Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(424,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.424");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.r (of order \(6\), degree \(2\), not 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 424.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.424 |
Dual form | 525.2.r.g.499.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | −2.09077 | − | 1.62132i | −0.790237 | − | 0.612801i | ||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70711 | + | 2.95680i | −0.514712 | + | 0.891507i | 0.485142 | + | 0.874435i | \(0.338768\pi\) |
−0.999854 | + | 0.0170722i | \(0.994565\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.58579i | − | 0.439818i | −0.975520 | − | 0.219909i | \(-0.929424\pi\) | ||
0.975520 | − | 0.219909i | \(-0.0705760\pi\) | |||||||
\(14\) | 3.70711 | + | 0.507306i | 0.990766 | + | 0.135583i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −5.40629 | − | 3.12132i | −1.31122 | − | 0.757031i | −0.328919 | − | 0.944358i | \(-0.606684\pi\) |
−0.982298 | + | 0.187327i | \(0.940018\pi\) | |||||||
\(18\) | −1.22474 | − | 0.707107i | −0.288675 | − | 0.166667i | ||||
\(19\) | −3.32843 | − | 5.76500i | −0.763594 | − | 1.32258i | −0.940987 | − | 0.338443i | \(-0.890100\pi\) |
0.177393 | − | 0.984140i | \(-0.443233\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 2.44949i | −0.218218 | − | 0.534522i | ||||
\(22\) | − | 4.82843i | − | 1.02942i | ||||||
\(23\) | −5.40629 | + | 3.12132i | −1.12729 | + | 0.650840i | −0.943252 | − | 0.332079i | \(-0.892250\pi\) |
−0.184037 | + | 0.982919i | \(0.558917\pi\) | |||||||
\(24\) | 1.41421 | − | 2.44949i | 0.288675 | − | 0.500000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.12132 | + | 1.94218i | 0.219909 | + | 0.380894i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.242641 | 0.0450572 | 0.0225286 | − | 0.999746i | \(-0.492828\pi\) | ||||
0.0225286 | + | 0.999746i | \(0.492828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0857864 | − | 0.148586i | 0.0154077 | − | 0.0266869i | −0.858219 | − | 0.513284i | \(-0.828429\pi\) |
0.873626 | + | 0.486597i | \(0.161762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.95680 | + | 1.70711i | −0.514712 | + | 0.297169i | ||||
\(34\) | 8.82843 | 1.51406 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.83743 | − | 2.79289i | 0.795269 | − | 0.459149i | −0.0465451 | − | 0.998916i | \(-0.514821\pi\) |
0.841814 | + | 0.539767i | \(0.181488\pi\) | |||||||
\(38\) | 8.15295 | + | 4.70711i | 1.32258 | + | 0.763594i | ||||
\(39\) | 0.792893 | − | 1.37333i | 0.126965 | − | 0.219909i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24264 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(42\) | 2.95680 | + | 2.29289i | 0.456243 | + | 0.353801i | ||||
\(43\) | − | 10.4142i | − | 1.58815i | −0.607818 | − | 0.794076i | \(-0.707955\pi\) | ||
0.607818 | − | 0.794076i | \(-0.292045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.41421 | − | 7.64564i | 0.650840 | − | 1.12729i | ||||
\(47\) | −8.06591 | + | 4.65685i | −1.17653 | + | 0.679272i | −0.955210 | − | 0.295928i | \(-0.904371\pi\) |
−0.221324 | + | 0.975200i | \(0.571038\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | 1.74264 | + | 6.77962i | 0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.12132 | − | 5.40629i | −0.437072 | − | 0.757031i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.01461 | − | 0.585786i | −0.139368 | − | 0.0804640i | 0.428695 | − | 0.903449i | \(-0.358974\pi\) |
−0.568063 | + | 0.822985i | \(0.692307\pi\) | |||||||
\(54\) | −0.707107 | − | 1.22474i | −0.0962250 | − | 0.166667i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.58579 | + | 5.91359i | −0.612801 | + | 0.790237i | ||||
\(57\) | − | 6.65685i | − | 0.881722i | ||||||
\(58\) | −0.297173 | + | 0.171573i | −0.0390207 | + | 0.0225286i | ||||
\(59\) | 0.707107 | − | 1.22474i | 0.0920575 | − | 0.159448i | −0.816319 | − | 0.577601i | \(-0.803989\pi\) |
0.908377 | + | 0.418153i | \(0.137322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24264 | − | 10.8126i | −0.799288 | − | 1.38441i | −0.920080 | − | 0.391730i | \(-0.871877\pi\) |
0.120792 | − | 0.992678i | \(-0.461457\pi\) | |||||||
\(62\) | 0.242641i | 0.0308154i | ||||||||
\(63\) | 0.358719 | − | 2.62132i | 0.0451944 | − | 0.330255i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.41421 | − | 4.18154i | 0.297169 | − | 0.514712i | ||||
\(67\) | 10.1567 | + | 5.86396i | 1.24084 | + | 0.716397i | 0.969264 | − | 0.246021i | \(-0.0791234\pi\) |
0.271571 | + | 0.962418i | \(0.412457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.24264 | −0.751526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.41421 | −0.405193 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(72\) | 2.44949 | − | 1.41421i | 0.288675 | − | 0.166667i | ||||
\(73\) | −1.79360 | − | 1.03553i | −0.209925 | − | 0.121200i | 0.391352 | − | 0.920241i | \(-0.372008\pi\) |
−0.601276 | + | 0.799041i | \(0.705341\pi\) | |||||||
\(74\) | −3.94975 | + | 6.84116i | −0.459149 | + | 0.795269i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.36308 | − | 3.41421i | 0.953062 | − | 0.389086i | ||||
\(78\) | 2.24264i | 0.253929i | ||||||||
\(79\) | −2.32843 | − | 4.03295i | −0.261969 | − | 0.453743i | 0.704796 | − | 0.709410i | \(-0.251038\pi\) |
−0.966765 | + | 0.255667i | \(0.917705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.74666 | + | 1.58579i | −0.303318 | + | 0.175121i | ||||
\(83\) | 5.41421i | 0.594287i | 0.954833 | + | 0.297144i | \(0.0960340\pi\) | ||||
−0.954833 | + | 0.297144i | \(0.903966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.36396 | + | 12.7548i | 0.794076 | + | 1.37538i | ||||
\(87\) | 0.210133 | + | 0.121320i | 0.0225286 | + | 0.0130069i | ||||
\(88\) | 8.36308 | + | 4.82843i | 0.891507 | + | 0.514712i | ||||
\(89\) | −1.87868 | − | 3.25397i | −0.199140 | − | 0.344920i | 0.749110 | − | 0.662446i | \(-0.230481\pi\) |
−0.948250 | + | 0.317526i | \(0.897148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.57107 | + | 3.31552i | −0.269521 | + | 0.347560i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.148586 | − | 0.0857864i | 0.0154077 | − | 0.00889564i | ||||
\(94\) | 6.58579 | − | 11.4069i | 0.679272 | − | 1.17653i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8284i | 1.09946i | 0.835342 | + | 0.549730i | \(0.185269\pi\) | ||||
−0.835342 | + | 0.549730i | \(0.814731\pi\) | |||||||
\(98\) | −6.92820 | − | 7.07107i | −0.699854 | − | 0.714286i | ||||
\(99\) | −3.41421 | −0.343141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.12132 | − | 5.40629i | 0.310583 | − | 0.537946i | −0.667906 | − | 0.744246i | \(-0.732809\pi\) |
0.978489 | + | 0.206300i | \(0.0661424\pi\) | |||||||
\(102\) | 7.64564 | + | 4.41421i | 0.757031 | + | 0.437072i | ||||
\(103\) | −1.07616 | + | 0.621320i | −0.106037 | + | 0.0612205i | −0.552081 | − | 0.833791i | \(-0.686166\pi\) |
0.446044 | + | 0.895011i | \(0.352833\pi\) | |||||||
\(104\) | −4.48528 | −0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.65685 | 0.160928 | ||||||||
\(107\) | −13.3491 | + | 7.70711i | −1.29051 | + | 0.745074i | −0.978744 | − | 0.205086i | \(-0.934253\pi\) |
−0.311762 | + | 0.950160i | \(0.600919\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.74264 | + | 11.6786i | −0.645828 | + | 1.11861i | 0.338282 | + | 0.941045i | \(0.390154\pi\) |
−0.984110 | + | 0.177562i | \(0.943179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.58579 | 0.530179 | ||||||||
\(112\) | 1.43488 | − | 10.4853i | 0.135583 | − | 0.990766i | ||||
\(113\) | − | 4.34315i | − | 0.408569i | −0.978912 | − | 0.204284i | \(-0.934513\pi\) | ||
0.978912 | − | 0.204284i | \(-0.0654867\pi\) | |||||||
\(114\) | 4.70711 | + | 8.15295i | 0.440861 | + | 0.763594i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.37333 | − | 0.792893i | 0.126965 | − | 0.0733030i | ||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | 6.24264 | + | 15.2913i | 0.572262 | + | 1.40175i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.328427 | − | 0.568852i | −0.0298570 | − | 0.0517139i | ||||
\(122\) | 15.2913 | + | 8.82843i | 1.38441 | + | 0.799288i | ||||
\(123\) | 1.94218 | + | 1.12132i | 0.175121 | + | 0.101106i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.41421 | + | 3.46410i | 0.125988 | + | 0.308607i | ||||
\(127\) | 18.0711i | 1.60355i | 0.597627 | + | 0.801774i | \(0.296110\pi\) | ||||
−0.597627 | + | 0.801774i | \(0.703890\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.866025 | − | 0.500000i | ||||
\(129\) | 5.20711 | − | 9.01897i | 0.458460 | − | 0.794076i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.24264 | + | 9.08052i | 0.458052 | + | 0.793369i | 0.998858 | − | 0.0477784i | \(-0.0152141\pi\) |
−0.540806 | + | 0.841147i | \(0.681881\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.38794 | + | 17.4497i | −0.207061 | + | 1.51308i | ||||
\(134\) | −16.5858 | −1.43279 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.82843 | + | 15.2913i | −0.757031 | + | 1.31122i | ||||
\(137\) | −2.53653 | − | 1.46447i | −0.216710 | − | 0.125118i | 0.387716 | − | 0.921779i | \(-0.373264\pi\) |
−0.604426 | + | 0.796661i | \(0.706598\pi\) | |||||||
\(138\) | 7.64564 | − | 4.41421i | 0.650840 | − | 0.375763i | ||||
\(139\) | −11.4853 | −0.974169 | −0.487084 | − | 0.873355i | \(-0.661940\pi\) | ||||
−0.487084 | + | 0.873355i | \(0.661940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.31371 | −0.784356 | ||||||||
\(142\) | 4.18154 | − | 2.41421i | 0.350907 | − | 0.202596i | ||||
\(143\) | 4.68885 | + | 2.70711i | 0.392101 | + | 0.226380i | ||||
\(144\) | −2.00000 | + | 3.46410i | −0.166667 | + | 0.288675i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.92893 | 0.242400 | ||||||||
\(147\) | −1.88064 | + | 6.74264i | −0.155112 | + | 0.556124i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.82843 | + | 15.2913i | 0.723253 | + | 1.25271i | 0.959689 | + | 0.281064i | \(0.0906873\pi\) |
−0.236436 | + | 0.971647i | \(0.575979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.24264 | − | 5.61642i | 0.263882 | − | 0.457058i | −0.703388 | − | 0.710806i | \(-0.748330\pi\) |
0.967270 | + | 0.253749i | \(0.0816636\pi\) | |||||||
\(152\) | −16.3059 | + | 9.41421i | −1.32258 | + | 0.763594i | ||||
\(153\) | − | 6.24264i | − | 0.504688i | ||||||
\(154\) | −7.82843 | + | 10.0951i | −0.630833 | + | 0.813489i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.9795 | − | 8.07107i | −1.11569 | − | 0.644141i | −0.175390 | − | 0.984499i | \(-0.556118\pi\) |
−0.940296 | + | 0.340358i | \(0.889452\pi\) | |||||||
\(158\) | 5.70346 | + | 3.29289i | 0.453743 | + | 0.261969i | ||||
\(159\) | −0.585786 | − | 1.01461i | −0.0464559 | − | 0.0804640i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3640 | + | 2.23936i | 1.28966 | + | 0.176486i | ||||
\(162\) | − | 1.41421i | − | 0.111111i | ||||||
\(163\) | −16.7262 | + | 9.65685i | −1.31009 | + | 0.756383i | −0.982111 | − | 0.188301i | \(-0.939702\pi\) |
−0.327983 | + | 0.944684i | \(0.606369\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.82843 | − | 6.63103i | −0.297144 | − | 0.514668i | ||||
\(167\) | − | 11.7574i | − | 0.909812i | −0.890540 | − | 0.454906i | \(-0.849673\pi\) | ||
0.890540 | − | 0.454906i | \(-0.150327\pi\) | |||||||
\(168\) | −6.92820 | + | 2.82843i | −0.534522 | + | 0.218218i | ||||
\(169\) | 10.4853 | 0.806560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.32843 | − | 5.76500i | 0.254531 | − | 0.440861i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.44949 | + | 1.41421i | −0.186231 | + | 0.107521i | −0.590217 | − | 0.807245i | \(-0.700958\pi\) |
0.403986 | + | 0.914765i | \(0.367625\pi\) | |||||||
\(174\) | −0.343146 | −0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.6569 | −1.02942 | ||||||||
\(177\) | 1.22474 | − | 0.707107i | 0.0920575 | − | 0.0531494i | ||||
\(178\) | 4.60181 | + | 2.65685i | 0.344920 | + | 0.199140i | ||||
\(179\) | 9.82843 | − | 17.0233i | 0.734611 | − | 1.27238i | −0.220283 | − | 0.975436i | \(-0.570698\pi\) |
0.954894 | − | 0.296948i | \(-0.0959687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.656854 | 0.0488236 | 0.0244118 | − | 0.999702i | \(-0.492229\pi\) | ||||
0.0244118 | + | 0.999702i | \(0.492229\pi\) | |||||||
\(182\) | 0.804479 | − | 5.87868i | 0.0596319 | − | 0.435757i | ||||
\(183\) | − | 12.4853i | − | 0.922939i | ||||||
\(184\) | 8.82843 | + | 15.2913i | 0.650840 | + | 1.12729i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.121320 | + | 0.210133i | −0.00889564 | + | 0.0154077i | ||||
\(187\) | 18.4582 | − | 10.6569i | 1.34980 | − | 0.779306i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.62132 | − | 2.09077i | 0.117934 | − | 0.152081i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.48528 | − | 16.4290i | −0.686331 | − | 1.18876i | −0.973017 | − | 0.230735i | \(-0.925887\pi\) |
0.286686 | − | 0.958025i | \(-0.407446\pi\) | |||||||
\(192\) | −6.92820 | − | 4.00000i | −0.500000 | − | 0.288675i | ||||
\(193\) | 5.85204 | + | 3.37868i | 0.421239 | + | 0.243203i | 0.695607 | − | 0.718422i | \(-0.255135\pi\) |
−0.274368 | + | 0.961625i | \(0.588469\pi\) | |||||||
\(194\) | −7.65685 | − | 13.2621i | −0.549730 | − | 0.952160i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.55635i | − | 0.395873i | −0.980215 | − | 0.197937i | \(-0.936576\pi\) | ||
0.980215 | − | 0.197937i | \(-0.0634241\pi\) | |||||||
\(198\) | 4.18154 | − | 2.41421i | 0.297169 | − | 0.171571i | ||||
\(199\) | 2.75736 | − | 4.77589i | 0.195464 | − | 0.338554i | −0.751589 | − | 0.659632i | \(-0.770712\pi\) |
0.947053 | + | 0.321079i | \(0.104045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.86396 | + | 10.1567i | 0.413612 | + | 0.716397i | ||||
\(202\) | 8.82843i | 0.621166i | ||||||||
\(203\) | −0.507306 | − | 0.393398i | −0.0356059 | − | 0.0276111i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.878680 | − | 1.52192i | 0.0612205 | − | 0.106037i | ||||
\(207\) | −5.40629 | − | 3.12132i | −0.375763 | − | 0.216947i | ||||
\(208\) | 5.49333 | − | 3.17157i | 0.380894 | − | 0.219909i | ||||
\(209\) | 22.7279 | 1.57212 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.142136 | 0.00978502 | 0.00489251 | − | 0.999988i | \(-0.498443\pi\) | ||||
0.00489251 | + | 0.999988i | \(0.498443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.95680 | − | 1.70711i | −0.202596 | − | 0.116969i | ||||
\(214\) | 10.8995 | − | 18.8785i | 0.745074 | − | 1.29051i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.82843 | 0.192450 | ||||||||
\(217\) | −0.420266 | + | 0.171573i | −0.0285295 | + | 0.0116471i | ||||
\(218\) | − | 19.0711i | − | 1.29166i | ||||||
\(219\) | −1.03553 | − | 1.79360i | −0.0699749 | − | 0.121200i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.94975 | + | 8.57321i | −0.332956 | + | 0.576697i | ||||
\(222\) | −6.84116 | + | 3.94975i | −0.459149 | + | 0.265090i | ||||
\(223\) | 17.1716i | 1.14989i | 0.818191 | + | 0.574947i | \(0.194977\pi\) | ||||
−0.818191 | + | 0.574947i | \(0.805023\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.07107 | + | 5.31925i | 0.204284 | + | 0.353831i | ||||
\(227\) | 19.9801 | + | 11.5355i | 1.32613 | + | 0.765640i | 0.984698 | − | 0.174267i | \(-0.0557556\pi\) |
0.341429 | + | 0.939907i | \(0.389089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.15685 | − | 12.3960i | −0.472938 | − | 0.819153i | 0.526582 | − | 0.850124i | \(-0.323473\pi\) |
−0.999520 | + | 0.0309713i | \(0.990140\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.94975 | + | 1.22474i | 0.588850 | + | 0.0805823i | ||||
\(232\) | − | 0.686292i | − | 0.0450572i | ||||||
\(233\) | −19.4728 | + | 11.2426i | −1.27571 | + | 0.736530i | −0.976056 | − | 0.217519i | \(-0.930204\pi\) |
−0.299651 | + | 0.954049i | \(0.596870\pi\) | |||||||
\(234\) | −1.12132 | + | 1.94218i | −0.0733030 | + | 0.126965i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.65685i | − | 0.302495i | ||||||
\(238\) | −18.4582 | − | 14.3137i | −1.19647 | − | 0.927820i | ||||
\(239\) | −17.3137 | −1.11993 | −0.559965 | − | 0.828516i | \(-0.689186\pi\) | ||||
−0.559965 | + | 0.828516i | \(0.689186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.17157 | − | 8.95743i | 0.333130 | − | 0.576999i | −0.649994 | − | 0.759940i | \(-0.725228\pi\) |
0.983124 | + | 0.182941i | \(0.0585618\pi\) | |||||||
\(242\) | 0.804479 | + | 0.464466i | 0.0517139 | + | 0.0298570i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.17157 | −0.202212 | ||||||||
\(247\) | −9.14207 | + | 5.27817i | −0.581696 | + | 0.335842i | ||||
\(248\) | −0.420266 | − | 0.242641i | −0.0266869 | − | 0.0154077i | ||||
\(249\) | −2.70711 | + | 4.68885i | −0.171556 | + | 0.297144i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.41421 | −0.341742 | −0.170871 | − | 0.985293i | \(-0.554658\pi\) | ||||
−0.170871 | + | 0.985293i | \(0.554658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.3137i | − | 1.33998i | ||||||
\(254\) | −12.7782 | − | 22.1324i | −0.801774 | − | 1.38871i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.8937 | − | 14.9497i | 1.61521 | − | 0.932540i | 0.627069 | − | 0.778964i | \(-0.284254\pi\) |
0.988137 | − | 0.153576i | \(-0.0490790\pi\) | |||||||
\(258\) | 14.7279i | 0.916920i | ||||||||
\(259\) | −14.6421 | − | 2.00373i | −0.909818 | − | 0.124506i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.121320 | + | 0.210133i | 0.00750954 | + | 0.0130069i | ||||
\(262\) | −12.8418 | − | 7.41421i | −0.793369 | − | 0.458052i | ||||
\(263\) | −1.01461 | − | 0.585786i | −0.0625636 | − | 0.0361211i | 0.468392 | − | 0.883521i | \(-0.344834\pi\) |
−0.530956 | + | 0.847400i | \(0.678167\pi\) | |||||||
\(264\) | 4.82843 | + | 8.36308i | 0.297169 | + | 0.514712i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.41421 | − | 23.0600i | −0.577222 | − | 1.41390i | ||||
\(267\) | − | 3.75736i | − | 0.229947i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.07107 | − | 7.05130i | 0.248217 | − | 0.429925i | −0.714814 | − | 0.699315i | \(-0.753489\pi\) |
0.963031 | + | 0.269390i | \(0.0868219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0711 | − | 17.4436i | −0.611774 | − | 1.05962i | −0.990941 | − | 0.134295i | \(-0.957123\pi\) |
0.379168 | − | 0.925328i | \(-0.376210\pi\) | |||||||
\(272\) | − | 24.9706i | − | 1.51406i | ||||||
\(273\) | −3.88437 | + | 1.58579i | −0.235093 | + | 0.0959762i | ||||
\(274\) | 4.14214 | 0.250236 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2518 | − | 11.6924i | −1.21681 | − | 0.702528i | −0.252578 | − | 0.967576i | \(-0.581279\pi\) |
−0.964235 | + | 0.265049i | \(0.914612\pi\) | |||||||
\(278\) | 14.0665 | − | 8.12132i | 0.843655 | − | 0.487084i | ||||
\(279\) | 0.171573 | 0.0102718 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.65685 | 0.576080 | 0.288040 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288040 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(282\) | 11.4069 | − | 6.58579i | 0.679272 | − | 0.392178i | ||||
\(283\) | 11.4685 | + | 6.62132i | 0.681729 | + | 0.393597i | 0.800506 | − | 0.599324i | \(-0.204564\pi\) |
−0.118777 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.65685 | −0.452759 | ||||||||
\(287\) | −4.68885 | − | 3.63604i | −0.276774 | − | 0.214629i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.9853 | + | 19.0271i | 0.646193 | + | 1.11924i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.41421 | + | 9.37769i | −0.317387 | + | 0.549730i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 15.3137i | − | 0.894636i | −0.894375 | − | 0.447318i | \(-0.852379\pi\) | ||
0.894375 | − | 0.447318i | \(-0.147621\pi\) | |||||||
\(294\) | −2.46447 | − | 9.58783i | −0.143731 | − | 0.559173i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.89949 | − | 13.6823i | −0.459149 | − | 0.795269i | ||||
\(297\) | −2.95680 | − | 1.70711i | −0.171571 | − | 0.0990564i | ||||
\(298\) | −21.6251 | − | 12.4853i | −1.25271 | − | 0.723253i | ||||
\(299\) | 4.94975 | + | 8.57321i | 0.286251 | + | 0.495802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8848 | + | 21.7737i | −0.973222 | + | 1.25502i | ||||
\(302\) | 9.17157i | 0.527765i | ||||||||
\(303\) | 5.40629 | − | 3.12132i | 0.310583 | − | 0.179315i | ||||
\(304\) | 13.3137 | − | 23.0600i | 0.763594 | − | 1.32258i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.41421 | + | 7.64564i | 0.252344 | + | 0.437072i | ||||
\(307\) | − | 1.58579i | − | 0.0905056i | −0.998976 | − | 0.0452528i | \(-0.985591\pi\) | ||
0.998976 | − | 0.0452528i | \(-0.0144093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.24264 | −0.0706914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.53553 | − | 14.7840i | 0.484006 | − | 0.838323i | −0.515826 | − | 0.856694i | \(-0.672515\pi\) |
0.999831 | + | 0.0183712i | \(0.00584805\pi\) | |||||||
\(312\) | −3.88437 | − | 2.24264i | −0.219909 | − | 0.126965i | ||||
\(313\) | 22.7013 | − | 13.1066i | 1.28315 | − | 0.740829i | 0.305730 | − | 0.952118i | \(-0.401100\pi\) |
0.977424 | + | 0.211289i | \(0.0677662\pi\) | |||||||
\(314\) | 22.8284 | 1.28828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0870399 | + | 0.0502525i | −0.00488865 | + | 0.00282246i | −0.502442 | − | 0.864611i | \(-0.667565\pi\) |
0.497554 | + | 0.867433i | \(0.334232\pi\) | |||||||
\(318\) | 1.43488 | + | 0.828427i | 0.0804640 | + | 0.0464559i | ||||
\(319\) | −0.414214 | + | 0.717439i | −0.0231915 | + | 0.0401689i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.4142 | −0.860338 | ||||||||
\(322\) | −21.6251 | + | 8.82843i | −1.20512 | + | 0.491989i | ||||
\(323\) | 41.5563i | 2.31226i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.6569 | − | 23.6544i | 0.756383 | − | 1.31009i | ||||
\(327\) | −11.6786 | + | 6.74264i | −0.645828 | + | 0.372869i | ||||
\(328\) | − | 6.34315i | − | 0.350242i | ||||||
\(329\) | 24.4142 | + | 3.34101i | 1.34600 | + | 0.184196i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8137 | + | 23.9260i | 0.759270 | + | 1.31509i | 0.943223 | + | 0.332159i | \(0.107777\pi\) |
−0.183953 | + | 0.982935i | \(0.558889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.83743 | + | 2.79289i | 0.265090 | + | 0.153050i | ||||
\(334\) | 8.31371 | + | 14.3998i | 0.454906 | + | 0.787920i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.48528 | − | 8.36308i | 0.353801 | − | 0.456243i | ||||
\(337\) | 0.899495i | 0.0489986i | 0.999700 | + | 0.0244993i | \(0.00779915\pi\) | ||||
−0.999700 | + | 0.0244993i | \(0.992201\pi\) | |||||||
\(338\) | −12.8418 | + | 7.41421i | −0.698502 | + | 0.403280i | ||||
\(339\) | 2.17157 | − | 3.76127i | 0.117944 | − | 0.204284i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.292893 | + | 0.507306i | 0.0158611 | + | 0.0274722i | ||||
\(342\) | 9.41421i | 0.509062i | ||||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | −29.4558 | −1.58815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | − | 3.46410i | 0.107521 | − | 0.186231i | ||||
\(347\) | −21.6251 | − | 12.4853i | −1.16090 | − | 0.670245i | −0.209379 | − | 0.977835i | \(-0.567144\pi\) |
−0.951519 | + | 0.307589i | \(0.900478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6274 | 0.890045 | 0.445023 | − | 0.895519i | \(-0.353196\pi\) | ||||
0.445023 | + | 0.895519i | \(0.353196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.58579 | 0.0846430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.10911 | − | 2.94975i | −0.271931 | − | 0.156999i | 0.357834 | − | 0.933785i | \(-0.383515\pi\) |
−0.629765 | + | 0.776786i | \(0.716849\pi\) | |||||||
\(354\) | −1.00000 | + | 1.73205i | −0.0531494 | + | 0.0920575i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.23936 | + | 16.3640i | −0.118519 | + | 0.866073i | ||||
\(358\) | 27.7990i | 1.46922i | ||||||||
\(359\) | −13.2929 | − | 23.0240i | −0.701572 | − | 1.21516i | −0.967914 | − | 0.251280i | \(-0.919149\pi\) |
0.266342 | − | 0.963878i | \(-0.414185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6569 | + | 21.9223i | −0.666150 | + | 1.15381i | ||||
\(362\) | −0.804479 | + | 0.464466i | −0.0422825 | + | 0.0244118i | ||||
\(363\) | − | 0.656854i | − | 0.0344759i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.82843 | + | 15.2913i | 0.461469 | + | 0.799288i | ||||
\(367\) | −16.9618 | − | 9.79289i | −0.885398 | − | 0.511185i | −0.0129637 | − | 0.999916i | \(-0.504127\pi\) |
−0.872434 | + | 0.488731i | \(0.837460\pi\) | |||||||
\(368\) | −21.6251 | − | 12.4853i | −1.12729 | − | 0.650840i | ||||
\(369\) | 1.12132 | + | 1.94218i | 0.0583736 | + | 0.101106i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.17157 | + | 2.86976i | 0.0608250 | + | 0.148990i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.6646 | − | 9.62132i | 0.862861 | − | 0.498173i | −0.00210826 | − | 0.999998i | \(-0.500671\pi\) |
0.864969 | + | 0.501825i | \(0.167338\pi\) | |||||||
\(374\) | −15.0711 | + | 26.1039i | −0.779306 | + | 1.34980i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.1716 | + | 22.8138i | 0.679272 | + | 1.17653i | ||||
\(377\) | − | 0.384776i | − | 0.0198170i | ||||||
\(378\) | −0.507306 | + | 3.70711i | −0.0260930 | + | 0.190673i | ||||
\(379\) | −14.7990 | −0.760173 | −0.380087 | − | 0.924951i | \(-0.624106\pi\) | ||||
−0.380087 | + | 0.924951i | \(0.624106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.03553 | + | 15.6500i | −0.462904 | + | 0.801774i | ||||
\(382\) | 23.2341 | + | 13.4142i | 1.18876 | + | 0.686331i | ||||
\(383\) | 10.8126 | − | 6.24264i | 0.552497 | − | 0.318984i | −0.197632 | − | 0.980276i | \(-0.563325\pi\) |
0.750128 | + | 0.661292i | \(0.229992\pi\) | |||||||
\(384\) | 11.3137 | 0.577350 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.55635 | −0.486405 | ||||||||
\(387\) | 9.01897 | − | 5.20711i | 0.458460 | − | 0.264692i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.43503 | − | 14.6099i | 0.427673 | − | 0.740751i | −0.568993 | − | 0.822342i | \(-0.692667\pi\) |
0.996666 | + | 0.0815911i | \(0.0260002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.9706 | 1.97083 | ||||||||
\(392\) | 19.1757 | − | 4.92893i | 0.968517 | − | 0.248949i | ||||
\(393\) | 10.4853i | 0.528912i | ||||||||
\(394\) | 3.92893 | + | 6.80511i | 0.197937 | + | 0.342836i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.9692 | − | 12.1066i | 1.05242 | − | 0.607613i | 0.129092 | − | 0.991633i | \(-0.458794\pi\) |
0.923325 | + | 0.384020i | \(0.125461\pi\) | |||||||
\(398\) | 7.79899i | 0.390928i | ||||||||
\(399\) | −10.7929 | + | 13.9180i | −0.540320 | + | 0.696769i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.242641 | − | 0.420266i | −0.0121169 | − | 0.0209871i | 0.859903 | − | 0.510457i | \(-0.170524\pi\) |
−0.872020 | + | 0.489470i | \(0.837190\pi\) | |||||||
\(402\) | −14.3637 | − | 8.29289i | −0.716397 | − | 0.413612i | ||||
\(403\) | −0.235626 | − | 0.136039i | −0.0117374 | − | 0.00677658i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.899495 | + | 0.123093i | 0.0446412 | + | 0.00610901i | ||||
\(407\) | 19.0711i | 0.945318i | ||||||||
\(408\) | −15.2913 | + | 8.82843i | −0.757031 | + | 0.437072i | ||||
\(409\) | −13.1569 | + | 22.7883i | −0.650565 | + | 1.12681i | 0.332422 | + | 0.943131i | \(0.392134\pi\) |
−0.982986 | + | 0.183680i | \(0.941199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.46447 | − | 2.53653i | −0.0722368 | − | 0.125118i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.46410 | + | 1.41421i | −0.170457 | + | 0.0695889i | ||||
\(414\) | 8.82843 | 0.433894 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.94655 | − | 5.74264i | −0.487084 | − | 0.281218i | ||||
\(418\) | −27.8359 | + | 16.0711i | −1.36150 | + | 0.786062i | ||||
\(419\) | 3.17157 | 0.154941 | 0.0774707 | − | 0.996995i | \(-0.475316\pi\) | ||||
0.0774707 | + | 0.996995i | \(0.475316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4853 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266390\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266390\pi\) | |||||||
\(422\) | −0.174080 | + | 0.100505i | −0.00847408 | + | 0.00489251i | ||||
\(423\) | −8.06591 | − | 4.65685i | −0.392178 | − | 0.226424i | ||||
\(424\) | −1.65685 | + | 2.86976i | −0.0804640 | + | 0.139368i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.82843 | 0.233938 | ||||||||
\(427\) | −4.47871 | + | 32.7279i | −0.216740 | + | 1.58382i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.70711 | + | 4.68885i | 0.130700 | + | 0.226380i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.4142 | + | 31.8944i | −0.886981 | + | 1.53630i | −0.0435558 | + | 0.999051i | \(0.513869\pi\) |
−0.843426 | + | 0.537246i | \(0.819465\pi\) | |||||||
\(432\) | −3.46410 | + | 2.00000i | −0.166667 | + | 0.0962250i | ||||
\(433\) | − | 24.5563i | − | 1.18010i | −0.807366 | − | 0.590051i | \(-0.799107\pi\) | ||
0.807366 | − | 0.590051i | \(-0.200893\pi\) | |||||||
\(434\) | 0.393398 | − | 0.507306i | 0.0188837 | − | 0.0243515i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.9889 | + | 20.7782i | 1.72158 | + | 0.993955i | ||||
\(438\) | 2.53653 | + | 1.46447i | 0.121200 | + | 0.0699749i | ||||
\(439\) | 0.171573 | + | 0.297173i | 0.00818873 | + | 0.0141833i | 0.870091 | − | 0.492892i | \(-0.164060\pi\) |
−0.861902 | + | 0.507075i | \(0.830727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 4.89898i | −0.238095 | + | 0.233285i | ||||
\(442\) | − | 14.0000i | − | 0.665912i | ||||||
\(443\) | 0.420266 | − | 0.242641i | 0.0199674 | − | 0.0115282i | −0.489983 | − | 0.871732i | \(-0.662997\pi\) |
0.509950 | + | 0.860204i | \(0.329664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.1421 | − | 21.0308i | −0.574947 | − | 0.995837i | ||||
\(447\) | 17.6569i | 0.835141i | ||||||||
\(448\) | 16.7262 | + | 12.9706i | 0.790237 | + | 0.612801i | ||||
\(449\) | 6.97056 | 0.328961 | 0.164481 | − | 0.986380i | \(-0.447405\pi\) | ||||
0.164481 | + | 0.986380i | \(0.447405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.82843 | + | 6.63103i | −0.180274 | + | 0.312243i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.61642 | − | 3.24264i | 0.263882 | − | 0.152353i | ||||
\(454\) | −32.6274 | −1.53128 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.8284 | −0.881722 | ||||||||
\(457\) | 18.0995 | − | 10.4497i | 0.846659 | − | 0.488819i | −0.0128634 | − | 0.999917i | \(-0.504095\pi\) |
0.859522 | + | 0.511099i | \(0.170761\pi\) | |||||||
\(458\) | 17.5306 | + | 10.1213i | 0.819153 | + | 0.472938i | ||||
\(459\) | 3.12132 | − | 5.40629i | 0.145691 | − | 0.252344i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.0711 | −1.26083 | −0.630413 | − | 0.776260i | \(-0.717114\pi\) | ||||
−0.630413 | + | 0.776260i | \(0.717114\pi\) | |||||||
\(462\) | −11.8272 | + | 4.82843i | −0.550250 | + | 0.224639i | ||||
\(463\) | − | 10.4142i | − | 0.483990i | −0.970278 | − | 0.241995i | \(-0.922198\pi\) | ||
0.970278 | − | 0.241995i | \(-0.0778017\pi\) | |||||||
\(464\) | 0.485281 | + | 0.840532i | 0.0225286 | + | 0.0390207i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.8995 | − | 27.5387i | 0.736530 | − | 1.27571i | ||||
\(467\) | −5.79050 | + | 3.34315i | −0.267952 | + | 0.154702i | −0.627957 | − | 0.778248i | \(-0.716109\pi\) |
0.360004 | + | 0.932951i | \(0.382775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7279 | − | 28.7274i | −0.541545 | − | 1.32651i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.07107 | − | 13.9795i | −0.371895 | − | 0.644141i | ||||
\(472\) | −3.46410 | − | 2.00000i | −0.159448 | − | 0.0920575i | ||||
\(473\) | 30.7927 | + | 17.7782i | 1.41585 | + | 0.817441i | ||||
\(474\) | 3.29289 | + | 5.70346i | 0.151248 | + | 0.261969i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.17157i | − | 0.0536426i | ||||||
\(478\) | 21.2049 | − | 12.2426i | 0.969888 | − | 0.559965i | ||||
\(479\) | −17.3137 | + | 29.9882i | −0.791084 | + | 1.37020i | 0.134213 | + | 0.990953i | \(0.457149\pi\) |
−0.925297 | + | 0.379244i | \(0.876184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.42893 | − | 7.67114i | −0.201942 | − | 0.349774i | ||||
\(482\) | 14.6274i | 0.666261i | ||||||||
\(483\) | 13.0519 | + | 10.1213i | 0.593883 | + | 0.460536i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.707107 | − | 1.22474i | 0.0320750 | − | 0.0555556i | ||||
\(487\) | 0.778985 | + | 0.449747i | 0.0352992 | + | 0.0203800i | 0.517546 | − | 0.855656i | \(-0.326846\pi\) |
−0.482247 | + | 0.876036i | \(0.660179\pi\) | |||||||
\(488\) | −30.5826 | + | 17.6569i | −1.38441 | + | 0.799288i | ||||
\(489\) | −19.3137 | −0.873396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1421 | −0.457708 | −0.228854 | − | 0.973461i | \(-0.573498\pi\) | ||||
−0.228854 | + | 0.973461i | \(0.573498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.31178 | − | 0.757359i | −0.0590798 | − | 0.0341097i | ||||
\(494\) | 7.46447 | − | 12.9288i | 0.335842 | − | 0.581696i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.686292 | 0.0308154 | ||||||||
\(497\) | 7.13834 | + | 5.53553i | 0.320198 | + | 0.248303i | ||||
\(498\) | − | 7.65685i | − | 0.343112i | ||||||
\(499\) | 4.39949 | + | 7.62015i | 0.196948 | + | 0.341125i | 0.947538 | − | 0.319645i | \(-0.103564\pi\) |
−0.750589 | + | 0.660769i | \(0.770230\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.87868 | − | 10.1822i | 0.262640 | − | 0.454906i | ||||
\(502\) | 6.63103 | − | 3.82843i | 0.295957 | − | 0.170871i | ||||
\(503\) | − | 18.4853i | − | 0.824218i | −0.911135 | − | 0.412109i | \(-0.864792\pi\) | ||
0.911135 | − | 0.412109i | \(-0.135208\pi\) | |||||||
\(504\) | −7.41421 | − | 1.01461i | −0.330255 | − | 0.0451944i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.0711 | + | 26.1039i | 0.669991 | + | 1.16046i | ||||
\(507\) | 9.08052 | + | 5.24264i | 0.403280 | + | 0.232834i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.89949 | + | 11.9503i | 0.305815 | + | 0.529687i | 0.977442 | − | 0.211202i | \(-0.0677378\pi\) |
−0.671628 | + | 0.740889i | \(0.734405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.07107 | + | 5.07306i | 0.0916186 | + | 0.224419i | ||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 5.76500 | − | 3.32843i | 0.254531 | − | 0.146954i | ||||
\(514\) | −21.1421 | + | 36.6193i | −0.932540 | + | 1.61521i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 31.7990i | − | 1.39852i | ||||||
\(518\) | 19.3497 | − | 7.89949i | 0.850178 | − | 0.347084i | ||||
\(519\) | −2.82843 | −0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5563 | − | 33.8726i | 0.856779 | − | 1.48399i | −0.0182053 | − | 0.999834i | \(-0.505795\pi\) |
0.874985 | − | 0.484151i | \(-0.160871\pi\) | |||||||
\(522\) | −0.297173 | − | 0.171573i | −0.0130069 | − | 0.00750954i | ||||
\(523\) | −6.56948 | + | 3.79289i | −0.287263 | + | 0.165852i | −0.636707 | − | 0.771106i | \(-0.719704\pi\) |
0.349444 | + | 0.936957i | \(0.386371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.65685 | 0.0722423 | ||||||||
\(527\) | −0.927572 | + | 0.535534i | −0.0404057 | + | 0.0233282i | ||||
\(528\) | −11.8272 | − | 6.82843i | −0.514712 | − | 0.297169i | ||||
\(529\) | 7.98528 | − | 13.8309i | 0.347186 | − | 0.601344i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.41421 | 0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.55635i | − | 0.154043i | ||||||
\(534\) | 2.65685 | + | 4.60181i | 0.114973 | + | 0.199140i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16.5858 | − | 28.7274i | 0.716397 | − | 1.24084i | ||||
\(537\) | 17.0233 | − | 9.82843i | 0.734611 | − | 0.424128i | ||||
\(538\) | 11.5147i | 0.496435i | ||||||||
\(539\) | −23.0208 | − | 6.42090i | −0.991577 | − | 0.276568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.1569 | − | 27.9845i | −0.694637 | − | 1.20315i | −0.970303 | − | 0.241894i | \(-0.922231\pi\) |
0.275665 | − | 0.961254i | \(-0.411102\pi\) | |||||||
\(542\) | 24.6690 | + | 14.2426i | 1.05962 | + | 0.611774i | ||||
\(543\) | 0.568852 | + | 0.328427i | 0.0244118 | + | 0.0140942i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.63604 | − | 4.68885i | 0.155608 | − | 0.200664i | ||||
\(547\) | 31.7990i | 1.35963i | 0.733385 | + | 0.679813i | \(0.237939\pi\) | ||||
−0.733385 | + | 0.679813i | \(0.762061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.24264 | − | 10.8126i | 0.266429 | − | 0.461469i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.807612 | − | 1.39882i | −0.0344054 | − | 0.0595919i | ||||
\(552\) | 17.6569i | 0.751526i | ||||||||
\(553\) | −1.67050 | + | 12.2071i | −0.0710371 | + | 0.519099i | ||||
\(554\) | 33.0711 | 1.40506 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.22538 | − | 4.17157i | −0.306149 | − | 0.176755i | 0.339053 | − | 0.940767i | \(-0.389893\pi\) |
−0.645202 | + | 0.764012i | \(0.723227\pi\) | |||||||
\(558\) | −0.210133 | + | 0.121320i | −0.00889564 | + | 0.00513590i | ||||
\(559\) | −16.5147 | −0.698498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.3137 | 0.899865 | ||||||||
\(562\) | −11.8272 | + | 6.82843i | −0.498900 | + | 0.288040i | ||||
\(563\) | 12.3705 | + | 7.14214i | 0.521356 | + | 0.301005i | 0.737489 | − | 0.675359i | \(-0.236011\pi\) |
−0.216133 | + | 0.976364i | \(0.569345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.7279 | −0.787193 | ||||||||
\(567\) | 2.44949 | − | 1.00000i | 0.102869 | − | 0.0419961i | ||||
\(568\) | 9.65685i | 0.405193i | ||||||||
\(569\) | −18.4350 | − | 31.9304i | −0.772837 | − | 1.33859i | −0.936002 | − | 0.351994i | \(-0.885504\pi\) |
0.163166 | − | 0.986599i | \(-0.447829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.9853 | + | 24.2232i | −0.585266 | + | 1.01371i | 0.409576 | + | 0.912276i | \(0.365677\pi\) |
−0.994842 | + | 0.101434i | \(0.967657\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 18.9706i | − | 0.792507i | ||||||
\(574\) | 8.31371 | + | 1.13770i | 0.347007 | + | 0.0474869i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.00000 | − | 6.92820i | −0.166667 | − | 0.288675i | ||||
\(577\) | 5.67796 | + | 3.27817i | 0.236377 | + | 0.136472i | 0.613510 | − | 0.789687i | \(-0.289757\pi\) |
−0.377134 | + | 0.926159i | \(0.623090\pi\) | |||||||
\(578\) | −26.9083 | − | 15.5355i | −1.11924 | − | 0.646193i | ||||
\(579\) | 3.37868 | + | 5.85204i | 0.140413 | + | 0.243203i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.77817 | − | 11.3199i | 0.364180 | − | 0.469628i | ||||
\(582\) | − | 15.3137i | − | 0.634774i | ||||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | −2.92893 | + | 5.07306i | −0.121200 | + | 0.209925i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.8284 | + | 18.7554i | 0.447318 | + | 0.774778i | ||||
\(587\) | − | 30.2426i | − | 1.24825i | −0.781326 | − | 0.624124i | \(-0.785456\pi\) | ||
0.781326 | − | 0.624124i | \(-0.214544\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.14214 | −0.0470609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.77817 | − | 4.81194i | 0.114279 | − | 0.197937i | ||||
\(592\) | 19.3497 | + | 11.1716i | 0.795269 | + | 0.459149i | ||||
\(593\) | 11.6170 | − | 6.70711i | 0.477055 | − | 0.275428i | −0.242133 | − | 0.970243i | \(-0.577847\pi\) |
0.719188 | + | 0.694815i | \(0.244514\pi\) | |||||||
\(594\) | 4.82843 | 0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.77589 | − | 2.75736i | 0.195464 | − | 0.112851i | ||||
\(598\) | −12.1244 | − | 7.00000i | −0.495802 | − | 0.286251i | ||||
\(599\) | −21.0711 | + | 36.4962i | −0.860940 | + | 1.49119i | 0.0100818 | + | 0.999949i | \(0.496791\pi\) |
−0.871022 | + | 0.491243i | \(0.836543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.1716 | −0.985979 | −0.492990 | − | 0.870035i | \(-0.664096\pi\) | ||||
−0.492990 | + | 0.870035i | \(0.664096\pi\) | |||||||
\(602\) | 5.28319 | − | 38.6066i | 0.215327 | − | 1.57349i | ||||
\(603\) | 11.7279i | 0.477598i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.41421 | + | 7.64564i | −0.179315 | + | 0.310583i | ||||
\(607\) | 1.07616 | − | 0.621320i | 0.0436799 | − | 0.0252186i | −0.478001 | − | 0.878359i | \(-0.658638\pi\) |
0.521681 | + | 0.853141i | \(0.325305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.242641 | − | 0.594346i | −0.00983230 | − | 0.0240841i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.38478 | + | 12.7908i | 0.298756 | + | 0.517461i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.78335 | − | 5.07107i | −0.354756 | − | 0.204818i | 0.312022 | − | 0.950075i | \(-0.398994\pi\) |
−0.666778 | + | 0.745256i | \(0.732327\pi\) | |||||||
\(614\) | 1.12132 | + | 1.94218i | 0.0452528 | + | 0.0783802i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.65685 | − | 23.6544i | −0.389086 | − | 0.953062i | ||||
\(617\) | 8.82843i | 0.355419i | 0.984083 | + | 0.177710i | \(0.0568688\pi\) | ||||
−0.984083 | + | 0.177710i | \(0.943131\pi\) | |||||||
\(618\) | 1.52192 | − | 0.878680i | 0.0612205 | − | 0.0353457i | ||||
\(619\) | 19.9853 | − | 34.6155i | 0.803276 | − | 1.39132i | −0.114172 | − | 0.993461i | \(-0.536422\pi\) |
0.917449 | − | 0.397854i | \(-0.130245\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.12132 | − | 5.40629i | −0.125254 | − | 0.216947i | ||||
\(622\) | 24.1421i | 0.968011i | ||||||||
\(623\) | −1.34784 | + | 9.84924i | −0.0540000 | + | 0.394602i | ||||
\(624\) | 6.34315 | 0.253929 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.5355 | + | 32.1045i | −0.740829 | + | 1.28315i | ||||
\(627\) | 19.6830 | + | 11.3640i | 0.786062 | + | 0.453833i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.8701 | −1.39036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −11.4069 | + | 6.58579i | −0.453743 | + | 0.261969i | ||||
\(633\) | 0.123093 | + | 0.0710678i | 0.00489251 | + | 0.00282469i | ||||
\(634\) | 0.0710678 | − | 0.123093i | 0.00282246 | − | 0.00488865i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.7510 | − | 2.76346i | 0.425971 | − | 0.109492i | ||||
\(638\) | − | 1.17157i | − | 0.0463830i | ||||||
\(639\) | −1.70711 | − | 2.95680i | −0.0675321 | − | 0.116969i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.60660 | − | 11.4430i | 0.260945 | − | 0.451970i | −0.705548 | − | 0.708662i | \(-0.749299\pi\) |
0.966493 | + | 0.256692i | \(0.0826325\pi\) | |||||||
\(642\) | 18.8785 | − | 10.8995i | 0.745074 | − | 0.430169i | ||||
\(643\) | 24.5563i | 0.968408i | 0.874955 | + | 0.484204i | \(0.160891\pi\) | ||||
−0.874955 | + | 0.484204i | \(0.839109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −29.3848 | − | 50.8959i | −1.15613 | − | 2.00247i | ||||
\(647\) | 8.32703 | + | 4.80761i | 0.327369 | + | 0.189007i | 0.654673 | − | 0.755913i | \(-0.272807\pi\) |
−0.327303 | + | 0.944919i | \(0.606140\pi\) | |||||||
\(648\) | 2.44949 | + | 1.41421i | 0.0962250 | + | 0.0555556i | ||||
\(649\) | 2.41421 | + | 4.18154i | 0.0947662 | + | 0.164140i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.449747 | − | 0.0615465i | −0.0176270 | − | 0.00241220i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.71807 | − | 3.87868i | 0.262898 | − | 0.151784i | −0.362758 | − | 0.931884i | \(-0.618165\pi\) |
0.625656 | + | 0.780099i | \(0.284831\pi\) | |||||||
\(654\) | 9.53553 | − | 16.5160i | 0.372869 | − | 0.645828i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.48528 | + | 7.76874i | 0.175121 | + | 0.303318i | ||||
\(657\) | − | 2.07107i | − | 0.0808001i | ||||||
\(658\) | −32.2636 | + | 13.1716i | −1.25777 | + | 0.513481i | ||||
\(659\) | 27.3137 | 1.06399 | 0.531996 | − | 0.846747i | \(-0.321442\pi\) | ||||
0.531996 | + | 0.846747i | \(0.321442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1569 | + | 27.9845i | −0.628429 | + | 1.08847i | 0.359438 | + | 0.933169i | \(0.382968\pi\) |
−0.987867 | + | 0.155302i | \(0.950365\pi\) | |||||||
\(662\) | −33.8365 | − | 19.5355i | −1.31509 | − | 0.759270i | ||||
\(663\) | −8.57321 | + | 4.94975i | −0.332956 | + | 0.192232i | ||||
\(664\) | 15.3137 | 0.594287 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.89949 | −0.306099 | ||||||||
\(667\) | −1.31178 | + | 0.757359i | −0.0507925 | + | 0.0293251i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.58579 | + | 14.8710i | −0.331946 | + | 0.574947i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.6274 | 1.64561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.27208i | 0.0875822i | 0.999041 | + | 0.0437911i | \(0.0139436\pi\) | ||||
−0.999041 | + | 0.0437911i | \(0.986056\pi\) | |||||||
\(674\) | −0.636039 | − | 1.10165i | −0.0244993 | − | 0.0424340i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.37706 | + | 1.94975i | −0.129791 | + | 0.0749349i | −0.563490 | − | 0.826123i | \(-0.690542\pi\) |
0.433699 | + | 0.901058i | \(0.357208\pi\) | |||||||
\(678\) | 6.14214i | 0.235887i | ||||||||
\(679\) | 17.5563 | − | 22.6398i | 0.673751 | − | 0.868834i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.5355 | + | 19.9801i | 0.442043 | + | 0.765640i | ||||
\(682\) | −0.717439 | − | 0.414214i | −0.0274722 | − | 0.0158611i | ||||
\(683\) | −17.8278 | − | 10.2929i | −0.682162 | − | 0.393847i | 0.118507 | − | 0.992953i | \(-0.462189\pi\) |
−0.800669 | + | 0.599107i | \(0.795523\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.02082 | + | 26.0168i | 0.115335 | + | 0.993327i | ||||
\(687\) | − | 14.3137i | − | 0.546102i | ||||||
\(688\) | 36.0759 | − | 20.8284i | 1.37538 | − | 0.794076i | ||||
\(689\) | −0.928932 | + | 1.60896i | −0.0353895 | + | 0.0612964i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1569 | − | 26.2524i | −0.576594 | − | 0.998690i | −0.995866 | − | 0.0908295i | \(-0.971048\pi\) |
0.419273 | − | 0.907860i | \(-0.362285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.13834 | + | 5.53553i | 0.271163 | + | 0.210278i | ||||
\(694\) | 35.3137 | 1.34049 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.343146 | − | 0.594346i | 0.0130069 | − | 0.0225286i | ||||
\(697\) | −12.1244 | − | 7.00000i | −0.459243 | − | 0.265144i | ||||
\(698\) | −20.3643 | + | 11.7574i | −0.770802 | + | 0.445023i | ||||
\(699\) | −22.4853 | −0.850471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.2132 | 1.55660 | 0.778301 | − | 0.627892i | \(-0.216082\pi\) | ||||
0.778301 | + | 0.627892i | \(0.216082\pi\) | |||||||
\(702\) | −1.94218 | + | 1.12132i | −0.0733030 | + | 0.0423215i | ||||
\(703\) | −32.2021 | − | 18.5919i | −1.21452 | − | 0.701206i | ||||
\(704\) | 13.6569 | − | 23.6544i | 0.514712 | − | 0.891507i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.34315 | 0.313998 | ||||||||
\(707\) | −15.2913 | + | 6.24264i | −0.575088 | + | 0.234779i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.55635 | − | 9.62388i | −0.208673 | − | 0.361432i | 0.742624 | − | 0.669709i | \(-0.233581\pi\) |
−0.951297 | + | 0.308277i | \(0.900248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.32843 | − | 4.03295i | 0.0873228 | − | 0.151248i | ||||
\(712\) | −9.20361 | + | 5.31371i | −0.344920 | + | 0.199140i | ||||
\(713\) | 1.07107i | 0.0401118i | ||||||||
\(714\) | −8.82843 | − | 21.6251i | −0.330396 | − | 0.809301i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.9941 | − | 8.65685i | −0.559965 | − | 0.323296i | ||||
\(718\) | 32.5608 | + | 18.7990i | 1.21516 | + | 0.701572i | ||||
\(719\) | 8.75736 | + | 15.1682i | 0.326594 | + | 0.565678i | 0.981834 | − | 0.189743i | \(-0.0607656\pi\) |
−0.655239 | + | 0.755421i | \(0.727432\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.25736 | + | 0.445759i | 0.121310 | + | 0.0166009i | ||||
\(722\) | − | 35.7990i | − | 1.33230i | ||||||
\(723\) | 8.95743 | − | 5.17157i | 0.333130 | − | 0.192333i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.464466 | + | 0.804479i | 0.0172380 | + | 0.0298570i | ||||
\(727\) | − | 4.75736i | − | 0.176441i | −0.996101 | − | 0.0882203i | \(-0.971882\pi\) | ||
0.996101 | − | 0.0882203i | \(-0.0281180\pi\) | |||||||
\(728\) | 9.37769 | + | 7.27208i | 0.347560 | + | 0.269521i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.5061 | + | 56.3022i | −1.20228 | + | 2.08241i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.31615 | + | 5.37868i | −0.344100 | + | 0.198666i | −0.662083 | − | 0.749430i | \(-0.730328\pi\) |
0.317984 | + | 0.948096i | \(0.396994\pi\) | |||||||
\(734\) | 27.6985 | 1.02237 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.6771 | + | 20.0208i | −1.27735 | + | 0.737476i | ||||
\(738\) | −2.74666 | − | 1.58579i | −0.101106 | − | 0.0583736i | ||||
\(739\) | −17.5711 | + | 30.4340i | −0.646362 | + | 1.11953i | 0.337623 | + | 0.941281i | \(0.390377\pi\) |
−0.983985 | + | 0.178251i | \(0.942956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.5563 | −0.387797 | ||||||||
\(742\) | −3.46410 | − | 2.68629i | −0.127171 | − | 0.0986169i | ||||
\(743\) | − | 4.72792i | − | 0.173451i | −0.996232 | − | 0.0867253i | \(-0.972360\pi\) | ||
0.996232 | − | 0.0867253i | \(-0.0276402\pi\) | |||||||
\(744\) | −0.242641 | − | 0.420266i | −0.00889564 | − | 0.0154077i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.6066 | + | 23.5673i | −0.498173 | + | 0.862861i | ||||
\(747\) | −4.68885 | + | 2.70711i | −0.171556 | + | 0.0990479i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.4056 | + | 5.52938i | 1.47639 | + | 0.202039i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.81371 | − | 16.9978i | −0.358107 | − | 0.620260i | 0.629537 | − | 0.776970i | \(-0.283244\pi\) |
−0.987645 | + | 0.156710i | \(0.949911\pi\) | |||||||
\(752\) | −32.2636 | − | 18.6274i | −1.17653 | − | 0.679272i | ||||
\(753\) | −4.68885 | − | 2.70711i | −0.170871 | − | 0.0986525i | ||||
\(754\) | 0.272078 | + | 0.471253i | 0.00990849 | + | 0.0171620i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.5980i | − | 1.51190i | −0.654627 | − | 0.755952i | \(-0.727174\pi\) | ||
0.654627 | − | 0.755952i | \(-0.272826\pi\) | |||||||
\(758\) | 18.1250 | − | 10.4645i | 0.658329 | − | 0.380087i | ||||
\(759\) | 10.6569 | − | 18.4582i | 0.386819 | − | 0.669991i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4645 | + | 18.1250i | 0.379337 | + | 0.657030i | 0.990966 | − | 0.134114i | \(-0.0428189\pi\) |
−0.611629 | + | 0.791145i | \(0.709486\pi\) | |||||||
\(762\) | − | 25.5563i | − | 0.925809i | ||||||
\(763\) | 33.0321 | − | 13.4853i | 1.19584 | − | 0.488200i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.82843 | + | 15.2913i | −0.318984 | + | 0.552497i | ||||
\(767\) | −1.94218 | − | 1.12132i | −0.0701282 | − | 0.0404885i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9706 | 0.575913 | 0.287957 | − | 0.957643i | \(-0.407024\pi\) | ||||
0.287957 | + | 0.957643i | \(0.407024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.8995 | 1.07680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.5891 | − | 12.4645i | −0.776506 | − | 0.448316i | 0.0586849 | − | 0.998277i | \(-0.481309\pi\) |
−0.835190 | + | 0.549961i | \(0.814643\pi\) | |||||||
\(774\) | −7.36396 | + | 12.7548i | −0.264692 | + | 0.458460i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 30.6274 | 1.09946 | ||||||||
\(777\) | −11.6786 | − | 9.05635i | −0.418967 | − | 0.324895i | ||||
\(778\) | 23.8579i | 0.855346i | ||||||||
\(779\) | −7.46447 | − | 12.9288i | −0.267442 | − | 0.463224i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.82843 | − | 10.0951i | 0.208558 | − | 0.361232i | ||||
\(782\) | −47.7290 | + | 27.5563i | −1.70679 | + | 0.985413i | ||||
\(783\) | 0.242641i | 0.00867127i | ||||||||
\(784\) | −20.0000 | + | 19.5959i | −0.714286 | + | 0.699854i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.41421 | − | 12.8418i | −0.264456 | − | 0.458052i | ||||
\(787\) | 11.4069 | + | 6.58579i | 0.406613 | + | 0.234758i | 0.689333 | − | 0.724444i | \(-0.257904\pi\) |
−0.282721 | + | 0.959202i | \(0.591237\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.585786 | − | 1.01461i | −0.0208545 | − | 0.0361211i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.04163 | + | 9.08052i | −0.250372 | + | 0.322866i | ||||
\(792\) | 9.65685i | 0.343141i | ||||||||
\(793\) | −17.1464 | + | 9.89949i | −0.608888 | + | 0.351541i | ||||
\(794\) | −17.1213 | + | 29.6550i | −0.607613 | + | 1.05242i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 10.4437i | − | 0.369933i | −0.982745 | − | 0.184967i | \(-0.940782\pi\) | ||
0.982745 | − | 0.184967i | \(-0.0592177\pi\) | |||||||
\(798\) | 3.37706 | − | 24.6777i | 0.119547 | − | 0.873580i | ||||
\(799\) | 58.1421 | 2.05692 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.87868 | − | 3.25397i | 0.0663799 | − | 0.114973i | ||||
\(802\) | 0.594346 | + | 0.343146i | 0.0209871 | + | 0.0121169i | ||||
\(803\) | 6.12372 | − | 3.53553i | 0.216102 | − | 0.124766i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.384776 | 0.0135532 | ||||||||
\(807\) | 7.05130 | − | 4.07107i | 0.248217 | − | 0.143308i | ||||
\(808\) | −15.2913 | − | 8.82843i | −0.537946 | − | 0.310583i | ||||
\(809\) | −2.31371 | + | 4.00746i | −0.0813457 | + | 0.140895i | −0.903828 | − | 0.427896i | \(-0.859255\pi\) |
0.822483 | + | 0.568790i | \(0.192588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9706 | −0.806606 | −0.403303 | − | 0.915067i | \(-0.632138\pi\) | ||||
−0.403303 | + | 0.915067i | \(0.632138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 20.1421i | − | 0.706416i | ||||||
\(814\) | −13.4853 | − | 23.3572i | −0.472659 | − | 0.818669i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.4853 | − | 21.6251i | 0.437072 | − | 0.757031i | ||||
\(817\) | −60.0380 | + | 34.6630i | −2.10046 | + | 1.21270i | ||||
\(818\) | − | 37.2132i | − | 1.30113i | ||||||
\(819\) | −4.15685 | − | 0.568852i | −0.145252 | − | 0.0198773i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.77817 | − | 11.7401i | −0.236560 | − | 0.409734i | 0.723165 | − | 0.690675i | \(-0.242687\pi\) |
−0.959725 | + | 0.280942i | \(0.909353\pi\) | |||||||
\(822\) | 3.58719 | + | 2.07107i | 0.125118 | + | 0.0722368i | ||||
\(823\) | −19.2987 | − | 11.1421i | −0.672712 | − | 0.388390i | 0.124391 | − | 0.992233i | \(-0.460302\pi\) |
−0.797103 | + | 0.603843i | \(0.793635\pi\) | |||||||
\(824\) | 1.75736 | + | 3.04384i | 0.0612205 | + | 0.106037i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.24264 | − | 4.18154i | 0.112826 | − | 0.145494i | ||||
\(827\) | − | 12.8284i | − | 0.446088i | −0.974808 | − | 0.223044i | \(-0.928401\pi\) | ||
0.974808 | − | 0.223044i | \(-0.0715994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.32843 | + | 16.1573i | −0.323990 | + | 0.561167i | −0.981307 | − | 0.192447i | \(-0.938358\pi\) |
0.657318 | + | 0.753614i | \(0.271691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.6924 | − | 20.2518i | −0.405604 | − | 0.702528i | ||||
\(832\) | 12.6863i | 0.439818i | ||||||||
\(833\) | 11.7401 | − | 42.0919i | 0.406772 | − | 1.45840i | ||||
\(834\) | 16.2426 | 0.562437 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.148586 | + | 0.0857864i | 0.00513590 | + | 0.00296521i | ||||
\(838\) | −3.88437 | + | 2.24264i | −0.134183 | + | 0.0774707i | ||||
\(839\) | 7.27208 | 0.251060 | 0.125530 | − | 0.992090i | \(-0.459937\pi\) | ||||
0.125530 | + | 0.992090i | \(0.459937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9411 | −0.997970 | ||||||||
\(842\) | −33.6625 | + | 19.4350i | −1.16008 | + | 0.669775i | ||||
\(843\) | 8.36308 | + | 4.82843i | 0.288040 | + | 0.166300i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.1716 | 0.452848 | ||||||||
\(847\) | −0.235626 | + | 1.72183i | −0.00809622 | + | 0.0591626i | ||||
\(848\) | − | 4.68629i | − | 0.160928i | ||||||
\(849\) | 6.62132 | + | 11.4685i | 0.227243 | + | 0.393597i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.4350 | + | 30.1984i | −0.597665 | + | 1.03519i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0122i | 1.30151i | 0.759287 | + | 0.650756i | \(0.225548\pi\) | ||||
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(854\) | −17.6569 | − | 43.2503i | −0.604205 | − | 1.47999i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.7990 | + | 37.7570i | 0.745074 | + | 1.29051i | ||||
\(857\) | −5.40629 | − | 3.12132i | −0.184675 | − | 0.106622i | 0.404812 | − | 0.914400i | \(-0.367337\pi\) |
−0.589487 | + | 0.807778i | \(0.700670\pi\) | |||||||
\(858\) | −6.63103 | − | 3.82843i | −0.226380 | − | 0.130700i | ||||
\(859\) | 7.82843 | + | 13.5592i | 0.267102 | + | 0.462635i | 0.968112 | − | 0.250517i | \(-0.0806004\pi\) |
−0.701010 | + | 0.713152i | \(0.747267\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.24264 | − | 5.49333i | −0.0764290 | − | 0.187212i | ||||
\(862\) | − | 52.0833i | − | 1.77396i | ||||||
\(863\) | −8.48617 | + | 4.89949i | −0.288873 | + | 0.166781i | −0.637433 | − | 0.770505i | \(-0.720004\pi\) |
0.348561 | + | 0.937286i | \(0.386671\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.3640 | + | 30.0753i | 0.590051 | + | 1.02200i | ||||
\(867\) | 21.9706i | 0.746159i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.8995 | 0.539353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.29899 | − | 16.1063i | 0.315084 | − | 0.545742i | ||||
\(872\) | 33.0321 | + | 19.0711i | 1.11861 | + | 0.645828i | ||||
\(873\) | −9.37769 | + | 5.41421i | −0.317387 | + | 0.183243i | ||||
\(874\) | −58.7696 | −1.98791 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5885 | − | 9.00000i | 0.526385 | − | 0.303908i | −0.213158 | − | 0.977018i | \(-0.568375\pi\) |
0.739543 | + | 0.673109i | \(0.235042\pi\) | |||||||
\(878\) | −0.420266 | − | 0.242641i | −0.0141833 | − | 0.00818873i | ||||
\(879\) | 7.65685 | − | 13.2621i | 0.258259 | − | 0.447318i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6569 | −0.729638 | −0.364819 | − | 0.931078i | \(-0.618869\pi\) | ||||
−0.364819 | + | 0.931078i | \(0.618869\pi\) | |||||||
\(882\) | 2.65962 | − | 9.53553i | 0.0895542 | − | 0.321078i | ||||
\(883\) | 8.07107i | 0.271613i | 0.990735 | + | 0.135807i | \(0.0433626\pi\) | ||||
−0.990735 | + | 0.135807i | \(0.956637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.343146 | + | 0.594346i | −0.0115282 | + | 0.0199674i | ||||
\(887\) | −4.51477 | + | 2.60660i | −0.151591 | + | 0.0875211i | −0.573877 | − | 0.818942i | \(-0.694561\pi\) |
0.422286 | + | 0.906463i | \(0.361228\pi\) | |||||||
\(888\) | − | 15.7990i | − | 0.530179i | ||||||
\(889\) | 29.2990 | − | 37.7825i | 0.982657 | − | 1.26718i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.70711 | − | 2.95680i | −0.0571902 | − | 0.0990564i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.6936 | + | 31.0000i | 1.79679 | + | 1.03738i | ||||
\(894\) | −12.4853 | − | 21.6251i | −0.417570 | − | 0.723253i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.6569 | − | 4.05845i | −0.990766 | − | 0.135583i | ||||
\(897\) | 9.89949i | 0.330535i | ||||||||
\(898\) | −8.53716 | + | 4.92893i | −0.284889 | + | 0.164481i | ||||
\(899\) | 0.0208153 | − | 0.0360531i | 0.000694228 | − | 0.00120244i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.65685 | + | 6.33386i | 0.121827 | + | 0.211011i | ||||
\(902\) | − | 10.8284i | − | 0.360547i | ||||||
\(903\) | −25.5095 | + | 10.4142i | −0.848903 | + | 0.346563i | ||||
\(904\) | −12.2843 | −0.408569 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.58579 | + | 7.94282i | −0.152353 | + | 0.263882i | ||||
\(907\) | −7.46100 | − | 4.30761i | −0.247739 | − | 0.143032i | 0.370990 | − | 0.928637i | \(-0.379018\pi\) |
−0.618728 | + | 0.785605i | \(0.712352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.24264 | 0.207055 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24264 | 0.140565 | 0.0702825 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | 23.0600 | − | 13.3137i | 0.763594 | − | 0.440861i | ||||
\(913\) | −16.0087 | − | 9.24264i | −0.529811 | − | 0.305887i | ||||
\(914\) | −14.7782 | + | 25.5965i | −0.488819 | + | 0.846659i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.76127 | − | 27.4853i | 0.124208 | − | 0.907644i | ||||
\(918\) | 8.82843i | 0.291382i | ||||||||
\(919\) | −23.3284 | − | 40.4060i | −0.769534 | − | 1.33287i | −0.937816 | − | 0.347133i | \(-0.887155\pi\) |
0.168282 | − | 0.985739i | \(-0.446178\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.792893 | − | 1.37333i | 0.0261267 | − | 0.0452528i | ||||
\(922\) | 33.1552 | − | 19.1421i | 1.09191 | − | 0.630413i | ||||
\(923\) | 5.41421i | 0.178211i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.36396 | + | 12.7548i | 0.241995 | + | 0.419147i | ||||
\(927\) | −1.07616 | − | 0.621320i | −0.0353457 | − | 0.0204068i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.5061 | − | 44.1779i | −0.836828 | − | 1.44943i | −0.892533 | − | 0.450981i | \(-0.851074\pi\) |
0.0557056 | − | 0.998447i | \(-0.482259\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.2843 | − | 32.6118i | 1.09085 | − | 1.06881i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.7840 | − | 8.53553i | 0.484006 | − | 0.279441i | ||||
\(934\) | 4.72792 | − | 8.18900i | 0.154702 | − | 0.267952i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.24264 | − | 3.88437i | −0.0733030 | − | 0.126965i | ||||
\(937\) | 7.92893i | 0.259027i | 0.991578 | + | 0.129513i | \(0.0413415\pi\) | ||||
−0.991578 | + | 0.129513i | \(0.958658\pi\) | |||||||
\(938\) | 34.6771 | + | 26.8909i | 1.13225 | + | 0.878018i | ||||
\(939\) | 26.2132 | 0.855436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.63604 | − | 9.76191i | 0.183730 | − | 0.318229i | −0.759418 | − | 0.650603i | \(-0.774516\pi\) |
0.943148 | + | 0.332374i | \(0.107850\pi\) | |||||||
\(942\) | 19.7700 | + | 11.4142i | 0.644141 | + | 0.371895i | ||||
\(943\) | −12.1244 | + | 7.00000i | −0.394823 | + | 0.227951i | ||||
\(944\) | 5.65685 | 0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −50.2843 | −1.63488 | ||||||||
\(947\) | 4.26858 | − | 2.46447i | 0.138710 | − | 0.0800844i | −0.429039 | − | 0.903286i | \(-0.641148\pi\) |
0.567749 | + | 0.823202i | \(0.307814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.64214 | + | 2.84426i | −0.0533060 | + | 0.0923287i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.100505 | −0.00325910 | ||||||||
\(952\) | 43.2503 | − | 17.6569i | 1.40175 | − | 0.572262i | ||||
\(953\) | 48.4853i | 1.57059i | 0.619120 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(954\) | 0.828427 | + | 1.43488i | 0.0268213 | + | 0.0464559i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.717439 | + | 0.414214i | −0.0231915 | + | 0.0133896i | ||||
\(958\) | − | 48.9706i | − | 1.58217i | ||||||
\(959\) | 2.92893 | + | 7.17439i | 0.0945802 | + | 0.231673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4853 | + | 26.8213i | 0.499525 | + | 0.865203i | ||||
\(962\) | 10.8486 | + | 6.26346i | 0.349774 | + | 0.201942i | ||||
\(963\) | −13.3491 | − | 7.70711i | −0.430169 | − | 0.248358i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.1421 | − | 3.16693i | −0.744586 | − | 0.101894i | ||||
\(967\) | − | 23.3848i | − | 0.752004i | −0.926619 | − | 0.376002i | \(-0.877299\pi\) | ||
0.926619 | − | 0.376002i | \(-0.122701\pi\) | |||||||
\(968\) | −1.60896 | + | 0.928932i | −0.0517139 | + | 0.0298570i | ||||
\(969\) | −20.7782 | + | 35.9889i | −0.667491 | + | 1.15613i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.17157 | − | 12.4215i | −0.230147 | − | 0.398626i | 0.727704 | − | 0.685891i | \(-0.240587\pi\) |
−0.957851 | + | 0.287265i | \(0.907254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0131 | + | 18.6213i | 0.769824 | + | 0.596972i | ||||
\(974\) | −1.27208 | −0.0407600 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.9706 | − | 43.2503i | 0.799288 | − | 1.38441i | ||||
\(977\) | 11.8632 | + | 6.84924i | 0.379539 | + | 0.219127i | 0.677617 | − | 0.735415i | \(-0.263013\pi\) |
−0.298079 | + | 0.954541i | \(0.596346\pi\) | |||||||
\(978\) | 23.6544 | − | 13.6569i | 0.756383 | − | 0.436698i | ||||
\(979\) | 12.8284 | 0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.4853 | −0.430552 | ||||||||
\(982\) | 12.4215 | − | 7.17157i | 0.396387 | − | 0.228854i | ||||
\(983\) | −46.0330 | − | 26.5772i | −1.46822 | − | 0.847680i | −0.468858 | − | 0.883273i | \(-0.655335\pi\) |
−0.999366 | + | 0.0355935i | \(0.988668\pi\) | |||||||
\(984\) | 3.17157 | − | 5.49333i | 0.101106 | − | 0.175121i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.14214 | 0.0682195 | ||||||||
\(987\) | 19.4728 | + | 15.1005i | 0.619827 | + | 0.480654i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.5061 | + | 56.3022i | 1.03363 | + | 1.79031i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.3284 | − | 26.5496i | 0.486924 | − | 0.843376i | −0.512963 | − | 0.858410i | \(-0.671452\pi\) |
0.999887 | + | 0.0150341i | \(0.00478570\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.6274i | 0.876730i | ||||||||
\(994\) | −12.6569 | − | 1.73205i | −0.401451 | − | 0.0549373i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.655892 | + | 0.378680i | 0.0207723 | + | 0.0119929i | 0.510350 | − | 0.859967i | \(-0.329516\pi\) |
−0.489578 | + | 0.871960i | \(0.662849\pi\) | |||||||
\(998\) | −10.7765 | − | 6.22183i | −0.341125 | − | 0.196948i | ||||
\(999\) | 2.79289 | + | 4.83743i | 0.0883632 | + | 0.153050i |
(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 | 525.2.r.g.424.2 | 8 | ||
5.2 | odd | 4 | 105.2.i.c.46.1 | yes | 4 | ||
5.3 | odd | 4 | 525.2.i.g.151.2 | 4 | |||
5.4 | even | 2 | inner | 525.2.r.g.424.3 | 8 | ||
7.2 | even | 3 | inner | 525.2.r.g.499.3 | 8 | ||
15.2 | even | 4 | 315.2.j.d.46.2 | 4 | |||
20.7 | even | 4 | 1680.2.bg.p.1201.1 | 4 | |||
35.2 | odd | 12 | 105.2.i.c.16.1 | ✓ | 4 | ||
35.3 | even | 12 | 3675.2.a.x.1.1 | 2 | |||
35.9 | even | 6 | inner | 525.2.r.g.499.2 | 8 | ||
35.12 | even | 12 | 735.2.i.j.226.1 | 4 | |||
35.17 | even | 12 | 735.2.a.j.1.2 | 2 | |||
35.18 | odd | 12 | 3675.2.a.z.1.1 | 2 | |||
35.23 | odd | 12 | 525.2.i.g.226.2 | 4 | |||
35.27 | even | 4 | 735.2.i.j.361.1 | 4 | |||
35.32 | odd | 12 | 735.2.a.i.1.2 | 2 | |||
105.2 | even | 12 | 315.2.j.d.226.2 | 4 | |||
105.17 | odd | 12 | 2205.2.a.s.1.1 | 2 | |||
105.32 | even | 12 | 2205.2.a.u.1.1 | 2 | |||
140.107 | even | 12 | 1680.2.bg.p.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.c.16.1 | ✓ | 4 | 35.2 | odd | 12 | ||
105.2.i.c.46.1 | yes | 4 | 5.2 | odd | 4 | ||
315.2.j.d.46.2 | 4 | 15.2 | even | 4 | |||
315.2.j.d.226.2 | 4 | 105.2 | even | 12 | |||
525.2.i.g.151.2 | 4 | 5.3 | odd | 4 | |||
525.2.i.g.226.2 | 4 | 35.23 | odd | 12 | |||
525.2.r.g.424.2 | 8 | 1.1 | even | 1 | trivial | ||
525.2.r.g.424.3 | 8 | 5.4 | even | 2 | inner | ||
525.2.r.g.499.2 | 8 | 35.9 | even | 6 | inner | ||
525.2.r.g.499.3 | 8 | 7.2 | even | 3 | inner | ||
735.2.a.i.1.2 | 2 | 35.32 | odd | 12 | |||
735.2.a.j.1.2 | 2 | 35.17 | even | 12 | |||
735.2.i.j.226.1 | 4 | 35.12 | even | 12 | |||
735.2.i.j.361.1 | 4 | 35.27 | even | 4 | |||
1680.2.bg.p.961.1 | 4 | 140.107 | even | 12 | |||
1680.2.bg.p.1201.1 | 4 | 20.7 | even | 4 | |||
2205.2.a.s.1.1 | 2 | 105.17 | odd | 12 | |||
2205.2.a.u.1.1 | 2 | 105.32 | even | 12 | |||
3675.2.a.x.1.1 | 2 | 35.3 | even | 12 | |||
3675.2.a.z.1.1 | 2 | 35.18 | odd | 12 |