Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(269,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("370.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.n (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 359.3 | ||
Root | \(-0.396143 + 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.359 |
Dual form | 370.2.n.e.269.3 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||
\(3\) | −1.73205 | − | 1.00000i | −1.00000 | − | 0.577350i | −0.0917517 | − | 0.995782i | \(-0.529247\pi\) |
−0.908248 | + | 0.418432i | \(0.862580\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.469882 | + | 2.18614i | 0.210138 | + | 0.977672i | ||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | −3.73831 | − | 2.15831i | −1.41295 | − | 0.815765i | −0.417282 | − | 0.908777i | \(-0.637017\pi\) |
−0.995665 | + | 0.0930116i | \(0.970351\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1.50000 | + | 1.65831i | 0.474342 | + | 0.524404i | ||||
\(11\) | −2.31662 | −0.698489 | −0.349244 | − | 0.937032i | \(-0.613562\pi\) | ||||
−0.349244 | + | 0.937032i | \(0.613562\pi\) | |||||||
\(12\) | −1.73205 | + | 1.00000i | −0.500000 | + | 0.288675i | ||||
\(13\) | −3.46410 | − | 2.00000i | −0.960769 | − | 0.554700i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | −4.31662 | −1.15367 | ||||||||
\(15\) | 1.37228 | − | 4.25639i | 0.354322 | − | 1.09899i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.14023 | − | 0.658312i | 0.276547 | − | 0.159664i | −0.355312 | − | 0.934748i | \(-0.615626\pi\) |
0.631859 | + | 0.775083i | \(0.282292\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | −1.15831 | + | 2.00626i | −0.265735 | + | 0.460267i | −0.967756 | − | 0.251890i | \(-0.918948\pi\) |
0.702021 | + | 0.712156i | \(0.252281\pi\) | |||||||
\(20\) | 2.12819 | + | 0.686141i | 0.475879 | + | 0.153426i | ||||
\(21\) | 4.31662 | + | 7.47661i | 0.941965 | + | 1.63153i | ||||
\(22\) | −2.00626 | + | 1.15831i | −0.427735 | + | 0.246953i | ||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | −1.00000 | + | 1.73205i | −0.204124 | + | 0.353553i | ||||
\(25\) | −4.55842 | + | 2.05446i | −0.911684 | + | 0.410891i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | −3.73831 | + | 2.15831i | −0.706474 | + | 0.407883i | ||||
\(29\) | 3.31662 | 0.615882 | 0.307941 | − | 0.951405i | \(-0.400360\pi\) | ||||
0.307941 | + | 0.951405i | \(0.400360\pi\) | |||||||
\(30\) | −0.939764 | − | 4.37228i | −0.171577 | − | 0.798266i | ||||
\(31\) | −4.31662 | −0.775289 | −0.387644 | − | 0.921809i | \(-0.626711\pi\) | ||||
−0.387644 | + | 0.921809i | \(0.626711\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 4.01251 | + | 2.31662i | 0.698489 | + | 0.403273i | ||||
\(34\) | 0.658312 | − | 1.14023i | 0.112900 | − | 0.195548i | ||||
\(35\) | 2.96181 | − | 9.18662i | 0.500638 | − | 1.55282i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.59808 | + | 5.50000i | 0.427121 | + | 0.904194i | ||||
\(38\) | 2.31662i | 0.375806i | ||||||||
\(39\) | 4.00000 | + | 6.92820i | 0.640513 | + | 1.10940i | ||||
\(40\) | 2.18614 | − | 0.469882i | 0.345659 | − | 0.0742949i | ||||
\(41\) | 2.81662 | − | 4.87854i | 0.439883 | − | 0.761900i | −0.557797 | − | 0.829977i | \(-0.688353\pi\) |
0.997680 | + | 0.0680778i | \(0.0216866\pi\) | |||||||
\(42\) | 7.47661 | + | 4.31662i | 1.15367 | + | 0.666070i | ||||
\(43\) | − | 10.9499i | − | 1.66984i | −0.550371 | − | 0.834920i | \(-0.685514\pi\) | ||
0.550371 | − | 0.834920i | \(-0.314486\pi\) | |||||||
\(44\) | −1.15831 | + | 2.00626i | −0.174622 | + | 0.302454i | ||||
\(45\) | −1.65831 | + | 1.50000i | −0.247207 | + | 0.223607i | ||||
\(46\) | −3.00000 | − | 5.19615i | −0.442326 | − | 0.766131i | ||||
\(47\) | 2.31662i | 0.337914i | 0.985623 | + | 0.168957i | \(0.0540400\pi\) | ||||
−0.985623 | + | 0.168957i | \(0.945960\pi\) | |||||||
\(48\) | 2.00000i | 0.288675i | ||||||||
\(49\) | 5.81662 | + | 10.0747i | 0.830946 | + | 1.43924i | ||||
\(50\) | −2.92048 | + | 4.05842i | −0.413018 | + | 0.573948i | ||||
\(51\) | −2.63325 | −0.368729 | ||||||||
\(52\) | −3.46410 | + | 2.00000i | −0.480384 | + | 0.277350i | ||||
\(53\) | −4.01251 | + | 2.31662i | −0.551161 | + | 0.318213i | −0.749590 | − | 0.661902i | \(-0.769749\pi\) |
0.198429 | + | 0.980115i | \(0.436416\pi\) | |||||||
\(54\) | 2.00000 | + | 3.46410i | 0.272166 | + | 0.471405i | ||||
\(55\) | −1.08854 | − | 5.06447i | −0.146779 | − | 0.682893i | ||||
\(56\) | −2.15831 | + | 3.73831i | −0.288417 | + | 0.499552i | ||||
\(57\) | 4.01251 | − | 2.31662i | 0.531470 | − | 0.306844i | ||||
\(58\) | 2.87228 | − | 1.65831i | 0.377149 | − | 0.217747i | ||||
\(59\) | −0.316625 | − | 0.548410i | −0.0412210 | − | 0.0713969i | 0.844679 | − | 0.535273i | \(-0.179791\pi\) |
−0.885900 | + | 0.463877i | \(0.846458\pi\) | |||||||
\(60\) | −3.00000 | − | 3.31662i | −0.387298 | − | 0.428174i | ||||
\(61\) | 3.97494 | − | 6.88479i | 0.508939 | − | 0.881507i | −0.491008 | − | 0.871155i | \(-0.663371\pi\) |
0.999946 | − | 0.0103523i | \(-0.00329530\pi\) | |||||||
\(62\) | −3.73831 | + | 2.15831i | −0.474765 | + | 0.274106i | ||||
\(63\) | − | 4.31662i | − | 0.543844i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.74456 | − | 8.51278i | 0.340421 | − | 1.05588i | ||||
\(66\) | 4.63325 | 0.570314 | ||||||||
\(67\) | 7.20241 | + | 4.15831i | 0.879914 | + | 0.508019i | 0.870630 | − | 0.491938i | \(-0.163711\pi\) |
0.00928410 | + | 0.999957i | \(0.497045\pi\) | |||||||
\(68\) | − | 1.31662i | − | 0.159664i | ||||||
\(69\) | −6.00000 | + | 10.3923i | −0.722315 | + | 1.25109i | ||||
\(70\) | −2.02830 | − | 9.43675i | −0.242429 | − | 1.12791i | ||||
\(71\) | 7.15831 | − | 12.3986i | 0.849535 | − | 1.47144i | −0.0320881 | − | 0.999485i | \(-0.510216\pi\) |
0.881623 | − | 0.471953i | \(-0.156451\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 10.6332i | − | 1.24453i | −0.782808 | − | 0.622264i | \(-0.786213\pi\) | ||
0.782808 | − | 0.622264i | \(-0.213787\pi\) | |||||||
\(74\) | 5.00000 | + | 3.46410i | 0.581238 | + | 0.402694i | ||||
\(75\) | 9.94987 | + | 1.00000i | 1.14891 | + | 0.115470i | ||||
\(76\) | 1.15831 | + | 2.00626i | 0.132868 | + | 0.230133i | ||||
\(77\) | 8.66025 | + | 5.00000i | 0.986928 | + | 0.569803i | ||||
\(78\) | 6.92820 | + | 4.00000i | 0.784465 | + | 0.452911i | ||||
\(79\) | 4.47494 | − | 7.75082i | 0.503470 | − | 0.872035i | −0.496522 | − | 0.868024i | \(-0.665390\pi\) |
0.999992 | − | 0.00401119i | \(-0.00127680\pi\) | |||||||
\(80\) | 1.65831 | − | 1.50000i | 0.185405 | − | 0.167705i | ||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | − | 5.63325i | − | 0.622088i | ||||||
\(83\) | −5.74456 | + | 3.31662i | −0.630548 | + | 0.364047i | −0.780964 | − | 0.624576i | \(-0.785272\pi\) |
0.150416 | + | 0.988623i | \(0.451939\pi\) | |||||||
\(84\) | 8.63325 | 0.941965 | ||||||||
\(85\) | 1.97494 | + | 2.18338i | 0.214212 | + | 0.236820i | ||||
\(86\) | −5.47494 | − | 9.48287i | −0.590378 | − | 1.02256i | ||||
\(87\) | −5.74456 | − | 3.31662i | −0.615882 | − | 0.355580i | ||||
\(88\) | 2.31662i | 0.246953i | ||||||||
\(89\) | −0.816625 | − | 1.41444i | −0.0865621 | − | 0.149930i | 0.819494 | − | 0.573088i | \(-0.194255\pi\) |
−0.906056 | + | 0.423158i | \(0.860921\pi\) | |||||||
\(90\) | −0.686141 | + | 2.12819i | −0.0723256 | + | 0.224331i | ||||
\(91\) | 8.63325 | + | 14.9532i | 0.905010 | + | 1.56752i | ||||
\(92\) | −5.19615 | − | 3.00000i | −0.541736 | − | 0.312772i | ||||
\(93\) | 7.47661 | + | 4.31662i | 0.775289 | + | 0.447613i | ||||
\(94\) | 1.15831 | + | 2.00626i | 0.119471 | + | 0.206929i | ||||
\(95\) | −4.93023 | − | 1.58953i | −0.505831 | − | 0.163082i | ||||
\(96\) | 1.00000 | + | 1.73205i | 0.102062 | + | 0.176777i | ||||
\(97\) | 9.94987i | 1.01026i | 0.863044 | + | 0.505128i | \(0.168555\pi\) | ||||
−0.863044 | + | 0.505128i | \(0.831445\pi\) | |||||||
\(98\) | 10.0747 | + | 5.81662i | 1.01770 | + | 0.587568i | ||||
\(99\) | −1.15831 | − | 2.00626i | −0.116415 | − | 0.201636i | ||||
\(100\) | −0.500000 | + | 4.97494i | −0.0500000 | + | 0.497494i | ||||
\(101\) | −8.68338 | −0.864028 | −0.432014 | − | 0.901867i | \(-0.642197\pi\) | ||||
−0.432014 | + | 0.901867i | \(0.642197\pi\) | |||||||
\(102\) | −2.28046 | + | 1.31662i | −0.225799 | + | 0.130365i | ||||
\(103\) | 16.3166i | 1.60772i | 0.594815 | + | 0.803862i | \(0.297225\pi\) | ||||
−0.594815 | + | 0.803862i | \(0.702775\pi\) | |||||||
\(104\) | −2.00000 | + | 3.46410i | −0.196116 | + | 0.339683i | ||||
\(105\) | −14.3166 | + | 12.9499i | −1.39716 | + | 1.26378i | ||||
\(106\) | −2.31662 | + | 4.01251i | −0.225010 | + | 0.389730i | ||||
\(107\) | −5.47036 | − | 3.15831i | −0.528839 | − | 0.305326i | 0.211704 | − | 0.977334i | \(-0.432099\pi\) |
−0.740544 | + | 0.672008i | \(0.765432\pi\) | |||||||
\(108\) | 3.46410 | + | 2.00000i | 0.333333 | + | 0.192450i | ||||
\(109\) | −7.97494 | − | 13.8130i | −0.763860 | − | 1.32305i | −0.940847 | − | 0.338832i | \(-0.889968\pi\) |
0.176987 | − | 0.984213i | \(-0.443365\pi\) | |||||||
\(110\) | −3.47494 | − | 3.84169i | −0.331322 | − | 0.366291i | ||||
\(111\) | 1.00000 | − | 12.1244i | 0.0949158 | − | 1.15079i | ||||
\(112\) | 4.31662i | 0.407883i | ||||||||
\(113\) | −16.1369 | + | 9.31662i | −1.51803 | + | 0.876434i | −0.518254 | + | 0.855227i | \(0.673418\pi\) |
−0.999775 | + | 0.0212074i | \(0.993249\pi\) | |||||||
\(114\) | 2.31662 | − | 4.01251i | 0.216972 | − | 0.375806i | ||||
\(115\) | 13.1168 | − | 2.81929i | 1.22315 | − | 0.262900i | ||||
\(116\) | 1.65831 | − | 2.87228i | 0.153970 | − | 0.266685i | ||||
\(117\) | − | 4.00000i | − | 0.369800i | ||||||
\(118\) | −0.548410 | − | 0.316625i | −0.0504853 | − | 0.0291477i | ||||
\(119\) | −5.68338 | −0.520994 | ||||||||
\(120\) | −4.25639 | − | 1.37228i | −0.388553 | − | 0.125272i | ||||
\(121\) | −5.63325 | −0.512114 | ||||||||
\(122\) | − | 7.94987i | − | 0.719748i | ||||||
\(123\) | −9.75707 | + | 5.63325i | −0.879766 | + | 0.507933i | ||||
\(124\) | −2.15831 | + | 3.73831i | −0.193822 | + | 0.335710i | ||||
\(125\) | −6.63325 | − | 9.00000i | −0.593296 | − | 0.804984i | ||||
\(126\) | −2.15831 | − | 3.73831i | −0.192278 | − | 0.333035i | ||||
\(127\) | −12.6728 | + | 7.31662i | −1.12453 | + | 0.649245i | −0.942553 | − | 0.334058i | \(-0.891582\pi\) |
−0.181974 | + | 0.983303i | \(0.558249\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −10.9499 | + | 18.9657i | −0.964083 | + | 1.66984i | ||||
\(130\) | −1.87953 | − | 8.74456i | −0.164845 | − | 0.766949i | ||||
\(131\) | 7.31662 | + | 12.6728i | 0.639256 | + | 1.10722i | 0.985596 | + | 0.169116i | \(0.0540911\pi\) |
−0.346340 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(132\) | 4.01251 | − | 2.31662i | 0.349244 | − | 0.201636i | ||||
\(133\) | 8.66025 | − | 5.00000i | 0.750939 | − | 0.433555i | ||||
\(134\) | 8.31662 | 0.718447 | ||||||||
\(135\) | −8.74456 | + | 1.87953i | −0.752612 | + | 0.161764i | ||||
\(136\) | −0.658312 | − | 1.14023i | −0.0564498 | − | 0.0977740i | ||||
\(137\) | − | 4.68338i | − | 0.400128i | −0.979783 | − | 0.200064i | \(-0.935885\pi\) | ||
0.979783 | − | 0.200064i | \(-0.0641150\pi\) | |||||||
\(138\) | 12.0000i | 1.02151i | ||||||||
\(139\) | 9.94987 | + | 17.2337i | 0.843937 | + | 1.46174i | 0.886541 | + | 0.462650i | \(0.153101\pi\) |
−0.0426035 | + | 0.999092i | \(0.513565\pi\) | |||||||
\(140\) | −6.47494 | − | 7.15831i | −0.547232 | − | 0.604988i | ||||
\(141\) | 2.31662 | − | 4.01251i | 0.195095 | − | 0.337914i | ||||
\(142\) | − | 14.3166i | − | 1.20142i | ||||||
\(143\) | 8.02502 | + | 4.63325i | 0.671086 | + | 0.387452i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 1.55842 | + | 7.25061i | 0.129420 | + | 0.602130i | ||||
\(146\) | −5.31662 | − | 9.20866i | −0.440007 | − | 0.762114i | ||||
\(147\) | − | 23.2665i | − | 1.91899i | ||||||
\(148\) | 6.06218 | + | 0.500000i | 0.498308 | + | 0.0410997i | ||||
\(149\) | −3.94987 | −0.323586 | −0.161793 | − | 0.986825i | \(-0.551728\pi\) | ||||
−0.161793 | + | 0.986825i | \(0.551728\pi\) | |||||||
\(150\) | 9.11684 | − | 4.10891i | 0.744387 | − | 0.335491i | ||||
\(151\) | 1.31662 | − | 2.28046i | 0.107145 | − | 0.185581i | −0.807467 | − | 0.589912i | \(-0.799162\pi\) |
0.914613 | + | 0.404331i | \(0.132496\pi\) | |||||||
\(152\) | 2.00626 | + | 1.15831i | 0.162729 | + | 0.0939515i | ||||
\(153\) | 1.14023 | + | 0.658312i | 0.0921822 | + | 0.0532214i | ||||
\(154\) | 10.0000 | 0.805823 | ||||||||
\(155\) | −2.02830 | − | 9.43675i | −0.162917 | − | 0.757978i | ||||
\(156\) | 8.00000 | 0.640513 | ||||||||
\(157\) | −2.59808 | + | 1.50000i | −0.207349 | + | 0.119713i | −0.600079 | − | 0.799941i | \(-0.704864\pi\) |
0.392730 | + | 0.919654i | \(0.371531\pi\) | |||||||
\(158\) | − | 8.94987i | − | 0.712014i | ||||||
\(159\) | 9.26650 | 0.734881 | ||||||||
\(160\) | 0.686141 | − | 2.12819i | 0.0542442 | − | 0.168249i | ||||
\(161\) | −12.9499 | + | 22.4298i | −1.02059 | + | 1.76772i | ||||
\(162\) | − | 11.0000i | − | 0.864242i | ||||||
\(163\) | 20.9720 | − | 12.1082i | 1.64265 | − | 0.948386i | 0.662768 | − | 0.748825i | \(-0.269382\pi\) |
0.979885 | − | 0.199562i | \(-0.0639518\pi\) | |||||||
\(164\) | −2.81662 | − | 4.87854i | −0.219941 | − | 0.380950i | ||||
\(165\) | −3.17906 | + | 9.86046i | −0.247490 | + | 0.767635i | ||||
\(166\) | −3.31662 | + | 5.74456i | −0.257420 | + | 0.445865i | ||||
\(167\) | −14.9532 | − | 8.63325i | −1.15712 | − | 0.668061i | −0.206504 | − | 0.978446i | \(-0.566209\pi\) |
−0.950611 | + | 0.310385i | \(0.899542\pi\) | |||||||
\(168\) | 7.47661 | − | 4.31662i | 0.576833 | − | 0.333035i | ||||
\(169\) | 1.50000 | + | 2.59808i | 0.115385 | + | 0.199852i | ||||
\(170\) | 2.80203 | + | 0.903390i | 0.214906 | + | 0.0692868i | ||||
\(171\) | −2.31662 | −0.177157 | ||||||||
\(172\) | −9.48287 | − | 5.47494i | −0.723062 | − | 0.417460i | ||||
\(173\) | 12.3552 | − | 7.13325i | 0.939345 | − | 0.542331i | 0.0495899 | − | 0.998770i | \(-0.484209\pi\) |
0.889755 | + | 0.456439i | \(0.150875\pi\) | |||||||
\(174\) | −6.63325 | −0.502865 | ||||||||
\(175\) | 21.4749 | + | 2.15831i | 1.62335 | + | 0.163153i | ||||
\(176\) | 1.15831 | + | 2.00626i | 0.0873111 | + | 0.151227i | ||||
\(177\) | 1.26650i | 0.0951959i | ||||||||
\(178\) | −1.41444 | − | 0.816625i | −0.106016 | − | 0.0612086i | ||||
\(179\) | −21.2665 | −1.58953 | −0.794766 | − | 0.606915i | \(-0.792407\pi\) | ||||
−0.794766 | + | 0.606915i | \(0.792407\pi\) | |||||||
\(180\) | 0.469882 | + | 2.18614i | 0.0350229 | + | 0.162945i | ||||
\(181\) | −3.34169 | + | 5.78797i | −0.248386 | + | 0.430217i | −0.963078 | − | 0.269222i | \(-0.913233\pi\) |
0.714692 | + | 0.699439i | \(0.246567\pi\) | |||||||
\(182\) | 14.9532 | + | 8.63325i | 1.10841 | + | 0.639939i | ||||
\(183\) | −13.7696 | + | 7.94987i | −1.01788 | + | 0.587672i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −10.8030 | + | 8.26411i | −0.794251 | + | 0.607589i | ||||
\(186\) | 8.63325 | 0.633021 | ||||||||
\(187\) | −2.64149 | + | 1.52506i | −0.193165 | + | 0.111524i | ||||
\(188\) | 2.00626 | + | 1.15831i | 0.146321 | + | 0.0844786i | ||||
\(189\) | 8.63325 | − | 14.9532i | 0.627977 | − | 1.08769i | ||||
\(190\) | −5.06447 | + | 1.08854i | −0.367415 | + | 0.0789710i | ||||
\(191\) | −6.63325 | −0.479965 | −0.239983 | − | 0.970777i | \(-0.577142\pi\) | ||||
−0.239983 | + | 0.970777i | \(0.577142\pi\) | |||||||
\(192\) | 1.73205 | + | 1.00000i | 0.125000 | + | 0.0721688i | ||||
\(193\) | 5.31662i | 0.382699i | 0.981522 | + | 0.191350i | \(0.0612864\pi\) | ||||
−0.981522 | + | 0.191350i | \(0.938714\pi\) | |||||||
\(194\) | 4.97494 | + | 8.61684i | 0.357180 | + | 0.618653i | ||||
\(195\) | −13.2665 | + | 12.0000i | −0.950034 | + | 0.859338i | ||||
\(196\) | 11.6332 | 0.830946 | ||||||||
\(197\) | 15.2708 | − | 8.81662i | 1.08800 | − | 0.628159i | 0.154959 | − | 0.987921i | \(-0.450476\pi\) |
0.933044 | + | 0.359762i | \(0.117142\pi\) | |||||||
\(198\) | −2.00626 | − | 1.15831i | −0.142578 | − | 0.0823177i | ||||
\(199\) | −2.94987 | −0.209111 | −0.104556 | − | 0.994519i | \(-0.533342\pi\) | ||||
−0.104556 | + | 0.994519i | \(0.533342\pi\) | |||||||
\(200\) | 2.05446 | + | 4.55842i | 0.145272 | + | 0.322329i | ||||
\(201\) | −8.31662 | − | 14.4048i | −0.586609 | − | 1.01604i | ||||
\(202\) | −7.52002 | + | 4.34169i | −0.529107 | + | 0.305480i | ||||
\(203\) | −12.3986 | − | 7.15831i | −0.870208 | − | 0.502415i | ||||
\(204\) | −1.31662 | + | 2.28046i | −0.0921822 | + | 0.159664i | ||||
\(205\) | 11.9886 | + | 3.86520i | 0.837324 | + | 0.269957i | ||||
\(206\) | 8.15831 | + | 14.1306i | 0.568417 | + | 0.984526i | ||||
\(207\) | 5.19615 | − | 3.00000i | 0.361158 | − | 0.208514i | ||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 2.68338 | − | 4.64774i | 0.185613 | − | 0.321491i | ||||
\(210\) | −5.92362 | + | 18.3732i | −0.408769 | + | 1.26787i | ||||
\(211\) | −7.68338 | −0.528945 | −0.264473 | − | 0.964393i | \(-0.585198\pi\) | ||||
−0.264473 | + | 0.964393i | \(0.585198\pi\) | |||||||
\(212\) | 4.63325i | 0.318213i | ||||||||
\(213\) | −24.7971 | + | 14.3166i | −1.69907 | + | 0.980959i | ||||
\(214\) | −6.31662 | −0.431796 | ||||||||
\(215\) | 23.9380 | − | 5.14515i | 1.63256 | − | 0.350896i | ||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 16.1369 | + | 9.31662i | 1.09544 | + | 0.632454i | ||||
\(218\) | −13.8130 | − | 7.97494i | −0.935534 | − | 0.540131i | ||||
\(219\) | −10.6332 | + | 18.4173i | −0.718528 | + | 1.24453i | ||||
\(220\) | −4.93023 | − | 1.58953i | −0.332396 | − | 0.107166i | ||||
\(221\) | −5.26650 | −0.354263 | ||||||||
\(222\) | −5.19615 | − | 11.0000i | −0.348743 | − | 0.738272i | ||||
\(223\) | − | 26.6332i | − | 1.78349i | −0.452534 | − | 0.891747i | \(-0.649480\pi\) | ||
0.452534 | − | 0.891747i | \(-0.350520\pi\) | |||||||
\(224\) | 2.15831 | + | 3.73831i | 0.144208 | + | 0.249776i | ||||
\(225\) | −4.05842 | − | 2.92048i | −0.270561 | − | 0.194699i | ||||
\(226\) | −9.31662 | + | 16.1369i | −0.619733 | + | 1.07341i | ||||
\(227\) | 11.2149 | + | 6.47494i | 0.744360 | + | 0.429757i | 0.823653 | − | 0.567095i | \(-0.191933\pi\) |
−0.0792922 | + | 0.996851i | \(0.525266\pi\) | |||||||
\(228\) | − | 4.63325i | − | 0.306844i | ||||||
\(229\) | 7.97494 | − | 13.8130i | 0.526999 | − | 0.912788i | −0.472506 | − | 0.881327i | \(-0.656651\pi\) |
0.999505 | − | 0.0314612i | \(-0.0100161\pi\) | |||||||
\(230\) | 9.94987 | − | 9.00000i | 0.656075 | − | 0.593442i | ||||
\(231\) | −10.0000 | − | 17.3205i | −0.657952 | − | 1.13961i | ||||
\(232\) | − | 3.31662i | − | 0.217747i | ||||||
\(233\) | − | 8.05013i | − | 0.527381i | −0.964607 | − | 0.263691i | \(-0.915060\pi\) | ||
0.964607 | − | 0.263691i | \(-0.0849398\pi\) | |||||||
\(234\) | −2.00000 | − | 3.46410i | −0.130744 | − | 0.226455i | ||||
\(235\) | −5.06447 | + | 1.08854i | −0.330369 | + | 0.0710085i | ||||
\(236\) | −0.633250 | −0.0412210 | ||||||||
\(237\) | −15.5016 | + | 8.94987i | −1.00694 | + | 0.581357i | ||||
\(238\) | −4.92195 | + | 2.84169i | −0.319042 | + | 0.184199i | ||||
\(239\) | −0.841688 | − | 1.45785i | −0.0544442 | − | 0.0943002i | 0.837519 | − | 0.546409i | \(-0.184005\pi\) |
−0.891963 | + | 0.452108i | \(0.850672\pi\) | |||||||
\(240\) | −4.37228 | + | 0.939764i | −0.282230 | + | 0.0606615i | ||||
\(241\) | −1.36675 | + | 2.36728i | −0.0880401 | + | 0.152490i | −0.906683 | − | 0.421813i | \(-0.861394\pi\) |
0.818642 | + | 0.574303i | \(0.194727\pi\) | |||||||
\(242\) | −4.87854 | + | 2.81662i | −0.313604 | + | 0.181059i | ||||
\(243\) | −8.66025 | + | 5.00000i | −0.555556 | + | 0.320750i | ||||
\(244\) | −3.97494 | − | 6.88479i | −0.254469 | − | 0.440754i | ||||
\(245\) | −19.2916 | + | 17.4499i | −1.23249 | + | 1.11483i | ||||
\(246\) | −5.63325 | + | 9.75707i | −0.359163 | + | 0.622088i | ||||
\(247\) | 8.02502 | − | 4.63325i | 0.510620 | − | 0.294807i | ||||
\(248\) | 4.31662i | 0.274106i | ||||||||
\(249\) | 13.2665 | 0.840730 | ||||||||
\(250\) | −10.2446 | − | 4.47760i | −0.647923 | − | 0.283189i | ||||
\(251\) | −4.31662 | −0.272463 | −0.136231 | − | 0.990677i | \(-0.543499\pi\) | ||||
−0.136231 | + | 0.990677i | \(0.543499\pi\) | |||||||
\(252\) | −3.73831 | − | 2.15831i | −0.235491 | − | 0.135961i | ||||
\(253\) | 13.8997i | 0.873870i | ||||||||
\(254\) | −7.31662 | + | 12.6728i | −0.459086 | + | 0.795160i | ||||
\(255\) | −1.23732 | − | 5.75665i | −0.0774838 | − | 0.360496i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.4482 | − | 8.34169i | 0.901256 | − | 0.520340i | 0.0236483 | − | 0.999720i | \(-0.492472\pi\) |
0.877607 | + | 0.479380i | \(0.159138\pi\) | |||||||
\(258\) | 21.8997i | 1.36342i | ||||||||
\(259\) | 2.15831 | − | 26.1681i | 0.134111 | − | 1.62601i | ||||
\(260\) | −6.00000 | − | 6.63325i | −0.372104 | − | 0.411377i | ||||
\(261\) | 1.65831 | + | 2.87228i | 0.102647 | + | 0.177790i | ||||
\(262\) | 12.6728 | + | 7.31662i | 0.782926 | + | 0.452023i | ||||
\(263\) | −11.4891 | − | 6.63325i | −0.708450 | − | 0.409024i | 0.102037 | − | 0.994781i | \(-0.467464\pi\) |
−0.810487 | + | 0.585757i | \(0.800797\pi\) | |||||||
\(264\) | 2.31662 | − | 4.01251i | 0.142578 | − | 0.246953i | ||||
\(265\) | −6.94987 | − | 7.68338i | −0.426927 | − | 0.471986i | ||||
\(266\) | 5.00000 | − | 8.66025i | 0.306570 | − | 0.530994i | ||||
\(267\) | 3.26650i | 0.199907i | ||||||||
\(268\) | 7.20241 | − | 4.15831i | 0.439957 | − | 0.254009i | ||||
\(269\) | 25.2665 | 1.54053 | 0.770263 | − | 0.637727i | \(-0.220125\pi\) | ||||
0.770263 | + | 0.637727i | \(0.220125\pi\) | |||||||
\(270\) | −6.63325 | + | 6.00000i | −0.403687 | + | 0.365148i | ||||
\(271\) | 2.79156 | + | 4.83513i | 0.169575 | + | 0.293713i | 0.938271 | − | 0.345902i | \(-0.112427\pi\) |
−0.768695 | + | 0.639615i | \(0.779094\pi\) | |||||||
\(272\) | −1.14023 | − | 0.658312i | −0.0691366 | − | 0.0399161i | ||||
\(273\) | − | 34.5330i | − | 2.09003i | ||||||
\(274\) | −2.34169 | − | 4.05592i | −0.141467 | − | 0.245027i | ||||
\(275\) | 10.5602 | − | 4.75940i | 0.636801 | − | 0.287003i | ||||
\(276\) | 6.00000 | + | 10.3923i | 0.361158 | + | 0.625543i | ||||
\(277\) | 6.61059 | + | 3.81662i | 0.397192 | + | 0.229319i | 0.685272 | − | 0.728288i | \(-0.259684\pi\) |
−0.288080 | + | 0.957606i | \(0.593017\pi\) | |||||||
\(278\) | 17.2337 | + | 9.94987i | 1.03361 | + | 0.596754i | ||||
\(279\) | −2.15831 | − | 3.73831i | −0.129215 | − | 0.223807i | ||||
\(280\) | −9.18662 | − | 2.96181i | −0.549005 | − | 0.177002i | ||||
\(281\) | −14.8166 | − | 25.6631i | −0.883886 | − | 1.53093i | −0.846985 | − | 0.531616i | \(-0.821585\pi\) |
−0.0369003 | − | 0.999319i | \(-0.511748\pi\) | |||||||
\(282\) | − | 4.63325i | − | 0.275906i | ||||||
\(283\) | 1.45785 | + | 0.841688i | 0.0866599 | + | 0.0500331i | 0.542704 | − | 0.839924i | \(-0.317401\pi\) |
−0.456044 | + | 0.889957i | \(0.650734\pi\) | |||||||
\(284\) | −7.15831 | − | 12.3986i | −0.424768 | − | 0.735719i | ||||
\(285\) | 6.94987 | + | 7.68338i | 0.411675 | + | 0.455124i | ||||
\(286\) | 9.26650 | 0.547940 | ||||||||
\(287\) | −21.0588 | + | 12.1583i | −1.24306 | + | 0.717682i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −7.63325 | + | 13.2212i | −0.449015 | + | 0.777716i | ||||
\(290\) | 4.97494 | + | 5.50000i | 0.292138 | + | 0.322971i | ||||
\(291\) | 9.94987 | − | 17.2337i | 0.583272 | − | 1.01026i | ||||
\(292\) | −9.20866 | − | 5.31662i | −0.538896 | − | 0.311132i | ||||
\(293\) | −13.5388 | − | 7.81662i | −0.790945 | − | 0.456652i | 0.0493504 | − | 0.998782i | \(-0.484285\pi\) |
−0.840295 | + | 0.542129i | \(0.817618\pi\) | |||||||
\(294\) | −11.6332 | − | 20.1494i | −0.678465 | − | 1.17514i | ||||
\(295\) | 1.05013 | − | 0.949874i | 0.0611407 | − | 0.0553038i | ||||
\(296\) | 5.50000 | − | 2.59808i | 0.319681 | − | 0.151010i | ||||
\(297\) | − | 9.26650i | − | 0.537697i | ||||||
\(298\) | −3.42069 | + | 1.97494i | −0.198155 | + | 0.114405i | ||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 5.84096 | − | 8.11684i | 0.337228 | − | 0.468626i | ||||
\(301\) | −23.6332 | + | 40.9340i | −1.36220 | + | 2.35940i | ||||
\(302\) | − | 2.63325i | − | 0.151526i | ||||||
\(303\) | 15.0400 | + | 8.68338i | 0.864028 | + | 0.498847i | ||||
\(304\) | 2.31662 | 0.132868 | ||||||||
\(305\) | 16.9189 | + | 5.45473i | 0.968772 | + | 0.312337i | ||||
\(306\) | 1.31662 | 0.0752664 | ||||||||
\(307\) | 22.3166i | 1.27368i | 0.770997 | + | 0.636839i | \(0.219758\pi\) | ||||
−0.770997 | + | 0.636839i | \(0.780242\pi\) | |||||||
\(308\) | 8.66025 | − | 5.00000i | 0.493464 | − | 0.284901i | ||||
\(309\) | 16.3166 | − | 28.2612i | 0.928220 | − | 1.60772i | ||||
\(310\) | −6.47494 | − | 7.15831i | −0.367752 | − | 0.406565i | ||||
\(311\) | 11.7916 | + | 20.4236i | 0.668638 | + | 1.15812i | 0.978285 | + | 0.207264i | \(0.0664558\pi\) |
−0.309647 | + | 0.950852i | \(0.600211\pi\) | |||||||
\(312\) | 6.92820 | − | 4.00000i | 0.392232 | − | 0.226455i | ||||
\(313\) | −20.7412 | + | 11.9749i | −1.17236 | + | 0.676863i | −0.954235 | − | 0.299057i | \(-0.903328\pi\) |
−0.218127 | + | 0.975920i | \(0.569995\pi\) | |||||||
\(314\) | −1.50000 | + | 2.59808i | −0.0846499 | + | 0.146618i | ||||
\(315\) | 9.43675 | − | 2.02830i | 0.531701 | − | 0.114282i | ||||
\(316\) | −4.47494 | − | 7.75082i | −0.251735 | − | 0.436018i | ||||
\(317\) | 18.7349 | − | 10.8166i | 1.05226 | − | 0.607522i | 0.128978 | − | 0.991647i | \(-0.458830\pi\) |
0.923281 | + | 0.384125i | \(0.125497\pi\) | |||||||
\(318\) | 8.02502 | − | 4.63325i | 0.450021 | − | 0.259820i | ||||
\(319\) | −7.68338 | −0.430186 | ||||||||
\(320\) | −0.469882 | − | 2.18614i | −0.0262672 | − | 0.122209i | ||||
\(321\) | 6.31662 | + | 10.9407i | 0.352560 | + | 0.610651i | ||||
\(322\) | 25.8997i | 1.44334i | ||||||||
\(323\) | 3.05013i | 0.169714i | ||||||||
\(324\) | −5.50000 | − | 9.52628i | −0.305556 | − | 0.529238i | ||||
\(325\) | 19.8997 | + | 2.00000i | 1.10384 | + | 0.110940i | ||||
\(326\) | 12.1082 | − | 20.9720i | 0.670610 | − | 1.16153i | ||||
\(327\) | 31.8997i | 1.76406i | ||||||||
\(328\) | −4.87854 | − | 2.81662i | −0.269372 | − | 0.155522i | ||||
\(329\) | 5.00000 | − | 8.66025i | 0.275659 | − | 0.477455i | ||||
\(330\) | 2.17708 | + | 10.1289i | 0.119844 | + | 0.557580i | ||||
\(331\) | −2.94987 | − | 5.10933i | −0.162140 | − | 0.280834i | 0.773496 | − | 0.633801i | \(-0.218506\pi\) |
−0.935636 | + | 0.352967i | \(0.885173\pi\) | |||||||
\(332\) | 6.63325i | 0.364047i | ||||||||
\(333\) | −3.46410 | + | 5.00000i | −0.189832 | + | 0.273998i | ||||
\(334\) | −17.2665 | −0.944781 | ||||||||
\(335\) | −5.70637 | + | 17.6994i | −0.311773 | + | 0.967021i | ||||
\(336\) | 4.31662 | − | 7.47661i | 0.235491 | − | 0.407883i | ||||
\(337\) | −6.88479 | − | 3.97494i | −0.375039 | − | 0.216529i | 0.300619 | − | 0.953744i | \(-0.402807\pi\) |
−0.675657 | + | 0.737216i | \(0.736140\pi\) | |||||||
\(338\) | 2.59808 | + | 1.50000i | 0.141317 | + | 0.0815892i | ||||
\(339\) | 37.2665 | 2.02404 | ||||||||
\(340\) | 2.87833 | − | 0.618658i | 0.156099 | − | 0.0335514i | ||||
\(341\) | 10.0000 | 0.541530 | ||||||||
\(342\) | −2.00626 | + | 1.15831i | −0.108486 | + | 0.0626344i | ||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | −10.9499 | −0.590378 | ||||||||
\(345\) | −25.5383 | − | 8.23369i | −1.37494 | − | 0.443287i | ||||
\(346\) | 7.13325 | − | 12.3552i | 0.383486 | − | 0.664217i | ||||
\(347\) | − | 11.2665i | − | 0.604817i | −0.953178 | − | 0.302409i | \(-0.902209\pi\) | ||
0.953178 | − | 0.302409i | \(-0.0977907\pi\) | |||||||
\(348\) | −5.74456 | + | 3.31662i | −0.307941 | + | 0.177790i | ||||
\(349\) | −17.6583 | − | 30.5851i | −0.945228 | − | 1.63718i | −0.755294 | − | 0.655386i | \(-0.772506\pi\) |
−0.189933 | − | 0.981797i | \(-0.560827\pi\) | |||||||
\(350\) | 19.6770 | − | 8.86832i | 1.05178 | − | 0.474031i | ||||
\(351\) | 8.00000 | − | 13.8564i | 0.427008 | − | 0.739600i | ||||
\(352\) | 2.00626 | + | 1.15831i | 0.106934 | + | 0.0617383i | ||||
\(353\) | 16.6419 | − | 9.60819i | 0.885757 | − | 0.511392i | 0.0132049 | − | 0.999913i | \(-0.495797\pi\) |
0.872552 | + | 0.488521i | \(0.162463\pi\) | |||||||
\(354\) | 0.633250 | + | 1.09682i | 0.0336568 | + | 0.0582953i | ||||
\(355\) | 30.4686 | + | 9.82322i | 1.61710 | + | 0.521362i | ||||
\(356\) | −1.63325 | −0.0865621 | ||||||||
\(357\) | 9.84389 | + | 5.68338i | 0.520994 | + | 0.300796i | ||||
\(358\) | −18.4173 | + | 10.6332i | −0.973386 | + | 0.561985i | ||||
\(359\) | −4.63325 | −0.244534 | −0.122267 | − | 0.992497i | \(-0.539016\pi\) | ||||
−0.122267 | + | 0.992497i | \(0.539016\pi\) | |||||||
\(360\) | 1.50000 | + | 1.65831i | 0.0790569 | + | 0.0874007i | ||||
\(361\) | 6.81662 | + | 11.8067i | 0.358770 | + | 0.621407i | ||||
\(362\) | 6.68338i | 0.351270i | ||||||||
\(363\) | 9.75707 | + | 5.63325i | 0.512114 | + | 0.295669i | ||||
\(364\) | 17.2665 | 0.905010 | ||||||||
\(365\) | 23.2458 | − | 4.99637i | 1.21674 | − | 0.261522i | ||||
\(366\) | −7.94987 | + | 13.7696i | −0.415547 | + | 0.719748i | ||||
\(367\) | −3.46410 | − | 2.00000i | −0.180825 | − | 0.104399i | 0.406855 | − | 0.913493i | \(-0.366625\pi\) |
−0.587680 | + | 0.809093i | \(0.699959\pi\) | |||||||
\(368\) | −5.19615 | + | 3.00000i | −0.270868 | + | 0.156386i | ||||
\(369\) | 5.63325 | 0.293255 | ||||||||
\(370\) | −5.22360 | + | 12.5584i | −0.271562 | + | 0.652881i | ||||
\(371\) | 20.0000 | 1.03835 | ||||||||
\(372\) | 7.47661 | − | 4.31662i | 0.387644 | − | 0.223807i | ||||
\(373\) | 19.8318 | + | 11.4499i | 1.02685 | + | 0.592852i | 0.916081 | − | 0.400994i | \(-0.131335\pi\) |
0.110769 | + | 0.993846i | \(0.464669\pi\) | |||||||
\(374\) | −1.52506 | + | 2.64149i | −0.0788591 | + | 0.136588i | ||||
\(375\) | 2.48913 | + | 22.2217i | 0.128538 | + | 1.14752i | ||||
\(376\) | 2.31662 | 0.119471 | ||||||||
\(377\) | −11.4891 | − | 6.63325i | −0.591720 | − | 0.341630i | ||||
\(378\) | − | 17.2665i | − | 0.888093i | ||||||
\(379\) | 16.4749 | + | 28.5354i | 0.846261 | + | 1.46577i | 0.884522 | + | 0.466499i | \(0.154485\pi\) |
−0.0382612 | + | 0.999268i | \(0.512182\pi\) | |||||||
\(380\) | −3.84169 | + | 3.47494i | −0.197074 | + | 0.178261i | ||||
\(381\) | 29.2665 | 1.49937 | ||||||||
\(382\) | −5.74456 | + | 3.31662i | −0.293917 | + | 0.169693i | ||||
\(383\) | −20.5104 | − | 11.8417i | −1.04803 | − | 0.605082i | −0.125935 | − | 0.992039i | \(-0.540193\pi\) |
−0.922098 | + | 0.386957i | \(0.873526\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | −6.86141 | + | 21.2819i | −0.349690 | + | 1.08463i | ||||
\(386\) | 2.65831 | + | 4.60433i | 0.135305 | + | 0.234354i | ||||
\(387\) | 9.48287 | − | 5.47494i | 0.482041 | − | 0.278307i | ||||
\(388\) | 8.61684 | + | 4.97494i | 0.437454 | + | 0.252564i | ||||
\(389\) | 4.02506 | − | 6.97161i | 0.204079 | − | 0.353475i | −0.745760 | − | 0.666215i | \(-0.767913\pi\) |
0.949839 | + | 0.312740i | \(0.101247\pi\) | |||||||
\(390\) | −5.48913 | + | 17.0256i | −0.277953 | + | 0.862122i | ||||
\(391\) | −3.94987 | − | 6.84138i | −0.199754 | − | 0.345984i | ||||
\(392\) | 10.0747 | − | 5.81662i | 0.508849 | − | 0.293784i | ||||
\(393\) | − | 29.2665i | − | 1.47630i | ||||||
\(394\) | 8.81662 | − | 15.2708i | 0.444175 | − | 0.769334i | ||||
\(395\) | 19.0471 | + | 6.14087i | 0.958362 | + | 0.308981i | ||||
\(396\) | −2.31662 | −0.116415 | ||||||||
\(397\) | − | 10.8997i | − | 0.547043i | −0.961866 | − | 0.273521i | \(-0.911812\pi\) | ||
0.961866 | − | 0.273521i | \(-0.0881884\pi\) | |||||||
\(398\) | −2.55467 | + | 1.47494i | −0.128054 | + | 0.0739319i | ||||
\(399\) | −20.0000 | −1.00125 | ||||||||
\(400\) | 4.05842 | + | 2.92048i | 0.202921 | + | 0.146024i | ||||
\(401\) | −10.7335 | −0.536005 | −0.268003 | − | 0.963418i | \(-0.586364\pi\) | ||||
−0.268003 | + | 0.963418i | \(0.586364\pi\) | |||||||
\(402\) | −14.4048 | − | 8.31662i | −0.718447 | − | 0.414796i | ||||
\(403\) | 14.9532 | + | 8.63325i | 0.744873 | + | 0.430053i | ||||
\(404\) | −4.34169 | + | 7.52002i | −0.216007 | + | 0.374135i | ||||
\(405\) | 23.4101 | + | 7.54755i | 1.16326 | + | 0.375041i | ||||
\(406\) | −14.3166 | −0.710522 | ||||||||
\(407\) | −6.01877 | − | 12.7414i | −0.298339 | − | 0.631570i | ||||
\(408\) | 2.63325i | 0.130365i | ||||||||
\(409\) | 16.0831 | + | 27.8568i | 0.795259 | + | 1.37743i | 0.922674 | + | 0.385580i | \(0.125999\pi\) |
−0.127415 | + | 0.991849i | \(0.540668\pi\) | |||||||
\(410\) | 12.3151 | − | 2.64696i | 0.608198 | − | 0.130724i | ||||
\(411\) | −4.68338 | + | 8.11184i | −0.231014 | + | 0.400128i | ||||
\(412\) | 14.1306 | + | 8.15831i | 0.696165 | + | 0.401931i | ||||
\(413\) | 2.73350i | 0.134507i | ||||||||
\(414\) | 3.00000 | − | 5.19615i | 0.147442 | − | 0.255377i | ||||
\(415\) | −9.94987 | − | 11.0000i | −0.488420 | − | 0.539969i | ||||
\(416\) | 2.00000 | + | 3.46410i | 0.0980581 | + | 0.169842i | ||||
\(417\) | − | 39.7995i | − | 1.94899i | ||||||
\(418\) | − | 5.36675i | − | 0.262496i | ||||||
\(419\) | −18.4749 | − | 31.9995i | −0.902560 | − | 1.56328i | −0.824160 | − | 0.566357i | \(-0.808352\pi\) |
−0.0784000 | − | 0.996922i | \(-0.524981\pi\) | |||||||
\(420\) | 4.05661 | + | 18.8735i | 0.197942 | + | 0.920932i | ||||
\(421\) | 2.05013 | 0.0999170 | 0.0499585 | − | 0.998751i | \(-0.484091\pi\) | ||||
0.0499585 | + | 0.998751i | \(0.484091\pi\) | |||||||
\(422\) | −6.65400 | + | 3.84169i | −0.323912 | + | 0.187010i | ||||
\(423\) | −2.00626 | + | 1.15831i | −0.0975475 | + | 0.0563191i | ||||
\(424\) | 2.31662 | + | 4.01251i | 0.112505 | + | 0.194865i | ||||
\(425\) | −3.84518 | + | 5.34342i | −0.186519 | + | 0.259194i | ||||
\(426\) | −14.3166 | + | 24.7971i | −0.693643 | + | 1.20142i | ||||
\(427\) | −29.7191 | + | 17.1583i | −1.43821 | + | 0.830349i | ||||
\(428\) | −5.47036 | + | 3.15831i | −0.264420 | + | 0.152663i | ||||
\(429\) | −9.26650 | − | 16.0500i | −0.447391 | − | 0.774904i | ||||
\(430\) | 18.1583 | − | 16.4248i | 0.875672 | − | 0.792075i | ||||
\(431\) | 18.1583 | − | 31.4511i | 0.874655 | − | 1.51495i | 0.0175255 | − | 0.999846i | \(-0.494421\pi\) |
0.857130 | − | 0.515101i | \(-0.172245\pi\) | |||||||
\(432\) | 3.46410 | − | 2.00000i | 0.166667 | − | 0.0962250i | ||||
\(433\) | 3.94987i | 0.189819i | 0.995486 | + | 0.0949094i | \(0.0302561\pi\) | ||||
−0.995486 | + | 0.0949094i | \(0.969744\pi\) | |||||||
\(434\) | 18.6332 | 0.894425 | ||||||||
\(435\) | 4.55134 | − | 14.1168i | 0.218220 | − | 0.676851i | ||||
\(436\) | −15.9499 | −0.763860 | ||||||||
\(437\) | 12.0375 | + | 6.94987i | 0.575833 | + | 0.332458i | ||||
\(438\) | 21.2665i | 1.01615i | ||||||||
\(439\) | 6.00000 | − | 10.3923i | 0.286364 | − | 0.495998i | −0.686575 | − | 0.727059i | \(-0.740887\pi\) |
0.972939 | + | 0.231062i | \(0.0742199\pi\) | |||||||
\(440\) | −5.06447 | + | 1.08854i | −0.241439 | + | 0.0518941i | ||||
\(441\) | −5.81662 | + | 10.0747i | −0.276982 | + | 0.479747i | ||||
\(442\) | −4.56092 | + | 2.63325i | −0.216941 | + | 0.125251i | ||||
\(443\) | 1.26650i | 0.0601732i | 0.999547 | + | 0.0300866i | \(0.00957831\pi\) | ||||
−0.999547 | + | 0.0300866i | \(0.990422\pi\) | |||||||
\(444\) | −10.0000 | − | 6.92820i | −0.474579 | − | 0.328798i | ||||
\(445\) | 2.70844 | − | 2.44987i | 0.128392 | − | 0.116135i | ||||
\(446\) | −13.3166 | − | 23.0651i | −0.630560 | − | 1.09216i | ||||
\(447\) | 6.84138 | + | 3.94987i | 0.323586 | + | 0.186823i | ||||
\(448\) | 3.73831 | + | 2.15831i | 0.176618 | + | 0.101971i | ||||
\(449\) | 6.63325 | − | 11.4891i | 0.313042 | − | 0.542205i | −0.665977 | − | 0.745972i | \(-0.731985\pi\) |
0.979019 | + | 0.203767i | \(0.0653185\pi\) | |||||||
\(450\) | −4.97494 | − | 0.500000i | −0.234521 | − | 0.0235702i | ||||
\(451\) | −6.52506 | + | 11.3017i | −0.307253 | + | 0.532178i | ||||
\(452\) | 18.6332i | 0.876434i | ||||||||
\(453\) | −4.56092 | + | 2.63325i | −0.214291 | + | 0.123721i | ||||
\(454\) | 12.9499 | 0.607768 | ||||||||
\(455\) | −28.6332 | + | 25.8997i | −1.34235 | + | 1.21420i | ||||
\(456\) | −2.31662 | − | 4.01251i | −0.108486 | − | 0.187903i | ||||
\(457\) | 25.9374 | + | 14.9749i | 1.21330 | + | 0.700498i | 0.963476 | − | 0.267794i | \(-0.0862946\pi\) |
0.249822 | + | 0.968292i | \(0.419628\pi\) | |||||||
\(458\) | − | 15.9499i | − | 0.745289i | ||||||
\(459\) | 2.63325 | + | 4.56092i | 0.122910 | + | 0.212886i | ||||
\(460\) | 4.11684 | − | 12.7692i | 0.191949 | − | 0.595365i | ||||
\(461\) | 2.68338 | + | 4.64774i | 0.124977 | + | 0.216467i | 0.921724 | − | 0.387846i | \(-0.126781\pi\) |
−0.796747 | + | 0.604313i | \(0.793448\pi\) | |||||||
\(462\) | −17.3205 | − | 10.0000i | −0.805823 | − | 0.465242i | ||||
\(463\) | −8.84764 | − | 5.10819i | −0.411185 | − | 0.237398i | 0.280114 | − | 0.959967i | \(-0.409628\pi\) |
−0.691299 | + | 0.722569i | \(0.742961\pi\) | |||||||
\(464\) | −1.65831 | − | 2.87228i | −0.0769852 | − | 0.133342i | ||||
\(465\) | −5.92362 | + | 18.3732i | −0.274701 | + | 0.852038i | ||||
\(466\) | −4.02506 | − | 6.97161i | −0.186457 | − | 0.322954i | ||||
\(467\) | 13.8997i | 0.643204i | 0.946875 | + | 0.321602i | \(0.104221\pi\) | ||||
−0.946875 | + | 0.321602i | \(0.895779\pi\) | |||||||
\(468\) | −3.46410 | − | 2.00000i | −0.160128 | − | 0.0924500i | ||||
\(469\) | −17.9499 | − | 31.0901i | −0.828848 | − | 1.43561i | ||||
\(470\) | −3.84169 | + | 3.47494i | −0.177204 | + | 0.160287i | ||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | −0.548410 | + | 0.316625i | −0.0252426 | + | 0.0145738i | ||||
\(473\) | 25.3668i | 1.16636i | ||||||||
\(474\) | −8.94987 | + | 15.5016i | −0.411081 | + | 0.712014i | ||||
\(475\) | 1.15831 | − | 11.5251i | 0.0531470 | − | 0.528806i | ||||
\(476\) | −2.84169 | + | 4.92195i | −0.130249 | + | 0.225597i | ||||
\(477\) | −4.01251 | − | 2.31662i | −0.183720 | − | 0.106071i | ||||
\(478\) | −1.45785 | − | 0.841688i | −0.0666803 | − | 0.0384979i | ||||
\(479\) | −18.3166 | − | 31.7253i | −0.836908 | − | 1.44957i | −0.892467 | − | 0.451112i | \(-0.851028\pi\) |
0.0555595 | − | 0.998455i | \(-0.482306\pi\) | |||||||
\(480\) | −3.31662 | + | 3.00000i | −0.151383 | + | 0.136931i | ||||
\(481\) | 2.00000 | − | 24.2487i | 0.0911922 | − | 1.10565i | ||||
\(482\) | 2.73350i | 0.124508i | ||||||||
\(483\) | 44.8597 | − | 25.8997i | 2.04119 | − | 1.17848i | ||||
\(484\) | −2.81662 | + | 4.87854i | −0.128028 | + | 0.221752i | ||||
\(485\) | −21.7518 | + | 4.67527i | −0.987699 | + | 0.212293i | ||||
\(486\) | −5.00000 | + | 8.66025i | −0.226805 | + | 0.392837i | ||||
\(487\) | − | 18.0000i | − | 0.815658i | −0.913058 | − | 0.407829i | \(-0.866286\pi\) | ||
0.913058 | − | 0.407829i | \(-0.133714\pi\) | |||||||
\(488\) | −6.88479 | − | 3.97494i | −0.311660 | − | 0.179937i | ||||
\(489\) | −48.4327 | −2.19020 | ||||||||
\(490\) | −7.98205 | + | 24.7578i | −0.360592 | + | 1.11844i | ||||
\(491\) | 17.6834 | 0.798040 | 0.399020 | − | 0.916942i | \(-0.369350\pi\) | ||||
0.399020 | + | 0.916942i | \(0.369350\pi\) | |||||||
\(492\) | 11.2665i | 0.507933i | ||||||||
\(493\) | 3.78172 | − | 2.18338i | 0.170320 | − | 0.0983343i | ||||
\(494\) | 4.63325 | − | 8.02502i | 0.208460 | − | 0.361063i | ||||
\(495\) | 3.84169 | − | 3.47494i | 0.172671 | − | 0.156187i | ||||
\(496\) | 2.15831 | + | 3.73831i | 0.0969111 | + | 0.167855i | ||||
\(497\) | −53.5199 | + | 30.8997i | −2.40070 | + | 1.38604i | ||||
\(498\) | 11.4891 | − | 6.63325i | 0.514840 | − | 0.297243i | ||||
\(499\) | 1.47494 | − | 2.55467i | 0.0660273 | − | 0.114363i | −0.831122 | − | 0.556090i | \(-0.812301\pi\) |
0.897149 | + | 0.441728i | \(0.145634\pi\) | |||||||
\(500\) | −11.1109 | + | 1.24456i | −0.496892 | + | 0.0556585i | ||||
\(501\) | 17.2665 | + | 29.9065i | 0.771410 | + | 1.33612i | ||||
\(502\) | −3.73831 | + | 2.15831i | −0.166849 | + | 0.0963302i | ||||
\(503\) | −6.56718 | + | 3.79156i | −0.292816 | + | 0.169057i | −0.639211 | − | 0.769031i | \(-0.720739\pi\) |
0.346395 | + | 0.938089i | \(0.387406\pi\) | |||||||
\(504\) | −4.31662 | −0.192278 | ||||||||
\(505\) | −4.08016 | − | 18.9831i | −0.181565 | − | 0.844736i | ||||
\(506\) | 6.94987 | + | 12.0375i | 0.308960 | + | 0.535134i | ||||
\(507\) | − | 6.00000i | − | 0.266469i | ||||||
\(508\) | 14.6332i | 0.649245i | ||||||||
\(509\) | 2.65831 | + | 4.60433i | 0.117828 | + | 0.204083i | 0.918907 | − | 0.394475i | \(-0.129074\pi\) |
−0.801079 | + | 0.598559i | \(0.795740\pi\) | |||||||
\(510\) | −3.94987 | − | 4.36675i | −0.174903 | − | 0.193363i | ||||
\(511\) | −22.9499 | + | 39.7503i | −1.01524 | + | 1.75845i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −8.02502 | − | 4.63325i | −0.354313 | − | 0.204563i | ||||
\(514\) | 8.34169 | − | 14.4482i | 0.367936 | − | 0.637284i | ||||
\(515\) | −35.6704 | + | 7.66689i | −1.57183 | + | 0.337843i | ||||
\(516\) | 10.9499 | + | 18.9657i | 0.482041 | + | 0.834920i | ||||
\(517\) | − | 5.36675i | − | 0.236029i | ||||||
\(518\) | −11.2149 | − | 23.7414i | −0.492755 | − | 1.04314i | ||||
\(519\) | −28.5330 | −1.25246 | ||||||||
\(520\) | −8.51278 | − | 2.74456i | −0.373310 | − | 0.120357i | ||||
\(521\) | 1.36675 | − | 2.36728i | 0.0598784 | − | 0.103712i | −0.834532 | − | 0.550959i | \(-0.814262\pi\) |
0.894411 | + | 0.447247i | \(0.147595\pi\) | |||||||
\(522\) | 2.87228 | + | 1.65831i | 0.125716 | + | 0.0725824i | ||||
\(523\) | 34.5542 | + | 19.9499i | 1.51095 | + | 0.872347i | 0.999918 | + | 0.0127850i | \(0.00406969\pi\) |
0.511031 | + | 0.859562i | \(0.329264\pi\) | |||||||
\(524\) | 14.6332 | 0.639256 | ||||||||
\(525\) | −35.0374 | − | 25.2132i | −1.52916 | − | 1.10040i | ||||
\(526\) | −13.2665 | −0.578447 | ||||||||
\(527\) | −4.92195 | + | 2.84169i | −0.214403 | + | 0.123786i | ||||
\(528\) | − | 4.63325i | − | 0.201636i | ||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −9.86046 | − | 3.17906i | −0.428311 | − | 0.138090i | ||||
\(531\) | 0.316625 | − | 0.548410i | 0.0137403 | − | 0.0237990i | ||||
\(532\) | − | 10.0000i | − | 0.433555i | ||||||
\(533\) | −19.5141 | + | 11.2665i | −0.845252 | + | 0.488006i | ||||
\(534\) | 1.63325 | + | 2.82887i | 0.0706776 | + | 0.122417i | ||||
\(535\) | 4.33409 | − | 13.4430i | 0.187379 | − | 0.581192i | ||||
\(536\) | 4.15831 | − | 7.20241i | 0.179612 | − | 0.311097i | ||||
\(537\) | 36.8347 | + | 21.2665i | 1.58953 | + | 0.917717i | ||||
\(538\) | 21.8814 | − | 12.6332i | 0.943375 | − | 0.544658i | ||||
\(539\) | −13.4749 | − | 23.3393i | −0.580407 | − | 1.00529i | ||||
\(540\) | −2.74456 | + | 8.51278i | −0.118107 | + | 0.366332i | ||||
\(541\) | −21.9499 | −0.943699 | −0.471849 | − | 0.881679i | \(-0.656413\pi\) | ||||
−0.471849 | + | 0.881679i | \(0.656413\pi\) | |||||||
\(542\) | 4.83513 | + | 2.79156i | 0.207686 | + | 0.119908i | ||||
\(543\) | 11.5759 | − | 6.68338i | 0.496771 | − | 0.286811i | ||||
\(544\) | −1.31662 | −0.0564498 | ||||||||
\(545\) | 26.4499 | − | 23.9248i | 1.13299 | − | 1.02483i | ||||
\(546\) | −17.2665 | − | 29.9065i | −0.738938 | − | 1.27988i | ||||
\(547\) | − | 28.3166i | − | 1.21073i | −0.795947 | − | 0.605366i | \(-0.793027\pi\) | ||
0.795947 | − | 0.605366i | \(-0.206973\pi\) | |||||||
\(548\) | −4.05592 | − | 2.34169i | −0.173260 | − | 0.100032i | ||||
\(549\) | 7.94987 | 0.339292 | ||||||||
\(550\) | 6.76566 | − | 9.40184i | 0.288489 | − | 0.400896i | ||||
\(551\) | −3.84169 | + | 6.65400i | −0.163661 | + | 0.283470i | ||||
\(552\) | 10.3923 | + | 6.00000i | 0.442326 | + | 0.255377i | ||||
\(553\) | −33.4574 | + | 19.3166i | −1.42275 | + | 0.821426i | ||||
\(554\) | 7.63325 | 0.324306 | ||||||||
\(555\) | 26.9754 | − | 3.51087i | 1.14504 | − | 0.149028i | ||||
\(556\) | 19.8997 | 0.843937 | ||||||||
\(557\) | −10.6231 | + | 6.13325i | −0.450115 | + | 0.259874i | −0.707879 | − | 0.706334i | \(-0.750348\pi\) |
0.257764 | + | 0.966208i | \(0.417014\pi\) | |||||||
\(558\) | −3.73831 | − | 2.15831i | −0.158255 | − | 0.0913686i | ||||
\(559\) | −21.8997 | + | 37.9315i | −0.926261 | + | 1.60433i | ||||
\(560\) | −9.43675 | + | 2.02830i | −0.398775 | + | 0.0857115i | ||||
\(561\) | 6.10025 | 0.257553 | ||||||||
\(562\) | −25.6631 | − | 14.8166i | −1.08253 | − | 0.625002i | ||||
\(563\) | 44.5330i | 1.87684i | 0.345494 | + | 0.938421i | \(0.387711\pi\) | ||||
−0.345494 | + | 0.938421i | \(0.612289\pi\) | |||||||
\(564\) | −2.31662 | − | 4.01251i | −0.0975475 | − | 0.168957i | ||||
\(565\) | −27.9499 | − | 30.8997i | −1.17586 | − | 1.29996i | ||||
\(566\) | 1.68338 | 0.0707575 | ||||||||
\(567\) | −41.1214 | + | 23.7414i | −1.72694 | + | 0.997047i | ||||
\(568\) | −12.3986 | − | 7.15831i | −0.520232 | − | 0.300356i | ||||
\(569\) | 32.1662 | 1.34848 | 0.674240 | − | 0.738513i | \(-0.264471\pi\) | ||||
0.674240 | + | 0.738513i | \(0.264471\pi\) | |||||||
\(570\) | 9.86046 | + | 3.17906i | 0.413009 | + | 0.133156i | ||||
\(571\) | 18.2665 | + | 31.6385i | 0.764429 | + | 1.32403i | 0.940548 | + | 0.339661i | \(0.110312\pi\) |
−0.176119 | + | 0.984369i | \(0.556354\pi\) | |||||||
\(572\) | 8.02502 | − | 4.63325i | 0.335543 | − | 0.193726i | ||||
\(573\) | 11.4891 | + | 6.63325i | 0.479965 | + | 0.277108i | ||||
\(574\) | −12.1583 | + | 21.0588i | −0.507478 | + | 0.878978i | ||||
\(575\) | 12.3267 | + | 27.3505i | 0.514060 | + | 1.14060i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −15.5885 | + | 9.00000i | −0.648956 | + | 0.374675i | −0.788056 | − | 0.615603i | \(-0.788912\pi\) |
0.139100 | + | 0.990278i | \(0.455579\pi\) | |||||||
\(578\) | 15.2665i | 0.635003i | ||||||||
\(579\) | 5.31662 | − | 9.20866i | 0.220951 | − | 0.382699i | ||||
\(580\) | 7.05842 | + | 2.27567i | 0.293085 | + | 0.0944921i | ||||
\(581\) | 28.6332 | 1.18791 | ||||||||
\(582\) | − | 19.8997i | − | 0.824871i | ||||||
\(583\) | 9.29548 | − | 5.36675i | 0.384980 | − | 0.222268i | ||||
\(584\) | −10.6332 | −0.440007 | ||||||||
\(585\) | 8.74456 | − | 1.87953i | 0.361543 | − | 0.0777089i | ||||
\(586\) | −15.6332 | −0.645804 | ||||||||
\(587\) | 6.29297 | + | 3.63325i | 0.259739 | + | 0.149960i | 0.624215 | − | 0.781252i | \(-0.285419\pi\) |
−0.364477 | + | 0.931213i | \(0.618752\pi\) | |||||||
\(588\) | −20.1494 | − | 11.6332i | −0.830946 | − | 0.479747i | ||||
\(589\) | 5.00000 | − | 8.66025i | 0.206021 | − | 0.356840i | ||||
\(590\) | 0.434498 | − | 1.34768i | 0.0178880 | − | 0.0554830i | ||||
\(591\) | −35.2665 | −1.45067 | ||||||||
\(592\) | 3.46410 | − | 5.00000i | 0.142374 | − | 0.205499i | ||||
\(593\) | − | 29.8496i | − | 1.22578i | −0.790169 | − | 0.612889i | \(-0.790007\pi\) | ||
0.790169 | − | 0.612889i | \(-0.209993\pi\) | |||||||
\(594\) | −4.63325 | − | 8.02502i | −0.190105 | − | 0.329271i | ||||
\(595\) | −2.67052 | − | 12.4247i | −0.109480 | − | 0.509361i | ||||
\(596\) | −1.97494 | + | 3.42069i | −0.0808966 | + | 0.140117i | ||||
\(597\) | 5.10933 | + | 2.94987i | 0.209111 | + | 0.120730i | ||||
\(598\) | 24.0000i | 0.981433i | ||||||||
\(599\) | −0.791562 | + | 1.37103i | −0.0323423 | + | 0.0560186i | −0.881744 | − | 0.471729i | \(-0.843630\pi\) |
0.849401 | + | 0.527748i | \(0.176963\pi\) | |||||||
\(600\) | 1.00000 | − | 9.94987i | 0.0408248 | − | 0.406202i | ||||
\(601\) | −17.5000 | − | 30.3109i | −0.713840 | − | 1.23641i | −0.963405 | − | 0.268049i | \(-0.913621\pi\) |
0.249565 | − | 0.968358i | \(-0.419712\pi\) | |||||||
\(602\) | 47.2665i | 1.92644i | ||||||||
\(603\) | 8.31662i | 0.338679i | ||||||||
\(604\) | −1.31662 | − | 2.28046i | −0.0535727 | − | 0.0927906i | ||||
\(605\) | −2.64696 | − | 12.3151i | −0.107614 | − | 0.500679i | ||||
\(606\) | 17.3668 | 0.705476 | ||||||||
\(607\) | −7.28923 | + | 4.20844i | −0.295861 | + | 0.170815i | −0.640582 | − | 0.767890i | \(-0.721307\pi\) |
0.344721 | + | 0.938705i | \(0.387973\pi\) | |||||||
\(608\) | 2.00626 | − | 1.15831i | 0.0813644 | − | 0.0469758i | ||||
\(609\) | 14.3166 | + | 24.7971i | 0.580139 | + | 1.00483i | ||||
\(610\) | 17.3795 | − | 3.73550i | 0.703677 | − | 0.151246i | ||||
\(611\) | 4.63325 | − | 8.02502i | 0.187441 | − | 0.324658i | ||||
\(612\) | 1.14023 | − | 0.658312i | 0.0460911 | − | 0.0266107i | ||||
\(613\) | −0.317615 | + | 0.183375i | −0.0128284 | + | 0.00740645i | −0.506400 | − | 0.862298i | \(-0.669024\pi\) |
0.493572 | + | 0.869705i | \(0.335691\pi\) | |||||||
\(614\) | 11.1583 | + | 19.3268i | 0.450313 | + | 0.779965i | ||||
\(615\) | −16.8997 | − | 18.6834i | −0.681464 | − | 0.753386i | ||||
\(616\) | 5.00000 | − | 8.66025i | 0.201456 | − | 0.348932i | ||||
\(617\) | 31.1769 | − | 18.0000i | 1.25514 | − | 0.724653i | 0.283011 | − | 0.959117i | \(-0.408667\pi\) |
0.972125 | + | 0.234464i | \(0.0753335\pi\) | |||||||
\(618\) | − | 32.6332i | − | 1.31270i | ||||||
\(619\) | 3.05013 | 0.122595 | 0.0612974 | − | 0.998120i | \(-0.480476\pi\) | ||||
0.0612974 | + | 0.998120i | \(0.480476\pi\) | |||||||
\(620\) | −9.18662 | − | 2.96181i | −0.368943 | − | 0.118949i | ||||
\(621\) | 24.0000 | 0.963087 | ||||||||
\(622\) | 20.4236 | + | 11.7916i | 0.818911 | + | 0.472799i | ||||
\(623\) | 7.05013i | 0.282457i | ||||||||
\(624\) | 4.00000 | − | 6.92820i | 0.160128 | − | 0.277350i | ||||
\(625\) | 16.5584 | − | 18.7302i | 0.662337 | − | 0.749206i | ||||
\(626\) | −11.9749 | + | 20.7412i | −0.478615 | + | 0.828985i | ||||
\(627\) | −9.29548 | + | 5.36675i | −0.371226 | + | 0.214327i | ||||
\(628\) | 3.00000i | 0.119713i | ||||||||
\(629\) | 6.58312 | + | 4.56092i | 0.262486 | + | 0.181856i | ||||
\(630\) | 7.15831 | − | 6.47494i | 0.285194 | − | 0.257968i | ||||
\(631\) | −5.00000 | − | 8.66025i | −0.199047 | − | 0.344759i | 0.749173 | − | 0.662375i | \(-0.230451\pi\) |
−0.948220 | + | 0.317615i | \(0.897118\pi\) | |||||||
\(632\) | −7.75082 | − | 4.47494i | −0.308311 | − | 0.178003i | ||||
\(633\) | 13.3080 | + | 7.68338i | 0.528945 | + | 0.305387i | ||||
\(634\) | 10.8166 | − | 18.7349i | 0.429583 | − | 0.744060i | ||||
\(635\) | −21.9499 | − | 24.2665i | −0.871054 | − | 0.962987i | ||||
\(636\) | 4.63325 | − | 8.02502i | 0.183720 | − | 0.318213i | ||||
\(637\) | − | 46.5330i | − | 1.84370i | ||||||
\(638\) | −6.65400 | + | 3.84169i | −0.263434 | + | 0.152094i | ||||
\(639\) | 14.3166 | 0.566357 | ||||||||
\(640\) | −1.50000 | − | 1.65831i | −0.0592927 | − | 0.0655506i | ||||
\(641\) | −8.13325 | − | 14.0872i | −0.321244 | − | 0.556411i | 0.659501 | − | 0.751704i | \(-0.270768\pi\) |
−0.980745 | + | 0.195293i | \(0.937434\pi\) | |||||||
\(642\) | 10.9407 | + | 6.31662i | 0.431796 | + | 0.249297i | ||||
\(643\) | − | 22.8496i | − | 0.901101i | −0.892751 | − | 0.450551i | \(-0.851228\pi\) | ||
0.892751 | − | 0.450551i | \(-0.148772\pi\) | |||||||
\(644\) | 12.9499 | + | 22.4298i | 0.510297 | + | 0.883860i | ||||
\(645\) | −46.6069 | − | 15.0263i | −1.83515 | − | 0.591660i | ||||
\(646\) | 1.52506 | + | 2.64149i | 0.0600028 | + | 0.103928i | ||||
\(647\) | 9.56969 | + | 5.52506i | 0.376223 | + | 0.217213i | 0.676174 | − | 0.736742i | \(-0.263637\pi\) |
−0.299950 | + | 0.953955i | \(0.596970\pi\) | |||||||
\(648\) | −9.52628 | − | 5.50000i | −0.374228 | − | 0.216060i | ||||
\(649\) | 0.733501 | + | 1.27046i | 0.0287924 | + | 0.0498699i | ||||
\(650\) | 18.2337 | − | 8.21782i | 0.715184 | − | 0.322330i | ||||
\(651\) | −18.6332 | − | 32.2737i | −0.730295 | − | 1.26491i | ||||
\(652\) | − | 24.2164i | − | 0.948386i | ||||||
\(653\) | −9.43946 | − | 5.44987i | −0.369395 | − | 0.213270i | 0.303799 | − | 0.952736i | \(-0.401745\pi\) |
−0.673194 | + | 0.739466i | \(0.735078\pi\) | |||||||
\(654\) | 15.9499 | + | 27.6260i | 0.623689 | + | 1.08026i | ||||
\(655\) | −24.2665 | + | 21.9499i | −0.948171 | + | 0.857653i | ||||
\(656\) | −5.63325 | −0.219941 | ||||||||
\(657\) | 9.20866 | − | 5.31662i | 0.359264 | − | 0.207421i | ||||
\(658\) | − | 10.0000i | − | 0.389841i | ||||||
\(659\) | −14.3166 | + | 24.7971i | −0.557697 | + | 0.965959i | 0.439992 | + | 0.898002i | \(0.354981\pi\) |
−0.997688 | + | 0.0679569i | \(0.978352\pi\) | |||||||
\(660\) | 6.94987 | + | 7.68338i | 0.270523 | + | 0.299075i | ||||
\(661\) | −19.9749 | + | 34.5976i | −0.776935 | + | 1.34569i | 0.156765 | + | 0.987636i | \(0.449893\pi\) |
−0.933700 | + | 0.358055i | \(0.883440\pi\) | |||||||
\(662\) | −5.10933 | − | 2.94987i | −0.198580 | − | 0.114650i | ||||
\(663\) | 9.12184 | + | 5.26650i | 0.354263 | + | 0.204534i | ||||
\(664\) | 3.31662 | + | 5.74456i | 0.128710 | + | 0.222932i | ||||
\(665\) | 15.0000 | + | 16.5831i | 0.581675 | + | 0.643066i | ||||
\(666\) | −0.500000 | + | 6.06218i | −0.0193746 | + | 0.234905i | ||||
\(667\) | − | 19.8997i | − | 0.770521i | ||||||
\(668\) | −14.9532 | + | 8.63325i | −0.578558 | + | 0.334030i | ||||
\(669\) | −26.6332 | + | 46.1301i | −1.02970 | + | 1.78349i | ||||
\(670\) | 3.90783 | + | 18.1813i | 0.150973 | + | 0.702405i | ||||
\(671\) | −9.20844 | + | 15.9495i | −0.355488 | + | 0.615723i | ||||
\(672\) | − | 8.63325i | − | 0.333035i | ||||||
\(673\) | 41.4824 | + | 23.9499i | 1.59903 | + | 0.923200i | 0.991675 | + | 0.128769i | \(0.0411025\pi\) |
0.607354 | + | 0.794431i | \(0.292231\pi\) | |||||||
\(674\) | −7.94987 | −0.306218 | ||||||||
\(675\) | −8.21782 | − | 18.2337i | −0.316304 | − | 0.701815i | ||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 21.6332i | 0.831433i | 0.909494 | + | 0.415717i | \(0.136469\pi\) | ||||
−0.909494 | + | 0.415717i | \(0.863531\pi\) | |||||||
\(678\) | 32.2737 | − | 18.6332i | 1.23947 | − | 0.715606i | ||||
\(679\) | 21.4749 | − | 37.1957i | 0.824132 | − | 1.42744i | ||||
\(680\) | 2.18338 | − | 1.97494i | 0.0837286 | − | 0.0757354i | ||||
\(681\) | −12.9499 | − | 22.4298i | −0.496240 | − | 0.859513i | ||||
\(682\) | 8.66025 | − | 5.00000i | 0.331618 | − | 0.191460i | ||||
\(683\) | 28.9970 | − | 16.7414i | 1.10954 | − | 0.640593i | 0.170830 | − | 0.985301i | \(-0.445355\pi\) |
0.938710 | + | 0.344707i | \(0.112022\pi\) | |||||||
\(684\) | −1.15831 | + | 2.00626i | −0.0442892 | + | 0.0767111i | ||||
\(685\) | 10.2385 | − | 2.20063i | 0.391194 | − | 0.0840819i | ||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | −27.6260 | + | 15.9499i | −1.05400 | + | 0.608526i | ||||
\(688\) | −9.48287 | + | 5.47494i | −0.361531 | + | 0.208730i | ||||
\(689\) | 18.5330 | 0.706051 | ||||||||
\(690\) | −26.2337 | + | 5.63858i | −0.998699 | + | 0.214657i | ||||
\(691\) | 17.1583 | + | 29.7191i | 0.652733 | + | 1.13057i | 0.982457 | + | 0.186489i | \(0.0597110\pi\) |
−0.329724 | + | 0.944077i | \(0.606956\pi\) | |||||||
\(692\) | − | 14.2665i | − | 0.542331i | ||||||
\(693\) | 10.0000i | 0.379869i | ||||||||
\(694\) | −5.63325 | − | 9.75707i | −0.213835 | − | 0.370373i | ||||
\(695\) | −33.0000 | + | 29.8496i | −1.25176 | + | 1.13226i | ||||
\(696\) | −3.31662 | + | 5.74456i | −0.125716 | + | 0.217747i | ||||
\(697\) | − | 7.41688i | − | 0.280934i | ||||||
\(698\) | −30.5851 | − | 17.6583i | −1.15766 | − | 0.668377i | ||||
\(699\) | −8.05013 | + | 13.9432i | −0.304484 | + | 0.527381i | ||||
\(700\) | 12.6066 | − | 17.5187i | 0.476486 | − | 0.662144i | ||||
\(701\) | 8.26650 | + | 14.3180i | 0.312221 | + | 0.540783i | 0.978843 | − | 0.204613i | \(-0.0655936\pi\) |
−0.666622 | + | 0.745396i | \(0.732260\pi\) | |||||||
\(702\) | − | 16.0000i | − | 0.603881i | ||||||
\(703\) | −14.0438 | − | 1.15831i | −0.529672 | − | 0.0436866i | ||||
\(704\) | 2.31662 | 0.0873111 | ||||||||
\(705\) | 9.86046 | + | 3.17906i | 0.371366 | + | 0.119730i | ||||
\(706\) | 9.60819 | − | 16.6419i | 0.361609 | − | 0.626325i | ||||
\(707\) | 32.4611 | + | 18.7414i | 1.22083 | + | 0.704844i | ||||
\(708\) | 1.09682 | + | 0.633250i | 0.0412210 | + | 0.0237990i | ||||
\(709\) | −18.5330 | −0.696021 | −0.348011 | − | 0.937491i | \(-0.613143\pi\) | ||||
−0.348011 | + | 0.937491i | \(0.613143\pi\) | |||||||
\(710\) | 31.2982 | − | 6.72712i | 1.17460 | − | 0.252464i | ||||
\(711\) | 8.94987 | 0.335647 | ||||||||
\(712\) | −1.41444 | + | 0.816625i | −0.0530082 | + | 0.0306043i | ||||
\(713\) | 25.8997i | 0.969953i | ||||||||
\(714\) | 11.3668 | 0.425390 | ||||||||
\(715\) | −6.35812 | + | 19.7209i | −0.237780 | + | 0.737520i | ||||
\(716\) | −10.6332 | + | 18.4173i | −0.397383 | + | 0.688288i | ||||
\(717\) | 3.36675i | 0.125734i | ||||||||
\(718\) | −4.01251 | + | 2.31662i | −0.149746 | + | 0.0864557i | ||||
\(719\) | 10.5831 | + | 18.3305i | 0.394684 | + | 0.683613i | 0.993061 | − | 0.117602i | \(-0.0375208\pi\) |
−0.598377 | + | 0.801215i | \(0.704187\pi\) | |||||||
\(720\) | 2.12819 | + | 0.686141i | 0.0793131 | + | 0.0255710i | ||||
\(721\) | 35.2164 | − | 60.9965i | 1.31153 | − | 2.27163i | ||||
\(722\) | 11.8067 | + | 6.81662i | 0.439401 | + | 0.253689i | ||||
\(723\) | 4.73456 | − | 2.73350i | 0.176080 | − | 0.101660i | ||||
\(724\) | 3.34169 | + | 5.78797i | 0.124193 | + | 0.215108i | ||||
\(725\) | −15.1186 | + | 6.81386i | −0.561490 | + | 0.253060i | ||||
\(726\) | 11.2665 | 0.418139 | ||||||||
\(727\) | −14.4048 | − | 8.31662i | −0.534245 | − | 0.308447i | 0.208498 | − | 0.978023i | \(-0.433142\pi\) |
−0.742743 | + | 0.669576i | \(0.766476\pi\) | |||||||
\(728\) | 14.9532 | − | 8.63325i | 0.554203 | − | 0.319970i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 17.6332 | − | 15.9499i | 0.652636 | − | 0.590331i | ||||
\(731\) | −7.20844 | − | 12.4854i | −0.266614 | − | 0.461788i | ||||
\(732\) | 15.8997i | 0.587672i | ||||||||
\(733\) | −31.1769 | − | 18.0000i | −1.15155 | − | 0.664845i | −0.202282 | − | 0.979327i | \(-0.564836\pi\) |
−0.949263 | + | 0.314482i | \(0.898169\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | 50.8638 | − | 10.9325i | 1.87614 | − | 0.403252i | ||||
\(736\) | −3.00000 | + | 5.19615i | −0.110581 | + | 0.191533i | ||||
\(737\) | −16.6853 | − | 9.63325i | −0.614610 | − | 0.354845i | ||||
\(738\) | 4.87854 | − | 2.81662i | 0.179581 | − | 0.103681i | ||||
\(739\) | 11.8997 | 0.437739 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(740\) | 1.75544 | + | 13.4877i | 0.0645312 | + | 0.495818i | ||||
\(741\) | −18.5330 | −0.680827 | ||||||||
\(742\) | 17.3205 | − | 10.0000i | 0.635856 | − | 0.367112i | ||||
\(743\) | 25.5329 | + | 14.7414i | 0.936712 | + | 0.540811i | 0.888928 | − | 0.458047i | \(-0.151451\pi\) |
0.0477838 | + | 0.998858i | \(0.484784\pi\) | |||||||
\(744\) | 4.31662 | − | 7.47661i | 0.158255 | − | 0.274106i | ||||
\(745\) | −1.85597 | − | 8.63498i | −0.0679976 | − | 0.316361i | ||||
\(746\) | 22.8997 | 0.838419 | ||||||||
\(747\) | −5.74456 | − | 3.31662i | −0.210183 | − | 0.121349i | ||||
\(748\) | 3.05013i | 0.111524i | ||||||||
\(749\) | 13.6332 | + | 23.6135i | 0.498148 | + | 0.862818i | ||||
\(750\) | 13.2665 | + | 18.0000i | 0.484424 | + | 0.657267i | ||||
\(751\) | −24.2164 | −0.883668 | −0.441834 | − | 0.897097i | \(-0.645672\pi\) | ||||
−0.441834 | + | 0.897097i | \(0.645672\pi\) | |||||||
\(752\) | 2.00626 | − | 1.15831i | 0.0731606 | − | 0.0422393i | ||||
\(753\) | 7.47661 | + | 4.31662i | 0.272463 | + | 0.157307i | ||||
\(754\) | −13.2665 | −0.483137 | ||||||||
\(755\) | 5.60407 | + | 1.80678i | 0.203953 | + | 0.0657554i | ||||
\(756\) | −8.63325 | − | 14.9532i | −0.313988 | − | 0.543844i | ||||
\(757\) | 9.61310 | − | 5.55013i | 0.349394 | − | 0.201723i | −0.315024 | − | 0.949084i | \(-0.602013\pi\) |
0.664418 | + | 0.747361i | \(0.268679\pi\) | |||||||
\(758\) | 28.5354 | + | 16.4749i | 1.03645 | + | 0.598397i | ||||
\(759\) | 13.8997 | − | 24.0751i | 0.504529 | − | 0.873870i | ||||
\(760\) | −1.58953 | + | 4.93023i | −0.0576583 | + | 0.178838i | ||||
\(761\) | 10.1332 | + | 17.5513i | 0.367330 | + | 0.636234i | 0.989147 | − | 0.146928i | \(-0.0469386\pi\) |
−0.621817 | + | 0.783162i | \(0.713605\pi\) | |||||||
\(762\) | 25.3455 | − | 14.6332i | 0.918172 | − | 0.530107i | ||||
\(763\) | 68.8496i | 2.49252i | ||||||||
\(764\) | −3.31662 | + | 5.74456i | −0.119991 | + | 0.207831i | ||||
\(765\) | −0.903390 | + | 2.80203i | −0.0326621 | + | 0.101308i | ||||
\(766\) | −23.6834 | −0.855715 | ||||||||
\(767\) | 2.53300i | 0.0914613i | ||||||||
\(768\) | 1.73205 | − | 1.00000i | 0.0625000 | − | 0.0360844i | ||||
\(769\) | 2.73350 | 0.0985726 | 0.0492863 | − | 0.998785i | \(-0.484305\pi\) | ||||
0.0492863 | + | 0.998785i | \(0.484305\pi\) | |||||||
\(770\) | 4.69882 | + | 21.8614i | 0.169334 | + | 0.787830i | ||||
\(771\) | −33.3668 | −1.20167 | ||||||||
\(772\) | 4.60433 | + | 2.65831i | 0.165714 | + | 0.0956748i | ||||
\(773\) | −31.3209 | − | 18.0831i | −1.12653 | − | 0.650405i | −0.183473 | − | 0.983025i | \(-0.558734\pi\) |
−0.943061 | + | 0.332620i | \(0.892067\pi\) | |||||||
\(774\) | 5.47494 | − | 9.48287i | 0.196793 | − | 0.340855i | ||||
\(775\) | 19.6770 | − | 8.86832i | 0.706819 | − | 0.318559i | ||||
\(776\) | 9.94987 | 0.357180 | ||||||||
\(777\) | −29.9065 | + | 43.1662i | −1.07289 | + | 1.54858i | ||||
\(778\) | − | 8.05013i | − | 0.288611i | ||||||
\(779\) | 6.52506 | + | 11.3017i | 0.233785 | + | 0.404927i | ||||
\(780\) | 3.75906 | + | 17.4891i | 0.134596 | + | 0.626211i | ||||
\(781\) | −16.5831 | + | 28.7228i | −0.593391 | + | 1.02778i | ||||
\(782\) | −6.84138 | − | 3.94987i | −0.244647 | − | 0.141247i | ||||
\(783\) | 13.2665i | 0.474106i | ||||||||
\(784\) | 5.81662 | − | 10.0747i | 0.207737 | − | 0.359810i | ||||
\(785\) | −4.50000 | − | 4.97494i | −0.160612 | − | 0.177563i | ||||
\(786\) | −14.6332 | − | 25.3455i | −0.521951 | − | 0.904045i | ||||
\(787\) | − | 24.0000i | − | 0.855508i | −0.903895 | − | 0.427754i | \(-0.859305\pi\) | ||
0.903895 | − | 0.427754i | \(-0.140695\pi\) | |||||||
\(788\) | − | 17.6332i | − | 0.628159i | ||||||
\(789\) | 13.2665 | + | 22.9783i | 0.472300 | + | 0.818047i | ||||
\(790\) | 19.5657 | − | 4.20538i | 0.696116 | − | 0.149621i | ||||
\(791\) | 80.4327 | 2.85986 | ||||||||
\(792\) | −2.00626 | + | 1.15831i | −0.0712892 | + | 0.0411588i | ||||
\(793\) | −27.5392 | + | 15.8997i | −0.977945 | + | 0.564617i | ||||
\(794\) | −5.44987 | − | 9.43946i | −0.193409 | − | 0.334994i | ||||
\(795\) | 4.35416 | + | 20.2579i | 0.154426 | + | 0.718473i | ||||
\(796\) | −1.47494 | + | 2.55467i | −0.0522778 | + | 0.0905477i | ||||
\(797\) | 23.5267 | − | 13.5831i | 0.833357 | − | 0.481139i | −0.0216436 | − | 0.999766i | \(-0.506890\pi\) |
0.855001 | + | 0.518627i | \(0.173557\pi\) | |||||||
\(798\) | −17.3205 | + | 10.0000i | −0.613139 | + | 0.353996i | ||||
\(799\) | 1.52506 | + | 2.64149i | 0.0539528 | + | 0.0934491i | ||||
\(800\) | 4.97494 | + | 0.500000i | 0.175891 | + | 0.0176777i | ||||
\(801\) | 0.816625 | − | 1.41444i | 0.0288540 | − | 0.0499766i | ||||
\(802\) | −9.29548 | + | 5.36675i | −0.328235 | + | 0.189507i | ||||
\(803\) | 24.6332i | 0.869289i | ||||||||
\(804\) | −16.6332 | −0.586609 | ||||||||
\(805\) | −55.1197 | − | 17.7709i | −1.94271 | − | 0.626341i | ||||
\(806\) | 17.2665 | 0.608186 | ||||||||
\(807\) | −43.7629 | − | 25.2665i | −1.54053 | − | 0.889423i | ||||
\(808\) | 8.68338i | 0.305480i | ||||||||
\(809\) | 0.949874 | − | 1.64523i | 0.0333958 | − | 0.0578432i | −0.848844 | − | 0.528643i | \(-0.822701\pi\) |
0.882240 | + | 0.470799i | \(0.156034\pi\) | |||||||
\(810\) | 24.0475 | − | 5.16870i | 0.844945 | − | 0.181610i | ||||
\(811\) | −12.9499 | + | 22.4298i | −0.454732 | + | 0.787618i | −0.998673 | − | 0.0515052i | \(-0.983598\pi\) |
0.543941 | + | 0.839123i | \(0.316931\pi\) | |||||||
\(812\) | −12.3986 | + | 7.15831i | −0.435104 | + | 0.251208i | ||||
\(813\) | − | 11.1662i | − | 0.391617i | ||||||
\(814\) | −11.5831 | − | 8.02502i | −0.405988 | − | 0.281277i | ||||
\(815\) | 36.3246 | + | 40.1583i | 1.27239 | + | 1.40668i | ||||
\(816\) | 1.31662 | + | 2.28046i | 0.0460911 | + | 0.0798321i | ||||
\(817\) | 21.9683 | + | 12.6834i | 0.768572 | + | 0.443735i | ||||
\(818\) | 27.8568 | + | 16.0831i | 0.973990 | + | 0.562333i | ||||
\(819\) | −8.63325 | + | 14.9532i | −0.301670 | + | 0.522508i | ||||
\(820\) | 9.34169 | − | 8.44987i | 0.326226 | − | 0.295082i | ||||
\(821\) | 5.26650 | − | 9.12184i | 0.183802 | − | 0.318355i | −0.759370 | − | 0.650659i | \(-0.774493\pi\) |
0.943172 | + | 0.332304i | \(0.107826\pi\) | |||||||
\(822\) | 9.36675i | 0.326703i | ||||||||
\(823\) | −12.1244 | + | 7.00000i | −0.422628 | + | 0.244005i | −0.696201 | − | 0.717847i | \(-0.745128\pi\) |
0.273573 | + | 0.961851i | \(0.411795\pi\) | |||||||
\(824\) | 16.3166 | 0.568417 | ||||||||
\(825\) | −23.0501 | − | 2.31662i | −0.802502 | − | 0.0806545i | ||||
\(826\) | 1.36675 | + | 2.36728i | 0.0475553 | + | 0.0823682i | ||||
\(827\) | −22.9783 | − | 13.2665i | −0.799032 | − | 0.461321i | 0.0441005 | − | 0.999027i | \(-0.485958\pi\) |
−0.843133 | + | 0.537706i | \(0.819291\pi\) | |||||||
\(828\) | − | 6.00000i | − | 0.208514i | ||||||
\(829\) | −27.9499 | − | 48.4106i | −0.970739 | − | 1.68137i | −0.693333 | − | 0.720617i | \(-0.743859\pi\) |
−0.277406 | − | 0.960753i | \(-0.589475\pi\) | |||||||
\(830\) | −14.1168 | − | 4.55134i | −0.490003 | − | 0.157979i | ||||
\(831\) | −7.63325 | − | 13.2212i | −0.264794 | − | 0.458638i | ||||
\(832\) | 3.46410 | + | 2.00000i | 0.120096 | + | 0.0693375i | ||||
\(833\) | 13.2646 | + | 7.65831i | 0.459591 | + | 0.265345i | ||||
\(834\) | −19.8997 | − | 34.4674i | −0.689072 | − | 1.19351i | ||||
\(835\) | 11.8472 | − | 36.7465i | 0.409991 | − | 1.27166i | ||||
\(836\) | −2.68338 | − | 4.64774i | −0.0928065 | − | 0.160746i | ||||
\(837\) | − | 17.2665i | − | 0.596818i | ||||||
\(838\) | −31.9995 | − | 18.4749i | −1.10541 | − | 0.638206i | ||||
\(839\) | −9.94987 | − | 17.2337i | −0.343508 | − | 0.594973i | 0.641574 | − | 0.767061i | \(-0.278282\pi\) |
−0.985082 | + | 0.172088i | \(0.944949\pi\) | |||||||
\(840\) | 12.9499 | + | 14.3166i | 0.446813 | + | 0.493970i | ||||
\(841\) | −18.0000 | −0.620690 | ||||||||
\(842\) | 1.77546 | − | 1.02506i | 0.0611864 | − | 0.0353260i | ||||
\(843\) | 59.2665i | 2.04125i | ||||||||
\(844\) | −3.84169 | + | 6.65400i | −0.132236 | + | 0.229040i | ||||
\(845\) | −4.97494 | + | 4.50000i | −0.171143 | + | 0.154805i | ||||
\(846\) | −1.15831 | + | 2.00626i | −0.0398236 | + | 0.0689765i | ||||
\(847\) | 21.0588 | + | 12.1583i | 0.723589 | + | 0.417765i | ||||
\(848\) | 4.01251 | + | 2.31662i | 0.137790 | + | 0.0795532i | ||||
\(849\) | −1.68338 | − | 2.91569i | −0.0577733 | − | 0.100066i | ||||
\(850\) | −0.658312 | + | 6.55013i | −0.0225799 | + | 0.224667i | ||||
\(851\) | 33.0000 | − | 15.5885i | 1.13123 | − | 0.534365i | ||||
\(852\) | 28.6332i | 0.980959i | ||||||||
\(853\) | 48.6414 | − | 28.0831i | 1.66545 | − | 0.961548i | 0.695406 | − | 0.718617i | \(-0.255225\pi\) |
0.970044 | − | 0.242931i | \(-0.0781088\pi\) | |||||||
\(854\) | −17.1583 | + | 29.7191i | −0.587145 | + | 1.01697i | ||||
\(855\) | −1.08854 | − | 5.06447i | −0.0372273 | − | 0.173201i | ||||
\(856\) | −3.15831 | + | 5.47036i | −0.107949 | + | 0.186973i | ||||
\(857\) | − | 26.5831i | − | 0.908062i | −0.890986 | − | 0.454031i | \(-0.849985\pi\) | ||
0.890986 | − | 0.454031i | \(-0.150015\pi\) | |||||||
\(858\) | −16.0500 | − | 9.26650i | −0.547940 | − | 0.316353i | ||||
\(859\) | 24.9499 | 0.851279 | 0.425639 | − | 0.904893i | \(-0.360049\pi\) | ||||
0.425639 | + | 0.904893i | \(0.360049\pi\) | |||||||
\(860\) | 7.51315 | − | 23.3035i | 0.256196 | − | 0.794641i | ||||
\(861\) | 48.6332 | 1.65742 | ||||||||
\(862\) | − | 36.3166i | − | 1.23695i | ||||||
\(863\) | −6.37979 | + | 3.68338i | −0.217171 | + | 0.125384i | −0.604640 | − | 0.796499i | \(-0.706683\pi\) |
0.387469 | + | 0.921883i | \(0.373349\pi\) | |||||||
\(864\) | 2.00000 | − | 3.46410i | 0.0680414 | − | 0.117851i | ||||
\(865\) | 21.3997 | + | 23.6583i | 0.727613 | + | 0.804407i | ||||
\(866\) | 1.97494 | + | 3.42069i | 0.0671111 | + | 0.116240i | ||||
\(867\) | 26.4424 | − | 15.2665i | 0.898029 | − | 0.518477i | ||||
\(868\) | 16.1369 | − | 9.31662i | 0.547721 | − | 0.316227i | ||||
\(869\) | −10.3668 | + | 17.9557i | −0.351668 | + | 0.609107i | ||||
\(870\) | −3.11684 | − | 14.5012i | −0.105671 | − | 0.491637i | ||||
\(871\) | −16.6332 | − | 28.8096i | −0.563596 | − | 0.976177i | ||||
\(872\) | −13.8130 | + | 7.97494i | −0.467767 | + | 0.270065i | ||||
\(873\) | −8.61684 | + | 4.97494i | −0.291636 | + | 0.168376i | ||||
\(874\) | 13.8997 | 0.470166 | ||||||||
\(875\) | 5.37231 | + | 47.9614i | 0.181617 | + | 1.62139i | ||||
\(876\) | 10.6332 | + | 18.4173i | 0.359264 | + | 0.622264i | ||||
\(877\) | 15.0000i | 0.506514i | 0.967399 | + | 0.253257i | \(0.0815018\pi\) | ||||
−0.967399 | + | 0.253257i | \(0.918498\pi\) | |||||||
\(878\) | − | 12.0000i | − | 0.404980i | ||||||
\(879\) | 15.6332 | + | 27.0776i | 0.527296 | + | 0.913304i | ||||
\(880\) | −3.84169 | + | 3.47494i | −0.129503 | + | 0.117140i | ||||
\(881\) | 18.8166 | − | 32.5914i | 0.633948 | − | 1.09803i | −0.352789 | − | 0.935703i | \(-0.614767\pi\) |
0.986737 | − | 0.162327i | \(-0.0519001\pi\) | |||||||
\(882\) | 11.6332i | 0.391712i | ||||||||
\(883\) | −27.6260 | − | 15.9499i | −0.929689 | − | 0.536756i | −0.0429756 | − | 0.999076i | \(-0.513684\pi\) |
−0.886713 | + | 0.462320i | \(0.847017\pi\) | |||||||
\(884\) | −2.63325 | + | 4.56092i | −0.0885658 | + | 0.153400i | ||||
\(885\) | −2.76875 | + | 0.595105i | −0.0930704 | + | 0.0200042i | ||||
\(886\) | 0.633250 | + | 1.09682i | 0.0212744 | + | 0.0368484i | ||||
\(887\) | 31.2665i | 1.04983i | 0.851156 | + | 0.524913i | \(0.175902\pi\) | ||||
−0.851156 | + | 0.524913i | \(0.824098\pi\) | |||||||
\(888\) | −12.1244 | − | 1.00000i | −0.406867 | − | 0.0335578i | ||||
\(889\) | 63.1662 | 2.11853 | ||||||||
\(890\) | 1.12064 | − | 3.47587i | 0.0375639 | − | 0.116512i | ||||
\(891\) | −12.7414 | + | 22.0688i | −0.426854 | + | 0.739333i | ||||
\(892\) | −23.0651 | − | 13.3166i | −0.772276 | − | 0.445874i | ||||
\(893\) | −4.64774 | − | 2.68338i | −0.155531 | − | 0.0897957i | ||||
\(894\) | 7.89975 | 0.264207 | ||||||||
\(895\) | −9.99274 | − | 46.4916i | −0.334021 | − | 1.55404i | ||||
\(896\) | 4.31662 | 0.144208 | ||||||||
\(897\) | 41.5692 | − | 24.0000i | 1.38796 | − | 0.801337i | ||||
\(898\) | − | 13.2665i | − | 0.442709i | ||||||
\(899\) | −14.3166 | −0.477486 | ||||||||
\(900\) | −4.55842 | + | 2.05446i | −0.151947 | + | 0.0684819i | ||||
\(901\) | −3.05013 | + | 5.28297i | −0.101614 | + | 0.176001i | ||||
\(902\) | 13.0501i | 0.434522i | ||||||||
\(903\) | 81.8680 | − | 47.2665i | 2.72440 | − | 1.57293i | ||||
\(904\) | 9.31662 | + | 16.1369i | 0.309866 | + | 0.536704i | ||||
\(905\) | −14.2235 | − | 4.58574i | −0.472806 | − | 0.152435i | ||||
\(906\) | −2.63325 | + | 4.56092i | −0.0874839 | + | 0.151526i | ||||
\(907\) | 29.6322 | + | 17.1082i | 0.983923 | + | 0.568068i | 0.903452 | − | 0.428689i | \(-0.141024\pi\) |
0.0804705 | + | 0.996757i | \(0.474358\pi\) | |||||||
\(908\) | 11.2149 | − | 6.47494i | 0.372180 | − | 0.214878i | ||||
\(909\) | −4.34169 | − | 7.52002i | −0.144005 | − | 0.249423i | ||||
\(910\) | −11.8472 | + | 36.7465i | −0.392732 | + | 1.21813i | ||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −4.01251 | − | 2.31662i | −0.132868 | − | 0.0767111i | ||||
\(913\) | 13.3080 | − | 7.68338i | 0.440430 | − | 0.254283i | ||||
\(914\) | 29.9499 | 0.990654 | ||||||||
\(915\) | −23.8496 | − | 26.3668i | −0.788444 | − | 0.871658i | ||||
\(916\) | −7.97494 | − | 13.8130i | −0.263499 | − | 0.456394i | ||||
\(917\) | − | 63.1662i | − | 2.08593i | ||||||
\(918\) | 4.56092 | + | 2.63325i | 0.150533 | + | 0.0869102i | ||||
\(919\) | 55.8997 | 1.84396 | 0.921981 | − | 0.387234i | \(-0.126570\pi\) | ||||
0.921981 | + | 0.387234i | \(0.126570\pi\) | |||||||
\(920\) | −2.81929 | − | 13.1168i | −0.0929493 | − | 0.432450i | ||||
\(921\) | 22.3166 | − | 38.6535i | 0.735358 | − | 1.27368i | ||||
\(922\) | 4.64774 | + | 2.68338i | 0.153065 | + | 0.0883723i | ||||
\(923\) | −49.5942 | + | 28.6332i | −1.63241 | + | 0.942475i | ||||
\(924\) | −20.0000 | −0.657952 | ||||||||
\(925\) | −23.1426 | − | 19.7337i | −0.760925 | − | 0.648840i | ||||
\(926\) | −10.2164 | −0.335731 | ||||||||
\(927\) | −14.1306 | + | 8.15831i | −0.464110 | + | 0.267954i | ||||
\(928\) | −2.87228 | − | 1.65831i | −0.0942873 | − | 0.0544368i | ||||
\(929\) | 8.44987 | − | 14.6356i | 0.277231 | − | 0.480179i | −0.693464 | − | 0.720491i | \(-0.743916\pi\) |
0.970696 | + | 0.240312i | \(0.0772498\pi\) | |||||||
\(930\) | 4.05661 | + | 18.8735i | 0.133021 | + | 0.618886i | ||||
\(931\) | −26.9499 | −0.883246 | ||||||||
\(932\) | −6.97161 | − | 4.02506i | −0.228363 | − | 0.131845i | ||||
\(933\) | − | 47.1662i | − | 1.54415i | ||||||
\(934\) | 6.94987 | + | 12.0375i | 0.227407 | + | 0.393880i | ||||
\(935\) | −4.57519 | − | 5.05806i | −0.149625 | − | 0.165416i | ||||
\(936\) | −4.00000 | −0.130744 | ||||||||
\(937\) | 12.0809 | − | 6.97494i | 0.394667 | − | 0.227861i | −0.289513 | − | 0.957174i | \(-0.593493\pi\) |
0.684180 | + | 0.729313i | \(0.260160\pi\) | |||||||
\(938\) | −31.0901 | − | 17.9499i | −1.01513 | − | 0.586084i | ||||
\(939\) | 47.8997 | 1.56315 | ||||||||
\(940\) | −1.58953 | + | 4.93023i | −0.0518448 | + | 0.160806i | ||||
\(941\) | 1.70844 | + | 2.95910i | 0.0556935 | + | 0.0964640i | 0.892528 | − | 0.450992i | \(-0.148930\pi\) |
−0.836835 | + | 0.547456i | \(0.815596\pi\) | |||||||
\(942\) | 5.19615 | − | 3.00000i | 0.169300 | − | 0.0977453i | ||||
\(943\) | −29.2712 | − | 16.8997i | −0.953202 | − | 0.550332i | ||||
\(944\) | −0.316625 | + | 0.548410i | −0.0103053 | + | 0.0178492i | ||||
\(945\) | 36.7465 | + | 11.8472i | 1.19536 | + | 0.385391i | ||||
\(946\) | 12.6834 | + | 21.9683i | 0.412372 | + | 0.714249i | ||||
\(947\) | −18.4173 | + | 10.6332i | −0.598483 | + | 0.345534i | −0.768444 | − | 0.639916i | \(-0.778969\pi\) |
0.169962 | + | 0.985451i | \(0.445636\pi\) | |||||||
\(948\) | 17.8997i | 0.581357i | ||||||||
\(949\) | −21.2665 | + | 36.8347i | −0.690340 | + | 1.19570i | ||||
\(950\) | −4.75940 | − | 10.5602i | −0.154415 | − | 0.342617i | ||||
\(951\) | −43.2665 | −1.40301 | ||||||||
\(952\) | 5.68338i | 0.184199i | ||||||||
\(953\) | −11.0275 | + | 6.36675i | −0.357217 | + | 0.206239i | −0.667859 | − | 0.744288i | \(-0.732789\pi\) |
0.310642 | + | 0.950527i | \(0.399456\pi\) | |||||||
\(954\) | −4.63325 | −0.150007 | ||||||||
\(955\) | −3.11684 | − | 14.5012i | −0.100859 | − | 0.469248i | ||||
\(956\) | −1.68338 | −0.0544442 | ||||||||
\(957\) | 13.3080 | + | 7.68338i | 0.430186 | + | 0.248368i | ||||
\(958\) | −31.7253 | − | 18.3166i | −1.02500 | − | 0.591783i | ||||
\(959\) | −10.1082 | + | 17.5079i | −0.326410 | + | 0.565359i | ||||
\(960\) | −1.37228 | + | 4.25639i | −0.0442902 | + | 0.137374i | ||||
\(961\) | −12.3668 | −0.398927 | ||||||||
\(962\) | −10.3923 | − | 22.0000i | −0.335061 | − | 0.709308i | ||||
\(963\) | − | 6.31662i | − | 0.203550i | ||||||
\(964\) | 1.36675 | + | 2.36728i | 0.0440201 | + | 0.0762450i | ||||
\(965\) | −11.6229 | + | 2.49819i | −0.374154 | + | 0.0804194i | ||||
\(966\) | 25.8997 | − | 44.8597i | 0.833311 | − | 1.44334i | ||||
\(967\) | −2.36728 | − | 1.36675i | −0.0761266 | − | 0.0439517i | 0.461454 | − | 0.887164i | \(-0.347328\pi\) |
−0.537580 | + | 0.843213i | \(0.680661\pi\) | |||||||
\(968\) | 5.63325i | 0.181059i | ||||||||
\(969\) | 3.05013 | − | 5.28297i | 0.0979842 | − | 0.169714i | ||||
\(970\) | −16.5000 | + | 14.9248i | −0.529783 | + | 0.479207i | ||||
\(971\) | −9.94987 | − | 17.2337i | −0.319307 | − | 0.553055i | 0.661037 | − | 0.750353i | \(-0.270117\pi\) |
−0.980344 | + | 0.197298i | \(0.936783\pi\) | |||||||
\(972\) | 10.0000i | 0.320750i | ||||||||
\(973\) | − | 85.8997i | − | 2.75382i | ||||||
\(974\) | −9.00000 | − | 15.5885i | −0.288379 | − | 0.499486i | ||||
\(975\) | −32.4674 | − | 23.3639i | −1.03979 | − | 0.748242i | ||||
\(976\) | −7.94987 | −0.254469 | ||||||||
\(977\) | 51.7011 | − | 29.8496i | 1.65406 | − | 0.954974i | 0.678687 | − | 0.734428i | \(-0.262549\pi\) |
0.975376 | − | 0.220547i | \(-0.0707841\pi\) | |||||||
\(978\) | −41.9440 | + | 24.2164i | −1.34122 | + | 0.774354i | ||||
\(979\) | 1.89181 | + | 3.27672i | 0.0604626 | + | 0.104724i | ||||
\(980\) | 5.46625 | + | 25.4319i | 0.174613 | + | 0.812393i | ||||
\(981\) | 7.97494 | − | 13.8130i | 0.254620 | − | 0.441015i | ||||
\(982\) | 15.3143 | − | 8.84169i | 0.488697 | − | 0.282150i | ||||
\(983\) | 26.2550 | − | 15.1583i | 0.837403 | − | 0.483475i | −0.0189774 | − | 0.999820i | \(-0.506041\pi\) |
0.856381 | + | 0.516345i | \(0.172708\pi\) | |||||||
\(984\) | 5.63325 | + | 9.75707i | 0.179581 | + | 0.311044i | ||||
\(985\) | 26.4499 | + | 29.2414i | 0.842763 | + | 0.931710i | ||||
\(986\) | 2.18338 | − | 3.78172i | 0.0695328 | − | 0.120434i | ||||
\(987\) | −17.3205 | + | 10.0000i | −0.551318 | + | 0.318304i | ||||
\(988\) | − | 9.26650i | − | 0.294807i | ||||||
\(989\) | −65.6992 | −2.08911 | ||||||||
\(990\) | 1.58953 | − | 4.93023i | 0.0505186 | − | 0.156693i | ||||
\(991\) | 46.3166 | 1.47130 | 0.735648 | − | 0.677364i | \(-0.236878\pi\) | ||||
0.735648 | + | 0.677364i | \(0.236878\pi\) | |||||||
\(992\) | 3.73831 | + | 2.15831i | 0.118691 | + | 0.0685265i | ||||
\(993\) | 11.7995i | 0.374446i | ||||||||
\(994\) | −30.8997 | + | 53.5199i | −0.980081 | + | 1.69755i | ||||
\(995\) | −1.38609 | − | 6.44884i | −0.0439421 | − | 0.204442i | ||||
\(996\) | 6.63325 | − | 11.4891i | 0.210183 | − | 0.364047i | ||||
\(997\) | −27.5392 | + | 15.8997i | −0.872174 | + | 0.503550i | −0.868070 | − | 0.496441i | \(-0.834640\pi\) |
−0.00410416 | + | 0.999992i | \(0.501306\pi\) | |||||||
\(998\) | − | 2.94987i | − | 0.0933766i | ||||||
\(999\) | −22.0000 | + | 10.3923i | −0.696049 | + | 0.328798i |
(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 | 370.2.n.e.359.3 | yes | 8 | |
5.4 | even | 2 | inner | 370.2.n.e.359.1 | yes | 8 | |
37.10 | even | 3 | inner | 370.2.n.e.269.1 | ✓ | 8 | |
185.84 | even | 6 | inner | 370.2.n.e.269.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.n.e.269.1 | ✓ | 8 | 37.10 | even | 3 | inner | |
370.2.n.e.269.3 | yes | 8 | 185.84 | even | 6 | inner | |
370.2.n.e.359.1 | yes | 8 | 5.4 | even | 2 | inner | |
370.2.n.e.359.3 | yes | 8 | 1.1 | even | 1 | trivial |