Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1099.6 | ||
Character | \(\chi\) | \(=\) | 1110.1099 |
Dual form | 1110.2.bb.d.1009.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.64155 | + | 1.51833i | 0.734123 | + | 0.679016i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.09384 | + | 0.631530i | 0.413434 | + | 0.238696i | 0.692264 | − | 0.721644i | \(-0.256613\pi\) |
−0.278830 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −2.18079 | − | 0.494135i | −0.689625 | − | 0.156259i | ||||
\(11\) | −4.99195 | −1.50513 | −0.752564 | − | 0.658519i | \(-0.771183\pi\) | ||||
−0.752564 | + | 0.658519i | \(0.771183\pi\) | |||||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | 4.64326 | + | 2.68079i | 1.28781 | + | 0.743516i | 0.978263 | − | 0.207368i | \(-0.0664898\pi\) |
0.309545 | + | 0.950885i | \(0.399823\pi\) | |||||||
\(14\) | −1.26306 | −0.337567 | ||||||||
\(15\) | −0.662460 | − | 2.13568i | −0.171046 | − | 0.551431i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.69192 | + | 2.13153i | −0.895422 | + | 0.516972i | −0.875712 | − | 0.482834i | \(-0.839608\pi\) |
−0.0197097 | + | 0.999806i | \(0.506274\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | −3.67492 | + | 6.36515i | −0.843085 | + | 1.46027i | 0.0441891 | + | 0.999023i | \(0.485930\pi\) |
−0.887274 | + | 0.461243i | \(0.847404\pi\) | |||||||
\(20\) | 2.13568 | − | 0.662460i | 0.477554 | − | 0.148130i | ||||
\(21\) | −0.631530 | − | 1.09384i | −0.137811 | − | 0.238696i | ||||
\(22\) | 4.32315 | − | 2.49597i | 0.921699 | − | 0.532143i | ||||
\(23\) | − | 7.94839i | − | 1.65735i | −0.559728 | − | 0.828677i | \(-0.689094\pi\) | ||
0.559728 | − | 0.828677i | \(-0.310906\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0.389366 | + | 4.98482i | 0.0778733 | + | 0.996963i | ||||
\(26\) | −5.36157 | −1.05149 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.09384 | − | 0.631530i | 0.206717 | − | 0.119348i | ||||
\(29\) | 0.263060 | 0.0488491 | 0.0244245 | − | 0.999702i | \(-0.492225\pi\) | ||||
0.0244245 | + | 0.999702i | \(0.492225\pi\) | |||||||
\(30\) | 1.64155 | + | 1.51833i | 0.299704 | + | 0.277207i | ||||
\(31\) | −8.35352 | −1.50034 | −0.750168 | − | 0.661247i | \(-0.770027\pi\) | ||||
−0.750168 | + | 0.661247i | \(0.770027\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 4.32315 | + | 2.49597i | 0.752564 | + | 0.434493i | ||||
\(34\) | 2.13153 | − | 3.69192i | 0.365554 | − | 0.633159i | ||||
\(35\) | 0.836727 | + | 2.69750i | 0.141433 | + | 0.455960i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.93579 | − | 1.32904i | 0.975839 | − | 0.218492i | ||||
\(38\) | − | 7.34984i | − | 1.19230i | ||||||
\(39\) | −2.68079 | − | 4.64326i | −0.429269 | − | 0.743516i | ||||
\(40\) | −1.51833 | + | 1.64155i | −0.240069 | + | 0.259552i | ||||
\(41\) | 3.74009 | − | 6.47803i | 0.584104 | − | 1.01170i | −0.410882 | − | 0.911689i | \(-0.634779\pi\) |
0.994986 | − | 0.100010i | \(-0.0318875\pi\) | |||||||
\(42\) | 1.09384 | + | 0.631530i | 0.168784 | + | 0.0974472i | ||||
\(43\) | 11.0032i | 1.67798i | 0.544150 | + | 0.838988i | \(0.316852\pi\) | ||||
−0.544150 | + | 0.838988i | \(0.683148\pi\) | |||||||
\(44\) | −2.49597 | + | 4.32315i | −0.376282 | + | 0.651740i | ||||
\(45\) | −0.494135 | + | 2.18079i | −0.0736613 | + | 0.325092i | ||||
\(46\) | 3.97419 | + | 6.88350i | 0.585963 | + | 1.01492i | ||||
\(47\) | 3.66980i | 0.535296i | 0.963517 | + | 0.267648i | \(0.0862464\pi\) | ||||
−0.963517 | + | 0.267648i | \(0.913754\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −2.70234 | − | 4.68059i | −0.386048 | − | 0.668656i | ||||
\(50\) | −2.82961 | − | 4.12229i | −0.400167 | − | 0.582980i | ||||
\(51\) | 4.26306 | 0.596948 | ||||||||
\(52\) | 4.64326 | − | 2.68079i | 0.643904 | − | 0.371758i | ||||
\(53\) | −7.06383 | + | 4.07831i | −0.970292 | + | 0.560198i | −0.899325 | − | 0.437280i | \(-0.855942\pi\) |
−0.0709668 | + | 0.997479i | \(0.522608\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −8.19452 | − | 7.57941i | −1.10495 | − | 1.02201i | ||||
\(56\) | −0.631530 | + | 1.09384i | −0.0843918 | + | 0.146171i | ||||
\(57\) | 6.36515 | − | 3.67492i | 0.843085 | − | 0.486755i | ||||
\(58\) | −0.227817 | + | 0.131530i | −0.0299138 | + | 0.0172708i | ||||
\(59\) | −2.45264 | − | 4.24810i | −0.319307 | − | 0.553055i | 0.661037 | − | 0.750353i | \(-0.270117\pi\) |
−0.980344 | + | 0.197298i | \(0.936783\pi\) | |||||||
\(60\) | −2.18079 | − | 0.494135i | −0.281538 | − | 0.0637926i | ||||
\(61\) | 0.390022 | − | 0.675539i | 0.0499373 | − | 0.0864939i | −0.839976 | − | 0.542623i | \(-0.817431\pi\) |
0.889914 | + | 0.456129i | \(0.150765\pi\) | |||||||
\(62\) | 7.23436 | − | 4.17676i | 0.918765 | − | 0.530449i | ||||
\(63\) | 1.26306i | 0.159131i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.55183 | + | 11.4506i | 0.440550 | + | 1.42028i | ||||
\(66\) | −4.99195 | −0.614466 | ||||||||
\(67\) | 3.05829 | + | 1.76570i | 0.373629 | + | 0.215715i | 0.675043 | − | 0.737779i | \(-0.264125\pi\) |
−0.301414 | + | 0.953494i | \(0.597458\pi\) | |||||||
\(68\) | 4.26306i | 0.516972i | ||||||||
\(69\) | −3.97419 | + | 6.88350i | −0.478437 | + | 0.828677i | ||||
\(70\) | −2.07338 | − | 1.91774i | −0.247816 | − | 0.229214i | ||||
\(71\) | −0.141422 | + | 0.244950i | −0.0167837 | + | 0.0290702i | −0.874295 | − | 0.485394i | \(-0.838676\pi\) |
0.857512 | + | 0.514465i | \(0.172009\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 1.54371i | 0.180677i | 0.995911 | + | 0.0903387i | \(0.0287950\pi\) | ||||
−0.995911 | + | 0.0903387i | \(0.971205\pi\) | |||||||
\(74\) | −4.47603 | + | 4.11888i | −0.520328 | + | 0.478810i | ||||
\(75\) | 2.15521 | − | 4.51166i | 0.248862 | − | 0.520962i | ||||
\(76\) | 3.67492 | + | 6.36515i | 0.421542 | + | 0.730133i | ||||
\(77\) | −5.46040 | − | 3.15256i | −0.622271 | − | 0.359268i | ||||
\(78\) | 4.64326 | + | 2.68079i | 0.525746 | + | 0.303539i | ||||
\(79\) | −4.05244 | + | 7.01903i | −0.455935 | + | 0.789703i | −0.998741 | − | 0.0501551i | \(-0.984028\pi\) |
0.542806 | + | 0.839858i | \(0.317362\pi\) | |||||||
\(80\) | 0.494135 | − | 2.18079i | 0.0552460 | − | 0.243819i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 7.48019i | 0.826048i | ||||||||
\(83\) | −11.9301 | + | 6.88783i | −1.30950 | + | 0.756038i | −0.982012 | − | 0.188819i | \(-0.939534\pi\) |
−0.327484 | + | 0.944857i | \(0.606201\pi\) | |||||||
\(84\) | −1.26306 | −0.137811 | ||||||||
\(85\) | −9.29683 | − | 2.10653i | −1.00838 | − | 0.228485i | ||||
\(86\) | −5.50161 | − | 9.52907i | −0.593254 | − | 1.02755i | ||||
\(87\) | −0.227817 | − | 0.131530i | −0.0244245 | − | 0.0141015i | ||||
\(88\) | − | 4.99195i | − | 0.532143i | ||||||
\(89\) | 6.52339 | + | 11.2988i | 0.691478 | + | 1.19768i | 0.971354 | + | 0.237639i | \(0.0763734\pi\) |
−0.279876 | + | 0.960036i | \(0.590293\pi\) | |||||||
\(90\) | −0.662460 | − | 2.13568i | −0.0698294 | − | 0.225121i | ||||
\(91\) | 3.38600 | + | 5.86472i | 0.354949 | + | 0.614789i | ||||
\(92\) | −6.88350 | − | 3.97419i | −0.717655 | − | 0.414338i | ||||
\(93\) | 7.23436 | + | 4.17676i | 0.750168 | + | 0.433110i | ||||
\(94\) | −1.83490 | − | 3.17814i | −0.189256 | − | 0.327800i | ||||
\(95\) | −15.6969 | + | 4.86898i | −1.61047 | + | 0.499546i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 6.02010i | 0.611249i | 0.952152 | + | 0.305624i | \(0.0988651\pi\) | ||||
−0.952152 | + | 0.305624i | \(0.901135\pi\) | |||||||
\(98\) | 4.68059 | + | 2.70234i | 0.472811 | + | 0.272977i | ||||
\(99\) | −2.49597 | − | 4.32315i | −0.250855 | − | 0.434493i | ||||
\(100\) | 4.51166 | + | 2.15521i | 0.451166 | + | 0.215521i | ||||
\(101\) | −19.5101 | −1.94133 | −0.970665 | − | 0.240435i | \(-0.922710\pi\) | ||||
−0.970665 | + | 0.240435i | \(0.922710\pi\) | |||||||
\(102\) | −3.69192 | + | 2.13153i | −0.365554 | + | 0.211053i | ||||
\(103\) | − | 8.49192i | − | 0.836733i | −0.908278 | − | 0.418367i | \(-0.862603\pi\) | ||
0.908278 | − | 0.418367i | \(-0.137397\pi\) | |||||||
\(104\) | −2.68079 | + | 4.64326i | −0.262873 | + | 0.455309i | ||||
\(105\) | 0.624123 | − | 2.75447i | 0.0609081 | − | 0.268808i | ||||
\(106\) | 4.07831 | − | 7.06383i | 0.396120 | − | 0.686100i | ||||
\(107\) | 13.5483 | + | 7.82214i | 1.30977 | + | 0.756195i | 0.982057 | − | 0.188583i | \(-0.0603896\pi\) |
0.327711 | + | 0.944778i | \(0.393723\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 5.13717 | + | 8.89784i | 0.492051 | + | 0.852258i | 0.999958 | − | 0.00915400i | \(-0.00291385\pi\) |
−0.507907 | + | 0.861412i | \(0.669581\pi\) | |||||||
\(110\) | 10.8864 | + | 2.46670i | 1.03797 | + | 0.235190i | ||||
\(111\) | −5.80507 | − | 1.81692i | −0.550993 | − | 0.172454i | ||||
\(112\) | − | 1.26306i | − | 0.119348i | ||||||
\(113\) | −15.6594 | + | 9.04098i | −1.47312 | + | 0.850503i | −0.999542 | − | 0.0302513i | \(-0.990369\pi\) |
−0.473573 | + | 0.880755i | \(0.657036\pi\) | |||||||
\(114\) | −3.67492 | + | 6.36515i | −0.344188 | + | 0.596151i | ||||
\(115\) | 12.0682 | − | 13.0477i | 1.12537 | − | 1.21670i | ||||
\(116\) | 0.131530 | − | 0.227817i | 0.0122123 | − | 0.0211523i | ||||
\(117\) | 5.36157i | 0.495678i | ||||||||
\(118\) | 4.24810 | + | 2.45264i | 0.391069 | + | 0.225784i | ||||
\(119\) | −5.38450 | −0.493597 | ||||||||
\(120\) | 2.13568 | − | 0.662460i | 0.194960 | − | 0.0604740i | ||||
\(121\) | 13.9195 | 1.26541 | ||||||||
\(122\) | 0.780045i | 0.0706219i | ||||||||
\(123\) | −6.47803 | + | 3.74009i | −0.584104 | + | 0.337233i | ||||
\(124\) | −4.17676 | + | 7.23436i | −0.375084 | + | 0.649665i | ||||
\(125\) | −6.92942 | + | 8.77401i | −0.619786 | + | 0.784771i | ||||
\(126\) | −0.631530 | − | 1.09384i | −0.0562612 | − | 0.0974472i | ||||
\(127\) | −3.82426 | + | 2.20794i | −0.339348 | + | 0.195923i | −0.659984 | − | 0.751280i | \(-0.729437\pi\) |
0.320635 | + | 0.947203i | \(0.396104\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.50161 | − | 9.52907i | 0.484390 | − | 0.838988i | ||||
\(130\) | −8.80129 | − | 8.14062i | −0.771924 | − | 0.713980i | ||||
\(131\) | 4.83306 | + | 8.37111i | 0.422267 | + | 0.731388i | 0.996161 | − | 0.0875420i | \(-0.0279012\pi\) |
−0.573894 | + | 0.818930i | \(0.694568\pi\) | |||||||
\(132\) | 4.32315 | − | 2.49597i | 0.376282 | − | 0.217247i | ||||
\(133\) | −8.03957 | + | 4.64165i | −0.697119 | + | 0.402482i | ||||
\(134\) | −3.53141 | −0.305067 | ||||||||
\(135\) | 1.51833 | − | 1.64155i | 0.130677 | − | 0.141282i | ||||
\(136\) | −2.13153 | − | 3.69192i | −0.182777 | − | 0.316579i | ||||
\(137\) | − | 14.3318i | − | 1.22445i | −0.790684 | − | 0.612225i | \(-0.790275\pi\) | ||
0.790684 | − | 0.612225i | \(-0.209725\pi\) | |||||||
\(138\) | − | 7.94839i | − | 0.676612i | ||||||
\(139\) | −3.79794 | − | 6.57823i | −0.322137 | − | 0.557958i | 0.658791 | − | 0.752326i | \(-0.271068\pi\) |
−0.980929 | + | 0.194367i | \(0.937735\pi\) | |||||||
\(140\) | 2.75447 | + | 0.624123i | 0.232795 | + | 0.0527480i | ||||
\(141\) | 1.83490 | − | 3.17814i | 0.154527 | − | 0.267648i | ||||
\(142\) | − | 0.282844i | − | 0.0237357i | ||||||
\(143\) | −23.1789 | − | 13.3823i | −1.93832 | − | 1.11909i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0.431826 | + | 0.399412i | 0.0358612 | + | 0.0331693i | ||||
\(146\) | −0.771854 | − | 1.33689i | −0.0638791 | − | 0.110642i | ||||
\(147\) | 5.40468i | 0.445770i | ||||||||
\(148\) | 1.81692 | − | 5.80507i | 0.149350 | − | 0.477174i | ||||
\(149\) | −2.64733 | −0.216877 | −0.108439 | − | 0.994103i | \(-0.534585\pi\) | ||||
−0.108439 | + | 0.994103i | \(0.534585\pi\) | |||||||
\(150\) | 0.389366 | + | 4.98482i | 0.0317916 | + | 0.407009i | ||||
\(151\) | −2.35137 | + | 4.07269i | −0.191352 | + | 0.331431i | −0.945698 | − | 0.325045i | \(-0.894620\pi\) |
0.754347 | + | 0.656476i | \(0.227954\pi\) | |||||||
\(152\) | −6.36515 | − | 3.67492i | −0.516282 | − | 0.298076i | ||||
\(153\) | −3.69192 | − | 2.13153i | −0.298474 | − | 0.172324i | ||||
\(154\) | 6.30513 | 0.508082 | ||||||||
\(155\) | −13.7127 | − | 12.6834i | −1.10143 | − | 1.01875i | ||||
\(156\) | −5.36157 | −0.429269 | ||||||||
\(157\) | 11.7867 | − | 6.80507i | 0.940683 | − | 0.543104i | 0.0505086 | − | 0.998724i | \(-0.483916\pi\) |
0.890174 | + | 0.455620i | \(0.150582\pi\) | |||||||
\(158\) | − | 8.10488i | − | 0.644790i | ||||||
\(159\) | 8.15661 | 0.646861 | ||||||||
\(160\) | 0.662460 | + | 2.13568i | 0.0523720 | + | 0.168841i | ||||
\(161\) | 5.01965 | − | 8.69428i | 0.395604 | − | 0.685205i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 10.5279 | − | 6.07828i | 0.824609 | − | 0.476088i | −0.0273945 | − | 0.999625i | \(-0.508721\pi\) |
0.852003 | + | 0.523537i | \(0.175388\pi\) | |||||||
\(164\) | −3.74009 | − | 6.47803i | −0.292052 | − | 0.505849i | ||||
\(165\) | 3.30696 | + | 10.6612i | 0.257447 | + | 0.829975i | ||||
\(166\) | 6.88783 | − | 11.9301i | 0.534600 | − | 0.925954i | ||||
\(167\) | 17.1266 | + | 9.88805i | 1.32530 | + | 0.765160i | 0.984568 | − | 0.175001i | \(-0.0559930\pi\) |
0.340728 | + | 0.940162i | \(0.389326\pi\) | |||||||
\(168\) | 1.09384 | − | 0.631530i | 0.0843918 | − | 0.0487236i | ||||
\(169\) | 7.87323 | + | 13.6368i | 0.605633 | + | 1.04899i | ||||
\(170\) | 9.10455 | − | 2.82411i | 0.698287 | − | 0.216599i | ||||
\(171\) | −7.34984 | −0.562057 | ||||||||
\(172\) | 9.52907 | + | 5.50161i | 0.726585 | + | 0.419494i | ||||
\(173\) | 4.03173 | − | 2.32772i | 0.306527 | − | 0.176973i | −0.338844 | − | 0.940842i | \(-0.610036\pi\) |
0.645371 | + | 0.763869i | \(0.276703\pi\) | |||||||
\(174\) | 0.263060 | 0.0199426 | ||||||||
\(175\) | −2.72216 | + | 5.69850i | −0.205776 | + | 0.430766i | ||||
\(176\) | 2.49597 | + | 4.32315i | 0.188141 | + | 0.325870i | ||||
\(177\) | 4.90528i | 0.368704i | ||||||||
\(178\) | −11.2988 | − | 6.52339i | −0.846884 | − | 0.488949i | ||||
\(179\) | 18.0339 | 1.34792 | 0.673958 | − | 0.738770i | \(-0.264593\pi\) | ||||
0.673958 | + | 0.738770i | \(0.264593\pi\) | |||||||
\(180\) | 1.64155 | + | 1.51833i | 0.122354 | + | 0.113169i | ||||
\(181\) | 6.41934 | − | 11.1186i | 0.477146 | − | 0.826440i | −0.522511 | − | 0.852632i | \(-0.675005\pi\) |
0.999657 | + | 0.0261920i | \(0.00833811\pi\) | |||||||
\(182\) | −5.86472 | − | 3.38600i | −0.434722 | − | 0.250987i | ||||
\(183\) | −0.675539 | + | 0.390022i | −0.0499373 | + | 0.0288313i | ||||
\(184\) | 7.94839 | 0.585963 | ||||||||
\(185\) | 11.7618 | + | 6.83080i | 0.864745 | + | 0.502210i | ||||
\(186\) | −8.35352 | −0.612510 | ||||||||
\(187\) | 18.4299 | − | 10.6405i | 1.34772 | − | 0.778109i | ||||
\(188\) | 3.17814 | + | 1.83490i | 0.231790 | + | 0.133824i | ||||
\(189\) | 0.631530 | − | 1.09384i | 0.0459371 | − | 0.0795653i | ||||
\(190\) | 11.1595 | − | 12.0651i | 0.809593 | − | 0.875296i | ||||
\(191\) | −4.45352 | −0.322246 | −0.161123 | − | 0.986934i | \(-0.551512\pi\) | ||||
−0.161123 | + | 0.986934i | \(0.551512\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 8.79974i | 0.633419i | 0.948523 | + | 0.316709i | \(0.102578\pi\) | ||||
−0.948523 | + | 0.316709i | \(0.897422\pi\) | |||||||
\(194\) | −3.01005 | − | 5.21356i | −0.216109 | − | 0.374312i | ||||
\(195\) | 2.64934 | − | 11.6924i | 0.189723 | − | 0.837314i | ||||
\(196\) | −5.40468 | −0.386048 | ||||||||
\(197\) | 7.01557 | − | 4.05044i | 0.499839 | − | 0.288582i | −0.228808 | − | 0.973472i | \(-0.573483\pi\) |
0.728647 | + | 0.684889i | \(0.240149\pi\) | |||||||
\(198\) | 4.32315 | + | 2.49597i | 0.307233 | + | 0.177381i | ||||
\(199\) | 0.881703 | 0.0625023 | 0.0312511 | − | 0.999512i | \(-0.490051\pi\) | ||||
0.0312511 | + | 0.999512i | \(0.490051\pi\) | |||||||
\(200\) | −4.98482 | + | 0.389366i | −0.352480 | + | 0.0275324i | ||||
\(201\) | −1.76570 | − | 3.05829i | −0.124543 | − | 0.215715i | ||||
\(202\) | 16.8963 | − | 9.75507i | 1.18882 | − | 0.686364i | ||||
\(203\) | 0.287747 | + | 0.166131i | 0.0201959 | + | 0.0116601i | ||||
\(204\) | 2.13153 | − | 3.69192i | 0.149237 | − | 0.258486i | ||||
\(205\) | 15.9753 | − | 4.95532i | 1.11576 | − | 0.346095i | ||||
\(206\) | 4.24596 | + | 7.35421i | 0.295830 | + | 0.512392i | ||||
\(207\) | 6.88350 | − | 3.97419i | 0.478437 | − | 0.276226i | ||||
\(208\) | − | 5.36157i | − | 0.371758i | ||||||
\(209\) | 18.3450 | − | 31.7745i | 1.26895 | − | 2.19789i | ||||
\(210\) | 0.836727 | + | 2.69750i | 0.0577396 | + | 0.186145i | ||||
\(211\) | −20.2451 | −1.39373 | −0.696866 | − | 0.717201i | \(-0.745423\pi\) | ||||
−0.696866 | + | 0.717201i | \(0.745423\pi\) | |||||||
\(212\) | 8.15661i | 0.560198i | ||||||||
\(213\) | 0.244950 | − | 0.141422i | 0.0167837 | − | 0.00969008i | ||||
\(214\) | −15.6443 | −1.06942 | ||||||||
\(215\) | −16.7065 | + | 18.0623i | −1.13937 | + | 1.23184i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −9.13743 | − | 5.27550i | −0.620289 | − | 0.358124i | ||||
\(218\) | −8.89784 | − | 5.13717i | −0.602637 | − | 0.347933i | ||||
\(219\) | 0.771854 | − | 1.33689i | 0.0521571 | − | 0.0903387i | ||||
\(220\) | −10.6612 | + | 3.30696i | −0.718779 | + | 0.222955i | ||||
\(221\) | −22.8567 | −1.53751 | ||||||||
\(222\) | 5.93579 | − | 1.32904i | 0.398384 | − | 0.0891991i | ||||
\(223\) | − | 18.1705i | − | 1.21679i | −0.793635 | − | 0.608394i | \(-0.791814\pi\) | ||
0.793635 | − | 0.608394i | \(-0.208186\pi\) | |||||||
\(224\) | 0.631530 | + | 1.09384i | 0.0421959 | + | 0.0730854i | ||||
\(225\) | −4.12229 | + | 2.82961i | −0.274820 | + | 0.188641i | ||||
\(226\) | 9.04098 | − | 15.6594i | 0.601397 | − | 1.04165i | ||||
\(227\) | 9.88733 | + | 5.70845i | 0.656245 | + | 0.378883i | 0.790845 | − | 0.612017i | \(-0.209642\pi\) |
−0.134600 | + | 0.990900i | \(0.542975\pi\) | |||||||
\(228\) | − | 7.34984i | − | 0.486755i | ||||||
\(229\) | 7.27924 | − | 12.6080i | 0.481026 | − | 0.833161i | −0.518737 | − | 0.854934i | \(-0.673598\pi\) |
0.999763 | + | 0.0217727i | \(0.00693103\pi\) | |||||||
\(230\) | −3.92758 | + | 17.3337i | −0.258977 | + | 1.14295i | ||||
\(231\) | 3.15256 | + | 5.46040i | 0.207424 | + | 0.359268i | ||||
\(232\) | 0.263060i | 0.0172708i | ||||||||
\(233\) | 2.82229i | 0.184895i | 0.995718 | + | 0.0924473i | \(0.0294690\pi\) | ||||
−0.995718 | + | 0.0924473i | \(0.970531\pi\) | |||||||
\(234\) | −2.68079 | − | 4.64326i | −0.175249 | − | 0.303539i | ||||
\(235\) | −5.57196 | + | 6.02416i | −0.363475 | + | 0.392973i | ||||
\(236\) | −4.90528 | −0.319307 | ||||||||
\(237\) | 7.01903 | − | 4.05244i | 0.455935 | − | 0.263234i | ||||
\(238\) | 4.66312 | − | 2.69225i | 0.302265 | − | 0.174513i | ||||
\(239\) | 11.2761 | + | 19.5308i | 0.729390 | + | 1.26334i | 0.957141 | + | 0.289621i | \(0.0935294\pi\) |
−0.227751 | + | 0.973719i | \(0.573137\pi\) | |||||||
\(240\) | −1.51833 | + | 1.64155i | −0.0980076 | + | 0.105962i | ||||
\(241\) | −2.91315 | + | 5.04572i | −0.187652 | + | 0.325023i | −0.944467 | − | 0.328606i | \(-0.893421\pi\) |
0.756815 | + | 0.653629i | \(0.226754\pi\) | |||||||
\(242\) | −12.0547 | + | 6.95976i | −0.774903 | + | 0.447390i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −0.390022 | − | 0.675539i | −0.0249686 | − | 0.0432469i | ||||
\(245\) | 2.67064 | − | 11.7865i | 0.170621 | − | 0.753009i | ||||
\(246\) | 3.74009 | − | 6.47803i | 0.238460 | − | 0.413024i | ||||
\(247\) | −34.1272 | + | 19.7034i | −2.17146 | + | 1.25369i | ||||
\(248\) | − | 8.35352i | − | 0.530449i | ||||||
\(249\) | 13.7757 | 0.872997 | ||||||||
\(250\) | 1.61405 | − | 11.0632i | 0.102081 | − | 0.699700i | ||||
\(251\) | 20.3308 | 1.28327 | 0.641633 | − | 0.767012i | \(-0.278257\pi\) | ||||
0.641633 | + | 0.767012i | \(0.278257\pi\) | |||||||
\(252\) | 1.09384 | + | 0.631530i | 0.0689056 | + | 0.0397827i | ||||
\(253\) | 39.6779i | 2.49453i | ||||||||
\(254\) | 2.20794 | − | 3.82426i | 0.138538 | − | 0.239956i | ||||
\(255\) | 6.99802 | + | 6.47272i | 0.438233 | + | 0.405337i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.32463 | + | 4.80623i | −0.519276 | + | 0.299804i | −0.736638 | − | 0.676287i | \(-0.763588\pi\) |
0.217362 | + | 0.976091i | \(0.430255\pi\) | |||||||
\(258\) | 11.0032i | 0.685031i | ||||||||
\(259\) | 7.33215 | + | 2.29488i | 0.455598 | + | 0.142597i | ||||
\(260\) | 11.6924 | + | 2.64934i | 0.725135 | + | 0.164305i | ||||
\(261\) | 0.131530 | + | 0.227817i | 0.00814151 | + | 0.0141015i | ||||
\(262\) | −8.37111 | − | 4.83306i | −0.517169 | − | 0.298588i | ||||
\(263\) | 4.05962 | + | 2.34382i | 0.250327 | + | 0.144526i | 0.619914 | − | 0.784670i | \(-0.287168\pi\) |
−0.369587 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(264\) | −2.49597 | + | 4.32315i | −0.153617 | + | 0.266072i | ||||
\(265\) | −17.7878 | − | 4.03047i | −1.09270 | − | 0.247590i | ||||
\(266\) | 4.64165 | − | 8.03957i | 0.284598 | − | 0.492938i | ||||
\(267\) | − | 13.0468i | − | 0.798450i | ||||||
\(268\) | 3.05829 | − | 1.76570i | 0.186815 | − | 0.107857i | ||||
\(269\) | 18.0324 | 1.09945 | 0.549727 | − | 0.835344i | \(-0.314732\pi\) | ||||
0.549727 | + | 0.835344i | \(0.314732\pi\) | |||||||
\(270\) | −0.494135 | + | 2.18079i | −0.0300721 | + | 0.132718i | ||||
\(271\) | 1.40902 | + | 2.44050i | 0.0855920 | + | 0.148250i | 0.905643 | − | 0.424040i | \(-0.139389\pi\) |
−0.820051 | + | 0.572290i | \(0.806055\pi\) | |||||||
\(272\) | 3.69192 | + | 2.13153i | 0.223855 | + | 0.129243i | ||||
\(273\) | − | 6.77199i | − | 0.409860i | ||||||
\(274\) | 7.16590 | + | 12.4117i | 0.432908 | + | 0.749819i | ||||
\(275\) | −1.94370 | − | 24.8839i | −0.117209 | − | 1.50056i | ||||
\(276\) | 3.97419 | + | 6.88350i | 0.239218 | + | 0.414338i | ||||
\(277\) | −16.3046 | − | 9.41347i | −0.979649 | − | 0.565601i | −0.0774850 | − | 0.996994i | \(-0.524689\pi\) |
−0.902164 | + | 0.431393i | \(0.858022\pi\) | |||||||
\(278\) | 6.57823 | + | 3.79794i | 0.394536 | + | 0.227786i | ||||
\(279\) | −4.17676 | − | 7.23436i | −0.250056 | − | 0.433110i | ||||
\(280\) | −2.69750 | + | 0.836727i | −0.161206 | + | 0.0500040i | ||||
\(281\) | 8.14090 | + | 14.1005i | 0.485646 | + | 0.841163i | 0.999864 | − | 0.0164965i | \(-0.00525125\pi\) |
−0.514218 | + | 0.857659i | \(0.671918\pi\) | |||||||
\(282\) | 3.66980i | 0.218534i | ||||||||
\(283\) | 9.11635 | + | 5.26333i | 0.541911 | + | 0.312872i | 0.745853 | − | 0.666111i | \(-0.232042\pi\) |
−0.203942 | + | 0.978983i | \(0.565376\pi\) | |||||||
\(284\) | 0.141422 | + | 0.244950i | 0.00839185 | + | 0.0145351i | ||||
\(285\) | 16.0284 | + | 3.63182i | 0.949443 | + | 0.215130i | ||||
\(286\) | 26.7647 | 1.58263 | ||||||||
\(287\) | 8.18214 | − | 4.72396i | 0.482977 | − | 0.278847i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 0.586842 | − | 1.01644i | 0.0345201 | − | 0.0597906i | ||||
\(290\) | −0.573679 | − | 0.129987i | −0.0336876 | − | 0.00763312i | ||||
\(291\) | 3.01005 | − | 5.21356i | 0.176452 | − | 0.305624i | ||||
\(292\) | 1.33689 | + | 0.771854i | 0.0782356 | + | 0.0451693i | ||||
\(293\) | 4.47258 | + | 2.58224i | 0.261291 | + | 0.150856i | 0.624923 | − | 0.780686i | \(-0.285130\pi\) |
−0.363632 | + | 0.931542i | \(0.618464\pi\) | |||||||
\(294\) | −2.70234 | − | 4.68059i | −0.157604 | − | 0.272977i | ||||
\(295\) | 2.42387 | − | 10.6974i | 0.141123 | − | 0.622825i | ||||
\(296\) | 1.32904 | + | 5.93579i | 0.0772487 | + | 0.345011i | ||||
\(297\) | 4.99195i | 0.289662i | ||||||||
\(298\) | 2.29265 | − | 1.32366i | 0.132810 | − | 0.0766778i | ||||
\(299\) | 21.3079 | − | 36.9064i | 1.23227 | − | 2.13435i | ||||
\(300\) | −2.82961 | − | 4.12229i | −0.163368 | − | 0.238001i | ||||
\(301\) | −6.94887 | + | 12.0358i | −0.400526 | + | 0.693731i | ||||
\(302\) | − | 4.70273i | − | 0.270612i | ||||||
\(303\) | 16.8963 | + | 9.75507i | 0.970665 | + | 0.560414i | ||||
\(304\) | 7.34984 | 0.421542 | ||||||||
\(305\) | 1.66593 | − | 0.516748i | 0.0953908 | − | 0.0295889i | ||||
\(306\) | 4.26306 | 0.243703 | ||||||||
\(307\) | − | 15.5648i | − | 0.888333i | −0.895944 | − | 0.444166i | \(-0.853500\pi\) | ||
0.895944 | − | 0.444166i | \(-0.146500\pi\) | |||||||
\(308\) | −5.46040 | + | 3.15256i | −0.311135 | + | 0.179634i | ||||
\(309\) | −4.24596 | + | 7.35421i | −0.241544 | + | 0.418367i | ||||
\(310\) | 18.2172 | + | 4.12777i | 1.03467 | + | 0.234441i | ||||
\(311\) | −8.92380 | − | 15.4565i | −0.506022 | − | 0.876456i | −0.999976 | − | 0.00696784i | \(-0.997782\pi\) |
0.493954 | − | 0.869488i | \(-0.335551\pi\) | |||||||
\(312\) | 4.64326 | − | 2.68079i | 0.262873 | − | 0.151770i | ||||
\(313\) | 5.50514 | − | 3.17839i | 0.311169 | − | 0.179653i | −0.336281 | − | 0.941762i | \(-0.609169\pi\) |
0.647449 | + | 0.762108i | \(0.275836\pi\) | |||||||
\(314\) | −6.80507 | + | 11.7867i | −0.384032 | + | 0.665163i | ||||
\(315\) | −1.91774 | + | 2.07338i | −0.108052 | + | 0.116821i | ||||
\(316\) | 4.05244 | + | 7.01903i | 0.227968 | + | 0.394851i | ||||
\(317\) | 13.7824 | − | 7.95728i | 0.774097 | − | 0.446925i | −0.0602370 | − | 0.998184i | \(-0.519186\pi\) |
0.834334 | + | 0.551259i | \(0.185852\pi\) | |||||||
\(318\) | −7.06383 | + | 4.07831i | −0.396120 | + | 0.228700i | ||||
\(319\) | −1.31318 | −0.0735241 | ||||||||
\(320\) | −1.64155 | − | 1.51833i | −0.0917654 | − | 0.0848771i | ||||
\(321\) | −7.82214 | − | 13.5483i | −0.436589 | − | 0.756195i | ||||
\(322\) | 10.0393i | 0.559468i | ||||||||
\(323\) | − | 31.3328i | − | 1.74341i | ||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −11.5553 | + | 24.1896i | −0.640973 | + | 1.34180i | ||||
\(326\) | −6.07828 | + | 10.5279i | −0.336645 | + | 0.583086i | ||||
\(327\) | − | 10.2743i | − | 0.568172i | ||||||
\(328\) | 6.47803 | + | 3.74009i | 0.357689 | + | 0.206512i | ||||
\(329\) | −2.31759 | + | 4.01419i | −0.127773 | + | 0.221309i | ||||
\(330\) | −8.19452 | − | 7.57941i | −0.451094 | − | 0.417233i | ||||
\(331\) | 3.96108 | + | 6.86079i | 0.217721 | + | 0.377103i | 0.954111 | − | 0.299454i | \(-0.0968045\pi\) |
−0.736390 | + | 0.676557i | \(0.763471\pi\) | |||||||
\(332\) | 13.7757i | 0.756038i | ||||||||
\(333\) | 4.11888 | + | 4.47603i | 0.225713 | + | 0.245285i | ||||
\(334\) | −19.7761 | −1.08210 | ||||||||
\(335\) | 2.33941 | + | 7.54197i | 0.127816 | + | 0.412062i | ||||
\(336\) | −0.631530 | + | 1.09384i | −0.0344528 | + | 0.0596740i | ||||
\(337\) | 30.5973 | + | 17.6654i | 1.66674 | + | 0.962295i | 0.969376 | + | 0.245581i | \(0.0789787\pi\) |
0.697367 | + | 0.716714i | \(0.254355\pi\) | |||||||
\(338\) | −13.6368 | − | 7.87323i | −0.741746 | − | 0.428247i | ||||
\(339\) | 18.0820 | 0.982077 | ||||||||
\(340\) | −6.47272 | + | 6.99802i | −0.351033 | + | 0.379521i | ||||
\(341\) | 41.7003 | 2.25820 | ||||||||
\(342\) | 6.36515 | − | 3.67492i | 0.344188 | − | 0.198717i | ||||
\(343\) | − | 15.6679i | − | 0.845985i | ||||||
\(344\) | −11.0032 | −0.593254 | ||||||||
\(345\) | −16.9752 | + | 5.26549i | −0.913916 | + | 0.283484i | ||||
\(346\) | −2.32772 | + | 4.03173i | −0.125139 | + | 0.216747i | ||||
\(347\) | − | 3.87172i | − | 0.207845i | −0.994585 | − | 0.103923i | \(-0.966861\pi\) | ||
0.994585 | − | 0.103923i | \(-0.0331394\pi\) | |||||||
\(348\) | −0.227817 | + | 0.131530i | −0.0122123 | + | 0.00705076i | ||||
\(349\) | −7.16648 | − | 12.4127i | −0.383613 | − | 0.664437i | 0.607963 | − | 0.793966i | \(-0.291987\pi\) |
−0.991576 | + | 0.129528i | \(0.958654\pi\) | |||||||
\(350\) | −0.491793 | − | 6.29612i | −0.0262875 | − | 0.336542i | ||||
\(351\) | 2.68079 | − | 4.64326i | 0.143090 | − | 0.247839i | ||||
\(352\) | −4.32315 | − | 2.49597i | −0.230425 | − | 0.133036i | ||||
\(353\) | −1.29700 | + | 0.748825i | −0.0690325 | + | 0.0398559i | −0.534119 | − | 0.845409i | \(-0.679357\pi\) |
0.465086 | + | 0.885265i | \(0.346023\pi\) | |||||||
\(354\) | −2.45264 | − | 4.24810i | −0.130356 | − | 0.225784i | ||||
\(355\) | −0.604066 | + | 0.187373i | −0.0320605 | + | 0.00994471i | ||||
\(356\) | 13.0468 | 0.691478 | ||||||||
\(357\) | 4.66312 | + | 2.69225i | 0.246798 | + | 0.142489i | ||||
\(358\) | −15.6178 | + | 9.01694i | −0.825426 | + | 0.476560i | ||||
\(359\) | −8.83396 | −0.466239 | −0.233119 | − | 0.972448i | \(-0.574893\pi\) | ||||
−0.233119 | + | 0.972448i | \(0.574893\pi\) | |||||||
\(360\) | −2.18079 | − | 0.494135i | −0.114938 | − | 0.0260432i | ||||
\(361\) | −17.5101 | − | 30.3284i | −0.921584 | − | 1.59623i | ||||
\(362\) | 12.8387i | 0.674786i | ||||||||
\(363\) | −12.0547 | − | 6.95976i | −0.632706 | − | 0.365293i | ||||
\(364\) | 6.77199 | 0.354949 | ||||||||
\(365\) | −2.34385 | + | 2.53407i | −0.122683 | + | 0.132639i | ||||
\(366\) | 0.390022 | − | 0.675539i | 0.0203868 | − | 0.0353110i | ||||
\(367\) | 15.9066 | + | 9.18365i | 0.830315 | + | 0.479383i | 0.853961 | − | 0.520338i | \(-0.174194\pi\) |
−0.0236452 | + | 0.999720i | \(0.507527\pi\) | |||||||
\(368\) | −6.88350 | + | 3.97419i | −0.358827 | + | 0.207169i | ||||
\(369\) | 7.48019 | 0.389403 | ||||||||
\(370\) | −13.6014 | − | 0.0347405i | −0.707104 | − | 0.00180607i | ||||
\(371\) | −10.3023 | −0.534868 | ||||||||
\(372\) | 7.23436 | − | 4.17676i | 0.375084 | − | 0.216555i | ||||
\(373\) | 7.08648 | + | 4.09138i | 0.366924 | + | 0.211844i | 0.672114 | − | 0.740448i | \(-0.265387\pi\) |
−0.305190 | + | 0.952292i | \(0.598720\pi\) | |||||||
\(374\) | −10.6405 | + | 18.4299i | −0.550206 | + | 0.952985i | ||||
\(375\) | 10.3881 | − | 4.13380i | 0.536437 | − | 0.213469i | ||||
\(376\) | −3.66980 | −0.189256 | ||||||||
\(377\) | 1.22146 | + | 0.705209i | 0.0629083 | + | 0.0363201i | ||||
\(378\) | 1.26306i | 0.0649648i | ||||||||
\(379\) | −13.6863 | − | 23.7054i | −0.703019 | − | 1.21766i | −0.967402 | − | 0.253247i | \(-0.918502\pi\) |
0.264383 | − | 0.964418i | \(-0.414832\pi\) | |||||||
\(380\) | −3.63182 | + | 16.0284i | −0.186308 | + | 0.822242i | ||||
\(381\) | 4.41588 | 0.226232 | ||||||||
\(382\) | 3.85686 | − | 2.22676i | 0.197334 | − | 0.113931i | ||||
\(383\) | −29.9910 | − | 17.3153i | −1.53247 | − | 0.884771i | −0.999247 | − | 0.0387959i | \(-0.987648\pi\) |
−0.533222 | − | 0.845975i | \(-0.679019\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.17689 | − | 13.4658i | −0.212874 | − | 0.686279i | ||||
\(386\) | −4.39987 | − | 7.62080i | −0.223947 | − | 0.387888i | ||||
\(387\) | −9.52907 | + | 5.50161i | −0.484390 | + | 0.279663i | ||||
\(388\) | 5.21356 | + | 3.01005i | 0.264678 | + | 0.152812i | ||||
\(389\) | −10.0409 | + | 17.3913i | −0.509093 | + | 0.881775i | 0.490851 | + | 0.871243i | \(0.336686\pi\) |
−0.999945 | + | 0.0105319i | \(0.996648\pi\) | |||||||
\(390\) | 3.55183 | + | 11.4506i | 0.179854 | + | 0.579825i | ||||
\(391\) | 16.9422 | + | 29.3448i | 0.856805 | + | 1.48403i | ||||
\(392\) | 4.68059 | − | 2.70234i | 0.236405 | − | 0.136489i | ||||
\(393\) | − | 9.66613i | − | 0.487592i | ||||||
\(394\) | −4.05044 | + | 7.01557i | −0.204058 | + | 0.353440i | ||||
\(395\) | −17.3095 | + | 5.36916i | −0.870934 | + | 0.270152i | ||||
\(396\) | −4.99195 | −0.250855 | ||||||||
\(397\) | 19.1670i | 0.961964i | 0.876730 | + | 0.480982i | \(0.159720\pi\) | ||||
−0.876730 | + | 0.480982i | \(0.840280\pi\) | |||||||
\(398\) | −0.763578 | + | 0.440852i | −0.0382747 | + | 0.0220979i | ||||
\(399\) | 9.28330 | 0.464746 | ||||||||
\(400\) | 4.12229 | − | 2.82961i | 0.206115 | − | 0.141480i | ||||
\(401\) | −2.28974 | −0.114344 | −0.0571721 | − | 0.998364i | \(-0.518208\pi\) | ||||
−0.0571721 | + | 0.998364i | \(0.518208\pi\) | |||||||
\(402\) | 3.05829 | + | 1.76570i | 0.152533 | + | 0.0880653i | ||||
\(403\) | −38.7876 | − | 22.3940i | −1.93215 | − | 1.11552i | ||||
\(404\) | −9.75507 | + | 16.8963i | −0.485333 | + | 0.840621i | ||||
\(405\) | −2.13568 | + | 0.662460i | −0.106123 | + | 0.0329179i | ||||
\(406\) | −0.332261 | −0.0164898 | ||||||||
\(407\) | −29.6312 | + | 6.63448i | −1.46876 | + | 0.328859i | ||||
\(408\) | 4.26306i | 0.211053i | ||||||||
\(409\) | −18.8834 | − | 32.7070i | −0.933724 | − | 1.61726i | −0.776893 | − | 0.629632i | \(-0.783206\pi\) |
−0.156831 | − | 0.987625i | \(-0.550128\pi\) | |||||||
\(410\) | −11.3574 | + | 12.2791i | −0.560900 | + | 0.606421i | ||||
\(411\) | −7.16590 | + | 12.4117i | −0.353468 | + | 0.612225i | ||||
\(412\) | −7.35421 | − | 4.24596i | −0.362316 | − | 0.209183i | ||||
\(413\) | − | 6.19567i | − | 0.304869i | ||||||
\(414\) | −3.97419 | + | 6.88350i | −0.195321 | + | 0.338306i | ||||
\(415\) | −30.0418 | − | 6.80704i | −1.47469 | − | 0.334145i | ||||
\(416\) | 2.68079 | + | 4.64326i | 0.131436 | + | 0.227654i | ||||
\(417\) | 7.59589i | 0.371972i | ||||||||
\(418\) | 36.6900i | 1.79457i | ||||||||
\(419\) | 8.70163 | + | 15.0717i | 0.425103 | + | 0.736299i | 0.996430 | − | 0.0844228i | \(-0.0269047\pi\) |
−0.571327 | + | 0.820722i | \(0.693571\pi\) | |||||||
\(420\) | −2.07338 | − | 1.91774i | −0.101170 | − | 0.0935761i | ||||
\(421\) | 6.81109 | 0.331952 | 0.165976 | − | 0.986130i | \(-0.446923\pi\) | ||||
0.165976 | + | 0.986130i | \(0.446923\pi\) | |||||||
\(422\) | 17.5328 | − | 10.1226i | 0.853484 | − | 0.492759i | ||||
\(423\) | −3.17814 | + | 1.83490i | −0.154527 | + | 0.0892159i | ||||
\(424\) | −4.07831 | − | 7.06383i | −0.198060 | − | 0.343050i | ||||
\(425\) | −12.0628 | − | 17.5736i | −0.585132 | − | 0.852444i | ||||
\(426\) | −0.141422 | + | 0.244950i | −0.00685192 | + | 0.0118679i | ||||
\(427\) | 0.853246 | − | 0.492622i | 0.0412915 | − | 0.0238396i | ||||
\(428\) | 13.5483 | − | 7.82214i | 0.654884 | − | 0.378097i | ||||
\(429\) | 13.3823 | + | 23.1789i | 0.646106 | + | 1.11909i | ||||
\(430\) | 5.43708 | − | 23.9957i | 0.262199 | − | 1.15717i | ||||
\(431\) | 10.8020 | − | 18.7097i | 0.520316 | − | 0.901214i | −0.479405 | − | 0.877594i | \(-0.659148\pi\) |
0.999721 | − | 0.0236199i | \(-0.00751915\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 4.55525i | 0.218911i | 0.993992 | + | 0.109456i | \(0.0349108\pi\) | ||||
−0.993992 | + | 0.109456i | \(0.965089\pi\) | |||||||
\(434\) | 10.5510 | 0.506464 | ||||||||
\(435\) | −0.174267 | − | 0.561814i | −0.00835546 | − | 0.0269369i | ||||
\(436\) | 10.2743 | 0.492051 | ||||||||
\(437\) | 50.5927 | + | 29.2097i | 2.42018 | + | 1.39729i | ||||
\(438\) | 1.54371i | 0.0737612i | ||||||||
\(439\) | 6.18014 | − | 10.7043i | 0.294962 | − | 0.510889i | −0.680014 | − | 0.733199i | \(-0.738026\pi\) |
0.974976 | + | 0.222310i | \(0.0713597\pi\) | |||||||
\(440\) | 7.57941 | − | 8.19452i | 0.361334 | − | 0.390659i | ||||
\(441\) | 2.70234 | − | 4.68059i | 0.128683 | − | 0.222885i | ||||
\(442\) | 19.7945 | − | 11.4284i | 0.941528 | − | 0.543591i | ||||
\(443\) | 13.2381i | 0.628960i | 0.949264 | + | 0.314480i | \(0.101830\pi\) | ||||
−0.949264 | + | 0.314480i | \(0.898170\pi\) | |||||||
\(444\) | −4.47603 | + | 4.11888i | −0.212423 | + | 0.195473i | ||||
\(445\) | −6.44687 | + | 28.4522i | −0.305611 | + | 1.34877i | ||||
\(446\) | 9.08526 | + | 15.7361i | 0.430200 | + | 0.745127i | ||||
\(447\) | 2.29265 | + | 1.32366i | 0.108439 | + | 0.0626071i | ||||
\(448\) | −1.09384 | − | 0.631530i | −0.0516792 | − | 0.0298370i | ||||
\(449\) | −18.3409 | + | 31.7673i | −0.865559 | + | 1.49919i | 0.000932977 | 1.00000i | \(0.499703\pi\) | |
−0.866492 | + | 0.499192i | \(0.833630\pi\) | |||||||
\(450\) | 2.15521 | − | 4.51166i | 0.101597 | − | 0.212682i | ||||
\(451\) | −18.6703 | + | 32.3380i | −0.879152 | + | 1.52274i | ||||
\(452\) | 18.0820i | 0.850503i | ||||||||
\(453\) | 4.07269 | − | 2.35137i | 0.191352 | − | 0.110477i | ||||
\(454\) | −11.4169 | −0.535822 | ||||||||
\(455\) | −3.34628 | + | 14.7683i | −0.156876 | + | 0.692347i | ||||
\(456\) | 3.67492 | + | 6.36515i | 0.172094 | + | 0.298076i | ||||
\(457\) | 32.3173 | + | 18.6584i | 1.51174 | + | 0.872803i | 0.999906 | + | 0.0137183i | \(0.00436681\pi\) |
0.511833 | + | 0.859085i | \(0.328967\pi\) | |||||||
\(458\) | 14.5585i | 0.680273i | ||||||||
\(459\) | 2.13153 | + | 3.69192i | 0.0994913 | + | 0.172324i | ||||
\(460\) | −5.26549 | − | 16.9752i | −0.245505 | − | 0.791475i | ||||
\(461\) | −11.8742 | − | 20.5667i | −0.553036 | − | 0.957887i | −0.998053 | − | 0.0623650i | \(-0.980136\pi\) |
0.445017 | − | 0.895522i | \(-0.353198\pi\) | |||||||
\(462\) | −5.46040 | − | 3.15256i | −0.254041 | − | 0.146671i | ||||
\(463\) | 24.5010 | + | 14.1457i | 1.13866 | + | 0.657405i | 0.946098 | − | 0.323880i | \(-0.104987\pi\) |
0.192561 | + | 0.981285i | \(0.438321\pi\) | |||||||
\(464\) | −0.131530 | − | 0.227817i | −0.00610614 | − | 0.0105761i | ||||
\(465\) | 5.53387 | + | 17.8405i | 0.256627 | + | 0.827332i | ||||
\(466\) | −1.41115 | − | 2.44418i | −0.0653701 | − | 0.113224i | ||||
\(467\) | − | 19.4357i | − | 0.899378i | −0.893185 | − | 0.449689i | \(-0.851535\pi\) | ||
0.893185 | − | 0.449689i | \(-0.148465\pi\) | |||||||
\(468\) | 4.64326 | + | 2.68079i | 0.214635 | + | 0.123919i | ||||
\(469\) | 2.23019 | + | 3.86280i | 0.102981 | + | 0.178368i | ||||
\(470\) | 1.81338 | − | 8.00306i | 0.0836449 | − | 0.369153i | ||||
\(471\) | −13.6101 | −0.627122 | ||||||||
\(472\) | 4.24810 | − | 2.45264i | 0.195535 | − | 0.112892i | ||||
\(473\) | − | 54.9275i | − | 2.52557i | ||||||
\(474\) | −4.05244 | + | 7.01903i | −0.186135 | + | 0.322395i | ||||
\(475\) | −33.1600 | − | 15.8404i | −1.52149 | − | 0.726809i | ||||
\(476\) | −2.69225 | + | 4.66312i | −0.123399 | + | 0.213734i | ||||
\(477\) | −7.06383 | − | 4.07831i | −0.323431 | − | 0.186733i | ||||
\(478\) | −19.5308 | − | 11.2761i | −0.893317 | − | 0.515757i | ||||
\(479\) | −18.7548 | − | 32.4842i | −0.856926 | − | 1.48424i | −0.874846 | − | 0.484401i | \(-0.839038\pi\) |
0.0179197 | − | 0.999839i | \(-0.494296\pi\) | |||||||
\(480\) | 0.494135 | − | 2.18079i | 0.0225541 | − | 0.0995388i | ||||
\(481\) | 31.1243 | + | 9.74154i | 1.41915 | + | 0.444176i | ||||
\(482\) | − | 5.82630i | − | 0.265380i | ||||||
\(483\) | −8.69428 | + | 5.01965i | −0.395604 | + | 0.228402i | ||||
\(484\) | 6.95976 | − | 12.0547i | 0.316353 | − | 0.547939i | ||||
\(485\) | −9.14048 | + | 9.88229i | −0.415048 | + | 0.448732i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | − | 17.3440i | − | 0.785931i | −0.919553 | − | 0.392965i | \(-0.871449\pi\) | ||
0.919553 | − | 0.392965i | \(-0.128551\pi\) | |||||||
\(488\) | 0.675539 | + | 0.390022i | 0.0305802 | + | 0.0176555i | ||||
\(489\) | −12.1566 | −0.549739 | ||||||||
\(490\) | 3.58038 | + | 11.5427i | 0.161745 | + | 0.521445i | ||||
\(491\) | −2.30071 | −0.103829 | −0.0519147 | − | 0.998652i | \(-0.516532\pi\) | ||||
−0.0519147 | + | 0.998652i | \(0.516532\pi\) | |||||||
\(492\) | 7.48019i | 0.337233i | ||||||||
\(493\) | −0.971197 | + | 0.560721i | −0.0437405 | + | 0.0252536i | ||||
\(494\) | 19.7034 | − | 34.1272i | 0.886496 | − | 1.53546i | ||||
\(495\) | 2.46670 | − | 10.8864i | 0.110870 | − | 0.489306i | ||||
\(496\) | 4.17676 | + | 7.23436i | 0.187542 | + | 0.324832i | ||||
\(497\) | −0.309387 | + | 0.178625i | −0.0138779 | + | 0.00801241i | ||||
\(498\) | −11.9301 | + | 6.88783i | −0.534600 | + | 0.308651i | ||||
\(499\) | −2.18307 | + | 3.78119i | −0.0977276 | + | 0.169269i | −0.910744 | − | 0.412972i | \(-0.864491\pi\) |
0.813016 | + | 0.582241i | \(0.197824\pi\) | |||||||
\(500\) | 4.13380 | + | 10.3881i | 0.184869 | + | 0.464568i | ||||
\(501\) | −9.88805 | − | 17.1266i | −0.441766 | − | 0.765160i | ||||
\(502\) | −17.6070 | + | 10.1654i | −0.785837 | + | 0.453703i | ||||
\(503\) | 18.1801 | − | 10.4963i | 0.810608 | − | 0.468005i | −0.0365587 | − | 0.999332i | \(-0.511640\pi\) |
0.847167 | + | 0.531327i | \(0.178306\pi\) | |||||||
\(504\) | −1.26306 | −0.0562612 | ||||||||
\(505\) | −32.0268 | − | 29.6228i | −1.42518 | − | 1.31820i | ||||
\(506\) | −19.8390 | − | 34.3621i | −0.881949 | − | 1.52758i | ||||
\(507\) | − | 15.7465i | − | 0.699325i | ||||||
\(508\) | 4.41588i | 0.195923i | ||||||||
\(509\) | −18.8359 | − | 32.6247i | −0.834886 | − | 1.44607i | −0.894123 | − | 0.447821i | \(-0.852200\pi\) |
0.0592368 | − | 0.998244i | \(-0.481133\pi\) | |||||||
\(510\) | −9.29683 | − | 2.10653i | −0.411670 | − | 0.0932786i | ||||
\(511\) | −0.974898 | + | 1.68857i | −0.0431270 | + | 0.0746981i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 6.36515 | + | 3.67492i | 0.281028 | + | 0.162252i | ||||
\(514\) | 4.80623 | − | 8.32463i | 0.211993 | − | 0.367184i | ||||
\(515\) | 12.8935 | − | 13.9399i | 0.568156 | − | 0.614265i | ||||
\(516\) | −5.50161 | − | 9.52907i | −0.242195 | − | 0.419494i | ||||
\(517\) | − | 18.3195i | − | 0.805689i | ||||||
\(518\) | −7.49727 | + | 1.67865i | −0.329411 | + | 0.0737558i | ||||
\(519\) | −4.65544 | −0.204351 | ||||||||
\(520\) | −11.4506 | + | 3.55183i | −0.502143 | + | 0.155758i | ||||
\(521\) | −18.1788 | + | 31.4866i | −0.796428 | + | 1.37945i | 0.125501 | + | 0.992094i | \(0.459946\pi\) |
−0.921929 | + | 0.387360i | \(0.873387\pi\) | |||||||
\(522\) | −0.227817 | − | 0.131530i | −0.00997128 | − | 0.00575692i | ||||
\(523\) | −35.0328 | − | 20.2262i | −1.53188 | − | 0.884430i | −0.999275 | − | 0.0380645i | \(-0.987881\pi\) |
−0.532602 | − | 0.846366i | \(-0.678786\pi\) | |||||||
\(524\) | 9.66613 | 0.422267 | ||||||||
\(525\) | 5.20671 | − | 3.57397i | 0.227239 | − | 0.155981i | ||||
\(526\) | −4.68764 | −0.204391 | ||||||||
\(527\) | 30.8405 | − | 17.8058i | 1.34343 | − | 0.775632i | ||||
\(528\) | − | 4.99195i | − | 0.217247i | ||||||
\(529\) | −40.1769 | −1.74682 | ||||||||
\(530\) | 17.4199 | − | 5.40343i | 0.756674 | − | 0.234710i | ||||
\(531\) | 2.45264 | − | 4.24810i | 0.106436 | − | 0.184352i | ||||
\(532\) | 9.28330i | 0.402482i | ||||||||
\(533\) | 34.7324 | − | 20.0528i | 1.50443 | − | 0.868582i | ||||
\(534\) | 6.52339 | + | 11.2988i | 0.282295 | + | 0.488949i | ||||
\(535\) | 10.3637 | + | 33.4112i | 0.448062 | + | 1.44449i | ||||
\(536\) | −1.76570 | + | 3.05829i | −0.0762667 | + | 0.132098i | ||||
\(537\) | −15.6178 | − | 9.01694i | −0.673958 | − | 0.389110i | ||||
\(538\) | −15.6165 | + | 9.01620i | −0.673276 | + | 0.388716i | ||||
\(539\) | 13.4899 | + | 23.3652i | 0.581052 | + | 1.00641i | ||||
\(540\) | −0.662460 | − | 2.13568i | −0.0285077 | − | 0.0919052i | ||||
\(541\) | 13.0090 | 0.559299 | 0.279649 | − | 0.960102i | \(-0.409782\pi\) | ||||
0.279649 | + | 0.960102i | \(0.409782\pi\) | |||||||
\(542\) | −2.44050 | − | 1.40902i | −0.104828 | − | 0.0605227i | ||||
\(543\) | −11.1186 | + | 6.41934i | −0.477146 | + | 0.275480i | ||||
\(544\) | −4.26306 | −0.182777 | ||||||||
\(545\) | −5.07691 | + | 22.4061i | −0.217471 | + | 0.959773i | ||||
\(546\) | 3.38600 | + | 5.86472i | 0.144907 | + | 0.250987i | ||||
\(547\) | − | 24.6188i | − | 1.05262i | −0.850292 | − | 0.526312i | \(-0.823574\pi\) | ||
0.850292 | − | 0.526312i | \(-0.176426\pi\) | |||||||
\(548\) | −12.4117 | − | 7.16590i | −0.530202 | − | 0.306112i | ||||
\(549\) | 0.780045 | 0.0332915 | ||||||||
\(550\) | 14.1253 | + | 20.5783i | 0.602303 | + | 0.877460i | ||||
\(551\) | −0.966726 | + | 1.67442i | −0.0411839 | + | 0.0713327i | ||||
\(552\) | −6.88350 | − | 3.97419i | −0.292981 | − | 0.169153i | ||||
\(553\) | −8.86546 | + | 5.11848i | −0.376998 | + | 0.217660i | ||||
\(554\) | 18.8269 | 0.799880 | ||||||||
\(555\) | −6.77063 | − | 11.7966i | −0.287397 | − | 0.500736i | ||||
\(556\) | −7.59589 | −0.322137 | ||||||||
\(557\) | −12.1937 | + | 7.04001i | −0.516662 | + | 0.298295i | −0.735568 | − | 0.677451i | \(-0.763085\pi\) |
0.218906 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(558\) | 7.23436 | + | 4.17676i | 0.306255 | + | 0.176816i | ||||
\(559\) | −29.4973 | + | 51.0908i | −1.24760 | + | 2.16091i | ||||
\(560\) | 1.91774 | − | 2.07338i | 0.0810392 | − | 0.0876161i | ||||
\(561\) | −21.2810 | −0.898483 | ||||||||
\(562\) | −14.1005 | − | 8.14090i | −0.594792 | − | 0.343403i | ||||
\(563\) | 18.2964i | 0.771101i | 0.922687 | + | 0.385551i | \(0.125989\pi\) | ||||
−0.922687 | + | 0.385551i | \(0.874011\pi\) | |||||||
\(564\) | −1.83490 | − | 3.17814i | −0.0772633 | − | 0.133824i | ||||
\(565\) | −39.4329 | − | 8.93493i | −1.65895 | − | 0.375895i | ||||
\(566\) | −10.5267 | −0.442468 | ||||||||
\(567\) | −1.09384 | + | 0.631530i | −0.0459371 | + | 0.0265218i | ||||
\(568\) | −0.244950 | − | 0.141422i | −0.0102779 | − | 0.00593394i | ||||
\(569\) | 25.3625 | 1.06325 | 0.531625 | − | 0.846980i | \(-0.321581\pi\) | ||||
0.531625 | + | 0.846980i | \(0.321581\pi\) | |||||||
\(570\) | −15.6969 | + | 4.86898i | −0.657473 | + | 0.203939i | ||||
\(571\) | 21.1056 | + | 36.5560i | 0.883241 | + | 1.52982i | 0.847716 | + | 0.530450i | \(0.177977\pi\) |
0.0355254 | + | 0.999369i | \(0.488690\pi\) | |||||||
\(572\) | −23.1789 | + | 13.3823i | −0.969158 | + | 0.559544i | ||||
\(573\) | 3.85686 | + | 2.22676i | 0.161123 | + | 0.0930243i | ||||
\(574\) | −4.72396 | + | 8.18214i | −0.197174 | + | 0.341516i | ||||
\(575\) | 39.6212 | − | 3.09483i | 1.65232 | − | 0.129064i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 0.213185 | − | 0.123082i | 0.00887501 | − | 0.00512399i | −0.495556 | − | 0.868576i | \(-0.665036\pi\) |
0.504431 | + | 0.863452i | \(0.331702\pi\) | |||||||
\(578\) | 1.17368i | 0.0488188i | ||||||||
\(579\) | 4.39987 | − | 7.62080i | 0.182852 | − | 0.316709i | ||||
\(580\) | 0.561814 | − | 0.174267i | 0.0233281 | − | 0.00723604i | ||||
\(581\) | −17.3995 | −0.721853 | ||||||||
\(582\) | 6.02010i | 0.249541i | ||||||||
\(583\) | 35.2623 | − | 20.3587i | 1.46041 | − | 0.843171i | ||||
\(584\) | −1.54371 | −0.0638791 | ||||||||
\(585\) | −8.14062 | + | 8.80129i | −0.336573 | + | 0.363888i | ||||
\(586\) | −5.16449 | −0.213343 | ||||||||
\(587\) | 24.5330 | + | 14.1641i | 1.01258 | + | 0.584616i | 0.911947 | − | 0.410307i | \(-0.134579\pi\) |
0.100637 | + | 0.994923i | \(0.467912\pi\) | |||||||
\(588\) | 4.68059 | + | 2.70234i | 0.193024 | + | 0.111443i | ||||
\(589\) | 30.6985 | − | 53.1714i | 1.26491 | − | 2.19089i | ||||
\(590\) | 3.24955 | + | 10.4761i | 0.133782 | + | 0.431296i | ||||
\(591\) | −8.10089 | −0.333226 | ||||||||
\(592\) | −4.11888 | − | 4.47603i | −0.169285 | − | 0.183964i | ||||
\(593\) | 32.0201i | 1.31491i | 0.753494 | + | 0.657455i | \(0.228367\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(594\) | −2.49597 | − | 4.32315i | −0.102411 | − | 0.177381i | ||||
\(595\) | −8.83892 | − | 8.17544i | −0.362361 | − | 0.335160i | ||||
\(596\) | −1.32366 | + | 2.29265i | −0.0542194 | + | 0.0939107i | ||||
\(597\) | −0.763578 | − | 0.440852i | −0.0312511 | − | 0.0180429i | ||||
\(598\) | 42.6159i | 1.74269i | ||||||||
\(599\) | 8.52695 | − | 14.7691i | 0.348402 | − | 0.603449i | −0.637564 | − | 0.770397i | \(-0.720058\pi\) |
0.985966 | + | 0.166948i | \(0.0533912\pi\) | |||||||
\(600\) | 4.51166 | + | 2.15521i | 0.184188 | + | 0.0879860i | ||||
\(601\) | −5.27568 | − | 9.13774i | −0.215199 | − | 0.372736i | 0.738135 | − | 0.674653i | \(-0.235707\pi\) |
−0.953334 | + | 0.301917i | \(0.902373\pi\) | |||||||
\(602\) | − | 13.8977i | − | 0.566429i | ||||||
\(603\) | 3.53141i | 0.143810i | ||||||||
\(604\) | 2.35137 | + | 4.07269i | 0.0956758 | + | 0.165715i | ||||
\(605\) | 22.8496 | + | 21.1344i | 0.928968 | + | 0.859235i | ||||
\(606\) | −19.5101 | −0.792545 | ||||||||
\(607\) | 9.55271 | − | 5.51526i | 0.387733 | − | 0.223858i | −0.293445 | − | 0.955976i | \(-0.594802\pi\) |
0.681177 | + | 0.732118i | \(0.261468\pi\) | |||||||
\(608\) | −6.36515 | + | 3.67492i | −0.258141 | + | 0.149038i | ||||
\(609\) | −0.166131 | − | 0.287747i | −0.00673195 | − | 0.0116601i | ||||
\(610\) | −1.18436 | + | 1.28048i | −0.0479535 | + | 0.0518452i | ||||
\(611\) | −9.83796 | + | 17.0398i | −0.398001 | + | 0.689358i | ||||
\(612\) | −3.69192 | + | 2.13153i | −0.149237 | + | 0.0861620i | ||||
\(613\) | −18.5126 | + | 10.6883i | −0.747717 | + | 0.431695i | −0.824869 | − | 0.565325i | \(-0.808751\pi\) |
0.0771512 | + | 0.997019i | \(0.475418\pi\) | |||||||
\(614\) | 7.78242 | + | 13.4796i | 0.314073 | + | 0.543990i | ||||
\(615\) | −16.3127 | − | 3.69622i | −0.657791 | − | 0.149046i | ||||
\(616\) | 3.15256 | − | 5.46040i | 0.127020 | − | 0.220006i | ||||
\(617\) | −2.11476 | + | 1.22095i | −0.0851368 | + | 0.0491538i | −0.541964 | − | 0.840402i | \(-0.682319\pi\) |
0.456827 | + | 0.889555i | \(0.348986\pi\) | |||||||
\(618\) | − | 8.49192i | − | 0.341595i | ||||||
\(619\) | 41.1110 | 1.65239 | 0.826196 | − | 0.563382i | \(-0.190500\pi\) | ||||
0.826196 | + | 0.563382i | \(0.190500\pi\) | |||||||
\(620\) | −17.8405 | + | 5.53387i | −0.716491 | + | 0.222246i | ||||
\(621\) | −7.94839 | −0.318958 | ||||||||
\(622\) | 15.4565 | + | 8.92380i | 0.619748 | + | 0.357812i | ||||
\(623\) | 16.4789i | 0.660212i | ||||||||
\(624\) | −2.68079 | + | 4.64326i | −0.107317 | + | 0.185879i | ||||
\(625\) | −24.6968 | + | 3.88184i | −0.987872 | + | 0.155274i | ||||
\(626\) | −3.17839 | + | 5.50514i | −0.127034 | + | 0.220029i | ||||
\(627\) | −31.7745 | + | 18.3450i | −1.26895 | + | 0.732629i | ||||
\(628\) | − | 13.6101i | − | 0.543104i | ||||||
\(629\) | −19.0816 | + | 17.5590i | −0.760833 | + | 0.700124i | ||||
\(630\) | 0.624123 | − | 2.75447i | 0.0248656 | − | 0.109741i | ||||
\(631\) | 8.88206 | + | 15.3842i | 0.353589 | + | 0.612434i | 0.986875 | − | 0.161483i | \(-0.0516278\pi\) |
−0.633286 | + | 0.773918i | \(0.718294\pi\) | |||||||
\(632\) | −7.01903 | − | 4.05244i | −0.279202 | − | 0.161197i | ||||
\(633\) | 17.5328 | + | 10.1226i | 0.696866 | + | 0.402336i | ||||
\(634\) | −7.95728 | + | 13.7824i | −0.316024 | + | 0.547369i | ||||
\(635\) | −9.63009 | − | 2.18204i | −0.382158 | − | 0.0865917i | ||||
\(636\) | 4.07831 | − | 7.06383i | 0.161715 | − | 0.280099i | ||||
\(637\) | − | 28.9776i | − | 1.14813i | ||||||
\(638\) | 1.13725 | − | 0.656592i | 0.0450242 | − | 0.0259947i | ||||
\(639\) | −0.282844 | −0.0111891 | ||||||||
\(640\) | 2.18079 | + | 0.494135i | 0.0862032 | + | 0.0195324i | ||||
\(641\) | 10.1835 | + | 17.6384i | 0.402225 | + | 0.696674i | 0.993994 | − | 0.109433i | \(-0.0349036\pi\) |
−0.591769 | + | 0.806108i | \(0.701570\pi\) | |||||||
\(642\) | 13.5483 | + | 7.82214i | 0.534710 | + | 0.308715i | ||||
\(643\) | 3.70473i | 0.146100i | 0.997328 | + | 0.0730502i | \(0.0232733\pi\) | ||||
−0.997328 | + | 0.0730502i | \(0.976727\pi\) | |||||||
\(644\) | −5.01965 | − | 8.69428i | −0.197802 | − | 0.342603i | ||||
\(645\) | 23.4994 | − | 7.28919i | 0.925288 | − | 0.287012i | ||||
\(646\) | 15.6664 | + | 27.1350i | 0.616387 | + | 1.06761i | ||||
\(647\) | 3.89440 | + | 2.24843i | 0.153105 | + | 0.0883950i | 0.574595 | − | 0.818438i | \(-0.305160\pi\) |
−0.421490 | + | 0.906833i | \(0.638493\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 12.2434 | + | 21.2063i | 0.480597 | + | 0.832419i | ||||
\(650\) | −2.08762 | − | 26.7265i | −0.0818831 | − | 1.04830i | ||||
\(651\) | 5.27550 | + | 9.13743i | 0.206763 | + | 0.358124i | ||||
\(652\) | − | 12.1566i | − | 0.476088i | ||||||
\(653\) | −19.3934 | − | 11.1968i | −0.758921 | − | 0.438163i | 0.0699875 | − | 0.997548i | \(-0.477704\pi\) |
−0.828908 | + | 0.559385i | \(0.811037\pi\) | |||||||
\(654\) | 5.13717 | + | 8.89784i | 0.200879 | + | 0.347933i | ||||
\(655\) | −4.77637 | + | 21.0798i | −0.186628 | + | 0.823655i | ||||
\(656\) | −7.48019 | −0.292052 | ||||||||
\(657\) | −1.33689 | + | 0.771854i | −0.0521571 | + | 0.0301129i | ||||
\(658\) | − | 4.63518i | − | 0.180698i | ||||||
\(659\) | 1.35816 | − | 2.35241i | 0.0529065 | − | 0.0916368i | −0.838359 | − | 0.545118i | \(-0.816485\pi\) |
0.891266 | + | 0.453481i | \(0.149818\pi\) | |||||||
\(660\) | 10.8864 | + | 2.46670i | 0.423751 | + | 0.0960160i | ||||
\(661\) | 3.15588 | − | 5.46614i | 0.122749 | − | 0.212608i | −0.798102 | − | 0.602523i | \(-0.794162\pi\) |
0.920851 | + | 0.389915i | \(0.127495\pi\) | |||||||
\(662\) | −6.86079 | − | 3.96108i | −0.266652 | − | 0.153952i | ||||
\(663\) | 19.7945 | + | 11.4284i | 0.768754 | + | 0.443841i | ||||
\(664\) | −6.88783 | − | 11.9301i | −0.267300 | − | 0.462977i | ||||
\(665\) | −20.2449 | − | 4.58720i | −0.785063 | − | 0.177884i | ||||
\(666\) | −5.80507 | − | 1.81692i | −0.224942 | − | 0.0704042i | ||||
\(667\) | − | 2.09091i | − | 0.0809602i | ||||||
\(668\) | 17.1266 | − | 9.88805i | 0.662648 | − | 0.382580i | ||||
\(669\) | −9.08526 | + | 15.7361i | −0.351256 | + | 0.608394i | ||||
\(670\) | −5.79698 | − | 5.36183i | −0.223957 | − | 0.207146i | ||||
\(671\) | −1.94697 | + | 3.37225i | −0.0751620 | + | 0.130184i | ||||
\(672\) | − | 1.26306i | − | 0.0487236i | ||||||
\(673\) | −3.67729 | − | 2.12308i | −0.141749 | − | 0.0818388i | 0.427448 | − | 0.904040i | \(-0.359413\pi\) |
−0.569197 | + | 0.822201i | \(0.692746\pi\) | |||||||
\(674\) | −35.3308 | −1.36089 | ||||||||
\(675\) | 4.98482 | − | 0.389366i | 0.191866 | − | 0.0149867i | ||||
\(676\) | 15.7465 | 0.605633 | ||||||||
\(677\) | 38.4405i | 1.47739i | 0.674041 | + | 0.738693i | \(0.264557\pi\) | ||||
−0.674041 | + | 0.738693i | \(0.735443\pi\) | |||||||
\(678\) | −15.6594 | + | 9.04098i | −0.601397 | + | 0.347217i | ||||
\(679\) | −3.80187 | + | 6.58504i | −0.145903 | + | 0.252711i | ||||
\(680\) | 2.10653 | − | 9.29683i | 0.0807817 | − | 0.356517i | ||||
\(681\) | −5.70845 | − | 9.88733i | −0.218748 | − | 0.378883i | ||||
\(682\) | −36.1135 | + | 20.8502i | −1.38286 | + | 0.798394i | ||||
\(683\) | 41.5997 | − | 24.0176i | 1.59177 | − | 0.919009i | 0.598766 | − | 0.800924i | \(-0.295658\pi\) |
0.993004 | − | 0.118085i | \(-0.0376754\pi\) | |||||||
\(684\) | −3.67492 | + | 6.36515i | −0.140514 | + | 0.243378i | ||||
\(685\) | 21.7604 | − | 23.5264i | 0.831421 | − | 0.898896i | ||||
\(686\) | 7.83393 | + | 13.5688i | 0.299101 | + | 0.518058i | ||||
\(687\) | −12.6080 | + | 7.27924i | −0.481026 | + | 0.277720i | ||||
\(688\) | 9.52907 | − | 5.50161i | 0.363292 | − | 0.209747i | ||||
\(689\) | −43.7323 | −1.66607 | ||||||||
\(690\) | 12.0682 | − | 13.0477i | 0.459430 | − | 0.496716i | ||||
\(691\) | 15.9446 | + | 27.6169i | 0.606561 | + | 1.05060i | 0.991803 | + | 0.127779i | \(0.0407849\pi\) |
−0.385241 | + | 0.922816i | \(0.625882\pi\) | |||||||
\(692\) | − | 4.65544i | − | 0.176973i | ||||||
\(693\) | − | 6.30513i | − | 0.239512i | ||||||
\(694\) | 1.93586 | + | 3.35301i | 0.0734843 | + | 0.127279i | ||||
\(695\) | 3.75340 | − | 16.5650i | 0.142374 | − | 0.628347i | ||||
\(696\) | 0.131530 | − | 0.227817i | 0.00498564 | − | 0.00863538i | ||||
\(697\) | 31.8885i | 1.20786i | ||||||||
\(698\) | 12.4127 | + | 7.16648i | 0.469828 | + | 0.271255i | ||||
\(699\) | 1.41115 | − | 2.44418i | 0.0533745 | − | 0.0924473i | ||||
\(700\) | 3.57397 | + | 5.20671i | 0.135083 | + | 0.196795i | ||||
\(701\) | −1.65838 | − | 2.87241i | −0.0626363 | − | 0.108489i | 0.833007 | − | 0.553263i | \(-0.186617\pi\) |
−0.895643 | + | 0.444774i | \(0.853284\pi\) | |||||||
\(702\) | 5.36157i | 0.202360i | ||||||||
\(703\) | −13.3541 | + | 42.6663i | −0.503658 | + | 1.60919i | ||||
\(704\) | 4.99195 | 0.188141 | ||||||||
\(705\) | 7.83754 | − | 2.43110i | 0.295179 | − | 0.0915604i | ||||
\(706\) | 0.748825 | − | 1.29700i | 0.0281824 | − | 0.0488134i | ||||
\(707\) | −21.3410 | − | 12.3212i | −0.802611 | − | 0.463388i | ||||
\(708\) | 4.24810 | + | 2.45264i | 0.159653 | + | 0.0921759i | ||||
\(709\) | −17.1332 | −0.643449 | −0.321724 | − | 0.946833i | \(-0.604262\pi\) | ||||
−0.321724 | + | 0.946833i | \(0.604262\pi\) | |||||||
\(710\) | 0.429450 | − | 0.464302i | 0.0161170 | − | 0.0174250i | ||||
\(711\) | −8.10488 | −0.303957 | ||||||||
\(712\) | −11.2988 | + | 6.52339i | −0.423442 | + | 0.244474i | ||||
\(713\) | 66.3970i | 2.48659i | ||||||||
\(714\) | −5.38450 | −0.201510 | ||||||||
\(715\) | −17.7305 | − | 57.1609i | −0.663084 | − | 2.13770i | ||||
\(716\) | 9.01694 | − | 15.6178i | 0.336979 | − | 0.583664i | ||||
\(717\) | − | 22.5522i | − | 0.842227i | ||||||
\(718\) | 7.65044 | − | 4.41698i | 0.285512 | − | 0.164840i | ||||
\(719\) | −4.90657 | − | 8.49843i | −0.182984 | − | 0.316938i | 0.759911 | − | 0.650027i | \(-0.225242\pi\) |
−0.942895 | + | 0.333089i | \(0.891909\pi\) | |||||||
\(720\) | 2.13568 | − | 0.662460i | 0.0795923 | − | 0.0246884i | ||||
\(721\) | 5.36290 | − | 9.28882i | 0.199725 | − | 0.345934i | ||||
\(722\) | 30.3284 | + | 17.5101i | 1.12871 | + | 0.651658i | ||||
\(723\) | 5.04572 | − | 2.91315i | 0.187652 | − | 0.108341i | ||||
\(724\) | −6.41934 | − | 11.1186i | −0.238573 | − | 0.413220i | ||||
\(725\) | 0.102427 | + | 1.31131i | 0.00380404 | + | 0.0487007i | ||||
\(726\) | 13.9195 | 0.516602 | ||||||||
\(727\) | −17.4136 | − | 10.0537i | −0.645835 | − | 0.372873i | 0.141024 | − | 0.990006i | \(-0.454961\pi\) |
−0.786859 | + | 0.617133i | \(0.788294\pi\) | |||||||
\(728\) | −5.86472 | + | 3.38600i | −0.217361 | + | 0.125493i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0.762801 | − | 3.36650i | 0.0282325 | − | 0.124600i | ||||
\(731\) | −23.4537 | − | 40.6230i | −0.867466 | − | 1.50250i | ||||
\(732\) | 0.780045i | 0.0288313i | ||||||||
\(733\) | −15.5016 | − | 8.94984i | −0.572564 | − | 0.330570i | 0.185609 | − | 0.982624i | \(-0.440574\pi\) |
−0.758173 | + | 0.652054i | \(0.773908\pi\) | |||||||
\(734\) | −18.3673 | −0.677950 | ||||||||
\(735\) | −8.20607 | + | 8.87204i | −0.302685 | + | 0.327250i | ||||
\(736\) | 3.97419 | − | 6.88350i | 0.146491 | − | 0.253729i | ||||
\(737\) | −15.2668 | − | 8.81429i | −0.562360 | − | 0.324679i | ||||
\(738\) | −6.47803 | + | 3.74009i | −0.238460 | + | 0.137675i | ||||
\(739\) | 20.5194 | 0.754818 | 0.377409 | − | 0.926047i | \(-0.376815\pi\) | ||||
0.377409 | + | 0.926047i | \(0.376815\pi\) | |||||||
\(740\) | 11.7966 | − | 6.77063i | 0.433650 | − | 0.248893i | ||||
\(741\) | 39.4067 | 1.44764 | ||||||||
\(742\) | 8.92205 | − | 5.15115i | 0.327539 | − | 0.189105i | ||||
\(743\) | 5.03166 | + | 2.90503i | 0.184594 | + | 0.106575i | 0.589449 | − | 0.807805i | \(-0.299345\pi\) |
−0.404855 | + | 0.914381i | \(0.632678\pi\) | |||||||
\(744\) | −4.17676 | + | 7.23436i | −0.153127 | + | 0.265224i | ||||
\(745\) | −4.34572 | − | 4.01951i | −0.159215 | − | 0.147263i | ||||
\(746\) | −8.18276 | −0.299592 | ||||||||
\(747\) | −11.9301 | − | 6.88783i | −0.436499 | − | 0.252013i | ||||
\(748\) | − | 21.2810i | − | 0.778109i | ||||||
\(749\) | 9.87983 | + | 17.1124i | 0.361001 | + | 0.625273i | ||||
\(750\) | −6.92942 | + | 8.77401i | −0.253027 | + | 0.320381i | ||||
\(751\) | 21.8875 | 0.798687 | 0.399343 | − | 0.916801i | \(-0.369238\pi\) | ||||
0.399343 | + | 0.916801i | \(0.369238\pi\) | |||||||
\(752\) | 3.17814 | − | 1.83490i | 0.115895 | − | 0.0669120i | ||||
\(753\) | −17.6070 | − | 10.1654i | −0.641633 | − | 0.370447i | ||||
\(754\) | −1.41042 | −0.0513644 | ||||||||
\(755\) | −10.0436 | + | 3.11537i | −0.365522 | + | 0.113380i | ||||
\(756\) | −0.631530 | − | 1.09384i | −0.0229685 | − | 0.0397827i | ||||
\(757\) | 2.78518 | − | 1.60802i | 0.101229 | − | 0.0584445i | −0.448531 | − | 0.893767i | \(-0.648053\pi\) |
0.549760 | + | 0.835323i | \(0.314719\pi\) | |||||||
\(758\) | 23.7054 | + | 13.6863i | 0.861019 | + | 0.497110i | ||||
\(759\) | 19.8390 | − | 34.3621i | 0.720109 | − | 1.24726i | ||||
\(760\) | −4.86898 | − | 15.6969i | −0.176616 | − | 0.569388i | ||||
\(761\) | 3.34598 | + | 5.79541i | 0.121292 | + | 0.210083i | 0.920277 | − | 0.391267i | \(-0.127963\pi\) |
−0.798986 | + | 0.601350i | \(0.794630\pi\) | |||||||
\(762\) | −3.82426 | + | 2.20794i | −0.138538 | + | 0.0799852i | ||||
\(763\) | 12.9771i | 0.469803i | ||||||||
\(764\) | −2.22676 | + | 3.85686i | −0.0805614 | + | 0.139536i | ||||
\(765\) | −2.82411 | − | 9.10455i | −0.102106 | − | 0.329176i | ||||
\(766\) | 34.6306 | 1.25126 | ||||||||
\(767\) | − | 26.3000i | − | 0.949639i | ||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 26.6101 | 0.959585 | 0.479793 | − | 0.877382i | \(-0.340712\pi\) | ||||
0.479793 | + | 0.877382i | \(0.340712\pi\) | |||||||
\(770\) | 10.3502 | + | 9.57325i | 0.372995 | + | 0.344996i | ||||
\(771\) | 9.61245 | 0.346184 | ||||||||
\(772\) | 7.62080 | + | 4.39987i | 0.274278 | + | 0.158355i | ||||
\(773\) | 24.3315 | + | 14.0478i | 0.875145 | + | 0.505265i | 0.869054 | − | 0.494716i | \(-0.164728\pi\) |
0.00609016 | + | 0.999981i | \(0.498061\pi\) | |||||||
\(774\) | 5.50161 | − | 9.52907i | 0.197751 | − | 0.342515i | ||||
\(775\) | −3.25258 | − | 41.6408i | −0.116836 | − | 1.49578i | ||||
\(776\) | −6.02010 | −0.216109 | ||||||||
\(777\) | −5.20239 | − | 5.65350i | −0.186635 | − | 0.202818i | ||||
\(778\) | − | 20.0818i | − | 0.719966i | ||||||
\(779\) | 27.4891 | + | 47.6125i | 0.984899 | + | 1.70590i | ||||
\(780\) | −8.80129 | − | 8.14062i | −0.315137 | − | 0.291481i | ||||
\(781\) | 0.705971 | − | 1.22278i | 0.0252616 | − | 0.0437544i | ||||
\(782\) | −29.3448 | − | 16.9422i | −1.04937 | − | 0.605853i | ||||
\(783\) | − | 0.263060i | − | 0.00940101i | ||||||
\(784\) | −2.70234 | + | 4.68059i | −0.0965121 | + | 0.167164i | ||||
\(785\) | 29.6808 | + | 6.72525i | 1.05935 | + | 0.240034i | ||||
\(786\) | 4.83306 | + | 8.37111i | 0.172390 | + | 0.298588i | ||||
\(787\) | 50.6929i | 1.80701i | 0.428579 | + | 0.903504i | \(0.359014\pi\) | ||||
−0.428579 | + | 0.903504i | \(0.640986\pi\) | |||||||
\(788\) | − | 8.10089i | − | 0.288582i | ||||||
\(789\) | −2.34382 | − | 4.05962i | −0.0834422 | − | 0.144526i | ||||
\(790\) | 12.3059 | − | 13.3046i | 0.437823 | − | 0.473355i | ||||
\(791\) | −22.8386 | −0.812047 | ||||||||
\(792\) | 4.32315 | − | 2.49597i | 0.153617 | − | 0.0886905i | ||||
\(793\) | 3.62195 | − | 2.09113i | 0.128619 | − | 0.0742583i | ||||
\(794\) | −9.58350 | − | 16.5991i | −0.340106 | − | 0.589081i | ||||
\(795\) | 13.3895 | + | 12.3844i | 0.474876 | + | 0.439230i | ||||
\(796\) | 0.440852 | − | 0.763578i | 0.0156256 | − | 0.0270643i | ||||
\(797\) | 19.0649 | − | 11.0071i | 0.675312 | − | 0.389892i | −0.122774 | − | 0.992435i | \(-0.539179\pi\) |
0.798086 | + | 0.602543i | \(0.205846\pi\) | |||||||
\(798\) | −8.03957 | + | 4.64165i | −0.284598 | + | 0.164313i | ||||
\(799\) | −7.82229 | − | 13.5486i | −0.276733 | − | 0.479315i | ||||
\(800\) | −2.15521 | + | 4.51166i | −0.0761981 | + | 0.159511i | ||||
\(801\) | −6.52339 | + | 11.2988i | −0.230493 | + | 0.399225i | ||||
\(802\) | 1.98297 | − | 1.14487i | 0.0700212 | − | 0.0404268i | ||||
\(803\) | − | 7.70611i | − | 0.271943i | ||||||
\(804\) | −3.53141 | −0.124543 | ||||||||
\(805\) | 21.4408 | − | 6.65063i | 0.755687 | − | 0.234404i | ||||
\(806\) | 44.7880 | 1.57759 | ||||||||
\(807\) | −15.6165 | − | 9.01620i | −0.549727 | − | 0.317385i | ||||
\(808\) | − | 19.5101i | − | 0.686364i | ||||||
\(809\) | −1.43253 | + | 2.48122i | −0.0503652 | + | 0.0872350i | −0.890109 | − | 0.455748i | \(-0.849372\pi\) |
0.839744 | + | 0.542983i | \(0.182705\pi\) | |||||||
\(810\) | 1.51833 | − | 1.64155i | 0.0533486 | − | 0.0576782i | ||||
\(811\) | −15.7472 | + | 27.2749i | −0.552958 | + | 0.957752i | 0.445101 | + | 0.895480i | \(0.353168\pi\) |
−0.998059 | + | 0.0622713i | \(0.980166\pi\) | |||||||
\(812\) | 0.287747 | − | 0.166131i | 0.0100979 | − | 0.00583004i | ||||
\(813\) | − | 2.81804i | − | 0.0988331i | ||||||
\(814\) | 22.3441 | − | 20.5612i | 0.783160 | − | 0.720670i | ||||
\(815\) | 26.5109 | + | 6.00699i | 0.928636 | + | 0.210416i | ||||
\(816\) | −2.13153 | − | 3.69192i | −0.0746185 | − | 0.129243i | ||||
\(817\) | −70.0372 | − | 40.4360i | −2.45029 | − | 1.41468i | ||||
\(818\) | 32.7070 | + | 18.8834i | 1.14357 | + | 0.660243i | ||||
\(819\) | −3.38600 | + | 5.86472i | −0.118316 | + | 0.204930i | ||||
\(820\) | 3.69622 | − | 16.3127i | 0.129078 | − | 0.569664i | ||||
\(821\) | 1.88493 | − | 3.26480i | 0.0657846 | − | 0.113942i | −0.831257 | − | 0.555888i | \(-0.812378\pi\) |
0.897042 | + | 0.441946i | \(0.145712\pi\) | |||||||
\(822\) | − | 14.3318i | − | 0.499879i | ||||||
\(823\) | −0.802289 | + | 0.463202i | −0.0279660 | + | 0.0161462i | −0.513918 | − | 0.857839i | \(-0.671806\pi\) |
0.485952 | + | 0.873986i | \(0.338473\pi\) | |||||||
\(824\) | 8.49192 | 0.295830 | ||||||||
\(825\) | −10.7587 | + | 22.5220i | −0.374569 | + | 0.784114i | ||||
\(826\) | 3.09783 | + | 5.36560i | 0.107787 | + | 0.186693i | ||||
\(827\) | 18.2258 | + | 10.5227i | 0.633773 | + | 0.365909i | 0.782212 | − | 0.623012i | \(-0.214091\pi\) |
−0.148439 | + | 0.988922i | \(0.547425\pi\) | |||||||
\(828\) | − | 7.94839i | − | 0.276226i | ||||||
\(829\) | 22.5048 | + | 38.9795i | 0.781624 | + | 1.35381i | 0.930995 | + | 0.365032i | \(0.118942\pi\) |
−0.149371 | + | 0.988781i | \(0.547725\pi\) | |||||||
\(830\) | 29.4205 | − | 9.12582i | 1.02120 | − | 0.316762i | ||||
\(831\) | 9.41347 | + | 16.3046i | 0.326550 | + | 0.565601i | ||||
\(832\) | −4.64326 | − | 2.68079i | −0.160976 | − | 0.0929396i | ||||
\(833\) | 19.9536 | + | 11.5202i | 0.691352 | + | 0.399152i | ||||
\(834\) | −3.79794 | − | 6.57823i | −0.131512 | − | 0.227786i | ||||
\(835\) | 13.1009 | + | 42.2355i | 0.453374 | + | 1.46162i | ||||
\(836\) | −18.3450 | − | 31.7745i | −0.634475 | − | 1.09894i | ||||
\(837\) | 8.35352i | 0.288740i | ||||||||
\(838\) | −15.0717 | − | 8.70163i | −0.520642 | − | 0.300593i | ||||
\(839\) | −6.26844 | − | 10.8572i | −0.216410 | − | 0.374834i | 0.737298 | − | 0.675568i | \(-0.236102\pi\) |
−0.953708 | + | 0.300734i | \(0.902768\pi\) | |||||||
\(840\) | 2.75447 | + | 0.624123i | 0.0950381 | + | 0.0215343i | ||||
\(841\) | −28.9308 | −0.997614 | ||||||||
\(842\) | −5.89858 | + | 3.40555i | −0.203278 | + | 0.117363i | ||||
\(843\) | − | 16.2818i | − | 0.560775i | ||||||
\(844\) | −10.1226 | + | 17.5328i | −0.348433 | + | 0.603504i | ||||
\(845\) | −7.78088 | + | 34.3397i | −0.267671 | + | 1.18132i | ||||
\(846\) | 1.83490 | − | 3.17814i | 0.0630852 | − | 0.109267i | ||||
\(847\) | 15.2258 | + | 8.79060i | 0.523163 | + | 0.302049i | ||||
\(848\) | 7.06383 | + | 4.07831i | 0.242573 | + | 0.140050i | ||||
\(849\) | −5.26333 | − | 9.11635i | −0.180637 | − | 0.312872i | ||||
\(850\) | 19.2335 | + | 9.18778i | 0.659703 | + | 0.315138i | ||||
\(851\) | −10.5637 | − | 47.1800i | −0.362119 | − | 1.61731i | ||||
\(852\) | − | 0.282844i | − | 0.00969008i | ||||||
\(853\) | 20.5299 | − | 11.8529i | 0.702930 | − | 0.405837i | −0.105508 | − | 0.994418i | \(-0.533647\pi\) |
0.808438 | + | 0.588582i | \(0.200314\pi\) | |||||||
\(854\) | −0.492622 | + | 0.853246i | −0.0168572 | + | 0.0291975i | ||||
\(855\) | −12.0651 | − | 11.1595i | −0.412619 | − | 0.381646i | ||||
\(856\) | −7.82214 | + | 13.5483i | −0.267355 | + | 0.463073i | ||||
\(857\) | − | 28.1064i | − | 0.960096i | −0.877242 | − | 0.480048i | \(-0.840619\pi\) | ||
0.877242 | − | 0.480048i | \(-0.159381\pi\) | |||||||
\(858\) | −23.1789 | − | 13.3823i | −0.791314 | − | 0.456866i | ||||
\(859\) | −55.4336 | −1.89137 | −0.945685 | − | 0.325085i | \(-0.894607\pi\) | ||||
−0.945685 | + | 0.325085i | \(0.894607\pi\) | |||||||
\(860\) | 7.28919 | + | 23.4994i | 0.248559 | + | 0.801323i | ||||
\(861\) | −9.44793 | −0.321984 | ||||||||
\(862\) | 21.6041i | 0.735838i | ||||||||
\(863\) | 4.37677 | − | 2.52693i | 0.148987 | − | 0.0860177i | −0.423653 | − | 0.905824i | \(-0.639252\pi\) |
0.572640 | + | 0.819807i | \(0.305919\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 10.1525 | + | 2.30042i | 0.345196 | + | 0.0782165i | ||||
\(866\) | −2.27763 | − | 3.94496i | −0.0773969 | − | 0.134055i | ||||
\(867\) | −1.01644 | + | 0.586842i | −0.0345201 | + | 0.0199302i | ||||
\(868\) | −9.13743 | + | 5.27550i | −0.310145 | + | 0.179062i | ||||
\(869\) | 20.2296 | − | 35.0386i | 0.686241 | − | 1.18860i | ||||
\(870\) | 0.431826 | + | 0.399412i | 0.0146403 | + | 0.0135413i | ||||
\(871\) | 9.46695 | + | 16.3972i | 0.320775 | + | 0.555599i | ||||
\(872\) | −8.89784 | + | 5.13717i | −0.301319 | + | 0.173966i | ||||
\(873\) | −5.21356 | + | 3.01005i | −0.176452 | + | 0.101875i | ||||
\(874\) | −58.4194 | −1.97607 | ||||||||
\(875\) | −13.1207 | + | 5.22124i | −0.443562 | + | 0.176510i | ||||
\(876\) | −0.771854 | − | 1.33689i | −0.0260785 | − | 0.0451693i | ||||
\(877\) | − | 21.0116i | − | 0.709511i | −0.934959 | − | 0.354755i | \(-0.884564\pi\) | ||
0.934959 | − | 0.354755i | \(-0.115436\pi\) | |||||||
\(878\) | 12.3603i | 0.417139i | ||||||||
\(879\) | −2.58224 | − | 4.47258i | −0.0870969 | − | 0.150856i | ||||
\(880\) | −2.46670 | + | 10.8864i | −0.0831523 | + | 0.366979i | ||||
\(881\) | −2.01042 | + | 3.48216i | −0.0677329 | + | 0.117317i | −0.897903 | − | 0.440193i | \(-0.854910\pi\) |
0.830170 | + | 0.557510i | \(0.188243\pi\) | |||||||
\(882\) | 5.40468i | 0.181985i | ||||||||
\(883\) | 36.6621 | + | 21.1669i | 1.23378 | + | 0.712323i | 0.967816 | − | 0.251661i | \(-0.0809767\pi\) |
0.265963 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(884\) | −11.4284 | + | 19.7945i | −0.384377 | + | 0.665761i | ||||
\(885\) | −7.44782 | + | 8.05226i | −0.250356 | + | 0.270674i | ||||
\(886\) | −6.61903 | − | 11.4645i | −0.222371 | − | 0.385158i | ||||
\(887\) | 55.2976i | 1.85671i | 0.371694 | + | 0.928355i | \(0.378777\pi\) | ||||
−0.371694 | + | 0.928355i | \(0.621223\pi\) | |||||||
\(888\) | 1.81692 | − | 5.80507i | 0.0609718 | − | 0.194805i | ||||
\(889\) | −5.57752 | −0.187064 | ||||||||
\(890\) | −8.64297 | − | 27.8638i | −0.289713 | − | 0.933997i | ||||
\(891\) | 2.49597 | − | 4.32315i | 0.0836182 | − | 0.144831i | ||||
\(892\) | −15.7361 | − | 9.08526i | −0.526885 | − | 0.304197i | ||||
\(893\) | −23.3588 | − | 13.4862i | −0.781674 | − | 0.451300i | ||||
\(894\) | −2.64733 | −0.0885399 | ||||||||
\(895\) | 29.6035 | + | 27.3813i | 0.989536 | + | 0.915257i | ||||
\(896\) | 1.26306 | 0.0421959 | ||||||||
\(897\) | −36.9064 | + | 21.3079i | −1.23227 | + | 0.711451i | ||||
\(898\) | − | 36.6817i | − | 1.22408i | ||||||
\(899\) | −2.19748 | −0.0732901 | ||||||||
\(900\) | 0.389366 | + | 4.98482i | 0.0129789 | + | 0.166161i | ||||
\(901\) | 17.3861 | − | 30.1135i | 0.579214 | − | 1.00323i | ||||
\(902\) | − | 37.3407i | − | 1.24331i | ||||||
\(903\) | 12.0358 | − | 6.94887i | 0.400526 | − | 0.231244i | ||||
\(904\) | −9.04098 | − | 15.6594i | −0.300698 | − | 0.520825i | ||||
\(905\) | 27.4194 | − | 8.50510i | 0.911450 | − | 0.282719i | ||||
\(906\) | −2.35137 | + | 4.07269i | −0.0781189 | + | 0.135306i | ||||
\(907\) | −5.91799 | − | 3.41675i | −0.196504 | − | 0.113451i | 0.398520 | − | 0.917160i | \(-0.369524\pi\) |
−0.595024 | + | 0.803708i | \(0.702857\pi\) | |||||||
\(908\) | 9.88733 | − | 5.70845i | 0.328123 | − | 0.189442i | ||||
\(909\) | −9.75507 | − | 16.8963i | −0.323555 | − | 0.560414i | ||||
\(910\) | −4.48617 | − | 14.4628i | −0.148715 | − | 0.479438i | ||||
\(911\) | −16.0278 | −0.531025 | −0.265513 | − | 0.964107i | \(-0.585541\pi\) | ||||
−0.265513 | + | 0.964107i | \(0.585541\pi\) | |||||||
\(912\) | −6.36515 | − | 3.67492i | −0.210771 | − | 0.121689i | ||||
\(913\) | 59.5543 | − | 34.3837i | 1.97096 | − | 1.13793i | ||||
\(914\) | −37.3168 | −1.23433 | ||||||||
\(915\) | −1.70111 | − | 0.385448i | −0.0562370 | − | 0.0127425i | ||||
\(916\) | −7.27924 | − | 12.6080i | −0.240513 | − | 0.416580i | ||||
\(917\) | 12.2089i | 0.403174i | ||||||||
\(918\) | −3.69192 | − | 2.13153i | −0.121851 | − | 0.0703510i | ||||
\(919\) | 18.8381 | 0.621412 | 0.310706 | − | 0.950506i | \(-0.399434\pi\) | ||||
0.310706 | + | 0.950506i | \(0.399434\pi\) | |||||||
\(920\) | 13.0477 | + | 12.0682i | 0.430169 | + | 0.397878i | ||||
\(921\) | −7.78242 | + | 13.4796i | −0.256440 | + | 0.444166i | ||||
\(922\) | 20.5667 | + | 11.8742i | 0.677328 | + | 0.391056i | ||||
\(923\) | −1.31332 | + | 0.758245i | −0.0432284 | + | 0.0249579i | ||||
\(924\) | 6.30513 | 0.207424 | ||||||||
\(925\) | 8.93620 | + | 29.0714i | 0.293820 | + | 0.955861i | ||||
\(926\) | −28.2913 | −0.929711 | ||||||||
\(927\) | 7.35421 | − | 4.24596i | 0.241544 | − | 0.139456i | ||||
\(928\) | 0.227817 | + | 0.131530i | 0.00747846 | + | 0.00431769i | ||||
\(929\) | 23.3315 | − | 40.4114i | 0.765482 | − | 1.32585i | −0.174509 | − | 0.984656i | \(-0.555834\pi\) |
0.939991 | − | 0.341199i | \(-0.110833\pi\) | |||||||
\(930\) | −13.7127 | − | 12.6834i | −0.449658 | − | 0.415904i | ||||
\(931\) | 39.7235 | 1.30189 | ||||||||
\(932\) | 2.44418 | + | 1.41115i | 0.0800617 | + | 0.0462236i | ||||
\(933\) | 17.8476i | 0.584304i | ||||||||
\(934\) | 9.71786 | + | 16.8318i | 0.317978 | + | 0.550754i | ||||
\(935\) | 46.4092 | + | 10.5157i | 1.51774 | + | 0.343899i | ||||
\(936\) | −5.36157 | −0.175249 | ||||||||
\(937\) | −42.9876 | + | 24.8189i | −1.40434 | + | 0.810798i | −0.994835 | − | 0.101507i | \(-0.967633\pi\) |
−0.409509 | + | 0.912306i | \(0.634300\pi\) | |||||||
\(938\) | −3.86280 | − | 2.23019i | −0.126125 | − | 0.0728183i | ||||
\(939\) | −6.35678 | −0.207446 | ||||||||
\(940\) | 2.43110 | + | 7.83754i | 0.0792936 | + | 0.255632i | ||||
\(941\) | −13.5062 | − | 23.3935i | −0.440291 | − | 0.762606i | 0.557420 | − | 0.830231i | \(-0.311791\pi\) |
−0.997711 | + | 0.0676245i | \(0.978458\pi\) | |||||||
\(942\) | 11.7867 | − | 6.80507i | 0.384032 | − | 0.221721i | ||||
\(943\) | −51.4899 | − | 29.7277i | −1.67674 | − | 0.968067i | ||||
\(944\) | −2.45264 | + | 4.24810i | −0.0798267 | + | 0.138264i | ||||
\(945\) | 2.69750 | − | 0.836727i | 0.0877496 | − | 0.0272187i | ||||
\(946\) | 27.4637 | + | 47.5686i | 0.892923 | + | 1.54659i | ||||
\(947\) | −8.58103 | + | 4.95426i | −0.278846 | + | 0.160992i | −0.632901 | − | 0.774233i | \(-0.718136\pi\) |
0.354055 | + | 0.935225i | \(0.384803\pi\) | |||||||
\(948\) | − | 8.10488i | − | 0.263234i | ||||||
\(949\) | −4.13835 | + | 7.16784i | −0.134337 | + | 0.232678i | ||||
\(950\) | 36.6376 | − | 2.86178i | 1.18868 | − | 0.0928485i | ||||
\(951\) | −15.9146 | −0.516065 | ||||||||
\(952\) | − | 5.38450i | − | 0.174513i | ||||||
\(953\) | 21.1411 | − | 12.2058i | 0.684828 | − | 0.395386i | −0.116844 | − | 0.993150i | \(-0.537278\pi\) |
0.801672 | + | 0.597765i | \(0.203944\pi\) | |||||||
\(954\) | 8.15661 | 0.264080 | ||||||||
\(955\) | −7.31068 | − | 6.76190i | −0.236568 | − | 0.218810i | ||||
\(956\) | 22.5522 | 0.729390 | ||||||||
\(957\) | 1.13725 | + | 0.656592i | 0.0367621 | + | 0.0212246i | ||||
\(958\) | 32.4842 | + | 18.7548i | 1.04952 | + | 0.605939i | ||||
\(959\) | 9.05097 | − | 15.6767i | 0.292271 | − | 0.506228i | ||||
\(960\) | 0.662460 | + | 2.13568i | 0.0213808 | + | 0.0689289i | ||||
\(961\) | 38.7813 | 1.25101 | ||||||||
\(962\) | −31.8252 | + | 7.12573i | −1.02609 | + | 0.229743i | ||||
\(963\) | 15.6443i | 0.504130i | ||||||||
\(964\) | 2.91315 | + | 5.04572i | 0.0938262 | + | 0.162512i | ||||
\(965\) | −13.3609 | + | 14.4452i | −0.430102 | + | 0.465007i | ||||
\(966\) | 5.01965 | − | 8.69428i | 0.161504 | − | 0.279734i | ||||
\(967\) | 1.75442 | + | 1.01292i | 0.0564184 | + | 0.0325732i | 0.527944 | − | 0.849279i | \(-0.322963\pi\) |
−0.471525 | + | 0.881852i | \(0.656296\pi\) | |||||||
\(968\) | 13.9195i | 0.447390i | ||||||||
\(969\) | −15.6664 | + | 27.1350i | −0.503278 | + | 0.871703i | ||||
\(970\) | 2.97474 | − | 13.1286i | 0.0955133 | − | 0.421532i | ||||
\(971\) | −2.26173 | − | 3.91744i | −0.0725824 | − | 0.125716i | 0.827450 | − | 0.561539i | \(-0.189791\pi\) |
−0.900032 | + | 0.435823i | \(0.856457\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 9.59407i | − | 0.307572i | ||||||
\(974\) | 8.67199 | + | 15.0203i | 0.277868 | + | 0.481282i | ||||
\(975\) | 22.1020 | − | 15.1712i | 0.707830 | − | 0.485866i | ||||
\(976\) | −0.780045 | −0.0249686 | ||||||||
\(977\) | 11.9433 | − | 6.89545i | 0.382099 | − | 0.220605i | −0.296632 | − | 0.954992i | \(-0.595863\pi\) |
0.678731 | + | 0.734387i | \(0.262530\pi\) | |||||||
\(978\) | 10.5279 | − | 6.07828i | 0.336645 | − | 0.194362i | ||||
\(979\) | −32.5644 | − | 56.4032i | −1.04076 | − | 1.80265i | ||||
\(980\) | −8.87204 | − | 8.20607i | −0.283407 | − | 0.262133i | ||||
\(981\) | −5.13717 | + | 8.89784i | −0.164017 | + | 0.284086i | ||||
\(982\) | 1.99247 | − | 1.15035i | 0.0635823 | − | 0.0367092i | ||||
\(983\) | −35.1161 | + | 20.2743i | −1.12003 | + | 0.646649i | −0.941408 | − | 0.337269i | \(-0.890497\pi\) |
−0.178621 | + | 0.983918i | \(0.557163\pi\) | |||||||
\(984\) | −3.74009 | − | 6.47803i | −0.119230 | − | 0.206512i | ||||
\(985\) | 17.6663 | + | 4.00293i | 0.562895 | + | 0.127544i | ||||
\(986\) | 0.560721 | − | 0.971197i | 0.0178570 | − | 0.0309292i | ||||
\(987\) | 4.01419 | − | 2.31759i | 0.127773 | − | 0.0737697i | ||||
\(988\) | 39.4067i | 1.25369i | ||||||||
\(989\) | 87.4579 | 2.78100 | ||||||||
\(990\) | 3.30696 | + | 10.6612i | 0.105102 | + | 0.338836i | ||||
\(991\) | 3.39031 | 0.107697 | 0.0538483 | − | 0.998549i | \(-0.482851\pi\) | ||||
0.0538483 | + | 0.998549i | \(0.482851\pi\) | |||||||
\(992\) | −7.23436 | − | 4.17676i | −0.229691 | − | 0.132612i | ||||
\(993\) | − | 7.92216i | − | 0.251402i | ||||||
\(994\) | 0.178625 | − | 0.309387i | 0.00566563 | − | 0.00981315i | ||||
\(995\) | 1.44736 | + | 1.33871i | 0.0458844 | + | 0.0424401i | ||||
\(996\) | 6.88783 | − | 11.9301i | 0.218249 | − | 0.378019i | ||||
\(997\) | 17.2302 | − | 9.94785i | 0.545686 | − | 0.315052i | −0.201694 | − | 0.979448i | \(-0.564645\pi\) |
0.747380 | + | 0.664397i | \(0.231311\pi\) | |||||||
\(998\) | − | 4.36614i | − | 0.138208i | ||||||
\(999\) | −1.32904 | − | 5.93579i | −0.0420489 | − | 0.187800i |
(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 | 1110.2.bb.d.1099.6 | yes | 28 | |
5.4 | even | 2 | inner | 1110.2.bb.d.1099.9 | yes | 28 | |
37.10 | even | 3 | inner | 1110.2.bb.d.1009.9 | yes | 28 | |
185.84 | even | 6 | inner | 1110.2.bb.d.1009.6 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.d.1009.6 | ✓ | 28 | 185.84 | even | 6 | inner | |
1110.2.bb.d.1009.9 | yes | 28 | 37.10 | even | 3 | inner | |
1110.2.bb.d.1099.6 | yes | 28 | 1.1 | even | 1 | trivial | |
1110.2.bb.d.1099.9 | yes | 28 | 5.4 | even | 2 | inner |