Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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 | 487.7 | ||
Character | \(\chi\) | \(=\) | 1110.487 |
Dual form | 1110.2.o.a.253.7 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.866398 | − | 2.06140i | −0.387465 | − | 0.921884i | ||||
\(6\) | 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 | \(0.806624\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.866398 | + | 2.06140i | 0.273979 | + | 0.651871i | ||||
\(11\) | − | 3.51735i | − | 1.06052i | −0.847835 | − | 0.530260i | \(-0.822094\pi\) | ||
0.847835 | − | 0.530260i | \(-0.177906\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | 6.87657 | 1.90722 | 0.953609 | − | 0.301047i | \(-0.0973362\pi\) | ||||
0.953609 | + | 0.301047i | \(0.0973362\pi\) | |||||||
\(14\) | 0.662100 | + | 0.662100i | 0.176954 | + | 0.176954i | ||||
\(15\) | −0.844991 | + | 2.07026i | −0.218176 | + | 0.534540i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.17458i | − | 0.527412i | −0.964603 | − | 0.263706i | \(-0.915055\pi\) | ||
0.964603 | − | 0.263706i | \(-0.0849449\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.01389 | + | 1.01389i | −0.232601 | + | 0.232601i | −0.813778 | − | 0.581176i | \(-0.802593\pi\) |
0.581176 | + | 0.813778i | \(0.302593\pi\) | |||||||
\(20\) | −0.866398 | − | 2.06140i | −0.193732 | − | 0.460942i | ||||
\(21\) | 0.936350i | 0.204328i | ||||||||
\(22\) | 3.51735i | 0.749901i | ||||||||
\(23\) | 9.57399 | 1.99632 | 0.998158 | − | 0.0606732i | \(-0.0193247\pi\) | ||||
0.998158 | + | 0.0606732i | \(0.0193247\pi\) | |||||||
\(24\) | 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 | −0.972006 | − | 0.234958i | \(-0.924505\pi\) |
−0.234958 | − | 0.972006i | \(-0.575495\pi\) | |||||||
\(30\) | 0.844991 | − | 2.07026i | 0.154274 | − | 0.377977i | ||||
\(31\) | 2.38699 | − | 2.38699i | 0.428716 | − | 0.428716i | −0.459475 | − | 0.888191i | \(-0.651962\pi\) |
0.888191 | + | 0.459475i | \(0.151962\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.48714 | + | 2.48714i | −0.432956 | + | 0.432956i | ||||
\(34\) | 2.17458i | 0.372937i | ||||||||
\(35\) | −0.791208 | + | 1.93849i | −0.133739 | + | 0.327665i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −5.95481 | − | 1.24106i | −0.978965 | − | 0.204029i | ||||
\(38\) | 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 | \(-0.912402\pi\) | ||
0.962372 | − | 0.271736i | \(-0.0875977\pi\) | |||||||
\(42\) | − | 0.936350i | − | 0.144482i | ||||||
\(43\) | 2.74581 | 0.418732 | 0.209366 | − | 0.977837i | \(-0.432860\pi\) | ||||
0.209366 | + | 0.977837i | \(0.432860\pi\) | |||||||
\(44\) | − | 3.51735i | − | 0.530260i | ||||||
\(45\) | 2.06140 | − | 0.866398i | 0.307295 | − | 0.129155i | ||||
\(46\) | −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 | ||||||
\(50\) | 3.49871 | − | 3.57198i | 0.494792 | − | 0.505154i | ||||
\(51\) | −1.53766 | + | 1.53766i | −0.215315 | + | 0.215315i | ||||
\(52\) | 6.87657 | 0.953609 | ||||||||
\(53\) | −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 | ||||
\(55\) | −7.25065 | + | 3.04742i | −0.977677 | + | 0.410914i | ||||
\(56\) | 0.662100 | + | 0.662100i | 0.0884768 | + | 0.0884768i | ||||
\(57\) | 1.43385 | 0.189918 | ||||||||
\(58\) | 6.49970 | + | 6.49970i | 0.853452 | + | 0.853452i | ||||
\(59\) | −3.45523 | + | 3.45523i | −0.449833 | + | 0.449833i | −0.895299 | − | 0.445466i | \(-0.853038\pi\) |
0.445466 | + | 0.895299i | \(0.353038\pi\) | |||||||
\(60\) | −0.844991 | + | 2.07026i | −0.109088 | + | 0.267270i | ||||
\(61\) | −9.99355 | + | 9.99355i | −1.27954 | + | 1.27954i | −0.338619 | + | 0.940924i | \(0.609960\pi\) |
−0.940924 | + | 0.338619i | \(0.890040\pi\) | |||||||
\(62\) | −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 | −0.773819 | − | 0.633406i | \(-0.781656\pi\) |
0.633406 | + | 0.773819i | \(0.281656\pi\) | |||||||
\(68\) | − | 2.17458i | − | 0.263706i | ||||||
\(69\) | −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 | \(0.643204\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −0.292649 | − | 0.292649i | −0.0342519 | − | 0.0342519i | 0.689773 | − | 0.724025i | \(-0.257710\pi\) |
−0.724025 | + | 0.689773i | \(0.757710\pi\) | |||||||
\(74\) | 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 | \(-0.531848\pi\) |
0.994999 | + | 0.0998861i | \(0.0318478\pi\) | |||||||
\(80\) | −0.866398 | − | 2.06140i | −0.0968662 | − | 0.230471i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 3.47992i | 0.384293i | ||||||||
\(83\) | −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 | ||||||||
\(87\) | 9.19196i | 0.985481i | ||||||||
\(88\) | 3.51735i | 0.374951i | ||||||||
\(89\) | −6.43088 | − | 6.43088i | −0.681672 | − | 0.681672i | 0.278705 | − | 0.960377i | \(-0.410095\pi\) |
−0.960377 | + | 0.278705i | \(0.910095\pi\) | |||||||
\(90\) | −2.06140 | + | 0.866398i | −0.217290 | + | 0.0913264i | ||||
\(91\) | −4.55298 | − | 4.55298i | −0.477282 | − | 0.477282i | ||||
\(92\) | 9.57399 | 0.998158 | ||||||||
\(93\) | −3.37571 | −0.350045 | ||||||||
\(94\) | −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 | ||||
\(97\) | 0.301015i | 0.0305635i | 0.999883 | + | 0.0152817i | \(0.00486451\pi\) | ||||
−0.999883 | + | 0.0152817i | \(0.995135\pi\) | |||||||
\(98\) | 6.12325i | 0.618541i | ||||||||
\(99\) | 3.51735 | 0.353507 | ||||||||
\(100\) | −3.49871 | + | 3.57198i | −0.349871 | + | 0.357198i | ||||
\(101\) | − | 7.88206i | − | 0.784294i | −0.919903 | − | 0.392147i | \(-0.871732\pi\) | ||
0.919903 | − | 0.392147i | \(-0.128268\pi\) | |||||||
\(102\) | 1.53766 | − | 1.53766i | 0.152251 | − | 0.152251i | ||||
\(103\) | 3.81714i | 0.376114i | 0.982158 | + | 0.188057i | \(0.0602190\pi\) | ||||
−0.982158 | + | 0.188057i | \(0.939781\pi\) | |||||||
\(104\) | −6.87657 | −0.674304 | ||||||||
\(105\) | 1.93019 | − | 0.811252i | 0.188367 | − | 0.0791701i | ||||
\(106\) | 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 | \(-0.792268\pi\) |
0.607261 | + | 0.794502i | \(0.292268\pi\) | |||||||
\(110\) | 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 | ||||
\(113\) | − | 18.3281i | − | 1.72416i | −0.506773 | − | 0.862079i | \(-0.669162\pi\) | ||
0.506773 | − | 0.862079i | \(-0.330838\pi\) | |||||||
\(114\) | −1.43385 | −0.134292 | ||||||||
\(115\) | −8.29489 | − | 19.7358i | −0.773502 | − | 1.84037i | ||||
\(116\) | −6.49970 | − | 6.49970i | −0.603482 | − | 0.603482i | ||||
\(117\) | 6.87657i | 0.635739i | ||||||||
\(118\) | 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 | ||||
\(125\) | 10.3945 | + | 4.11747i | 0.929716 | + | 0.368278i | ||||
\(126\) | −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 | \(0.754944\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.94158 | − | 1.94158i | −0.170947 | − | 0.170947i | ||||
\(130\) | 5.95785 | + | 14.1753i | 0.522538 | + | 1.24326i | ||||
\(131\) | −1.31529 | + | 1.31529i | −0.114917 | + | 0.114917i | −0.762227 | − | 0.647310i | \(-0.775894\pi\) |
0.647310 | + | 0.762227i | \(0.275894\pi\) | |||||||
\(132\) | −2.48714 | + | 2.48714i | −0.216478 | + | 0.216478i | ||||
\(133\) | 1.34259 | 0.116417 | ||||||||
\(134\) | 1.14933 | − | 1.14933i | 0.0992872 | − | 0.0992872i | ||||
\(135\) | −2.07026 | − | 0.844991i | −0.178180 | − | 0.0727253i | ||||
\(136\) | 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 | \(-0.771115\pi\) | ||||
−0.752422 | + | 0.658681i | \(0.771115\pi\) | |||||||
\(140\) | −0.791208 | + | 1.93849i | −0.0668693 | + | 0.163832i | ||||
\(141\) | − | 5.07803i | − | 0.427647i | ||||||
\(142\) | 7.32848 | 0.614992 | ||||||||
\(143\) | − | 24.1873i | − | 2.02264i | ||||||
\(144\) | 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 | ||||
\(148\) | −5.95481 | − | 1.24106i | −0.489482 | − | 0.102015i | ||||
\(149\) | 10.6094i | 0.869159i | 0.900633 | + | 0.434579i | \(0.143103\pi\) | ||||
−0.900633 | + | 0.434579i | \(0.856897\pi\) | |||||||
\(150\) | −4.99973 | + | 0.0518094i | −0.408226 | + | 0.00423022i | ||||
\(151\) | 3.90183i | 0.317526i | 0.987317 | + | 0.158763i | \(0.0507506\pi\) | ||||
−0.987317 | + | 0.158763i | \(0.949249\pi\) | |||||||
\(152\) | 1.01389 | − | 1.01389i | 0.0822370 | − | 0.0822370i | ||||
\(153\) | 2.17458 | 0.175804 | ||||||||
\(154\) | 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 | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.39725i | 0.736049i | 0.929816 | + | 0.368025i | \(0.119966\pi\) | ||||
−0.929816 | + | 0.368025i | \(0.880034\pi\) | |||||||
\(164\) | − | 3.47992i | − | 0.271736i | ||||||
\(165\) | 7.28184 | + | 2.97213i | 0.566890 | + | 0.231380i | ||||
\(166\) | 1.46770 | − | 1.46770i | 0.113916 | − | 0.113916i | ||||
\(167\) | − | 18.3360i | − | 1.41888i | −0.704765 | − | 0.709441i | \(-0.748948\pi\) | ||
0.704765 | − | 0.709441i | \(-0.251052\pi\) | |||||||
\(168\) | − | 0.936350i | − | 0.0722410i | ||||||
\(169\) | 34.2873 | 2.63748 | ||||||||
\(170\) | 4.48266 | − | 1.88405i | 0.343805 | − | 0.144500i | ||||
\(171\) | −1.01389 | − | 1.01389i | −0.0775338 | − | 0.0775338i | ||||
\(172\) | 2.74581 | 0.209366 | ||||||||
\(173\) | 5.06991 | + | 5.06991i | 0.385458 | + | 0.385458i | 0.873064 | − | 0.487606i | \(-0.162130\pi\) |
−0.487606 | + | 0.873064i | \(0.662130\pi\) | |||||||
\(174\) | − | 9.19196i | − | 0.696841i | ||||||
\(175\) | 4.68150 | − | 0.0485117i | 0.353888 | − | 0.00366714i | ||||
\(176\) | − | 3.51735i | − | 0.265130i | ||||||
\(177\) | 4.88643 | 0.367287 | ||||||||
\(178\) | 6.43088 | + | 6.43088i | 0.482015 | + | 0.482015i | ||||
\(179\) | 14.7313 | + | 14.7313i | 1.10107 | + | 1.10107i | 0.994282 | + | 0.106786i | \(0.0340560\pi\) |
0.106786 | + | 0.994282i | \(0.465944\pi\) | |||||||
\(180\) | 2.06140 | − | 0.866398i | 0.153647 | − | 0.0645775i | ||||
\(181\) | −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 | ||||
\(183\) | 14.1330 | 1.04474 | ||||||||
\(184\) | −9.57399 | −0.705804 | ||||||||
\(185\) | 2.60092 | + | 13.3505i | 0.191223 | + | 0.981547i | ||||
\(186\) | 3.37571 | 0.247519 | ||||||||
\(187\) | −7.64874 | −0.559331 | ||||||||
\(188\) | 3.59071 | + | 3.59071i | 0.261879 | + | 0.261879i | ||||
\(189\) | −0.936350 | −0.0681095 | ||||||||
\(190\) | −2.96845 | − | 1.21159i | −0.215354 | − | 0.0878981i | ||||
\(191\) | 0.841106 | + | 0.841106i | 0.0608603 | + | 0.0608603i | 0.736882 | − | 0.676022i | \(-0.236297\pi\) |
−0.676022 | + | 0.736882i | \(0.736297\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 2.71107 | 0.195147 | 0.0975736 | − | 0.995228i | \(-0.468892\pi\) | ||||
0.0975736 | + | 0.995228i | \(0.468892\pi\) | |||||||
\(194\) | − | 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 | \(0.500574\pi\) | |||||||
\(198\) | −3.51735 | −0.249967 | ||||||||
\(199\) | 2.28257 | + | 2.28257i | 0.161807 | + | 0.161807i | 0.783367 | − | 0.621560i | \(-0.213501\pi\) |
−0.621560 | + | 0.783367i | \(0.713501\pi\) | |||||||
\(200\) | 3.49871 | − | 3.57198i | 0.247396 | − | 0.252577i | ||||
\(201\) | 1.62540 | 0.114647 | ||||||||
\(202\) | 7.88206i | 0.554580i | ||||||||
\(203\) | 8.60689i | 0.604085i | ||||||||
\(204\) | −1.53766 | + | 1.53766i | −0.107658 | + | 0.107658i | ||||
\(205\) | −7.17349 | + | 3.01499i | −0.501018 | + | 0.210576i | ||||
\(206\) | − | 3.81714i | − | 0.265953i | ||||||
\(207\) | 9.57399i | 0.665438i | ||||||||
\(208\) | 6.87657 | 0.476805 | ||||||||
\(209\) | 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 | ||||
\(217\) | −3.16085 | −0.214572 | ||||||||
\(218\) | 1.95485 | − | 1.95485i | 0.132399 | − | 0.132399i | ||||
\(219\) | 0.413868i | 0.0279666i | ||||||||
\(220\) | −7.25065 | + | 3.04742i | −0.488839 | + | 0.205457i | ||||
\(221\) | − | 14.9536i | − | 1.00589i | ||||||
\(222\) | −3.33312 | − | 5.08825i | −0.223705 | − | 0.341501i | ||||
\(223\) | 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 | ||||||||
\(227\) | 28.0799i | 1.86373i | 0.362805 | + | 0.931865i | \(0.381819\pi\) | ||||
−0.362805 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(228\) | 1.43385 | 0.0949591 | ||||||||
\(229\) | 0.286568i | 0.0189369i | 0.999955 | + | 0.00946847i | \(0.00301395\pi\) | ||||
−0.999955 | + | 0.00946847i | \(0.996986\pi\) | |||||||
\(230\) | 8.29489 | + | 19.7358i | 0.546949 | + | 1.30134i | ||||
\(231\) | 3.29347 | 0.216694 | ||||||||
\(232\) | 6.49970 | + | 6.49970i | 0.426726 | + | 0.426726i | ||||
\(233\) | 10.2080 | + | 10.2080i | 0.668751 | + | 0.668751i | 0.957427 | − | 0.288676i | \(-0.0932150\pi\) |
−0.288676 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(234\) | − | 6.87657i | − | 0.449536i | ||||||
\(235\) | 4.29089 | − | 10.5129i | 0.279907 | − | 0.685783i | ||||
\(236\) | −3.45523 | + | 3.45523i | −0.224916 | + | 0.224916i | ||||
\(237\) | −11.2514 | −0.730857 | ||||||||
\(238\) | 1.43979 | − | 1.43979i | 0.0933275 | − | 0.0933275i | ||||
\(239\) | −16.6011 | + | 16.6011i | −1.07384 | + | 1.07384i | −0.0767893 | + | 0.997047i | \(0.524467\pi\) |
−0.997047 | + | 0.0767893i | \(0.975533\pi\) | |||||||
\(240\) | −0.844991 | + | 2.07026i | −0.0545440 | + | 0.133635i | ||||
\(241\) | −17.4511 | − | 17.4511i | −1.12412 | − | 1.12412i | −0.991115 | − | 0.133010i | \(-0.957536\pi\) |
−0.133010 | − | 0.991115i | \(-0.542464\pi\) | |||||||
\(242\) | 1.37173 | 0.0881784 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −9.99355 | + | 9.99355i | −0.639771 | + | 0.639771i | ||||
\(245\) | −12.6224 | + | 5.30517i | −0.806418 | + | 0.338935i | ||||
\(246\) | 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 | −0.737736 | − | 0.675089i | \(-0.764105\pi\) |
0.675089 | + | 0.737736i | \(0.264105\pi\) | |||||||
\(252\) | 0.662100 | − | 0.662100i | 0.0417084 | − | 0.0417084i | ||||
\(253\) | − | 33.6751i | − | 2.11713i | ||||||
\(254\) | 0.247513 | + | 0.247513i | 0.0155303 | + | 0.0155303i | ||||
\(255\) | 4.50195 | + | 1.83750i | 0.281923 | + | 0.115069i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.19465i | 0.573546i | 0.957998 | + | 0.286773i | \(0.0925826\pi\) | ||||
−0.957998 | + | 0.286773i | \(0.907417\pi\) | |||||||
\(258\) | 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 | 0.946748 | − | 0.321974i | \(-0.104346\pi\) |
−0.321974 | + | 0.946748i | \(0.604346\pi\) | |||||||
\(264\) | 2.48714 | − | 2.48714i | 0.153073 | − | 0.153073i | ||||
\(265\) | 8.59132 | + | 3.50660i | 0.527761 | + | 0.215409i | ||||
\(266\) | −1.34259 | −0.0823193 | ||||||||
\(267\) | 9.09463i | 0.556582i | ||||||||
\(268\) | −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 | \(0.303571\pi\) | |||||||
\(272\) | − | 2.17458i | − | 0.131853i | ||||||
\(273\) | 6.43888i | 0.389699i | ||||||||
\(274\) | 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 | ||||
\(277\) | 2.31001 | 0.138795 | 0.0693974 | − | 0.997589i | \(-0.477892\pi\) | ||||
0.0693974 | + | 0.997589i | \(0.477892\pi\) | |||||||
\(278\) | 17.7419 | 1.06409 | ||||||||
\(279\) | 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 | 0.159251 | − | 0.987238i | \(-0.449092\pi\) |
−0.987238 | + | 0.159251i | \(0.949092\pi\) | |||||||
\(282\) | 5.07803i | 0.302392i | ||||||||
\(283\) | − | 20.9115i | − | 1.24306i | −0.783389 | − | 0.621531i | \(-0.786511\pi\) | ||
0.783389 | − | 0.621531i | \(-0.213489\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 12.2712 | 0.721836 | ||||||||
\(290\) | 7.76713 | − | 19.0298i | 0.456101 | − | 1.11747i | ||||
\(291\) | 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 | ||||
\(298\) | − | 10.6094i | − | 0.614588i | ||||||
\(299\) | 65.8363 | 3.80741 | ||||||||
\(300\) | 4.99973 | − | 0.0518094i | 0.288660 | − | 0.00299122i | ||||
\(301\) | −1.81800 | − | 1.81800i | −0.104788 | − | 0.104788i | ||||
\(302\) | − | 3.90183i | − | 0.224525i | ||||||
\(303\) | −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 | −0.307022 | − | 0.951703i | \(-0.599332\pi\) |
0.951703 | + | 0.307022i | \(0.0993324\pi\) | |||||||
\(308\) | −2.32883 | + | 2.32883i | −0.132698 | + | 0.132698i | ||||
\(309\) | 2.69912 | − | 2.69912i | 0.153548 | − | 0.153548i | ||||
\(310\) | 6.98861 | + | 2.85245i | 0.396927 | + | 0.162008i | ||||
\(311\) | 9.84746 | − | 9.84746i | 0.558398 | − | 0.558398i | −0.370453 | − | 0.928851i | \(-0.620798\pi\) |
0.928851 | + | 0.370453i | \(0.120798\pi\) | |||||||
\(312\) | 4.86247 | + | 4.86247i | 0.275283 | + | 0.275283i | ||||
\(313\) | −12.1322 | −0.685752 | −0.342876 | − | 0.939381i | \(-0.611401\pi\) | ||||
−0.342876 | + | 0.939381i | \(0.611401\pi\) | |||||||
\(314\) | −1.75656 | − | 1.75656i | −0.0991282 | − | 0.0991282i | ||||
\(315\) | −1.93849 | − | 0.791208i | −0.109222 | − | 0.0445795i | ||||
\(316\) | 7.95594 | − | 7.95594i | 0.447556 | − | 0.447556i | ||||
\(317\) | −9.66544 | + | 9.66544i | −0.542865 | + | 0.542865i | −0.924368 | − | 0.381502i | \(-0.875407\pi\) |
0.381502 | + | 0.924368i | \(0.375407\pi\) | |||||||
\(318\) | −4.14987 | −0.232713 | ||||||||
\(319\) | −22.8617 | + | 22.8617i | −1.28001 | + | 1.28001i | ||||
\(320\) | −0.866398 | − | 2.06140i | −0.0484331 | − | 0.115236i | ||||
\(321\) | 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 | ||||||||
\(325\) | −24.0591 | + | 24.5630i | −1.33456 | + | 1.36251i | ||||
\(326\) | − | 9.39725i | − | 0.520465i | ||||||
\(327\) | 2.76458 | 0.152882 | ||||||||
\(328\) | 3.47992i | 0.192146i | ||||||||
\(329\) | − | 4.75481i | − | 0.262141i | ||||||
\(330\) | −7.28184 | − | 2.97213i | −0.400852 | − | 0.163610i | ||||
\(331\) | 23.0765 | + | 23.0765i | 1.26840 | + | 1.26840i | 0.946914 | + | 0.321487i | \(0.104183\pi\) |
0.321487 | + | 0.946914i | \(0.395817\pi\) | |||||||
\(332\) | −1.46770 | + | 1.46770i | −0.0805508 | + | 0.0805508i | ||||
\(333\) | 1.24106 | − | 5.95481i | 0.0680097 | − | 0.326322i | ||||
\(334\) | 18.3360i | 1.00330i | ||||||||
\(335\) | 3.36501 | + | 1.37345i | 0.183850 | + | 0.0750396i | ||||
\(336\) | 0.936350i | 0.0510821i | ||||||||
\(337\) | 10.8978 | − | 10.8978i | 0.593640 | − | 0.593640i | −0.344973 | − | 0.938613i | \(-0.612112\pi\) |
0.938613 | + | 0.344973i | \(0.112112\pi\) | |||||||
\(338\) | −34.2873 | −1.86498 | ||||||||
\(339\) | −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 | ||||
\(347\) | 0.330476 | 0.0177409 | 0.00887043 | − | 0.999961i | \(-0.497176\pi\) | ||||
0.00887043 | + | 0.999961i | \(0.497176\pi\) | |||||||
\(348\) | 9.19196i | 0.492741i | ||||||||
\(349\) | − | 35.7141i | − | 1.91173i | −0.293799 | − | 0.955867i | \(-0.594920\pi\) | ||
0.293799 | − | 0.955867i | \(-0.405080\pi\) | |||||||
\(350\) | −4.68150 | + | 0.0485117i | −0.250237 | + | 0.00259306i | ||||
\(351\) | 4.86247 | − | 4.86247i | 0.259540 | − | 0.259540i | ||||
\(352\) | 3.51735i | 0.187475i | ||||||||
\(353\) | 19.1728i | 1.02047i | 0.860036 | + | 0.510233i | \(0.170441\pi\) | ||||
−0.860036 | + | 0.510233i | \(0.829559\pi\) | |||||||
\(354\) | −4.88643 | −0.259711 | ||||||||
\(355\) | 6.34938 | + | 15.1069i | 0.336990 | + | 0.801791i | ||||
\(356\) | −6.43088 | − | 6.43088i | −0.340836 | − | 0.340836i | ||||
\(357\) | 2.03617 | 0.107765 | ||||||||
\(358\) | −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 | ||||||||
\(362\) | 4.07298 | 0.214071 | ||||||||
\(363\) | 0.969963 | + | 0.969963i | 0.0509098 | + | 0.0509098i | ||||
\(364\) | −4.55298 | − | 4.55298i | −0.238641 | − | 0.238641i | ||||
\(365\) | −0.349715 | + | 0.856815i | −0.0183049 | + | 0.0448477i | ||||
\(366\) | −14.1330 | −0.738744 | ||||||||
\(367\) | 17.2144 | + | 17.2144i | 0.898582 | + | 0.898582i | 0.995311 | − | 0.0967284i | \(-0.0308378\pi\) |
−0.0967284 | + | 0.995311i | \(0.530838\pi\) | |||||||
\(368\) | 9.57399 | 0.499079 | ||||||||
\(369\) | 3.47992 | 0.181157 | ||||||||
\(370\) | −2.60092 | − | 13.3505i | −0.135215 | − | 0.694058i | ||||
\(371\) | 3.88573 | 0.201737 | ||||||||
\(372\) | −3.37571 | −0.175023 | ||||||||
\(373\) | −13.8033 | − | 13.8033i | −0.714705 | − | 0.714705i | 0.252811 | − | 0.967516i | \(-0.418645\pi\) |
−0.967516 | + | 0.252811i | \(0.918645\pi\) | |||||||
\(374\) | 7.64874 | 0.395507 | ||||||||
\(375\) | −4.43856 | − | 10.2615i | −0.229206 | − | 0.529904i | ||||
\(376\) | −3.59071 | − | 3.59071i | −0.185177 | − | 0.185177i | ||||
\(377\) | −44.6956 | − | 44.6956i | −2.30194 | − | 2.30194i | ||||
\(378\) | 0.936350 | 0.0481607 | ||||||||
\(379\) | − | 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 | ||||
\(383\) | 28.2223 | 1.44209 | 0.721047 | − | 0.692887i | \(-0.243661\pi\) | ||||
0.721047 | + | 0.692887i | \(0.243661\pi\) | |||||||
\(384\) | 0.707107 | + | 0.707107i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | 6.81835 | + | 2.78295i | 0.347495 | + | 0.141832i | ||||
\(386\) | −2.71107 | −0.137990 | ||||||||
\(387\) | 2.74581i | 0.139577i | ||||||||
\(388\) | 0.301015i | 0.0152817i | ||||||||
\(389\) | −15.3299 | + | 15.3299i | −0.777258 | + | 0.777258i | −0.979364 | − | 0.202106i | \(-0.935222\pi\) |
0.202106 | + | 0.979364i | \(0.435222\pi\) | |||||||
\(390\) | 5.81065 | − | 14.2363i | 0.294234 | − | 0.720884i | ||||
\(391\) | − | 20.8194i | − | 1.05288i | ||||||
\(392\) | 6.12325i | 0.309271i | ||||||||
\(393\) | 1.86010 | 0.0938295 | ||||||||
\(394\) | −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 | −0.441748 | − | 0.897139i | \(-0.645642\pi\) |
0.897139 | + | 0.441748i | \(0.145642\pi\) | |||||||
\(398\) | −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 | −0.165182 | + | 0.986263i | \(0.552821\pi\) |
−0.986263 | + | 0.165182i | \(0.947179\pi\) | |||||||
\(402\) | −1.62540 | −0.0810677 | ||||||||
\(403\) | 16.4143 | − | 16.4143i | 0.817655 | − | 0.817655i | ||||
\(404\) | − | 7.88206i | − | 0.392147i | ||||||
\(405\) | 0.866398 | + | 2.06140i | 0.0430517 | + | 0.102432i | ||||
\(406\) | − | 8.60689i | − | 0.427153i | ||||||
\(407\) | −4.36524 | + | 20.9451i | −0.216377 | + | 1.03821i | ||||
\(408\) | 1.53766 | − | 1.53766i | 0.0761254 | − | 0.0761254i | ||||
\(409\) | 12.7245 | + | 12.7245i | 0.629185 | + | 0.629185i | 0.947863 | − | 0.318678i | \(-0.103239\pi\) |
−0.318678 | + | 0.947863i | \(0.603239\pi\) | |||||||
\(410\) | 7.17349 | − | 3.01499i | 0.354273 | − | 0.148900i | ||||
\(411\) | 19.3502i | 0.954477i | ||||||||
\(412\) | 3.81714i | 0.188057i | ||||||||
\(413\) | 4.57541 | 0.225141 | ||||||||
\(414\) | − | 9.57399i | − | 0.470536i | ||||||
\(415\) | 4.29714 | + | 1.75390i | 0.210938 | + | 0.0860958i | ||||
\(416\) | −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 | \(0.968244\pi\) | |||||||
\(420\) | 1.93019 | − | 0.811252i | 0.0941836 | − | 0.0395850i | ||||
\(421\) | −5.38925 | + | 5.38925i | −0.262656 | + | 0.262656i | −0.826132 | − | 0.563476i | \(-0.809464\pi\) |
0.563476 | + | 0.826132i | \(0.309464\pi\) | |||||||
\(422\) | −16.7409 | −0.814936 | ||||||||
\(423\) | −3.59071 | + | 3.59071i | −0.174586 | + | 0.174586i | ||||
\(424\) | 2.93440 | − | 2.93440i | 0.142507 | − | 0.142507i | ||||
\(425\) | 7.76754 | + | 7.60821i | 0.376781 | + | 0.369052i | ||||
\(426\) | −5.18202 | − | 5.18202i | −0.251070 | − | 0.251070i | ||||
\(427\) | 13.2334 | 0.640411 | ||||||||
\(428\) | −3.39625 | − | 3.39625i | −0.164164 | − | 0.164164i | ||||
\(429\) | −17.1030 | + | 17.1030i | −0.825741 | + | 0.825741i | ||||
\(430\) | 2.37896 | + | 5.66020i | 0.114724 | + | 0.272959i | ||||
\(431\) | 9.41260 | − | 9.41260i | 0.453389 | − | 0.453389i | −0.443089 | − | 0.896478i | \(-0.646117\pi\) |
0.896478 | + | 0.443089i | \(0.146117\pi\) | |||||||
\(432\) | 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 | ||||
\(438\) | − | 0.413868i | − | 0.0197754i | ||||||
\(439\) | −3.41744 | − | 3.41744i | −0.163106 | − | 0.163106i | 0.620835 | − | 0.783941i | \(-0.286794\pi\) |
−0.783941 | + | 0.620835i | \(0.786794\pi\) | |||||||
\(440\) | 7.25065 | − | 3.04742i | 0.345661 | − | 0.145280i | ||||
\(441\) | 6.12325 | 0.291583 | ||||||||
\(442\) | 14.9536i | 0.711272i | ||||||||
\(443\) | −10.8466 | − | 10.8466i | −0.515340 | − | 0.515340i | 0.400818 | − | 0.916158i | \(-0.368726\pi\) |
−0.916158 | + | 0.400818i | \(0.868726\pi\) | |||||||
\(444\) | 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 | \(-0.637397\pi\) |
0.908279 | + | 0.418366i | \(0.137397\pi\) | |||||||
\(450\) | 3.57198 | + | 3.49871i | 0.168385 | + | 0.164931i | ||||
\(451\) | −12.2401 | −0.576363 | ||||||||
\(452\) | − | 18.3281i | − | 0.862079i | ||||||
\(453\) | 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 | ||||||||
\(457\) | − | 13.7780i | − | 0.644509i | −0.946653 | − | 0.322254i | \(-0.895559\pi\) | ||
0.946653 | − | 0.322254i | \(-0.104441\pi\) | |||||||
\(458\) | − | 0.286568i | − | 0.0133904i | ||||||
\(459\) | −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 | −0.913253 | − | 0.407393i | \(-0.866438\pi\) |
−0.407393 | − | 0.913253i | \(-0.633562\pi\) | |||||||
\(462\) | −3.29347 | −0.153226 | ||||||||
\(463\) | −27.1414 | −1.26137 | −0.630683 | − | 0.776040i | \(-0.717225\pi\) | ||||
−0.630683 | + | 0.776040i | \(0.717225\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | 15.3540i | 0.710500i | 0.934771 | + | 0.355250i | \(0.115604\pi\) | ||||
−0.934771 | + | 0.355250i | \(0.884396\pi\) | |||||||
\(468\) | 6.87657i | 0.317870i | ||||||||
\(469\) | 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 | ||||
\(473\) | − | 9.65796i | − | 0.444074i | ||||||
\(474\) | 11.2514 | 0.516794 | ||||||||
\(475\) | −0.0742869 | − | 7.16887i | −0.00340852 | − | 0.328930i | ||||
\(476\) | −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 | \(-0.631033\pi\) |
0.916461 | + | 0.400123i | \(0.131033\pi\) | |||||||
\(480\) | 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 | ||||
\(483\) | 8.96461i | 0.407904i | ||||||||
\(484\) | −1.37173 | −0.0623516 | ||||||||
\(485\) | 0.620511 | − | 0.260799i | 0.0281760 | − | 0.0118423i | ||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | − | 21.7950i | − | 0.987628i | −0.869568 | − | 0.493814i | \(-0.835602\pi\) | ||
0.869568 | − | 0.493814i | \(-0.164398\pi\) | |||||||
\(488\) | 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 | ||||
\(495\) | −3.04742 | − | 7.25065i | −0.136971 | − | 0.325892i | ||||
\(496\) | 2.38699 | − | 2.38699i | 0.107179 | − | 0.107179i | ||||
\(497\) | 4.85218 | + | 4.85218i | 0.217650 | + | 0.217650i | ||||
\(498\) | −2.07565 | −0.0930120 | ||||||||
\(499\) | −31.1536 | − | 31.1536i | −1.39463 | − | 1.39463i | −0.814592 | − | 0.580034i | \(-0.803039\pi\) |
−0.580034 | − | 0.814592i | \(-0.696961\pi\) | |||||||
\(500\) | 10.3945 | + | 4.11747i | 0.464858 | + | 0.184139i | ||||
\(501\) | −12.9655 | + | 12.9655i | −0.579256 | + | 0.579256i | ||||
\(502\) | 0.992524 | − | 0.992524i | 0.0442985 | − | 0.0442985i | ||||
\(503\) | −0.724954 | −0.0323241 | −0.0161621 | − | 0.999869i | \(-0.505145\pi\) | ||||
−0.0161621 | + | 0.999869i | \(0.505145\pi\) | |||||||
\(504\) | −0.662100 | + | 0.662100i | −0.0294923 | + | 0.0294923i | ||||
\(505\) | −16.2480 | + | 6.82900i | −0.723029 | + | 0.303886i | ||||
\(506\) | 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 | \(-0.676271\pi\) | ||||
−0.525899 | + | 0.850547i | \(0.676271\pi\) | |||||||
\(510\) | −4.50195 | − | 1.83750i | −0.199350 | − | 0.0813658i | ||||
\(511\) | 0.387525i | 0.0171431i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.43385i | 0.0633061i | ||||||||
\(514\) | − | 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 | ||||
\(518\) | −3.12097 | − | 4.76438i | −0.137128 | − | 0.209335i | ||||
\(519\) | − | 7.16994i | − | 0.314725i | ||||||
\(520\) | 5.95785 | + | 14.1753i | 0.261269 | + | 0.621630i | ||||
\(521\) | 23.1177i | 1.01281i | 0.862297 | + | 0.506403i | \(0.169025\pi\) | ||||
−0.862297 | + | 0.506403i | \(0.830975\pi\) | |||||||
\(522\) | −6.49970 | + | 6.49970i | −0.284484 | + | 0.284484i | ||||
\(523\) | 15.4427 | 0.675261 | 0.337631 | − | 0.941279i | \(-0.390375\pi\) | ||||
0.337631 | + | 0.941279i | \(0.390375\pi\) | |||||||
\(524\) | −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 | ||||
\(532\) | 1.34259 | 0.0582085 | ||||||||
\(533\) | − | 23.9299i | − | 1.03652i | ||||||
\(534\) | − | 9.09463i | − | 0.393563i | ||||||
\(535\) | −4.05851 | + | 9.94353i | −0.175465 | + | 0.429896i | ||||
\(536\) | 1.14933 | − | 1.14933i | 0.0496436 | − | 0.0496436i | ||||
\(537\) | − | 20.8332i | − | 0.899018i | ||||||
\(538\) | 25.8428i | 1.11416i | ||||||||
\(539\) | −21.5376 | −0.927690 | ||||||||
\(540\) | −2.07026 | − | 0.844991i | −0.0890899 | − | 0.0363626i | ||||
\(541\) | 3.85083 | + | 3.85083i | 0.165560 | + | 0.165560i | 0.785025 | − | 0.619465i | \(-0.212650\pi\) |
−0.619465 | + | 0.785025i | \(0.712650\pi\) | |||||||
\(542\) | −19.0523 | −0.818365 | ||||||||
\(543\) | 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 | ||||||
\(547\) | 5.49141 | 0.234796 | 0.117398 | − | 0.993085i | \(-0.462545\pi\) | ||||
0.117398 | + | 0.993085i | \(0.462545\pi\) | |||||||
\(548\) | −13.6827 | − | 13.6827i | −0.584495 | − | 0.584495i | ||||
\(549\) | −9.99355 | − | 9.99355i | −0.426514 | − | 0.426514i | ||||
\(550\) | −12.5639 | − | 12.3062i | −0.535726 | − | 0.524737i | ||||
\(551\) | 13.1799 | 0.561483 | ||||||||
\(552\) | 6.76983 | + | 6.76983i | 0.288143 | + | 0.288143i | ||||
\(553\) | −10.5352 | −0.448004 | ||||||||
\(554\) | −2.31001 | −0.0981428 | ||||||||
\(555\) | 7.60109 | − | 11.2793i | 0.322648 | − | 0.478781i | ||||
\(556\) | −17.7419 | −0.752422 | ||||||||
\(557\) | −20.3979 | −0.864285 | −0.432142 | − | 0.901805i | \(-0.642242\pi\) | ||||
−0.432142 | + | 0.901805i | \(0.642242\pi\) | |||||||
\(558\) | −2.38699 | − | 2.38699i | −0.101049 | − | 0.101049i | ||||
\(559\) | 18.8818 | 0.798613 | ||||||||
\(560\) | −0.791208 | + | 1.93849i | −0.0334346 | + | 0.0819162i | ||||
\(561\) | 5.40848 | + | 5.40848i | 0.228346 | + | 0.228346i | ||||
\(562\) | 13.8796 | + | 13.8796i | 0.585475 | + | 0.585475i | ||||
\(563\) | 41.6497 | 1.75533 | 0.877663 | − | 0.479278i | \(-0.159101\pi\) | ||||
0.877663 | + | 0.479278i | \(0.159101\pi\) | |||||||
\(564\) | − | 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 | ||||
\(568\) | 7.32848 | 0.307496 | ||||||||
\(569\) | 29.9799 | + | 29.9799i | 1.25682 | + | 1.25682i | 0.952602 | + | 0.304220i | \(0.0983957\pi\) |
0.304220 | + | 0.952602i | \(0.401604\pi\) | |||||||
\(570\) | 1.24229 | + | 2.95573i | 0.0520336 | + | 0.123802i | ||||
\(571\) | −33.5003 | −1.40195 | −0.700973 | − | 0.713188i | \(-0.747250\pi\) | ||||
−0.700973 | + | 0.713188i | \(0.747250\pi\) | |||||||
\(572\) | − | 24.1873i | − | 1.01132i | ||||||
\(573\) | − | 1.18950i | − | 0.0496922i | ||||||
\(574\) | 2.30405 | − | 2.30405i | 0.0961693 | − | 0.0961693i | ||||
\(575\) | −33.4966 | + | 34.1981i | −1.39691 | + | 1.42616i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | 11.2900i | 0.470008i | 0.971994 | + | 0.235004i | \(0.0755104\pi\) | ||||
−0.971994 | + | 0.235004i | \(0.924490\pi\) | |||||||
\(578\) | −12.2712 | −0.510415 | ||||||||
\(579\) | −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 | ||||
\(587\) | −0.261793 | −0.0108053 | −0.00540267 | − | 0.999985i | \(-0.501720\pi\) | ||||
−0.00540267 | + | 0.999985i | \(0.501720\pi\) | |||||||
\(588\) | −4.32979 | + | 4.32979i | −0.178558 | + | 0.178558i | ||||
\(589\) | 4.84027i | 0.199440i | ||||||||
\(590\) | −10.1162 | − | 4.12899i | −0.416477 | − | 0.169988i | ||||
\(591\) | − | 19.8136i | − | 0.815023i | ||||||
\(592\) | −5.95481 | − | 1.24106i | −0.244741 | − | 0.0510073i | ||||
\(593\) | −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 | ||||||||
\(597\) | − | 3.22805i | − | 0.132115i | ||||||
\(598\) | −65.8363 | −2.69225 | ||||||||
\(599\) | − | 40.4441i | − | 1.65250i | −0.563303 | − | 0.826251i | \(-0.690470\pi\) | ||
0.563303 | − | 0.826251i | \(-0.309530\pi\) | |||||||
\(600\) | −4.99973 | + | 0.0518094i | −0.204113 | + | 0.00211511i | ||||
\(601\) | 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 | ||||||||
\(605\) | 1.18847 | + | 2.82769i | 0.0483181 | + | 0.114962i | ||||
\(606\) | 5.57346 | − | 5.57346i | 0.226406 | − | 0.226406i | ||||
\(607\) | −14.3687 | −0.583208 | −0.291604 | − | 0.956539i | \(-0.594189\pi\) | ||||
−0.291604 | + | 0.956539i | \(0.594189\pi\) | |||||||
\(608\) | 1.01389 | − | 1.01389i | 0.0411185 | − | 0.0411185i | ||||
\(609\) | 6.08599 | − | 6.08599i | 0.246617 | − | 0.246617i | ||||
\(610\) | −29.2590 | − | 11.9423i | −1.18466 | − | 0.483528i | ||||
\(611\) | 24.6918 | + | 24.6918i | 0.998922 | + | 0.998922i | ||||
\(612\) | 2.17458 | 0.0879020 | ||||||||
\(613\) | −10.7011 | − | 10.7011i | −0.432213 | − | 0.432213i | 0.457167 | − | 0.889381i | \(-0.348864\pi\) |
−0.889381 | + | 0.457167i | \(0.848864\pi\) | |||||||
\(614\) | −11.2957 | + | 11.2957i | −0.455858 | + | 0.455858i | ||||
\(615\) | 7.20434 | + | 2.94050i | 0.290507 | + | 0.118572i | ||||
\(616\) | 2.32883 | − | 2.32883i | 0.0938314 | − | 0.0938314i | ||||
\(617\) | 14.0957 | − | 14.0957i | 0.567470 | − | 0.567470i | −0.363949 | − | 0.931419i | \(-0.618572\pi\) |
0.931419 | + | 0.363949i | \(0.118572\pi\) | |||||||
\(618\) | −2.69912 | + | 2.69912i | −0.108575 | + | 0.108575i | ||||
\(619\) | −4.28502 | −0.172230 | −0.0861148 | − | 0.996285i | \(-0.527445\pi\) | ||||
−0.0861148 | + | 0.996285i | \(0.527445\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | 8.51576i | 0.341177i | ||||||||
\(624\) | −4.86247 | − | 4.86247i | −0.194655 | − | 0.194655i | ||||
\(625\) | −0.518066 | − | 24.9946i | −0.0207226 | − | 0.999785i | ||||
\(626\) | 12.1322 | 0.484900 | ||||||||
\(627\) | − | 5.04335i | − | 0.201412i | ||||||
\(628\) | 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 | −0.884565 | − | 0.466416i | \(-0.845545\pi\) |
0.466416 | + | 0.884565i | \(0.345545\pi\) | |||||||
\(632\) | −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 | ||||
\(635\) | −0.295777 | + | 0.724667i | −0.0117376 | + | 0.0287575i | ||||
\(636\) | 4.14987 | 0.164553 | ||||||||
\(637\) | − | 42.1070i | − | 1.66834i | ||||||
\(638\) | 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 | \(0.192251\pi\) | |||||||
\(642\) | − | 4.80302i | − | 0.189560i | ||||||
\(643\) | − | 25.1480i | − | 0.991742i | −0.868396 | − | 0.495871i | \(-0.834849\pi\) | ||
0.868396 | − | 0.495871i | \(-0.165151\pi\) | |||||||
\(644\) | −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 | ||||
\(647\) | −29.9330 | −1.17679 | −0.588394 | − | 0.808575i | \(-0.700239\pi\) | ||||
−0.588394 | + | 0.808575i | \(0.700239\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 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 | ||||
\(652\) | 9.39725i | 0.368025i | ||||||||
\(653\) | 16.5783i | 0.648759i | 0.945927 | + | 0.324380i | \(0.105156\pi\) | ||||
−0.945927 | + | 0.324380i | \(0.894844\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | 4.75481i | 0.185362i | ||||||||
\(659\) | 19.3767 | 0.754807 | 0.377404 | − | 0.926049i | \(-0.376817\pi\) | ||||
0.377404 | + | 0.926049i | \(0.376817\pi\) | |||||||
\(660\) | 7.28184 | + | 2.97213i | 0.283445 | + | 0.115690i | ||||
\(661\) | −11.4801 | + | 11.4801i | −0.446523 | + | 0.446523i | −0.894197 | − | 0.447674i | \(-0.852252\pi\) |
0.447674 | + | 0.894197i | \(0.352252\pi\) | |||||||
\(662\) | −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 | ||||
\(668\) | − | 18.3360i | − | 0.709441i | ||||||
\(669\) | −23.3764 | −0.903784 | ||||||||
\(670\) | −3.36501 | − | 1.37345i | −0.130002 | − | 0.0530610i | ||||
\(671\) | 35.1508 | + | 35.1508i | 1.35698 | + | 1.35698i | ||||
\(672\) | − | 0.936350i | − | 0.0361205i | ||||||
\(673\) | 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 | −0.236635 | − | 0.971599i | \(-0.576045\pi\) |
0.971599 | + | 0.236635i | \(0.0760446\pi\) | |||||||
\(678\) | 12.9599 | − | 12.9599i | 0.497722 | − | 0.497722i | ||||
\(679\) | 0.199302 | − | 0.199302i | 0.00764851 | − | 0.00764851i | ||||
\(680\) | 4.48266 | − | 1.88405i | 0.171902 | − | 0.0722500i | ||||
\(681\) | 19.8555 | − | 19.8555i | 0.760865 | − | 0.760865i | ||||
\(682\) | 8.39587 | + | 8.39587i | 0.321494 | + | 0.321494i | ||||
\(683\) | −5.31945 | −0.203543 | −0.101772 | − | 0.994808i | \(-0.532451\pi\) | ||||
−0.101772 | + | 0.994808i | \(0.532451\pi\) | |||||||
\(684\) | −1.01389 | − | 1.01389i | −0.0387669 | − | 0.0387669i | ||||
\(685\) | −16.3508 | + | 40.0601i | −0.624732 | + | 1.53062i | ||||
\(686\) | 8.68890 | − | 8.68890i | 0.331744 | − | 0.331744i | ||||
\(687\) | 0.202634 | − | 0.202634i | 0.00773097 | − | 0.00773097i | ||||
\(688\) | 2.74581 | 0.104683 | ||||||||
\(689\) | −20.1786 | + | 20.1786i | −0.768745 | + | 0.768745i | ||||
\(690\) | 8.08994 | − | 19.8207i | 0.307979 | − | 0.754561i | ||||
\(691\) | − | 35.7436i | − | 1.35975i | −0.733328 | − | 0.679875i | \(-0.762034\pi\) | ||
0.733328 | − | 0.679875i | \(-0.237966\pi\) | |||||||
\(692\) | 5.06991 | + | 5.06991i | 0.192729 | + | 0.192729i | ||||
\(693\) | −2.32883 | − | 2.32883i | −0.0884651 | − | 0.0884651i | ||||
\(694\) | −0.330476 | −0.0125447 | ||||||||
\(695\) | 15.3715 | + | 36.5730i | 0.583074 | + | 1.38729i | ||||
\(696\) | − | 9.19196i | − | 0.348420i | ||||||
\(697\) | −7.56735 | −0.286634 | ||||||||
\(698\) | 35.7141i | 1.35180i | ||||||||
\(699\) | − | 14.4363i | − | 0.546033i | ||||||
\(700\) | 4.68150 | − | 0.0485117i | 0.176944 | − | 0.00183357i | ||||
\(701\) | −20.6265 | − | 20.6265i | −0.779051 | − | 0.779051i | 0.200618 | − | 0.979669i | \(-0.435705\pi\) |
−0.979669 | + | 0.200618i | \(0.935705\pi\) | |||||||
\(702\) | −4.86247 | + | 4.86247i | −0.183522 | + | 0.183522i | ||||
\(703\) | 7.29579 | − | 4.77920i | 0.275166 | − | 0.180251i | ||||
\(704\) | − | 3.51735i | − | 0.132565i | ||||||
\(705\) | −10.4678 | + | 4.39959i | −0.394241 | + | 0.165698i | ||||
\(706\) | − | 19.1728i | − | 0.721579i | ||||||
\(707\) | −5.21871 | + | 5.21871i | −0.196270 | + | 0.196270i | ||||
\(708\) | 4.88643 | 0.183643 | ||||||||
\(709\) | −7.74624 | + | 7.74624i | −0.290916 | + | 0.290916i | −0.837442 | − | 0.546526i | \(-0.815950\pi\) |
0.546526 | + | 0.837442i | \(0.315950\pi\) | |||||||
\(710\) | −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 | ||||
\(717\) | 23.4775 | 0.876784 | ||||||||
\(718\) | 6.91664i | 0.258127i | ||||||||
\(719\) | 28.4115i | 1.05957i | 0.848132 | + | 0.529785i | \(0.177727\pi\) | ||||
−0.848132 | + | 0.529785i | \(0.822273\pi\) | |||||||
\(720\) | 2.06140 | − | 0.866398i | 0.0768237 | − | 0.0322887i | ||||
\(721\) | 2.52733 | − | 2.52733i | 0.0941226 | − | 0.0941226i | ||||
\(722\) | − | 16.9441i | − | 0.630593i | ||||||
\(723\) | 24.6796i | 0.917844i | ||||||||
\(724\) | −4.07298 | −0.151371 | ||||||||
\(725\) | 45.9573 | − | 0.476230i | 1.70681 | − | 0.0176867i | ||||
\(726\) | −0.969963 | − | 0.969963i | −0.0359987 | − | 0.0359987i | ||||
\(727\) | 10.2341 | 0.379561 | 0.189780 | − | 0.981827i | \(-0.439222\pi\) | ||||
0.189780 | + | 0.981827i | \(0.439222\pi\) | |||||||
\(728\) | 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 | ||||||
\(732\) | 14.1330 | 0.522371 | ||||||||
\(733\) | −27.1770 | − | 27.1770i | −1.00380 | − | 1.00380i | −0.999993 | − | 0.00381081i | \(-0.998787\pi\) |
−0.00381081 | − | 0.999993i | \(-0.501213\pi\) | |||||||
\(734\) | −17.2144 | − | 17.2144i | −0.635394 | − | 0.635394i | ||||
\(735\) | 12.6767 | + | 5.17409i | 0.467588 | + | 0.190849i | ||||
\(736\) | −9.57399 | −0.352902 | ||||||||
\(737\) | 4.04260 | + | 4.04260i | 0.148911 | + | 0.148911i | ||||
\(738\) | −3.47992 | −0.128098 | ||||||||
\(739\) | 17.3037 | 0.636527 | 0.318264 | − | 0.948002i | \(-0.396900\pi\) | ||||
0.318264 | + | 0.948002i | \(0.396900\pi\) | |||||||
\(740\) | 2.60092 | + | 13.3505i | 0.0956116 | + | 0.490773i | ||||
\(741\) | 9.85998 | 0.362215 | ||||||||
\(742\) | −3.88573 | −0.142650 | ||||||||
\(743\) | 24.1248 | + | 24.1248i | 0.885055 | + | 0.885055i | 0.994043 | − | 0.108988i | \(-0.0347611\pi\) |
−0.108988 | + | 0.994043i | \(0.534761\pi\) | |||||||
\(744\) | 3.37571 | 0.123760 | ||||||||
\(745\) | 21.8703 | − | 9.19199i | 0.801264 | − | 0.336769i | ||||
\(746\) | 13.8033 | + | 13.8033i | 0.505373 | + | 0.505373i | ||||
\(747\) | −1.46770 | − | 1.46770i | −0.0537005 | − | 0.0537005i | ||||
\(748\) | −7.64874 | −0.279666 | ||||||||
\(749\) | 4.49731i | 0.164328i | ||||||||
\(750\) | 4.43856 | + | 10.2615i | 0.162073 | + | 0.374698i | ||||
\(751\) | − | 49.1232i | − | 1.79253i | −0.443517 | − | 0.896266i | \(-0.646270\pi\) | ||
0.443517 | − | 0.896266i | \(-0.353730\pi\) | |||||||
\(752\) | 3.59071 | + | 3.59071i | 0.130940 | + | 0.130940i | ||||
\(753\) | 1.40364 | 0.0511515 | ||||||||
\(754\) | 44.6956 | + | 44.6956i | 1.62772 | + | 1.62772i | ||||
\(755\) | 8.04321 | − | 3.38053i | 0.292722 | − | 0.123030i | ||||
\(756\) | −0.936350 | −0.0340547 | ||||||||
\(757\) | − | 20.9126i | − | 0.760081i | −0.924970 | − | 0.380040i | \(-0.875910\pi\) | ||
0.924970 | − | 0.380040i | \(-0.124090\pi\) | |||||||
\(758\) | 0.729632i | 0.0265014i | ||||||||
\(759\) | −23.8119 | + | 23.8119i | −0.864316 | + | 0.864316i | ||||
\(760\) | −2.96845 | − | 1.21159i | −0.107677 | − | 0.0439491i | ||||
\(761\) | − | 22.5447i | − | 0.817245i | −0.912704 | − | 0.408622i | \(-0.866009\pi\) | ||
0.912704 | − | 0.408622i | \(-0.133991\pi\) | |||||||
\(762\) | − | 0.350036i | − | 0.0126805i | ||||||
\(763\) | 2.58862 | 0.0937142 | ||||||||
\(764\) | 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 | \(-0.235439\pi\) |
−0.674033 | + | 0.738701i | \(0.735439\pi\) | |||||||
\(770\) | −6.81835 | − | 2.78295i | −0.245716 | − | 0.100291i | ||||
\(771\) | 6.50160 | − | 6.50160i | 0.234149 | − | 0.234149i | ||||
\(772\) | 2.71107 | 0.0975736 | ||||||||
\(773\) | −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 | ||||||
\(775\) | 0.174894 | + | 16.8777i | 0.00628236 | + | 0.606263i | ||||
\(776\) | − | 0.301015i | − | 0.0108058i | ||||||
\(777\) | 1.16207 | − | 5.57579i | 0.0416890 | − | 0.200030i | ||||
\(778\) | 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 | ||||||||
\(782\) | 20.8194i | 0.744499i | ||||||||
\(783\) | −9.19196 | −0.328494 | ||||||||
\(784\) | − | 6.12325i | − | 0.218687i | ||||||
\(785\) | 2.09908 | − | 5.14283i | 0.0749194 | − | 0.183556i | ||||
\(786\) | −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 | ||||||
\(790\) | 23.2933 | + | 9.50733i | 0.828740 | + | 0.338256i | ||||
\(791\) | −12.1350 | + | 12.1350i | −0.431471 | + | 0.431471i | ||||
\(792\) | −3.51735 | −0.124984 | ||||||||
\(793\) | −68.7214 | + | 68.7214i | −2.44037 | + | 2.44037i | ||||
\(794\) | −9.07360 | + | 9.07360i | −0.322010 | + | 0.322010i | ||||
\(795\) | −3.59544 | − | 8.55453i | −0.127517 | − | 0.303398i | ||||
\(796\) | 2.28257 | + | 2.28257i | 0.0809037 | + | 0.0809037i | ||||
\(797\) | 18.1150 | 0.641667 | 0.320833 | − | 0.947136i | \(-0.396037\pi\) | ||||
0.320833 | + | 0.947136i | \(0.396037\pi\) | |||||||
\(798\) | 0.949352 | + | 0.949352i | 0.0336067 | + | 0.0336067i | ||||
\(799\) | 7.80827 | − | 7.80827i | 0.276237 | − | 0.276237i | ||||
\(800\) | 3.49871 | − | 3.57198i | 0.123698 | − | 0.126289i | ||||
\(801\) | 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 | ||||
\(808\) | 7.88206i | 0.277290i | ||||||||
\(809\) | 8.19124 | + | 8.19124i | 0.287989 | + | 0.287989i | 0.836284 | − | 0.548296i | \(-0.184723\pi\) |
−0.548296 | + | 0.836284i | \(0.684723\pi\) | |||||||
\(810\) | −0.866398 | − | 2.06140i | −0.0304421 | − | 0.0724301i | ||||
\(811\) | 42.4868 | 1.49191 | 0.745956 | − | 0.665995i | \(-0.231993\pi\) | ||||
0.745956 | + | 0.665995i | \(0.231993\pi\) | |||||||
\(812\) | 8.60689i | 0.302043i | ||||||||
\(813\) | −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 | ||||
\(820\) | −7.17349 | + | 3.01499i | −0.250509 | + | 0.105288i | ||||
\(821\) | 47.2026 | 1.64738 | 0.823691 | − | 0.567039i | \(-0.191911\pi\) | ||||
0.823691 | + | 0.567039i | \(0.191911\pi\) | |||||||
\(822\) | − | 19.3502i | − | 0.674917i | ||||||
\(823\) | 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 | ||||||||
\(827\) | − | 8.86372i | − | 0.308222i | −0.988054 | − | 0.154111i | \(-0.950749\pi\) | ||
0.988054 | − | 0.154111i | \(-0.0492513\pi\) | |||||||
\(828\) | 9.57399i | 0.332719i | ||||||||
\(829\) | −12.4726 | − | 12.4726i | −0.433190 | − | 0.433190i | 0.456522 | − | 0.889712i | \(-0.349095\pi\) |
−0.889712 | + | 0.456522i | \(0.849095\pi\) | |||||||
\(830\) | −4.29714 | − | 1.75390i | −0.149156 | − | 0.0608789i | ||||
\(831\) | −1.63342 | − | 1.63342i | −0.0566628 | − | 0.0566628i | ||||
\(832\) | 6.87657 | 0.238402 | ||||||||
\(833\) | −13.3155 | −0.461354 | ||||||||
\(834\) | −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 | ||||
\(837\) | − | 3.37571i | − | 0.116682i | ||||||
\(838\) | − | 4.07751i | − | 0.140855i | ||||||
\(839\) | −52.3150 | −1.80611 | −0.903056 | − | 0.429522i | \(-0.858682\pi\) | ||||
−0.903056 | + | 0.429522i | \(0.858682\pi\) | |||||||
\(840\) | −1.93019 | + | 0.811252i | −0.0665978 | + | 0.0279909i | ||||
\(841\) | 55.4921i | 1.91352i | ||||||||
\(842\) | 5.38925 | − | 5.38925i | 0.185726 | − | 0.185726i | ||||
\(843\) | 19.6287i | 0.676048i | ||||||||
\(844\) | 16.7409 | 0.576247 | ||||||||
\(845\) | −29.7064 | − | 70.6797i | −1.02193 | − | 2.43145i | ||||
\(846\) | 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 | ||||
\(853\) | − | 38.2913i | − | 1.31107i | −0.755165 | − | 0.655535i | \(-0.772443\pi\) | ||
0.755165 | − | 0.655535i | \(-0.227557\pi\) | |||||||
\(854\) | −13.2334 | −0.452839 | ||||||||
\(855\) | −1.21159 | + | 2.96845i | −0.0414356 | + | 0.101519i | ||||
\(856\) | 3.39625 | + | 3.39625i | 0.116081 | + | 0.116081i | ||||
\(857\) | 23.6239i | 0.806978i | 0.914984 | + | 0.403489i | \(0.132203\pi\) | ||||
−0.914984 | + | 0.403489i | \(0.867797\pi\) | |||||||
\(858\) | 17.1030 | − | 17.1030i | 0.583887 | − | 0.583887i | ||||
\(859\) | −25.3164 | + | 25.3164i | −0.863785 | + | 0.863785i | −0.991775 | − | 0.127991i | \(-0.959147\pi\) |
0.127991 | + | 0.991775i | \(0.459147\pi\) | |||||||
\(860\) | −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 | ||||
\(865\) | 6.05853 | − | 14.8437i | 0.205996 | − | 0.504699i | ||||
\(866\) | −18.0950 | + | 18.0950i | −0.614892 | + | 0.614892i | ||||
\(867\) | −8.67706 | − | 8.67706i | −0.294688 | − | 0.294688i | ||||
\(868\) | −3.16085 | −0.107286 | ||||||||
\(869\) | −27.9838 | − | 27.9838i | −0.949285 | − | 0.949285i | ||||
\(870\) | −18.9483 | + | 7.96389i | −0.642407 | + | 0.270001i | ||||
\(871\) | −7.90347 | + | 7.90347i | −0.267799 | + | 0.267799i | ||||
\(872\) | 1.95485 | − | 1.95485i | 0.0661997 | − | 0.0661997i | ||||
\(873\) | −0.301015 | −0.0101878 | ||||||||
\(874\) | 9.70693 | − | 9.70693i | 0.328342 | − | 0.328342i | ||||
\(875\) | −4.15604 | − | 9.60840i | −0.140500 | − | 0.324823i | ||||
\(876\) | 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 | ||||||||
\(880\) | −7.25065 | + | 3.04742i | −0.244419 | + | 0.102729i | ||||
\(881\) | 12.7644i | 0.430043i | 0.976609 | + | 0.215022i | \(0.0689822\pi\) | ||||
−0.976609 | + | 0.215022i | \(0.931018\pi\) | |||||||
\(882\) | −6.12325 | −0.206180 | ||||||||
\(883\) | 23.3191i | 0.784751i | 0.919805 | + | 0.392376i | \(0.128347\pi\) | ||||
−0.919805 | + | 0.392376i | \(0.871653\pi\) | |||||||
\(884\) | − | 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 | −0.573970 | − | 0.818876i | \(-0.694597\pi\) |
0.818876 | + | 0.573970i | \(0.194597\pi\) | |||||||
\(888\) | −3.33312 | − | 5.08825i | −0.111852 | − | 0.170750i | ||||
\(889\) | 0.327756i | 0.0109926i | ||||||||
\(890\) | 7.68489 | − | 18.8283i | 0.257598 | − | 0.631125i | ||||
\(891\) | 3.51735i | 0.117836i | ||||||||
\(892\) | 16.5296 | − | 16.5296i | 0.553452 | − | 0.553452i | ||||
\(893\) | −7.28113 | −0.243654 | ||||||||
\(894\) | −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 | ||||
\(902\) | 12.2401 | 0.407550 | ||||||||
\(903\) | 2.57104i | 0.0855588i | ||||||||
\(904\) | 18.3281i | 0.609582i | ||||||||
\(905\) | 3.52882 | + | 8.39602i | 0.117302 | + | 0.279093i | ||||
\(906\) | −2.75901 | + | 2.75901i | −0.0916619 | + | 0.0916619i | ||||
\(907\) | 49.3619i | 1.63904i | 0.573054 | + | 0.819518i | \(0.305759\pi\) | ||||
−0.573054 | + | 0.819518i | \(0.694241\pi\) | |||||||
\(908\) | 28.0799i | 0.931865i | ||||||||
\(909\) | 7.88206 | 0.261431 | ||||||||
\(910\) | 5.44080 | − | 13.3302i | 0.180361 | − | 0.441891i | ||||
\(911\) | 6.70882 | + | 6.70882i | 0.222273 | + | 0.222273i | 0.809455 | − | 0.587182i | \(-0.199763\pi\) |
−0.587182 | + | 0.809455i | \(0.699763\pi\) | |||||||
\(912\) | 1.43385 | 0.0474795 | ||||||||
\(913\) | 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 | ||||||||
\(917\) | 1.74170 | 0.0575161 | ||||||||
\(918\) | 1.53766 | + | 1.53766i | 0.0507503 | + | 0.0507503i | ||||
\(919\) | 19.7075 | + | 19.7075i | 0.650090 | + | 0.650090i | 0.953015 | − | 0.302924i | \(-0.0979630\pi\) |
−0.302924 | + | 0.953015i | \(0.597963\pi\) | |||||||
\(920\) | 8.29489 | + | 19.7358i | 0.273474 | + | 0.650670i | ||||
\(921\) | −15.9746 | −0.526380 | ||||||||
\(922\) | 28.3555 | + | 28.3555i | 0.933838 | + | 0.933838i | ||||
\(923\) | −50.3948 | −1.65877 | ||||||||
\(924\) | 3.29347 | 0.108347 | ||||||||
\(925\) | 25.2672 | − | 16.9283i | 0.830780 | − | 0.556601i | ||||
\(926\) | 27.1414 | 0.891921 | ||||||||
\(927\) | −3.81714 | −0.125371 | ||||||||
\(928\) | 6.49970 | + | 6.49970i | 0.213363 | + | 0.213363i | ||||
\(929\) | 32.0555 | 1.05171 | 0.525853 | − | 0.850575i | \(-0.323746\pi\) | ||||
0.525853 | + | 0.850575i | \(0.323746\pi\) | |||||||
\(930\) | −2.92471 | − | 6.95868i | −0.0959050 | − | 0.228184i | ||||
\(931\) | 6.20827 | + | 6.20827i | 0.203468 | + | 0.203468i | ||||
\(932\) | 10.2080 | + | 10.2080i | 0.334375 | + | 0.334375i | ||||
\(933\) | −13.9264 | −0.455930 | ||||||||
\(934\) | − | 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 | \(0.488622\pi\) | |||||||
\(938\) | −1.52195 | −0.0496933 | ||||||||
\(939\) | 8.57876 | + | 8.57876i | 0.279957 | + | 0.279957i | ||||
\(940\) | 4.29089 | − | 10.5129i | 0.139953 | − | 0.342891i | ||||
\(941\) | 22.9702 | 0.748808 | 0.374404 | − | 0.927266i | \(-0.377847\pi\) | ||||
0.374404 | + | 0.927266i | \(0.377847\pi\) | |||||||
\(942\) | 2.48415i | 0.0809378i | ||||||||
\(943\) | − | 33.3167i | − | 1.08494i | ||||||
\(944\) | −3.45523 | + | 3.45523i | −0.112458 | + | 0.112458i | ||||
\(945\) | 0.811252 | + | 1.93019i | 0.0263900 | + | 0.0627891i | ||||
\(946\) | 9.65796i | 0.314007i | ||||||||
\(947\) | 47.0948i | 1.53037i | 0.643808 | + | 0.765187i | \(0.277353\pi\) | ||||
−0.643808 | + | 0.765187i | \(0.722647\pi\) | |||||||
\(948\) | −11.2514 | −0.365428 | ||||||||
\(949\) | −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 | 0.859602 | − | 0.510964i | \(-0.170711\pi\) |
−0.510964 | + | 0.859602i | \(0.670711\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 32.3313 | 1.04512 | ||||||||
\(958\) | −11.3006 | + | 11.3006i | −0.365106 | + | 0.365106i | ||||
\(959\) | 18.1186i | 0.585080i | ||||||||
\(960\) | −0.844991 | + | 2.07026i | −0.0272720 | + | 0.0668175i | ||||
\(961\) | 19.6046i | 0.632405i | ||||||||
\(962\) | 40.9487 | + | 8.53425i | 1.32024 | + | 0.275155i | ||||
\(963\) | 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 | ||||||
\(967\) | 25.7099i | 0.826776i | 0.910555 | + | 0.413388i | \(0.135655\pi\) | ||||
−0.910555 | + | 0.413388i | \(0.864345\pi\) | |||||||
\(968\) | 1.37173 | 0.0440892 | ||||||||
\(969\) | − | 3.11802i | − | 0.100165i | ||||||
\(970\) | −0.620511 | + | 0.260799i | −0.0199234 | + | 0.00837375i | ||||
\(971\) | −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 | ||||||||
\(975\) | 34.3810 | − | 0.356271i | 1.10107 | − | 0.0114098i | ||||
\(976\) | −9.99355 | + | 9.99355i | −0.319886 | + | 0.319886i | ||||
\(977\) | −6.00481 | −0.192111 | −0.0960554 | − | 0.995376i | \(-0.530623\pi\) | ||||
−0.0960554 | + | 0.995376i | \(0.530623\pi\) | |||||||
\(978\) | −6.64486 | + | 6.64486i | −0.212479 | + | 0.212479i | ||||
\(979\) | −22.6196 | + | 22.6196i | −0.722926 | + | 0.722926i | ||||
\(980\) | −12.6224 | + | 5.30517i | −0.403209 | + | 0.169467i | ||||
\(981\) | −1.95485 | − | 1.95485i | −0.0624137 | − | 0.0624137i | ||||
\(982\) | 6.69716 | 0.213715 | ||||||||
\(983\) | 16.8252 | + | 16.8252i | 0.536640 | + | 0.536640i | 0.922540 | − | 0.385901i | \(-0.126109\pi\) |
−0.385901 | + | 0.922540i | \(0.626109\pi\) | |||||||
\(984\) | 2.46067 | − | 2.46067i | 0.0784434 | − | 0.0784434i | ||||
\(985\) | 16.7423 | − | 41.0194i | 0.533455 | − | 1.30699i | ||||
\(986\) | 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 | −0.286491 | − | 0.958083i | \(-0.592489\pi\) |
0.958083 | + | 0.286491i | \(0.0924887\pi\) | |||||||
\(992\) | −2.38699 | + | 2.38699i | −0.0757870 | + | 0.0757870i | ||||
\(993\) | − | 32.6352i | − | 1.03565i | ||||||
\(994\) | −4.85218 | − | 4.85218i | −0.153902 | − | 0.153902i | ||||
\(995\) | 2.72767 | − | 6.68291i | 0.0864731 | − | 0.211862i | ||||
\(996\) | 2.07565 | 0.0657694 | ||||||||
\(997\) | − | 51.0135i | − | 1.61561i | −0.589447 | − | 0.807807i | \(-0.700654\pi\) | ||
0.589447 | − | 0.807807i | \(-0.299346\pi\) | |||||||
\(998\) | 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.o.a.487.7 | yes | 36 | |
5.3 | odd | 4 | 1110.2.l.a.43.12 | ✓ | 36 | ||
37.31 | odd | 4 | 1110.2.l.a.697.12 | yes | 36 | ||
185.68 | even | 4 | inner | 1110.2.o.a.253.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.12 | ✓ | 36 | 5.3 | odd | 4 | ||
1110.2.l.a.697.12 | yes | 36 | 37.31 | odd | 4 | ||
1110.2.o.a.253.7 | yes | 36 | 185.68 | even | 4 | inner | |
1110.2.o.a.487.7 | yes | 36 | 1.1 | even | 1 | trivial |