Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), 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: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 697.12 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.a.43.12 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.06140 | + | 0.866398i | −0.921884 | + | 0.387465i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −0.662100 | − | 0.662100i | −0.250250 | − | 0.250250i | 0.570823 | − | 0.821073i | \(-0.306624\pi\) |
−0.821073 | + | 0.570823i | \(0.806624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.866398 | + | 2.06140i | 0.273979 | + | 0.651871i | ||||
\(11\) | 3.51735i | 1.06052i | 0.847835 | + | 0.530260i | \(0.177906\pi\) | ||||
−0.847835 | + | 0.530260i | \(0.822094\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | − | 6.87657i | − | 1.90722i | −0.301047 | − | 0.953609i | \(-0.597336\pi\) | ||
0.301047 | − | 0.953609i | \(-0.402664\pi\) | |||||||
\(14\) | −0.662100 | + | 0.662100i | −0.176954 | + | 0.176954i | ||||
\(15\) | −2.07026 | − | 0.844991i | −0.534540 | − | 0.218176i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.17458 | −0.527412 | −0.263706 | − | 0.964603i | \(-0.584945\pi\) | ||||
−0.263706 | + | 0.964603i | \(0.584945\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.01389 | + | 1.01389i | 0.232601 | + | 0.232601i | 0.813778 | − | 0.581176i | \(-0.197407\pi\) |
−0.581176 | + | 0.813778i | \(0.697407\pi\) | |||||||
\(20\) | 2.06140 | − | 0.866398i | 0.460942 | − | 0.193732i | ||||
\(21\) | − | 0.936350i | − | 0.204328i | ||||||
\(22\) | 3.51735 | 0.749901 | ||||||||
\(23\) | − | 9.57399i | − | 1.99632i | −0.0606732 | − | 0.998158i | \(-0.519325\pi\) | ||
0.0606732 | − | 0.998158i | \(-0.480675\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 3.49871 | − | 3.57198i | 0.699742 | − | 0.714396i | ||||
\(26\) | −6.87657 | −1.34861 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0.662100 | + | 0.662100i | 0.125125 | + | 0.125125i | ||||
\(29\) | 6.49970 | − | 6.49970i | 1.20696 | − | 1.20696i | 0.234958 | − | 0.972006i | \(-0.424505\pi\) |
0.972006 | − | 0.234958i | \(-0.0754952\pi\) | |||||||
\(30\) | −0.844991 | + | 2.07026i | −0.154274 | + | 0.377977i | ||||
\(31\) | 2.38699 | + | 2.38699i | 0.428716 | + | 0.428716i | 0.888191 | − | 0.459475i | \(-0.151962\pi\) |
−0.459475 | + | 0.888191i | \(0.651962\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.48714 | + | 2.48714i | −0.432956 | + | 0.432956i | ||||
\(34\) | 2.17458i | 0.372937i | ||||||||
\(35\) | 1.93849 | + | 0.791208i | 0.327665 | + | 0.133739i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −1.24106 | − | 5.95481i | −0.204029 | − | 0.978965i | ||||
\(38\) | 1.01389 | − | 1.01389i | 0.164474 | − | 0.164474i | ||||
\(39\) | 4.86247 | − | 4.86247i | 0.778619 | − | 0.778619i | ||||
\(40\) | −0.866398 | − | 2.06140i | −0.136990 | − | 0.325935i | ||||
\(41\) | 3.47992i | 0.543472i | 0.962372 | + | 0.271736i | \(0.0875977\pi\) | ||||
−0.962372 | + | 0.271736i | \(0.912402\pi\) | |||||||
\(42\) | −0.936350 | −0.144482 | ||||||||
\(43\) | − | 2.74581i | − | 0.418732i | −0.977837 | − | 0.209366i | \(-0.932860\pi\) | ||
0.977837 | − | 0.209366i | \(-0.0671400\pi\) | |||||||
\(44\) | − | 3.51735i | − | 0.530260i | ||||||
\(45\) | −0.866398 | − | 2.06140i | −0.129155 | − | 0.307295i | ||||
\(46\) | −9.57399 | −1.41161 | ||||||||
\(47\) | 3.59071 | + | 3.59071i | 0.523759 | + | 0.523759i | 0.918704 | − | 0.394946i | \(-0.129237\pi\) |
−0.394946 | + | 0.918704i | \(0.629237\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 6.12325i | − | 0.874750i | ||||||
\(50\) | −3.57198 | − | 3.49871i | −0.505154 | − | 0.494792i | ||||
\(51\) | −1.53766 | − | 1.53766i | −0.215315 | − | 0.215315i | ||||
\(52\) | 6.87657i | 0.953609i | ||||||||
\(53\) | −2.93440 | + | 2.93440i | −0.403071 | + | 0.403071i | −0.879314 | − | 0.476243i | \(-0.841998\pi\) |
0.476243 | + | 0.879314i | \(0.341998\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | −3.04742 | − | 7.25065i | −0.410914 | − | 0.977677i | ||||
\(56\) | 0.662100 | − | 0.662100i | 0.0884768 | − | 0.0884768i | ||||
\(57\) | 1.43385i | 0.189918i | ||||||||
\(58\) | −6.49970 | − | 6.49970i | −0.853452 | − | 0.853452i | ||||
\(59\) | 3.45523 | + | 3.45523i | 0.449833 | + | 0.449833i | 0.895299 | − | 0.445466i | \(-0.146962\pi\) |
−0.445466 | + | 0.895299i | \(0.646962\pi\) | |||||||
\(60\) | 2.07026 | + | 0.844991i | 0.267270 | + | 0.109088i | ||||
\(61\) | −9.99355 | − | 9.99355i | −1.27954 | − | 1.27954i | −0.940924 | − | 0.338619i | \(-0.890040\pi\) |
−0.338619 | − | 0.940924i | \(-0.609960\pi\) | |||||||
\(62\) | 2.38699 | − | 2.38699i | 0.303148 | − | 0.303148i | ||||
\(63\) | 0.662100 | − | 0.662100i | 0.0834167 | − | 0.0834167i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.95785 | + | 14.1753i | 0.738980 | + | 1.75824i | ||||
\(66\) | 2.48714 | + | 2.48714i | 0.306146 | + | 0.306146i | ||||
\(67\) | 1.14933 | − | 1.14933i | 0.140413 | − | 0.140413i | −0.633406 | − | 0.773819i | \(-0.718344\pi\) |
0.773819 | + | 0.633406i | \(0.218344\pi\) | |||||||
\(68\) | 2.17458 | 0.263706 | ||||||||
\(69\) | 6.76983 | − | 6.76983i | 0.814992 | − | 0.814992i | ||||
\(70\) | 0.791208 | − | 1.93849i | 0.0945674 | − | 0.231694i | ||||
\(71\) | −7.32848 | −0.869730 | −0.434865 | − | 0.900496i | \(-0.643204\pi\) | ||||
−0.434865 | + | 0.900496i | \(0.643204\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.292649 | + | 0.292649i | 0.0342519 | + | 0.0342519i | 0.724025 | − | 0.689773i | \(-0.242290\pi\) |
−0.689773 | + | 0.724025i | \(0.742290\pi\) | |||||||
\(74\) | −5.95481 | + | 1.24106i | −0.692233 | + | 0.144270i | ||||
\(75\) | 4.99973 | − | 0.0518094i | 0.577319 | − | 0.00598243i | ||||
\(76\) | −1.01389 | − | 1.01389i | −0.116301 | − | 0.116301i | ||||
\(77\) | 2.32883 | − | 2.32883i | 0.265395 | − | 0.265395i | ||||
\(78\) | −4.86247 | − | 4.86247i | −0.550567 | − | 0.550567i | ||||
\(79\) | −7.95594 | − | 7.95594i | −0.895113 | − | 0.895113i | 0.0998861 | − | 0.994999i | \(-0.468152\pi\) |
−0.994999 | + | 0.0998861i | \(0.968152\pi\) | |||||||
\(80\) | −2.06140 | + | 0.866398i | −0.230471 | + | 0.0968662i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 3.47992 | 0.384293 | ||||||||
\(83\) | −1.46770 | + | 1.46770i | −0.161102 | + | 0.161102i | −0.783055 | − | 0.621953i | \(-0.786339\pi\) |
0.621953 | + | 0.783055i | \(0.286339\pi\) | |||||||
\(84\) | 0.936350i | 0.102164i | ||||||||
\(85\) | 4.48266 | − | 1.88405i | 0.486213 | − | 0.204354i | ||||
\(86\) | −2.74581 | −0.296088 | ||||||||
\(87\) | 9.19196 | 0.985481 | ||||||||
\(88\) | −3.51735 | −0.374951 | ||||||||
\(89\) | 6.43088 | − | 6.43088i | 0.681672 | − | 0.681672i | −0.278705 | − | 0.960377i | \(-0.589905\pi\) |
0.960377 | + | 0.278705i | \(0.0899052\pi\) | |||||||
\(90\) | −2.06140 | + | 0.866398i | −0.217290 | + | 0.0913264i | ||||
\(91\) | −4.55298 | + | 4.55298i | −0.477282 | + | 0.477282i | ||||
\(92\) | 9.57399i | 0.998158i | ||||||||
\(93\) | 3.37571i | 0.350045i | ||||||||
\(94\) | 3.59071 | − | 3.59071i | 0.370353 | − | 0.370353i | ||||
\(95\) | −2.96845 | − | 1.21159i | −0.304556 | − | 0.124307i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 0.301015 | 0.0305635 | 0.0152817 | − | 0.999883i | \(-0.495135\pi\) | ||||
0.0152817 | + | 0.999883i | \(0.495135\pi\) | |||||||
\(98\) | −6.12325 | −0.618541 | ||||||||
\(99\) | −3.51735 | −0.353507 | ||||||||
\(100\) | −3.49871 | + | 3.57198i | −0.349871 | + | 0.357198i | ||||
\(101\) | 7.88206i | 0.784294i | 0.919903 | + | 0.392147i | \(0.128268\pi\) | ||||
−0.919903 | + | 0.392147i | \(0.871732\pi\) | |||||||
\(102\) | −1.53766 | + | 1.53766i | −0.152251 | + | 0.152251i | ||||
\(103\) | −3.81714 | −0.376114 | −0.188057 | − | 0.982158i | \(-0.560219\pi\) | ||||
−0.188057 | + | 0.982158i | \(0.560219\pi\) | |||||||
\(104\) | 6.87657 | 0.674304 | ||||||||
\(105\) | 0.811252 | + | 1.93019i | 0.0791701 | + | 0.188367i | ||||
\(106\) | 2.93440 | + | 2.93440i | 0.285014 | + | 0.285014i | ||||
\(107\) | −3.39625 | − | 3.39625i | −0.328328 | − | 0.328328i | 0.523622 | − | 0.851950i | \(-0.324580\pi\) |
−0.851950 | + | 0.523622i | \(0.824580\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 1.95485 | + | 1.95485i | 0.187241 | + | 0.187241i | 0.794502 | − | 0.607261i | \(-0.207732\pi\) |
−0.607261 | + | 0.794502i | \(0.707732\pi\) | |||||||
\(110\) | −7.25065 | + | 3.04742i | −0.691322 | + | 0.290560i | ||||
\(111\) | 3.33312 | − | 5.08825i | 0.316366 | − | 0.482955i | ||||
\(112\) | −0.662100 | − | 0.662100i | −0.0625625 | − | 0.0625625i | ||||
\(113\) | 18.3281 | 1.72416 | 0.862079 | − | 0.506773i | \(-0.169162\pi\) | ||||
0.862079 | + | 0.506773i | \(0.169162\pi\) | |||||||
\(114\) | 1.43385 | 0.134292 | ||||||||
\(115\) | 8.29489 | + | 19.7358i | 0.773502 | + | 1.84037i | ||||
\(116\) | −6.49970 | + | 6.49970i | −0.603482 | + | 0.603482i | ||||
\(117\) | 6.87657 | 0.635739 | ||||||||
\(118\) | 3.45523 | − | 3.45523i | 0.318080 | − | 0.318080i | ||||
\(119\) | 1.43979 | + | 1.43979i | 0.131985 | + | 0.131985i | ||||
\(120\) | 0.844991 | − | 2.07026i | 0.0771368 | − | 0.188988i | ||||
\(121\) | −1.37173 | −0.124703 | ||||||||
\(122\) | −9.99355 | + | 9.99355i | −0.904773 | + | 0.904773i | ||||
\(123\) | −2.46067 | + | 2.46067i | −0.221871 | + | 0.221871i | ||||
\(124\) | −2.38699 | − | 2.38699i | −0.214358 | − | 0.214358i | ||||
\(125\) | −4.11747 | + | 10.3945i | −0.368278 | + | 0.929716i | ||||
\(126\) | −0.662100 | − | 0.662100i | −0.0589845 | − | 0.0589845i | ||||
\(127\) | −0.247513 | − | 0.247513i | −0.0219632 | − | 0.0219632i | 0.696040 | − | 0.718003i | \(-0.254944\pi\) |
−0.718003 | + | 0.696040i | \(0.754944\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 1.94158 | − | 1.94158i | 0.170947 | − | 0.170947i | ||||
\(130\) | 14.1753 | − | 5.95785i | 1.24326 | − | 0.522538i | ||||
\(131\) | −1.31529 | − | 1.31529i | −0.114917 | − | 0.114917i | 0.647310 | − | 0.762227i | \(-0.275894\pi\) |
−0.762227 | + | 0.647310i | \(0.775894\pi\) | |||||||
\(132\) | 2.48714 | − | 2.48714i | 0.216478 | − | 0.216478i | ||||
\(133\) | − | 1.34259i | − | 0.116417i | ||||||
\(134\) | −1.14933 | − | 1.14933i | −0.0992872 | − | 0.0992872i | ||||
\(135\) | 0.844991 | − | 2.07026i | 0.0727253 | − | 0.178180i | ||||
\(136\) | − | 2.17458i | − | 0.186468i | ||||||
\(137\) | −13.6827 | − | 13.6827i | −1.16899 | − | 1.16899i | −0.982447 | − | 0.186544i | \(-0.940271\pi\) |
−0.186544 | − | 0.982447i | \(-0.559729\pi\) | |||||||
\(138\) | −6.76983 | − | 6.76983i | −0.576287 | − | 0.576287i | ||||
\(139\) | 17.7419 | 1.50484 | 0.752422 | − | 0.658681i | \(-0.228885\pi\) | ||||
0.752422 | + | 0.658681i | \(0.228885\pi\) | |||||||
\(140\) | −1.93849 | − | 0.791208i | −0.163832 | − | 0.0668693i | ||||
\(141\) | 5.07803i | 0.427647i | ||||||||
\(142\) | 7.32848i | 0.614992i | ||||||||
\(143\) | 24.1873 | 2.02264 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −7.76713 | + | 19.0298i | −0.645025 | + | 1.58034i | ||||
\(146\) | 0.292649 | − | 0.292649i | 0.0242198 | − | 0.0242198i | ||||
\(147\) | 4.32979 | − | 4.32979i | 0.357115 | − | 0.357115i | ||||
\(148\) | 1.24106 | + | 5.95481i | 0.102015 | + | 0.489482i | ||||
\(149\) | 10.6094i | 0.869159i | 0.900633 | + | 0.434579i | \(0.143103\pi\) | ||||
−0.900633 | + | 0.434579i | \(0.856897\pi\) | |||||||
\(150\) | −0.0518094 | − | 4.99973i | −0.00423022 | − | 0.408226i | ||||
\(151\) | − | 3.90183i | − | 0.317526i | −0.987317 | − | 0.158763i | \(-0.949249\pi\) | ||
0.987317 | − | 0.158763i | \(-0.0507506\pi\) | |||||||
\(152\) | −1.01389 | + | 1.01389i | −0.0822370 | + | 0.0822370i | ||||
\(153\) | − | 2.17458i | − | 0.175804i | ||||||
\(154\) | −2.32883 | − | 2.32883i | −0.187663 | − | 0.187663i | ||||
\(155\) | −6.98861 | − | 2.85245i | −0.561339 | − | 0.229114i | ||||
\(156\) | −4.86247 | + | 4.86247i | −0.389309 | + | 0.389309i | ||||
\(157\) | 1.75656 | + | 1.75656i | 0.140188 | + | 0.140188i | 0.773718 | − | 0.633530i | \(-0.218395\pi\) |
−0.633530 | + | 0.773718i | \(0.718395\pi\) | |||||||
\(158\) | −7.95594 | + | 7.95594i | −0.632940 | + | 0.632940i | ||||
\(159\) | −4.14987 | −0.329106 | ||||||||
\(160\) | 0.866398 | + | 2.06140i | 0.0684948 | + | 0.162968i | ||||
\(161\) | −6.33894 | + | 6.33894i | −0.499578 | + | 0.499578i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −9.39725 | −0.736049 | −0.368025 | − | 0.929816i | \(-0.619966\pi\) | ||||
−0.368025 | + | 0.929816i | \(0.619966\pi\) | |||||||
\(164\) | − | 3.47992i | − | 0.271736i | ||||||
\(165\) | 2.97213 | − | 7.28184i | 0.231380 | − | 0.566890i | ||||
\(166\) | 1.46770 | + | 1.46770i | 0.113916 | + | 0.113916i | ||||
\(167\) | −18.3360 | −1.41888 | −0.709441 | − | 0.704765i | \(-0.751052\pi\) | ||||
−0.709441 | + | 0.704765i | \(0.751052\pi\) | |||||||
\(168\) | 0.936350 | 0.0722410 | ||||||||
\(169\) | −34.2873 | −2.63748 | ||||||||
\(170\) | −1.88405 | − | 4.48266i | −0.144500 | − | 0.343805i | ||||
\(171\) | −1.01389 | + | 1.01389i | −0.0775338 | + | 0.0775338i | ||||
\(172\) | 2.74581i | 0.209366i | ||||||||
\(173\) | −5.06991 | − | 5.06991i | −0.385458 | − | 0.385458i | 0.487606 | − | 0.873064i | \(-0.337870\pi\) |
−0.873064 | + | 0.487606i | \(0.837870\pi\) | |||||||
\(174\) | − | 9.19196i | − | 0.696841i | ||||||
\(175\) | −4.68150 | + | 0.0485117i | −0.353888 | + | 0.00366714i | ||||
\(176\) | 3.51735i | 0.265130i | ||||||||
\(177\) | 4.88643i | 0.367287i | ||||||||
\(178\) | −6.43088 | − | 6.43088i | −0.482015 | − | 0.482015i | ||||
\(179\) | −14.7313 | + | 14.7313i | −1.10107 | + | 1.10107i | −0.106786 | + | 0.994282i | \(0.534056\pi\) |
−0.994282 | + | 0.106786i | \(0.965944\pi\) | |||||||
\(180\) | 0.866398 | + | 2.06140i | 0.0645775 | + | 0.153647i | ||||
\(181\) | −4.07298 | −0.302742 | −0.151371 | − | 0.988477i | \(-0.548369\pi\) | ||||
−0.151371 | + | 0.988477i | \(0.548369\pi\) | |||||||
\(182\) | 4.55298 | + | 4.55298i | 0.337489 | + | 0.337489i | ||||
\(183\) | − | 14.1330i | − | 1.04474i | ||||||
\(184\) | 9.57399 | 0.705804 | ||||||||
\(185\) | 7.71755 | + | 11.2000i | 0.567406 | + | 0.823438i | ||||
\(186\) | 3.37571 | 0.247519 | ||||||||
\(187\) | − | 7.64874i | − | 0.559331i | ||||||
\(188\) | −3.59071 | − | 3.59071i | −0.261879 | − | 0.261879i | ||||
\(189\) | 0.936350 | 0.0681095 | ||||||||
\(190\) | −1.21159 | + | 2.96845i | −0.0878981 | + | 0.215354i | ||||
\(191\) | 0.841106 | − | 0.841106i | 0.0608603 | − | 0.0608603i | −0.676022 | − | 0.736882i | \(-0.736297\pi\) |
0.736882 | + | 0.676022i | \(0.236297\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | − | 2.71107i | − | 0.195147i | −0.995228 | − | 0.0975736i | \(-0.968892\pi\) | ||
0.995228 | − | 0.0975736i | \(-0.0311081\pi\) | |||||||
\(194\) | − | 0.301015i | − | 0.0216116i | ||||||
\(195\) | −5.81065 | + | 14.2363i | −0.416109 | + | 1.01948i | ||||
\(196\) | 6.12325i | 0.437375i | ||||||||
\(197\) | 14.0103 | + | 14.0103i | 0.998195 | + | 0.998195i | 0.999998 | − | 0.00180312i | \(-0.000573952\pi\) |
−0.00180312 | + | 0.999998i | \(0.500574\pi\) | |||||||
\(198\) | 3.51735i | 0.249967i | ||||||||
\(199\) | −2.28257 | + | 2.28257i | −0.161807 | + | 0.161807i | −0.783367 | − | 0.621560i | \(-0.786499\pi\) |
0.621560 | + | 0.783367i | \(0.286499\pi\) | |||||||
\(200\) | 3.57198 | + | 3.49871i | 0.252577 | + | 0.247396i | ||||
\(201\) | 1.62540 | 0.114647 | ||||||||
\(202\) | 7.88206 | 0.554580 | ||||||||
\(203\) | −8.60689 | −0.604085 | ||||||||
\(204\) | 1.53766 | + | 1.53766i | 0.107658 | + | 0.107658i | ||||
\(205\) | −3.01499 | − | 7.17349i | −0.210576 | − | 0.501018i | ||||
\(206\) | 3.81714i | 0.265953i | ||||||||
\(207\) | 9.57399 | 0.665438 | ||||||||
\(208\) | − | 6.87657i | − | 0.476805i | ||||||
\(209\) | −3.56619 | + | 3.56619i | −0.246678 | + | 0.246678i | ||||
\(210\) | 1.93019 | − | 0.811252i | 0.133196 | − | 0.0559817i | ||||
\(211\) | 16.7409 | 1.15249 | 0.576247 | − | 0.817276i | \(-0.304517\pi\) | ||||
0.576247 | + | 0.817276i | \(0.304517\pi\) | |||||||
\(212\) | 2.93440 | − | 2.93440i | 0.201536 | − | 0.201536i | ||||
\(213\) | −5.18202 | − | 5.18202i | −0.355066 | − | 0.355066i | ||||
\(214\) | −3.39625 | + | 3.39625i | −0.232163 | + | 0.232163i | ||||
\(215\) | 2.37896 | + | 5.66020i | 0.162244 | + | 0.386022i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | − | 3.16085i | − | 0.214572i | ||||||
\(218\) | 1.95485 | − | 1.95485i | 0.132399 | − | 0.132399i | ||||
\(219\) | 0.413868i | 0.0279666i | ||||||||
\(220\) | 3.04742 | + | 7.25065i | 0.205457 | + | 0.488839i | ||||
\(221\) | 14.9536i | 1.00589i | ||||||||
\(222\) | −5.08825 | − | 3.33312i | −0.341501 | − | 0.223705i | ||||
\(223\) | 16.5296 | − | 16.5296i | 1.10690 | − | 1.10690i | 0.113349 | − | 0.993555i | \(-0.463842\pi\) |
0.993555 | − | 0.113349i | \(-0.0361580\pi\) | |||||||
\(224\) | −0.662100 | + | 0.662100i | −0.0442384 | + | 0.0442384i | ||||
\(225\) | 3.57198 | + | 3.49871i | 0.238132 | + | 0.233247i | ||||
\(226\) | − | 18.3281i | − | 1.21916i | ||||||
\(227\) | 28.0799 | 1.86373 | 0.931865 | − | 0.362805i | \(-0.118181\pi\) | ||||
0.931865 | + | 0.362805i | \(0.118181\pi\) | |||||||
\(228\) | − | 1.43385i | − | 0.0949591i | ||||||
\(229\) | 0.286568i | 0.0189369i | 0.999955 | + | 0.00946847i | \(0.00301395\pi\) | ||||
−0.999955 | + | 0.00946847i | \(0.996986\pi\) | |||||||
\(230\) | 19.7358 | − | 8.29489i | 1.30134 | − | 0.546949i | ||||
\(231\) | 3.29347 | 0.216694 | ||||||||
\(232\) | 6.49970 | + | 6.49970i | 0.426726 | + | 0.426726i | ||||
\(233\) | −10.2080 | − | 10.2080i | −0.668751 | − | 0.668751i | 0.288676 | − | 0.957427i | \(-0.406785\pi\) |
−0.957427 | + | 0.288676i | \(0.906785\pi\) | |||||||
\(234\) | − | 6.87657i | − | 0.449536i | ||||||
\(235\) | −10.5129 | − | 4.29089i | −0.685783 | − | 0.279907i | ||||
\(236\) | −3.45523 | − | 3.45523i | −0.224916 | − | 0.224916i | ||||
\(237\) | − | 11.2514i | − | 0.730857i | ||||||
\(238\) | 1.43979 | − | 1.43979i | 0.0933275 | − | 0.0933275i | ||||
\(239\) | 16.6011 | + | 16.6011i | 1.07384 | + | 1.07384i | 0.997047 | + | 0.0767893i | \(0.0244669\pi\) |
0.0767893 | + | 0.997047i | \(0.475533\pi\) | |||||||
\(240\) | −2.07026 | − | 0.844991i | −0.133635 | − | 0.0545440i | ||||
\(241\) | −17.4511 | + | 17.4511i | −1.12412 | + | 1.12412i | −0.133010 | + | 0.991115i | \(0.542464\pi\) |
−0.991115 | + | 0.133010i | \(0.957536\pi\) | |||||||
\(242\) | 1.37173i | 0.0881784i | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 9.99355 | + | 9.99355i | 0.639771 | + | 0.639771i | ||||
\(245\) | 5.30517 | + | 12.6224i | 0.338935 | + | 0.806418i | ||||
\(246\) | 2.46067 | + | 2.46067i | 0.156887 | + | 0.156887i | ||||
\(247\) | 6.97206 | − | 6.97206i | 0.443622 | − | 0.443622i | ||||
\(248\) | −2.38699 | + | 2.38699i | −0.151574 | + | 0.151574i | ||||
\(249\) | −2.07565 | −0.131539 | ||||||||
\(250\) | 10.3945 | + | 4.11747i | 0.657408 | + | 0.260412i | ||||
\(251\) | −0.992524 | − | 0.992524i | −0.0626476 | − | 0.0626476i | 0.675089 | − | 0.737736i | \(-0.264105\pi\) |
−0.737736 | + | 0.675089i | \(0.764105\pi\) | |||||||
\(252\) | −0.662100 | + | 0.662100i | −0.0417084 | + | 0.0417084i | ||||
\(253\) | 33.6751 | 2.11713 | ||||||||
\(254\) | −0.247513 | + | 0.247513i | −0.0155303 | + | 0.0155303i | ||||
\(255\) | 4.50195 | + | 1.83750i | 0.281923 | + | 0.115069i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.19465 | 0.573546 | 0.286773 | − | 0.957998i | \(-0.407417\pi\) | ||||
0.286773 | + | 0.957998i | \(0.407417\pi\) | |||||||
\(258\) | −1.94158 | − | 1.94158i | −0.120877 | − | 0.120877i | ||||
\(259\) | −3.12097 | + | 4.76438i | −0.193928 | + | 0.296044i | ||||
\(260\) | −5.95785 | − | 14.1753i | −0.369490 | − | 0.879118i | ||||
\(261\) | 6.49970 | + | 6.49970i | 0.402321 | + | 0.402321i | ||||
\(262\) | −1.31529 | + | 1.31529i | −0.0812588 | + | 0.0812588i | ||||
\(263\) | −10.1321 | − | 10.1321i | −0.624774 | − | 0.624774i | 0.321974 | − | 0.946748i | \(-0.395654\pi\) |
−0.946748 | + | 0.321974i | \(0.895654\pi\) | |||||||
\(264\) | −2.48714 | − | 2.48714i | −0.153073 | − | 0.153073i | ||||
\(265\) | 3.50660 | − | 8.59132i | 0.215409 | − | 0.527761i | ||||
\(266\) | −1.34259 | −0.0823193 | ||||||||
\(267\) | 9.09463 | 0.556582 | ||||||||
\(268\) | −1.14933 | + | 1.14933i | −0.0702067 | + | 0.0702067i | ||||
\(269\) | − | 25.8428i | − | 1.57566i | −0.615890 | − | 0.787832i | \(-0.711204\pi\) | ||
0.615890 | − | 0.787832i | \(-0.288796\pi\) | |||||||
\(270\) | −2.07026 | − | 0.844991i | −0.125992 | − | 0.0514245i | ||||
\(271\) | 19.0523 | 1.15734 | 0.578672 | − | 0.815561i | \(-0.303571\pi\) | ||||
0.578672 | + | 0.815561i | \(0.303571\pi\) | |||||||
\(272\) | −2.17458 | −0.131853 | ||||||||
\(273\) | −6.43888 | −0.389699 | ||||||||
\(274\) | −13.6827 | + | 13.6827i | −0.826601 | + | 0.826601i | ||||
\(275\) | 12.5639 | + | 12.3062i | 0.757631 | + | 0.742090i | ||||
\(276\) | −6.76983 | + | 6.76983i | −0.407496 | + | 0.407496i | ||||
\(277\) | 2.31001i | 0.138795i | 0.997589 | + | 0.0693974i | \(0.0221077\pi\) | ||||
−0.997589 | + | 0.0693974i | \(0.977892\pi\) | |||||||
\(278\) | − | 17.7419i | − | 1.06409i | ||||||
\(279\) | −2.38699 | + | 2.38699i | −0.142905 | + | 0.142905i | ||||
\(280\) | −0.791208 | + | 1.93849i | −0.0472837 | + | 0.115847i | ||||
\(281\) | −13.8796 | + | 13.8796i | −0.827987 | + | 0.827987i | −0.987238 | − | 0.159251i | \(-0.949092\pi\) |
0.159251 | + | 0.987238i | \(0.449092\pi\) | |||||||
\(282\) | 5.07803 | 0.302392 | ||||||||
\(283\) | 20.9115 | 1.24306 | 0.621531 | − | 0.783389i | \(-0.286511\pi\) | ||||
0.621531 | + | 0.783389i | \(0.286511\pi\) | |||||||
\(284\) | 7.32848 | 0.434865 | ||||||||
\(285\) | −1.24229 | − | 2.95573i | −0.0735866 | − | 0.175083i | ||||
\(286\) | − | 24.1873i | − | 1.43023i | ||||||
\(287\) | 2.30405 | − | 2.30405i | 0.136004 | − | 0.136004i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −12.2712 | −0.721836 | ||||||||
\(290\) | 19.0298 | + | 7.76713i | 1.11747 | + | 0.456101i | ||||
\(291\) | 0.212850 | + | 0.212850i | 0.0124775 | + | 0.0124775i | ||||
\(292\) | −0.292649 | − | 0.292649i | −0.0171260 | − | 0.0171260i | ||||
\(293\) | −6.11142 | + | 6.11142i | −0.357033 | + | 0.357033i | −0.862718 | − | 0.505685i | \(-0.831240\pi\) |
0.505685 | + | 0.862718i | \(0.331240\pi\) | |||||||
\(294\) | −4.32979 | − | 4.32979i | −0.252518 | − | 0.252518i | ||||
\(295\) | −10.1162 | − | 4.12899i | −0.588988 | − | 0.240399i | ||||
\(296\) | 5.95481 | − | 1.24106i | 0.346116 | − | 0.0721352i | ||||
\(297\) | −2.48714 | − | 2.48714i | −0.144319 | − | 0.144319i | ||||
\(298\) | 10.6094 | 0.614588 | ||||||||
\(299\) | −65.8363 | −3.80741 | ||||||||
\(300\) | −4.99973 | + | 0.0518094i | −0.288660 | + | 0.00299122i | ||||
\(301\) | −1.81800 | + | 1.81800i | −0.104788 | + | 0.104788i | ||||
\(302\) | −3.90183 | −0.224525 | ||||||||
\(303\) | −5.57346 | + | 5.57346i | −0.320187 | + | 0.320187i | ||||
\(304\) | 1.01389 | + | 1.01389i | 0.0581503 | + | 0.0581503i | ||||
\(305\) | 29.2590 | + | 11.9423i | 1.67537 | + | 0.683812i | ||||
\(306\) | −2.17458 | −0.124312 | ||||||||
\(307\) | −11.2957 | + | 11.2957i | −0.644681 | + | 0.644681i | −0.951703 | − | 0.307022i | \(-0.900668\pi\) |
0.307022 | + | 0.951703i | \(0.400668\pi\) | |||||||
\(308\) | −2.32883 | + | 2.32883i | −0.132698 | + | 0.132698i | ||||
\(309\) | −2.69912 | − | 2.69912i | −0.153548 | − | 0.153548i | ||||
\(310\) | −2.85245 | + | 6.98861i | −0.162008 | + | 0.396927i | ||||
\(311\) | 9.84746 | + | 9.84746i | 0.558398 | + | 0.558398i | 0.928851 | − | 0.370453i | \(-0.120798\pi\) |
−0.370453 | + | 0.928851i | \(0.620798\pi\) | |||||||
\(312\) | 4.86247 | + | 4.86247i | 0.275283 | + | 0.275283i | ||||
\(313\) | 12.1322i | 0.685752i | 0.939381 | + | 0.342876i | \(0.111401\pi\) | ||||
−0.939381 | + | 0.342876i | \(0.888599\pi\) | |||||||
\(314\) | 1.75656 | − | 1.75656i | 0.0991282 | − | 0.0991282i | ||||
\(315\) | −0.791208 | + | 1.93849i | −0.0445795 | + | 0.109222i | ||||
\(316\) | 7.95594 | + | 7.95594i | 0.447556 | + | 0.447556i | ||||
\(317\) | 9.66544 | − | 9.66544i | 0.542865 | − | 0.542865i | −0.381502 | − | 0.924368i | \(-0.624593\pi\) |
0.924368 | + | 0.381502i | \(0.124593\pi\) | |||||||
\(318\) | 4.14987i | 0.232713i | ||||||||
\(319\) | 22.8617 | + | 22.8617i | 1.28001 | + | 1.28001i | ||||
\(320\) | 2.06140 | − | 0.866398i | 0.115236 | − | 0.0484331i | ||||
\(321\) | − | 4.80302i | − | 0.268079i | ||||||
\(322\) | 6.33894 | + | 6.33894i | 0.353255 | + | 0.353255i | ||||
\(323\) | −2.20477 | − | 2.20477i | −0.122677 | − | 0.122677i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −24.5630 | − | 24.0591i | −1.36251 | − | 1.33456i | ||||
\(326\) | 9.39725i | 0.520465i | ||||||||
\(327\) | 2.76458i | 0.152882i | ||||||||
\(328\) | −3.47992 | −0.192146 | ||||||||
\(329\) | − | 4.75481i | − | 0.262141i | ||||||
\(330\) | −7.28184 | − | 2.97213i | −0.400852 | − | 0.163610i | ||||
\(331\) | 23.0765 | − | 23.0765i | 1.26840 | − | 1.26840i | 0.321487 | − | 0.946914i | \(-0.395817\pi\) |
0.946914 | − | 0.321487i | \(-0.104183\pi\) | |||||||
\(332\) | 1.46770 | − | 1.46770i | 0.0805508 | − | 0.0805508i | ||||
\(333\) | 5.95481 | − | 1.24106i | 0.326322 | − | 0.0680097i | ||||
\(334\) | 18.3360i | 1.00330i | ||||||||
\(335\) | −1.37345 | + | 3.36501i | −0.0750396 | + | 0.183850i | ||||
\(336\) | − | 0.936350i | − | 0.0510821i | ||||||
\(337\) | −10.8978 | + | 10.8978i | −0.593640 | + | 0.593640i | −0.938613 | − | 0.344973i | \(-0.887888\pi\) |
0.344973 | + | 0.938613i | \(0.387888\pi\) | |||||||
\(338\) | 34.2873i | 1.86498i | ||||||||
\(339\) | 12.9599 | + | 12.9599i | 0.703885 | + | 0.703885i | ||||
\(340\) | −4.48266 | + | 1.88405i | −0.243107 | + | 0.102177i | ||||
\(341\) | −8.39587 | + | 8.39587i | −0.454662 | + | 0.454662i | ||||
\(342\) | 1.01389 | + | 1.01389i | 0.0548247 | + | 0.0548247i | ||||
\(343\) | −8.68890 | + | 8.68890i | −0.469156 | + | 0.469156i | ||||
\(344\) | 2.74581 | 0.148044 | ||||||||
\(345\) | −8.08994 | + | 19.8207i | −0.435548 | + | 1.06711i | ||||
\(346\) | −5.06991 | + | 5.06991i | −0.272560 | + | 0.272560i | ||||
\(347\) | 0.330476i | 0.0177409i | 0.999961 | + | 0.00887043i | \(0.00282358\pi\) | ||||
−0.999961 | + | 0.00887043i | \(0.997176\pi\) | |||||||
\(348\) | −9.19196 | −0.492741 | ||||||||
\(349\) | − | 35.7141i | − | 1.91173i | −0.293799 | − | 0.955867i | \(-0.594920\pi\) | ||
0.293799 | − | 0.955867i | \(-0.405080\pi\) | |||||||
\(350\) | 0.0485117 | + | 4.68150i | 0.00259306 | + | 0.250237i | ||||
\(351\) | 4.86247 | + | 4.86247i | 0.259540 | + | 0.259540i | ||||
\(352\) | 3.51735 | 0.187475 | ||||||||
\(353\) | −19.1728 | −1.02047 | −0.510233 | − | 0.860036i | \(-0.670441\pi\) | ||||
−0.510233 | + | 0.860036i | \(0.670441\pi\) | |||||||
\(354\) | 4.88643 | 0.259711 | ||||||||
\(355\) | 15.1069 | − | 6.34938i | 0.801791 | − | 0.336990i | ||||
\(356\) | −6.43088 | + | 6.43088i | −0.340836 | + | 0.340836i | ||||
\(357\) | 2.03617i | 0.107765i | ||||||||
\(358\) | 14.7313 | + | 14.7313i | 0.778573 | + | 0.778573i | ||||
\(359\) | − | 6.91664i | − | 0.365046i | −0.983202 | − | 0.182523i | \(-0.941574\pi\) | ||
0.983202 | − | 0.182523i | \(-0.0584264\pi\) | |||||||
\(360\) | 2.06140 | − | 0.866398i | 0.108645 | − | 0.0456632i | ||||
\(361\) | − | 16.9441i | − | 0.891793i | ||||||
\(362\) | 4.07298i | 0.214071i | ||||||||
\(363\) | −0.969963 | − | 0.969963i | −0.0509098 | − | 0.0509098i | ||||
\(364\) | 4.55298 | − | 4.55298i | 0.238641 | − | 0.238641i | ||||
\(365\) | −0.856815 | − | 0.349715i | −0.0448477 | − | 0.0183049i | ||||
\(366\) | −14.1330 | −0.738744 | ||||||||
\(367\) | 17.2144 | + | 17.2144i | 0.898582 | + | 0.898582i | 0.995311 | − | 0.0967284i | \(-0.0308378\pi\) |
−0.0967284 | + | 0.995311i | \(0.530838\pi\) | |||||||
\(368\) | − | 9.57399i | − | 0.499079i | ||||||
\(369\) | −3.47992 | −0.181157 | ||||||||
\(370\) | 11.2000 | − | 7.71755i | 0.582259 | − | 0.401217i | ||||
\(371\) | 3.88573 | 0.201737 | ||||||||
\(372\) | − | 3.37571i | − | 0.175023i | ||||||
\(373\) | 13.8033 | + | 13.8033i | 0.714705 | + | 0.714705i | 0.967516 | − | 0.252811i | \(-0.0813549\pi\) |
−0.252811 | + | 0.967516i | \(0.581355\pi\) | |||||||
\(374\) | −7.64874 | −0.395507 | ||||||||
\(375\) | −10.2615 | + | 4.43856i | −0.529904 | + | 0.229206i | ||||
\(376\) | −3.59071 | + | 3.59071i | −0.185177 | + | 0.185177i | ||||
\(377\) | −44.6956 | − | 44.6956i | −2.30194 | − | 2.30194i | ||||
\(378\) | − | 0.936350i | − | 0.0481607i | ||||||
\(379\) | − | 0.729632i | − | 0.0374787i | −0.999824 | − | 0.0187393i | \(-0.994035\pi\) | ||
0.999824 | − | 0.0187393i | \(-0.00596527\pi\) | |||||||
\(380\) | 2.96845 | + | 1.21159i | 0.152278 | + | 0.0621533i | ||||
\(381\) | − | 0.350036i | − | 0.0179329i | ||||||
\(382\) | −0.841106 | − | 0.841106i | −0.0430347 | − | 0.0430347i | ||||
\(383\) | − | 28.2223i | − | 1.44209i | −0.692887 | − | 0.721047i | \(-0.743661\pi\) | ||
0.692887 | − | 0.721047i | \(-0.256339\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −2.78295 | + | 6.81835i | −0.141832 | + | 0.347495i | ||||
\(386\) | −2.71107 | −0.137990 | ||||||||
\(387\) | 2.74581 | 0.139577 | ||||||||
\(388\) | −0.301015 | −0.0152817 | ||||||||
\(389\) | 15.3299 | + | 15.3299i | 0.777258 | + | 0.777258i | 0.979364 | − | 0.202106i | \(-0.0647784\pi\) |
−0.202106 | + | 0.979364i | \(0.564778\pi\) | |||||||
\(390\) | 14.2363 | + | 5.81065i | 0.720884 | + | 0.294234i | ||||
\(391\) | 20.8194i | 1.05288i | ||||||||
\(392\) | 6.12325 | 0.309271 | ||||||||
\(393\) | − | 1.86010i | − | 0.0938295i | ||||||
\(394\) | 14.0103 | − | 14.0103i | 0.705831 | − | 0.705831i | ||||
\(395\) | 23.2933 | + | 9.50733i | 1.17202 | + | 0.478366i | ||||
\(396\) | 3.51735 | 0.176753 | ||||||||
\(397\) | −9.07360 | + | 9.07360i | −0.455391 | + | 0.455391i | −0.897139 | − | 0.441748i | \(-0.854358\pi\) |
0.441748 | + | 0.897139i | \(0.354358\pi\) | |||||||
\(398\) | 2.28257 | + | 2.28257i | 0.114415 | + | 0.114415i | ||||
\(399\) | 0.949352 | − | 0.949352i | 0.0475271 | − | 0.0475271i | ||||
\(400\) | 3.49871 | − | 3.57198i | 0.174935 | − | 0.178599i | ||||
\(401\) | −23.0577 | − | 23.0577i | −1.15144 | − | 1.15144i | −0.986263 | − | 0.165182i | \(-0.947179\pi\) |
−0.165182 | − | 0.986263i | \(-0.552821\pi\) | |||||||
\(402\) | − | 1.62540i | − | 0.0810677i | ||||||
\(403\) | 16.4143 | − | 16.4143i | 0.817655 | − | 0.817655i | ||||
\(404\) | − | 7.88206i | − | 0.392147i | ||||||
\(405\) | 2.06140 | − | 0.866398i | 0.102432 | − | 0.0430517i | ||||
\(406\) | 8.60689i | 0.427153i | ||||||||
\(407\) | 20.9451 | − | 4.36524i | 1.03821 | − | 0.216377i | ||||
\(408\) | 1.53766 | − | 1.53766i | 0.0761254 | − | 0.0761254i | ||||
\(409\) | −12.7245 | + | 12.7245i | −0.629185 | + | 0.629185i | −0.947863 | − | 0.318678i | \(-0.896761\pi\) |
0.318678 | + | 0.947863i | \(0.396761\pi\) | |||||||
\(410\) | −7.17349 | + | 3.01499i | −0.354273 | + | 0.148900i | ||||
\(411\) | − | 19.3502i | − | 0.954477i | ||||||
\(412\) | 3.81714 | 0.188057 | ||||||||
\(413\) | − | 4.57541i | − | 0.225141i | ||||||
\(414\) | − | 9.57399i | − | 0.470536i | ||||||
\(415\) | 1.75390 | − | 4.29714i | 0.0860958 | − | 0.210938i | ||||
\(416\) | −6.87657 | −0.337152 | ||||||||
\(417\) | 12.5454 | + | 12.5454i | 0.614350 | + | 0.614350i | ||||
\(418\) | 3.56619 | + | 3.56619i | 0.174428 | + | 0.174428i | ||||
\(419\) | 4.07751i | 0.199200i | 0.995028 | + | 0.0995998i | \(0.0317563\pi\) | ||||
−0.995028 | + | 0.0995998i | \(0.968244\pi\) | |||||||
\(420\) | −0.811252 | − | 1.93019i | −0.0395850 | − | 0.0941836i | ||||
\(421\) | −5.38925 | − | 5.38925i | −0.262656 | − | 0.262656i | 0.563476 | − | 0.826132i | \(-0.309464\pi\) |
−0.826132 | + | 0.563476i | \(0.809464\pi\) | |||||||
\(422\) | − | 16.7409i | − | 0.814936i | ||||||
\(423\) | −3.59071 | + | 3.59071i | −0.174586 | + | 0.174586i | ||||
\(424\) | −2.93440 | − | 2.93440i | −0.142507 | − | 0.142507i | ||||
\(425\) | −7.60821 | + | 7.76754i | −0.369052 | + | 0.376781i | ||||
\(426\) | −5.18202 | + | 5.18202i | −0.251070 | + | 0.251070i | ||||
\(427\) | 13.2334i | 0.640411i | ||||||||
\(428\) | 3.39625 | + | 3.39625i | 0.164164 | + | 0.164164i | ||||
\(429\) | 17.1030 | + | 17.1030i | 0.825741 | + | 0.825741i | ||||
\(430\) | 5.66020 | − | 2.37896i | 0.272959 | − | 0.114724i | ||||
\(431\) | 9.41260 | + | 9.41260i | 0.453389 | + | 0.453389i | 0.896478 | − | 0.443089i | \(-0.146117\pi\) |
−0.443089 | + | 0.896478i | \(0.646117\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 18.0950 | − | 18.0950i | 0.869588 | − | 0.869588i | −0.122839 | − | 0.992427i | \(-0.539200\pi\) |
0.992427 | + | 0.122839i | \(0.0391998\pi\) | |||||||
\(434\) | −3.16085 | −0.151726 | ||||||||
\(435\) | −18.9483 | + | 7.96389i | −0.908500 | + | 0.381840i | ||||
\(436\) | −1.95485 | − | 1.95485i | −0.0936205 | − | 0.0936205i | ||||
\(437\) | 9.70693 | − | 9.70693i | 0.464346 | − | 0.464346i | ||||
\(438\) | 0.413868 | 0.0197754 | ||||||||
\(439\) | 3.41744 | − | 3.41744i | 0.163106 | − | 0.163106i | −0.620835 | − | 0.783941i | \(-0.713206\pi\) |
0.783941 | + | 0.620835i | \(0.213206\pi\) | |||||||
\(440\) | 7.25065 | − | 3.04742i | 0.345661 | − | 0.145280i | ||||
\(441\) | 6.12325 | 0.291583 | ||||||||
\(442\) | 14.9536 | 0.711272 | ||||||||
\(443\) | 10.8466 | + | 10.8466i | 0.515340 | + | 0.515340i | 0.916158 | − | 0.400818i | \(-0.131274\pi\) |
−0.400818 | + | 0.916158i | \(0.631274\pi\) | |||||||
\(444\) | −3.33312 | + | 5.08825i | −0.158183 | + | 0.241478i | ||||
\(445\) | −7.68489 | + | 18.8283i | −0.364299 | + | 0.892546i | ||||
\(446\) | −16.5296 | − | 16.5296i | −0.782700 | − | 0.782700i | ||||
\(447\) | −7.50200 | + | 7.50200i | −0.354833 | + | 0.354833i | ||||
\(448\) | 0.662100 | + | 0.662100i | 0.0312813 | + | 0.0312813i | ||||
\(449\) | −10.3811 | − | 10.3811i | −0.489913 | − | 0.489913i | 0.418366 | − | 0.908279i | \(-0.362603\pi\) |
−0.908279 | + | 0.418366i | \(0.862603\pi\) | |||||||
\(450\) | 3.49871 | − | 3.57198i | 0.164931 | − | 0.168385i | ||||
\(451\) | −12.2401 | −0.576363 | ||||||||
\(452\) | −18.3281 | −0.862079 | ||||||||
\(453\) | 2.75901 | − | 2.75901i | 0.129630 | − | 0.129630i | ||||
\(454\) | − | 28.0799i | − | 1.31786i | ||||||
\(455\) | 5.44080 | − | 13.3302i | 0.255069 | − | 0.624928i | ||||
\(456\) | −1.43385 | −0.0671462 | ||||||||
\(457\) | −13.7780 | −0.644509 | −0.322254 | − | 0.946653i | \(-0.604441\pi\) | ||||
−0.322254 | + | 0.946653i | \(0.604441\pi\) | |||||||
\(458\) | 0.286568 | 0.0133904 | ||||||||
\(459\) | 1.53766 | − | 1.53766i | 0.0717717 | − | 0.0717717i | ||||
\(460\) | −8.29489 | − | 19.7358i | −0.386751 | − | 0.920186i | ||||
\(461\) | −28.3555 | + | 28.3555i | −1.32065 | + | 1.32065i | −0.407393 | + | 0.913253i | \(0.633562\pi\) |
−0.913253 | + | 0.407393i | \(0.866438\pi\) | |||||||
\(462\) | − | 3.29347i | − | 0.153226i | ||||||
\(463\) | 27.1414i | 1.26137i | 0.776040 | + | 0.630683i | \(0.217225\pi\) | ||||
−0.776040 | + | 0.630683i | \(0.782775\pi\) | |||||||
\(464\) | 6.49970 | − | 6.49970i | 0.301741 | − | 0.301741i | ||||
\(465\) | −2.92471 | − | 6.95868i | −0.135630 | − | 0.322701i | ||||
\(466\) | −10.2080 | + | 10.2080i | −0.472878 | + | 0.472878i | ||||
\(467\) | 15.3540 | 0.710500 | 0.355250 | − | 0.934771i | \(-0.384396\pi\) | ||||
0.355250 | + | 0.934771i | \(0.384396\pi\) | |||||||
\(468\) | −6.87657 | −0.317870 | ||||||||
\(469\) | −1.52195 | −0.0702769 | ||||||||
\(470\) | −4.29089 | + | 10.5129i | −0.197924 | + | 0.484922i | ||||
\(471\) | 2.48415i | 0.114463i | ||||||||
\(472\) | −3.45523 | + | 3.45523i | −0.159040 | + | 0.159040i | ||||
\(473\) | 9.65796 | 0.444074 | ||||||||
\(474\) | −11.2514 | −0.516794 | ||||||||
\(475\) | 7.16887 | − | 0.0742869i | 0.328930 | − | 0.00340852i | ||||
\(476\) | −1.43979 | − | 1.43979i | −0.0659925 | − | 0.0659925i | ||||
\(477\) | −2.93440 | − | 2.93440i | −0.134357 | − | 0.134357i | ||||
\(478\) | 16.6011 | − | 16.6011i | 0.759317 | − | 0.759317i | ||||
\(479\) | −11.3006 | − | 11.3006i | −0.516338 | − | 0.516338i | 0.400123 | − | 0.916461i | \(-0.368967\pi\) |
−0.916461 | + | 0.400123i | \(0.868967\pi\) | |||||||
\(480\) | −0.844991 | + | 2.07026i | −0.0385684 | + | 0.0944942i | ||||
\(481\) | −40.9487 | + | 8.53425i | −1.86710 | + | 0.389128i | ||||
\(482\) | 17.4511 | + | 17.4511i | 0.794876 | + | 0.794876i | ||||
\(483\) | −8.96461 | −0.407904 | ||||||||
\(484\) | 1.37173 | 0.0623516 | ||||||||
\(485\) | −0.620511 | + | 0.260799i | −0.0281760 | + | 0.0118423i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | −21.7950 | −0.987628 | −0.493814 | − | 0.869568i | \(-0.664398\pi\) | ||||
−0.493814 | + | 0.869568i | \(0.664398\pi\) | |||||||
\(488\) | 9.99355 | − | 9.99355i | 0.452387 | − | 0.452387i | ||||
\(489\) | −6.64486 | − | 6.64486i | −0.300491 | − | 0.300491i | ||||
\(490\) | 12.6224 | − | 5.30517i | 0.570224 | − | 0.239663i | ||||
\(491\) | −6.69716 | −0.302239 | −0.151119 | − | 0.988516i | \(-0.548288\pi\) | ||||
−0.151119 | + | 0.988516i | \(0.548288\pi\) | |||||||
\(492\) | 2.46067 | − | 2.46067i | 0.110936 | − | 0.110936i | ||||
\(493\) | −14.1341 | + | 14.1341i | −0.636567 | + | 0.636567i | ||||
\(494\) | −6.97206 | − | 6.97206i | −0.313688 | − | 0.313688i | ||||
\(495\) | 7.25065 | − | 3.04742i | 0.325892 | − | 0.136971i | ||||
\(496\) | 2.38699 | + | 2.38699i | 0.107179 | + | 0.107179i | ||||
\(497\) | 4.85218 | + | 4.85218i | 0.217650 | + | 0.217650i | ||||
\(498\) | 2.07565i | 0.0930120i | ||||||||
\(499\) | 31.1536 | − | 31.1536i | 1.39463 | − | 1.39463i | 0.580034 | − | 0.814592i | \(-0.303039\pi\) |
0.814592 | − | 0.580034i | \(-0.196961\pi\) | |||||||
\(500\) | 4.11747 | − | 10.3945i | 0.184139 | − | 0.464858i | ||||
\(501\) | −12.9655 | − | 12.9655i | −0.579256 | − | 0.579256i | ||||
\(502\) | −0.992524 | + | 0.992524i | −0.0442985 | + | 0.0442985i | ||||
\(503\) | 0.724954i | 0.0323241i | 0.999869 | + | 0.0161621i | \(0.00514477\pi\) | ||||
−0.999869 | + | 0.0161621i | \(0.994855\pi\) | |||||||
\(504\) | 0.662100 | + | 0.662100i | 0.0294923 | + | 0.0294923i | ||||
\(505\) | −6.82900 | − | 16.2480i | −0.303886 | − | 0.723029i | ||||
\(506\) | − | 33.6751i | − | 1.49704i | ||||||
\(507\) | −24.2448 | − | 24.2448i | −1.07675 | − | 1.07675i | ||||
\(508\) | 0.247513 | + | 0.247513i | 0.0109816 | + | 0.0109816i | ||||
\(509\) | 23.7296 | 1.05180 | 0.525899 | − | 0.850547i | \(-0.323729\pi\) | ||||
0.525899 | + | 0.850547i | \(0.323729\pi\) | |||||||
\(510\) | 1.83750 | − | 4.50195i | 0.0813658 | − | 0.199350i | ||||
\(511\) | − | 0.387525i | − | 0.0171431i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.43385 | −0.0633061 | ||||||||
\(514\) | − | 9.19465i | − | 0.405559i | ||||||
\(515\) | 7.86864 | − | 3.30716i | 0.346734 | − | 0.145731i | ||||
\(516\) | −1.94158 | + | 1.94158i | −0.0854733 | + | 0.0854733i | ||||
\(517\) | −12.6298 | + | 12.6298i | −0.555456 | + | 0.555456i | ||||
\(518\) | 4.76438 | + | 3.12097i | 0.209335 | + | 0.137128i | ||||
\(519\) | − | 7.16994i | − | 0.314725i | ||||||
\(520\) | −14.1753 | + | 5.95785i | −0.621630 | + | 0.261269i | ||||
\(521\) | − | 23.1177i | − | 1.01281i | −0.862297 | − | 0.506403i | \(-0.830975\pi\) | ||
0.862297 | − | 0.506403i | \(-0.169025\pi\) | |||||||
\(522\) | 6.49970 | − | 6.49970i | 0.284484 | − | 0.284484i | ||||
\(523\) | − | 15.4427i | − | 0.675261i | −0.941279 | − | 0.337631i | \(-0.890375\pi\) | ||
0.941279 | − | 0.337631i | \(-0.109625\pi\) | |||||||
\(524\) | 1.31529 | + | 1.31529i | 0.0574586 | + | 0.0574586i | ||||
\(525\) | −3.34462 | − | 3.27602i | −0.145971 | − | 0.142977i | ||||
\(526\) | −10.1321 | + | 10.1321i | −0.441782 | + | 0.441782i | ||||
\(527\) | −5.19069 | − | 5.19069i | −0.226110 | − | 0.226110i | ||||
\(528\) | −2.48714 | + | 2.48714i | −0.108239 | + | 0.108239i | ||||
\(529\) | −68.6613 | −2.98528 | ||||||||
\(530\) | −8.59132 | − | 3.50660i | −0.373183 | − | 0.152317i | ||||
\(531\) | −3.45523 | + | 3.45523i | −0.149944 | + | 0.149944i | ||||
\(532\) | 1.34259i | 0.0582085i | ||||||||
\(533\) | 23.9299 | 1.03652 | ||||||||
\(534\) | − | 9.09463i | − | 0.393563i | ||||||
\(535\) | 9.94353 | + | 4.05851i | 0.429896 | + | 0.175465i | ||||
\(536\) | 1.14933 | + | 1.14933i | 0.0496436 | + | 0.0496436i | ||||
\(537\) | −20.8332 | −0.899018 | ||||||||
\(538\) | −25.8428 | −1.11416 | ||||||||
\(539\) | 21.5376 | 0.927690 | ||||||||
\(540\) | −0.844991 | + | 2.07026i | −0.0363626 | + | 0.0890899i | ||||
\(541\) | 3.85083 | − | 3.85083i | 0.165560 | − | 0.165560i | −0.619465 | − | 0.785025i | \(-0.712650\pi\) |
0.785025 | + | 0.619465i | \(0.212650\pi\) | |||||||
\(542\) | − | 19.0523i | − | 0.818365i | ||||||
\(543\) | −2.88003 | − | 2.88003i | −0.123594 | − | 0.123594i | ||||
\(544\) | 2.17458i | 0.0932342i | ||||||||
\(545\) | −5.72341 | − | 2.33605i | −0.245164 | − | 0.100065i | ||||
\(546\) | 6.43888i | 0.275559i | ||||||||
\(547\) | 5.49141i | 0.234796i | 0.993085 | + | 0.117398i | \(0.0374552\pi\) | ||||
−0.993085 | + | 0.117398i | \(0.962545\pi\) | |||||||
\(548\) | 13.6827 | + | 13.6827i | 0.584495 | + | 0.584495i | ||||
\(549\) | 9.99355 | − | 9.99355i | 0.426514 | − | 0.426514i | ||||
\(550\) | 12.3062 | − | 12.5639i | 0.524737 | − | 0.535726i | ||||
\(551\) | 13.1799 | 0.561483 | ||||||||
\(552\) | 6.76983 | + | 6.76983i | 0.288143 | + | 0.288143i | ||||
\(553\) | 10.5352i | 0.448004i | ||||||||
\(554\) | 2.31001 | 0.0981428 | ||||||||
\(555\) | −2.46244 | + | 13.3767i | −0.104525 | + | 0.567810i | ||||
\(556\) | −17.7419 | −0.752422 | ||||||||
\(557\) | − | 20.3979i | − | 0.864285i | −0.901805 | − | 0.432142i | \(-0.857758\pi\) | ||
0.901805 | − | 0.432142i | \(-0.142242\pi\) | |||||||
\(558\) | 2.38699 | + | 2.38699i | 0.101049 | + | 0.101049i | ||||
\(559\) | −18.8818 | −0.798613 | ||||||||
\(560\) | 1.93849 | + | 0.791208i | 0.0819162 | + | 0.0334346i | ||||
\(561\) | 5.40848 | − | 5.40848i | 0.228346 | − | 0.228346i | ||||
\(562\) | 13.8796 | + | 13.8796i | 0.585475 | + | 0.585475i | ||||
\(563\) | − | 41.6497i | − | 1.75533i | −0.479278 | − | 0.877663i | \(-0.659101\pi\) | ||
0.479278 | − | 0.877663i | \(-0.340899\pi\) | |||||||
\(564\) | − | 5.07803i | − | 0.213824i | ||||||
\(565\) | −37.7814 | + | 15.8794i | −1.58948 | + | 0.668051i | ||||
\(566\) | − | 20.9115i | − | 0.878978i | ||||||
\(567\) | 0.662100 | + | 0.662100i | 0.0278056 | + | 0.0278056i | ||||
\(568\) | − | 7.32848i | − | 0.307496i | ||||||
\(569\) | −29.9799 | + | 29.9799i | −1.25682 | + | 1.25682i | −0.304220 | + | 0.952602i | \(0.598396\pi\) |
−0.952602 | + | 0.304220i | \(0.901604\pi\) | |||||||
\(570\) | −2.95573 | + | 1.24229i | −0.123802 | + | 0.0520336i | ||||
\(571\) | −33.5003 | −1.40195 | −0.700973 | − | 0.713188i | \(-0.747250\pi\) | ||||
−0.700973 | + | 0.713188i | \(0.747250\pi\) | |||||||
\(572\) | −24.1873 | −1.01132 | ||||||||
\(573\) | 1.18950 | 0.0496922 | ||||||||
\(574\) | −2.30405 | − | 2.30405i | −0.0961693 | − | 0.0961693i | ||||
\(575\) | −34.1981 | − | 33.4966i | −1.42616 | − | 1.39691i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 11.2900 | 0.470008 | 0.235004 | − | 0.971994i | \(-0.424490\pi\) | ||||
0.235004 | + | 0.971994i | \(0.424490\pi\) | |||||||
\(578\) | 12.2712i | 0.510415i | ||||||||
\(579\) | 1.91702 | − | 1.91702i | 0.0796685 | − | 0.0796685i | ||||
\(580\) | 7.76713 | − | 19.0298i | 0.322512 | − | 0.790168i | ||||
\(581\) | 1.94353 | 0.0806313 | ||||||||
\(582\) | 0.212850 | − | 0.212850i | 0.00882291 | − | 0.00882291i | ||||
\(583\) | −10.3213 | − | 10.3213i | −0.427465 | − | 0.427465i | ||||
\(584\) | −0.292649 | + | 0.292649i | −0.0121099 | + | 0.0121099i | ||||
\(585\) | −14.1753 | + | 5.95785i | −0.586078 | + | 0.246327i | ||||
\(586\) | 6.11142 | + | 6.11142i | 0.252461 | + | 0.252461i | ||||
\(587\) | − | 0.261793i | − | 0.0108053i | −0.999985 | − | 0.00540267i | \(-0.998280\pi\) | ||
0.999985 | − | 0.00540267i | \(-0.00171973\pi\) | |||||||
\(588\) | −4.32979 | + | 4.32979i | −0.178558 | + | 0.178558i | ||||
\(589\) | 4.84027i | 0.199440i | ||||||||
\(590\) | −4.12899 | + | 10.1162i | −0.169988 | + | 0.416477i | ||||
\(591\) | 19.8136i | 0.815023i | ||||||||
\(592\) | −1.24106 | − | 5.95481i | −0.0510073 | − | 0.244741i | ||||
\(593\) | −23.9024 | + | 23.9024i | −0.981553 | + | 0.981553i | −0.999833 | − | 0.0182800i | \(-0.994181\pi\) |
0.0182800 | + | 0.999833i | \(0.494181\pi\) | |||||||
\(594\) | −2.48714 | + | 2.48714i | −0.102049 | + | 0.102049i | ||||
\(595\) | −4.21540 | − | 1.72054i | −0.172814 | − | 0.0705354i | ||||
\(596\) | − | 10.6094i | − | 0.434579i | ||||||
\(597\) | −3.22805 | −0.132115 | ||||||||
\(598\) | 65.8363i | 2.69225i | ||||||||
\(599\) | − | 40.4441i | − | 1.65250i | −0.563303 | − | 0.826251i | \(-0.690470\pi\) | ||
0.563303 | − | 0.826251i | \(-0.309530\pi\) | |||||||
\(600\) | 0.0518094 | + | 4.99973i | 0.00211511 | + | 0.204113i | ||||
\(601\) | 38.4258 | 1.56742 | 0.783710 | − | 0.621127i | \(-0.213325\pi\) | ||||
0.783710 | + | 0.621127i | \(0.213325\pi\) | |||||||
\(602\) | 1.81800 | + | 1.81800i | 0.0740961 | + | 0.0740961i | ||||
\(603\) | 1.14933 | + | 1.14933i | 0.0468044 | + | 0.0468044i | ||||
\(604\) | 3.90183i | 0.158763i | ||||||||
\(605\) | 2.82769 | − | 1.18847i | 0.114962 | − | 0.0483181i | ||||
\(606\) | 5.57346 | + | 5.57346i | 0.226406 | + | 0.226406i | ||||
\(607\) | − | 14.3687i | − | 0.583208i | −0.956539 | − | 0.291604i | \(-0.905811\pi\) | ||
0.956539 | − | 0.291604i | \(-0.0941890\pi\) | |||||||
\(608\) | 1.01389 | − | 1.01389i | 0.0411185 | − | 0.0411185i | ||||
\(609\) | −6.08599 | − | 6.08599i | −0.246617 | − | 0.246617i | ||||
\(610\) | 11.9423 | − | 29.2590i | 0.483528 | − | 1.18466i | ||||
\(611\) | 24.6918 | − | 24.6918i | 0.998922 | − | 0.998922i | ||||
\(612\) | 2.17458i | 0.0879020i | ||||||||
\(613\) | 10.7011 | + | 10.7011i | 0.432213 | + | 0.432213i | 0.889381 | − | 0.457167i | \(-0.151136\pi\) |
−0.457167 | + | 0.889381i | \(0.651136\pi\) | |||||||
\(614\) | 11.2957 | + | 11.2957i | 0.455858 | + | 0.455858i | ||||
\(615\) | 2.94050 | − | 7.20434i | 0.118572 | − | 0.290507i | ||||
\(616\) | 2.32883 | + | 2.32883i | 0.0938314 | + | 0.0938314i | ||||
\(617\) | −14.0957 | + | 14.0957i | −0.567470 | + | 0.567470i | −0.931419 | − | 0.363949i | \(-0.881428\pi\) |
0.363949 | + | 0.931419i | \(0.381428\pi\) | |||||||
\(618\) | −2.69912 | + | 2.69912i | −0.108575 | + | 0.108575i | ||||
\(619\) | 4.28502 | 0.172230 | 0.0861148 | − | 0.996285i | \(-0.472555\pi\) | ||||
0.0861148 | + | 0.996285i | \(0.472555\pi\) | |||||||
\(620\) | 6.98861 | + | 2.85245i | 0.280669 | + | 0.114557i | ||||
\(621\) | 6.76983 | + | 6.76983i | 0.271664 | + | 0.271664i | ||||
\(622\) | 9.84746 | − | 9.84746i | 0.394847 | − | 0.394847i | ||||
\(623\) | −8.51576 | −0.341177 | ||||||||
\(624\) | 4.86247 | − | 4.86247i | 0.194655 | − | 0.194655i | ||||
\(625\) | −0.518066 | − | 24.9946i | −0.0207226 | − | 0.999785i | ||||
\(626\) | 12.1322 | 0.484900 | ||||||||
\(627\) | −5.04335 | −0.201412 | ||||||||
\(628\) | −1.75656 | − | 1.75656i | −0.0700942 | − | 0.0700942i | ||||
\(629\) | 2.69878 | + | 12.9492i | 0.107607 | + | 0.516318i | ||||
\(630\) | 1.93849 | + | 0.791208i | 0.0772313 | + | 0.0315225i | ||||
\(631\) | −10.5038 | − | 10.5038i | −0.418149 | − | 0.418149i | 0.466416 | − | 0.884565i | \(-0.345545\pi\) |
−0.884565 | + | 0.466416i | \(0.845545\pi\) | |||||||
\(632\) | 7.95594 | − | 7.95594i | 0.316470 | − | 0.316470i | ||||
\(633\) | 11.8376 | + | 11.8376i | 0.470504 | + | 0.470504i | ||||
\(634\) | −9.66544 | − | 9.66544i | −0.383864 | − | 0.383864i | ||||
\(635\) | 0.724667 | + | 0.295777i | 0.0287575 | + | 0.0117376i | ||||
\(636\) | 4.14987 | 0.164553 | ||||||||
\(637\) | −42.1070 | −1.66834 | ||||||||
\(638\) | 22.8617 | − | 22.8617i | 0.905103 | − | 0.905103i | ||||
\(639\) | − | 7.32848i | − | 0.289910i | ||||||
\(640\) | −0.866398 | − | 2.06140i | −0.0342474 | − | 0.0814838i | ||||
\(641\) | 41.6777 | 1.64617 | 0.823085 | − | 0.567919i | \(-0.192251\pi\) | ||||
0.823085 | + | 0.567919i | \(0.192251\pi\) | |||||||
\(642\) | −4.80302 | −0.189560 | ||||||||
\(643\) | 25.1480 | 0.991742 | 0.495871 | − | 0.868396i | \(-0.334849\pi\) | ||||
0.495871 | + | 0.868396i | \(0.334849\pi\) | |||||||
\(644\) | 6.33894 | − | 6.33894i | 0.249789 | − | 0.249789i | ||||
\(645\) | −2.32018 | + | 5.68455i | −0.0913572 | + | 0.223829i | ||||
\(646\) | −2.20477 | + | 2.20477i | −0.0867456 | + | 0.0867456i | ||||
\(647\) | − | 29.9330i | − | 1.17679i | −0.808575 | − | 0.588394i | \(-0.799761\pi\) | ||
0.808575 | − | 0.588394i | \(-0.200239\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −12.1532 | + | 12.1532i | −0.477057 | + | 0.477057i | ||||
\(650\) | −24.0591 | + | 24.5630i | −0.943677 | + | 0.963439i | ||||
\(651\) | 2.23506 | − | 2.23506i | 0.0875988 | − | 0.0875988i | ||||
\(652\) | 9.39725 | 0.368025 | ||||||||
\(653\) | −16.5783 | −0.648759 | −0.324380 | − | 0.945927i | \(-0.605156\pi\) | ||||
−0.324380 | + | 0.945927i | \(0.605156\pi\) | |||||||
\(654\) | 2.76458 | 0.108104 | ||||||||
\(655\) | 3.85089 | + | 1.57177i | 0.150467 | + | 0.0614140i | ||||
\(656\) | 3.47992i | 0.135868i | ||||||||
\(657\) | −0.292649 | + | 0.292649i | −0.0114173 | + | 0.0114173i | ||||
\(658\) | −4.75481 | −0.185362 | ||||||||
\(659\) | −19.3767 | −0.754807 | −0.377404 | − | 0.926049i | \(-0.623183\pi\) | ||||
−0.377404 | + | 0.926049i | \(0.623183\pi\) | |||||||
\(660\) | −2.97213 | + | 7.28184i | −0.115690 | + | 0.283445i | ||||
\(661\) | −11.4801 | − | 11.4801i | −0.446523 | − | 0.446523i | 0.447674 | − | 0.894197i | \(-0.352252\pi\) |
−0.894197 | + | 0.447674i | \(0.852252\pi\) | |||||||
\(662\) | −23.0765 | − | 23.0765i | −0.896895 | − | 0.896895i | ||||
\(663\) | −10.5738 | + | 10.5738i | −0.410653 | + | 0.410653i | ||||
\(664\) | −1.46770 | − | 1.46770i | −0.0569580 | − | 0.0569580i | ||||
\(665\) | 1.16321 | + | 2.76760i | 0.0451075 | + | 0.107323i | ||||
\(666\) | −1.24106 | − | 5.95481i | −0.0480901 | − | 0.230744i | ||||
\(667\) | −62.2280 | − | 62.2280i | −2.40948 | − | 2.40948i | ||||
\(668\) | 18.3360 | 0.709441 | ||||||||
\(669\) | 23.3764 | 0.903784 | ||||||||
\(670\) | 3.36501 | + | 1.37345i | 0.130002 | + | 0.0530610i | ||||
\(671\) | 35.1508 | − | 35.1508i | 1.35698 | − | 1.35698i | ||||
\(672\) | −0.936350 | −0.0361205 | ||||||||
\(673\) | 24.2873 | − | 24.2873i | 0.936205 | − | 0.936205i | −0.0618787 | − | 0.998084i | \(-0.519709\pi\) |
0.998084 | + | 0.0618787i | \(0.0197092\pi\) | |||||||
\(674\) | 10.8978 | + | 10.8978i | 0.419767 | + | 0.419767i | ||||
\(675\) | 0.0518094 | + | 4.99973i | 0.00199414 | + | 0.192440i | ||||
\(676\) | 34.2873 | 1.31874 | ||||||||
\(677\) | −19.1232 | + | 19.1232i | −0.734963 | + | 0.734963i | −0.971599 | − | 0.236635i | \(-0.923955\pi\) |
0.236635 | + | 0.971599i | \(0.423955\pi\) | |||||||
\(678\) | 12.9599 | − | 12.9599i | 0.497722 | − | 0.497722i | ||||
\(679\) | −0.199302 | − | 0.199302i | −0.00764851 | − | 0.00764851i | ||||
\(680\) | 1.88405 | + | 4.48266i | 0.0722500 | + | 0.171902i | ||||
\(681\) | 19.8555 | + | 19.8555i | 0.760865 | + | 0.760865i | ||||
\(682\) | 8.39587 | + | 8.39587i | 0.321494 | + | 0.321494i | ||||
\(683\) | 5.31945i | 0.203543i | 0.994808 | + | 0.101772i | \(0.0324511\pi\) | ||||
−0.994808 | + | 0.101772i | \(0.967549\pi\) | |||||||
\(684\) | 1.01389 | − | 1.01389i | 0.0387669 | − | 0.0387669i | ||||
\(685\) | 40.0601 | + | 16.3508i | 1.53062 | + | 0.624732i | ||||
\(686\) | 8.68890 | + | 8.68890i | 0.331744 | + | 0.331744i | ||||
\(687\) | −0.202634 | + | 0.202634i | −0.00773097 | + | 0.00773097i | ||||
\(688\) | − | 2.74581i | − | 0.104683i | ||||||
\(689\) | 20.1786 | + | 20.1786i | 0.768745 | + | 0.768745i | ||||
\(690\) | 19.8207 | + | 8.08994i | 0.754561 | + | 0.307979i | ||||
\(691\) | 35.7436i | 1.35975i | 0.733328 | + | 0.679875i | \(0.237966\pi\) | ||||
−0.733328 | + | 0.679875i | \(0.762034\pi\) | |||||||
\(692\) | 5.06991 | + | 5.06991i | 0.192729 | + | 0.192729i | ||||
\(693\) | 2.32883 | + | 2.32883i | 0.0884651 | + | 0.0884651i | ||||
\(694\) | 0.330476 | 0.0125447 | ||||||||
\(695\) | −36.5730 | + | 15.3715i | −1.38729 | + | 0.583074i | ||||
\(696\) | 9.19196i | 0.348420i | ||||||||
\(697\) | − | 7.56735i | − | 0.286634i | ||||||
\(698\) | −35.7141 | −1.35180 | ||||||||
\(699\) | − | 14.4363i | − | 0.546033i | ||||||
\(700\) | 4.68150 | − | 0.0485117i | 0.176944 | − | 0.00183357i | ||||
\(701\) | −20.6265 | + | 20.6265i | −0.779051 | + | 0.779051i | −0.979669 | − | 0.200618i | \(-0.935705\pi\) |
0.200618 | + | 0.979669i | \(0.435705\pi\) | |||||||
\(702\) | 4.86247 | − | 4.86247i | 0.183522 | − | 0.183522i | ||||
\(703\) | 4.77920 | − | 7.29579i | 0.180251 | − | 0.275166i | ||||
\(704\) | − | 3.51735i | − | 0.132565i | ||||||
\(705\) | −4.39959 | − | 10.4678i | −0.165698 | − | 0.394241i | ||||
\(706\) | 19.1728i | 0.721579i | ||||||||
\(707\) | 5.21871 | − | 5.21871i | 0.196270 | − | 0.196270i | ||||
\(708\) | − | 4.88643i | − | 0.183643i | ||||||
\(709\) | 7.74624 | + | 7.74624i | 0.290916 | + | 0.290916i | 0.837442 | − | 0.546526i | \(-0.184050\pi\) |
−0.546526 | + | 0.837442i | \(0.684050\pi\) | |||||||
\(710\) | −6.34938 | − | 15.1069i | −0.238288 | − | 0.566952i | ||||
\(711\) | 7.95594 | − | 7.95594i | 0.298371 | − | 0.298371i | ||||
\(712\) | 6.43088 | + | 6.43088i | 0.241007 | + | 0.241007i | ||||
\(713\) | 22.8530 | − | 22.8530i | 0.855852 | − | 0.855852i | ||||
\(714\) | 2.03617 | 0.0762016 | ||||||||
\(715\) | −49.8596 | + | 20.9558i | −1.86464 | + | 0.783704i | ||||
\(716\) | 14.7313 | − | 14.7313i | 0.550534 | − | 0.550534i | ||||
\(717\) | 23.4775i | 0.876784i | ||||||||
\(718\) | −6.91664 | −0.258127 | ||||||||
\(719\) | 28.4115i | 1.05957i | 0.848132 | + | 0.529785i | \(0.177727\pi\) | ||||
−0.848132 | + | 0.529785i | \(0.822273\pi\) | |||||||
\(720\) | −0.866398 | − | 2.06140i | −0.0322887 | − | 0.0768237i | ||||
\(721\) | 2.52733 | + | 2.52733i | 0.0941226 | + | 0.0941226i | ||||
\(722\) | −16.9441 | −0.630593 | ||||||||
\(723\) | −24.6796 | −0.917844 | ||||||||
\(724\) | 4.07298 | 0.151371 | ||||||||
\(725\) | −0.476230 | − | 45.9573i | −0.0176867 | − | 1.70681i | ||||
\(726\) | −0.969963 | + | 0.969963i | −0.0359987 | + | 0.0359987i | ||||
\(727\) | 10.2341i | 0.379561i | 0.981827 | + | 0.189780i | \(0.0607776\pi\) | ||||
−0.981827 | + | 0.189780i | \(0.939222\pi\) | |||||||
\(728\) | −4.55298 | − | 4.55298i | −0.168745 | − | 0.168745i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −0.349715 | + | 0.856815i | −0.0129435 | + | 0.0317121i | ||||
\(731\) | 5.97097i | 0.220844i | ||||||||
\(732\) | 14.1330i | 0.522371i | ||||||||
\(733\) | 27.1770 | + | 27.1770i | 1.00380 | + | 1.00380i | 0.999993 | + | 0.00381081i | \(0.00121302\pi\) |
0.00381081 | + | 0.999993i | \(0.498787\pi\) | |||||||
\(734\) | 17.2144 | − | 17.2144i | 0.635394 | − | 0.635394i | ||||
\(735\) | −5.17409 | + | 12.6767i | −0.190849 | + | 0.467588i | ||||
\(736\) | −9.57399 | −0.352902 | ||||||||
\(737\) | 4.04260 | + | 4.04260i | 0.148911 | + | 0.148911i | ||||
\(738\) | 3.47992i | 0.128098i | ||||||||
\(739\) | −17.3037 | −0.636527 | −0.318264 | − | 0.948002i | \(-0.603100\pi\) | ||||
−0.318264 | + | 0.948002i | \(0.603100\pi\) | |||||||
\(740\) | −7.71755 | − | 11.2000i | −0.283703 | − | 0.411719i | ||||
\(741\) | 9.85998 | 0.362215 | ||||||||
\(742\) | − | 3.88573i | − | 0.142650i | ||||||
\(743\) | −24.1248 | − | 24.1248i | −0.885055 | − | 0.885055i | 0.108988 | − | 0.994043i | \(-0.465239\pi\) |
−0.994043 | + | 0.108988i | \(0.965239\pi\) | |||||||
\(744\) | −3.37571 | −0.123760 | ||||||||
\(745\) | −9.19199 | − | 21.8703i | −0.336769 | − | 0.801264i | ||||
\(746\) | 13.8033 | − | 13.8033i | 0.505373 | − | 0.505373i | ||||
\(747\) | −1.46770 | − | 1.46770i | −0.0537005 | − | 0.0537005i | ||||
\(748\) | 7.64874i | 0.279666i | ||||||||
\(749\) | 4.49731i | 0.164328i | ||||||||
\(750\) | 4.43856 | + | 10.2615i | 0.162073 | + | 0.374698i | ||||
\(751\) | 49.1232i | 1.79253i | 0.443517 | + | 0.896266i | \(0.353730\pi\) | ||||
−0.443517 | + | 0.896266i | \(0.646270\pi\) | |||||||
\(752\) | 3.59071 | + | 3.59071i | 0.130940 | + | 0.130940i | ||||
\(753\) | − | 1.40364i | − | 0.0511515i | ||||||
\(754\) | −44.6956 | + | 44.6956i | −1.62772 | + | 1.62772i | ||||
\(755\) | 3.38053 | + | 8.04321i | 0.123030 | + | 0.292722i | ||||
\(756\) | −0.936350 | −0.0340547 | ||||||||
\(757\) | −20.9126 | −0.760081 | −0.380040 | − | 0.924970i | \(-0.624090\pi\) | ||||
−0.380040 | + | 0.924970i | \(0.624090\pi\) | |||||||
\(758\) | −0.729632 | −0.0265014 | ||||||||
\(759\) | 23.8119 | + | 23.8119i | 0.864316 | + | 0.864316i | ||||
\(760\) | 1.21159 | − | 2.96845i | 0.0439491 | − | 0.107677i | ||||
\(761\) | 22.5447i | 0.817245i | 0.912704 | + | 0.408622i | \(0.133991\pi\) | ||||
−0.912704 | + | 0.408622i | \(0.866009\pi\) | |||||||
\(762\) | −0.350036 | −0.0126805 | ||||||||
\(763\) | − | 2.58862i | − | 0.0937142i | ||||||
\(764\) | −0.841106 | + | 0.841106i | −0.0304301 | + | 0.0304301i | ||||
\(765\) | 1.88405 | + | 4.48266i | 0.0681179 | + | 0.162071i | ||||
\(766\) | −28.2223 | −1.01971 | ||||||||
\(767\) | 23.7601 | − | 23.7601i | 0.857929 | − | 0.857929i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −1.79332 | + | 1.79332i | −0.0646688 | + | 0.0646688i | −0.738701 | − | 0.674033i | \(-0.764561\pi\) |
0.674033 | + | 0.738701i | \(0.264561\pi\) | |||||||
\(770\) | 6.81835 | + | 2.78295i | 0.245716 | + | 0.100291i | ||||
\(771\) | 6.50160 | + | 6.50160i | 0.234149 | + | 0.234149i | ||||
\(772\) | 2.71107i | 0.0975736i | ||||||||
\(773\) | −10.3091 | + | 10.3091i | −0.370791 | + | 0.370791i | −0.867765 | − | 0.496974i | \(-0.834444\pi\) |
0.496974 | + | 0.867765i | \(0.334444\pi\) | |||||||
\(774\) | − | 2.74581i | − | 0.0986961i | ||||||
\(775\) | 16.8777 | − | 0.174894i | 0.606263 | − | 0.00628236i | ||||
\(776\) | 0.301015i | 0.0108058i | ||||||||
\(777\) | −5.57579 | + | 1.16207i | −0.200030 | + | 0.0416890i | ||||
\(778\) | 15.3299 | − | 15.3299i | 0.549604 | − | 0.549604i | ||||
\(779\) | −3.52824 | + | 3.52824i | −0.126412 | + | 0.126412i | ||||
\(780\) | 5.81065 | − | 14.2363i | 0.208055 | − | 0.509742i | ||||
\(781\) | − | 25.7768i | − | 0.922367i | ||||||
\(782\) | 20.8194 | 0.744499 | ||||||||
\(783\) | 9.19196i | 0.328494i | ||||||||
\(784\) | − | 6.12325i | − | 0.218687i | ||||||
\(785\) | −5.14283 | − | 2.09908i | −0.183556 | − | 0.0749194i | ||||
\(786\) | −1.86010 | −0.0663475 | ||||||||
\(787\) | 34.8286 | + | 34.8286i | 1.24151 | + | 1.24151i | 0.959376 | + | 0.282129i | \(0.0910406\pi\) |
0.282129 | + | 0.959376i | \(0.408959\pi\) | |||||||
\(788\) | −14.0103 | − | 14.0103i | −0.499098 | − | 0.499098i | ||||
\(789\) | − | 14.3290i | − | 0.510126i | ||||||
\(790\) | 9.50733 | − | 23.2933i | 0.338256 | − | 0.828740i | ||||
\(791\) | −12.1350 | − | 12.1350i | −0.431471 | − | 0.431471i | ||||
\(792\) | − | 3.51735i | − | 0.124984i | ||||||
\(793\) | −68.7214 | + | 68.7214i | −2.44037 | + | 2.44037i | ||||
\(794\) | 9.07360 | + | 9.07360i | 0.322010 | + | 0.322010i | ||||
\(795\) | 8.55453 | − | 3.59544i | 0.303398 | − | 0.127517i | ||||
\(796\) | 2.28257 | − | 2.28257i | 0.0809037 | − | 0.0809037i | ||||
\(797\) | 18.1150i | 0.641667i | 0.947136 | + | 0.320833i | \(0.103963\pi\) | ||||
−0.947136 | + | 0.320833i | \(0.896037\pi\) | |||||||
\(798\) | −0.949352 | − | 0.949352i | −0.0336067 | − | 0.0336067i | ||||
\(799\) | −7.80827 | − | 7.80827i | −0.276237 | − | 0.276237i | ||||
\(800\) | −3.57198 | − | 3.49871i | −0.126289 | − | 0.123698i | ||||
\(801\) | 6.43088 | + | 6.43088i | 0.227224 | + | 0.227224i | ||||
\(802\) | −23.0577 | + | 23.0577i | −0.814194 | + | 0.814194i | ||||
\(803\) | −1.02935 | + | 1.02935i | −0.0363249 | + | 0.0363249i | ||||
\(804\) | −1.62540 | −0.0573235 | ||||||||
\(805\) | 7.57502 | − | 18.5591i | 0.266984 | − | 0.654122i | ||||
\(806\) | −16.4143 | − | 16.4143i | −0.578169 | − | 0.578169i | ||||
\(807\) | 18.2736 | − | 18.2736i | 0.643262 | − | 0.643262i | ||||
\(808\) | −7.88206 | −0.277290 | ||||||||
\(809\) | −8.19124 | + | 8.19124i | −0.287989 | + | 0.287989i | −0.836284 | − | 0.548296i | \(-0.815277\pi\) |
0.548296 | + | 0.836284i | \(0.315277\pi\) | |||||||
\(810\) | −0.866398 | − | 2.06140i | −0.0304421 | − | 0.0724301i | ||||
\(811\) | 42.4868 | 1.49191 | 0.745956 | − | 0.665995i | \(-0.231993\pi\) | ||||
0.745956 | + | 0.665995i | \(0.231993\pi\) | |||||||
\(812\) | 8.60689 | 0.302043 | ||||||||
\(813\) | 13.4720 | + | 13.4720i | 0.472483 | + | 0.472483i | ||||
\(814\) | −4.36524 | − | 20.9451i | −0.153002 | − | 0.734127i | ||||
\(815\) | 19.3714 | − | 8.14175i | 0.678552 | − | 0.285193i | ||||
\(816\) | −1.53766 | − | 1.53766i | −0.0538288 | − | 0.0538288i | ||||
\(817\) | 2.78394 | − | 2.78394i | 0.0973976 | − | 0.0973976i | ||||
\(818\) | 12.7245 | + | 12.7245i | 0.444901 | + | 0.444901i | ||||
\(819\) | −4.55298 | − | 4.55298i | −0.159094 | − | 0.159094i | ||||
\(820\) | 3.01499 | + | 7.17349i | 0.105288 | + | 0.250509i | ||||
\(821\) | 47.2026 | 1.64738 | 0.823691 | − | 0.567039i | \(-0.191911\pi\) | ||||
0.823691 | + | 0.567039i | \(0.191911\pi\) | |||||||
\(822\) | −19.3502 | −0.674917 | ||||||||
\(823\) | 10.8159 | − | 10.8159i | 0.377018 | − | 0.377018i | −0.493007 | − | 0.870025i | \(-0.664102\pi\) |
0.870025 | + | 0.493007i | \(0.164102\pi\) | |||||||
\(824\) | − | 3.81714i | − | 0.132976i | ||||||
\(825\) | 0.182232 | + | 17.5858i | 0.00634449 | + | 0.612259i | ||||
\(826\) | −4.57541 | −0.159199 | ||||||||
\(827\) | −8.86372 | −0.308222 | −0.154111 | − | 0.988054i | \(-0.549251\pi\) | ||||
−0.154111 | + | 0.988054i | \(0.549251\pi\) | |||||||
\(828\) | −9.57399 | −0.332719 | ||||||||
\(829\) | 12.4726 | − | 12.4726i | 0.433190 | − | 0.433190i | −0.456522 | − | 0.889712i | \(-0.650905\pi\) |
0.889712 | + | 0.456522i | \(0.150905\pi\) | |||||||
\(830\) | −4.29714 | − | 1.75390i | −0.149156 | − | 0.0608789i | ||||
\(831\) | −1.63342 | + | 1.63342i | −0.0566628 | + | 0.0566628i | ||||
\(832\) | 6.87657i | 0.238402i | ||||||||
\(833\) | 13.3155i | 0.461354i | ||||||||
\(834\) | 12.5454 | − | 12.5454i | 0.434411 | − | 0.434411i | ||||
\(835\) | 37.7977 | − | 15.8863i | 1.30804 | − | 0.549767i | ||||
\(836\) | 3.56619 | − | 3.56619i | 0.123339 | − | 0.123339i | ||||
\(837\) | −3.37571 | −0.116682 | ||||||||
\(838\) | 4.07751 | 0.140855 | ||||||||
\(839\) | 52.3150 | 1.80611 | 0.903056 | − | 0.429522i | \(-0.141318\pi\) | ||||
0.903056 | + | 0.429522i | \(0.141318\pi\) | |||||||
\(840\) | −1.93019 | + | 0.811252i | −0.0665978 | + | 0.0279909i | ||||
\(841\) | − | 55.4921i | − | 1.91352i | ||||||
\(842\) | −5.38925 | + | 5.38925i | −0.185726 | + | 0.185726i | ||||
\(843\) | −19.6287 | −0.676048 | ||||||||
\(844\) | −16.7409 | −0.576247 | ||||||||
\(845\) | 70.6797 | − | 29.7064i | 2.43145 | − | 1.02193i | ||||
\(846\) | 3.59071 | + | 3.59071i | 0.123451 | + | 0.123451i | ||||
\(847\) | 0.908225 | + | 0.908225i | 0.0312070 | + | 0.0312070i | ||||
\(848\) | −2.93440 | + | 2.93440i | −0.100768 | + | 0.100768i | ||||
\(849\) | 14.7867 | + | 14.7867i | 0.507478 | + | 0.507478i | ||||
\(850\) | 7.76754 | + | 7.60821i | 0.266424 | + | 0.260960i | ||||
\(851\) | −57.0113 | + | 11.8819i | −1.95432 | + | 0.407307i | ||||
\(852\) | 5.18202 | + | 5.18202i | 0.177533 | + | 0.177533i | ||||
\(853\) | 38.2913 | 1.31107 | 0.655535 | − | 0.755165i | \(-0.272443\pi\) | ||||
0.655535 | + | 0.755165i | \(0.272443\pi\) | |||||||
\(854\) | 13.2334 | 0.452839 | ||||||||
\(855\) | 1.21159 | − | 2.96845i | 0.0414356 | − | 0.101519i | ||||
\(856\) | 3.39625 | − | 3.39625i | 0.116081 | − | 0.116081i | ||||
\(857\) | 23.6239 | 0.806978 | 0.403489 | − | 0.914984i | \(-0.367797\pi\) | ||||
0.403489 | + | 0.914984i | \(0.367797\pi\) | |||||||
\(858\) | 17.1030 | − | 17.1030i | 0.583887 | − | 0.583887i | ||||
\(859\) | 25.3164 | + | 25.3164i | 0.863785 | + | 0.863785i | 0.991775 | − | 0.127991i | \(-0.0408527\pi\) |
−0.127991 | + | 0.991775i | \(0.540853\pi\) | |||||||
\(860\) | −2.37896 | − | 5.66020i | −0.0811220 | − | 0.193011i | ||||
\(861\) | 3.25842 | 0.111047 | ||||||||
\(862\) | 9.41260 | − | 9.41260i | 0.320594 | − | 0.320594i | ||||
\(863\) | −22.2626 | + | 22.2626i | −0.757827 | + | 0.757827i | −0.975927 | − | 0.218099i | \(-0.930014\pi\) |
0.218099 | + | 0.975927i | \(0.430014\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 14.8437 | + | 6.05853i | 0.504699 | + | 0.205996i | ||||
\(866\) | −18.0950 | − | 18.0950i | −0.614892 | − | 0.614892i | ||||
\(867\) | −8.67706 | − | 8.67706i | −0.294688 | − | 0.294688i | ||||
\(868\) | 3.16085i | 0.107286i | ||||||||
\(869\) | 27.9838 | − | 27.9838i | 0.949285 | − | 0.949285i | ||||
\(870\) | 7.96389 | + | 18.9483i | 0.270001 | + | 0.642407i | ||||
\(871\) | −7.90347 | − | 7.90347i | −0.267799 | − | 0.267799i | ||||
\(872\) | −1.95485 | + | 1.95485i | −0.0661997 | + | 0.0661997i | ||||
\(873\) | 0.301015i | 0.0101878i | ||||||||
\(874\) | −9.70693 | − | 9.70693i | −0.328342 | − | 0.328342i | ||||
\(875\) | 9.60840 | − | 4.15604i | 0.324823 | − | 0.140500i | ||||
\(876\) | − | 0.413868i | − | 0.0139833i | ||||||
\(877\) | 13.1660 | + | 13.1660i | 0.444583 | + | 0.444583i | 0.893549 | − | 0.448966i | \(-0.148208\pi\) |
−0.448966 | + | 0.893549i | \(0.648208\pi\) | |||||||
\(878\) | −3.41744 | − | 3.41744i | −0.115333 | − | 0.115333i | ||||
\(879\) | −8.64286 | −0.291516 | ||||||||
\(880\) | −3.04742 | − | 7.25065i | −0.102729 | − | 0.244419i | ||||
\(881\) | − | 12.7644i | − | 0.430043i | −0.976609 | − | 0.215022i | \(-0.931018\pi\) | ||
0.976609 | − | 0.215022i | \(-0.0689822\pi\) | |||||||
\(882\) | − | 6.12325i | − | 0.206180i | ||||||
\(883\) | −23.3191 | −0.784751 | −0.392376 | − | 0.919805i | \(-0.628347\pi\) | ||||
−0.392376 | + | 0.919805i | \(0.628347\pi\) | |||||||
\(884\) | − | 14.9536i | − | 0.502945i | ||||||
\(885\) | −4.23360 | − | 10.0729i | −0.142311 | − | 0.338596i | ||||
\(886\) | 10.8466 | − | 10.8466i | 0.364400 | − | 0.364400i | ||||
\(887\) | −7.29393 | + | 7.29393i | −0.244906 | + | 0.244906i | −0.818876 | − | 0.573970i | \(-0.805403\pi\) |
0.573970 | + | 0.818876i | \(0.305403\pi\) | |||||||
\(888\) | 5.08825 | + | 3.33312i | 0.170750 | + | 0.111852i | ||||
\(889\) | 0.327756i | 0.0109926i | ||||||||
\(890\) | 18.8283 | + | 7.68489i | 0.631125 | + | 0.257598i | ||||
\(891\) | − | 3.51735i | − | 0.117836i | ||||||
\(892\) | −16.5296 | + | 16.5296i | −0.553452 | + | 0.553452i | ||||
\(893\) | 7.28113i | 0.243654i | ||||||||
\(894\) | 7.50200 | + | 7.50200i | 0.250905 | + | 0.250905i | ||||
\(895\) | 17.6039 | − | 43.1302i | 0.588432 | − | 1.44168i | ||||
\(896\) | 0.662100 | − | 0.662100i | 0.0221192 | − | 0.0221192i | ||||
\(897\) | −46.5533 | − | 46.5533i | −1.55437 | − | 1.55437i | ||||
\(898\) | −10.3811 | + | 10.3811i | −0.346421 | + | 0.346421i | ||||
\(899\) | 31.0294 | 1.03489 | ||||||||
\(900\) | −3.57198 | − | 3.49871i | −0.119066 | − | 0.116624i | ||||
\(901\) | 6.38108 | − | 6.38108i | 0.212585 | − | 0.212585i | ||||
\(902\) | 12.2401i | 0.407550i | ||||||||
\(903\) | −2.57104 | −0.0855588 | ||||||||
\(904\) | 18.3281i | 0.609582i | ||||||||
\(905\) | 8.39602 | − | 3.52882i | 0.279093 | − | 0.117302i | ||||
\(906\) | −2.75901 | − | 2.75901i | −0.0916619 | − | 0.0916619i | ||||
\(907\) | 49.3619 | 1.63904 | 0.819518 | − | 0.573054i | \(-0.194241\pi\) | ||||
0.819518 | + | 0.573054i | \(0.194241\pi\) | |||||||
\(908\) | −28.0799 | −0.931865 | ||||||||
\(909\) | −7.88206 | −0.261431 | ||||||||
\(910\) | −13.3302 | − | 5.44080i | −0.441891 | − | 0.180361i | ||||
\(911\) | 6.70882 | − | 6.70882i | 0.222273 | − | 0.222273i | −0.587182 | − | 0.809455i | \(-0.699763\pi\) |
0.809455 | + | 0.587182i | \(0.199763\pi\) | |||||||
\(912\) | 1.43385i | 0.0474795i | ||||||||
\(913\) | −5.16243 | − | 5.16243i | −0.170851 | − | 0.170851i | ||||
\(914\) | 13.7780i | 0.455737i | ||||||||
\(915\) | 12.2448 | + | 29.1337i | 0.404801 | + | 0.963131i | ||||
\(916\) | − | 0.286568i | − | 0.00946847i | ||||||
\(917\) | 1.74170i | 0.0575161i | ||||||||
\(918\) | −1.53766 | − | 1.53766i | −0.0507503 | − | 0.0507503i | ||||
\(919\) | −19.7075 | + | 19.7075i | −0.650090 | + | 0.650090i | −0.953015 | − | 0.302924i | \(-0.902037\pi\) |
0.302924 | + | 0.953015i | \(0.402037\pi\) | |||||||
\(920\) | −19.7358 | + | 8.29489i | −0.650670 | + | 0.273474i | ||||
\(921\) | −15.9746 | −0.526380 | ||||||||
\(922\) | 28.3555 | + | 28.3555i | 0.933838 | + | 0.933838i | ||||
\(923\) | 50.3948i | 1.65877i | ||||||||
\(924\) | −3.29347 | −0.108347 | ||||||||
\(925\) | −25.6126 | − | 16.4011i | −0.842136 | − | 0.539265i | ||||
\(926\) | 27.1414 | 0.891921 | ||||||||
\(927\) | − | 3.81714i | − | 0.125371i | ||||||
\(928\) | −6.49970 | − | 6.49970i | −0.213363 | − | 0.213363i | ||||
\(929\) | −32.0555 | −1.05171 | −0.525853 | − | 0.850575i | \(-0.676254\pi\) | ||||
−0.525853 | + | 0.850575i | \(0.676254\pi\) | |||||||
\(930\) | −6.95868 | + | 2.92471i | −0.228184 | + | 0.0959050i | ||||
\(931\) | 6.20827 | − | 6.20827i | 0.203468 | − | 0.203468i | ||||
\(932\) | 10.2080 | + | 10.2080i | 0.334375 | + | 0.334375i | ||||
\(933\) | 13.9264i | 0.455930i | ||||||||
\(934\) | − | 15.3540i | − | 0.502400i | ||||||
\(935\) | 6.62685 | + | 15.7671i | 0.216721 | + | 0.515639i | ||||
\(936\) | 6.87657i | 0.224768i | ||||||||
\(937\) | 31.6848 | + | 31.6848i | 1.03510 | + | 1.03510i | 0.999361 | + | 0.0357367i | \(0.0113778\pi\) |
0.0357367 | + | 0.999361i | \(0.488622\pi\) | |||||||
\(938\) | 1.52195i | 0.0496933i | ||||||||
\(939\) | −8.57876 | + | 8.57876i | −0.279957 | + | 0.279957i | ||||
\(940\) | 10.5129 | + | 4.29089i | 0.342891 | + | 0.139953i | ||||
\(941\) | 22.9702 | 0.748808 | 0.374404 | − | 0.927266i | \(-0.377847\pi\) | ||||
0.374404 | + | 0.927266i | \(0.377847\pi\) | |||||||
\(942\) | 2.48415 | 0.0809378 | ||||||||
\(943\) | 33.3167 | 1.08494 | ||||||||
\(944\) | 3.45523 | + | 3.45523i | 0.112458 | + | 0.112458i | ||||
\(945\) | −1.93019 | + | 0.811252i | −0.0627891 | + | 0.0263900i | ||||
\(946\) | − | 9.65796i | − | 0.314007i | ||||||
\(947\) | 47.0948 | 1.53037 | 0.765187 | − | 0.643808i | \(-0.222647\pi\) | ||||
0.765187 | + | 0.643808i | \(0.222647\pi\) | |||||||
\(948\) | 11.2514i | 0.365428i | ||||||||
\(949\) | 2.01242 | − | 2.01242i | 0.0653259 | − | 0.0653259i | ||||
\(950\) | −0.0742869 | − | 7.16887i | −0.00241019 | − | 0.232589i | ||||
\(951\) | 13.6690 | 0.443248 | ||||||||
\(952\) | −1.43979 | + | 1.43979i | −0.0466637 | + | 0.0466637i | ||||
\(953\) | −10.7627 | − | 10.7627i | −0.348638 | − | 0.348638i | 0.510964 | − | 0.859602i | \(-0.329289\pi\) |
−0.859602 | + | 0.510964i | \(0.829289\pi\) | |||||||
\(954\) | −2.93440 | + | 2.93440i | −0.0950048 | + | 0.0950048i | ||||
\(955\) | −1.00512 | + | 2.46258i | −0.0325249 | + | 0.0796874i | ||||
\(956\) | −16.6011 | − | 16.6011i | −0.536918 | − | 0.536918i | ||||
\(957\) | 32.3313i | 1.04512i | ||||||||
\(958\) | −11.3006 | + | 11.3006i | −0.365106 | + | 0.365106i | ||||
\(959\) | 18.1186i | 0.585080i | ||||||||
\(960\) | 2.07026 | + | 0.844991i | 0.0668175 | + | 0.0272720i | ||||
\(961\) | − | 19.6046i | − | 0.632405i | ||||||
\(962\) | 8.53425 | + | 40.9487i | 0.275155 | + | 1.32024i | ||||
\(963\) | 3.39625 | − | 3.39625i | 0.109443 | − | 0.109443i | ||||
\(964\) | 17.4511 | − | 17.4511i | 0.562062 | − | 0.562062i | ||||
\(965\) | 2.34887 | + | 5.58860i | 0.0756127 | + | 0.179903i | ||||
\(966\) | 8.96461i | 0.288432i | ||||||||
\(967\) | 25.7099 | 0.826776 | 0.413388 | − | 0.910555i | \(-0.364345\pi\) | ||||
0.413388 | + | 0.910555i | \(0.364345\pi\) | |||||||
\(968\) | − | 1.37173i | − | 0.0440892i | ||||||
\(969\) | − | 3.11802i | − | 0.100165i | ||||||
\(970\) | 0.260799 | + | 0.620511i | 0.00837375 | + | 0.0199234i | ||||
\(971\) | −7.16138 | −0.229820 | −0.114910 | − | 0.993376i | \(-0.536658\pi\) | ||||
−0.114910 | + | 0.993376i | \(0.536658\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −11.7469 | − | 11.7469i | −0.376587 | − | 0.376587i | ||||
\(974\) | 21.7950i | 0.698358i | ||||||||
\(975\) | −0.356271 | − | 34.3810i | −0.0114098 | − | 1.10107i | ||||
\(976\) | −9.99355 | − | 9.99355i | −0.319886 | − | 0.319886i | ||||
\(977\) | − | 6.00481i | − | 0.192111i | −0.995376 | − | 0.0960554i | \(-0.969377\pi\) | ||
0.995376 | − | 0.0960554i | \(-0.0306226\pi\) | |||||||
\(978\) | −6.64486 | + | 6.64486i | −0.212479 | + | 0.212479i | ||||
\(979\) | 22.6196 | + | 22.6196i | 0.722926 | + | 0.722926i | ||||
\(980\) | −5.30517 | − | 12.6224i | −0.169467 | − | 0.403209i | ||||
\(981\) | −1.95485 | + | 1.95485i | −0.0624137 | + | 0.0624137i | ||||
\(982\) | 6.69716i | 0.213715i | ||||||||
\(983\) | −16.8252 | − | 16.8252i | −0.536640 | − | 0.536640i | 0.385901 | − | 0.922540i | \(-0.373891\pi\) |
−0.922540 | + | 0.385901i | \(0.873891\pi\) | |||||||
\(984\) | −2.46067 | − | 2.46067i | −0.0784434 | − | 0.0784434i | ||||
\(985\) | −41.0194 | − | 16.7423i | −1.30699 | − | 0.533455i | ||||
\(986\) | 14.1341 | + | 14.1341i | 0.450121 | + | 0.450121i | ||||
\(987\) | 3.36216 | − | 3.36216i | 0.107019 | − | 0.107019i | ||||
\(988\) | −6.97206 | + | 6.97206i | −0.221811 | + | 0.221811i | ||||
\(989\) | −26.2883 | −0.835921 | ||||||||
\(990\) | −3.04742 | − | 7.25065i | −0.0968534 | − | 0.230441i | ||||
\(991\) | 21.1418 | + | 21.1418i | 0.671592 | + | 0.671592i | 0.958083 | − | 0.286491i | \(-0.0924887\pi\) |
−0.286491 | + | 0.958083i | \(0.592489\pi\) | |||||||
\(992\) | 2.38699 | − | 2.38699i | 0.0757870 | − | 0.0757870i | ||||
\(993\) | 32.6352 | 1.03565 | ||||||||
\(994\) | 4.85218 | − | 4.85218i | 0.153902 | − | 0.153902i | ||||
\(995\) | 2.72767 | − | 6.68291i | 0.0864731 | − | 0.211862i | ||||
\(996\) | 2.07565 | 0.0657694 | ||||||||
\(997\) | −51.0135 | −1.61561 | −0.807807 | − | 0.589447i | \(-0.799346\pi\) | ||||
−0.807807 | + | 0.589447i | \(0.799346\pi\) | |||||||
\(998\) | −31.1536 | − | 31.1536i | −0.986150 | − | 0.986150i | ||||
\(999\) | 5.08825 | + | 3.33312i | 0.160985 | + | 0.105455i |
(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.l.a.697.12 | yes | 36 | |
5.3 | odd | 4 | 1110.2.o.a.253.7 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.o.a.487.7 | yes | 36 | ||
185.43 | even | 4 | inner | 1110.2.l.a.43.12 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.12 | ✓ | 36 | 185.43 | even | 4 | inner | |
1110.2.l.a.697.12 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.253.7 | yes | 36 | 5.3 | odd | 4 | ||
1110.2.o.a.487.7 | yes | 36 | 37.6 | odd | 4 |