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 | 439.3 | ||
Character | \(\chi\) | \(=\) | 930.439 |
Dual form | 930.2.s.c.769.9 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −0.291362 | − | 2.21700i | −0.130301 | − | 0.991474i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 3.11266 | + | 1.79709i | 1.17647 | + | 0.679238i | 0.955196 | − | 0.295973i | \(-0.0956439\pi\) |
0.221278 | + | 0.975211i | \(0.428977\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −2.21700 | + | 0.291362i | −0.701078 | + | 0.0921368i | ||||
\(11\) | 2.97645 | + | 5.15537i | 0.897434 | + | 1.55440i | 0.830763 | + | 0.556626i | \(0.187904\pi\) |
0.0666710 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −4.69019 | + | 2.70788i | −1.30082 | + | 0.751031i | −0.980546 | − | 0.196292i | \(-0.937110\pi\) |
−0.320279 | + | 0.947323i | \(0.603777\pi\) | |||||||
\(14\) | 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 | \(-0.547432\pi\) |
−0.930659 | + | 0.365888i | \(0.880765\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | −2.31842 | + | 4.01562i | −0.531882 | + | 0.921247i | 0.467425 | + | 0.884033i | \(0.345182\pi\) |
−0.999307 | + | 0.0372146i | \(0.988151\pi\) | |||||||
\(20\) | 0.291362 | + | 2.21700i | 0.0651505 | + | 0.495737i | ||||
\(21\) | −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 | ||||
\(25\) | −4.83022 | + | 1.29190i | −0.966043 | + | 0.258380i | ||||
\(26\) | 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 | \(-0.571111\pi\) |
−0.955278 | + | 0.295709i | \(0.904444\pi\) | |||||||
\(38\) | 4.01562 | + | 2.31842i | 0.651420 | + | 0.376098i | ||||
\(39\) | 5.41576 | 0.867216 | ||||||||
\(40\) | 2.21700 | − | 0.291362i | 0.350539 | − | 0.0460684i | ||||
\(41\) | 4.35396 | + | 7.54127i | 0.679974 | + | 1.17775i | 0.974988 | + | 0.222256i | \(0.0713421\pi\) |
−0.295015 | + | 0.955493i | \(0.595325\pi\) | |||||||
\(42\) | −3.11266 | + | 1.79709i | −0.480293 | + | 0.277298i | ||||
\(43\) | 1.99052 | + | 1.14923i | 0.303552 | + | 0.175256i | 0.644037 | − | 0.764994i | \(-0.277258\pi\) |
−0.340486 | + | 0.940250i | \(0.610591\pi\) | |||||||
\(44\) | −2.97645 | − | 5.15537i | −0.448717 | − | 0.777201i | ||||
\(45\) | 1.77430 | − | 1.36083i | 0.264497 | − | 0.202860i | ||||
\(46\) | 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 | ||||
\(50\) | 1.29190 | + | 4.83022i | 0.182703 | + | 0.683096i | ||||
\(51\) | 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 | \(-0.556782\pi\) |
0.763561 | + | 0.645735i | \(0.223449\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 10.5622 | − | 8.10088i | 1.42421 | − | 1.09232i | ||||
\(56\) | −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 | 0.00562217 | − | 0.999984i | \(-0.498210\pi\) |
0.863201 | − | 0.504861i | \(-0.168456\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | 7.36993 | + | 9.60920i | 0.914127 | + | 1.19187i | ||||
\(66\) | −5.95290 | −0.732752 | ||||||||
\(67\) | −4.83998 | + | 2.79437i | −0.591298 | + | 0.341386i | −0.765611 | − | 0.643304i | \(-0.777563\pi\) |
0.174313 | + | 0.984690i | \(0.444230\pi\) | |||||||
\(68\) | 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 | 0.688825 | − | 0.724927i | \(-0.258127\pi\) |
−0.972218 | + | 0.234077i | \(0.924793\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 1.61832 | − | 0.934337i | 0.189410 | − | 0.109356i | −0.402296 | − | 0.915509i | \(-0.631788\pi\) |
0.591706 | + | 0.806154i | \(0.298455\pi\) | |||||||
\(74\) | −4.13288 | + | 7.15835i | −0.480437 | + | 0.832142i | ||||
\(75\) | 4.82904 | + | 1.29629i | 0.557610 | + | 0.149682i | ||||
\(76\) | 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 | −0.956433 | − | 0.291952i | \(-0.905695\pi\) |
0.731054 | + | 0.682319i | \(0.239029\pi\) | |||||||
\(80\) | −0.291362 | − | 2.21700i | −0.0325753 | − | 0.247869i | ||||
\(81\) | −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 | \(-0.849757\pi\) |
−0.0515731 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(84\) | 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 | \(0.288775\pi\) | |||||||
\(90\) | −1.36083 | − | 1.77430i | −0.143444 | − | 0.187028i | ||||
\(91\) | −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 | ||||
\(100\) | 4.83022 | − | 1.29190i | 0.483022 | − | 0.129190i | ||||
\(101\) | −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 | \(-0.640354\pi\) |
0.569801 | + | 0.821783i | \(0.307020\pi\) | |||||||
\(104\) | −2.70788 | − | 4.69019i | −0.265530 | − | 0.459911i | ||||
\(105\) | −6.37717 | + | 4.89107i | −0.622348 | + | 0.477320i | ||||
\(106\) | −2.46356 | − | 4.26701i | −0.239282 | − | 0.414449i | ||||
\(107\) | 2.12044 | + | 1.22423i | 0.204990 | + | 0.118351i | 0.598981 | − | 0.800763i | \(-0.295572\pi\) |
−0.393991 | + | 0.919114i | \(0.628906\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 1.67713 | 0.160640 | 0.0803201 | − | 0.996769i | \(-0.474406\pi\) | ||||
0.0803201 | + | 0.996769i | \(0.474406\pi\) | |||||||
\(110\) | −8.10088 | − | 10.5622i | −0.772389 | − | 1.00707i | ||||
\(111\) | 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 | \(-0.725214\pi\) |
0.333174 | + | 0.942865i | \(0.391880\pi\) | |||||||
\(114\) | −2.31842 | − | 4.01562i | −0.217140 | − | 0.376098i | ||||
\(115\) | 20.0966 | − | 2.64113i | 1.87402 | − | 0.246286i | ||||
\(116\) | −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 | \(-0.123693\pi\) |
0.134595 | + | 0.990901i | \(0.457027\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.14923 | − | 1.99052i | −0.101184 | − | 0.175256i | ||||
\(130\) | 9.60920 | − | 7.36993i | 0.842782 | − | 0.646386i | ||||
\(131\) | 10.1483 | − | 17.5774i | 0.886663 | − | 1.53575i | 0.0428672 | − | 0.999081i | \(-0.486351\pi\) |
0.843796 | − | 0.536664i | \(-0.180316\pi\) | |||||||
\(132\) | 5.95290i | 0.518134i | ||||||||
\(133\) | −14.4329 | + | 8.33284i | −1.25149 | + | 0.722549i | ||||
\(134\) | 2.79437 | + | 4.83998i | 0.241396 | + | 0.418111i | ||||
\(135\) | −2.21700 | + | 0.291362i | −0.190809 | + | 0.0250765i | ||||
\(136\) | 2.56882 | − | 4.44932i | 0.220274 | − | 0.381526i | ||||
\(137\) | −10.9454 | + | 6.31936i | −0.935133 | + | 0.539899i | −0.888431 | − | 0.459010i | \(-0.848204\pi\) |
−0.0467015 | + | 0.998909i | \(0.514871\pi\) | |||||||
\(138\) | −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 | ||||
\(145\) | −1.60887 | − | 12.2421i | −0.133609 | − | 1.01665i | ||||
\(146\) | −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 | −0.850416 | − | 0.526111i | \(-0.823650\pi\) |
0.880833 | + | 0.473427i | \(0.156983\pi\) | |||||||
\(150\) | 1.29629 | − | 4.82904i | 0.105841 | − | 0.394290i | ||||
\(151\) | −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 | ||||||||
\(155\) | 12.1590 | + | 2.67552i | 0.976635 | + | 0.214903i | ||||
\(156\) | −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 | ||||||||
\(160\) | −2.21700 | + | 0.291362i | −0.175270 | + | 0.0230342i | ||||
\(161\) | −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 | ||||
\(165\) | −13.1976 | + | 1.73445i | −1.02743 | + | 0.135027i | ||||
\(166\) | 4.95606 | + | 8.58415i | 0.384665 | + | 0.666259i | ||||
\(167\) | 10.0883 | + | 5.82450i | 0.780658 | + | 0.450713i | 0.836663 | − | 0.547717i | \(-0.184503\pi\) |
−0.0560056 | + | 0.998430i | \(0.517836\pi\) | |||||||
\(168\) | 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 | \(-0.524186\pi\) |
0.825573 | + | 0.564296i | \(0.190852\pi\) | |||||||
\(174\) | −2.76095 | + | 4.78210i | −0.209307 | + | 0.362530i | ||||
\(175\) | −17.3565 | − | 4.65910i | −1.31203 | − | 0.352195i | ||||
\(176\) | 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 | −0.972963 | − | 0.230960i | \(-0.925813\pi\) |
0.686499 | + | 0.727131i | \(0.259147\pi\) | |||||||
\(180\) | −1.77430 | + | 1.36083i | −0.132249 | + | 0.101430i | ||||
\(181\) | −2.30528 | − | 3.99286i | −0.171350 | − | 0.296787i | 0.767542 | − | 0.640999i | \(-0.221480\pi\) |
−0.938892 | + | 0.344212i | \(0.888146\pi\) | |||||||
\(182\) | 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 | 0.998081 | + | 0.0619254i | \(0.0197241\pi\) |
−0.445411 | + | 0.895326i | \(0.646943\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 3.56077 | + | 2.05581i | 0.256310 | + | 0.147981i | 0.622650 | − | 0.782500i | \(-0.286056\pi\) |
−0.366340 | + | 0.930481i | \(0.619389\pi\) | |||||||
\(194\) | −6.45060 | −0.463126 | ||||||||
\(195\) | −1.57795 | − | 12.0068i | −0.112999 | − | 0.859823i | ||||
\(196\) | −2.95909 | − | 5.12530i | −0.211364 | − | 0.366093i | ||||
\(197\) | 10.0616 | − | 5.80908i | 0.716861 | − | 0.413880i | −0.0967354 | − | 0.995310i | \(-0.530840\pi\) |
0.813596 | + | 0.581430i | \(0.197507\pi\) | |||||||
\(198\) | 5.15537 | + | 2.97645i | 0.366376 | + | 0.211527i | ||||
\(199\) | −2.53294 | − | 4.38718i | −0.179555 | − | 0.310999i | 0.762173 | − | 0.647373i | \(-0.224132\pi\) |
−0.941728 | + | 0.336375i | \(0.890799\pi\) | |||||||
\(200\) | −1.29190 | − | 4.83022i | −0.0913513 | − | 0.341548i | ||||
\(201\) | 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 | ||||
\(205\) | 15.4505 | − | 11.8500i | 1.07911 | − | 0.827638i | ||||
\(206\) | −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 | ||||||||
\(210\) | 4.89107 | + | 6.37717i | 0.337516 | + | 0.440067i | ||||
\(211\) | −3.91582 | + | 6.78240i | −0.269576 | + | 0.466920i | −0.968752 | − | 0.248030i | \(-0.920217\pi\) |
0.699176 | + | 0.714949i | \(0.253550\pi\) | |||||||
\(212\) | −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 | ||||||||
\(220\) | −10.5622 | + | 8.10088i | −0.712106 | + | 0.546162i | ||||
\(221\) | 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 | \(-0.192745\pi\) |
−0.0818361 | + | 0.996646i | \(0.526078\pi\) | |||||||
\(224\) | 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 | \(-0.701824\pi\) |
0.401496 | + | 0.915861i | \(0.368490\pi\) | |||||||
\(228\) | −4.01562 | + | 2.31842i | −0.265941 | + | 0.153541i | ||||
\(229\) | −2.61956 | + | 4.53720i | −0.173105 | + | 0.299827i | −0.939504 | − | 0.342538i | \(-0.888713\pi\) |
0.766399 | + | 0.642365i | \(0.222047\pi\) | |||||||
\(230\) | −2.64113 | − | 20.0966i | −0.174151 | − | 1.32513i | ||||
\(231\) | 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 | ||||
\(235\) | −11.2088 | + | 1.47307i | −0.731180 | + | 0.0960928i | ||||
\(236\) | −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 | 0.961286 | + | 0.275551i | \(0.0888604\pi\) |
−0.242009 | + | 0.970274i | \(0.577806\pi\) | |||||||
\(240\) | −0.856175 | + | 2.06566i | −0.0552659 | + | 0.133338i | ||||
\(241\) | −1.12616 | + | 1.95057i | −0.0725424 | + | 0.125647i | −0.900015 | − | 0.435859i | \(-0.856445\pi\) |
0.827473 | + | 0.561506i | \(0.189778\pi\) | |||||||
\(242\) | 21.1631 | + | 12.2185i | 1.36042 | + | 0.785437i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −1.14657 | −0.0734019 | ||||||||
\(245\) | 10.5006 | − | 8.05363i | 0.670861 | − | 0.514528i | ||||
\(246\) | −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 | −0.519905 | − | 0.854224i | \(-0.674033\pi\) |
0.999732 | + | 0.0231388i | \(0.00736598\pi\) | |||||||
\(252\) | − | 3.59419i | − | 0.226413i | ||||||
\(253\) | −46.7321 | + | 26.9808i | −2.93802 | + | 1.69627i | ||||
\(254\) | 6.89703 | − | 11.9460i | 0.432758 | − | 0.749559i | ||||
\(255\) | 9.11572 | − | 6.99145i | 0.570848 | − | 0.437821i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.77882 | + | 1.60435i | −0.173338 | + | 0.100077i | −0.584159 | − | 0.811639i | \(-0.698576\pi\) |
0.410821 | + | 0.911716i | \(0.365242\pi\) | |||||||
\(258\) | −1.99052 | + | 1.14923i | −0.123925 | + | 0.0715479i | ||||
\(259\) | −14.8543 | − | 25.7285i | −0.923003 | − | 1.59869i | ||||
\(260\) | −7.36993 | − | 9.60920i | −0.457064 | − | 0.595937i | ||||
\(261\) | 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 | ||||||||
\(265\) | −6.70496 | − | 8.74219i | −0.411883 | − | 0.537028i | ||||
\(266\) | 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 | 0.999938 | + | 0.0111673i | \(0.00355472\pi\) |
−0.490298 | + | 0.871555i | \(0.663112\pi\) | |||||||
\(270\) | 0.291362 | + | 2.21700i | 0.0177317 | + | 0.134923i | ||||
\(271\) | −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 | ||||
\(285\) | −6.30995 | − | 8.22716i | −0.373769 | − | 0.487335i | ||||
\(286\) | −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 | ||||
\(290\) | −12.2421 | + | 1.60887i | −0.718878 | + | 0.0944761i | ||||
\(291\) | −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 | \(-0.417977\pi\) |
−0.710011 | + | 0.704190i | \(0.751310\pi\) | |||||||
\(294\) | −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 | ||||
\(300\) | −4.82904 | − | 1.29629i | −0.278805 | − | 0.0748412i | ||||
\(301\) | 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 | ||||
\(305\) | −0.334068 | − | 2.54196i | −0.0191287 | − | 0.145552i | ||||
\(306\) | −5.13764 | −0.293699 | ||||||||
\(307\) | 14.7208 | + | 8.49904i | 0.840158 | + | 0.485066i | 0.857318 | − | 0.514787i | \(-0.172129\pi\) |
−0.0171597 | + | 0.999853i | \(0.505462\pi\) | |||||||
\(308\) | − | 21.3959i | − | 1.21914i | ||||||
\(309\) | −1.67601 | −0.0953446 | ||||||||
\(310\) | 2.67552 | − | 12.1590i | 0.151960 | − | 0.690585i | ||||
\(311\) | −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 | 0.981969 | + | 0.189041i | \(0.0605381\pi\) |
0.654699 | + | 0.755889i | \(0.272795\pi\) | |||||||
\(314\) | −7.83784 | −0.442315 | ||||||||
\(315\) | 7.96833 | − | 1.04721i | 0.448964 | − | 0.0590036i | ||||
\(316\) | 2.00321 | − | 3.46966i | 0.112689 | − | 0.195184i | ||||
\(317\) | 12.0309 | + | 6.94602i | 0.675720 | + | 0.390127i | 0.798241 | − | 0.602339i | \(-0.205764\pi\) |
−0.122520 | + | 0.992466i | \(0.539098\pi\) | |||||||
\(318\) | 4.92712i | 0.276299i | ||||||||
\(319\) | 16.4356 | + | 28.4674i | 0.920219 | + | 1.59387i | ||||
\(320\) | 0.291362 | + | 2.21700i | 0.0162876 | + | 0.123934i | ||||
\(321\) | −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 | ||||
\(330\) | 1.73445 | + | 13.1976i | 0.0954784 | + | 0.726505i | ||||
\(331\) | −2.20296 | − | 3.81564i | −0.121086 | − | 0.209726i | 0.799110 | − | 0.601184i | \(-0.205304\pi\) |
−0.920196 | + | 0.391458i | \(0.871971\pi\) | |||||||
\(332\) | 8.58415 | − | 4.95606i | 0.471116 | − | 0.271999i | ||||
\(333\) | − | 8.26575i | − | 0.452960i | ||||||
\(334\) | 5.82450 | − | 10.0883i | 0.318702 | − | 0.552008i | ||||
\(335\) | 7.60531 | + | 9.91609i | 0.415522 | + | 0.541774i | ||||
\(336\) | −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 | \(-0.640579\pi\) |
−0.996643 | + | 0.0818642i | \(0.973913\pi\) | |||||||
\(348\) | 4.78210 | + | 2.76095i | 0.256347 | + | 0.148002i | ||||
\(349\) | 15.2039 | 0.813846 | 0.406923 | − | 0.913462i | \(-0.366602\pi\) | ||||
0.406923 | + | 0.913462i | \(0.366602\pi\) | |||||||
\(350\) | −4.65910 | + | 17.3565i | −0.249040 | + | 0.927743i | ||||
\(351\) | 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 | \(-0.444469\pi\) |
−0.766095 | + | 0.642728i | \(0.777803\pi\) | |||||||
\(354\) | 6.67355 | + | 11.5589i | 0.354695 | + | 0.614350i | ||||
\(355\) | −8.47374 | + | 6.49908i | −0.449740 | + | 0.344935i | ||||
\(356\) | −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 | 0.999299 | − | 0.0374444i | \(-0.0119217\pi\) |
−0.532077 | + | 0.846696i | \(0.678588\pi\) | |||||||
\(360\) | 1.36083 | + | 1.77430i | 0.0717220 | + | 0.0935139i | ||||
\(361\) | −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 | ||||||||
\(365\) | −2.54295 | − | 3.31559i | −0.133104 | − | 0.173546i | ||||
\(366\) | −0.573287 | + | 0.992962i | −0.0299662 | + | 0.0519030i | ||||
\(367\) | −3.85157 | + | 2.22370i | −0.201050 | + | 0.116076i | −0.597145 | − | 0.802133i | \(-0.703698\pi\) |
0.396095 | + | 0.918210i | \(0.370365\pi\) | |||||||
\(368\) | 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 | ||||||||
\(375\) | 1.46688 | − | 11.0837i | 0.0757492 | − | 0.572359i | ||||
\(376\) | 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 | −0.955869 | − | 0.293792i | \(-0.905083\pi\) |
0.732366 | + | 0.680911i | \(0.238416\pi\) | |||||||
\(380\) | −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 | \(-0.414178\pi\) |
0.967919 | + | 0.251261i | \(0.0808451\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 47.4347 | − | 6.23394i | 2.41750 | − | 0.317711i | ||||
\(386\) | 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 | −0.0929919 | − | 0.995667i | \(-0.529643\pi\) |
0.908769 | − | 0.417300i | \(-0.137024\pi\) | |||||||
\(390\) | −12.0068 | + | 1.57795i | −0.607987 | + | 0.0799025i | ||||
\(391\) | 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 | \(-0.296338\pi\) |
−0.396199 | + | 0.918165i | \(0.629671\pi\) | |||||||
\(398\) | −4.38718 | + | 2.53294i | −0.219909 | + | 0.126965i | ||||
\(399\) | 16.6657 | 0.834328 | ||||||||
\(400\) | −4.83022 | + | 1.29190i | −0.241511 | + | 0.0645951i | ||||
\(401\) | 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 | −0.527041 | − | 0.849840i | \(-0.676699\pi\) |
0.999503 | + | 0.0315108i | \(0.0100319\pi\) | |||||||
\(410\) | −11.8500 | − | 15.4505i | −0.585229 | − | 0.763044i | ||||
\(411\) | 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 | ||||
\(415\) | 13.4887 | + | 17.5871i | 0.662134 | + | 0.863316i | ||||
\(416\) | 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 | \(0.769403\pi\) | |||||||
\(420\) | 6.37717 | − | 4.89107i | 0.311174 | − | 0.238660i | ||||
\(421\) | 17.2976 | + | 29.9603i | 0.843032 | + | 1.46017i | 0.887319 | + | 0.461156i | \(0.152565\pi\) |
−0.0442873 | + | 0.999019i | \(0.514102\pi\) | |||||||
\(422\) | 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 | ||||
\(425\) | 24.8099 | + | 6.65986i | 1.20346 | + | 0.323051i | ||||
\(426\) | 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 | −0.760113 | − | 0.649791i | \(-0.774856\pi\) |
0.942792 | + | 0.333381i | \(0.108190\pi\) | |||||||
\(432\) | − | 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 | 0.961706 | − | 0.274082i | \(-0.0883741\pi\) |
−0.718215 | + | 0.695821i | \(0.755041\pi\) | |||||||
\(440\) | 8.10088 | + | 10.5622i | 0.386195 | + | 0.503535i | ||||
\(441\) | −2.95909 | + | 5.12530i | −0.140909 | + | 0.244062i | ||||
\(442\) | − | 27.8242i | − | 1.32346i | ||||||
\(443\) | 33.0182 | − | 19.0631i | 1.56874 | − | 0.905715i | 0.572429 | − | 0.819955i | \(-0.306001\pi\) |
0.996316 | − | 0.0857604i | \(-0.0273320\pi\) | |||||||
\(444\) | −4.13288 | − | 7.15835i | −0.196138 | − | 0.339720i | ||||
\(445\) | −3.38609 | − | 25.7651i | −0.160516 | − | 1.22138i | ||||
\(446\) | 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 | ||||
\(455\) | 5.67144 | + | 43.1546i | 0.265881 | + | 2.02312i | ||||
\(456\) | 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 | ||||
\(460\) | −20.0966 | + | 2.64113i | −0.937009 | + | 0.123143i | ||||
\(461\) | −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 | ||||||||
\(465\) | −9.19225 | − | 8.39658i | −0.426280 | − | 0.389382i | ||||
\(466\) | −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 | ||||||||
\(470\) | 1.47307 | + | 11.2088i | 0.0679478 | + | 0.517022i | ||||
\(471\) | −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 | ||||
\(475\) | 6.01069 | − | 22.3915i | 0.275789 | − | 1.02739i | ||||
\(476\) | 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 | −0.963062 | − | 0.269281i | \(-0.913214\pi\) |
0.714735 | + | 0.699395i | \(0.246547\pi\) | |||||||
\(480\) | 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 | ||||
\(485\) | −14.3010 | + | 1.87946i | −0.649375 | + | 0.0853419i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −27.4811 | + | 15.8662i | −1.24529 | + | 0.718966i | −0.970166 | − | 0.242444i | \(-0.922051\pi\) |
−0.275120 | + | 0.961410i | \(0.588718\pi\) | |||||||
\(488\) | 1.14657i | 0.0519030i | ||||||||
\(489\) | −5.38408 | + | 9.32551i | −0.243477 | + | 0.421714i | ||||
\(490\) | −8.05363 | − | 10.5006i | −0.363826 | − | 0.474370i | ||||
\(491\) | −3.62646 | − | 6.28121i | −0.163660 | − | 0.283467i | 0.772519 | − | 0.634992i | \(-0.218997\pi\) |
−0.936179 | + | 0.351525i | \(0.885663\pi\) | |||||||
\(492\) | 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 | −0.508977 | − | 0.860780i | \(-0.669976\pi\) |
0.999946 | + | 0.0103971i | \(0.00330957\pi\) | |||||||
\(500\) | −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 | \(-0.393659\pi\) |
−0.654194 | + | 0.756327i | \(0.726992\pi\) | |||||||
\(504\) | −3.59419 | −0.160098 | ||||||||
\(505\) | 2.84582 | + | 21.6542i | 0.126638 | + | 0.963598i | ||||
\(506\) | 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 | 0.714413 | − | 0.699724i | \(-0.246694\pi\) |
−0.963185 | + | 0.268838i | \(0.913360\pi\) | |||||||
\(510\) | −6.99145 | − | 9.11572i | −0.309586 | − | 0.403651i | ||||
\(511\) | 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 | ||||
\(515\) | −2.28076 | − | 2.97374i | −0.100502 | − | 0.131039i | ||||
\(516\) | 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 | ||||||||
\(520\) | −9.60920 | + | 7.36993i | −0.421391 | + | 0.323193i | ||||
\(521\) | 13.8234 | − | 23.9428i | 0.605613 | − | 1.04895i | −0.386341 | − | 0.922356i | \(-0.626261\pi\) |
0.991954 | − | 0.126597i | \(-0.0404054\pi\) | |||||||
\(522\) | 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 | ||||||||
\(530\) | −8.74219 | + | 6.70496i | −0.379736 | + | 0.291245i | ||||
\(531\) | 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 | ||||
\(540\) | 2.21700 | − | 0.291362i | 0.0954047 | − | 0.0125382i | ||||
\(541\) | 2.94961 | − | 5.10887i | 0.126813 | − | 0.219647i | −0.795627 | − | 0.605787i | \(-0.792858\pi\) |
0.922440 | + | 0.386140i | \(0.126192\pi\) | |||||||
\(542\) | 8.95467i | 0.384636i | ||||||||
\(543\) | 4.61056i | 0.197858i | ||||||||
\(544\) | −2.56882 | + | 4.44932i | −0.110137 | + | 0.190763i | ||||
\(545\) | −0.488653 | − | 3.71821i | −0.0209316 | − | 0.159271i | ||||
\(546\) | 9.73264 | − | 16.8574i | 0.416518 | − | 0.721431i | ||||
\(547\) | 9.81072 | − | 5.66422i | 0.419476 | − | 0.242185i | −0.275377 | − | 0.961336i | \(-0.588803\pi\) |
0.694853 | + | 0.719152i | \(0.255469\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | 14.6659 | − | 11.2483i | 0.622534 | − | 0.477463i | ||||
\(556\) | 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 | \(-0.398097\pi\) |
0.979373 | + | 0.202061i | \(0.0647639\pi\) | |||||||
\(564\) | 2.52791 | − | 4.37847i | 0.106444 | − | 0.184367i | ||||
\(565\) | 5.29147 | + | 6.89922i | 0.222614 | + | 0.290253i | ||||
\(566\) | 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 | 0.918177 | − | 0.396170i | \(-0.129661\pi\) |
−0.802182 | + | 0.597080i | \(0.796328\pi\) | |||||||
\(570\) | −8.22716 | + | 6.30995i | −0.344598 | + | 0.264295i | ||||
\(571\) | 22.6987 | + | 39.3153i | 0.949911 | + | 1.64529i | 0.745606 | + | 0.666387i | \(0.232160\pi\) |
0.204305 | + | 0.978907i | \(0.434506\pi\) | |||||||
\(572\) | 27.9202 | + | 16.1198i | 1.16740 | + | 0.674001i | ||||
\(573\) | − | 15.2761i | − | 0.638168i | ||||||
\(574\) | 31.2979 | 1.30635 | ||||||||
\(575\) | −11.7108 | − | 43.7847i | −0.488373 | − | 1.82595i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 10.3544 | + | 5.97812i | 0.431060 | + | 0.248872i | 0.699798 | − | 0.714341i | \(-0.253273\pi\) |
−0.268738 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(578\) | 8.13659 | − | 4.69766i | 0.338437 | − | 0.195397i | ||||
\(579\) | −2.05581 | − | 3.56077i | −0.0854366 | − | 0.147981i | ||||
\(580\) | 1.60887 | + | 12.2421i | 0.0668047 | + | 0.508324i | ||||
\(581\) | −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 | ||||
\(595\) | −32.7636 | + | 25.1286i | −1.34318 | + | 1.03017i | ||||
\(596\) | −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 | 0.875515 | − | 0.483192i | \(-0.160523\pi\) |
−0.856214 | + | 0.516622i | \(0.827189\pi\) | |||||||
\(600\) | −1.29629 | + | 4.82904i | −0.0529207 | + | 0.197145i | ||||
\(601\) | 16.3314 | − | 28.2868i | 0.666172 | − | 1.15384i | −0.312795 | − | 0.949821i | \(-0.601265\pi\) |
0.978966 | − | 0.204022i | \(-0.0654015\pi\) | |||||||
\(602\) | 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 | \(-0.693128\pi\) |
0.426363 | + | 0.904552i | \(0.359795\pi\) | |||||||
\(608\) | 4.01562 | + | 2.31842i | 0.162855 | + | 0.0940244i | ||||
\(609\) | −9.92336 | − | 17.1878i | −0.402115 | − | 0.696483i | ||||
\(610\) | −2.54196 | + | 0.334068i | −0.102921 | + | 0.0135260i | ||||
\(611\) | 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 | \(-0.387412\pi\) |
−0.639227 | + | 0.769018i | \(0.720745\pi\) | |||||||
\(614\) | 8.49904 | − | 14.7208i | 0.342993 | − | 0.594082i | ||||
\(615\) | −19.3055 | + | 2.53715i | −0.778472 | + | 0.102308i | ||||
\(616\) | −21.3959 | −0.862063 | ||||||||
\(617\) | −6.05354 | − | 3.49502i | −0.243706 | − | 0.140704i | 0.373173 | − | 0.927762i | \(-0.378270\pi\) |
−0.616879 | + | 0.787058i | \(0.711603\pi\) | |||||||
\(618\) | 1.67601i | 0.0674188i | ||||||||
\(619\) | 21.1473 | 0.849982 | 0.424991 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424991 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(620\) | −12.1590 | − | 2.67552i | −0.488318 | − | 0.107452i | ||||
\(621\) | 9.06476 | 0.363756 | ||||||||
\(622\) | 17.4831i | 0.701010i | ||||||||
\(623\) | 36.1740 | + | 20.8851i | 1.44928 | + | 0.836744i | ||||
\(624\) | 5.41576 | 0.216804 | ||||||||
\(625\) | 21.6620 | − | 12.4803i | 0.866479 | − | 0.499213i | ||||
\(626\) | 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 | ||||
\(630\) | −1.04721 | − | 7.96833i | −0.0417218 | − | 0.317466i | ||||
\(631\) | 10.9873 | + | 19.0306i | 0.437399 | + | 0.757598i | 0.997488 | − | 0.0708346i | \(-0.0225662\pi\) |
−0.560089 | + | 0.828433i | \(0.689233\pi\) | |||||||
\(632\) | −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 | ||||
\(640\) | 2.21700 | − | 0.291362i | 0.0876348 | − | 0.0115171i | ||||
\(641\) | −19.2323 | − | 33.3113i | −0.759631 | − | 1.31572i | −0.943039 | − | 0.332682i | \(-0.892046\pi\) |
0.183409 | − | 0.983037i | \(-0.441287\pi\) | |||||||
\(642\) | −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 | ||||
\(645\) | −4.07816 | + | 3.12781i | −0.160577 | + | 0.123157i | ||||
\(646\) | −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 | \(0.567038\pi\) | |||||||
\(660\) | 13.1976 | − | 1.73445i | 0.513716 | − | 0.0675134i | ||||
\(661\) | −18.9020 | − | 32.7391i | −0.735201 | − | 1.27341i | −0.954635 | − | 0.297778i | \(-0.903755\pi\) |
0.219434 | − | 0.975627i | \(-0.429579\pi\) | |||||||
\(662\) | −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 | ||||
\(665\) | 22.6791 | + | 29.5699i | 0.879460 | + | 1.14667i | ||||
\(666\) | −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 | ||||
\(670\) | 9.91609 | − | 7.60531i | 0.383092 | − | 0.293819i | ||||
\(671\) | 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 | \(-0.614789\pi\) |
0.633894 | + | 0.773420i | \(0.281455\pi\) | |||||||
\(674\) | 8.34153 | 0.321304 | ||||||||
\(675\) | 1.29190 | + | 4.83022i | 0.0497253 | + | 0.185915i | ||||
\(676\) | −8.16525 | + | 14.1426i | −0.314048 | + | 0.543948i | ||||
\(677\) | −5.96039 | + | 3.44123i | −0.229076 | + | 0.132257i | −0.610146 | − | 0.792289i | \(-0.708889\pi\) |
0.381070 | + | 0.924546i | \(0.375556\pi\) | |||||||
\(678\) | − | 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 | ||||||||
\(685\) | 17.1991 | + | 22.4249i | 0.657145 | + | 0.856811i | ||||
\(686\) | −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 | −0.801683 | − | 0.597749i | \(-0.796062\pi\) |
−0.116825 | − | 0.993153i | \(-0.537272\pi\) | |||||||
\(692\) | −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 | ||||
\(695\) | 1.93112 | + | 14.6941i | 0.0732516 | + | 0.557379i | ||||
\(696\) | 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 | ||||
\(700\) | 17.3565 | + | 4.65910i | 0.656013 | + | 0.176098i | ||||
\(701\) | 7.46350 | − | 12.9272i | 0.281893 | − | 0.488252i | −0.689958 | − | 0.723849i | \(-0.742371\pi\) |
0.971851 | + | 0.235597i | \(0.0757045\pi\) | |||||||
\(702\) | 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 | \(0.735651\pi\) | |||||||
\(710\) | 6.49908 | + | 8.47374i | 0.243906 | + | 0.318014i | ||||
\(711\) | −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 | −0.0591865 | − | 0.998247i | \(-0.518851\pi\) |
0.894100 | − | 0.447866i | \(-0.147816\pi\) | |||||||
\(720\) | 1.77430 | − | 1.36083i | 0.0661243 | − | 0.0507151i | ||||
\(721\) | 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 | ||||
\(725\) | −26.6719 | + | 7.13374i | −0.990571 | + | 0.264941i | ||||
\(726\) | −12.2185 | − | 21.1631i | −0.453472 | − | 0.785437i | ||||
\(727\) | −6.22980 | − | 3.59677i | −0.231050 | − | 0.133397i | 0.380006 | − | 0.924984i | \(-0.375922\pi\) |
−0.611057 | + | 0.791587i | \(0.709255\pi\) | |||||||
\(728\) | − | 19.4653i | − | 0.721431i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −3.31559 | + | 2.54295i | −0.122715 | + | 0.0941186i | ||||
\(731\) | −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 | \(-0.715053\pi\) |
0.363095 | + | 0.931752i | \(0.381720\pi\) | |||||||
\(734\) | 2.22370 | + | 3.85157i | 0.0820784 | + | 0.142164i | ||||
\(735\) | −13.1206 | + | 1.72433i | −0.483962 | + | 0.0636030i | ||||
\(736\) | 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 | −0.998879 | − | 0.0473456i | \(-0.984924\pi\) |
0.458437 | − | 0.888727i | \(-0.348410\pi\) | |||||||
\(740\) | 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 | ||||
\(750\) | −11.0837 | − | 1.46688i | −0.404719 | − | 0.0535628i | ||||
\(751\) | −9.28329 | + | 16.0791i | −0.338752 | + | 0.586736i | −0.984198 | − | 0.177070i | \(-0.943338\pi\) |
0.645446 | + | 0.763806i | \(0.276671\pi\) | |||||||
\(752\) | − | 5.05582i | − | 0.184367i | ||||||
\(753\) | −13.1669 | + | 7.60189i | −0.479827 | + | 0.277028i | ||||
\(754\) | 14.9526 | + | 25.8987i | 0.544543 | + | 0.943176i | ||||
\(755\) | 1.19927 | + | 9.12536i | 0.0436459 | + | 0.332106i | ||||
\(756\) | −1.79709 | + | 3.11266i | −0.0653597 | + | 0.113206i | ||||
\(757\) | 10.6644 | − | 6.15708i | 0.387603 | − | 0.223783i | −0.293518 | − | 0.955954i | \(-0.594826\pi\) |
0.681121 | + | 0.732171i | \(0.261493\pi\) | |||||||
\(758\) | 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 | −0.530012 | − | 0.847990i | \(-0.677813\pi\) |
0.999387 | + | 0.0350090i | \(0.0111460\pi\) | |||||||
\(762\) | −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 | ||||
\(765\) | −11.3902 | + | 1.49691i | −0.411812 | + | 0.0541210i | ||||
\(766\) | −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 | 0.294123 | + | 0.955768i | \(0.404973\pi\) |
−0.974780 | + | 0.223166i | \(0.928361\pi\) | |||||||
\(770\) | −6.23394 | − | 47.4347i | −0.224656 | − | 1.70943i | ||||
\(771\) | 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 | ||||||||
\(775\) | 2.38897 | − | 27.7361i | 0.0858145 | − | 0.996311i | ||||
\(776\) | 6.45060 | 0.231563 | ||||||||
\(777\) | 29.7087i | 1.06579i | ||||||||
\(778\) | −27.8681 | − | 16.0896i | −0.999118 | − | 0.576841i | ||||
\(779\) | −40.3772 | −1.44666 | ||||||||
\(780\) | 1.57795 | + | 12.0068i | 0.0564996 | + | 0.429911i | ||||
\(781\) | 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 | ||||
\(785\) | −17.3765 | + | 2.28365i | −0.620195 | + | 0.0815070i | ||||
\(786\) | 10.1483 | + | 17.5774i | 0.361979 | + | 0.626965i | ||||
\(787\) | −9.92956 | − | 5.73283i | −0.353951 | − | 0.204353i | 0.312473 | − | 0.949927i | \(-0.398843\pi\) |
−0.666424 | + | 0.745573i | \(0.732176\pi\) | |||||||
\(788\) | −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 | ||||
\(795\) | 1.43558 | + | 10.9234i | 0.0509146 | + | 0.387415i | ||||
\(796\) | 2.53294 | + | 4.38718i | 0.0897776 | + | 0.155499i | ||||
\(797\) | −6.64854 | + | 3.83854i | −0.235504 | + | 0.135968i | −0.613108 | − | 0.789999i | \(-0.710081\pi\) |
0.377605 | + | 0.925967i | \(0.376748\pi\) | |||||||
\(798\) | − | 16.6657i | − | 0.589959i | ||||||
\(799\) | −12.9875 | + | 22.4950i | −0.459464 | + | 0.795815i | ||||
\(800\) | 1.29190 | + | 4.83022i | 0.0456756 | + | 0.170774i | ||||
\(801\) | 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 | −0.697140 | − | 0.716935i | \(-0.745544\pi\) |
0.969454 | + | 0.245273i | \(0.0788777\pi\) | |||||||
\(810\) | 0.856175 | − | 2.06566i | 0.0300829 | − | 0.0725800i | ||||
\(811\) | 11.1715 | + | 19.3496i | 0.392284 | + | 0.679456i | 0.992750 | − | 0.120194i | \(-0.0383517\pi\) |
−0.600466 | + | 0.799650i | \(0.705018\pi\) | |||||||
\(812\) | −17.1878 | − | 9.92336i | −0.603172 | − | 0.348242i | ||||
\(813\) | 7.75497 | + | 4.47734i | 0.271979 | + | 0.157027i | ||||
\(814\) | −49.2052 | −1.72464 | ||||||||
\(815\) | −23.8731 | + | 3.13744i | −0.836237 | + | 0.109900i | ||||
\(816\) | 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 | ||||
\(820\) | −15.4505 | + | 11.8500i | −0.539553 | + | 0.413819i | ||||
\(821\) | −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 | \(-0.284276\pi\) |
−0.361130 | + | 0.932515i | \(0.617609\pi\) | |||||||
\(824\) | 0.838003 | + | 1.45146i | 0.0291932 | + | 0.0505641i | ||||
\(825\) | 7.69057 | + | 28.7538i | 0.267751 | + | 1.00108i | ||||
\(826\) | −23.9860 | − | 41.5450i | −0.834580 | − | 1.44553i | ||||
\(827\) | 13.0149 | − | 7.51413i | 0.452571 | − | 0.261292i | −0.256344 | − | 0.966586i | \(-0.582518\pi\) |
0.708915 | + | 0.705294i | \(0.249185\pi\) | |||||||
\(828\) | 7.85031 | − | 4.53238i | 0.272817 | − | 0.157511i | ||||
\(829\) | −26.0810 | −0.905831 | −0.452916 | − | 0.891553i | \(-0.649616\pi\) | ||||
−0.452916 | + | 0.891553i | \(0.649616\pi\) | |||||||
\(830\) | 17.5871 | − | 13.4887i | 0.610457 | − | 0.468200i | ||||
\(831\) | −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 | \(0.135662\pi\) | |||||||
\(840\) | −4.89107 | − | 6.37717i | −0.168758 | − | 0.220033i | ||||
\(841\) | 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 | ||||
\(850\) | 6.65986 | − | 24.8099i | 0.228431 | − | 0.850971i | ||||
\(851\) | 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 | ||||
\(855\) | 1.35100 | + | 10.2799i | 0.0462032 | + | 0.351565i | ||||
\(856\) | −1.22423 | + | 2.12044i | −0.0418435 | + | 0.0724750i | ||||
\(857\) | −10.8217 | + | 6.24790i | −0.369662 | + | 0.213424i | −0.673311 | − | 0.739360i | \(-0.735128\pi\) |
0.303649 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(858\) | 27.9202 | − | 16.1198i | 0.953182 | − | 0.550320i | ||||
\(859\) | −11.5649 | − | 20.0310i | −0.394589 | − | 0.683447i | 0.598460 | − | 0.801153i | \(-0.295780\pi\) |
−0.993049 | + | 0.117705i | \(0.962446\pi\) | |||||||
\(860\) | −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 | \(-0.772395\pi\) |
0.190277 | + | 0.981730i | \(0.439061\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −15.4940 | − | 20.2016i | −0.526811 | − | 0.686876i | ||||
\(866\) | 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 | ||||
\(875\) | −5.27223 | + | 39.8369i | −0.178234 | + | 1.34673i | ||||
\(876\) | 1.86867 | 0.0631366 | ||||||||
\(877\) | −4.46956 | + | 2.58050i | −0.150926 | + | 0.0871374i | −0.573561 | − | 0.819163i | \(-0.694439\pi\) |
0.422635 | + | 0.906300i | \(0.361105\pi\) | |||||||
\(878\) | 8.83640 | − | 5.10170i | 0.298214 | − | 0.172174i | ||||
\(879\) | 4.49828 | + | 7.79125i | 0.151723 | + | 0.262792i | ||||
\(880\) | 10.5622 | − | 8.10088i | 0.356053 | − | 0.273081i | ||||
\(881\) | 3.89978 | + | 6.75462i | 0.131387 | + | 0.227569i | 0.924211 | − | 0.381881i | \(-0.124724\pi\) |
−0.792824 | + | 0.609450i | \(0.791390\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | 18.1631 | + | 23.6818i | 0.610547 | + | 0.796055i | ||||
\(886\) | −19.0631 | − | 33.0182i | −0.640437 | − | 1.10927i | ||||
\(887\) | −11.7260 | − | 6.76998i | −0.393719 | − | 0.227314i | 0.290051 | − | 0.957011i | \(-0.406328\pi\) |
−0.683770 | + | 0.729697i | \(0.739661\pi\) | |||||||
\(888\) | −7.15835 | + | 4.13288i | −0.240219 | + | 0.138690i | ||||
\(889\) | 24.7892 | + | 42.9362i | 0.831404 | + | 1.44003i | ||||
\(890\) | −25.7651 | + | 3.38609i | −0.863649 | + | 0.113502i | ||||
\(891\) | −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 | ||||
\(905\) | −8.18052 | + | 6.27419i | −0.271930 | + | 0.208561i | ||||
\(906\) | 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 | ||||
\(910\) | 43.1546 | − | 5.67144i | 1.43056 | − | 0.188006i | ||||
\(911\) | −12.5857 | + | 21.7991i | −0.416982 | + | 0.722235i | −0.995634 | − | 0.0933398i | \(-0.970246\pi\) |
0.578652 | + | 0.815575i | \(0.303579\pi\) | |||||||
\(912\) | 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 | 0.973232 | − | 0.229824i | \(-0.0738151\pi\) |
−0.685650 | + | 0.727932i | \(0.740482\pi\) | |||||||
\(920\) | 2.64113 | + | 20.0966i | 0.0870753 | + | 0.662565i | ||||
\(921\) | −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 | ||||
\(925\) | 39.9157 | + | 10.7148i | 1.31242 | + | 0.352300i | ||||
\(926\) | 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 | \(0.879051\pi\) | |||||||
\(930\) | −8.39658 | + | 9.19225i | −0.275335 | + | 0.301426i | ||||
\(931\) | −27.4417 | −0.899365 | ||||||||
\(932\) | 14.5392i | 0.476246i | ||||||||
\(933\) | 15.1408 | + | 8.74157i | 0.495689 | + | 0.286186i | ||||
\(934\) | −21.0286 | −0.688077 | ||||||||
\(935\) | −67.8046 | + | 8.91098i | −2.21745 | + | 0.291420i | ||||
\(936\) | 2.70788 | − | 4.69019i | 0.0885099 | − | 0.153304i | ||||
\(937\) | 21.7524 | + | 12.5588i | 0.710620 | + | 0.410277i | 0.811291 | − | 0.584643i | \(-0.198765\pi\) |
−0.100670 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(938\) | 20.0869i | 0.655862i | ||||||||
\(939\) | −16.7175 | − | 28.9556i | −0.545556 | − | 0.944931i | ||||
\(940\) | 11.2088 | − | 1.47307i | 0.365590 | − | 0.0480464i | ||||
\(941\) | 18.6613 | + | 32.3224i | 0.608343 | + | 1.05368i | 0.991514 | + | 0.130003i | \(0.0414987\pi\) |
−0.383171 | + | 0.923677i | \(0.625168\pi\) | |||||||
\(942\) | 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 | \(-0.0307250\pi\) |
0.414209 | + | 0.910182i | \(0.364058\pi\) | |||||||
\(948\) | −3.46966 | + | 2.00321i | −0.112689 | + | 0.0650613i | ||||
\(949\) | −5.06015 | + | 8.76444i | −0.164259 | + | 0.284506i | ||||
\(950\) | −22.3915 | − | 6.01069i | −0.726476 | − | 0.195012i | ||||
\(951\) | −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 | ||||
\(955\) | 27.1044 | − | 20.7881i | 0.877077 | − | 0.672688i | ||||
\(956\) | −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 | \(-0.233863\pi\) |
−0.209540 | + | 0.977800i | \(0.567197\pi\) | |||||||
\(968\) | −21.1631 | − | 12.2185i | −0.680208 | − | 0.392718i | ||||
\(969\) | −23.8224 | −0.765286 | ||||||||
\(970\) | 1.87946 | + | 14.3010i | 0.0603458 | + | 0.459178i | ||||
\(971\) | −19.6700 | − | 34.0694i | −0.631240 | − | 1.09334i | −0.987299 | − | 0.158876i | \(-0.949213\pi\) |
0.356058 | − | 0.934464i | \(-0.384120\pi\) | |||||||
\(972\) | −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 | ||||
\(975\) | −26.1593 | + | 6.99664i | −0.837769 | + | 0.224072i | ||||
\(976\) | 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 | ||||
\(980\) | −10.5006 | + | 8.05363i | −0.335430 | + | 0.257264i | ||||
\(981\) | 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 | \(-0.831501\pi\) |
0.00575657 | + | 0.999983i | \(0.498168\pi\) | |||||||
\(984\) | 8.70791 | 0.277598 | ||||||||
\(985\) | −15.8103 | − | 20.6141i | −0.503759 | − | 0.656820i | ||||
\(986\) | −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 | ||||||||
\(995\) | −8.98839 | + | 6.89379i | −0.284951 | + | 0.218548i | ||||
\(996\) | −9.91212 | −0.314078 | ||||||||
\(997\) | 35.5407 | − | 20.5194i | 1.12558 | − | 0.649856i | 0.182764 | − | 0.983157i | \(-0.441496\pi\) |
0.942821 | + | 0.333300i | \(0.108162\pi\) | |||||||
\(998\) | −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.439.3 | ✓ | 24 | |
5.4 | even | 2 | inner | 930.2.s.c.439.8 | yes | 24 | |
31.25 | even | 3 | inner | 930.2.s.c.769.2 | yes | 24 | |
155.149 | even | 6 | inner | 930.2.s.c.769.9 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.s.c.439.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
930.2.s.c.439.8 | yes | 24 | 5.4 | even | 2 | inner | |
930.2.s.c.769.2 | yes | 24 | 31.25 | even | 3 | inner | |
930.2.s.c.769.9 | yes | 24 | 155.149 | even | 6 | inner |