Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 943.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.943 |
Dual form | 950.2.q.c.407.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258819 | + | 0.965926i | −0.183013 | + | 0.683013i | ||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | −0.0310384 | − | 0.999518i | \(-0.509881\pi\) |
−0.526639 | + | 0.850089i | \(0.676548\pi\) | |||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −2.44949 | + | 2.44949i | −0.925820 | + | 0.925820i | −0.997433 | − | 0.0716124i | \(-0.977186\pi\) |
0.0716124 | + | 0.997433i | \(0.477186\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −1.73205 | − | 1.00000i | −0.577350 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 0.517638 | + | 1.93185i | 0.143567 | + | 0.535799i | 0.999815 | + | 0.0192343i | \(0.00612285\pi\) |
−0.856248 | + | 0.516565i | \(0.827210\pi\) | |||||||
\(14\) | −1.73205 | − | 3.00000i | −0.462910 | − | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −1.67303 | − | 0.448288i | −0.405770 | − | 0.108726i | 0.0501604 | − | 0.998741i | \(-0.484027\pi\) |
−0.455930 | + | 0.890015i | \(0.650693\pi\) | |||||||
\(18\) | 1.41421 | − | 1.41421i | 0.333333 | − | 0.333333i | ||||
\(19\) | 2.59808 | − | 3.50000i | 0.596040 | − | 0.802955i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 1.73205i | 0.654654 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.34607 | − | 0.896575i | 0.697703 | − | 0.186949i | 0.107501 | − | 0.994205i | \(-0.465715\pi\) |
0.590201 | + | 0.807256i | \(0.299048\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 3.53553 | + | 3.53553i | 0.680414 | + | 0.680414i | ||||
\(28\) | 3.34607 | − | 0.896575i | 0.632347 | − | 0.169437i | ||||
\(29\) | −1.73205 | + | 3.00000i | −0.321634 | + | 0.557086i | −0.980825 | − | 0.194889i | \(-0.937565\pi\) |
0.659192 | + | 0.751975i | \(0.270899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.3923i | − | 1.86651i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | −0.965926 | + | 0.258819i | −0.170753 | + | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.866025 | − | 1.50000i | 0.148522 | − | 0.257248i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | + | 1.73205i | 0.166667 | + | 0.288675i | ||||
\(37\) | −2.82843 | − | 2.82843i | −0.464991 | − | 0.464991i | 0.435297 | − | 0.900287i | \(-0.356644\pi\) |
−0.900287 | + | 0.435297i | \(0.856644\pi\) | |||||||
\(38\) | 2.70831 | + | 3.41542i | 0.439346 | + | 0.554054i | ||||
\(39\) | − | 2.00000i | − | 0.320256i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | − | 3.46410i | 0.937043 | − | 0.541002i | 0.0480106 | − | 0.998847i | \(-0.484712\pi\) |
0.889032 | + | 0.457845i | \(0.151379\pi\) | |||||||
\(42\) | 0.896575 | + | 3.34607i | 0.138345 | + | 0.516309i | ||||
\(43\) | 0.896575 | − | 3.34607i | 0.136726 | − | 0.510270i | −0.863258 | − | 0.504762i | \(-0.831580\pi\) |
0.999985 | − | 0.00550783i | \(-0.00175320\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.46410i | 0.510754i | ||||||||
\(47\) | −1.79315 | − | 6.69213i | −0.261558 | − | 0.976148i | −0.964324 | − | 0.264726i | \(-0.914718\pi\) |
0.702766 | − | 0.711421i | \(-0.251948\pi\) | |||||||
\(48\) | −0.258819 | − | 0.965926i | −0.0373573 | − | 0.139419i | ||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50000 | + | 0.866025i | 0.210042 | + | 0.121268i | ||||
\(52\) | 0.517638 | − | 1.93185i | 0.0717835 | − | 0.267900i | ||||
\(53\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(54\) | −4.33013 | + | 2.50000i | −0.589256 | + | 0.340207i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.46410i | 0.462910i | ||||||||
\(57\) | −3.41542 | + | 2.70831i | −0.452383 | + | 0.358724i | ||||
\(58\) | −2.44949 | − | 2.44949i | −0.321634 | − | 0.321634i | ||||
\(59\) | −2.59808 | − | 4.50000i | −0.338241 | − | 0.585850i | 0.645861 | − | 0.763455i | \(-0.276498\pi\) |
−0.984102 | + | 0.177605i | \(0.943165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 10.0382 | + | 2.68973i | 1.27485 | + | 0.341596i | ||||
\(63\) | 6.69213 | − | 1.79315i | 0.843129 | − | 0.225916i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72741 | − | 2.07055i | 0.944053 | − | 0.252958i | 0.246216 | − | 0.969215i | \(-0.420813\pi\) |
0.697837 | + | 0.716257i | \(0.254146\pi\) | |||||||
\(68\) | 1.22474 | + | 1.22474i | 0.148522 | + | 0.148522i | ||||
\(69\) | −3.46410 | −0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | − | 6.92820i | 1.42414 | − | 0.822226i | 0.427489 | − | 0.904021i | \(-0.359398\pi\) |
0.996649 | + | 0.0817942i | \(0.0260650\pi\) | |||||||
\(72\) | −1.93185 | + | 0.517638i | −0.227671 | + | 0.0610042i | ||||
\(73\) | −2.24144 | + | 8.36516i | −0.262341 | + | 0.979068i | 0.701518 | + | 0.712652i | \(0.252506\pi\) |
−0.963858 | + | 0.266416i | \(0.914160\pi\) | |||||||
\(74\) | 3.46410 | − | 2.00000i | 0.402694 | − | 0.232495i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | + | 1.73205i | −0.458831 | + | 0.198680i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.93185 | + | 0.517638i | 0.218739 | + | 0.0586110i | ||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.79315 | + | 6.69213i | 0.198020 | + | 0.739022i | ||||
\(83\) | −1.22474 | − | 1.22474i | −0.134433 | − | 0.134433i | 0.636688 | − | 0.771121i | \(-0.280304\pi\) |
−0.771121 | + | 0.636688i | \(0.780304\pi\) | |||||||
\(84\) | −3.46410 | −0.377964 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.00000 | + | 1.73205i | 0.323498 | + | 0.186772i | ||||
\(87\) | 2.44949 | − | 2.44949i | 0.262613 | − | 0.262613i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.33013 | + | 7.50000i | −0.458993 | + | 0.794998i | −0.998908 | − | 0.0467209i | \(-0.985123\pi\) |
0.539915 | + | 0.841719i | \(0.318456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | − | 3.46410i | −0.628971 | − | 0.363137i | ||||
\(92\) | −3.34607 | − | 0.896575i | −0.348851 | − | 0.0934745i | ||||
\(93\) | −2.68973 | + | 10.0382i | −0.278912 | + | 1.04091i | ||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.81173 | − | 6.76148i | 0.183954 | − | 0.686524i | −0.810898 | − | 0.585187i | \(-0.801021\pi\) |
0.994852 | − | 0.101337i | \(-0.0323122\pi\) | |||||||
\(98\) | 4.82963 | + | 1.29410i | 0.487866 | + | 0.130723i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | −1.22474 | + | 1.22474i | −0.121268 | + | 0.121268i | ||||
\(103\) | 2.82843 | − | 2.82843i | 0.278693 | − | 0.278693i | −0.553894 | − | 0.832587i | \(-0.686859\pi\) |
0.832587 | + | 0.553894i | \(0.186859\pi\) | |||||||
\(104\) | 1.73205 | + | 1.00000i | 0.169842 | + | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.6066 | − | 10.6066i | −1.02538 | − | 1.02538i | −0.999669 | − | 0.0257094i | \(-0.991816\pi\) |
−0.0257094 | − | 0.999669i | \(-0.508184\pi\) | |||||||
\(108\) | −1.29410 | − | 4.82963i | −0.124524 | − | 0.464731i | ||||
\(109\) | 8.66025 | + | 15.0000i | 0.829502 | + | 1.43674i | 0.898430 | + | 0.439118i | \(0.144709\pi\) |
−0.0689276 | + | 0.997622i | \(0.521958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | + | 3.46410i | 0.189832 | + | 0.328798i | ||||
\(112\) | −3.34607 | − | 0.896575i | −0.316173 | − | 0.0847184i | ||||
\(113\) | 6.36396 | − | 6.36396i | 0.598671 | − | 0.598671i | −0.341288 | − | 0.939959i | \(-0.610863\pi\) |
0.939959 | + | 0.341288i | \(0.110863\pi\) | |||||||
\(114\) | −1.73205 | − | 4.00000i | −0.162221 | − | 0.374634i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | − | 1.73205i | 0.278543 | − | 0.160817i | ||||
\(117\) | 1.03528 | − | 3.86370i | 0.0957113 | − | 0.357199i | ||||
\(118\) | 5.01910 | − | 1.34486i | 0.462045 | − | 0.123805i | ||||
\(119\) | 5.19615 | − | 3.00000i | 0.476331 | − | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 5.65685 | + | 5.65685i | 0.512148 | + | 0.512148i | ||||
\(123\) | −6.69213 | + | 1.79315i | −0.603409 | + | 0.161683i | ||||
\(124\) | −5.19615 | + | 9.00000i | −0.466628 | + | 0.808224i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.92820i | 0.617213i | ||||||||
\(127\) | −3.86370 | + | 1.03528i | −0.342848 | + | 0.0918659i | −0.426135 | − | 0.904660i | \(-0.640125\pi\) |
0.0832864 | + | 0.996526i | \(0.473458\pi\) | |||||||
\(128\) | 0.965926 | + | 0.258819i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | −1.73205 | + | 3.00000i | −0.152499 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.20925 | + | 14.9372i | 0.191567 | + | 1.29522i | ||||
\(134\) | 8.00000i | 0.691095i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | + | 0.866025i | −0.128624 | + | 0.0742611i | ||||
\(137\) | −4.03459 | − | 15.0573i | −0.344698 | − | 1.28643i | −0.892964 | − | 0.450127i | \(-0.851379\pi\) |
0.548266 | − | 0.836304i | \(-0.315288\pi\) | |||||||
\(138\) | 0.896575 | − | 3.34607i | 0.0763216 | − | 0.284836i | ||||
\(139\) | 13.8564 | + | 8.00000i | 1.17529 | + | 0.678551i | 0.954919 | − | 0.296866i | \(-0.0959415\pi\) |
0.220366 | + | 0.975417i | \(0.429275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820i | 0.583460i | ||||||||
\(142\) | 3.58630 | + | 13.3843i | 0.300956 | + | 1.12318i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 2.00000i | − | 0.166667i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.50000 | − | 4.33013i | −0.620704 | − | 0.358364i | ||||
\(147\) | −1.29410 | + | 4.82963i | −0.106735 | + | 0.398341i | ||||
\(148\) | 1.03528 | + | 3.86370i | 0.0850992 | + | 0.317594i | ||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.7846i | 1.69143i | 0.533637 | + | 0.845714i | \(0.320825\pi\) | ||||
−0.533637 | + | 0.845714i | \(0.679175\pi\) | |||||||
\(152\) | −0.637756 | − | 4.31199i | −0.0517289 | − | 0.349749i | ||||
\(153\) | 2.44949 | + | 2.44949i | 0.198030 | + | 0.198030i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | 16.7303 | + | 4.48288i | 1.33523 | + | 0.357773i | 0.854661 | − | 0.519187i | \(-0.173765\pi\) |
0.480565 | + | 0.876959i | \(0.340432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | + | 10.3923i | −0.472866 | + | 0.819028i | ||||
\(162\) | −0.965926 | + | 0.258819i | −0.0758903 | + | 0.0203347i | ||||
\(163\) | −12.2474 | − | 12.2474i | −0.959294 | − | 0.959294i | 0.0399091 | − | 0.999203i | \(-0.487293\pi\) |
−0.999203 | + | 0.0399091i | \(0.987293\pi\) | |||||||
\(164\) | −6.92820 | −0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50000 | − | 0.866025i | 0.116423 | − | 0.0672166i | ||||
\(167\) | −17.3867 | + | 4.65874i | −1.34542 | + | 0.360504i | −0.858442 | − | 0.512910i | \(-0.828568\pi\) |
−0.486978 | + | 0.873414i | \(0.661901\pi\) | |||||||
\(168\) | 0.896575 | − | 3.34607i | 0.0691723 | − | 0.258155i | ||||
\(169\) | 7.79423 | − | 4.50000i | 0.599556 | − | 0.346154i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.00000 | + | 3.46410i | −0.611775 | + | 0.264906i | ||||
\(172\) | −2.44949 | + | 2.44949i | −0.186772 | + | 0.186772i | ||||
\(173\) | −17.3867 | − | 4.65874i | −1.32188 | − | 0.354198i | −0.472200 | − | 0.881491i | \(-0.656540\pi\) |
−0.849683 | + | 0.527294i | \(0.823207\pi\) | |||||||
\(174\) | 1.73205 | + | 3.00000i | 0.131306 | + | 0.227429i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.34486 | + | 5.01910i | 0.101086 | + | 0.377258i | ||||
\(178\) | −6.12372 | − | 6.12372i | −0.458993 | − | 0.458993i | ||||
\(179\) | −8.66025 | −0.647298 | −0.323649 | − | 0.946177i | \(-0.604910\pi\) | ||||
−0.323649 | + | 0.946177i | \(0.604910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | − | 3.46410i | −0.445976 | − | 0.257485i | 0.260153 | − | 0.965567i | \(-0.416227\pi\) |
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 4.89898 | − | 4.89898i | 0.363137 | − | 0.363137i | ||||
\(183\) | −5.65685 | + | 5.65685i | −0.418167 | + | 0.418167i | ||||
\(184\) | 1.73205 | − | 3.00000i | 0.127688 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.00000 | − | 5.19615i | −0.659912 | − | 0.381000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.79315 | + | 6.69213i | −0.130779 | + | 0.488074i | ||||
\(189\) | −17.3205 | −1.25988 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | −0.258819 | + | 0.965926i | −0.0186787 | + | 0.0697097i | ||||
\(193\) | −10.6252 | − | 2.84701i | −0.764817 | − | 0.204932i | −0.144737 | − | 0.989470i | \(-0.546234\pi\) |
−0.620081 | + | 0.784538i | \(0.712900\pi\) | |||||||
\(194\) | 6.06218 | + | 3.50000i | 0.435239 | + | 0.251285i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.50000 | + | 4.33013i | −0.178571 | + | 0.309295i | ||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.46410 | + | 2.00000i | 0.245564 | + | 0.141776i | 0.617731 | − | 0.786389i | \(-0.288052\pi\) |
−0.372168 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | −4.24264 | − | 4.24264i | −0.298511 | − | 0.298511i | ||||
\(203\) | −3.10583 | − | 11.5911i | −0.217986 | − | 0.813536i | ||||
\(204\) | −0.866025 | − | 1.50000i | −0.0606339 | − | 0.105021i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | −6.69213 | − | 1.79315i | −0.465135 | − | 0.124633i | ||||
\(208\) | −1.41421 | + | 1.41421i | −0.0980581 | + | 0.0980581i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.50000 | + | 2.59808i | −0.309793 | + | 0.178859i | −0.646834 | − | 0.762631i | \(-0.723907\pi\) |
0.337041 | + | 0.941490i | \(0.390574\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.3843 | + | 3.58630i | −0.917074 | + | 0.245729i | ||||
\(214\) | 12.9904 | − | 7.50000i | 0.888004 | − | 0.512689i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 25.4558 | + | 25.4558i | 1.72806 | + | 1.72806i | ||||
\(218\) | −16.7303 | + | 4.48288i | −1.13312 | + | 0.303619i | ||||
\(219\) | 4.33013 | − | 7.50000i | 0.292603 | − | 0.506803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.46410i | − | 0.233021i | ||||||
\(222\) | −3.86370 | + | 1.03528i | −0.259315 | + | 0.0694832i | ||||
\(223\) | 1.93185 | + | 0.517638i | 0.129366 | + | 0.0346636i | 0.322921 | − | 0.946426i | \(-0.395335\pi\) |
−0.193555 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(224\) | 1.73205 | − | 3.00000i | 0.115728 | − | 0.200446i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.50000 | + | 7.79423i | 0.299336 | + | 0.518464i | ||||
\(227\) | −19.0919 | − | 19.0919i | −1.26717 | − | 1.26717i | −0.947542 | − | 0.319631i | \(-0.896441\pi\) |
−0.319631 | − | 0.947542i | \(-0.603559\pi\) | |||||||
\(228\) | 4.31199 | − | 0.637756i | 0.285569 | − | 0.0422365i | ||||
\(229\) | − | 22.0000i | − | 1.45380i | −0.686743 | − | 0.726900i | \(-0.740960\pi\) | ||
0.686743 | − | 0.726900i | \(-0.259040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.896575 | + | 3.34607i | 0.0588631 | + | 0.219680i | ||||
\(233\) | −5.82774 | + | 21.7494i | −0.381788 | + | 1.42485i | 0.461380 | + | 0.887202i | \(0.347354\pi\) |
−0.843168 | + | 0.537650i | \(0.819312\pi\) | |||||||
\(234\) | 3.46410 | + | 2.00000i | 0.226455 | + | 0.130744i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.19615i | 0.338241i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.55291 | + | 5.79555i | 0.100660 | + | 0.375670i | ||||
\(239\) | − | 18.0000i | − | 1.16432i | −0.813073 | − | 0.582162i | \(-0.802207\pi\) | ||
0.813073 | − | 0.582162i | \(-0.197793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | 2.84701 | − | 10.6252i | 0.183013 | − | 0.683013i | ||||
\(243\) | −4.14110 | − | 15.4548i | −0.265652 | − | 0.991427i | ||||
\(244\) | −6.92820 | + | 4.00000i | −0.443533 | + | 0.256074i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 6.92820i | − | 0.441726i | ||||||
\(247\) | 8.10634 | + | 3.20736i | 0.515794 | + | 0.204080i | ||||
\(248\) | −7.34847 | − | 7.34847i | −0.466628 | − | 0.466628i | ||||
\(249\) | 0.866025 | + | 1.50000i | 0.0548821 | + | 0.0950586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.00000 | + | 10.3923i | −0.378717 | + | 0.655956i | −0.990876 | − | 0.134778i | \(-0.956968\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(252\) | −6.69213 | − | 1.79315i | −0.421565 | − | 0.112958i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 4.00000i | − | 0.250982i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.69333 | + | 2.32937i | −0.542275 | + | 0.145302i | −0.519551 | − | 0.854440i | \(-0.673901\pi\) |
−0.0227244 | + | 0.999742i | \(0.507234\pi\) | |||||||
\(258\) | −2.44949 | − | 2.44949i | −0.152499 | − | 0.152499i | ||||
\(259\) | 13.8564 | 0.860995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | − | 3.46410i | 0.371391 | − | 0.214423i | ||||
\(262\) | 14.4889 | − | 3.88229i | 0.895126 | − | 0.239848i | ||||
\(263\) | 6.27603 | − | 23.4225i | 0.386996 | − | 1.44429i | −0.447999 | − | 0.894034i | \(-0.647863\pi\) |
0.834996 | − | 0.550257i | \(-0.185470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.0000 | − | 1.73205i | −0.919709 | − | 0.106199i | ||||
\(267\) | 6.12372 | − | 6.12372i | 0.374766 | − | 0.374766i | ||||
\(268\) | −7.72741 | − | 2.07055i | −0.472026 | − | 0.126479i | ||||
\(269\) | 12.1244 | + | 21.0000i | 0.739235 | + | 1.28039i | 0.952840 | + | 0.303473i | \(0.0981461\pi\) |
−0.213605 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | −0.448288 | − | 1.67303i | −0.0271814 | − | 0.101443i | ||||
\(273\) | 4.89898 | + | 4.89898i | 0.296500 | + | 0.296500i | ||||
\(274\) | 15.5885 | 0.941733 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | + | 1.73205i | 0.180579 | + | 0.104257i | ||||
\(277\) | 17.1464 | − | 17.1464i | 1.03023 | − | 1.03023i | 0.0307004 | − | 0.999529i | \(-0.490226\pi\) |
0.999529 | − | 0.0307004i | \(-0.00977377\pi\) | |||||||
\(278\) | −11.3137 | + | 11.3137i | −0.678551 | + | 0.678551i | ||||
\(279\) | −10.3923 | + | 18.0000i | −0.622171 | + | 1.07763i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5000 | − | 6.06218i | −0.626377 | − | 0.361639i | 0.152970 | − | 0.988231i | \(-0.451116\pi\) |
−0.779348 | + | 0.626592i | \(0.784449\pi\) | |||||||
\(282\) | −6.69213 | − | 1.79315i | −0.398511 | − | 0.106781i | ||||
\(283\) | 0.896575 | − | 3.34607i | 0.0532959 | − | 0.198903i | −0.934144 | − | 0.356895i | \(-0.883835\pi\) |
0.987440 | + | 0.157992i | \(0.0505021\pi\) | |||||||
\(284\) | −13.8564 | −0.822226 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.21166 | + | 23.1822i | −0.366663 | + | 1.36840i | ||||
\(288\) | 1.93185 | + | 0.517638i | 0.113835 | + | 0.0305021i | ||||
\(289\) | −12.1244 | − | 7.00000i | −0.713197 | − | 0.411765i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.50000 | + | 6.06218i | −0.205174 | + | 0.355371i | ||||
\(292\) | 6.12372 | − | 6.12372i | 0.358364 | − | 0.358364i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | −4.33013 | − | 2.50000i | −0.252538 | − | 0.145803i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.46410 | + | 6.00000i | 0.200334 | + | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | + | 10.3923i | 0.345834 | + | 0.599002i | ||||
\(302\) | −20.0764 | − | 5.37945i | −1.15527 | − | 0.309553i | ||||
\(303\) | 4.24264 | − | 4.24264i | 0.243733 | − | 0.243733i | ||||
\(304\) | 4.33013 | + | 0.500000i | 0.248350 | + | 0.0286770i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00000 | + | 1.73205i | −0.171499 | + | 0.0990148i | ||||
\(307\) | −2.84701 | + | 10.6252i | −0.162487 | + | 0.606411i | 0.835860 | + | 0.548943i | \(0.184970\pi\) |
−0.998347 | + | 0.0574685i | \(0.981697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.46410 | + | 2.00000i | −0.197066 | + | 0.113776i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | −1.41421 | − | 1.41421i | −0.0800641 | − | 0.0800641i | ||||
\(313\) | 18.4034 | − | 4.93117i | 1.04022 | − | 0.278726i | 0.302015 | − | 0.953303i | \(-0.402341\pi\) |
0.738204 | + | 0.674577i | \(0.235674\pi\) | |||||||
\(314\) | −8.66025 | + | 15.0000i | −0.488726 | + | 0.846499i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5911 | − | 3.10583i | 0.651022 | − | 0.174441i | 0.0818309 | − | 0.996646i | \(-0.473923\pi\) |
0.569191 | + | 0.822206i | \(0.307257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.50000 | + | 12.9904i | 0.418609 | + | 0.725052i | ||||
\(322\) | −8.48528 | − | 8.48528i | −0.472866 | − | 0.472866i | ||||
\(323\) | −5.91567 | + | 4.69093i | −0.329157 | + | 0.261010i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.0000 | − | 8.66025i | 0.830773 | − | 0.479647i | ||||
\(327\) | −4.48288 | − | 16.7303i | −0.247904 | − | 0.925189i | ||||
\(328\) | 1.79315 | − | 6.69213i | 0.0990102 | − | 0.369511i | ||||
\(329\) | 20.7846 | + | 12.0000i | 1.14589 | + | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.19615i | − | 0.285606i | −0.989751 | − | 0.142803i | \(-0.954388\pi\) | ||
0.989751 | − | 0.142803i | \(-0.0456116\pi\) | |||||||
\(332\) | 0.448288 | + | 1.67303i | 0.0246030 | + | 0.0918196i | ||||
\(333\) | 2.07055 | + | 7.72741i | 0.113466 | + | 0.423459i | ||||
\(334\) | − | 18.0000i | − | 0.984916i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.00000 | + | 1.73205i | 0.163663 | + | 0.0944911i | ||||
\(337\) | −5.69402 | + | 21.2504i | −0.310173 | + | 1.15758i | 0.618227 | + | 0.785999i | \(0.287851\pi\) |
−0.928400 | + | 0.371582i | \(0.878816\pi\) | |||||||
\(338\) | 2.32937 | + | 8.69333i | 0.126701 | + | 0.472855i | ||||
\(339\) | −7.79423 | + | 4.50000i | −0.423324 | + | 0.244406i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.27551 | − | 8.62398i | −0.0689718 | − | 0.466332i | ||||
\(343\) | −4.89898 | − | 4.89898i | −0.264520 | − | 0.264520i | ||||
\(344\) | −1.73205 | − | 3.00000i | −0.0933859 | − | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.00000 | − | 15.5885i | 0.483843 | − | 0.838041i | ||||
\(347\) | 3.34607 | + | 0.896575i | 0.179626 | + | 0.0481307i | 0.347511 | − | 0.937676i | \(-0.387027\pi\) |
−0.167885 | + | 0.985807i | \(0.553694\pi\) | |||||||
\(348\) | −3.34607 | + | 0.896575i | −0.179368 | + | 0.0480615i | ||||
\(349\) | 28.0000i | 1.49881i | 0.662114 | + | 0.749403i | \(0.269659\pi\) | ||||
−0.662114 | + | 0.749403i | \(0.730341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | + | 8.66025i | −0.266880 | + | 0.462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.67423 | − | 3.67423i | −0.195560 | − | 0.195560i | 0.602534 | − | 0.798093i | \(-0.294158\pi\) |
−0.798093 | + | 0.602534i | \(0.794158\pi\) | |||||||
\(354\) | −5.19615 | −0.276172 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.50000 | − | 4.33013i | 0.397499 | − | 0.229496i | ||||
\(357\) | −5.79555 | + | 1.55291i | −0.306733 | + | 0.0821889i | ||||
\(358\) | 2.24144 | − | 8.36516i | 0.118464 | − | 0.442113i | ||||
\(359\) | 10.3923 | − | 6.00000i | 0.548485 | − | 0.316668i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.50000 | − | 18.1865i | −0.289474 | − | 0.957186i | ||||
\(362\) | 4.89898 | − | 4.89898i | 0.257485 | − | 0.257485i | ||||
\(363\) | 10.6252 | + | 2.84701i | 0.557678 | + | 0.149429i | ||||
\(364\) | 3.46410 | + | 6.00000i | 0.181568 | + | 0.314485i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.00000 | − | 6.92820i | −0.209083 | − | 0.362143i | ||||
\(367\) | 7.17260 | + | 26.7685i | 0.374407 | + | 1.39731i | 0.854209 | + | 0.519929i | \(0.174042\pi\) |
−0.479803 | + | 0.877376i | \(0.659292\pi\) | |||||||
\(368\) | 2.44949 | + | 2.44949i | 0.127688 | + | 0.127688i | ||||
\(369\) | −13.8564 | −0.721336 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.34847 | − | 7.34847i | 0.381000 | − | 0.381000i | ||||
\(373\) | 7.07107 | − | 7.07107i | 0.366126 | − | 0.366126i | −0.499936 | − | 0.866062i | \(-0.666643\pi\) |
0.866062 | + | 0.499936i | \(0.166643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | − | 3.46410i | −0.309426 | − | 0.178647i | ||||
\(377\) | −6.69213 | − | 1.79315i | −0.344662 | − | 0.0923520i | ||||
\(378\) | 4.48288 | − | 16.7303i | 0.230574 | − | 0.860515i | ||||
\(379\) | 5.19615 | 0.266908 | 0.133454 | − | 0.991055i | \(-0.457393\pi\) | ||||
0.133454 | + | 0.991055i | \(0.457393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | 0.204926 | ||||||||
\(382\) | −1.55291 | + | 5.79555i | −0.0794540 | + | 0.296526i | ||||
\(383\) | −23.1822 | − | 6.21166i | −1.18456 | − | 0.317401i | −0.387824 | − | 0.921733i | \(-0.626773\pi\) |
−0.796732 | + | 0.604333i | \(0.793440\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.50000 | − | 9.52628i | 0.279943 | − | 0.484875i | ||||
\(387\) | −4.89898 | + | 4.89898i | −0.249029 | + | 0.249029i | ||||
\(388\) | −4.94975 | + | 4.94975i | −0.251285 | + | 0.251285i | ||||
\(389\) | −25.9808 | − | 15.0000i | −1.31728 | − | 0.760530i | −0.333987 | − | 0.942578i | \(-0.608394\pi\) |
−0.983290 | + | 0.182047i | \(0.941728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | −3.53553 | − | 3.53553i | −0.178571 | − | 0.178571i | ||||
\(393\) | 3.88229 | + | 14.4889i | 0.195835 | + | 0.730868i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.1146 | + | 8.06918i | 1.51141 | + | 0.404980i | 0.916903 | − | 0.399111i | \(-0.130681\pi\) |
0.594505 | + | 0.804092i | \(0.297348\pi\) | |||||||
\(398\) | −2.82843 | + | 2.82843i | −0.141776 | + | 0.141776i | ||||
\(399\) | 1.73205 | − | 15.0000i | 0.0867110 | − | 0.750939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | + | 17.3205i | −1.49813 | + | 0.864945i | −0.999998 | − | 0.00215698i | \(-0.999313\pi\) |
−0.498131 | + | 0.867102i | \(0.665980\pi\) | |||||||
\(402\) | 2.07055 | − | 7.72741i | 0.103270 | − | 0.385408i | ||||
\(403\) | 20.0764 | − | 5.37945i | 1.00008 | − | 0.267970i | ||||
\(404\) | 5.19615 | − | 3.00000i | 0.258518 | − | 0.149256i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.67303 | − | 0.448288i | 0.0828275 | − | 0.0221936i | ||||
\(409\) | 3.46410 | − | 6.00000i | 0.171289 | − | 0.296681i | −0.767582 | − | 0.640951i | \(-0.778540\pi\) |
0.938871 | + | 0.344270i | \(0.111874\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.5885i | 0.768922i | ||||||||
\(412\) | −3.86370 | + | 1.03528i | −0.190351 | + | 0.0510044i | ||||
\(413\) | 17.3867 | + | 4.65874i | 0.855542 | + | 0.229242i | ||||
\(414\) | 3.46410 | − | 6.00000i | 0.170251 | − | 0.294884i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | −11.3137 | − | 11.3137i | −0.554035 | − | 0.554035i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 21.0000i | − | 1.02592i | −0.858413 | − | 0.512959i | \(-0.828549\pi\) | ||
0.858413 | − | 0.512959i | \(-0.171451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.0000 | − | 19.0526i | 1.60832 | − | 0.928565i | 0.618576 | − | 0.785725i | \(-0.287710\pi\) |
0.989746 | − | 0.142840i | \(-0.0456234\pi\) | |||||||
\(422\) | −1.34486 | − | 5.01910i | −0.0654669 | − | 0.244326i | ||||
\(423\) | −3.58630 | + | 13.3843i | −0.174372 | + | 0.650765i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 13.8564i | − | 0.671345i | ||||||
\(427\) | 7.17260 | + | 26.7685i | 0.347107 | + | 1.29542i | ||||
\(428\) | 3.88229 | + | 14.4889i | 0.187657 | + | 0.700347i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0000 | + | 12.1244i | 1.01153 | + | 0.584010i | 0.911641 | − | 0.410988i | \(-0.134816\pi\) |
0.0998939 | + | 0.994998i | \(0.468150\pi\) | |||||||
\(432\) | −1.29410 | + | 4.82963i | −0.0622622 | + | 0.232366i | ||||
\(433\) | 9.05867 | + | 33.8074i | 0.435332 | + | 1.62468i | 0.740271 | + | 0.672308i | \(0.234697\pi\) |
−0.304939 | + | 0.952372i | \(0.598636\pi\) | |||||||
\(434\) | −31.1769 | + | 18.0000i | −1.49654 | + | 0.864028i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 17.3205i | − | 0.829502i | ||||||
\(437\) | 5.55532 | − | 14.0406i | 0.265747 | − | 0.671653i | ||||
\(438\) | 6.12372 | + | 6.12372i | 0.292603 | + | 0.292603i | ||||
\(439\) | −3.46410 | − | 6.00000i | −0.165333 | − | 0.286364i | 0.771441 | − | 0.636301i | \(-0.219536\pi\) |
−0.936773 | + | 0.349937i | \(0.886203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 8.66025i | −0.238095 | + | 0.412393i | ||||
\(442\) | 3.34607 | + | 0.896575i | 0.159156 | + | 0.0426457i | ||||
\(443\) | 23.4225 | − | 6.27603i | 1.11283 | − | 0.298183i | 0.344854 | − | 0.938656i | \(-0.387928\pi\) |
0.767980 | + | 0.640473i | \(0.221262\pi\) | |||||||
\(444\) | − | 4.00000i | − | 0.189832i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.00000 | + | 1.73205i | −0.0473514 | + | 0.0820150i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.44949 | + | 2.44949i | 0.115728 | + | 0.115728i | ||||
\(449\) | −25.9808 | −1.22611 | −0.613054 | − | 0.790041i | \(-0.710059\pi\) | ||||
−0.613054 | + | 0.790041i | \(0.710059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.69333 | + | 2.32937i | −0.408900 | + | 0.109564i | ||||
\(453\) | 5.37945 | − | 20.0764i | 0.252749 | − | 0.943271i | ||||
\(454\) | 23.3827 | − | 13.5000i | 1.09740 | − | 0.633586i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.500000 | + | 4.33013i | −0.0234146 | + | 0.202777i | ||||
\(457\) | −13.4722 | + | 13.4722i | −0.630203 | + | 0.630203i | −0.948119 | − | 0.317916i | \(-0.897017\pi\) |
0.317916 | + | 0.948119i | \(0.397017\pi\) | |||||||
\(458\) | 21.2504 | + | 5.69402i | 0.992964 | + | 0.266064i | ||||
\(459\) | −4.33013 | − | 7.50000i | −0.202113 | − | 0.350070i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.00000 | − | 15.5885i | −0.419172 | − | 0.726027i | 0.576685 | − | 0.816967i | \(-0.304346\pi\) |
−0.995856 | + | 0.0909401i | \(0.971013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.34847 | + | 7.34847i | 0.341512 | + | 0.341512i | 0.856936 | − | 0.515423i | \(-0.172365\pi\) |
−0.515423 | + | 0.856936i | \(0.672365\pi\) | |||||||
\(464\) | −3.46410 | −0.160817 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.5000 | − | 11.2583i | −0.903320 | − | 0.521532i | ||||
\(467\) | 25.7196 | − | 25.7196i | 1.19016 | − | 1.19016i | 0.213142 | − | 0.977021i | \(-0.431630\pi\) |
0.977021 | − | 0.213142i | \(-0.0683696\pi\) | |||||||
\(468\) | −2.82843 | + | 2.82843i | −0.130744 | + | 0.130744i | ||||
\(469\) | −13.8564 | + | 24.0000i | −0.639829 | + | 1.10822i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0000 | − | 8.66025i | −0.691164 | − | 0.399043i | ||||
\(472\) | −5.01910 | − | 1.34486i | −0.231023 | − | 0.0619023i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.3867 | + | 4.65874i | 0.795248 | + | 0.213086i | ||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | − | 6.92820i | 0.182384 | − | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.48528 | − | 8.48528i | 0.386094 | − | 0.386094i | ||||
\(484\) | 9.52628 | + | 5.50000i | 0.433013 | + | 0.250000i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.0000 | 0.725775 | ||||||||
\(487\) | −11.3137 | − | 11.3137i | −0.512673 | − | 0.512673i | 0.402671 | − | 0.915345i | \(-0.368082\pi\) |
−0.915345 | + | 0.402671i | \(0.868082\pi\) | |||||||
\(488\) | −2.07055 | − | 7.72741i | −0.0937295 | − | 0.349803i | ||||
\(489\) | 8.66025 | + | 15.0000i | 0.391630 | + | 0.678323i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | + | 20.7846i | 0.541552 | + | 0.937996i | 0.998815 | + | 0.0486647i | \(0.0154966\pi\) |
−0.457263 | + | 0.889332i | \(0.651170\pi\) | |||||||
\(492\) | 6.69213 | + | 1.79315i | 0.301705 | + | 0.0808415i | ||||
\(493\) | 4.24264 | − | 4.24264i | 0.191079 | − | 0.191079i | ||||
\(494\) | −5.19615 | + | 7.00000i | −0.233786 | + | 0.314945i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.00000 | − | 5.19615i | 0.404112 | − | 0.233314i | ||||
\(497\) | −12.4233 | + | 46.3644i | −0.557262 | + | 2.07973i | ||||
\(498\) | −1.67303 | + | 0.448288i | −0.0749704 | + | 0.0200883i | ||||
\(499\) | 26.8468 | − | 15.5000i | 1.20183 | − | 0.693875i | 0.240866 | − | 0.970558i | \(-0.422569\pi\) |
0.960961 | + | 0.276683i | \(0.0892352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | −8.48528 | − | 8.48528i | −0.378717 | − | 0.378717i | ||||
\(503\) | 40.1528 | − | 10.7589i | 1.79032 | − | 0.479716i | 0.797923 | − | 0.602760i | \(-0.205932\pi\) |
0.992401 | + | 0.123044i | \(0.0392655\pi\) | |||||||
\(504\) | 3.46410 | − | 6.00000i | 0.154303 | − | 0.267261i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.69333 | + | 2.32937i | −0.386084 | + | 0.103451i | ||||
\(508\) | 3.86370 | + | 1.03528i | 0.171424 | + | 0.0459330i | ||||
\(509\) | 12.1244 | − | 21.0000i | 0.537403 | − | 0.930809i | −0.461640 | − | 0.887067i | \(-0.652739\pi\) |
0.999043 | − | 0.0437414i | \(-0.0139278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0000 | − | 25.9808i | −0.663561 | − | 1.14932i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 21.5600 | − | 3.18878i | 0.951895 | − | 0.140788i | ||||
\(514\) | − | 9.00000i | − | 0.396973i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.00000 | − | 1.73205i | 0.132068 | − | 0.0762493i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.58630 | + | 13.3843i | −0.157573 | + | 0.588071i | ||||
\(519\) | 15.5885 | + | 9.00000i | 0.684257 | + | 0.395056i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.7846i | − | 0.910590i | −0.890341 | − | 0.455295i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455295i | \(-0.150466\pi\) | |||||||
\(522\) | 1.79315 | + | 6.69213i | 0.0784841 | + | 0.292907i | ||||
\(523\) | 7.50575 | + | 28.0118i | 0.328204 | + | 1.22487i | 0.911052 | + | 0.412292i | \(0.135272\pi\) |
−0.582848 | + | 0.812581i | \(0.698062\pi\) | |||||||
\(524\) | 15.0000i | 0.655278i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0000 | + | 12.1244i | 0.915644 | + | 0.528647i | ||||
\(527\) | −4.65874 | + | 17.3867i | −0.202938 | + | 0.757375i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.52628 | + | 5.50000i | −0.414186 | + | 0.239130i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923i | 0.450988i | ||||||||
\(532\) | 5.55532 | − | 14.0406i | 0.240854 | − | 0.608737i | ||||
\(533\) | 9.79796 | + | 9.79796i | 0.424397 | + | 0.424397i | ||||
\(534\) | 4.33013 | + | 7.50000i | 0.187383 | + | 0.324557i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | − | 6.92820i | 0.172774 | − | 0.299253i | ||||
\(537\) | 8.36516 | + | 2.24144i | 0.360983 | + | 0.0967252i | ||||
\(538\) | −23.4225 | + | 6.27603i | −1.00981 | + | 0.270579i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | + | 1.73205i | −0.0429934 | + | 0.0744667i | −0.886721 | − | 0.462304i | \(-0.847023\pi\) |
0.843728 | + | 0.536771i | \(0.180356\pi\) | |||||||
\(542\) | 1.93185 | − | 0.517638i | 0.0829801 | − | 0.0222345i | ||||
\(543\) | 4.89898 | + | 4.89898i | 0.210235 | + | 0.210235i | ||||
\(544\) | 1.73205 | 0.0742611 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.00000 | + | 3.46410i | −0.256776 | + | 0.148250i | ||||
\(547\) | 6.76148 | − | 1.81173i | 0.289100 | − | 0.0774641i | −0.111355 | − | 0.993781i | \(-0.535519\pi\) |
0.400455 | + | 0.916317i | \(0.368852\pi\) | |||||||
\(548\) | −4.03459 | + | 15.0573i | −0.172349 | + | 0.643216i | ||||
\(549\) | −13.8564 | + | 8.00000i | −0.591377 | + | 0.341432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 13.8564i | 0.255609 | + | 0.590303i | ||||
\(552\) | −2.44949 | + | 2.44949i | −0.104257 | + | 0.104257i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.1244 | + | 21.0000i | 0.515115 | + | 0.892205i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | − | 13.8564i | −0.339276 | − | 0.587643i | ||||
\(557\) | −6.27603 | − | 23.4225i | −0.265924 | − | 0.992441i | −0.961682 | − | 0.274166i | \(-0.911598\pi\) |
0.695759 | − | 0.718276i | \(-0.255068\pi\) | |||||||
\(558\) | −14.6969 | − | 14.6969i | −0.622171 | − | 0.622171i | ||||
\(559\) | 6.92820 | 0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.57321 | − | 8.57321i | 0.361639 | − | 0.361639i | ||||
\(563\) | 14.8492 | − | 14.8492i | 0.625821 | − | 0.625821i | −0.321193 | − | 0.947014i | \(-0.604084\pi\) |
0.947014 | + | 0.321193i | \(0.104084\pi\) | |||||||
\(564\) | 3.46410 | − | 6.00000i | 0.145865 | − | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.00000 | + | 1.73205i | 0.126099 | + | 0.0728035i | ||||
\(567\) | −3.34607 | − | 0.896575i | −0.140522 | − | 0.0376526i | ||||
\(568\) | 3.58630 | − | 13.3843i | 0.150478 | − | 0.561591i | ||||
\(569\) | −39.8372 | −1.67006 | −0.835030 | − | 0.550204i | \(-0.814550\pi\) | ||||
−0.835030 | + | 0.550204i | \(0.814550\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.79555 | − | 1.55291i | −0.242113 | − | 0.0648739i | ||||
\(574\) | −20.7846 | − | 12.0000i | −0.867533 | − | 0.500870i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | + | 1.73205i | −0.0416667 | + | 0.0721688i | ||||
\(577\) | 29.3939 | − | 29.3939i | 1.22368 | − | 1.22368i | 0.257370 | − | 0.966313i | \(-0.417144\pi\) |
0.966313 | − | 0.257370i | \(-0.0828560\pi\) | |||||||
\(578\) | 9.89949 | − | 9.89949i | 0.411765 | − | 0.411765i | ||||
\(579\) | 9.52628 | + | 5.50000i | 0.395899 | + | 0.228572i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | −4.94975 | − | 4.94975i | −0.205174 | − | 0.205174i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.33013 | + | 7.50000i | 0.179182 | + | 0.310352i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.4416 | + | 7.62089i | 1.17391 | + | 0.314548i | 0.792508 | − | 0.609862i | \(-0.208775\pi\) |
0.381401 | + | 0.924410i | \(0.375442\pi\) | |||||||
\(588\) | 3.53553 | − | 3.53553i | 0.145803 | − | 0.145803i | ||||
\(589\) | −36.3731 | − | 27.0000i | −1.49873 | − | 1.11252i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.03528 | − | 3.86370i | 0.0425496 | − | 0.158797i | ||||
\(593\) | 20.0764 | − | 5.37945i | 0.824439 | − | 0.220908i | 0.178153 | − | 0.984003i | \(-0.442988\pi\) |
0.646286 | + | 0.763095i | \(0.276321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.82843 | − | 2.82843i | −0.115760 | − | 0.115760i | ||||
\(598\) | −6.69213 | + | 1.79315i | −0.273662 | + | 0.0733274i | ||||
\(599\) | 13.8564 | − | 24.0000i | 0.566157 | − | 0.980613i | −0.430784 | − | 0.902455i | \(-0.641763\pi\) |
0.996941 | − | 0.0781581i | \(-0.0249039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.5167i | − | 0.918474i | −0.888314 | − | 0.459237i | \(-0.848123\pi\) | ||
0.888314 | − | 0.459237i | \(-0.151877\pi\) | |||||||
\(602\) | −11.5911 | + | 3.10583i | −0.472418 | + | 0.126584i | ||||
\(603\) | −15.4548 | − | 4.14110i | −0.629369 | − | 0.168639i | ||||
\(604\) | 10.3923 | − | 18.0000i | 0.422857 | − | 0.732410i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.00000 | + | 5.19615i | 0.121867 | + | 0.211079i | ||||
\(607\) | −24.0416 | − | 24.0416i | −0.975820 | − | 0.975820i | 0.0238948 | − | 0.999714i | \(-0.492393\pi\) |
−0.999714 | + | 0.0238948i | \(0.992393\pi\) | |||||||
\(608\) | −1.60368 | + | 4.05317i | −0.0650379 | + | 0.164378i | ||||
\(609\) | 12.0000i | 0.486265i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | − | 6.92820i | 0.485468 | − | 0.280285i | ||||
\(612\) | −0.896575 | − | 3.34607i | −0.0362419 | − | 0.135257i | ||||
\(613\) | 0.896575 | − | 3.34607i | 0.0362123 | − | 0.135146i | −0.945453 | − | 0.325758i | \(-0.894380\pi\) |
0.981665 | + | 0.190612i | \(0.0610472\pi\) | |||||||
\(614\) | −9.52628 | − | 5.50000i | −0.384449 | − | 0.221962i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.2072 | + | 41.8258i | 0.451185 | + | 1.68384i | 0.699069 | + | 0.715054i | \(0.253598\pi\) |
−0.247884 | + | 0.968790i | \(0.579735\pi\) | |||||||
\(618\) | −1.03528 | − | 3.86370i | −0.0416449 | − | 0.155421i | ||||
\(619\) | − | 44.0000i | − | 1.76851i | −0.467005 | − | 0.884255i | \(-0.654667\pi\) | ||
0.467005 | − | 0.884255i | \(-0.345333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0000 | + | 8.66025i | 0.601929 | + | 0.347524i | ||||
\(622\) | −7.76457 | + | 28.9778i | −0.311331 | + | 1.16190i | ||||
\(623\) | −7.76457 | − | 28.9778i | −0.311081 | − | 1.16097i | ||||
\(624\) | 1.73205 | − | 1.00000i | 0.0693375 | − | 0.0400320i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.0526i | 0.761493i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.2474 | − | 12.2474i | −0.488726 | − | 0.488726i | ||||
\(629\) | 3.46410 | + | 6.00000i | 0.138123 | + | 0.239236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | − | 6.92820i | 0.159237 | − | 0.275807i | −0.775356 | − | 0.631524i | \(-0.782430\pi\) |
0.934594 | + | 0.355716i | \(0.115763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.01910 | − | 1.34486i | 0.199491 | − | 0.0534535i | ||||
\(634\) | 12.0000i | 0.476581i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.65926 | − | 2.58819i | 0.382714 | − | 0.102548i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.7128 | −1.09630 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | + | 6.06218i | −0.414725 | + | 0.239442i | −0.692818 | − | 0.721113i | \(-0.743631\pi\) |
0.278093 | + | 0.960554i | \(0.410298\pi\) | |||||||
\(642\) | −14.4889 | + | 3.88229i | −0.571831 | + | 0.153222i | ||||
\(643\) | −2.24144 | + | 8.36516i | −0.0883937 | + | 0.329890i | −0.995935 | − | 0.0900726i | \(-0.971290\pi\) |
0.907541 | + | 0.419962i | \(0.137957\pi\) | |||||||
\(644\) | 10.3923 | − | 6.00000i | 0.409514 | − | 0.236433i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | − | 6.92820i | −0.118033 | − | 0.272587i | ||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0.965926 | + | 0.258819i | 0.0379452 | + | 0.0101674i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | − | 31.1769i | −0.705476 | − | 1.22192i | ||||
\(652\) | 4.48288 | + | 16.7303i | 0.175563 | + | 0.655210i | ||||
\(653\) | −34.2929 | − | 34.2929i | −1.34198 | − | 1.34198i | −0.894084 | − | 0.447899i | \(-0.852172\pi\) |
−0.447899 | − | 0.894084i | \(-0.647828\pi\) | |||||||
\(654\) | 17.3205 | 0.677285 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.00000 | + | 3.46410i | 0.234261 | + | 0.135250i | ||||
\(657\) | 12.2474 | − | 12.2474i | 0.477818 | − | 0.477818i | ||||
\(658\) | −16.9706 | + | 16.9706i | −0.661581 | + | 0.661581i | ||||
\(659\) | 0.866025 | − | 1.50000i | 0.0337356 | − | 0.0584317i | −0.848665 | − | 0.528931i | \(-0.822593\pi\) |
0.882400 | + | 0.470500i | \(0.155926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.00000 | − | 3.46410i | −0.233373 | − | 0.134738i | 0.378754 | − | 0.925497i | \(-0.376353\pi\) |
−0.612127 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(662\) | 5.01910 | + | 1.34486i | 0.195073 | + | 0.0522696i | ||||
\(663\) | −0.896575 | + | 3.34607i | −0.0348201 | + | 0.129950i | ||||
\(664\) | −1.73205 | −0.0672166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | −3.10583 | + | 11.5911i | −0.120258 | + | 0.448810i | ||||
\(668\) | 17.3867 | + | 4.65874i | 0.672710 | + | 0.180252i | ||||
\(669\) | −1.73205 | − | 1.00000i | −0.0669650 | − | 0.0386622i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.44949 | + | 2.44949i | −0.0944911 | + | 0.0944911i | ||||
\(673\) | −32.5269 | + | 32.5269i | −1.25382 | + | 1.25382i | −0.299827 | + | 0.953994i | \(0.596929\pi\) |
−0.953994 | + | 0.299827i | \(0.903071\pi\) | |||||||
\(674\) | −19.0526 | − | 11.0000i | −0.733877 | − | 0.423704i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −21.2132 | − | 21.2132i | −0.815290 | − | 0.815290i | 0.170132 | − | 0.985421i | \(-0.445581\pi\) |
−0.985421 | + | 0.170132i | \(0.945581\pi\) | |||||||
\(678\) | −2.32937 | − | 8.69333i | −0.0894590 | − | 0.333865i | ||||
\(679\) | 12.1244 | + | 21.0000i | 0.465290 | + | 0.805906i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5000 | + | 23.3827i | 0.517321 | + | 0.896026i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.3345 | + | 23.3345i | −0.892871 | + | 0.892871i | −0.994792 | − | 0.101922i | \(-0.967501\pi\) |
0.101922 | + | 0.994792i | \(0.467501\pi\) | |||||||
\(684\) | 8.66025 | + | 1.00000i | 0.331133 | + | 0.0382360i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.00000 | − | 3.46410i | 0.229081 | − | 0.132260i | ||||
\(687\) | −5.69402 | + | 21.2504i | −0.217240 | + | 0.810752i | ||||
\(688\) | 3.34607 | − | 0.896575i | 0.127568 | − | 0.0341816i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.0000 | 1.63580 | 0.817899 | − | 0.575362i | \(-0.195139\pi\) | ||||
0.817899 | + | 0.575362i | \(0.195139\pi\) | |||||||
\(692\) | 12.7279 | + | 12.7279i | 0.483843 | + | 0.483843i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.73205 | + | 3.00000i | −0.0657477 | + | 0.113878i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 3.46410i | − | 0.131306i | ||||||
\(697\) | −11.5911 | + | 3.10583i | −0.439045 | + | 0.117642i | ||||
\(698\) | −27.0459 | − | 7.24693i | −1.02370 | − | 0.274300i | ||||
\(699\) | 11.2583 | − | 19.5000i | 0.425829 | − | 0.737558i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(702\) | −7.07107 | − | 7.07107i | −0.266880 | − | 0.266880i | ||||
\(703\) | −17.2480 | + | 2.55103i | −0.650519 | + | 0.0962138i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.50000 | − | 2.59808i | 0.169360 | − | 0.0977799i | ||||
\(707\) | −5.37945 | − | 20.0764i | −0.202315 | − | 0.755050i | ||||
\(708\) | 1.34486 | − | 5.01910i | 0.0505431 | − | 0.188629i | ||||
\(709\) | 6.92820 | + | 4.00000i | 0.260194 | + | 0.150223i | 0.624423 | − | 0.781086i | \(-0.285334\pi\) |
−0.364229 | + | 0.931309i | \(0.618667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.24144 | + | 8.36516i | 0.0840015 | + | 0.313498i | ||||
\(713\) | −9.31749 | − | 34.7733i | −0.348943 | − | 1.30227i | ||||
\(714\) | − | 6.00000i | − | 0.224544i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.50000 | + | 4.33013i | 0.280288 | + | 0.161824i | ||||
\(717\) | −4.65874 | + | 17.3867i | −0.173984 | + | 0.649317i | ||||
\(718\) | 3.10583 | + | 11.5911i | 0.115908 | + | 0.432576i | ||||
\(719\) | −31.1769 | + | 18.0000i | −1.16270 | + | 0.671287i | −0.951950 | − | 0.306253i | \(-0.900925\pi\) |
−0.210752 | + | 0.977539i | \(0.567591\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8564i | 0.516040i | ||||||||
\(722\) | 18.9903 | − | 0.605571i | 0.706748 | − | 0.0225370i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.46410 | + | 6.00000i | 0.128742 | + | 0.222988i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.50000 | + | 9.52628i | −0.204124 | + | 0.353553i | ||||
\(727\) | −10.0382 | − | 2.68973i | −0.372296 | − | 0.0997564i | 0.0678194 | − | 0.997698i | \(-0.478396\pi\) |
−0.440115 | + | 0.897941i | \(0.645062\pi\) | |||||||
\(728\) | −6.69213 | + | 1.79315i | −0.248027 | + | 0.0664586i | ||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | + | 5.19615i | −0.110959 | + | 0.192187i | ||||
\(732\) | 7.72741 | − | 2.07055i | 0.285613 | − | 0.0765298i | ||||
\(733\) | −7.34847 | − | 7.34847i | −0.271422 | − | 0.271422i | 0.558251 | − | 0.829672i | \(-0.311473\pi\) |
−0.829672 | + | 0.558251i | \(0.811473\pi\) | |||||||
\(734\) | −27.7128 | −1.02290 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | + | 1.73205i | −0.110581 | + | 0.0638442i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.58630 | − | 13.3843i | 0.132014 | − | 0.492681i | ||||
\(739\) | −21.6506 | + | 12.5000i | −0.796431 | + | 0.459820i | −0.842222 | − | 0.539131i | \(-0.818753\pi\) |
0.0457903 | + | 0.998951i | \(0.485419\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00000 | − | 5.19615i | −0.257151 | − | 0.190885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.79555 | − | 1.55291i | −0.212618 | − | 0.0569709i | 0.150938 | − | 0.988543i | \(-0.451771\pi\) |
−0.363556 | + | 0.931572i | \(0.618437\pi\) | |||||||
\(744\) | 5.19615 | + | 9.00000i | 0.190500 | + | 0.329956i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0.896575 | + | 3.34607i | 0.0328040 | + | 0.122426i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.9615 | 1.89863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.00000 | − | 5.19615i | −0.328415 | − | 0.189610i | 0.326722 | − | 0.945120i | \(-0.394056\pi\) |
−0.655137 | + | 0.755510i | \(0.727389\pi\) | |||||||
\(752\) | 4.89898 | − | 4.89898i | 0.178647 | − | 0.178647i | ||||
\(753\) | 8.48528 | − | 8.48528i | 0.309221 | − | 0.309221i | ||||
\(754\) | 3.46410 | − | 6.00000i | 0.126155 | − | 0.218507i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15.0000 | + | 8.66025i | 0.545545 | + | 0.314970i | ||||
\(757\) | −33.4607 | − | 8.96575i | −1.21615 | − | 0.325866i | −0.406977 | − | 0.913439i | \(-0.633417\pi\) |
−0.809171 | + | 0.587573i | \(0.800084\pi\) | |||||||
\(758\) | −1.34486 | + | 5.01910i | −0.0488476 | + | 0.182302i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | −1.03528 | + | 3.86370i | −0.0375041 | + | 0.139967i | ||||
\(763\) | −57.9555 | − | 15.5291i | −2.09813 | − | 0.562193i | ||||
\(764\) | −5.19615 | − | 3.00000i | −0.187990 | − | 0.108536i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | − | 20.7846i | 0.433578 | − | 0.750978i | ||||
\(767\) | 7.34847 | − | 7.34847i | 0.265338 | − | 0.265338i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | 19.9186 | + | 11.5000i | 0.718283 | + | 0.414701i | 0.814120 | − | 0.580696i | \(-0.197220\pi\) |
−0.0958377 | + | 0.995397i | \(0.530553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.00000 | 0.324127 | ||||||||
\(772\) | 7.77817 | + | 7.77817i | 0.279943 | + | 0.279943i | ||||
\(773\) | 4.65874 | + | 17.3867i | 0.167563 | + | 0.625355i | 0.997699 | + | 0.0677939i | \(0.0215960\pi\) |
−0.830136 | + | 0.557561i | \(0.811737\pi\) | |||||||
\(774\) | −3.46410 | − | 6.00000i | −0.124515 | − | 0.215666i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.50000 | − | 6.06218i | −0.125643 | − | 0.217620i | ||||
\(777\) | −13.3843 | − | 3.58630i | −0.480158 | − | 0.128658i | ||||
\(778\) | 21.2132 | − | 21.2132i | 0.760530 | − | 0.760530i | ||||
\(779\) | 3.46410 | − | 30.0000i | 0.124114 | − | 1.07486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.55291 | − | 5.79555i | 0.0555321 | − | 0.207249i | ||||
\(783\) | −16.7303 | + | 4.48288i | −0.597893 | + | 0.160205i | ||||
\(784\) | 4.33013 | − | 2.50000i | 0.154647 | − | 0.0892857i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.0000 | −0.535032 | ||||||||
\(787\) | 9.19239 | + | 9.19239i | 0.327673 | + | 0.327673i | 0.851701 | − | 0.524028i | \(-0.175571\pi\) |
−0.524028 | + | 0.851701i | \(0.675571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.1244 | + | 21.0000i | −0.431638 | + | 0.747620i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1769i | 1.10852i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4548 | + | 4.14110i | 0.548817 | + | 0.147055i | ||||
\(794\) | −15.5885 | + | 27.0000i | −0.553214 | + | 0.958194i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.00000 | − | 3.46410i | −0.0708881 | − | 0.122782i | ||||
\(797\) | −8.48528 | − | 8.48528i | −0.300564 | − | 0.300564i | 0.540670 | − | 0.841235i | \(-0.318171\pi\) |
−0.841235 | + | 0.540670i | \(0.818171\pi\) | |||||||
\(798\) | 14.0406 | + | 5.55532i | 0.497032 | + | 0.196656i | ||||
\(799\) | 12.0000i | 0.424529i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0000 | − | 8.66025i | 0.529999 | − | 0.305995i | ||||
\(802\) | −8.96575 | − | 33.4607i | −0.316592 | − | 1.18154i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.92820 | + | 4.00000i | 0.244339 | + | 0.141069i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.7846i | 0.732107i | ||||||||
\(807\) | −6.27603 | − | 23.4225i | −0.220927 | − | 0.824510i | ||||
\(808\) | 1.55291 | + | 5.79555i | 0.0546313 | + | 0.203887i | ||||
\(809\) | − | 51.0000i | − | 1.79306i | −0.442978 | − | 0.896532i | \(-0.646078\pi\) | ||
0.442978 | − | 0.896532i | \(-0.353922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0000 | − | 8.66025i | −0.526721 | − | 0.304103i | 0.212959 | − | 0.977061i | \(-0.431690\pi\) |
−0.739680 | + | 0.672958i | \(0.765023\pi\) | |||||||
\(812\) | −3.10583 | + | 11.5911i | −0.108993 | + | 0.406768i | ||||
\(813\) | 0.517638 | + | 1.93185i | 0.0181544 | + | 0.0677530i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.73205i | 0.0606339i | ||||||||
\(817\) | −9.38186 | − | 11.8313i | −0.328230 | − | 0.413926i | ||||
\(818\) | 4.89898 | + | 4.89898i | 0.171289 | + | 0.171289i | ||||
\(819\) | 6.92820 | + | 12.0000i | 0.242091 | + | 0.419314i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0000 | + | 36.3731i | −0.732905 | + | 1.26943i | 0.222731 | + | 0.974880i | \(0.428503\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(822\) | −15.0573 | − | 4.03459i | −0.525183 | − | 0.140722i | ||||
\(823\) | −26.7685 | + | 7.17260i | −0.933092 | + | 0.250021i | −0.693173 | − | 0.720772i | \(-0.743788\pi\) |
−0.239919 | + | 0.970793i | \(0.577121\pi\) | |||||||
\(824\) | − | 4.00000i | − | 0.139347i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.00000 | + | 15.5885i | −0.313150 | + | 0.542392i | ||||
\(827\) | −34.7733 | + | 9.31749i | −1.20919 | + | 0.324001i | −0.806443 | − | 0.591312i | \(-0.798610\pi\) |
−0.402744 | + | 0.915313i | \(0.631944\pi\) | |||||||
\(828\) | 4.89898 | + | 4.89898i | 0.170251 | + | 0.170251i | ||||
\(829\) | 45.0333 | 1.56407 | 0.782036 | − | 0.623233i | \(-0.214181\pi\) | ||||
0.782036 | + | 0.623233i | \(0.214181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0000 | + | 12.1244i | −0.728482 | + | 0.420589i | ||||
\(832\) | 1.93185 | − | 0.517638i | 0.0669749 | − | 0.0179459i | ||||
\(833\) | −2.24144 | + | 8.36516i | −0.0776612 | + | 0.289836i | ||||
\(834\) | 13.8564 | − | 8.00000i | 0.479808 | − | 0.277017i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.7423 | − | 36.7423i | 1.27000 | − | 1.27000i | ||||
\(838\) | 20.2844 | + | 5.43520i | 0.700714 | + | 0.187756i | ||||
\(839\) | 24.2487 | + | 42.0000i | 0.837158 | + | 1.45000i | 0.892261 | + | 0.451520i | \(0.149118\pi\) |
−0.0551024 | + | 0.998481i | \(0.517549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.50000 | + | 14.7224i | 0.293103 | + | 0.507670i | ||||
\(842\) | 9.86233 | + | 36.8067i | 0.339878 | + | 1.26844i | ||||
\(843\) | 8.57321 | + | 8.57321i | 0.295277 | + | 0.295277i | ||||
\(844\) | 5.19615 | 0.178859 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0000 | − | 6.92820i | −0.412568 | − | 0.238197i | ||||
\(847\) | 26.9444 | − | 26.9444i | 0.925820 | − | 0.925820i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.73205 | + | 3.00000i | −0.0594438 | + | 0.102960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | − | 6.92820i | −0.411355 | − | 0.237496i | ||||
\(852\) | 13.3843 | + | 3.58630i | 0.458537 | + | 0.122865i | ||||
\(853\) | −5.37945 | + | 20.0764i | −0.184189 | + | 0.687403i | 0.810614 | + | 0.585581i | \(0.199134\pi\) |
−0.994803 | + | 0.101821i | \(0.967533\pi\) | |||||||
\(854\) | −27.7128 | −0.948313 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0000 | −0.512689 | ||||||||
\(857\) | −7.76457 | + | 28.9778i | −0.265233 | + | 0.989862i | 0.696875 | + | 0.717193i | \(0.254573\pi\) |
−0.962108 | + | 0.272669i | \(0.912093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.866025 | − | 0.500000i | −0.0295484 | − | 0.0170598i | 0.485153 | − | 0.874429i | \(-0.338764\pi\) |
−0.514701 | + | 0.857369i | \(0.672097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 20.7846i | 0.408959 | − | 0.708338i | ||||
\(862\) | −17.1464 | + | 17.1464i | −0.584010 | + | 0.584010i | ||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | −4.33013 | − | 2.50000i | −0.147314 | − | 0.0850517i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −35.0000 | −1.18935 | ||||||||
\(867\) | 9.89949 | + | 9.89949i | 0.336204 | + | 0.336204i | ||||
\(868\) | −9.31749 | − | 34.7733i | −0.316256 | − | 1.18028i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | + | 13.8564i | 0.271070 | + | 0.469506i | ||||
\(872\) | 16.7303 | + | 4.48288i | 0.566560 | + | 0.151809i | ||||
\(873\) | −9.89949 | + | 9.89949i | −0.335047 | + | 0.335047i | ||||
\(874\) | 12.1244 | + | 9.00000i | 0.410112 | + | 0.304430i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.50000 | + | 4.33013i | −0.253402 | + | 0.146301i | ||||
\(877\) | −0.517638 | + | 1.93185i | −0.0174794 | + | 0.0652340i | −0.974115 | − | 0.226054i | \(-0.927417\pi\) |
0.956635 | + | 0.291288i | \(0.0940839\pi\) | |||||||
\(878\) | 6.69213 | − | 1.79315i | 0.225848 | − | 0.0605159i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.0000 | −1.51609 | −0.758044 | − | 0.652203i | \(-0.773845\pi\) | ||||
−0.758044 | + | 0.652203i | \(0.773845\pi\) | |||||||
\(882\) | −7.07107 | − | 7.07107i | −0.238095 | − | 0.238095i | ||||
\(883\) | 1.67303 | − | 0.448288i | 0.0563020 | − | 0.0150861i | −0.230558 | − | 0.973059i | \(-0.574055\pi\) |
0.286860 | + | 0.957972i | \(0.407389\pi\) | |||||||
\(884\) | −1.73205 | + | 3.00000i | −0.0582552 | + | 0.100901i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.2487i | 0.814651i | ||||||||
\(887\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(888\) | 3.86370 | + | 1.03528i | 0.129657 | + | 0.0347416i | ||||
\(889\) | 6.92820 | − | 12.0000i | 0.232364 | − | 0.402467i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.41421 | − | 1.41421i | −0.0473514 | − | 0.0473514i | ||||
\(893\) | −28.0812 | − | 11.1106i | −0.939702 | − | 0.371803i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.00000 | + | 1.73205i | −0.100223 | + | 0.0578638i | ||||
\(897\) | −1.79315 | − | 6.69213i | −0.0598716 | − | 0.223444i | ||||
\(898\) | 6.72432 | − | 25.0955i | 0.224393 | − | 0.837447i | ||||
\(899\) | 31.1769 | + | 18.0000i | 1.03981 | + | 0.600334i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.10583 | − | 11.5911i | −0.103356 | − | 0.385728i | ||||
\(904\) | − | 9.00000i | − | 0.299336i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.0000 | + | 10.3923i | 0.598010 | + | 0.345261i | ||||
\(907\) | 9.57630 | − | 35.7393i | 0.317976 | − | 1.18670i | −0.603211 | − | 0.797582i | \(-0.706112\pi\) |
0.921187 | − | 0.389121i | \(-0.127221\pi\) | |||||||
\(908\) | 6.98811 | + | 26.0800i | 0.231909 | + | 0.865495i | ||||
\(909\) | 10.3923 | − | 6.00000i | 0.344691 | − | 0.199007i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −4.05317 | − | 1.60368i | −0.134214 | − | 0.0531032i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −9.52628 | − | 16.5000i | −0.315101 | − | 0.545771i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.0000 | + | 19.0526i | −0.363450 | + | 0.629514i | ||||
\(917\) | 50.1910 | + | 13.4486i | 1.65745 | + | 0.444113i | ||||
\(918\) | 8.36516 | − | 2.24144i | 0.276092 | − | 0.0739785i | ||||
\(919\) | 32.0000i | 1.05558i | 0.849374 | + | 0.527791i | \(0.176980\pi\) | ||||
−0.849374 | + | 0.527791i | \(0.823020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.50000 | − | 9.52628i | 0.181231 | − | 0.313902i | ||||
\(922\) | 17.3867 | − | 4.65874i | 0.572599 | − | 0.153428i | ||||
\(923\) | 19.5959 | + | 19.5959i | 0.645007 | + | 0.645007i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.00000 | + | 5.19615i | −0.295758 | + | 0.170756i | ||||
\(927\) | −7.72741 | + | 2.07055i | −0.253801 | + | 0.0680059i | ||||
\(928\) | 0.896575 | − | 3.34607i | 0.0294315 | − | 0.109840i | ||||
\(929\) | −18.1865 | + | 10.5000i | −0.596681 | + | 0.344494i | −0.767735 | − | 0.640768i | \(-0.778616\pi\) |
0.171054 | + | 0.985262i | \(0.445283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5000 | − | 12.9904i | −0.573539 | − | 0.425743i | ||||
\(932\) | 15.9217 | − | 15.9217i | 0.521532 | − | 0.521532i | ||||
\(933\) | −28.9778 | − | 7.76457i | −0.948690 | − | 0.254201i | ||||
\(934\) | 18.1865 | + | 31.5000i | 0.595082 | + | 1.03071i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | − | 3.46410i | −0.0653720 | − | 0.113228i | ||||
\(937\) | 11.2072 | + | 41.8258i | 0.366123 | + | 1.36639i | 0.865892 | + | 0.500231i | \(0.166752\pi\) |
−0.499769 | + | 0.866159i | \(0.666582\pi\) | |||||||
\(938\) | −19.5959 | − | 19.5959i | −0.639829 | − | 0.639829i | ||||
\(939\) | −19.0526 | −0.621757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000 | + | 6.92820i | 0.391189 | + | 0.225853i | 0.682675 | − | 0.730722i | \(-0.260816\pi\) |
−0.291486 | + | 0.956575i | \(0.594150\pi\) | |||||||
\(942\) | 12.2474 | − | 12.2474i | 0.399043 | − | 0.399043i | ||||
\(943\) | 16.9706 | − | 16.9706i | 0.552638 | − | 0.552638i | ||||
\(944\) | 2.59808 | − | 4.50000i | 0.0845602 | − | 0.146463i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.8831 | − | 15.2418i | −1.84845 | − | 0.495291i | −0.849001 | − | 0.528392i | \(-0.822795\pi\) |
−0.999452 | + | 0.0331004i | \(0.989462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.3205 | −0.562247 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 1.55291 | − | 5.79555i | 0.0503302 | − | 0.187835i | ||||
\(953\) | 5.79555 | + | 1.55291i | 0.187736 | + | 0.0503038i | 0.351462 | − | 0.936202i | \(-0.385685\pi\) |
−0.163726 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | + | 15.5885i | −0.291081 | + | 0.504167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.7654 | + | 27.0000i | 1.51013 | + | 0.871875i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −77.0000 | −2.48387 | ||||||||
\(962\) | 5.65685 | + | 5.65685i | 0.182384 | + | 0.182384i | ||||
\(963\) | 7.76457 | + | 28.9778i | 0.250210 | + | 0.933796i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.00000 | + | 10.3923i | 0.193047 | + | 0.334367i | ||||
\(967\) | 26.7685 | + | 7.17260i | 0.860818 | + | 0.230655i | 0.662113 | − | 0.749404i | \(-0.269660\pi\) |
0.198705 | + | 0.980059i | \(0.436327\pi\) | |||||||
\(968\) | −7.77817 | + | 7.77817i | −0.250000 | + | 0.250000i | ||||
\(969\) | 6.92820 | − | 3.00000i | 0.222566 | − | 0.0963739i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5000 | − | 14.7224i | 0.818334 | − | 0.472465i | −0.0315077 | − | 0.999504i | \(-0.510031\pi\) |
0.849842 | + | 0.527038i | \(0.176698\pi\) | |||||||
\(972\) | −4.14110 | + | 15.4548i | −0.132826 | + | 0.495713i | ||||
\(973\) | −53.5370 | + | 14.3452i | −1.71632 | + | 0.459886i | ||||
\(974\) | 13.8564 | − | 8.00000i | 0.443988 | − | 0.256337i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | 4.24264 | + | 4.24264i | 0.135734 | + | 0.135734i | 0.771709 | − | 0.635975i | \(-0.219402\pi\) |
−0.635975 | + | 0.771709i | \(0.719402\pi\) | |||||||
\(978\) | −16.7303 | + | 4.48288i | −0.534977 | + | 0.143347i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 34.6410i | − | 1.10600i | ||||||
\(982\) | −23.1822 | + | 6.21166i | −0.739774 | + | 0.198222i | ||||
\(983\) | −57.9555 | − | 15.5291i | −1.84849 | − | 0.495303i | −0.849040 | − | 0.528328i | \(-0.822819\pi\) |
−0.999455 | + | 0.0330251i | \(0.989486\pi\) | |||||||
\(984\) | −3.46410 | + | 6.00000i | −0.110432 | + | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.00000 | + | 5.19615i | 0.0955395 | + | 0.165479i | ||||
\(987\) | −16.9706 | − | 16.9706i | −0.540179 | − | 0.540179i | ||||
\(988\) | −5.41662 | − | 6.83083i | −0.172326 | − | 0.217318i | ||||
\(989\) | − | 12.0000i | − | 0.381578i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0000 | + | 24.2487i | −1.33417 | + | 0.770286i | −0.985936 | − | 0.167121i | \(-0.946553\pi\) |
−0.348238 | + | 0.937406i | \(0.613220\pi\) | |||||||
\(992\) | 2.68973 | + | 10.0382i | 0.0853989 | + | 0.318713i | ||||
\(993\) | −1.34486 | + | 5.01910i | −0.0426779 | + | 0.159276i | ||||
\(994\) | −41.5692 | − | 24.0000i | −1.31850 | − | 0.761234i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1.73205i | − | 0.0548821i | ||||||
\(997\) | −6.27603 | − | 23.4225i | −0.198764 | − | 0.741797i | −0.991260 | − | 0.131920i | \(-0.957886\pi\) |
0.792497 | − | 0.609876i | \(-0.208781\pi\) | |||||||
\(998\) | 8.02339 | + | 29.9437i | 0.253976 | + | 0.947851i | ||||
\(999\) | − | 20.0000i | − | 0.632772i |
(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 | 950.2.q.c.943.1 | yes | 8 | |
5.2 | odd | 4 | inner | 950.2.q.c.107.1 | ✓ | 8 | |
5.3 | odd | 4 | inner | 950.2.q.c.107.2 | yes | 8 | |
5.4 | even | 2 | inner | 950.2.q.c.943.2 | yes | 8 | |
19.8 | odd | 6 | inner | 950.2.q.c.293.1 | yes | 8 | |
95.8 | even | 12 | inner | 950.2.q.c.407.2 | yes | 8 | |
95.27 | even | 12 | inner | 950.2.q.c.407.1 | yes | 8 | |
95.84 | odd | 6 | inner | 950.2.q.c.293.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.q.c.107.1 | ✓ | 8 | 5.2 | odd | 4 | inner | |
950.2.q.c.107.2 | yes | 8 | 5.3 | odd | 4 | inner | |
950.2.q.c.293.1 | yes | 8 | 19.8 | odd | 6 | inner | |
950.2.q.c.293.2 | yes | 8 | 95.84 | odd | 6 | inner | |
950.2.q.c.407.1 | yes | 8 | 95.27 | even | 12 | inner | |
950.2.q.c.407.2 | yes | 8 | 95.8 | even | 12 | inner | |
950.2.q.c.943.1 | yes | 8 | 1.1 | even | 1 | trivial | |
950.2.q.c.943.2 | yes | 8 | 5.4 | even | 2 | inner |