Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(187,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.187");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cz (of order \(6\), 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: | \(4.02446026187\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 283.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.283 |
Dual form | 504.2.cz.a.187.2 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.258819 | + | 0.965926i | ||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | −1.73205 | − | 1.73205i | −0.707107 | − | 0.707107i | ||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −0.633975 | − | 2.36603i | −0.200480 | − | 0.748203i | ||||
\(11\) | −5.00000 | −1.50756 | −0.753778 | − | 0.657129i | \(-0.771771\pi\) | ||||
−0.753778 | + | 0.657129i | \(0.771771\pi\) | |||||||
\(12\) | 1.73205 | − | 3.00000i | 0.500000 | − | 0.866025i | ||||
\(13\) | 0.866025 | − | 1.50000i | 0.240192 | − | 0.416025i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) |
0.960769 | + | 0.277350i | \(0.0894562\pi\) | |||||||
\(14\) | −3.09808 | + | 2.09808i | −0.827996 | + | 0.560734i | ||||
\(15\) | 2.59808 | − | 1.50000i | 0.670820 | − | 0.387298i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 1.50000 | + | 0.866025i | 0.363803 | + | 0.210042i | 0.670748 | − | 0.741685i | \(-0.265973\pi\) |
−0.306944 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(18\) | 4.09808 | + | 1.09808i | 0.965926 | + | 0.258819i | ||||
\(19\) | −1.50000 | + | 0.866025i | −0.344124 | + | 0.198680i | −0.662094 | − | 0.749421i | \(-0.730332\pi\) |
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(20\) | 3.00000 | − | 1.73205i | 0.670820 | − | 0.387298i | ||||
\(21\) | −3.46410 | − | 3.00000i | −0.755929 | − | 0.654654i | ||||
\(22\) | −1.83013 | − | 6.83013i | −0.390184 | − | 1.45619i | ||||
\(23\) | − | 7.00000i | − | 1.45960i | −0.683660 | − | 0.729800i | \(-0.739613\pi\) | ||
0.683660 | − | 0.729800i | \(-0.260387\pi\) | |||||||
\(24\) | 4.73205 | + | 1.26795i | 0.965926 | + | 0.258819i | ||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 2.36603 | + | 0.633975i | 0.464016 | + | 0.124333i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −4.00000 | − | 3.46410i | −0.755929 | − | 0.654654i | ||||
\(29\) | 6.06218 | − | 3.50000i | 1.12572 | − | 0.649934i | 0.182864 | − | 0.983138i | \(-0.441463\pi\) |
0.942855 | + | 0.333205i | \(0.108130\pi\) | |||||||
\(30\) | 3.00000 | + | 3.00000i | 0.547723 | + | 0.547723i | ||||
\(31\) | 3.46410 | + | 6.00000i | 0.622171 | + | 1.07763i | 0.989081 | + | 0.147375i | \(0.0470825\pi\) |
−0.366910 | + | 0.930257i | \(0.619584\pi\) | |||||||
\(32\) | 5.46410 | + | 1.46410i | 0.965926 | + | 0.258819i | ||||
\(33\) | 7.50000 | − | 4.33013i | 1.30558 | − | 0.753778i | ||||
\(34\) | −0.633975 | + | 2.36603i | −0.108726 | + | 0.405770i | ||||
\(35\) | −1.50000 | − | 4.33013i | −0.253546 | − | 0.731925i | ||||
\(36\) | 6.00000i | 1.00000i | ||||||||
\(37\) | 0.866025 | − | 0.500000i | 0.142374 | − | 0.0821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | −1.73205 | − | 1.73205i | −0.280976 | − | 0.280976i | ||||
\(39\) | 3.00000i | 0.480384i | ||||||||
\(40\) | 3.46410 | + | 3.46410i | 0.547723 | + | 0.547723i | ||||
\(41\) | −10.5000 | − | 6.06218i | −1.63982 | − | 0.946753i | −0.980892 | − | 0.194551i | \(-0.937675\pi\) |
−0.658932 | − | 0.752202i | \(-0.728992\pi\) | |||||||
\(42\) | 2.83013 | − | 5.83013i | 0.436698 | − | 0.899608i | ||||
\(43\) | −4.50000 | − | 7.79423i | −0.686244 | − | 1.18861i | −0.973044 | − | 0.230618i | \(-0.925925\pi\) |
0.286801 | − | 0.957990i | \(-0.407408\pi\) | |||||||
\(44\) | 8.66025 | − | 5.00000i | 1.30558 | − | 0.753778i | ||||
\(45\) | −2.59808 | + | 4.50000i | −0.387298 | + | 0.670820i | ||||
\(46\) | 9.56218 | − | 2.56218i | 1.40987 | − | 0.377773i | ||||
\(47\) | −1.73205 | + | 3.00000i | −0.252646 | + | 0.437595i | −0.964253 | − | 0.264982i | \(-0.914634\pi\) |
0.711608 | + | 0.702577i | \(0.247967\pi\) | |||||||
\(48\) | 6.92820i | 1.00000i | ||||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | −0.732051 | − | 2.73205i | −0.103528 | − | 0.386370i | ||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 3.46410i | 0.480384i | ||||||||
\(53\) | −9.52628 | − | 5.50000i | −1.30854 | − | 0.755483i | −0.326683 | − | 0.945134i | \(-0.605931\pi\) |
−0.981852 | + | 0.189651i | \(0.939264\pi\) | |||||||
\(54\) | −7.09808 | + | 1.90192i | −0.965926 | + | 0.258819i | ||||
\(55\) | 8.66025 | 1.16775 | ||||||||
\(56\) | 3.26795 | − | 6.73205i | 0.436698 | − | 0.899608i | ||||
\(57\) | 1.50000 | − | 2.59808i | 0.198680 | − | 0.344124i | ||||
\(58\) | 7.00000 | + | 7.00000i | 0.919145 | + | 0.919145i | ||||
\(59\) | −6.00000 | + | 3.46410i | −0.781133 | + | 0.450988i | −0.836832 | − | 0.547460i | \(-0.815595\pi\) |
0.0556984 | + | 0.998448i | \(0.482261\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | −1.73205 | + | 3.00000i | −0.221766 | + | 0.384111i | −0.955344 | − | 0.295495i | \(-0.904516\pi\) |
0.733578 | + | 0.679605i | \(0.237849\pi\) | |||||||
\(62\) | −6.92820 | + | 6.92820i | −0.879883 | + | 0.879883i | ||||
\(63\) | 7.79423 | + | 1.50000i | 0.981981 | + | 0.188982i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −1.50000 | + | 2.59808i | −0.186052 | + | 0.322252i | ||||
\(66\) | 8.66025 | + | 8.66025i | 1.06600 | + | 1.06600i | ||||
\(67\) | 4.00000 | + | 6.92820i | 0.488678 | + | 0.846415i | 0.999915 | − | 0.0130248i | \(-0.00414604\pi\) |
−0.511237 | + | 0.859440i | \(0.670813\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 6.06218 | + | 10.5000i | 0.729800 | + | 1.26405i | ||||
\(70\) | 5.36603 | − | 3.63397i | 0.641363 | − | 0.434343i | ||||
\(71\) | 10.0000i | 1.18678i | 0.804914 | + | 0.593391i | \(0.202211\pi\) | ||||
−0.804914 | + | 0.593391i | \(0.797789\pi\) | |||||||
\(72\) | −8.19615 | + | 2.19615i | −0.965926 | + | 0.258819i | ||||
\(73\) | −7.50000 | − | 4.33013i | −0.877809 | − | 0.506803i | −0.00787336 | − | 0.999969i | \(-0.502506\pi\) |
−0.869935 | + | 0.493166i | \(0.835840\pi\) | |||||||
\(74\) | 1.00000 | + | 1.00000i | 0.116248 | + | 0.116248i | ||||
\(75\) | 3.00000 | − | 1.73205i | 0.346410 | − | 0.200000i | ||||
\(76\) | 1.73205 | − | 3.00000i | 0.198680 | − | 0.344124i | ||||
\(77\) | −4.33013 | − | 12.5000i | −0.493464 | − | 1.42451i | ||||
\(78\) | −4.09808 | + | 1.09808i | −0.464016 | + | 0.124333i | ||||
\(79\) | −5.19615 | − | 3.00000i | −0.584613 | − | 0.337526i | 0.178352 | − | 0.983967i | \(-0.442924\pi\) |
−0.762964 | + | 0.646440i | \(0.776257\pi\) | |||||||
\(80\) | −3.46410 | + | 6.00000i | −0.387298 | + | 0.670820i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 4.43782 | − | 16.5622i | 0.490075 | − | 1.82899i | ||||
\(83\) | −13.5000 | + | 7.79423i | −1.48182 | + | 0.855528i | −0.999787 | − | 0.0206268i | \(-0.993434\pi\) |
−0.482030 | + | 0.876155i | \(0.660100\pi\) | |||||||
\(84\) | 9.00000 | + | 1.73205i | 0.981981 | + | 0.188982i | ||||
\(85\) | −2.59808 | − | 1.50000i | −0.281801 | − | 0.162698i | ||||
\(86\) | 9.00000 | − | 9.00000i | 0.970495 | − | 0.970495i | ||||
\(87\) | −6.06218 | + | 10.5000i | −0.649934 | + | 1.12572i | ||||
\(88\) | 10.0000 | + | 10.0000i | 1.06600 | + | 1.06600i | ||||
\(89\) | 7.50000 | − | 4.33013i | 0.794998 | − | 0.458993i | −0.0467209 | − | 0.998908i | \(-0.514877\pi\) |
0.841719 | + | 0.539915i | \(0.181544\pi\) | |||||||
\(90\) | −7.09808 | − | 1.90192i | −0.748203 | − | 0.200480i | ||||
\(91\) | 4.50000 | + | 0.866025i | 0.471728 | + | 0.0907841i | ||||
\(92\) | 7.00000 | + | 12.1244i | 0.729800 | + | 1.26405i | ||||
\(93\) | −10.3923 | − | 6.00000i | −1.07763 | − | 0.622171i | ||||
\(94\) | −4.73205 | − | 1.26795i | −0.488074 | − | 0.130779i | ||||
\(95\) | 2.59808 | − | 1.50000i | 0.266557 | − | 0.153897i | ||||
\(96\) | −9.46410 | + | 2.53590i | −0.965926 | + | 0.258819i | ||||
\(97\) | −1.50000 | + | 0.866025i | −0.152302 | + | 0.0879316i | −0.574214 | − | 0.818705i | \(-0.694692\pi\) |
0.421912 | + | 0.906637i | \(0.361359\pi\) | |||||||
\(98\) | −7.92820 | − | 5.92820i | −0.800869 | − | 0.598839i | ||||
\(99\) | −7.50000 | + | 12.9904i | −0.753778 | + | 1.30558i | ||||
\(100\) | 3.46410 | − | 2.00000i | 0.346410 | − | 0.200000i | ||||
\(101\) | 1.73205 | 0.172345 | 0.0861727 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861727 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(102\) | −1.09808 | − | 4.09808i | −0.108726 | − | 0.405770i | ||||
\(103\) | −5.19615 | −0.511992 | −0.255996 | − | 0.966678i | \(-0.582403\pi\) | ||||
−0.255996 | + | 0.966678i | \(0.582403\pi\) | |||||||
\(104\) | −4.73205 | + | 1.26795i | −0.464016 | + | 0.124333i | ||||
\(105\) | 6.00000 | + | 5.19615i | 0.585540 | + | 0.507093i | ||||
\(106\) | 4.02628 | − | 15.0263i | 0.391067 | − | 1.45948i | ||||
\(107\) | −2.50000 | − | 4.33013i | −0.241684 | − | 0.418609i | 0.719510 | − | 0.694482i | \(-0.244366\pi\) |
−0.961194 | + | 0.275873i | \(0.911033\pi\) | |||||||
\(108\) | −5.19615 | − | 9.00000i | −0.500000 | − | 0.866025i | ||||
\(109\) | −4.33013 | − | 2.50000i | −0.414751 | − | 0.239457i | 0.278078 | − | 0.960558i | \(-0.410303\pi\) |
−0.692829 | + | 0.721102i | \(0.743636\pi\) | |||||||
\(110\) | 3.16987 | + | 11.8301i | 0.302236 | + | 1.12796i | ||||
\(111\) | −0.866025 | + | 1.50000i | −0.0821995 | + | 0.142374i | ||||
\(112\) | 10.3923 | + | 2.00000i | 0.981981 | + | 0.188982i | ||||
\(113\) | 0.500000 | − | 0.866025i | 0.0470360 | − | 0.0814688i | −0.841549 | − | 0.540181i | \(-0.818356\pi\) |
0.888585 | + | 0.458712i | \(0.151689\pi\) | |||||||
\(114\) | 4.09808 | + | 1.09808i | 0.383820 | + | 0.102844i | ||||
\(115\) | 12.1244i | 1.13060i | ||||||||
\(116\) | −7.00000 | + | 12.1244i | −0.649934 | + | 1.12572i | ||||
\(117\) | −2.59808 | − | 4.50000i | −0.240192 | − | 0.416025i | ||||
\(118\) | −6.92820 | − | 6.92820i | −0.637793 | − | 0.637793i | ||||
\(119\) | −0.866025 | + | 4.50000i | −0.0793884 | + | 0.412514i | ||||
\(120\) | −8.19615 | − | 2.19615i | −0.748203 | − | 0.200480i | ||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | −4.73205 | − | 1.26795i | −0.428420 | − | 0.114795i | ||||
\(123\) | 21.0000 | 1.89351 | ||||||||
\(124\) | −12.0000 | − | 6.92820i | −1.07763 | − | 0.622171i | ||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0.803848 | + | 11.1962i | 0.0716124 | + | 0.997433i | ||||
\(127\) | − | 18.0000i | − | 1.59724i | −0.601834 | − | 0.798621i | \(-0.705563\pi\) | ||
0.601834 | − | 0.798621i | \(-0.294437\pi\) | |||||||
\(128\) | −10.9282 | + | 2.92820i | −0.965926 | + | 0.258819i | ||||
\(129\) | 13.5000 | + | 7.79423i | 1.18861 | + | 0.686244i | ||||
\(130\) | −4.09808 | − | 1.09808i | −0.359425 | − | 0.0963077i | ||||
\(131\) | − | 8.66025i | − | 0.756650i | −0.925673 | − | 0.378325i | \(-0.876500\pi\) | ||
0.925673 | − | 0.378325i | \(-0.123500\pi\) | |||||||
\(132\) | −8.66025 | + | 15.0000i | −0.753778 | + | 1.30558i | ||||
\(133\) | −3.46410 | − | 3.00000i | −0.300376 | − | 0.260133i | ||||
\(134\) | −8.00000 | + | 8.00000i | −0.691095 | + | 0.691095i | ||||
\(135\) | − | 9.00000i | − | 0.774597i | ||||||
\(136\) | −1.26795 | − | 4.73205i | −0.108726 | − | 0.405770i | ||||
\(137\) | −13.0000 | −1.11066 | −0.555332 | − | 0.831628i | \(-0.687409\pi\) | ||||
−0.555332 | + | 0.831628i | \(0.687409\pi\) | |||||||
\(138\) | −12.1244 | + | 12.1244i | −1.03209 | + | 1.03209i | ||||
\(139\) | 13.5000 | + | 7.79423i | 1.14506 | + | 0.661098i | 0.947677 | − | 0.319230i | \(-0.103424\pi\) |
0.197378 | + | 0.980328i | \(0.436757\pi\) | |||||||
\(140\) | 6.92820 | + | 6.00000i | 0.585540 | + | 0.507093i | ||||
\(141\) | − | 6.00000i | − | 0.505291i | ||||||
\(142\) | −13.6603 | + | 3.66025i | −1.14634 | + | 0.307162i | ||||
\(143\) | −4.33013 | + | 7.50000i | −0.362103 | + | 0.627182i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.500000 | − | 0.866025i | ||||
\(145\) | −10.5000 | + | 6.06218i | −0.871978 | + | 0.503436i | ||||
\(146\) | 3.16987 | − | 11.8301i | 0.262341 | − | 0.979068i | ||||
\(147\) | 4.50000 | − | 11.2583i | 0.371154 | − | 0.928571i | ||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | 11.0000i | 0.901155i | 0.892737 | + | 0.450578i | \(0.148782\pi\) | ||||
−0.892737 | + | 0.450578i | \(0.851218\pi\) | |||||||
\(150\) | 3.46410 | + | 3.46410i | 0.282843 | + | 0.282843i | ||||
\(151\) | − | 5.00000i | − | 0.406894i | −0.979086 | − | 0.203447i | \(-0.934786\pi\) | ||
0.979086 | − | 0.203447i | \(-0.0652145\pi\) | |||||||
\(152\) | 4.73205 | + | 1.26795i | 0.383820 | + | 0.102844i | ||||
\(153\) | 4.50000 | − | 2.59808i | 0.363803 | − | 0.210042i | ||||
\(154\) | 15.4904 | − | 10.4904i | 1.24825 | − | 0.845339i | ||||
\(155\) | −6.00000 | − | 10.3923i | −0.481932 | − | 0.834730i | ||||
\(156\) | −3.00000 | − | 5.19615i | −0.240192 | − | 0.416025i | ||||
\(157\) | 10.3923 | + | 18.0000i | 0.829396 | + | 1.43656i | 0.898513 | + | 0.438948i | \(0.144649\pi\) |
−0.0691164 | + | 0.997609i | \(0.522018\pi\) | |||||||
\(158\) | 2.19615 | − | 8.19615i | 0.174717 | − | 0.652051i | ||||
\(159\) | 19.0526 | 1.51097 | ||||||||
\(160\) | −9.46410 | − | 2.53590i | −0.748203 | − | 0.200480i | ||||
\(161\) | 17.5000 | − | 6.06218i | 1.37919 | − | 0.477767i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.707107 | − | 0.707107i | ||||
\(163\) | 3.50000 | + | 6.06218i | 0.274141 | + | 0.474826i | 0.969918 | − | 0.243432i | \(-0.0782731\pi\) |
−0.695777 | + | 0.718258i | \(0.744940\pi\) | |||||||
\(164\) | 24.2487 | 1.89351 | ||||||||
\(165\) | −12.9904 | + | 7.50000i | −1.01130 | + | 0.583874i | ||||
\(166\) | −15.5885 | − | 15.5885i | −1.20990 | − | 1.20990i | ||||
\(167\) | −4.33013 | + | 7.50000i | −0.335075 | + | 0.580367i | −0.983499 | − | 0.180912i | \(-0.942095\pi\) |
0.648424 | + | 0.761279i | \(0.275428\pi\) | |||||||
\(168\) | 0.928203 | + | 12.9282i | 0.0716124 | + | 0.997433i | ||||
\(169\) | 5.00000 | + | 8.66025i | 0.384615 | + | 0.666173i | ||||
\(170\) | 1.09808 | − | 4.09808i | 0.0842186 | − | 0.314308i | ||||
\(171\) | 5.19615i | 0.397360i | ||||||||
\(172\) | 15.5885 | + | 9.00000i | 1.18861 | + | 0.686244i | ||||
\(173\) | 1.73205 | − | 3.00000i | 0.131685 | − | 0.228086i | −0.792641 | − | 0.609689i | \(-0.791294\pi\) |
0.924326 | + | 0.381603i | \(0.124628\pi\) | |||||||
\(174\) | −16.5622 | − | 4.43782i | −1.25558 | − | 0.336430i | ||||
\(175\) | −1.73205 | − | 5.00000i | −0.130931 | − | 0.377964i | ||||
\(176\) | −10.0000 | + | 17.3205i | −0.753778 | + | 1.30558i | ||||
\(177\) | 6.00000 | − | 10.3923i | 0.450988 | − | 0.781133i | ||||
\(178\) | 8.66025 | + | 8.66025i | 0.649113 | + | 0.649113i | ||||
\(179\) | −5.50000 | + | 9.52628i | −0.411089 | + | 0.712028i | −0.995009 | − | 0.0997838i | \(-0.968185\pi\) |
0.583920 | + | 0.811811i | \(0.301518\pi\) | |||||||
\(180\) | − | 10.3923i | − | 0.774597i | ||||||
\(181\) | 3.46410 | 0.257485 | 0.128742 | − | 0.991678i | \(-0.458906\pi\) | ||||
0.128742 | + | 0.991678i | \(0.458906\pi\) | |||||||
\(182\) | 0.464102 | + | 6.46410i | 0.0344015 | + | 0.479151i | ||||
\(183\) | − | 6.00000i | − | 0.443533i | ||||||
\(184\) | −14.0000 | + | 14.0000i | −1.03209 | + | 1.03209i | ||||
\(185\) | −1.50000 | + | 0.866025i | −0.110282 | + | 0.0636715i | ||||
\(186\) | 4.39230 | − | 16.3923i | 0.322059 | − | 1.20194i | ||||
\(187\) | −7.50000 | − | 4.33013i | −0.548454 | − | 0.316650i | ||||
\(188\) | − | 6.92820i | − | 0.505291i | ||||||
\(189\) | −12.9904 | + | 4.50000i | −0.944911 | + | 0.327327i | ||||
\(190\) | 3.00000 | + | 3.00000i | 0.217643 | + | 0.217643i | ||||
\(191\) | −12.1244 | − | 7.00000i | −0.877288 | − | 0.506502i | −0.00752447 | − | 0.999972i | \(-0.502395\pi\) |
−0.869763 | + | 0.493469i | \(0.835728\pi\) | |||||||
\(192\) | −6.92820 | − | 12.0000i | −0.500000 | − | 0.866025i | ||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | −1.73205 | − | 1.73205i | −0.124354 | − | 0.124354i | ||||
\(195\) | − | 5.19615i | − | 0.372104i | ||||||
\(196\) | 5.19615 | − | 13.0000i | 0.371154 | − | 0.928571i | ||||
\(197\) | 8.00000i | 0.569976i | 0.958531 | + | 0.284988i | \(0.0919897\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908010\pi\) | |||||||
\(198\) | −20.4904 | − | 5.49038i | −1.45619 | − | 0.390184i | ||||
\(199\) | 4.33013 | − | 7.50000i | 0.306955 | − | 0.531661i | −0.670740 | − | 0.741693i | \(-0.734023\pi\) |
0.977695 | + | 0.210032i | \(0.0673567\pi\) | |||||||
\(200\) | 4.00000 | + | 4.00000i | 0.282843 | + | 0.282843i | ||||
\(201\) | −12.0000 | − | 6.92820i | −0.846415 | − | 0.488678i | ||||
\(202\) | 0.633975 | + | 2.36603i | 0.0446063 | + | 0.166473i | ||||
\(203\) | 14.0000 | + | 12.1244i | 0.982607 | + | 0.850963i | ||||
\(204\) | 5.19615 | − | 3.00000i | 0.363803 | − | 0.210042i | ||||
\(205\) | 18.1865 | + | 10.5000i | 1.27020 | + | 0.733352i | ||||
\(206\) | −1.90192 | − | 7.09808i | −0.132513 | − | 0.494546i | ||||
\(207\) | −18.1865 | − | 10.5000i | −1.26405 | − | 0.729800i | ||||
\(208\) | −3.46410 | − | 6.00000i | −0.240192 | − | 0.416025i | ||||
\(209\) | 7.50000 | − | 4.33013i | 0.518786 | − | 0.299521i | ||||
\(210\) | −4.90192 | + | 10.0981i | −0.338265 | + | 0.696833i | ||||
\(211\) | 4.50000 | − | 7.79423i | 0.309793 | − | 0.536577i | −0.668524 | − | 0.743690i | \(-0.733074\pi\) |
0.978317 | + | 0.207114i | \(0.0664070\pi\) | |||||||
\(212\) | 22.0000 | 1.51097 | ||||||||
\(213\) | −8.66025 | − | 15.0000i | −0.593391 | − | 1.02778i | ||||
\(214\) | 5.00000 | − | 5.00000i | 0.341793 | − | 0.341793i | ||||
\(215\) | 7.79423 | + | 13.5000i | 0.531562 | + | 0.920692i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | −12.0000 | + | 13.8564i | −0.814613 | + | 0.940634i | ||||
\(218\) | 1.83013 | − | 6.83013i | 0.123952 | − | 0.462595i | ||||
\(219\) | 15.0000 | 1.01361 | ||||||||
\(220\) | −15.0000 | + | 8.66025i | −1.01130 | + | 0.583874i | ||||
\(221\) | 2.59808 | − | 1.50000i | 0.174766 | − | 0.100901i | ||||
\(222\) | −2.36603 | − | 0.633975i | −0.158797 | − | 0.0425496i | ||||
\(223\) | −6.06218 | − | 10.5000i | −0.405953 | − | 0.703132i | 0.588478 | − | 0.808513i | \(-0.299727\pi\) |
−0.994432 | + | 0.105381i | \(0.966394\pi\) | |||||||
\(224\) | 1.07180 | + | 14.9282i | 0.0716124 | + | 0.997433i | ||||
\(225\) | −3.00000 | + | 5.19615i | −0.200000 | + | 0.346410i | ||||
\(226\) | 1.36603 | + | 0.366025i | 0.0908667 | + | 0.0243476i | ||||
\(227\) | − | 19.0526i | − | 1.26456i | −0.774739 | − | 0.632281i | \(-0.782119\pi\) | ||
0.774739 | − | 0.632281i | \(-0.217881\pi\) | |||||||
\(228\) | 6.00000i | 0.397360i | ||||||||
\(229\) | −12.1244 | −0.801200 | −0.400600 | − | 0.916253i | \(-0.631198\pi\) | ||||
−0.400600 | + | 0.916253i | \(0.631198\pi\) | |||||||
\(230\) | −16.5622 | + | 4.43782i | −1.09208 | + | 0.292621i | ||||
\(231\) | 17.3205 | + | 15.0000i | 1.13961 | + | 0.986928i | ||||
\(232\) | −19.1244 | − | 5.12436i | −1.25558 | − | 0.336430i | ||||
\(233\) | 5.50000 | + | 9.52628i | 0.360317 | + | 0.624087i | 0.988013 | − | 0.154371i | \(-0.0493352\pi\) |
−0.627696 | + | 0.778459i | \(0.716002\pi\) | |||||||
\(234\) | 5.19615 | − | 5.19615i | 0.339683 | − | 0.339683i | ||||
\(235\) | 3.00000 | − | 5.19615i | 0.195698 | − | 0.338960i | ||||
\(236\) | 6.92820 | − | 12.0000i | 0.450988 | − | 0.781133i | ||||
\(237\) | 10.3923 | 0.675053 | ||||||||
\(238\) | −6.46410 | + | 0.464102i | −0.419005 | + | 0.0300832i | ||||
\(239\) | 4.33013 | + | 2.50000i | 0.280093 | + | 0.161712i | 0.633465 | − | 0.773771i | \(-0.281632\pi\) |
−0.353373 | + | 0.935483i | \(0.614965\pi\) | |||||||
\(240\) | − | 12.0000i | − | 0.774597i | ||||||
\(241\) | − | 5.19615i | − | 0.334714i | −0.985896 | − | 0.167357i | \(-0.946477\pi\) | ||
0.985896 | − | 0.167357i | \(-0.0535232\pi\) | |||||||
\(242\) | 5.12436 | + | 19.1244i | 0.329406 | + | 1.22936i | ||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | 9.52628 | − | 7.50000i | 0.608612 | − | 0.479157i | ||||
\(246\) | 7.68653 | + | 28.6865i | 0.490075 | + | 1.82899i | ||||
\(247\) | 3.00000i | 0.190885i | ||||||||
\(248\) | 5.07180 | − | 18.9282i | 0.322059 | − | 1.20194i | ||||
\(249\) | 13.5000 | − | 23.3827i | 0.855528 | − | 1.48182i | ||||
\(250\) | 4.43782 | + | 16.5622i | 0.280673 | + | 1.04748i | ||||
\(251\) | − | 13.8564i | − | 0.874609i | −0.899314 | − | 0.437304i | \(-0.855933\pi\) | ||
0.899314 | − | 0.437304i | \(-0.144067\pi\) | |||||||
\(252\) | −15.0000 | + | 5.19615i | −0.944911 | + | 0.327327i | ||||
\(253\) | 35.0000i | 2.20043i | ||||||||
\(254\) | 24.5885 | − | 6.58846i | 1.54282 | − | 0.413397i | ||||
\(255\) | 5.19615 | 0.325396 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 22.5167i | 1.40455i | 0.711905 | + | 0.702275i | \(0.247832\pi\) | ||||
−0.711905 | + | 0.702275i | \(0.752168\pi\) | |||||||
\(258\) | −5.70577 | + | 21.2942i | −0.355226 | + | 1.32572i | ||||
\(259\) | 2.00000 | + | 1.73205i | 0.124274 | + | 0.107624i | ||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | − | 21.0000i | − | 1.29987i | ||||||
\(262\) | 11.8301 | − | 3.16987i | 0.730868 | − | 0.195835i | ||||
\(263\) | 13.0000i | 0.801614i | 0.916162 | + | 0.400807i | \(0.131270\pi\) | ||||
−0.916162 | + | 0.400807i | \(0.868730\pi\) | |||||||
\(264\) | −23.6603 | − | 6.33975i | −1.45619 | − | 0.390184i | ||||
\(265\) | 16.5000 | + | 9.52628i | 1.01359 | + | 0.585195i | ||||
\(266\) | 2.83013 | − | 5.83013i | 0.173526 | − | 0.357468i | ||||
\(267\) | −7.50000 | + | 12.9904i | −0.458993 | + | 0.794998i | ||||
\(268\) | −13.8564 | − | 8.00000i | −0.846415 | − | 0.488678i | ||||
\(269\) | −0.866025 | + | 1.50000i | −0.0528025 | + | 0.0914566i | −0.891219 | − | 0.453574i | \(-0.850149\pi\) |
0.838416 | + | 0.545031i | \(0.183482\pi\) | |||||||
\(270\) | 12.2942 | − | 3.29423i | 0.748203 | − | 0.200480i | ||||
\(271\) | 7.79423 | + | 13.5000i | 0.473466 | + | 0.820067i | 0.999539 | − | 0.0303728i | \(-0.00966946\pi\) |
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | 6.00000 | − | 3.46410i | 0.363803 | − | 0.210042i | ||||
\(273\) | −7.50000 | + | 2.59808i | −0.453921 | + | 0.157243i | ||||
\(274\) | −4.75833 | − | 17.7583i | −0.287461 | − | 1.07282i | ||||
\(275\) | 10.0000 | 0.603023 | ||||||||
\(276\) | −21.0000 | − | 12.1244i | −1.26405 | − | 0.729800i | ||||
\(277\) | − | 21.0000i | − | 1.26177i | −0.775877 | − | 0.630884i | \(-0.782692\pi\) | ||
0.775877 | − | 0.630884i | \(-0.217308\pi\) | |||||||
\(278\) | −5.70577 | + | 21.2942i | −0.342209 | + | 1.27714i | ||||
\(279\) | 20.7846 | 1.24434 | ||||||||
\(280\) | −5.66025 | + | 11.6603i | −0.338265 | + | 0.696833i | ||||
\(281\) | 5.50000 | + | 9.52628i | 0.328102 | + | 0.568290i | 0.982135 | − | 0.188176i | \(-0.0602575\pi\) |
−0.654033 | + | 0.756466i | \(0.726924\pi\) | |||||||
\(282\) | 8.19615 | − | 2.19615i | 0.488074 | − | 0.130779i | ||||
\(283\) | −12.0000 | + | 6.92820i | −0.713326 | + | 0.411839i | −0.812291 | − | 0.583252i | \(-0.801780\pi\) |
0.0989653 | + | 0.995091i | \(0.468447\pi\) | |||||||
\(284\) | −10.0000 | − | 17.3205i | −0.593391 | − | 1.02778i | ||||
\(285\) | −2.59808 | + | 4.50000i | −0.153897 | + | 0.266557i | ||||
\(286\) | −11.8301 | − | 3.16987i | −0.699530 | − | 0.187439i | ||||
\(287\) | 6.06218 | − | 31.5000i | 0.357839 | − | 1.85939i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.707107 | − | 0.707107i | ||||
\(289\) | −7.00000 | − | 12.1244i | −0.411765 | − | 0.713197i | ||||
\(290\) | −12.1244 | − | 12.1244i | −0.711967 | − | 0.711967i | ||||
\(291\) | 1.50000 | − | 2.59808i | 0.0879316 | − | 0.152302i | ||||
\(292\) | 17.3205 | 1.01361 | ||||||||
\(293\) | 0.866025 | − | 1.50000i | 0.0505937 | − | 0.0876309i | −0.839619 | − | 0.543175i | \(-0.817222\pi\) |
0.890213 | + | 0.455544i | \(0.150555\pi\) | |||||||
\(294\) | 17.0263 | + | 2.02628i | 0.992993 | + | 0.118175i | ||||
\(295\) | 10.3923 | − | 6.00000i | 0.605063 | − | 0.349334i | ||||
\(296\) | −2.73205 | − | 0.732051i | −0.158797 | − | 0.0425496i | ||||
\(297\) | − | 25.9808i | − | 1.50756i | ||||||
\(298\) | −15.0263 | + | 4.02628i | −0.870449 | + | 0.233236i | ||||
\(299\) | −10.5000 | − | 6.06218i | −0.607231 | − | 0.350585i | ||||
\(300\) | −3.46410 | + | 6.00000i | −0.200000 | + | 0.346410i | ||||
\(301\) | 15.5885 | − | 18.0000i | 0.898504 | − | 1.03750i | ||||
\(302\) | 6.83013 | − | 1.83013i | 0.393030 | − | 0.105312i | ||||
\(303\) | −2.59808 | + | 1.50000i | −0.149256 | + | 0.0861727i | ||||
\(304\) | 6.92820i | 0.397360i | ||||||||
\(305\) | 3.00000 | − | 5.19615i | 0.171780 | − | 0.297531i | ||||
\(306\) | 5.19615 | + | 5.19615i | 0.297044 | + | 0.297044i | ||||
\(307\) | − | 6.92820i | − | 0.395413i | −0.980261 | − | 0.197707i | \(-0.936651\pi\) | ||
0.980261 | − | 0.197707i | \(-0.0633494\pi\) | |||||||
\(308\) | 20.0000 | + | 17.3205i | 1.13961 | + | 0.986928i | ||||
\(309\) | 7.79423 | − | 4.50000i | 0.443398 | − | 0.255996i | ||||
\(310\) | 12.0000 | − | 12.0000i | 0.681554 | − | 0.681554i | ||||
\(311\) | 10.3923 | + | 18.0000i | 0.589294 | + | 1.02069i | 0.994325 | + | 0.106384i | \(0.0339272\pi\) |
−0.405032 | + | 0.914303i | \(0.632739\pi\) | |||||||
\(312\) | 6.00000 | − | 6.00000i | 0.339683 | − | 0.339683i | ||||
\(313\) | −9.00000 | − | 5.19615i | −0.508710 | − | 0.293704i | 0.223593 | − | 0.974683i | \(-0.428221\pi\) |
−0.732303 | + | 0.680979i | \(0.761555\pi\) | |||||||
\(314\) | −20.7846 | + | 20.7846i | −1.17294 | + | 1.17294i | ||||
\(315\) | −13.5000 | − | 2.59808i | −0.760639 | − | 0.146385i | ||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | 12.1244 | + | 7.00000i | 0.680972 | + | 0.393159i | 0.800221 | − | 0.599705i | \(-0.204715\pi\) |
−0.119249 | + | 0.992864i | \(0.538049\pi\) | |||||||
\(318\) | 6.97372 | + | 26.0263i | 0.391067 | + | 1.45948i | ||||
\(319\) | −30.3109 | + | 17.5000i | −1.69708 | + | 0.979812i | ||||
\(320\) | − | 13.8564i | − | 0.774597i | ||||||
\(321\) | 7.50000 | + | 4.33013i | 0.418609 | + | 0.241684i | ||||
\(322\) | 14.6865 | + | 21.6865i | 0.818449 | + | 1.20854i | ||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 15.5885 | + | 9.00000i | 0.866025 | + | 0.500000i | ||||
\(325\) | −1.73205 | + | 3.00000i | −0.0960769 | + | 0.166410i | ||||
\(326\) | −7.00000 | + | 7.00000i | −0.387694 | + | 0.387694i | ||||
\(327\) | 8.66025 | 0.478913 | ||||||||
\(328\) | 8.87564 | + | 33.1244i | 0.490075 | + | 1.82899i | ||||
\(329\) | −9.00000 | − | 1.73205i | −0.496186 | − | 0.0954911i | ||||
\(330\) | −15.0000 | − | 15.0000i | −0.825723 | − | 0.825723i | ||||
\(331\) | −3.00000 | + | 5.19615i | −0.164895 | + | 0.285606i | −0.936618 | − | 0.350352i | \(-0.886062\pi\) |
0.771723 | + | 0.635959i | \(0.219395\pi\) | |||||||
\(332\) | 15.5885 | − | 27.0000i | 0.855528 | − | 1.48182i | ||||
\(333\) | − | 3.00000i | − | 0.164399i | ||||||
\(334\) | −11.8301 | − | 3.16987i | −0.647316 | − | 0.173448i | ||||
\(335\) | −6.92820 | − | 12.0000i | −0.378528 | − | 0.655630i | ||||
\(336\) | −17.3205 | + | 6.00000i | −0.944911 | + | 0.327327i | ||||
\(337\) | 4.50000 | − | 7.79423i | 0.245131 | − | 0.424579i | −0.717038 | − | 0.697034i | \(-0.754502\pi\) |
0.962168 | + | 0.272456i | \(0.0878358\pi\) | |||||||
\(338\) | −10.0000 | + | 10.0000i | −0.543928 | + | 0.543928i | ||||
\(339\) | 1.73205i | 0.0940721i | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | −17.3205 | − | 30.0000i | −0.937958 | − | 1.62459i | ||||
\(342\) | −7.09808 | + | 1.90192i | −0.383820 | + | 0.102844i | ||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | −6.58846 | + | 24.5885i | −0.355226 | + | 1.32572i | ||||
\(345\) | −10.5000 | − | 18.1865i | −0.565301 | − | 0.979130i | ||||
\(346\) | 4.73205 | + | 1.26795i | 0.254397 | + | 0.0681654i | ||||
\(347\) | −8.00000 | − | 13.8564i | −0.429463 | − | 0.743851i | 0.567363 | − | 0.823468i | \(-0.307964\pi\) |
−0.996826 | + | 0.0796169i | \(0.974630\pi\) | |||||||
\(348\) | − | 24.2487i | − | 1.29987i | ||||||
\(349\) | −6.06218 | − | 10.5000i | −0.324501 | − | 0.562052i | 0.656910 | − | 0.753969i | \(-0.271863\pi\) |
−0.981411 | + | 0.191917i | \(0.938530\pi\) | |||||||
\(350\) | 6.19615 | − | 4.19615i | 0.331198 | − | 0.224294i | ||||
\(351\) | 7.79423 | + | 4.50000i | 0.416025 | + | 0.240192i | ||||
\(352\) | −27.3205 | − | 7.32051i | −1.45619 | − | 0.390184i | ||||
\(353\) | − | 5.19615i | − | 0.276563i | −0.990393 | − | 0.138282i | \(-0.955842\pi\) | ||
0.990393 | − | 0.138282i | \(-0.0441579\pi\) | |||||||
\(354\) | 16.3923 | + | 4.39230i | 0.871241 | + | 0.233448i | ||||
\(355\) | − | 17.3205i | − | 0.919277i | ||||||
\(356\) | −8.66025 | + | 15.0000i | −0.458993 | + | 0.794998i | ||||
\(357\) | −2.59808 | − | 7.50000i | −0.137505 | − | 0.396942i | ||||
\(358\) | −15.0263 | − | 4.02628i | −0.794164 | − | 0.212795i | ||||
\(359\) | 6.06218 | − | 3.50000i | 0.319950 | − | 0.184723i | −0.331421 | − | 0.943483i | \(-0.607528\pi\) |
0.651370 | + | 0.758760i | \(0.274195\pi\) | |||||||
\(360\) | 14.1962 | − | 3.80385i | 0.748203 | − | 0.200480i | ||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 1.26795 | + | 4.73205i | 0.0666419 | + | 0.248711i | ||||
\(363\) | −21.0000 | + | 12.1244i | −1.10221 | + | 0.636364i | ||||
\(364\) | −8.66025 | + | 3.00000i | −0.453921 | + | 0.157243i | ||||
\(365\) | 12.9904 | + | 7.50000i | 0.679948 | + | 0.392568i | ||||
\(366\) | 8.19615 | − | 2.19615i | 0.428420 | − | 0.114795i | ||||
\(367\) | −36.3731 | −1.89866 | −0.949329 | − | 0.314283i | \(-0.898236\pi\) | ||||
−0.949329 | + | 0.314283i | \(0.898236\pi\) | |||||||
\(368\) | −24.2487 | − | 14.0000i | −1.26405 | − | 0.729800i | ||||
\(369\) | −31.5000 | + | 18.1865i | −1.63982 | + | 0.946753i | ||||
\(370\) | −1.73205 | − | 1.73205i | −0.0900450 | − | 0.0900450i | ||||
\(371\) | 5.50000 | − | 28.5788i | 0.285546 | − | 1.48374i | ||||
\(372\) | 24.0000 | 1.24434 | ||||||||
\(373\) | − | 3.00000i | − | 0.155334i | −0.996979 | − | 0.0776671i | \(-0.975253\pi\) | ||
0.996979 | − | 0.0776671i | \(-0.0247471\pi\) | |||||||
\(374\) | 3.16987 | − | 11.8301i | 0.163910 | − | 0.611721i | ||||
\(375\) | −18.1865 | + | 10.5000i | −0.939149 | + | 0.542218i | ||||
\(376\) | 9.46410 | − | 2.53590i | 0.488074 | − | 0.130779i | ||||
\(377\) | − | 12.1244i | − | 0.624436i | ||||||
\(378\) | −10.9019 | − | 16.0981i | −0.560734 | − | 0.827996i | ||||
\(379\) | 18.0000 | 0.924598 | 0.462299 | − | 0.886724i | \(-0.347025\pi\) | ||||
0.462299 | + | 0.886724i | \(0.347025\pi\) | |||||||
\(380\) | −3.00000 | + | 5.19615i | −0.153897 | + | 0.266557i | ||||
\(381\) | 15.5885 | + | 27.0000i | 0.798621 | + | 1.38325i | ||||
\(382\) | 5.12436 | − | 19.1244i | 0.262185 | − | 0.978487i | ||||
\(383\) | −36.3731 | −1.85858 | −0.929288 | − | 0.369355i | \(-0.879579\pi\) | ||||
−0.929288 | + | 0.369355i | \(0.879579\pi\) | |||||||
\(384\) | 13.8564 | − | 13.8564i | 0.707107 | − | 0.707107i | ||||
\(385\) | 7.50000 | + | 21.6506i | 0.382235 | + | 1.10342i | ||||
\(386\) | −6.00000 | + | 6.00000i | −0.305392 | + | 0.305392i | ||||
\(387\) | −27.0000 | −1.37249 | ||||||||
\(388\) | 1.73205 | − | 3.00000i | 0.0879316 | − | 0.152302i | ||||
\(389\) | − | 1.00000i | − | 0.0507020i | −0.999679 | − | 0.0253510i | \(-0.991930\pi\) | ||
0.999679 | − | 0.0253510i | \(-0.00807034\pi\) | |||||||
\(390\) | 7.09808 | − | 1.90192i | 0.359425 | − | 0.0963077i | ||||
\(391\) | 6.06218 | − | 10.5000i | 0.306578 | − | 0.531008i | ||||
\(392\) | 19.6603 | + | 2.33975i | 0.992993 | + | 0.118175i | ||||
\(393\) | 7.50000 | + | 12.9904i | 0.378325 | + | 0.655278i | ||||
\(394\) | −10.9282 | + | 2.92820i | −0.550555 | + | 0.147521i | ||||
\(395\) | 9.00000 | + | 5.19615i | 0.452839 | + | 0.261447i | ||||
\(396\) | − | 30.0000i | − | 1.50756i | ||||||
\(397\) | 16.4545 | + | 28.5000i | 0.825827 | + | 1.43037i | 0.901286 | + | 0.433225i | \(0.142624\pi\) |
−0.0754589 | + | 0.997149i | \(0.524042\pi\) | |||||||
\(398\) | 11.8301 | + | 3.16987i | 0.592991 | + | 0.158891i | ||||
\(399\) | 7.79423 | + | 1.50000i | 0.390199 | + | 0.0750939i | ||||
\(400\) | −4.00000 | + | 6.92820i | −0.200000 | + | 0.346410i | ||||
\(401\) | 25.0000 | 1.24844 | 0.624220 | − | 0.781248i | \(-0.285417\pi\) | ||||
0.624220 | + | 0.781248i | \(0.285417\pi\) | |||||||
\(402\) | 5.07180 | − | 18.9282i | 0.252958 | − | 0.944053i | ||||
\(403\) | 12.0000 | 0.597763 | ||||||||
\(404\) | −3.00000 | + | 1.73205i | −0.149256 | + | 0.0861727i | ||||
\(405\) | 7.79423 | + | 13.5000i | 0.387298 | + | 0.670820i | ||||
\(406\) | −11.4378 | + | 23.5622i | −0.567650 | + | 1.16937i | ||||
\(407\) | −4.33013 | + | 2.50000i | −0.214636 | + | 0.123920i | ||||
\(408\) | 6.00000 | + | 6.00000i | 0.297044 | + | 0.297044i | ||||
\(409\) | −27.0000 | + | 15.5885i | −1.33506 | + | 0.770800i | −0.986071 | − | 0.166326i | \(-0.946810\pi\) |
−0.348993 | + | 0.937125i | \(0.613476\pi\) | |||||||
\(410\) | −7.68653 | + | 28.6865i | −0.379611 | + | 1.41673i | ||||
\(411\) | 19.5000 | − | 11.2583i | 0.961864 | − | 0.555332i | ||||
\(412\) | 9.00000 | − | 5.19615i | 0.443398 | − | 0.255996i | ||||
\(413\) | −13.8564 | − | 12.0000i | −0.681829 | − | 0.590481i | ||||
\(414\) | 7.68653 | − | 28.6865i | 0.377773 | − | 1.40987i | ||||
\(415\) | 23.3827 | − | 13.5000i | 1.14781 | − | 0.662689i | ||||
\(416\) | 6.92820 | − | 6.92820i | 0.339683 | − | 0.339683i | ||||
\(417\) | −27.0000 | −1.32220 | ||||||||
\(418\) | 8.66025 | + | 8.66025i | 0.423587 | + | 0.423587i | ||||
\(419\) | −1.50000 | − | 0.866025i | −0.0732798 | − | 0.0423081i | 0.462912 | − | 0.886404i | \(-0.346804\pi\) |
−0.536192 | + | 0.844096i | \(0.680138\pi\) | |||||||
\(420\) | −15.5885 | − | 3.00000i | −0.760639 | − | 0.146385i | ||||
\(421\) | −12.9904 | + | 7.50000i | −0.633112 | + | 0.365528i | −0.781956 | − | 0.623333i | \(-0.785778\pi\) |
0.148844 | + | 0.988861i | \(0.452445\pi\) | |||||||
\(422\) | 12.2942 | + | 3.29423i | 0.598474 | + | 0.160361i | ||||
\(423\) | 5.19615 | + | 9.00000i | 0.252646 | + | 0.437595i | ||||
\(424\) | 8.05256 | + | 30.0526i | 0.391067 | + | 1.45948i | ||||
\(425\) | −3.00000 | − | 1.73205i | −0.145521 | − | 0.0840168i | ||||
\(426\) | 17.3205 | − | 17.3205i | 0.839181 | − | 0.839181i | ||||
\(427\) | −9.00000 | − | 1.73205i | −0.435541 | − | 0.0838198i | ||||
\(428\) | 8.66025 | + | 5.00000i | 0.418609 | + | 0.241684i | ||||
\(429\) | − | 15.0000i | − | 0.724207i | ||||||
\(430\) | −15.5885 | + | 15.5885i | −0.751742 | + | 0.751742i | ||||
\(431\) | 4.33013 | + | 2.50000i | 0.208575 | + | 0.120421i | 0.600649 | − | 0.799513i | \(-0.294909\pi\) |
−0.392074 | + | 0.919934i | \(0.628242\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.866025 | + | 0.500000i | ||||
\(433\) | − | 31.1769i | − | 1.49827i | −0.662419 | − | 0.749133i | \(-0.730470\pi\) | ||
0.662419 | − | 0.749133i | \(-0.269530\pi\) | |||||||
\(434\) | −23.3205 | − | 11.3205i | −1.11942 | − | 0.543402i | ||||
\(435\) | 10.5000 | − | 18.1865i | 0.503436 | − | 0.871978i | ||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | 6.06218 | + | 10.5000i | 0.289993 | + | 0.502283i | ||||
\(438\) | 5.49038 | + | 20.4904i | 0.262341 | + | 0.979068i | ||||
\(439\) | −13.8564 | + | 24.0000i | −0.661330 | + | 1.14546i | 0.318936 | + | 0.947776i | \(0.396674\pi\) |
−0.980266 | + | 0.197681i | \(0.936659\pi\) | |||||||
\(440\) | −17.3205 | − | 17.3205i | −0.825723 | − | 0.825723i | ||||
\(441\) | 3.00000 | + | 20.7846i | 0.142857 | + | 0.989743i | ||||
\(442\) | 3.00000 | + | 3.00000i | 0.142695 | + | 0.142695i | ||||
\(443\) | −13.0000 | + | 22.5167i | −0.617649 | + | 1.06980i | 0.372265 | + | 0.928126i | \(0.378581\pi\) |
−0.989914 | + | 0.141672i | \(0.954752\pi\) | |||||||
\(444\) | − | 3.46410i | − | 0.164399i | ||||||
\(445\) | −12.9904 | + | 7.50000i | −0.615803 | + | 0.355534i | ||||
\(446\) | 12.1244 | − | 12.1244i | 0.574105 | − | 0.574105i | ||||
\(447\) | −9.52628 | − | 16.5000i | −0.450578 | − | 0.780423i | ||||
\(448\) | −20.0000 | + | 6.92820i | −0.944911 | + | 0.327327i | ||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | −8.19615 | − | 2.19615i | −0.386370 | − | 0.103528i | ||||
\(451\) | 52.5000 | + | 30.3109i | 2.47213 | + | 1.42728i | ||||
\(452\) | 2.00000i | 0.0940721i | ||||||||
\(453\) | 4.33013 | + | 7.50000i | 0.203447 | + | 0.352381i | ||||
\(454\) | 26.0263 | − | 6.97372i | 1.22147 | − | 0.327293i | ||||
\(455\) | −7.79423 | − | 1.50000i | −0.365399 | − | 0.0703211i | ||||
\(456\) | −8.19615 | + | 2.19615i | −0.383820 | + | 0.102844i | ||||
\(457\) | −12.0000 | + | 20.7846i | −0.561336 | + | 0.972263i | 0.436044 | + | 0.899925i | \(0.356379\pi\) |
−0.997380 | + | 0.0723376i | \(0.976954\pi\) | |||||||
\(458\) | −4.43782 | − | 16.5622i | −0.207366 | − | 0.773900i | ||||
\(459\) | −4.50000 | + | 7.79423i | −0.210042 | + | 0.363803i | ||||
\(460\) | −12.1244 | − | 21.0000i | −0.565301 | − | 0.979130i | ||||
\(461\) | 2.59808 | + | 4.50000i | 0.121004 | + | 0.209586i | 0.920164 | − | 0.391533i | \(-0.128055\pi\) |
−0.799160 | + | 0.601119i | \(0.794722\pi\) | |||||||
\(462\) | −14.1506 | + | 29.1506i | −0.658347 | + | 1.35621i | ||||
\(463\) | −7.79423 | − | 4.50000i | −0.362229 | − | 0.209133i | 0.307829 | − | 0.951442i | \(-0.400397\pi\) |
−0.670058 | + | 0.742309i | \(0.733731\pi\) | |||||||
\(464\) | − | 28.0000i | − | 1.29987i | ||||||
\(465\) | 18.0000 | + | 10.3923i | 0.834730 | + | 0.481932i | ||||
\(466\) | −11.0000 | + | 11.0000i | −0.509565 | + | 0.509565i | ||||
\(467\) | 7.50000 | − | 4.33013i | 0.347059 | − | 0.200374i | −0.316330 | − | 0.948649i | \(-0.602451\pi\) |
0.663389 | + | 0.748275i | \(0.269117\pi\) | |||||||
\(468\) | 9.00000 | + | 5.19615i | 0.416025 | + | 0.240192i | ||||
\(469\) | −13.8564 | + | 16.0000i | −0.639829 | + | 0.738811i | ||||
\(470\) | 8.19615 | + | 2.19615i | 0.378060 | + | 0.101301i | ||||
\(471\) | −31.1769 | − | 18.0000i | −1.43656 | − | 0.829396i | ||||
\(472\) | 18.9282 | + | 5.07180i | 0.871241 | + | 0.233448i | ||||
\(473\) | 22.5000 | + | 38.9711i | 1.03455 | + | 1.79190i | ||||
\(474\) | 3.80385 | + | 14.1962i | 0.174717 | + | 0.652051i | ||||
\(475\) | 3.00000 | − | 1.73205i | 0.137649 | − | 0.0794719i | ||||
\(476\) | −3.00000 | − | 8.66025i | −0.137505 | − | 0.396942i | ||||
\(477\) | −28.5788 | + | 16.5000i | −1.30854 | + | 0.755483i | ||||
\(478\) | −1.83013 | + | 6.83013i | −0.0837081 | + | 0.312403i | ||||
\(479\) | −1.73205 | −0.0791394 | −0.0395697 | − | 0.999217i | \(-0.512599\pi\) | ||||
−0.0395697 | + | 0.999217i | \(0.512599\pi\) | |||||||
\(480\) | 16.3923 | − | 4.39230i | 0.748203 | − | 0.200480i | ||||
\(481\) | − | 1.73205i | − | 0.0789747i | ||||||
\(482\) | 7.09808 | − | 1.90192i | 0.323309 | − | 0.0866303i | ||||
\(483\) | −21.0000 | + | 24.2487i | −0.955533 | + | 1.10335i | ||||
\(484\) | −24.2487 | + | 14.0000i | −1.10221 | + | 0.636364i | ||||
\(485\) | 2.59808 | − | 1.50000i | 0.117973 | − | 0.0681115i | ||||
\(486\) | −5.70577 | + | 21.2942i | −0.258819 | + | 0.965926i | ||||
\(487\) | −19.9186 | − | 11.5000i | −0.902597 | − | 0.521115i | −0.0245553 | − | 0.999698i | \(-0.507817\pi\) |
−0.878042 | + | 0.478584i | \(0.841150\pi\) | |||||||
\(488\) | 9.46410 | − | 2.53590i | 0.428420 | − | 0.114795i | ||||
\(489\) | −10.5000 | − | 6.06218i | −0.474826 | − | 0.274141i | ||||
\(490\) | 13.7321 | + | 10.2679i | 0.620351 | + | 0.463859i | ||||
\(491\) | −18.5000 | + | 32.0429i | −0.834893 | + | 1.44608i | 0.0592240 | + | 0.998245i | \(0.481137\pi\) |
−0.894117 | + | 0.447833i | \(0.852196\pi\) | |||||||
\(492\) | −36.3731 | + | 21.0000i | −1.63982 | + | 0.946753i | ||||
\(493\) | 12.1244 | 0.546054 | ||||||||
\(494\) | −4.09808 | + | 1.09808i | −0.184381 | + | 0.0494048i | ||||
\(495\) | 12.9904 | − | 22.5000i | 0.583874 | − | 1.01130i | ||||
\(496\) | 27.7128 | 1.24434 | ||||||||
\(497\) | −25.0000 | + | 8.66025i | −1.12140 | + | 0.388465i | ||||
\(498\) | 36.8827 | + | 9.88269i | 1.65275 | + | 0.442854i | ||||
\(499\) | −15.0000 | −0.671492 | −0.335746 | − | 0.941953i | \(-0.608988\pi\) | ||||
−0.335746 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(500\) | −21.0000 | + | 12.1244i | −0.939149 | + | 0.542218i | ||||
\(501\) | − | 15.0000i | − | 0.670151i | ||||||
\(502\) | 18.9282 | − | 5.07180i | 0.844807 | − | 0.226365i | ||||
\(503\) | −6.92820 | −0.308913 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(504\) | −12.5885 | − | 18.5885i | −0.560734 | − | 0.827996i | ||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | −47.8109 | + | 12.8109i | −2.12545 | + | 0.569513i | ||||
\(507\) | −15.0000 | − | 8.66025i | −0.666173 | − | 0.384615i | ||||
\(508\) | 18.0000 | + | 31.1769i | 0.798621 | + | 1.38325i | ||||
\(509\) | 32.9090 | 1.45866 | 0.729332 | − | 0.684160i | \(-0.239831\pi\) | ||||
0.729332 | + | 0.684160i | \(0.239831\pi\) | |||||||
\(510\) | 1.90192 | + | 7.09808i | 0.0842186 | + | 0.314308i | ||||
\(511\) | 4.33013 | − | 22.5000i | 0.191554 | − | 0.995341i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | −4.50000 | − | 7.79423i | −0.198680 | − | 0.344124i | ||||
\(514\) | −30.7583 | + | 8.24167i | −1.35669 | + | 0.363524i | ||||
\(515\) | 9.00000 | 0.396587 | ||||||||
\(516\) | −31.1769 | −1.37249 | ||||||||
\(517\) | 8.66025 | − | 15.0000i | 0.380878 | − | 0.659699i | ||||
\(518\) | −1.63397 | + | 3.36603i | −0.0717927 | + | 0.147895i | ||||
\(519\) | 6.00000i | 0.263371i | ||||||||
\(520\) | 8.19615 | − | 2.19615i | 0.359425 | − | 0.0963077i | ||||
\(521\) | −4.50000 | − | 2.59808i | −0.197149 | − | 0.113824i | 0.398176 | − | 0.917309i | \(-0.369643\pi\) |
−0.595325 | + | 0.803485i | \(0.702977\pi\) | |||||||
\(522\) | 28.6865 | − | 7.68653i | 1.25558 | − | 0.336430i | ||||
\(523\) | 10.5000 | − | 6.06218i | 0.459133 | − | 0.265081i | −0.252547 | − | 0.967585i | \(-0.581268\pi\) |
0.711680 | + | 0.702504i | \(0.247935\pi\) | |||||||
\(524\) | 8.66025 | + | 15.0000i | 0.378325 | + | 0.655278i | ||||
\(525\) | 6.92820 | + | 6.00000i | 0.302372 | + | 0.261861i | ||||
\(526\) | −17.7583 | + | 4.75833i | −0.774300 | + | 0.207473i | ||||
\(527\) | 12.0000i | 0.522728i | ||||||||
\(528\) | − | 34.6410i | − | 1.50756i | ||||||
\(529\) | −26.0000 | −1.13043 | ||||||||
\(530\) | −6.97372 | + | 26.0263i | −0.302919 | + | 1.13051i | ||||
\(531\) | 20.7846i | 0.901975i | ||||||||
\(532\) | 9.00000 | + | 1.73205i | 0.390199 | + | 0.0750939i | ||||
\(533\) | −18.1865 | + | 10.5000i | −0.787746 | + | 0.454805i | ||||
\(534\) | −20.4904 | − | 5.49038i | −0.886706 | − | 0.237592i | ||||
\(535\) | 4.33013 | + | 7.50000i | 0.187208 | + | 0.324253i | ||||
\(536\) | 5.85641 | − | 21.8564i | 0.252958 | − | 0.944053i | ||||
\(537\) | − | 19.0526i | − | 0.822179i | ||||||
\(538\) | −2.36603 | − | 0.633975i | −0.102007 | − | 0.0273326i | ||||
\(539\) | 27.5000 | − | 21.6506i | 1.18451 | − | 0.932559i | ||||
\(540\) | 9.00000 | + | 15.5885i | 0.387298 | + | 0.670820i | ||||
\(541\) | −2.59808 | + | 1.50000i | −0.111700 | + | 0.0644900i | −0.554809 | − | 0.831978i | \(-0.687209\pi\) |
0.443109 | + | 0.896468i | \(0.353875\pi\) | |||||||
\(542\) | −15.5885 | + | 15.5885i | −0.669582 | + | 0.669582i | ||||
\(543\) | −5.19615 | + | 3.00000i | −0.222988 | + | 0.128742i | ||||
\(544\) | 6.92820 | + | 6.92820i | 0.297044 | + | 0.297044i | ||||
\(545\) | 7.50000 | + | 4.33013i | 0.321265 | + | 0.185482i | ||||
\(546\) | −6.29423 | − | 9.29423i | −0.269368 | − | 0.397756i | ||||
\(547\) | −18.5000 | − | 32.0429i | −0.791003 | − | 1.37006i | −0.925347 | − | 0.379122i | \(-0.876226\pi\) |
0.134344 | − | 0.990935i | \(-0.457107\pi\) | |||||||
\(548\) | 22.5167 | − | 13.0000i | 0.961864 | − | 0.555332i | ||||
\(549\) | 5.19615 | + | 9.00000i | 0.221766 | + | 0.384111i | ||||
\(550\) | 3.66025 | + | 13.6603i | 0.156074 | + | 0.582475i | ||||
\(551\) | −6.06218 | + | 10.5000i | −0.258257 | + | 0.447315i | ||||
\(552\) | 8.87564 | − | 33.1244i | 0.377773 | − | 1.40987i | ||||
\(553\) | 3.00000 | − | 15.5885i | 0.127573 | − | 0.662889i | ||||
\(554\) | 28.6865 | − | 7.68653i | 1.21877 | − | 0.326570i | ||||
\(555\) | 1.50000 | − | 2.59808i | 0.0636715 | − | 0.110282i | ||||
\(556\) | −31.1769 | −1.32220 | ||||||||
\(557\) | 40.7032 | + | 23.5000i | 1.72465 | + | 0.995727i | 0.908498 | + | 0.417889i | \(0.137230\pi\) |
0.816152 | + | 0.577838i | \(0.196103\pi\) | |||||||
\(558\) | 7.60770 | + | 28.3923i | 0.322059 | + | 1.20194i | ||||
\(559\) | −15.5885 | −0.659321 | ||||||||
\(560\) | −18.0000 | − | 3.46410i | −0.760639 | − | 0.146385i | ||||
\(561\) | 15.0000 | 0.633300 | ||||||||
\(562\) | −11.0000 | + | 11.0000i | −0.464007 | + | 0.464007i | ||||
\(563\) | 3.00000 | − | 1.73205i | 0.126435 | − | 0.0729972i | −0.435449 | − | 0.900214i | \(-0.643410\pi\) |
0.561884 | + | 0.827216i | \(0.310077\pi\) | |||||||
\(564\) | 6.00000 | + | 10.3923i | 0.252646 | + | 0.437595i | ||||
\(565\) | −0.866025 | + | 1.50000i | −0.0364340 | + | 0.0631055i | ||||
\(566\) | −13.8564 | − | 13.8564i | −0.582428 | − | 0.582428i | ||||
\(567\) | 15.5885 | − | 18.0000i | 0.654654 | − | 0.755929i | ||||
\(568\) | 20.0000 | − | 20.0000i | 0.839181 | − | 0.839181i | ||||
\(569\) | −10.0000 | + | 17.3205i | −0.419222 | + | 0.726113i | −0.995861 | − | 0.0908852i | \(-0.971030\pi\) |
0.576640 | + | 0.816999i | \(0.304364\pi\) | |||||||
\(570\) | −7.09808 | − | 1.90192i | −0.297306 | − | 0.0796628i | ||||
\(571\) | −13.0000 | − | 22.5167i | −0.544033 | − | 0.942293i | −0.998667 | − | 0.0516146i | \(-0.983563\pi\) |
0.454634 | − | 0.890678i | \(-0.349770\pi\) | |||||||
\(572\) | − | 17.3205i | − | 0.724207i | ||||||
\(573\) | 24.2487 | 1.01300 | ||||||||
\(574\) | 45.2487 | − | 3.24871i | 1.88864 | − | 0.135599i | ||||
\(575\) | 14.0000i | 0.583840i | ||||||||
\(576\) | 20.7846 | + | 12.0000i | 0.866025 | + | 0.500000i | ||||
\(577\) | −28.5000 | − | 16.4545i | −1.18647 | − | 0.685009i | −0.228968 | − | 0.973434i | \(-0.573535\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 14.0000 | − | 14.0000i | 0.582323 | − | 0.582323i | ||||
\(579\) | −9.00000 | − | 5.19615i | −0.374027 | − | 0.215945i | ||||
\(580\) | 12.1244 | − | 21.0000i | 0.503436 | − | 0.871978i | ||||
\(581\) | −31.1769 | − | 27.0000i | −1.29344 | − | 1.12015i | ||||
\(582\) | 4.09808 | + | 1.09808i | 0.169871 | + | 0.0455167i | ||||
\(583\) | 47.6314 | + | 27.5000i | 1.97269 | + | 1.13893i | ||||
\(584\) | 6.33975 | + | 23.6603i | 0.262341 | + | 0.979068i | ||||
\(585\) | 4.50000 | + | 7.79423i | 0.186052 | + | 0.322252i | ||||
\(586\) | 2.36603 | + | 0.633975i | 0.0977396 | + | 0.0261892i | ||||
\(587\) | −7.50000 | + | 4.33013i | −0.309558 | + | 0.178723i | −0.646729 | − | 0.762720i | \(-0.723863\pi\) |
0.337171 | + | 0.941444i | \(0.390530\pi\) | |||||||
\(588\) | 3.46410 | + | 24.0000i | 0.142857 | + | 0.989743i | ||||
\(589\) | −10.3923 | − | 6.00000i | −0.428207 | − | 0.247226i | ||||
\(590\) | 12.0000 | + | 12.0000i | 0.494032 | + | 0.494032i | ||||
\(591\) | −6.92820 | − | 12.0000i | −0.284988 | − | 0.493614i | ||||
\(592\) | − | 4.00000i | − | 0.164399i | ||||||
\(593\) | −25.5000 | + | 14.7224i | −1.04716 | + | 0.604578i | −0.921853 | − | 0.387540i | \(-0.873325\pi\) |
−0.125307 | + | 0.992118i | \(0.539991\pi\) | |||||||
\(594\) | 35.4904 | − | 9.50962i | 1.45619 | − | 0.390184i | ||||
\(595\) | 1.50000 | − | 7.79423i | 0.0614940 | − | 0.319532i | ||||
\(596\) | −11.0000 | − | 19.0526i | −0.450578 | − | 0.780423i | ||||
\(597\) | 15.0000i | 0.613909i | ||||||||
\(598\) | 4.43782 | − | 16.5622i | 0.181476 | − | 0.677278i | ||||
\(599\) | 38.1051 | − | 22.0000i | 1.55693 | − | 0.898896i | 0.559385 | − | 0.828908i | \(-0.311037\pi\) |
0.997548 | − | 0.0699877i | \(-0.0222960\pi\) | |||||||
\(600\) | −9.46410 | − | 2.53590i | −0.386370 | − | 0.103528i | ||||
\(601\) | 7.50000 | − | 4.33013i | 0.305931 | − | 0.176630i | −0.339173 | − | 0.940724i | \(-0.610147\pi\) |
0.645104 | + | 0.764094i | \(0.276814\pi\) | |||||||
\(602\) | 30.2942 | + | 14.7058i | 1.23470 | + | 0.599362i | ||||
\(603\) | 24.0000 | 0.977356 | ||||||||
\(604\) | 5.00000 | + | 8.66025i | 0.203447 | + | 0.352381i | ||||
\(605\) | −24.2487 | −0.985850 | ||||||||
\(606\) | −3.00000 | − | 3.00000i | −0.121867 | − | 0.121867i | ||||
\(607\) | 36.3731 | 1.47634 | 0.738169 | − | 0.674616i | \(-0.235691\pi\) | ||||
0.738169 | + | 0.674616i | \(0.235691\pi\) | |||||||
\(608\) | −9.46410 | + | 2.53590i | −0.383820 | + | 0.102844i | ||||
\(609\) | −31.5000 | − | 6.06218i | −1.27644 | − | 0.245652i | ||||
\(610\) | 8.19615 | + | 2.19615i | 0.331853 | + | 0.0889196i | ||||
\(611\) | 3.00000 | + | 5.19615i | 0.121367 | + | 0.210214i | ||||
\(612\) | −5.19615 | + | 9.00000i | −0.210042 | + | 0.363803i | ||||
\(613\) | −18.1865 | − | 10.5000i | −0.734547 | − | 0.424091i | 0.0855362 | − | 0.996335i | \(-0.472740\pi\) |
−0.820083 | + | 0.572244i | \(0.806073\pi\) | |||||||
\(614\) | 9.46410 | − | 2.53590i | 0.381940 | − | 0.102341i | ||||
\(615\) | −36.3731 | −1.46670 | ||||||||
\(616\) | −16.3397 | + | 33.6603i | −0.658347 | + | 1.35621i | ||||
\(617\) | −11.5000 | + | 19.9186i | −0.462973 | + | 0.801892i | −0.999107 | − | 0.0422403i | \(-0.986550\pi\) |
0.536135 | + | 0.844132i | \(0.319884\pi\) | |||||||
\(618\) | 9.00000 | + | 9.00000i | 0.362033 | + | 0.362033i | ||||
\(619\) | − | 32.9090i | − | 1.32272i | −0.750067 | − | 0.661361i | \(-0.769979\pi\) | ||
0.750067 | − | 0.661361i | \(-0.230021\pi\) | |||||||
\(620\) | 20.7846 | + | 12.0000i | 0.834730 | + | 0.481932i | ||||
\(621\) | 36.3731 | 1.45960 | ||||||||
\(622\) | −20.7846 | + | 20.7846i | −0.833387 | + | 0.833387i | ||||
\(623\) | 17.3205 | + | 15.0000i | 0.693932 | + | 0.600962i | ||||
\(624\) | 10.3923 | + | 6.00000i | 0.416025 | + | 0.240192i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 3.80385 | − | 14.1962i | 0.152032 | − | 0.567392i | ||||
\(627\) | −7.50000 | + | 12.9904i | −0.299521 | + | 0.518786i | ||||
\(628\) | −36.0000 | − | 20.7846i | −1.43656 | − | 0.829396i | ||||
\(629\) | 1.73205 | 0.0690614 | ||||||||
\(630\) | −1.39230 | − | 19.3923i | −0.0554708 | − | 0.772608i | ||||
\(631\) | − | 42.0000i | − | 1.67199i | −0.548734 | − | 0.835997i | \(-0.684890\pi\) | ||
0.548734 | − | 0.835997i | \(-0.315110\pi\) | |||||||
\(632\) | 4.39230 | + | 16.3923i | 0.174717 | + | 0.652051i | ||||
\(633\) | 15.5885i | 0.619586i | ||||||||
\(634\) | −5.12436 | + | 19.1244i | −0.203514 | + | 0.759525i | ||||
\(635\) | 31.1769i | 1.23722i | ||||||||
\(636\) | −33.0000 | + | 19.0526i | −1.30854 | + | 0.755483i | ||||
\(637\) | 1.73205 | + | 12.0000i | 0.0686264 | + | 0.475457i | ||||
\(638\) | −35.0000 | − | 35.0000i | −1.38566 | − | 1.38566i | ||||
\(639\) | 25.9808 | + | 15.0000i | 1.02778 | + | 0.593391i | ||||
\(640\) | 18.9282 | − | 5.07180i | 0.748203 | − | 0.200480i | ||||
\(641\) | 11.0000 | 0.434474 | 0.217237 | − | 0.976119i | \(-0.430296\pi\) | ||||
0.217237 | + | 0.976119i | \(0.430296\pi\) | |||||||
\(642\) | −3.16987 | + | 11.8301i | −0.125105 | + | 0.466898i | ||||
\(643\) | −10.5000 | − | 6.06218i | −0.414080 | − | 0.239069i | 0.278462 | − | 0.960447i | \(-0.410176\pi\) |
−0.692541 | + | 0.721378i | \(0.743509\pi\) | |||||||
\(644\) | −24.2487 | + | 28.0000i | −0.955533 | + | 1.10335i | ||||
\(645\) | −23.3827 | − | 13.5000i | −0.920692 | − | 0.531562i | ||||
\(646\) | −1.09808 | − | 4.09808i | −0.0432032 | − | 0.161237i | ||||
\(647\) | −16.4545 | + | 28.5000i | −0.646892 | + | 1.12045i | 0.336968 | + | 0.941516i | \(0.390598\pi\) |
−0.983861 | + | 0.178935i | \(0.942735\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.258819 | + | 0.965926i | ||||
\(649\) | 30.0000 | − | 17.3205i | 1.17760 | − | 0.679889i | ||||
\(650\) | −4.73205 | − | 1.26795i | −0.185606 | − | 0.0497331i | ||||
\(651\) | 6.00000 | − | 31.1769i | 0.235159 | − | 1.22192i | ||||
\(652\) | −12.1244 | − | 7.00000i | −0.474826 | − | 0.274141i | ||||
\(653\) | 13.0000i | 0.508729i | 0.967108 | + | 0.254365i | \(0.0818663\pi\) | ||||
−0.967108 | + | 0.254365i | \(0.918134\pi\) | |||||||
\(654\) | 3.16987 | + | 11.8301i | 0.123952 | + | 0.462595i | ||||
\(655\) | 15.0000i | 0.586098i | ||||||||
\(656\) | −42.0000 | + | 24.2487i | −1.63982 | + | 0.946753i | ||||
\(657\) | −22.5000 | + | 12.9904i | −0.877809 | + | 0.506803i | ||||
\(658\) | −0.928203 | − | 12.9282i | −0.0361851 | − | 0.503994i | ||||
\(659\) | −2.50000 | − | 4.33013i | −0.0973862 | − | 0.168678i | 0.813216 | − | 0.581962i | \(-0.197715\pi\) |
−0.910602 | + | 0.413284i | \(0.864382\pi\) | |||||||
\(660\) | 15.0000 | − | 25.9808i | 0.583874 | − | 1.01130i | ||||
\(661\) | 1.73205 | + | 3.00000i | 0.0673690 | + | 0.116686i | 0.897742 | − | 0.440521i | \(-0.145206\pi\) |
−0.830373 | + | 0.557207i | \(0.811873\pi\) | |||||||
\(662\) | −8.19615 | − | 2.19615i | −0.318553 | − | 0.0853559i | ||||
\(663\) | −2.59808 | + | 4.50000i | −0.100901 | + | 0.174766i | ||||
\(664\) | 42.5885 | + | 11.4115i | 1.65275 | + | 0.442854i | ||||
\(665\) | 6.00000 | + | 5.19615i | 0.232670 | + | 0.201498i | ||||
\(666\) | 4.09808 | − | 1.09808i | 0.158797 | − | 0.0425496i | ||||
\(667\) | −24.5000 | − | 42.4352i | −0.948644 | − | 1.64310i | ||||
\(668\) | − | 17.3205i | − | 0.670151i | ||||||
\(669\) | 18.1865 | + | 10.5000i | 0.703132 | + | 0.405953i | ||||
\(670\) | 13.8564 | − | 13.8564i | 0.535320 | − | 0.535320i | ||||
\(671\) | 8.66025 | − | 15.0000i | 0.334325 | − | 0.579069i | ||||
\(672\) | −14.5359 | − | 21.4641i | −0.560734 | − | 0.827996i | ||||
\(673\) | 7.50000 | + | 12.9904i | 0.289104 | + | 0.500742i | 0.973596 | − | 0.228278i | \(-0.0733094\pi\) |
−0.684492 | + | 0.729020i | \(0.739976\pi\) | |||||||
\(674\) | 12.2942 | + | 3.29423i | 0.473556 | + | 0.126889i | ||||
\(675\) | − | 10.3923i | − | 0.400000i | ||||||
\(676\) | −17.3205 | − | 10.0000i | −0.666173 | − | 0.384615i | ||||
\(677\) | 10.3923 | − | 18.0000i | 0.399409 | − | 0.691796i | −0.594244 | − | 0.804285i | \(-0.702549\pi\) |
0.993653 | + | 0.112488i | \(0.0358821\pi\) | |||||||
\(678\) | −2.36603 | + | 0.633975i | −0.0908667 | + | 0.0243476i | ||||
\(679\) | −3.46410 | − | 3.00000i | −0.132940 | − | 0.115129i | ||||
\(680\) | 2.19615 | + | 8.19615i | 0.0842186 | + | 0.314308i | ||||
\(681\) | 16.5000 | + | 28.5788i | 0.632281 | + | 1.09514i | ||||
\(682\) | 34.6410 | − | 34.6410i | 1.32647 | − | 1.32647i | ||||
\(683\) | −0.500000 | + | 0.866025i | −0.0191320 | + | 0.0331375i | −0.875433 | − | 0.483340i | \(-0.839424\pi\) |
0.856301 | + | 0.516477i | \(0.172757\pi\) | |||||||
\(684\) | −5.19615 | − | 9.00000i | −0.198680 | − | 0.344124i | ||||
\(685\) | 22.5167 | 0.860317 | ||||||||
\(686\) | 7.95448 | − | 24.9545i | 0.303704 | − | 0.952767i | ||||
\(687\) | 18.1865 | − | 10.5000i | 0.693860 | − | 0.400600i | ||||
\(688\) | −36.0000 | −1.37249 | ||||||||
\(689\) | −16.5000 | + | 9.52628i | −0.628600 | + | 0.362922i | ||||
\(690\) | 21.0000 | − | 21.0000i | 0.799456 | − | 0.799456i | ||||
\(691\) | 33.0000 | + | 19.0526i | 1.25538 | + | 0.724793i | 0.972173 | − | 0.234265i | \(-0.0752685\pi\) |
0.283206 | + | 0.959059i | \(0.408602\pi\) | |||||||
\(692\) | 6.92820i | 0.263371i | ||||||||
\(693\) | −38.9711 | − | 7.50000i | −1.48039 | − | 0.284901i | ||||
\(694\) | 16.0000 | − | 16.0000i | 0.607352 | − | 0.607352i | ||||
\(695\) | −23.3827 | − | 13.5000i | −0.886956 | − | 0.512084i | ||||
\(696\) | 33.1244 | − | 8.87564i | 1.25558 | − | 0.336430i | ||||
\(697\) | −10.5000 | − | 18.1865i | −0.397716 | − | 0.688864i | ||||
\(698\) | 12.1244 | − | 12.1244i | 0.458914 | − | 0.458914i | ||||
\(699\) | −16.5000 | − | 9.52628i | −0.624087 | − | 0.360317i | ||||
\(700\) | 8.00000 | + | 6.92820i | 0.302372 | + | 0.261861i | ||||
\(701\) | 44.0000i | 1.66186i | 0.556379 | + | 0.830929i | \(0.312190\pi\) | ||||
−0.556379 | + | 0.830929i | \(0.687810\pi\) | |||||||
\(702\) | −3.29423 | + | 12.2942i | −0.124333 | + | 0.464016i | ||||
\(703\) | −0.866025 | + | 1.50000i | −0.0326628 | + | 0.0565736i | ||||
\(704\) | − | 40.0000i | − | 1.50756i | ||||||
\(705\) | 10.3923i | 0.391397i | ||||||||
\(706\) | 7.09808 | − | 1.90192i | 0.267140 | − | 0.0715798i | ||||
\(707\) | 1.50000 | + | 4.33013i | 0.0564133 | + | 0.162851i | ||||
\(708\) | 24.0000i | 0.901975i | ||||||||
\(709\) | 45.0333 | + | 26.0000i | 1.69126 | + | 0.976450i | 0.953502 | + | 0.301388i | \(0.0974498\pi\) |
0.737760 | + | 0.675063i | \(0.235884\pi\) | |||||||
\(710\) | 23.6603 | − | 6.33975i | 0.887954 | − | 0.237926i | ||||
\(711\) | −15.5885 | + | 9.00000i | −0.584613 | + | 0.337526i | ||||
\(712\) | −23.6603 | − | 6.33975i | −0.886706 | − | 0.237592i | ||||
\(713\) | 42.0000 | − | 24.2487i | 1.57291 | − | 0.908121i | ||||
\(714\) | 9.29423 | − | 6.29423i | 0.347828 | − | 0.235556i | ||||
\(715\) | 7.50000 | − | 12.9904i | 0.280484 | − | 0.485813i | ||||
\(716\) | − | 22.0000i | − | 0.822179i | ||||||
\(717\) | −8.66025 | −0.323423 | ||||||||
\(718\) | 7.00000 | + | 7.00000i | 0.261238 | + | 0.261238i | ||||
\(719\) | −23.3827 | − | 40.5000i | −0.872027 | − | 1.51040i | −0.859896 | − | 0.510469i | \(-0.829472\pi\) |
−0.0121307 | − | 0.999926i | \(-0.503861\pi\) | |||||||
\(720\) | 10.3923 | + | 18.0000i | 0.387298 | + | 0.670820i | ||||
\(721\) | −4.50000 | − | 12.9904i | −0.167589 | − | 0.483787i | ||||
\(722\) | −21.8564 | − | 5.85641i | −0.813411 | − | 0.217953i | ||||
\(723\) | 4.50000 | + | 7.79423i | 0.167357 | + | 0.289870i | ||||
\(724\) | −6.00000 | + | 3.46410i | −0.222988 | + | 0.128742i | ||||
\(725\) | −12.1244 | + | 7.00000i | −0.450287 | + | 0.259973i | ||||
\(726\) | −24.2487 | − | 24.2487i | −0.899954 | − | 0.899954i | ||||
\(727\) | −16.4545 | − | 28.5000i | −0.610263 | − | 1.05701i | −0.991196 | − | 0.132404i | \(-0.957730\pi\) |
0.380933 | − | 0.924603i | \(-0.375603\pi\) | |||||||
\(728\) | −7.26795 | − | 10.7321i | −0.269368 | − | 0.397756i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −5.49038 | + | 20.4904i | −0.203208 | + | 0.758383i | ||||
\(731\) | − | 15.5885i | − | 0.576560i | ||||||
\(732\) | 6.00000 | + | 10.3923i | 0.221766 | + | 0.384111i | ||||
\(733\) | 8.66025 | 0.319874 | 0.159937 | − | 0.987127i | \(-0.448871\pi\) | ||||
0.159937 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(734\) | −13.3135 | − | 49.6865i | −0.491409 | − | 1.83396i | ||||
\(735\) | −7.79423 | + | 19.5000i | −0.287494 | + | 0.719268i | ||||
\(736\) | 10.2487 | − | 38.2487i | 0.377773 | − | 1.40987i | ||||
\(737\) | −20.0000 | − | 34.6410i | −0.736709 | − | 1.27602i | ||||
\(738\) | −36.3731 | − | 36.3731i | −1.33891 | − | 1.33891i | ||||
\(739\) | 11.5000 | − | 19.9186i | 0.423034 | − | 0.732717i | −0.573200 | − | 0.819415i | \(-0.694298\pi\) |
0.996235 | + | 0.0866983i | \(0.0276316\pi\) | |||||||
\(740\) | 1.73205 | − | 3.00000i | 0.0636715 | − | 0.110282i | ||||
\(741\) | −2.59808 | − | 4.50000i | −0.0954427 | − | 0.165312i | ||||
\(742\) | 41.0526 | − | 2.94744i | 1.50709 | − | 0.108204i | ||||
\(743\) | −16.4545 | − | 9.50000i | −0.603656 | − | 0.348521i | 0.166822 | − | 0.985987i | \(-0.446649\pi\) |
−0.770479 | + | 0.637466i | \(0.779983\pi\) | |||||||
\(744\) | 8.78461 | + | 32.7846i | 0.322059 | + | 1.20194i | ||||
\(745\) | − | 19.0526i | − | 0.698032i | ||||||
\(746\) | 4.09808 | − | 1.09808i | 0.150041 | − | 0.0402034i | ||||
\(747\) | 46.7654i | 1.71106i | ||||||||
\(748\) | 17.3205 | 0.633300 | ||||||||
\(749\) | 8.66025 | − | 10.0000i | 0.316439 | − | 0.365392i | ||||
\(750\) | −21.0000 | − | 21.0000i | −0.766812 | − | 0.766812i | ||||
\(751\) | 47.0000i | 1.71505i | 0.514439 | + | 0.857527i | \(0.328000\pi\) | ||||
−0.514439 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(752\) | 6.92820 | + | 12.0000i | 0.252646 | + | 0.437595i | ||||
\(753\) | 12.0000 | + | 20.7846i | 0.437304 | + | 0.757433i | ||||
\(754\) | 16.5622 | − | 4.43782i | 0.603159 | − | 0.161616i | ||||
\(755\) | 8.66025i | 0.315179i | ||||||||
\(756\) | 18.0000 | − | 20.7846i | 0.654654 | − | 0.755929i | ||||
\(757\) | − | 26.0000i | − | 0.944986i | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||
0.881334 | − | 0.472493i | \(-0.156646\pi\) | |||||||
\(758\) | 6.58846 | + | 24.5885i | 0.239304 | + | 0.893093i | ||||
\(759\) | −30.3109 | − | 52.5000i | −1.10022 | − | 1.90563i | ||||
\(760\) | −8.19615 | − | 2.19615i | −0.297306 | − | 0.0796628i | ||||
\(761\) | − | 43.3013i | − | 1.56967i | −0.619705 | − | 0.784835i | \(-0.712748\pi\) | ||
0.619705 | − | 0.784835i | \(-0.287252\pi\) | |||||||
\(762\) | −31.1769 | + | 31.1769i | −1.12942 | + | 1.12942i | ||||
\(763\) | 2.50000 | − | 12.9904i | 0.0905061 | − | 0.470283i | ||||
\(764\) | 28.0000 | 1.01300 | ||||||||
\(765\) | −7.79423 | + | 4.50000i | −0.281801 | + | 0.162698i | ||||
\(766\) | −13.3135 | − | 49.6865i | −0.481035 | − | 1.79525i | ||||
\(767\) | 12.0000i | 0.433295i | ||||||||
\(768\) | 24.0000 | + | 13.8564i | 0.866025 | + | 0.500000i | ||||
\(769\) | 19.5000 | + | 11.2583i | 0.703188 | + | 0.405986i | 0.808534 | − | 0.588450i | \(-0.200262\pi\) |
−0.105346 | + | 0.994436i | \(0.533595\pi\) | |||||||
\(770\) | −26.8301 | + | 18.1699i | −0.966891 | + | 0.654797i | ||||
\(771\) | −19.5000 | − | 33.7750i | −0.702275 | − | 1.21638i | ||||
\(772\) | −10.3923 | − | 6.00000i | −0.374027 | − | 0.215945i | ||||
\(773\) | 25.1147 | − | 43.5000i | 0.903314 | − | 1.56459i | 0.0801501 | − | 0.996783i | \(-0.474460\pi\) |
0.823164 | − | 0.567803i | \(-0.192207\pi\) | |||||||
\(774\) | −9.88269 | − | 36.8827i | −0.355226 | − | 1.32572i | ||||
\(775\) | −6.92820 | − | 12.0000i | −0.248868 | − | 0.431053i | ||||
\(776\) | 4.73205 | + | 1.26795i | 0.169871 | + | 0.0455167i | ||||
\(777\) | −4.50000 | − | 0.866025i | −0.161437 | − | 0.0310685i | ||||
\(778\) | 1.36603 | − | 0.366025i | 0.0489744 | − | 0.0131226i | ||||
\(779\) | 21.0000 | 0.752403 | ||||||||
\(780\) | 5.19615 | + | 9.00000i | 0.186052 | + | 0.322252i | ||||
\(781\) | − | 50.0000i | − | 1.78914i | ||||||
\(782\) | 16.5622 | + | 4.43782i | 0.592262 | + | 0.158696i | ||||
\(783\) | 18.1865 | + | 31.5000i | 0.649934 | + | 1.12572i | ||||
\(784\) | 4.00000 | + | 27.7128i | 0.142857 | + | 0.989743i | ||||
\(785\) | −18.0000 | − | 31.1769i | −0.642448 | − | 1.11275i | ||||
\(786\) | −15.0000 | + | 15.0000i | −0.535032 | + | 0.535032i | ||||
\(787\) | −36.0000 | + | 20.7846i | −1.28326 | + | 0.740891i | −0.977443 | − | 0.211199i | \(-0.932263\pi\) |
−0.305818 | + | 0.952090i | \(0.598930\pi\) | |||||||
\(788\) | −8.00000 | − | 13.8564i | −0.284988 | − | 0.493614i | ||||
\(789\) | −11.2583 | − | 19.5000i | −0.400807 | − | 0.694218i | ||||
\(790\) | −3.80385 | + | 14.1962i | −0.135335 | + | 0.505076i | ||||
\(791\) | 2.59808 | + | 0.500000i | 0.0923770 | + | 0.0177780i | ||||
\(792\) | 40.9808 | − | 10.9808i | 1.45619 | − | 0.390184i | ||||
\(793\) | 3.00000 | + | 5.19615i | 0.106533 | + | 0.184521i | ||||
\(794\) | −32.9090 | + | 32.9090i | −1.16790 | + | 1.16790i | ||||
\(795\) | −33.0000 | −1.17039 | ||||||||
\(796\) | 17.3205i | 0.613909i | ||||||||
\(797\) | −12.9904 | + | 22.5000i | −0.460143 | + | 0.796991i | −0.998968 | − | 0.0454270i | \(-0.985535\pi\) |
0.538825 | + | 0.842418i | \(0.318868\pi\) | |||||||
\(798\) | 0.803848 | + | 11.1962i | 0.0284559 | + | 0.396339i | ||||
\(799\) | −5.19615 | + | 3.00000i | −0.183827 | + | 0.106132i | ||||
\(800\) | −10.9282 | − | 2.92820i | −0.386370 | − | 0.103528i | ||||
\(801\) | − | 25.9808i | − | 0.917985i | ||||||
\(802\) | 9.15064 | + | 34.1506i | 0.323120 | + | 1.20590i | ||||
\(803\) | 37.5000 | + | 21.6506i | 1.32335 | + | 0.764034i | ||||
\(804\) | 27.7128 | 0.977356 | ||||||||
\(805\) | −30.3109 | + | 10.5000i | −1.06832 | + | 0.370076i | ||||
\(806\) | 4.39230 | + | 16.3923i | 0.154712 | + | 0.577394i | ||||
\(807\) | − | 3.00000i | − | 0.105605i | ||||||
\(808\) | −3.46410 | − | 3.46410i | −0.121867 | − | 0.121867i | ||||
\(809\) | 2.50000 | − | 4.33013i | 0.0878953 | − | 0.152239i | −0.818726 | − | 0.574184i | \(-0.805319\pi\) |
0.906621 | + | 0.421945i | \(0.138653\pi\) | |||||||
\(810\) | −15.5885 | + | 15.5885i | −0.547723 | + | 0.547723i | ||||
\(811\) | 41.5692i | 1.45969i | 0.683611 | + | 0.729846i | \(0.260408\pi\) | ||||
−0.683611 | + | 0.729846i | \(0.739592\pi\) | |||||||
\(812\) | −36.3731 | − | 7.00000i | −1.27644 | − | 0.245652i | ||||
\(813\) | −23.3827 | − | 13.5000i | −0.820067 | − | 0.473466i | ||||
\(814\) | −5.00000 | − | 5.00000i | −0.175250 | − | 0.175250i | ||||
\(815\) | −6.06218 | − | 10.5000i | −0.212349 | − | 0.367799i | ||||
\(816\) | −6.00000 | + | 10.3923i | −0.210042 | + | 0.363803i | ||||
\(817\) | 13.5000 | + | 7.79423i | 0.472305 | + | 0.272686i | ||||
\(818\) | −31.1769 | − | 31.1769i | −1.09008 | − | 1.09008i | ||||
\(819\) | 9.00000 | − | 10.3923i | 0.314485 | − | 0.363137i | ||||
\(820\) | −42.0000 | −1.46670 | ||||||||
\(821\) | 1.73205 | + | 1.00000i | 0.0604490 | + | 0.0349002i | 0.529920 | − | 0.848048i | \(-0.322222\pi\) |
−0.469471 | + | 0.882948i | \(0.655555\pi\) | |||||||
\(822\) | 22.5167 | + | 22.5167i | 0.785359 | + | 0.785359i | ||||
\(823\) | 46.7654 | − | 27.0000i | 1.63014 | − | 0.941161i | 0.646090 | − | 0.763261i | \(-0.276403\pi\) |
0.984049 | − | 0.177899i | \(-0.0569301\pi\) | |||||||
\(824\) | 10.3923 | + | 10.3923i | 0.362033 | + | 0.362033i | ||||
\(825\) | −15.0000 | + | 8.66025i | −0.522233 | + | 0.301511i | ||||
\(826\) | 11.3205 | − | 23.3205i | 0.393891 | − | 0.811424i | ||||
\(827\) | −38.0000 | −1.32139 | −0.660695 | − | 0.750655i | \(-0.729738\pi\) | ||||
−0.660695 | + | 0.750655i | \(0.729738\pi\) | |||||||
\(828\) | 42.0000 | 1.45960 | ||||||||
\(829\) | 11.2583 | − | 19.5000i | 0.391018 | − | 0.677263i | −0.601566 | − | 0.798823i | \(-0.705456\pi\) |
0.992584 | + | 0.121560i | \(0.0387897\pi\) | |||||||
\(830\) | 27.0000 | + | 27.0000i | 0.937184 | + | 0.937184i | ||||
\(831\) | 18.1865 | + | 31.5000i | 0.630884 | + | 1.09272i | ||||
\(832\) | 12.0000 | + | 6.92820i | 0.416025 | + | 0.240192i | ||||
\(833\) | −12.0000 | + | 1.73205i | −0.415775 | + | 0.0600120i | ||||
\(834\) | −9.88269 | − | 36.8827i | −0.342209 | − | 1.27714i | ||||
\(835\) | 7.50000 | − | 12.9904i | 0.259548 | − | 0.449551i | ||||
\(836\) | −8.66025 | + | 15.0000i | −0.299521 | + | 0.518786i | ||||
\(837\) | −31.1769 | + | 18.0000i | −1.07763 | + | 0.622171i | ||||
\(838\) | 0.633975 | − | 2.36603i | 0.0219003 | − | 0.0817330i | ||||
\(839\) | −7.79423 | − | 13.5000i | −0.269087 | − | 0.466072i | 0.699540 | − | 0.714594i | \(-0.253388\pi\) |
−0.968626 | + | 0.248522i | \(0.920055\pi\) | |||||||
\(840\) | −1.60770 | − | 22.3923i | −0.0554708 | − | 0.772608i | ||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | −15.0000 | − | 15.0000i | −0.516934 | − | 0.516934i | ||||
\(843\) | −16.5000 | − | 9.52628i | −0.568290 | − | 0.328102i | ||||
\(844\) | 18.0000i | 0.619586i | ||||||||
\(845\) | −8.66025 | − | 15.0000i | −0.297922 | − | 0.516016i | ||||
\(846\) | −10.3923 | + | 10.3923i | −0.357295 | + | 0.357295i | ||||
\(847\) | 12.1244 | + | 35.0000i | 0.416598 | + | 1.20261i | ||||
\(848\) | −38.1051 | + | 22.0000i | −1.30854 | + | 0.755483i | ||||
\(849\) | 12.0000 | − | 20.7846i | 0.411839 | − | 0.713326i | ||||
\(850\) | 1.26795 | − | 4.73205i | 0.0434903 | − | 0.162308i | ||||
\(851\) | −3.50000 | − | 6.06218i | −0.119978 | − | 0.207809i | ||||
\(852\) | 30.0000 | + | 17.3205i | 1.02778 | + | 0.593391i | ||||
\(853\) | 9.52628 | + | 16.5000i | 0.326174 | + | 0.564949i | 0.981749 | − | 0.190180i | \(-0.0609073\pi\) |
−0.655576 | + | 0.755130i | \(0.727574\pi\) | |||||||
\(854\) | −0.928203 | − | 12.9282i | −0.0317625 | − | 0.442394i | ||||
\(855\) | − | 9.00000i | − | 0.307794i | ||||||
\(856\) | −3.66025 | + | 13.6603i | −0.125105 | + | 0.466898i | ||||
\(857\) | 15.5885i | 0.532492i | 0.963905 | + | 0.266246i | \(0.0857833\pi\) | ||||
−0.963905 | + | 0.266246i | \(0.914217\pi\) | |||||||
\(858\) | 20.4904 | − | 5.49038i | 0.699530 | − | 0.187439i | ||||
\(859\) | 29.4449i | 1.00465i | 0.864680 | + | 0.502323i | \(0.167521\pi\) | ||||
−0.864680 | + | 0.502323i | \(0.832479\pi\) | |||||||
\(860\) | −27.0000 | − | 15.5885i | −0.920692 | − | 0.531562i | ||||
\(861\) | 18.1865 | + | 52.5000i | 0.619795 | + | 1.78920i | ||||
\(862\) | −1.83013 | + | 6.83013i | −0.0623344 | + | 0.232635i | ||||
\(863\) | −19.9186 | + | 11.5000i | −0.678036 | + | 0.391465i | −0.799115 | − | 0.601178i | \(-0.794698\pi\) |
0.121078 | + | 0.992643i | \(0.461365\pi\) | |||||||
\(864\) | −7.60770 | + | 28.3923i | −0.258819 | + | 0.965926i | ||||
\(865\) | −3.00000 | + | 5.19615i | −0.102003 | + | 0.176674i | ||||
\(866\) | 42.5885 | − | 11.4115i | 1.44721 | − | 0.387780i | ||||
\(867\) | 21.0000 | + | 12.1244i | 0.713197 | + | 0.411765i | ||||
\(868\) | 6.92820 | − | 36.0000i | 0.235159 | − | 1.22192i | ||||
\(869\) | 25.9808 | + | 15.0000i | 0.881337 | + | 0.508840i | ||||
\(870\) | 28.6865 | + | 7.68653i | 0.972565 | + | 0.260598i | ||||
\(871\) | 13.8564 | 0.469506 | ||||||||
\(872\) | 3.66025 | + | 13.6603i | 0.123952 | + | 0.462595i | ||||
\(873\) | 5.19615i | 0.175863i | ||||||||
\(874\) | −12.1244 | + | 12.1244i | −0.410112 | + | 0.410112i | ||||
\(875\) | 10.5000 | + | 30.3109i | 0.354965 | + | 1.02470i | ||||
\(876\) | −25.9808 | + | 15.0000i | −0.877809 | + | 0.506803i | ||||
\(877\) | − | 45.0000i | − | 1.51954i | −0.650191 | − | 0.759771i | \(-0.725311\pi\) | ||
0.650191 | − | 0.759771i | \(-0.274689\pi\) | |||||||
\(878\) | −37.8564 | − | 10.1436i | −1.27759 | − | 0.342330i | ||||
\(879\) | 3.00000i | 0.101187i | ||||||||
\(880\) | 17.3205 | − | 30.0000i | 0.583874 | − | 1.01130i | ||||
\(881\) | 10.3923i | 0.350126i | 0.984557 | + | 0.175063i | \(0.0560129\pi\) | ||||
−0.984557 | + | 0.175063i | \(0.943987\pi\) | |||||||
\(882\) | −27.2942 | + | 11.7058i | −0.919044 | + | 0.394154i | ||||
\(883\) | −54.0000 | −1.81724 | −0.908622 | − | 0.417619i | \(-0.862865\pi\) | ||||
−0.908622 | + | 0.417619i | \(0.862865\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | −10.3923 | + | 18.0000i | −0.349334 | + | 0.605063i | ||||
\(886\) | −35.5167 | − | 9.51666i | −1.19321 | − | 0.319718i | ||||
\(887\) | 25.9808 | 0.872349 | 0.436174 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436174 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(888\) | 4.73205 | − | 1.26795i | 0.158797 | − | 0.0425496i | ||||
\(889\) | 45.0000 | − | 15.5885i | 1.50925 | − | 0.522820i | ||||
\(890\) | −15.0000 | − | 15.0000i | −0.502801 | − | 0.502801i | ||||
\(891\) | 22.5000 | + | 38.9711i | 0.753778 | + | 1.30558i | ||||
\(892\) | 21.0000 | + | 12.1244i | 0.703132 | + | 0.405953i | ||||
\(893\) | − | 6.00000i | − | 0.200782i | ||||||
\(894\) | 19.0526 | − | 19.0526i | 0.637213 | − | 0.637213i | ||||
\(895\) | 9.52628 | − | 16.5000i | 0.318428 | − | 0.551534i | ||||
\(896\) | −16.7846 | − | 24.7846i | −0.560734 | − | 0.827996i | ||||
\(897\) | 21.0000 | 0.701170 | ||||||||
\(898\) | 8.05256 | + | 30.0526i | 0.268717 | + | 1.00287i | ||||
\(899\) | 42.0000 | + | 24.2487i | 1.40078 | + | 0.808740i | ||||
\(900\) | − | 12.0000i | − | 0.400000i | ||||||
\(901\) | −9.52628 | − | 16.5000i | −0.317366 | − | 0.549695i | ||||
\(902\) | −22.1891 | + | 82.8109i | −0.738817 | + | 2.75730i | ||||
\(903\) | −7.79423 | + | 40.5000i | −0.259376 | + | 1.34776i | ||||
\(904\) | −2.73205 | + | 0.732051i | −0.0908667 | + | 0.0243476i | ||||
\(905\) | −6.00000 | −0.199447 | ||||||||
\(906\) | −8.66025 | + | 8.66025i | −0.287718 | + | 0.287718i | ||||
\(907\) | 39.0000 | 1.29497 | 0.647487 | − | 0.762077i | \(-0.275820\pi\) | ||||
0.647487 | + | 0.762077i | \(0.275820\pi\) | |||||||
\(908\) | 19.0526 | + | 33.0000i | 0.632281 | + | 1.09514i | ||||
\(909\) | 2.59808 | − | 4.50000i | 0.0861727 | − | 0.149256i | ||||
\(910\) | −0.803848 | − | 11.1962i | −0.0266473 | − | 0.371149i | ||||
\(911\) | 45.8993 | − | 26.5000i | 1.52071 | − | 0.877984i | 0.521012 | − | 0.853549i | \(-0.325555\pi\) |
0.999701 | − | 0.0244347i | \(-0.00777857\pi\) | |||||||
\(912\) | −6.00000 | − | 10.3923i | −0.198680 | − | 0.344124i | ||||
\(913\) | 67.5000 | − | 38.9711i | 2.23392 | − | 1.28976i | ||||
\(914\) | −32.7846 | − | 8.78461i | −1.08442 | − | 0.290569i | ||||
\(915\) | 10.3923i | 0.343559i | ||||||||
\(916\) | 21.0000 | − | 12.1244i | 0.693860 | − | 0.400600i | ||||
\(917\) | 21.6506 | − | 7.50000i | 0.714967 | − | 0.247672i | ||||
\(918\) | −12.2942 | − | 3.29423i | −0.405770 | − | 0.108726i | ||||
\(919\) | 16.4545 | − | 9.50000i | 0.542783 | − | 0.313376i | −0.203423 | − | 0.979091i | \(-0.565207\pi\) |
0.746206 | + | 0.665715i | \(0.231873\pi\) | |||||||
\(920\) | 24.2487 | − | 24.2487i | 0.799456 | − | 0.799456i | ||||
\(921\) | 6.00000 | + | 10.3923i | 0.197707 | + | 0.342438i | ||||
\(922\) | −5.19615 | + | 5.19615i | −0.171126 | + | 0.171126i | ||||
\(923\) | 15.0000 | + | 8.66025i | 0.493731 | + | 0.285056i | ||||
\(924\) | −45.0000 | − | 8.66025i | −1.48039 | − | 0.284901i | ||||
\(925\) | −1.73205 | + | 1.00000i | −0.0569495 | + | 0.0328798i | ||||
\(926\) | 3.29423 | − | 12.2942i | 0.108255 | − | 0.404013i | ||||
\(927\) | −7.79423 | + | 13.5000i | −0.255996 | + | 0.443398i | ||||
\(928\) | 38.2487 | − | 10.2487i | 1.25558 | − | 0.336430i | ||||
\(929\) | 15.0000 | + | 8.66025i | 0.492134 | + | 0.284134i | 0.725459 | − | 0.688265i | \(-0.241627\pi\) |
−0.233325 | + | 0.972399i | \(0.574961\pi\) | |||||||
\(930\) | −7.60770 | + | 28.3923i | −0.249466 | + | 0.931020i | ||||
\(931\) | 4.50000 | − | 11.2583i | 0.147482 | − | 0.368977i | ||||
\(932\) | −19.0526 | − | 11.0000i | −0.624087 | − | 0.360317i | ||||
\(933\) | −31.1769 | − | 18.0000i | −1.02069 | − | 0.589294i | ||||
\(934\) | 8.66025 | + | 8.66025i | 0.283372 | + | 0.283372i | ||||
\(935\) | 12.9904 | + | 7.50000i | 0.424831 | + | 0.245276i | ||||
\(936\) | −3.80385 | + | 14.1962i | −0.124333 | + | 0.464016i | ||||
\(937\) | − | 17.3205i | − | 0.565836i | −0.959144 | − | 0.282918i | \(-0.908698\pi\) | ||
0.959144 | − | 0.282918i | \(-0.0913025\pi\) | |||||||
\(938\) | −26.9282 | − | 13.0718i | −0.879237 | − | 0.426809i | ||||
\(939\) | 18.0000 | 0.587408 | ||||||||
\(940\) | 12.0000i | 0.391397i | ||||||||
\(941\) | −22.5167 | − | 39.0000i | −0.734022 | − | 1.27136i | −0.955151 | − | 0.296119i | \(-0.904307\pi\) |
0.221129 | − | 0.975245i | \(-0.429026\pi\) | |||||||
\(942\) | 13.1769 | − | 49.1769i | 0.429327 | − | 1.60227i | ||||
\(943\) | −42.4352 | + | 73.5000i | −1.38188 | + | 2.39349i | ||||
\(944\) | 27.7128i | 0.901975i | ||||||||
\(945\) | 22.5000 | − | 7.79423i | 0.731925 | − | 0.253546i | ||||
\(946\) | −45.0000 | + | 45.0000i | −1.46308 | + | 1.46308i | ||||
\(947\) | 13.0000 | − | 22.5167i | 0.422443 | − | 0.731693i | −0.573735 | − | 0.819041i | \(-0.694506\pi\) |
0.996178 | + | 0.0873481i | \(0.0278392\pi\) | |||||||
\(948\) | −18.0000 | + | 10.3923i | −0.584613 | + | 0.337526i | ||||
\(949\) | −12.9904 | + | 7.50000i | −0.421686 | + | 0.243460i | ||||
\(950\) | 3.46410 | + | 3.46410i | 0.112390 | + | 0.112390i | ||||
\(951\) | −24.2487 | −0.786318 | ||||||||
\(952\) | 10.7321 | − | 7.26795i | 0.347828 | − | 0.235556i | ||||
\(953\) | 20.0000 | 0.647864 | 0.323932 | − | 0.946080i | \(-0.394995\pi\) | ||||
0.323932 | + | 0.946080i | \(0.394995\pi\) | |||||||
\(954\) | −33.0000 | − | 33.0000i | −1.06841 | − | 1.06841i | ||||
\(955\) | 21.0000 | + | 12.1244i | 0.679544 | + | 0.392335i | ||||
\(956\) | −10.0000 | −0.323423 | ||||||||
\(957\) | 30.3109 | − | 52.5000i | 0.979812 | − | 1.69708i | ||||
\(958\) | −0.633975 | − | 2.36603i | −0.0204828 | − | 0.0764428i | ||||
\(959\) | −11.2583 | − | 32.5000i | −0.363550 | − | 1.04948i | ||||
\(960\) | 12.0000 | + | 20.7846i | 0.387298 | + | 0.670820i | ||||
\(961\) | −8.50000 | + | 14.7224i | −0.274194 | + | 0.474917i | ||||
\(962\) | 2.36603 | − | 0.633975i | 0.0762837 | − | 0.0204402i | ||||
\(963\) | −15.0000 | −0.483368 | ||||||||
\(964\) | 5.19615 | + | 9.00000i | 0.167357 | + | 0.289870i | ||||
\(965\) | −5.19615 | − | 9.00000i | −0.167270 | − | 0.289720i | ||||
\(966\) | −40.8109 | − | 19.8109i | −1.31307 | − | 0.637405i | ||||
\(967\) | 28.5788 | + | 16.5000i | 0.919033 | + | 0.530604i | 0.883327 | − | 0.468758i | \(-0.155298\pi\) |
0.0357069 | + | 0.999362i | \(0.488632\pi\) | |||||||
\(968\) | −28.0000 | − | 28.0000i | −0.899954 | − | 0.899954i | ||||
\(969\) | 4.50000 | − | 2.59808i | 0.144561 | − | 0.0834622i | ||||
\(970\) | 3.00000 | + | 3.00000i | 0.0963242 | + | 0.0963242i | ||||
\(971\) | −7.50000 | + | 4.33013i | −0.240686 | + | 0.138960i | −0.615492 | − | 0.788143i | \(-0.711043\pi\) |
0.374806 | + | 0.927103i | \(0.377709\pi\) | |||||||
\(972\) | −31.1769 | −1.00000 | ||||||||
\(973\) | −7.79423 | + | 40.5000i | −0.249871 | + | 1.29837i | ||||
\(974\) | 8.41858 | − | 31.4186i | 0.269749 | − | 1.00672i | ||||
\(975\) | − | 6.00000i | − | 0.192154i | ||||||
\(976\) | 6.92820 | + | 12.0000i | 0.221766 | + | 0.384111i | ||||
\(977\) | 10.0000 | + | 17.3205i | 0.319928 | + | 0.554132i | 0.980473 | − | 0.196655i | \(-0.0630078\pi\) |
−0.660544 | + | 0.750787i | \(0.729674\pi\) | |||||||
\(978\) | 4.43782 | − | 16.5622i | 0.141906 | − | 0.529600i | ||||
\(979\) | −37.5000 | + | 21.6506i | −1.19851 | + | 0.691957i | ||||
\(980\) | −9.00000 | + | 22.5167i | −0.287494 | + | 0.719268i | ||||
\(981\) | −12.9904 | + | 7.50000i | −0.414751 | + | 0.239457i | ||||
\(982\) | −50.5429 | − | 13.5429i | −1.61289 | − | 0.432173i | ||||
\(983\) | 29.4449 | 0.939145 | 0.469573 | − | 0.882894i | \(-0.344408\pi\) | ||||
0.469573 | + | 0.882894i | \(0.344408\pi\) | |||||||
\(984\) | −42.0000 | − | 42.0000i | −1.33891 | − | 1.33891i | ||||
\(985\) | − | 13.8564i | − | 0.441502i | ||||||
\(986\) | 4.43782 | + | 16.5622i | 0.141329 | + | 0.527447i | ||||
\(987\) | 15.0000 | − | 5.19615i | 0.477455 | − | 0.165395i | ||||
\(988\) | −3.00000 | − | 5.19615i | −0.0954427 | − | 0.165312i | ||||
\(989\) | −54.5596 | + | 31.5000i | −1.73489 | + | 1.00164i | ||||
\(990\) | 35.4904 | + | 9.50962i | 1.12796 | + | 0.302236i | ||||
\(991\) | 47.6314 | + | 27.5000i | 1.51306 | + | 0.873566i | 0.999883 | + | 0.0152841i | \(0.00486527\pi\) |
0.513178 | + | 0.858282i | \(0.328468\pi\) | |||||||
\(992\) | 10.1436 | + | 37.8564i | 0.322059 | + | 1.20194i | ||||
\(993\) | − | 10.3923i | − | 0.329790i | ||||||
\(994\) | −20.9808 | − | 30.9808i | −0.665469 | − | 0.982650i | ||||
\(995\) | −7.50000 | + | 12.9904i | −0.237766 | + | 0.411823i | ||||
\(996\) | 54.0000i | 1.71106i | ||||||||
\(997\) | 50.2295 | 1.59078 | 0.795392 | − | 0.606096i | \(-0.207265\pi\) | ||||
0.795392 | + | 0.606096i | \(0.207265\pi\) | |||||||
\(998\) | −5.49038 | − | 20.4904i | −0.173795 | − | 0.648612i | ||||
\(999\) | 2.59808 | + | 4.50000i | 0.0821995 | + | 0.142374i |
(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 | 504.2.cz.a.283.2 | yes | 4 | |
7.5 | odd | 6 | 504.2.bf.a.355.1 | yes | 4 | ||
8.3 | odd | 2 | inner | 504.2.cz.a.283.1 | yes | 4 | |
9.7 | even | 3 | 504.2.bf.a.115.1 | ✓ | 4 | ||
56.19 | even | 6 | 504.2.bf.a.355.2 | yes | 4 | ||
63.61 | odd | 6 | inner | 504.2.cz.a.187.1 | yes | 4 | |
72.43 | odd | 6 | 504.2.bf.a.115.2 | yes | 4 | ||
504.187 | even | 6 | inner | 504.2.cz.a.187.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bf.a.115.1 | ✓ | 4 | 9.7 | even | 3 | ||
504.2.bf.a.115.2 | yes | 4 | 72.43 | odd | 6 | ||
504.2.bf.a.355.1 | yes | 4 | 7.5 | odd | 6 | ||
504.2.bf.a.355.2 | yes | 4 | 56.19 | even | 6 | ||
504.2.cz.a.187.1 | yes | 4 | 63.61 | odd | 6 | inner | |
504.2.cz.a.187.2 | yes | 4 | 504.187 | even | 6 | inner | |
504.2.cz.a.283.1 | yes | 4 | 8.3 | odd | 2 | inner | |
504.2.cz.a.283.2 | yes | 4 | 1.1 | even | 1 | trivial |