Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(439,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 769.2 | ||
Character | \(\chi\) | \(=\) | 930.769 |
Dual form | 930.2.s.c.439.8 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.77430 | + | 1.36083i | −0.793492 | + | 0.608581i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −3.11266 | + | 1.79709i | −1.17647 | + | 0.679238i | −0.955196 | − | 0.295973i | \(-0.904356\pi\) |
−0.221278 | + | 0.975211i | \(0.571023\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.36083 | + | 1.77430i | 0.430332 | + | 0.561083i | ||||
\(11\) | 2.97645 | − | 5.15537i | 0.897434 | − | 1.55440i | 0.0666710 | − | 0.997775i | \(-0.478762\pi\) |
0.830763 | − | 0.556626i | \(-0.187904\pi\) | |||||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | 4.69019 | + | 2.70788i | 1.30082 | + | 0.751031i | 0.980546 | − | 0.196292i | \(-0.0628900\pi\) |
0.320279 | + | 0.947323i | \(0.396223\pi\) | |||||||
\(14\) | 1.79709 | + | 3.11266i | 0.480293 | + | 0.831893i | ||||
\(15\) | −0.856175 | + | 2.06566i | −0.221063 | + | 0.533352i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.44932 | − | 2.56882i | 1.07912 | − | 0.623030i | 0.148461 | − | 0.988918i | \(-0.452568\pi\) |
0.930659 | + | 0.365888i | \(0.119235\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | −2.31842 | − | 4.01562i | −0.531882 | − | 0.921247i | −0.999307 | − | 0.0372146i | \(-0.988151\pi\) |
0.467425 | − | 0.884033i | \(-0.345182\pi\) | |||||||
\(20\) | 1.77430 | − | 1.36083i | 0.396746 | − | 0.304291i | ||||
\(21\) | −1.79709 | + | 3.11266i | −0.392158 | + | 0.679238i | ||||
\(22\) | −5.15537 | − | 2.97645i | −1.09913 | − | 0.634582i | ||||
\(23\) | 9.06476i | 1.89013i | 0.326879 | + | 0.945066i | \(0.394003\pi\) | ||||
−0.326879 | + | 0.945066i | \(0.605997\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 1.29629 | − | 4.82904i | 0.259258 | − | 0.965808i | ||||
\(26\) | 2.70788 | − | 4.69019i | 0.531059 | − | 0.919822i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.11266 | − | 1.79709i | 0.588237 | − | 0.339619i | ||||
\(29\) | 5.52189 | 1.02539 | 0.512695 | − | 0.858571i | \(-0.328647\pi\) | ||||
0.512695 | + | 0.858571i | \(0.328647\pi\) | |||||||
\(30\) | 2.06566 | + | 0.856175i | 0.377137 | + | 0.156315i | ||||
\(31\) | −1.89486 | − | 5.23541i | −0.340328 | − | 0.940307i | ||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 5.95290i | − | 1.03627i | ||||||
\(34\) | −2.56882 | − | 4.44932i | −0.440549 | − | 0.763053i | ||||
\(35\) | 3.07725 | − | 7.42438i | 0.520151 | − | 1.25495i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 7.15835 | − | 4.13288i | 1.17683 | − | 0.679441i | 0.221548 | − | 0.975150i | \(-0.428889\pi\) |
0.955278 | + | 0.295709i | \(0.0955558\pi\) | |||||||
\(38\) | −4.01562 | + | 2.31842i | −0.651420 | + | 0.376098i | ||||
\(39\) | 5.41576 | 0.867216 | ||||||||
\(40\) | −1.36083 | − | 1.77430i | −0.215166 | − | 0.280542i | ||||
\(41\) | 4.35396 | − | 7.54127i | 0.679974 | − | 1.17775i | −0.295015 | − | 0.955493i | \(-0.595325\pi\) |
0.974988 | − | 0.222256i | \(-0.0713421\pi\) | |||||||
\(42\) | 3.11266 | + | 1.79709i | 0.480293 | + | 0.277298i | ||||
\(43\) | −1.99052 | + | 1.14923i | −0.303552 | + | 0.175256i | −0.644037 | − | 0.764994i | \(-0.722742\pi\) |
0.340486 | + | 0.940250i | \(0.389409\pi\) | |||||||
\(44\) | −2.97645 | + | 5.15537i | −0.448717 | + | 0.777201i | ||||
\(45\) | 0.291362 | + | 2.21700i | 0.0434337 | + | 0.330491i | ||||
\(46\) | 9.06476 | 1.33653 | ||||||||
\(47\) | − | 5.05582i | − | 0.737467i | −0.929535 | − | 0.368734i | \(-0.879791\pi\) | ||
0.929535 | − | 0.368734i | \(-0.120209\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 2.95909 | − | 5.12530i | 0.422727 | − | 0.732185i | ||||
\(50\) | −4.82904 | − | 1.29629i | −0.682930 | − | 0.183323i | ||||
\(51\) | 2.56882 | − | 4.44932i | 0.359707 | − | 0.623030i | ||||
\(52\) | −4.69019 | − | 2.70788i | −0.650412 | − | 0.375516i | ||||
\(53\) | −4.26701 | − | 2.46356i | −0.586119 | − | 0.338396i | 0.177443 | − | 0.984131i | \(-0.443218\pi\) |
−0.763561 | + | 0.645735i | \(0.776551\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.73445 | + | 13.1976i | 0.233873 | + | 1.77957i | ||||
\(56\) | −1.79709 | − | 3.11266i | −0.240147 | − | 0.415946i | ||||
\(57\) | −4.01562 | − | 2.31842i | −0.531882 | − | 0.307082i | ||||
\(58\) | − | 5.52189i | − | 0.725060i | ||||||
\(59\) | 6.67355 | + | 11.5589i | 0.868823 | + | 1.50485i | 0.863201 | + | 0.504861i | \(0.168456\pi\) |
0.00562217 | + | 0.999984i | \(0.498210\pi\) | |||||||
\(60\) | 0.856175 | − | 2.06566i | 0.110532 | − | 0.266676i | ||||
\(61\) | 1.14657 | 0.146804 | 0.0734019 | − | 0.997302i | \(-0.476614\pi\) | ||||
0.0734019 | + | 0.997302i | \(0.476614\pi\) | |||||||
\(62\) | −5.23541 | + | 1.89486i | −0.664897 | + | 0.240648i | ||||
\(63\) | 3.59419i | 0.452825i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −12.0068 | + | 1.57795i | −1.48926 | + | 0.195720i | ||||
\(66\) | −5.95290 | −0.732752 | ||||||||
\(67\) | 4.83998 | + | 2.79437i | 0.591298 | + | 0.341386i | 0.765611 | − | 0.643304i | \(-0.222437\pi\) |
−0.174313 | + | 0.984690i | \(0.555770\pi\) | |||||||
\(68\) | −4.44932 | + | 2.56882i | −0.539560 | + | 0.311515i | ||||
\(69\) | 4.53238 | + | 7.85031i | 0.545634 | + | 0.945066i | ||||
\(70\) | −7.42438 | − | 3.07725i | −0.887383 | − | 0.367802i | ||||
\(71\) | −2.38791 | + | 4.13598i | −0.283393 | + | 0.490851i | −0.972218 | − | 0.234077i | \(-0.924793\pi\) |
0.688825 | + | 0.724927i | \(0.258127\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −1.61832 | − | 0.934337i | −0.189410 | − | 0.109356i | 0.402296 | − | 0.915509i | \(-0.368212\pi\) |
−0.591706 | + | 0.806154i | \(0.701545\pi\) | |||||||
\(74\) | −4.13288 | − | 7.15835i | −0.480437 | − | 0.832142i | ||||
\(75\) | −1.29190 | − | 4.83022i | −0.149176 | − | 0.557745i | ||||
\(76\) | 2.31842 | + | 4.01562i | 0.265941 | + | 0.460624i | ||||
\(77\) | 21.3959i | 2.43828i | ||||||||
\(78\) | − | 5.41576i | − | 0.613215i | ||||||
\(79\) | −2.00321 | − | 3.46966i | −0.225379 | − | 0.390368i | 0.731054 | − | 0.682319i | \(-0.239029\pi\) |
−0.956433 | + | 0.291952i | \(0.905695\pi\) | |||||||
\(80\) | −1.77430 | + | 1.36083i | −0.198373 | + | 0.152145i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −7.54127 | − | 4.35396i | −0.832794 | − | 0.480814i | ||||
\(83\) | 8.58415 | + | 4.95606i | 0.942233 | + | 0.543998i | 0.890659 | − | 0.454671i | \(-0.150243\pi\) |
0.0515731 | + | 0.998669i | \(0.483576\pi\) | |||||||
\(84\) | 1.79709 | − | 3.11266i | 0.196079 | − | 0.339619i | ||||
\(85\) | −4.39872 | + | 10.6126i | −0.477108 | + | 1.15110i | ||||
\(86\) | 1.14923 | + | 1.99052i | 0.123925 | + | 0.214644i | ||||
\(87\) | 4.78210 | − | 2.76095i | 0.512695 | − | 0.296004i | ||||
\(88\) | 5.15537 | + | 2.97645i | 0.549564 | + | 0.317291i | ||||
\(89\) | 11.6216 | 1.23189 | 0.615943 | − | 0.787790i | \(-0.288775\pi\) | ||||
0.615943 | + | 0.787790i | \(0.288775\pi\) | |||||||
\(90\) | 2.21700 | − | 0.291362i | 0.233693 | − | 0.0307123i | ||||
\(91\) | −19.4653 | −2.04051 | ||||||||
\(92\) | − | 9.06476i | − | 0.945066i | ||||||
\(93\) | −4.25870 | − | 3.58656i | −0.441607 | − | 0.371909i | ||||
\(94\) | −5.05582 | −0.521468 | ||||||||
\(95\) | 9.57816 | + | 3.96995i | 0.982698 | + | 0.407308i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 6.45060i | − | 0.654959i | −0.944858 | − | 0.327479i | \(-0.893801\pi\) | ||
0.944858 | − | 0.327479i | \(-0.106199\pi\) | |||||||
\(98\) | −5.12530 | − | 2.95909i | −0.517733 | − | 0.298913i | ||||
\(99\) | −2.97645 | − | 5.15537i | −0.299145 | − | 0.518134i | ||||
\(100\) | −1.29629 | + | 4.82904i | −0.129629 | + | 0.482904i | ||||
\(101\) | −9.76731 | −0.971884 | −0.485942 | − | 0.873991i | \(-0.661523\pi\) | ||||
−0.485942 | + | 0.873991i | \(0.661523\pi\) | |||||||
\(102\) | −4.44932 | − | 2.56882i | −0.440549 | − | 0.254351i | ||||
\(103\) | −1.45146 | − | 0.838003i | −0.143017 | − | 0.0825709i | 0.426784 | − | 0.904354i | \(-0.359646\pi\) |
−0.569801 | + | 0.821783i | \(0.692980\pi\) | |||||||
\(104\) | −2.70788 | + | 4.69019i | −0.265530 | + | 0.459911i | ||||
\(105\) | −1.04721 | − | 7.96833i | −0.102197 | − | 0.777629i | ||||
\(106\) | −2.46356 | + | 4.26701i | −0.239282 | + | 0.414449i | ||||
\(107\) | −2.12044 | + | 1.22423i | −0.204990 | + | 0.118351i | −0.598981 | − | 0.800763i | \(-0.704428\pi\) |
0.393991 | + | 0.919114i | \(0.371094\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 1.67713 | 0.160640 | 0.0803201 | − | 0.996769i | \(-0.474406\pi\) | ||||
0.0803201 | + | 0.996769i | \(0.474406\pi\) | |||||||
\(110\) | 13.1976 | − | 1.73445i | 1.25834 | − | 0.165373i | ||||
\(111\) | 4.13288 | − | 7.15835i | 0.392275 | − | 0.679441i | ||||
\(112\) | −3.11266 | + | 1.79709i | −0.294118 | + | 0.169809i | ||||
\(113\) | 3.36747 | + | 1.94421i | 0.316785 | + | 0.182896i | 0.649959 | − | 0.759970i | \(-0.274786\pi\) |
−0.333174 | + | 0.942865i | \(0.608120\pi\) | |||||||
\(114\) | −2.31842 | + | 4.01562i | −0.217140 | + | 0.376098i | ||||
\(115\) | −12.3356 | − | 16.0836i | −1.15030 | − | 1.49980i | ||||
\(116\) | −5.52189 | −0.512695 | ||||||||
\(117\) | 4.69019 | − | 2.70788i | 0.433608 | − | 0.250344i | ||||
\(118\) | 11.5589 | − | 6.67355i | 1.06409 | − | 0.614350i | ||||
\(119\) | −9.23282 | + | 15.9917i | −0.846371 | + | 1.46596i | ||||
\(120\) | −2.06566 | − | 0.856175i | −0.188568 | − | 0.0781577i | ||||
\(121\) | −12.2185 | − | 21.1631i | −1.11078 | − | 1.92392i | ||||
\(122\) | − | 1.14657i | − | 0.103806i | ||||||
\(123\) | − | 8.70791i | − | 0.785166i | ||||||
\(124\) | 1.89486 | + | 5.23541i | 0.170164 | + | 0.470153i | ||||
\(125\) | 4.27149 | + | 10.3322i | 0.382054 | + | 0.924140i | ||||
\(126\) | 3.59419 | 0.320196 | ||||||||
\(127\) | −11.9460 | + | 6.89703i | −1.06004 | + | 0.612013i | −0.925443 | − | 0.378888i | \(-0.876307\pi\) |
−0.134595 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.14923 | + | 1.99052i | −0.101184 | + | 0.175256i | ||||
\(130\) | 1.57795 | + | 12.0068i | 0.138395 | + | 1.05306i | ||||
\(131\) | 10.1483 | + | 17.5774i | 0.886663 | + | 1.53575i | 0.843796 | + | 0.536664i | \(0.180316\pi\) |
0.0428672 | + | 0.999081i | \(0.486351\pi\) | |||||||
\(132\) | 5.95290i | 0.518134i | ||||||||
\(133\) | 14.4329 | + | 8.33284i | 1.25149 | + | 0.722549i | ||||
\(134\) | 2.79437 | − | 4.83998i | 0.241396 | − | 0.418111i | ||||
\(135\) | 1.36083 | + | 1.77430i | 0.117122 | + | 0.152708i | ||||
\(136\) | 2.56882 | + | 4.44932i | 0.220274 | + | 0.381526i | ||||
\(137\) | 10.9454 | + | 6.31936i | 0.935133 | + | 0.539899i | 0.888431 | − | 0.459010i | \(-0.151796\pi\) |
0.0467015 | + | 0.998909i | \(0.485129\pi\) | |||||||
\(138\) | 7.85031 | − | 4.53238i | 0.668263 | − | 0.385822i | ||||
\(139\) | −6.62791 | −0.562172 | −0.281086 | − | 0.959683i | \(-0.590695\pi\) | ||||
−0.281086 | + | 0.959683i | \(0.590695\pi\) | |||||||
\(140\) | −3.07725 | + | 7.42438i | −0.260075 | + | 0.627475i | ||||
\(141\) | −2.52791 | − | 4.37847i | −0.212888 | − | 0.368734i | ||||
\(142\) | 4.13598 | + | 2.38791i | 0.347084 | + | 0.200389i | ||||
\(143\) | 27.9202 | − | 16.1198i | 2.33481 | − | 1.34800i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −9.79750 | + | 7.51435i | −0.813638 | + | 0.624033i | ||||
\(146\) | −0.934337 | + | 1.61832i | −0.0773263 | + | 0.133933i | ||||
\(147\) | − | 5.91818i | − | 0.488123i | ||||||
\(148\) | −7.15835 | + | 4.13288i | −0.588413 | + | 0.339720i | ||||
\(149\) | 0.371288 | + | 0.643090i | 0.0304171 | + | 0.0526840i | 0.880833 | − | 0.473427i | \(-0.156983\pi\) |
−0.850416 | + | 0.526111i | \(0.823650\pi\) | |||||||
\(150\) | −4.83022 | + | 1.29190i | −0.394386 | + | 0.105483i | ||||
\(151\) | −4.11608 | −0.334962 | −0.167481 | − | 0.985875i | \(-0.553563\pi\) | ||||
−0.167481 | + | 0.985875i | \(0.553563\pi\) | |||||||
\(152\) | 4.01562 | − | 2.31842i | 0.325710 | − | 0.188049i | ||||
\(153\) | − | 5.13764i | − | 0.415353i | ||||||
\(154\) | 21.3959 | 1.72413 | ||||||||
\(155\) | 10.4866 | + | 6.71060i | 0.842300 | + | 0.539008i | ||||
\(156\) | −5.41576 | −0.433608 | ||||||||
\(157\) | − | 7.83784i | − | 0.625528i | −0.949831 | − | 0.312764i | \(-0.898745\pi\) | ||
0.949831 | − | 0.312764i | \(-0.101255\pi\) | |||||||
\(158\) | −3.46966 | + | 2.00321i | −0.276032 | + | 0.159367i | ||||
\(159\) | −4.92712 | −0.390746 | ||||||||
\(160\) | 1.36083 | + | 1.77430i | 0.107583 | + | 0.140271i | ||||
\(161\) | −16.2902 | − | 28.2155i | −1.28385 | − | 2.22369i | ||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | − | 10.7682i | − | 0.843428i | −0.906729 | − | 0.421714i | \(-0.861429\pi\) | ||
0.906729 | − | 0.421714i | \(-0.138571\pi\) | |||||||
\(164\) | −4.35396 | + | 7.54127i | −0.339987 | + | 0.588874i | ||||
\(165\) | 8.10088 | + | 10.5622i | 0.630653 | + | 0.822270i | ||||
\(166\) | 4.95606 | − | 8.58415i | 0.384665 | − | 0.666259i | ||||
\(167\) | −10.0883 | + | 5.82450i | −0.780658 | + | 0.450713i | −0.836663 | − | 0.547717i | \(-0.815497\pi\) |
0.0560056 | + | 0.998430i | \(0.482164\pi\) | |||||||
\(168\) | −3.11266 | − | 1.79709i | −0.240147 | − | 0.138649i | ||||
\(169\) | 8.16525 | + | 14.1426i | 0.628096 | + | 1.08790i | ||||
\(170\) | 10.6126 | + | 4.39872i | 0.813951 | + | 0.337366i | ||||
\(171\) | −4.63684 | −0.354588 | ||||||||
\(172\) | 1.99052 | − | 1.14923i | 0.151776 | − | 0.0876279i | ||||
\(173\) | −9.86029 | − | 5.69284i | −0.749664 | − | 0.432819i | 0.0759084 | − | 0.997115i | \(-0.475814\pi\) |
−0.825573 | + | 0.564296i | \(0.809148\pi\) | |||||||
\(174\) | −2.76095 | − | 4.78210i | −0.209307 | − | 0.362530i | ||||
\(175\) | 4.64334 | + | 17.3607i | 0.351003 | + | 1.31235i | ||||
\(176\) | 2.97645 | − | 5.15537i | 0.224359 | − | 0.388600i | ||||
\(177\) | 11.5589 | + | 6.67355i | 0.868823 | + | 0.501615i | ||||
\(178\) | − | 11.6216i | − | 0.871075i | ||||||
\(179\) | −3.83263 | − | 6.63830i | −0.286464 | − | 0.496170i | 0.686499 | − | 0.727131i | \(-0.259147\pi\) |
−0.972963 | + | 0.230960i | \(0.925813\pi\) | |||||||
\(180\) | −0.291362 | − | 2.21700i | −0.0217168 | − | 0.165246i | ||||
\(181\) | −2.30528 | + | 3.99286i | −0.171350 | + | 0.296787i | −0.938892 | − | 0.344212i | \(-0.888146\pi\) |
0.767542 | + | 0.640999i | \(0.221480\pi\) | |||||||
\(182\) | 19.4653i | 1.44286i | ||||||||
\(183\) | 0.992962 | − | 0.573287i | 0.0734019 | − | 0.0423786i | ||||
\(184\) | −9.06476 | −0.668263 | ||||||||
\(185\) | −7.07693 | + | 17.0743i | −0.520306 | + | 1.25532i | ||||
\(186\) | −3.58656 | + | 4.25870i | −0.262980 | + | 0.312263i | ||||
\(187\) | − | 30.5839i | − | 2.23651i | ||||||
\(188\) | 5.05582i | 0.368734i | ||||||||
\(189\) | 1.79709 | + | 3.11266i | 0.130719 | + | 0.226413i | ||||
\(190\) | 3.96995 | − | 9.57816i | 0.288010 | − | 0.694873i | ||||
\(191\) | 7.63804 | − | 13.2295i | 0.552669 | − | 0.957251i | −0.445411 | − | 0.895326i | \(-0.646943\pi\) |
0.998081 | − | 0.0619254i | \(-0.0197241\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −3.56077 | + | 2.05581i | −0.256310 | + | 0.147981i | −0.622650 | − | 0.782500i | \(-0.713944\pi\) |
0.366340 | + | 0.930481i | \(0.380611\pi\) | |||||||
\(194\) | −6.45060 | −0.463126 | ||||||||
\(195\) | −9.60920 | + | 7.36993i | −0.688129 | + | 0.527772i | ||||
\(196\) | −2.95909 | + | 5.12530i | −0.211364 | + | 0.366093i | ||||
\(197\) | −10.0616 | − | 5.80908i | −0.716861 | − | 0.413880i | 0.0967354 | − | 0.995310i | \(-0.469160\pi\) |
−0.813596 | + | 0.581430i | \(0.802493\pi\) | |||||||
\(198\) | −5.15537 | + | 2.97645i | −0.366376 | + | 0.211527i | ||||
\(199\) | −2.53294 | + | 4.38718i | −0.179555 | + | 0.310999i | −0.941728 | − | 0.336375i | \(-0.890799\pi\) |
0.762173 | + | 0.647373i | \(0.224132\pi\) | |||||||
\(200\) | 4.82904 | + | 1.29629i | 0.341465 | + | 0.0916614i | ||||
\(201\) | 5.58873 | 0.394199 | ||||||||
\(202\) | 9.76731i | 0.687226i | ||||||||
\(203\) | −17.1878 | + | 9.92336i | −1.20634 | + | 0.696483i | ||||
\(204\) | −2.56882 | + | 4.44932i | −0.179853 | + | 0.311515i | ||||
\(205\) | 2.53715 | + | 19.3055i | 0.177203 | + | 1.34835i | ||||
\(206\) | −0.838003 | + | 1.45146i | −0.0583864 | + | 0.101128i | ||||
\(207\) | 7.85031 | + | 4.53238i | 0.545634 | + | 0.315022i | ||||
\(208\) | 4.69019 | + | 2.70788i | 0.325206 | + | 0.187758i | ||||
\(209\) | −27.6027 | −1.90932 | ||||||||
\(210\) | −7.96833 | + | 1.04721i | −0.549867 | + | 0.0722643i | ||||
\(211\) | −3.91582 | − | 6.78240i | −0.269576 | − | 0.466920i | 0.699176 | − | 0.714949i | \(-0.253550\pi\) |
−0.968752 | + | 0.248030i | \(0.920217\pi\) | |||||||
\(212\) | 4.26701 | + | 2.46356i | 0.293059 | + | 0.169198i | ||||
\(213\) | 4.77582i | 0.327234i | ||||||||
\(214\) | 1.22423 | + | 2.12044i | 0.0836870 | + | 0.144950i | ||||
\(215\) | 1.96788 | − | 4.74784i | 0.134208 | − | 0.323800i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 15.3066 | + | 12.8908i | 1.03908 | + | 0.875083i | ||||
\(218\) | − | 1.67713i | − | 0.113590i | ||||||
\(219\) | −1.86867 | −0.126273 | ||||||||
\(220\) | −1.73445 | − | 13.1976i | −0.116937 | − | 0.889783i | ||||
\(221\) | 27.8242 | 1.87166 | ||||||||
\(222\) | −7.15835 | − | 4.13288i | −0.480437 | − | 0.277381i | ||||
\(223\) | −11.0560 | + | 6.38320i | −0.740366 | + | 0.427451i | −0.822203 | − | 0.569195i | \(-0.807255\pi\) |
0.0818361 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(224\) | 1.79709 | + | 3.11266i | 0.120073 | + | 0.207973i | ||||
\(225\) | −3.53393 | − | 3.53714i | −0.235595 | − | 0.235809i | ||||
\(226\) | 1.94421 | − | 3.36747i | 0.129327 | − | 0.224001i | ||||
\(227\) | 2.87642 | + | 1.66070i | 0.190915 | + | 0.110225i | 0.592411 | − | 0.805636i | \(-0.298176\pi\) |
−0.401496 | + | 0.915861i | \(0.631510\pi\) | |||||||
\(228\) | 4.01562 | + | 2.31842i | 0.265941 | + | 0.153541i | ||||
\(229\) | −2.61956 | − | 4.53720i | −0.173105 | − | 0.299827i | 0.766399 | − | 0.642365i | \(-0.222047\pi\) |
−0.939504 | + | 0.342538i | \(0.888713\pi\) | |||||||
\(230\) | −16.0836 | + | 12.3356i | −1.06052 | + | 0.813384i | ||||
\(231\) | 10.6979 | + | 18.5294i | 0.703872 | + | 1.21914i | ||||
\(232\) | 5.52189i | 0.362530i | ||||||||
\(233\) | − | 14.5392i | − | 0.952492i | −0.879312 | − | 0.476246i | \(-0.841997\pi\) | ||
0.879312 | − | 0.476246i | \(-0.158003\pi\) | |||||||
\(234\) | −2.70788 | − | 4.69019i | −0.177020 | − | 0.306607i | ||||
\(235\) | 6.88011 | + | 8.97055i | 0.448809 | + | 0.585174i | ||||
\(236\) | −6.67355 | − | 11.5589i | −0.434411 | − | 0.752423i | ||||
\(237\) | −3.46966 | − | 2.00321i | −0.225379 | − | 0.130123i | ||||
\(238\) | 15.9917 | + | 9.23282i | 1.03659 | + | 0.598475i | ||||
\(239\) | 11.1198 | − | 19.2600i | 0.719278 | − | 1.24583i | −0.242009 | − | 0.970274i | \(-0.577806\pi\) |
0.961286 | − | 0.275551i | \(-0.0888604\pi\) | |||||||
\(240\) | −0.856175 | + | 2.06566i | −0.0552659 | + | 0.133338i | ||||
\(241\) | −1.12616 | − | 1.95057i | −0.0725424 | − | 0.125647i | 0.827473 | − | 0.561506i | \(-0.189778\pi\) |
−0.900015 | + | 0.435859i | \(0.856445\pi\) | |||||||
\(242\) | −21.1631 | + | 12.2185i | −1.36042 | + | 0.785437i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −1.14657 | −0.0734019 | ||||||||
\(245\) | 1.72433 | + | 13.1206i | 0.110164 | + | 0.838247i | ||||
\(246\) | −8.70791 | −0.555196 | ||||||||
\(247\) | − | 25.1121i | − | 1.59784i | ||||||
\(248\) | 5.23541 | − | 1.89486i | 0.332449 | − | 0.120324i | ||||
\(249\) | 9.91212 | 0.628155 | ||||||||
\(250\) | 10.3322 | − | 4.27149i | 0.653466 | − | 0.270153i | ||||
\(251\) | 7.60189 | + | 13.1669i | 0.479827 | + | 0.831085i | 0.999732 | − | 0.0231388i | \(-0.00736598\pi\) |
−0.519905 | + | 0.854224i | \(0.674033\pi\) | |||||||
\(252\) | − | 3.59419i | − | 0.226413i | ||||||
\(253\) | 46.7321 | + | 26.9808i | 2.93802 | + | 1.69627i | ||||
\(254\) | 6.89703 | + | 11.9460i | 0.432758 | + | 0.749559i | ||||
\(255\) | 1.49691 | + | 11.3902i | 0.0937403 | + | 0.713280i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.77882 | + | 1.60435i | 0.173338 | + | 0.100077i | 0.584159 | − | 0.811639i | \(-0.301424\pi\) |
−0.410821 | + | 0.911716i | \(0.634758\pi\) | |||||||
\(258\) | 1.99052 | + | 1.14923i | 0.123925 | + | 0.0715479i | ||||
\(259\) | −14.8543 | + | 25.7285i | −0.923003 | + | 1.59869i | ||||
\(260\) | 12.0068 | − | 1.57795i | 0.744629 | − | 0.0978602i | ||||
\(261\) | 2.76095 | − | 4.78210i | 0.170898 | − | 0.296004i | ||||
\(262\) | 17.5774 | − | 10.1483i | 1.08594 | − | 0.626965i | ||||
\(263\) | 21.1070i | 1.30151i | 0.759286 | + | 0.650757i | \(0.225549\pi\) | ||||
−0.759286 | + | 0.650757i | \(0.774451\pi\) | |||||||
\(264\) | 5.95290 | 0.366376 | ||||||||
\(265\) | 10.9234 | − | 1.43558i | 0.671022 | − | 0.0881867i | ||||
\(266\) | 8.33284 | − | 14.4329i | 0.510919 | − | 0.884938i | ||||
\(267\) | 10.0646 | − | 5.81080i | 0.615943 | − | 0.355615i | ||||
\(268\) | −4.83998 | − | 2.79437i | −0.295649 | − | 0.170693i | ||||
\(269\) | 8.35872 | − | 14.4777i | 0.509640 | − | 0.882722i | −0.490298 | − | 0.871555i | \(-0.663112\pi\) |
0.999938 | − | 0.0111673i | \(-0.00355472\pi\) | |||||||
\(270\) | 1.77430 | − | 1.36083i | 0.107981 | − | 0.0828174i | ||||
\(271\) | −8.95467 | −0.543958 | −0.271979 | − | 0.962303i | \(-0.587678\pi\) | ||||
−0.271979 | + | 0.962303i | \(0.587678\pi\) | |||||||
\(272\) | 4.44932 | − | 2.56882i | 0.269780 | − | 0.155758i | ||||
\(273\) | −16.8574 | + | 9.73264i | −1.02026 | + | 0.589046i | ||||
\(274\) | 6.31936 | − | 10.9454i | 0.381766 | − | 0.661239i | ||||
\(275\) | −21.0371 | − | 21.0562i | −1.26859 | − | 1.26974i | ||||
\(276\) | −4.53238 | − | 7.85031i | −0.272817 | − | 0.472533i | ||||
\(277\) | − | 0.851610i | − | 0.0511683i | −0.999673 | − | 0.0255842i | \(-0.991855\pi\) | ||
0.999673 | − | 0.0255842i | \(-0.00814458\pi\) | |||||||
\(278\) | 6.62791i | 0.397515i | ||||||||
\(279\) | −5.48143 | − | 0.976703i | −0.328165 | − | 0.0584737i | ||||
\(280\) | 7.42438 | + | 3.07725i | 0.443692 | + | 0.183901i | ||||
\(281\) | 3.72310 | 0.222102 | 0.111051 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111051 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(282\) | −4.37847 | + | 2.52791i | −0.260734 | + | 0.150535i | ||||
\(283\) | 21.3862i | 1.27128i | 0.771988 | + | 0.635638i | \(0.219263\pi\) | ||||
−0.771988 | + | 0.635638i | \(0.780737\pi\) | |||||||
\(284\) | 2.38791 | − | 4.13598i | 0.141696 | − | 0.245425i | ||||
\(285\) | 10.2799 | − | 1.35100i | 0.608929 | − | 0.0800264i | ||||
\(286\) | −16.1198 | − | 27.9202i | −0.953182 | − | 1.65096i | ||||
\(287\) | 31.2979i | 1.84745i | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 4.69766 | − | 8.13659i | 0.276333 | − | 0.478623i | ||||
\(290\) | 7.51435 | + | 9.79750i | 0.441258 | + | 0.575329i | ||||
\(291\) | −3.22530 | − | 5.58638i | −0.189070 | − | 0.327479i | ||||
\(292\) | 1.61832 | + | 0.934337i | 0.0947050 | + | 0.0546779i | ||||
\(293\) | 7.79125 | − | 4.49828i | 0.455170 | − | 0.262792i | −0.254841 | − | 0.966983i | \(-0.582023\pi\) |
0.710011 | + | 0.704190i | \(0.248690\pi\) | |||||||
\(294\) | −5.91818 | −0.345155 | ||||||||
\(295\) | −27.5706 | − | 11.4275i | −1.60522 | − | 0.665333i | ||||
\(296\) | 4.13288 | + | 7.15835i | 0.240219 | + | 0.416071i | ||||
\(297\) | −5.15537 | − | 2.97645i | −0.299145 | − | 0.172711i | ||||
\(298\) | 0.643090 | − | 0.371288i | 0.0372532 | − | 0.0215082i | ||||
\(299\) | −24.5463 | + | 42.5154i | −1.41955 | + | 2.45873i | ||||
\(300\) | 1.29190 | + | 4.83022i | 0.0745880 | + | 0.278873i | ||||
\(301\) | 4.13054 | − | 7.15431i | 0.238081 | − | 0.412368i | ||||
\(302\) | 4.11608i | 0.236854i | ||||||||
\(303\) | −8.45874 | + | 4.88366i | −0.485942 | + | 0.280559i | ||||
\(304\) | −2.31842 | − | 4.01562i | −0.132971 | − | 0.230312i | ||||
\(305\) | −2.03437 | + | 1.56029i | −0.116488 | + | 0.0893420i | ||||
\(306\) | −5.13764 | −0.293699 | ||||||||
\(307\) | −14.7208 | + | 8.49904i | −0.840158 | + | 0.485066i | −0.857318 | − | 0.514787i | \(-0.827871\pi\) |
0.0171597 | + | 0.999853i | \(0.494538\pi\) | |||||||
\(308\) | − | 21.3959i | − | 1.21914i | ||||||
\(309\) | −1.67601 | −0.0953446 | ||||||||
\(310\) | 6.71060 | − | 10.4866i | 0.381137 | − | 0.595596i | ||||
\(311\) | −17.4831 | −0.991378 | −0.495689 | − | 0.868500i | \(-0.665084\pi\) | ||||
−0.495689 | + | 0.868500i | \(0.665084\pi\) | |||||||
\(312\) | 5.41576i | 0.306607i | ||||||||
\(313\) | −28.9556 | + | 16.7175i | −1.63667 | + | 0.944931i | −0.654699 | + | 0.755889i | \(0.727205\pi\) |
−0.981969 | + | 0.189041i | \(0.939462\pi\) | |||||||
\(314\) | −7.83784 | −0.442315 | ||||||||
\(315\) | −4.89107 | − | 6.37717i | −0.275581 | − | 0.359313i | ||||
\(316\) | 2.00321 | + | 3.46966i | 0.112689 | + | 0.195184i | ||||
\(317\) | −12.0309 | + | 6.94602i | −0.675720 | + | 0.390127i | −0.798241 | − | 0.602339i | \(-0.794236\pi\) |
0.122520 | + | 0.992466i | \(0.460902\pi\) | |||||||
\(318\) | 4.92712i | 0.276299i | ||||||||
\(319\) | 16.4356 | − | 28.4674i | 0.920219 | − | 1.59387i | ||||
\(320\) | 1.77430 | − | 1.36083i | 0.0991864 | − | 0.0760727i | ||||
\(321\) | −1.22423 | + | 2.12044i | −0.0683301 | + | 0.118351i | ||||
\(322\) | −28.2155 | + | 16.2902i | −1.57239 | + | 0.907818i | ||||
\(323\) | −20.6308 | − | 11.9112i | −1.14793 | − | 0.662758i | ||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 19.1563 | − | 19.1389i | 1.06260 | − | 1.06164i | ||||
\(326\) | −10.7682 | −0.596394 | ||||||||
\(327\) | 1.45244 | − | 0.838566i | 0.0803201 | − | 0.0463728i | ||||
\(328\) | 7.54127 | + | 4.35396i | 0.416397 | + | 0.240407i | ||||
\(329\) | 9.08578 | + | 15.7370i | 0.500915 | + | 0.867611i | ||||
\(330\) | 10.5622 | − | 8.10088i | 0.581432 | − | 0.445939i | ||||
\(331\) | −2.20296 | + | 3.81564i | −0.121086 | + | 0.209726i | −0.920196 | − | 0.391458i | \(-0.871971\pi\) |
0.799110 | + | 0.601184i | \(0.205304\pi\) | |||||||
\(332\) | −8.58415 | − | 4.95606i | −0.471116 | − | 0.271999i | ||||
\(333\) | − | 8.26575i | − | 0.452960i | ||||||
\(334\) | 5.82450 | + | 10.0883i | 0.318702 | + | 0.552008i | ||||
\(335\) | −12.3902 | + | 1.62834i | −0.676951 | + | 0.0889660i | ||||
\(336\) | −1.79709 | + | 3.11266i | −0.0980395 | + | 0.169809i | ||||
\(337\) | 8.34153i | 0.454392i | 0.973849 | + | 0.227196i | \(0.0729558\pi\) | ||||
−0.973849 | + | 0.227196i | \(0.927044\pi\) | |||||||
\(338\) | 14.1426 | − | 8.16525i | 0.769258 | − | 0.444131i | ||||
\(339\) | 3.88842 | 0.211190 | ||||||||
\(340\) | 4.39872 | − | 10.6126i | 0.238554 | − | 0.575551i | ||||
\(341\) | −32.6304 | − | 5.81422i | −1.76704 | − | 0.314858i | ||||
\(342\) | 4.63684i | 0.250732i | ||||||||
\(343\) | − | 3.88826i | − | 0.209946i | ||||||
\(344\) | −1.14923 | − | 1.99052i | −0.0619623 | − | 0.107322i | ||||
\(345\) | −18.7247 | − | 7.76102i | −1.00811 | − | 0.417839i | ||||
\(346\) | −5.69284 | + | 9.86029i | −0.306049 | + | 0.530093i | ||||
\(347\) | 26.5275 | − | 15.3156i | 1.42407 | − | 0.822186i | 0.427425 | − | 0.904051i | \(-0.359421\pi\) |
0.996643 | + | 0.0818642i | \(0.0260874\pi\) | |||||||
\(348\) | −4.78210 | + | 2.76095i | −0.256347 | + | 0.148002i | ||||
\(349\) | 15.2039 | 0.813846 | 0.406923 | − | 0.913462i | \(-0.366602\pi\) | ||||
0.406923 | + | 0.913462i | \(0.366602\pi\) | |||||||
\(350\) | 17.3607 | − | 4.64334i | 0.927969 | − | 0.248197i | ||||
\(351\) | 2.70788 | − | 4.69019i | 0.144536 | − | 0.250344i | ||||
\(352\) | −5.15537 | − | 2.97645i | −0.274782 | − | 0.158645i | ||||
\(353\) | 11.1325 | − | 6.42736i | 0.592524 | − | 0.342094i | −0.173571 | − | 0.984821i | \(-0.555531\pi\) |
0.766095 | + | 0.642728i | \(0.222197\pi\) | |||||||
\(354\) | 6.67355 | − | 11.5589i | 0.354695 | − | 0.614350i | ||||
\(355\) | −1.39149 | − | 10.5880i | −0.0738528 | − | 0.561953i | ||||
\(356\) | −11.6216 | −0.615943 | ||||||||
\(357\) | 18.4656i | 0.977305i | ||||||||
\(358\) | −6.63830 | + | 3.83263i | −0.350845 | + | 0.202561i | ||||
\(359\) | 8.85258 | − | 15.3331i | 0.467222 | − | 0.809251i | −0.532077 | − | 0.846696i | \(-0.678588\pi\) |
0.999299 | + | 0.0374444i | \(0.0119217\pi\) | |||||||
\(360\) | −2.21700 | + | 0.291362i | −0.116846 | + | 0.0153561i | ||||
\(361\) | −1.25016 | + | 2.16534i | −0.0657978 | + | 0.113965i | ||||
\(362\) | 3.99286 | + | 2.30528i | 0.209860 | + | 0.121163i | ||||
\(363\) | −21.1631 | − | 12.2185i | −1.11078 | − | 0.641307i | ||||
\(364\) | 19.4653 | 1.02026 | ||||||||
\(365\) | 4.14286 | − | 0.544461i | 0.216847 | − | 0.0284984i | ||||
\(366\) | −0.573287 | − | 0.992962i | −0.0299662 | − | 0.0519030i | ||||
\(367\) | 3.85157 | + | 2.22370i | 0.201050 | + | 0.116076i | 0.597145 | − | 0.802133i | \(-0.296302\pi\) |
−0.396095 | + | 0.918210i | \(0.629635\pi\) | |||||||
\(368\) | 9.06476i | 0.472533i | ||||||||
\(369\) | −4.35396 | − | 7.54127i | −0.226658 | − | 0.392583i | ||||
\(370\) | 17.0743 | + | 7.07693i | 0.887649 | + | 0.367912i | ||||
\(371\) | 17.7090 | 0.919405 | ||||||||
\(372\) | 4.25870 | + | 3.58656i | 0.220804 | + | 0.185955i | ||||
\(373\) | − | 17.9531i | − | 0.929577i | −0.885422 | − | 0.464788i | \(-0.846130\pi\) | ||
0.885422 | − | 0.464788i | \(-0.153870\pi\) | |||||||
\(374\) | −30.5839 | −1.58145 | ||||||||
\(375\) | 8.86532 | + | 6.81220i | 0.457803 | + | 0.351780i | ||||
\(376\) | 5.05582 | 0.260734 | ||||||||
\(377\) | 25.8987 | + | 14.9526i | 1.33385 | + | 0.770100i | ||||
\(378\) | 3.11266 | − | 1.79709i | 0.160098 | − | 0.0924325i | ||||
\(379\) | −4.35115 | − | 7.53641i | −0.223503 | − | 0.387119i | 0.732366 | − | 0.680911i | \(-0.238416\pi\) |
−0.955869 | + | 0.293792i | \(0.905083\pi\) | |||||||
\(380\) | −9.57816 | − | 3.96995i | −0.491349 | − | 0.203654i | ||||
\(381\) | −6.89703 | + | 11.9460i | −0.353346 | + | 0.612013i | ||||
\(382\) | −13.2295 | − | 7.63804i | −0.676879 | − | 0.390796i | ||||
\(383\) | −24.1554 | − | 13.9461i | −1.23428 | − | 0.712613i | −0.266362 | − | 0.963873i | \(-0.585822\pi\) |
−0.967919 | + | 0.251261i | \(0.919155\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −29.1161 | − | 37.9627i | −1.48389 | − | 1.93476i | ||||
\(386\) | 2.05581 | + | 3.56077i | 0.104638 | + | 0.181238i | ||||
\(387\) | 2.29846i | 0.116837i | ||||||||
\(388\) | 6.45060i | 0.327479i | ||||||||
\(389\) | 16.0896 | + | 27.8681i | 0.815777 | + | 1.41297i | 0.908769 | + | 0.417300i | \(0.137024\pi\) |
−0.0929919 | + | 0.995667i | \(0.529643\pi\) | |||||||
\(390\) | 7.36993 | + | 9.60920i | 0.373191 | + | 0.486581i | ||||
\(391\) | 23.2857 | + | 40.3320i | 1.17761 | + | 2.03968i | ||||
\(392\) | 5.12530 | + | 2.95909i | 0.258867 | + | 0.149457i | ||||
\(393\) | 17.5774 | + | 10.1483i | 0.886663 | + | 0.511915i | ||||
\(394\) | −5.80908 | + | 10.0616i | −0.292657 | + | 0.506897i | ||||
\(395\) | 8.27592 | + | 3.43020i | 0.416407 | + | 0.172592i | ||||
\(396\) | 2.97645 | + | 5.15537i | 0.149572 | + | 0.259067i | ||||
\(397\) | −4.00201 | + | 2.31056i | −0.200855 | + | 0.115964i | −0.597054 | − | 0.802201i | \(-0.703662\pi\) |
0.396199 | + | 0.918165i | \(0.370329\pi\) | |||||||
\(398\) | 4.38718 | + | 2.53294i | 0.219909 | + | 0.126965i | ||||
\(399\) | 16.6657 | 0.834328 | ||||||||
\(400\) | 1.29629 | − | 4.82904i | 0.0648144 | − | 0.241452i | ||||
\(401\) | 2.12856 | 0.106295 | 0.0531477 | − | 0.998587i | \(-0.483075\pi\) | ||||
0.0531477 | + | 0.998587i | \(0.483075\pi\) | |||||||
\(402\) | − | 5.58873i | − | 0.278741i | ||||||
\(403\) | 5.28959 | − | 29.6861i | 0.263493 | − | 1.47877i | ||||
\(404\) | 9.76731 | 0.485942 | ||||||||
\(405\) | 2.06566 | + | 0.856175i | 0.102644 | + | 0.0425437i | ||||
\(406\) | 9.92336 | + | 17.1878i | 0.492488 | + | 0.853014i | ||||
\(407\) | − | 49.2052i | − | 2.43901i | ||||||
\(408\) | 4.44932 | + | 2.56882i | 0.220274 | + | 0.127175i | ||||
\(409\) | 9.55496 | + | 16.5497i | 0.472463 | + | 0.818329i | 0.999503 | − | 0.0315108i | \(-0.0100319\pi\) |
−0.527041 | + | 0.849840i | \(0.676699\pi\) | |||||||
\(410\) | 19.3055 | − | 2.53715i | 0.953429 | − | 0.125301i | ||||
\(411\) | 12.6387 | 0.623422 | ||||||||
\(412\) | 1.45146 | + | 0.838003i | 0.0715085 | + | 0.0412854i | ||||
\(413\) | −41.5450 | − | 23.9860i | −2.04429 | − | 1.18027i | ||||
\(414\) | 4.53238 | − | 7.85031i | 0.222754 | − | 0.385822i | ||||
\(415\) | −21.9752 | + | 2.88802i | −1.07872 | + | 0.141767i | ||||
\(416\) | 2.70788 | − | 4.69019i | 0.132765 | − | 0.229955i | ||||
\(417\) | −5.73994 | + | 3.31395i | −0.281086 | + | 0.162285i | ||||
\(418\) | 27.6027i | 1.35009i | ||||||||
\(419\) | −30.6580 | −1.49774 | −0.748870 | − | 0.662717i | \(-0.769403\pi\) | ||||
−0.748870 | + | 0.662717i | \(0.769403\pi\) | |||||||
\(420\) | 1.04721 | + | 7.96833i | 0.0510986 | + | 0.388815i | ||||
\(421\) | 17.2976 | − | 29.9603i | 0.843032 | − | 1.46017i | −0.0442873 | − | 0.999019i | \(-0.514102\pi\) |
0.887319 | − | 0.461156i | \(-0.152565\pi\) | |||||||
\(422\) | −6.78240 | + | 3.91582i | −0.330162 | + | 0.190619i | ||||
\(423\) | −4.37847 | − | 2.52791i | −0.212888 | − | 0.122911i | ||||
\(424\) | 2.46356 | − | 4.26701i | 0.119641 | − | 0.207224i | ||||
\(425\) | −6.63732 | − | 24.8159i | −0.321958 | − | 1.20375i | ||||
\(426\) | 4.77582 | 0.231389 | ||||||||
\(427\) | −3.56889 | + | 2.06050i | −0.172711 | + | 0.0997146i | ||||
\(428\) | 2.12044 | − | 1.22423i | 0.102495 | − | 0.0591756i | ||||
\(429\) | 16.1198 | − | 27.9202i | 0.778270 | − | 1.34800i | ||||
\(430\) | −4.74784 | − | 1.96788i | −0.228961 | − | 0.0948997i | ||||
\(431\) | 3.79252 | + | 6.56884i | 0.182679 | + | 0.316410i | 0.942792 | − | 0.333381i | \(-0.108190\pi\) |
−0.760113 | + | 0.649791i | \(0.774856\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 23.7371i | 1.14073i | 0.821390 | + | 0.570366i | \(0.193199\pi\) | ||||
−0.821390 | + | 0.570366i | \(0.806801\pi\) | |||||||
\(434\) | 12.8908 | − | 15.3066i | 0.618777 | − | 0.734739i | ||||
\(435\) | −4.72771 | + | 11.4064i | −0.226676 | + | 0.546893i | ||||
\(436\) | −1.67713 | −0.0803201 | ||||||||
\(437\) | 36.4007 | − | 21.0159i | 1.74128 | − | 1.00533i | ||||
\(438\) | 1.86867i | 0.0892887i | ||||||||
\(439\) | 5.10170 | − | 8.83640i | 0.243491 | − | 0.421738i | −0.718215 | − | 0.695821i | \(-0.755041\pi\) |
0.961706 | + | 0.274082i | \(0.0883741\pi\) | |||||||
\(440\) | −13.1976 | + | 1.73445i | −0.629172 | + | 0.0826867i | ||||
\(441\) | −2.95909 | − | 5.12530i | −0.140909 | − | 0.244062i | ||||
\(442\) | − | 27.8242i | − | 1.32346i | ||||||
\(443\) | −33.0182 | − | 19.0631i | −1.56874 | − | 0.905715i | −0.996316 | − | 0.0857604i | \(-0.972668\pi\) |
−0.572429 | − | 0.819955i | \(-0.693999\pi\) | |||||||
\(444\) | −4.13288 | + | 7.15835i | −0.196138 | + | 0.339720i | ||||
\(445\) | −20.6202 | + | 15.8150i | −0.977492 | + | 0.749703i | ||||
\(446\) | 6.38320 | + | 11.0560i | 0.302253 | + | 0.523518i | ||||
\(447\) | 0.643090 | + | 0.371288i | 0.0304171 | + | 0.0175613i | ||||
\(448\) | 3.11266 | − | 1.79709i | 0.147059 | − | 0.0849047i | ||||
\(449\) | 30.7843 | 1.45280 | 0.726400 | − | 0.687272i | \(-0.241192\pi\) | ||||
0.726400 | + | 0.687272i | \(0.241192\pi\) | |||||||
\(450\) | −3.53714 | + | 3.53393i | −0.166742 | + | 0.166591i | ||||
\(451\) | −25.9187 | − | 44.8925i | −1.22046 | − | 2.11390i | ||||
\(452\) | −3.36747 | − | 1.94421i | −0.158392 | − | 0.0914479i | ||||
\(453\) | −3.56463 | + | 2.05804i | −0.167481 | + | 0.0966951i | ||||
\(454\) | 1.66070 | − | 2.87642i | 0.0779407 | − | 0.134997i | ||||
\(455\) | 34.5373 | − | 26.4889i | 1.61913 | − | 1.24182i | ||||
\(456\) | 2.31842 | − | 4.01562i | 0.108570 | − | 0.188049i | ||||
\(457\) | 22.5321i | 1.05401i | 0.849862 | + | 0.527005i | \(0.176685\pi\) | ||||
−0.849862 | + | 0.527005i | \(0.823315\pi\) | |||||||
\(458\) | −4.53720 | + | 2.61956i | −0.212010 | + | 0.122404i | ||||
\(459\) | −2.56882 | − | 4.44932i | −0.119902 | − | 0.207677i | ||||
\(460\) | 12.3356 | + | 16.0836i | 0.575150 | + | 0.749902i | ||||
\(461\) | −40.8334 | −1.90180 | −0.950899 | − | 0.309500i | \(-0.899838\pi\) | ||||
−0.950899 | + | 0.309500i | \(0.899838\pi\) | |||||||
\(462\) | 18.5294 | − | 10.6979i | 0.862063 | − | 0.497713i | ||||
\(463\) | 3.98680i | 0.185282i | 0.995700 | + | 0.0926412i | \(0.0295310\pi\) | ||||
−0.995700 | + | 0.0926412i | \(0.970469\pi\) | |||||||
\(464\) | 5.52189 | 0.256347 | ||||||||
\(465\) | 12.4369 | + | 0.568274i | 0.576749 | + | 0.0263531i | ||||
\(466\) | −14.5392 | −0.673513 | ||||||||
\(467\) | − | 21.0286i | − | 0.973087i | −0.873656 | − | 0.486544i | \(-0.838257\pi\) | ||
0.873656 | − | 0.486544i | \(-0.161743\pi\) | |||||||
\(468\) | −4.69019 | + | 2.70788i | −0.216804 | + | 0.125172i | ||||
\(469\) | −20.0869 | −0.927529 | ||||||||
\(470\) | 8.97055 | − | 6.88011i | 0.413780 | − | 0.317356i | ||||
\(471\) | −3.91892 | − | 6.78777i | −0.180574 | − | 0.312764i | ||||
\(472\) | −11.5589 | + | 6.67355i | −0.532043 | + | 0.307175i | ||||
\(473\) | 13.6825i | 0.629122i | ||||||||
\(474\) | −2.00321 | + | 3.46966i | −0.0920105 | + | 0.159367i | ||||
\(475\) | −22.3970 | + | 5.99035i | −1.02764 | + | 0.274856i | ||||
\(476\) | 9.23282 | − | 15.9917i | 0.423185 | − | 0.732979i | ||||
\(477\) | −4.26701 | + | 2.46356i | −0.195373 | + | 0.112799i | ||||
\(478\) | −19.2600 | − | 11.1198i | −0.880932 | − | 0.508606i | ||||
\(479\) | −5.43490 | − | 9.41352i | −0.248327 | − | 0.430115i | 0.714735 | − | 0.699395i | \(-0.246547\pi\) |
−0.963062 | + | 0.269281i | \(0.913214\pi\) | |||||||
\(480\) | 2.06566 | + | 0.856175i | 0.0942842 | + | 0.0390789i | ||||
\(481\) | 44.7654 | 2.04113 | ||||||||
\(482\) | −1.95057 | + | 1.12616i | −0.0888459 | + | 0.0512952i | ||||
\(483\) | −28.2155 | − | 16.2902i | −1.28385 | − | 0.741230i | ||||
\(484\) | 12.2185 | + | 21.1631i | 0.555388 | + | 0.961960i | ||||
\(485\) | 8.77816 | + | 11.4453i | 0.398596 | + | 0.519704i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 27.4811 | + | 15.8662i | 1.24529 | + | 0.718966i | 0.970166 | − | 0.242444i | \(-0.0779489\pi\) |
0.275120 | + | 0.961410i | \(0.411282\pi\) | |||||||
\(488\) | 1.14657i | 0.0519030i | ||||||||
\(489\) | −5.38408 | − | 9.32551i | −0.243477 | − | 0.421714i | ||||
\(490\) | 13.1206 | − | 1.72433i | 0.592730 | − | 0.0778975i | ||||
\(491\) | −3.62646 | + | 6.28121i | −0.163660 | + | 0.283467i | −0.936179 | − | 0.351525i | \(-0.885663\pi\) |
0.772519 | + | 0.634992i | \(0.218997\pi\) | |||||||
\(492\) | 8.70791i | 0.392583i | ||||||||
\(493\) | 24.5687 | − | 14.1847i | 1.10652 | − | 0.638849i | ||||
\(494\) | −25.1121 | −1.12984 | ||||||||
\(495\) | 12.2967 | + | 5.09673i | 0.552695 | + | 0.229081i | ||||
\(496\) | −1.89486 | − | 5.23541i | −0.0850819 | − | 0.235077i | ||||
\(497\) | − | 17.1652i | − | 0.769964i | ||||||
\(498\) | − | 9.91212i | − | 0.444173i | ||||||
\(499\) | 10.9674 | + | 18.9961i | 0.490969 | + | 0.850383i | 0.999946 | − | 0.0103971i | \(-0.00330957\pi\) |
−0.508977 | + | 0.860780i | \(0.669976\pi\) | |||||||
\(500\) | −4.27149 | − | 10.3322i | −0.191027 | − | 0.462070i | ||||
\(501\) | −5.82450 | + | 10.0883i | −0.260219 | + | 0.450713i | ||||
\(502\) | 13.1669 | − | 7.60189i | 0.587666 | − | 0.339289i | ||||
\(503\) | 7.31796 | − | 4.22503i | 0.326292 | − | 0.188385i | −0.327902 | − | 0.944712i | \(-0.606341\pi\) |
0.654194 | + | 0.756327i | \(0.273008\pi\) | |||||||
\(504\) | −3.59419 | −0.160098 | ||||||||
\(505\) | 17.3302 | − | 13.2916i | 0.771182 | − | 0.591470i | ||||
\(506\) | 26.9808 | − | 46.7321i | 1.19944 | − | 2.07750i | ||||
\(507\) | 14.1426 | + | 8.16525i | 0.628096 | + | 0.362632i | ||||
\(508\) | 11.9460 | − | 6.89703i | 0.530019 | − | 0.306006i | ||||
\(509\) | −5.61256 | + | 9.72123i | −0.248772 | + | 0.430886i | −0.963185 | − | 0.268838i | \(-0.913360\pi\) |
0.714413 | + | 0.699724i | \(0.246694\pi\) | |||||||
\(510\) | 11.3902 | − | 1.49691i | 0.504365 | − | 0.0662844i | ||||
\(511\) | 6.71636 | 0.297114 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −4.01562 | + | 2.31842i | −0.177294 | + | 0.102361i | ||||
\(514\) | 1.60435 | − | 2.77882i | 0.0707650 | − | 0.122568i | ||||
\(515\) | 3.71571 | − | 0.488325i | 0.163734 | − | 0.0215181i | ||||
\(516\) | 1.14923 | − | 1.99052i | 0.0505920 | − | 0.0876279i | ||||
\(517\) | −26.0646 | − | 15.0484i | −1.14632 | − | 0.661828i | ||||
\(518\) | 25.7285 | + | 14.8543i | 1.13044 | + | 0.652662i | ||||
\(519\) | −11.3857 | −0.499776 | ||||||||
\(520\) | −1.57795 | − | 12.0068i | −0.0691976 | − | 0.526532i | ||||
\(521\) | 13.8234 | + | 23.9428i | 0.605613 | + | 1.04895i | 0.991954 | + | 0.126597i | \(0.0404054\pi\) |
−0.386341 | + | 0.922356i | \(0.626261\pi\) | |||||||
\(522\) | −4.78210 | − | 2.76095i | −0.209307 | − | 0.120843i | ||||
\(523\) | 36.5883i | 1.59989i | 0.600070 | + | 0.799947i | \(0.295139\pi\) | ||||
−0.600070 | + | 0.799947i | \(0.704861\pi\) | |||||||
\(524\) | −10.1483 | − | 17.5774i | −0.443331 | − | 0.767873i | ||||
\(525\) | 12.7016 | + | 12.7131i | 0.554343 | + | 0.554847i | ||||
\(526\) | 21.1070 | 0.920310 | ||||||||
\(527\) | −21.8797 | − | 18.4265i | −0.953094 | − | 0.802669i | ||||
\(528\) | − | 5.95290i | − | 0.259067i | ||||||
\(529\) | −59.1698 | −2.57260 | ||||||||
\(530\) | −1.43558 | − | 10.9234i | −0.0623574 | − | 0.474484i | ||||
\(531\) | 13.3471 | 0.579215 | ||||||||
\(532\) | −14.4329 | − | 8.33284i | −0.625746 | − | 0.361275i | ||||
\(533\) | 40.8418 | − | 23.5800i | 1.76905 | − | 1.02136i | ||||
\(534\) | −5.81080 | − | 10.0646i | −0.251458 | − | 0.435538i | ||||
\(535\) | 2.09632 | − | 5.05771i | 0.0906318 | − | 0.218664i | ||||
\(536\) | −2.79437 | + | 4.83998i | −0.120698 | + | 0.209055i | ||||
\(537\) | −6.63830 | − | 3.83263i | −0.286464 | − | 0.165390i | ||||
\(538\) | −14.4777 | − | 8.35872i | −0.624179 | − | 0.360370i | ||||
\(539\) | −17.6152 | − | 30.5104i | −0.758740 | − | 1.31418i | ||||
\(540\) | −1.36083 | − | 1.77430i | −0.0585608 | − | 0.0763538i | ||||
\(541\) | 2.94961 | + | 5.10887i | 0.126813 | + | 0.219647i | 0.922440 | − | 0.386140i | \(-0.126192\pi\) |
−0.795627 | + | 0.605787i | \(0.792858\pi\) | |||||||
\(542\) | 8.95467i | 0.384636i | ||||||||
\(543\) | 4.61056i | 0.197858i | ||||||||
\(544\) | −2.56882 | − | 4.44932i | −0.110137 | − | 0.190763i | ||||
\(545\) | −2.97574 | + | 2.28229i | −0.127467 | + | 0.0977626i | ||||
\(546\) | 9.73264 | + | 16.8574i | 0.416518 | + | 0.721431i | ||||
\(547\) | −9.81072 | − | 5.66422i | −0.419476 | − | 0.242185i | 0.275377 | − | 0.961336i | \(-0.411197\pi\) |
−0.694853 | + | 0.719152i | \(0.744531\pi\) | |||||||
\(548\) | −10.9454 | − | 6.31936i | −0.467566 | − | 0.269950i | ||||
\(549\) | 0.573287 | − | 0.992962i | 0.0244673 | − | 0.0423786i | ||||
\(550\) | −21.0562 | + | 21.0371i | −0.897841 | + | 0.897026i | ||||
\(551\) | −12.8021 | − | 22.1738i | −0.545387 | − | 0.944637i | ||||
\(552\) | −7.85031 | + | 4.53238i | −0.334131 | + | 0.192911i | ||||
\(553\) | 12.4706 | + | 7.19992i | 0.530305 | + | 0.306172i | ||||
\(554\) | −0.851610 | −0.0361815 | ||||||||
\(555\) | 2.40833 | + | 18.3252i | 0.102228 | + | 0.777862i | ||||
\(556\) | 6.62791 | 0.281086 | ||||||||
\(557\) | 6.90212i | 0.292452i | 0.989251 | + | 0.146226i | \(0.0467127\pi\) | ||||
−0.989251 | + | 0.146226i | \(0.953287\pi\) | |||||||
\(558\) | −0.976703 | + | 5.48143i | −0.0413471 | + | 0.232047i | ||||
\(559\) | −12.4479 | −0.526490 | ||||||||
\(560\) | 3.07725 | − | 7.42438i | 0.130038 | − | 0.313737i | ||||
\(561\) | −15.2919 | − | 26.4864i | −0.645626 | − | 1.11826i | ||||
\(562\) | − | 3.72310i | − | 0.157050i | ||||||
\(563\) | −30.7052 | − | 17.7277i | −1.29407 | − | 0.747131i | −0.314697 | − | 0.949192i | \(-0.601903\pi\) |
−0.979373 | + | 0.202061i | \(0.935236\pi\) | |||||||
\(564\) | 2.52791 | + | 4.37847i | 0.106444 | + | 0.184367i | ||||
\(565\) | −8.62064 | + | 1.13294i | −0.362673 | + | 0.0476630i | ||||
\(566\) | 21.3862 | 0.898927 | ||||||||
\(567\) | 3.11266 | + | 1.79709i | 0.130719 | + | 0.0754708i | ||||
\(568\) | −4.13598 | − | 2.38791i | −0.173542 | − | 0.100194i | ||||
\(569\) | 2.76691 | − | 4.79243i | 0.115995 | − | 0.200909i | −0.802182 | − | 0.597080i | \(-0.796328\pi\) |
0.918177 | + | 0.396170i | \(0.129661\pi\) | |||||||
\(570\) | −1.35100 | − | 10.2799i | −0.0565872 | − | 0.430578i | ||||
\(571\) | 22.6987 | − | 39.3153i | 0.949911 | − | 1.64529i | 0.204305 | − | 0.978907i | \(-0.434506\pi\) |
0.745606 | − | 0.666387i | \(-0.232160\pi\) | |||||||
\(572\) | −27.9202 | + | 16.1198i | −1.16740 | + | 0.674001i | ||||
\(573\) | − | 15.2761i | − | 0.638168i | ||||||
\(574\) | 31.2979 | 1.30635 | ||||||||
\(575\) | 43.7741 | + | 11.7505i | 1.82551 | + | 0.490031i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −10.3544 | + | 5.97812i | −0.431060 | + | 0.248872i | −0.699798 | − | 0.714341i | \(-0.746727\pi\) |
0.268738 | + | 0.963213i | \(0.413393\pi\) | |||||||
\(578\) | −8.13659 | − | 4.69766i | −0.338437 | − | 0.195397i | ||||
\(579\) | −2.05581 | + | 3.56077i | −0.0854366 | + | 0.147981i | ||||
\(580\) | 9.79750 | − | 7.51435i | 0.406819 | − | 0.312016i | ||||
\(581\) | −35.6260 | −1.47802 | ||||||||
\(582\) | −5.58638 | + | 3.22530i | −0.231563 | + | 0.133693i | ||||
\(583\) | −25.4011 | + | 14.6653i | −1.05201 | + | 0.607376i | ||||
\(584\) | 0.934337 | − | 1.61832i | 0.0386631 | − | 0.0669665i | ||||
\(585\) | −4.63684 | + | 11.1871i | −0.191710 | + | 0.462532i | ||||
\(586\) | −4.49828 | − | 7.79125i | −0.185822 | − | 0.321854i | ||||
\(587\) | − | 24.8671i | − | 1.02637i | −0.858277 | − | 0.513187i | \(-0.828465\pi\) | ||
0.858277 | − | 0.513187i | \(-0.171535\pi\) | |||||||
\(588\) | 5.91818i | 0.244062i | ||||||||
\(589\) | −16.6303 | + | 19.7469i | −0.685241 | + | 0.813659i | ||||
\(590\) | −11.4275 | + | 27.5706i | −0.470461 | + | 1.13506i | ||||
\(591\) | −11.6182 | −0.477907 | ||||||||
\(592\) | 7.15835 | − | 4.13288i | 0.294206 | − | 0.169860i | ||||
\(593\) | 43.5200i | 1.78715i | 0.448910 | + | 0.893577i | \(0.351812\pi\) | ||||
−0.448910 | + | 0.893577i | \(0.648188\pi\) | |||||||
\(594\) | −2.97645 | + | 5.15537i | −0.122125 | + | 0.211527i | ||||
\(595\) | −5.38018 | − | 40.9384i | −0.220566 | − | 1.67831i | ||||
\(596\) | −0.371288 | − | 0.643090i | −0.0152086 | − | 0.0263420i | ||||
\(597\) | 5.06587i | 0.207332i | ||||||||
\(598\) | 42.5154 | + | 24.5463i | 1.73858 | + | 1.00377i | ||||
\(599\) | 0.472384 | − | 0.818193i | 0.0193011 | − | 0.0334304i | −0.856214 | − | 0.516622i | \(-0.827189\pi\) |
0.875515 | + | 0.483192i | \(0.160523\pi\) | |||||||
\(600\) | 4.83022 | − | 1.29190i | 0.197193 | − | 0.0527417i | ||||
\(601\) | 16.3314 | + | 28.2868i | 0.666172 | + | 1.15384i | 0.978966 | + | 0.204022i | \(0.0654015\pi\) |
−0.312795 | + | 0.949821i | \(0.601265\pi\) | |||||||
\(602\) | −7.15431 | − | 4.13054i | −0.291588 | − | 0.168348i | ||||
\(603\) | 4.83998 | − | 2.79437i | 0.197099 | − | 0.113795i | ||||
\(604\) | 4.11608 | 0.167481 | ||||||||
\(605\) | 50.4787 | + | 20.9224i | 2.05225 | + | 0.850617i | ||||
\(606\) | 4.88366 | + | 8.45874i | 0.198385 | + | 0.343613i | ||||
\(607\) | 3.54336 | + | 2.04576i | 0.143820 | + | 0.0830347i | 0.570184 | − | 0.821517i | \(-0.306872\pi\) |
−0.426363 | + | 0.904552i | \(0.640205\pi\) | |||||||
\(608\) | −4.01562 | + | 2.31842i | −0.162855 | + | 0.0940244i | ||||
\(609\) | −9.92336 | + | 17.1878i | −0.402115 | + | 0.696483i | ||||
\(610\) | 1.56029 | + | 2.03437i | 0.0631743 | + | 0.0823691i | ||||
\(611\) | 13.6906 | − | 23.7128i | 0.553861 | − | 0.959315i | ||||
\(612\) | 5.13764i | 0.207677i | ||||||||
\(613\) | 7.25064 | − | 4.18616i | 0.292851 | − | 0.169077i | −0.346376 | − | 0.938096i | \(-0.612588\pi\) |
0.639227 | + | 0.769018i | \(0.279255\pi\) | |||||||
\(614\) | 8.49904 | + | 14.7208i | 0.342993 | + | 0.594082i | ||||
\(615\) | 11.8500 | + | 15.4505i | 0.477837 | + | 0.623022i | ||||
\(616\) | −21.3959 | −0.862063 | ||||||||
\(617\) | 6.05354 | − | 3.49502i | 0.243706 | − | 0.140704i | −0.373173 | − | 0.927762i | \(-0.621730\pi\) |
0.616879 | + | 0.787058i | \(0.288397\pi\) | |||||||
\(618\) | 1.67601i | 0.0674188i | ||||||||
\(619\) | 21.1473 | 0.849982 | 0.424991 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424991 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(620\) | −10.4866 | − | 6.71060i | −0.421150 | − | 0.269504i | ||||
\(621\) | 9.06476 | 0.363756 | ||||||||
\(622\) | 17.4831i | 0.701010i | ||||||||
\(623\) | −36.1740 | + | 20.8851i | −1.44928 | + | 0.836744i | ||||
\(624\) | 5.41576 | 0.216804 | ||||||||
\(625\) | −21.6393 | − | 12.5197i | −0.865571 | − | 0.500786i | ||||
\(626\) | 16.7175 | + | 28.9556i | 0.668167 | + | 1.15730i | ||||
\(627\) | −23.9046 | + | 13.8013i | −0.954659 | + | 0.551173i | ||||
\(628\) | 7.83784i | 0.312764i | ||||||||
\(629\) | 21.2332 | − | 36.7770i | 0.846624 | − | 1.46640i | ||||
\(630\) | −6.37717 | + | 4.89107i | −0.254073 | + | 0.194865i | ||||
\(631\) | 10.9873 | − | 19.0306i | 0.437399 | − | 0.757598i | −0.560089 | − | 0.828433i | \(-0.689233\pi\) |
0.997488 | + | 0.0708346i | \(0.0225662\pi\) | |||||||
\(632\) | 3.46966 | − | 2.00321i | 0.138016 | − | 0.0796835i | ||||
\(633\) | −6.78240 | − | 3.91582i | −0.269576 | − | 0.155640i | ||||
\(634\) | 6.94602 | + | 12.0309i | 0.275862 | + | 0.477806i | ||||
\(635\) | 11.8101 | − | 28.4939i | 0.468671 | − | 1.13075i | ||||
\(636\) | 4.92712 | 0.195373 | ||||||||
\(637\) | 27.7574 | − | 16.0257i | 1.09979 | − | 0.634963i | ||||
\(638\) | −28.4674 | − | 16.4356i | −1.12703 | − | 0.650693i | ||||
\(639\) | 2.38791 | + | 4.13598i | 0.0944643 | + | 0.163617i | ||||
\(640\) | −1.36083 | − | 1.77430i | −0.0537915 | − | 0.0701354i | ||||
\(641\) | −19.2323 | + | 33.3113i | −0.759631 | + | 1.31572i | 0.183409 | + | 0.983037i | \(0.441287\pi\) |
−0.943039 | + | 0.332682i | \(0.892046\pi\) | |||||||
\(642\) | 2.12044 | + | 1.22423i | 0.0836870 | + | 0.0483167i | ||||
\(643\) | 20.6335i | 0.813704i | 0.913494 | + | 0.406852i | \(0.133374\pi\) | ||||
−0.913494 | + | 0.406852i | \(0.866626\pi\) | |||||||
\(644\) | 16.2902 | + | 28.2155i | 0.641924 | + | 1.11185i | ||||
\(645\) | −0.669683 | − | 5.09569i | −0.0263688 | − | 0.200643i | ||||
\(646\) | −11.9112 | + | 20.6308i | −0.468640 | + | 0.811709i | ||||
\(647\) | − | 4.89104i | − | 0.192287i | −0.995367 | − | 0.0961434i | \(-0.969349\pi\) | ||
0.995367 | − | 0.0961434i | \(-0.0306507\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 79.4541 | 3.11884 | ||||||||
\(650\) | −19.1389 | − | 19.1563i | −0.750690 | − | 0.751372i | ||||
\(651\) | 19.7013 | + | 3.51045i | 0.772154 | + | 0.137585i | ||||
\(652\) | 10.7682i | 0.421714i | ||||||||
\(653\) | 12.9123i | 0.505297i | 0.967558 | + | 0.252648i | \(0.0813016\pi\) | ||||
−0.967558 | + | 0.252648i | \(0.918698\pi\) | |||||||
\(654\) | −0.838566 | − | 1.45244i | −0.0327905 | − | 0.0567949i | ||||
\(655\) | −41.9260 | − | 17.3775i | −1.63819 | − | 0.678994i | ||||
\(656\) | 4.35396 | − | 7.54127i | 0.169993 | − | 0.294437i | ||||
\(657\) | −1.61832 | + | 0.934337i | −0.0631366 | + | 0.0364520i | ||||
\(658\) | 15.7370 | − | 9.08578i | 0.613493 | − | 0.354201i | ||||
\(659\) | −10.7331 | −0.418103 | −0.209051 | − | 0.977905i | \(-0.567038\pi\) | ||||
−0.209051 | + | 0.977905i | \(0.567038\pi\) | |||||||
\(660\) | −8.10088 | − | 10.5622i | −0.315327 | − | 0.411135i | ||||
\(661\) | −18.9020 | + | 32.7391i | −0.735201 | + | 1.27341i | 0.219434 | + | 0.975627i | \(0.429579\pi\) |
−0.954635 | + | 0.297778i | \(0.903755\pi\) | |||||||
\(662\) | 3.81564 | + | 2.20296i | 0.148299 | + | 0.0856204i | ||||
\(663\) | 24.0965 | − | 13.9121i | 0.935830 | − | 0.540302i | ||||
\(664\) | −4.95606 | + | 8.58415i | −0.192332 | + | 0.333130i | ||||
\(665\) | −36.9479 | + | 4.85575i | −1.43278 | + | 0.188298i | ||||
\(666\) | −8.26575 | −0.320291 | ||||||||
\(667\) | 50.0546i | 1.93812i | ||||||||
\(668\) | 10.0883 | − | 5.82450i | 0.390329 | − | 0.225356i | ||||
\(669\) | −6.38320 | + | 11.0560i | −0.246789 | + | 0.427451i | ||||
\(670\) | 1.62834 | + | 12.3902i | 0.0629084 | + | 0.478677i | ||||
\(671\) | 3.41272 | − | 5.91101i | 0.131747 | − | 0.228192i | ||||
\(672\) | 3.11266 | + | 1.79709i | 0.120073 | + | 0.0693244i | ||||
\(673\) | −7.29082 | − | 4.20935i | −0.281040 | − | 0.162259i | 0.352854 | − | 0.935678i | \(-0.385211\pi\) |
−0.633894 | + | 0.773420i | \(0.718545\pi\) | |||||||
\(674\) | 8.34153 | 0.321304 | ||||||||
\(675\) | −4.82904 | − | 1.29629i | −0.185870 | − | 0.0498942i | ||||
\(676\) | −8.16525 | − | 14.1426i | −0.314048 | − | 0.543948i | ||||
\(677\) | 5.96039 | + | 3.44123i | 0.229076 | + | 0.132257i | 0.610146 | − | 0.792289i | \(-0.291111\pi\) |
−0.381070 | + | 0.924546i | \(0.624444\pi\) | |||||||
\(678\) | − | 3.88842i | − | 0.149334i | ||||||
\(679\) | 11.5923 | + | 20.0785i | 0.444873 | + | 0.770542i | ||||
\(680\) | −10.6126 | − | 4.39872i | −0.406976 | − | 0.168683i | ||||
\(681\) | 3.32141 | 0.127277 | ||||||||
\(682\) | −5.81422 | + | 32.6304i | −0.222638 | + | 1.24948i | ||||
\(683\) | − | 17.2994i | − | 0.661945i | −0.943640 | − | 0.330973i | \(-0.892623\pi\) | ||
0.943640 | − | 0.330973i | \(-0.107377\pi\) | |||||||
\(684\) | 4.63684 | 0.177294 | ||||||||
\(685\) | −28.0201 | + | 3.68244i | −1.07059 | + | 0.140699i | ||||
\(686\) | −3.88826 | −0.148454 | ||||||||
\(687\) | −4.53720 | − | 2.61956i | −0.173105 | − | 0.0999423i | ||||
\(688\) | −1.99052 | + | 1.14923i | −0.0758880 | + | 0.0438139i | ||||
\(689\) | −13.3421 | − | 23.1091i | −0.508292 | − | 0.880387i | ||||
\(690\) | −7.76102 | + | 18.7247i | −0.295457 | + | 0.712838i | ||||
\(691\) | −24.1447 | + | 41.8198i | −0.918508 | + | 1.59090i | −0.116825 | + | 0.993153i | \(0.537272\pi\) |
−0.801683 | + | 0.597749i | \(0.796062\pi\) | |||||||
\(692\) | 9.86029 | + | 5.69284i | 0.374832 | + | 0.216409i | ||||
\(693\) | 18.5294 | + | 10.6979i | 0.703872 | + | 0.406381i | ||||
\(694\) | −15.3156 | − | 26.5275i | −0.581374 | − | 1.00697i | ||||
\(695\) | 11.7599 | − | 9.01945i | 0.446079 | − | 0.342127i | ||||
\(696\) | 2.76095 | + | 4.78210i | 0.104653 | + | 0.181265i | ||||
\(697\) | − | 44.7381i | − | 1.69458i | ||||||
\(698\) | − | 15.2039i | − | 0.575476i | ||||||
\(699\) | −7.26958 | − | 12.5913i | −0.274961 | − | 0.476246i | ||||
\(700\) | −4.64334 | − | 17.3607i | −0.175502 | − | 0.656173i | ||||
\(701\) | 7.46350 | + | 12.9272i | 0.281893 | + | 0.488252i | 0.971851 | − | 0.235597i | \(-0.0757045\pi\) |
−0.689958 | + | 0.723849i | \(0.742371\pi\) | |||||||
\(702\) | −4.69019 | − | 2.70788i | −0.177020 | − | 0.102202i | ||||
\(703\) | −33.1922 | − | 19.1635i | −1.25187 | − | 0.722765i | ||||
\(704\) | −2.97645 | + | 5.15537i | −0.112179 | + | 0.194300i | ||||
\(705\) | 10.4436 | + | 4.32867i | 0.393329 | + | 0.163027i | ||||
\(706\) | −6.42736 | − | 11.1325i | −0.241897 | − | 0.418977i | ||||
\(707\) | 30.4023 | − | 17.5528i | 1.14340 | − | 0.660140i | ||||
\(708\) | −11.5589 | − | 6.67355i | −0.434411 | − | 0.250808i | ||||
\(709\) | −35.9212 | −1.34905 | −0.674525 | − | 0.738252i | \(-0.735651\pi\) | ||||
−0.674525 | + | 0.738252i | \(0.735651\pi\) | |||||||
\(710\) | −10.5880 | + | 1.39149i | −0.397361 | + | 0.0522218i | ||||
\(711\) | −4.00642 | −0.150253 | ||||||||
\(712\) | 11.6216i | 0.435538i | ||||||||
\(713\) | 47.4577 | − | 17.1765i | 1.77730 | − | 0.643264i | ||||
\(714\) | 18.4656 | 0.691059 | ||||||||
\(715\) | −27.6027 | + | 66.5960i | −1.03228 | + | 2.49055i | ||||
\(716\) | 3.83263 | + | 6.63830i | 0.143232 | + | 0.248085i | ||||
\(717\) | − | 22.2395i | − | 0.830550i | ||||||
\(718\) | −15.3331 | − | 8.85258i | −0.572227 | − | 0.330376i | ||||
\(719\) | 22.3875 | + | 38.7763i | 0.834914 | + | 1.44611i | 0.894100 | + | 0.447866i | \(0.147816\pi\) |
−0.0591865 | + | 0.998247i | \(0.518851\pi\) | |||||||
\(720\) | 0.291362 | + | 2.21700i | 0.0108584 | + | 0.0826229i | ||||
\(721\) | 6.02388 | 0.224341 | ||||||||
\(722\) | 2.16534 | + | 1.25016i | 0.0805856 | + | 0.0465261i | ||||
\(723\) | −1.95057 | − | 1.12616i | −0.0725424 | − | 0.0418824i | ||||
\(724\) | 2.30528 | − | 3.99286i | 0.0856751 | − | 0.148394i | ||||
\(725\) | 7.15796 | − | 26.6654i | 0.265840 | − | 0.990330i | ||||
\(726\) | −12.2185 | + | 21.1631i | −0.453472 | + | 0.785437i | ||||
\(727\) | 6.22980 | − | 3.59677i | 0.231050 | − | 0.133397i | −0.380006 | − | 0.924984i | \(-0.624078\pi\) |
0.611057 | + | 0.791587i | \(0.290745\pi\) | |||||||
\(728\) | − | 19.4653i | − | 0.721431i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.544461 | − | 4.14286i | −0.0201514 | − | 0.153334i | ||||
\(731\) | −5.90432 | + | 10.2266i | −0.218379 | + | 0.378244i | ||||
\(732\) | −0.992962 | + | 0.573287i | −0.0367009 | + | 0.0211893i | ||||
\(733\) | 7.10090 | + | 4.09970i | 0.262278 | + | 0.151426i | 0.625373 | − | 0.780326i | \(-0.284947\pi\) |
−0.363095 | + | 0.931752i | \(0.618280\pi\) | |||||||
\(734\) | 2.22370 | − | 3.85157i | 0.0820784 | − | 0.142164i | ||||
\(735\) | 8.05363 | + | 10.5006i | 0.297063 | + | 0.387322i | ||||
\(736\) | 9.06476 | 0.334131 | ||||||||
\(737\) | 28.8120 | − | 16.6346i | 1.06130 | − | 0.612743i | ||||
\(738\) | −7.54127 | + | 4.35396i | −0.277598 | + | 0.160271i | ||||
\(739\) | −14.6917 | + | 25.4467i | −0.540442 | + | 0.936073i | 0.458437 | + | 0.888727i | \(0.348410\pi\) |
−0.998879 | + | 0.0473456i | \(0.984924\pi\) | |||||||
\(740\) | 7.07693 | − | 17.0743i | 0.260153 | − | 0.627662i | ||||
\(741\) | −12.5560 | − | 21.7477i | −0.461257 | − | 0.798921i | ||||
\(742\) | − | 17.7090i | − | 0.650117i | ||||||
\(743\) | 4.08220i | 0.149761i | 0.997193 | + | 0.0748807i | \(0.0238576\pi\) | ||||
−0.997193 | + | 0.0748807i | \(0.976142\pi\) | |||||||
\(744\) | 3.58656 | − | 4.25870i | 0.131490 | − | 0.156132i | ||||
\(745\) | −1.53391 | − | 0.635776i | −0.0561982 | − | 0.0232930i | ||||
\(746\) | −17.9531 | −0.657310 | ||||||||
\(747\) | 8.58415 | − | 4.95606i | 0.314078 | − | 0.181333i | ||||
\(748\) | 30.5839i | 1.11826i | ||||||||
\(749\) | 4.40013 | − | 7.62125i | 0.160777 | − | 0.278474i | ||||
\(750\) | 6.81220 | − | 8.86532i | 0.248746 | − | 0.323716i | ||||
\(751\) | −9.28329 | − | 16.0791i | −0.338752 | − | 0.586736i | 0.645446 | − | 0.763806i | \(-0.276671\pi\) |
−0.984198 | + | 0.177070i | \(0.943338\pi\) | |||||||
\(752\) | − | 5.05582i | − | 0.184367i | ||||||
\(753\) | 13.1669 | + | 7.60189i | 0.479827 | + | 0.277028i | ||||
\(754\) | 14.9526 | − | 25.8987i | 0.544543 | − | 0.943176i | ||||
\(755\) | 7.30316 | − | 5.60128i | 0.265789 | − | 0.203851i | ||||
\(756\) | −1.79709 | − | 3.11266i | −0.0653597 | − | 0.113206i | ||||
\(757\) | −10.6644 | − | 6.15708i | −0.387603 | − | 0.223783i | 0.293518 | − | 0.955954i | \(-0.405174\pi\) |
−0.681121 | + | 0.732171i | \(0.738507\pi\) | |||||||
\(758\) | −7.53641 | + | 4.35115i | −0.273735 | + | 0.158041i | ||||
\(759\) | 53.9616 | 1.95868 | ||||||||
\(760\) | −3.96995 | + | 9.57816i | −0.144005 | + | 0.347436i | ||||
\(761\) | 12.9483 | + | 22.4271i | 0.469375 | + | 0.812981i | 0.999387 | − | 0.0350090i | \(-0.0111460\pi\) |
−0.530012 | + | 0.847990i | \(0.677813\pi\) | |||||||
\(762\) | 11.9460 | + | 6.89703i | 0.432758 | + | 0.249853i | ||||
\(763\) | −5.22034 | + | 3.01396i | −0.188989 | + | 0.109113i | ||||
\(764\) | −7.63804 | + | 13.2295i | −0.276335 | + | 0.478626i | ||||
\(765\) | 6.99145 | + | 9.11572i | 0.252776 | + | 0.329579i | ||||
\(766\) | −13.9461 | + | 24.1554i | −0.503893 | + | 0.872769i | ||||
\(767\) | 72.2848i | 2.61005i | ||||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | −18.8752 | − | 32.6928i | −0.680658 | − | 1.17893i | −0.974780 | − | 0.223166i | \(-0.928361\pi\) |
0.294123 | − | 0.955768i | \(-0.404973\pi\) | |||||||
\(770\) | −37.9627 | + | 29.1161i | −1.36808 | + | 1.04927i | ||||
\(771\) | 3.20871 | 0.115559 | ||||||||
\(772\) | 3.56077 | − | 2.05581i | 0.128155 | − | 0.0739903i | ||||
\(773\) | 38.3339i | 1.37877i | 0.724393 | + | 0.689387i | \(0.242120\pi\) | ||||
−0.724393 | + | 0.689387i | \(0.757880\pi\) | |||||||
\(774\) | 2.29846 | 0.0826164 | ||||||||
\(775\) | −27.7383 | + | 2.36378i | −0.996389 | + | 0.0849096i | ||||
\(776\) | 6.45060 | 0.231563 | ||||||||
\(777\) | 29.7087i | 1.06579i | ||||||||
\(778\) | 27.8681 | − | 16.0896i | 0.999118 | − | 0.576841i | ||||
\(779\) | −40.3772 | −1.44666 | ||||||||
\(780\) | 9.60920 | − | 7.36993i | 0.344064 | − | 0.263886i | ||||
\(781\) | 14.2150 | + | 24.6211i | 0.508653 | + | 0.881012i | ||||
\(782\) | 40.3320 | − | 23.2857i | 1.44227 | − | 0.832695i | ||||
\(783\) | − | 5.52189i | − | 0.197336i | ||||||
\(784\) | 2.95909 | − | 5.12530i | 0.105682 | − | 0.183046i | ||||
\(785\) | 10.6660 | + | 13.9067i | 0.380685 | + | 0.496351i | ||||
\(786\) | 10.1483 | − | 17.5774i | 0.361979 | − | 0.626965i | ||||
\(787\) | 9.92956 | − | 5.73283i | 0.353951 | − | 0.204353i | −0.312473 | − | 0.949927i | \(-0.601157\pi\) |
0.666424 | + | 0.745573i | \(0.267824\pi\) | |||||||
\(788\) | 10.0616 | + | 5.80908i | 0.358430 | + | 0.206940i | ||||
\(789\) | 10.5535 | + | 18.2792i | 0.375715 | + | 0.650757i | ||||
\(790\) | 3.43020 | − | 8.27592i | 0.122041 | − | 0.294444i | ||||
\(791\) | −13.9757 | −0.496919 | ||||||||
\(792\) | 5.15537 | − | 2.97645i | 0.183188 | − | 0.105764i | ||||
\(793\) | 5.37765 | + | 3.10479i | 0.190966 | + | 0.110254i | ||||
\(794\) | 2.31056 | + | 4.00201i | 0.0819987 | + | 0.142026i | ||||
\(795\) | 8.74219 | − | 6.70496i | 0.310054 | − | 0.237801i | ||||
\(796\) | 2.53294 | − | 4.38718i | 0.0897776 | − | 0.155499i | ||||
\(797\) | 6.64854 | + | 3.83854i | 0.235504 | + | 0.135968i | 0.613108 | − | 0.789999i | \(-0.289919\pi\) |
−0.377605 | + | 0.925967i | \(0.623252\pi\) | |||||||
\(798\) | − | 16.6657i | − | 0.589959i | ||||||
\(799\) | −12.9875 | − | 22.4950i | −0.459464 | − | 0.795815i | ||||
\(800\) | −4.82904 | − | 1.29629i | −0.170732 | − | 0.0458307i | ||||
\(801\) | 5.81080 | − | 10.0646i | 0.205314 | − | 0.355615i | ||||
\(802\) | − | 2.12856i | − | 0.0751621i | ||||||
\(803\) | −9.63370 | + | 5.56202i | −0.339966 | + | 0.196279i | ||||
\(804\) | −5.58873 | −0.197099 | ||||||||
\(805\) | 67.3002 | + | 27.8946i | 2.37202 | + | 0.983154i | ||||
\(806\) | −29.6861 | − | 5.28959i | −1.04565 | − | 0.186318i | ||||
\(807\) | − | 16.7174i | − | 0.588482i | ||||||
\(808\) | − | 9.76731i | − | 0.343613i | ||||||
\(809\) | 7.74541 | + | 13.4154i | 0.272314 | + | 0.471662i | 0.969454 | − | 0.245273i | \(-0.0788777\pi\) |
−0.697140 | + | 0.716935i | \(0.745544\pi\) | |||||||
\(810\) | 0.856175 | − | 2.06566i | 0.0300829 | − | 0.0725800i | ||||
\(811\) | 11.1715 | − | 19.3496i | 0.392284 | − | 0.679456i | −0.600466 | − | 0.799650i | \(-0.705018\pi\) |
0.992750 | + | 0.120194i | \(0.0383517\pi\) | |||||||
\(812\) | 17.1878 | − | 9.92336i | 0.603172 | − | 0.348242i | ||||
\(813\) | −7.75497 | + | 4.47734i | −0.271979 | + | 0.157027i | ||||
\(814\) | −49.2052 | −1.72464 | ||||||||
\(815\) | 14.6536 | + | 19.1060i | 0.513295 | + | 0.669253i | ||||
\(816\) | 2.56882 | − | 4.44932i | 0.0899267 | − | 0.155758i | ||||
\(817\) | 9.22974 | + | 5.32879i | 0.322908 | + | 0.186431i | ||||
\(818\) | 16.5497 | − | 9.55496i | 0.578646 | − | 0.334081i | ||||
\(819\) | −9.73264 | + | 16.8574i | −0.340086 | + | 0.589046i | ||||
\(820\) | −2.53715 | − | 19.3055i | −0.0886013 | − | 0.674176i | ||||
\(821\) | −18.0664 | −0.630521 | −0.315260 | − | 0.949005i | \(-0.602092\pi\) | ||||
−0.315260 | + | 0.949005i | \(0.602092\pi\) | |||||||
\(822\) | − | 12.6387i | − | 0.440826i | ||||||
\(823\) | −7.62776 | + | 4.40389i | −0.265887 | + | 0.153510i | −0.627017 | − | 0.779006i | \(-0.715724\pi\) |
0.361130 | + | 0.932515i | \(0.382391\pi\) | |||||||
\(824\) | 0.838003 | − | 1.45146i | 0.0291932 | − | 0.0505641i | ||||
\(825\) | −28.7468 | − | 7.71668i | −1.00084 | − | 0.268660i | ||||
\(826\) | −23.9860 | + | 41.5450i | −0.834580 | + | 1.44553i | ||||
\(827\) | −13.0149 | − | 7.51413i | −0.452571 | − | 0.261292i | 0.256344 | − | 0.966586i | \(-0.417482\pi\) |
−0.708915 | + | 0.705294i | \(0.750815\pi\) | |||||||
\(828\) | −7.85031 | − | 4.53238i | −0.272817 | − | 0.157511i | ||||
\(829\) | −26.0810 | −0.905831 | −0.452916 | − | 0.891553i | \(-0.649616\pi\) | ||||
−0.452916 | + | 0.891553i | \(0.649616\pi\) | |||||||
\(830\) | 2.88802 | + | 21.9752i | 0.100244 | + | 0.762771i | ||||
\(831\) | −0.425805 | − | 0.737516i | −0.0147710 | − | 0.0255842i | ||||
\(832\) | −4.69019 | − | 2.70788i | −0.162603 | − | 0.0938789i | ||||
\(833\) | − | 30.4055i | − | 1.05349i | ||||||
\(834\) | 3.31395 | + | 5.73994i | 0.114753 | + | 0.198758i | ||||
\(835\) | 9.97358 | − | 24.0629i | 0.345150 | − | 0.832731i | ||||
\(836\) | 27.6027 | 0.954659 | ||||||||
\(837\) | −5.23541 | + | 1.89486i | −0.180962 | + | 0.0654961i | ||||
\(838\) | 30.6580i | 1.05906i | ||||||||
\(839\) | 52.7488 | 1.82109 | 0.910545 | − | 0.413410i | \(-0.135662\pi\) | ||||
0.910545 | + | 0.413410i | \(0.135662\pi\) | |||||||
\(840\) | 7.96833 | − | 1.04721i | 0.274933 | − | 0.0361322i | ||||
\(841\) | 1.49128 | 0.0514236 | ||||||||
\(842\) | −29.9603 | − | 17.2976i | −1.03250 | − | 0.596114i | ||||
\(843\) | 3.22430 | − | 1.86155i | 0.111051 | − | 0.0641152i | ||||
\(844\) | 3.91582 | + | 6.78240i | 0.134788 | + | 0.233460i | ||||
\(845\) | −33.7333 | − | 13.9818i | −1.16046 | − | 0.480988i | ||||
\(846\) | −2.52791 | + | 4.37847i | −0.0869113 | + | 0.150535i | ||||
\(847\) | 76.0642 | + | 43.9157i | 2.61360 | + | 1.50896i | ||||
\(848\) | −4.26701 | − | 2.46356i | −0.146530 | − | 0.0845990i | ||||
\(849\) | 10.6931 | + | 18.5210i | 0.366986 | + | 0.635638i | ||||
\(850\) | −24.8159 | + | 6.63732i | −0.851178 | + | 0.227658i | ||||
\(851\) | 37.4635 | + | 64.8887i | 1.28423 | + | 2.22436i | ||||
\(852\) | − | 4.77582i | − | 0.163617i | ||||||
\(853\) | 12.6356i | 0.432634i | 0.976323 | + | 0.216317i | \(0.0694045\pi\) | ||||
−0.976323 | + | 0.216317i | \(0.930596\pi\) | |||||||
\(854\) | 2.06050 | + | 3.56889i | 0.0705089 | + | 0.122125i | ||||
\(855\) | 8.22716 | − | 6.30995i | 0.281363 | − | 0.215796i | ||||
\(856\) | −1.22423 | − | 2.12044i | −0.0418435 | − | 0.0724750i | ||||
\(857\) | 10.8217 | + | 6.24790i | 0.369662 | + | 0.213424i | 0.673311 | − | 0.739360i | \(-0.264872\pi\) |
−0.303649 | + | 0.952784i | \(0.598205\pi\) | |||||||
\(858\) | −27.9202 | − | 16.1198i | −0.953182 | − | 0.550320i | ||||
\(859\) | −11.5649 | + | 20.0310i | −0.394589 | + | 0.683447i | −0.993049 | − | 0.117705i | \(-0.962446\pi\) |
0.598460 | + | 0.801153i | \(0.295780\pi\) | |||||||
\(860\) | −1.96788 | + | 4.74784i | −0.0671042 | + | 0.161900i | ||||
\(861\) | 15.6489 | + | 27.1047i | 0.533314 | + | 0.923727i | ||||
\(862\) | 6.56884 | − | 3.79252i | 0.223736 | − | 0.129174i | ||||
\(863\) | 16.5917 | + | 9.57921i | 0.564787 | + | 0.326080i | 0.755065 | − | 0.655650i | \(-0.227605\pi\) |
−0.190277 | + | 0.981730i | \(0.560939\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 25.2421 | − | 3.31736i | 0.858258 | − | 0.112794i | ||||
\(866\) | 23.7371 | 0.806620 | ||||||||
\(867\) | − | 9.39532i | − | 0.319082i | ||||||
\(868\) | −15.3066 | − | 12.8908i | −0.519539 | − | 0.437542i | ||||
\(869\) | −23.8498 | −0.809051 | ||||||||
\(870\) | 11.4064 | + | 4.72771i | 0.386712 | + | 0.160284i | ||||
\(871\) | 15.1336 | + | 26.2122i | 0.512783 | + | 0.888167i | ||||
\(872\) | 1.67713i | 0.0567949i | ||||||||
\(873\) | −5.58638 | − | 3.22530i | −0.189070 | − | 0.109160i | ||||
\(874\) | −21.0159 | − | 36.4007i | −0.710874 | − | 1.23127i | ||||
\(875\) | −31.8636 | − | 24.4843i | −1.07719 | − | 0.827721i | ||||
\(876\) | 1.86867 | 0.0631366 | ||||||||
\(877\) | 4.46956 | + | 2.58050i | 0.150926 | + | 0.0871374i | 0.573561 | − | 0.819163i | \(-0.305561\pi\) |
−0.422635 | + | 0.906300i | \(0.638895\pi\) | |||||||
\(878\) | −8.83640 | − | 5.10170i | −0.298214 | − | 0.172174i | ||||
\(879\) | 4.49828 | − | 7.79125i | 0.151723 | − | 0.262792i | ||||
\(880\) | 1.73445 | + | 13.1976i | 0.0584683 | + | 0.444891i | ||||
\(881\) | 3.89978 | − | 6.75462i | 0.131387 | − | 0.227569i | −0.792824 | − | 0.609450i | \(-0.791390\pi\) |
0.924211 | + | 0.381881i | \(0.124724\pi\) | |||||||
\(882\) | −5.12530 | + | 2.95909i | −0.172578 | + | 0.0996378i | ||||
\(883\) | 12.4007i | 0.417316i | 0.977989 | + | 0.208658i | \(0.0669096\pi\) | ||||
−0.977989 | + | 0.208658i | \(0.933090\pi\) | |||||||
\(884\) | −27.8242 | −0.935830 | ||||||||
\(885\) | −29.5906 | + | 3.88884i | −0.994677 | + | 0.130722i | ||||
\(886\) | −19.0631 | + | 33.0182i | −0.640437 | + | 1.10927i | ||||
\(887\) | 11.7260 | − | 6.76998i | 0.393719 | − | 0.227314i | −0.290051 | − | 0.957011i | \(-0.593672\pi\) |
0.683770 | + | 0.729697i | \(0.260339\pi\) | |||||||
\(888\) | 7.15835 | + | 4.13288i | 0.240219 | + | 0.138690i | ||||
\(889\) | 24.7892 | − | 42.9362i | 0.831404 | − | 1.44003i | ||||
\(890\) | 15.8150 | + | 20.6202i | 0.530120 | + | 0.691191i | ||||
\(891\) | −5.95290 | −0.199430 | ||||||||
\(892\) | 11.0560 | − | 6.38320i | 0.370183 | − | 0.213725i | ||||
\(893\) | −20.3023 | + | 11.7215i | −0.679390 | + | 0.392246i | ||||
\(894\) | 0.371288 | − | 0.643090i | 0.0124177 | − | 0.0215082i | ||||
\(895\) | 15.8338 | + | 6.56280i | 0.529267 | + | 0.219370i | ||||
\(896\) | −1.79709 | − | 3.11266i | −0.0600367 | − | 0.103987i | ||||
\(897\) | 49.0926i | 1.63915i | ||||||||
\(898\) | − | 30.7843i | − | 1.02728i | ||||||
\(899\) | −10.4632 | − | 28.9093i | −0.348968 | − | 0.964181i | ||||
\(900\) | 3.53393 | + | 3.53714i | 0.117798 | + | 0.117905i | ||||
\(901\) | −25.3137 | −0.843323 | ||||||||
\(902\) | −44.8925 | + | 25.9187i | −1.49476 | + | 0.862998i | ||||
\(903\) | − | 8.26109i | − | 0.274912i | ||||||
\(904\) | −1.94421 | + | 3.36747i | −0.0646634 | + | 0.112000i | ||||
\(905\) | −1.34334 | − | 10.2216i | −0.0446542 | − | 0.339779i | ||||
\(906\) | 2.05804 | + | 3.56463i | 0.0683738 | + | 0.118427i | ||||
\(907\) | − | 47.5948i | − | 1.58036i | −0.612876 | − | 0.790179i | \(-0.709987\pi\) | ||
0.612876 | − | 0.790179i | \(-0.290013\pi\) | |||||||
\(908\) | −2.87642 | − | 1.66070i | −0.0954574 | − | 0.0551124i | ||||
\(909\) | −4.88366 | + | 8.45874i | −0.161981 | + | 0.280559i | ||||
\(910\) | −26.4889 | − | 34.5373i | −0.878099 | − | 1.14490i | ||||
\(911\) | −12.5857 | − | 21.7991i | −0.416982 | − | 0.722235i | 0.578652 | − | 0.815575i | \(-0.303579\pi\) |
−0.995634 | + | 0.0933398i | \(0.970246\pi\) | |||||||
\(912\) | −4.01562 | − | 2.31842i | −0.132971 | − | 0.0767706i | ||||
\(913\) | 51.1006 | − | 29.5029i | 1.69118 | − | 0.976405i | ||||
\(914\) | 22.5321 | 0.745297 | ||||||||
\(915\) | −0.981668 | + | 2.36844i | −0.0324529 | + | 0.0782981i | ||||
\(916\) | 2.61956 | + | 4.53720i | 0.0865525 | + | 0.149913i | ||||
\(917\) | −63.1765 | − | 36.4750i | −2.08627 | − | 1.20451i | ||||
\(918\) | −4.44932 | + | 2.56882i | −0.146850 | + | 0.0847837i | ||||
\(919\) | 8.71806 | − | 15.1001i | 0.287582 | − | 0.498107i | −0.685650 | − | 0.727932i | \(-0.740482\pi\) |
0.973232 | + | 0.229824i | \(0.0738151\pi\) | |||||||
\(920\) | 16.0836 | − | 12.3356i | 0.530261 | − | 0.406692i | ||||
\(921\) | −8.49904 | + | 14.7208i | −0.280053 | + | 0.485066i | ||||
\(922\) | 40.8334i | 1.34477i | ||||||||
\(923\) | −22.3995 | + | 12.9324i | −0.737289 | + | 0.425674i | ||||
\(924\) | −10.6979 | − | 18.5294i | −0.351936 | − | 0.609571i | ||||
\(925\) | −10.6785 | − | 39.9254i | −0.351108 | − | 1.31274i | ||||
\(926\) | 3.98680 | 0.131014 | ||||||||
\(927\) | −1.45146 | + | 0.838003i | −0.0476723 | + | 0.0275236i | ||||
\(928\) | − | 5.52189i | − | 0.181265i | ||||||
\(929\) | −56.6111 | −1.85735 | −0.928675 | − | 0.370894i | \(-0.879051\pi\) | ||||
−0.928675 | + | 0.370894i | \(0.879051\pi\) | |||||||
\(930\) | 0.568274 | − | 12.4369i | 0.0186344 | − | 0.407823i | ||||
\(931\) | −27.4417 | −0.899365 | ||||||||
\(932\) | 14.5392i | 0.476246i | ||||||||
\(933\) | −15.1408 | + | 8.74157i | −0.495689 | + | 0.286186i | ||||
\(934\) | −21.0286 | −0.688077 | ||||||||
\(935\) | 41.6194 | + | 54.2650i | 1.36110 | + | 1.77465i | ||||
\(936\) | 2.70788 | + | 4.69019i | 0.0885099 | + | 0.153304i | ||||
\(937\) | −21.7524 | + | 12.5588i | −0.710620 | + | 0.410277i | −0.811291 | − | 0.584643i | \(-0.801235\pi\) |
0.100670 | + | 0.994920i | \(0.467901\pi\) | |||||||
\(938\) | 20.0869i | 0.655862i | ||||||||
\(939\) | −16.7175 | + | 28.9556i | −0.545556 | + | 0.944931i | ||||
\(940\) | −6.88011 | − | 8.97055i | −0.224404 | − | 0.292587i | ||||
\(941\) | 18.6613 | − | 32.3224i | 0.608343 | − | 1.05368i | −0.383171 | − | 0.923677i | \(-0.625168\pi\) |
0.991514 | − | 0.130003i | \(-0.0414987\pi\) | |||||||
\(942\) | −6.78777 | + | 3.91892i | −0.221157 | + | 0.127685i | ||||
\(943\) | 68.3598 | + | 39.4675i | 2.22610 | + | 1.28524i | ||||
\(944\) | 6.67355 | + | 11.5589i | 0.217206 | + | 0.376211i | ||||
\(945\) | −7.42438 | − | 3.07725i | −0.241515 | − | 0.100103i | ||||
\(946\) | 13.6825 | 0.444856 | ||||||||
\(947\) | −43.3767 | + | 25.0436i | −1.40955 | + | 0.813806i | −0.995345 | − | 0.0963757i | \(-0.969275\pi\) |
−0.414209 | + | 0.910182i | \(0.635942\pi\) | |||||||
\(948\) | 3.46966 | + | 2.00321i | 0.112689 | + | 0.0650613i | ||||
\(949\) | −5.06015 | − | 8.76444i | −0.164259 | − | 0.284506i | ||||
\(950\) | 5.99035 | + | 22.3970i | 0.194353 | + | 0.726653i | ||||
\(951\) | −6.94602 | + | 12.0309i | −0.225240 | + | 0.390127i | ||||
\(952\) | −15.9917 | − | 9.23282i | −0.518294 | − | 0.299237i | ||||
\(953\) | 1.90903i | 0.0618394i | 0.999522 | + | 0.0309197i | \(0.00984361\pi\) | ||||
−0.999522 | + | 0.0309197i | \(0.990156\pi\) | |||||||
\(954\) | 2.46356 | + | 4.26701i | 0.0797607 | + | 0.138150i | ||||
\(955\) | 4.45087 | + | 33.8671i | 0.144027 | + | 1.09592i | ||||
\(956\) | −11.1198 | + | 19.2600i | −0.359639 | + | 0.622913i | ||||
\(957\) | − | 32.8713i | − | 1.06258i | ||||||
\(958\) | −9.41352 | + | 5.43490i | −0.304137 | + | 0.175594i | ||||
\(959\) | −45.4259 | −1.46688 | ||||||||
\(960\) | 0.856175 | − | 2.06566i | 0.0276329 | − | 0.0666690i | ||||
\(961\) | −23.8190 | + | 19.8408i | −0.768354 | + | 0.640025i | ||||
\(962\) | − | 44.7654i | − | 1.44329i | ||||||
\(963\) | 2.44847i | 0.0789008i | ||||||||
\(964\) | 1.12616 | + | 1.95057i | 0.0362712 | + | 0.0628235i | ||||
\(965\) | 3.52027 | − | 8.49323i | 0.113322 | − | 0.273407i | ||||
\(966\) | −16.2902 | + | 28.2155i | −0.524129 | + | 0.907818i | ||||
\(967\) | −16.5586 | + | 9.56013i | −0.532490 | + | 0.307433i | −0.742030 | − | 0.670367i | \(-0.766137\pi\) |
0.209540 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(968\) | 21.1631 | − | 12.2185i | 0.680208 | − | 0.392718i | ||||
\(969\) | −23.8224 | −0.765286 | ||||||||
\(970\) | 11.4453 | − | 8.77816i | 0.367486 | − | 0.281850i | ||||
\(971\) | −19.6700 | + | 34.0694i | −0.631240 | + | 1.09334i | 0.356058 | + | 0.934464i | \(0.384120\pi\) |
−0.987299 | + | 0.158876i | \(0.949213\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | 20.6304 | − | 11.9110i | 0.661380 | − | 0.381848i | ||||
\(974\) | 15.8662 | − | 27.4811i | 0.508386 | − | 0.880550i | ||||
\(975\) | 7.02039 | − | 26.1530i | 0.224832 | − | 0.837565i | ||||
\(976\) | 1.14657 | 0.0367009 | ||||||||
\(977\) | − | 11.3539i | − | 0.363244i | −0.983368 | − | 0.181622i | \(-0.941865\pi\) | ||
0.983368 | − | 0.181622i | \(-0.0581347\pi\) | |||||||
\(978\) | −9.32551 | + | 5.38408i | −0.298197 | + | 0.172164i | ||||
\(979\) | 34.5911 | − | 59.9136i | 1.10554 | − | 1.91485i | ||||
\(980\) | −1.72433 | − | 13.1206i | −0.0550818 | − | 0.419123i | ||||
\(981\) | 0.838566 | − | 1.45244i | 0.0267734 | − | 0.0463728i | ||||
\(982\) | 6.28121 | + | 3.62646i | 0.200441 | + | 0.115725i | ||||
\(983\) | 26.8812 | + | 15.5199i | 0.857376 | + | 0.495006i | 0.863133 | − | 0.504977i | \(-0.168499\pi\) |
−0.00575657 | + | 0.999983i | \(0.501832\pi\) | |||||||
\(984\) | 8.70791 | 0.277598 | ||||||||
\(985\) | 25.7575 | − | 3.38509i | 0.820702 | − | 0.107858i | ||||
\(986\) | −14.1847 | − | 24.5687i | −0.451734 | − | 0.782426i | ||||
\(987\) | 15.7370 | + | 9.08578i | 0.500915 | + | 0.289204i | ||||
\(988\) | 25.1121i | 0.798921i | ||||||||
\(989\) | −10.4175 | − | 18.0436i | −0.331257 | − | 0.573753i | ||||
\(990\) | 5.09673 | − | 12.2967i | 0.161985 | − | 0.390815i | ||||
\(991\) | −5.06121 | −0.160775 | −0.0803874 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803874 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(992\) | −5.23541 | + | 1.89486i | −0.166224 | + | 0.0601620i | ||||
\(993\) | 4.40592i | 0.139818i | ||||||||
\(994\) | −17.1652 | −0.544447 | ||||||||
\(995\) | −1.47600 | − | 11.2311i | −0.0467925 | − | 0.356049i | ||||
\(996\) | −9.91212 | −0.314078 | ||||||||
\(997\) | −35.5407 | − | 20.5194i | −1.12558 | − | 0.649856i | −0.182764 | − | 0.983157i | \(-0.558504\pi\) |
−0.942821 | + | 0.333300i | \(0.891838\pi\) | |||||||
\(998\) | 18.9961 | − | 10.9674i | 0.601312 | − | 0.347167i | ||||
\(999\) | −4.13288 | − | 7.15835i | −0.130758 | − | 0.226480i |
(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 | 930.2.s.c.769.2 | yes | 24 | |
5.4 | even | 2 | inner | 930.2.s.c.769.9 | yes | 24 | |
31.5 | even | 3 | inner | 930.2.s.c.439.3 | ✓ | 24 | |
155.129 | even | 6 | inner | 930.2.s.c.439.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.s.c.439.3 | ✓ | 24 | 31.5 | even | 3 | inner | |
930.2.s.c.439.8 | yes | 24 | 155.129 | even | 6 | inner | |
930.2.s.c.769.2 | yes | 24 | 1.1 | even | 1 | trivial | |
930.2.s.c.769.9 | yes | 24 | 5.4 | even | 2 | inner |