LMFDB - Embedded newform 256.2.m.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([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("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15776 + 0.812153i) q^{2} +(-0.322964 + 2.17724i) q^{3} +(0.680816 - 1.88056i) q^{4} +(0.378649 + 0.0186018i) q^{5} +(-1.39434 - 2.78302i) q^{6} +(1.23593 + 0.660620i) q^{7} +(0.739076 + 2.73016i) q^{8} +(-1.76526 - 0.535486i) q^{9} +O(q^{10})$	\(q+(-1.15776 + 0.812153i) q^{2} +(-0.322964 + 2.17724i) q^{3} +(0.680816 - 1.88056i) q^{4} +(0.378649 + 0.0186018i) q^{5} +(-1.39434 - 2.78302i) q^{6} +(1.23593 + 0.660620i) q^{7} +(0.739076 + 2.73016i) q^{8} +(-1.76526 - 0.535486i) q^{9} +(-0.453492 + 0.285984i) q^{10} +(2.70367 + 4.51080i) q^{11} +(3.87455 + 2.08965i) q^{12} +(-4.27193 + 4.71335i) q^{13} +(-1.96744 + 0.238927i) q^{14} +(-0.162790 + 0.818403i) q^{15} +(-3.07298 - 2.56063i) q^{16} +(-0.969103 - 4.87201i) q^{17} +(2.47865 - 0.813697i) q^{18} +(-3.27063 - 6.91516i) q^{19} +(0.292772 - 0.699406i) q^{20} +(-1.83749 + 2.47757i) q^{21} +(-6.79366 - 3.02663i) q^{22} +(4.50298 + 3.69550i) q^{23} +(-6.18291 + 0.727408i) q^{24} +(-4.83289 - 0.475999i) q^{25} +(1.11791 - 8.92639i) q^{26} +(-1.08723 + 2.29876i) q^{27} +(2.08378 - 1.87448i) q^{28} +(0.112655 - 0.0282185i) q^{29} +(-0.476196 - 1.07972i) q^{30} +(4.91305 + 2.03505i) q^{31} +(5.63739 + 0.468862i) q^{32} +(-10.6943 + 4.42972i) q^{33} +(5.07880 + 4.85356i) q^{34} +(0.455696 + 0.273134i) q^{35} +(-2.20883 + 2.95510i) q^{36} +(1.28732 + 3.59781i) q^{37} +(9.40277 + 5.34985i) q^{38} +(-8.88243 - 10.8233i) q^{39} +(0.229065 + 1.04752i) q^{40} +(1.50676 - 0.148403i) q^{41} +(0.115209 - 4.36076i) q^{42} +(-0.807932 + 0.119845i) q^{43} +(10.3235 - 2.01337i) q^{44} +(-0.658453 - 0.235598i) q^{45} +(-8.21468 - 0.621395i) q^{46} +(-3.12116 + 4.67114i) q^{47} +(6.56756 - 5.86363i) q^{48} +(-2.79788 - 4.18732i) q^{49} +(5.98192 - 3.37396i) q^{50} +(10.9205 - 0.536491i) q^{51} +(5.95532 + 11.2425i) q^{52} +(8.01418 + 2.00745i) q^{53} +(-0.608190 - 3.54441i) q^{54} +(0.939832 + 1.75830i) q^{55} +(-0.890149 + 3.86254i) q^{56} +(16.1123 - 4.88761i) q^{57} +(-0.107509 + 0.124163i) q^{58} +(7.07858 + 7.81001i) q^{59} +(1.42822 + 0.863318i) q^{60} +(-0.548580 - 0.739674i) q^{61} +(-7.34090 + 1.63404i) q^{62} +(-1.82799 - 1.82799i) q^{63} +(-6.90753 + 4.03559i) q^{64} +(-1.70524 + 1.70524i) q^{65} +(8.78381 - 13.8140i) q^{66} +(6.00143 - 4.45097i) q^{67} +(-9.82186 - 1.49449i) q^{68} +(-9.50030 + 8.61057i) q^{69} +(-0.749413 + 0.0538715i) q^{70} +(-2.32729 - 7.67204i) q^{71} +(0.157299 - 5.21521i) q^{72} +(10.0070 - 5.34888i) q^{73} +(-4.41238 - 3.11990i) q^{74} +(2.59721 - 10.3687i) q^{75} +(-15.2310 + 1.44264i) q^{76} +(0.361630 + 7.36115i) q^{77} +(19.0739 + 5.31686i) q^{78} +(8.14727 - 5.44383i) q^{79} +(-1.11595 - 1.02674i) q^{80} +(-9.25524 - 6.18416i) q^{81} +(-1.62394 + 1.39553i) q^{82} +(3.74796 - 10.4749i) q^{83} +(3.40822 + 5.14228i) q^{84} +(-0.276321 - 1.86281i) q^{85} +(0.838059 - 0.794917i) q^{86} +(0.0250553 + 0.254390i) q^{87} +(-10.3170 + 10.7153i) q^{88} +(1.21435 - 0.996594i) q^{89} +(0.953672 - 0.261998i) q^{90} +(-8.39356 + 3.00326i) q^{91} +(10.0153 - 5.95215i) q^{92} +(-6.01754 + 10.0397i) q^{93} +(-0.180129 - 7.94292i) q^{94} +(-1.10978 - 2.67926i) q^{95} +(-2.84150 + 12.1225i) q^{96} +(3.14107 - 7.58322i) q^{97} +(6.64002 + 2.57561i) q^{98} +(-2.35721 - 9.41052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.15776	+	0.812153i	−0.818660	+	0.574279i
$2$	−1.15776	+	0.812153i	−0.818660	+	0.574279i
$3$	−0.322964	+	2.17724i	−0.186463	+	1.25703i	0.670600	+	0.741820i	$0.266037\pi$
$3$	−0.322964	+	2.17724i	−0.186463	+	1.25703i	−0.857063	+	0.515212i	$0.827713\pi$
$4$	0.680816	−	1.88056i	0.340408	−	0.940278i
$5$	0.378649	+	0.0186018i	0.169337	+	0.00831899i	0.133560	−	0.991041i	$-0.457359\pi$
$5$	0.378649	+	0.0186018i	0.169337	+	0.00831899i	0.0357774	+	0.999360i	$0.488609\pi$
$6$	−1.39434	−	2.78302i	−0.569237	−	1.13616i
$7$	1.23593	+	0.660620i	0.467139	+	0.249691i	0.688134	−	0.725584i	$-0.258430\pi$
$7$	1.23593	+	0.660620i	0.467139	+	0.249691i	−0.220995	+	0.975275i	$0.570930\pi$
$8$	0.739076	+	2.73016i	0.261303	+	0.965257i
$9$	−1.76526	−	0.535486i	−0.588420	−	0.178495i
$10$	−0.453492	+	0.285984i	−0.143407	+	0.0904361i
$11$	2.70367	+	4.51080i	0.815187	+	1.36006i	0.930336	+	0.366709i	$0.119515\pi$
$11$	2.70367	+	4.51080i	0.815187	+	1.36006i	−0.115149	+	0.993348i	$0.536735\pi$
$12$	3.87455	+	2.08965i	1.11849	+	0.603231i
$13$	−4.27193	+	4.71335i	−1.18482	+	1.30725i	−0.243435	+	0.969917i	$0.578274\pi$
$13$	−4.27193	+	4.71335i	−1.18482	+	1.30725i	−0.941386	+	0.337331i	$0.890476\pi$
$14$	−1.96744	+	0.238927i	−0.525820	+	0.0638559i
$15$	−0.162790	+	0.818403i	−0.0420323	+	0.211311i
$16$	−3.07298	−	2.56063i	−0.768245	−	0.640156i
$17$	−0.969103	−	4.87201i	−0.235042	−	1.18164i	−0.900384	−	0.435097i	$-0.856714\pi$
$17$	−0.969103	−	4.87201i	−0.235042	−	1.18164i	0.665342	−	0.746539i	$-0.268286\pi$
$18$	2.47865	−	0.813697i	0.584222	−	0.191790i
$19$	−3.27063	−	6.91516i	−0.750333	−	1.58645i	−0.808749	−	0.588155i	$-0.799855\pi$
$19$	−3.27063	−	6.91516i	−0.750333	−	1.58645i	0.0584151	−	0.998292i	$-0.481395\pi$
$20$	0.292772	−	0.699406i	0.0654658	−	0.156392i
$21$	−1.83749	+	2.47757i	−0.400974	+	0.540650i
$22$	−6.79366	−	3.02663i	−1.44841	−	0.645280i
$23$	4.50298	+	3.69550i	0.938937	+	0.770565i	0.973464	−	0.228838i	$-0.0734927\pi$
$23$	4.50298	+	3.69550i	0.938937	+	0.770565i	−0.0345278	+	0.999404i	$0.510993\pi$
$24$	−6.18291	+	0.727408i	−1.26208	+	0.148481i
$25$	−4.83289	−	0.475999i	−0.966579	−	0.0951997i
$26$	1.11791	−	8.92639i	0.219241	−	1.75061i
$27$	−1.08723	+	2.29876i	−0.209238	+	0.442397i
$28$	2.08378	−	1.87448i	0.393797	−	0.354244i
$29$	0.112655	−	0.0282185i	0.0209195	−	0.00524005i	−0.232506	−	0.972595i	$-0.574693\pi$
$29$	0.112655	−	0.0282185i	0.0209195	−	0.00524005i	0.253426	+	0.967355i	$0.418443\pi$
$30$	−0.476196	−	1.07972i	−0.0869411	−	0.197130i
$31$	4.91305	+	2.03505i	0.882410	+	0.365506i	0.777431	−	0.628968i	$-0.216523\pi$
$31$	4.91305	+	2.03505i	0.882410	+	0.365506i	0.104979	+	0.994474i	$0.466523\pi$
$32$	5.63739	+	0.468862i	0.996559	+	0.0828838i
$33$	−10.6943	+	4.42972i	−1.86164	+	0.771115i
$34$	5.07880	+	4.85356i	0.871008	+	0.832378i
$35$	0.455696	+	0.273134i	0.0770267	+	0.0461680i
$36$	−2.20883	+	2.95510i	−0.368138	+	0.492517i
$37$	1.28732	+	3.59781i	0.211634	+	0.591477i	0.999710	−	0.0241016i	$-0.00767254\pi$
$37$	1.28732	+	3.59781i	0.211634	+	0.591477i	−0.788076	+	0.615578i	$0.788923\pi$
$38$	9.40277	+	5.34985i	1.52533	+	0.867860i
$39$	−8.88243	−	10.8233i	−1.42233	−	1.73311i
$40$	0.229065	+	1.04752i	0.0362183	+	0.165627i
$41$	1.50676	−	0.148403i	0.235316	−	0.0231767i	0.0203285	−	0.999793i	$-0.493529\pi$
$41$	1.50676	−	0.148403i	0.235316	−	0.0231767i	0.214988	+	0.976617i	$0.431029\pi$
$42$	0.115209	−	4.36076i	0.0177771	−	0.672879i
$43$	−0.807932	+	0.119845i	−0.123209	+	0.0182763i	−0.208050	−	0.978118i	$-0.566712\pi$
$43$	−0.807932	+	0.119845i	−0.123209	+	0.0182763i	0.0848414	+	0.996394i	$0.472962\pi$
$44$	10.3235	−	2.01337i	1.55633	−	0.303528i
$45$	−0.658453	−	0.235598i	−0.0981564	−	0.0351209i
$46$	−8.21468	−	0.621395i	−1.21119	−	0.0916197i
$47$	−3.12116	+	4.67114i	−0.455268	+	0.681356i	−0.986106	−	0.166117i	$-0.946877\pi$
$47$	−3.12116	+	4.67114i	−0.455268	+	0.681356i	0.530838	+	0.847473i	$0.321877\pi$
$48$	6.56756	−	5.86363i	0.947946	−	0.846343i
$49$	−2.79788	−	4.18732i	−0.399697	−	0.598189i
$50$	5.98192	−	3.37396i	0.845971	−	0.477149i
$51$	10.9205	−	0.536491i	1.52918	−	0.0751238i
$52$	5.95532	+	11.2425i	0.825854	+	1.55906i
$53$	8.01418	+	2.00745i	1.10083	+	0.275744i	0.750493	−	0.660879i	$-0.229816\pi$
$53$	8.01418	+	2.00745i	1.10083	+	0.275744i	0.350340	+	0.936623i	$0.386066\pi$
$54$	−0.608190	−	3.54441i	−0.0827642	−	0.482333i
$55$	0.939832	+	1.75830i	0.126727	+	0.237089i
$56$	−0.890149	+	3.86254i	−0.118951	+	0.516154i
$57$	16.1123	−	4.88761i	2.13412	−	0.647379i
$58$	−0.107509	+	0.124163i	−0.0141167	+	0.0163034i
$59$	7.07858	+	7.81001i	0.921553	+	1.01678i	0.999803	+	0.0198429i	$0.00631659\pi$
$59$	7.07858	+	7.81001i	0.921553	+	1.01678i	−0.0782505	+	0.996934i	$0.524933\pi$
$60$	1.42822	+	0.863318i	0.184383	+	0.111454i
$61$	−0.548580	−	0.739674i	−0.0702385	−	0.0947056i	0.766691	−	0.642016i	$-0.221902\pi$
$61$	−0.548580	−	0.739674i	−0.0702385	−	0.0947056i	−0.836930	+	0.547310i	$0.815652\pi$
$62$	−7.34090	+	1.63404i	−0.932296	+	0.207524i
$63$	−1.82799	−	1.82799i	−0.230305	−	0.230305i
$64$	−6.90753	+	4.03559i	−0.863441	+	0.504449i
$65$	−1.70524	+	1.70524i	−0.211509	+	0.211509i
$66$	8.78381	−	13.8140i	1.08121	−	1.70038i
$67$	6.00143	−	4.45097i	0.733192	−	0.543772i	−0.163438	−	0.986554i	$-0.552258\pi$
$67$	6.00143	−	4.45097i	0.733192	−	0.543772i	0.896630	+	0.442781i	$0.146008\pi$
$68$	−9.82186	−	1.49449i	−1.19108	−	0.181234i
$69$	−9.50030	+	8.61057i	−1.14370	+	1.03659i
$70$	−0.749413	+	0.0538715i	−0.0895720	+	0.00643887i
$71$	−2.32729	−	7.67204i	−0.276198	−	0.910503i	−0.979812	−	0.199921i	$-0.935932\pi$
$71$	−2.32729	−	7.67204i	−0.276198	−	0.910503i	0.703614	−	0.710582i	$-0.251568\pi$
$72$	0.157299	−	5.21521i	0.0185379	−	0.614618i
$73$	10.0070	−	5.34888i	1.17124	−	0.626039i	0.233150	−	0.972441i	$-0.425097\pi$
$73$	10.0070	−	5.34888i	1.17124	−	0.626039i	0.938086	+	0.346402i	$0.112597\pi$
$74$	−4.41238	−	3.11990i	−0.512928	−	0.362681i
$75$	2.59721	−	10.3687i	0.299900	−	1.19727i
$76$	−15.2310	+	1.44264i	−1.74712	+	0.165483i
$77$	0.361630	+	7.36115i	0.0412116	+	0.838880i
$78$	19.0739	+	5.31686i	2.15969	+	0.602016i
$79$	8.14727	−	5.44383i	0.916640	−	0.612479i	−0.00522688	−	0.999986i	$-0.501664\pi$
$79$	8.14727	−	5.44383i	0.916640	−	0.612479i	0.921867	+	0.387507i	$0.126664\pi$
$80$	−1.11595	−	1.02674i	−0.124767	−	0.114793i
$81$	−9.25524	−	6.18416i	−1.02836	−	0.687128i
$82$	−1.62394	+	1.39553i	−0.179334	+	0.154111i
$83$	3.74796	−	10.4749i	0.411392	−	1.14976i	−0.539969	−	0.841685i	$-0.681564\pi$
$83$	3.74796	−	10.4749i	0.411392	−	1.14976i	0.951361	−	0.308079i	$-0.0996861\pi$
$84$	3.40822	+	5.14228i	0.371867	+	0.561068i
$85$	−0.276321	−	1.86281i	−0.0299713	−	0.202050i
$86$	0.838059	−	0.794917i	0.0903702	−	0.0857181i
$87$	0.0250553	+	0.254390i	0.00268621	+	0.0272735i
$88$	−10.3170	+	10.7153i	−1.09979	+	1.14225i
$89$	1.21435	−	0.996594i	0.128721	−	0.105639i	−0.567830	−	0.823146i	$-0.692217\pi$
$89$	1.21435	−	0.996594i	0.128721	−	0.105639i	0.696551	+	0.717507i	$0.254717\pi$
$90$	0.953672	−	0.261998i	0.100526	−	0.0276170i
$91$	−8.39356	+	3.00326i	−0.879884	+	0.314828i
$92$	10.0153	−	5.95215i	1.04417	−	0.620555i
$93$	−6.01754	+	10.0397i	−0.623990	+	1.04106i
$94$	−0.180129	−	7.94292i	−0.0185789	−	0.819250i
$95$	−1.10978	−	2.67926i	−0.113862	−	0.274886i
$96$	−2.84150	+	12.1225i	−0.290009	+	1.23725i
$97$	3.14107	−	7.58322i	0.318928	−	0.769960i	−0.680384	−	0.732856i	$-0.738187\pi$
$97$	3.14107	−	7.58322i	0.318928	−	0.769960i	0.999311	−	0.0371036i	$-0.0118132\pi$
$98$	6.64002	+	2.57561i	0.670743	+	0.260176i
$99$	−2.35721	−	9.41052i	−0.236909	−	0.945792i
$100$	−4.18545	+	8.76446i	−0.418545	+	0.876446i
$101$	0.609349	+	0.288201i	0.0606325	+	0.0286770i	0.457631	−	0.889142i	$-0.348698\pi$
$101$	0.609349	+	0.288201i	0.0606325	+	0.0286770i	−0.396998	+	0.917819i	$0.629948\pi$
$102$	−12.2076	+	9.49027i	−1.20874	+	0.939677i
$103$	−1.09579	+	11.1257i	−0.107971	+	1.09625i	0.776647	+	0.629936i	$0.216919\pi$
$103$	−1.09579	+	11.1257i	−0.107971	+	1.09625i	−0.884618	+	0.466316i	$0.845581\pi$
$104$	−16.0255	−	8.17953i	−1.57143	−	0.802069i
$105$	−0.741852	+	0.903949i	−0.0723973	+	0.0882164i
$106$	−10.9089	+	4.18460i	−1.05956	+	0.406444i
$107$	8.20763	+	6.08720i	0.793462	+	0.588471i	0.914691	−	0.404153i	$-0.132434\pi$
$107$	8.20763	+	6.08720i	0.793462	+	0.588471i	−0.121229	+	0.992625i	$0.538684\pi$
$108$	3.58274	+	3.60964i	0.344749	+	0.347337i
$109$	4.78189	−	2.26166i	0.458022	−	0.216628i	−0.184597	−	0.982814i	$-0.559098\pi$
$109$	4.78189	−	2.26166i	0.458022	−	0.216628i	0.642619	+	0.766186i	$0.277848\pi$
$110$	−2.51611	−	1.27240i	−0.239902	−	0.121319i
$111$	−8.24907	+	1.64084i	−0.782967	+	0.155742i
$112$	−2.10640	−	5.19483i	−0.199036	−	0.490866i
$113$	1.10946	+	0.220686i	0.104369	+	0.0207604i	0.246999	−	0.969016i	$-0.420556\pi$
$113$	1.10946	+	0.220686i	0.104369	+	0.0207604i	−0.142629	+	0.989776i	$0.545556\pi$
$114$	−14.6847	+	18.7443i	−1.37535	+	1.75557i
$115$	1.63631	+	1.48306i	0.152586	+	0.138296i
$116$	0.0236306	−	0.231065i	0.00219405	−	0.0214539i
$117$	10.0650	−	6.03274i	0.930511	−	0.557727i
$118$	−14.5382	−	3.29323i	−1.33835	−	0.303166i
$119$	2.02080	−	6.66169i	0.185247	−	0.610676i
$120$	−2.35468	+	0.160419i	−0.214952	+	0.0146441i
$121$	−7.85212	+	14.6903i	−0.713829	+	1.33548i
$122$	1.23585	+	0.410835i	0.111889	+	0.0371952i
$123$	−0.163519	+	3.32851i	−0.0147440	+	0.300122i
$124$	7.17191	−	7.85377i	0.644057	−	0.705289i
$125$	−3.69613	−	0.548269i	−0.330592	−	0.0490386i
$126$	3.60099	+	0.631768i	0.320801	+	0.0562823i
$127$			4.73578i			0.420233i	0.977676	+	0.210116i	$0.0673843\pi$
$127$			4.73578i			0.420233i	−0.977676	+	0.210116i	$0.932616\pi$
$128$	4.71975	−	10.2822i	0.417171	−	0.908828i
$129$		−	1.79777i		−	0.158285i
$130$	0.589343	−	3.35917i	0.0516888	−	0.294619i
$131$	−0.907116	−	0.134558i	−0.0792551	−	0.0117564i	0.106985	−	0.994261i	$-0.465880\pi$
$131$	−0.907116	−	0.134558i	−0.0792551	−	0.0117564i	−0.186240	+	0.982504i	$0.559630\pi$
$132$	1.04949	+	23.1270i	0.0913463	+	2.01295i
$133$	0.526017	−	10.7073i	0.0456115	−	0.928443i
$134$	−3.33336	+	10.0272i	−0.287958	+	0.866221i
$135$	−0.454441	+	0.850199i	−0.0391120	+	0.0731734i
$136$	12.5851	−	6.24659i	1.07916	−	0.535641i
$137$	1.16680	−	3.84643i	0.0996866	−	0.328623i	−0.892885	−	0.450285i	$-0.851322\pi$
$137$	1.16680	−	3.84643i	0.0996866	−	0.328623i	0.992572	+	0.121662i	$0.0388224\pi$
$138$	4.00597	−	17.6847i	0.341011	−	1.50542i
$139$	2.41027	−	1.44466i	0.204437	−	0.122535i	−0.408221	−	0.912883i	$-0.633851\pi$
$139$	2.41027	−	1.44466i	0.204437	−	0.122535i	0.612657	+	0.790349i	$0.290101\pi$
$140$	0.823888	−	0.671008i	0.0696313	−	0.0567105i
$141$	−9.16219	−	8.30413i	−0.771596	−	0.699334i
$142$	8.92530	+	6.99227i	0.748995	+	0.586778i
$143$	−32.8109	−	6.52649i	−2.74378	−	0.545772i
$144$	4.05343	+	6.16571i	0.337786	+	0.513809i
$145$	0.0431815	−	0.00858933i	0.00358603	−	0.000713305i
$146$	−7.24165	+	14.3200i	−0.599323	+	1.18513i
$147$	10.0204	−	4.73931i	0.826471	−	0.390892i
$148$	7.64231	+	0.0285761i	0.628194	+	0.00234894i
$149$	13.2805	+	9.84950i	1.08798	+	0.806902i	0.982266	−	0.187494i	$-0.0600366\pi$
$149$	13.2805	+	9.84950i	1.08798	+	0.806902i	0.105716	+	0.994396i	$0.466287\pi$
$150$	5.41398	+	14.1137i	0.442050	+	1.15238i
$151$	−1.84715	+	2.25075i	−0.150319	+	0.183164i	−0.842726	−	0.538343i	$-0.819050\pi$
$151$	−1.84715	+	2.25075i	−0.150319	+	0.183164i	0.692407	+	0.721507i	$0.256550\pi$
$152$	16.4622	−	14.0402i	1.33526	−	1.13881i
$153$	−0.898174	+	9.11931i	−0.0726130	+	0.737252i
$154$	−6.39705	−	8.22874i	−0.515489	−	0.663091i
$155$	1.82246	+	0.861962i	0.146384	+	0.0692344i
$156$	−26.4011	+	9.33525i	−2.11378	+	0.747418i
$157$	−3.11735	−	12.4452i	−0.248792	−	0.993232i	−0.957662	−	0.287894i	$-0.907045\pi$
$157$	−3.11735	−	12.4452i	−0.248792	−	0.993232i	0.708871	−	0.705339i	$-0.249205\pi$
$158$	−5.01136	+	12.9195i	−0.398683	+	1.02782i
$159$	−6.95899	+	16.8005i	−0.551884	+	1.33237i
$160$	2.12587	+	0.282400i	0.168065	+	0.0223257i
$161$	3.12406	+	7.54215i	0.246211	+	0.594405i
$162$	15.7378	−	0.356902i	1.23648	−	0.0280409i
$163$	−10.2114	+	17.0367i	−0.799818	+	1.33442i	0.139101	+	0.990278i	$0.455579\pi$
$163$	−10.2114	+	17.0367i	−0.799818	+	1.33442i	−0.938919	+	0.344138i	$0.888171\pi$
$164$	0.746747	−	2.93458i	0.0583111	−	0.229152i
$165$	−4.13178	+	1.47838i	−0.321659	+	0.115091i
$166$	4.16794	+	15.1713i	0.323495	+	1.17752i
$167$	2.61910	−	2.14944i	0.202672	−	0.166328i	−0.527583	−	0.849504i	$-0.676901\pi$
$167$	2.61910	−	2.14944i	0.202672	−	0.166328i	0.730254	+	0.683175i	$0.239401\pi$
$168$	−8.12221	−	3.18553i	−0.626642	−	0.245769i
$169$	−2.69205	−	27.3328i	−0.207081	−	2.10253i
$170$	1.83280	+	1.93227i	0.140569	+	0.148198i
$171$	2.07054	+	13.9584i	0.158338	+	1.06743i
$172$	−0.324677	+	1.60095i	−0.0247564	+	0.122072i
$173$	1.45174	−	4.05735i	0.110374	−	0.308474i	−0.873638	−	0.486576i	$-0.838246\pi$
$173$	1.45174	−	4.05735i	0.110374	−	0.308474i	0.984012	+	0.178102i	$0.0569956\pi$
$174$	−0.235612	−	0.274174i	−0.0178617	−	0.0207851i
$175$	−5.65868	−	3.78101i	−0.427756	−	0.285818i
$176$	3.24215	−	20.7847i	0.244386	−	1.56670i
$177$	−19.2904	+	12.8894i	−1.44996	+	0.968830i
$178$	−0.596543	+	2.14006i	−0.0447128	+	0.160404i
$179$	0.0936494	+	1.90628i	0.00699969	+	0.142482i	0.999751	+	0.0222982i	$0.00709834\pi$
$179$	0.0936494	+	1.90628i	0.00699969	+	0.142482i	−0.992752	+	0.120184i	$0.961652\pi$
$180$	−0.891341	+	1.07786i	−0.0664366	+	0.0803388i
$181$	6.18648	−	24.6978i	0.459837	−	1.83577i	−0.0838401	−	0.996479i	$-0.526718\pi$
$181$	6.18648	−	24.6978i	0.459837	−	1.83577i	0.543677	−	0.839294i	$-0.317032\pi$
$182$	7.27862	−	10.2939i	0.539527	−	0.763035i
$183$	1.78762	−	0.955504i	0.132145	−	0.0706329i
$184$	−6.76126	+	15.0251i	−0.498447	+	1.10767i
$185$	0.420515	+	1.38625i	0.0309169	+	0.101919i
$186$	−1.18687	−	16.5107i	−0.0870254	−	1.21062i
$187$	19.3565	−	17.5437i	1.41549	−	1.28292i
$188$	6.65941	+	9.04970i	0.485687	+	0.660017i
$189$	−2.86236	+	2.12287i	−0.208206	+	0.154416i
$190$	3.46083	+	2.20062i	0.251075	+	0.159650i
$191$	−1.64258	+	1.64258i	−0.118853	+	0.118853i	−0.764032	−	0.645179i	$-0.776783\pi$
$191$	−1.64258	+	1.64258i	−0.118853	+	0.118853i	0.645179	+	0.764032i	$0.276783\pi$
$192$	−6.55558	−	16.3427i	−0.473109	−	1.17943i
$193$	3.79311	+	3.79311i	0.273034	+	0.273034i	0.830320	−	0.557286i	$-0.188157\pi$
$193$	3.79311	+	3.79311i	0.273034	+	0.273034i	−0.557286	+	0.830320i	$0.688157\pi$
$194$	2.52213	+	11.3306i	0.181078	+	0.813489i
$195$	−3.16199	−	4.26345i	−0.226435	−	0.305312i
$196$	−9.77933	+	2.41077i	−0.698524	+	0.172198i
$197$	−15.7475	−	17.3747i	−1.12196	−	1.23789i	−0.968306	−	0.249769i	$-0.919645\pi$
$197$	−15.7475	−	17.3747i	−1.12196	−	1.23789i	−0.153655	−	0.988124i	$-0.549105\pi$
$198$	10.3719	+	8.98070i	0.737096	+	0.638231i
$199$	4.23289	−	1.28403i	0.300061	−	0.0910226i	−0.136664	−	0.990617i	$-0.543638\pi$
$199$	4.23289	−	1.28403i	0.300061	−	0.0910226i	0.436725	+	0.899595i	$0.356138\pi$
$200$	−2.27233	−	13.5464i	−0.160678	−	0.957873i
$201$	7.75259	+	14.5041i	0.546826	+	1.02304i
$202$	−0.939543	+	0.161217i	−0.0661060	+	0.0113432i
$203$	0.157875	+	0.0395458i	0.0110807	+	0.00277557i
$204$	6.42597	−	20.9019i	0.449908	−	1.46343i
$205$	0.573294	−	0.0281641i	0.0400406	−	0.00196707i
$206$	−7.76714	−	13.7709i	−0.541162	−	0.959463i
$207$	−5.97005	−	8.93481i	−0.414947	−	0.621012i
$208$	25.1967	−	3.54521i	1.74708	−	0.245816i
$209$	22.3502	−	33.4495i	1.54600	−	2.31375i
$210$	0.124742	−	1.64905i	0.00860799	−	0.113795i
$211$	−6.80891	−	2.43627i	−0.468745	−	0.167720i	0.0919131	−	0.995767i	$-0.470702\pi$
$211$	−6.80891	−	2.43627i	−0.468745	−	0.167720i	−0.560658	+	0.828047i	$0.689452\pi$
$212$	9.23130	−	13.7044i	0.634008	−	0.941223i
$213$	17.4555	−	2.58928i	1.19603	−	0.177415i
$214$	−14.4462	−	0.381660i	−0.987522	−	0.0260898i
$215$	−0.308152	+	0.0303503i	−0.0210158	+	0.00206988i
$216$	−7.07953	−	1.26936i	−0.481701	−	0.0863689i
$217$	4.72781	+	5.76085i	0.320944	+	0.391072i
$218$	−3.69946	+	6.50208i	−0.250559	+	0.440377i
$219$	8.41390	+	23.5153i	0.568558	+	1.58901i
$220$	3.94644	−	0.570326i	0.266069	−	0.0384514i
$221$	27.1034	+	16.2452i	1.82317	+	1.09277i
$222$	8.21783	−	8.59920i	0.551544	−	0.577141i
$223$	−16.9035	+	7.00164i	−1.13194	+	0.468865i	−0.868440	−	0.495795i	$-0.834877\pi$
$223$	−16.9035	+	7.00164i	−1.13194	+	0.468865i	−0.263499	+	0.964660i	$0.584877\pi$
$224$	6.65770	+	4.30366i	0.444836	+	0.287550i
$225$	8.27643	+	3.42821i	0.551762	+	0.228547i
$226$	−1.46372	+	0.645552i	−0.0973654	+	0.0429415i
$227$	−23.3166	+	5.84051i	−1.54758	+	0.387648i	−0.920321	−	0.391164i	$-0.872073\pi$
$227$	−23.3166	+	5.84051i	−1.54758	+	0.387648i	−0.627258	+	0.778812i	$0.715823\pi$
$228$	1.77809	−	33.6276i	0.117757	−	2.22704i
$229$	−8.53428	+	18.0442i	−0.563961	+	1.19239i	0.397538	+	0.917586i	$0.369865\pi$
$229$	−8.53428	+	18.0442i	−0.563961	+	1.19239i	−0.961499	+	0.274809i	$0.911385\pi$
$230$	−3.09892	−	0.388099i	−0.204337	−	0.0255905i
$231$	−16.1438	−	1.59003i	−1.06218	−	0.104616i
$232$	0.160302	+	0.286710i	0.0105243	+	0.0188234i
$233$	−2.81201	−	2.30776i	−0.184221	−	0.151186i	0.537763	−	0.843096i	$-0.319270\pi$
$233$	−2.81201	−	2.30776i	−0.184221	−	0.151186i	−0.721984	+	0.691910i	$0.756770\pi$
$234$	−6.75337	+	15.1588i	−0.441481	+	0.990961i
$235$	−1.26871	+	1.71066i	−0.0827618	+	0.111591i
$236$	19.5064	−	7.99448i	1.26976	−	0.520396i
$237$	9.22128	+	19.4968i	0.598986	+	1.26645i
$238$	3.07070	+	9.35383i	0.199044	+	0.606319i
$239$	4.70807	+	23.6691i	0.304540	+	1.53103i	0.765401	+	0.643554i	$0.222541\pi$
$239$	4.70807	+	23.6691i	0.304540	+	1.53103i	−0.460861	+	0.887472i	$0.652459\pi$
$240$	2.59587	−	2.09809i	0.167563	−	0.135431i
$241$	0.272146	−	1.36817i	0.0175304	−	0.0881314i	−0.971030	−	0.238959i	$-0.923194\pi$
$241$	0.272146	−	1.36817i	0.0175304	−	0.0881314i	0.988560	+	0.150828i	$0.0481938\pi$
$242$	−2.83988	−	23.3849i	−0.182554	−	1.50324i
$243$	11.3304	−	12.5011i	0.726844	−	0.801949i
$244$	−1.76448	+	0.528053i	−0.112959	+	0.0338051i
$245$	−0.981522	−	1.63757i	−0.0627071	−	0.104621i
$246$	−2.51394	−	3.98642i	−0.160283	−	0.254165i
$247$	46.5655	+	14.1255i	2.96289	+	0.898783i
$248$	−1.92489	+	14.9175i	−0.122231	+	0.947260i
$249$	21.5958	+	11.5432i	1.36858	+	0.731522i
$250$	4.72451	−	2.36706i	0.298804	−	0.149706i
$251$	−19.8214	−	0.973764i	−1.25112	−	0.0614634i	−0.587307	−	0.809364i	$-0.699812\pi$
$251$	−19.8214	−	0.973764i	−1.25112	−	0.0614634i	−0.663810	+	0.747901i	$0.731062\pi$
$252$	−4.68217	+	2.19311i	−0.294949	+	0.138153i
$253$	−4.49509	+	30.3035i	−0.282604	+	1.90516i
$254$	−3.84618	−	5.48290i	−0.241331	−	0.344028i
$255$	4.14503			0.259572
$256$	2.88640	+	15.7375i	0.180400	+	0.983593i
$257$	−3.39100			−0.211525			−0.105762	−	0.994391i	$-0.533728\pi$
$257$	−3.39100			−0.211525			−0.105762	+	0.994391i	$0.533728\pi$
$258$	1.46006	+	2.08139i	0.0908996	+	0.129582i
$259$	−0.785748	+	5.29708i	−0.0488240	+	0.329145i
$260$	2.04584	+	4.36775i	0.126878	+	0.270876i
$261$	−0.213976	−	0.0105120i	−0.0132448	−	0.000650673i
$262$	1.15950	−	0.580931i	0.0716344	−	0.0358900i
$263$	2.00753	+	1.07305i	0.123790	+	0.0661670i	0.532129	−	0.846663i	$-0.321392\pi$
$263$	2.00753	+	1.07305i	0.123790	+	0.0661670i	−0.408340	+	0.912830i	$0.633892\pi$
$264$	−19.9977	−	25.9232i	−1.23078	−	1.59546i
$265$	2.99722	+	0.909196i	0.184118	+	0.0558515i
$266$	8.08698	+	12.8237i	0.495844	+	0.786272i
$267$	1.77764	+	2.96581i	0.108790	+	0.181504i
$268$	−4.28442	−	14.3163i	−0.261712	−	0.874509i
$269$	−15.7403	+	17.3667i	−0.959702	+	1.05887i	0.0385198	+	0.999258i	$0.487736\pi$
$269$	−15.7403	+	17.3667i	−0.959702	+	1.05887i	−0.998222	+	0.0596101i	$0.981014\pi$
$270$	−0.164358	−	1.35340i	−0.0100025	−	0.0823654i
$271$	5.50202	−	27.6605i	0.334224	−	1.68026i	−0.338973	−	0.940796i	$-0.610080\pi$
$271$	5.50202	−	27.6605i	0.334224	−	1.68026i	0.673198	−	0.739463i	$-0.264920\pi$
$272$	−9.49736	+	17.4531i	−0.575862	+	1.05825i
$273$	−3.82802	−	19.2448i	−0.231682	−	1.16475i
$274$	1.77301	+	5.40086i	0.107112	+	0.326278i
$275$	−10.9194	−	23.0872i	−0.658465	−	1.39221i
$276$	9.72470	+	23.7281i	0.585358	+	1.42826i
$277$	12.1283	−	16.3531i	0.728720	−	0.982565i	−0.271080	−	0.962557i	$-0.587381\pi$
$277$	12.1283	−	16.3531i	0.728720	−	0.982565i	0.999800	−	0.0200084i	$-0.00636931\pi$
$278$	−1.61723	+	3.63008i	−0.0969950	+	0.217718i
$279$	−7.58307	−	6.22327i	−0.453987	−	0.372577i
$280$	−0.408904	+	1.44599i	−0.0244367	+	0.0864144i
$281$	12.0878	+	1.19055i	0.721098	+	0.0710220i	0.451907	−	0.892065i	$-0.350744\pi$
$281$	12.0878	+	1.19055i	0.721098	+	0.0710220i	0.269191	+	0.963087i	$0.413244\pi$
$282$	17.3518	+	2.17309i	1.03329	+	0.129405i
$283$	1.75535	−	3.71137i	0.104345	−	0.220618i	−0.845062	−	0.534669i	$-0.820436\pi$
$283$	1.75535	−	3.71137i	0.104345	−	0.220618i	0.949406	+	0.314051i	$0.101686\pi$
$284$	−16.0121	−	0.846655i	−0.950146	−	0.0502397i
$285$	6.19182	−	1.55097i	0.366771	−	0.0918715i
$286$	43.2876	−	19.0913i	2.55965	−	1.12889i
$287$	1.96029	+	0.811980i	0.115712	+	0.0479297i
$288$	−9.70040	−	3.84641i	−0.571601	−	0.226652i
$289$	−7.09136	+	2.93734i	−0.417139	+	0.172785i
$290$	−0.0430180	+	0.0450144i	−0.00252610	+	0.00264333i
$291$	15.4961	+	9.28799i	0.908396	+	0.544471i
$292$	−3.24590	−	22.4604i	−0.189952	−	1.31440i
$293$	−9.68135	−	27.0576i	−0.565590	−	1.58072i	−0.794495	−	0.607271i	$-0.792264\pi$
$293$	−9.68135	−	27.0576i	−0.565590	−	1.58072i	0.228905	−	0.973449i	$-0.426486\pi$
$294$	−7.75221	+	13.6251i	−0.452118	+	0.794632i
$295$	2.53502	+	3.08893i	0.147594	+	0.179844i
$296$	−8.87117	+	6.17364i	−0.515626	+	0.358835i
$297$	−13.3088	+	1.31080i	−0.772253	+	0.0760603i
$298$	−23.3749	−	0.617552i	−1.35407	−	0.0357739i
$299$	−36.6546	+	5.43720i	−2.11979	+	0.314441i
$300$	−17.7306	−	11.9434i	−1.02368	−	0.689550i
$301$	−1.07772	−	0.385615i	−0.0621189	−	0.0222265i
$302$	0.310596	−	4.10600i	0.0178728	−	0.236274i
$303$	−0.824280	+	1.23362i	−0.0473537	+	0.0708698i
$304$	−7.65657	+	29.6250i	−0.439134	+	1.69911i
$305$	−0.193960	−	0.290281i	−0.0111061	−	0.0166215i
$306$	−6.36640	−	11.2874i	−0.363943	−	0.645259i
$307$	−10.9629	+	0.538571i	−0.625683	+	0.0307378i	−0.359440	−	0.933168i	$-0.617032\pi$
$307$	−10.9629	+	0.538571i	−0.625683	+	0.0307378i	−0.266243	+	0.963906i	$0.585782\pi$
$308$	14.0892	+	4.33152i	0.802809	+	0.246811i
$309$	−23.8695	−	5.97901i	−1.35789	−	0.340134i
$310$	−2.81002	+	0.482175i	−0.159598	+	0.0273857i
$311$	9.31773	+	17.4322i	0.528360	+	0.988492i	0.994595	+	0.103831i	$0.0331101\pi$
$311$	9.31773	+	17.4322i	0.528360	+	0.988492i	−0.466235	+	0.884661i	$0.654390\pi$
$312$	22.9845	−	32.2497i	1.30124	−	1.82578i
$313$	−0.138478	+	0.0420070i	−0.00782727	+	0.00237438i	−0.294196	−	0.955745i	$-0.595052\pi$
$313$	−0.138478	+	0.0420070i	−0.00782727	+	0.00237438i	0.286369	+	0.958120i	$0.407552\pi$
$314$	13.7165	+	11.8768i	0.774068	+	0.670244i
$315$	−0.658163	−	0.726171i	−0.0370833	−	0.0409151i
$316$	−4.69064	−	19.0276i	−0.263869	−	1.07039i
$317$	3.20199	+	4.31739i	0.179842	+	0.242489i	0.883925	−	0.467629i	$-0.154892\pi$
$317$	3.20199	+	4.31739i	0.179842	+	0.242489i	−0.704083	+	0.710118i	$0.748642\pi$
$318$	−5.58772	−	25.1027i	−0.313344	−	1.40769i
$319$	0.431869	+	0.431869i	0.0241800	+	0.0241800i
$320$	−2.69060	+	1.39958i	−0.150409	+	0.0782389i
$321$	−15.9041	+	15.9041i	−0.887679	+	0.887679i
$322$	−9.74230	−	6.19479i	−0.542917	−	0.345222i
$323$	−30.5212	+	22.6360i	−1.69824	+	1.25950i
$324$	−17.9308	+	13.1947i	−0.996154	+	0.733040i
$325$	22.8894	−	20.7457i	1.26967	−	1.15076i
$326$	−2.01404	−	28.0176i	−0.111548	−	1.55175i
$327$	3.37982	+	11.1418i	0.186904	+	0.616141i
$328$	1.51877	+	4.00401i	0.0838603	+	0.221085i
$329$	−6.94339	+	3.71132i	−0.382802	+	0.204612i
$330$	3.58295	−	5.06724i	0.197235	−	0.278942i
$331$	5.54418	−	22.1336i	0.304736	−	1.21657i	−0.603244	−	0.797557i	$-0.706125\pi$
$331$	5.54418	−	22.1336i	0.304736	−	1.21657i	0.907979	−	0.419015i	$-0.137625\pi$
$332$	−17.1469	−	14.1797i	−0.941057	−	0.778212i
$333$	−0.345874	−	7.04042i	−0.0189538	−	0.385812i
$334$	−1.28661	+	4.61564i	−0.0704004	+	0.252557i
$335$	2.35523	−	1.57372i	0.128680	−	0.0859813i
$336$	11.9907	−	2.90839i	0.654147	−	0.158666i
$337$	18.8565	+	12.5995i	1.02718	+	0.686340i	0.950503	−	0.310716i	$-0.100569\pi$
$337$	18.8565	+	12.5995i	1.02718	+	0.686340i	0.0766777	+	0.997056i	$0.475569\pi$
$338$	25.3152	+	29.4585i	1.37696	+	1.60233i
$339$	−0.838803	+	2.34430i	−0.0455575	+	0.127325i
$340$	−3.69124	−	0.748592i	−0.200185	−	0.0405981i
$341$	4.10355	+	27.6639i	0.222220	+	1.49808i
$342$	−13.7336	−	14.4789i	−0.742627	−	0.782931i
$343$	−1.65330	−	16.7862i	−0.0892697	−	0.906371i
$344$	−0.924321	−	2.11721i	−0.0498360	−	0.114152i
$345$	−3.75745	+	3.08366i	−0.202294	+	0.166019i
$346$	1.61442	+	5.87647i	0.0867916	+	0.315921i
$347$	−5.24354	+	1.87617i	−0.281488	+	0.100718i	−0.473849	−	0.880606i	$-0.657136\pi$
$347$	−5.24354	+	1.87617i	−0.281488	+	0.100718i	0.192361	+	0.981324i	$0.438386\pi$
$348$	0.495453	+	0.126075i	0.0265591	+	0.00675834i
$349$	2.04431	−	3.41073i	0.109429	−	0.182572i	−0.798142	−	0.602469i	$-0.794184\pi$
$349$	2.04431	−	3.41073i	0.109429	−	0.182572i	0.907572	+	0.419897i	$0.137934\pi$
$350$	9.62215	−	0.218211i	0.514326	−	0.0116639i
$351$	−6.19028	−	14.9447i	−0.330413	−	0.797687i
$352$	13.1267	+	26.6968i	0.699655	+	1.42294i
$353$	0.405973	−	0.980107i	0.0216078	−	0.0521658i	−0.912707	−	0.408614i	$-0.866012\pi$
$353$	0.405973	−	0.980107i	0.0216078	−	0.0521658i	0.934315	+	0.356448i	$0.116012\pi$
$354$	11.8655	−	30.5896i	0.630643	−	1.62582i
$355$	−0.738511	−	2.94830i	−0.0391961	−	0.156480i
$356$	−1.04740	−	2.96216i	−0.0555121	−	0.156994i
$357$	13.8515	+	6.55126i	0.733097	+	0.346729i
$358$	−1.65661	−	2.13095i	−0.0875547	−	0.112624i
$359$	0.0310010	−	0.314758i	0.00163617	−	0.0166123i	−0.994332	−	0.106320i	$-0.966093\pi$
$359$	0.0310010	−	0.314758i	0.00163617	−	0.0166123i	0.995968	+	0.0897076i	$0.0285932\pi$
$360$	0.156574	−	1.97181i	0.00825215	−	0.103923i
$361$	−25.0690	+	30.5466i	−1.31942	+	1.60772i
$362$	12.8959	+	33.6185i	0.677795	+	1.76695i
$363$	−29.4484	−	21.8404i	−1.54564	−	1.14632i
$364$	−0.0666671	+	17.8292i	−0.00349430	+	0.934505i
$365$	3.88865	−	1.83920i	0.203542	−	0.0962680i
$366$	−1.29362	+	2.55807i	−0.0676187	+	0.133712i
$367$	20.4759	−	4.07292i	1.06884	−	0.212605i	0.370832	−	0.928700i	$-0.379072\pi$
$367$	20.4759	−	4.07292i	1.06884	−	0.212605i	0.698003	+	0.716095i	$0.254072\pi$
$368$	−4.37477	−	22.8866i	−0.228051	−	1.19305i
$369$	−2.73929	−	0.544879i	−0.142602	−	0.0283653i
$370$	−1.61271	−	1.26343i	−0.0838406	−	0.0656824i
$371$	8.57883	+	7.77540i	0.445391	+	0.403679i
$372$	14.7833	+	18.1515i	0.766478	+	0.941110i
$373$	−29.2949	+	17.5587i	−1.51683	+	0.909154i	−0.518287	+	0.855207i	$0.673430\pi$
$373$	−29.2949	+	17.5587i	−1.51683	+	0.909154i	−0.998544	+	0.0539471i	$0.982820\pi$
$374$	−8.16202	+	36.0319i	−0.422048	+	1.86316i
$375$	2.38743	−	7.87030i	0.123286	−	0.406420i
$376$	−15.0597	−	5.06892i	−0.776647	−	0.261410i
$377$	−0.348250	+	0.651529i	−0.0179358	+	0.0335555i
$378$	1.58983	−	4.78244i	0.0817719	−	0.245982i
$379$	−0.251391	+	5.11718i	−0.0129131	+	0.262852i	0.983654	+	0.180067i	$0.0576314\pi$
$379$	−0.251391	+	5.11718i	−0.0129131	+	0.262852i	−0.996567	+	0.0827848i	$0.973619\pi$
$380$	−5.79405	+	0.262930i	−0.297229	+	0.0134880i
$381$	−10.3109	−	1.52948i	−0.528246	−	0.0783579i
$382$	0.567688	−	3.23574i	0.0290455	−	0.165555i
$383$		−	1.16877i		−	0.0597212i	−0.999554	−	0.0298606i	$-0.990494\pi$
$383$		−	1.16877i		−	0.0597212i	0.999554	−	0.0298606i	$-0.00950634\pi$
$384$	20.8626	+	13.5968i	1.06464	+	0.693860i
$385$			2.79402i			0.142396i
$386$	−7.47210	−	1.31093i	−0.380320	−	0.0667244i
$387$	1.49039	+	0.221078i	0.0757606	+	0.0112380i
$388$	−12.1222	−	11.0697i	−0.615410	−	0.561981i
$389$	−1.63924	+	33.3675i	−0.0831128	+	1.69180i	0.489524	+	0.871990i	$0.337171\pi$
$389$	−1.63924	+	33.3675i	−0.0831128	+	1.69180i	−0.572637	+	0.819809i	$0.694079\pi$
$390$	7.12340	+	2.36803i	0.360707	+	0.119910i
$391$	13.6407	−	25.5199i	0.689838	−	1.29060i
$392$	9.36421	−	10.7334i	0.472964	−	0.542119i
$393$	0.585931	−	1.93156i	0.0295563	−	0.0974341i
$394$	32.3427	+	7.32633i	1.62940	+	0.369095i
$395$	3.18622	−	1.90975i	0.160316	−	0.0960898i
$396$	−19.3018	−	1.97396i	−0.969953	−	0.0991954i
$397$	−9.57363	−	8.67703i	−0.480487	−	0.435488i	0.395035	−	0.918666i	$-0.370732\pi$
$397$	−9.57363	−	8.67703i	−0.480487	−	0.435488i	−0.875522	+	0.483178i	$0.839482\pi$
$398$	−3.85784	+	4.92435i	−0.193376	+	0.246835i
$399$	23.1426	+	4.60334i	1.15858	+	0.230455i
$400$	13.6325	+	13.8380i	0.681626	+	0.691898i
$401$	12.7339	−	2.53294i	0.635903	−	0.126489i	0.133397	−	0.991063i	$-0.457411\pi$
$401$	12.7339	−	2.53294i	0.635903	−	0.126489i	0.502506	+	0.864574i	$0.332411\pi$
$402$	−20.7552	−	10.4960i	−1.03517	−	0.523491i
$403$	−30.5801	+	14.4633i	−1.52330	+	0.720470i
$404$	0.956832	−	0.949703i	0.0476042	−	0.0472495i
$405$	−3.38945	−	2.51379i	−0.168423	−	0.124911i
$406$	−0.214899	+	0.0824345i	−0.0106653	+	0.00409116i
$407$	−12.7485	+	15.5341i	−0.631921	+	0.769998i
$408$	9.53582	+	29.4183i	0.472093	+	1.45642i
$409$	2.44729	−	24.8478i	0.121011	−	1.22864i	−0.722438	−	0.691435i	$-0.756979\pi$
$409$	2.44729	−	24.8478i	0.121011	−	1.22864i	0.843449	−	0.537209i	$-0.180521\pi$
$410$	−0.640863	+	0.498209i	−0.0316500	+	0.0246048i
$411$	7.99778	+	3.78267i	0.394501	+	0.186585i
$412$	20.1765	+	9.63528i	0.994027	+	0.474696i
$413$	3.58920	+	14.3289i	0.176613	+	0.705079i
$414$	14.1683	+	5.49577i	0.696335	+	0.270103i
$415$	1.61401	−	3.89657i	0.0792288	−	0.191275i
$416$	−26.2925	+	24.5681i	−1.28909	+	1.20455i
$417$	2.36695	+	5.71432i	0.115910	+	0.279831i
$418$	1.28988	+	56.8782i	0.0630903	+	2.78200i
$419$	19.9894	−	33.3504i	0.976548	−	1.62927i	0.219821	−	0.975540i	$-0.429453\pi$
$419$	19.9894	−	33.3504i	0.976548	−	1.62927i	0.756727	−	0.653731i	$-0.226797\pi$
$420$	1.19486	+	2.01052i	0.0583033	+	0.0981031i
$421$	3.93065	−	1.40641i	0.191568	−	0.0685442i	−0.239358	−	0.970931i	$-0.576937\pi$
$421$	3.93065	−	1.40641i	0.191568	−	0.0685442i	0.430926	+	0.902387i	$0.358187\pi$
$422$	9.86171	−	2.70926i	0.480061	−	0.131885i
$423$	8.01099	−	6.57445i	0.389508	−	0.319661i
$424$	0.442441	+	23.3636i	0.0214869	+	1.13464i
$425$	2.36450	+	24.0072i	0.114695	+	1.16452i
$426$	−18.1064	+	17.1743i	−0.877258	+	0.832098i
$427$	−0.189364	−	1.27659i	−0.00916399	−	0.0617786i
$428$	17.0352	−	11.2906i	0.823427	−	0.545754i
$429$	24.8065	−	69.3294i	1.19767	−	3.34726i
$430$	0.332117	−	0.285405i	0.0160161	−	0.0137634i
$431$	−1.19670	−	0.799608i	−0.0576429	−	0.0385158i	0.526415	−	0.850228i	$-0.323536\pi$
$431$	−1.19670	−	0.799608i	−0.0576429	−	0.0385158i	−0.584058	+	0.811712i	$0.698536\pi$
$432$	9.22731	−	4.28005i	0.443949	−	0.205924i
$433$	4.07928	−	2.72569i	0.196038	−	0.130988i	−0.453677	−	0.891166i	$-0.649888\pi$
$433$	4.07928	−	2.72569i	0.196038	−	0.130988i	0.649715	+	0.760178i	$0.274888\pi$
$434$	−10.1524	−	2.82998i	−0.487328	−	0.135843i
$435$	0.00475502	+	0.0967907i	0.000227986	+	0.00464076i
$436$	−0.997599	−	10.5324i	−0.0477763	−	0.504410i
$437$	10.8274	−	43.2255i	0.517945	−	2.06775i
$438$	−28.8393	−	20.3917i	−1.37799	−	0.974351i
$439$	27.9285	−	14.9281i	1.33296	−	0.712480i	0.357759	−	0.933814i	$-0.383541\pi$
$439$	27.9285	−	14.9281i	1.33296	−	0.712480i	0.975198	+	0.221334i	$0.0710410\pi$
$440$	−4.10584	+	3.86541i	−0.195738	+	0.184276i
$441$	2.69673	+	8.88994i	0.128416	+	0.423331i
$442$	−44.5728	+	3.20411i	−2.12011	+	0.152404i
$443$	−20.5951	+	18.6663i	−0.978501	+	0.886861i	−0.993592	−	0.113025i	$-0.963946\pi$
$443$	−20.5951	+	18.6663i	−0.978501	+	0.886861i	0.0150916	+	0.999886i	$0.495196\pi$
$444$	−2.53040	+	16.6299i	−0.120088	+	0.789222i
$445$	0.478352	−	0.354770i	0.0226761	−	0.0168177i
$446$	13.8837	−	21.8344i	0.657414	−	1.03389i
$447$	−25.7339	+	25.7339i	−1.21717	+	1.21717i
$448$	−11.2032	+	0.424468i	−0.529303	+	0.0200542i
$449$	−16.0320	−	16.0320i	−0.756598	−	0.756598i	0.219104	−	0.975702i	$-0.429687\pi$
$449$	−16.0320	−	16.0320i	−0.756598	−	0.756598i	−0.975702	+	0.219104i	$0.929687\pi$
$450$	−12.3664	+	2.75268i	−0.582955	+	0.129763i
$451$	4.74320	+	6.39546i	0.223348	+	0.301151i
$452$	1.17035	−	1.93616i	0.0550487	−	0.0910693i
$453$	−4.30388	−	4.74860i	−0.202214	−	0.223109i
$454$	22.2517	−	25.6986i	1.04432	−	1.20609i
$455$	−3.23408	+	0.981047i	−0.151616	+	0.0459922i
$456$	25.2522	+	40.3768i	1.18254	+	1.89082i
$457$	−6.09550	−	11.4039i	−0.285135	−	0.533451i	0.698053	−	0.716046i	$-0.254050\pi$
$457$	−6.09550	−	11.4039i	−0.285135	−	0.533451i	−0.983188	+	0.182596i	$0.941550\pi$
$458$	−4.77401	−	27.8220i	−0.223075	−	1.30004i
$459$	12.2532	+	3.06927i	0.571932	+	0.143261i
$460$	3.90300	−	2.06747i	0.181978	−	0.0963964i
$461$	−23.3475	+	1.14699i	−1.08740	+	0.0534205i	−0.584861	−	0.811134i	$-0.698851\pi$
$461$	−23.3475	+	1.14699i	−1.08740	+	0.0534205i	−0.502539	+	0.864554i	$0.667601\pi$
$462$	19.9820	−	11.2704i	0.929646	−	0.524345i
$463$	6.28264	+	9.40263i	0.291979	+	0.436977i	0.948239	−	0.317557i	$-0.102863\pi$
$463$	6.28264	+	9.40263i	0.291979	+	0.436977i	−0.656260	+	0.754535i	$0.727863\pi$
$464$	−0.418443	−	0.201752i	−0.0194257	−	0.00936608i
$465$	−2.46529	+	3.68957i	−0.114325	+	0.171100i
$466$	5.12989	+	0.388048i	0.237638	+	0.0179760i
$467$	29.1371	+	10.4254i	1.34830	+	0.482431i	0.909333	−	0.416070i	$-0.136593\pi$
$467$	29.1371	+	10.4254i	1.34830	+	0.482431i	0.438972	+	0.898501i	$0.355343\pi$
$468$	−4.49247	−	23.0350i	−0.207665	−	1.06479i
$469$	10.3578	−	1.53643i	0.478278	−	0.0709458i
$470$	0.0795470	−	3.01093i	0.00366923	−	0.138884i
$471$	28.1029	−	2.76790i	1.29492	−	0.127538i
$472$	−16.0910	+	25.0978i	−0.740646	+	1.15522i
$473$	−2.72498	−	3.32040i	−0.125295	−	0.152672i
$474$	−26.5104	−	15.0835i	−1.21766	−	0.692807i
$475$	12.5150	+	34.9771i	0.574227	+	1.60486i
$476$	−11.1519	−	8.33561i	−0.511146	−	0.382062i
$477$	−13.0722	−	7.83515i	−0.598533	−	0.358747i
$478$	−24.6737	−	23.5794i	−1.12855	−	1.07850i
$479$	−4.53169	+	1.87709i	−0.207058	+	0.0857663i	−0.483802	−	0.875177i	$-0.660745\pi$
$479$	−4.53169	+	1.87709i	−0.207058	+	0.0857663i	0.276744	+	0.960944i	$0.410745\pi$
$480$	−1.30143	+	4.53733i	−0.0594019	+	0.207100i
$481$	−22.4571	−	9.30203i	−1.02395	−	0.424136i
$482$	0.796082	+	1.80503i	0.0362605	+	0.0822170i
$483$	−17.4301	+	4.36600i	−0.793095	+	0.198660i
$484$	22.2800	+	24.7677i	1.01273	+	1.12581i
$485$	1.33043	−	2.81295i	0.0604115	−	0.127729i
$486$	−2.96502	+	23.6753i	−0.134496	+	1.07393i
$487$	−28.7131	−	2.82800i	−1.30112	−	0.128149i	−0.576384	−	0.817179i	$-0.695537\pi$
$487$	−28.7131	−	2.82800i	−1.30112	−	0.128149i	−0.724732	+	0.689030i	$0.758037\pi$
$488$	1.61399	−	2.04439i	0.0730617	−	0.0925450i
$489$	−33.7951	−	27.7349i	−1.52827	−	1.25422i
$490$	2.46632	+	1.09877i	0.111417	+	0.0496373i
$491$	8.07413	−	10.8867i	0.364380	−	0.491310i	−0.582529	−	0.812810i	$-0.697937\pi$
$491$	8.07413	−	10.8867i	0.364380	−	0.491310i	0.946910	+	0.321500i	$0.104187\pi$
$492$	6.14813	+	2.57361i	0.277179	+	0.116027i
$493$	−0.246655	−	0.521508i	−0.0111088	−	0.0234875i
$494$	−65.3837	+	21.4644i	−2.94175	+	0.965727i
$495$	−0.717503	−	3.60713i	−0.0322493	−	0.162128i
$496$	−9.88669	−	18.8341i	−0.443925	−	0.845678i
$497$	2.19193	−	11.0196i	0.0983215	−	0.494296i
$498$	−34.3777	+	4.17484i	−1.54050	+	0.187079i
$499$	6.71183	−	7.40537i	0.300463	−	0.331510i	−0.571942	−	0.820294i	$-0.693810\pi$
$499$	6.71183	−	7.40537i	0.300463	−	0.331510i	0.872404	+	0.488785i	$0.162560\pi$
$500$	−3.54743	+	6.57750i	−0.158646	+	0.294155i
$501$	3.83398	+	6.39660i	0.171289	+	0.285779i
$502$	23.7393	−	14.9706i	1.05954	−	0.668172i
$503$	1.30947	+	0.397225i	0.0583866	+	0.0177114i	0.319343	−	0.947639i	$-0.396538\pi$
$503$	1.30947	+	0.397225i	0.0583866	+	0.0177114i	−0.260956	+	0.965351i	$0.584038\pi$
$504$	3.63968	−	6.34174i	0.162124	−	0.282483i
$505$	0.225368	+	0.120462i	0.0100288	+	0.00536048i
$506$	−19.4068	−	38.7348i	−0.862737	−	1.72197i
$507$	60.3797	+	2.96626i	2.68156	+	0.131736i
$508$	8.90590	+	3.22420i	0.395135	+	0.143051i
$509$	−3.21646	+	21.6836i	−0.142567	+	0.961109i	0.793319	+	0.608806i	$0.208351\pi$
$509$	−3.21646	+	21.6836i	−0.142567	+	0.961109i	−0.935886	+	0.352303i	$0.885399\pi$
$510$	−4.79895	+	3.36639i	−0.212501	+	0.149066i
$511$	15.9016			0.703446
$512$	−16.1230	−	15.8760i	−0.712543	−	0.701629i
$513$	19.4522			0.858837
$514$	3.92596	−	2.75401i	0.173167	−	0.121474i
$515$	−0.621879	+	4.19236i	−0.0274032	+	0.184738i
$516$	−3.38081	−	1.22395i	−0.148832	−	0.0538815i
$517$	−29.5092	−	1.44969i	−1.29781	−	0.0637574i
$518$	−3.39233	−	6.77090i	−0.149051	−	0.297496i
$519$	8.36497	+	4.47117i	0.367181	+	0.196263i
$520$	−5.91588	−	3.39527i	−0.259428	−	0.148893i
$521$	6.72370	+	2.03961i	0.294571	+	0.0893570i	0.434111	−	0.900859i	$-0.357063\pi$
$521$	6.72370	+	2.03961i	0.294571	+	0.0893570i	−0.139540	+	0.990216i	$0.544563\pi$
$522$	0.256270	−	0.161611i	0.0112166	−	0.00707350i
$523$	−8.31662	−	13.8754i	−0.363660	−	0.606731i	0.620459	−	0.784239i	$-0.286946\pi$
$523$	−8.31662	−	13.8754i	−0.363660	−	0.606731i	−0.984119	+	0.177508i	$0.943196\pi$
$524$	−0.870623	+	1.61427i	−0.0380334	+	0.0705199i
$525$	10.0597	−	11.0992i	0.439042	−	0.484409i
$526$	−3.19572	+	0.388090i	−0.139340	+	0.0169215i
$527$	5.15354	−	25.9086i	0.224492	−	1.12860i
$528$	44.2062	+	13.7716i	1.92383	+	0.599334i
$529$	2.13303	+	10.7235i	0.0927406	+	0.466239i
$530$	−4.20847	+	1.38157i	−0.182804	+	0.0600115i
$531$	−8.31339	−	17.5772i	−0.360770	−	0.762785i
$532$	−19.7776	−	8.27892i	−0.857467	−	0.358937i
$533$	−5.73731	+	7.73586i	−0.248510	+	0.335077i
$534$	−4.46676	−	1.98998i	−0.193296	−	0.0861149i
$535$	2.99458	+	2.45759i	0.129467	+	0.106251i
$536$	16.5874	+	13.0953i	0.716465	+	0.565629i
$537$	−4.18068	−	0.411761i	−0.180409	−	0.0177688i
$538$	4.11904	−	32.8900i	0.177584	−	1.41799i
$539$	11.3236	−	23.9418i	0.487743	−	1.03125i
$540$	1.28946	+	1.43343i	0.0554893	+	0.0616850i
$541$	8.67022	−	2.17178i	0.372762	−	0.0933720i	−0.0520719	−	0.998643i	$-0.516583\pi$
$541$	8.67022	−	2.17178i	0.372762	−	0.0933720i	0.424834	+	0.905271i	$0.360333\pi$
$542$	16.0946	+	36.4928i	0.691321	+	1.56750i
$543$	51.7751	+	21.4460i	2.22188	+	0.920334i
$544$	−3.17891	−	27.9198i	−0.136295	−	1.19705i
$545$	1.85273	−	0.767425i	0.0793621	−	0.0328729i
$546$	20.0616	+	19.1719i	0.858558	+	0.820481i
$547$	−6.49813	−	3.89483i	−0.277840	−	0.166531i	0.368395	−	0.929669i	$-0.379907\pi$
$547$	−6.49813	−	3.89483i	−0.277840	−	0.166531i	−0.646235	+	0.763139i	$0.723657\pi$
$548$	−6.43905	−	4.81295i	−0.275063	−	0.205599i
$549$	0.572301	+	1.59948i	0.0244252	+	0.0682639i
$550$	31.3924	+	17.8612i	1.33857	+	0.761602i
$551$	−0.563588	−	0.686733i	−0.0240096	−	0.0292558i
$552$	−30.5297	−	19.5735i	−1.29943	−	0.833102i
$553$	13.6658	−	1.34596i	0.581129	−	0.0572362i
$554$	−0.760432	+	28.7831i	−0.0323077	+	1.22288i
$555$	−3.15402	+	0.467855i	−0.133881	+	0.0198593i
$556$	−1.07581	−	5.51620i	−0.0456247	−	0.233939i
$557$	−21.3741	−	7.64778i	−0.905650	−	0.324047i	−0.157455	−	0.987526i	$-0.550329\pi$
$557$	−21.3741	−	7.64778i	−0.905650	−	0.324047i	−0.748195	+	0.663479i	$0.769079\pi$
$558$	13.8336	+	1.04644i	0.585624	+	0.0442992i
$559$	2.88656	−	4.32004i	0.122088	−	0.182718i
$560$	−0.700951	−	2.00620i	−0.0296206	−	0.0847775i
$561$	31.9455	+	47.8098i	1.34874	+	2.01853i
$562$	−14.9617	+	8.43878i	−0.631121	+	0.355968i
$563$	−3.58272	+	0.176008i	−0.150994	+	0.00741784i	−0.124424	−	0.992229i	$-0.539708\pi$
$563$	−3.58272	+	0.176008i	−0.150994	+	0.00741784i	−0.0265695	+	0.999647i	$0.508458\pi$
$564$	−21.8541	+	11.5764i	−0.920225	+	0.487456i
$565$	0.415992	+	0.104200i	0.0175009	+	0.00438375i
$566$	0.981928	+	5.72249i	0.0412735	+	0.240534i
$567$	−7.35349	−	13.7574i	−0.308817	−	0.577757i
$568$	19.2258	−	12.0241i	0.806698	−	0.504519i
$569$	34.7496	−	10.5412i	1.45678	−	0.441910i	0.540124	−	0.841585i	$-0.318377\pi$
$569$	34.7496	−	10.5412i	1.45678	−	0.441910i	0.916657	+	0.399676i	$0.130877\pi$
$570$	−5.90901	+	6.82435i	−0.247501	+	0.285841i
$571$	−22.9846	−	25.3596i	−0.961876	−	1.06127i	−0.998081	−	0.0619223i	$-0.980277\pi$
$571$	−22.9846	−	25.3596i	−0.961876	−	1.06127i	0.0362049	−	0.999344i	$-0.488473\pi$
$572$	−34.6116	+	57.2593i	−1.44718	+	2.39413i
$573$	−3.04581	−	4.10679i	−0.127240	−	0.171564i
$574$	−2.92900	+	0.651980i	−0.122254	+	0.0272131i
$575$	−20.0034	−	20.0034i	−0.834199	−	0.834199i
$576$	14.3546	−	3.42499i	0.598108	−	0.142708i
$577$	−19.0324	+	19.0324i	−0.792329	+	0.792329i	−0.981872	−	0.189543i	$-0.939299\pi$
$577$	−19.0324	+	19.0324i	−0.792329	+	0.792329i	0.189543	+	0.981872i	$0.439299\pi$
$578$	5.82453	−	9.16000i	0.242268	−	0.381006i
$579$	−9.48356	+	7.03349i	−0.394123	+	0.292302i
$580$	0.0132459	−	0.0870530i	0.000550008	−	0.00361468i
$581$	11.5521	−	10.4702i	0.479263	−	0.434379i
$582$	−25.4840	+	1.83191i	−1.05635	+	0.0759353i
$583$	12.6125	+	41.5778i	0.522356	+	1.72198i
$584$	21.9993	+	23.3676i	0.910336	+	0.966958i
$585$	3.92333	−	2.09706i	0.162210	−	0.0867028i
$586$	33.1835	+	23.4634i	1.37080	+	0.969265i
$587$	5.28362	−	21.0934i	0.218078	−	0.870617i	−0.757833	−	0.652449i	$-0.773742\pi$
$587$	5.28362	−	21.0934i	0.218078	−	0.870617i	0.975911	−	0.218169i	$-0.0700082\pi$
$588$	−2.09047	−	22.0706i	−0.0862094	−	0.910175i
$589$	−1.99604	−	40.6304i	−0.0822456	−	1.67415i
$590$	−5.44362	−	1.51741i	−0.224110	−	0.0624710i
$591$	42.9147	−	28.6747i	1.76528	−	1.17952i
$592$	5.25675	−	14.3523i	0.216051	−	0.589877i
$593$	−17.6719	−	11.8080i	−0.725699	−	0.484896i	0.137028	−	0.990567i	$-0.456245\pi$
$593$	−17.6719	−	11.8080i	−0.725699	−	0.484896i	−0.862726	+	0.505671i	$0.831245\pi$
$594$	14.3438	−	12.3263i	0.588533	−	0.505756i
$595$	0.889093	−	2.48485i	0.0364493	−	0.101869i
$596$	27.5641	−	18.2690i	1.12907	−	0.748329i
$597$	1.42858	+	9.63072i	0.0584680	+	0.394159i
$598$	38.0214	−	36.0641i	1.55481	−	1.47477i
$599$	−2.49286	−	25.3104i	−0.101855	−	1.03416i	−0.901236	−	0.433330i	$-0.857339\pi$
$599$	−2.49286	−	25.3104i	−0.101855	−	1.03416i	0.799380	−	0.600826i	$-0.205161\pi$
$600$	30.2276	−	0.572426i	1.23404	−	0.0233692i
$601$	−30.3396	+	24.8991i	−1.23758	+	1.01565i	−0.238571	+	0.971125i	$0.576679\pi$
$601$	−30.3396	+	24.8991i	−1.23758	+	1.01565i	−0.999008	+	0.0445294i	$0.985821\pi$
$602$	1.56092	−	0.428825i	0.0636185	−	0.0174776i
$603$	−12.9775	+	4.64343i	−0.528486	+	0.189095i
$604$	2.97510	+	5.00601i	0.121055	+	0.203692i
$605$	−3.24646	+	5.41639i	−0.131987	+	0.220208i
$606$	−0.0475712	−	2.09768i	−0.00193245	−	0.0852125i
$607$	13.0089	+	31.4063i	0.528016	+	1.27474i	0.932821	+	0.360340i	$0.117339\pi$
$607$	13.0089	+	31.4063i	0.528016	+	1.27474i	−0.404805	+	0.914403i	$0.632661\pi$
$608$	−15.1956	−	40.5169i	−0.616261	−	1.64318i
$609$	−0.137089	+	0.330962i	−0.00555512	+	0.0134112i
$610$	0.460312	+	0.178551i	0.0186375	+	0.00722933i
$611$	−8.68336	−	34.6659i	−0.351291	−	1.40243i
$612$	16.5379	+	7.89764i	0.668504	+	0.319243i
$613$	−32.0770	−	15.1713i	−1.29558	−	0.612762i	−0.349570	−	0.936910i	$-0.613672\pi$
$613$	−32.0770	−	15.1713i	−1.29558	−	0.612762i	−0.946006	+	0.324148i	$0.894922\pi$
$614$	12.2550	−	9.52705i	0.494570	−	0.384480i
$615$	−0.123833	+	1.25730i	−0.00499342	+	0.0506991i
$616$	−19.8298	+	6.42776i	−0.798966	+	0.258982i
$617$	−0.292563	+	0.356489i	−0.0117781	+	0.0143517i	−0.778866	−	0.627190i	$-0.784205\pi$
$617$	−0.292563	+	0.356489i	−0.0117781	+	0.0143517i	0.767088	+	0.641542i	$0.221705\pi$
$618$	32.4911	−	12.4635i	1.30698	−	0.501354i
$619$	−4.81190	−	3.56875i	−0.193407	−	0.143440i	0.494663	−	0.869085i	$-0.335292\pi$
$619$	−4.81190	−	3.56875i	−0.193407	−	0.143440i	−0.688069	+	0.725645i	$0.741542\pi$
$620$	2.86173	−	2.84041i	0.114930	−	0.114074i
$621$	−13.3909	+	6.33341i	−0.537357	+	0.254151i
$622$	−24.9453	−	12.6149i	−1.00022	−	0.505813i
$623$	2.15923	−	0.429498i	0.0865078	−	0.0172075i
$624$	−0.418829	+	56.0043i	−0.0167666	+	2.24197i
$625$	22.4255	+	4.46071i	0.897020	+	0.178428i
$626$	0.126209	−	0.161100i	0.00504432	−	0.00643884i
$627$	65.6093	+	59.4648i	2.62018	+	2.37480i
$628$	−25.5262	−	2.61052i	−1.01861	−	0.104171i
$629$	16.2810	−	9.75847i	0.649167	−	0.389096i
$630$	1.35176	+	0.306203i	0.0538553	+	0.0121994i
$631$	3.55414	−	11.7164i	0.141488	−	0.466423i	−0.857344	−	0.514744i	$-0.827887\pi$
$631$	3.55414	−	11.7164i	0.141488	−	0.466423i	0.998832	+	0.0483207i	$0.0153870\pi$
$632$	20.8840	+	18.2199i	0.830720	+	0.724750i
$633$	7.50338	−	14.0378i	0.298233	−	0.557954i
$634$	−7.21352	−	2.39799i	−0.286486	−	0.0952365i
$635$	−0.0880942	+	1.79320i	−0.00349591	+	0.0711609i
$636$	26.8565	+	24.5248i	1.06493	+	0.972472i
$637$	31.6887	+	4.70057i	1.25555	+	0.186243i
$638$	−0.850745	−	0.149257i	−0.0336813	−	0.00590915i
$639$			14.7894i			0.585059i
$640$	1.97839	−	3.80555i	0.0782029	−	0.150428i
$641$			7.59428i			0.299956i	0.988689	+	0.149978i	$0.0479203\pi$
$641$			7.59428i			0.299956i	−0.988689	+	0.149978i	$0.952080\pi$
$642$	5.49656	−	31.3296i	0.216932	−	1.23648i
$643$	1.47938	+	0.219446i	0.0583412	+	0.00865409i	0.175837	−	0.984419i	$-0.443737\pi$
$643$	1.47938	+	0.219446i	0.0583412	+	0.00865409i	−0.117496	+	0.993073i	$0.537487\pi$
$644$	16.3104	−	0.740153i	0.642718	−	0.0291661i
$645$	0.0334418	−	0.680724i	0.00131677	−	0.0268035i
$646$	16.9523	−	50.9949i	0.666978	−	2.00637i
$647$	−13.0573	+	24.4285i	−0.513336	+	0.960384i	0.483062	+	0.875586i	$0.339525\pi$
$647$	−13.0573	+	24.4285i	−0.513336	+	0.960384i	−0.996398	+	0.0847980i	$0.972975\pi$
$648$	10.0434	−	29.8388i	0.394542	−	1.17218i
$649$	−16.0912	+	53.0457i	−0.631637	+	2.08223i
$650$	−9.65170	+	42.6082i	−0.378571	+	1.67123i
$651$	−14.0697	+	8.43304i	−0.551434	+	0.330517i
$652$	25.0864	+	30.8020i	0.982457	+	1.20630i
$653$	13.3019	+	12.0562i	0.520545	+	0.471794i	0.889036	−	0.457837i	$-0.151376\pi$
$653$	13.3019	+	12.0562i	0.520545	+	0.471794i	−0.368492	+	0.929631i	$0.620126\pi$
$654$	−12.9618	−	10.1546i	−0.506848	−	0.397075i
$655$	−0.340976	−	0.0678242i	−0.0133230	−	0.00265011i
$656$	−5.01025	−	3.40221i	−0.195617	−	0.132834i
$657$	−20.5293	+	4.08353i	−0.800924	+	0.159314i
$658$	5.02462	−	9.93592i	0.195880	−	0.387342i
$659$	−23.0238	+	10.8895i	−0.896880	+	0.424193i	−0.819679	−	0.572823i	$-0.805848\pi$
$659$	−23.0238	+	10.8895i	−0.896880	+	0.424193i	−0.0772010	+	0.997016i	$0.524598\pi$
$660$	−0.0328173	+	8.77655i	−0.00127741	+	0.341627i
$661$	−15.0019	−	11.1262i	−0.583508	−	0.432759i	0.263258	−	0.964726i	$-0.415203\pi$
$661$	−15.0019	−	11.1262i	−0.583508	−	0.432759i	−0.846765	+	0.531967i	$0.821453\pi$
$662$	11.5570	+	30.1281i	0.449177	+	1.17096i
$663$	−44.1231	+	53.7642i	−1.71360	+	2.08803i
$664$	31.3680	+	2.49081i	1.21732	+	0.0966623i
$665$	0.398351	−	4.04453i	0.0154474	−	0.156840i
$666$	6.11833	+	7.87021i	0.237081	+	0.304964i
$667$	0.611564	+	0.289248i	0.0236798	+	0.0111997i
$668$	−2.25901	−	6.38873i	−0.0874038	−	0.247187i
$669$	−9.78507	−	39.0642i	−0.378313	−	1.51031i
$670$	−1.44870	+	3.73479i	−0.0559680	+	0.144288i
$671$	1.85334	−	4.47437i	0.0715475	−	0.172731i
$672$	−11.5203	+	13.1055i	−0.444405	+	0.505556i
$673$	13.8767	+	33.5014i	0.534908	+	1.29138i	0.928238	+	0.371986i	$0.121323\pi$
$673$	13.8767	+	33.5014i	0.534908	+	1.29138i	−0.393330	+	0.919397i	$0.628677\pi$
$674$	−32.0641	+	0.727149i	−1.23506	+	0.0280087i
$675$	6.34869	−	10.5921i	0.244361	−	0.407692i
$676$	−53.2337	−	13.5461i	−2.04745	−	0.521004i
$677$	2.06170	−	0.737689i	0.0792376	−	0.0283517i	−0.296973	−	0.954886i	$-0.595977\pi$
$677$	2.06170	−	0.737689i	0.0792376	−	0.0283517i	0.376210	+	0.926534i	$0.377227\pi$
$678$	−0.932795	−	3.39537i	−0.0358238	−	0.130398i
$679$	8.89179	−	7.29730i	0.341236	−	0.280045i
$680$	4.88154	−	2.13116i	0.187198	−	0.0817262i
$681$	−5.18579	−	52.6522i	−0.198720	−	2.01764i
$682$	−27.2182	−	28.6954i	−1.04224	−	1.09880i
$683$	0.593223	+	3.99918i	0.0226990	+	0.153024i	0.997562	−	0.0697787i	$-0.0222293\pi$
$683$	0.593223	+	3.99918i	0.0226990	+	0.153024i	−0.974863	+	0.222803i	$0.928479\pi$
$684$	27.6593	+	5.60937i	1.05758	+	0.214480i
$685$	0.513359	−	1.43474i	0.0196144	−	0.0548187i
$686$	15.5471	+	18.0917i	0.593591	+	0.690744i
$687$	−36.5304	−	24.4088i	−1.39372	−	0.931254i
$688$	2.78964	+	1.70053i	0.106354	+	0.0648321i
$689$	−43.6979	+	29.1980i	−1.66476	+	1.11235i
$690$	1.84582	−	6.62176i	0.0702693	−	0.252086i
$691$	−0.0587507	−	1.19590i	−0.00223498	−	0.0454941i	0.997419	−	0.0718020i	$-0.0228750\pi$
$691$	−0.0587507	−	1.19590i	−0.00223498	−	0.0454941i	−0.999654	+	0.0263079i	$0.991625\pi$
$692$	−6.64170	−	5.49239i	−0.252479	−	0.208789i
$693$	3.30342	−	13.1880i	0.125487	−	0.500970i
$694$	4.54702	−	6.43070i	0.172603	−	0.244106i
$695$	0.939520	−	0.502184i	0.0356380	−	0.0190489i
$696$	−0.676008	+	0.256419i	−0.0256240	+	0.00971953i
$697$	−2.18323	−	7.19713i	−0.0826956	−	0.272611i
$698$	0.403210	+	5.60910i	0.0152617	+	0.212307i
$699$	5.93274	−	5.37712i	0.224397	−	0.203381i
$700$	−10.9629	+	8.06729i	−0.414360	+	0.304915i
$701$	5.30854	−	3.93708i	0.200501	−	0.148702i	−0.490791	−	0.871278i	$-0.663292\pi$
$701$	5.30854	−	3.93708i	0.200501	−	0.148702i	0.691292	+	0.722576i	$0.257042\pi$
$702$	19.3042	+	12.2749i	0.728590	+	0.463285i
$703$	20.6691	−	20.6691i	0.779550	−	0.779550i
$704$	−36.8794	−	20.2476i	−1.38995	−	0.763110i
$705$	−3.31478	−	3.31478i	−0.124842	−	0.124842i
$706$	0.325976	+	1.46444i	0.0122683	+	0.0551149i
$707$	0.562724	+	0.758745i	0.0211634	+	0.0285355i
$708$	11.1061	+	45.0520i	0.417392	+	1.69316i
$709$	19.6813	+	21.7150i	0.739147	+	0.815523i	0.988233	−	0.152958i	$-0.0488800\pi$
$709$	19.6813	+	21.7150i	0.739147	+	0.815523i	−0.249085	+	0.968482i	$0.580130\pi$
$710$	3.24949	+	2.81364i	0.121951	+	0.105594i
$711$	−17.2972	+	5.24704i	−0.648694	+	0.196779i
$712$	3.61836	+	2.57882i	0.135604	+	0.0966453i
$713$	14.6028	+	27.3200i	0.546880	+	1.02314i
$714$	−21.3573	+	3.66472i	−0.799277	+	0.137149i
$715$	−12.3024	−	3.08159i	−0.460083	−	0.115245i
$716$	3.64862	+	1.12171i	0.136355	+	0.0419203i
$717$	−53.0539	+	2.60637i	−1.98133	+	0.0973367i
$718$	0.219740	+	0.389592i	0.00820062	+	0.0145394i
$719$	−14.0973	−	21.0981i	−0.525740	−	0.786825i	0.469638	−	0.882859i	$-0.344384\pi$
$719$	−14.0973	−	21.0981i	−0.525740	−	0.786825i	−0.995378	+	0.0960337i	$0.969384\pi$
$720$	1.42013	+	2.41004i	0.0529252	+	0.0898169i
$721$	−8.70421	+	13.0268i	−0.324162	+	0.485142i
$722$	4.21533	−	55.7255i	0.156878	−	2.07389i
$723$	2.89094	+	1.03440i	0.107515	+	0.0384696i
$724$	−42.2337	−	28.4487i	−1.56960	−	1.05729i
$725$	−0.557880	+	0.0827538i	−0.0207192	+	0.00307340i
$726$	51.8319	+	1.36937i	1.92366	+	0.0508220i
$727$	−7.83751	+	0.771927i	−0.290677	+	0.0286292i	−0.242305	−	0.970200i	$-0.577903\pi$
$727$	−7.83751	+	0.771927i	−0.290677	+	0.0286292i	−0.0483723	+	0.998829i	$0.515403\pi$
$728$	−14.4029	−	20.6961i	−0.533806	−	0.767049i
$729$	2.37409	+	2.89284i	0.0879293	+	0.107142i
$730$	−3.00842	+	5.28753i	−0.111347	+	0.195700i
$731$	1.36686	+	3.82011i	0.0505551	+	0.141292i
$732$	−0.579836	−	4.01225i	−0.0214314	−	0.148297i
$733$	−13.2950	−	7.96871i	−0.491062	−	0.294331i	0.247058	−	0.969001i	$-0.420536\pi$
$733$	−13.2950	−	7.96871i	−0.491062	−	0.294331i	−0.738120	+	0.674670i	$0.764286\pi$
$734$	−20.3984	+	21.3450i	−0.752918	+	0.787860i
$735$	3.88238	−	1.60814i	0.143204	−	0.0593170i
$736$	23.6524	+	22.9443i	0.871838	+	0.845737i
$737$	36.3033	+	15.0373i	1.33725	+	0.553907i
$738$	3.61397	−	1.59389i	0.133032	−	0.0586717i
$739$	27.1621	−	6.80375i	0.999174	−	0.250280i	0.291310	−	0.956629i	$-0.405909\pi$
$739$	27.1621	−	6.80375i	0.999174	−	0.250280i	0.707864	+	0.706349i	$0.249659\pi$
$740$	2.89322	+	0.152981i	0.106357	+	0.00562370i
$741$	−45.7936	+	96.8224i	−1.68227	+	3.55686i
$742$	−16.2470	−	2.03473i	−0.596448	−	0.0746971i
$743$	−2.11378	−	0.208189i	−0.0775471	−	0.00763772i	0.0591692	−	0.998248i	$-0.481155\pi$
$743$	−2.11378	−	0.208189i	−0.0775471	−	0.00763772i	−0.136716	+	0.990610i	$0.543655\pi$
$744$	−31.8573	−	9.00876i	−1.16794	−	0.330277i
$745$	4.84543	+	3.97654i	0.177523	+	0.145689i
$746$	19.6561	−	44.1206i	0.719661	−	1.61537i
$747$	−12.2253	+	16.4839i	−0.447299	+	0.603113i
$748$	−19.8137	−	48.3451i	−0.724461	−	1.76767i
$749$	6.12276	+	12.9455i	0.223721	+	0.473018i
$750$	3.62781	+	11.0509i	0.132469	+	0.403521i
$751$	9.76321	+	49.0830i	0.356265	+	1.79106i	0.578085	+	0.815976i	$0.303800\pi$
$751$	9.76321	+	49.0830i	0.356265	+	1.79106i	−0.221821	+	0.975087i	$0.571200\pi$
$752$	21.5523	−	6.36221i	0.785931	−	0.232006i
$753$	8.52172	−	42.8416i	0.310549	−	1.56123i
$754$	−0.125952	−	1.03715i	−0.00458689	−	0.0377706i
$755$	−0.741288	+	0.817885i	−0.0269782	+	0.0297659i
$756$	2.04343	+	6.82810i	0.0743189	+	0.248336i
$757$	8.25966	+	13.7804i	0.300202	+	0.500857i	0.970457	−	0.241274i	$-0.0775651\pi$
$757$	8.25966	+	13.7804i	0.300202	+	0.500857i	−0.670255	+	0.742131i	$0.733815\pi$
$758$	−3.86488	−	6.12863i	−0.140379	−	0.222602i
$759$	−64.5262	−	19.5738i	−2.34215	−	0.710485i
$760$	6.49458	−	5.01006i	0.235583	−	0.181734i
$761$	−1.36636	−	0.730333i	−0.0495304	−	0.0264745i	0.446446	−	0.894811i	$-0.352690\pi$
$761$	−1.36636	−	0.730333i	−0.0495304	−	0.0264745i	−0.495976	+	0.868336i	$0.665190\pi$
$762$	13.1798	−	6.60329i	0.477453	−	0.239212i
$763$	7.40419	+	0.363745i	0.268050	+	0.0131684i
$764$	1.97067	+	4.20726i	0.0712963	+	0.152213i
$765$	−0.509728	+	3.43631i	−0.0184293	+	0.124240i
$766$	0.949217	+	1.35315i	0.0342966	+	0.0488913i
$767$	−67.0505			−2.42105
$768$	−35.1966	+	1.20175i	−1.27005	+	0.0433643i
$769$	−35.1360			−1.26704			−0.633519	−	0.773727i	$-0.718390\pi$
$769$	−35.1360			−1.26704			−0.633519	+	0.773727i	$0.718390\pi$
$770$	−2.26917	−	3.23480i	−0.0817751	−	0.116574i
$771$	1.09517	−	7.38302i	0.0394415	−	0.265893i
$772$	9.71557	−	4.55074i	0.349671	−	0.163785i
$773$	44.3067	+	2.17665i	1.59360	+	0.0782885i	0.826386	−	0.563103i	$-0.190393\pi$
$773$	44.3067	+	2.17665i	1.59360	+	0.0782885i	0.767213	+	0.641392i	$0.221643\pi$
$774$	−1.90506	+	0.954467i	−0.0684760	+	0.0343076i
$775$	−22.7756	−	12.1738i	−0.818123	−	0.437296i
$776$	23.0249	+	2.97105i	0.826546	+	0.106654i
$777$	−11.2793	−	3.42153i	−0.404642	−	0.122747i
$778$	−25.2017	−	39.9629i	−0.903523	−	1.43274i
$779$	−5.95428	−	9.93412i	−0.213334	−	0.355927i
$780$	−10.1704	+	3.04367i	−0.364158	+	0.108981i
$781$	28.3148	−	31.2406i	1.01318	−	1.11788i
$782$	4.93343	+	40.6242i	0.176419	+	1.45272i
$783$	−0.0576143	+	0.289646i	−0.00205897	+	0.0103511i
$784$	−2.12434	+	20.0319i	−0.0758693	+	0.715424i
$785$	−0.948879	−	4.77034i	−0.0338669	−	0.170261i
$786$	0.890351	+	2.71214i	0.0317578	+	0.0967389i
$787$	−12.2874	−	25.9794i	−0.437997	−	0.926067i	−0.995398	−	0.0958239i	$-0.969451\pi$
$787$	−12.2874	−	25.9794i	−0.437997	−	0.926067i	0.557401	−	0.830243i	$-0.311799\pi$
$788$	−43.3951	+	17.7850i	−1.54589	+	0.633566i
$789$	−2.98465	+	4.02433i	−0.106256	+	0.143270i
$790$	−2.13787	+	4.79873i	−0.0760621	+	0.170731i
$791$	1.22543	+	1.00569i	0.0435714	+	0.0357581i
$792$	23.9500	−	13.3907i	0.851028	−	0.475816i
$793$	5.82984	+	0.574189i	0.207024	+	0.0203901i
$794$	18.1310	+	2.27067i	0.643447	+	0.0805831i
$795$	−2.94753	+	6.23204i	−0.104538	+	0.221028i
$796$	0.467124	−	8.83437i	0.0165568	−	0.313126i
$797$	−36.3146	+	9.09634i	−1.28633	+	0.322209i	−0.825057	−	0.565049i	$-0.808857\pi$
$797$	−36.3146	+	9.09634i	−1.28633	+	0.322209i	−0.461273	+	0.887258i	$0.652607\pi$
$798$	−30.5321	+	13.4657i	−1.08083	+	0.476682i
$799$	25.7826	+	10.6795i	0.912122	+	0.377813i
$800$	−27.0217	−	4.94935i	−0.955363	−	0.174986i
$801$	−2.67731	+	1.10898i	−0.0945982	+	0.0391839i
$802$	−12.6857	+	13.2744i	−0.447948	+	0.468737i
$803$	51.1834	+	30.6782i	1.80622	+	1.08261i
$804$	32.5538	−	4.70457i	1.14808	−	0.165917i
$805$	1.04262	+	2.91394i	0.0367477	+	0.102703i
$806$	23.6580	−	41.5808i	0.833318	−	1.46462i
$807$	−32.7280	−	39.8792i	−1.15208	−	1.40382i
$808$	−0.336478	+	1.87662i	−0.0118373	+	0.0660193i
$809$	37.5749	−	3.70081i	1.32106	−	0.130113i	0.587218	−	0.809429i	$-0.300223\pi$
$809$	37.5749	−	3.70081i	1.32106	−	0.130113i	0.733846	+	0.679315i	$0.237723\pi$
$810$	5.96575	+	0.157612i	0.209615	+	0.00553791i
$811$	−45.7794	+	6.79073i	−1.60753	+	0.238455i	−0.889291	−	0.457341i	$-0.848802\pi$
$811$	−45.7794	+	6.79073i	−1.60753	+	0.238455i	−0.718239	+	0.695796i	$0.755052\pi$
$812$	0.181852	−	0.269970i	0.00638176	−	0.00947410i
$813$	58.4468	+	20.9126i	2.04982	+	0.733437i
$814$	2.14365	−	28.3385i	0.0751350	−	0.993265i
$815$	−4.18345	+	6.26097i	−0.146540	+	0.219312i
$816$	−34.9323	−	26.3148i	−1.22288	−	0.921201i
$817$	3.47120	+	5.19501i	0.121442	+	0.181751i
$818$	17.3468	+	30.7553i	0.606517	+	1.07534i
$819$	16.4250	−	0.806910i	0.573937	−	0.0281957i
$820$	0.337343	−	1.09729i	0.0117805	−	0.0383189i
$821$	−33.9721	−	8.50956i	−1.18563	−	0.296986i	−0.400491	−	0.916301i	$-0.631160\pi$
$821$	−33.9721	−	8.50956i	−1.18563	−	0.296986i	−0.785143	+	0.619315i	$0.787410\pi$
$822$	−12.3316	+	2.11600i	−0.430114	+	0.0738038i
$823$	−15.3428	−	28.7043i	−0.534815	−	1.00057i	−0.993700	−	0.112073i	$-0.964251\pi$
$823$	−15.3428	−	28.7043i	−0.534815	−	1.00057i	0.458885	−	0.888496i	$-0.348249\pi$
$824$	−31.1849	+	5.23109i	−1.08638	+	0.182234i
$825$	53.7929	−	16.3179i	1.87283	−	0.568117i
$826$	−15.7927	−	13.6744i	−0.549498	−	0.475795i
$827$	28.6007	+	31.5560i	0.994545	+	1.09731i	0.995254	+	0.0973111i	$0.0310242\pi$
$827$	28.6007	+	31.5560i	0.994545	+	1.09731i	−0.000709427		1.00000i	$0.500226\pi$
$828$	−20.8669	+	5.14405i	−0.725175	+	0.178768i
$829$	−0.168456	−	0.227137i	−0.00585073	−	0.00788880i	0.800272	−	0.599637i	$-0.204688\pi$
$829$	−0.168456	−	0.227137i	−0.00585073	−	0.00788880i	−0.806123	+	0.591748i	$0.798438\pi$
$830$	1.29597	+	5.82212i	0.0449838	+	0.202089i
$831$	31.6878	+	31.6878i	1.09924	+	1.09924i
$832$	10.4874	−	49.7974i	0.363583	−	1.72641i
$833$	−17.6892	+	17.6892i	−0.612896	+	0.612896i
$834$	−7.38126	−	4.69349i	−0.255592	−	0.162522i
$835$	1.03170	−	0.765162i	0.0357035	−	0.0264795i
$836$	−47.6872	−	64.8037i	−1.64930	−	2.24128i
$837$	−10.0197	+	9.08135i	−0.346332	+	0.313897i
$838$	3.94261	+	54.8462i	0.136195	+	1.89463i
$839$	−0.655399	−	2.16056i	−0.0226269	−	0.0745908i	0.944900	−	0.327360i	$-0.106159\pi$
$839$	−0.655399	−	2.16056i	−0.0226269	−	0.0745908i	−0.967527	+	0.252769i	$0.918659\pi$
$840$	−3.01621	−	1.35729i	−0.104069	−	0.0468308i
$841$	−25.5638	+	13.6641i	−0.881511	+	0.471177i
$842$	−3.40853	+	4.82057i	−0.117466	+	0.166128i
$843$	−6.49603	+	25.9336i	−0.223735	+	0.893200i
$844$	−9.21716	+	11.1459i	−0.317268	+	0.383657i
$845$	−0.510901	−	10.3996i	−0.0175755	−	0.357758i
$846$	−3.93535	+	14.1178i	−0.135300	+	0.485379i
$847$	−19.4094	+	12.9689i	−0.666915	+	0.445618i
$848$	−19.4871	−	26.6902i	−0.669189	−	0.916544i
$849$	7.51364	+	5.02046i	0.257868	+	0.172302i
$850$	−22.2350	−	25.8742i	−0.762655	−	0.887479i
$851$	−7.49895	+	20.9582i	−0.257061	+	0.718437i
$852$	7.01471	−	34.5889i	0.240320	−	1.18500i
$853$	7.62619	+	51.4116i	0.261116	+	1.76030i	0.582006	+	0.813184i	$0.302268\pi$
$853$	7.62619	+	51.4116i	0.261116	+	1.76030i	−0.320890	+	0.947116i	$0.603982\pi$
$854$	1.25603	+	1.32419i	0.0429803	+	0.0453130i
$855$	0.524355	+	5.32386i	0.0179326	+	0.182072i
$856$	−10.5529	+	26.9070i	−0.360692	+	0.919664i
$857$	−30.4655	+	25.0024i	−1.04068	+	0.854066i	−0.989487	−	0.144623i	$-0.953803\pi$
$857$	−30.4655	+	25.0024i	−1.04068	+	0.854066i	−0.0511957	+	0.998689i	$0.516303\pi$
$858$	27.5861	+	100.413i	0.941776	+	3.42806i
$859$	−35.4422	+	12.6814i	−1.20927	+	0.432685i	−0.862882	−	0.505405i	$-0.831343\pi$
$859$	−35.4422	+	12.6814i	−1.20927	+	0.432685i	−0.346392	+	0.938090i	$0.612593\pi$
$860$	−0.152719	+	0.600160i	−0.00520769	+	0.0204653i
$861$	−2.40098	+	4.00580i	−0.0818252	+	0.136517i
$862$	2.03489	−	0.0461473i	0.0693087	−	0.00157178i
$863$	0.158613	+	0.382927i	0.00539926	+	0.0130350i	0.926556	−	0.376156i	$-0.122754\pi$
$863$	0.158613	+	0.382927i	0.00539926	+	0.0130350i	−0.921157	+	0.389191i	$0.872754\pi$
$864$	−7.20696	+	12.4493i	−0.245186	+	0.423532i
$865$	0.625174	−	1.50930i	0.0212566	−	0.0513179i
$866$	−2.50915	+	6.46869i	−0.0852645	+	0.219815i
$867$	−4.10505	−	16.3883i	−0.139415	−	0.556575i
$868$	14.0524	−	4.96882i	0.476968	−	0.168653i
$869$	46.5836	+	22.0324i	1.58024	+	0.747398i
$870$	−0.0841140	−	0.108199i	−0.00285173	−	0.00366827i
$871$	−4.65875	+	47.3011i	−0.157856	+	1.60274i
$872$	9.70888	+	11.3838i	0.328784	+	0.385503i
$873$	−9.60553	+	11.7044i	−0.325098	+	0.396133i
$874$	22.5701	+	58.8382i	0.763446	+	1.99023i
$875$	−4.20597	−	3.11936i	−0.142188	−	0.105454i
$876$	49.9501	+	0.186773i	1.68766	+	0.00631049i
$877$	47.7629	−	22.5902i	1.61284	−	0.762816i	0.613207	−	0.789923i	$-0.289879\pi$
$877$	47.7629	−	22.5902i	1.61284	−	0.762816i	0.999633	+	0.0271065i	$0.00862933\pi$
$878$	−20.2106	+	39.9654i	−0.682076	+	1.34877i
$879$	62.0376	−	12.3400i	2.09248	−	0.416219i
$880$	1.61427	−	7.80978i	0.0544170	−	0.263268i
$881$	31.4434	+	6.25448i	1.05935	+	0.210719i	0.693871	−	0.720099i	$-0.255904\pi$
$881$	31.4434	+	6.25448i	1.05935	+	0.210719i	0.365484	+	0.930818i	$0.380904\pi$
$882$	−10.3422	−	8.10226i	−0.348239	−	0.272817i
$883$	−17.9546	−	16.2731i	−0.604220	−	0.547633i	0.311091	−	0.950380i	$-0.399305\pi$
$883$	−17.9546	−	16.2731i	−0.604220	−	0.547633i	−0.915311	+	0.402747i	$0.868055\pi$
$884$	49.0024	−	39.9095i	1.64813	−	1.34230i
$885$	−7.54406	+	4.52173i	−0.253591	+	0.151996i
$886$	8.68427	−	38.3374i	0.291754	−	1.28797i
$887$	5.55940	−	18.3269i	0.186666	−	0.615357i	−0.812795	−	0.582549i	$-0.802055\pi$
$887$	5.55940	−	18.3269i	0.186666	−	0.615357i	0.999462	−	0.0328072i	$-0.0104447\pi$
$888$	−10.5764	−	21.3086i	−0.354922	−	0.715068i
$889$	−3.12855	+	5.85311i	−0.104928	+	0.196307i
$890$	−0.265689	+	0.799234i	−0.00890593	+	0.0267904i
$891$	2.87237	−	58.4685i	0.0962280	−	1.95877i
$892$	1.65883	+	36.5547i	0.0555417	+	1.22394i
$893$	42.5099	+	6.30574i	1.42254	+	0.211014i
$894$	8.89381	−	50.6935i	0.297454	−	1.69544i
$895$			0.723552i			0.0241857i
$896$	12.6259	−	9.59018i	0.421803	−	0.320385i
$897$		−	81.5621i		−	2.72328i
$898$	31.5817	+	5.54078i	1.05389	+	0.184898i
$899$	0.610904	+	0.0906191i	0.0203748	+	0.00302232i
$900$	12.0817	−	13.2303i	0.402722	−	0.441010i
$901$	2.01374	−	40.9906i	0.0670873	−	1.36559i
$902$	−10.6856	−	3.55221i	−0.355791	−	0.118276i
$903$	1.18764	−	2.22193i	0.0395223	−	0.0739410i
$904$	0.217470	+	3.19211i	0.00723296	+	0.106168i
$905$	2.80193	−	9.23672i	0.0931392	−	0.307039i
$906$	8.83944	+	2.00233i	0.293671	+	0.0665229i
$907$	−8.33721	+	4.99713i	−0.276832	+	0.165927i	−0.645781	−	0.763523i	$-0.723468\pi$
$907$	−8.33721	+	4.99713i	−0.276832	+	0.165927i	0.368948	+	0.929450i	$0.379718\pi$
$908$	−4.89093	+	47.8245i	−0.162311	+	1.58711i
$909$	−0.921333	−	0.835047i	−0.0305587	−	0.0276968i
$910$	2.94753	−	3.76238i	0.0977095	−	0.124722i
$911$	16.2423	+	3.23079i	0.538131	+	0.107041i	0.456671	−	0.889636i	$-0.349042\pi$
$911$	16.2423	+	3.23079i	0.538131	+	0.107041i	0.0814603	+	0.996677i	$0.474042\pi$
$912$	−62.0280	−	26.2380i	−2.05395	−	0.868827i
$913$	57.3832	−	11.4142i	1.89911	−	0.377756i
$914$	16.3188	+	8.25248i	0.539778	+	0.272968i
$915$	0.694655	−	0.328547i	0.0229646	−	0.0108614i
$916$	28.1229	+	28.3340i	0.929206	+	0.936181i
$917$	−1.03224	−	0.765564i	−0.0340877	−	0.0252812i
$918$	−16.6790	+	6.39801i	−0.550489	+	0.211166i
$919$	−11.5807	+	14.1111i	−0.382012	+	0.465483i	−0.928147	−	0.372214i	$-0.878599\pi$
$919$	−11.5807	+	14.1111i	−0.382012	+	0.465483i	0.546135	+	0.837697i	$0.316099\pi$
$920$	−2.83964	+	5.56347i	−0.0936201	+	0.183422i
$921$	2.36800	−	24.0427i	0.0780284	−	0.792235i
$922$	26.0992	−	20.2896i	0.859533	−	0.668204i
$923$	46.1030	+	21.8051i	1.51750	+	0.717724i
$924$	−13.9811	+	29.2768i	−0.459944	+	0.963136i
$925$	−4.50892	−	18.0006i	−0.148252	−	0.591856i
$926$	−14.9102	−	5.78353i	−0.489978	−	0.190059i
$927$	7.89203	−	19.0531i	0.259208	−	0.625784i
$928$	0.648309	−	0.106259i	0.0212818	−	0.00348814i
$929$	−0.311517	−	0.752068i	−0.0102205	−	0.0246746i	0.918687	−	0.394987i	$-0.129251\pi$
$929$	−0.311517	−	0.752068i	−0.0102205	−	0.0246746i	−0.928907	+	0.370312i	$0.879251\pi$
$930$	−0.142278	−	6.27382i	−0.00466547	−	0.205727i
$931$	−19.8052	+	33.0430i	−0.649089	+	1.08294i
$932$	−6.25434	+	3.71699i	−0.204868	+	0.121754i
$933$	−40.9635	+	14.6570i	−1.34109	+	0.479848i
$934$	−42.2008	+	11.5936i	−1.38085	+	0.379355i
$935$	7.65567	−	6.28285i	0.250367	−	0.205471i
$936$	23.9091	+	23.0204i	0.781495	+	0.752446i
$937$	−4.79541	−	48.6887i	−0.156659	−	1.59059i	−0.676576	−	0.736372i	$-0.736537\pi$
$937$	−4.79541	−	48.6887i	−0.156659	−	1.59059i	0.519917	−	0.854217i	$-0.325963\pi$
$938$	−10.7440	+	10.1909i	−0.350804	+	0.332745i
$939$	−0.0467359	−	0.315068i	−0.00152517	−	0.0102819i
$940$	2.35324	+	3.55054i	0.0767541	+	0.115806i
$941$	−3.65076	+	10.2032i	−0.119012	+	0.332615i	−0.986246	−	0.165285i	$-0.947145\pi$
$941$	−3.65076	+	10.2032i	−0.119012	+	0.332615i	0.867234	+	0.497900i	$0.165895\pi$
$942$	−30.2885	+	26.0284i	−0.986853	+	0.848053i
$943$	7.33334	+	4.89998i	0.238806	+	0.159565i
$944$	−1.75382	−	42.1256i	−0.0570819	−	1.37107i
$945$	−1.12332	+	0.750576i	−0.0365415	+	0.0244162i
$946$	5.85154	+	1.63112i	0.190250	+	0.0530324i
$947$	−1.18449	−	24.1108i	−0.0384907	−	0.783497i	−0.938008	−	0.346612i	$-0.887332\pi$
$947$	−1.18449	−	24.1108i	−0.0384907	−	0.783497i	0.899518	−	0.436884i	$-0.143918\pi$
$948$	42.9427	−	4.06742i	1.39471	−	0.132104i
$949$	−17.5383	+	70.0168i	−0.569317	+	2.27284i
$950$	−42.8961	−	30.3310i	−1.39173	−	0.984066i
$951$	−10.4341	+	5.57716i	−0.338350	+	0.180852i
$952$	19.6810	+	0.593610i	0.637865	+	0.0192390i
$953$	−12.6759	−	41.7867i	−0.410611	−	1.35360i	−0.881822	−	0.471583i	$-0.843683\pi$
$953$	−12.6759	−	41.7867i	−0.410611	−	1.35360i	0.471211	−	0.882021i	$-0.343817\pi$
$954$	21.4978	−	1.54537i	0.696016	−	0.0500330i
$955$	−0.652517	+	0.591407i	−0.0211149	+	0.0191375i
$956$	47.7164	+	7.26050i	1.54326	+	0.234821i
$957$	−1.07976	+	0.800806i	−0.0349038	+	0.0258864i
$958$	3.72213	−	5.85364i	0.120256	−	0.189123i
$959$	3.98312	−	3.98312i	0.128622	−	0.128622i
$960$	−2.17826	−	6.31010i	−0.0703030	−	0.203658i
$961$	−1.92369	−	1.92369i	−0.0620547	−	0.0620547i
$962$	33.5546	−	7.46906i	1.08184	−	0.240812i
$963$	−11.2290	−	15.1406i	−0.361850	−	0.487898i
$964$	−2.38763	−	1.44326i	−0.0769005	−	0.0464841i
$965$	1.36570	+	1.50682i	0.0439634	+	0.0485061i
$966$	16.6340	−	19.2107i	0.535189	−	0.618093i
$967$	−31.1083	+	9.43661i	−1.00038	+	0.303461i	−0.747662	−	0.664080i	$-0.768824\pi$
$967$	−31.1083	+	9.43661i	−1.00038	+	0.303461i	−0.252715	+	0.967541i	$0.581324\pi$
$968$	−45.9101	−	10.5803i	−1.47561	−	0.340063i
$969$	−39.4269	−	73.7626i	−1.26658	−	2.36960i
$970$	0.744230	+	4.33723i	0.0238958	+	0.139260i
$971$	38.5106	+	9.64641i	1.23586	+	0.309568i	0.805232	−	0.592959i	$-0.202041\pi$
$971$	38.5106	+	9.64641i	1.23586	+	0.309568i	0.430632	+	0.902527i	$0.358291\pi$
$972$	−15.7952	−	29.8184i	−0.506631	−	0.956425i
$973$	3.93331	−	0.193231i	0.126096	−	0.00619470i
$974$	35.5397	−	20.0453i	1.13876	−	0.642293i
$975$	37.7760	+	56.5358i	1.20980	+	1.81059i
$976$	−0.208255	+	3.67771i	−0.00666607	+	0.117721i
$977$	17.7269	−	26.5301i	0.567133	−	0.848774i	−0.431442	−	0.902141i	$-0.641995\pi$
$977$	17.7269	−	26.5301i	0.567133	−	0.848774i	0.998575	+	0.0533665i	$0.0169952\pi$
$978$	61.6516	+	4.66360i	1.97140	+	0.149126i
$979$	7.77865	+	2.78324i	0.248607	+	0.0889529i
$980$	−3.74778	+	0.730922i	−0.119718	+	0.0233484i
$981$	−9.65237	+	1.43179i	−0.308176	+	0.0457136i
$982$	−0.506239	+	19.1616i	−0.0161547	+	0.611472i
$983$	1.71301	−	0.168717i	0.0546366	−	0.00538123i	−0.0706619	−	0.997500i	$-0.522511\pi$
$983$	1.71301	−	0.168717i	0.0546366	−	0.00538123i	0.125298	+	0.992119i	$0.460011\pi$
$984$	−9.20822	+	2.01359i	−0.293547	+	0.0641910i
$985$	−5.63956	−	6.87183i	−0.179691	−	0.218955i
$986$	0.709112	+	0.403460i	0.0225827	+	0.0128488i
$987$	−5.83799	−	16.3161i	−0.185825	−	0.519347i
$988$	58.2663	−	77.9521i	1.85370	−	2.47999i
$989$	−4.08099	−	2.44605i	−0.129768	−	0.0777800i
$990$	3.76024	+	3.59347i	0.119508	+	0.114208i
$991$	10.7118	−	4.43695i	0.340270	−	0.140944i	−0.206004	−	0.978551i	$-0.566046\pi$
$991$	10.7118	−	4.43695i	0.340270	−	0.140944i	0.546274	+	0.837607i	$0.316046\pi$
$992$	26.7426	+	13.7759i	0.849079	+	0.437386i
$993$	46.3996	+	19.2194i	1.47245	+	0.609908i
$994$	6.41185	+	14.5382i	0.203372	+	0.461124i
$995$	1.62666	−	0.407458i	0.0515687	−	0.0129173i
$996$	36.4105	−	32.7534i	1.15371	−	1.03783i
$997$	7.29913	−	15.4327i	0.231166	−	0.488759i	−0.754748	−	0.656015i	$-0.772241\pi$
$997$	7.29913	−	15.4327i	0.231166	−	0.488759i	0.985913	+	0.167256i	$0.0534907\pi$
$998$	−1.75640	+	14.0247i	−0.0555980	+	0.443943i
$999$	−9.67012	−	0.952424i	−0.305949	−	0.0301334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.6	✓	992
256.205	even	64	inner	256.2.m.a.205.6	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.6	✓	992	1.1	even	1	trivial
256.2.m.a.205.6	yes	992	256.205	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15776 + 0.812153i) q^{2} +(-0.322964 + 2.17724i) q^{3} +(0.680816 - 1.88056i) q^{4} +(0.378649 + 0.0186018i) q^{5} +(-1.39434 - 2.78302i) q^{6} +(1.23593 + 0.660620i) q^{7} +(0.739076 + 2.73016i) q^{8} +(-1.76526 - 0.535486i) q^{9} +O(q^{10})\)	\(q+(-1.15776 + 0.812153i) q^{2} +(-0.322964 + 2.17724i) q^{3} +(0.680816 - 1.88056i) q^{4} +(0.378649 + 0.0186018i) q^{5} +(-1.39434 - 2.78302i) q^{6} +(1.23593 + 0.660620i) q^{7} +(0.739076 + 2.73016i) q^{8} +(-1.76526 - 0.535486i) q^{9} +(-0.453492 + 0.285984i) q^{10} +(2.70367 + 4.51080i) q^{11} +(3.87455 + 2.08965i) q^{12} +(-4.27193 + 4.71335i) q^{13} +(-1.96744 + 0.238927i) q^{14} +(-0.162790 + 0.818403i) q^{15} +(-3.07298 - 2.56063i) q^{16} +(-0.969103 - 4.87201i) q^{17} +(2.47865 - 0.813697i) q^{18} +(-3.27063 - 6.91516i) q^{19} +(0.292772 - 0.699406i) q^{20} +(-1.83749 + 2.47757i) q^{21} +(-6.79366 - 3.02663i) q^{22} +(4.50298 + 3.69550i) q^{23} +(-6.18291 + 0.727408i) q^{24} +(-4.83289 - 0.475999i) q^{25} +(1.11791 - 8.92639i) q^{26} +(-1.08723 + 2.29876i) q^{27} +(2.08378 - 1.87448i) q^{28} +(0.112655 - 0.0282185i) q^{29} +(-0.476196 - 1.07972i) q^{30} +(4.91305 + 2.03505i) q^{31} +(5.63739 + 0.468862i) q^{32} +(-10.6943 + 4.42972i) q^{33} +(5.07880 + 4.85356i) q^{34} +(0.455696 + 0.273134i) q^{35} +(-2.20883 + 2.95510i) q^{36} +(1.28732 + 3.59781i) q^{37} +(9.40277 + 5.34985i) q^{38} +(-8.88243 - 10.8233i) q^{39} +(0.229065 + 1.04752i) q^{40} +(1.50676 - 0.148403i) q^{41} +(0.115209 - 4.36076i) q^{42} +(-0.807932 + 0.119845i) q^{43} +(10.3235 - 2.01337i) q^{44} +(-0.658453 - 0.235598i) q^{45} +(-8.21468 - 0.621395i) q^{46} +(-3.12116 + 4.67114i) q^{47} +(6.56756 - 5.86363i) q^{48} +(-2.79788 - 4.18732i) q^{49} +(5.98192 - 3.37396i) q^{50} +(10.9205 - 0.536491i) q^{51} +(5.95532 + 11.2425i) q^{52} +(8.01418 + 2.00745i) q^{53} +(-0.608190 - 3.54441i) q^{54} +(0.939832 + 1.75830i) q^{55} +(-0.890149 + 3.86254i) q^{56} +(16.1123 - 4.88761i) q^{57} +(-0.107509 + 0.124163i) q^{58} +(7.07858 + 7.81001i) q^{59} +(1.42822 + 0.863318i) q^{60} +(-0.548580 - 0.739674i) q^{61} +(-7.34090 + 1.63404i) q^{62} +(-1.82799 - 1.82799i) q^{63} +(-6.90753 + 4.03559i) q^{64} +(-1.70524 + 1.70524i) q^{65} +(8.78381 - 13.8140i) q^{66} +(6.00143 - 4.45097i) q^{67} +(-9.82186 - 1.49449i) q^{68} +(-9.50030 + 8.61057i) q^{69} +(-0.749413 + 0.0538715i) q^{70} +(-2.32729 - 7.67204i) q^{71} +(0.157299 - 5.21521i) q^{72} +(10.0070 - 5.34888i) q^{73} +(-4.41238 - 3.11990i) q^{74} +(2.59721 - 10.3687i) q^{75} +(-15.2310 + 1.44264i) q^{76} +(0.361630 + 7.36115i) q^{77} +(19.0739 + 5.31686i) q^{78} +(8.14727 - 5.44383i) q^{79} +(-1.11595 - 1.02674i) q^{80} +(-9.25524 - 6.18416i) q^{81} +(-1.62394 + 1.39553i) q^{82} +(3.74796 - 10.4749i) q^{83} +(3.40822 + 5.14228i) q^{84} +(-0.276321 - 1.86281i) q^{85} +(0.838059 - 0.794917i) q^{86} +(0.0250553 + 0.254390i) q^{87} +(-10.3170 + 10.7153i) q^{88} +(1.21435 - 0.996594i) q^{89} +(0.953672 - 0.261998i) q^{90} +(-8.39356 + 3.00326i) q^{91} +(10.0153 - 5.95215i) q^{92} +(-6.01754 + 10.0397i) q^{93} +(-0.180129 - 7.94292i) q^{94} +(-1.10978 - 2.67926i) q^{95} +(-2.84150 + 12.1225i) q^{96} +(3.14107 - 7.58322i) q^{97} +(6.64002 + 2.57561i) q^{98} +(-2.35721 - 9.41052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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