||||
\(95\) | −0.757359 | + | 1.31178i | −0.0777034 | + | 0.134586i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −9.65685 | −0.980505 | −0.490252 | − | 0.871580i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871580i | \(0.663095\pi\) | |||||||
\(98\) | 5.00000 | + | 4.89898i | 0.505076 | + | 0.494872i | ||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 2.41421 | + | 4.18154i | 0.241421 | + | 0.418154i | ||||
\(101\) | −1.58579 | + | 2.74666i | −0.157792 | + | 0.273303i | −0.934072 | − | 0.357085i | \(-0.883771\pi\) |
0.776280 | + | 0.630388i | \(0.217104\pi\) | |||||||
\(102\) | −1.62132 | + | 2.80821i | −0.160535 | + | 0.278054i | ||||
\(103\) | 4.44975 | + | 7.70719i | 0.438447 | + | 0.759412i | 0.997570 | − | 0.0696727i | \(-0.0221955\pi\) |
−0.559123 | + | 0.829085i | \(0.688862\pi\) | |||||||
\(104\) | 1.82843 | 0.179292 | ||||||||
\(105\) | −1.08579 | + | 0.148586i | −0.105962 | + | 0.0145006i | ||||
\(106\) | 10.0711 | 0.978189 | ||||||||
\(107\) | −2.82843 | − | 4.89898i | −0.273434 | − | 0.473602i | 0.696305 | − | 0.717746i | \(-0.254826\pi\) |
−0.969739 | + | 0.244144i | \(0.921493\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −7.41421 | + | 12.8418i | −0.710153 | + | 1.23002i | 0.254647 | + | 0.967034i | \(0.418041\pi\) |
−0.964799 | + | 0.262987i | \(0.915292\pi\) | |||||||
\(110\) | 0.414214 | + | 0.717439i | 0.0394937 | + | 0.0684051i | ||||
\(111\) | −3.17157 | −0.301032 | ||||||||
\(112\) | 1.62132 | + | 2.09077i | 0.153200 | + | 0.197559i | ||||
\(113\) | −13.7279 | −1.29141 | −0.645707 | − | 0.763585i | \(-0.723437\pi\) | ||||
−0.645707 | + | 0.763585i | \(0.723437\pi\) | |||||||
\(114\) | 1.82843 | + | 3.16693i | 0.171248 | + | 0.296610i | ||||
\(115\) | −0.207107 | + | 0.358719i | −0.0193128 | + | 0.0334508i | ||||
\(116\) | 0.585786 | − | 1.01461i | 0.0543889 | − | 0.0942043i | ||||
\(117\) | 0.914214 | + | 1.58346i | 0.0845191 | + | 0.146391i | ||||
\(118\) | −1.65685 | −0.152526 | ||||||||
\(119\) | −3.24264 | + | 7.94282i | −0.297252 | + | 0.728117i | ||||
\(120\) | −0.414214 | −0.0378124 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −1.00000 | + | 1.73205i | −0.0905357 | + | 0.156813i | ||||
\(123\) | 5.41421 | − | 9.37769i | 0.488183 | − | 0.845558i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | −4.07107 | −0.364127 | ||||||||
\(126\) | −1.00000 | + | 2.44949i | −0.0890871 | + | 0.218218i | ||||
\(127\) | 4.82843 | 0.428454 | 0.214227 | − | 0.976784i | \(-0.431277\pi\) | ||||
0.214227 | + | 0.976784i | \(0.431277\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.82843 | − | 10.0951i | 0.513164 | − | 0.888827i | ||||
\(130\) | −0.378680 | + | 0.655892i | −0.0332124 | + | 0.0575256i | ||||
\(131\) | −9.57107 | − | 16.5776i | −0.836228 | − | 1.44839i | −0.893027 | − | 0.450004i | \(-0.851423\pi\) |
0.0567985 | − | 0.998386i | \(-0.481911\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | 5.92893 | + | 7.64564i | 0.514104 | + | 0.662961i | ||||
\(134\) | −14.8995 | −1.28712 | ||||||||
\(135\) | −0.207107 | − | 0.358719i | −0.0178249 | − | 0.0308737i | ||||
\(136\) | −1.62132 | + | 2.80821i | −0.139027 | + | 0.240802i | ||||
\(137\) | 5.20711 | − | 9.01897i | 0.444873 | − | 0.770543i | −0.553170 | − | 0.833068i | \(-0.686582\pi\) |
0.998043 | + | 0.0625253i | \(0.0199154\pi\) | |||||||
\(138\) | 0.500000 | + | 0.866025i | 0.0425628 | + | 0.0737210i | ||||
\(139\) | −13.3137 | −1.12925 | −0.564627 | − | 0.825346i | \(-0.690980\pi\) | ||||
−0.564627 | + | 0.825346i | \(0.690980\pi\) | |||||||
\(140\) | −1.08579 | + | 0.148586i | −0.0917657 | + | 0.0125578i | ||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | −4.91421 | − | 8.51167i | −0.412392 | − | 0.714283i | ||||
\(143\) | 1.82843 | − | 3.16693i | 0.152901 | − | 0.264832i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0.242641 | + | 0.420266i | 0.0201502 | + | 0.0349012i | ||||
\(146\) | 10.6569 | 0.881968 | ||||||||
\(147\) | −1.74264 | + | 6.77962i | −0.143731 | + | 0.559173i | ||||
\(148\) | −3.17157 | −0.260702 | ||||||||
\(149\) | −0.378680 | − | 0.655892i | −0.0310226 | − | 0.0537328i | 0.850097 | − | 0.526626i | \(-0.176543\pi\) |
−0.881120 | + | 0.472893i | \(0.843210\pi\) | |||||||
\(150\) | −2.41421 | + | 4.18154i | −0.197120 | + | 0.341421i | ||||
\(151\) | −7.07107 | + | 12.2474i | −0.575435 | + | 0.996683i | 0.420559 | + | 0.907265i | \(0.361834\pi\) |
−0.995994 | + | 0.0894180i | \(0.971499\pi\) | |||||||
\(152\) | 1.82843 | + | 3.16693i | 0.148305 | + | 0.256872i | ||||
\(153\) | −3.24264 | −0.262152 | ||||||||
\(154\) | 5.24264 | − | 0.717439i | 0.422464 | − | 0.0578129i | ||||
\(155\) | −0.828427 | −0.0665409 | ||||||||
\(156\) | 0.914214 | + | 1.58346i | 0.0731957 | + | 0.126779i | ||||
\(157\) | 2.17157 | − | 3.76127i | 0.173310 | − | 0.300182i | −0.766265 | − | 0.642525i | \(-0.777887\pi\) |
0.939575 | + | 0.342342i | \(0.111220\pi\) | |||||||
\(158\) | −5.00000 | + | 8.66025i | −0.397779 | + | 0.688973i | ||||
\(159\) | 5.03553 | + | 8.72180i | 0.399344 | + | 0.691684i | ||||
\(160\) | −0.414214 | −0.0327465 | ||||||||
\(161\) | 1.62132 | + | 2.09077i | 0.127778 | + | 0.164776i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.82843 | + | 8.36308i | 0.378192 | + | 0.655047i | 0.990799 | − | 0.135340i | \(-0.0432127\pi\) |
−0.612608 | + | 0.790387i | \(0.709879\pi\) | |||||||
\(164\) | 5.41421 | − | 9.37769i | 0.422779 | − | 0.732275i | ||||
\(165\) | −0.414214 | + | 0.717439i | −0.0322465 | + | 0.0558525i | ||||
\(166\) | 6.41421 | + | 11.1097i | 0.497840 | + | 0.862283i | ||||
\(167\) | −14.7990 | −1.14518 | −0.572590 | − | 0.819842i | \(-0.694061\pi\) | ||||
−0.572590 | + | 0.819842i | \(0.694061\pi\) | |||||||
\(168\) | −1.00000 | + | 2.44949i | −0.0771517 | + | 0.188982i | ||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | −0.671573 | − | 1.16320i | −0.0515073 | − | 0.0892132i | ||||
\(171\) | −1.82843 | + | 3.16693i | −0.139823 | + | 0.242181i | ||||
\(172\) | 5.82843 | − | 10.0951i | 0.444413 | − | 0.769747i | ||||
\(173\) | −7.65685 | − | 13.2621i | −0.582140 | − | 1.00830i | −0.995225 | − | 0.0976036i | \(-0.968882\pi\) |
0.413086 | − | 0.910692i | \(-0.364451\pi\) | |||||||
\(174\) | 1.17157 | 0.0888167 | ||||||||
\(175\) | −4.82843 | + | 11.8272i | −0.364995 | + | 0.894051i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | −0.828427 | − | 1.43488i | −0.0622684 | − | 0.107852i | ||||
\(178\) | 0.585786 | − | 1.01461i | 0.0439065 | − | 0.0760484i | ||||
\(179\) | −5.98528 | + | 10.3668i | −0.447361 | + | 0.774852i | −0.998213 | − | 0.0597508i | \(-0.980969\pi\) |
0.550852 | + | 0.834603i | \(0.314303\pi\) | |||||||
\(180\) | −0.207107 | − | 0.358719i | −0.0154368 | − | 0.0267374i | ||||
\(181\) | 13.3137 | 0.989600 | 0.494800 | − | 0.869007i | \(-0.335241\pi\) | ||||
0.494800 | + | 0.869007i | \(0.335241\pi\) | |||||||
\(182\) | 2.96447 | + | 3.82282i | 0.219741 | + | 0.283366i | ||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 0.656854 | − | 1.13770i | 0.0482929 | − | 0.0836457i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | 3.24264 | + | 5.61642i | 0.237125 | + | 0.410713i | ||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | −2.62132 | + | 0.358719i | −0.190673 | + | 0.0260930i | ||||
\(190\) | −1.51472 | −0.109889 | ||||||||
\(191\) | 5.41421 | + | 9.37769i | 0.391759 | + | 0.678546i | 0.992682 | − | 0.120761i | \(-0.0385335\pi\) |
−0.600923 | + | 0.799307i | \(0.705200\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −5.74264 | + | 9.94655i | −0.413364 | + | 0.715968i | −0.995255 | − | 0.0972989i | \(-0.968980\pi\) |
0.581891 | + | 0.813267i | \(0.302313\pi\) | |||||||
\(194\) | −4.82843 | − | 8.36308i | −0.346661 | − | 0.600434i | ||||
\(195\) | −0.757359 | −0.0542356 | ||||||||
\(196\) | −1.74264 | + | 6.77962i | −0.124474 | + | 0.484258i | ||||
\(197\) | −7.17157 | −0.510953 | −0.255477 | − | 0.966815i | \(-0.582232\pi\) | ||||
−0.255477 | + | 0.966815i | \(0.582232\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | 8.17157 | − | 14.1536i | 0.579267 | − | 1.00332i | −0.416296 | − | 0.909229i | \(-0.636672\pi\) |
0.995564 | − | 0.0940915i | \(-0.0299946\pi\) | |||||||
\(200\) | −2.41421 | + | 4.18154i | −0.170711 | + | 0.295680i | ||||
\(201\) | −7.44975 | − | 12.9033i | −0.525465 | − | 0.910132i | ||||
\(202\) | −3.17157 | −0.223151 | ||||||||
\(203\) | 3.07107 | − | 0.420266i | 0.215547 | − | 0.0294969i | ||||
\(204\) | −3.24264 | −0.227030 | ||||||||
\(205\) | 2.24264 | + | 3.88437i | 0.156633 | + | 0.271296i | ||||
\(206\) | −4.44975 | + | 7.70719i | −0.310029 | + | 0.536985i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 0.914214 | + | 1.58346i | 0.0633893 | + | 0.109793i | ||||
\(209\) | 7.31371 | 0.505900 | ||||||||
\(210\) | −0.671573 | − | 0.866025i | −0.0463429 | − | 0.0597614i | ||||
\(211\) | −16.8284 | −1.15852 | −0.579258 | − | 0.815144i | \(-0.696658\pi\) | ||||
−0.579258 | + | 0.815144i | \(0.696658\pi\) | |||||||
\(212\) | 5.03553 | + | 8.72180i | 0.345842 | + | 0.599016i | ||||
\(213\) | 4.91421 | − | 8.51167i | 0.336716 | − | 0.583210i | ||||
\(214\) | 2.82843 | − | 4.89898i | 0.193347 | − | 0.334887i | ||||
\(215\) | 2.41421 | + | 4.18154i | 0.164648 | + | 0.285179i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.00000 | + | 4.89898i | −0.135769 | + | 0.332564i | ||||
\(218\) | −14.8284 | −1.00431 | ||||||||
\(219\) | 5.32843 | + | 9.22911i | 0.360062 | + | 0.623645i | ||||
\(220\) | −0.414214 | + | 0.717439i | −0.0279263 | + | 0.0483697i | ||||
\(221\) | −2.96447 | + | 5.13461i | −0.199412 | + | 0.345391i | ||||
\(222\) | −1.58579 | − | 2.74666i | −0.106431 | − | 0.184344i | ||||
\(223\) | 4.48528 | 0.300357 | 0.150178 | − | 0.988659i | \(-0.452015\pi\) | ||||
0.150178 | + | 0.988659i | \(0.452015\pi\) | |||||||
\(224\) | −1.00000 | + | 2.44949i | −0.0668153 | + | 0.163663i | ||||
\(225\) | −4.82843 | −0.321895 | ||||||||
\(226\) | −6.86396 | − | 11.8887i | −0.456584 | − | 0.790827i | ||||
\(227\) | −11.4853 | + | 19.8931i | −0.762305 | + | 1.32035i | 0.179355 | + | 0.983784i | \(0.442599\pi\) |
−0.941660 | + | 0.336566i | \(0.890734\pi\) | |||||||
\(228\) | −1.82843 | + | 3.16693i | −0.121091 | + | 0.209735i | ||||
\(229\) | 13.0711 | + | 22.6398i | 0.863760 | + | 1.49608i | 0.868273 | + | 0.496087i | \(0.165230\pi\) |
−0.00451223 | + | 0.999990i | \(0.501436\pi\) | |||||||
\(230\) | −0.414214 | −0.0273124 | ||||||||
\(231\) | 3.24264 | + | 4.18154i | 0.213350 | + | 0.275125i | ||||
\(232\) | 1.17157 | 0.0769175 | ||||||||
\(233\) | 4.00000 | + | 6.92820i | 0.262049 | + | 0.453882i | 0.966786 | − | 0.255586i | \(-0.0822686\pi\) |
−0.704737 | + | 0.709468i | \(0.748935\pi\) | |||||||
\(234\) | −0.914214 | + | 1.58346i | −0.0597640 | + | 0.103514i | ||||
\(235\) | −1.86396 | + | 3.22848i | −0.121591 | + | 0.210603i | ||||
\(236\) | −0.828427 | − | 1.43488i | −0.0539260 | − | 0.0934026i | ||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | −8.50000 | + | 1.16320i | −0.550973 | + | 0.0753989i | ||||
\(239\) | 21.6569 | 1.40087 | 0.700433 | − | 0.713718i | \(-0.252990\pi\) | ||||
0.700433 | + | 0.713718i | \(0.252990\pi\) | |||||||
\(240\) | −0.207107 | − | 0.358719i | −0.0133687 | − | 0.0231552i | ||||
\(241\) | 3.58579 | − | 6.21076i | 0.230981 | − | 0.400070i | −0.727116 | − | 0.686514i | \(-0.759140\pi\) |
0.958097 | + | 0.286444i | \(0.0924732\pi\) | |||||||
\(242\) | −3.50000 | + | 6.06218i | −0.224989 | + | 0.389692i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | −2.07107 | − | 2.02922i | −0.132316 | − | 0.129642i | ||||
\(246\) | 10.8284 | 0.690395 | ||||||||
\(247\) | 3.34315 | + | 5.79050i | 0.212719 | + | 0.368441i | ||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | −6.41421 | + | 11.1097i | −0.406484 | + | 0.704051i | ||||
\(250\) | −2.03553 | − | 3.52565i | −0.128738 | − | 0.222982i | ||||
\(251\) | −5.31371 | −0.335398 | −0.167699 | − | 0.985838i | \(-0.553634\pi\) | ||||
−0.167699 | + | 0.985838i | \(0.553634\pi\) | |||||||
\(252\) | −2.62132 | + | 0.358719i | −0.165128 | + | 0.0225972i | ||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 2.41421 | + | 4.18154i | 0.151481 | + | 0.262373i | ||||
\(255\) | 0.671573 | − | 1.16320i | 0.0420555 | − | 0.0728423i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −11.2426 | − | 19.4728i | −0.701297 | − | 1.21468i | −0.968011 | − | 0.250906i | \(-0.919272\pi\) |
0.266715 | − | 0.963775i | \(-0.414062\pi\) | |||||||
\(258\) | 11.6569 | 0.725724 | ||||||||
\(259\) | −5.14214 | − | 6.63103i | −0.319517 | − | 0.412032i | ||||
\(260\) | −0.757359 | −0.0469694 | ||||||||
\(261\) | 0.585786 | + | 1.01461i | 0.0362593 | + | 0.0628029i | ||||
\(262\) | 9.57107 | − | 16.5776i | 0.591303 | − | 1.02417i | ||||
\(263\) | 1.65685 | − | 2.86976i | 0.102166 | − | 0.176957i | −0.810411 | − | 0.585862i | \(-0.800756\pi\) |
0.912577 | + | 0.408905i | \(0.134089\pi\) | |||||||
\(264\) | 1.00000 | + | 1.73205i | 0.0615457 | + | 0.106600i | ||||
\(265\) | −4.17157 | −0.256258 | ||||||||
\(266\) | −3.65685 | + | 8.95743i | −0.224216 | + | 0.549215i | ||||
\(267\) | 1.17157 | 0.0716991 | ||||||||
\(268\) | −7.44975 | − | 12.9033i | −0.455066 | − | 0.788197i | ||||
\(269\) | 6.00000 | − | 10.3923i | 0.365826 | − | 0.633630i | −0.623082 | − | 0.782157i | \(-0.714120\pi\) |
0.988908 | + | 0.148527i | \(0.0474530\pi\) | |||||||
\(270\) | 0.207107 | − | 0.358719i | 0.0126041 | − | 0.0218310i | ||||
\(271\) | −13.1421 | − | 22.7628i | −0.798328 | − | 1.38274i | −0.920704 | − | 0.390261i | \(-0.872385\pi\) |
0.122377 | − | 0.992484i | \(-0.460948\pi\) | |||||||
\(272\) | −3.24264 | −0.196614 | ||||||||
\(273\) | −1.82843 | + | 4.47871i | −0.110661 | + | 0.271064i | ||||
\(274\) | 10.4142 | 0.629146 | ||||||||
\(275\) | 4.82843 | + | 8.36308i | 0.291165 | + | 0.504313i | ||||
\(276\) | −0.500000 | + | 0.866025i | −0.0300965 | + | 0.0521286i | ||||
\(277\) | 15.6421 | − | 27.0930i | 0.939845 | − | 1.62786i | 0.174087 | − | 0.984730i | \(-0.444303\pi\) |
0.765758 | − | 0.643129i | \(-0.222364\pi\) | |||||||
\(278\) | −6.65685 | − | 11.5300i | −0.399252 | − | 0.691524i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | −0.671573 | − | 0.866025i | −0.0401342 | − | 0.0517549i | ||||
\(281\) | −16.4142 | −0.979190 | −0.489595 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489595 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(282\) | 4.50000 | + | 7.79423i | 0.267971 | + | 0.464140i | ||||
\(283\) | −3.69239 | + | 6.39540i | −0.219490 | + | 0.380167i | −0.954652 | − | 0.297724i | \(-0.903773\pi\) |
0.735162 | + | 0.677891i | \(0.237106\pi\) | |||||||
\(284\) | 4.91421 | − | 8.51167i | 0.291605 | − | 0.505075i | ||||
\(285\) | −0.757359 | − | 1.31178i | −0.0448621 | − | 0.0777034i | ||||
\(286\) | 3.65685 | 0.216234 | ||||||||
\(287\) | 28.3848 | − | 3.88437i | 1.67550 | − | 0.229287i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 3.24264 | + | 5.61642i | 0.190744 | + | 0.330378i | ||||
\(290\) | −0.242641 | + | 0.420266i | −0.0142484 | + | 0.0246789i | ||||
\(291\) | 4.82843 | − | 8.36308i | 0.283047 | − | 0.490252i | ||||
\(292\) | 5.32843 | + | 9.22911i | 0.311823 | + | 0.540093i | ||||
\(293\) | −6.41421 | −0.374722 | −0.187361 | − | 0.982291i | \(-0.559993\pi\) | ||||
−0.187361 | + | 0.982291i | \(0.559993\pi\) | |||||||
\(294\) | −6.74264 | + | 1.88064i | −0.393239 | + | 0.109681i | ||||
\(295\) | 0.686292 | 0.0399574 | ||||||||
\(296\) | −1.58579 | − | 2.74666i | −0.0921720 | − | 0.159647i | ||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 0.378680 | − | 0.655892i | 0.0219363 | − | 0.0379948i | ||||
\(299\) | 0.914214 | + | 1.58346i | 0.0528703 | + | 0.0915741i | ||||
\(300\) | −4.82843 | −0.278769 | ||||||||
\(301\) | 30.5563 | − | 4.18154i | 1.76124 | − | 0.241020i | ||||
\(302\) | −14.1421 | −0.813788 | ||||||||
\(303\) | −1.58579 | − | 2.74666i | −0.0911011 | − | 0.157792i | ||||
\(304\) | −1.82843 | + | 3.16693i | −0.104867 | + | 0.181636i | ||||
\(305\) | 0.414214 | − | 0.717439i | 0.0237178 | − | 0.0410804i | ||||
\(306\) | −1.62132 | − | 2.80821i | −0.0926847 | − | 0.160535i | ||||
\(307\) | 14.1421 | 0.807134 | 0.403567 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403567 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(308\) | 3.24264 | + | 4.18154i | 0.184767 | + | 0.238265i | ||||
\(309\) | −8.89949 | −0.506275 | ||||||||
\(310\) | −0.414214 | − | 0.717439i | −0.0235257 | − | 0.0407478i | ||||
\(311\) | −3.15685 | + | 5.46783i | −0.179009 | + | 0.310052i | −0.941541 | − | 0.336898i | \(-0.890622\pi\) |
0.762533 | + | 0.646950i | \(0.223956\pi\) | |||||||
\(312\) | −0.914214 | + | 1.58346i | −0.0517572 | + | 0.0896460i | ||||
\(313\) | 0.485281 | + | 0.840532i | 0.0274297 | + | 0.0475097i | 0.879414 | − | 0.476057i | \(-0.157934\pi\) |
−0.851985 | + | 0.523567i | \(0.824601\pi\) | |||||||
\(314\) | 4.34315 | 0.245098 | ||||||||
\(315\) | 0.414214 | − | 1.01461i | 0.0233383 | − | 0.0571669i | ||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −6.31371 | − | 10.9357i | −0.354613 | − | 0.614208i | 0.632438 | − | 0.774611i | \(-0.282054\pi\) |
−0.987052 | + | 0.160403i | \(0.948721\pi\) | |||||||
\(318\) | −5.03553 | + | 8.72180i | −0.282379 | + | 0.489094i | ||||
\(319\) | 1.17157 | − | 2.02922i | 0.0655955 | − | 0.113615i | ||||
\(320\) | −0.207107 | − | 0.358719i | −0.0115776 | − | 0.0200530i | ||||
\(321\) | 5.65685 | 0.315735 | ||||||||
\(322\) | −1.00000 | + | 2.44949i | −0.0557278 | + | 0.136505i | ||||
\(323\) | −11.8579 | −0.659789 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −4.41421 | + | 7.64564i | −0.244857 | + | 0.424104i | ||||
\(326\) | −4.82843 | + | 8.36308i | −0.267422 | + | 0.463188i | ||||
\(327\) | −7.41421 | − | 12.8418i | −0.410007 | − | 0.710153i | ||||
\(328\) | 10.8284 | 0.597900 | ||||||||
\(329\) | 14.5919 | + | 18.8169i | 0.804477 | + | 1.03741i | ||||
\(330\) | −0.828427 | −0.0456034 | ||||||||
\(331\) | 8.75736 | + | 15.1682i | 0.481348 | + | 0.833719i | 0.999771 | − | 0.0214052i | \(-0.00681400\pi\) |
−0.518423 | + | 0.855124i | \(0.673481\pi\) | |||||||
\(332\) | −6.41421 | + | 11.1097i | −0.352026 | + | 0.609726i | ||||
\(333\) | 1.58579 | − | 2.74666i | 0.0869006 | − | 0.150516i | ||||
\(334\) | −7.39949 | − | 12.8163i | −0.404882 | − | 0.701277i | ||||
\(335\) | 6.17157 | 0.337189 | ||||||||
\(336\) | −2.62132 | + | 0.358719i | −0.143005 | + | 0.0195698i | ||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −4.82843 | − | 8.36308i | −0.262632 | − | 0.454892i | ||||
\(339\) | 6.86396 | − | 11.8887i | 0.372799 | − | 0.645707i | ||||
\(340\) | 0.671573 | − | 1.16320i | 0.0364212 | − | 0.0630833i | ||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | −3.65685 | −0.197740 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 11.6569 | 0.628495 | ||||||||
\(345\) | −0.207107 | − | 0.358719i | −0.0111503 | − | 0.0193128i | ||||
\(346\) | 7.65685 | − | 13.2621i | 0.411635 | − | 0.712973i | ||||
\(347\) | 10.6716 | − | 18.4837i | 0.572880 | − | 0.992257i | −0.423388 | − | 0.905948i | \(-0.639159\pi\) |
0.996268 | − | 0.0863091i | \(-0.0275073\pi\) | |||||||
\(348\) | 0.585786 | + | 1.01461i | 0.0314014 | + | 0.0543889i | ||||
\(349\) | 3.14214 | 0.168195 | 0.0840973 | − | 0.996458i | \(-0.473199\pi\) | ||||
0.0840973 | + | 0.996458i | \(0.473199\pi\) | |||||||
\(350\) | −12.6569 | + | 1.73205i | −0.676537 | + | 0.0925820i | ||||
\(351\) | −1.82843 | −0.0975942 | ||||||||
\(352\) | 1.00000 | + | 1.73205i | 0.0533002 | + | 0.0923186i | ||||
\(353\) | 13.0711 | − | 22.6398i | 0.695703 | − | 1.20499i | −0.274240 | − | 0.961661i | \(-0.588426\pi\) |
0.969943 | − | 0.243331i | \(-0.0782402\pi\) | |||||||
\(354\) | 0.828427 | − | 1.43488i | 0.0440304 | − | 0.0762629i | ||||
\(355\) | 2.03553 | + | 3.52565i | 0.108035 | + | 0.187122i | ||||
\(356\) | 1.17157 | 0.0620932 | ||||||||
\(357\) | −5.25736 | − | 6.77962i | −0.278249 | − | 0.358815i | ||||
\(358\) | −11.9706 | −0.632664 | ||||||||
\(359\) | 3.48528 | + | 6.03668i | 0.183946 | + | 0.318604i | 0.943221 | − | 0.332166i | \(-0.107779\pi\) |
−0.759275 | + | 0.650770i | \(0.774446\pi\) | |||||||
\(360\) | 0.207107 | − | 0.358719i | 0.0109155 | − | 0.0189062i | ||||
\(361\) | 2.81371 | − | 4.87349i | 0.148090 | − | 0.256499i | ||||
\(362\) | 6.65685 | + | 11.5300i | 0.349876 | + | 0.606004i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | −1.82843 | + | 4.47871i | −0.0958356 | + | 0.234748i | ||||
\(365\) | −4.41421 | −0.231050 | ||||||||
\(366\) | −1.00000 | − | 1.73205i | −0.0522708 | − | 0.0905357i | ||||
\(367\) | 16.3492 | − | 28.3177i | 0.853424 | − | 1.47817i | −0.0246764 | − | 0.999695i | \(-0.507856\pi\) |
0.878100 | − | 0.478477i | \(-0.158811\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | 5.41421 | + | 9.37769i | 0.281853 | + | 0.488183i | ||||
\(370\) | 1.31371 | 0.0682965 | ||||||||
\(371\) | −10.0711 | + | 24.6690i | −0.522864 | + | 1.28075i | ||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | 5.82843 | + | 10.0951i | 0.301785 | + | 0.522706i | 0.976540 | − | 0.215335i | \(-0.0690844\pi\) |
−0.674756 | + | 0.738041i | \(0.735751\pi\) | |||||||
\(374\) | −3.24264 | + | 5.61642i | −0.167673 | + | 0.290418i | ||||
\(375\) | 2.03553 | − | 3.52565i | 0.105115 | − | 0.182064i | ||||
\(376\) | 4.50000 | + | 7.79423i | 0.232070 | + | 0.401957i | ||||
\(377\) | 2.14214 | 0.110326 | ||||||||
\(378\) | −1.62132 | − | 2.09077i | −0.0833917 | − | 0.107538i | ||||
\(379\) | 0.899495 | 0.0462040 | 0.0231020 | − | 0.999733i | \(-0.492646\pi\) | ||||
0.0231020 | + | 0.999733i | \(0.492646\pi\) | |||||||
\(380\) | −0.757359 | − | 1.31178i | −0.0388517 | − | 0.0672931i | ||||
\(381\) | −2.41421 | + | 4.18154i | −0.123684 | + | 0.214227i | ||||
\(382\) | −5.41421 | + | 9.37769i | −0.277015 | + | 0.479805i | ||||
\(383\) | 3.82843 | + | 6.63103i | 0.195623 | + | 0.338830i | 0.947105 | − | 0.320925i | \(-0.103994\pi\) |
−0.751481 | + | 0.659754i | \(0.770660\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.17157 | + | 0.297173i | −0.110674 | + | 0.0151453i | ||||
\(386\) | −11.4853 | −0.584585 | ||||||||
\(387\) | 5.82843 | + | 10.0951i | 0.296276 | + | 0.513164i | ||||
\(388\) | 4.82843 | − | 8.36308i | 0.245126 | − | 0.424571i | ||||
\(389\) | −6.72792 | + | 11.6531i | −0.341119 | + | 0.590836i | −0.984641 | − | 0.174592i | \(-0.944139\pi\) |
0.643522 | + | 0.765428i | \(0.277473\pi\) | |||||||
\(390\) | −0.378680 | − | 0.655892i | −0.0191752 | − | 0.0332124i | ||||
\(391\) | −3.24264 | −0.163987 | ||||||||
\(392\) | −6.74264 | + | 1.88064i | −0.340555 | + | 0.0949865i | ||||
\(393\) | 19.1421 | 0.965593 | ||||||||
\(394\) | −3.58579 | − | 6.21076i | −0.180649 | − | 0.312894i | ||||
\(395\) | 2.07107 | − | 3.58719i | 0.104207 | − | 0.180491i | ||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | −1.32843 | − | 2.30090i | −0.0666718 | − | 0.115479i | 0.830763 | − | 0.556627i | \(-0.187905\pi\) |
−0.897434 | + | 0.441148i | \(0.854571\pi\) | |||||||
\(398\) | 16.3431 | 0.819208 | ||||||||
\(399\) | −9.58579 | + | 1.31178i | −0.479890 | + | 0.0656714i | ||||
\(400\) | −4.82843 | −0.241421 | ||||||||
\(401\) | −13.3492 | − | 23.1216i | −0.666629 | − | 1.15464i | −0.978841 | − | 0.204623i | \(-0.934403\pi\) |
0.312211 | − | 0.950013i | \(-0.398930\pi\) | |||||||
\(402\) | 7.44975 | − | 12.9033i | 0.371560 | − | 0.643560i | ||||
\(403\) | −1.82843 | + | 3.16693i | −0.0910804 | + | 0.157756i | ||||
\(404\) | −1.58579 | − | 2.74666i | −0.0788958 | − | 0.136652i | ||||
\(405\) | 0.414214 | 0.0205824 | ||||||||
\(406\) | 1.89949 | + | 2.44949i | 0.0942704 | + | 0.121566i | ||||
\(407\) | −6.34315 | −0.314418 | ||||||||
\(408\) | −1.62132 | − | 2.80821i | −0.0802673 | − | 0.139027i | ||||
\(409\) | −6.39949 | + | 11.0843i | −0.316435 | + | 0.548081i | −0.979741 | − | 0.200267i | \(-0.935819\pi\) |
0.663307 | + | 0.748348i | \(0.269152\pi\) | |||||||
\(410\) | −2.24264 | + | 3.88437i | −0.110756 | + | 0.191835i | ||||
\(411\) | 5.20711 | + | 9.01897i | 0.256848 | + | 0.444873i | ||||
\(412\) | −8.89949 | −0.438447 | ||||||||
\(413\) | 1.65685 | − | 4.05845i | 0.0815285 | − | 0.199703i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −2.65685 | − | 4.60181i | −0.130420 | − | 0.225894i | ||||
\(416\) | −0.914214 | + | 1.58346i | −0.0448230 | + | 0.0776357i | ||||
\(417\) | 6.65685 | − | 11.5300i | 0.325988 | − | 0.564627i | ||||
\(418\) | 3.65685 | + | 6.33386i | 0.178863 | + | 0.309799i | ||||
\(419\) | 24.4853 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(420\) | 0.414214 | − | 1.01461i | 0.0202116 | − | 0.0495080i | ||||
\(421\) | 15.3137 | 0.746344 | 0.373172 | − | 0.927762i | \(-0.378270\pi\) | ||||
0.373172 | + | 0.927762i | \(0.378270\pi\) | |||||||
\(422\) | −8.41421 | − | 14.5738i | −0.409598 | − | 0.709444i | ||||
\(423\) | −4.50000 | + | 7.79423i | −0.218797 | + | 0.378968i | ||||
\(424\) | −5.03553 | + | 8.72180i | −0.244547 | + | 0.423568i | ||||
\(425\) | −7.82843 | − | 13.5592i | −0.379734 | − | 0.657719i | ||||
\(426\) | 9.82843 | 0.476189 | ||||||||
\(427\) | −3.24264 | − | 4.18154i | −0.156922 | − | 0.202359i | ||||
\(428\) | 5.65685 | 0.273434 | ||||||||
\(429\) | 1.82843 | + | 3.16693i | 0.0882773 | + | 0.152901i | ||||
\(430\) | −2.41421 | + | 4.18154i | −0.116424 | + | 0.201652i | ||||
\(431\) | 2.34315 | − | 4.05845i | 0.112865 | − | 0.195489i | −0.804059 | − | 0.594549i | \(-0.797330\pi\) |
0.916924 | + | 0.399061i | \(0.130664\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | −5.24264 | + | 0.717439i | −0.251655 | + | 0.0344382i | ||||
\(435\) | −0.485281 | −0.0232675 | ||||||||
\(436\) | −7.41421 | − | 12.8418i | −0.355076 | − | 0.615010i | ||||
\(437\) | −1.82843 | + | 3.16693i | −0.0874655 | + | 0.151495i | ||||
\(438\) | −5.32843 | + | 9.22911i | −0.254602 | + | 0.440984i | ||||
\(439\) | 1.48528 | + | 2.57258i | 0.0708886 | + | 0.122783i | 0.899291 | − | 0.437351i | \(-0.144083\pi\) |
−0.828402 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(440\) | −0.828427 | −0.0394937 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | −5.92893 | −0.282011 | ||||||||
\(443\) | 8.57107 | + | 14.8455i | 0.407224 | + | 0.705332i | 0.994577 | − | 0.103998i | \(-0.0331636\pi\) |
−0.587354 | + | 0.809330i | \(0.699830\pi\) | |||||||
\(444\) | 1.58579 | − | 2.74666i | 0.0752581 | − | 0.130351i | ||||
\(445\) | −0.242641 | + | 0.420266i | −0.0115023 | + | 0.0199225i | ||||
\(446\) | 2.24264 | + | 3.88437i | 0.106192 | + | 0.183930i | ||||
\(447\) | 0.757359 | 0.0358219 | ||||||||
\(448\) | −2.62132 | + | 0.358719i | −0.123846 | + | 0.0169479i | ||||
\(449\) | 26.4853 | 1.24992 | 0.624959 | − | 0.780658i | \(-0.285116\pi\) | ||||
0.624959 | + | 0.780658i | \(0.285116\pi\) | |||||||
\(450\) | −2.41421 | − | 4.18154i | −0.113807 | − | 0.197120i | ||||
\(451\) | 10.8284 | − | 18.7554i | 0.509891 | − | 0.883157i | ||||
\(452\) | 6.86396 | − | 11.8887i | 0.322854 | − | 0.559199i | ||||
\(453\) | −7.07107 | − | 12.2474i | −0.332228 | − | 0.575435i | ||||
\(454\) | −22.9706 | −1.07806 | ||||||||
\(455\) | −1.22792 | − | 1.58346i | −0.0575659 | − | 0.0742340i | ||||
\(456\) | −3.65685 | −0.171248 | ||||||||
\(457\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(458\) | −13.0711 | + | 22.6398i | −0.610771 | + | 1.05789i | ||||
\(459\) | 1.62132 | − | 2.80821i | 0.0756768 | − | 0.131076i | ||||
\(460\) | −0.207107 | − | 0.358719i | −0.00965640 | − | 0.0167254i | ||||
\(461\) | 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 | ||||
\(463\) | 10.6274 | 0.493898 | 0.246949 | − | 0.969028i | \(-0.420572\pi\) | ||||
0.246949 | + | 0.969028i | \(0.420572\pi\) | |||||||
\(464\) | 0.585786 | + | 1.01461i | 0.0271945 | + | 0.0471022i | ||||
\(465\) | 0.414214 | − | 0.717439i | 0.0192087 | − | 0.0332704i | ||||
\(466\) | −4.00000 | + | 6.92820i | −0.185296 | + | 0.320943i | ||||
\(467\) | −5.17157 | − | 8.95743i | −0.239312 | − | 0.414500i | 0.721205 | − | 0.692722i | \(-0.243588\pi\) |
−0.960517 | + | 0.278221i | \(0.910255\pi\) | |||||||
\(468\) | −1.82843 | −0.0845191 | ||||||||
\(469\) | 14.8995 | − | 36.4962i | 0.687995 | − | 1.68524i | ||||
\(470\) | −3.72792 | −0.171956 | ||||||||
\(471\) | 2.17157 | + | 3.76127i | 0.100061 | + | 0.173310i | ||||
\(472\) | 0.828427 | − | 1.43488i | 0.0381314 | − | 0.0660456i | ||||
\(473\) | 11.6569 | − | 20.1903i | 0.535983 | − | 0.928349i | ||||
\(474\) | −5.00000 | − | 8.66025i | −0.229658 | − | 0.397779i | ||||
\(475\) | −17.6569 | −0.810152 | ||||||||
\(476\) | −5.25736 | − | 6.77962i | −0.240971 | − | 0.310743i | ||||
\(477\) | −10.0711 | −0.461123 | ||||||||
\(478\) | 10.8284 | + | 18.7554i | 0.495281 | + | 0.857851i | ||||
\(479\) | −17.0711 | + | 29.5680i | −0.779997 | + | 1.35099i | 0.151946 | + | 0.988389i | \(0.451446\pi\) |
−0.931943 | + | 0.362606i | \(0.881887\pi\) | |||||||
\(480\) | 0.207107 | − | 0.358719i | 0.00945309 | − | 0.0163732i | ||||
\(481\) | −2.89949 | − | 5.02207i | −0.132206 | − | 0.228987i | ||||
\(482\) | 7.17157 | 0.326656 | ||||||||
\(483\) | −2.62132 | + | 0.358719i | −0.119274 | + | 0.0163223i | ||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 2.00000 | + | 3.46410i | 0.0908153 | + | 0.157297i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 16.3848 | − | 28.3793i | 0.742465 | − | 1.28599i | −0.208905 | − | 0.977936i | \(-0.566990\pi\) |
0.951370 | − | 0.308051i | \(-0.0996768\pi\) | |||||||
\(488\) | −1.00000 | − | 1.73205i | −0.0452679 | − | 0.0784063i | ||||
\(489\) | −9.65685 | −0.436698 | ||||||||
\(490\) | 0.721825 | − | 2.80821i | 0.0326087 | − | 0.126862i | ||||
\(491\) | −11.3431 | −0.511909 | −0.255955 | − | 0.966689i | \(-0.582390\pi\) | ||||
−0.255955 | + | 0.966689i | \(0.582390\pi\) | |||||||
\(492\) | 5.41421 | + | 9.37769i | 0.244092 | + | 0.422779i | ||||
\(493\) | −1.89949 | + | 3.29002i | −0.0855489 | + | 0.148175i | ||||
\(494\) | −3.34315 | + | 5.79050i | −0.150415 | + | 0.260527i | ||||
\(495\) | −0.414214 | − | 0.717439i | −0.0186175 | − | 0.0322465i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 25.7635 | − | 3.52565i | 1.15565 | − | 0.158147i | ||||
\(498\) | −12.8284 | −0.574856 | ||||||||
\(499\) | −0.585786 | − | 1.01461i | −0.0262234 | − | 0.0454203i | 0.852616 | − | 0.522538i | \(-0.175015\pi\) |
−0.878839 | + | 0.477118i | \(0.841681\pi\) | |||||||
\(500\) | 2.03553 | − | 3.52565i | 0.0910318 | − | 0.157672i | ||||
\(501\) | 7.39949 | − | 12.8163i | 0.330585 | − | 0.572590i | ||||
\(502\) | −2.65685 | − | 4.60181i | −0.118581 | − | 0.205389i | ||||
\(503\) | 43.6569 | 1.94656 | 0.973281 | − | 0.229615i | \(-0.0737468\pi\) | ||||
0.973281 | + | 0.229615i | \(0.0737468\pi\) | |||||||
\(504\) | −1.62132 | − | 2.09077i | −0.0722193 | − | 0.0931303i | ||||
\(505\) | 1.31371 | 0.0584593 | ||||||||
\(506\) | 1.00000 | + | 1.73205i | 0.0444554 | + | 0.0769991i | ||||
\(507\) | 4.82843 | − | 8.36308i | 0.214438 | − | 0.371417i | ||||
\(508\) | −2.41421 | + | 4.18154i | −0.107113 | + | 0.185526i | ||||
\(509\) | −7.92893 | − | 13.7333i | −0.351444 | − | 0.608718i | 0.635059 | − | 0.772464i | \(-0.280976\pi\) |
−0.986503 | + | 0.163745i | \(0.947642\pi\) | |||||||
\(510\) | 1.34315 | 0.0594755 | ||||||||
\(511\) | −10.6569 | + | 26.1039i | −0.471431 | + | 1.15477i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.82843 | − | 3.16693i | −0.0807270 | − | 0.139823i | ||||
\(514\) | 11.2426 | − | 19.4728i | 0.495892 | − | 0.858909i | ||||
\(515\) | 1.84315 | − | 3.19242i | 0.0812187 | − | 0.140675i | ||||
\(516\) | 5.82843 | + | 10.0951i | 0.256582 | + | 0.444413i | ||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 3.17157 | − | 7.76874i | 0.139351 | − | 0.341339i | ||||
\(519\) | 15.3137 | 0.672197 | ||||||||
\(520\) | −0.378680 | − | 0.655892i | −0.0166062 | − | 0.0287628i | ||||
\(521\) | −12.7929 | + | 22.1579i | −0.560467 | + | 0.970757i | 0.436989 | + | 0.899467i | \(0.356045\pi\) |
−0.997456 | + | 0.0712901i | \(0.977288\pi\) | |||||||
\(522\) | −0.585786 | + | 1.01461i | −0.0256392 | + | 0.0444084i | ||||
\(523\) | 7.03553 | + | 12.1859i | 0.307642 | + | 0.532852i | 0.977846 | − | 0.209325i | \(-0.0671266\pi\) |
−0.670204 | + | 0.742177i | \(0.733793\pi\) | |||||||
\(524\) | 19.1421 | 0.836228 | ||||||||
\(525\) | −7.82843 | − | 10.0951i | −0.341661 | − | 0.440588i | ||||
\(526\) | 3.31371 | 0.144485 | ||||||||
\(527\) | −3.24264 | − | 5.61642i | −0.141252 | − | 0.244655i | ||||
\(528\) | −1.00000 | + | 1.73205i | −0.0435194 | + | 0.0753778i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −2.08579 | − | 3.61269i | −0.0906008 | − | 0.156925i | ||||
\(531\) | 1.65685 | 0.0719014 | ||||||||
\(532\) | −9.58579 | + | 1.31178i | −0.415597 | + | 0.0568731i | ||||
\(533\) | 19.7990 | 0.857589 | ||||||||
\(534\) | 0.585786 | + | 1.01461i | 0.0253495 | + | 0.0439065i | ||||
\(535\) | −1.17157 | + | 2.02922i | −0.0506515 | + | 0.0877310i | ||||
\(536\) | 7.44975 | − | 12.9033i | 0.321780 | − | 0.557339i | ||||
\(537\) | −5.98528 | − | 10.3668i | −0.258284 | − | 0.447361i | ||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | −3.48528 | + | 13.5592i | −0.150122 | + | 0.584038i | ||||
\(540\) | 0.414214 | 0.0178249 | ||||||||
\(541\) | −6.42893 | − | 11.1352i | −0.276401 | − | 0.478741i | 0.694086 | − | 0.719892i | \(-0.255809\pi\) |
−0.970488 | + | 0.241151i | \(0.922475\pi\) | |||||||
\(542\) | 13.1421 | − | 22.7628i | 0.564503 | − | 0.977748i | ||||
\(543\) | −6.65685 | + | 11.5300i | −0.285673 | + | 0.494800i | ||||
\(544\) | −1.62132 | − | 2.80821i | −0.0695135 | − | 0.120401i | ||||
\(545\) | 6.14214 | 0.263100 | ||||||||
\(546\) | −4.79289 | + | 0.655892i | −0.205117 | + | 0.0280696i | ||||
\(547\) | −34.2843 | −1.46589 | −0.732945 | − | 0.680288i | \(-0.761855\pi\) | ||||
−0.732945 | + | 0.680288i | \(0.761855\pi\) | |||||||
\(548\) | 5.20711 | + | 9.01897i | 0.222437 | + | 0.385271i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | −4.82843 | + | 8.36308i | −0.205885 | + | 0.356603i | ||||
\(551\) | 2.14214 | + | 3.71029i | 0.0912580 | + | 0.158064i | ||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −16.2132 | − | 20.9077i | −0.689456 | − | 0.889086i | ||||
\(554\) | 31.2843 | 1.32914 | ||||||||
\(555\) | 0.656854 | + | 1.13770i | 0.0278819 | + | 0.0482929i | ||||
\(556\) | 6.65685 | − | 11.5300i | 0.282314 | − | 0.488981i | ||||
\(557\) | 11.8995 | − | 20.6105i | 0.504198 | − | 0.873296i | −0.495790 | − | 0.868442i | \(-0.665122\pi\) |
0.999988 | − | 0.00485398i | \(-0.00154508\pi\) | |||||||
\(558\) | −1.00000 | − | 1.73205i | −0.0423334 | − | 0.0733236i | ||||
\(559\) | 21.3137 | 0.901474 | ||||||||
\(560\) | 0.414214 | − | 1.01461i | 0.0175037 | − | 0.0428752i | ||||
\(561\) | −6.48528 | −0.273809 | ||||||||
\(562\) | −8.20711 | − | 14.2151i | −0.346196 | − | 0.599629i | ||||
\(563\) | 2.72792 | − | 4.72490i | 0.114968 | − | 0.199131i | −0.802799 | − | 0.596250i | \(-0.796657\pi\) |
0.917767 | + | 0.397119i | \(0.129990\pi\) | |||||||
\(564\) | −4.50000 | + | 7.79423i | −0.189484 | + | 0.328196i | ||||
\(565\) | 2.84315 | + | 4.92447i | 0.119612 | + | 0.207174i | ||||
\(566\) | −7.38478 | −0.310405 | ||||||||
\(567\) | 1.00000 | − | 2.44949i | 0.0419961 | − | 0.102869i | ||||
\(568\) | 9.82843 | 0.412392 | ||||||||
\(569\) | −5.20711 | − | 9.01897i | −0.218293 | − | 0.378095i | 0.735993 | − | 0.676989i | \(-0.236716\pi\) |
−0.954286 | + | 0.298894i | \(0.903382\pi\) | |||||||
\(570\) | 0.757359 | − | 1.31178i | 0.0317223 | − | 0.0549446i | ||||
\(571\) | 10.4497 | − | 18.0995i | 0.437308 | − | 0.757440i | −0.560173 | − | 0.828376i | \(-0.689265\pi\) |
0.997481 | + | 0.0709357i | \(0.0225985\pi\) | |||||||
\(572\) | 1.82843 | + | 3.16693i | 0.0764504 | + | 0.132416i | ||||
\(573\) | −10.8284 | −0.452364 | ||||||||
\(574\) | 17.5563 | + | 22.6398i | 0.732788 | + | 0.944965i | ||||
\(575\) | −4.82843 | −0.201359 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 15.9706 | − | 27.6618i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648435\pi\) | |||||||
\(578\) | −3.24264 | + | 5.61642i | −0.134876 | + | 0.233612i | ||||
\(579\) | −5.74264 | − | 9.94655i | −0.238656 | − | 0.413364i | ||||
\(580\) | −0.485281 | −0.0201502 | ||||||||
\(581\) | −33.6274 | + | 4.60181i | −1.39510 | + | 0.190915i | ||||
\(582\) | 9.65685 | 0.400289 | ||||||||
\(583\) | 10.0711 | + | 17.4436i | 0.417101 | + | 0.722440i | ||||
\(584\) | −5.32843 | + | 9.22911i | −0.220492 | + | 0.381903i | ||||
\(585\) | 0.378680 | − | 0.655892i | 0.0156565 | − | 0.0271178i | ||||
\(586\) | −3.20711 | − | 5.55487i | −0.132484 | − | 0.229470i | ||||
\(587\) | 1.14214 | 0.0471410 | 0.0235705 | − | 0.999722i | \(-0.492497\pi\) | ||||
0.0235705 | + | 0.999722i | \(0.492497\pi\) | |||||||
\(588\) | −5.00000 | − | 4.89898i | −0.206197 | − | 0.202031i | ||||
\(589\) | −7.31371 | −0.301356 | ||||||||
\(590\) | 0.343146 | + | 0.594346i | 0.0141271 | + | 0.0244688i | ||||
\(591\) | 3.58579 | − | 6.21076i | 0.147500 | − | 0.255477i | ||||
\(592\) | 1.58579 | − | 2.74666i | 0.0651754 | − | 0.112887i | ||||
\(593\) | 1.92893 | + | 3.34101i | 0.0792118 | + | 0.137199i | 0.902910 | − | 0.429830i | \(-0.141426\pi\) |
−0.823698 | + | 0.567028i | \(0.808093\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 3.52082 | − | 0.481813i | 0.144339 | − | 0.0197524i | ||||
\(596\) | 0.757359 | 0.0310226 | ||||||||
\(597\) | 8.17157 | + | 14.1536i | 0.334440 | + | 0.579267i | ||||
\(598\) | −0.914214 | + | 1.58346i | −0.0373850 | + | 0.0647527i | ||||
\(599\) | 3.08579 | − | 5.34474i | 0.126082 | − | 0.218380i | −0.796073 | − | 0.605200i | \(-0.793093\pi\) |
0.922155 | + | 0.386820i | \(0.126426\pi\) | |||||||
\(600\) | −2.41421 | − | 4.18154i | −0.0985599 | − | 0.170711i | ||||
\(601\) | −14.2843 | −0.582668 | −0.291334 | − | 0.956621i | \(-0.594099\pi\) | ||||
−0.291334 | + | 0.956621i | \(0.594099\pi\) | |||||||
\(602\) | 18.8995 | + | 24.3718i | 0.770286 | + | 0.993321i | ||||
\(603\) | 14.8995 | 0.606754 | ||||||||
\(604\) | −7.07107 | − | 12.2474i | −0.287718 | − | 0.498342i | ||||
\(605\) | 1.44975 | − | 2.51104i | 0.0589406 | − | 0.102088i | ||||
\(606\) | 1.58579 | − | 2.74666i | 0.0644182 | − | 0.111576i | ||||
\(607\) | −18.0711 | − | 31.3000i | −0.733482 | − | 1.27043i | −0.955386 | − | 0.295360i | \(-0.904561\pi\) |
0.221904 | − | 0.975068i | \(-0.428773\pi\) | |||||||
\(608\) | −3.65685 | −0.148305 | ||||||||
\(609\) | −1.17157 | + | 2.86976i | −0.0474745 | + | 0.116288i | ||||
\(610\) | 0.828427 | 0.0335420 | ||||||||
\(611\) | 8.22792 | + | 14.2512i | 0.332866 | + | 0.576541i | ||||
\(612\) | 1.62132 | − | 2.80821i | 0.0655380 | − | 0.113515i | ||||
\(613\) | 8.89949 | − | 15.4144i | 0.359447 | − | 0.622581i | −0.628421 | − | 0.777873i | \(-0.716299\pi\) |
0.987869 | + | 0.155292i | \(0.0496319\pi\) | |||||||
\(614\) | 7.07107 | + | 12.2474i | 0.285365 | + | 0.494267i | ||||
\(615\) | −4.48528 | −0.180864 | ||||||||
\(616\) | −2.00000 | + | 4.89898i | −0.0805823 | + | 0.197386i | ||||
\(617\) | −36.0711 | −1.45217 | −0.726083 | − | 0.687607i | \(-0.758661\pi\) | ||||
−0.726083 | + | 0.687607i | \(0.758661\pi\) | |||||||
\(618\) | −4.44975 | − | 7.70719i | −0.178995 | − | 0.310029i | ||||
\(619\) | −14.9645 | + | 25.9192i | −0.601473 | + | 1.04178i | 0.391126 | + | 0.920337i | \(0.372086\pi\) |
−0.992598 | + | 0.121444i | \(0.961248\pi\) | |||||||
\(620\) | 0.414214 | − | 0.717439i | 0.0166352 | − | 0.0288130i | ||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | −6.31371 | −0.253157 | ||||||||
\(623\) | 1.89949 | + | 2.44949i | 0.0761017 | + | 0.0981367i | ||||
\(624\) | −1.82843 | −0.0731957 | ||||||||
\(625\) | −11.2279 | − | 19.4473i | −0.449117 | − | 0.777893i | ||||
\(626\) | −0.485281 | + | 0.840532i | −0.0193957 | + | 0.0335944i | ||||
\(627\) | −3.65685 | + | 6.33386i | −0.146041 | + | 0.252950i | ||||
\(628\) | 2.17157 | + | 3.76127i | 0.0866552 | + | 0.150091i | ||||
\(629\) | 10.2843 | 0.410061 | ||||||||
\(630\) | 1.08579 | − | 0.148586i | 0.0432588 | − | 0.00591983i | ||||
\(631\) | −46.5563 | −1.85338 | −0.926689 | − | 0.375828i | \(-0.877358\pi\) | ||||
−0.926689 | + | 0.375828i | \(0.877358\pi\) | |||||||
\(632\) | −5.00000 | − | 8.66025i | −0.198889 | − | 0.344486i | ||||
\(633\) | 8.41421 | − | 14.5738i | 0.334435 | − | 0.579258i | ||||
\(634\) | 6.31371 | − | 10.9357i | 0.250749 | − | 0.434311i | ||||
\(635\) | −1.00000 | − | 1.73205i | −0.0396838 | − | 0.0687343i | ||||
\(636\) | −10.0711 | −0.399344 | ||||||||
\(637\) | −12.3284 | + | 3.43861i | −0.488470 | + | 0.136243i | ||||
\(638\) | 2.34315 | 0.0927660 | ||||||||
\(639\) | 4.91421 | + | 8.51167i | 0.194403 | + | 0.336716i | ||||
\(640\) | 0.207107 | − | 0.358719i | 0.00818661 | − | 0.0141796i | ||||
\(641\) | 5.30761 | − | 9.19305i | 0.209638 | − | 0.363104i | −0.741962 | − | 0.670441i | \(-0.766105\pi\) |
0.951601 | + | 0.307338i | \(0.0994381\pi\) | |||||||
\(642\) | 2.82843 | + | 4.89898i | 0.111629 | + | 0.193347i | ||||
\(643\) | 6.68629 | 0.263682 | 0.131841 | − | 0.991271i | \(-0.457911\pi\) | ||||
0.131841 | + | 0.991271i | \(0.457911\pi\) | |||||||
\(644\) | −2.62132 | + | 0.358719i | −0.103294 | + | 0.0141355i | ||||
\(645\) | −4.82843 | −0.190119 | ||||||||
\(646\) | −5.92893 | − | 10.2692i | −0.233271 | − | 0.404037i | ||||
\(647\) | 10.8284 | − | 18.7554i | 0.425709 | − | 0.737350i | −0.570777 | − | 0.821105i | \(-0.693358\pi\) |
0.996486 | + | 0.0837548i | \(0.0266913\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −1.65685 | − | 2.86976i | −0.0650372 | − | 0.112648i | ||||
\(650\) | −8.82843 | −0.346279 | ||||||||
\(651\) | −3.24264 | − | 4.18154i | −0.127089 | − | 0.163887i | ||||
\(652\) | −9.65685 | −0.378192 | ||||||||
\(653\) | 15.9706 | + | 27.6618i | 0.624976 | + | 1.08249i | 0.988545 | + | 0.150924i | \(0.0482248\pi\) |
−0.363569 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(654\) | 7.41421 | − | 12.8418i | 0.289919 | − | 0.502154i | ||||
\(655\) | −3.96447 | + | 6.86666i | −0.154905 | + | 0.268302i | ||||
\(656\) | 5.41421 | + | 9.37769i | 0.211390 | + | 0.366137i | ||||
\(657\) | −10.6569 | −0.415763 | ||||||||
\(658\) | −9.00000 | + | 22.0454i | −0.350857 | + | 0.859419i | ||||
\(659\) | 27.4558 | 1.06953 | 0.534764 | − | 0.845002i | \(-0.320401\pi\) | ||||
0.534764 | + | 0.845002i | \(0.320401\pi\) | |||||||
\(660\) | −0.414214 | − | 0.717439i | −0.0161232 | − | 0.0279263i | ||||
\(661\) | −8.72792 | + | 15.1172i | −0.339477 | + | 0.587991i | −0.984334 | − | 0.176312i | \(-0.943583\pi\) |
0.644858 | + | 0.764303i | \(0.276917\pi\) | |||||||
\(662\) | −8.75736 | + | 15.1682i | −0.340364 | + | 0.589528i | ||||
\(663\) | −2.96447 | − | 5.13461i | −0.115130 | − | 0.199412i | ||||
\(664\) | −12.8284 | −0.497840 | ||||||||
\(665\) | 1.51472 | − | 3.71029i | 0.0587383 | − | 0.143879i | ||||
\(666\) | 3.17157 | 0.122896 | ||||||||
\(667\) | 0.585786 | + | 1.01461i | 0.0226817 | + | 0.0392859i | ||||
\(668\) | 7.39949 | − | 12.8163i | 0.286295 | − | 0.495878i | ||||
\(669\) | −2.24264 | + | 3.88437i | −0.0867055 | + | 0.150178i | ||||
\(670\) | 3.08579 | + | 5.34474i | 0.119214 | + | 0.206485i | ||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | −1.62132 | − | 2.09077i | −0.0625438 | − | 0.0806532i | ||||
\(673\) | −29.3137 | −1.12996 | −0.564980 | − | 0.825104i | \(-0.691116\pi\) | ||||
−0.564980 | + | 0.825104i | \(0.691116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.41421 | − | 4.18154i | 0.0929231 | − | 0.160948i | ||||
\(676\) | 4.82843 | − | 8.36308i | 0.185709 | − | 0.321657i | ||||
\(677\) | 10.1360 | + | 17.5561i | 0.389560 | + | 0.674737i | 0.992390 | − | 0.123132i | \(-0.0392939\pi\) |
−0.602831 | + | 0.797869i | \(0.705961\pi\) | |||||||
\(678\) | 13.7279 | 0.527218 | ||||||||
\(679\) | 25.3137 | − | 3.46410i | 0.971451 | − | 0.132940i | ||||
\(680\) | 1.34315 | 0.0515073 | ||||||||
\(681\) | −11.4853 | − | 19.8931i | −0.440117 | − | 0.762305i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | 22.5711 | − | 39.0942i | 0.863658 | − | 1.49590i | −0.00471573 | − | 0.999989i | \(-0.501501\pi\) |
0.868374 | − | 0.495910i | \(-0.165166\pi\) | |||||||
\(684\) | −1.82843 | − | 3.16693i | −0.0699117 | − | 0.121091i | ||||
\(685\) | −4.31371 | −0.164818 | ||||||||
\(686\) | −14.8640 | − | 11.0482i | −0.567509 | − | 0.421822i | ||||
\(687\) | −26.1421 | −0.997385 | ||||||||
\(688\) | 5.82843 | + | 10.0951i | 0.222207 | + | 0.384873i | ||||
\(689\) | −9.20711 | + | 15.9472i | −0.350763 | + | 0.607539i | ||||
\(690\) | 0.207107 | − | 0.358719i | 0.00788442 | − | 0.0136562i | ||||
\(691\) | −8.07107 | − | 13.9795i | −0.307038 | − | 0.531805i | 0.670675 | − | 0.741751i | \(-0.266005\pi\) |
−0.977713 | + | 0.209946i | \(0.932671\pi\) | |||||||
\(692\) | 15.3137 | 0.582140 | ||||||||
\(693\) | −5.24264 | + | 0.717439i | −0.199151 | + | 0.0272533i | ||||
\(694\) | 21.3431 | 0.810175 | ||||||||
\(695\) | 2.75736 | + | 4.77589i | 0.104593 | + | 0.181160i | ||||
\(696\) | −0.585786 | + | 1.01461i | −0.0222042 | + | 0.0384588i | ||||
\(697\) | −17.5563 | + | 30.4085i | −0.664994 | + | 1.15180i | ||||
\(698\) | 1.57107 | + | 2.72117i | 0.0594658 | + | 0.102998i | ||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | −7.82843 | − | 10.0951i | −0.295887 | − | 0.381560i | ||||
\(701\) | 45.3848 | 1.71416 | 0.857080 | − | 0.515184i | \(-0.172276\pi\) | ||||
0.857080 | + | 0.515184i | \(0.172276\pi\) | |||||||
\(702\) | −0.914214 | − | 1.58346i | −0.0345048 | − | 0.0597640i | ||||
\(703\) | 5.79899 | − | 10.0441i | 0.218713 | − | 0.378822i | ||||
\(704\) | −1.00000 | + | 1.73205i | −0.0376889 | + | 0.0652791i | ||||
\(705\) | −1.86396 | − | 3.22848i | −0.0702008 | − | 0.121591i | ||||
\(706\) | 26.1421 | 0.983872 | ||||||||
\(707\) | 3.17157 | − | 7.76874i | 0.119279 | − | 0.292173i | ||||
\(708\) | 1.65685 | 0.0622684 | ||||||||
\(709\) | 19.0711 | + | 33.0321i | 0.716229 | + | 1.24054i | 0.962484 | + | 0.271340i | \(0.0874667\pi\) |
−0.246255 | + | 0.969205i | \(0.579200\pi\) | |||||||
\(710\) | −2.03553 | + | 3.52565i | −0.0763922 | + | 0.132315i | ||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | 0.585786 | + | 1.01461i | 0.0219533 | + | 0.0380242i | ||||
\(713\) | −2.00000 | −0.0749006 | ||||||||
\(714\) | 3.24264 | − | 7.94282i | 0.121353 | − | 0.297252i | ||||
\(715\) | −1.51472 | −0.0566473 | ||||||||
\(716\) | −5.98528 | − | 10.3668i | −0.223680 | − | 0.387426i | ||||
\(717\) | −10.8284 | + | 18.7554i | −0.404395 | + | 0.700433i | ||||
\(718\) | −3.48528 | + | 6.03668i | −0.130070 | + | 0.225287i | ||||
\(719\) | −1.67157 | − | 2.89525i | −0.0623391 | − | 0.107975i | 0.833171 | − | 0.553015i | \(-0.186523\pi\) |
−0.895511 | + | 0.445040i | \(0.853189\pi\) | |||||||
\(720\) | 0.414214 | 0.0154368 | ||||||||
\(721\) | −14.4289 | − | 18.6068i | −0.537362 | − | 0.692953i | ||||
\(722\) | 5.62742 | 0.209431 | ||||||||
\(723\) | 3.58579 | + | 6.21076i | 0.133357 | + | 0.230981i | ||||
\(724\) | −6.65685 | + | 11.5300i | −0.247400 | + | 0.428509i | ||||
\(725\) | −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 | \(0.784195\pi\) | |||||||
\(728\) | −4.79289 | + | 0.655892i | −0.177636 | + | 0.0243090i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.20711 | − | 3.82282i | −0.0816887 | − | 0.141489i | ||||
\(731\) | −18.8995 | + | 32.7349i | −0.699023 | + | 1.21074i | ||||
\(732\) | 1.00000 | − | 1.73205i | 0.0369611 | − | 0.0640184i | ||||
\(733\) | −4.24264 | − | 7.34847i | −0.156706 | − | 0.271422i | 0.776973 | − | 0.629534i | \(-0.216754\pi\) |
−0.933679 | + | 0.358112i | \(0.883421\pi\) | |||||||
\(734\) | 32.6985 | 1.20692 | ||||||||
\(735\) | 2.79289 | − | 0.778985i | 0.103017 | − | 0.0287333i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −14.8995 | − | 25.8067i | −0.548830 | − | 0.950601i | ||||
\(738\) | −5.41421 | + | 9.37769i | −0.199300 | + | 0.345198i | ||||
\(739\) | −22.6274 | + | 39.1918i | −0.832363 | + | 1.44169i | 0.0637965 | + | 0.997963i | \(0.479679\pi\) |
−0.896160 | + | 0.443732i | \(0.853654\pi\) | |||||||
\(740\) | 0.656854 | + | 1.13770i | 0.0241464 | + | 0.0418229i | ||||
\(741\) | −6.68629 | −0.245627 | ||||||||
\(742\) | −26.3995 | + | 3.61269i | −0.969156 | + | 0.132626i | ||||
\(743\) | −35.4558 | −1.30075 | −0.650374 | − | 0.759614i | \(-0.725388\pi\) | ||||
−0.650374 | + | 0.759614i | \(0.725388\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | −0.156854 | + | 0.271680i | −0.00574670 | + | 0.00995357i | ||||
\(746\) | −5.82843 | + | 10.0951i | −0.213394 | + | 0.369609i | ||||
\(747\) | −6.41421 | − | 11.1097i | −0.234684 | − | 0.406484i | ||||
\(748\) | −6.48528 | −0.237125 | ||||||||
\(749\) | 9.17157 | + | 11.8272i | 0.335122 | + | 0.432156i | ||||
\(750\) | 4.07107 | 0.148654 | ||||||||
\(751\) | 20.7990 | + | 36.0249i | 0.758966 | + | 1.31457i | 0.943378 | + | 0.331719i | \(0.107628\pi\) |
−0.184412 | + | 0.982849i | \(0.559038\pi\) | |||||||
\(752\) | −4.50000 | + | 7.79423i | −0.164098 | + | 0.284226i | ||||
\(753\) | 2.65685 | − | 4.60181i | 0.0968212 | − | 0.167699i | ||||
\(754\) | 1.07107 | + | 1.85514i | 0.0390060 | + | 0.0675604i | ||||
\(755\) | 5.85786 | 0.213190 | ||||||||
\(756\) | 1.00000 | − | 2.44949i | 0.0363696 | − | 0.0890871i | ||||
\(757\) | −4.97056 | −0.180658 | −0.0903291 | − | 0.995912i | \(-0.528792\pi\) | ||||
−0.0903291 | + | 0.995912i | \(0.528792\pi\) | |||||||
\(758\) | 0.449747 | + | 0.778985i | 0.0163356 | + | 0.0282940i | ||||
\(759\) | −1.00000 | + | 1.73205i | −0.0362977 | + | 0.0628695i | ||||
\(760\) | 0.757359 | − | 1.31178i | 0.0274723 | − | 0.0475834i | ||||
\(761\) | 5.17157 | + | 8.95743i | 0.187469 | + | 0.324706i | 0.944406 | − | 0.328782i | \(-0.106638\pi\) |
−0.756936 | + | 0.653488i | \(0.773305\pi\) | |||||||
\(762\) | −4.82843 | −0.174915 | ||||||||
\(763\) | 14.8284 | − | 36.3221i | 0.536825 | − | 1.31495i | ||||
\(764\) | −10.8284 | −0.391759 | ||||||||
\(765\) | 0.671573 | + | 1.16320i | 0.0242808 | + | 0.0420555i | ||||
\(766\) | −3.82843 | + | 6.63103i | −0.138327 | + | 0.239589i | ||||
\(767\) | 1.51472 | − | 2.62357i | 0.0546933 | − | 0.0947316i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 10.6863 | 0.385358 | 0.192679 | − | 0.981262i | \(-0.438282\pi\) | ||||
0.192679 | + | 0.981262i | \(0.438282\pi\) | |||||||
\(770\) | −1.34315 | − | 1.73205i | −0.0484036 | − | 0.0624188i | ||||
\(771\) | 22.4853 | 0.809788 | ||||||||
\(772\) | −5.74264 | − | 9.94655i | −0.206682 | − | 0.357984i | ||||
\(773\) | 4.62132 | − | 8.00436i | 0.166217 | − | 0.287897i | −0.770870 | − | 0.636993i | \(-0.780178\pi\) |
0.937087 | + | 0.349096i | \(0.113511\pi\) | |||||||
\(774\) | −5.82843 | + | 10.0951i | −0.209498 | + | 0.362862i | ||||
\(775\) | −4.82843 | − | 8.36308i | −0.173442 | − | 0.300411i | ||||
\(776\) | 9.65685 | 0.346661 | ||||||||
\(777\) | 8.31371 | − | 1.13770i | 0.298253 | − | 0.0408149i | ||||
\(778\) | −13.4558 | −0.482415 | ||||||||
\(779\) | 19.7990 | + | 34.2929i | 0.709372 | + | 1.22867i | ||||
\(780\) | 0.378680 | − | 0.655892i | 0.0135589 | − | 0.0234847i | ||||
\(781\) | 9.82843 | − | 17.0233i | 0.351689 | − | 0.609143i | ||||
\(782\) | −1.62132 | − | 2.80821i | −0.0579783 | − | 0.100421i | ||||
\(783\) | −1.17157 | −0.0418686 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | −1.79899 | −0.0642087 | ||||||||
\(786\) | 9.57107 | + | 16.5776i | 0.341389 | + | 0.591303i | ||||
\(787\) | −5.52082 | + | 9.56233i | −0.196796 | + | 0.340860i | −0.947488 | − | 0.319792i | \(-0.896387\pi\) |
0.750692 | + | 0.660652i | \(0.229720\pi\) | |||||||
\(788\) | 3.58579 | − | 6.21076i | 0.127738 | − | 0.221249i | ||||
\(789\) | 1.65685 | + | 2.86976i | 0.0589856 | + | 0.102166i | ||||
\(790\) | 4.14214 | 0.147371 | ||||||||
\(791\) | 35.9853 | − | 4.92447i | 1.27949 | − | 0.175094i | ||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | −1.82843 | − | 3.16693i | −0.0649294 | − | 0.112461i | ||||
\(794\) | 1.32843 | − | 2.30090i | 0.0471441 | − | 0.0816560i | ||||
\(795\) | 2.08579 | − | 3.61269i | 0.0739752 | − | 0.128129i | ||||
\(796\) | 8.17157 | + | 14.1536i | 0.289634 | + | 0.501660i | ||||
\(797\) | 13.8701 | 0.491303 | 0.245651 | − | 0.969358i | \(-0.420998\pi\) | ||||
0.245651 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(798\) | −5.92893 | − | 7.64564i | −0.209882 | − | 0.270653i | ||||
\(799\) | −29.1838 | −1.03245 | ||||||||
\(800\) | −2.41421 | − | 4.18154i | −0.0853553 | − | 0.147840i | ||||
\(801\) | −0.585786 | + | 1.01461i | −0.0206977 | + | 0.0358495i | ||||
\(802\) | 13.3492 | − | 23.1216i | 0.471378 | − | 0.816451i | ||||
\(803\) | 10.6569 | + | 18.4582i | 0.376072 | + | 0.651376i | ||||
\(804\) | 14.8995 | 0.525465 | ||||||||
\(805\) | 0.414214 | − | 1.01461i | 0.0145991 | − | 0.0357604i | ||||
\(806\) | −3.65685 | −0.128807 | ||||||||
\(807\) | 6.00000 | + | 10.3923i | 0.211210 | + | 0.365826i | ||||
\(808\) | 1.58579 | − | 2.74666i | 0.0557878 | − | 0.0966273i | ||||
\(809\) | −2.07107 | + | 3.58719i | −0.0728149 | + | 0.126119i | −0.900134 | − | 0.435613i | \(-0.856532\pi\) |
0.827319 | + | 0.561732i | \(0.189865\pi\) | |||||||
\(810\) | 0.207107 | + | 0.358719i | 0.00727699 | + | 0.0126041i | ||||
\(811\) | −41.1127 | −1.44366 | −0.721831 | − | 0.692069i | \(-0.756699\pi\) | ||||
−0.721831 | + | 0.692069i | \(0.756699\pi\) | |||||||
\(812\) | −1.17157 | + | 2.86976i | −0.0411141 | + | 0.100709i | ||||
\(813\) | 26.2843 | 0.921830 | ||||||||
\(814\) | −3.17157 | − | 5.49333i | −0.111164 | − | 0.192541i | ||||
\(815\) | 2.00000 | − | 3.46410i | 0.0700569 | − | 0.121342i | ||||
\(816\) | 1.62132 | − | 2.80821i | 0.0567576 | − | 0.0983070i | ||||
\(817\) | 21.3137 | + | 36.9164i | 0.745672 | + | 1.29154i | ||||
\(818\) | −12.7990 | −0.447506 | ||||||||
\(819\) | −2.96447 | − | 3.82282i | −0.103587 | − | 0.133580i | ||||
\(820\) | −4.48528 | −0.156633 | ||||||||
\(821\) | −27.1421 | − | 47.0116i | −0.947267 | − | 1.64071i | −0.751147 | − | 0.660135i | \(-0.770499\pi\) |
−0.196120 | − | 0.980580i | \(-0.562834\pi\) | |||||||
\(822\) | −5.20711 | + | 9.01897i | −0.181619 | + | 0.314573i | ||||
\(823\) | −12.8995 | + | 22.3426i | −0.449648 | + | 0.778813i | −0.998363 | − | 0.0571962i | \(-0.981784\pi\) |
0.548715 | + | 0.836010i | \(0.315117\pi\) | |||||||
\(824\) | −4.44975 | − | 7.70719i | −0.155014 | − | 0.268493i | ||||
\(825\) | −9.65685 | −0.336209 | ||||||||
\(826\) | 4.34315 | − | 0.594346i | 0.151117 | − | 0.0206799i | ||||
\(827\) | 2.62742 | 0.0913642 | 0.0456821 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456821 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | −10.9142 | + | 18.9040i | −0.379066 | + | 0.656562i | −0.990927 | − | 0.134404i | \(-0.957088\pi\) |
0.611860 | + | 0.790966i | \(0.290421\pi\) | |||||||
\(830\) | 2.65685 | − | 4.60181i | 0.0922208 | − | 0.159731i | ||||
\(831\) | 15.6421 | + | 27.0930i | 0.542620 | + | 0.939845i | ||||
\(832\) | −1.82843 | −0.0633893 | ||||||||
\(833\) | 5.65076 | − | 21.9839i | 0.195787 | − | 0.761696i | ||||
\(834\) | 13.3137 | 0.461016 | ||||||||
\(835\) | 3.06497 | + | 5.30869i | 0.106068 | + | 0.183715i | ||||
\(836\) | −3.65685 | + | 6.33386i | −0.126475 | + | 0.219061i | ||||
\(837\) | 1.00000 | − | 1.73205i | 0.0345651 | − | 0.0598684i | ||||
\(838\) | 12.2426 | + | 21.2049i | 0.422915 | + | 0.732510i | ||||
\(839\) | −8.97056 | −0.309698 | −0.154849 | − | 0.987938i | \(-0.549489\pi\) | ||||
−0.154849 | + | 0.987938i | \(0.549489\pi\) | |||||||
\(840\) | 1.08579 | − | 0.148586i | 0.0374632 | − | 0.00512672i | ||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | 7.65685 | + | 13.2621i | 0.263873 | + | 0.457041i | ||||
\(843\) | 8.20711 | − | 14.2151i | 0.282668 | − | 0.489595i | ||||
\(844\) | 8.41421 | − | 14.5738i | 0.289629 | − | 0.501652i | ||||
\(845\) | 2.00000 | + | 3.46410i | 0.0688021 | + | 0.119169i | ||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | −11.3492 | − | 14.6354i | −0.389965 | − | 0.502878i | ||||
\(848\) | −10.0711 | −0.345842 | ||||||||
\(849\) | −3.69239 | − | 6.39540i | −0.126722 | − | 0.219490i | ||||
\(850\) | 7.82843 | − | 13.5592i | 0.268513 | − | 0.465078i | ||||
\(851\) | 1.58579 | − | 2.74666i | 0.0543601 | − | 0.0941544i | ||||
\(852\) | 4.91421 | + | 8.51167i | 0.168358 | + | 0.291605i | ||||
\(853\) | 48.9117 | 1.67470 | 0.837352 | − | 0.546664i | \(-0.184102\pi\) | ||||
0.837352 | + | 0.546664i | \(0.184102\pi\) | |||||||
\(854\) | 2.00000 | − | 4.89898i | 0.0684386 | − | 0.167640i | ||||
\(855\) | 1.51472 | 0.0518023 | ||||||||
\(856\) | 2.82843 | + | 4.89898i | 0.0966736 | + | 0.167444i | ||||
\(857\) | −22.3137 | + | 38.6485i | −0.762222 | + | 1.32021i | 0.179481 | + | 0.983761i | \(0.442558\pi\) |
−0.941703 | + | 0.336445i | \(0.890775\pi\) | |||||||
\(858\) | −1.82843 | + | 3.16693i | −0.0624215 | + | 0.108117i | ||||
\(859\) | 6.34315 | + | 10.9867i | 0.216425 | + | 0.374860i | 0.953713 | − | 0.300720i | \(-0.0972269\pi\) |
−0.737287 | + | 0.675579i | \(0.763894\pi\) | |||||||
\(860\) | −4.82843 | −0.164648 | ||||||||
\(861\) | −10.8284 | + | 26.5241i | −0.369032 | + | 0.903940i | ||||
\(862\) | 4.68629 | 0.159616 | ||||||||
\(863\) | −15.6716 | − | 27.1440i | −0.533467 | − | 0.923991i | −0.999236 | − | 0.0390850i | \(-0.987556\pi\) |
0.465769 | − | 0.884906i | \(-0.345778\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −3.17157 | + | 5.49333i | −0.107837 | + | 0.186779i | ||||
\(866\) | −7.00000 | − | 12.1244i | −0.237870 | − | 0.412002i | ||||
\(867\) | −6.48528 | −0.220252 | ||||||||
\(868\) | −3.24264 | − | 4.18154i | −0.110062 | − | 0.141931i | ||||
\(869\) | −20.0000 | −0.678454 | ||||||||
\(870\) | −0.242641 | − | 0.420266i | −0.00822629 | − | 0.0142484i | ||||
\(871\) | 13.6213 | − | 23.5928i | 0.461541 | − | 0.799412i | ||||
\(872\) | 7.41421 | − | 12.8418i | 0.251077 | − | 0.434878i | ||||
\(873\) | 4.82843 | + | 8.36308i | 0.163417 | + | 0.283047i | ||||
\(874\) | −3.65685 | −0.123695 | ||||||||
\(875\) | 10.6716 | − | 1.46037i | 0.360765 | − | 0.0493696i | ||||
\(876\) | −10.6569 | −0.360062 | ||||||||
\(877\) | 20.1569 | + | 34.9127i | 0.680649 | + | 1.17892i | 0.974783 | + | 0.223154i | \(0.0716353\pi\) |
−0.294135 | + | 0.955764i | \(0.595031\pi\) | |||||||
\(878\) | −1.48528 | + | 2.57258i | −0.0501258 | + | 0.0868205i | ||||
\(879\) | 3.20711 | − | 5.55487i | 0.108173 | − | 0.187361i | ||||
\(880\) | −0.414214 | − | 0.717439i | −0.0139631 | − | 0.0241849i | ||||
\(881\) | −31.7279 | −1.06894 | −0.534470 | − | 0.845187i | \(-0.679489\pi\) | ||||
−0.534470 | + | 0.845187i | \(0.679489\pi\) | |||||||
\(882\) | 1.74264 | − | 6.77962i | 0.0586778 | − | 0.228282i | ||||
\(883\) | 12.2843 | 0.413399 | 0.206699 | − | 0.978405i | \(-0.433728\pi\) | ||||
0.206699 | + | 0.978405i | \(0.433728\pi\) | |||||||
\(884\) | −2.96447 | − | 5.13461i | −0.0997058 | − | 0.172695i | ||||
\(885\) | −0.343146 | + | 0.594346i | −0.0115347 | + | 0.0199787i | ||||
\(886\) | −8.57107 | + | 14.8455i | −0.287951 | + | 0.498745i | ||||
\(887\) | −3.51472 | − | 6.08767i | −0.118013 | − | 0.204404i | 0.800967 | − | 0.598708i | \(-0.204319\pi\) |
−0.918980 | + | 0.394304i | \(0.870986\pi\) | |||||||
\(888\) | 3.17157 | 0.106431 | ||||||||
\(889\) | −12.6569 | + | 1.73205i | −0.424497 | + | 0.0580911i | ||||
\(890\) | −0.485281 | −0.0162667 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | −2.24264 | + | 3.88437i | −0.0750892 | + | 0.130058i | ||||
\(893\) | −16.4558 | + | 28.5024i | −0.550674 | + | 0.953795i | ||||
\(894\) | 0.378680 | + | 0.655892i | 0.0126649 | + | 0.0219363i | ||||
\(895\) | 4.95837 | 0.165740 | ||||||||
\(896\) | −1.62132 | − | 2.09077i | −0.0541645 | − | 0.0698477i | ||||
\(897\) | −1.82843 | −0.0610494 | ||||||||
\(898\) | 13.2426 | + | 22.9369i | 0.441913 | + | 0.765415i | ||||
\(899\) | −1.17157 | + | 2.02922i | −0.0390741 | + | 0.0676784i | ||||
\(900\) | 2.41421 | − | 4.18154i | 0.0804738 | − | 0.139385i | ||||
\(901\) | −16.3284 | − | 28.2817i | −0.543979 | − | 0.942199i | ||||
\(902\) | 21.6569 | 0.721094 | ||||||||
\(903\) | −11.6569 | + | 28.5533i | −0.387916 | + | 0.950196i | ||||
\(904\) | 13.7279 | 0.456584 | ||||||||
\(905\) | −2.75736 | − | 4.77589i | −0.0916577 | − | 0.158756i | ||||
\(906\) | 7.07107 | − | 12.2474i | 0.234920 | − | 0.406894i | ||||
\(907\) | −11.5503 | + | 20.0056i | −0.383520 | + | 0.664276i | −0.991563 | − | 0.129628i | \(-0.958622\pi\) |
0.608043 | + | 0.793904i | \(0.291955\pi\) | |||||||
\(908\) | −11.4853 | − | 19.8931i | −0.381152 | − | 0.660175i | ||||
\(909\) | 3.17157 | 0.105194 | ||||||||
\(910\) | 0.757359 | − | 1.85514i | 0.0251062 | − | 0.0614974i | ||||
\(911\) | −8.48528 | −0.281130 | −0.140565 | − | 0.990071i | \(-0.544892\pi\) | ||||
−0.140565 | + | 0.990071i | \(0.544892\pi\) | |||||||
\(912\) | −1.82843 | − | 3.16693i | −0.0605453 | − | 0.104867i | ||||
\(913\) | −12.8284 | + | 22.2195i | −0.424559 | + | 0.735358i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.414214 | + | 0.717439i | 0.0136935 | + | 0.0237178i | ||||
\(916\) | −26.1421 | −0.863760 | ||||||||
\(917\) | 31.0355 | + | 40.0218i | 1.02488 | + | 1.32164i | ||||
\(918\) | 3.24264 | 0.107023 | ||||||||
\(919\) | −0.863961 | − | 1.49642i | −0.0284994 | − | 0.0493625i | 0.851424 | − | 0.524478i | \(-0.175740\pi\) |
−0.879923 | + | 0.475116i | \(0.842406\pi\) | |||||||
\(920\) | 0.207107 | − | 0.358719i | 0.00682811 | − | 0.0118266i | ||||
\(921\) | −7.07107 | + | 12.2474i | −0.233000 | + | 0.403567i | ||||
\(922\) | 7.00000 | + | 12.1244i | 0.230533 | + | 0.399294i | ||||
\(923\) | 17.9706 | 0.591508 | ||||||||
\(924\) | −5.24264 | + | 0.717439i | −0.172470 | + | 0.0236020i | ||||
\(925\) | 15.3137 | 0.503512 | ||||||||
\(926\) | 5.31371 | + | 9.20361i | 0.174619 | + | 0.302449i | ||||
\(927\) | 4.44975 | − | 7.70719i | 0.146149 | − | 0.253137i | ||||
\(928\) | −0.585786 | + | 1.01461i | −0.0192294 | + | 0.0333063i | ||||
\(929\) | 25.3137 | + | 43.8446i | 0.830516 | + | 1.43850i | 0.897630 | + | 0.440750i | \(0.145288\pi\) |
−0.0671139 | + | 0.997745i | \(0.521379\pi\) | |||||||
\(930\) | 0.828427 | 0.0271652 | ||||||||
\(931\) | −18.2843 | − | 17.9149i | −0.599243 | − | 0.587136i | ||||
\(932\) | −8.00000 | −0.262049 | ||||||||
\(933\) | −3.15685 | − | 5.46783i | −0.103351 | − | 0.179009i | ||||
\(934\) | 5.17157 | − | 8.95743i | 0.169219 | − | 0.293096i | ||||
\(935\) | 1.34315 | − | 2.32640i | 0.0439256 | − | 0.0760813i | ||||
\(936\) | −0.914214 | − | 1.58346i | −0.0298820 | − | 0.0517572i | ||||
\(937\) | −12.4853 | −0.407876 | −0.203938 | − | 0.978984i | \(-0.565374\pi\) | ||||
−0.203938 | + | 0.978984i | \(0.565374\pi\) | |||||||
\(938\) | 39.0563 | − | 5.34474i | 1.27524 | − | 0.174512i | ||||
\(939\) | −0.970563 | −0.0316731 | ||||||||
\(940\) | −1.86396 | − | 3.22848i | −0.0607957 | − | 0.105301i | ||||
\(941\) | −24.2426 | + | 41.9895i | −0.790288 | + | 1.36882i | 0.135501 | + | 0.990777i | \(0.456735\pi\) |
−0.925789 | + | 0.378041i | \(0.876598\pi\) | |||||||
\(942\) | −2.17157 | + | 3.76127i | −0.0707537 | + | 0.122549i | ||||
\(943\) | 5.41421 | + | 9.37769i | 0.176311 | + | 0.305380i | ||||
\(944\) | 1.65685 | 0.0539260 | ||||||||
\(945\) | 0.671573 | + | 0.866025i | 0.0218463 | + | 0.0281718i | ||||
\(946\) | 23.3137 | 0.757994 | ||||||||
\(947\) | 17.1569 | + | 29.7165i | 0.557523 | + | 0.965658i | 0.997702 | + | 0.0677482i | \(0.0215814\pi\) |
−0.440180 | + | 0.897910i | \(0.645085\pi\) | |||||||
\(948\) | 5.00000 | − | 8.66025i | 0.162392 | − | 0.281272i | ||||
\(949\) | −9.74264 | + | 16.8747i | −0.316259 | + | 0.547778i | ||||
\(950\) | −8.82843 | − | 15.2913i | −0.286432 | − | 0.496115i | ||||
\(951\) | 12.6274 | 0.409472 | ||||||||
\(952\) | 3.24264 | − | 7.94282i | 0.105095 | − | 0.257428i | ||||
\(953\) | −27.7990 | −0.900498 | −0.450249 | − | 0.892903i | \(-0.648665\pi\) | ||||
−0.450249 | + | 0.892903i | \(0.648665\pi\) | |||||||
\(954\) | −5.03553 | − | 8.72180i | −0.163031 | − | 0.282379i | ||||
\(955\) | 2.24264 | − | 3.88437i | 0.0725701 | − | 0.125695i | ||||
\(956\) | −10.8284 | + | 18.7554i | −0.350216 | + | 0.606593i | ||||
\(957\) | 1.17157 | + | 2.02922i | 0.0378716 | + | 0.0655955i | ||||
\(958\) | −34.1421 | −1.10308 | ||||||||
\(959\) | −10.4142 | + | 25.5095i | −0.336292 | + | 0.823745i | ||||
\(960\) | 0.414214 | 0.0133687 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 2.89949 | − | 5.02207i | 0.0934835 | − | 0.161918i | ||||
\(963\) | −2.82843 | + | 4.89898i | −0.0911448 | + | 0.157867i | ||||
\(964\) | 3.58579 | + | 6.21076i | 0.115490 | + | 0.200035i | ||||
\(965\) | 4.75736 | 0.153145 | ||||||||
\(966\) | −1.62132 | − | 2.09077i | −0.0521651 | − | 0.0672694i | ||||
\(967\) | −5.17157 | −0.166307 | −0.0831533 | − | 0.996537i | \(-0.526499\pi\) | ||||
−0.0831533 | + | 0.996537i | \(0.526499\pi\) | |||||||
\(968\) | −3.50000 | − | 6.06218i | −0.112494 | − | 0.194846i | ||||
\(969\) | 5.92893 | − | 10.2692i | 0.190465 | − | 0.329895i | ||||
\(970\) | −2.00000 | + | 3.46410i | −0.0642161 | + | 0.111226i | ||||
\(971\) | −1.17157 | − | 2.02922i | −0.0375976 | − | 0.0651209i | 0.846614 | − | 0.532207i | \(-0.178637\pi\) |
−0.884212 | + | 0.467086i | \(0.845304\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 34.8995 | − | 4.77589i | 1.11883 | − | 0.153108i | ||||
\(974\) | 32.7696 | 1.05000 | ||||||||
\(975\) | −4.41421 | − | 7.64564i | −0.141368 | − | 0.244857i | ||||
\(976\) | 1.00000 | − | 1.73205i | 0.0320092 | − | 0.0554416i | ||||
\(977\) | 23.1777 | − | 40.1449i | 0.741519 | − | 1.28435i | −0.210284 | − | 0.977640i | \(-0.567439\pi\) |
0.951803 | − | 0.306709i | \(-0.0992278\pi\) | |||||||
\(978\) | −4.82843 | − | 8.36308i | −0.154396 | − | 0.267422i | ||||
\(979\) | 2.34315 | 0.0748873 | ||||||||
\(980\) | 2.79289 | − | 0.778985i | 0.0892157 | − | 0.0248838i | ||||
\(981\) | 14.8284 | 0.473435 | ||||||||
\(982\) | −5.67157 | − | 9.82345i | −0.180987 | − | 0.313479i | ||||
\(983\) | −25.7279 | + | 44.5621i | −0.820593 | + | 1.42131i | 0.0846478 | + | 0.996411i | \(0.473023\pi\) |
−0.905241 | + | 0.424898i | \(0.860310\pi\) | |||||||
\(984\) | −5.41421 | + | 9.37769i | −0.172599 | + | 0.298950i | ||||
\(985\) | 1.48528 | + | 2.57258i | 0.0473250 | + | 0.0819693i | ||||
\(986\) | −3.79899 | −0.120984 | ||||||||
\(987\) | −23.5919 | + | 3.22848i | −0.750938 | + | 0.102763i | ||||
\(988\) | −6.68629 | −0.212719 | ||||||||
\(989\) | 5.82843 | + | 10.0951i | 0.185333 | + | 0.321007i | ||||
\(990\) | 0.414214 | − | 0.717439i | 0.0131646 | − | 0.0228017i | ||||
\(991\) | 23.9706 | − | 41.5182i | 0.761450 | − | 1.31887i | −0.180653 | − | 0.983547i | \(-0.557821\pi\) |
0.942103 | − | 0.335323i | \(-0.108846\pi\) | |||||||
\(992\) | −1.00000 | − | 1.73205i | −0.0317500 | − | 0.0549927i | ||||
\(993\) | −17.5147 | −0.555813 | ||||||||
\(994\) | 15.9350 | + | 20.5490i | 0.505428 | + | 0.651774i | ||||
\(995\) | −6.76955 | −0.214609 | ||||||||
\(996\) | −6.41421 | − | 11.1097i | −0.203242 | − | 0.352026i | ||||
\(997\) | −10.3137 | + | 17.8639i | −0.326638 | + | 0.565754i | −0.981843 | − | 0.189698i | \(-0.939249\pi\) |
0.655204 | + | 0.755452i | \(0.272583\pi\) | |||||||
\(998\) | 0.585786 | − | 1.01461i | 0.0185427 | − | 0.0321170i | ||||
\(999\) | 1.58579 | + | 2.74666i | 0.0501721 | + | 0.0869006i |
(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.277.1 | ✓ | 4 | |
7.2 | even | 3 | inner | 966.2.i.j.415.1 | yes | 4 | |
7.3 | odd | 6 | 6762.2.a.bt.1.1 | 2 | |||
7.4 | even | 3 | 6762.2.a.bv.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.j.277.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
966.2.i.j.415.1 | yes | 4 | 7.2 | even | 3 | inner | |
6762.2.a.bt.1.1 | 2 | 7.3 | odd | 6 | |||
6762.2.a.bv.1.2 | 2 | 7.4 | even | 3 |