Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(439,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.o (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 439.11 | ||
Character | \(\chi\) | \(=\) | 770.439 |
Dual form | 770.2.o.a.549.11 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.340512 | − | 0.589784i | −0.196595 | − | 0.340512i | 0.750827 | − | 0.660498i | \(-0.229655\pi\) |
−0.947422 | + | 0.319986i | \(0.896322\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.37482 | − | 1.76348i | 0.614838 | − | 0.788653i | ||||
\(6\) | 0.681024 | 0.278027 | ||||||||
\(7\) | 2.52726 | − | 0.782908i | 0.955215 | − | 0.295911i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.26810 | − | 2.19642i | 0.422701 | − | 0.732140i | ||||
\(10\) | 0.839811 | + | 2.07237i | 0.265571 | + | 0.655341i | ||||
\(11\) | −3.24014 | − | 0.708161i | −0.976939 | − | 0.213519i | ||||
\(12\) | −0.340512 | + | 0.589784i | −0.0982973 | + | 0.170256i | ||||
\(13\) | − | 2.05099i | − | 0.568842i | −0.958699 | − | 0.284421i | \(-0.908199\pi\) | ||
0.958699 | − | 0.284421i | \(-0.0918013\pi\) | |||||||
\(14\) | −0.585613 | + | 2.58013i | −0.156512 | + | 0.689568i | ||||
\(15\) | −1.50822 | − | 0.210360i | −0.389420 | − | 0.0543147i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.89411 | − | 1.67092i | 0.701925 | − | 0.405257i | −0.106139 | − | 0.994351i | \(-0.533849\pi\) |
0.808064 | + | 0.589095i | \(0.200515\pi\) | |||||||
\(18\) | 1.26810 | + | 2.19642i | 0.298895 | + | 0.517701i | ||||
\(19\) | −2.31422 | + | 4.00835i | −0.530919 | + | 0.919578i | 0.468430 | + | 0.883501i | \(0.344820\pi\) |
−0.999349 | + | 0.0360778i | \(0.988514\pi\) | |||||||
\(20\) | −2.21463 | − | 0.308888i | −0.495206 | − | 0.0690694i | ||||
\(21\) | −1.32231 | − | 1.22395i | −0.288552 | − | 0.267088i | ||||
\(22\) | 2.23336 | − | 2.45196i | 0.476153 | − | 0.522760i | ||||
\(23\) | −2.24798 | − | 1.29787i | −0.468737 | − | 0.270625i | 0.246974 | − | 0.969022i | \(-0.420564\pi\) |
−0.715711 | + | 0.698397i | \(0.753897\pi\) | |||||||
\(24\) | −0.340512 | − | 0.589784i | −0.0695067 | − | 0.120389i | ||||
\(25\) | −1.21974 | − | 4.84894i | −0.243948 | − | 0.969788i | ||||
\(26\) | 1.77621 | + | 1.02549i | 0.348343 | + | 0.201116i | ||||
\(27\) | −3.77029 | −0.725593 | ||||||||
\(28\) | −1.94165 | − | 1.79722i | −0.366937 | − | 0.339643i | ||||
\(29\) | 0.208603i | 0.0387366i | 0.999812 | + | 0.0193683i | \(0.00616551\pi\) | ||||
−0.999812 | + | 0.0193683i | \(0.993834\pi\) | |||||||
\(30\) | 0.936285 | − | 1.20097i | 0.170942 | − | 0.219267i | ||||
\(31\) | −7.69058 | + | 4.44016i | −1.38127 | + | 0.797476i | −0.992310 | − | 0.123778i | \(-0.960499\pi\) |
−0.388960 | + | 0.921255i | \(0.627165\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.685645 | + | 2.15212i | 0.119355 | + | 0.374636i | ||||
\(34\) | 3.34183i | 0.573120i | ||||||||
\(35\) | 2.09389 | − | 5.53314i | 0.353931 | − | 0.935271i | ||||
\(36\) | −2.53621 | −0.422701 | ||||||||
\(37\) | 3.14069 | + | 1.81328i | 0.516326 | + | 0.298101i | 0.735430 | − | 0.677600i | \(-0.236980\pi\) |
−0.219104 | + | 0.975702i | \(0.570313\pi\) | |||||||
\(38\) | −2.31422 | − | 4.00835i | −0.375416 | − | 0.650240i | ||||
\(39\) | −1.20964 | + | 0.698386i | −0.193697 | + | 0.111831i | ||||
\(40\) | 1.37482 | − | 1.76348i | 0.217378 | − | 0.278831i | ||||
\(41\) | −6.23454 | −0.973671 | −0.486836 | − | 0.873494i | \(-0.661849\pi\) | ||||
−0.486836 | + | 0.873494i | \(0.661849\pi\) | |||||||
\(42\) | 1.72113 | − | 0.533179i | 0.265576 | − | 0.0822713i | ||||
\(43\) | 6.55137 | 0.999074 | 0.499537 | − | 0.866292i | \(-0.333503\pi\) | ||||
0.499537 | + | 0.866292i | \(0.333503\pi\) | |||||||
\(44\) | 1.00678 | + | 3.16012i | 0.151778 | + | 0.476407i | ||||
\(45\) | −2.12993 | − | 5.25596i | −0.317512 | − | 0.783512i | ||||
\(46\) | 2.24798 | − | 1.29787i | 0.331447 | − | 0.191361i | ||||
\(47\) | 6.57571 | − | 11.3895i | 0.959166 | − | 1.66132i | 0.234633 | − | 0.972084i | \(-0.424611\pi\) |
0.724533 | − | 0.689240i | \(-0.242056\pi\) | |||||||
\(48\) | 0.681024 | 0.0982973 | ||||||||
\(49\) | 5.77411 | − | 3.95723i | 0.824873 | − | 0.565318i | ||||
\(50\) | 4.80918 | + | 1.36814i | 0.680120 | + | 0.193485i | ||||
\(51\) | −1.97096 | − | 1.13793i | −0.275990 | − | 0.159343i | ||||
\(52\) | −1.77621 | + | 1.02549i | −0.246316 | + | 0.142210i | ||||
\(53\) | −3.20093 | + | 1.84806i | −0.439682 | + | 0.253850i | −0.703463 | − | 0.710732i | \(-0.748364\pi\) |
0.263781 | + | 0.964583i | \(0.415030\pi\) | |||||||
\(54\) | 1.88514 | − | 3.26517i | 0.256536 | − | 0.444333i | ||||
\(55\) | −5.70344 | + | 4.74034i | −0.769052 | + | 0.639187i | ||||
\(56\) | 2.52726 | − | 0.782908i | 0.337720 | − | 0.104620i | ||||
\(57\) | 3.15208 | 0.417503 | ||||||||
\(58\) | −0.180656 | − | 0.104302i | −0.0237213 | − | 0.0136955i | ||||
\(59\) | 4.99271 | − | 2.88254i | 0.649995 | − | 0.375275i | −0.138459 | − | 0.990368i | \(-0.544215\pi\) |
0.788454 | + | 0.615093i | \(0.210882\pi\) | |||||||
\(60\) | 0.571931 | + | 1.41133i | 0.0738360 | + | 0.182202i | ||||
\(61\) | 5.38616 | − | 9.32910i | 0.689627 | − | 1.19447i | −0.282331 | − | 0.959317i | \(-0.591108\pi\) |
0.971959 | − | 0.235152i | \(-0.0755589\pi\) | |||||||
\(62\) | − | 8.88032i | − | 1.12780i | ||||||
\(63\) | 1.48523 | − | 6.54374i | 0.187122 | − | 0.824433i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.61688 | − | 2.81974i | −0.448619 | − | 0.349746i | ||||
\(66\) | −2.20661 | − | 0.482275i | −0.271615 | − | 0.0593639i | ||||
\(67\) | −1.44891 | + | 0.836530i | −0.177013 | + | 0.102198i | −0.585888 | − | 0.810392i | \(-0.699254\pi\) |
0.408876 | + | 0.912590i | \(0.365921\pi\) | |||||||
\(68\) | −2.89411 | − | 1.67092i | −0.350963 | − | 0.202628i | ||||
\(69\) | 1.76777i | 0.212814i | ||||||||
\(70\) | 3.74490 | + | 4.57993i | 0.447601 | + | 0.547406i | ||||
\(71\) | 5.74537 | 0.681850 | 0.340925 | − | 0.940091i | \(-0.389260\pi\) | ||||
0.340925 | + | 0.940091i | \(0.389260\pi\) | |||||||
\(72\) | 1.26810 | − | 2.19642i | 0.149447 | − | 0.258850i | ||||
\(73\) | −6.62663 | + | 3.82589i | −0.775589 | + | 0.447786i | −0.834865 | − | 0.550455i | \(-0.814454\pi\) |
0.0592759 | + | 0.998242i | \(0.481121\pi\) | |||||||
\(74\) | −3.14069 | + | 1.81328i | −0.365098 | + | 0.210789i | ||||
\(75\) | −2.44449 | + | 2.37051i | −0.282266 | + | 0.273722i | ||||
\(76\) | 4.62844 | 0.530919 | ||||||||
\(77\) | −8.74311 | + | 0.747023i | −0.996370 | + | 0.0851312i | ||||
\(78\) | − | 1.39677i | − | 0.158153i | ||||||
\(79\) | 13.3578 | + | 7.71215i | 1.50287 | + | 0.867685i | 0.999994 | + | 0.00332822i | \(0.00105941\pi\) |
0.502880 | + | 0.864356i | \(0.332274\pi\) | |||||||
\(80\) | 0.839811 | + | 2.07237i | 0.0938937 | + | 0.231698i | ||||
\(81\) | −2.52048 | − | 4.36560i | −0.280053 | − | 0.485067i | ||||
\(82\) | 3.11727 | − | 5.39927i | 0.344245 | − | 0.596250i | ||||
\(83\) | − | 1.84746i | − | 0.202785i | −0.994846 | − | 0.101393i | \(-0.967670\pi\) | ||
0.994846 | − | 0.101393i | \(-0.0323298\pi\) | |||||||
\(84\) | −0.398816 | + | 1.75713i | −0.0435144 | + | 0.191718i | ||||
\(85\) | 1.03225 | − | 7.40093i | 0.111963 | − | 0.802743i | ||||
\(86\) | −3.27568 | + | 5.67365i | −0.353226 | + | 0.611806i | ||||
\(87\) | 0.123031 | − | 0.0710319i | 0.0131903 | − | 0.00761542i | ||||
\(88\) | −3.24014 | − | 0.708161i | −0.345400 | − | 0.0754902i | ||||
\(89\) | 15.0268 | + | 8.67572i | 1.59284 | + | 0.919624i | 0.992818 | + | 0.119638i | \(0.0381733\pi\) |
0.600018 | + | 0.799986i | \(0.295160\pi\) | |||||||
\(90\) | 5.61676 | + | 0.783403i | 0.592058 | + | 0.0825779i | ||||
\(91\) | −1.60574 | − | 5.18339i | −0.168327 | − | 0.543367i | ||||
\(92\) | 2.59575i | 0.270625i | ||||||||
\(93\) | 5.23747 | + | 3.02386i | 0.543101 | + | 0.313559i | ||||
\(94\) | 6.57571 | + | 11.3895i | 0.678233 | + | 1.17473i | ||||
\(95\) | 3.88702 | + | 9.59185i | 0.398799 | + | 0.984103i | ||||
\(96\) | −0.340512 | + | 0.589784i | −0.0347534 | + | 0.0601946i | ||||
\(97\) | 5.95329 | 0.604465 | 0.302233 | − | 0.953234i | \(-0.402268\pi\) | ||||
0.302233 | + | 0.953234i | \(0.402268\pi\) | |||||||
\(98\) | 0.540006 | + | 6.97914i | 0.0545488 | + | 0.705000i | ||||
\(99\) | −5.66425 | + | 6.21868i | −0.569279 | + | 0.625001i | ||||
\(100\) | −3.58944 | + | 3.48080i | −0.358944 | + | 0.348080i | ||||
\(101\) | −2.30017 | − | 3.98401i | −0.228876 | − | 0.396424i | 0.728600 | − | 0.684940i | \(-0.240172\pi\) |
−0.957475 | + | 0.288516i | \(0.906838\pi\) | |||||||
\(102\) | 1.97096 | − | 1.13793i | 0.195154 | − | 0.112672i | ||||
\(103\) | −2.02004 | + | 3.49881i | −0.199040 | + | 0.344748i | −0.948217 | − | 0.317622i | \(-0.897116\pi\) |
0.749177 | + | 0.662369i | \(0.230449\pi\) | |||||||
\(104\) | − | 2.05099i | − | 0.201116i | ||||||
\(105\) | −3.97635 | + | 0.649160i | −0.388052 | + | 0.0633515i | ||||
\(106\) | − | 3.69612i | − | 0.358999i | ||||||
\(107\) | −4.80623 | + | 8.32464i | −0.464636 | + | 0.804773i | −0.999185 | − | 0.0403642i | \(-0.987148\pi\) |
0.534549 | + | 0.845138i | \(0.320482\pi\) | |||||||
\(108\) | 1.88514 | + | 3.26517i | 0.181398 | + | 0.314191i | ||||
\(109\) | −15.1014 | + | 8.71882i | −1.44646 | + | 0.835112i | −0.998268 | − | 0.0588278i | \(-0.981264\pi\) |
−0.448188 | + | 0.893939i | \(0.647930\pi\) | |||||||
\(110\) | −1.25353 | − | 7.30949i | −0.119520 | − | 0.696933i | ||||
\(111\) | − | 2.46977i | − | 0.234420i | ||||||
\(112\) | −0.585613 | + | 2.58013i | −0.0553352 | + | 0.243799i | ||||
\(113\) | − | 10.5976i | − | 0.996934i | −0.866909 | − | 0.498467i | \(-0.833896\pi\) | ||
0.866909 | − | 0.498467i | \(-0.166104\pi\) | |||||||
\(114\) | −1.57604 | + | 2.72978i | −0.147610 | + | 0.255668i | ||||
\(115\) | −5.37935 | + | 2.17994i | −0.501627 | + | 0.203280i | ||||
\(116\) | 0.180656 | − | 0.104302i | 0.0167735 | − | 0.00968416i | ||||
\(117\) | −4.50483 | − | 2.60087i | −0.416472 | − | 0.240450i | ||||
\(118\) | 5.76508i | 0.530719i | ||||||||
\(119\) | 6.00601 | − | 6.48867i | 0.550570 | − | 0.594815i | ||||
\(120\) | −1.50822 | − | 0.210360i | −0.137681 | − | 0.0192032i | ||||
\(121\) | 9.99702 | + | 4.58908i | 0.908820 | + | 0.417189i | ||||
\(122\) | 5.38616 | + | 9.32910i | 0.487640 | + | 0.844617i | ||||
\(123\) | 2.12294 | + | 3.67703i | 0.191419 | + | 0.331547i | ||||
\(124\) | 7.69058 | + | 4.44016i | 0.690635 | + | 0.398738i | ||||
\(125\) | −10.2279 | − | 4.51543i | −0.914815 | − | 0.403872i | ||||
\(126\) | 4.92442 | + | 4.55812i | 0.438703 | + | 0.406070i | ||||
\(127\) | −12.3526 | −1.09612 | −0.548059 | − | 0.836440i | \(-0.684633\pi\) | ||||
−0.548059 | + | 0.836440i | \(0.684633\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.23082 | − | 3.86389i | −0.196413 | − | 0.340197i | ||||
\(130\) | 4.25041 | − | 1.72244i | 0.372785 | − | 0.151068i | ||||
\(131\) | 3.55442 | − | 6.15643i | 0.310551 | − | 0.537890i | −0.667931 | − | 0.744223i | \(-0.732820\pi\) |
0.978482 | + | 0.206333i | \(0.0661532\pi\) | |||||||
\(132\) | 1.52097 | − | 1.66985i | 0.132383 | − | 0.145341i | ||||
\(133\) | −2.71048 | + | 11.9420i | −0.235028 | + | 1.03550i | ||||
\(134\) | − | 1.67306i | − | 0.144530i | ||||||
\(135\) | −5.18347 | + | 6.64884i | −0.446122 | + | 0.572241i | ||||
\(136\) | 2.89411 | − | 1.67092i | 0.248168 | − | 0.143280i | ||||
\(137\) | 16.1860 | − | 9.34499i | 1.38286 | − | 0.798397i | 0.390366 | − | 0.920660i | \(-0.372349\pi\) |
0.992498 | + | 0.122263i | \(0.0390153\pi\) | |||||||
\(138\) | −1.53093 | − | 0.883883i | −0.130322 | − | 0.0752412i | ||||
\(139\) | −19.6113 | −1.66341 | −0.831706 | − | 0.555216i | \(-0.812636\pi\) | ||||
−0.831706 | + | 0.555216i | \(0.812636\pi\) | |||||||
\(140\) | −5.83878 | + | 0.953212i | −0.493467 | + | 0.0805611i | ||||
\(141\) | −8.95643 | −0.754268 | ||||||||
\(142\) | −2.87268 | + | 4.97564i | −0.241070 | + | 0.417546i | ||||
\(143\) | −1.45243 | + | 6.64549i | −0.121458 | + | 0.555724i | ||||
\(144\) | 1.26810 | + | 2.19642i | 0.105675 | + | 0.183035i | ||||
\(145\) | 0.367868 | + | 0.286792i | 0.0305498 | + | 0.0238168i | ||||
\(146\) | − | 7.65178i | − | 0.633266i | ||||||
\(147\) | −4.30006 | − | 2.05799i | −0.354663 | − | 0.169741i | ||||
\(148\) | − | 3.62656i | − | 0.298101i | ||||||
\(149\) | 4.37001 | + | 2.52303i | 0.358005 | + | 0.206694i | 0.668205 | − | 0.743977i | \(-0.267063\pi\) |
−0.310200 | + | 0.950671i | \(0.600396\pi\) | |||||||
\(150\) | −0.830673 | − | 3.30225i | −0.0678241 | − | 0.269627i | ||||
\(151\) | 2.05768 | − | 1.18800i | 0.167452 | − | 0.0966784i | −0.413932 | − | 0.910308i | \(-0.635845\pi\) |
0.581384 | + | 0.813629i | \(0.302512\pi\) | |||||||
\(152\) | −2.31422 | + | 4.00835i | −0.187708 | + | 0.325120i | ||||
\(153\) | − | 8.47558i | − | 0.685210i | ||||||
\(154\) | 3.72461 | − | 7.94527i | 0.300138 | − | 0.640248i | ||||
\(155\) | −2.74302 | + | 19.6666i | −0.220325 | + | 1.57966i | ||||
\(156\) | 1.20964 | + | 0.698386i | 0.0968487 | + | 0.0559157i | ||||
\(157\) | −0.279611 | − | 0.484300i | −0.0223154 | − | 0.0386513i | 0.854652 | − | 0.519201i | \(-0.173770\pi\) |
−0.876967 | + | 0.480550i | \(0.840437\pi\) | |||||||
\(158\) | −13.3578 | + | 7.71215i | −1.06269 | + | 0.613546i | ||||
\(159\) | 2.17991 | + | 1.25857i | 0.172878 | + | 0.0998113i | ||||
\(160\) | −2.21463 | − | 0.308888i | −0.175082 | − | 0.0244197i | ||||
\(161\) | −6.69736 | − | 1.52010i | −0.527826 | − | 0.119801i | ||||
\(162\) | 5.04096 | 0.396055 | ||||||||
\(163\) | 19.0284 | + | 10.9861i | 1.49042 | + | 0.860495i | 0.999940 | − | 0.0109567i | \(-0.00348771\pi\) |
0.490481 | + | 0.871452i | \(0.336821\pi\) | |||||||
\(164\) | 3.11727 | + | 5.39927i | 0.243418 | + | 0.421612i | ||||
\(165\) | 4.73786 | + | 1.74966i | 0.368842 | + | 0.136211i | ||||
\(166\) | 1.59995 | + | 0.923730i | 0.124180 | + | 0.0716954i | ||||
\(167\) | − | 10.5810i | − | 0.818786i | −0.912358 | − | 0.409393i | \(-0.865741\pi\) | ||
0.912358 | − | 0.409393i | \(-0.134259\pi\) | |||||||
\(168\) | −1.32231 | − | 1.22395i | −0.102018 | − | 0.0944298i | ||||
\(169\) | 8.79345 | 0.676419 | ||||||||
\(170\) | 5.89326 | + | 4.59442i | 0.451993 | + | 0.352376i | ||||
\(171\) | 5.86934 | + | 10.1660i | 0.448840 | + | 0.777413i | ||||
\(172\) | −3.27568 | − | 5.67365i | −0.249769 | − | 0.432612i | ||||
\(173\) | −3.43353 | − | 1.98235i | −0.261046 | − | 0.150715i | 0.363766 | − | 0.931491i | \(-0.381491\pi\) |
−0.624812 | + | 0.780775i | \(0.714824\pi\) | |||||||
\(174\) | 0.142064i | 0.0107698i | ||||||||
\(175\) | −6.87888 | − | 11.2996i | −0.519994 | − | 0.854170i | ||||
\(176\) | 2.23336 | − | 2.45196i | 0.168346 | − | 0.184824i | ||||
\(177\) | −3.40015 | − | 1.96308i | −0.255571 | − | 0.147554i | ||||
\(178\) | −15.0268 | + | 8.67572i | −1.12630 | + | 0.650272i | ||||
\(179\) | −0.740004 | − | 1.28173i | −0.0553105 | − | 0.0958006i | 0.837044 | − | 0.547135i | \(-0.184282\pi\) |
−0.892355 | + | 0.451334i | \(0.850948\pi\) | |||||||
\(180\) | −3.48683 | + | 4.47256i | −0.259893 | + | 0.333365i | ||||
\(181\) | − | 10.8158i | − | 0.803935i | −0.915654 | − | 0.401967i | \(-0.868326\pi\) | ||
0.915654 | − | 0.401967i | \(-0.131674\pi\) | |||||||
\(182\) | 5.29181 | + | 1.20109i | 0.392255 | + | 0.0890304i | ||||
\(183\) | −7.33621 | −0.542308 | ||||||||
\(184\) | −2.24798 | − | 1.29787i | −0.165724 | − | 0.0956806i | ||||
\(185\) | 7.51557 | − | 3.04562i | 0.552556 | − | 0.223919i | ||||
\(186\) | −5.23747 | + | 3.02386i | −0.384030 | + | 0.221720i | ||||
\(187\) | −10.5606 | + | 3.36451i | −0.772268 | + | 0.246037i | ||||
\(188\) | −13.1514 | −0.959166 | ||||||||
\(189\) | −9.52851 | + | 2.95179i | −0.693097 | + | 0.214711i | ||||
\(190\) | −10.2503 | − | 1.42967i | −0.743634 | − | 0.103719i | ||||
\(191\) | −8.82641 | + | 15.2878i | −0.638657 | + | 1.10619i | 0.347071 | + | 0.937839i | \(0.387176\pi\) |
−0.985728 | + | 0.168347i | \(0.946157\pi\) | |||||||
\(192\) | −0.340512 | − | 0.589784i | −0.0245743 | − | 0.0425640i | ||||
\(193\) | 10.8787 | + | 18.8425i | 0.783066 | + | 1.35631i | 0.930147 | + | 0.367186i | \(0.119679\pi\) |
−0.147081 | + | 0.989124i | \(0.546988\pi\) | |||||||
\(194\) | −2.97665 | + | 5.15570i | −0.213711 | + | 0.370158i | ||||
\(195\) | −0.431446 | + | 3.09334i | −0.0308965 | + | 0.221518i | ||||
\(196\) | −6.31412 | − | 3.02191i | −0.451008 | − | 0.215851i | ||||
\(197\) | −3.55637 | −0.253381 | −0.126690 | − | 0.991942i | \(-0.540435\pi\) | ||||
−0.126690 | + | 0.991942i | \(0.540435\pi\) | |||||||
\(198\) | −2.55341 | − | 8.01473i | −0.181463 | − | 0.569582i | ||||
\(199\) | −9.05521 | + | 5.22803i | −0.641907 | + | 0.370605i | −0.785349 | − | 0.619054i | \(-0.787516\pi\) |
0.143442 | + | 0.989659i | \(0.454183\pi\) | |||||||
\(200\) | −1.21974 | − | 4.84894i | −0.0862487 | − | 0.342872i | ||||
\(201\) | 0.986744 | + | 0.569697i | 0.0695996 | + | 0.0401833i | ||||
\(202\) | 4.60034 | 0.323679 | ||||||||
\(203\) | 0.163317 | + | 0.527195i | 0.0114626 | + | 0.0370018i | ||||
\(204\) | 2.27587i | 0.159343i | ||||||||
\(205\) | −8.57137 | + | 10.9945i | −0.598650 | + | 0.767889i | ||||
\(206\) | −2.02004 | − | 3.49881i | −0.140743 | − | 0.243773i | ||||
\(207\) | −5.70135 | + | 3.29168i | −0.396271 | + | 0.228787i | ||||
\(208\) | 1.77621 | + | 1.02549i | 0.123158 | + | 0.0711052i | ||||
\(209\) | 10.3370 | − | 11.3488i | 0.715022 | − | 0.785011i | ||||
\(210\) | 1.42599 | − | 3.76820i | 0.0984024 | − | 0.260031i | ||||
\(211\) | 24.6765i | 1.69880i | 0.527747 | + | 0.849402i | \(0.323037\pi\) | ||||
−0.527747 | + | 0.849402i | \(0.676963\pi\) | |||||||
\(212\) | 3.20093 | + | 1.84806i | 0.219841 | + | 0.126925i | ||||
\(213\) | −1.95637 | − | 3.38853i | −0.134048 | − | 0.232178i | ||||
\(214\) | −4.80623 | − | 8.32464i | −0.328547 | − | 0.569061i | ||||
\(215\) | 9.00695 | − | 11.5532i | 0.614269 | − | 0.787923i | ||||
\(216\) | −3.77029 | −0.256536 | ||||||||
\(217\) | −15.9599 | + | 17.2425i | −1.08343 | + | 1.17050i | ||||
\(218\) | − | 17.4376i | − | 1.18103i | ||||||
\(219\) | 4.51290 | + | 2.60552i | 0.304953 | + | 0.176065i | ||||
\(220\) | 6.95697 | + | 2.56915i | 0.469039 | + | 0.173212i | ||||
\(221\) | −3.42703 | − | 5.93579i | −0.230527 | − | 0.399285i | ||||
\(222\) | 2.13889 | + | 1.23489i | 0.143553 | + | 0.0828801i | ||||
\(223\) | 25.7283 | 1.72290 | 0.861448 | − | 0.507846i | \(-0.169558\pi\) | ||||
0.861448 | + | 0.507846i | \(0.169558\pi\) | |||||||
\(224\) | −1.94165 | − | 1.79722i | −0.129732 | − | 0.120082i | ||||
\(225\) | −12.1971 | − | 3.46990i | −0.813138 | − | 0.231326i | ||||
\(226\) | 9.17775 | + | 5.29878i | 0.610495 | + | 0.352470i | ||||
\(227\) | 9.94984 | − | 5.74454i | 0.660394 | − | 0.381279i | −0.132033 | − | 0.991245i | \(-0.542150\pi\) |
0.792427 | + | 0.609967i | \(0.208817\pi\) | |||||||
\(228\) | −1.57604 | − | 2.72978i | −0.104376 | − | 0.180784i | ||||
\(229\) | 16.3220 | + | 9.42353i | 1.07859 | + | 0.622725i | 0.930516 | − | 0.366252i | \(-0.119359\pi\) |
0.148075 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(230\) | 0.801795 | − | 5.74862i | 0.0528688 | − | 0.379053i | ||||
\(231\) | 3.41772 | + | 4.90218i | 0.224869 | + | 0.322540i | ||||
\(232\) | 0.208603i | 0.0136955i | ||||||||
\(233\) | 4.53084 | − | 7.84765i | 0.296825 | − | 0.514116i | −0.678583 | − | 0.734524i | \(-0.737405\pi\) |
0.975408 | + | 0.220408i | \(0.0707388\pi\) | |||||||
\(234\) | 4.50483 | − | 2.60087i | 0.294490 | − | 0.170024i | ||||
\(235\) | −11.0447 | − | 27.2546i | −0.720477 | − | 1.77790i | ||||
\(236\) | −4.99271 | − | 2.88254i | −0.324998 | − | 0.187637i | ||||
\(237\) | − | 10.5043i | − | 0.682329i | ||||||
\(238\) | 2.61635 | + | 8.44569i | 0.169593 | + | 0.547453i | ||||
\(239\) | 19.0580i | 1.23276i | 0.787450 | + | 0.616379i | \(0.211401\pi\) | ||||
−0.787450 | + | 0.616379i | \(0.788599\pi\) | |||||||
\(240\) | 0.936285 | − | 1.20097i | 0.0604370 | − | 0.0775225i | ||||
\(241\) | −3.67875 | − | 6.37178i | −0.236969 | − | 0.410442i | 0.722874 | − | 0.690980i | \(-0.242821\pi\) |
−0.959843 | + | 0.280537i | \(0.909487\pi\) | |||||||
\(242\) | −8.97277 | + | 6.36313i | −0.576791 | + | 0.409037i | ||||
\(243\) | −7.37194 | + | 12.7686i | −0.472910 | + | 0.819105i | ||||
\(244\) | −10.7723 | −0.689627 | ||||||||
\(245\) | 0.959858 | − | 15.6230i | 0.0613231 | − | 0.998118i | ||||
\(246\) | −4.24587 | −0.270707 | ||||||||
\(247\) | 8.22108 | + | 4.74644i | 0.523095 | + | 0.302009i | ||||
\(248\) | −7.69058 | + | 4.44016i | −0.488353 | + | 0.281950i | ||||
\(249\) | −1.08960 | + | 0.629082i | −0.0690508 | + | 0.0398665i | ||||
\(250\) | 9.02445 | − | 6.59995i | 0.570756 | − | 0.417417i | ||||
\(251\) | 9.88938i | 0.624212i | 0.950047 | + | 0.312106i | \(0.101034\pi\) | ||||
−0.950047 | + | 0.312106i | \(0.898966\pi\) | |||||||
\(252\) | −6.40966 | + | 1.98562i | −0.403771 | + | 0.125082i | ||||
\(253\) | 6.36468 | + | 5.79723i | 0.400144 | + | 0.364469i | ||||
\(254\) | 6.17631 | − | 10.6977i | 0.387536 | − | 0.671233i | ||||
\(255\) | −4.71644 | + | 1.91130i | −0.295355 | + | 0.119690i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −8.66287 | + | 15.0045i | −0.540375 | + | 0.935957i | 0.458508 | + | 0.888690i | \(0.348384\pi\) |
−0.998882 | + | 0.0472660i | \(0.984949\pi\) | |||||||
\(258\) | 4.46164 | 0.277770 | ||||||||
\(259\) | 9.35698 | + | 2.12376i | 0.581414 | + | 0.131964i | ||||
\(260\) | −0.633525 | + | 4.54218i | −0.0392896 | + | 0.281694i | ||||
\(261\) | 0.458180 | + | 0.264530i | 0.0283606 | + | 0.0163740i | ||||
\(262\) | 3.55442 | + | 6.15643i | 0.219593 | + | 0.380346i | ||||
\(263\) | −5.94935 | − | 10.3046i | −0.366853 | − | 0.635407i | 0.622219 | − | 0.782843i | \(-0.286231\pi\) |
−0.989072 | + | 0.147436i | \(0.952898\pi\) | |||||||
\(264\) | 0.685645 | + | 2.15212i | 0.0421985 | + | 0.132454i | ||||
\(265\) | −1.14169 | + | 8.18553i | −0.0701332 | + | 0.502833i | ||||
\(266\) | −8.98681 | − | 8.31833i | −0.551017 | − | 0.510029i | ||||
\(267\) | − | 11.8167i | − | 0.723173i | ||||||
\(268\) | 1.44891 | + | 0.836530i | 0.0885064 | + | 0.0510992i | ||||
\(269\) | 0.208607 | − | 0.120439i | 0.0127190 | − | 0.00734332i | −0.493627 | − | 0.869674i | \(-0.664329\pi\) |
0.506346 | + | 0.862330i | \(0.330996\pi\) | |||||||
\(270\) | −3.16633 | − | 7.81344i | −0.192697 | − | 0.475511i | ||||
\(271\) | 4.79043 | − | 8.29727i | 0.290998 | − | 0.504024i | −0.683048 | − | 0.730374i | \(-0.739346\pi\) |
0.974046 | + | 0.226350i | \(0.0726793\pi\) | |||||||
\(272\) | 3.34183i | 0.202628i | ||||||||
\(273\) | −2.51031 | + | 2.71204i | −0.151931 | + | 0.164140i | ||||
\(274\) | 18.6900i | 1.12910i | ||||||||
\(275\) | 0.518299 | + | 16.5750i | 0.0312546 | + | 0.999511i | ||||
\(276\) | 1.53093 | − | 0.883883i | 0.0921512 | − | 0.0532035i | ||||
\(277\) | 12.4107 | + | 21.4960i | 0.745687 | + | 1.29157i | 0.949873 | + | 0.312635i | \(0.101212\pi\) |
−0.204186 | + | 0.978932i | \(0.565455\pi\) | |||||||
\(278\) | 9.80567 | − | 16.9839i | 0.588105 | − | 1.01863i | ||||
\(279\) | 22.5223i | 1.34838i | ||||||||
\(280\) | 2.09389 | − | 5.53314i | 0.125134 | − | 0.330668i | ||||
\(281\) | − | 23.1359i | − | 1.38017i | −0.723726 | − | 0.690087i | \(-0.757572\pi\) | ||
0.723726 | − | 0.690087i | \(-0.242428\pi\) | |||||||
\(282\) | 4.47822 | − | 7.75650i | 0.266674 | − | 0.461893i | ||||
\(283\) | 26.4747 | − | 15.2852i | 1.57376 | − | 0.908610i | 0.578057 | − | 0.815996i | \(-0.303811\pi\) |
0.995702 | − | 0.0926142i | \(-0.0295223\pi\) | |||||||
\(284\) | −2.87268 | − | 4.97564i | −0.170462 | − | 0.295250i | ||||
\(285\) | 4.33354 | − | 5.55864i | 0.256697 | − | 0.329265i | ||||
\(286\) | −5.02895 | − | 4.58059i | −0.297368 | − | 0.270856i | ||||
\(287\) | −15.7563 | + | 4.88107i | −0.930066 | + | 0.288121i | ||||
\(288\) | −2.53621 | −0.149447 | ||||||||
\(289\) | −2.91608 | + | 5.05079i | −0.171534 | + | 0.297105i | ||||
\(290\) | −0.432303 | + | 0.175187i | −0.0253857 | + | 0.0102873i | ||||
\(291\) | −2.02717 | − | 3.51116i | −0.118835 | − | 0.205828i | ||||
\(292\) | 6.62663 | + | 3.82589i | 0.387794 | + | 0.223893i | ||||
\(293\) | − | 4.51666i | − | 0.263866i | −0.991259 | − | 0.131933i | \(-0.957882\pi\) | ||
0.991259 | − | 0.131933i | \(-0.0421184\pi\) | |||||||
\(294\) | 3.93231 | − | 2.69497i | 0.229337 | − | 0.157174i | ||||
\(295\) | 1.78076 | − | 12.7675i | 0.103680 | − | 0.743354i | ||||
\(296\) | 3.14069 | + | 1.81328i | 0.182549 | + | 0.105395i | ||||
\(297\) | 12.2163 | + | 2.66997i | 0.708860 | + | 0.154927i | ||||
\(298\) | −4.37001 | + | 2.52303i | −0.253148 | + | 0.146155i | ||||
\(299\) | −2.66193 | + | 4.61059i | −0.153943 | + | 0.266637i | ||||
\(300\) | 3.27516 | + | 0.931739i | 0.189092 | + | 0.0537940i | ||||
\(301\) | 16.5570 | − | 5.12912i | 0.954331 | − | 0.295638i | ||||
\(302\) | 2.37601i | 0.136724i | ||||||||
\(303\) | −1.56647 | + | 2.71321i | −0.0899915 | + | 0.155870i | ||||
\(304\) | −2.31422 | − | 4.00835i | −0.132730 | − | 0.229895i | ||||
\(305\) | −9.04671 | − | 22.3242i | −0.518013 | − | 1.27828i | ||||
\(306\) | 7.34007 | + | 4.23779i | 0.419604 | + | 0.242258i | ||||
\(307\) | 30.0596i | 1.71559i | 0.513992 | + | 0.857795i | \(0.328166\pi\) | ||||
−0.513992 | + | 0.857795i | \(0.671834\pi\) | |||||||
\(308\) | 5.01850 | + | 7.19824i | 0.285955 | + | 0.410158i | ||||
\(309\) | 2.75139 | 0.156521 | ||||||||
\(310\) | −15.6603 | − | 12.2088i | −0.889445 | − | 0.693416i | ||||
\(311\) | −0.971429 | + | 0.560855i | −0.0550847 | + | 0.0318032i | −0.527289 | − | 0.849686i | \(-0.676792\pi\) |
0.472205 | + | 0.881489i | \(0.343458\pi\) | |||||||
\(312\) | −1.20964 | + | 0.698386i | −0.0684824 | + | 0.0395383i | ||||
\(313\) | 10.3195 | − | 17.8740i | 0.583294 | − | 1.01030i | −0.411791 | − | 0.911278i | \(-0.635097\pi\) |
0.995086 | − | 0.0990174i | \(-0.0315699\pi\) | |||||||
\(314\) | 0.559221 | 0.0315587 | ||||||||
\(315\) | −9.49783 | − | 11.6156i | −0.535142 | − | 0.654467i | ||||
\(316\) | − | 15.4243i | − | 0.867685i | ||||||
\(317\) | −18.3880 | − | 10.6163i | −1.03277 | − | 0.596272i | −0.114995 | − | 0.993366i | \(-0.536685\pi\) |
−0.917778 | + | 0.397095i | \(0.870019\pi\) | |||||||
\(318\) | −2.17991 | + | 1.25857i | −0.122243 | + | 0.0705772i | ||||
\(319\) | 0.147725 | − | 0.675904i | 0.00827099 | − | 0.0378433i | ||||
\(320\) | 1.37482 | − | 1.76348i | 0.0768548 | − | 0.0985817i | ||||
\(321\) | 6.54632 | 0.365380 | ||||||||
\(322\) | 4.66513 | − | 5.04003i | 0.259977 | − | 0.280870i | ||||
\(323\) | 15.4675i | 0.860634i | ||||||||
\(324\) | −2.52048 | + | 4.36560i | −0.140027 | + | 0.242533i | ||||
\(325\) | −9.94512 | + | 2.50167i | −0.551656 | + | 0.138768i | ||||
\(326\) | −19.0284 | + | 10.9861i | −1.05389 | + | 0.608462i | ||||
\(327\) | 10.2844 | + | 5.93773i | 0.568731 | + | 0.328357i | ||||
\(328\) | −6.23454 | −0.344245 | ||||||||
\(329\) | 7.70164 | − | 33.9323i | 0.424605 | − | 1.87075i | ||||
\(330\) | −3.88418 | + | 3.22828i | −0.213817 | + | 0.177711i | ||||
\(331\) | −8.87838 | + | 15.3778i | −0.488000 | + | 0.845241i | −0.999905 | − | 0.0138013i | \(-0.995607\pi\) |
0.511905 | + | 0.859042i | \(0.328940\pi\) | |||||||
\(332\) | −1.59995 | + | 0.923730i | −0.0878085 | + | 0.0506963i | ||||
\(333\) | 7.96544 | − | 4.59885i | 0.436503 | − | 0.252015i | ||||
\(334\) | 9.16345 | + | 5.29052i | 0.501402 | + | 0.289484i | ||||
\(335\) | −0.516788 | + | 3.70521i | −0.0282351 | + | 0.202437i | ||||
\(336\) | 1.72113 | − | 0.533179i | 0.0938951 | − | 0.0290873i | ||||
\(337\) | 11.5799 | 0.630798 | 0.315399 | − | 0.948959i | \(-0.397862\pi\) | ||||
0.315399 | + | 0.948959i | \(0.397862\pi\) | |||||||
\(338\) | −4.39672 | + | 7.61535i | −0.239150 | + | 0.414220i | ||||
\(339\) | −6.25027 | + | 3.60860i | −0.339468 | + | 0.195992i | ||||
\(340\) | −6.92551 | + | 2.80651i | −0.375589 | + | 0.152204i | ||||
\(341\) | 28.0629 | − | 8.94057i | 1.51969 | − | 0.484159i | ||||
\(342\) | −11.7387 | −0.634755 | ||||||||
\(343\) | 11.4945 | − | 14.5216i | 0.620647 | − | 0.784090i | ||||
\(344\) | 6.55137 | 0.353226 | ||||||||
\(345\) | 3.11743 | + | 2.43036i | 0.167837 | + | 0.130846i | ||||
\(346\) | 3.43353 | − | 1.98235i | 0.184588 | − | 0.106572i | ||||
\(347\) | −4.34117 | − | 7.51913i | −0.233046 | − | 0.403648i | 0.725657 | − | 0.688057i | \(-0.241536\pi\) |
−0.958703 | + | 0.284409i | \(0.908203\pi\) | |||||||
\(348\) | −0.123031 | − | 0.0710319i | −0.00659515 | − | 0.00380771i | ||||
\(349\) | 10.3147 | 0.552134 | 0.276067 | − | 0.961138i | \(-0.410969\pi\) | ||||
0.276067 | + | 0.961138i | \(0.410969\pi\) | |||||||
\(350\) | 13.2252 | − | 0.307484i | 0.706916 | − | 0.0164357i | ||||
\(351\) | 7.73282i | 0.412747i | ||||||||
\(352\) | 1.00678 | + | 3.16012i | 0.0536618 | + | 0.168435i | ||||
\(353\) | −5.58273 | − | 9.66958i | −0.297139 | − | 0.514660i | 0.678341 | − | 0.734747i | \(-0.262699\pi\) |
−0.975480 | + | 0.220087i | \(0.929366\pi\) | |||||||
\(354\) | 3.40015 | − | 1.96308i | 0.180716 | − | 0.104336i | ||||
\(355\) | 7.89885 | − | 10.1319i | 0.419227 | − | 0.537743i | ||||
\(356\) | − | 17.3514i | − | 0.919624i | ||||||
\(357\) | −5.87203 | − | 1.33278i | −0.310781 | − | 0.0705381i | ||||
\(358\) | 1.48001 | 0.0782209 | ||||||||
\(359\) | 16.5110 | + | 9.53265i | 0.871419 | + | 0.503114i | 0.867820 | − | 0.496879i | \(-0.165521\pi\) |
0.00359971 | + | 0.999994i | \(0.498854\pi\) | |||||||
\(360\) | −2.12993 | − | 5.25596i | −0.112257 | − | 0.277013i | ||||
\(361\) | −1.21124 | − | 2.09793i | −0.0637496 | − | 0.110418i | ||||
\(362\) | 9.36679 | + | 5.40792i | 0.492308 | + | 0.284234i | ||||
\(363\) | −0.697537 | − | 7.45872i | −0.0366112 | − | 0.391481i | ||||
\(364\) | −3.68608 | + | 3.98230i | −0.193203 | + | 0.208729i | ||||
\(365\) | −2.36354 | + | 16.9459i | −0.123713 | + | 0.886987i | ||||
\(366\) | 3.66810 | − | 6.35334i | 0.191735 | − | 0.332095i | ||||
\(367\) | −3.01556 | − | 5.22310i | −0.157411 | − | 0.272644i | 0.776523 | − | 0.630088i | \(-0.216981\pi\) |
−0.933934 | + | 0.357445i | \(0.883648\pi\) | |||||||
\(368\) | 2.24798 | − | 1.29787i | 0.117184 | − | 0.0676564i | ||||
\(369\) | −7.90604 | + | 13.6937i | −0.411572 | + | 0.712863i | ||||
\(370\) | −1.12020 | + | 8.03148i | −0.0582364 | + | 0.417537i | ||||
\(371\) | −6.64273 | + | 7.17656i | −0.344873 | + | 0.372589i | ||||
\(372\) | − | 6.04771i | − | 0.313559i | ||||||
\(373\) | 0.803802 | − | 1.39223i | 0.0416193 | − | 0.0720867i | −0.844465 | − | 0.535610i | \(-0.820082\pi\) |
0.886085 | + | 0.463523i | \(0.153415\pi\) | |||||||
\(374\) | 2.36656 | − | 10.8280i | 0.122372 | − | 0.559903i | ||||
\(375\) | 0.819610 | + | 7.56984i | 0.0423245 | + | 0.390905i | ||||
\(376\) | 6.57571 | − | 11.3895i | 0.339116 | − | 0.587367i | ||||
\(377\) | 0.427843 | 0.0220350 | ||||||||
\(378\) | 2.20793 | − | 9.72783i | 0.113564 | − | 0.500345i | ||||
\(379\) | −21.0081 | −1.07912 | −0.539558 | − | 0.841949i | \(-0.681409\pi\) | ||||
−0.539558 | + | 0.841949i | \(0.681409\pi\) | |||||||
\(380\) | 6.36328 | − | 8.16218i | 0.326429 | − | 0.418711i | ||||
\(381\) | 4.20622 | + | 7.28538i | 0.215491 | + | 0.373241i | ||||
\(382\) | −8.82641 | − | 15.2878i | −0.451598 | − | 0.782191i | ||||
\(383\) | 15.2258 | − | 26.3718i | 0.778000 | − | 1.34754i | −0.155092 | − | 0.987900i | \(-0.549567\pi\) |
0.933093 | − | 0.359636i | \(-0.117099\pi\) | |||||||
\(384\) | 0.681024 | 0.0347534 | ||||||||
\(385\) | −10.7028 | + | 16.4453i | −0.545467 | + | 0.838132i | ||||
\(386\) | −21.7574 | −1.10742 | ||||||||
\(387\) | 8.30781 | − | 14.3896i | 0.422310 | − | 0.731462i | ||||
\(388\) | −2.97665 | − | 5.15570i | −0.151116 | − | 0.261741i | ||||
\(389\) | 14.4555 | + | 25.0377i | 0.732924 | + | 1.26946i | 0.955628 | + | 0.294575i | \(0.0951781\pi\) |
−0.222705 | + | 0.974886i | \(0.571489\pi\) | |||||||
\(390\) | −2.46318 | − | 1.92031i | −0.124728 | − | 0.0972387i | ||||
\(391\) | −8.67456 | −0.438691 | ||||||||
\(392\) | 5.77411 | − | 3.95723i | 0.291637 | − | 0.199870i | ||||
\(393\) | −4.84129 | −0.244211 | ||||||||
\(394\) | 1.77819 | − | 3.07991i | 0.0895837 | − | 0.155164i | ||||
\(395\) | 31.9649 | − | 12.9535i | 1.60833 | − | 0.651761i | ||||
\(396\) | 8.21766 | + | 1.79604i | 0.412953 | + | 0.0902545i | ||||
\(397\) | −11.2369 | + | 19.4629i | −0.563963 | + | 0.976813i | 0.433182 | + | 0.901306i | \(0.357391\pi\) |
−0.997145 | + | 0.0755063i | \(0.975943\pi\) | |||||||
\(398\) | − | 10.4561i | − | 0.524115i | ||||||
\(399\) | 7.96613 | − | 2.46779i | 0.398806 | − | 0.123544i | ||||
\(400\) | 4.80918 | + | 1.36814i | 0.240459 | + | 0.0684072i | ||||
\(401\) | −10.8958 | + | 18.8721i | −0.544111 | + | 0.942429i | 0.454551 | + | 0.890721i | \(0.349800\pi\) |
−0.998662 | + | 0.0517079i | \(0.983534\pi\) | |||||||
\(402\) | −0.986744 | + | 0.569697i | −0.0492143 | + | 0.0284139i | ||||
\(403\) | 9.10672 | + | 15.7733i | 0.453638 | + | 0.785724i | ||||
\(404\) | −2.30017 | + | 3.98401i | −0.114438 | + | 0.198212i | ||||
\(405\) | −11.1639 | − | 1.55709i | −0.554737 | − | 0.0773725i | ||||
\(406\) | −0.538223 | − | 0.122161i | −0.0267116 | − | 0.00606273i | ||||
\(407\) | −8.89218 | − | 8.09939i | −0.440769 | − | 0.401472i | ||||
\(408\) | −1.97096 | − | 1.13793i | −0.0975771 | − | 0.0563361i | ||||
\(409\) | 6.88836 | + | 11.9310i | 0.340608 | + | 0.589950i | 0.984546 | − | 0.175128i | \(-0.0560339\pi\) |
−0.643938 | + | 0.765078i | \(0.722701\pi\) | |||||||
\(410\) | −5.23583 | − | 12.9203i | −0.258579 | − | 0.638087i | ||||
\(411\) | −11.0231 | − | 6.36416i | −0.543727 | − | 0.313921i | ||||
\(412\) | 4.04007 | 0.199040 | ||||||||
\(413\) | 10.3611 | − | 11.1938i | 0.509837 | − | 0.550809i | ||||
\(414\) | − | 6.58335i | − | 0.323554i | ||||||
\(415\) | −3.25796 | − | 2.53993i | −0.159927 | − | 0.124680i | ||||
\(416\) | −1.77621 | + | 1.02549i | −0.0870858 | + | 0.0502790i | ||||
\(417\) | 6.67790 | + | 11.5665i | 0.327018 | + | 0.566412i | ||||
\(418\) | 4.65985 | + | 14.6265i | 0.227920 | + | 0.715403i | ||||
\(419\) | − | 3.32031i | − | 0.162208i | −0.996706 | − | 0.0811039i | \(-0.974155\pi\) | ||
0.996706 | − | 0.0811039i | \(-0.0258446\pi\) | |||||||
\(420\) | 2.55036 | + | 3.11904i | 0.124445 | + | 0.152194i | ||||
\(421\) | −1.32850 | −0.0647471 | −0.0323735 | − | 0.999476i | \(-0.510307\pi\) | ||||
−0.0323735 | + | 0.999476i | \(0.510307\pi\) | |||||||
\(422\) | −21.3705 | − | 12.3383i | −1.04030 | − | 0.600618i | ||||
\(423\) | −16.6774 | − | 28.8860i | −0.810881 | − | 1.40449i | ||||
\(424\) | −3.20093 | + | 1.84806i | −0.155451 | + | 0.0897497i | ||||
\(425\) | −11.6322 | − | 11.9953i | −0.564247 | − | 0.581857i | ||||
\(426\) | 3.91273 | 0.189573 | ||||||||
\(427\) | 6.30841 | − | 27.7940i | 0.305285 | − | 1.34504i | ||||
\(428\) | 9.61247 | 0.464636 | ||||||||
\(429\) | 4.41397 | − | 1.40625i | 0.213109 | − | 0.0678943i | ||||
\(430\) | 5.50191 | + | 13.5769i | 0.265326 | + | 0.654734i | ||||
\(431\) | 18.2668 | − | 10.5464i | 0.879882 | − | 0.508000i | 0.00926235 | − | 0.999957i | \(-0.497052\pi\) |
0.870619 | + | 0.491957i | \(0.163718\pi\) | |||||||
\(432\) | 1.88514 | − | 3.26517i | 0.0906991 | − | 0.157095i | ||||
\(433\) | 5.00434 | 0.240493 | 0.120247 | − | 0.992744i | \(-0.461631\pi\) | ||||
0.120247 | + | 0.992744i | \(0.461631\pi\) | |||||||
\(434\) | −6.95248 | − | 22.4429i | −0.333730 | − | 1.07729i | ||||
\(435\) | 0.0438818 | − | 0.314619i | 0.00210397 | − | 0.0150848i | ||||
\(436\) | 15.1014 | + | 8.71882i | 0.723228 | + | 0.417556i | ||||
\(437\) | 10.4047 | − | 6.00714i | 0.497723 | − | 0.287360i | ||||
\(438\) | −4.51290 | + | 2.60552i | −0.215635 | + | 0.124497i | ||||
\(439\) | 4.57091 | − | 7.91705i | 0.218158 | − | 0.377860i | −0.736087 | − | 0.676887i | \(-0.763329\pi\) |
0.954245 | + | 0.299027i | \(0.0966620\pi\) | |||||||
\(440\) | −5.70344 | + | 4.74034i | −0.271901 | + | 0.225987i | ||||
\(441\) | −1.36957 | − | 17.7005i | −0.0652174 | − | 0.842883i | ||||
\(442\) | 6.85406 | 0.326014 | ||||||||
\(443\) | −4.23828 | − | 2.44697i | −0.201367 | − | 0.116259i | 0.395926 | − | 0.918282i | \(-0.370424\pi\) |
−0.597293 | + | 0.802023i | \(0.703757\pi\) | |||||||
\(444\) | −2.13889 | + | 1.23489i | −0.101507 | + | 0.0586051i | ||||
\(445\) | 35.9586 | − | 14.5719i | 1.70460 | − | 0.690775i | ||||
\(446\) | −12.8642 | + | 22.2814i | −0.609136 | + | 1.05505i | ||||
\(447\) | − | 3.43648i | − | 0.162540i | ||||||
\(448\) | 2.52726 | − | 0.782908i | 0.119402 | − | 0.0369889i | ||||
\(449\) | 3.19516 | 0.150789 | 0.0753945 | − | 0.997154i | \(-0.475978\pi\) | ||||
0.0753945 | + | 0.997154i | \(0.475978\pi\) | |||||||
\(450\) | 9.10355 | − | 8.82802i | 0.429146 | − | 0.416157i | ||||
\(451\) | 20.2008 | + | 4.41506i | 0.951218 | + | 0.207897i | ||||
\(452\) | −9.17775 | + | 5.29878i | −0.431685 | + | 0.249234i | ||||
\(453\) | −1.40133 | − | 0.809059i | −0.0658403 | − | 0.0380129i | ||||
\(454\) | 11.4891i | 0.539210i | ||||||||
\(455\) | −11.3484 | − | 4.29454i | −0.532022 | − | 0.201331i | ||||
\(456\) | 3.15208 | 0.147610 | ||||||||
\(457\) | 7.73790 | − | 13.4024i | 0.361964 | − | 0.626939i | −0.626320 | − | 0.779566i | \(-0.715440\pi\) |
0.988284 | + | 0.152626i | \(0.0487731\pi\) | |||||||
\(458\) | −16.3220 | + | 9.42353i | −0.762679 | + | 0.440333i | ||||
\(459\) | −10.9116 | + | 6.29984i | −0.509312 | + | 0.294051i | ||||
\(460\) | 4.57756 | + | 3.56869i | 0.213430 | + | 0.166391i | ||||
\(461\) | 2.55725 | 0.119103 | 0.0595515 | − | 0.998225i | \(-0.481033\pi\) | ||||
0.0595515 | + | 0.998225i | \(0.481033\pi\) | |||||||
\(462\) | −5.95427 | + | 0.508741i | −0.277018 | + | 0.0236688i | ||||
\(463\) | 32.5823i | 1.51423i | 0.653283 | + | 0.757113i | \(0.273391\pi\) | ||||
−0.653283 | + | 0.757113i | \(0.726609\pi\) | |||||||
\(464\) | −0.180656 | − | 0.104302i | −0.00838673 | − | 0.00484208i | ||||
\(465\) | 12.5331 | − | 5.07893i | 0.581209 | − | 0.235530i | ||||
\(466\) | 4.53084 | + | 7.84765i | 0.209887 | + | 0.363535i | ||||
\(467\) | −0.161793 | + | 0.280233i | −0.00748687 | + | 0.0129676i | −0.869745 | − | 0.493502i | \(-0.835717\pi\) |
0.862258 | + | 0.506470i | \(0.169050\pi\) | |||||||
\(468\) | 5.20173i | 0.240450i | ||||||||
\(469\) | −3.00686 | + | 3.24850i | −0.138844 | + | 0.150002i | ||||
\(470\) | 29.1255 | + | 4.06231i | 1.34346 | + | 0.187381i | ||||
\(471\) | −0.190422 | + | 0.329820i | −0.00877416 | + | 0.0151973i | ||||
\(472\) | 4.99271 | − | 2.88254i | 0.229808 | − | 0.132680i | ||||
\(473\) | −21.2274 | − | 4.63942i | −0.976035 | − | 0.213321i | ||||
\(474\) | 9.09701 | + | 5.25216i | 0.417839 | + | 0.241240i | ||||
\(475\) | 22.2590 | + | 6.33238i | 1.02131 | + | 0.290549i | ||||
\(476\) | −8.62235 | − | 1.95702i | −0.395205 | − | 0.0896999i | ||||
\(477\) | 9.37411i | 0.429211i | ||||||||
\(478\) | −16.5047 | − | 9.52898i | −0.754906 | − | 0.435845i | ||||
\(479\) | −12.2943 | − | 21.2944i | −0.561743 | − | 0.972968i | −0.997345 | − | 0.0728280i | \(-0.976798\pi\) |
0.435601 | − | 0.900140i | \(-0.356536\pi\) | |||||||
\(480\) | 0.571931 | + | 1.41133i | 0.0261050 | + | 0.0644183i | ||||
\(481\) | 3.71901 | − | 6.44152i | 0.169572 | − | 0.293708i | ||||
\(482\) | 7.35750 | 0.335125 | ||||||||
\(483\) | 1.38400 | + | 4.46761i | 0.0629741 | + | 0.203283i | ||||
\(484\) | −1.02425 | − | 10.9522i | −0.0465567 | − | 0.497828i | ||||
\(485\) | 8.18471 | − | 10.4985i | 0.371648 | − | 0.476714i | ||||
\(486\) | −7.37194 | − | 12.7686i | −0.334398 | − | 0.579194i | ||||
\(487\) | 26.5133 | − | 15.3075i | 1.20143 | − | 0.693648i | 0.240560 | − | 0.970634i | \(-0.422669\pi\) |
0.960874 | + | 0.276986i | \(0.0893355\pi\) | |||||||
\(488\) | 5.38616 | − | 9.32910i | 0.243820 | − | 0.422309i | ||||
\(489\) | − | 14.9635i | − | 0.676675i | ||||||
\(490\) | 13.0500 | + | 8.64277i | 0.589539 | + | 0.390441i | ||||
\(491\) | − | 12.1960i | − | 0.550399i | −0.961387 | − | 0.275200i | \(-0.911256\pi\) | ||
0.961387 | − | 0.275200i | \(-0.0887439\pi\) | |||||||
\(492\) | 2.12294 | − | 3.67703i | 0.0957093 | − | 0.165773i | ||||
\(493\) | 0.348559 | + | 0.603721i | 0.0156983 | + | 0.0271902i | ||||
\(494\) | −8.22108 | + | 4.74644i | −0.369884 | + | 0.213553i | ||||
\(495\) | 3.17922 | + | 18.5384i | 0.142895 | + | 0.833238i | ||||
\(496\) | − | 8.88032i | − | 0.398738i | ||||||
\(497\) | 14.5201 | − | 4.49810i | 0.651314 | − | 0.201767i | ||||
\(498\) | − | 1.25816i | − | 0.0563797i | ||||||
\(499\) | −3.86443 | + | 6.69338i | −0.172995 | + | 0.299637i | −0.939466 | − | 0.342643i | \(-0.888678\pi\) |
0.766470 | + | 0.642280i | \(0.222011\pi\) | |||||||
\(500\) | 1.20350 | + | 11.1154i | 0.0538220 | + | 0.497095i | ||||
\(501\) | −6.24053 | + | 3.60297i | −0.278806 | + | 0.160969i | ||||
\(502\) | −8.56446 | − | 4.94469i | −0.382250 | − | 0.220692i | ||||
\(503\) | − | 3.46254i | − | 0.154387i | −0.997016 | − | 0.0771936i | \(-0.975404\pi\) | ||
0.997016 | − | 0.0771936i | \(-0.0245960\pi\) | |||||||
\(504\) | 1.48523 | − | 6.54374i | 0.0661576 | − | 0.291481i | ||||
\(505\) | −10.1881 | − | 1.42099i | −0.453363 | − | 0.0632332i | ||||
\(506\) | −8.20289 | + | 2.61336i | −0.364663 | + | 0.116178i | ||||
\(507\) | −2.99427 | − | 5.18623i | −0.132980 | − | 0.230329i | ||||
\(508\) | 6.17631 | + | 10.6977i | 0.274030 | + | 0.474633i | ||||
\(509\) | 2.67778 | + | 1.54601i | 0.118690 | + | 0.0685259i | 0.558170 | − | 0.829727i | \(-0.311504\pi\) |
−0.439480 | + | 0.898253i | \(0.644837\pi\) | |||||||
\(510\) | 0.702988 | − | 5.04021i | 0.0311288 | − | 0.223184i | ||||
\(511\) | −13.7519 | + | 14.8571i | −0.608349 | + | 0.657238i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.72528 | − | 15.1126i | 0.385231 | − | 0.667239i | ||||
\(514\) | −8.66287 | − | 15.0045i | −0.382103 | − | 0.661821i | ||||
\(515\) | 3.39290 | + | 8.37253i | 0.149509 | + | 0.368938i | ||||
\(516\) | −2.23082 | + | 3.86389i | −0.0982064 | + | 0.170098i | ||||
\(517\) | −29.3718 | + | 32.2468i | −1.29177 | + | 1.41821i | ||||
\(518\) | −6.51772 | + | 7.04150i | −0.286372 | + | 0.309386i | ||||
\(519\) | 2.70005i | 0.118519i | ||||||||
\(520\) | −3.61688 | − | 2.81974i | −0.158611 | − | 0.123654i | ||||
\(521\) | −11.0075 | + | 6.35516i | −0.482245 | + | 0.278424i | −0.721352 | − | 0.692569i | \(-0.756479\pi\) |
0.239106 | + | 0.970993i | \(0.423146\pi\) | |||||||
\(522\) | −0.458180 | + | 0.264530i | −0.0200540 | + | 0.0115782i | ||||
\(523\) | −5.73591 | − | 3.31163i | −0.250814 | − | 0.144808i | 0.369323 | − | 0.929301i | \(-0.379590\pi\) |
−0.620137 | + | 0.784494i | \(0.712923\pi\) | |||||||
\(524\) | −7.10883 | −0.310551 | ||||||||
\(525\) | −4.32198 | + | 7.90470i | −0.188627 | + | 0.344990i | ||||
\(526\) | 11.8987 | 0.518808 | ||||||||
\(527\) | −14.8383 | + | 25.7006i | −0.646365 | + | 1.11954i | ||||
\(528\) | −2.20661 | − | 0.482275i | −0.0960305 | − | 0.0209883i | ||||
\(529\) | −8.13105 | − | 14.0834i | −0.353524 | − | 0.612321i | ||||
\(530\) | −6.51804 | − | 5.08150i | −0.283125 | − | 0.220726i | ||||
\(531\) | − | 14.6214i | − | 0.634516i | ||||||
\(532\) | 11.6973 | − | 3.62365i | 0.507142 | − | 0.157105i | ||||
\(533\) | 12.7870i | 0.553865i | ||||||||
\(534\) | 10.2336 | + | 5.90837i | 0.442851 | + | 0.255680i | ||||
\(535\) | 8.07265 | + | 19.9206i | 0.349011 | + | 0.861242i | ||||
\(536\) | −1.44891 | + | 0.836530i | −0.0625835 | + | 0.0361326i | ||||
\(537\) | −0.503961 | + | 0.872886i | −0.0217475 | + | 0.0376678i | ||||
\(538\) | 0.240879i | 0.0103850i | ||||||||
\(539\) | −21.5113 | + | 8.73298i | −0.926556 | + | 0.376156i | ||||
\(540\) | 8.34980 | + | 1.16460i | 0.359318 | + | 0.0501162i | ||||
\(541\) | −9.24839 | − | 5.33956i | −0.397619 | − | 0.229566i | 0.287837 | − | 0.957679i | \(-0.407064\pi\) |
−0.685456 | + | 0.728114i | \(0.740397\pi\) | |||||||
\(542\) | 4.79043 | + | 8.29727i | 0.205767 | + | 0.356398i | ||||
\(543\) | −6.37901 | + | 3.68292i | −0.273749 | + | 0.158049i | ||||
\(544\) | −2.89411 | − | 1.67092i | −0.124084 | − | 0.0716400i | ||||
\(545\) | −5.38627 | + | 38.6179i | −0.230723 | + | 1.65421i | ||||
\(546\) | −1.09354 | − | 3.53001i | −0.0467994 | − | 0.151071i | ||||
\(547\) | −29.6241 | −1.26663 | −0.633317 | − | 0.773893i | \(-0.718307\pi\) | ||||
−0.633317 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(548\) | −16.1860 | − | 9.34499i | −0.691432 | − | 0.399198i | ||||
\(549\) | −13.6604 | − | 23.6605i | −0.583012 | − | 1.00981i | ||||
\(550\) | −14.6135 | − | 7.83865i | −0.623123 | − | 0.334241i | ||||
\(551\) | −0.836155 | − | 0.482754i | −0.0356214 | − | 0.0205660i | ||||
\(552\) | 1.76777i | 0.0752412i | ||||||||
\(553\) | 39.7967 | + | 9.03267i | 1.69233 | + | 0.384108i | ||||
\(554\) | −24.8214 | −1.05456 | ||||||||
\(555\) | −4.35540 | − | 3.39549i | −0.184876 | − | 0.144131i | ||||
\(556\) | 9.80567 | + | 16.9839i | 0.415853 | + | 0.720279i | ||||
\(557\) | −1.83613 | − | 3.18026i | −0.0777991 | − | 0.134752i | 0.824501 | − | 0.565861i | \(-0.191456\pi\) |
−0.902300 | + | 0.431109i | \(0.858123\pi\) | |||||||
\(558\) | −19.5049 | − | 11.2612i | −0.825709 | − | 0.476723i | ||||
\(559\) | − | 13.4368i | − | 0.568315i | ||||||
\(560\) | 3.74490 | + | 4.57993i | 0.158251 | + | 0.193537i | ||||
\(561\) | 5.58035 | + | 5.08282i | 0.235602 | + | 0.214597i | ||||
\(562\) | 20.0363 | + | 11.5680i | 0.845181 | + | 0.487965i | ||||
\(563\) | −24.2556 | + | 14.0040i | −1.02225 | + | 0.590198i | −0.914756 | − | 0.404007i | \(-0.867617\pi\) |
−0.107498 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(564\) | 4.47822 | + | 7.75650i | 0.188567 | + | 0.326608i | ||||
\(565\) | −18.6886 | − | 14.5697i | −0.786236 | − | 0.612953i | ||||
\(566\) | 30.5704i | 1.28497i | ||||||||
\(567\) | −9.78778 | − | 9.05971i | −0.411048 | − | 0.380472i | ||||
\(568\) | 5.74537 | 0.241070 | ||||||||
\(569\) | 7.59248 | + | 4.38352i | 0.318293 | + | 0.183767i | 0.650632 | − | 0.759394i | \(-0.274504\pi\) |
−0.332338 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(570\) | 2.64715 | + | 6.53228i | 0.110877 | + | 0.273607i | ||||
\(571\) | −21.6883 | + | 12.5217i | −0.907626 | + | 0.524018i | −0.879667 | − | 0.475591i | \(-0.842234\pi\) |
−0.0279594 | + | 0.999609i | \(0.508901\pi\) | |||||||
\(572\) | 6.48138 | − | 2.06490i | 0.271000 | − | 0.0863380i | ||||
\(573\) | 12.0220 | 0.502226 | ||||||||
\(574\) | 3.65103 | − | 16.0859i | 0.152391 | − | 0.671413i | ||||
\(575\) | −3.55136 | + | 12.4834i | −0.148102 | + | 0.520594i | ||||
\(576\) | 1.26810 | − | 2.19642i | 0.0528376 | − | 0.0915175i | ||||
\(577\) | −12.2420 | − | 21.2037i | −0.509640 | − | 0.882722i | −0.999938 | − | 0.0111668i | \(-0.996445\pi\) |
0.490298 | − | 0.871555i | \(-0.336888\pi\) | |||||||
\(578\) | −2.91608 | − | 5.05079i | −0.121293 | − | 0.210085i | ||||
\(579\) | 7.40866 | − | 12.8322i | 0.307893 | − | 0.533287i | ||||
\(580\) | 0.0644350 | − | 0.461979i | 0.00267552 | − | 0.0191826i | ||||
\(581\) | −1.44639 | − | 4.66902i | −0.0600064 | − | 0.193703i | ||||
\(582\) | 4.05434 | 0.168058 | ||||||||
\(583\) | 11.6802 | − | 3.72119i | 0.483744 | − | 0.154116i | ||||
\(584\) | −6.62663 | + | 3.82589i | −0.274212 | + | 0.158316i | ||||
\(585\) | −10.7799 | + | 4.36847i | −0.445694 | + | 0.180614i | ||||
\(586\) | 3.91154 | + | 2.25833i | 0.161584 | + | 0.0932907i | ||||
\(587\) | 3.07712 | 0.127006 | 0.0635031 | − | 0.997982i | \(-0.479773\pi\) | ||||
0.0635031 | + | 0.997982i | \(0.479773\pi\) | |||||||
\(588\) | 0.367757 | + | 4.75296i | 0.0151660 | + | 0.196009i | ||||
\(589\) | − | 41.1021i | − | 1.69358i | ||||||
\(590\) | 10.1666 | + | 7.92595i | 0.418553 | + | 0.326306i | ||||
\(591\) | 1.21099 | + | 2.09749i | 0.0498134 | + | 0.0862793i | ||||
\(592\) | −3.14069 | + | 1.81328i | −0.129082 | + | 0.0745253i | ||||
\(593\) | −24.6596 | − | 14.2372i | −1.01265 | − | 0.584652i | −0.100682 | − | 0.994919i | \(-0.532102\pi\) |
−0.911966 | + | 0.410266i | \(0.865436\pi\) | |||||||
\(594\) | −8.42040 | + | 9.24461i | −0.345493 | + | 0.379311i | ||||
\(595\) | −3.18547 | − | 19.5122i | −0.130592 | − | 0.799924i | ||||
\(596\) | − | 5.04605i | − | 0.206694i | ||||||
\(597\) | 6.16681 | + | 3.56041i | 0.252391 | + | 0.145718i | ||||
\(598\) | −2.66193 | − | 4.61059i | −0.108854 | − | 0.188541i | ||||
\(599\) | −13.1686 | − | 22.8086i | −0.538053 | − | 0.931934i | −0.999009 | − | 0.0445115i | \(-0.985827\pi\) |
0.460956 | − | 0.887423i | \(-0.347506\pi\) | |||||||
\(600\) | −2.44449 | + | 2.37051i | −0.0997960 | + | 0.0967755i | ||||
\(601\) | −28.6070 | −1.16690 | −0.583452 | − | 0.812148i | \(-0.698298\pi\) | ||||
−0.583452 | + | 0.812148i | \(0.698298\pi\) | |||||||
\(602\) | −3.83657 | + | 16.9034i | −0.156367 | + | 0.688930i | ||||
\(603\) | 4.24322i | 0.172797i | ||||||||
\(604\) | −2.05768 | − | 1.18800i | −0.0837259 | − | 0.0483392i | ||||
\(605\) | 21.8369 | − | 11.3204i | 0.887795 | − | 0.460240i | ||||
\(606\) | −1.56647 | − | 2.71321i | −0.0636336 | − | 0.110217i | ||||
\(607\) | −6.93601 | − | 4.00451i | −0.281524 | − | 0.162538i | 0.352589 | − | 0.935778i | \(-0.385301\pi\) |
−0.634113 | + | 0.773240i | \(0.718635\pi\) | |||||||
\(608\) | 4.62844 | 0.187708 | ||||||||
\(609\) | 0.255320 | − | 0.275838i | 0.0103461 | − | 0.0111775i | ||||
\(610\) | 23.8567 | + | 3.32744i | 0.965930 | + | 0.134724i | ||||
\(611\) | −23.3597 | − | 13.4867i | −0.945031 | − | 0.545614i | ||||
\(612\) | −7.34007 | + | 4.23779i | −0.296705 | + | 0.171302i | ||||
\(613\) | 12.8523 | + | 22.2608i | 0.519099 | + | 0.899105i | 0.999754 | + | 0.0221956i | \(0.00706566\pi\) |
−0.480655 | + | 0.876910i | \(0.659601\pi\) | |||||||
\(614\) | −26.0324 | − | 15.0298i | −1.05058 | − | 0.606553i | ||||
\(615\) | 9.40303 | + | 1.31150i | 0.379167 | + | 0.0528847i | ||||
\(616\) | −8.74311 | + | 0.747023i | −0.352270 | + | 0.0300984i | ||||
\(617\) | 32.5391i | 1.30998i | 0.755640 | + | 0.654988i | \(0.227326\pi\) | ||||
−0.755640 | + | 0.654988i | \(0.772674\pi\) | |||||||
\(618\) | −1.37569 | + | 2.38277i | −0.0553385 | + | 0.0958491i | ||||
\(619\) | −33.3383 | + | 19.2479i | −1.33998 | + | 0.773637i | −0.986804 | − | 0.161920i | \(-0.948231\pi\) |
−0.353175 | + | 0.935557i | \(0.614898\pi\) | |||||||
\(620\) | 18.4033 | − | 7.45779i | 0.739095 | − | 0.299512i | ||||
\(621\) | 8.47555 | + | 4.89336i | 0.340112 | + | 0.196364i | ||||
\(622\) | − | 1.12171i | − | 0.0449765i | ||||||
\(623\) | 44.7689 | + | 10.1612i | 1.79363 | + | 0.407101i | ||||
\(624\) | − | 1.39677i | − | 0.0559157i | ||||||
\(625\) | −22.0245 | + | 11.8289i | −0.880979 | + | 0.473156i | ||||
\(626\) | 10.3195 | + | 17.8740i | 0.412451 | + | 0.714387i | ||||
\(627\) | −10.2132 | − | 2.23218i | −0.407875 | − | 0.0891447i | ||||
\(628\) | −0.279611 | + | 0.484300i | −0.0111577 | + | 0.0193257i | ||||
\(629\) | 12.1193 | 0.483230 | ||||||||
\(630\) | 14.8084 | − | 2.41754i | 0.589979 | − | 0.0963172i | ||||
\(631\) | 41.5135 | 1.65262 | 0.826312 | − | 0.563212i | \(-0.190435\pi\) | ||||
0.826312 | + | 0.563212i | \(0.190435\pi\) | |||||||
\(632\) | 13.3578 | + | 7.71215i | 0.531346 | + | 0.306773i | ||||
\(633\) | 14.5538 | − | 8.40266i | 0.578463 | − | 0.333976i | ||||
\(634\) | 18.3880 | − | 10.6163i | 0.730281 | − | 0.421628i | ||||
\(635\) | −16.9826 | + | 21.7836i | −0.673935 | + | 0.864457i | ||||
\(636\) | − | 2.51714i | − | 0.0998113i | ||||||
\(637\) | −8.11623 | − | 11.8426i | −0.321577 | − | 0.469222i | ||||
\(638\) | 0.511487 | + | 0.465885i | 0.0202500 | + | 0.0184446i | ||||
\(639\) | 7.28572 | − | 12.6192i | 0.288219 | − | 0.499209i | ||||
\(640\) | 0.839811 | + | 2.07237i | 0.0331964 | + | 0.0819176i | ||||
\(641\) | 6.91276 | + | 11.9732i | 0.273038 | + | 0.472915i | 0.969638 | − | 0.244544i | \(-0.0786383\pi\) |
−0.696601 | + | 0.717459i | \(0.745305\pi\) | |||||||
\(642\) | −3.27316 | + | 5.66928i | −0.129181 | + | 0.223749i | ||||
\(643\) | −1.24361 | −0.0490430 | −0.0245215 | − | 0.999699i | \(-0.507806\pi\) | ||||
−0.0245215 | + | 0.999699i | \(0.507806\pi\) | |||||||
\(644\) | 2.03223 | + | 6.56014i | 0.0800812 | + | 0.258506i | ||||
\(645\) | −9.88088 | − | 1.37815i | −0.389059 | − | 0.0542644i | ||||
\(646\) | −13.3952 | − | 7.73374i | −0.527028 | − | 0.304280i | ||||
\(647\) | 5.28986 | + | 9.16230i | 0.207966 | + | 0.360207i | 0.951074 | − | 0.308964i | \(-0.0999824\pi\) |
−0.743108 | + | 0.669172i | \(0.766649\pi\) | |||||||
\(648\) | −2.52048 | − | 4.36560i | −0.0990138 | − | 0.171497i | ||||
\(649\) | −18.2184 | + | 5.80420i | −0.715134 | + | 0.227835i | ||||
\(650\) | 2.80605 | − | 9.86357i | 0.110062 | − | 0.386881i | ||||
\(651\) | 15.6039 | + | 3.54162i | 0.611564 | + | 0.138807i | ||||
\(652\) | − | 21.9721i | − | 0.860495i | ||||||
\(653\) | 15.2726 | + | 8.81765i | 0.597663 | + | 0.345061i | 0.768122 | − | 0.640304i | \(-0.221192\pi\) |
−0.170458 | + | 0.985365i | \(0.554525\pi\) | |||||||
\(654\) | −10.2844 | + | 5.93773i | −0.402154 | + | 0.232183i | ||||
\(655\) | −5.97007 | − | 14.7321i | −0.233270 | − | 0.575632i | ||||
\(656\) | 3.11727 | − | 5.39927i | 0.121709 | − | 0.210806i | ||||
\(657\) | 19.4065i | 0.757119i | ||||||||
\(658\) | 25.5355 | + | 23.6360i | 0.995476 | + | 0.921427i | ||||
\(659\) | 14.3408i | 0.558639i | 0.960198 | + | 0.279319i | \(0.0901088\pi\) | ||||
−0.960198 | + | 0.279319i | \(0.909891\pi\) | |||||||
\(660\) | −0.853686 | − | 4.97794i | −0.0332297 | − | 0.193766i | ||||
\(661\) | −19.0348 | + | 10.9898i | −0.740369 | + | 0.427452i | −0.822203 | − | 0.569194i | \(-0.807255\pi\) |
0.0818346 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(662\) | −8.87838 | − | 15.3778i | −0.345068 | − | 0.597676i | ||||
\(663\) | −2.33389 | + | 4.04242i | −0.0906408 | + | 0.156994i | ||||
\(664\) | − | 1.84746i | − | 0.0716954i | ||||||
\(665\) | 17.3330 | + | 21.1979i | 0.672147 | + | 0.822021i | ||||
\(666\) | 9.19770i | 0.356403i | ||||||||
\(667\) | 0.270741 | − | 0.468937i | 0.0104831 | − | 0.0181573i | ||||
\(668\) | −9.16345 | + | 5.29052i | −0.354545 | + | 0.204696i | ||||
\(669\) | −8.76080 | − | 15.1742i | −0.338712 | − | 0.586667i | ||||
\(670\) | −2.95041 | − | 2.30016i | −0.113984 | − | 0.0888628i | ||||
\(671\) | −24.0584 | + | 26.4133i | −0.928765 | + | 1.01968i | ||||
\(672\) | −0.398816 | + | 1.75713i | −0.0153847 | + | 0.0677827i | ||||
\(673\) | −17.7793 | −0.685341 | −0.342670 | − | 0.939456i | \(-0.611331\pi\) | ||||
−0.342670 | + | 0.939456i | \(0.611331\pi\) | |||||||
\(674\) | −5.78996 | + | 10.0285i | −0.223021 | + | 0.386284i | ||||
\(675\) | 4.59877 | + | 18.2819i | 0.177007 | + | 0.703671i | ||||
\(676\) | −4.39672 | − | 7.61535i | −0.169105 | − | 0.292898i | ||||
\(677\) | 21.8386 | + | 12.6085i | 0.839325 | + | 0.484585i | 0.857035 | − | 0.515259i | \(-0.172304\pi\) |
−0.0177096 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(678\) | − | 7.21719i | − | 0.277175i | ||||||
\(679\) | 15.0455 | − | 4.66088i | 0.577395 | − | 0.178868i | ||||
\(680\) | 1.03225 | − | 7.40093i | 0.0395850 | − | 0.283813i | ||||
\(681\) | −6.77608 | − | 3.91217i | −0.259660 | − | 0.149915i | ||||
\(682\) | −6.28870 | + | 28.7735i | −0.240807 | + | 1.10179i | ||||
\(683\) | −18.6523 | + | 10.7689i | −0.713712 | + | 0.412062i | −0.812434 | − | 0.583053i | \(-0.801858\pi\) |
0.0987218 | + | 0.995115i | \(0.468525\pi\) | |||||||
\(684\) | 5.86934 | − | 10.1660i | 0.224420 | − | 0.388707i | ||||
\(685\) | 5.77311 | − | 41.3914i | 0.220579 | − | 1.58148i | ||||
\(686\) | 6.82876 | + | 17.2153i | 0.260723 | + | 0.657285i | ||||
\(687\) | − | 12.8353i | − | 0.489697i | ||||||
\(688\) | −3.27568 | + | 5.67365i | −0.124884 | + | 0.216306i | ||||
\(689\) | 3.79035 | + | 6.56507i | 0.144401 | + | 0.250109i | ||||
\(690\) | −3.66347 | + | 1.48459i | −0.139466 | + | 0.0565174i | ||||
\(691\) | −25.7641 | − | 14.8749i | −0.980114 | − | 0.565869i | −0.0778094 | − | 0.996968i | \(-0.524793\pi\) |
−0.902305 | + | 0.431099i | \(0.858126\pi\) | |||||||
\(692\) | 3.96470i | 0.150715i | ||||||||
\(693\) | −9.44639 | + | 20.1508i | −0.358839 | + | 0.765467i | ||||
\(694\) | 8.68234 | 0.329577 | ||||||||
\(695\) | −26.9621 | + | 34.5843i | −1.02273 | + | 1.31186i | ||||
\(696\) | 0.123031 | − | 0.0710319i | 0.00466347 | − | 0.00269246i | ||||
\(697\) | −18.0435 | + | 10.4174i | −0.683445 | + | 0.394587i | ||||
\(698\) | −5.15736 | + | 8.93281i | −0.195209 | + | 0.338112i | ||||
\(699\) | −6.17122 | −0.233417 | ||||||||
\(700\) | −6.34630 | + | 11.6071i | −0.239868 | + | 0.438707i | ||||
\(701\) | 27.1878i | 1.02687i | 0.858128 | + | 0.513435i | \(0.171627\pi\) | ||||
−0.858128 | + | 0.513435i | \(0.828373\pi\) | |||||||
\(702\) | −6.69682 | − | 3.86641i | −0.252755 | − | 0.145928i | ||||
\(703\) | −14.5365 | + | 8.39266i | −0.548255 | + | 0.316535i | ||||
\(704\) | −3.24014 | − | 0.708161i | −0.122117 | − | 0.0266898i | ||||
\(705\) | −12.3135 | + | 15.7945i | −0.463753 | + | 0.594856i | ||||
\(706\) | 11.1655 | 0.420218 | ||||||||
\(707\) | −8.93225 | − | 8.26782i | −0.335932 | − | 0.310944i | ||||
\(708\) | 3.92616i | 0.147554i | ||||||||
\(709\) | 18.0630 | − | 31.2859i | 0.678368 | − | 1.17497i | −0.297104 | − | 0.954845i | \(-0.596021\pi\) |
0.975472 | − | 0.220123i | \(-0.0706460\pi\) | |||||||
\(710\) | 4.82502 | + | 11.9065i | 0.181080 | + | 0.446844i | ||||
\(711\) | 33.8782 | − | 19.5596i | 1.27053 | − | 0.733542i | ||||
\(712\) | 15.0268 | + | 8.67572i | 0.563152 | + | 0.325136i | ||||
\(713\) | 23.0511 | 0.863270 | ||||||||
\(714\) | 4.09023 | − | 4.41894i | 0.153073 | − | 0.165375i | ||||
\(715\) | 9.72238 | + | 11.6977i | 0.363596 | + | 0.437469i | ||||
\(716\) | −0.740004 | + | 1.28173i | −0.0276553 | + | 0.0479003i | ||||
\(717\) | 11.2401 | − | 6.48946i | 0.419769 | − | 0.242353i | ||||
\(718\) | −16.5110 | + | 9.53265i | −0.616187 | + | 0.355755i | ||||
\(719\) | 24.3745 | + | 14.0726i | 0.909016 | + | 0.524821i | 0.880114 | − | 0.474762i | \(-0.157466\pi\) |
0.0289015 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(720\) | 5.61676 | + | 0.783403i | 0.209324 | + | 0.0291957i | ||||
\(721\) | −2.36592 | + | 10.4239i | −0.0881114 | + | 0.388206i | ||||
\(722\) | 2.42248 | 0.0901555 | ||||||||
\(723\) | −2.50532 | + | 4.33933i | −0.0931737 | + | 0.161382i | ||||
\(724\) | −9.36679 | + | 5.40792i | −0.348114 | + | 0.200984i | ||||
\(725\) | 1.01150 | − | 0.254442i | 0.0375663 | − | 0.00944973i | ||||
\(726\) | 6.80821 | + | 3.12527i | 0.252676 | + | 0.115990i | ||||
\(727\) | −6.28055 | −0.232933 | −0.116466 | − | 0.993195i | \(-0.537157\pi\) | ||||
−0.116466 | + | 0.993195i | \(0.537157\pi\) | |||||||
\(728\) | −1.60574 | − | 5.18339i | −0.0595125 | − | 0.192109i | ||||
\(729\) | −5.08195 | −0.188220 | ||||||||
\(730\) | −13.4938 | − | 10.5198i | −0.499427 | − | 0.389356i | ||||
\(731\) | 18.9604 | − | 10.9468i | 0.701276 | − | 0.404882i | ||||
\(732\) | 3.66810 | + | 6.35334i | 0.135577 | + | 0.234826i | ||||
\(733\) | −32.5279 | − | 18.7800i | −1.20144 | − | 0.693655i | −0.240569 | − | 0.970632i | \(-0.577334\pi\) |
−0.960876 | + | 0.276978i | \(0.910667\pi\) | |||||||
\(734\) | 6.03112 | 0.222613 | ||||||||
\(735\) | −9.54105 | + | 4.75372i | −0.351927 | + | 0.175343i | ||||
\(736\) | 2.59575i | 0.0956806i | ||||||||
\(737\) | 5.28708 | − | 1.68441i | 0.194752 | − | 0.0620461i | ||||
\(738\) | −7.90604 | − | 13.6937i | −0.291025 | − | 0.504071i | ||||
\(739\) | −9.42805 | + | 5.44329i | −0.346817 | + | 0.200235i | −0.663282 | − | 0.748369i | \(-0.730837\pi\) |
0.316466 | + | 0.948604i | \(0.397504\pi\) | |||||||
\(740\) | −6.39537 | − | 4.98586i | −0.235098 | − | 0.183284i | ||||
\(741\) | − | 6.46488i | − | 0.237493i | ||||||
\(742\) | −2.89372 | − | 9.34106i | −0.106232 | − | 0.342921i | ||||
\(743\) | −18.1135 | −0.664520 | −0.332260 | − | 0.943188i | \(-0.607811\pi\) | ||||
−0.332260 | + | 0.943188i | \(0.607811\pi\) | |||||||
\(744\) | 5.23747 | + | 3.02386i | 0.192015 | + | 0.110860i | ||||
\(745\) | 10.4573 | − | 4.23773i | 0.383125 | − | 0.155258i | ||||
\(746\) | 0.803802 | + | 1.39223i | 0.0294293 | + | 0.0509730i | ||||
\(747\) | −4.05780 | − | 2.34277i | −0.148467 | − | 0.0857175i | ||||
\(748\) | 8.19405 | + | 7.46350i | 0.299604 | + | 0.272893i | ||||
\(749\) | −5.62918 | + | 24.8014i | −0.205686 | + | 0.906223i | ||||
\(750\) | −6.96548 | − | 3.07512i | −0.254343 | − | 0.112287i | ||||
\(751\) | 15.8194 | − | 27.4001i | 0.577260 | − | 0.999843i | −0.418533 | − | 0.908202i | \(-0.637455\pi\) |
0.995792 | − | 0.0916410i | \(-0.0292112\pi\) | |||||||
\(752\) | 6.57571 | + | 11.3895i | 0.239792 | + | 0.415331i | ||||
\(753\) | 5.83260 | − | 3.36745i | 0.212552 | − | 0.122717i | ||||
\(754\) | −0.213921 | + | 0.370523i | −0.00779056 | + | 0.0134936i | ||||
\(755\) | 0.733920 | − | 5.26198i | 0.0267101 | − | 0.191503i | ||||
\(756\) | 7.32058 | + | 6.77604i | 0.266247 | + | 0.246442i | ||||
\(757\) | 28.5956i | 1.03932i | 0.854372 | + | 0.519662i | \(0.173942\pi\) | ||||
−0.854372 | + | 0.519662i | \(0.826058\pi\) | |||||||
\(758\) | 10.5041 | − | 18.1936i | 0.381525 | − | 0.660821i | ||||
\(759\) | 1.25186 | − | 5.72781i | 0.0454398 | − | 0.207906i | ||||
\(760\) | 3.88702 | + | 9.59185i | 0.140997 | + | 0.347933i | ||||
\(761\) | −18.0463 | + | 31.2572i | −0.654179 | + | 1.13307i | 0.327920 | + | 0.944706i | \(0.393652\pi\) |
−0.982099 | + | 0.188366i | \(0.939681\pi\) | |||||||
\(762\) | −8.41243 | −0.304750 | ||||||||
\(763\) | −31.3393 | + | 33.8578i | −1.13456 | + | 1.22573i | ||||
\(764\) | 17.6528 | 0.638657 | ||||||||
\(765\) | −14.9465 | − | 11.6524i | −0.540393 | − | 0.421293i | ||||
\(766\) | 15.2258 | + | 26.3718i | 0.550129 | + | 0.952852i | ||||
\(767\) | −5.91206 | − | 10.2400i | −0.213472 | − | 0.369744i | ||||
\(768\) | −0.340512 | + | 0.589784i | −0.0122872 | + | 0.0212820i | ||||
\(769\) | 28.3685 | 1.02299 | 0.511497 | − | 0.859285i | \(-0.329091\pi\) | ||||
0.511497 | + | 0.859285i | \(0.329091\pi\) | |||||||
\(770\) | −8.89066 | − | 17.4916i | −0.320397 | − | 0.630354i | ||||
\(771\) | 11.7992 | 0.424939 | ||||||||
\(772\) | 10.8787 | − | 18.8425i | 0.391533 | − | 0.678155i | ||||
\(773\) | −14.6951 | − | 25.4526i | −0.528545 | − | 0.915466i | −0.999446 | − | 0.0332805i | \(-0.989405\pi\) |
0.470901 | − | 0.882186i | \(-0.343929\pi\) | |||||||
\(774\) | 8.30781 | + | 14.3896i | 0.298618 | + | 0.517222i | ||||
\(775\) | 30.9106 | + | 31.8753i | 1.11034 | + | 1.14500i | ||||
\(776\) | 5.95329 | 0.213711 | ||||||||
\(777\) | −1.93360 | − | 6.24176i | −0.0693677 | − | 0.223922i | ||||
\(778\) | −28.9110 | −1.03651 | ||||||||
\(779\) | 14.4281 | − | 24.9902i | 0.516940 | − | 0.895367i | ||||
\(780\) | 2.89463 | − | 1.17302i | 0.103644 | − | 0.0420010i | ||||
\(781\) | −18.6158 | − | 4.06865i | −0.666126 | − | 0.145588i | ||||
\(782\) | 4.33728 | − | 7.51239i | 0.155101 | − | 0.268642i | ||||
\(783\) | − | 0.786494i | − | 0.0281070i | ||||||
\(784\) | 0.540006 | + | 6.97914i | 0.0192859 | + | 0.249255i | ||||
\(785\) | −1.23847 | − | 0.172737i | −0.0442028 | − | 0.00616523i | ||||
\(786\) | 2.42064 | − | 4.19268i | 0.0863415 | − | 0.149548i | ||||
\(787\) | −25.2858 | + | 14.5988i | −0.901341 | + | 0.520390i | −0.877635 | − | 0.479329i | \(-0.840880\pi\) |
−0.0237062 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(788\) | 1.77819 | + | 3.07991i | 0.0633452 | + | 0.109717i | ||||
\(789\) | −4.05165 | + | 7.01766i | −0.144243 | + | 0.249835i | ||||
\(790\) | −4.76438 | + | 34.1591i | −0.169509 | + | 1.21533i | ||||
\(791\) | −8.29691 | − | 26.7828i | −0.295004 | − | 0.952287i | ||||
\(792\) | −5.66425 | + | 6.21868i | −0.201270 | + | 0.220971i | ||||
\(793\) | −19.1339 | − | 11.0470i | −0.679464 | − | 0.392289i | ||||
\(794\) | −11.2369 | − | 19.4629i | −0.398782 | − | 0.690711i | ||||
\(795\) | 5.21645 | − | 2.11392i | 0.185009 | − | 0.0749732i | ||||
\(796\) | 9.05521 | + | 5.22803i | 0.320953 | + | 0.185303i | ||||
\(797\) | 46.8193 | 1.65843 | 0.829213 | − | 0.558933i | \(-0.188789\pi\) | ||||
0.829213 | + | 0.558933i | \(0.188789\pi\) | |||||||
\(798\) | −1.84590 | + | 8.13277i | −0.0653441 | + | 0.287897i | ||||
\(799\) | − | 43.9499i | − | 1.55483i | ||||||
\(800\) | −3.58944 | + | 3.48080i | −0.126906 | + | 0.123065i | ||||
\(801\) | 38.1110 | − | 22.0034i | 1.34659 | − | 0.777452i | ||||
\(802\) | −10.8958 | − | 18.8721i | −0.384745 | − | 0.666398i | ||||
\(803\) | 24.1806 | − | 7.70369i | 0.853314 | − | 0.271857i | ||||
\(804\) | − | 1.13939i | − | 0.0401833i | ||||||
\(805\) | −11.8883 | + | 9.72081i | −0.419009 | + | 0.342614i | ||||
\(806\) | −18.2134 | −0.641541 | ||||||||
\(807\) | −0.142066 | − | 0.0820221i | −0.00500097 | − | 0.00288731i | ||||
\(808\) | −2.30017 | − | 3.98401i | −0.0809197 | − | 0.140157i | ||||
\(809\) | 21.5069 | − | 12.4170i | 0.756141 | − | 0.436558i | −0.0717676 | − | 0.997421i | \(-0.522864\pi\) |
0.827908 | + | 0.560863i | \(0.189531\pi\) | |||||||
\(810\) | 6.93041 | − | 8.88965i | 0.243510 | − | 0.312350i | ||||
\(811\) | 16.5834 | 0.582322 | 0.291161 | − | 0.956674i | \(-0.405958\pi\) | ||||
0.291161 | + | 0.956674i | \(0.405958\pi\) | |||||||
\(812\) | 0.374906 | − | 0.405034i | 0.0131566 | − | 0.0142139i | ||||
\(813\) | −6.52480 | −0.228835 | ||||||||
\(814\) | 11.4604 | − | 3.65116i | 0.401686 | − | 0.127973i | ||||
\(815\) | 45.5344 | − | 18.4524i | 1.59500 | − | 0.646360i | ||||
\(816\) | 1.97096 | − | 1.13793i | 0.0689974 | − | 0.0398357i | ||||
\(817\) | −15.1613 | + | 26.2602i | −0.530427 | + | 0.918727i | ||||
\(818\) | −13.7767 | −0.481692 | ||||||||
\(819\) | −13.4211 | − | 3.04620i | −0.468972 | − | 0.106443i | ||||
\(820\) | 13.8072 | + | 1.92577i | 0.482168 | + | 0.0672509i | ||||
\(821\) | 26.5267 | + | 15.3152i | 0.925789 | + | 0.534504i | 0.885477 | − | 0.464683i | \(-0.153832\pi\) |
0.0403114 | + | 0.999187i | \(0.487165\pi\) | |||||||
\(822\) | 11.0231 | − | 6.36416i | 0.384473 | − | 0.221976i | ||||
\(823\) | −24.0405 | + | 13.8798i | −0.837998 | + | 0.483819i | −0.856583 | − | 0.516009i | \(-0.827417\pi\) |
0.0185849 | + | 0.999827i | \(0.494084\pi\) | |||||||
\(824\) | −2.02004 | + | 3.49881i | −0.0703713 | + | 0.121887i | ||||
\(825\) | 9.59920 | − | 5.94968i | 0.334201 | − | 0.207141i | ||||
\(826\) | 4.51353 | + | 14.5699i | 0.157046 | + | 0.506951i | ||||
\(827\) | −16.1744 | −0.562438 | −0.281219 | − | 0.959644i | \(-0.590739\pi\) | ||||
−0.281219 | + | 0.959644i | \(0.590739\pi\) | |||||||
\(828\) | 5.70135 | + | 3.29168i | 0.198136 | + | 0.114394i | ||||
\(829\) | −8.64849 | + | 4.99321i | −0.300375 | + | 0.173421i | −0.642611 | − | 0.766192i | \(-0.722149\pi\) |
0.342237 | + | 0.939614i | \(0.388816\pi\) | |||||||
\(830\) | 3.82862 | − | 1.55152i | 0.132893 | − | 0.0538539i | ||||
\(831\) | 8.45199 | − | 14.6393i | 0.293196 | − | 0.507831i | ||||
\(832\) | − | 2.05099i | − | 0.0711052i | ||||||
\(833\) | 10.0987 | − | 21.1007i | 0.349900 | − | 0.731097i | ||||
\(834\) | −13.3558 | −0.462473 | ||||||||
\(835\) | −18.6595 | − | 14.5470i | −0.645738 | − | 0.503421i | ||||
\(836\) | −14.9968 | − | 3.27768i | −0.518675 | − | 0.113361i | ||||
\(837\) | 28.9957 | − | 16.7407i | 1.00224 | − | 0.578643i | ||||
\(838\) | 2.87547 | + | 1.66015i | 0.0993316 | + | 0.0573491i | ||||
\(839\) | 36.2333i | 1.25091i | 0.780259 | + | 0.625456i | \(0.215087\pi\) | ||||
−0.780259 | + | 0.625456i | \(0.784913\pi\) | |||||||
\(840\) | −3.97635 | + | 0.649160i | −0.137197 | + | 0.0223982i | ||||
\(841\) | 28.9565 | 0.998499 | ||||||||
\(842\) | 0.664249 | − | 1.15051i | 0.0228915 | − | 0.0396493i | ||||
\(843\) | −13.6452 | + | 7.87806i | −0.469966 | + | 0.271335i | ||||
\(844\) | 21.3705 | − | 12.3383i | 0.735603 | − | 0.424701i | ||||
\(845\) | 12.0894 | − | 15.5071i | 0.415888 | − | 0.533460i | ||||
\(846\) | 33.3547 | 1.14676 | ||||||||
\(847\) | 28.8579 | + | 3.77107i | 0.991570 | + | 0.129575i | ||||
\(848\) | − | 3.69612i | − | 0.126925i | ||||||
\(849\) | −18.0299 | − | 10.4096i | −0.618785 | − | 0.357256i | ||||
\(850\) | 16.2044 | − | 4.07617i | 0.555805 | − | 0.139811i | ||||
\(851\) | −4.70681 | − | 8.15244i | −0.161348 | − | 0.279462i | ||||
\(852\) | −1.95637 | + | 3.38853i | −0.0670240 | + | 0.116089i | ||||
\(853\) | − | 6.56955i | − | 0.224937i | −0.993655 | − | 0.112468i | \(-0.964124\pi\) | ||
0.993655 | − | 0.112468i | \(-0.0358757\pi\) | |||||||
\(854\) | 20.9161 | + | 19.3602i | 0.715733 | + | 0.662493i | ||||
\(855\) | 25.9969 | + | 3.62594i | 0.889074 | + | 0.124004i | ||||
\(856\) | −4.80623 | + | 8.32464i | −0.164274 | + | 0.284530i | ||||
\(857\) | −6.09840 | + | 3.52092i | −0.208318 | + | 0.120272i | −0.600529 | − | 0.799603i | \(-0.705043\pi\) |
0.392212 | + | 0.919875i | \(0.371710\pi\) | |||||||
\(858\) | −0.989140 | + | 4.52574i | −0.0337687 | + | 0.154506i | ||||
\(859\) | −6.18365 | − | 3.57013i | −0.210983 | − | 0.121811i | 0.390785 | − | 0.920482i | \(-0.372204\pi\) |
−0.601768 | + | 0.798671i | \(0.705537\pi\) | |||||||
\(860\) | −14.5089 | − | 2.02364i | −0.494748 | − | 0.0690055i | ||||
\(861\) | 8.24399 | + | 7.63076i | 0.280955 | + | 0.260056i | ||||
\(862\) | 21.0927i | 0.718420i | ||||||||
\(863\) | 40.0293 | + | 23.1109i | 1.36261 | + | 0.786706i | 0.989971 | − | 0.141269i | \(-0.0451182\pi\) |
0.372643 | + | 0.927975i | \(0.378452\pi\) | |||||||
\(864\) | 1.88514 | + | 3.26517i | 0.0641339 | + | 0.111083i | ||||
\(865\) | −8.21632 | + | 3.32959i | −0.279363 | + | 0.113210i | ||||
\(866\) | −2.50217 | + | 4.33389i | −0.0850272 | + | 0.147271i | ||||
\(867\) | 3.97184 | 0.134891 | ||||||||
\(868\) | 22.9124 | + | 5.20043i | 0.777696 | + | 0.176514i | ||||
\(869\) | −37.8198 | − | 34.4479i | −1.28295 | − | 1.16857i | ||||
\(870\) | 0.250527 | + | 0.195312i | 0.00849366 | + | 0.00662170i | ||||
\(871\) | 1.71571 | + | 2.97170i | 0.0581347 | + | 0.100692i | ||||
\(872\) | −15.1014 | + | 8.71882i | −0.511399 | + | 0.295257i | ||||
\(873\) | 7.54939 | − | 13.0759i | 0.255508 | − | 0.442553i | ||||
\(874\) | 12.0143i | 0.406389i | ||||||||
\(875\) | −29.3839 | − | 3.40413i | −0.993356 | − | 0.115081i | ||||
\(876\) | − | 5.21104i | − | 0.176065i | ||||||
\(877\) | −13.3820 | + | 23.1784i | −0.451879 | + | 0.782678i | −0.998503 | − | 0.0547006i | \(-0.982580\pi\) |
0.546624 | + | 0.837378i | \(0.315913\pi\) | |||||||
\(878\) | 4.57091 | + | 7.91705i | 0.154261 | + | 0.267187i | ||||
\(879\) | −2.66385 | + | 1.53798i | −0.0898495 | + | 0.0518746i | ||||
\(880\) | −1.25353 | − | 7.30949i | −0.0422566 | − | 0.246403i | ||||
\(881\) | − | 4.15297i | − | 0.139917i | −0.997550 | − | 0.0699586i | \(-0.977713\pi\) | ||
0.997550 | − | 0.0699586i | \(-0.0222867\pi\) | |||||||
\(882\) | 16.0139 | + | 7.66419i | 0.539216 | + | 0.258067i | ||||
\(883\) | − | 8.52040i | − | 0.286734i | −0.989670 | − | 0.143367i | \(-0.954207\pi\) | ||
0.989670 | − | 0.143367i | \(-0.0457930\pi\) | |||||||
\(884\) | −3.42703 | + | 5.93579i | −0.115264 | + | 0.199642i | ||||
\(885\) | −8.13645 | + | 3.29723i | −0.273504 | + | 0.110835i | ||||
\(886\) | 4.23828 | − | 2.44697i | 0.142388 | − | 0.0822076i | ||||
\(887\) | −1.73379 | − | 1.00101i | −0.0582150 | − | 0.0336105i | 0.470610 | − | 0.882341i | \(-0.344034\pi\) |
−0.528825 | + | 0.848731i | \(0.677367\pi\) | |||||||
\(888\) | − | 2.46977i | − | 0.0828801i | ||||||
\(889\) | −31.2183 | + | 9.67097i | −1.04703 | + | 0.324354i | ||||
\(890\) | −5.35965 | + | 38.4270i | −0.179656 | + | 1.28808i | ||||
\(891\) | 5.07516 | + | 15.9301i | 0.170024 | + | 0.533677i | ||||
\(892\) | −12.8642 | − | 22.2814i | −0.430724 | − | 0.746036i | ||||
\(893\) | 30.4353 | + | 52.7155i | 1.01848 | + | 1.76406i | ||||
\(894\) | 2.97608 | + | 1.71824i | 0.0995351 | + | 0.0574666i | ||||
\(895\) | −3.27767 | − | 0.457157i | −0.109561 | − | 0.0152811i | ||||
\(896\) | −0.585613 | + | 2.58013i | −0.0195640 | + | 0.0861960i | ||||
\(897\) | 3.62567 | 0.121058 | ||||||||
\(898\) | −1.59758 | + | 2.76709i | −0.0533120 | + | 0.0923390i | ||||
\(899\) | −0.926232 | − | 1.60428i | −0.0308916 | − | 0.0535058i | ||||
\(900\) | 3.09351 | + | 12.2979i | 0.103117 | + | 0.409931i | ||||
\(901\) | −6.17590 | + | 10.6970i | −0.205749 | + | 0.356368i | ||||
\(902\) | −13.9239 | + | 15.2869i | −0.463617 | + | 0.508997i | ||||
\(903\) | −8.66294 | − | 8.01855i | −0.288285 | − | 0.266840i | ||||
\(904\) | − | 10.5976i | − | 0.352470i | ||||||
\(905\) | −19.0735 | − | 14.8698i | −0.634026 | − | 0.494290i | ||||
\(906\) | 1.40133 | − | 0.809059i | 0.0465561 | − | 0.0268792i | ||||
\(907\) | 28.8503 | − | 16.6567i | 0.957958 | − | 0.553077i | 0.0624140 | − | 0.998050i | \(-0.480120\pi\) |
0.895544 | + | 0.444973i | \(0.146787\pi\) | |||||||
\(908\) | −9.94984 | − | 5.74454i | −0.330197 | − | 0.190639i | ||||
\(909\) | −11.6674 | −0.386984 | ||||||||
\(910\) | 9.39338 | − | 7.68074i | 0.311388 | − | 0.254614i | ||||
\(911\) | 7.49371 | 0.248278 | 0.124139 | − | 0.992265i | \(-0.460383\pi\) | ||||
0.124139 | + | 0.992265i | \(0.460383\pi\) | |||||||
\(912\) | −1.57604 | + | 2.72978i | −0.0521879 | + | 0.0903921i | ||||
\(913\) | −1.30830 | + | 5.98603i | −0.0432984 | + | 0.198109i | ||||
\(914\) | 7.73790 | + | 13.4024i | 0.255947 | + | 0.443313i | ||||
\(915\) | −10.0860 | + | 12.9373i | −0.333432 | + | 0.427693i | ||||
\(916\) | − | 18.8471i | − | 0.622725i | ||||||
\(917\) | 4.16302 | − | 18.3417i | 0.137475 | − | 0.605696i | ||||
\(918\) | − | 12.5997i | − | 0.415851i | ||||||
\(919\) | −43.7672 | − | 25.2690i | −1.44375 | − | 0.833547i | −0.445649 | − | 0.895208i | \(-0.647027\pi\) |
−0.998097 | + | 0.0616610i | \(0.980360\pi\) | |||||||
\(920\) | −5.37935 | + | 2.17994i | −0.177352 | + | 0.0718704i | ||||
\(921\) | 17.7287 | − | 10.2356i | 0.584179 | − | 0.337276i | ||||
\(922\) | −1.27863 | + | 2.21464i | −0.0421093 | + | 0.0729354i | ||||
\(923\) | − | 11.7837i | − | 0.387865i | ||||||
\(924\) | 2.53655 | − | 5.41092i | 0.0834464 | − | 0.178006i | ||||
\(925\) | 4.96165 | − | 17.4408i | 0.163138 | − | 0.573448i | ||||
\(926\) | −28.2171 | − | 16.2911i | −0.927271 | − | 0.535360i | ||||
\(927\) | 5.12323 | + | 8.87369i | 0.168269 | + | 0.291450i | ||||
\(928\) | 0.180656 | − | 0.104302i | 0.00593031 | − | 0.00342387i | ||||
\(929\) | −43.2077 | − | 24.9460i | −1.41760 | − | 0.818450i | −0.421510 | − | 0.906824i | \(-0.638500\pi\) |
−0.996087 | + | 0.0883737i | \(0.971833\pi\) | |||||||
\(930\) | −1.86806 | + | 13.3934i | −0.0612562 | + | 0.439188i | ||||
\(931\) | 2.49938 | + | 32.3026i | 0.0819140 | + | 1.05867i | ||||
\(932\) | −9.06168 | −0.296825 | ||||||||
\(933\) | 0.661566 | + | 0.381956i | 0.0216587 | + | 0.0125047i | ||||
\(934\) | −0.161793 | − | 0.280233i | −0.00529402 | − | 0.00916951i | ||||
\(935\) | −8.58569 | + | 23.2490i | −0.280782 | + | 0.760325i | ||||
\(936\) | −4.50483 | − | 2.60087i | −0.147245 | − | 0.0850119i | ||||
\(937\) | − | 46.4297i | − | 1.51679i | −0.651794 | − | 0.758396i | \(-0.725983\pi\) | ||
0.651794 | − | 0.758396i | \(-0.274017\pi\) | |||||||
\(938\) | −1.30985 | − | 4.22826i | −0.0427682 | − | 0.138058i | ||||
\(939\) | −14.0557 | −0.458690 | ||||||||
\(940\) | −18.0808 | + | 23.1923i | −0.589732 | + | 0.756450i | ||||
\(941\) | −18.9088 | − | 32.7510i | −0.616409 | − | 1.06765i | −0.990136 | − | 0.140112i | \(-0.955254\pi\) |
0.373727 | − | 0.927539i | \(-0.378080\pi\) | |||||||
\(942\) | −0.190422 | − | 0.329820i | −0.00620427 | − | 0.0107461i | ||||
\(943\) | 14.0151 | + | 8.09165i | 0.456396 | + | 0.263500i | ||||
\(944\) | 5.76508i | 0.187637i | ||||||||
\(945\) | −7.89456 | + | 20.8615i | −0.256810 | + | 0.678626i | ||||
\(946\) | 14.6315 | − | 16.0637i | 0.475712 | − | 0.522276i | ||||
\(947\) | 10.1023 | + | 5.83256i | 0.328280 | + | 0.189533i | 0.655077 | − | 0.755562i | \(-0.272636\pi\) |
−0.326797 | + | 0.945095i | \(0.605969\pi\) | |||||||
\(948\) | −9.09701 | + | 5.25216i | −0.295457 | + | 0.170582i | ||||
\(949\) | 7.84685 | + | 13.5911i | 0.254720 | + | 0.441187i | ||||
\(950\) | −16.6135 | + | 16.1107i | −0.539013 | + | 0.522699i | ||||
\(951\) | 14.4599i | 0.468895i | ||||||||
\(952\) | 6.00601 | − | 6.48867i | 0.194656 | − | 0.210299i | ||||
\(953\) | −31.7232 | −1.02761 | −0.513807 | − | 0.857906i | \(-0.671765\pi\) | ||||
−0.513807 | + | 0.857906i | \(0.671765\pi\) | |||||||
\(954\) | −8.11822 | − | 4.68706i | −0.262837 | − | 0.151749i | ||||
\(955\) | 14.8250 | + | 36.5832i | 0.479727 | + | 1.18380i | ||||
\(956\) | 16.5047 | − | 9.52898i | 0.533799 | − | 0.308189i | ||||
\(957\) | −0.448939 | + | 0.143028i | −0.0145121 | + | 0.00462343i | ||||
\(958\) | 24.5887 | 0.794425 | ||||||||
\(959\) | 33.5900 | − | 36.2894i | 1.08468 | − | 1.17185i | ||||
\(960\) | −1.50822 | − | 0.210360i | −0.0486775 | − | 0.00678934i | ||||
\(961\) | 23.9301 | − | 41.4481i | 0.771937 | − | 1.33703i | ||||
\(962\) | 3.71901 | + | 6.44152i | 0.119906 | + | 0.207683i | ||||
\(963\) | 12.1896 | + | 21.1130i | 0.392804 | + | 0.680357i | ||||
\(964\) | −3.67875 | + | 6.37178i | −0.118485 | + | 0.205221i | ||||
\(965\) | 48.1846 | + | 6.72060i | 1.55112 | + | 0.216344i | ||||
\(966\) | −4.56106 | − | 1.03523i | −0.146750 | − | 0.0333079i | ||||
\(967\) | 23.7319 | 0.763167 | 0.381583 | − | 0.924334i | \(-0.375379\pi\) | ||||
0.381583 | + | 0.924334i | \(0.375379\pi\) | |||||||
\(968\) | 9.99702 | + | 4.58908i | 0.321316 | + | 0.147499i | ||||
\(969\) | 9.12248 | − | 5.26686i | 0.293056 | − | 0.169196i | ||||
\(970\) | 4.99964 | + | 12.3374i | 0.160529 | + | 0.396131i | ||||
\(971\) | −44.9933 | − | 25.9769i | −1.44390 | − | 0.833637i | −0.445795 | − | 0.895135i | \(-0.647079\pi\) |
−0.998107 | + | 0.0614977i | \(0.980412\pi\) | |||||||
\(972\) | 14.7439 | 0.472910 | ||||||||
\(973\) | −49.5630 | + | 15.3539i | −1.58892 | + | 0.492223i | ||||
\(974\) | 30.6150i | 0.980967i | ||||||||
\(975\) | 4.86188 | + | 5.01363i | 0.155705 | + | 0.160565i | ||||
\(976\) | 5.38616 | + | 9.32910i | 0.172407 | + | 0.298617i | ||||
\(977\) | −12.5562 | + | 7.24930i | −0.401707 | + | 0.231926i | −0.687220 | − | 0.726449i | \(-0.741169\pi\) |
0.285513 | + | 0.958375i | \(0.407836\pi\) | |||||||
\(978\) | 12.9588 | + | 7.48177i | 0.414377 | + | 0.239241i | ||||
\(979\) | −42.5451 | − | 38.7519i | −1.35975 | − | 1.23852i | ||||
\(980\) | −14.0099 | + | 6.98025i | −0.447529 | + | 0.222976i | ||||
\(981\) | 44.2255i | 1.41201i | ||||||||
\(982\) | 10.5621 | + | 6.09802i | 0.337049 | + | 0.194595i | ||||
\(983\) | −12.6199 | − | 21.8583i | −0.402511 | − | 0.697170i | 0.591517 | − | 0.806293i | \(-0.298529\pi\) |
−0.994028 | + | 0.109122i | \(0.965196\pi\) | |||||||
\(984\) | 2.12294 | + | 3.67703i | 0.0676767 | + | 0.117219i | ||||
\(985\) | −4.88937 | + | 6.27160i | −0.155788 | + | 0.199830i | ||||
\(986\) | −0.697117 | −0.0222007 | ||||||||
\(987\) | −22.6353 | + | 7.01207i | −0.720488 | + | 0.223196i | ||||
\(988\) | − | 9.49288i | − | 0.302009i | ||||||
\(989\) | −14.7274 | − | 8.50285i | −0.468303 | − | 0.270375i | ||||
\(990\) | −17.6443 | − | 6.51591i | −0.560773 | − | 0.207089i | ||||
\(991\) | 3.63988 | + | 6.30446i | 0.115625 | + | 0.200268i | 0.918029 | − | 0.396513i | \(-0.129780\pi\) |
−0.802405 | + | 0.596780i | \(0.796446\pi\) | |||||||
\(992\) | 7.69058 | + | 4.44016i | 0.244176 | + | 0.140975i | ||||
\(993\) | 12.0928 | 0.383753 | ||||||||
\(994\) | −3.36456 | + | 14.8238i | −0.106717 | + | 0.470182i | ||||
\(995\) | −3.22975 | + | 23.1563i | −0.102390 | + | 0.734104i | ||||
\(996\) | 1.08960 | + | 0.629082i | 0.0345254 | + | 0.0199332i | ||||
\(997\) | 47.8438 | − | 27.6227i | 1.51523 | − | 0.874818i | 0.515389 | − | 0.856956i | \(-0.327647\pi\) |
0.999840 | − | 0.0178623i | \(-0.00568606\pi\) | |||||||
\(998\) | −3.86443 | − | 6.69338i | −0.122326 | − | 0.211875i | ||||
\(999\) | −11.8413 | − | 6.83658i | −0.374643 | − | 0.216300i |
(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 | 770.2.o.a.439.11 | ✓ | 48 | |
5.4 | even | 2 | 770.2.o.b.439.14 | yes | 48 | ||
7.3 | odd | 6 | inner | 770.2.o.a.549.14 | yes | 48 | |
11.10 | odd | 2 | 770.2.o.b.439.11 | yes | 48 | ||
35.24 | odd | 6 | 770.2.o.b.549.11 | yes | 48 | ||
55.54 | odd | 2 | inner | 770.2.o.a.439.14 | yes | 48 | |
77.10 | even | 6 | 770.2.o.b.549.14 | yes | 48 | ||
385.164 | even | 6 | inner | 770.2.o.a.549.11 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.o.a.439.11 | ✓ | 48 | 1.1 | even | 1 | trivial | |
770.2.o.a.439.14 | yes | 48 | 55.54 | odd | 2 | inner | |
770.2.o.a.549.11 | yes | 48 | 385.164 | even | 6 | inner | |
770.2.o.a.549.14 | yes | 48 | 7.3 | odd | 6 | inner | |
770.2.o.b.439.11 | yes | 48 | 11.10 | odd | 2 | ||
770.2.o.b.439.14 | yes | 48 | 5.4 | even | 2 | ||
770.2.o.b.549.11 | yes | 48 | 35.24 | odd | 6 | ||
770.2.o.b.549.14 | yes | 48 | 77.10 | even | 6 |