Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(0.838429221223\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.16 |
Dual form | 105.2.i.c.46.1 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.707107 | + | 1.22474i | 0.223607 | + | 0.387298i | ||||
\(11\) | −1.70711 | − | 2.95680i | −0.514712 | − | 0.891507i | −0.999854 | − | 0.0170722i | \(-0.994565\pi\) |
0.485142 | − | 0.874435i | \(-0.338768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58579 | −0.439818 | −0.219909 | − | 0.975520i | \(-0.570576\pi\) | ||||
−0.219909 | + | 0.975520i | \(0.570576\pi\) | |||||||
\(14\) | −3.70711 | + | 0.507306i | −0.990766 | + | 0.135583i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 3.12132 | + | 5.40629i | 0.757031 | + | 1.31122i | 0.944358 | + | 0.328919i | \(0.106684\pi\) |
−0.187327 | + | 0.982298i | \(0.559982\pi\) | |||||||
\(18\) | −0.707107 | − | 1.22474i | −0.166667 | − | 0.288675i | ||||
\(19\) | 3.32843 | − | 5.76500i | 0.763594 | − | 1.32258i | −0.177393 | − | 0.984140i | \(-0.556767\pi\) |
0.940987 | − | 0.338443i | \(-0.109900\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | + | 2.44949i | −0.218218 | + | 0.534522i | ||||
\(22\) | 4.82843 | 1.02942 | ||||||||
\(23\) | 3.12132 | − | 5.40629i | 0.650840 | − | 1.12729i | −0.332079 | − | 0.943252i | \(-0.607750\pi\) |
0.982919 | − | 0.184037i | \(-0.0589166\pi\) | |||||||
\(24\) | −1.41421 | − | 2.44949i | −0.288675 | − | 0.500000i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.12132 | − | 1.94218i | 0.219909 | − | 0.380894i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.242641 | −0.0450572 | −0.0225286 | − | 0.999746i | \(-0.507172\pi\) | ||||
−0.0225286 | + | 0.999746i | \(0.507172\pi\) | |||||||
\(30\) | −0.707107 | + | 1.22474i | −0.129099 | + | 0.223607i | ||||
\(31\) | 0.0857864 | + | 0.148586i | 0.0154077 | + | 0.0266869i | 0.873626 | − | 0.486597i | \(-0.161762\pi\) |
−0.858219 | + | 0.513284i | \(0.828429\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.70711 | − | 2.95680i | 0.297169 | − | 0.514712i | ||||
\(34\) | −8.82843 | −1.51406 | ||||||||
\(35\) | 2.62132 | − | 0.358719i | 0.443084 | − | 0.0606347i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.79289 | − | 4.83743i | 0.459149 | − | 0.795269i | −0.539767 | − | 0.841814i | \(-0.681488\pi\) |
0.998916 | + | 0.0465451i | \(0.0148211\pi\) | |||||||
\(38\) | 4.70711 | + | 8.15295i | 0.763594 | + | 1.32258i | ||||
\(39\) | −0.792893 | − | 1.37333i | −0.126965 | − | 0.219909i | ||||
\(40\) | −1.41421 | + | 2.44949i | −0.223607 | + | 0.387298i | ||||
\(41\) | 2.24264 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(42\) | −2.29289 | − | 2.95680i | −0.353801 | − | 0.456243i | ||||
\(43\) | −10.4142 | −1.58815 | −0.794076 | − | 0.607818i | \(-0.792045\pi\) | ||||
−0.794076 | + | 0.607818i | \(0.792045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 4.41421 | + | 7.64564i | 0.650840 | + | 1.12729i | ||||
\(47\) | −4.65685 | + | 8.06591i | −0.679272 | + | 1.17653i | 0.295928 | + | 0.955210i | \(0.404371\pi\) |
−0.975200 | + | 0.221324i | \(0.928962\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 1.41421 | 0.200000 | ||||||||
\(51\) | −3.12132 | + | 5.40629i | −0.437072 | + | 0.757031i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.585786 | − | 1.01461i | −0.0804640 | − | 0.139368i | 0.822985 | − | 0.568063i | \(-0.192307\pi\) |
−0.903449 | + | 0.428695i | \(0.858974\pi\) | |||||||
\(54\) | 0.707107 | − | 1.22474i | 0.0962250 | − | 0.166667i | ||||
\(55\) | −3.41421 | −0.460372 | ||||||||
\(56\) | −4.58579 | − | 5.91359i | −0.612801 | − | 0.790237i | ||||
\(57\) | 6.65685 | 0.881722 | ||||||||
\(58\) | 0.171573 | − | 0.297173i | 0.0225286 | − | 0.0390207i | ||||
\(59\) | −0.707107 | − | 1.22474i | −0.0920575 | − | 0.159448i | 0.816319 | − | 0.577601i | \(-0.196011\pi\) |
−0.908377 | + | 0.418153i | \(0.862678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24264 | + | 10.8126i | −0.799288 | + | 1.38441i | 0.120792 | + | 0.992678i | \(0.461457\pi\) |
−0.920080 | + | 0.391730i | \(0.871877\pi\) | |||||||
\(62\) | −0.242641 | −0.0308154 | ||||||||
\(63\) | −2.62132 | + | 0.358719i | −0.330255 | + | 0.0451944i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −0.792893 | + | 1.37333i | −0.0983463 | + | 0.170341i | ||||
\(66\) | 2.41421 | + | 4.18154i | 0.297169 | + | 0.514712i | ||||
\(67\) | −5.86396 | − | 10.1567i | −0.716397 | − | 1.24084i | −0.962418 | − | 0.271571i | \(-0.912457\pi\) |
0.246021 | − | 0.969264i | \(-0.420877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.24264 | 0.751526 | ||||||||
\(70\) | −1.41421 | + | 3.46410i | −0.169031 | + | 0.414039i | ||||
\(71\) | −3.41421 | −0.405193 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(72\) | 1.41421 | − | 2.44949i | 0.166667 | − | 0.288675i | ||||
\(73\) | −1.03553 | − | 1.79360i | −0.121200 | − | 0.209925i | 0.799041 | − | 0.601276i | \(-0.205341\pi\) |
−0.920241 | + | 0.391352i | \(0.872008\pi\) | |||||||
\(74\) | 3.94975 | + | 6.84116i | 0.459149 | + | 0.795269i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.41421 | − | 8.36308i | 0.389086 | − | 0.953062i | ||||
\(78\) | 2.24264 | 0.253929 | ||||||||
\(79\) | 2.32843 | − | 4.03295i | 0.261969 | − | 0.453743i | −0.704796 | − | 0.709410i | \(-0.748962\pi\) |
0.966765 | + | 0.255667i | \(0.0822950\pi\) | |||||||
\(80\) | −2.00000 | − | 3.46410i | −0.223607 | − | 0.387298i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.58579 | + | 2.74666i | −0.175121 | + | 0.303318i | ||||
\(83\) | 5.41421 | 0.594287 | 0.297144 | − | 0.954833i | \(-0.403966\pi\) | ||||
0.297144 | + | 0.954833i | \(0.403966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.24264 | 0.677109 | ||||||||
\(86\) | 7.36396 | − | 12.7548i | 0.794076 | − | 1.37538i | ||||
\(87\) | −0.121320 | − | 0.210133i | −0.0130069 | − | 0.0225286i | ||||
\(88\) | 4.82843 | + | 8.36308i | 0.514712 | + | 0.891507i | ||||
\(89\) | 1.87868 | − | 3.25397i | 0.199140 | − | 0.344920i | −0.749110 | − | 0.662446i | \(-0.769519\pi\) |
0.948250 | + | 0.317526i | \(0.102852\pi\) | |||||||
\(90\) | −1.41421 | −0.149071 | ||||||||
\(91\) | −2.57107 | − | 3.31552i | −0.269521 | − | 0.347560i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0857864 | + | 0.148586i | −0.00889564 | + | 0.0154077i | ||||
\(94\) | −6.58579 | − | 11.4069i | −0.679272 | − | 1.17653i | ||||
\(95\) | −3.32843 | − | 5.76500i | −0.341489 | − | 0.591477i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8284 | −1.09946 | −0.549730 | − | 0.835342i | \(-0.685269\pi\) | ||||
−0.549730 | + | 0.835342i | \(0.685269\pi\) | |||||||
\(98\) | −7.07107 | − | 6.92820i | −0.714286 | − | 0.699854i | ||||
\(99\) | 3.41421 | 0.343141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.12132 | + | 5.40629i | 0.310583 | + | 0.537946i | 0.978489 | − | 0.206300i | \(-0.0661424\pi\) |
−0.667906 | + | 0.744246i | \(0.732809\pi\) | |||||||
\(102\) | −4.41421 | − | 7.64564i | −0.437072 | − | 0.757031i | ||||
\(103\) | 0.621320 | − | 1.07616i | 0.0612205 | − | 0.106037i | −0.833791 | − | 0.552081i | \(-0.813834\pi\) |
0.895011 | + | 0.446044i | \(0.147167\pi\) | |||||||
\(104\) | 4.48528 | 0.439818 | ||||||||
\(105\) | 1.62132 | + | 2.09077i | 0.158225 | + | 0.204038i | ||||
\(106\) | 1.65685 | 0.160928 | ||||||||
\(107\) | −7.70711 | + | 13.3491i | −0.745074 | + | 1.29051i | 0.205086 | + | 0.978744i | \(0.434253\pi\) |
−0.950160 | + | 0.311762i | \(0.899081\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.74264 | + | 11.6786i | 0.645828 | + | 1.11861i | 0.984110 | + | 0.177562i | \(0.0568210\pi\) |
−0.338282 | + | 0.941045i | \(0.609846\pi\) | |||||||
\(110\) | 2.41421 | − | 4.18154i | 0.230186 | − | 0.398694i | ||||
\(111\) | 5.58579 | 0.530179 | ||||||||
\(112\) | 10.4853 | − | 1.43488i | 0.990766 | − | 0.135583i | ||||
\(113\) | −4.34315 | −0.408569 | −0.204284 | − | 0.978912i | \(-0.565487\pi\) | ||||
−0.204284 | + | 0.978912i | \(0.565487\pi\) | |||||||
\(114\) | −4.70711 | + | 8.15295i | −0.440861 | + | 0.763594i | ||||
\(115\) | −3.12132 | − | 5.40629i | −0.291065 | − | 0.504139i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.792893 | − | 1.37333i | 0.0733030 | − | 0.126965i | ||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | −6.24264 | + | 15.2913i | −0.572262 | + | 1.40175i | ||||
\(120\) | −2.82843 | −0.258199 | ||||||||
\(121\) | −0.328427 | + | 0.568852i | −0.0298570 | + | 0.0517139i | ||||
\(122\) | −8.82843 | − | 15.2913i | −0.799288 | − | 1.38441i | ||||
\(123\) | 1.12132 | + | 1.94218i | 0.101106 | + | 0.175121i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.41421 | − | 3.46410i | 0.125988 | − | 0.308607i | ||||
\(127\) | −18.0711 | −1.60355 | −0.801774 | − | 0.597627i | \(-0.796110\pi\) | ||||
−0.801774 | + | 0.597627i | \(0.796110\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.500000 | + | 0.866025i | ||||
\(129\) | −5.20711 | − | 9.01897i | −0.458460 | − | 0.794076i | ||||
\(130\) | −1.12132 | − | 1.94218i | −0.0983463 | − | 0.170341i | ||||
\(131\) | 5.24264 | − | 9.08052i | 0.458052 | − | 0.793369i | −0.540806 | − | 0.841147i | \(-0.681881\pi\) |
0.998858 | + | 0.0477784i | \(0.0152141\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.4497 | − | 2.38794i | 1.51308 | − | 0.207061i | ||||
\(134\) | 16.5858 | 1.43279 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −8.82843 | − | 15.2913i | −0.757031 | − | 1.31122i | ||||
\(137\) | 1.46447 | + | 2.53653i | 0.125118 | + | 0.216710i | 0.921779 | − | 0.387716i | \(-0.126736\pi\) |
−0.796661 | + | 0.604426i | \(0.793402\pi\) | |||||||
\(138\) | −4.41421 | + | 7.64564i | −0.375763 | + | 0.650840i | ||||
\(139\) | 11.4853 | 0.974169 | 0.487084 | − | 0.873355i | \(-0.338060\pi\) | ||||
0.487084 | + | 0.873355i | \(0.338060\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.31371 | −0.784356 | ||||||||
\(142\) | 2.41421 | − | 4.18154i | 0.202596 | − | 0.350907i | ||||
\(143\) | 2.70711 | + | 4.68885i | 0.226380 | + | 0.392101i | ||||
\(144\) | 2.00000 | + | 3.46410i | 0.166667 | + | 0.288675i | ||||
\(145\) | −0.121320 | + | 0.210133i | −0.0100751 | + | 0.0174506i | ||||
\(146\) | 2.92893 | 0.242400 | ||||||||
\(147\) | −6.74264 | + | 1.88064i | −0.556124 | + | 0.155112i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.82843 | + | 15.2913i | −0.723253 | + | 1.25271i | 0.236436 | + | 0.971647i | \(0.424021\pi\) |
−0.959689 | + | 0.281064i | \(0.909313\pi\) | |||||||
\(150\) | 0.707107 | + | 1.22474i | 0.0577350 | + | 0.100000i | ||||
\(151\) | 3.24264 | + | 5.61642i | 0.263882 | + | 0.457058i | 0.967270 | − | 0.253749i | \(-0.0816636\pi\) |
−0.703388 | + | 0.710806i | \(0.748330\pi\) | |||||||
\(152\) | −9.41421 | + | 16.3059i | −0.763594 | + | 1.32258i | ||||
\(153\) | −6.24264 | −0.504688 | ||||||||
\(154\) | 7.82843 | + | 10.0951i | 0.630833 | + | 0.813489i | ||||
\(155\) | 0.171573 | 0.0137811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.07107 | + | 13.9795i | 0.644141 | + | 1.11569i | 0.984499 | + | 0.175390i | \(0.0561185\pi\) |
−0.340358 | + | 0.940296i | \(0.610548\pi\) | |||||||
\(158\) | 3.29289 | + | 5.70346i | 0.261969 | + | 0.453743i | ||||
\(159\) | 0.585786 | − | 1.01461i | 0.0464559 | − | 0.0804640i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3640 | − | 2.23936i | 1.28966 | − | 0.176486i | ||||
\(162\) | 1.41421 | 0.111111 | ||||||||
\(163\) | 9.65685 | − | 16.7262i | 0.756383 | − | 1.31009i | −0.188301 | − | 0.982111i | \(-0.560298\pi\) |
0.944684 | − | 0.327983i | \(-0.106369\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.70711 | − | 2.95680i | −0.132898 | − | 0.230186i | ||||
\(166\) | −3.82843 | + | 6.63103i | −0.297144 | + | 0.514668i | ||||
\(167\) | 11.7574 | 0.909812 | 0.454906 | − | 0.890540i | \(-0.349673\pi\) | ||||
0.454906 | + | 0.890540i | \(0.349673\pi\) | |||||||
\(168\) | 2.82843 | − | 6.92820i | 0.218218 | − | 0.534522i | ||||
\(169\) | −10.4853 | −0.806560 | ||||||||
\(170\) | −4.41421 | + | 7.64564i | −0.338555 | + | 0.586394i | ||||
\(171\) | 3.32843 | + | 5.76500i | 0.254531 | + | 0.440861i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.41421 | − | 2.44949i | 0.107521 | − | 0.186231i | −0.807245 | − | 0.590217i | \(-0.799042\pi\) |
0.914765 | + | 0.403986i | \(0.132375\pi\) | |||||||
\(174\) | 0.343146 | 0.0260138 | ||||||||
\(175\) | 1.00000 | − | 2.44949i | 0.0755929 | − | 0.185164i | ||||
\(176\) | −13.6569 | −1.02942 | ||||||||
\(177\) | 0.707107 | − | 1.22474i | 0.0531494 | − | 0.0920575i | ||||
\(178\) | 2.65685 | + | 4.60181i | 0.199140 | + | 0.344920i | ||||
\(179\) | −9.82843 | − | 17.0233i | −0.734611 | − | 1.27238i | −0.954894 | − | 0.296948i | \(-0.904031\pi\) |
0.220283 | − | 0.975436i | \(-0.429302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.656854 | 0.0488236 | 0.0244118 | − | 0.999702i | \(-0.492229\pi\) | ||||
0.0244118 | + | 0.999702i | \(0.492229\pi\) | |||||||
\(182\) | 5.87868 | − | 0.804479i | 0.435757 | − | 0.0596319i | ||||
\(183\) | −12.4853 | −0.922939 | ||||||||
\(184\) | −8.82843 | + | 15.2913i | −0.650840 | + | 1.12729i | ||||
\(185\) | −2.79289 | − | 4.83743i | −0.205338 | − | 0.355655i | ||||
\(186\) | −0.121320 | − | 0.210133i | −0.00889564 | − | 0.0154077i | ||||
\(187\) | 10.6569 | − | 18.4582i | 0.779306 | − | 1.34980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.62132 | − | 2.09077i | −0.117934 | − | 0.152081i | ||||
\(190\) | 9.41421 | 0.682979 | ||||||||
\(191\) | −9.48528 | + | 16.4290i | −0.686331 | + | 1.18876i | 0.286686 | + | 0.958025i | \(0.407446\pi\) |
−0.973017 | + | 0.230735i | \(0.925887\pi\) | |||||||
\(192\) | 4.00000 | + | 6.92820i | 0.288675 | + | 0.500000i | ||||
\(193\) | 3.37868 | + | 5.85204i | 0.243203 | + | 0.421239i | 0.961625 | − | 0.274368i | \(-0.0884687\pi\) |
−0.718422 | + | 0.695607i | \(0.755135\pi\) | |||||||
\(194\) | 7.65685 | − | 13.2621i | 0.549730 | − | 0.952160i | ||||
\(195\) | −1.58579 | −0.113561 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.55635 | 0.395873 | 0.197937 | − | 0.980215i | \(-0.436576\pi\) | ||||
0.197937 | + | 0.980215i | \(0.436576\pi\) | |||||||
\(198\) | −2.41421 | + | 4.18154i | −0.171571 | + | 0.297169i | ||||
\(199\) | −2.75736 | − | 4.77589i | −0.195464 | − | 0.338554i | 0.751589 | − | 0.659632i | \(-0.229288\pi\) |
−0.947053 | + | 0.321079i | \(0.895955\pi\) | |||||||
\(200\) | 1.41421 | + | 2.44949i | 0.100000 | + | 0.173205i | ||||
\(201\) | 5.86396 | − | 10.1567i | 0.413612 | − | 0.716397i | ||||
\(202\) | −8.82843 | −0.621166 | ||||||||
\(203\) | −0.393398 | − | 0.507306i | −0.0276111 | − | 0.0356059i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.12132 | − | 1.94218i | 0.0783164 | − | 0.135648i | ||||
\(206\) | 0.878680 | + | 1.52192i | 0.0612205 | + | 0.106037i | ||||
\(207\) | 3.12132 | + | 5.40629i | 0.216947 | + | 0.375763i | ||||
\(208\) | −3.17157 | + | 5.49333i | −0.219909 | + | 0.380894i | ||||
\(209\) | −22.7279 | −1.57212 | ||||||||
\(210\) | −3.70711 | + | 0.507306i | −0.255815 | + | 0.0350074i | ||||
\(211\) | 0.142136 | 0.00978502 | 0.00489251 | − | 0.999988i | \(-0.498443\pi\) | ||||
0.00489251 | + | 0.999988i | \(0.498443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.70711 | − | 2.95680i | −0.116969 | − | 0.202596i | ||||
\(214\) | −10.8995 | − | 18.8785i | −0.745074 | − | 1.29051i | ||||
\(215\) | −5.20711 | + | 9.01897i | −0.355122 | + | 0.615089i | ||||
\(216\) | 2.82843 | 0.192450 | ||||||||
\(217\) | −0.171573 | + | 0.420266i | −0.0116471 | + | 0.0285295i | ||||
\(218\) | −19.0711 | −1.29166 | ||||||||
\(219\) | 1.03553 | − | 1.79360i | 0.0699749 | − | 0.121200i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.94975 | − | 8.57321i | −0.332956 | − | 0.576697i | ||||
\(222\) | −3.94975 | + | 6.84116i | −0.265090 | + | 0.459149i | ||||
\(223\) | 17.1716 | 1.14989 | 0.574947 | − | 0.818191i | \(-0.305023\pi\) | ||||
0.574947 | + | 0.818191i | \(0.305023\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.07107 | − | 5.31925i | 0.204284 | − | 0.353831i | ||||
\(227\) | −11.5355 | − | 19.9801i | −0.765640 | − | 1.32613i | −0.939907 | − | 0.341429i | \(-0.889089\pi\) |
0.174267 | − | 0.984698i | \(-0.444244\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.15685 | − | 12.3960i | 0.472938 | − | 0.819153i | −0.526582 | − | 0.850124i | \(-0.676527\pi\) |
0.999520 | + | 0.0309713i | \(0.00986003\pi\) | |||||||
\(230\) | 8.82843 | 0.582129 | ||||||||
\(231\) | 8.94975 | − | 1.22474i | 0.588850 | − | 0.0805823i | ||||
\(232\) | 0.686292 | 0.0450572 | ||||||||
\(233\) | 11.2426 | − | 19.4728i | 0.736530 | − | 1.27571i | −0.217519 | − | 0.976056i | \(-0.569796\pi\) |
0.954049 | − | 0.299651i | \(-0.0968703\pi\) | |||||||
\(234\) | 1.12132 | + | 1.94218i | 0.0733030 | + | 0.126965i | ||||
\(235\) | 4.65685 | + | 8.06591i | 0.303780 | + | 0.526162i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.65685 | 0.302495 | ||||||||
\(238\) | −14.3137 | − | 18.4582i | −0.927820 | − | 1.19647i | ||||
\(239\) | 17.3137 | 1.11993 | 0.559965 | − | 0.828516i | \(-0.310814\pi\) | ||||
0.559965 | + | 0.828516i | \(0.310814\pi\) | |||||||
\(240\) | 2.00000 | − | 3.46410i | 0.129099 | − | 0.223607i | ||||
\(241\) | 5.17157 | + | 8.95743i | 0.333130 | + | 0.576999i | 0.983124 | − | 0.182941i | \(-0.0585618\pi\) |
−0.649994 | + | 0.759940i | \(0.725228\pi\) | |||||||
\(242\) | −0.464466 | − | 0.804479i | −0.0298570 | − | 0.0517139i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | + | 4.89898i | 0.319438 | + | 0.312984i | ||||
\(246\) | −3.17157 | −0.202212 | ||||||||
\(247\) | −5.27817 | + | 9.14207i | −0.335842 | + | 0.581696i | ||||
\(248\) | −0.242641 | − | 0.420266i | −0.0154077 | − | 0.0266869i | ||||
\(249\) | 2.70711 | + | 4.68885i | 0.171556 | + | 0.297144i | ||||
\(250\) | 0.707107 | − | 1.22474i | 0.0447214 | − | 0.0774597i | ||||
\(251\) | −5.41421 | −0.341742 | −0.170871 | − | 0.985293i | \(-0.554658\pi\) | ||||
−0.170871 | + | 0.985293i | \(0.554658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.3137 | −1.33998 | ||||||||
\(254\) | 12.7782 | − | 22.1324i | 0.801774 | − | 1.38871i | ||||
\(255\) | 3.12132 | + | 5.40629i | 0.195465 | + | 0.338555i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9497 | − | 25.8937i | 0.932540 | − | 1.61521i | 0.153576 | − | 0.988137i | \(-0.450921\pi\) |
0.778964 | − | 0.627069i | \(-0.215746\pi\) | |||||||
\(258\) | 14.7279 | 0.916920 | ||||||||
\(259\) | 14.6421 | − | 2.00373i | 0.909818 | − | 0.124506i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.121320 | − | 0.210133i | 0.00750954 | − | 0.0130069i | ||||
\(262\) | 7.41421 | + | 12.8418i | 0.458052 | + | 0.793369i | ||||
\(263\) | −0.585786 | − | 1.01461i | −0.0361211 | − | 0.0625636i | 0.847400 | − | 0.530956i | \(-0.178167\pi\) |
−0.883521 | + | 0.468392i | \(0.844834\pi\) | |||||||
\(264\) | −4.82843 | + | 8.36308i | −0.297169 | + | 0.514712i | ||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | −9.41421 | + | 23.0600i | −0.577222 | + | 1.41390i | ||||
\(267\) | 3.75736 | 0.229947 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.07107 | − | 7.05130i | −0.248217 | − | 0.429925i | 0.714814 | − | 0.699315i | \(-0.246511\pi\) |
−0.963031 | + | 0.269390i | \(0.913178\pi\) | |||||||
\(270\) | −0.707107 | − | 1.22474i | −0.0430331 | − | 0.0745356i | ||||
\(271\) | −10.0711 | + | 17.4436i | −0.611774 | + | 1.05962i | 0.379168 | + | 0.925328i | \(0.376210\pi\) |
−0.990941 | + | 0.134295i | \(0.957123\pi\) | |||||||
\(272\) | 24.9706 | 1.51406 | ||||||||
\(273\) | 1.58579 | − | 3.88437i | 0.0959762 | − | 0.235093i | ||||
\(274\) | −4.14214 | −0.250236 | ||||||||
\(275\) | −1.70711 | + | 2.95680i | −0.102942 | + | 0.178301i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6924 | + | 20.2518i | 0.702528 | + | 1.21681i | 0.967576 | + | 0.252578i | \(0.0812786\pi\) |
−0.265049 | + | 0.964235i | \(0.585388\pi\) | |||||||
\(278\) | −8.12132 | + | 14.0665i | −0.487084 | + | 0.843655i | ||||
\(279\) | −0.171573 | −0.0102718 | ||||||||
\(280\) | −7.41421 | + | 1.01461i | −0.443084 | + | 0.0606347i | ||||
\(281\) | 9.65685 | 0.576080 | 0.288040 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288040 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(282\) | 6.58579 | − | 11.4069i | 0.392178 | − | 0.679272i | ||||
\(283\) | 6.62132 | + | 11.4685i | 0.393597 | + | 0.681729i | 0.992921 | − | 0.118777i | \(-0.0378973\pi\) |
−0.599324 | + | 0.800506i | \(0.704564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.32843 | − | 5.76500i | 0.197159 | − | 0.341489i | ||||
\(286\) | −7.65685 | −0.452759 | ||||||||
\(287\) | 3.63604 | + | 4.68885i | 0.214629 | + | 0.276774i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9853 | + | 19.0271i | −0.646193 | + | 1.11924i | ||||
\(290\) | −0.171573 | − | 0.297173i | −0.0100751 | − | 0.0174506i | ||||
\(291\) | −5.41421 | − | 9.37769i | −0.317387 | − | 0.549730i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3137 | −0.894636 | −0.447318 | − | 0.894375i | \(-0.647621\pi\) | ||||
−0.447318 | + | 0.894375i | \(0.647621\pi\) | |||||||
\(294\) | 2.46447 | − | 9.58783i | 0.143731 | − | 0.559173i | ||||
\(295\) | −1.41421 | −0.0823387 | ||||||||
\(296\) | −7.89949 | + | 13.6823i | −0.459149 | + | 0.795269i | ||||
\(297\) | 1.70711 | + | 2.95680i | 0.0990564 | + | 0.171571i | ||||
\(298\) | −12.4853 | − | 21.6251i | −0.723253 | − | 1.25271i | ||||
\(299\) | −4.94975 | + | 8.57321i | −0.286251 | + | 0.495802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8848 | − | 21.7737i | −0.973222 | − | 1.25502i | ||||
\(302\) | −9.17157 | −0.527765 | ||||||||
\(303\) | −3.12132 | + | 5.40629i | −0.179315 | + | 0.310583i | ||||
\(304\) | −13.3137 | − | 23.0600i | −0.763594 | − | 1.32258i | ||||
\(305\) | 6.24264 | + | 10.8126i | 0.357453 | + | 0.619126i | ||||
\(306\) | 4.41421 | − | 7.64564i | 0.252344 | − | 0.437072i | ||||
\(307\) | 1.58579 | 0.0905056 | 0.0452528 | − | 0.998976i | \(-0.485591\pi\) | ||||
0.0452528 | + | 0.998976i | \(0.485591\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.24264 | 0.0706914 | ||||||||
\(310\) | −0.121320 | + | 0.210133i | −0.00689053 | + | 0.0119348i | ||||
\(311\) | 8.53553 | + | 14.7840i | 0.484006 | + | 0.838323i | 0.999831 | − | 0.0183712i | \(-0.00584805\pi\) |
−0.515826 | + | 0.856694i | \(0.672515\pi\) | |||||||
\(312\) | 2.24264 | + | 3.88437i | 0.126965 | + | 0.219909i | ||||
\(313\) | −13.1066 | + | 22.7013i | −0.740829 | + | 1.28315i | 0.211289 | + | 0.977424i | \(0.432234\pi\) |
−0.952118 | + | 0.305730i | \(0.901100\pi\) | |||||||
\(314\) | −22.8284 | −1.28828 | ||||||||
\(315\) | −1.00000 | + | 2.44949i | −0.0563436 | + | 0.138013i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0502525 | + | 0.0870399i | −0.00282246 | + | 0.00488865i | −0.867433 | − | 0.497554i | \(-0.834232\pi\) |
0.864611 | + | 0.502442i | \(0.167565\pi\) | |||||||
\(318\) | 0.828427 | + | 1.43488i | 0.0464559 | + | 0.0804640i | ||||
\(319\) | 0.414214 | + | 0.717439i | 0.0231915 | + | 0.0401689i | ||||
\(320\) | 4.00000 | − | 6.92820i | 0.223607 | − | 0.387298i | ||||
\(321\) | −15.4142 | −0.860338 | ||||||||
\(322\) | −8.82843 | + | 21.6251i | −0.491989 | + | 1.20512i | ||||
\(323\) | 41.5563 | 2.31226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.792893 | + | 1.37333i | 0.0439818 | + | 0.0761787i | ||||
\(326\) | 13.6569 | + | 23.6544i | 0.756383 | + | 1.31009i | ||||
\(327\) | −6.74264 | + | 11.6786i | −0.372869 | + | 0.645828i | ||||
\(328\) | −6.34315 | −0.350242 | ||||||||
\(329\) | −24.4142 | + | 3.34101i | −1.34600 | + | 0.184196i | ||||
\(330\) | 4.82843 | 0.265796 | ||||||||
\(331\) | 13.8137 | − | 23.9260i | 0.759270 | − | 1.31509i | −0.183953 | − | 0.982935i | \(-0.558889\pi\) |
0.943223 | − | 0.332159i | \(-0.107777\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.79289 | + | 4.83743i | 0.153050 | + | 0.265090i | ||||
\(334\) | −8.31371 | + | 14.3998i | −0.454906 | + | 0.787920i | ||||
\(335\) | −11.7279 | −0.640765 | ||||||||
\(336\) | 6.48528 | + | 8.36308i | 0.353801 | + | 0.456243i | ||||
\(337\) | −0.899495 | −0.0489986 | −0.0244993 | − | 0.999700i | \(-0.507799\pi\) | ||||
−0.0244993 | + | 0.999700i | \(0.507799\pi\) | |||||||
\(338\) | 7.41421 | − | 12.8418i | 0.403280 | − | 0.698502i | ||||
\(339\) | −2.17157 | − | 3.76127i | −0.117944 | − | 0.204284i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.292893 | − | 0.507306i | 0.0158611 | − | 0.0274722i | ||||
\(342\) | −9.41421 | −0.509062 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 29.4558 | 1.58815 | ||||||||
\(345\) | 3.12132 | − | 5.40629i | 0.168046 | − | 0.291065i | ||||
\(346\) | 2.00000 | + | 3.46410i | 0.107521 | + | 0.186231i | ||||
\(347\) | 12.4853 | + | 21.6251i | 0.670245 | + | 1.16090i | 0.977835 | + | 0.209379i | \(0.0671443\pi\) |
−0.307589 | + | 0.951519i | \(0.599522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6274 | −0.890045 | −0.445023 | − | 0.895519i | \(-0.646804\pi\) | ||||
−0.445023 | + | 0.895519i | \(0.646804\pi\) | |||||||
\(350\) | 2.29289 | + | 2.95680i | 0.122560 | + | 0.158047i | ||||
\(351\) | 1.58579 | 0.0846430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.94975 | − | 5.10911i | −0.156999 | − | 0.271931i | 0.776786 | − | 0.629765i | \(-0.216849\pi\) |
−0.933785 | + | 0.357834i | \(0.883515\pi\) | |||||||
\(354\) | 1.00000 | + | 1.73205i | 0.0531494 | + | 0.0920575i | ||||
\(355\) | −1.70711 | + | 2.95680i | −0.0906038 | + | 0.156930i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.3640 | + | 2.23936i | −0.866073 | + | 0.118519i | ||||
\(358\) | 27.7990 | 1.46922 | ||||||||
\(359\) | 13.2929 | − | 23.0240i | 0.701572 | − | 1.21516i | −0.266342 | − | 0.963878i | \(-0.585815\pi\) |
0.967914 | − | 0.251280i | \(-0.0808515\pi\) | |||||||
\(360\) | −1.41421 | − | 2.44949i | −0.0745356 | − | 0.129099i | ||||
\(361\) | −12.6569 | − | 21.9223i | −0.666150 | − | 1.15381i | ||||
\(362\) | −0.464466 | + | 0.804479i | −0.0244118 | + | 0.0422825i | ||||
\(363\) | −0.656854 | −0.0344759 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.07107 | −0.108405 | ||||||||
\(366\) | 8.82843 | − | 15.2913i | 0.461469 | − | 0.799288i | ||||
\(367\) | 9.79289 | + | 16.9618i | 0.511185 | + | 0.885398i | 0.999916 | + | 0.0129637i | \(0.00412658\pi\) |
−0.488731 | + | 0.872434i | \(0.662540\pi\) | |||||||
\(368\) | −12.4853 | − | 21.6251i | −0.650840 | − | 1.12729i | ||||
\(369\) | −1.12132 | + | 1.94218i | −0.0583736 | + | 0.101106i | ||||
\(370\) | 7.89949 | 0.410675 | ||||||||
\(371\) | 1.17157 | − | 2.86976i | 0.0608250 | − | 0.148990i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.62132 | + | 16.6646i | −0.498173 | + | 0.862861i | −0.999998 | − | 0.00210826i | \(-0.999329\pi\) |
0.501825 | + | 0.864969i | \(0.332662\pi\) | |||||||
\(374\) | 15.0711 | + | 26.1039i | 0.779306 | + | 1.34980i | ||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 13.1716 | − | 22.8138i | 0.679272 | − | 1.17653i | ||||
\(377\) | 0.384776 | 0.0198170 | ||||||||
\(378\) | 3.70711 | − | 0.507306i | 0.190673 | − | 0.0260930i | ||||
\(379\) | 14.7990 | 0.760173 | 0.380087 | − | 0.924951i | \(-0.375894\pi\) | ||||
0.380087 | + | 0.924951i | \(0.375894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.03553 | − | 15.6500i | −0.462904 | − | 0.801774i | ||||
\(382\) | −13.4142 | − | 23.2341i | −0.686331 | − | 1.18876i | ||||
\(383\) | −6.24264 | + | 10.8126i | −0.318984 | + | 0.552497i | −0.980276 | − | 0.197632i | \(-0.936675\pi\) |
0.661292 | + | 0.750128i | \(0.270008\pi\) | |||||||
\(384\) | −11.3137 | −0.577350 | ||||||||
\(385\) | −5.53553 | − | 7.13834i | −0.282117 | − | 0.363803i | ||||
\(386\) | −9.55635 | −0.486405 | ||||||||
\(387\) | 5.20711 | − | 9.01897i | 0.264692 | − | 0.458460i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.43503 | − | 14.6099i | −0.427673 | − | 0.740751i | 0.568993 | − | 0.822342i | \(-0.307333\pi\) |
−0.996666 | + | 0.0815911i | \(0.974000\pi\) | |||||||
\(390\) | 1.12132 | − | 1.94218i | 0.0567803 | − | 0.0983463i | ||||
\(391\) | 38.9706 | 1.97083 | ||||||||
\(392\) | 4.92893 | − | 19.1757i | 0.248949 | − | 0.968517i | ||||
\(393\) | 10.4853 | 0.528912 | ||||||||
\(394\) | −3.92893 | + | 6.80511i | −0.197937 | + | 0.342836i | ||||
\(395\) | −2.32843 | − | 4.03295i | −0.117156 | − | 0.202920i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.1066 | − | 20.9692i | 0.607613 | − | 1.05242i | −0.384020 | − | 0.923325i | \(-0.625461\pi\) |
0.991633 | − | 0.129092i | \(-0.0412061\pi\) | |||||||
\(398\) | 7.79899 | 0.390928 | ||||||||
\(399\) | 10.7929 | + | 13.9180i | 0.540320 | + | 0.696769i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −0.242641 | + | 0.420266i | −0.0121169 | + | 0.0209871i | −0.872020 | − | 0.489470i | \(-0.837190\pi\) |
0.859903 | + | 0.510457i | \(0.170524\pi\) | |||||||
\(402\) | 8.29289 | + | 14.3637i | 0.413612 | + | 0.716397i | ||||
\(403\) | −0.136039 | − | 0.235626i | −0.00677658 | − | 0.0117374i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0.899495 | − | 0.123093i | 0.0446412 | − | 0.00610901i | ||||
\(407\) | −19.0711 | −0.945318 | ||||||||
\(408\) | 8.82843 | − | 15.2913i | 0.437072 | − | 0.757031i | ||||
\(409\) | 13.1569 | + | 22.7883i | 0.650565 | + | 1.12681i | 0.982986 | + | 0.183680i | \(0.0588010\pi\) |
−0.332422 | + | 0.943131i | \(0.607866\pi\) | |||||||
\(410\) | 1.58579 | + | 2.74666i | 0.0783164 | + | 0.135648i | ||||
\(411\) | −1.46447 | + | 2.53653i | −0.0722368 | + | 0.125118i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.41421 | − | 3.46410i | 0.0695889 | − | 0.170457i | ||||
\(414\) | −8.82843 | −0.433894 | ||||||||
\(415\) | 2.70711 | − | 4.68885i | 0.132887 | − | 0.230166i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.74264 | + | 9.94655i | 0.281218 | + | 0.487084i | ||||
\(418\) | 16.0711 | − | 27.8359i | 0.786062 | − | 1.36150i | ||||
\(419\) | −3.17157 | −0.154941 | −0.0774707 | − | 0.996995i | \(-0.524684\pi\) | ||||
−0.0774707 | + | 0.996995i | \(0.524684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4853 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266390\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266390\pi\) | |||||||
\(422\) | −0.100505 | + | 0.174080i | −0.00489251 | + | 0.00847408i | ||||
\(423\) | −4.65685 | − | 8.06591i | −0.226424 | − | 0.392178i | ||||
\(424\) | 1.65685 | + | 2.86976i | 0.0804640 | + | 0.139368i | ||||
\(425\) | 3.12132 | − | 5.40629i | 0.151406 | − | 0.262243i | ||||
\(426\) | 4.82843 | 0.233938 | ||||||||
\(427\) | −32.7279 | + | 4.47871i | −1.58382 | + | 0.216740i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.70711 | + | 4.68885i | −0.130700 | + | 0.226380i | ||||
\(430\) | −7.36396 | − | 12.7548i | −0.355122 | − | 0.615089i | ||||
\(431\) | −18.4142 | − | 31.8944i | −0.886981 | − | 1.53630i | −0.843426 | − | 0.537246i | \(-0.819465\pi\) |
−0.0435558 | − | 0.999051i | \(-0.513869\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | −24.5563 | −1.18010 | −0.590051 | − | 0.807366i | \(-0.700893\pi\) | ||||
−0.590051 | + | 0.807366i | \(0.700893\pi\) | |||||||
\(434\) | −0.393398 | − | 0.507306i | −0.0188837 | − | 0.0243515i | ||||
\(435\) | −0.242641 | −0.0116337 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7782 | − | 35.9889i | −0.993955 | − | 1.72158i | ||||
\(438\) | 1.46447 | + | 2.53653i | 0.0699749 | + | 0.121200i | ||||
\(439\) | −0.171573 | + | 0.297173i | −0.00818873 | + | 0.0141833i | −0.870091 | − | 0.492892i | \(-0.835940\pi\) |
0.861902 | + | 0.507075i | \(0.169273\pi\) | |||||||
\(440\) | 9.65685 | 0.460372 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | 14.0000 | 0.665912 | ||||||||
\(443\) | −0.242641 | + | 0.420266i | −0.0115282 | + | 0.0199674i | −0.871732 | − | 0.489983i | \(-0.837003\pi\) |
0.860204 | + | 0.509950i | \(0.170336\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.87868 | − | 3.25397i | −0.0890580 | − | 0.154253i | ||||
\(446\) | −12.1421 | + | 21.0308i | −0.574947 | + | 0.995837i | ||||
\(447\) | −17.6569 | −0.835141 | ||||||||
\(448\) | 12.9706 | + | 16.7262i | 0.612801 | + | 0.790237i | ||||
\(449\) | −6.97056 | −0.328961 | −0.164481 | − | 0.986380i | \(-0.552595\pi\) | ||||
−0.164481 | + | 0.986380i | \(0.552595\pi\) | |||||||
\(450\) | −0.707107 | + | 1.22474i | −0.0333333 | + | 0.0577350i | ||||
\(451\) | −3.82843 | − | 6.63103i | −0.180274 | − | 0.312243i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.24264 | + | 5.61642i | −0.152353 | + | 0.263882i | ||||
\(454\) | 32.6274 | 1.53128 | ||||||||
\(455\) | −4.15685 | + | 0.568852i | −0.194876 | + | 0.0266682i | ||||
\(456\) | −18.8284 | −0.881722 | ||||||||
\(457\) | 10.4497 | − | 18.0995i | 0.488819 | − | 0.846659i | −0.511099 | − | 0.859522i | \(-0.670761\pi\) |
0.999917 | + | 0.0128634i | \(0.00409467\pi\) | |||||||
\(458\) | 10.1213 | + | 17.5306i | 0.472938 | + | 0.819153i | ||||
\(459\) | −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 | \(0.717114\pi\) | |||||||
\(462\) | −4.82843 | + | 11.8272i | −0.224639 | + | 0.550250i | ||||
\(463\) | −10.4142 | −0.483990 | −0.241995 | − | 0.970278i | \(-0.577802\pi\) | ||||
−0.241995 | + | 0.970278i | \(0.577802\pi\) | |||||||
\(464\) | −0.485281 | + | 0.840532i | −0.0225286 | + | 0.0390207i | ||||
\(465\) | 0.0857864 | + | 0.148586i | 0.00397825 | + | 0.00689053i | ||||
\(466\) | 15.8995 | + | 27.5387i | 0.736530 | + | 1.27571i | ||||
\(467\) | −3.34315 | + | 5.79050i | −0.154702 | + | 0.267952i | −0.932951 | − | 0.360004i | \(-0.882775\pi\) |
0.778248 | + | 0.627957i | \(0.216109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7279 | − | 28.7274i | 0.541545 | − | 1.32651i | ||||
\(470\) | −13.1716 | −0.607559 | ||||||||
\(471\) | −8.07107 | + | 13.9795i | −0.371895 | + | 0.644141i | ||||
\(472\) | 2.00000 | + | 3.46410i | 0.0920575 | + | 0.159448i | ||||
\(473\) | 17.7782 | + | 30.7927i | 0.817441 | + | 1.41585i | ||||
\(474\) | −3.29289 | + | 5.70346i | −0.151248 | + | 0.261969i | ||||
\(475\) | −6.65685 | −0.305437 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.17157 | 0.0536426 | ||||||||
\(478\) | −12.2426 | + | 21.2049i | −0.559965 | + | 0.969888i | ||||
\(479\) | 17.3137 | + | 29.9882i | 0.791084 | + | 1.37020i | 0.925297 | + | 0.379244i | \(0.123816\pi\) |
−0.134213 | + | 0.990953i | \(0.542851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.42893 | + | 7.67114i | −0.201942 | + | 0.349774i | ||||
\(482\) | −14.6274 | −0.666261 | ||||||||
\(483\) | 10.1213 | + | 13.0519i | 0.460536 | + | 0.593883i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.41421 | + | 9.37769i | −0.245847 | + | 0.425819i | ||||
\(486\) | 0.707107 | + | 1.22474i | 0.0320750 | + | 0.0555556i | ||||
\(487\) | −0.449747 | − | 0.778985i | −0.0203800 | − | 0.0352992i | 0.855656 | − | 0.517546i | \(-0.173154\pi\) |
−0.876036 | + | 0.482247i | \(0.839821\pi\) | |||||||
\(488\) | 17.6569 | − | 30.5826i | 0.799288 | − | 1.38441i | ||||
\(489\) | 19.3137 | 0.873396 | ||||||||
\(490\) | −9.53553 | + | 2.65962i | −0.430772 | + | 0.120150i | ||||
\(491\) | −10.1421 | −0.457708 | −0.228854 | − | 0.973461i | \(-0.573498\pi\) | ||||
−0.228854 | + | 0.973461i | \(0.573498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.757359 | − | 1.31178i | −0.0341097 | − | 0.0590798i | ||||
\(494\) | −7.46447 | − | 12.9288i | −0.335842 | − | 0.581696i | ||||
\(495\) | 1.70711 | − | 2.95680i | 0.0767287 | − | 0.132898i | ||||
\(496\) | 0.686292 | 0.0308154 | ||||||||
\(497\) | −5.53553 | − | 7.13834i | −0.248303 | − | 0.320198i | ||||
\(498\) | −7.65685 | −0.343112 | ||||||||
\(499\) | −4.39949 | + | 7.62015i | −0.196948 | + | 0.341125i | −0.947538 | − | 0.319645i | \(-0.896436\pi\) |
0.750589 | + | 0.660769i | \(0.229770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.87868 | + | 10.1822i | 0.262640 | + | 0.454906i | ||||
\(502\) | 3.82843 | − | 6.63103i | 0.170871 | − | 0.295957i | ||||
\(503\) | −18.4853 | −0.824218 | −0.412109 | − | 0.911135i | \(-0.635208\pi\) | ||||
−0.412109 | + | 0.911135i | \(0.635208\pi\) | |||||||
\(504\) | 7.41421 | − | 1.01461i | 0.330255 | − | 0.0451944i | ||||
\(505\) | 6.24264 | 0.277794 | ||||||||
\(506\) | 15.0711 | − | 26.1039i | 0.669991 | − | 1.16046i | ||||
\(507\) | −5.24264 | − | 9.08052i | −0.232834 | − | 0.403280i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.89949 | + | 11.9503i | −0.305815 | + | 0.529687i | −0.977442 | − | 0.211202i | \(-0.932262\pi\) |
0.671628 | + | 0.740889i | \(0.265595\pi\) | |||||||
\(510\) | −8.82843 | −0.390929 | ||||||||
\(511\) | 2.07107 | − | 5.07306i | 0.0916186 | − | 0.224419i | ||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −3.32843 | + | 5.76500i | −0.146954 | + | 0.254531i | ||||
\(514\) | 21.1421 | + | 36.6193i | 0.932540 | + | 1.61521i | ||||
\(515\) | −0.621320 | − | 1.07616i | −0.0273786 | − | 0.0474212i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.7990 | 1.39852 | ||||||||
\(518\) | −7.89949 | + | 19.3497i | −0.347084 | + | 0.850178i | ||||
\(519\) | 2.82843 | 0.124154 | ||||||||
\(520\) | 2.24264 | − | 3.88437i | 0.0983463 | − | 0.170341i | ||||
\(521\) | 19.5563 | + | 33.8726i | 0.856779 | + | 1.48399i | 0.874985 | + | 0.484151i | \(0.160871\pi\) |
−0.0182053 | + | 0.999834i | \(0.505795\pi\) | |||||||
\(522\) | 0.171573 | + | 0.297173i | 0.00750954 | + | 0.0130069i | ||||
\(523\) | 3.79289 | − | 6.56948i | 0.165852 | − | 0.287263i | −0.771106 | − | 0.636707i | \(-0.780296\pi\) |
0.936957 | + | 0.349444i | \(0.113629\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.62132 | − | 0.358719i | 0.114404 | − | 0.0156558i | ||||
\(526\) | 1.65685 | 0.0722423 | ||||||||
\(527\) | −0.535534 | + | 0.927572i | −0.0233282 | + | 0.0404057i | ||||
\(528\) | −6.82843 | − | 11.8272i | −0.297169 | − | 0.514712i | ||||
\(529\) | −7.98528 | − | 13.8309i | −0.347186 | − | 0.601344i | ||||
\(530\) | 0.828427 | − | 1.43488i | 0.0359846 | − | 0.0623271i | ||||
\(531\) | 1.41421 | 0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.55635 | −0.154043 | ||||||||
\(534\) | −2.65685 | + | 4.60181i | −0.114973 | + | 0.199140i | ||||
\(535\) | 7.70711 | + | 13.3491i | 0.333207 | + | 0.577132i | ||||
\(536\) | 16.5858 | + | 28.7274i | 0.716397 | + | 1.24084i | ||||
\(537\) | 9.82843 | − | 17.0233i | 0.424128 | − | 0.734611i | ||||
\(538\) | 11.5147 | 0.496435 | ||||||||
\(539\) | 23.0208 | − | 6.42090i | 0.991577 | − | 0.276568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.1569 | + | 27.9845i | −0.694637 | + | 1.20315i | 0.275665 | + | 0.961254i | \(0.411102\pi\) |
−0.970303 | + | 0.241894i | \(0.922231\pi\) | |||||||
\(542\) | −14.2426 | − | 24.6690i | −0.611774 | − | 1.05962i | ||||
\(543\) | 0.328427 | + | 0.568852i | 0.0140942 | + | 0.0244118i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.4853 | 0.577646 | ||||||||
\(546\) | 3.63604 | + | 4.68885i | 0.155608 | + | 0.200664i | ||||
\(547\) | −31.7990 | −1.35963 | −0.679813 | − | 0.733385i | \(-0.737939\pi\) | ||||
−0.679813 | + | 0.733385i | \(0.737939\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.24264 | − | 10.8126i | −0.266429 | − | 0.461469i | ||||
\(550\) | −2.41421 | − | 4.18154i | −0.102942 | − | 0.178301i | ||||
\(551\) | −0.807612 | + | 1.39882i | −0.0344054 | + | 0.0595919i | ||||
\(552\) | −17.6569 | −0.751526 | ||||||||
\(553\) | 12.2071 | − | 1.67050i | 0.519099 | − | 0.0710371i | ||||
\(554\) | −33.0711 | −1.40506 | ||||||||
\(555\) | 2.79289 | − | 4.83743i | 0.118552 | − | 0.205338i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.17157 | + | 7.22538i | 0.176755 | + | 0.306149i | 0.940767 | − | 0.339053i | \(-0.110107\pi\) |
−0.764012 | + | 0.645202i | \(0.776773\pi\) | |||||||
\(558\) | 0.121320 | − | 0.210133i | 0.00513590 | − | 0.00889564i | ||||
\(559\) | 16.5147 | 0.698498 | ||||||||
\(560\) | 4.00000 | − | 9.79796i | 0.169031 | − | 0.414039i | ||||
\(561\) | 21.3137 | 0.899865 | ||||||||
\(562\) | −6.82843 | + | 11.8272i | −0.288040 | + | 0.498900i | ||||
\(563\) | 7.14214 | + | 12.3705i | 0.301005 | + | 0.521356i | 0.976364 | − | 0.216133i | \(-0.0693445\pi\) |
−0.675359 | + | 0.737489i | \(0.736011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.17157 | + | 3.76127i | −0.0913588 | + | 0.158238i | ||||
\(566\) | −18.7279 | −0.787193 | ||||||||
\(567\) | 1.00000 | − | 2.44949i | 0.0419961 | − | 0.102869i | ||||
\(568\) | 9.65685 | 0.405193 | ||||||||
\(569\) | 18.4350 | − | 31.9304i | 0.772837 | − | 1.33859i | −0.163166 | − | 0.986599i | \(-0.552171\pi\) |
0.936002 | − | 0.351994i | \(-0.114496\pi\) | |||||||
\(570\) | 4.70711 | + | 8.15295i | 0.197159 | + | 0.341489i | ||||
\(571\) | −13.9853 | − | 24.2232i | −0.585266 | − | 1.01371i | −0.994842 | − | 0.101434i | \(-0.967657\pi\) |
0.409576 | − | 0.912276i | \(-0.365677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.9706 | −0.792507 | ||||||||
\(574\) | −8.31371 | + | 1.13770i | −0.347007 | + | 0.0474869i | ||||
\(575\) | −6.24264 | −0.260336 | ||||||||
\(576\) | −4.00000 | + | 6.92820i | −0.166667 | + | 0.288675i | ||||
\(577\) | −3.27817 | − | 5.67796i | −0.136472 | − | 0.236377i | 0.789687 | − | 0.613510i | \(-0.210243\pi\) |
−0.926159 | + | 0.377134i | \(0.876910\pi\) | |||||||
\(578\) | −15.5355 | − | 26.9083i | −0.646193 | − | 1.11924i | ||||
\(579\) | −3.37868 | + | 5.85204i | −0.140413 | + | 0.243203i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.77817 | + | 11.3199i | 0.364180 | + | 0.469628i | ||||
\(582\) | 15.3137 | 0.634774 | ||||||||
\(583\) | −2.00000 | + | 3.46410i | −0.0828315 | + | 0.143468i | ||||
\(584\) | 2.92893 | + | 5.07306i | 0.121200 | + | 0.209925i | ||||
\(585\) | −0.792893 | − | 1.37333i | −0.0327821 | − | 0.0567803i | ||||
\(586\) | 10.8284 | − | 18.7554i | 0.447318 | − | 0.774778i | ||||
\(587\) | 30.2426 | 1.24825 | 0.624124 | − | 0.781326i | \(-0.285456\pi\) | ||||
0.624124 | + | 0.781326i | \(0.285456\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.14214 | 0.0470609 | ||||||||
\(590\) | 1.00000 | − | 1.73205i | 0.0411693 | − | 0.0713074i | ||||
\(591\) | 2.77817 | + | 4.81194i | 0.114279 | + | 0.197937i | ||||
\(592\) | −11.1716 | − | 19.3497i | −0.459149 | − | 0.795269i | ||||
\(593\) | −6.70711 | + | 11.6170i | −0.275428 | + | 0.477055i | −0.970243 | − | 0.242133i | \(-0.922153\pi\) |
0.694815 | + | 0.719188i | \(0.255486\pi\) | |||||||
\(594\) | −4.82843 | −0.198113 | ||||||||
\(595\) | 10.1213 | + | 13.0519i | 0.414934 | + | 0.535077i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.75736 | − | 4.77589i | 0.112851 | − | 0.195464i | ||||
\(598\) | −7.00000 | − | 12.1244i | −0.286251 | − | 0.495802i | ||||
\(599\) | 21.0711 | + | 36.4962i | 0.860940 | + | 1.49119i | 0.871022 | + | 0.491243i | \(0.163457\pi\) |
−0.0100818 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(600\) | −1.41421 | + | 2.44949i | −0.0577350 | + | 0.100000i | ||||
\(601\) | −24.1716 | −0.985979 | −0.492990 | − | 0.870035i | \(-0.664096\pi\) | ||||
−0.492990 | + | 0.870035i | \(0.664096\pi\) | |||||||
\(602\) | 38.6066 | − | 5.28319i | 1.57349 | − | 0.215327i | ||||
\(603\) | 11.7279 | 0.477598 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.328427 | + | 0.568852i | 0.0133525 | + | 0.0231271i | ||||
\(606\) | −4.41421 | − | 7.64564i | −0.179315 | − | 0.310583i | ||||
\(607\) | 0.621320 | − | 1.07616i | 0.0252186 | − | 0.0436799i | −0.853141 | − | 0.521681i | \(-0.825305\pi\) |
0.878359 | + | 0.478001i | \(0.158638\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.242641 | − | 0.594346i | 0.00983230 | − | 0.0240841i | ||||
\(610\) | −17.6569 | −0.714905 | ||||||||
\(611\) | 7.38478 | − | 12.7908i | 0.298756 | − | 0.517461i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.07107 | − | 8.78335i | −0.204818 | − | 0.354756i | 0.745256 | − | 0.666778i | \(-0.232327\pi\) |
−0.950075 | + | 0.312022i | \(0.898994\pi\) | |||||||
\(614\) | −1.12132 | + | 1.94218i | −0.0452528 | + | 0.0783802i | ||||
\(615\) | 2.24264 | 0.0904320 | ||||||||
\(616\) | −9.65685 | + | 23.6544i | −0.389086 | + | 0.953062i | ||||
\(617\) | −8.82843 | −0.355419 | −0.177710 | − | 0.984083i | \(-0.556869\pi\) | ||||
−0.177710 | + | 0.984083i | \(0.556869\pi\) | |||||||
\(618\) | −0.878680 | + | 1.52192i | −0.0353457 | + | 0.0612205i | ||||
\(619\) | −19.9853 | − | 34.6155i | −0.803276 | − | 1.39132i | −0.917449 | − | 0.397854i | \(-0.869755\pi\) |
0.114172 | − | 0.993461i | \(-0.463578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.12132 | + | 5.40629i | −0.125254 | + | 0.216947i | ||||
\(622\) | −24.1421 | −0.968011 | ||||||||
\(623\) | 9.84924 | − | 1.34784i | 0.394602 | − | 0.0540000i | ||||
\(624\) | −6.34315 | −0.253929 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −18.5355 | − | 32.1045i | −0.740829 | − | 1.28315i | ||||
\(627\) | −11.3640 | − | 19.6830i | −0.453833 | − | 0.786062i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.8701 | 1.39036 | ||||||||
\(630\) | −2.29289 | − | 2.95680i | −0.0913511 | − | 0.117802i | ||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −6.58579 | + | 11.4069i | −0.261969 | + | 0.453743i | ||||
\(633\) | 0.0710678 | + | 0.123093i | 0.00282469 | + | 0.00489251i | ||||
\(634\) | −0.0710678 | − | 0.123093i | −0.00282246 | − | 0.00488865i | ||||
\(635\) | −9.03553 | + | 15.6500i | −0.358564 | + | 0.621051i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.76346 | − | 10.7510i | 0.109492 | − | 0.425971i | ||||
\(638\) | −1.17157 | −0.0463830 | ||||||||
\(639\) | 1.70711 | − | 2.95680i | 0.0675321 | − | 0.116969i | ||||
\(640\) | 5.65685 | + | 9.79796i | 0.223607 | + | 0.387298i | ||||
\(641\) | 6.60660 | + | 11.4430i | 0.260945 | + | 0.451970i | 0.966493 | − | 0.256692i | \(-0.0826325\pi\) |
−0.705548 | + | 0.708662i | \(0.749299\pi\) | |||||||
\(642\) | 10.8995 | − | 18.8785i | 0.430169 | − | 0.745074i | ||||
\(643\) | 24.5563 | 0.968408 | 0.484204 | − | 0.874955i | \(-0.339109\pi\) | ||||
0.484204 | + | 0.874955i | \(0.339109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4142 | −0.410059 | ||||||||
\(646\) | −29.3848 | + | 50.8959i | −1.15613 | + | 2.00247i | ||||
\(647\) | −4.80761 | − | 8.32703i | −0.189007 | − | 0.327369i | 0.755913 | − | 0.654673i | \(-0.227193\pi\) |
−0.944919 | + | 0.327303i | \(0.893860\pi\) | |||||||
\(648\) | 1.41421 | + | 2.44949i | 0.0555556 | + | 0.0962250i | ||||
\(649\) | −2.41421 | + | 4.18154i | −0.0947662 | + | 0.164140i | ||||
\(650\) | −2.24264 | −0.0879636 | ||||||||
\(651\) | −0.449747 | + | 0.0615465i | −0.0176270 | + | 0.00241220i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.87868 | + | 6.71807i | −0.151784 | + | 0.262898i | −0.931884 | − | 0.362758i | \(-0.881835\pi\) |
0.780099 | + | 0.625656i | \(0.215169\pi\) | |||||||
\(654\) | −9.53553 | − | 16.5160i | −0.372869 | − | 0.645828i | ||||
\(655\) | −5.24264 | − | 9.08052i | −0.204847 | − | 0.354805i | ||||
\(656\) | 4.48528 | − | 7.76874i | 0.175121 | − | 0.303318i | ||||
\(657\) | 2.07107 | 0.0808001 | ||||||||
\(658\) | 13.1716 | − | 32.2636i | 0.513481 | − | 1.25777i | ||||
\(659\) | −27.3137 | −1.06399 | −0.531996 | − | 0.846747i | \(-0.678558\pi\) | ||||
−0.531996 | + | 0.846747i | \(0.678558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1569 | − | 27.9845i | −0.628429 | − | 1.08847i | −0.987867 | − | 0.155302i | \(-0.950365\pi\) |
0.359438 | − | 0.933169i | \(-0.382968\pi\) | |||||||
\(662\) | 19.5355 | + | 33.8365i | 0.759270 | + | 1.31509i | ||||
\(663\) | 4.94975 | − | 8.57321i | 0.192232 | − | 0.332956i | ||||
\(664\) | −15.3137 | −0.594287 | ||||||||
\(665\) | 6.65685 | − | 16.3059i | 0.258142 | − | 0.632316i | ||||
\(666\) | −7.89949 | −0.306099 | ||||||||
\(667\) | −0.757359 | + | 1.31178i | −0.0293251 | + | 0.0507925i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.58579 | + | 14.8710i | 0.331946 | + | 0.574947i | ||||
\(670\) | 8.29289 | − | 14.3637i | 0.320382 | − | 0.554919i | ||||
\(671\) | 42.6274 | 1.64561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.27208 | 0.0875822 | 0.0437911 | − | 0.999041i | \(-0.486056\pi\) | ||||
0.0437911 | + | 0.999041i | \(0.486056\pi\) | |||||||
\(674\) | 0.636039 | − | 1.10165i | 0.0244993 | − | 0.0424340i | ||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.94975 | + | 3.37706i | −0.0749349 | + | 0.129791i | −0.901058 | − | 0.433699i | \(-0.857208\pi\) |
0.826123 | + | 0.563490i | \(0.190542\pi\) | |||||||
\(678\) | 6.14214 | 0.235887 | ||||||||
\(679\) | −17.5563 | − | 22.6398i | −0.673751 | − | 0.868834i | ||||
\(680\) | −17.6569 | −0.677109 | ||||||||
\(681\) | 11.5355 | − | 19.9801i | 0.442043 | − | 0.765640i | ||||
\(682\) | 0.414214 | + | 0.717439i | 0.0158611 | + | 0.0274722i | ||||
\(683\) | −10.2929 | − | 17.8278i | −0.393847 | − | 0.682162i | 0.599107 | − | 0.800669i | \(-0.295523\pi\) |
−0.992953 | + | 0.118507i | \(0.962189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.92893 | 0.111909 | ||||||||
\(686\) | 3.02082 | − | 26.0168i | 0.115335 | − | 0.993327i | ||||
\(687\) | 14.3137 | 0.546102 | ||||||||
\(688\) | −20.8284 | + | 36.0759i | −0.794076 | + | 1.37538i | ||||
\(689\) | 0.928932 | + | 1.60896i | 0.0353895 | + | 0.0612964i | ||||
\(690\) | 4.41421 | + | 7.64564i | 0.168046 | + | 0.291065i | ||||
\(691\) | −15.1569 | + | 26.2524i | −0.576594 | + | 0.998690i | 0.419273 | + | 0.907860i | \(0.362285\pi\) |
−0.995866 | + | 0.0908295i | \(0.971048\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.53553 | + | 7.13834i | 0.210278 | + | 0.271163i | ||||
\(694\) | −35.3137 | −1.34049 | ||||||||
\(695\) | 5.74264 | − | 9.94655i | 0.217831 | − | 0.377294i | ||||
\(696\) | 0.343146 | + | 0.594346i | 0.0130069 | + | 0.0225286i | ||||
\(697\) | 7.00000 | + | 12.1244i | 0.265144 | + | 0.459243i | ||||
\(698\) | 11.7574 | − | 20.3643i | 0.445023 | − | 0.770802i | ||||
\(699\) | 22.4853 | 0.850471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.2132 | 1.55660 | 0.778301 | − | 0.627892i | \(-0.216082\pi\) | ||||
0.778301 | + | 0.627892i | \(0.216082\pi\) | |||||||
\(702\) | −1.12132 | + | 1.94218i | −0.0423215 | + | 0.0733030i | ||||
\(703\) | −18.5919 | − | 32.2021i | −0.701206 | − | 1.21452i | ||||
\(704\) | −13.6569 | − | 23.6544i | −0.514712 | − | 0.891507i | ||||
\(705\) | −4.65685 | + | 8.06591i | −0.175387 | + | 0.303780i | ||||
\(706\) | 8.34315 | 0.313998 | ||||||||
\(707\) | −6.24264 | + | 15.2913i | −0.234779 | + | 0.575088i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.55635 | − | 9.62388i | 0.208673 | − | 0.361432i | −0.742624 | − | 0.669709i | \(-0.766419\pi\) |
0.951297 | + | 0.308277i | \(0.0997522\pi\) | |||||||
\(710\) | −2.41421 | − | 4.18154i | −0.0906038 | − | 0.156930i | ||||
\(711\) | 2.32843 | + | 4.03295i | 0.0873228 | + | 0.151248i | ||||
\(712\) | −5.31371 | + | 9.20361i | −0.199140 | + | 0.344920i | ||||
\(713\) | 1.07107 | 0.0401118 | ||||||||
\(714\) | 8.82843 | − | 21.6251i | 0.330396 | − | 0.809301i | ||||
\(715\) | 5.41421 | 0.202480 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.65685 | + | 14.9941i | 0.323296 | + | 0.559965i | ||||
\(718\) | 18.7990 | + | 32.5608i | 0.701572 | + | 1.21516i | ||||
\(719\) | −8.75736 | + | 15.1682i | −0.326594 | + | 0.565678i | −0.981834 | − | 0.189743i | \(-0.939234\pi\) |
0.655239 | + | 0.755421i | \(0.272568\pi\) | |||||||
\(720\) | 4.00000 | 0.149071 | ||||||||
\(721\) | 3.25736 | − | 0.445759i | 0.121310 | − | 0.0166009i | ||||
\(722\) | 35.7990 | 1.33230 | ||||||||
\(723\) | −5.17157 | + | 8.95743i | −0.192333 | + | 0.333130i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.121320 | + | 0.210133i | 0.00450572 | + | 0.00780414i | ||||
\(726\) | 0.464466 | − | 0.804479i | 0.0172380 | − | 0.0298570i | ||||
\(727\) | 4.75736 | 0.176441 | 0.0882203 | − | 0.996101i | \(-0.471882\pi\) | ||||
0.0882203 | + | 0.996101i | \(0.471882\pi\) | |||||||
\(728\) | 7.27208 | + | 9.37769i | 0.269521 | + | 0.347560i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.46447 | − | 2.53653i | 0.0542023 | − | 0.0938812i | ||||
\(731\) | −32.5061 | − | 56.3022i | −1.20228 | − | 2.08241i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.37868 | − | 9.31615i | 0.198666 | − | 0.344100i | −0.749430 | − | 0.662083i | \(-0.769672\pi\) |
0.948096 | + | 0.317984i | \(0.103006\pi\) | |||||||
\(734\) | −27.6985 | −1.02237 | ||||||||
\(735\) | −1.74264 | + | 6.77962i | −0.0642783 | + | 0.250070i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.0208 | + | 34.6771i | −0.737476 | + | 1.27735i | ||||
\(738\) | −1.58579 | − | 2.74666i | −0.0583736 | − | 0.101106i | ||||
\(739\) | 17.5711 | + | 30.4340i | 0.646362 | + | 1.11953i | 0.983985 | + | 0.178251i | \(0.0570438\pi\) |
−0.337623 | + | 0.941281i | \(0.609623\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.5563 | −0.387797 | ||||||||
\(742\) | 2.68629 | + | 3.46410i | 0.0986169 | + | 0.127171i | ||||
\(743\) | −4.72792 | −0.173451 | −0.0867253 | − | 0.996232i | \(-0.527640\pi\) | ||||
−0.0867253 | + | 0.996232i | \(0.527640\pi\) | |||||||
\(744\) | 0.242641 | − | 0.420266i | 0.00889564 | − | 0.0154077i | ||||
\(745\) | 8.82843 | + | 15.2913i | 0.323449 | + | 0.560229i | ||||
\(746\) | −13.6066 | − | 23.5673i | −0.498173 | − | 0.862861i | ||||
\(747\) | −2.70711 | + | 4.68885i | −0.0990479 | + | 0.171556i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.4056 | + | 5.52938i | −1.47639 | + | 0.202039i | ||||
\(750\) | 1.41421 | 0.0516398 | ||||||||
\(751\) | −9.81371 | + | 16.9978i | −0.358107 | + | 0.620260i | −0.987645 | − | 0.156710i | \(-0.949911\pi\) |
0.629537 | + | 0.776970i | \(0.283244\pi\) | |||||||
\(752\) | 18.6274 | + | 32.2636i | 0.679272 | + | 1.17653i | ||||
\(753\) | −2.70711 | − | 4.68885i | −0.0986525 | − | 0.170871i | ||||
\(754\) | −0.272078 | + | 0.471253i | −0.00990849 | + | 0.0171620i | ||||
\(755\) | 6.48528 | 0.236024 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.5980 | 1.51190 | 0.755952 | − | 0.654627i | \(-0.227174\pi\) | ||||
0.755952 | + | 0.654627i | \(0.227174\pi\) | |||||||
\(758\) | −10.4645 | + | 18.1250i | −0.380087 | + | 0.658329i | ||||
\(759\) | −10.6569 | − | 18.4582i | −0.386819 | − | 0.669991i | ||||
\(760\) | 9.41421 | + | 16.3059i | 0.341489 | + | 0.591477i | ||||
\(761\) | 10.4645 | − | 18.1250i | 0.379337 | − | 0.657030i | −0.611629 | − | 0.791145i | \(-0.709486\pi\) |
0.990966 | + | 0.134114i | \(0.0428189\pi\) | |||||||
\(762\) | 25.5563 | 0.925809 | ||||||||
\(763\) | −13.4853 | + | 33.0321i | −0.488200 | + | 1.19584i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.12132 | + | 5.40629i | −0.112852 | + | 0.195465i | ||||
\(766\) | −8.82843 | − | 15.2913i | −0.318984 | − | 0.552497i | ||||
\(767\) | 1.12132 | + | 1.94218i | 0.0404885 | + | 0.0701282i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.9706 | −0.575913 | −0.287957 | − | 0.957643i | \(-0.592976\pi\) | ||||
−0.287957 | + | 0.957643i | \(0.592976\pi\) | |||||||
\(770\) | 12.6569 | − | 1.73205i | 0.456121 | − | 0.0624188i | ||||
\(771\) | 29.8995 | 1.07680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.4645 | − | 21.5891i | −0.448316 | − | 0.776506i | 0.549961 | − | 0.835190i | \(-0.314643\pi\) |
−0.998277 | + | 0.0586849i | \(0.981309\pi\) | |||||||
\(774\) | 7.36396 | + | 12.7548i | 0.264692 | + | 0.458460i | ||||
\(775\) | 0.0857864 | − | 0.148586i | 0.00308154 | − | 0.00533738i | ||||
\(776\) | 30.6274 | 1.09946 | ||||||||
\(777\) | 9.05635 | + | 11.6786i | 0.324895 | + | 0.418967i | ||||
\(778\) | 23.8579 | 0.855346 | ||||||||
\(779\) | 7.46447 | − | 12.9288i | 0.267442 | − | 0.463224i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.82843 | + | 10.0951i | 0.208558 | + | 0.361232i | ||||
\(782\) | −27.5563 | + | 47.7290i | −0.985413 | + | 1.70679i | ||||
\(783\) | 0.242641 | 0.00867127 | ||||||||
\(784\) | 20.0000 | + | 19.5959i | 0.714286 | + | 0.699854i | ||||
\(785\) | 16.1421 | 0.576138 | ||||||||
\(786\) | −7.41421 | + | 12.8418i | −0.264456 | + | 0.458052i | ||||
\(787\) | −6.58579 | − | 11.4069i | −0.234758 | − | 0.406613i | 0.724444 | − | 0.689333i | \(-0.242096\pi\) |
−0.959202 | + | 0.282721i | \(0.908763\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.585786 | − | 1.01461i | 0.0208545 | − | 0.0361211i | ||||
\(790\) | 6.58579 | 0.234312 | ||||||||
\(791\) | −7.04163 | − | 9.08052i | −0.250372 | − | 0.322866i | ||||
\(792\) | −9.65685 | −0.343141 | ||||||||
\(793\) | 9.89949 | − | 17.1464i | 0.351541 | − | 0.608888i | ||||
\(794\) | 17.1213 | + | 29.6550i | 0.607613 | + | 1.05242i | ||||
\(795\) | −0.585786 | − | 1.01461i | −0.0207757 | − | 0.0359846i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4437 | 0.369933 | 0.184967 | − | 0.982745i | \(-0.440782\pi\) | ||||
0.184967 | + | 0.982745i | \(0.440782\pi\) | |||||||
\(798\) | −24.6777 | + | 3.37706i | −0.873580 | + | 0.119547i | ||||
\(799\) | −58.1421 | −2.05692 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.87868 | + | 3.25397i | 0.0663799 | + | 0.114973i | ||||
\(802\) | −0.343146 | − | 0.594346i | −0.0121169 | − | 0.0209871i | ||||
\(803\) | −3.53553 | + | 6.12372i | −0.124766 | + | 0.216102i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.24264 | − | 15.2913i | 0.220024 | − | 0.538947i | ||||
\(806\) | 0.384776 | 0.0135532 | ||||||||
\(807\) | 4.07107 | − | 7.05130i | 0.143308 | − | 0.248217i | ||||
\(808\) | −8.82843 | − | 15.2913i | −0.310583 | − | 0.537946i | ||||
\(809\) | 2.31371 | + | 4.00746i | 0.0813457 | + | 0.140895i | 0.903828 | − | 0.427896i | \(-0.140745\pi\) |
−0.822483 | + | 0.568790i | \(0.807412\pi\) | |||||||
\(810\) | 0.707107 | − | 1.22474i | 0.0248452 | − | 0.0430331i | ||||
\(811\) | −22.9706 | −0.806606 | −0.403303 | − | 0.915067i | \(-0.632138\pi\) | ||||
−0.403303 | + | 0.915067i | \(0.632138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.1421 | −0.706416 | ||||||||
\(814\) | 13.4853 | − | 23.3572i | 0.472659 | − | 0.818669i | ||||
\(815\) | −9.65685 | − | 16.7262i | −0.338265 | − | 0.585892i | ||||
\(816\) | 12.4853 | + | 21.6251i | 0.437072 | + | 0.757031i | ||||
\(817\) | −34.6630 | + | 60.0380i | −1.21270 | + | 2.10046i | ||||
\(818\) | −37.2132 | −1.30113 | ||||||||
\(819\) | 4.15685 | − | 0.568852i | 0.145252 | − | 0.0198773i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.77817 | + | 11.7401i | −0.236560 | + | 0.409734i | −0.959725 | − | 0.280942i | \(-0.909353\pi\) |
0.723165 | + | 0.690675i | \(0.242687\pi\) | |||||||
\(822\) | −2.07107 | − | 3.58719i | −0.0722368 | − | 0.125118i | ||||
\(823\) | −11.1421 | − | 19.2987i | −0.388390 | − | 0.672712i | 0.603843 | − | 0.797103i | \(-0.293635\pi\) |
−0.992233 | + | 0.124391i | \(0.960302\pi\) | |||||||
\(824\) | −1.75736 | + | 3.04384i | −0.0612205 | + | 0.106037i | ||||
\(825\) | −3.41421 | −0.118868 | ||||||||
\(826\) | 3.24264 | + | 4.18154i | 0.112826 | + | 0.145494i | ||||
\(827\) | 12.8284 | 0.446088 | 0.223044 | − | 0.974808i | \(-0.428401\pi\) | ||||
0.223044 | + | 0.974808i | \(0.428401\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.32843 | + | 16.1573i | 0.323990 | + | 0.561167i | 0.981307 | − | 0.192447i | \(-0.0616424\pi\) |
−0.657318 | + | 0.753614i | \(0.728309\pi\) | |||||||
\(830\) | 3.82843 | + | 6.63103i | 0.132887 | + | 0.230166i | ||||
\(831\) | −11.6924 | + | 20.2518i | −0.405604 | + | 0.702528i | ||||
\(832\) | −12.6863 | −0.439818 | ||||||||
\(833\) | −42.0919 | + | 11.7401i | −1.45840 | + | 0.406772i | ||||
\(834\) | −16.2426 | −0.562437 | ||||||||
\(835\) | 5.87868 | − | 10.1822i | 0.203440 | − | 0.352369i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.0857864 | − | 0.148586i | −0.00296521 | − | 0.00513590i | ||||
\(838\) | 2.24264 | − | 3.88437i | 0.0774707 | − | 0.134183i | ||||
\(839\) | −7.27208 | −0.251060 | −0.125530 | − | 0.992090i | \(-0.540063\pi\) | ||||
−0.125530 | + | 0.992090i | \(0.540063\pi\) | |||||||
\(840\) | −4.58579 | − | 5.91359i | −0.158225 | − | 0.204038i | ||||
\(841\) | −28.9411 | −0.997970 | ||||||||
\(842\) | −19.4350 | + | 33.6625i | −0.669775 | + | 1.16008i | ||||
\(843\) | 4.82843 | + | 8.36308i | 0.166300 | + | 0.288040i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.24264 | + | 9.08052i | −0.180352 | + | 0.312379i | ||||
\(846\) | 13.1716 | 0.452848 | ||||||||
\(847\) | −1.72183 | + | 0.235626i | −0.0591626 | + | 0.00809622i | ||||
\(848\) | −4.68629 | −0.160928 | ||||||||
\(849\) | −6.62132 | + | 11.4685i | −0.227243 | + | 0.393597i | ||||
\(850\) | 4.41421 | + | 7.64564i | 0.151406 | + | 0.262243i | ||||
\(851\) | −17.4350 | − | 30.1984i | −0.597665 | − | 1.03519i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0122 | 1.30151 | 0.650756 | − | 0.759287i | \(-0.274452\pi\) | ||||
0.650756 | + | 0.759287i | \(0.274452\pi\) | |||||||
\(854\) | 17.6569 | − | 43.2503i | 0.604205 | − | 1.47999i | ||||
\(855\) | 6.65685 | 0.227660 | ||||||||
\(856\) | 21.7990 | − | 37.7570i | 0.745074 | − | 1.29051i | ||||
\(857\) | 3.12132 | + | 5.40629i | 0.106622 | + | 0.184675i | 0.914400 | − | 0.404812i | \(-0.132663\pi\) |
−0.807778 | + | 0.589487i | \(0.799330\pi\) | |||||||
\(858\) | −3.82843 | − | 6.63103i | −0.130700 | − | 0.226380i | ||||
\(859\) | −7.82843 | + | 13.5592i | −0.267102 | + | 0.462635i | −0.968112 | − | 0.250517i | \(-0.919400\pi\) |
0.701010 | + | 0.713152i | \(0.252733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.24264 | + | 5.49333i | −0.0764290 | + | 0.187212i | ||||
\(862\) | 52.0833 | 1.77396 | ||||||||
\(863\) | 4.89949 | − | 8.48617i | 0.166781 | − | 0.288873i | −0.770505 | − | 0.637433i | \(-0.779996\pi\) |
0.937286 | + | 0.348561i | \(0.113329\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.41421 | − | 2.44949i | −0.0480847 | − | 0.0832851i | ||||
\(866\) | 17.3640 | − | 30.0753i | 0.590051 | − | 1.02200i | ||||
\(867\) | −21.9706 | −0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.8995 | −0.539353 | ||||||||
\(870\) | 0.171573 | − | 0.297173i | 0.00581687 | − | 0.0100751i | ||||
\(871\) | 9.29899 | + | 16.1063i | 0.315084 | + | 0.545742i | ||||
\(872\) | −19.0711 | − | 33.0321i | −0.645828 | − | 1.11861i | ||||
\(873\) | 5.41421 | − | 9.37769i | 0.183243 | − | 0.317387i | ||||
\(874\) | 58.7696 | 1.98791 | ||||||||
\(875\) | −1.62132 | − | 2.09077i | −0.0548106 | − | 0.0706809i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.00000 | − | 15.5885i | 0.303908 | − | 0.526385i | −0.673109 | − | 0.739543i | \(-0.735042\pi\) |
0.977018 | + | 0.213158i | \(0.0683750\pi\) | |||||||
\(878\) | −0.242641 | − | 0.420266i | −0.00818873 | − | 0.0141833i | ||||
\(879\) | −7.65685 | − | 13.2621i | −0.258259 | − | 0.447318i | ||||
\(880\) | −6.82843 | + | 11.8272i | −0.230186 | + | 0.398694i | ||||
\(881\) | −21.6569 | −0.729638 | −0.364819 | − | 0.931078i | \(-0.618869\pi\) | ||||
−0.364819 | + | 0.931078i | \(0.618869\pi\) | |||||||
\(882\) | 9.53553 | − | 2.65962i | 0.321078 | − | 0.0895542i | ||||
\(883\) | 8.07107 | 0.271613 | 0.135807 | − | 0.990735i | \(-0.456637\pi\) | ||||
0.135807 | + | 0.990735i | \(0.456637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.707107 | − | 1.22474i | −0.0237691 | − | 0.0411693i | ||||
\(886\) | −0.343146 | − | 0.594346i | −0.0115282 | − | 0.0199674i | ||||
\(887\) | −2.60660 | + | 4.51477i | −0.0875211 | + | 0.151591i | −0.906463 | − | 0.422286i | \(-0.861228\pi\) |
0.818942 | + | 0.573877i | \(0.194561\pi\) | |||||||
\(888\) | −15.7990 | −0.530179 | ||||||||
\(889\) | −29.2990 | − | 37.7825i | −0.982657 | − | 1.26718i | ||||
\(890\) | 5.31371 | 0.178116 | ||||||||
\(891\) | −1.70711 | + | 2.95680i | −0.0571902 | + | 0.0990564i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.0000 | + | 53.6936i | 1.03738 | + | 1.79679i | ||||
\(894\) | 12.4853 | − | 21.6251i | 0.417570 | − | 0.723253i | ||||
\(895\) | −19.6569 | −0.657056 | ||||||||
\(896\) | −29.6569 | + | 4.05845i | −0.990766 | + | 0.135583i | ||||
\(897\) | −9.89949 | −0.330535 | ||||||||
\(898\) | 4.92893 | − | 8.53716i | 0.164481 | − | 0.284889i | ||||
\(899\) | −0.0208153 | − | 0.0360531i | −0.000694228 | − | 0.00120244i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.65685 | − | 6.33386i | 0.121827 | − | 0.211011i | ||||
\(902\) | 10.8284 | 0.360547 | ||||||||
\(903\) | 10.4142 | − | 25.5095i | 0.346563 | − | 0.848903i | ||||
\(904\) | 12.2843 | 0.408569 | ||||||||
\(905\) | 0.328427 | − | 0.568852i | 0.0109173 | − | 0.0189093i | ||||
\(906\) | −4.58579 | − | 7.94282i | −0.152353 | − | 0.263882i | ||||
\(907\) | 4.30761 | + | 7.46100i | 0.143032 | + | 0.247739i | 0.928637 | − | 0.370990i | \(-0.120982\pi\) |
−0.785605 | + | 0.618728i | \(0.787648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.24264 | −0.207055 | ||||||||
\(910\) | 2.24264 | − | 5.49333i | 0.0743428 | − | 0.182102i | ||||
\(911\) | 4.24264 | 0.140565 | 0.0702825 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | 13.3137 | − | 23.0600i | 0.440861 | − | 0.763594i | ||||
\(913\) | −9.24264 | − | 16.0087i | −0.305887 | − | 0.529811i | ||||
\(914\) | 14.7782 | + | 25.5965i | 0.488819 | + | 0.846659i | ||||
\(915\) | −6.24264 | + | 10.8126i | −0.206375 | + | 0.357453i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.4853 | − | 3.76127i | 0.907644 | − | 0.124208i | ||||
\(918\) | 8.82843 | 0.291382 | ||||||||
\(919\) | 23.3284 | − | 40.4060i | 0.769534 | − | 1.33287i | −0.168282 | − | 0.985739i | \(-0.553822\pi\) |
0.937816 | − | 0.347133i | \(-0.112845\pi\) | |||||||
\(920\) | 8.82843 | + | 15.2913i | 0.291065 | + | 0.504139i | ||||
\(921\) | 0.792893 | + | 1.37333i | 0.0261267 | + | 0.0452528i | ||||
\(922\) | 19.1421 | − | 33.1552i | 0.630413 | − | 1.09191i | ||||
\(923\) | 5.41421 | 0.178211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.58579 | −0.183660 | ||||||||
\(926\) | 7.36396 | − | 12.7548i | 0.241995 | − | 0.419147i | ||||
\(927\) | 0.621320 | + | 1.07616i | 0.0204068 | + | 0.0353457i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5061 | − | 44.1779i | 0.836828 | − | 1.44943i | −0.0557056 | − | 0.998447i | \(-0.517741\pi\) |
0.892533 | − | 0.450981i | \(-0.148926\pi\) | |||||||
\(930\) | −0.242641 | −0.00795650 | ||||||||
\(931\) | 33.2843 | + | 32.6118i | 1.09085 | + | 1.06881i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.53553 | + | 14.7840i | −0.279441 | + | 0.484006i | ||||
\(934\) | −4.72792 | − | 8.18900i | −0.154702 | − | 0.267952i | ||||
\(935\) | −10.6569 | − | 18.4582i | −0.348516 | − | 0.603648i | ||||
\(936\) | −2.24264 | + | 3.88437i | −0.0733030 | + | 0.126965i | ||||
\(937\) | −7.92893 | −0.259027 | −0.129513 | − | 0.991578i | \(-0.541342\pi\) | ||||
−0.129513 | + | 0.991578i | \(0.541342\pi\) | |||||||
\(938\) | 26.8909 | + | 34.6771i | 0.878018 | + | 1.13225i | ||||
\(939\) | −26.2132 | −0.855436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.63604 | + | 9.76191i | 0.183730 | + | 0.318229i | 0.943148 | − | 0.332374i | \(-0.107850\pi\) |
−0.759418 | + | 0.650603i | \(0.774516\pi\) | |||||||
\(942\) | −11.4142 | − | 19.7700i | −0.371895 | − | 0.644141i | ||||
\(943\) | 7.00000 | − | 12.1244i | 0.227951 | − | 0.394823i | ||||
\(944\) | −5.65685 | −0.184115 | ||||||||
\(945\) | −2.62132 | + | 0.358719i | −0.0852716 | + | 0.0116691i | ||||
\(946\) | −50.2843 | −1.63488 | ||||||||
\(947\) | 2.46447 | − | 4.26858i | 0.0800844 | − | 0.138710i | −0.823202 | − | 0.567749i | \(-0.807814\pi\) |
0.903286 | + | 0.429039i | \(0.141148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.64214 | + | 2.84426i | 0.0533060 | + | 0.0923287i | ||||
\(950\) | 4.70711 | − | 8.15295i | 0.152719 | − | 0.264517i | ||||
\(951\) | −0.100505 | −0.00325910 | ||||||||
\(952\) | 17.6569 | − | 43.2503i | 0.572262 | − | 1.40175i | ||||
\(953\) | 48.4853 | 1.57059 | 0.785296 | − | 0.619120i | \(-0.212511\pi\) | ||||
0.785296 | + | 0.619120i | \(0.212511\pi\) | |||||||
\(954\) | −0.828427 | + | 1.43488i | −0.0268213 | + | 0.0464559i | ||||
\(955\) | 9.48528 | + | 16.4290i | 0.306936 | + | 0.531630i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.414214 | + | 0.717439i | −0.0133896 | + | 0.0231915i | ||||
\(958\) | −48.9706 | −1.58217 | ||||||||
\(959\) | −2.92893 | + | 7.17439i | −0.0945802 | + | 0.231673i | ||||
\(960\) | 8.00000 | 0.258199 | ||||||||
\(961\) | 15.4853 | − | 26.8213i | 0.499525 | − | 0.865203i | ||||
\(962\) | −6.26346 | − | 10.8486i | −0.201942 | − | 0.349774i | ||||
\(963\) | −7.70711 | − | 13.3491i | −0.248358 | − | 0.430169i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.75736 | 0.217527 | ||||||||
\(966\) | −23.1421 | + | 3.16693i | −0.744586 | + | 0.101894i | ||||
\(967\) | 23.3848 | 0.752004 | 0.376002 | − | 0.926619i | \(-0.377299\pi\) | ||||
0.376002 | + | 0.926619i | \(0.377299\pi\) | |||||||
\(968\) | 0.928932 | − | 1.60896i | 0.0298570 | − | 0.0517139i | ||||
\(969\) | 20.7782 | + | 35.9889i | 0.667491 | + | 1.15613i | ||||
\(970\) | −7.65685 | − | 13.2621i | −0.245847 | − | 0.425819i | ||||
\(971\) | −7.17157 | + | 12.4215i | −0.230147 | + | 0.398626i | −0.957851 | − | 0.287265i | \(-0.907254\pi\) |
0.727704 | + | 0.685891i | \(0.240587\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.6213 | + | 24.0131i | 0.596972 | + | 0.769824i | ||||
\(974\) | 1.27208 | 0.0407600 | ||||||||
\(975\) | −0.792893 | + | 1.37333i | −0.0253929 | + | 0.0439818i | ||||
\(976\) | 24.9706 | + | 43.2503i | 0.799288 | + | 1.38441i | ||||
\(977\) | −6.84924 | − | 11.8632i | −0.219127 | − | 0.379539i | 0.735415 | − | 0.677617i | \(-0.236987\pi\) |
−0.954541 | + | 0.298079i | \(0.903654\pi\) | |||||||
\(978\) | −13.6569 | + | 23.6544i | −0.436698 | + | 0.756383i | ||||
\(979\) | −12.8284 | −0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.4853 | −0.430552 | ||||||||
\(982\) | 7.17157 | − | 12.4215i | 0.228854 | − | 0.396387i | ||||
\(983\) | −26.5772 | − | 46.0330i | −0.847680 | − | 1.46822i | −0.883273 | − | 0.468858i | \(-0.844665\pi\) |
0.0355935 | − | 0.999366i | \(-0.488668\pi\) | |||||||
\(984\) | −3.17157 | − | 5.49333i | −0.101106 | − | 0.175121i | ||||
\(985\) | 2.77817 | − | 4.81194i | 0.0885200 | − | 0.153321i | ||||
\(986\) | 2.14214 | 0.0682195 | ||||||||
\(987\) | −15.1005 | − | 19.4728i | −0.480654 | − | 0.619827i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.5061 | + | 56.3022i | −1.03363 | + | 1.79031i | ||||
\(990\) | 2.41421 | + | 4.18154i | 0.0767287 | + | 0.132898i | ||||
\(991\) | 15.3284 | + | 26.5496i | 0.486924 | + | 0.843376i | 0.999887 | − | 0.0150341i | \(-0.00478570\pi\) |
−0.512963 | + | 0.858410i | \(0.671452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.6274 | 0.876730 | ||||||||
\(994\) | 12.6569 | − | 1.73205i | 0.401451 | − | 0.0549373i | ||||
\(995\) | −5.51472 | −0.174828 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.378680 | − | 0.655892i | −0.0119929 | − | 0.0207723i | 0.859967 | − | 0.510350i | \(-0.170484\pi\) |
−0.871960 | + | 0.489578i | \(0.837151\pi\) | |||||||
\(998\) | −6.22183 | − | 10.7765i | −0.196948 | − | 0.341125i | ||||
\(999\) | −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 | 105.2.i.c.16.1 | ✓ | 4 | |
3.2 | odd | 2 | 315.2.j.d.226.2 | 4 | |||
4.3 | odd | 2 | 1680.2.bg.p.961.1 | 4 | |||
5.2 | odd | 4 | 525.2.r.g.499.2 | 8 | |||
5.3 | odd | 4 | 525.2.r.g.499.3 | 8 | |||
5.4 | even | 2 | 525.2.i.g.226.2 | 4 | |||
7.2 | even | 3 | 735.2.a.i.1.2 | 2 | |||
7.3 | odd | 6 | 735.2.i.j.361.1 | 4 | |||
7.4 | even | 3 | inner | 105.2.i.c.46.1 | yes | 4 | |
7.5 | odd | 6 | 735.2.a.j.1.2 | 2 | |||
7.6 | odd | 2 | 735.2.i.j.226.1 | 4 | |||
21.2 | odd | 6 | 2205.2.a.u.1.1 | 2 | |||
21.5 | even | 6 | 2205.2.a.s.1.1 | 2 | |||
21.11 | odd | 6 | 315.2.j.d.46.2 | 4 | |||
28.11 | odd | 6 | 1680.2.bg.p.1201.1 | 4 | |||
35.4 | even | 6 | 525.2.i.g.151.2 | 4 | |||
35.9 | even | 6 | 3675.2.a.z.1.1 | 2 | |||
35.18 | odd | 12 | 525.2.r.g.424.2 | 8 | |||
35.19 | odd | 6 | 3675.2.a.x.1.1 | 2 | |||
35.32 | odd | 12 | 525.2.r.g.424.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.c.16.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
105.2.i.c.46.1 | yes | 4 | 7.4 | even | 3 | inner | |
315.2.j.d.46.2 | 4 | 21.11 | odd | 6 | |||
315.2.j.d.226.2 | 4 | 3.2 | odd | 2 | |||
525.2.i.g.151.2 | 4 | 35.4 | even | 6 | |||
525.2.i.g.226.2 | 4 | 5.4 | even | 2 | |||
525.2.r.g.424.2 | 8 | 35.18 | odd | 12 | |||
525.2.r.g.424.3 | 8 | 35.32 | odd | 12 | |||
525.2.r.g.499.2 | 8 | 5.2 | odd | 4 | |||
525.2.r.g.499.3 | 8 | 5.3 | odd | 4 | |||
735.2.a.i.1.2 | 2 | 7.2 | even | 3 | |||
735.2.a.j.1.2 | 2 | 7.5 | odd | 6 | |||
735.2.i.j.226.1 | 4 | 7.6 | odd | 2 | |||
735.2.i.j.361.1 | 4 | 7.3 | odd | 6 | |||
1680.2.bg.p.961.1 | 4 | 4.3 | odd | 2 | |||
1680.2.bg.p.1201.1 | 4 | 28.11 | odd | 6 | |||
2205.2.a.s.1.1 | 2 | 21.5 | even | 6 | |||
2205.2.a.u.1.1 | 2 | 21.2 | odd | 6 | |||
3675.2.a.x.1.1 | 2 | 35.19 | odd | 6 | |||
3675.2.a.z.1.1 | 2 | 35.9 | even | 6 |