Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(101,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bi (of order \(10\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 101.16 | ||
Character | \(\chi\) | \(=\) | 825.101 |
Dual form | 825.2.bi.h.776.16 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.428747 | − | 1.31955i | 0.303170 | − | 0.933062i | −0.677183 | − | 0.735814i | \(-0.736800\pi\) |
0.980354 | − | 0.197248i | \(-0.0632004\pi\) | |||||||
\(3\) | 1.68532 | + | 0.399638i | 0.973017 | + | 0.230731i | ||||
\(4\) | 0.0606486 | + | 0.0440638i | 0.0303243 | + | 0.0220319i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.24992 | − | 2.05251i | 0.510277 | − | 0.837935i | ||||
\(7\) | 0.527114 | − | 0.725510i | 0.199230 | − | 0.274217i | −0.697699 | − | 0.716391i | \(-0.745793\pi\) |
0.896929 | + | 0.442174i | \(0.145793\pi\) | |||||||
\(8\) | 2.32910 | − | 1.69219i | 0.823461 | − | 0.598279i | ||||
\(9\) | 2.68058 | + | 1.34703i | 0.893526 | + | 0.449011i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.46596 | − | 2.21790i | 0.743514 | − | 0.668721i | ||||
\(12\) | 0.0846024 | + | 0.0984989i | 0.0244226 | + | 0.0284342i | ||||
\(13\) | −6.22748 | − | 2.02343i | −1.72719 | − | 0.561199i | −0.734153 | − | 0.678984i | \(-0.762421\pi\) |
−0.993039 | + | 0.117785i | \(0.962421\pi\) | |||||||
\(14\) | −0.731347 | − | 1.00661i | −0.195461 | − | 0.269029i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.18800 | − | 3.65629i | −0.297000 | − | 0.914072i | ||||
\(17\) | 0.994701 | + | 3.06137i | 0.241250 | + | 0.742492i | 0.996231 | + | 0.0867447i | \(0.0276464\pi\) |
−0.754980 | + | 0.655748i | \(0.772354\pi\) | |||||||
\(18\) | 2.92677 | − | 2.95962i | 0.689846 | − | 0.697588i | ||||
\(19\) | 0.445440 | + | 0.613095i | 0.102191 | + | 0.140654i | 0.857050 | − | 0.515233i | \(-0.172295\pi\) |
−0.754859 | + | 0.655887i | \(0.772295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.17829 | − | 1.01206i | 0.257125 | − | 0.220849i | ||||
\(22\) | −1.86935 | − | 4.20487i | −0.398547 | − | 0.896481i | ||||
\(23\) | 0.697650i | 0.145470i | 0.997351 | + | 0.0727350i | \(0.0231727\pi\) | ||||
−0.997351 | + | 0.0727350i | \(0.976827\pi\) | |||||||
\(24\) | 4.60153 | − | 1.92108i | 0.939283 | − | 0.392138i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.34003 | + | 7.34992i | −1.04727 | + | 1.44144i | ||||
\(27\) | 3.97929 | + | 3.34144i | 0.765815 | + | 0.643060i | ||||
\(28\) | 0.0639374 | − | 0.0207745i | 0.0120830 | − | 0.00392602i | ||||
\(29\) | 2.21328 | + | 1.60804i | 0.410996 | + | 0.298606i | 0.774005 | − | 0.633180i | \(-0.218251\pi\) |
−0.363009 | + | 0.931786i | \(0.618251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.39303 | + | 7.36499i | −0.429801 | + | 1.32279i | 0.468521 | + | 0.883452i | \(0.344787\pi\) |
−0.898322 | + | 0.439338i | \(0.855213\pi\) | |||||||
\(32\) | 0.423844 | 0.0749258 | ||||||||
\(33\) | 5.04227 | − | 2.75236i | 0.877747 | − | 0.479125i | ||||
\(34\) | 4.46611 | 0.765931 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.103218 | + | 0.199812i | 0.0172030 | + | 0.0333020i | ||||
\(37\) | −3.98689 | − | 2.89665i | −0.655441 | − | 0.476206i | 0.209679 | − | 0.977770i | \(-0.432758\pi\) |
−0.865120 | + | 0.501565i | \(0.832758\pi\) | |||||||
\(38\) | 0.999990 | − | 0.324916i | 0.162220 | − | 0.0527084i | ||||
\(39\) | −9.68663 | − | 5.89886i | −1.55110 | − | 0.944574i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66350 | − | 1.93515i | 0.415970 | − | 0.302220i | −0.360045 | − | 0.932935i | \(-0.617239\pi\) |
0.776014 | + | 0.630716i | \(0.217239\pi\) | |||||||
\(42\) | −0.830270 | − | 1.98874i | −0.128113 | − | 0.306869i | ||||
\(43\) | − | 7.94703i | − | 1.21191i | −0.795499 | − | 0.605955i | \(-0.792791\pi\) | ||
0.795499 | − | 0.605955i | \(-0.207209\pi\) | |||||||
\(44\) | 0.247286 | − | 0.0258529i | 0.0372797 | − | 0.00389747i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.920583 | + | 0.299116i | 0.135733 | + | 0.0441022i | ||||
\(47\) | −4.78514 | − | 6.58618i | −0.697984 | − | 0.960693i | −0.999973 | − | 0.00738149i | \(-0.997650\pi\) |
0.301988 | − | 0.953312i | \(-0.402350\pi\) | |||||||
\(48\) | −0.540962 | − | 6.63677i | −0.0780811 | − | 0.957935i | ||||
\(49\) | 1.91460 | + | 5.89254i | 0.273515 | + | 0.841792i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.452942 | + | 5.55690i | 0.0634246 | + | 0.778122i | ||||
\(52\) | −0.288528 | − | 0.397124i | −0.0400116 | − | 0.0550713i | ||||
\(53\) | 6.58232 | + | 2.13872i | 0.904151 | + | 0.293776i | 0.723949 | − | 0.689853i | \(-0.242325\pi\) |
0.180202 | + | 0.983630i | \(0.442325\pi\) | |||||||
\(54\) | 6.11531 | − | 3.81824i | 0.832188 | − | 0.519597i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2.58176i | − | 0.345002i | ||||||
\(57\) | 0.505690 | + | 1.21127i | 0.0669803 | + | 0.160437i | ||||
\(58\) | 3.07083 | − | 2.23109i | 0.403220 | − | 0.292956i | ||||
\(59\) | −7.04822 | + | 9.70104i | −0.917600 | + | 1.26297i | 0.0469036 | + | 0.998899i | \(0.485065\pi\) |
−0.964504 | + | 0.264069i | \(0.914935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65156 | − | 0.536624i | 0.211460 | − | 0.0687076i | −0.201371 | − | 0.979515i | \(-0.564540\pi\) |
0.412832 | + | 0.910807i | \(0.364540\pi\) | |||||||
\(62\) | 8.69246 | + | 6.31544i | 1.10394 | + | 0.802062i | ||||
\(63\) | 2.39026 | − | 1.23475i | 0.301144 | − | 0.155563i | ||||
\(64\) | 2.55772 | − | 7.87186i | 0.319715 | − | 0.983982i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.47002 | − | 7.83359i | −0.180947 | − | 0.964249i | ||||
\(67\) | −1.90261 | −0.232441 | −0.116220 | − | 0.993223i | \(-0.537078\pi\) | ||||
−0.116220 | + | 0.993223i | \(0.537078\pi\) | |||||||
\(68\) | −0.0745685 | + | 0.229498i | −0.00904276 | + | 0.0278308i | ||||
\(69\) | −0.278808 | + | 1.17576i | −0.0335645 | + | 0.141545i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.354205 | + | 0.115088i | −0.0420364 | + | 0.0136585i | −0.329960 | − | 0.943995i | \(-0.607035\pi\) |
0.287923 | + | 0.957653i | \(0.407035\pi\) | |||||||
\(72\) | 8.52277 | − | 1.39867i | 1.00442 | − | 0.164835i | ||||
\(73\) | −2.97667 | + | 4.09704i | −0.348393 | + | 0.479522i | −0.946869 | − | 0.321618i | \(-0.895773\pi\) |
0.598476 | + | 0.801141i | \(0.295773\pi\) | |||||||
\(74\) | −5.53164 | + | 4.01897i | −0.643040 | + | 0.467196i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0568111i | 0.00651668i | ||||||||
\(77\) | −0.309265 | − | 2.95816i | −0.0352441 | − | 0.337114i | ||||
\(78\) | −11.9370 | + | 10.2529i | −1.35159 | + | 1.16091i | ||||
\(79\) | −14.2056 | − | 4.61569i | −1.59826 | − | 0.519306i | −0.631583 | − | 0.775309i | \(-0.717594\pi\) |
−0.966676 | + | 0.256003i | \(0.917594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.37100 | + | 7.22166i | 0.596778 | + | 0.802407i | ||||
\(82\) | −1.41155 | − | 4.34432i | −0.155880 | − | 0.479749i | ||||
\(83\) | −0.265916 | − | 0.818406i | −0.0291881 | − | 0.0898317i | 0.935401 | − | 0.353588i | \(-0.115039\pi\) |
−0.964589 | + | 0.263756i | \(0.915039\pi\) | |||||||
\(84\) | 0.116057 | − | 0.00945978i | 0.0126629 | − | 0.00103215i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.4865 | − | 3.40727i | −1.13079 | − | 0.367415i | ||||
\(87\) | 3.08744 | + | 3.59457i | 0.331008 | + | 0.385378i | ||||
\(88\) | 1.99036 | − | 9.33856i | 0.212173 | − | 0.995494i | ||||
\(89\) | 5.24506i | 0.555976i | 0.960585 | + | 0.277988i | \(0.0896675\pi\) | ||||
−0.960585 | + | 0.277988i | \(0.910333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.75061 | + | 3.45152i | −0.497999 | + | 0.361818i | ||||
\(92\) | −0.0307411 | + | 0.0423115i | −0.00320498 | + | 0.00441128i | ||||
\(93\) | −6.97634 | + | 11.4560i | −0.723413 | + | 1.18793i | ||||
\(94\) | −10.7424 | + | 3.49042i | −1.10799 | + | 0.360009i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.714311 | + | 0.169384i | 0.0729041 | + | 0.0172877i | ||||
\(97\) | −3.83972 | + | 11.8174i | −0.389864 | + | 1.19988i | 0.543025 | + | 0.839716i | \(0.317279\pi\) |
−0.932890 | + | 0.360163i | \(0.882721\pi\) | |||||||
\(98\) | 8.59638 | 0.868366 | ||||||||
\(99\) | 9.59777 | − | 2.62351i | 0.964612 | − | 0.263673i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.08008 | + | 12.5572i | −0.405983 | + | 1.24949i | 0.514089 | + | 0.857737i | \(0.328130\pi\) |
−0.920072 | + | 0.391750i | \(0.871870\pi\) | |||||||
\(102\) | 7.52680 | + | 1.78483i | 0.745265 | + | 0.176724i | ||||
\(103\) | 0.353627 | + | 0.256925i | 0.0348439 | + | 0.0253156i | 0.605071 | − | 0.796172i | \(-0.293145\pi\) |
−0.570227 | + | 0.821487i | \(0.693145\pi\) | |||||||
\(104\) | −17.9284 | + | 5.82530i | −1.75803 | + | 0.571218i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.64430 | − | 7.76872i | 0.548223 | − | 0.754565i | ||||
\(107\) | 0.509781 | − | 0.370378i | 0.0492824 | − | 0.0358058i | −0.562871 | − | 0.826545i | \(-0.690303\pi\) |
0.612154 | + | 0.790739i | \(0.290303\pi\) | |||||||
\(108\) | 0.0941021 | + | 0.377996i | 0.00905498 | + | 0.0363727i | ||||
\(109\) | 2.55958i | 0.245164i | 0.992458 | + | 0.122582i | \(0.0391174\pi\) | ||||
−0.992458 | + | 0.122582i | \(0.960883\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.56156 | − | 6.47508i | −0.527880 | − | 0.614587i | ||||
\(112\) | −3.27888 | − | 1.06537i | −0.309825 | − | 0.100668i | ||||
\(113\) | −5.92260 | − | 8.15175i | −0.557151 | − | 0.766853i | 0.433810 | − | 0.901004i | \(-0.357169\pi\) |
−0.990961 | + | 0.134152i | \(0.957169\pi\) | |||||||
\(114\) | 1.81515 | − | 0.147952i | 0.170004 | − | 0.0138570i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0633759 | + | 0.195051i | 0.00588430 | + | 0.0181100i | ||||
\(117\) | −13.9676 | − | 13.8126i | −1.29131 | − | 1.27697i | ||||
\(118\) | 9.77910 | + | 13.4598i | 0.900239 | + | 1.23907i | ||||
\(119\) | 2.74538 | + | 0.892027i | 0.251668 | + | 0.0817720i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.16188 | − | 10.9385i | 0.105626 | − | 0.994406i | ||||
\(122\) | − | 2.40939i | − | 0.218136i | ||||||
\(123\) | 5.26221 | − | 2.19690i | 0.474477 | − | 0.198088i | ||||
\(124\) | −0.469663 | + | 0.341230i | −0.0421770 | + | 0.0306434i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.604491 | − | 3.68345i | −0.0538524 | − | 0.328148i | ||||
\(127\) | −4.43732 | + | 1.44177i | −0.393749 | + | 0.127937i | −0.499198 | − | 0.866488i | \(-0.666372\pi\) |
0.105449 | + | 0.994425i | \(0.466372\pi\) | |||||||
\(128\) | −8.60489 | − | 6.25182i | −0.760572 | − | 0.552588i | ||||
\(129\) | 3.17594 | − | 13.3933i | 0.279626 | − | 1.17921i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4283 | 1.17324 | 0.586618 | − | 0.809864i | \(-0.300459\pi\) | ||||
0.586618 | + | 0.809864i | \(0.300459\pi\) | |||||||
\(132\) | 0.427086 | + | 0.0552546i | 0.0371731 | + | 0.00480930i | ||||
\(133\) | 0.679604 | 0.0589291 | ||||||||
\(134\) | −0.815740 | + | 2.51059i | −0.0704692 | + | 0.216882i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.49718 | + | 5.44702i | 0.642878 | + | 0.467078i | ||||
\(137\) | −10.8493 | + | 3.52514i | −0.926915 | + | 0.301173i | −0.733300 | − | 0.679905i | \(-0.762021\pi\) |
−0.193614 | + | 0.981078i | \(0.562021\pi\) | |||||||
\(138\) | 1.43194 | + | 0.872005i | 0.121894 | + | 0.0742300i | ||||
\(139\) | 9.81539 | − | 13.5097i | 0.832531 | − | 1.14588i | −0.154916 | − | 0.987928i | \(-0.549511\pi\) |
0.987447 | − | 0.157953i | \(-0.0504894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.43238 | − | 13.0121i | −0.457489 | − | 1.09582i | ||||
\(142\) | 0.516735i | 0.0433634i | ||||||||
\(143\) | −19.8444 | + | 8.82221i | −1.65948 | + | 0.737750i | ||||
\(144\) | 1.74062 | − | 11.4012i | 0.145051 | − | 0.950103i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.13000 | + | 5.68446i | 0.341802 | + | 0.470450i | ||||
\(147\) | 0.871824 | + | 10.6959i | 0.0719068 | + | 0.882187i | ||||
\(148\) | −0.114162 | − | 0.351355i | −0.00938407 | − | 0.0288812i | ||||
\(149\) | −4.31014 | − | 13.2653i | −0.353101 | − | 1.08673i | −0.957103 | − | 0.289749i | \(-0.906428\pi\) |
0.604002 | − | 0.796983i | \(-0.293572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.48297 | − | 11.6758i | −0.690334 | − | 0.950164i | 0.309666 | − | 0.950846i | \(-0.399783\pi\) |
−1.00000 | 0.000681994i | \(0.999783\pi\) | ||||||||
\(152\) | 2.07495 | + | 0.674191i | 0.168300 | + | 0.0546841i | ||||
\(153\) | −1.45740 | + | 9.54615i | −0.117824 | + | 0.771760i | ||||
\(154\) | −4.03603 | − | 0.860212i | −0.325233 | − | 0.0693179i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.327554 | − | 0.784587i | −0.0262253 | − | 0.0628172i | ||||
\(157\) | −0.278110 | + | 0.202058i | −0.0221956 | + | 0.0161260i | −0.598828 | − | 0.800878i | \(-0.704367\pi\) |
0.576632 | + | 0.817004i | \(0.304367\pi\) | |||||||
\(158\) | −12.1813 | + | 16.7661i | −0.969089 | + | 1.33384i | ||||
\(159\) | 10.2386 | + | 6.23497i | 0.811971 | + | 0.494466i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.506152 | + | 0.367741i | 0.0398904 | + | 0.0289820i | ||||
\(162\) | 11.8321 | − | 3.99103i | 0.929620 | − | 0.313565i | ||||
\(163\) | −3.29710 | + | 10.1474i | −0.258249 | + | 0.794809i | 0.734923 | + | 0.678151i | \(0.237218\pi\) |
−0.993172 | + | 0.116659i | \(0.962782\pi\) | |||||||
\(164\) | 0.246808 | 0.0192725 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.19394 | −0.0926675 | ||||||||
\(167\) | −0.413471 | + | 1.27253i | −0.0319953 | + | 0.0984715i | −0.965779 | − | 0.259367i | \(-0.916486\pi\) |
0.933784 | + | 0.357838i | \(0.116486\pi\) | |||||||
\(168\) | 1.03177 | − | 4.35108i | 0.0796028 | − | 0.335693i | ||||
\(169\) | 24.1700 | + | 17.5605i | 1.85923 | + | 1.35081i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.368176 | + | 2.24347i | 0.0281551 | + | 0.171563i | ||||
\(172\) | 0.350176 | − | 0.481976i | 0.0267007 | − | 0.0367503i | ||||
\(173\) | 9.22022 | − | 6.69889i | 0.701001 | − | 0.509307i | −0.179257 | − | 0.983802i | \(-0.557369\pi\) |
0.880258 | + | 0.474495i | \(0.157369\pi\) | |||||||
\(174\) | 6.06694 | − | 2.53287i | 0.459934 | − | 0.192016i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.0388 | − | 6.38139i | −0.832082 | − | 0.481015i | ||||
\(177\) | −15.7554 | + | 13.5326i | −1.18425 | + | 1.01717i | ||||
\(178\) | 6.92112 | + | 2.24881i | 0.518760 | + | 0.168555i | ||||
\(179\) | 0.931229 | + | 1.28173i | 0.0696033 | + | 0.0958008i | 0.842399 | − | 0.538854i | \(-0.181142\pi\) |
−0.772796 | + | 0.634654i | \(0.781142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.63880 | + | 14.2768i | 0.344799 | + | 1.06118i | 0.961691 | + | 0.274135i | \(0.0883915\pi\) |
−0.616892 | + | 0.787048i | \(0.711609\pi\) | |||||||
\(182\) | 2.51764 | + | 7.74849i | 0.186620 | + | 0.574357i | ||||
\(183\) | 2.99785 | − | 0.244354i | 0.221608 | − | 0.0180632i | ||||
\(184\) | 1.18056 | + | 1.62489i | 0.0870317 | + | 0.119789i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.1256 | + | 14.1173i | 0.889095 | + | 1.03513i | ||||
\(187\) | 9.24270 | + | 5.34307i | 0.675893 | + | 0.390724i | ||||
\(188\) | − | 0.610294i | − | 0.0445103i | ||||||
\(189\) | 4.52179 | − | 1.12570i | 0.328912 | − | 0.0818825i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.33023 | + | 11.4656i | −0.602754 | + | 0.829620i | −0.995957 | − | 0.0898317i | \(-0.971367\pi\) |
0.393203 | + | 0.919452i | \(0.371367\pi\) | |||||||
\(192\) | 7.45647 | − | 12.2444i | 0.538124 | − | 0.883664i | ||||
\(193\) | −20.1414 | + | 6.54433i | −1.44981 | + | 0.471072i | −0.924941 | − | 0.380112i | \(-0.875886\pi\) |
−0.524869 | + | 0.851183i | \(0.675886\pi\) | |||||||
\(194\) | 13.9474 | + | 10.1334i | 1.00137 | + | 0.727535i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.143530 | + | 0.441739i | −0.0102521 | + | 0.0315528i | ||||
\(197\) | −12.2325 | −0.871530 | −0.435765 | − | 0.900061i | \(-0.643522\pi\) | ||||
−0.435765 | + | 0.900061i | \(0.643522\pi\) | |||||||
\(198\) | 0.653163 | − | 13.7896i | 0.0464183 | − | 0.979981i | ||||
\(199\) | −9.12394 | −0.646779 | −0.323390 | − | 0.946266i | \(-0.604822\pi\) | ||||
−0.323390 | + | 0.946266i | \(0.604822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.20650 | − | 0.760357i | −0.226169 | − | 0.0536314i | ||||
\(202\) | 14.8205 | + | 10.7677i | 1.04277 | + | 0.757614i | ||||
\(203\) | 2.33330 | − | 0.758135i | 0.163766 | − | 0.0532107i | ||||
\(204\) | −0.217388 | + | 0.356977i | −0.0152202 | + | 0.0249934i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.490642 | − | 0.356472i | 0.0341847 | − | 0.0248366i | ||||
\(207\) | −0.939758 | + | 1.87010i | −0.0653177 | + | 0.129981i | ||||
\(208\) | 25.1733i | 1.74545i | ||||||||
\(209\) | 2.45822 | + | 0.523927i | 0.170038 | + | 0.0362408i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.93176 | + | 1.92735i | 0.408359 | + | 0.132684i | 0.505991 | − | 0.862539i | \(-0.331127\pi\) |
−0.0976320 | + | 0.995223i | \(0.531127\pi\) | |||||||
\(212\) | 0.304968 | + | 0.419752i | 0.0209453 | + | 0.0288287i | ||||
\(213\) | −0.642941 | + | 0.0524060i | −0.0440536 | + | 0.00359080i | ||||
\(214\) | −0.270164 | − | 0.831480i | −0.0184680 | − | 0.0568388i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.9225 | + | 1.04882i | 1.01535 | + | 0.0713635i | ||||
\(217\) | 4.08197 | + | 5.61835i | 0.277102 | + | 0.381399i | ||||
\(218\) | 3.37750 | + | 1.09742i | 0.228753 | + | 0.0743263i | ||||
\(219\) | −6.65397 | + | 5.71521i | −0.449634 | + | 0.386198i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 21.0774i | − | 1.41782i | ||||||
\(222\) | −10.9287 | + | 4.56258i | −0.733485 | + | 0.306220i | ||||
\(223\) | 13.7966 | − | 10.0238i | 0.923891 | − | 0.671246i | −0.0205984 | − | 0.999788i | \(-0.506557\pi\) |
0.944489 | + | 0.328542i | \(0.106557\pi\) | |||||||
\(224\) | 0.223414 | − | 0.307503i | 0.0149275 | − | 0.0205459i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.2959 | + | 4.32011i | −0.884433 | + | 0.287370i | ||||
\(227\) | 4.29548 | + | 3.12085i | 0.285101 | + | 0.207138i | 0.721139 | − | 0.692790i | \(-0.243619\pi\) |
−0.436038 | + | 0.899928i | \(0.643619\pi\) | |||||||
\(228\) | −0.0227039 | + | 0.0957446i | −0.00150360 | + | 0.00634084i | ||||
\(229\) | 0.209053 | − | 0.643400i | 0.0138146 | − | 0.0425171i | −0.943912 | − | 0.330198i | \(-0.892884\pi\) |
0.957726 | + | 0.287681i | \(0.0928844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.660984 | − | 5.10903i | 0.0434896 | − | 0.336149i | ||||
\(232\) | 7.87606 | 0.517088 | ||||||||
\(233\) | −0.653719 | + | 2.01194i | −0.0428265 | + | 0.131807i | −0.970184 | − | 0.242371i | \(-0.922075\pi\) |
0.927357 | + | 0.374177i | \(0.122075\pi\) | |||||||
\(234\) | −24.2150 | + | 12.5088i | −1.58298 | + | 0.817729i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.854929 | + | 0.277783i | −0.0556511 | + | 0.0180822i | ||||
\(237\) | −22.0964 | − | 13.4560i | −1.43531 | − | 0.874062i | ||||
\(238\) | 2.35415 | − | 3.24021i | 0.152597 | − | 0.210031i | ||||
\(239\) | 6.90685 | − | 5.01812i | 0.446767 | − | 0.324595i | −0.341551 | − | 0.939863i | \(-0.610952\pi\) |
0.788318 | + | 0.615268i | \(0.210952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.62484i | 0.297912i | 0.988844 | + | 0.148956i | \(0.0475912\pi\) | ||||
−0.988844 | + | 0.148956i | \(0.952409\pi\) | |||||||
\(242\) | −13.9357 | − | 6.22300i | −0.895820 | − | 0.400030i | ||||
\(243\) | 6.16578 | + | 14.3172i | 0.395535 | + | 0.918451i | ||||
\(244\) | 0.123810 | + | 0.0402284i | 0.00792614 | + | 0.00257536i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.642758 | − | 7.88566i | −0.0409808 | − | 0.502771i | ||||
\(247\) | −1.53341 | − | 4.71935i | −0.0975686 | − | 0.300285i | ||||
\(248\) | 6.88935 | + | 21.2032i | 0.437474 | + | 1.34641i | ||||
\(249\) | −0.121086 | − | 1.48554i | −0.00767353 | − | 0.0941424i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8508 | + | 7.09975i | 1.37921 | + | 0.448132i | 0.902409 | − | 0.430880i | \(-0.141797\pi\) |
0.476799 | + | 0.879012i | \(0.341797\pi\) | |||||||
\(252\) | 0.199373 | + | 0.0304381i | 0.0125593 | + | 0.00191742i | ||||
\(253\) | 1.54731 | + | 1.72037i | 0.0972788 | + | 0.108159i | ||||
\(254\) | 6.47342i | 0.406179i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.45350 | − | 1.05603i | 0.0908435 | − | 0.0660016i | ||||
\(257\) | 10.2799 | − | 14.1491i | 0.641243 | − | 0.882595i | −0.357439 | − | 0.933937i | \(-0.616350\pi\) |
0.998681 | + | 0.0513419i | \(0.0163498\pi\) | |||||||
\(258\) | −16.3114 | − | 9.93313i | −1.01550 | − | 0.618410i | ||||
\(259\) | −4.20309 | + | 1.36567i | −0.261167 | + | 0.0848584i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.76678 | + | 7.29185i | 0.233158 | + | 0.451354i | ||||
\(262\) | 5.75735 | − | 17.7193i | 0.355690 | − | 1.09470i | ||||
\(263\) | 2.19449 | 0.135318 | 0.0676590 | − | 0.997709i | \(-0.478447\pi\) | ||||
0.0676590 | + | 0.997709i | \(0.478447\pi\) | |||||||
\(264\) | 7.08643 | − | 14.9430i | 0.436139 | − | 0.919678i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.291378 | − | 0.896771i | 0.0178656 | − | 0.0549845i | ||||
\(267\) | −2.09613 | + | 8.83959i | −0.128281 | + | 0.540974i | ||||
\(268\) | −0.115391 | − | 0.0838362i | −0.00704861 | − | 0.00512111i | ||||
\(269\) | 1.13650 | − | 0.369271i | 0.0692937 | − | 0.0225149i | −0.274165 | − | 0.961683i | \(-0.588401\pi\) |
0.343459 | + | 0.939168i | \(0.388401\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.08529 | − | 1.49377i | 0.0659264 | − | 0.0907399i | −0.774781 | − | 0.632230i | \(-0.782140\pi\) |
0.840707 | + | 0.541490i | \(0.182140\pi\) | |||||||
\(272\) | 10.0116 | − | 7.27382i | 0.607040 | − | 0.441040i | ||||
\(273\) | −9.38564 | + | 3.91837i | −0.568045 | + | 0.237151i | ||||
\(274\) | 15.8275i | 0.956176i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.0687177 | + | 0.0590229i | −0.00413632 | + | 0.00355276i | ||||
\(277\) | 28.6337 | + | 9.30364i | 1.72043 | + | 0.559002i | 0.992013 | − | 0.126132i | \(-0.0402564\pi\) |
0.728417 | + | 0.685134i | \(0.240256\pi\) | |||||||
\(278\) | −13.6184 | − | 18.7442i | −0.816779 | − | 1.12420i | ||||
\(279\) | −16.3356 | + | 16.5189i | −0.977986 | + | 0.988962i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00625 | − | 18.4853i | −0.358303 | − | 1.10274i | −0.954070 | − | 0.299585i | \(-0.903152\pi\) |
0.595767 | − | 0.803158i | \(-0.296848\pi\) | |||||||
\(282\) | −19.4992 | + | 1.58938i | −1.16116 | + | 0.0946462i | ||||
\(283\) | 12.5870 | + | 17.3245i | 0.748217 | + | 1.02983i | 0.998104 | + | 0.0615572i | \(0.0196066\pi\) |
−0.249887 | + | 0.968275i | \(0.580393\pi\) | |||||||
\(284\) | −0.0265533 | − | 0.00862768i | −0.00157565 | − | 0.000511958i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.13308 | + | 29.9682i | 0.185263 | + | 1.77206i | ||||
\(287\) | − | 2.95244i | − | 0.174277i | ||||||
\(288\) | 1.13615 | + | 0.570932i | 0.0669481 | + | 0.0336425i | ||||
\(289\) | 5.37071 | − | 3.90205i | 0.315924 | − | 0.229532i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.1938 | + | 18.3816i | −0.656195 | + | 1.07755i | ||||
\(292\) | −0.361062 | + | 0.117316i | −0.0211296 | + | 0.00686541i | ||||
\(293\) | −15.8153 | − | 11.4905i | −0.923938 | − | 0.671280i | 0.0205632 | − | 0.999789i | \(-0.493454\pi\) |
−0.944501 | + | 0.328508i | \(0.893454\pi\) | |||||||
\(294\) | 14.4876 | + | 3.43544i | 0.844935 | + | 0.200359i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.1875 | −0.824634 | ||||||||
\(297\) | 17.2237 | − | 0.585813i | 0.999422 | − | 0.0339923i | ||||
\(298\) | −19.3521 | −1.12104 | ||||||||
\(299\) | 1.41165 | − | 4.34460i | 0.0816376 | − | 0.251255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.76565 | − | 4.18899i | −0.332326 | − | 0.241449i | ||||
\(302\) | −19.0438 | + | 6.18772i | −1.09585 | + | 0.356063i | ||||
\(303\) | −11.8946 | + | 19.5323i | −0.683324 | + | 1.12210i | ||||
\(304\) | 1.71247 | − | 2.35701i | 0.0982169 | − | 0.135184i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.9718 | + | 6.01600i | 0.684380 | + | 0.343912i | ||||
\(307\) | − | 1.52564i | − | 0.0870730i | −0.999052 | − | 0.0435365i | \(-0.986138\pi\) | ||
0.999052 | − | 0.0435365i | \(-0.0138625\pi\) | |||||||
\(308\) | 0.111591 | − | 0.193036i | 0.00635850 | − | 0.0109992i | ||||
\(309\) | 0.493296 | + | 0.574323i | 0.0280626 | + | 0.0326721i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.08414 | − | 5.62134i | −0.231591 | − | 0.318757i | 0.677367 | − | 0.735645i | \(-0.263121\pi\) |
−0.908958 | + | 0.416888i | \(0.863121\pi\) | |||||||
\(312\) | −32.5431 | + | 2.65258i | −1.84239 | + | 0.150173i | ||||
\(313\) | −8.95555 | − | 27.5623i | −0.506197 | − | 1.55792i | −0.798748 | − | 0.601666i | \(-0.794504\pi\) |
0.292551 | − | 0.956250i | \(-0.405496\pi\) | |||||||
\(314\) | 0.147387 | + | 0.453611i | 0.00831754 | + | 0.0255988i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.658167 | − | 0.905889i | −0.0370248 | − | 0.0509602i | ||||
\(317\) | 12.1266 | + | 3.94019i | 0.681100 | + | 0.221303i | 0.629077 | − | 0.777343i | \(-0.283433\pi\) |
0.0520233 | + | 0.998646i | \(0.483433\pi\) | |||||||
\(318\) | 12.6171 | − | 10.8371i | 0.707533 | − | 0.607712i | ||||
\(319\) | 9.02432 | − | 0.943462i | 0.505265 | − | 0.0528237i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.00716 | − | 0.420475i | 0.0562141 | − | 0.0234686i | ||||
\(322\) | 0.702263 | − | 0.510224i | 0.0391356 | − | 0.0284337i | ||||
\(323\) | −1.43383 | + | 1.97350i | −0.0797807 | + | 0.109809i | ||||
\(324\) | 0.00752987 | + | 0.674650i | 0.000418326 | + | 0.0374806i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.9764 | + | 8.70138i | 0.663313 | + | 0.481925i | ||||
\(327\) | −1.02291 | + | 4.31371i | −0.0565670 | + | 0.238549i | ||||
\(328\) | 2.92893 | − | 9.01431i | 0.161723 | − | 0.497732i | ||||
\(329\) | −7.30065 | −0.402498 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.04823 | −0.112581 | −0.0562903 | − | 0.998414i | \(-0.517927\pi\) | ||||
−0.0562903 | + | 0.998414i | \(0.517927\pi\) | |||||||
\(332\) | 0.0199346 | − | 0.0613524i | 0.00109405 | − | 0.00336715i | ||||
\(333\) | −6.78529 | − | 13.1352i | −0.371832 | − | 0.719802i | ||||
\(334\) | 1.50189 | + | 1.09119i | 0.0821800 | + | 0.0597072i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.10019 | − | 3.10586i | −0.278238 | − | 0.169439i | ||||
\(337\) | −1.14962 | + | 1.58232i | −0.0626238 | + | 0.0861943i | −0.839180 | − | 0.543854i | \(-0.816965\pi\) |
0.776556 | + | 0.630048i | \(0.216965\pi\) | |||||||
\(338\) | 33.5348 | − | 24.3645i | 1.82405 | − | 1.32525i | ||||
\(339\) | −6.72369 | − | 16.1052i | −0.365181 | − | 0.874713i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4337 | + | 23.4692i | 0.565015 | + | 1.27093i | ||||
\(342\) | 3.11823 | + | 0.476057i | 0.168614 | + | 0.0257422i | ||||
\(343\) | 11.2545 | + | 3.65682i | 0.607687 | + | 0.197450i | ||||
\(344\) | −13.4479 | − | 18.5094i | −0.725061 | − | 0.997960i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.88636 | − | 15.0387i | −0.262692 | − | 0.808484i | ||||
\(347\) | 7.49213 | + | 23.0584i | 0.402199 | + | 1.23784i | 0.923212 | + | 0.384292i | \(0.125554\pi\) |
−0.521013 | + | 0.853549i | \(0.674446\pi\) | |||||||
\(348\) | 0.0288585 | + | 0.354050i | 0.00154698 | + | 0.0189791i | ||||
\(349\) | −16.3915 | − | 22.5610i | −0.877417 | − | 1.20766i | −0.977130 | − | 0.212645i | \(-0.931792\pi\) |
0.0997123 | − | 0.995016i | \(-0.468208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0198 | − | 28.8606i | −0.961826 | − | 1.54046i | ||||
\(352\) | 1.04518 | − | 0.940042i | 0.0557083 | − | 0.0501044i | ||||
\(353\) | 2.24413i | 0.119443i | 0.998215 | + | 0.0597215i | \(0.0190213\pi\) | ||||
−0.998215 | + | 0.0597215i | \(0.980979\pi\) | |||||||
\(354\) | 11.1018 | + | 26.5921i | 0.590055 | + | 1.41335i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.231117 | + | 0.318106i | −0.0122492 | + | 0.0168596i | ||||
\(357\) | 4.27034 | + | 2.60051i | 0.226010 | + | 0.137633i | ||||
\(358\) | 2.09056 | − | 0.679265i | 0.110490 | − | 0.0359003i | ||||
\(359\) | 5.48619 | + | 3.98595i | 0.289550 | + | 0.210370i | 0.723072 | − | 0.690773i | \(-0.242729\pi\) |
−0.433522 | + | 0.901143i | \(0.642729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.69385 | − | 17.5239i | 0.299677 | − | 0.922309i | ||||
\(362\) | 20.8277 | 1.09468 | ||||||||
\(363\) | 6.32957 | − | 17.9704i | 0.332216 | − | 0.943203i | ||||
\(364\) | −0.440205 | −0.0230730 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.962884 | − | 4.06058i | 0.0503307 | − | 0.212250i | ||||
\(367\) | −23.9070 | − | 17.3694i | −1.24793 | − | 0.906677i | −0.249834 | − | 0.968289i | \(-0.580376\pi\) |
−0.998100 | + | 0.0616119i | \(0.980376\pi\) | |||||||
\(368\) | 2.55081 | − | 0.828808i | 0.132970 | − | 0.0432046i | ||||
\(369\) | 9.74645 | − | 1.59949i | 0.507380 | − | 0.0832660i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.02130 | − | 3.64819i | 0.260693 | − | 0.189404i | ||||
\(372\) | −0.927899 | + | 0.387385i | −0.0481093 | + | 0.0200850i | ||||
\(373\) | 8.05921i | 0.417290i | 0.977991 | + | 0.208645i | \(0.0669053\pi\) | ||||
−0.977991 | + | 0.208645i | \(0.933095\pi\) | |||||||
\(374\) | 11.0132 | − | 9.90536i | 0.569480 | − | 0.512194i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.2901 | − | 7.24250i | −1.14953 | − | 0.373503i | ||||
\(377\) | −10.5294 | − | 14.4925i | −0.542291 | − | 0.746400i | ||||
\(378\) | 0.453291 | − | 6.44936i | 0.0233148 | − | 0.331719i | ||||
\(379\) | −7.73325 | − | 23.8005i | −0.397230 | − | 1.22255i | −0.927211 | − | 0.374540i | \(-0.877801\pi\) |
0.529981 | − | 0.848010i | \(-0.322199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.05448 | + | 0.656519i | −0.412644 | + | 0.0336345i | ||||
\(382\) | 11.5578 | + | 15.9080i | 0.591350 | + | 0.813923i | ||||
\(383\) | 23.6246 | + | 7.67611i | 1.20716 | + | 0.392231i | 0.842391 | − | 0.538867i | \(-0.181147\pi\) |
0.364771 | + | 0.931097i | \(0.381147\pi\) | |||||||
\(384\) | −12.0035 | − | 13.9751i | −0.612551 | − | 0.713166i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.3834i | 1.49558i | ||||||||
\(387\) | 10.7049 | − | 21.3026i | 0.544161 | − | 1.08287i | ||||
\(388\) | −0.753594 | + | 0.547518i | −0.0382580 | + | 0.0277960i | ||||
\(389\) | −10.0232 | + | 13.7958i | −0.508198 | + | 0.699475i | −0.983614 | − | 0.180286i | \(-0.942298\pi\) |
0.475416 | + | 0.879761i | \(0.342298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.13577 | + | 0.693953i | −0.108010 | + | 0.0350947i | ||||
\(392\) | 14.4306 | + | 10.4844i | 0.728855 | + | 0.529544i | ||||
\(393\) | 22.6309 | + | 5.36647i | 1.14158 | + | 0.270702i | ||||
\(394\) | −5.24465 | + | 16.1414i | −0.264222 | + | 0.813191i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.697693 | + | 0.263801i | 0.0350604 | + | 0.0132565i | ||||
\(397\) | −8.32149 | −0.417643 | −0.208822 | − | 0.977954i | \(-0.566963\pi\) | ||||
−0.208822 | + | 0.977954i | \(0.566963\pi\) | |||||||
\(398\) | −3.91187 | + | 12.0395i | −0.196084 | + | 0.603485i | ||||
\(399\) | 1.14535 | + | 0.271596i | 0.0573391 | + | 0.0135968i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.0428 | + | 4.23786i | −0.651327 | + | 0.211629i | −0.615999 | − | 0.787747i | \(-0.711247\pi\) |
−0.0353277 | + | 0.999376i | \(0.511247\pi\) | |||||||
\(402\) | −2.37811 | + | 3.90513i | −0.118609 | + | 0.194770i | ||||
\(403\) | 29.8051 | − | 41.0232i | 1.48470 | − | 2.04351i | ||||
\(404\) | −0.800768 | + | 0.581792i | −0.0398397 | + | 0.0289452i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 3.40395i | − | 0.168935i | ||||||
\(407\) | −16.2560 | + | 1.69950i | −0.805778 | + | 0.0842413i | ||||
\(408\) | 10.4583 | + | 12.1761i | 0.517762 | + | 0.602807i | ||||
\(409\) | −21.6718 | − | 7.04159i | −1.07160 | − | 0.348184i | −0.280490 | − | 0.959857i | \(-0.590497\pi\) |
−0.791111 | + | 0.611673i | \(0.790497\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.6932 | + | 1.60519i | −0.971394 | + | 0.0791781i | ||||
\(412\) | 0.0101259 | + | 0.0311643i | 0.000498867 | + | 0.00153535i | ||||
\(413\) | 3.32299 | + | 10.2271i | 0.163514 | + | 0.503243i | ||||
\(414\) | 2.06478 | + | 2.04186i | 0.101478 | + | 0.100352i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.63948 | − | 0.857619i | −0.129411 | − | 0.0420482i | ||||
\(417\) | 21.9410 | − | 18.8456i | 1.07446 | − | 0.922871i | ||||
\(418\) | 1.74530 | − | 3.01910i | 0.0853655 | − | 0.147669i | ||||
\(419\) | − | 30.6229i | − | 1.49603i | −0.663685 | − | 0.748013i | \(-0.731008\pi\) | ||
0.663685 | − | 0.748013i | \(-0.268992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6246 | − | 18.6173i | 1.24886 | − | 0.907353i | 0.250709 | − | 0.968063i | \(-0.419336\pi\) |
0.998155 | + | 0.0607095i | \(0.0193363\pi\) | |||||||
\(422\) | 5.08645 | − | 7.00090i | 0.247605 | − | 0.340799i | ||||
\(423\) | −3.95513 | − | 24.1005i | −0.192305 | − | 1.17181i | ||||
\(424\) | 18.9500 | − | 6.15723i | 0.920293 | − | 0.299021i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.206507 | + | 0.870861i | −0.0100053 | + | 0.0421934i | ||||
\(427\) | 0.481233 | − | 1.48108i | 0.0232885 | − | 0.0716746i | ||||
\(428\) | 0.0472377 | 0.00228332 | ||||||||
\(429\) | −36.9699 | + | 6.93760i | −1.78492 | + | 0.334950i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.62702 | − | 20.3959i | 0.319212 | − | 0.982434i | −0.654774 | − | 0.755825i | \(-0.727236\pi\) |
0.973986 | − | 0.226609i | \(-0.0727639\pi\) | |||||||
\(432\) | 7.48986 | − | 18.5191i | 0.360356 | − | 0.890999i | ||||
\(433\) | −18.1221 | − | 13.1665i | −0.870892 | − | 0.632740i | 0.0599343 | − | 0.998202i | \(-0.480911\pi\) |
−0.930826 | + | 0.365462i | \(0.880911\pi\) | |||||||
\(434\) | 9.16383 | − | 2.97751i | 0.439878 | − | 0.142925i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.112785 | + | 0.155235i | −0.00540142 | + | 0.00743442i | ||||
\(437\) | −0.427726 | + | 0.310761i | −0.0204609 | + | 0.0148657i | ||||
\(438\) | 4.68863 | + | 11.2306i | 0.224031 | + | 0.536620i | ||||
\(439\) | 19.2175i | 0.917200i | 0.888643 | + | 0.458600i | \(0.151649\pi\) | ||||
−0.888643 | + | 0.458600i | \(0.848351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.80521 | + | 18.3745i | −0.133582 | + | 0.874974i | ||||
\(442\) | −27.8126 | − | 9.03686i | −1.32291 | − | 0.429840i | ||||
\(443\) | 14.3128 | + | 19.6998i | 0.680019 | + | 0.935966i | 0.999934 | − | 0.0114800i | \(-0.00365427\pi\) |
−0.319915 | + | 0.947446i | \(0.603654\pi\) | |||||||
\(444\) | −0.0519843 | − | 0.637768i | −0.00246707 | − | 0.0302671i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.31168 | − | 22.5030i | −0.346218 | − | 1.06555i | ||||
\(447\) | −1.96264 | − | 24.0786i | −0.0928299 | − | 1.13888i | ||||
\(448\) | −4.36290 | − | 6.00502i | −0.206128 | − | 0.283710i | ||||
\(449\) | −7.10410 | − | 2.30826i | −0.335263 | − | 0.108934i | 0.136547 | − | 0.990634i | \(-0.456399\pi\) |
−0.471811 | + | 0.881700i | \(0.656399\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.27613 | − | 10.6794i | 0.107179 | − | 0.502872i | ||||
\(452\) | − | 0.755364i | − | 0.0355293i | ||||||
\(453\) | −9.63038 | − | 23.0675i | −0.452475 | − | 1.08381i | ||||
\(454\) | 5.95979 | − | 4.33004i | 0.279707 | − | 0.203219i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.22751 | + | 1.96545i | 0.151142 | + | 0.0920407i | ||||
\(457\) | −12.8323 | + | 4.16948i | −0.600272 | + | 0.195040i | −0.593362 | − | 0.804936i | \(-0.702200\pi\) |
−0.00691008 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(458\) | −0.759367 | − | 0.551712i | −0.0354829 | − | 0.0257798i | ||||
\(459\) | −6.27119 | + | 15.5058i | −0.292714 | + | 0.723751i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5766 | 0.725475 | 0.362737 | − | 0.931891i | \(-0.381842\pi\) | ||||
0.362737 | + | 0.931891i | \(0.381842\pi\) | |||||||
\(462\) | −6.45822 | − | 3.06268i | −0.300463 | − | 0.142489i | ||||
\(463\) | −31.2181 | −1.45083 | −0.725414 | − | 0.688313i | \(-0.758351\pi\) | ||||
−0.725414 | + | 0.688313i | \(0.758351\pi\) | |||||||
\(464\) | 3.25009 | − | 10.0027i | 0.150882 | − | 0.464366i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.37457 | + | 1.72523i | 0.110000 | + | 0.0799197i | ||||
\(467\) | 6.71752 | − | 2.18266i | 0.310850 | − | 0.101001i | −0.149438 | − | 0.988771i | \(-0.547746\pi\) |
0.460288 | + | 0.887770i | \(0.347746\pi\) | |||||||
\(468\) | −0.238481 | − | 1.45318i | −0.0110238 | − | 0.0671733i | ||||
\(469\) | −1.00289 | + | 1.38036i | −0.0463093 | + | 0.0637392i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.549453 | + | 0.229389i | −0.0253174 | + | 0.0105697i | ||||
\(472\) | 34.5216i | 1.58899i | ||||||||
\(473\) | −17.6257 | − | 19.5970i | −0.810429 | − | 0.901072i | ||||
\(474\) | −27.2296 | + | 23.3880i | −1.25070 | + | 1.07425i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.127197 | + | 0.175072i | 0.00583007 | + | 0.00802441i | ||||
\(477\) | 14.7635 | + | 14.5996i | 0.675973 | + | 0.668471i | ||||
\(478\) | −3.66036 | − | 11.2654i | −0.167421 | − | 0.515269i | ||||
\(479\) | 8.42706 | + | 25.9358i | 0.385042 | + | 1.18504i | 0.936450 | + | 0.350802i | \(0.114091\pi\) |
−0.551407 | + | 0.834236i | \(0.685909\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9671 | + | 26.1060i | 0.864826 | + | 1.19033i | ||||
\(482\) | 6.10270 | + | 1.98289i | 0.277970 | + | 0.0903180i | ||||
\(483\) | 0.706062 | + | 0.822037i | 0.0321269 | + | 0.0374040i | ||||
\(484\) | 0.552457 | − | 0.612206i | 0.0251117 | − | 0.0278275i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 21.5359 | − | 1.99756i | 0.976886 | − | 0.0906114i | ||||
\(487\) | 17.2161 | − | 12.5083i | 0.780137 | − | 0.566803i | −0.124883 | − | 0.992172i | \(-0.539855\pi\) |
0.905020 | + | 0.425368i | \(0.139855\pi\) | |||||||
\(488\) | 2.93857 | − | 4.04460i | 0.133023 | − | 0.183090i | ||||
\(489\) | −9.61197 | + | 15.7840i | −0.434668 | + | 0.713777i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.1024 | − | 21.1442i | −1.31337 | − | 0.954223i | −0.999989 | − | 0.00459659i | \(-0.998537\pi\) |
−0.313385 | − | 0.949626i | \(-0.601463\pi\) | |||||||
\(492\) | 0.415949 | + | 0.0986339i | 0.0187524 | + | 0.00444676i | ||||
\(493\) | −2.72127 | + | 8.37520i | −0.122560 | + | 0.377200i | ||||
\(494\) | −6.88486 | −0.309765 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.7714 | 1.33678 | ||||||||
\(497\) | −0.103209 | + | 0.317644i | −0.00462955 | + | 0.0142483i | ||||
\(498\) | −2.01216 | − | 0.477143i | −0.0901671 | − | 0.0213813i | ||||
\(499\) | 4.98953 | + | 3.62511i | 0.223362 | + | 0.162282i | 0.693839 | − | 0.720130i | \(-0.255918\pi\) |
−0.470477 | + | 0.882412i | \(0.655918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.20538 | + | 1.97938i | −0.0538525 | + | 0.0884321i | ||||
\(502\) | 18.7369 | − | 25.7892i | 0.836270 | − | 1.15103i | ||||
\(503\) | 24.7294 | − | 17.9669i | 1.10263 | − | 0.801106i | 0.121141 | − | 0.992635i | \(-0.461345\pi\) |
0.981487 | + | 0.191529i | \(0.0613447\pi\) | |||||||
\(504\) | 3.47772 | − | 6.92061i | 0.154910 | − | 0.308268i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.93352 | − | 1.30415i | 0.130411 | − | 0.0579766i | ||||
\(507\) | 33.7162 | + | 39.2543i | 1.49739 | + | 1.74335i | ||||
\(508\) | −0.332647 | − | 0.108084i | −0.0147588 | − | 0.00479544i | ||||
\(509\) | −0.464290 | − | 0.639040i | −0.0205793 | − | 0.0283249i | 0.798603 | − | 0.601858i | \(-0.205573\pi\) |
−0.819183 | + | 0.573533i | \(0.805573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.40340 | + | 4.31921i | 0.0620827 | + | 0.191071i | ||||
\(512\) | −7.34385 | − | 22.6020i | −0.324555 | − | 0.998879i | ||||
\(513\) | −0.276085 | + | 3.92809i | −0.0121894 | + | 0.173430i | ||||
\(514\) | −14.2629 | − | 19.6312i | −0.629110 | − | 0.865896i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.782773 | − | 0.672338i | 0.0344597 | − | 0.0295980i | ||||
\(517\) | −26.4074 | − | 5.62829i | −1.16140 | − | 0.247532i | ||||
\(518\) | 6.13171i | 0.269412i | ||||||||
\(519\) | 18.2161 | − | 7.60498i | 0.799599 | − | 0.333822i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.0782 | − | 31.7645i | 1.01108 | − | 1.39163i | 0.0928006 | − | 0.995685i | \(-0.470418\pi\) |
0.918275 | − | 0.395942i | \(-0.129582\pi\) | |||||||
\(522\) | 11.2369 | − | 1.84409i | 0.491828 | − | 0.0807138i | ||||
\(523\) | 17.8563 | − | 5.80188i | 0.780803 | − | 0.253698i | 0.108620 | − | 0.994083i | \(-0.465357\pi\) |
0.672183 | + | 0.740385i | \(0.265357\pi\) | |||||||
\(524\) | 0.814408 | + | 0.591702i | 0.0355776 | + | 0.0258486i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.940881 | − | 2.89574i | 0.0410244 | − | 0.126260i | ||||
\(527\) | −24.9273 | −1.08585 | ||||||||
\(528\) | −16.0536 | − | 15.1662i | −0.698645 | − | 0.660024i | ||||
\(529\) | 22.5133 | 0.978838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.9609 | + | 16.5102i | −1.38699 | + | 0.716482i | ||||
\(532\) | 0.0412170 | + | 0.0299459i | 0.00178698 | + | 0.00129832i | ||||
\(533\) | −20.5026 | + | 6.66169i | −0.888065 | + | 0.288550i | ||||
\(534\) | 10.7656 | + | 6.55590i | 0.465871 | + | 0.283701i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.43137 | + | 3.21958i | −0.191406 | + | 0.139065i | ||||
\(537\) | 1.05719 | + | 2.53227i | 0.0456210 | + | 0.109275i | ||||
\(538\) | − | 1.65799i | − | 0.0714811i | ||||||
\(539\) | 17.7904 | + | 10.2844i | 0.766286 | + | 0.442979i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.2488 | − | 9.17858i | −1.21451 | − | 0.394618i | −0.369429 | − | 0.929259i | \(-0.620447\pi\) |
−0.845079 | + | 0.534641i | \(0.820447\pi\) | |||||||
\(542\) | −1.50579 | − | 2.07254i | −0.0646790 | − | 0.0890230i | ||||
\(543\) | 2.11230 | + | 25.9147i | 0.0906475 | + | 1.11211i | ||||
\(544\) | 0.421598 | + | 1.29755i | 0.0180759 | + | 0.0556318i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.14642 | + | 14.0648i | 0.0490622 | + | 0.601918i | ||||
\(547\) | −9.51221 | − | 13.0924i | −0.406713 | − | 0.559792i | 0.555700 | − | 0.831383i | \(-0.312450\pi\) |
−0.962413 | + | 0.271591i | \(0.912450\pi\) | |||||||
\(548\) | −0.813323 | − | 0.264265i | −0.0347434 | − | 0.0112888i | ||||
\(549\) | 5.14998 | + | 0.786243i | 0.219796 | + | 0.0335560i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.07324i | 0.0883228i | ||||||||
\(552\) | 1.34024 | + | 3.21026i | 0.0570443 | + | 0.136638i | ||||
\(553\) | −10.8367 | + | 7.87333i | −0.460824 | + | 0.334808i | ||||
\(554\) | 24.5532 | − | 33.7946i | 1.04317 | − | 1.43580i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.19058 | − | 0.386843i | 0.0504918 | − | 0.0164058i | ||||
\(557\) | 20.8491 | + | 15.1478i | 0.883406 | + | 0.641832i | 0.934150 | − | 0.356880i | \(-0.116159\pi\) |
−0.0507444 | + | 0.998712i | \(0.516159\pi\) | |||||||
\(558\) | 14.7937 | + | 28.6381i | 0.626267 | + | 1.21235i | ||||
\(559\) | −16.0803 | + | 49.4900i | −0.680123 | + | 2.09320i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4416 | + | 12.6985i | 0.567503 | + | 0.536131i | ||||
\(562\) | −26.9675 | −1.13755 | ||||||||
\(563\) | 1.46581 | − | 4.51129i | 0.0617764 | − | 0.190128i | −0.915405 | − | 0.402533i | \(-0.868130\pi\) |
0.977182 | + | 0.212405i | \(0.0681297\pi\) | |||||||
\(564\) | 0.243897 | − | 1.02854i | 0.0102699 | − | 0.0433093i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28.2571 | − | 9.18129i | 1.18773 | − | 0.385918i | ||||
\(567\) | 8.07051 | − | 0.0900762i | 0.338930 | − | 0.00378284i | ||||
\(568\) | −0.630227 | + | 0.867434i | −0.0264438 | + | 0.0363967i | ||||
\(569\) | 31.8594 | − | 23.1472i | 1.33561 | − | 0.970380i | 0.336020 | − | 0.941855i | \(-0.390919\pi\) |
0.999593 | − | 0.0285253i | \(-0.00908112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.45810i | 0.228415i | 0.993457 | + | 0.114207i | \(0.0364328\pi\) | ||||
−0.993457 | + | 0.114207i | \(0.963567\pi\) | |||||||
\(572\) | −1.59228 | − | 0.339367i | −0.0665765 | − | 0.0141897i | ||||
\(573\) | −18.6212 | + | 15.9940i | −0.777910 | + | 0.668161i | ||||
\(574\) | −3.89589 | − | 1.26585i | −0.162611 | − | 0.0528357i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.4598 | − | 17.6558i | 0.727493 | − | 0.735658i | ||||
\(577\) | 5.16605 | + | 15.8995i | 0.215066 | + | 0.661904i | 0.999149 | + | 0.0412482i | \(0.0131334\pi\) |
−0.784083 | + | 0.620656i | \(0.786867\pi\) | |||||||
\(578\) | −2.84627 | − | 8.75991i | −0.118389 | − | 0.364364i | ||||
\(579\) | −36.5600 | + | 2.98000i | −1.51938 | + | 0.123844i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.733930 | − | 0.238468i | −0.0304485 | − | 0.00989333i | ||||
\(582\) | 19.4561 | + | 22.6519i | 0.806482 | + | 0.938951i | ||||
\(583\) | 20.9752 | − | 9.32489i | 0.868703 | − | 0.386197i | ||||
\(584\) | 14.5795i | 0.603304i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.9430 | + | 15.9425i | −0.906457 | + | 0.658579i | ||||
\(587\) | 7.78966 | − | 10.7215i | 0.321514 | − | 0.442525i | −0.617415 | − | 0.786638i | \(-0.711820\pi\) |
0.938929 | + | 0.344112i | \(0.111820\pi\) | |||||||
\(588\) | −0.418429 | + | 0.687110i | −0.0172557 | + | 0.0283359i | ||||
\(589\) | −5.58139 | + | 1.81350i | −0.229977 | + | 0.0747241i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.6156 | − | 4.88858i | −0.848014 | − | 0.201089i | ||||
\(592\) | −5.85454 | + | 18.0184i | −0.240620 | + | 0.740553i | ||||
\(593\) | 2.52752 | 0.103793 | 0.0518964 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518964 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(594\) | 6.61162 | − | 22.9787i | 0.271278 | − | 0.942828i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.323113 | − | 0.994440i | 0.0132352 | − | 0.0407338i | ||||
\(597\) | −15.3767 | − | 3.64628i | −0.629328 | − | 0.149232i | ||||
\(598\) | −5.12767 | − | 3.72547i | −0.209686 | − | 0.152346i | ||||
\(599\) | 39.2198 | − | 12.7433i | 1.60248 | − | 0.520677i | 0.634759 | − | 0.772710i | \(-0.281099\pi\) |
0.967719 | + | 0.252033i | \(0.0810992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3992 | + | 21.1951i | −0.628145 | + | 0.864567i | −0.997914 | − | 0.0645567i | \(-0.979437\pi\) |
0.369769 | + | 0.929124i | \(0.379437\pi\) | |||||||
\(602\) | −7.99958 | + | 5.81204i | −0.326039 | + | 0.236881i | ||||
\(603\) | −5.10010 | − | 2.56288i | −0.207692 | − | 0.104369i | ||||
\(604\) | − | 1.08191i | − | 0.0440224i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.6740 | + | 24.0699i | 0.839825 | + | 0.977771i | ||||
\(607\) | −16.5155 | − | 5.36623i | −0.670345 | − | 0.217808i | −0.0459818 | − | 0.998942i | \(-0.514642\pi\) |
−0.624364 | + | 0.781134i | \(0.714642\pi\) | |||||||
\(608\) | 0.188797 | + | 0.259857i | 0.00765673 | + | 0.0105386i | ||||
\(609\) | 4.23533 | − | 0.345221i | 0.171624 | − | 0.0139890i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.4727 | + | 50.6977i | 0.666413 | + | 2.05101i | ||||
\(612\) | −0.509029 | + | 0.514742i | −0.0205763 | + | 0.0208072i | ||||
\(613\) | −3.70849 | − | 5.10430i | −0.149784 | − | 0.206161i | 0.727531 | − | 0.686075i | \(-0.240668\pi\) |
−0.877315 | + | 0.479914i | \(0.840668\pi\) | |||||||
\(614\) | −2.01316 | − | 0.654115i | −0.0812445 | − | 0.0263979i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.72607 | − | 6.36651i | −0.230710 | − | 0.256514i | ||||
\(617\) | − | 33.6793i | − | 1.35588i | −0.735117 | − | 0.677940i | \(-0.762873\pi\) | ||
0.735117 | − | 0.677940i | \(-0.237127\pi\) | |||||||
\(618\) | 0.969347 | − | 0.404689i | 0.0389929 | − | 0.0162790i | ||||
\(619\) | 6.36477 | − | 4.62428i | 0.255822 | − | 0.185865i | −0.452481 | − | 0.891774i | \(-0.649461\pi\) |
0.708303 | + | 0.705909i | \(0.249461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.33115 | + | 2.77615i | −0.0935460 | + | 0.111403i | ||||
\(622\) | −9.16870 | + | 2.97909i | −0.367631 | + | 0.119451i | ||||
\(623\) | 3.80535 | + | 2.76475i | 0.152458 | + | 0.110767i | ||||
\(624\) | −10.0602 | + | 42.4249i | −0.402731 | + | 1.69836i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −40.2095 | −1.60710 | ||||||||
\(627\) | 3.93349 | + | 1.86538i | 0.157088 | + | 0.0744961i | ||||
\(628\) | −0.0257704 | −0.00102835 | ||||||||
\(629\) | 4.90195 | − | 15.0867i | 0.195454 | − | 0.601544i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4492 | + | 13.4041i | 0.734451 | + | 0.533610i | 0.890968 | − | 0.454065i | \(-0.150027\pi\) |
−0.156517 | + | 0.987675i | \(0.550027\pi\) | |||||||
\(632\) | −40.8969 | + | 13.2882i | −1.62679 | + | 0.528577i | ||||
\(633\) | 9.22665 | + | 5.61875i | 0.366726 | + | 0.223325i | ||||
\(634\) | 10.3985 | − | 14.3124i | 0.412979 | − | 0.568416i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.346218 | + | 0.829292i | 0.0137284 | + | 0.0328836i | ||||
\(637\) | − | 40.5698i | − | 1.60743i | ||||||
\(638\) | 2.62421 | − | 12.3125i | 0.103893 | − | 0.487458i | ||||
\(639\) | −1.10450 | − | 0.168623i | −0.0436934 | − | 0.00667064i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.8714 | + | 21.8451i | 0.626881 | + | 0.862828i | 0.997831 | − | 0.0658247i | \(-0.0209678\pi\) |
−0.370950 | + | 0.928653i | \(0.620968\pi\) | |||||||
\(642\) | −0.123021 | − | 1.50927i | −0.00485523 | − | 0.0595663i | ||||
\(643\) | 10.5161 | + | 32.3653i | 0.414716 | + | 1.27636i | 0.912505 | + | 0.409065i | \(0.134145\pi\) |
−0.497789 | + | 0.867298i | \(0.665855\pi\) | |||||||
\(644\) | 0.0144933 | + | 0.0446059i | 0.000571118 | + | 0.00175772i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.98938 | + | 2.73815i | 0.0782712 | + | 0.107731i | ||||
\(647\) | 20.7519 | + | 6.74272i | 0.815843 | + | 0.265084i | 0.687071 | − | 0.726591i | \(-0.258896\pi\) |
0.128773 | + | 0.991674i | \(0.458896\pi\) | |||||||
\(648\) | 24.7300 | + | 7.73121i | 0.971486 | + | 0.303711i | ||||
\(649\) | 4.13529 | + | 39.5546i | 0.162325 | + | 1.55265i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.63410 | + | 11.1000i | 0.181625 | + | 0.435044i | ||||
\(652\) | −0.647099 | + | 0.470145i | −0.0253424 | + | 0.0184123i | ||||
\(653\) | 11.2822 | − | 15.5286i | 0.441506 | − | 0.607680i | −0.529040 | − | 0.848597i | \(-0.677448\pi\) |
0.970546 | + | 0.240916i | \(0.0774480\pi\) | |||||||
\(654\) | 5.25358 | + | 3.19927i | 0.205431 | + | 0.125101i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.2397 | − | 7.43958i | −0.399793 | − | 0.290467i | ||||
\(657\) | −13.4981 | + | 6.97276i | −0.526610 | + | 0.272033i | ||||
\(658\) | −3.13014 | + | 9.63357i | −0.122025 | + | 0.375556i | ||||
\(659\) | 12.8998 | 0.502507 | 0.251253 | − | 0.967921i | \(-0.419157\pi\) | ||||
0.251253 | + | 0.967921i | \(0.419157\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.7036 | −1.31092 | −0.655459 | − | 0.755231i | \(-0.727525\pi\) | ||||
−0.655459 | + | 0.755231i | \(0.727525\pi\) | |||||||
\(662\) | −0.878172 | + | 2.70273i | −0.0341311 | + | 0.105045i | ||||
\(663\) | 8.42332 | − | 35.5220i | 0.327135 | − | 1.37956i | ||||
\(664\) | −2.00424 | − | 1.45617i | −0.0777797 | − | 0.0565102i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.2417 | + | 3.32186i | −0.784349 | + | 0.128719i | ||||
\(667\) | −1.12185 | + | 1.54409i | −0.0434382 | + | 0.0597876i | ||||
\(668\) | −0.0811490 | + | 0.0589582i | −0.00313975 | + | 0.00228116i | ||||
\(669\) | 27.2576 | − | 11.3797i | 1.05384 | − | 0.439964i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.88249 | − | 4.98627i | 0.111277 | − | 0.192493i | ||||
\(672\) | 0.499413 | − | 0.428955i | 0.0192653 | − | 0.0165473i | ||||
\(673\) | 17.5771 | + | 5.71116i | 0.677549 | + | 0.220149i | 0.627522 | − | 0.778599i | \(-0.284069\pi\) |
0.0500268 | + | 0.998748i | \(0.484069\pi\) | |||||||
\(674\) | 1.59505 | + | 2.19539i | 0.0614389 | + | 0.0845634i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.692093 | + | 2.13004i | 0.0266190 | + | 0.0819248i | ||||
\(677\) | 13.7407 | + | 42.2894i | 0.528096 | + | 1.62531i | 0.758110 | + | 0.652126i | \(0.226123\pi\) |
−0.230014 | + | 0.973187i | \(0.573877\pi\) | |||||||
\(678\) | −24.1343 | + | 1.96718i | −0.926874 | + | 0.0755493i | ||||
\(679\) | 6.54970 | + | 9.01489i | 0.251354 | + | 0.345960i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.99203 | + | 6.97626i | 0.229615 | + | 0.267331i | ||||
\(682\) | 35.4422 | − | 3.70536i | 1.35715 | − | 0.141886i | ||||
\(683\) | 33.7026i | 1.28959i | 0.764354 | + | 0.644797i | \(0.223058\pi\) | ||||
−0.764354 | + | 0.644797i | \(0.776942\pi\) | |||||||
\(684\) | −0.0765265 | + | 0.152287i | −0.00292606 | + | 0.00582282i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.65070 | − | 13.2831i | 0.368466 | − | 0.507149i | ||||
\(687\) | 0.609448 | − | 1.00079i | 0.0232519 | − | 0.0381824i | ||||
\(688\) | −29.0566 | + | 9.44107i | −1.10777 | + | 0.359937i | ||||
\(689\) | −36.6637 | − | 26.6377i | −1.39678 | − | 1.01482i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.77678 | + | 17.7791i | −0.219759 | + | 0.676349i | 0.779022 | + | 0.626996i | \(0.215716\pi\) |
−0.998781 | + | 0.0493527i | \(0.984284\pi\) | |||||||
\(692\) | 0.854372 | 0.0324783 | ||||||||
\(693\) | 3.15573 | − | 8.34617i | 0.119876 | − | 0.317045i | ||||
\(694\) | 33.6390 | 1.27692 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 13.2736 | + | 3.14758i | 0.503136 | + | 0.119309i | ||||
\(697\) | 8.57361 | + | 6.22909i | 0.324749 | + | 0.235944i | ||||
\(698\) | −36.7981 | + | 11.9564i | −1.39283 | + | 0.452558i | ||||
\(699\) | −1.90577 | + | 3.12950i | −0.0720829 | + | 0.118369i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.42323 | + | 1.03404i | −0.0537547 | + | 0.0390550i | −0.614338 | − | 0.789043i | \(-0.710577\pi\) |
0.560583 | + | 0.828098i | \(0.310577\pi\) | |||||||
\(702\) | −45.8089 | + | 11.4041i | −1.72895 | + | 0.430420i | ||||
\(703\) | − | 3.73462i | − | 0.140854i | ||||||
\(704\) | −11.1517 | − | 25.0844i | −0.420297 | − | 0.945405i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.96124 | + | 0.962166i | 0.111448 | + | 0.0362116i | ||||
\(707\) | 6.95970 | + | 9.57920i | 0.261746 | + | 0.360263i | ||||
\(708\) | −1.55184 | + | 0.126490i | −0.0583217 | + | 0.00475379i | ||||
\(709\) | −5.03949 | − | 15.5100i | −0.189262 | − | 0.582489i | 0.810734 | − | 0.585415i | \(-0.199069\pi\) |
−0.999996 | + | 0.00292630i | \(0.999069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.8618 | − | 31.5082i | −1.19491 | − | 1.18165i | ||||
\(712\) | 8.87564 | + | 12.2163i | 0.332629 | + | 0.457824i | ||||
\(713\) | −5.13818 | − | 1.66950i | −0.192426 | − | 0.0625231i | ||||
\(714\) | 5.26239 | − | 4.51996i | 0.196940 | − | 0.169155i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.118768i | 0.00443858i | ||||||||
\(717\) | 13.6457 | − | 5.69688i | 0.509607 | − | 0.212754i | ||||
\(718\) | 7.61184 | − | 5.53033i | 0.284072 | − | 0.206390i | ||||
\(719\) | 13.1663 | − | 18.1219i | 0.491020 | − | 0.675831i | −0.489556 | − | 0.871972i | \(-0.662841\pi\) |
0.980576 | + | 0.196141i | \(0.0628410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.372804 | − | 0.121131i | 0.0138839 | − | 0.00451116i | ||||
\(722\) | −20.6824 | − | 15.0266i | −0.769719 | − | 0.559234i | ||||
\(723\) | −1.84826 | + | 7.79431i | −0.0687376 | + | 0.289873i | ||||
\(724\) | −0.347751 | + | 1.07027i | −0.0129241 | + | 0.0397762i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −20.9991 | − | 16.0570i | −0.779349 | − | 0.595929i | ||||
\(727\) | −3.83594 | −0.142267 | −0.0711336 | − | 0.997467i | \(-0.522662\pi\) | ||||
−0.0711336 | + | 0.997467i | \(0.522662\pi\) | |||||||
\(728\) | −5.22401 | + | 16.0779i | −0.193615 | + | 0.595885i | ||||
\(729\) | 4.66956 | + | 26.5931i | 0.172947 | + | 0.984931i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.3288 | − | 7.90491i | 0.899834 | − | 0.292374i | ||||
\(732\) | 0.192583 | + | 0.117277i | 0.00711806 | + | 0.00433468i | ||||
\(733\) | −21.4067 | + | 29.4638i | −0.790676 | + | 1.08827i | 0.203348 | + | 0.979107i | \(0.434818\pi\) |
−0.994024 | + | 0.109165i | \(0.965182\pi\) | |||||||
\(734\) | −33.1699 | + | 24.0993i | −1.22432 | + | 0.889522i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.295695i | 0.0108995i | ||||||||
\(737\) | −4.69176 | + | 4.21979i | −0.172823 | + | 0.155438i | ||||
\(738\) | 2.06816 | − | 13.5467i | 0.0761301 | − | 0.498661i | ||||
\(739\) | −5.34301 | − | 1.73605i | −0.196546 | − | 0.0638616i | 0.209090 | − | 0.977896i | \(-0.432950\pi\) |
−0.405636 | + | 0.914035i | \(0.632950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.698246 | − | 8.56641i | −0.0256507 | − | 0.314695i | ||||
\(742\) | −2.66109 | − | 8.19000i | −0.0976917 | − | 0.300664i | ||||
\(743\) | 3.90188 | + | 12.0088i | 0.143146 | + | 0.440558i | 0.996768 | − | 0.0803349i | \(-0.0255990\pi\) |
−0.853622 | + | 0.520893i | \(0.825599\pi\) | |||||||
\(744\) | 3.13710 | + | 38.4874i | 0.115012 | + | 1.41102i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.6345 | + | 3.45537i | 0.389358 | + | 0.126510i | ||||
\(747\) | 0.389611 | − | 2.55200i | 0.0142551 | − | 0.0933728i | ||||
\(748\) | 0.325120 | + | 0.731318i | 0.0118876 | + | 0.0267396i | ||||
\(749\) | − | 0.565082i | − | 0.0206477i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0215 | − | 17.4526i | 0.876556 | − | 0.636855i | −0.0557822 | − | 0.998443i | \(-0.517765\pi\) |
0.932338 | + | 0.361588i | \(0.117765\pi\) | |||||||
\(752\) | −18.3962 | + | 25.3202i | −0.670841 | + | 0.923334i | ||||
\(753\) | 33.9881 | + | 20.6977i | 1.23860 | + | 0.754267i | ||||
\(754\) | −23.6380 | + | 7.68044i | −0.860844 | + | 0.279705i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.323843 | + | 0.130975i | 0.0117780 | + | 0.00476352i | ||||
\(757\) | 1.86354 | − | 5.73537i | 0.0677314 | − | 0.208456i | −0.911462 | − | 0.411384i | \(-0.865046\pi\) |
0.979194 | + | 0.202928i | \(0.0650457\pi\) | |||||||
\(758\) | −34.7215 | −1.26114 | ||||||||
\(759\) | 1.92019 | + | 3.51774i | 0.0696983 | + | 0.127686i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0839 | − | 34.1128i | 0.401792 | − | 1.23659i | −0.521752 | − | 0.853097i | \(-0.674721\pi\) |
0.923544 | − | 0.383492i | \(-0.125279\pi\) | |||||||
\(762\) | −2.58703 | + | 10.9098i | −0.0937182 | + | 0.395219i | ||||
\(763\) | 1.85700 | + | 1.34919i | 0.0672281 | + | 0.0488440i | ||||
\(764\) | −1.01043 | + | 0.328310i | −0.0365562 | + | 0.0118778i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.2580 | − | 27.8827i | 0.731951 | − | 1.00744i | ||||
\(767\) | 63.5220 | − | 46.1515i | 2.29365 | − | 1.66643i | ||||
\(768\) | 2.87163 | − | 1.19886i | 0.103621 | − | 0.0432603i | ||||
\(769\) | − | 27.6384i | − | 0.996666i | −0.866986 | − | 0.498333i | \(-0.833946\pi\) | ||
0.866986 | − | 0.498333i | \(-0.166054\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.9794 | − | 19.7374i | 0.827583 | − | 0.710825i | ||||
\(772\) | −1.50991 | − | 0.490601i | −0.0543430 | − | 0.0176571i | ||||
\(773\) | −23.8655 | − | 32.8480i | −0.858382 | − | 1.18146i | −0.981953 | − | 0.189126i | \(-0.939435\pi\) |
0.123571 | − | 0.992336i | \(-0.460565\pi\) | |||||||
\(774\) | −23.5202 | − | 23.2591i | −0.845415 | − | 0.836031i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.0543 | + | 34.0215i | 0.396825 | + | 1.22130i | ||||
\(777\) | −7.62931 | + | 0.621863i | −0.273700 | + | 0.0223092i | ||||
\(778\) | 13.9068 | + | 19.1411i | 0.498583 | + | 0.686240i | ||||
\(779\) | 2.37286 | + | 0.770989i | 0.0850166 | + | 0.0276236i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.618201 | + | 1.06939i | −0.0221210 | + | 0.0382659i | ||||
\(782\) | 3.11578i | 0.111420i | ||||||||
\(783\) | 3.43412 | + | 13.7944i | 0.122725 | + | 0.492972i | ||||
\(784\) | 19.2703 | − | 14.0007i | 0.688224 | − | 0.500024i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.7843 | − | 27.5618i | 0.598675 | − | 0.983096i | ||||
\(787\) | 33.9748 | − | 11.0391i | 1.21107 | − | 0.393501i | 0.367249 | − | 0.930123i | \(-0.380300\pi\) |
0.843823 | + | 0.536622i | \(0.180300\pi\) | |||||||
\(788\) | −0.741884 | − | 0.539010i | −0.0264285 | − | 0.0192014i | ||||
\(789\) | 3.69841 | + | 0.877002i | 0.131667 | + | 0.0312221i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.03606 | −0.321285 | ||||||||
\(792\) | 17.9147 | − | 22.3517i | 0.636570 | − | 0.794232i | ||||
\(793\) | −11.3709 | −0.403791 | ||||||||
\(794\) | −3.56782 | + | 10.9806i | −0.126617 | + | 0.389687i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.553354 | − | 0.402035i | −0.0196131 | − | 0.0142498i | ||||
\(797\) | 9.23655 | − | 3.00114i | 0.327175 | − | 0.106306i | −0.140824 | − | 0.990035i | \(-0.544975\pi\) |
0.467999 | + | 0.883729i | \(0.344975\pi\) | |||||||
\(798\) | 0.849449 | − | 1.39490i | 0.0300702 | − | 0.0493788i | ||||
\(799\) | 15.4030 | − | 21.2004i | 0.544918 | − | 0.750016i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.06528 | + | 14.0598i | −0.249639 | + | 0.496779i | ||||
\(802\) | 19.0276i | 0.671888i | ||||||||
\(803\) | 1.74646 | + | 16.7051i | 0.0616312 | + | 0.589509i | ||||
\(804\) | −0.160966 | − | 0.187405i | −0.00567682 | − | 0.00660927i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −41.3532 | − | 56.9178i | −1.45661 | − | 2.00485i | ||||
\(807\) | 2.06294 | − | 0.168150i | 0.0726188 | − | 0.00591915i | ||||
\(808\) | 11.7462 | + | 36.1512i | 0.413231 | + | 1.27179i | ||||
\(809\) | −0.455901 | − | 1.40312i | −0.0160286 | − | 0.0493310i | 0.942722 | − | 0.333579i | \(-0.108256\pi\) |
−0.958751 | + | 0.284248i | \(0.908256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.8256 | − | 25.9112i | −0.661056 | − | 0.909865i | 0.338460 | − | 0.940981i | \(-0.390094\pi\) |
−0.999516 | + | 0.0311156i | \(0.990094\pi\) | |||||||
\(812\) | 0.174918 | + | 0.0568342i | 0.00613841 | + | 0.00199449i | ||||
\(813\) | 2.42602 | − | 2.08375i | 0.0850841 | − | 0.0730802i | ||||
\(814\) | −4.72712 | + | 22.1792i | −0.165685 | + | 0.777380i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 19.7795 | − | 8.25769i | 0.692422 | − | 0.289077i | ||||
\(817\) | 4.87228 | − | 3.53992i | 0.170460 | − | 0.123846i | ||||
\(818\) | −18.5834 | + | 25.5779i | −0.649755 | + | 0.894311i | ||||
\(819\) | −17.3837 | + | 2.85284i | −0.607435 | + | 0.0996862i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5911 | + | 7.69491i | 0.369633 | + | 0.268554i | 0.757059 | − | 0.653347i | \(-0.226636\pi\) |
−0.387426 | + | 0.921901i | \(0.626636\pi\) | |||||||
\(822\) | −6.32529 | + | 26.6744i | −0.220620 | + | 0.930376i | ||||
\(823\) | −8.69247 | + | 26.7527i | −0.303001 | + | 0.932540i | 0.677415 | + | 0.735601i | \(0.263100\pi\) |
−0.980416 | + | 0.196939i | \(0.936900\pi\) | |||||||
\(824\) | 1.25840 | 0.0438384 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9199 | 0.519130 | ||||||||
\(827\) | −15.6650 | + | 48.2119i | −0.544726 | + | 1.67649i | 0.176916 | + | 0.984226i | \(0.443388\pi\) |
−0.721641 | + | 0.692267i | \(0.756612\pi\) | |||||||
\(828\) | −0.139399 | + | 0.0720099i | −0.00484444 | + | 0.00250252i | ||||
\(829\) | −42.3470 | − | 30.7669i | −1.47077 | − | 1.06858i | −0.980390 | − | 0.197069i | \(-0.936858\pi\) |
−0.490381 | − | 0.871508i | \(-0.663142\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.5387 | + | 27.1227i | 1.54503 | + | 0.940876i | ||||
\(832\) | −31.8563 | + | 43.8465i | −1.10442 | + | 1.52010i | ||||
\(833\) | −16.1348 | + | 11.7226i | −0.559038 | + | 0.406165i | ||||
\(834\) | −15.4605 | − | 37.0323i | −0.535352 | − | 1.28232i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.126001 | + | 0.140094i | 0.00435784 | + | 0.00484524i | ||||
\(837\) | −34.1322 | + | 21.3113i | −1.17978 | + | 0.736626i | ||||
\(838\) | −40.4084 | − | 13.1295i | −1.39588 | − | 0.453550i | ||||
\(839\) | 27.2838 | + | 37.5530i | 0.941943 | + | 1.29647i | 0.955015 | + | 0.296559i | \(0.0958391\pi\) |
−0.0130716 | + | 0.999915i | \(0.504161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.64868 | − | 20.4625i | −0.229265 | − | 0.705605i | ||||
\(842\) | −13.5800 | − | 41.7950i | −0.467998 | − | 1.44035i | ||||
\(843\) | −2.73498 | − | 33.5540i | −0.0941976 | − | 1.15566i | ||||
\(844\) | 0.274827 | + | 0.378267i | 0.00945993 | + | 0.0130205i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −33.4976 | − | 5.11404i | −1.15167 | − | 0.175824i | ||||
\(847\) | −7.32352 | − | 6.60877i | −0.251639 | − | 0.227080i | ||||
\(848\) | − | 26.6077i | − | 0.913711i | ||||||
\(849\) | 14.2895 | + | 34.2274i | 0.490414 | + | 1.17468i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.02084 | − | 2.78145i | 0.0692736 | − | 0.0953470i | ||||
\(852\) | −0.0413027 | − | 0.0251521i | −0.00141501 | − | 0.000861695i | ||||
\(853\) | −8.69949 | + | 2.82664i | −0.297865 | + | 0.0967822i | −0.454137 | − | 0.890932i | \(-0.650052\pi\) |
0.156272 | + | 0.987714i | \(0.450052\pi\) | |||||||
\(854\) | −1.74803 | − | 1.27002i | −0.0598165 | − | 0.0434592i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.560581 | − | 1.72529i | 0.0191603 | − | 0.0589693i | ||||
\(857\) | −56.3567 | −1.92511 | −0.962554 | − | 0.271092i | \(-0.912615\pi\) | ||||
−0.962554 | + | 0.271092i | \(0.912615\pi\) | |||||||
\(858\) | −6.69623 | + | 51.7580i | −0.228606 | + | 1.76699i | ||||
\(859\) | −8.91219 | −0.304080 | −0.152040 | − | 0.988374i | \(-0.548584\pi\) | ||||
−0.152040 | + | 0.988374i | \(0.548584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.17991 | − | 4.97580i | 0.0402112 | − | 0.169575i | ||||
\(862\) | −24.0720 | − | 17.4893i | −0.819896 | − | 0.595689i | ||||
\(863\) | 5.91241 | − | 1.92106i | 0.201261 | − | 0.0653936i | −0.206652 | − | 0.978415i | \(-0.566257\pi\) |
0.407913 | + | 0.913021i | \(0.366257\pi\) | |||||||
\(864\) | 1.68660 | + | 1.41625i | 0.0573793 | + | 0.0481818i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.1436 | + | 18.2679i | −0.854414 | + | 0.620768i | ||||
\(867\) | 10.6107 | − | 4.42984i | 0.360360 | − | 0.150445i | ||||
\(868\) | 0.520612i | 0.0176707i | ||||||||
\(869\) | −45.2676 | + | 20.1245i | −1.53560 | + | 0.682677i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.8485 | + | 3.84980i | 0.401470 | + | 0.130446i | ||||
\(872\) | 4.33130 | + | 5.96152i | 0.146676 | + | 0.201883i | ||||
\(873\) | −26.2112 | + | 26.5053i | −0.887113 | + | 0.897070i | ||||
\(874\) | 0.226678 | + | 0.697643i | 0.00766749 | + | 0.0235981i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.655388 | + | 0.0534205i | −0.0221435 | + | 0.00180491i | ||||
\(877\) | 11.8885 | + | 16.3632i | 0.401447 | + | 0.552545i | 0.961107 | − | 0.276178i | \(-0.0890679\pi\) |
−0.559659 | + | 0.828723i | \(0.689068\pi\) | |||||||
\(878\) | 25.3584 | + | 8.23945i | 0.855805 | + | 0.278068i | ||||
\(879\) | −22.0617 | − | 25.6855i | −0.744122 | − | 0.866349i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.2385i | 0.917689i | 0.888516 | + | 0.458845i | \(0.151737\pi\) | ||||
−0.888516 | + | 0.458845i | \(0.848263\pi\) | |||||||
\(882\) | 23.0433 | + | 11.5796i | 0.775907 | + | 0.389906i | ||||
\(883\) | 33.1640 | − | 24.0950i | 1.11606 | − | 0.810863i | 0.132450 | − | 0.991190i | \(-0.457716\pi\) |
0.983607 | + | 0.180327i | \(0.0577156\pi\) | |||||||
\(884\) | 0.928748 | − | 1.27831i | 0.0312372 | − | 0.0429943i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.1314 | − | 10.4401i | 1.07948 | − | 0.350743i | ||||
\(887\) | −9.60397 | − | 6.97769i | −0.322470 | − | 0.234288i | 0.414759 | − | 0.909931i | \(-0.363866\pi\) |
−0.737229 | + | 0.675643i | \(0.763866\pi\) | |||||||
\(888\) | −23.9105 | − | 5.66988i | −0.802383 | − | 0.190269i | ||||
\(889\) | −1.29295 | + | 3.97930i | −0.0433643 | + | 0.133462i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.2615 | + | 5.89598i | 0.980298 | + | 0.197523i | ||||
\(892\) | 1.27843 | 0.0428052 | ||||||||
\(893\) | 1.90646 | − | 5.86749i | 0.0637974 | − | 0.196348i | ||||
\(894\) | −32.6144 | − | 7.73385i | −1.09079 | − | 0.258659i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.07152 | + | 2.94751i | −0.303058 | + | 0.0984695i | ||||
\(897\) | 4.11534 | − | 6.75787i | 0.137407 | − | 0.225639i | ||||
\(898\) | −6.09173 | + | 8.38455i | −0.203284 | + | 0.279796i | ||||
\(899\) | −17.1397 | + | 12.4527i | −0.571639 | + | 0.415320i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.2783i | 0.742199i | ||||||||
\(902\) | −13.1161 | − | 7.58222i | −0.436717 | − | 0.252460i | ||||
\(903\) | −8.04286 | − | 9.36394i | −0.267649 | − | 0.311612i | ||||
\(904\) | −27.5886 | − | 8.96409i | −0.917584 | − | 0.298141i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −34.5678 | + | 2.81761i | −1.14844 | + | 0.0936088i | ||||
\(907\) | −2.58726 | − | 7.96276i | −0.0859085 | − | 0.264399i | 0.898869 | − | 0.438217i | \(-0.144390\pi\) |
−0.984778 | + | 0.173818i | \(0.944390\pi\) | |||||||
\(908\) | 0.122998 | + | 0.378550i | 0.00408185 | + | 0.0125626i | ||||
\(909\) | −27.8519 | + | 28.1645i | −0.923790 | + | 0.934158i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.6294 | − | 5.07829i | −0.517824 | − | 0.168251i | 0.0384333 | − | 0.999261i | \(-0.487763\pi\) |
−0.556258 | + | 0.831010i | \(0.687763\pi\) | |||||||
\(912\) | 3.82800 | − | 3.28794i | 0.126758 | − | 0.108875i | ||||
\(913\) | −2.47088 | − | 1.42838i | −0.0817741 | − | 0.0472724i | ||||
\(914\) | 18.7206i | 0.619221i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0410294 | − | 0.0298096i | 0.00135565 | − | 0.000984937i | ||||
\(917\) | 7.07824 | − | 9.74237i | 0.233744 | − | 0.321721i | ||||
\(918\) | 17.7720 | + | 14.9232i | 0.586562 | + | 0.492540i | ||||
\(919\) | 29.7484 | − | 9.66583i | 0.981308 | − | 0.318846i | 0.225936 | − | 0.974142i | \(-0.427456\pi\) |
0.755372 | + | 0.655296i | \(0.227456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.609705 | − | 2.57119i | 0.0200905 | − | 0.0847235i | ||||
\(922\) | 6.67843 | − | 20.5541i | 0.219942 | − | 0.676913i | ||||
\(923\) | 2.43868 | 0.0802701 | ||||||||
\(924\) | 0.265211 | − | 0.280730i | 0.00872479 | − | 0.00923533i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.3847 | + | 41.1938i | −0.439848 | + | 1.35371i | ||||
\(927\) | 0.601838 | + | 1.16506i | 0.0197670 | + | 0.0382655i | ||||
\(928\) | 0.938086 | + | 0.681559i | 0.0307942 | + | 0.0223733i | ||||
\(929\) | −30.5407 | + | 9.92327i | −1.00201 | + | 0.325572i | −0.763667 | − | 0.645610i | \(-0.776603\pi\) |
−0.238340 | + | 0.971182i | \(0.576603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.75985 | + | 3.79861i | −0.0904504 | + | 0.124494i | ||||
\(932\) | −0.128301 | + | 0.0932160i | −0.00420263 | + | 0.00305339i | ||||
\(933\) | −4.63657 | − | 11.1059i | −0.151794 | − | 0.363591i | ||||
\(934\) | − | 9.79991i | − | 0.320663i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −55.9055 | − | 8.53504i | −1.82733 | − | 0.278976i | ||||
\(937\) | 17.9384 | + | 5.82855i | 0.586023 | + | 0.190410i | 0.586997 | − | 0.809589i | \(-0.300310\pi\) |
−0.000973916 | 1.00000i | \(0.500310\pi\) | ||||||||
\(938\) | 1.39147 | + | 1.91519i | 0.0454331 | + | 0.0625333i | ||||
\(939\) | −4.07795 | − | 50.0302i | −0.133079 | − | 1.63267i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.7722 | − | 33.1533i | −0.351162 | − | 1.08077i | −0.958201 | − | 0.286094i | \(-0.907643\pi\) |
0.607039 | − | 0.794672i | \(-0.292357\pi\) | |||||||
\(942\) | 0.0671135 | + | 0.823380i | 0.00218668 | + | 0.0268272i | ||||
\(943\) | 1.35006 | + | 1.85819i | 0.0439639 | + | 0.0605111i | ||||
\(944\) | 43.8431 | + | 14.2455i | 1.42697 | + | 0.463651i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.4162 | + | 14.8558i | −1.08645 | + | 0.483003i | ||||
\(947\) | − | 2.29089i | − | 0.0744441i | −0.999307 | − | 0.0372220i | \(-0.988149\pi\) | ||
0.999307 | − | 0.0372220i | \(-0.0118509\pi\) | |||||||
\(948\) | −0.747191 | − | 1.78974i | −0.0242676 | − | 0.0581280i | ||||
\(949\) | 26.8273 | − | 19.4911i | 0.870850 | − | 0.632709i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.8626 | + | 11.4867i | 0.611661 | + | 0.372483i | ||||
\(952\) | 7.90373 | − | 2.56808i | 0.256161 | − | 0.0832319i | ||||
\(953\) | 9.93032 | + | 7.21480i | 0.321675 | + | 0.233710i | 0.736890 | − | 0.676013i | \(-0.236294\pi\) |
−0.415215 | + | 0.909723i | \(0.636294\pi\) | |||||||
\(954\) | 25.5947 | − | 13.2216i | 0.828660 | − | 0.428065i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.640008 | 0.0206993 | ||||||||
\(957\) | 15.5859 | + | 2.01643i | 0.503820 | + | 0.0651821i | ||||
\(958\) | 37.8367 | 1.22245 | ||||||||
\(959\) | −3.16127 | + | 9.72939i | −0.102083 | + | 0.314179i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4369 | − | 17.0279i | −0.756029 | − | 0.549287i | ||||
\(962\) | 42.5803 | − | 13.8352i | 1.37284 | − | 0.446064i | ||||
\(963\) | 1.86542 | − | 0.306134i | 0.0601123 | − | 0.00986502i | ||||
\(964\) | −0.203788 | + | 0.280490i | −0.00656356 | + | 0.00903396i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.38744 | − | 0.579237i | 0.0446402 | − | 0.0186367i | ||||
\(967\) | − | 19.7879i | − | 0.636335i | −0.948035 | − | 0.318167i | \(-0.896933\pi\) | ||
0.948035 | − | 0.318167i | \(-0.103067\pi\) | |||||||
\(968\) | −15.8038 | − | 27.4429i | −0.507954 | − | 0.882048i | ||||
\(969\) | −3.20515 | + | 2.75296i | −0.102964 | + | 0.0884378i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0957 | + | 13.8955i | 0.323986 | + | 0.445928i | 0.939679 | − | 0.342058i | \(-0.111124\pi\) |
−0.615693 | + | 0.787986i | \(0.711124\pi\) | |||||||
\(972\) | −0.256926 | + | 1.14001i | −0.00824090 | + | 0.0365658i | ||||
\(973\) | −4.62761 | − | 14.2423i | −0.148355 | − | 0.456588i | ||||
\(974\) | −9.12388 | − | 28.0804i | −0.292348 | − | 0.899755i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.92410 | − | 5.40106i | −0.125607 | − | 0.172884i | ||||
\(977\) | 8.05036 | + | 2.61572i | 0.257554 | + | 0.0836843i | 0.434948 | − | 0.900456i | \(-0.356767\pi\) |
−0.177394 | + | 0.984140i | \(0.556767\pi\) | |||||||
\(978\) | 16.7067 | + | 19.4508i | 0.534220 | + | 0.621969i | ||||
\(979\) | 11.6330 | + | 12.9341i | 0.371792 | + | 0.413376i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.44785 | + | 6.86117i | −0.110081 | + | 0.219060i | ||||
\(982\) | −40.3784 | + | 29.3366i | −1.28853 | + | 0.936168i | ||||
\(983\) | 22.0086 | − | 30.2923i | 0.701966 | − | 0.966173i | −0.297967 | − | 0.954576i | \(-0.596309\pi\) |
0.999933 | − | 0.0115969i | \(-0.00369149\pi\) | |||||||
\(984\) | 8.53863 | − | 14.0214i | 0.272202 | − | 0.446987i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.88475 | + | 7.18169i | 0.314795 | + | 0.228712i | ||||
\(987\) | −12.3039 | − | 2.91762i | −0.391638 | − | 0.0928689i | ||||
\(988\) | 0.114953 | − | 0.353790i | 0.00365715 | − | 0.0112556i | ||||
\(989\) | 5.54424 | 0.176297 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.33052 | −0.169329 | −0.0846647 | − | 0.996409i | \(-0.526982\pi\) | ||||
−0.0846647 | + | 0.996409i | \(0.526982\pi\) | |||||||
\(992\) | −1.01427 | + | 3.12161i | −0.0322031 | + | 0.0991111i | ||||
\(993\) | −3.45191 | − | 0.818550i | −0.109543 | − | 0.0259759i | ||||
\(994\) | 0.374896 | + | 0.272378i | 0.0118910 | + | 0.00863931i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.0581149 | − | 0.0954316i | 0.00184144 | − | 0.00302386i | ||||
\(997\) | 0.611544 | − | 0.841718i | 0.0193678 | − | 0.0266575i | −0.799223 | − | 0.601034i | \(-0.794756\pi\) |
0.818591 | + | 0.574377i | \(0.194756\pi\) | |||||||
\(998\) | 6.92275 | − | 5.02968i | 0.219136 | − | 0.159212i | ||||
\(999\) | −6.18604 | − | 24.8486i | −0.195718 | − | 0.786174i |
(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 | 825.2.bi.h.101.16 | 80 | ||
3.2 | odd | 2 | inner | 825.2.bi.h.101.6 | 80 | ||
5.2 | odd | 4 | 165.2.r.a.134.15 | yes | 80 | ||
5.3 | odd | 4 | 165.2.r.a.134.6 | yes | 80 | ||
5.4 | even | 2 | inner | 825.2.bi.h.101.5 | 80 | ||
11.6 | odd | 10 | inner | 825.2.bi.h.776.6 | 80 | ||
15.2 | even | 4 | 165.2.r.a.134.5 | ✓ | 80 | ||
15.8 | even | 4 | 165.2.r.a.134.16 | yes | 80 | ||
15.14 | odd | 2 | inner | 825.2.bi.h.101.15 | 80 | ||
33.17 | even | 10 | inner | 825.2.bi.h.776.16 | 80 | ||
55.17 | even | 20 | 165.2.r.a.149.16 | yes | 80 | ||
55.28 | even | 20 | 165.2.r.a.149.5 | yes | 80 | ||
55.39 | odd | 10 | inner | 825.2.bi.h.776.15 | 80 | ||
165.17 | odd | 20 | 165.2.r.a.149.6 | yes | 80 | ||
165.83 | odd | 20 | 165.2.r.a.149.15 | yes | 80 | ||
165.149 | even | 10 | inner | 825.2.bi.h.776.5 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.r.a.134.5 | ✓ | 80 | 15.2 | even | 4 | ||
165.2.r.a.134.6 | yes | 80 | 5.3 | odd | 4 | ||
165.2.r.a.134.15 | yes | 80 | 5.2 | odd | 4 | ||
165.2.r.a.134.16 | yes | 80 | 15.8 | even | 4 | ||
165.2.r.a.149.5 | yes | 80 | 55.28 | even | 20 | ||
165.2.r.a.149.6 | yes | 80 | 165.17 | odd | 20 | ||
165.2.r.a.149.15 | yes | 80 | 165.83 | odd | 20 | ||
165.2.r.a.149.16 | yes | 80 | 55.17 | even | 20 | ||
825.2.bi.h.101.5 | 80 | 5.4 | even | 2 | inner | ||
825.2.bi.h.101.6 | 80 | 3.2 | odd | 2 | inner | ||
825.2.bi.h.101.15 | 80 | 15.14 | odd | 2 | inner | ||
825.2.bi.h.101.16 | 80 | 1.1 | even | 1 | trivial | ||
825.2.bi.h.776.5 | 80 | 165.149 | even | 10 | inner | ||
825.2.bi.h.776.6 | 80 | 11.6 | odd | 10 | inner | ||
825.2.bi.h.776.15 | 80 | 55.39 | odd | 10 | inner | ||
825.2.bi.h.776.16 | 80 | 33.17 | even | 10 | inner |