LMFDB - Embedded newform 864.2.v.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39805 - 0.213220i) q^{2} +(1.90907 + 0.596184i) q^{4} +(0.0181233 - 0.00750691i) q^{5} +(-1.64798 + 1.64798i) q^{7} +(-2.54186 - 1.24055i) q^{8} +O(q^{10})$	\(q+(-1.39805 - 0.213220i) q^{2} +(1.90907 + 0.596184i) q^{4} +(0.0181233 - 0.00750691i) q^{5} +(-1.64798 + 1.64798i) q^{7} +(-2.54186 - 1.24055i) q^{8} +(-0.0269378 + 0.00663076i) q^{10} +(-1.05521 - 2.54750i) q^{11} +(-0.619443 - 0.256582i) q^{13} +(2.65534 - 1.95258i) q^{14} +(3.28913 + 2.27632i) q^{16} -1.88186i q^{17} +(7.70774 + 3.19265i) q^{19} +(0.0390742 - 0.00352644i) q^{20} +(0.932055 + 3.78652i) q^{22} +(2.54144 + 2.54144i) q^{23} +(-3.53526 + 3.53526i) q^{25} +(0.811303 + 0.490791i) q^{26} +(-4.12863 + 2.16362i) q^{28} +(-2.16330 + 5.22266i) q^{29} +8.26107 q^{31} +(-4.11300 - 3.88371i) q^{32} +(-0.401250 + 2.63092i) q^{34} +(-0.0174956 + 0.0422381i) q^{35} +(-5.35925 + 2.21987i) q^{37} +(-10.0951 - 6.10693i) q^{38} +(-0.0553795 - 0.00340128i) q^{40} +(3.00044 + 3.00044i) q^{41} +(-1.48765 - 3.59150i) q^{43} +(-0.495695 - 5.49247i) q^{44} +(-3.01116 - 4.09494i) q^{46} +7.48247i q^{47} +1.56829i q^{49} +(5.69625 - 4.18868i) q^{50} +(-1.02959 - 0.859136i) q^{52} +(1.80541 + 4.35866i) q^{53} +(-0.0382477 - 0.0382477i) q^{55} +(6.23334 - 2.14454i) q^{56} +(4.13797 - 6.84027i) q^{58} +(3.62927 - 1.50329i) q^{59} +(-0.177788 + 0.429218i) q^{61} +(-11.5494 - 1.76143i) q^{62} +(4.92209 + 6.30659i) q^{64} -0.0131525 q^{65} +(0.264108 - 0.637614i) q^{67} +(1.12193 - 3.59260i) q^{68} +(0.0334657 - 0.0553205i) q^{70} +(-10.9496 + 10.9496i) q^{71} +(1.35090 + 1.35090i) q^{73} +(7.96581 - 1.96079i) q^{74} +(12.8112 + 10.6902i) q^{76} +(5.93722 + 2.45928i) q^{77} +2.39418i q^{79} +(0.0766979 + 0.0165632i) q^{80} +(-3.55500 - 4.83450i) q^{82} +(13.6807 + 5.66672i) q^{83} +(-0.0141269 - 0.0341054i) q^{85} +(1.31402 + 5.33829i) q^{86} +(-0.478101 + 7.78443i) q^{88} +(-2.85123 + 2.85123i) q^{89} +(1.44368 - 0.597990i) q^{91} +(3.33663 + 6.36696i) q^{92} +(1.59541 - 10.4608i) q^{94} +0.163656 q^{95} -12.3625 q^{97} +(0.334392 - 2.19255i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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 $

$2$	−1.39805	−	0.213220i	−0.988569	−	0.150769i
$2$	−1.39805	−	0.213220i	−0.988569	−	0.150769i
$3$		0			0
$3$		0			0
$4$	1.90907	+	0.596184i	0.954537	+	0.298092i
$5$	0.0181233	−	0.00750691i	0.00810498	−	0.00335719i	−0.378627	−	0.925549i	$-0.623604\pi$
$5$	0.0181233	−	0.00750691i	0.00810498	−	0.00335719i	0.386732	+	0.922192i	$0.373604\pi$
$6$		0			0
$7$	−1.64798	+	1.64798i	−0.622880	+	0.622880i	−0.946267	−	0.323387i	$-0.895178\pi$
$7$	−1.64798	+	1.64798i	−0.622880	+	0.622880i	0.323387	+	0.946267i	$0.395178\pi$
$8$	−2.54186	−	1.24055i	−0.898683	−	0.438599i
$9$		0			0
$10$	−0.0269378	+	0.00663076i	−0.00851849	+	0.00209683i
$11$	−1.05521	−	2.54750i	−0.318158	−	0.768101i	−0.999352	−	0.0359982i	$-0.988539\pi$
$11$	−1.05521	−	2.54750i	−0.318158	−	0.768101i	0.681194	−	0.732103i	$-0.261461\pi$
$12$		0			0
$13$	−0.619443	−	0.256582i	−0.171803	−	0.0711630i	0.295124	−	0.955459i	$-0.404639\pi$
$13$	−0.619443	−	0.256582i	−0.171803	−	0.0711630i	−0.466927	+	0.884296i	$0.654639\pi$
$14$	2.65534	−	1.95258i	0.709671	−	0.521848i
$15$		0			0
$16$	3.28913	+	2.27632i	0.822282	+	0.569080i
$17$		−	1.88186i		−	0.456417i	−0.973612	−	0.228209i	$-0.926713\pi$
$17$		−	1.88186i		−	0.456417i	0.973612	−	0.228209i	$-0.0732868\pi$
$18$		0			0
$19$	7.70774	+	3.19265i	1.76828	+	0.732445i	0.995170	+	0.0981701i	$0.0312989\pi$
$19$	7.70774	+	3.19265i	1.76828	+	0.732445i	0.773108	+	0.634274i	$0.218701\pi$
$20$	0.0390742	−	0.00352644i	0.00873725	−	0.000788535i
$21$		0			0
$22$	0.932055	+	3.78652i	0.198715	+	0.807289i
$23$	2.54144	+	2.54144i	0.529926	+	0.529926i	0.920550	−	0.390624i	$-0.127741\pi$
$23$	2.54144	+	2.54144i	0.529926	+	0.529926i	−0.390624	+	0.920550i	$0.627741\pi$
$24$		0			0
$25$	−3.53526	+	3.53526i	−0.707052	+	0.707052i
$26$	0.811303	+	0.490791i	0.159110	+	0.0962521i
$27$		0			0
$28$	−4.12863	+	2.16362i	−0.780237	+	0.408886i
$29$	−2.16330	+	5.22266i	−0.401714	+	0.969823i	0.585536	+	0.810646i	$0.300884\pi$
$29$	−2.16330	+	5.22266i	−0.401714	+	0.969823i	−0.987250	+	0.159177i	$0.949116\pi$
$30$		0			0
$31$	8.26107			1.48373			0.741866	−	0.670548i	$-0.233941\pi$
$31$	8.26107			1.48373			0.741866	+	0.670548i	$0.233941\pi$
$32$	−4.11300	−	3.88371i	−0.727083	−	0.686550i
$33$		0			0
$34$	−0.401250	+	2.63092i	−0.0688137	+	0.451200i
$35$	−0.0174956	+	0.0422381i	−0.00295730	+	0.00713955i
$36$		0			0
$37$	−5.35925	+	2.21987i	−0.881056	+	0.364945i	−0.776906	−	0.629616i	$-0.783212\pi$
$37$	−5.35925	+	2.21987i	−0.881056	+	0.364945i	−0.104150	+	0.994562i	$0.533212\pi$
$38$	−10.0951	−	6.10693i	−1.63763	−	0.990674i
$39$		0			0
$40$	−0.0553795	−	0.00340128i	−0.00875626	−	0.000537789i
$41$	3.00044	+	3.00044i	0.468589	+	0.468589i	0.901457	−	0.432868i	$-0.142498\pi$
$41$	3.00044	+	3.00044i	0.468589	+	0.468589i	−0.432868	+	0.901457i	$0.642498\pi$
$42$		0			0
$43$	−1.48765	−	3.59150i	−0.226864	−	0.547699i	0.768928	−	0.639335i	$-0.220790\pi$
$43$	−1.48765	−	3.59150i	−0.226864	−	0.547699i	−0.995793	+	0.0916363i	$0.970790\pi$
$44$	−0.495695	−	5.49247i	−0.0747288	−	0.828021i
$45$		0			0
$46$	−3.01116	−	4.09494i	−0.443972	−	0.603765i
$47$			7.48247i			1.09143i	0.837971	+	0.545715i	$0.183742\pi$
$47$			7.48247i			1.09143i	−0.837971	+	0.545715i	$0.816258\pi$
$48$		0			0
$49$			1.56829i			0.224042i
$50$	5.69625	−	4.18868i	0.805572	−	0.592368i
$51$		0			0
$52$	−1.02959	−	0.859136i	−0.142779	−	0.119141i
$53$	1.80541	+	4.35866i	0.247993	+	0.598707i	0.998033	−	0.0626843i	$-0.0199661\pi$
$53$	1.80541	+	4.35866i	0.247993	+	0.598707i	−0.750041	+	0.661392i	$0.769966\pi$
$54$		0			0
$55$	−0.0382477	−	0.0382477i	−0.00515732	−	0.00515732i
$56$	6.23334	−	2.14454i	0.832966	−	0.286576i
$57$		0			0
$58$	4.13797	−	6.84027i	0.543342	−	0.898171i
$59$	3.62927	−	1.50329i	0.472491	−	0.195712i	−0.133715	−	0.991020i	$-0.542691\pi$
$59$	3.62927	−	1.50329i	0.472491	−	0.195712i	0.606206	+	0.795308i	$0.292691\pi$
$60$		0			0
$61$	−0.177788	+	0.429218i	−0.0227634	+	0.0549557i	−0.934853	−	0.355036i	$-0.884469\pi$
$61$	−0.177788	+	0.429218i	−0.0227634	+	0.0549557i	0.912089	+	0.409992i	$0.134469\pi$
$62$	−11.5494	−	1.76143i	−1.46677	−	0.223701i
$63$		0			0
$64$	4.92209	+	6.30659i	0.615261	+	0.788323i
$65$	−0.0131525			−0.00163136
$66$		0			0
$67$	0.264108	−	0.637614i	0.0322660	−	0.0778969i	−0.906925	−	0.421292i	$-0.861577\pi$
$67$	0.264108	−	0.637614i	0.0322660	−	0.0778969i	0.939191	+	0.343395i	$0.111577\pi$
$68$	1.12193	−	3.59260i	0.136054	−	0.435667i
$69$		0			0
$70$	0.0334657	−	0.0553205i	0.00399992	−	0.00661207i
$71$	−10.9496	+	10.9496i	−1.29948	+	1.29948i	−0.370740	+	0.928737i	$0.620896\pi$
$71$	−10.9496	+	10.9496i	−1.29948	+	1.29948i	−0.928737	+	0.370740i	$0.879104\pi$
$72$		0			0
$73$	1.35090	+	1.35090i	0.158111	+	0.158111i	0.781729	−	0.623618i	$-0.214338\pi$
$73$	1.35090	+	1.35090i	0.158111	+	0.158111i	−0.623618	+	0.781729i	$0.714338\pi$
$74$	7.96581	−	1.96079i	0.926007	−	0.227937i
$75$		0			0
$76$	12.8112	+	10.6902i	1.46955	+	1.22625i
$77$	5.93722	+	2.45928i	0.676609	+	0.280260i
$78$		0			0
$79$			2.39418i			0.269367i	0.990889	+	0.134683i	$0.0430017\pi$
$79$			2.39418i			0.269367i	−0.990889	+	0.134683i	$0.956998\pi$
$80$	0.0766979	+	0.0165632i	0.00857509	+	0.00185182i
$81$		0			0
$82$	−3.55500	−	4.83450i	−0.392584	−	0.533882i
$83$	13.6807	+	5.66672i	1.50165	+	0.622004i	0.973815	−	0.227343i	$-0.0730039\pi$
$83$	13.6807	+	5.66672i	1.50165	+	0.622004i	0.527835	+	0.849347i	$0.323004\pi$
$84$		0			0
$85$	−0.0141269	−	0.0341054i	−0.00153228	−	0.00369925i
$86$	1.31402	+	5.33829i	0.141695	+	0.575642i
$87$		0			0
$88$	−0.478101	+	7.78443i	−0.0509658	+	0.829823i
$89$	−2.85123	+	2.85123i	−0.302230	+	0.302230i	−0.841886	−	0.539656i	$-0.818554\pi$
$89$	−2.85123	+	2.85123i	−0.302230	+	0.302230i	0.539656	+	0.841886i	$0.318554\pi$
$90$		0			0
$91$	1.44368	−	0.597990i	0.151338	−	0.0626864i
$92$	3.33663	+	6.36696i	0.347868	+	0.663801i
$93$		0			0
$94$	1.59541	−	10.4608i	0.164554	−	1.07895i
$95$	0.163656			0.0167908
$96$		0			0
$97$	−12.3625			−1.25522			−0.627609	−	0.778528i	$-0.715967\pi$
$97$	−12.3625			−1.25522			−0.627609	+	0.778528i	$0.715967\pi$
$98$	0.334392	−	2.19255i	0.0337787	−	0.221481i
$99$		0			0
$100$	−8.85674	+	4.64141i	−0.885674	+	0.464141i
$101$	9.02332	−	3.73758i	0.897854	−	0.371903i	0.114459	−	0.993428i	$-0.463486\pi$
$101$	9.02332	−	3.73758i	0.897854	−	0.371903i	0.783394	+	0.621525i	$0.213486\pi$
$102$		0			0
$103$	5.66197	−	5.66197i	0.557891	−	0.557891i	−0.370816	−	0.928706i	$-0.620922\pi$
$103$	5.66197	−	5.66197i	0.557891	−	0.557891i	0.928706	+	0.370816i	$0.120922\pi$
$104$	1.25624	+	1.42064i	0.123184	+	0.139305i
$105$		0			0
$106$	−1.59470	−	6.47856i	−0.154891	−	0.629253i
$107$	3.03700	+	7.33197i	0.293598	+	0.708808i	1.00000		0.000996661i	$0.000317247\pi$
$107$	3.03700	+	7.33197i	0.293598	+	0.708808i	−0.706402	+	0.707811i	$0.749683\pi$
$108$		0			0
$109$	9.35178	+	3.87363i	0.895738	+	0.371027i	0.782580	−	0.622550i	$-0.213903\pi$
$109$	9.35178	+	3.87363i	0.895738	+	0.371027i	0.113158	+	0.993577i	$0.463903\pi$
$110$	0.0453170	+	0.0616274i	0.00432080	+	0.00587594i
$111$		0			0
$112$	−9.17177	+	1.66910i	−0.866651	+	0.157715i
$113$			6.04064i			0.568255i	0.958786	+	0.284128i	$0.0917040\pi$
$113$			6.04064i			0.568255i	−0.958786	+	0.284128i	$0.908296\pi$
$114$		0			0
$115$	0.0651375	+	0.0269808i	0.00607410	+	0.00251598i
$116$	−7.24356	+	8.68072i	−0.672547	+	0.805984i
$117$		0			0
$118$	−5.39442	+	1.32784i	−0.496597	+	0.122238i
$119$	3.10127	+	3.10127i	0.284293	+	0.284293i
$120$		0			0
$121$	2.40187	−	2.40187i	0.218352	−	0.218352i
$122$	0.340074	−	0.562159i	0.0307888	−	0.0508955i
$123$		0			0
$124$	15.7710	+	4.92512i	1.41628	+	0.442288i
$125$	−0.0750662	+	0.181226i	−0.00671412	+	0.0162093i
$126$		0			0
$127$	8.59459			0.762647			0.381323	−	0.924442i	$-0.375468\pi$
$127$	8.59459			0.762647			0.381323	+	0.924442i	$0.375468\pi$
$128$	−5.53662	−	9.86640i	−0.489373	−	0.872075i
$129$		0			0
$130$	0.0183878	+	0.00280437i	0.00161272	+	0.000245960i
$131$	5.02167	−	12.1234i	0.438745	−	1.05922i	−0.537638	−	0.843176i	$-0.680683\pi$
$131$	5.02167	−	12.1234i	0.438745	−	1.05922i	0.976383	−	0.216048i	$-0.0693168\pi$
$132$		0			0
$133$	−17.9637	+	7.44080i	−1.55765	+	0.645199i
$134$	−0.505188	+	0.835101i	−0.0436416	+	0.0721418i
$135$		0			0
$136$	−2.33453	+	4.78341i	−0.200184	+	0.410174i
$137$	−7.17068	−	7.17068i	−0.612633	−	0.612633i	0.330999	−	0.943631i	$-0.392614\pi$
$137$	−7.17068	−	7.17068i	−0.612633	−	0.612633i	−0.943631	+	0.330999i	$0.892614\pi$
$138$		0			0
$139$	3.55799	+	8.58975i	0.301785	+	0.728573i	0.999921	+	0.0126077i	$0.00401325\pi$
$139$	3.55799	+	8.58975i	0.301785	+	0.728573i	−0.698136	+	0.715966i	$0.745987\pi$
$140$	−0.0585821	+	0.0702051i	−0.00495109	+	0.00593342i
$141$		0			0
$142$	17.6427	−	12.9734i	1.48054	−	1.08870i
$143$			1.84878i			0.154603i
$144$		0			0
$145$			0.110891i			0.00920902i
$146$	−1.60058	−	2.17666i	−0.132465	−	0.180142i
$147$		0			0
$148$	−11.5547	+	1.04281i	−0.949788	+	0.0857182i
$149$	7.59472	+	18.3353i	0.622184	+	1.50208i	0.849134	+	0.528178i	$0.177125\pi$
$149$	7.59472	+	18.3353i	0.622184	+	1.50208i	−0.226950	+	0.973906i	$0.572875\pi$
$150$		0			0
$151$	−4.90316	−	4.90316i	−0.399014	−	0.399014i	0.478871	−	0.877885i	$-0.341046\pi$
$151$	−4.90316	−	4.90316i	−0.399014	−	0.399014i	−0.877885	+	0.478871i	$0.841046\pi$
$152$	−15.6314	−	17.6771i	−1.26787	−	1.43380i
$153$		0			0
$154$	−7.77614	−	4.70412i	−0.626620	−	0.379069i
$155$	0.149718	−	0.0620151i	0.0120256	−	0.00498117i
$156$		0			0
$157$	−1.32585	+	3.20089i	−0.105814	+	0.255459i	−0.967915	−	0.251279i	$-0.919149\pi$
$157$	−1.32585	+	3.20089i	−0.105814	+	0.255459i	0.862100	+	0.506738i	$0.169149\pi$
$158$	0.510488	−	3.34718i	0.0406122	−	0.266287i
$159$		0			0
$160$	−0.103696	−	0.0395096i	−0.00819787	−	0.00312351i
$161$	−8.37650			−0.660160
$162$		0			0
$163$	9.36500	−	22.6091i	0.733523	−	1.77088i	0.103043	−	0.994677i	$-0.467142\pi$
$163$	9.36500	−	22.6091i	0.733523	−	1.77088i	0.630480	−	0.776205i	$-0.282858\pi$
$164$	3.93924	+	7.51686i	0.307603	+	0.586969i
$165$		0			0
$166$	−17.9180	−	10.8393i	−1.39071	−	0.841296i
$167$	7.73912	−	7.73912i	0.598871	−	0.598871i	−0.341141	−	0.940012i	$-0.610813\pi$
$167$	7.73912	−	7.73912i	0.598871	−	0.598871i	0.940012	+	0.341141i	$0.110813\pi$
$168$		0			0
$169$	−8.87451	−	8.87451i	−0.682655	−	0.682655i
$170$	0.0124781	+	0.0506931i	0.000957030	+	0.00388798i
$171$		0			0
$172$	−0.698836	−	7.74335i	−0.0532858	−	0.590425i
$173$	7.47654	+	3.09689i	0.568431	+	0.235452i	0.648341	−	0.761350i	$-0.275463\pi$
$173$	7.47654	+	3.09689i	0.568431	+	0.235452i	−0.0799098	+	0.996802i	$0.525463\pi$
$174$		0			0
$175$		−	11.6521i		−	0.880817i
$176$	2.32821	−	10.7811i	0.175495	−	0.812653i
$177$		0			0
$178$	4.59410	−	3.37822i	0.344342	−	0.253208i
$179$	−18.2455	−	7.55754i	−1.36373	−	0.564877i	−0.423652	−	0.905825i	$-0.639252\pi$
$179$	−18.2455	−	7.55754i	−1.36373	−	0.564877i	−0.940082	+	0.340948i	$0.889252\pi$
$180$		0			0
$181$	−7.97121	−	19.2442i	−0.592496	−	1.43041i	−0.881085	−	0.472958i	$-0.843186\pi$
$181$	−7.97121	−	19.2442i	−0.592496	−	1.43041i	0.288589	−	0.957453i	$-0.406814\pi$
$182$	−2.14583	+	0.528198i	−0.159060	+	0.0391526i
$183$		0			0
$184$	−3.30720	−	9.61274i	−0.243810	−	0.708661i
$185$	−0.0804628	+	0.0804628i	−0.00591574	+	0.00591574i
$186$		0			0
$187$	−4.79403	+	1.98575i	−0.350574	+	0.145213i
$188$	−4.46093	+	14.2846i	−0.325347	+	1.04181i
$189$		0			0
$190$	−0.228800	−	0.0348949i	−0.0165989	−	0.00253154i
$191$	−11.3199			−0.819077			−0.409538	−	0.912293i	$-0.634310\pi$
$191$	−11.3199			−0.819077			−0.409538	+	0.912293i	$0.634310\pi$
$192$		0			0
$193$	−8.30651			−0.597915			−0.298958	−	0.954266i	$-0.596639\pi$
$193$	−8.30651			−0.597915			−0.298958	+	0.954266i	$0.596639\pi$
$194$	17.2833	+	2.63593i	1.24087	+	0.189249i
$195$		0			0
$196$	−0.934992	+	2.99399i	−0.0667851	+	0.213856i
$197$	−5.65696	+	2.34319i	−0.403042	+	0.166945i	−0.574990	−	0.818161i	$-0.694994\pi$
$197$	−5.65696	+	2.34319i	−0.403042	+	0.166945i	0.171948	+	0.985106i	$0.444994\pi$
$198$		0			0
$199$	5.31490	−	5.31490i	0.376763	−	0.376763i	−0.493170	−	0.869933i	$-0.664162\pi$
$199$	5.31490	−	5.31490i	0.376763	−	0.376763i	0.869933	+	0.493170i	$0.164162\pi$
$200$	13.3718	−	4.60048i	0.945528	−	0.325303i
$201$		0			0
$202$	−13.4120	+	3.30136i	−0.943662	+	0.232283i
$203$	−5.04178	−	12.1719i	−0.353864	−	0.854302i
$204$		0			0
$205$	0.0769017	+	0.0318537i	0.00537105	+	0.00222476i
$206$	−9.12295	+	6.70846i	−0.635626	+	0.467400i
$207$		0			0
$208$	−1.45337	−	2.25398i	−0.100773	−	0.156285i
$209$		−	23.0044i		−	1.59125i
$210$		0			0
$211$	5.97206	+	2.47371i	0.411133	+	0.170297i	0.578657	−	0.815571i	$-0.303577\pi$
$211$	5.97206	+	2.47371i	0.411133	+	0.170297i	−0.167524	+	0.985868i	$0.553577\pi$
$212$	0.848110	+	9.39736i	0.0582484	+	0.645413i
$213$		0			0
$214$	−2.68255	−	10.8980i	−0.183375	−	0.744971i
$215$	−0.0539221	−	0.0539221i	−0.00367746	−	0.00367746i
$216$		0			0
$217$	−13.6141	+	13.6141i	−0.924186	+	0.924186i
$218$	−12.2483	−	7.40951i	−0.829559	−	0.501836i
$219$		0			0
$220$	−0.0502151	−	0.0958205i	−0.00338550	−	0.00646021i
$221$	−0.482850	+	1.16570i	−0.0324800	+	0.0784136i
$222$		0			0
$223$	8.49180			0.568653			0.284326	−	0.958728i	$-0.408230\pi$
$223$	8.49180			0.568653			0.284326	+	0.958728i	$0.408230\pi$
$224$	13.1785	−	0.377869i	0.880523	−	0.0252475i
$225$		0			0
$226$	1.28799	−	8.44510i	0.0856756	−	0.561760i
$227$	−1.18368	+	2.85767i	−0.0785639	+	0.189670i	−0.958281	−	0.285827i	$-0.907732\pi$
$227$	−1.18368	+	2.85767i	−0.0785639	+	0.189670i	0.879717	+	0.475497i	$0.157732\pi$
$228$		0			0
$229$	−21.6401	+	8.96362i	−1.43002	+	0.592333i	−0.957356	−	0.288912i	$-0.906707\pi$
$229$	−21.6401	+	8.96362i	−1.43002	+	0.592333i	−0.472661	+	0.881244i	$0.656707\pi$
$230$	−0.0853125	−	0.0516091i	−0.00562534	−	0.00340300i
$231$		0			0
$232$	11.9777	−	10.5916i	0.786377	−	0.695372i
$233$	−16.9144	−	16.9144i	−1.10810	−	1.10810i	−0.993400	−	0.114698i	$-0.963410\pi$
$233$	−16.9144	−	16.9144i	−1.10810	−	1.10810i	−0.114698	−	0.993400i	$-0.536590\pi$
$234$		0			0
$235$	0.0561702	+	0.135607i	0.00366414	+	0.00884601i
$236$	7.82479	−	0.706185i	0.509350	−	0.0459688i
$237$		0			0
$238$	−3.67447	−	4.99698i	−0.238180	−	0.323906i
$239$			7.77197i			0.502727i	0.967893	+	0.251363i	$0.0808789\pi$
$239$			7.77197i			0.502727i	−0.967893	+	0.251363i	$0.919121\pi$
$240$		0			0
$241$		−	14.9502i		−	0.963030i	−0.876438	−	0.481515i	$-0.840087\pi$
$241$		−	14.9502i		−	0.963030i	0.876438	−	0.481515i	$-0.159913\pi$
$242$	−3.87006	+	2.84580i	−0.248777	+	0.182935i
$243$		0			0
$244$	−0.595303	+	0.713414i	−0.0381104	+	0.0456717i
$245$	0.0117730	+	0.0284226i	0.000752152	+	0.00181586i
$246$		0			0
$247$	−3.95533	−	3.95533i	−0.251672	−	0.251672i
$248$	−20.9985	−	10.2482i	−1.33340	−	0.650764i
$249$		0			0
$250$	0.143587	−	0.237357i	0.00908124	−	0.0150118i
$251$	23.5733	−	9.76437i	1.48793	−	0.616322i	0.517067	−	0.855945i	$-0.327024\pi$
$251$	23.5733	−	9.76437i	1.48793	−	0.616322i	0.970866	+	0.239623i	$0.0770239\pi$
$252$		0			0
$253$	3.79257	−	9.15607i	0.238437	−	0.575637i
$254$	−12.0157	−	1.83254i	−0.753929	−	0.114984i
$255$		0			0
$256$	5.63675	+	14.9742i	0.352297	+	0.935888i
$257$	−20.7757			−1.29595			−0.647976	−	0.761661i	$-0.724384\pi$
$257$	−20.7757			−1.29595			−0.647976	+	0.761661i	$0.724384\pi$
$258$		0			0
$259$	5.17365	−	12.4903i	0.321475	−	0.776108i
$260$	−0.0251090	−	0.00784129i	−0.00155720	−	0.000486296i
$261$		0			0
$262$	−9.60547	+	15.8783i	−0.593428	+	0.980967i
$263$	−20.5201	+	20.5201i	−1.26532	+	1.26532i	−0.316849	+	0.948476i	$0.602625\pi$
$263$	−20.5201	+	20.5201i	−1.26532	+	1.26532i	−0.948476	+	0.316849i	$0.897375\pi$
$264$		0			0
$265$	0.0654400	+	0.0654400i	0.00401995	+	0.00401995i
$266$	26.7006	−	6.57237i	1.63712	−	0.402978i
$267$		0			0
$268$	0.884338	−	1.05980i	0.0540195	−	0.0647373i
$269$	24.6774	+	10.2217i	1.50461	+	0.623228i	0.974436	−	0.224663i	$-0.0721282\pi$
$269$	24.6774	+	10.2217i	1.50461	+	0.623228i	0.530170	+	0.847891i	$0.322128\pi$
$270$		0			0
$271$			29.1471i			1.77056i	0.465057	+	0.885281i	$0.346034\pi$
$271$			29.1471i			1.77056i	−0.465057	+	0.885281i	$0.653966\pi$
$272$	4.28370	−	6.18967i	0.259738	−	0.375304i
$273$		0			0
$274$	8.49602	+	11.5539i	0.513263	+	0.697996i
$275$	12.7365	+	5.27565i	0.768042	+	0.318133i
$276$		0			0
$277$	−2.06050	−	4.97449i	−0.123803	−	0.298888i	0.849811	−	0.527088i	$-0.176716\pi$
$277$	−2.06050	−	4.97449i	−0.123803	−	0.298888i	−0.973614	+	0.228200i	$0.926716\pi$
$278$	−3.14273	−	12.7675i	−0.188489	−	0.765745i
$279$		0			0
$280$	0.0968698	−	0.0856593i	0.00578907	−	0.00511912i
$281$	2.37536	−	2.37536i	0.141702	−	0.141702i	−0.632697	−	0.774399i	$-0.718052\pi$
$281$	2.37536	−	2.37536i	0.141702	−	0.141702i	0.774399	+	0.632697i	$0.218052\pi$
$282$		0			0
$283$	−16.5935	+	6.87327i	−0.986384	+	0.408574i	−0.816787	−	0.576940i	$-0.804247\pi$
$283$	−16.5935	+	6.87327i	−0.986384	+	0.408574i	−0.169597	+	0.985513i	$0.554247\pi$
$284$	−27.4315	+	14.3756i	−1.62776	+	0.853035i
$285$		0			0
$286$	0.394197	−	2.58468i	0.0233094	−	0.152836i
$287$	−9.88934			−0.583749
$288$		0			0
$289$	13.4586			0.791683
$290$	0.0236443	−	0.155031i	0.00138844	−	0.00910375i
$291$		0			0
$292$	1.77358	+	3.38435i	0.103791	+	0.198054i
$293$	3.21895	−	1.33333i	0.188053	−	0.0778941i	−0.286670	−	0.958029i	$-0.592548\pi$
$293$	3.21895	−	1.33333i	0.188053	−	0.0778941i	0.474723	+	0.880135i	$0.342548\pi$
$294$		0			0
$295$	0.0544892	−	0.0544892i	0.00317248	−	0.00317248i
$296$	16.3763	+	1.00579i	0.951854	+	0.0584606i
$297$		0			0
$298$	−6.70833	−	27.2529i	−0.388603	−	1.57872i
$299$	−0.922189	−	2.22636i	−0.0533316	−	0.128754i
$300$		0			0
$301$	8.37036	+	3.46712i	0.482459	+	0.199841i
$302$	5.80940	+	7.90031i	0.334294	+	0.454612i
$303$		0			0
$304$	18.0843	+	28.0463i	1.03720	+	1.60857i
$305$			0.00911347i			0.000521836i
$306$		0			0
$307$	21.9668	+	9.09896i	1.25371	+	0.519305i	0.907974	−	0.419025i	$-0.137628\pi$
$307$	21.9668	+	9.09896i	1.25371	+	0.519305i	0.345739	+	0.938331i	$0.387628\pi$
$308$	9.86841	+	8.23461i	0.562305	+	0.469211i
$309$		0			0
$310$	−0.222535	+	0.0547772i	−0.0126392	+	0.00311114i
$311$	−22.2181	−	22.2181i	−1.25987	−	1.25987i	−0.951154	−	0.308718i	$-0.900100\pi$
$311$	−22.2181	−	22.2181i	−1.25987	−	1.25987i	−0.308718	−	0.951154i	$-0.599900\pi$
$312$		0			0
$313$	−17.3858	+	17.3858i	−0.982704	+	0.982704i	−0.999853	−	0.0171486i	$-0.994541\pi$
$313$	−17.3858	+	17.3858i	−0.982704	+	0.982704i	0.0171486	+	0.999853i	$0.494541\pi$
$314$	2.53610	−	4.19230i	0.143120	−	0.236585i
$315$		0			0
$316$	−1.42737	+	4.57067i	−0.0802960	+	0.257120i
$317$	7.61975	−	18.3957i	0.427968	−	1.03321i	−0.551963	−	0.833869i	$-0.686121\pi$
$317$	7.61975	−	18.3957i	0.427968	−	1.03321i	0.979931	−	0.199338i	$-0.0638790\pi$
$318$		0			0
$319$	15.5875			0.872731
$320$	0.136547	+	0.0773464i	0.00763323	+	0.00432379i
$321$		0			0
$322$	11.7107	+	1.78604i	0.652614	+	0.0995320i
$323$	6.00811	−	14.5049i	0.334300	−	0.807072i
$324$		0			0
$325$	3.09698	−	1.28281i	0.171789	−	0.0711575i
$326$	−17.9134	+	29.6118i	−0.992133	+	1.64005i
$327$		0			0
$328$	−3.90450	−	11.3489i	−0.215590	−	0.626636i
$329$	−12.3310	−	12.3310i	−0.679830	−	0.679830i
$330$		0			0
$331$	3.18689	+	7.69385i	0.175168	+	0.422892i	0.986941	−	0.161080i	$-0.0514977\pi$
$331$	3.18689	+	7.69385i	0.175168	+	0.422892i	−0.811774	+	0.583972i	$0.801498\pi$
$332$	22.7390	+	18.9744i	1.24797	+	1.04136i
$333$		0			0
$334$	−12.4698	+	9.16953i	−0.682317	+	0.501734i
$335$		−	0.0135383i		−	0.000739676i
$336$		0			0
$337$		−	35.6850i		−	1.94389i	−0.235212	−	0.971944i	$-0.575579\pi$
$337$		−	35.6850i		−	1.94389i	0.235212	−	0.971944i	$-0.424421\pi$
$338$	10.5148	+	14.2992i	0.571928	+	0.777775i
$339$		0			0
$340$	−0.00663625	−	0.0735320i	−0.000359901	−	0.00398783i
$341$	−8.71717	−	21.0451i	−0.472061	−	1.13966i
$342$		0			0
$343$	−14.1204	−	14.1204i	−0.762431	−	0.762431i
$344$	−0.674033	+	10.9746i	−0.0363414	+	0.591710i
$345$		0			0
$346$	−9.79224	−	5.92374i	−0.526434	−	0.318462i
$347$	14.4792	−	5.99748i	0.777284	−	0.321962i	0.0414653	−	0.999140i	$-0.486797\pi$
$347$	14.4792	−	5.99748i	0.777284	−	0.321962i	0.735819	+	0.677178i	$0.236797\pi$
$348$		0			0
$349$	−1.44972	+	3.49994i	−0.0776019	+	0.187347i	−0.957919	−	0.287038i	$-0.907330\pi$
$349$	−1.44972	+	3.49994i	−0.0776019	+	0.187347i	0.880317	+	0.474385i	$0.157330\pi$
$350$	−2.48447	+	16.2902i	−0.132800	+	0.870748i
$351$		0			0
$352$	−5.55368	+	14.5760i	−0.296012	+	0.776904i
$353$	−17.5215			−0.932577			−0.466289	−	0.884633i	$-0.654409\pi$
$353$	−17.5215			−0.932577			−0.466289	+	0.884633i	$0.654409\pi$
$354$		0			0
$355$	−0.116245	+	0.280640i	−0.00616964	+	0.0148948i
$356$	−7.14307	+	3.74335i	−0.378582	+	0.198397i
$357$		0			0
$358$	23.8967	+	14.4561i	1.26298	+	0.764030i
$359$	11.6241	−	11.6241i	0.613495	−	0.613495i	−0.330360	−	0.943855i	$-0.607170\pi$
$359$	11.6241	−	11.6241i	0.613495	−	0.613495i	0.943855	+	0.330360i	$0.107170\pi$
$360$		0			0
$361$	35.7813	+	35.7813i	1.88322	+	1.88322i
$362$	7.04088	+	28.6039i	0.370061	+	1.50339i
$363$		0			0
$364$	3.11260	−	0.280911i	0.163144	−	0.0147237i
$365$	0.0346238	+	0.0143417i	0.00181229	+	0.000750676i
$366$		0			0
$367$			12.0873i			0.630953i	0.948933	+	0.315476i	$0.102164\pi$
$367$			12.0873i			0.630953i	−0.948933	+	0.315476i	$0.897836\pi$
$368$	2.57399	+	14.1442i	0.134179	+	0.737319i
$369$		0			0
$370$	0.129647	−	0.0953345i	0.00674003	−	0.00495621i
$371$	−10.1583	−	4.20770i	−0.527392	−	0.218453i
$372$		0			0
$373$	7.01689	+	16.9403i	0.363321	+	0.877133i	0.994810	+	0.101749i	$0.0324439\pi$
$373$	7.01689	+	16.9403i	0.363321	+	0.877133i	−0.631490	+	0.775384i	$0.717556\pi$
$374$	7.12569	−	1.75399i	0.368461	−	0.0906969i
$375$		0			0
$376$	9.28235	−	19.0194i	0.478701	−	0.980849i
$377$	2.68008	−	2.68008i	0.138031	−	0.138031i
$378$		0			0
$379$	17.7984	−	7.37232i	0.914241	−	0.378691i	0.124562	−	0.992212i	$-0.460247\pi$
$379$	17.7984	−	7.37232i	0.914241	−	0.378691i	0.789678	+	0.613521i	$0.210247\pi$
$380$	0.312432	+	0.0975694i	0.0160274	+	0.00500520i
$381$		0			0
$382$	15.8257	+	2.41362i	0.809714	+	0.123492i
$383$	−20.4866			−1.04682			−0.523408	−	0.852082i	$-0.675340\pi$
$383$	−20.4866			−1.04682			−0.523408	+	0.852082i	$0.675340\pi$
$384$		0			0
$385$	0.126063			0.00642478
$386$	11.6129	+	1.77111i	0.591081	+	0.0901474i
$387$		0			0
$388$	−23.6009	−	7.37031i	−1.19815	−	0.374171i
$389$	17.1590	−	7.10747i	0.869994	−	0.360363i	0.0973859	−	0.995247i	$-0.468952\pi$
$389$	17.1590	−	7.10747i	0.869994	−	0.360363i	0.772608	+	0.634883i	$0.218952\pi$
$390$		0			0
$391$	4.78262	−	4.78262i	0.241867	−	0.241867i
$392$	1.94554	−	3.98638i	0.0982647	−	0.201343i
$393$		0			0
$394$	8.40832	−	2.06971i	0.423605	−	0.104271i
$395$	0.0179729	+	0.0433904i	0.000904315	+	0.00218321i
$396$		0			0
$397$	−7.40610	−	3.06771i	−0.371701	−	0.153964i	0.189010	−	0.981975i	$-0.439472\pi$
$397$	−7.40610	−	3.06771i	−0.371701	−	0.153964i	−0.560711	+	0.828011i	$0.689472\pi$
$398$	−8.56372	+	6.29724i	−0.429261	+	0.315652i
$399$		0			0
$400$	−19.6753	+	3.58055i	−0.983766	+	0.179028i
$401$			8.68253i			0.433585i	0.976218	+	0.216792i	$0.0695595\pi$
$401$			8.68253i			0.433585i	−0.976218	+	0.216792i	$0.930441\pi$
$402$		0			0
$403$	−5.11726	−	2.11964i	−0.254909	−	0.105587i
$404$	19.4545	−	1.75576i	0.967896	−	0.0873524i
$405$		0			0
$406$	4.45335	+	18.0920i	0.221016	+	0.897889i
$407$	11.3103	+	11.3103i	0.560630	+	0.560630i
$408$		0			0
$409$	−17.1998	+	17.1998i	−0.850477	+	0.850477i	−0.990192	−	0.139715i	$-0.955381\pi$
$409$	−17.1998	+	17.1998i	−0.850477	+	0.850477i	0.139715	+	0.990192i	$0.455381\pi$
$410$	−0.100720	−	0.0609300i	−0.00497422	−	0.00300912i
$411$		0			0
$412$	14.1847	−	7.43355i	0.698830	−	0.366225i
$413$	−3.50358	+	8.45838i	−0.172400	+	0.416210i
$414$		0			0
$415$	0.290478			0.0142590
$416$	1.55128	+	3.46106i	0.0760579	+	0.169692i
$417$		0			0
$418$	−4.90501	+	32.1613i	−0.239912	+	1.57306i
$419$	12.0889	−	29.1853i	0.590583	−	1.42579i	−0.292357	−	0.956309i	$-0.594440\pi$
$419$	12.0889	−	29.1853i	0.590583	−	1.42579i	0.882940	−	0.469485i	$-0.155560\pi$
$420$		0			0
$421$	9.66935	−	4.00518i	0.471255	−	0.195200i	−0.134400	−	0.990927i	$-0.542911\pi$
$421$	9.66935	−	4.00518i	0.471255	−	0.195200i	0.605656	+	0.795727i	$0.292911\pi$
$422$	−7.82178	−	4.73172i	−0.380758	−	0.230337i
$423$		0			0
$424$	0.818008	−	13.3188i	0.0397260	−	0.646817i
$425$	6.65285	+	6.65285i	0.322711	+	0.322711i
$426$		0			0
$427$	−0.414353	−	1.00034i	−0.0200519	−	0.0484096i
$428$	1.42666	+	15.8079i	0.0689601	+	0.764103i
$429$		0			0
$430$	0.0638884	+	0.0868830i	0.00308097	+	0.00418987i
$431$			26.3303i			1.26829i	0.773216	+	0.634143i	$0.218647\pi$
$431$			26.3303i			1.26829i	−0.773216	+	0.634143i	$0.781353\pi$
$432$		0			0
$433$		−	13.4509i		−	0.646409i	−0.946329	−	0.323205i	$-0.895240\pi$
$433$		−	13.4509i		−	0.646409i	0.946329	−	0.323205i	$-0.104760\pi$
$434$	21.9360	−	16.1304i	1.05296	−	0.774283i
$435$		0			0
$436$	15.5438	+	12.9704i	0.744415	+	0.621171i
$437$	11.4748	+	27.7027i	0.548915	+	1.32520i
$438$		0			0
$439$	−17.6157	−	17.6157i	−0.840751	−	0.840751i	0.148205	−	0.988957i	$-0.452650\pi$
$439$	−17.6157	−	17.6157i	−0.840751	−	0.840751i	−0.988957	+	0.148205i	$0.952650\pi$
$440$	0.0497722	+	0.144668i	0.00237280	+	0.00689680i
$441$		0			0
$442$	0.923598	−	1.52675i	0.0439311	−	0.0726203i
$443$	−14.8580	+	6.15440i	−0.705926	+	0.292404i	−0.706618	−	0.707596i	$-0.749780\pi$
$443$	−14.8580	+	6.15440i	−0.705926	+	0.292404i	0.000691537		1.00000i	$0.499780\pi$
$444$		0			0
$445$	−0.0302697	+	0.0730776i	−0.00143492	+	0.00346421i
$446$	−11.8719	−	1.81062i	−0.562152	−	0.0857354i
$447$		0			0
$448$	−18.5047	−	2.28163i	−0.874264	−	0.107797i
$449$	33.6931			1.59008			0.795038	−	0.606559i	$-0.207451\pi$
$449$	33.6931			1.59008			0.795038	+	0.606559i	$0.207451\pi$
$450$		0			0
$451$	4.47753	−	10.8097i	0.210839	−	0.509009i
$452$	−3.60133	+	11.5320i	−0.169392	+	0.542421i
$453$		0			0
$454$	2.26416	−	3.74277i	0.106262	−	0.175657i
$455$	0.0216751	−	0.0216751i	0.00101614	−	0.00101614i
$456$		0			0
$457$	22.2161	+	22.2161i	1.03923	+	1.03923i	0.999199	+	0.0400279i	$0.0127447\pi$
$457$	22.2161	+	22.2161i	1.03923	+	1.03923i	0.0400279	+	0.999199i	$0.487255\pi$
$458$	32.1651	−	7.91746i	1.50298	−	0.369959i
$459$		0			0
$460$	0.108267	+	0.0903423i	0.00504796	+	0.00421223i
$461$	−27.7443	−	11.4921i	−1.29218	−	0.535238i	−0.372545	−	0.928014i	$-0.621515\pi$
$461$	−27.7443	−	11.4921i	−1.29218	−	0.535238i	−0.919634	+	0.392776i	$0.871515\pi$
$462$		0			0
$463$			26.2164i			1.21838i	0.793025	+	0.609189i	$0.208505\pi$
$463$			26.2164i			1.21838i	−0.793025	+	0.609189i	$0.791495\pi$
$464$	−19.0038	+	12.2536i	−0.882229	+	0.568861i
$465$		0			0
$466$	20.0406	+	27.2536i	0.928364	+	1.26250i
$467$	7.19598	+	2.98067i	0.332990	+	0.137929i	0.542913	−	0.839789i	$-0.317321\pi$
$467$	7.19598	+	2.98067i	0.332990	+	0.137929i	−0.209923	+	0.977718i	$0.567321\pi$
$468$		0			0
$469$	0.615531	+	1.48602i	0.0284226	+	0.0686182i
$470$	−0.0496145	−	0.201561i	−0.00228855	−	0.00929733i
$471$		0			0
$472$	−11.0900	−	0.681121i	−0.510458	−	0.0313511i
$473$	−7.57958	+	7.57958i	−0.348509	+	0.348509i
$474$		0			0
$475$	−38.5358	+	15.9620i	−1.76814	+	0.732388i
$476$	4.07163	+	7.76948i	0.186623	+	0.356114i
$477$		0			0
$478$	1.65714	−	10.8656i	0.0757959	−	0.496980i
$479$	25.9107			1.18389			0.591945	−	0.805978i	$-0.298360\pi$
$479$	25.9107			1.18389			0.591945	+	0.805978i	$0.298360\pi$
$480$		0			0
$481$	3.88933			0.177338
$482$	−3.18769	+	20.9011i	−0.145195	+	0.952021i
$483$		0			0
$484$	6.01730	−	3.15339i	0.273514	−	0.143336i
$485$	−0.224049	+	0.0928039i	−0.0101735	+	0.00421401i
$486$		0			0
$487$	−17.7959	+	17.7959i	−0.806410	+	0.806410i	−0.984089	−	0.177678i	$-0.943141\pi$
$487$	−17.7959	+	17.7959i	−0.806410	+	0.806410i	0.177678	+	0.984089i	$0.443141\pi$
$488$	0.984376	−	0.870456i	0.0445606	−	0.0394037i
$489$		0			0
$490$	−0.0103990	−	0.0422464i	−0.000469779	−	0.00190850i
$491$	−15.3766	−	37.1223i	−0.693935	−	1.67531i	−0.736699	−	0.676221i	$-0.763616\pi$
$491$	−15.3766	−	37.1223i	−0.693935	−	1.67531i	0.0427643	−	0.999085i	$-0.486384\pi$
$492$		0			0
$493$	9.82829	+	4.07101i	0.442644	+	0.183349i
$494$	4.68639	+	6.37310i	0.210850	+	0.286739i
$495$		0			0
$496$	27.1717	+	18.8048i	1.22005	+	0.844362i
$497$		−	36.0895i		−	1.61884i
$498$		0			0
$499$	−22.8350	−	9.45856i	−1.02223	−	0.423423i	−0.192330	−	0.981330i	$-0.561605\pi$
$499$	−22.8350	−	9.45856i	−1.02223	−	0.423423i	−0.829903	+	0.557907i	$0.811605\pi$
$500$	−0.251351	+	0.301220i	−0.0112407	+	0.0134710i
$501$		0			0
$502$	−35.0385	+	8.62476i	−1.56385	+	0.384942i
$503$	5.89315	+	5.89315i	0.262762	+	0.262762i	0.826175	−	0.563413i	$-0.190512\pi$
$503$	5.89315	+	5.89315i	0.262762	+	0.262762i	−0.563413	+	0.826175i	$0.690512\pi$
$504$		0			0
$505$	0.135474	−	0.135474i	0.00602853	−	0.00602853i
$506$	−7.25445	+	11.9920i	−0.322500	+	0.533108i
$507$		0			0
$508$	16.4077	+	5.12396i	0.727975	+	0.227339i
$509$	−12.9851	+	31.3488i	−0.575554	+	1.38951i	0.321213	+	0.947007i	$0.395910\pi$
$509$	−12.9851	+	31.3488i	−0.575554	+	1.38951i	−0.896767	+	0.442503i	$0.854090\pi$
$510$		0			0
$511$	−4.45252			−0.196968
$512$	−4.68763	−	22.1365i	−0.207166	−	0.978306i
$513$		0			0
$514$	29.0454	+	4.42980i	1.28114	+	0.195390i
$515$	0.0601096	−	0.145117i	0.00264874	−	0.00639463i
$516$		0			0
$517$	19.0616	−	7.89558i	0.838329	−	0.347247i
$518$	−9.89618	+	16.3589i	−0.434813	+	0.718768i
$519$		0			0
$520$	0.0334317	+	0.0163163i	0.00146608	+	0.000715515i
$521$	−25.9040	−	25.9040i	−1.13487	−	1.13487i	−0.989355	−	0.145519i	$-0.953515\pi$
$521$	−25.9040	−	25.9040i	−1.13487	−	1.13487i	−0.145519	−	0.989355i	$-0.546485\pi$
$522$		0			0
$523$	9.34255	+	22.5549i	0.408521	+	0.986258i	0.985527	+	0.169518i	$0.0542210\pi$
$523$	9.34255	+	22.5549i	0.408521	+	0.986258i	−0.577006	+	0.816740i	$0.695779\pi$
$524$	16.8145	−	20.1506i	0.734544	−	0.880282i
$525$		0			0
$526$	33.0634	−	24.3128i	1.44163	−	1.06009i
$527$		−	15.5461i		−	0.677200i
$528$		0			0
$529$		−	10.0822i		−	0.438356i
$530$	−0.0775352	−	0.105441i	−0.00336791	−	0.00458008i
$531$		0			0
$532$	−38.7301	+	3.49538i	−1.67916	+	0.151544i
$533$	−1.08874	−	2.62846i	−0.0471587	−	0.113851i
$534$		0			0
$535$	0.110081	+	0.110081i	0.00475921	+	0.00475921i
$536$	−1.46232	+	1.29309i	−0.0631624	+	0.0558528i
$537$		0			0
$538$	−32.3207	−	19.5521i	−1.39344	−	0.842953i
$539$	3.99524	−	1.65488i	0.172087	−	0.0712808i
$540$		0			0
$541$	6.54031	−	15.7897i	0.281190	−	0.678853i	−0.718674	−	0.695347i	$-0.755251\pi$
$541$	6.54031	−	15.7897i	0.281190	−	0.678853i	0.999864	+	0.0164945i	$0.00525060\pi$
$542$	6.21476	−	40.7491i	0.266947	−	1.75032i
$543$		0			0
$544$	−7.30858	+	7.74008i	−0.313353	+	0.331853i
$545$	0.198564			0.00850554
$546$		0			0
$547$	0.933168	−	2.25287i	0.0398994	−	0.0963256i	−0.902674	−	0.430326i	$-0.858399\pi$
$547$	0.933168	−	2.25287i	0.0398994	−	0.0963256i	0.942573	+	0.334000i	$0.108399\pi$
$548$	−9.41432	−	17.9644i	−0.402160	−	0.767402i
$549$		0			0
$550$	−16.6814	−	10.0913i	−0.711298	−	0.430294i
$551$	−33.3483	+	33.3483i	−1.42068	+	1.42068i
$552$		0			0
$553$	−3.94558	−	3.94558i	−0.167783	−	0.167783i
$554$	1.82002	+	7.39391i	0.0773251	+	0.314137i
$555$		0			0
$556$	1.67140	+	18.5197i	0.0708831	+	0.785410i
$557$	16.6879	+	6.91234i	0.707087	+	0.292885i	0.707099	−	0.707115i	$-0.250004\pi$
$557$	16.6879	+	6.91234i	0.707087	+	0.292885i	−1.13924e−5		1.00000i	$0.500004\pi$
$558$		0			0
$559$			2.60643i			0.110240i
$560$	−0.153693	+	0.0991011i	−0.00649471	+	0.00418779i
$561$		0			0
$562$	−3.82734	+	2.81439i	−0.161447	+	0.118718i
$563$	−18.1908	−	7.53488i	−0.766651	−	0.317557i	−0.0351362	−	0.999383i	$-0.511187\pi$
$563$	−18.1908	−	7.53488i	−0.766651	−	0.317557i	−0.731515	+	0.681825i	$0.761187\pi$
$564$		0			0
$565$	0.0453465	+	0.109476i	0.00190774	+	0.00460570i
$566$	24.6641	−	6.07108i	1.03671	−	0.255187i
$567$		0			0
$568$	41.4158	−	14.2488i	1.73777	−	0.597867i
$569$	14.3479	−	14.3479i	0.601496	−	0.601496i	−0.339213	−	0.940709i	$-0.610161\pi$
$569$	14.3479	−	14.3479i	0.601496	−	0.601496i	0.940709	+	0.339213i	$0.110161\pi$
$570$		0			0
$571$	−28.1368	+	11.6547i	−1.17749	+	0.487732i	−0.883662	−	0.468126i	$-0.844929\pi$
$571$	−28.1368	+	11.6547i	−1.17749	+	0.487732i	−0.293828	+	0.955858i	$0.594929\pi$
$572$	−1.10221	+	3.52946i	−0.0460859	+	0.147574i
$573$		0			0
$574$	13.8258	+	2.10861i	0.577076	+	0.0880116i
$575$	−17.9693			−0.749371
$576$		0			0
$577$	17.0055			0.707949			0.353975	−	0.935255i	$-0.384830\pi$
$577$	17.0055			0.707949			0.353975	+	0.935255i	$0.384830\pi$
$578$	−18.8158	−	2.86965i	−0.782634	−	0.119362i
$579$		0			0
$580$	−0.0661116	+	0.211700i	−0.00274514	+	0.00879035i
$581$	−31.8842	+	13.2069i	−1.32278	+	0.547914i
$582$		0			0
$583$	9.19860	−	9.19860i	0.380967	−	0.380967i
$584$	−1.75794	−	5.10965i	−0.0727442	−	0.211439i
$585$		0			0
$586$	−4.78454	+	1.17772i	−0.197647	+	0.0486510i
$587$	−1.08676	−	2.62368i	−0.0448555	−	0.108291i	0.899864	−	0.436171i	$-0.143666\pi$
$587$	−1.08676	−	2.62368i	−0.0448555	−	0.108291i	−0.944719	+	0.327880i	$0.893666\pi$
$588$		0			0
$589$	63.6742	+	26.3747i	2.62365	+	1.08675i
$590$	−0.0877967	+	0.0645603i	−0.00361453	+	0.00265790i
$591$		0			0
$592$	−22.6804	−	4.89791i	−0.932159	−	0.201303i
$593$			0.349138i			0.0143374i	0.999974	+	0.00716869i	$0.00228189\pi$
$593$			0.349138i			0.0143374i	−0.999974	+	0.00716869i	$0.997718\pi$
$594$		0			0
$595$	0.0794861	+	0.0329242i	0.00325861	+	0.00134976i
$596$	3.56769	+	39.5313i	0.146138	+	1.61926i
$597$		0			0
$598$	0.814559	+	3.30919i	0.0333098	+	0.135323i
$599$	8.87418	+	8.87418i	0.362589	+	0.362589i	0.864765	−	0.502176i	$-0.167467\pi$
$599$	8.87418	+	8.87418i	0.362589	+	0.362589i	−0.502176	+	0.864765i	$0.667467\pi$
$600$		0			0
$601$	19.4058	−	19.4058i	0.791577	−	0.791577i	−0.190173	−	0.981751i	$-0.560905\pi$
$601$	19.4058	−	19.4058i	0.791577	−	0.791577i	0.981751	+	0.190173i	$0.0609050\pi$
$602$	−10.9629	−	6.63192i	−0.446814	−	0.270297i
$603$		0			0
$604$	−6.43732	−	12.2837i	−0.261931	−	0.499816i
$605$	0.0254991	−	0.0615604i	0.00103669	−	0.00250278i
$606$		0			0
$607$	20.7512			0.842264			0.421132	−	0.906999i	$-0.361633\pi$
$607$	20.7512			0.842264			0.421132	+	0.906999i	$0.361633\pi$
$608$	−19.3026	−	43.0660i	−0.782825	−	1.74656i
$609$		0			0
$610$	0.00194317	−	0.0127411i	7.86768e−5	−	0.000515870i
$611$	1.91986	−	4.63496i	0.0776694	−	0.187511i
$612$		0			0
$613$	−30.7279	+	12.7279i	−1.24109	+	0.514075i	−0.904054	−	0.427418i	$-0.859423\pi$
$613$	−30.7279	+	12.7279i	−1.24109	+	0.514075i	−0.337033	+	0.941493i	$0.609423\pi$
$614$	−28.7706	−	17.4046i	−1.16109	−	0.702391i
$615$		0			0
$616$	−12.0407	−	13.6165i	−0.485134	−	0.548625i
$617$	10.7091	+	10.7091i	0.431130	+	0.431130i	0.889013	−	0.457882i	$-0.151392\pi$
$617$	10.7091	+	10.7091i	0.431130	+	0.431130i	−0.457882	+	0.889013i	$0.651392\pi$
$618$		0			0
$619$	8.87671	+	21.4303i	0.356785	+	0.861355i	0.995748	+	0.0921180i	$0.0293637\pi$
$619$	8.87671	+	21.4303i	0.356785	+	0.861355i	−0.638963	+	0.769237i	$0.720636\pi$
$620$	0.322794	−	0.0291321i	0.0129637	−	0.00116997i
$621$		0			0
$622$	26.3246	+	35.7993i	1.05552	+	1.43542i
$623$		−	9.39757i		−	0.376506i
$624$		0			0
$625$		−	24.9942i		−	0.999769i
$626$	28.0132	−	20.5992i	1.11963	−	0.823309i
$627$		0			0
$628$	−4.43947	+	5.32028i	−0.177154	+	0.212302i
$629$	4.17748	+	10.0853i	0.166567	+	0.402129i
$630$		0			0
$631$	−14.1836	−	14.1836i	−0.564641	−	0.564641i	0.365981	−	0.930622i	$-0.380733\pi$
$631$	−14.1836	−	14.1836i	−0.564641	−	0.564641i	−0.930622	+	0.365981i	$0.880733\pi$
$632$	2.97009	−	6.08567i	0.118144	−	0.242075i
$633$		0			0
$634$	−14.5751	+	24.0934i	−0.578852	+	0.956871i
$635$	0.155762	−	0.0645188i	0.00618123	−	0.00256035i
$636$		0			0
$637$	0.402396	−	0.971469i	0.0159435	−	0.0384910i
$638$	−21.7920	−	3.32356i	−0.862754	−	0.131581i
$639$		0			0
$640$	−0.174408	−	0.137249i	−0.00689408	−	0.00542523i
$641$	−30.2696			−1.19558			−0.597788	−	0.801654i	$-0.703953\pi$
$641$	−30.2696			−1.19558			−0.597788	+	0.801654i	$0.703953\pi$
$642$		0			0
$643$	6.62030	−	15.9828i	0.261079	−	0.630301i	−0.737927	−	0.674881i	$-0.764195\pi$
$643$	6.62030	−	15.9828i	0.261079	−	0.630301i	0.999006	+	0.0445802i	$0.0141950\pi$
$644$	−15.9914	−	4.99393i	−0.630148	−	0.196789i
$645$		0			0
$646$	−11.4924	+	18.9974i	−0.452161	+	0.747444i
$647$	11.0743	−	11.0743i	0.435376	−	0.435376i	−0.455077	−	0.890452i	$-0.650388\pi$
$647$	11.0743	−	11.0743i	0.435376	−	0.435376i	0.890452	+	0.455077i	$0.150388\pi$
$648$		0			0
$649$	−7.65929	−	7.65929i	−0.300653	−	0.300653i
$650$	−4.60324	+	1.13309i	−0.180554	+	0.0444435i
$651$		0			0
$652$	31.3577	−	37.5792i	1.22806	−	1.47172i
$653$	6.81365	+	2.82231i	0.266639	+	0.110445i	0.511997	−	0.858987i	$-0.328906\pi$
$653$	6.81365	+	2.82231i	0.266639	+	0.110445i	−0.245359	+	0.969432i	$0.578906\pi$
$654$		0			0
$655$		−	0.257412i		−	0.0100579i
$656$	3.03887	+	16.6988i	0.118648	+	0.651977i
$657$		0			0
$658$	14.6101	+	19.8685i	0.569561	+	0.774556i
$659$	37.5899	+	15.5703i	1.46430	+	0.606531i	0.965550	−	0.260217i	$-0.0837942\pi$
$659$	37.5899	+	15.5703i	1.46430	+	0.606531i	0.498746	+	0.866748i	$0.333794\pi$
$660$		0			0
$661$	−0.233382	−	0.563433i	−0.00907750	−	0.0219150i	0.919276	−	0.393614i	$-0.128775\pi$
$661$	−0.233382	−	0.563433i	−0.00907750	−	0.0219150i	−0.928353	+	0.371699i	$0.878775\pi$
$662$	−2.81495	−	11.4359i	−0.109406	−	0.444468i
$663$		0			0
$664$	−27.7445	−	31.3755i	−1.07670	−	1.21761i
$665$	−0.269703	+	0.269703i	−0.0104586	+	0.0104586i
$666$		0			0
$667$	−18.7709	+	7.77517i	−0.726813	+	0.301056i
$668$	19.3885	−	10.1606i	0.750164	−	0.393126i
$669$		0			0
$670$	−0.00288664	+	0.0189272i	−0.000111520	+	0.000731220i
$671$	1.28104			0.0494539
$672$		0			0
$673$	10.7608			0.414800			0.207400	−	0.978256i	$-0.433500\pi$
$673$	10.7608			0.414800			0.207400	+	0.978256i	$0.433500\pi$
$674$	−7.60877	+	49.8894i	−0.293079	+	1.92167i
$675$		0			0
$676$	−11.6513	−	22.2329i	−0.448125	−	0.855113i
$677$	31.1860	−	12.9177i	1.19858	−	0.496467i	0.308038	−	0.951374i	$-0.400328\pi$
$677$	31.1860	−	12.9177i	1.19858	−	0.496467i	0.890539	+	0.454907i	$0.150328\pi$
$678$		0			0
$679$	20.3732	−	20.3732i	0.781850	−	0.781850i
$680$	−0.00640071	+	0.104216i	−0.000245456	+	0.00399651i
$681$		0			0
$682$	7.69977	+	31.2807i	0.294840	+	1.19780i
$683$	3.58373	+	8.65189i	0.137128	+	0.331055i	0.977494	−	0.210964i	$-0.0676601\pi$
$683$	3.58373	+	8.65189i	0.137128	+	0.331055i	−0.840366	+	0.542019i	$0.817660\pi$
$684$		0			0
$685$	−0.183786	−	0.0761266i	−0.00702210	−	0.00290865i
$686$	16.7303	+	22.7518i	0.638764	+	0.868667i
$687$		0			0
$688$	3.28233	−	15.1993i	0.125138	−	0.579467i
$689$		−	3.16318i		−	0.120507i
$690$		0			0
$691$	3.18865	+	1.32078i	0.121302	+	0.0502450i	0.442509	−	0.896764i	$-0.354088\pi$
$691$	3.18865	+	1.32078i	0.121302	+	0.0502450i	−0.321207	+	0.947009i	$0.604088\pi$
$692$	12.4270	+	10.3696i	0.472402	+	0.394192i
$693$		0			0
$694$	−21.5214	+	5.29751i	−0.816941	+	0.201091i
$695$	0.128965	+	0.128965i	0.00489192	+	0.00489192i
$696$		0			0
$697$	5.64639	−	5.64639i	0.213872	−	0.213872i
$698$	2.77304	−	4.58397i	0.104961	−	0.173506i
$699$		0			0
$700$	6.94680	−	22.2448i	0.262564	−	0.840773i
$701$	14.6916	−	35.4687i	0.554895	−	1.33964i	−0.358868	−	0.933388i	$-0.616837\pi$
$701$	14.6916	−	35.4687i	0.554895	−	1.33964i	0.913763	−	0.406247i	$-0.133163\pi$
$702$		0			0
$703$	−48.3950			−1.82525
$704$	10.8722	−	19.1938i	0.409762	−	0.723394i
$705$		0			0
$706$	24.4959	+	3.73594i	0.921917	+	0.140604i
$707$	−8.71081	+	21.0298i	−0.327604	+	0.790906i
$708$		0			0
$709$	−41.8642	+	17.3407i	−1.57224	+	0.651244i	−0.987161	−	0.159731i	$-0.948937\pi$
$709$	−41.8642	+	17.3407i	−1.57224	+	0.651244i	−0.585081	+	0.810975i	$0.698937\pi$
$710$	0.222354	−	0.367562i	0.00834479	−	0.0137944i
$711$		0			0
$712$	10.7845	−	3.71034i	0.404167	−	0.139051i
$713$	20.9950	+	20.9950i	0.786268	+	0.786268i
$714$		0			0
$715$	0.0138786	+	0.0335060i	0.000519031	+	0.00125305i
$716$	−30.3264	−	25.3056i	−1.13335	−	0.945715i
$717$		0			0
$718$	−18.7295	+	13.7725i	−0.698979	+	0.513986i
$719$			4.56519i			0.170253i	0.996370	+	0.0851264i	$0.0271294\pi$
$719$			4.56519i			0.170253i	−0.996370	+	0.0851264i	$0.972871\pi$
$720$		0			0
$721$			18.6617i			0.694997i
$722$	−42.3946	−	57.6532i	−1.57776	−	2.14563i
$723$		0			0
$724$	−3.74455	−	41.4909i	−0.139165	−	1.54200i
$725$	−10.8156	−	26.1113i	−0.401683	−	0.969748i
$726$		0			0
$727$	−4.04226	−	4.04226i	−0.149919	−	0.149919i	0.628163	−	0.778082i	$-0.283807\pi$
$727$	−4.04226	−	4.04226i	−0.149919	−	0.149919i	−0.778082	+	0.628163i	$0.783807\pi$
$728$	−4.41145	−	0.270941i	−0.163499	−	0.0100417i
$729$		0			0
$730$	−0.0453478	−	0.0274328i	−0.00167840	−	0.00101533i
$731$	−6.75869	+	2.79954i	−0.249979	+	0.103545i
$732$		0			0
$733$	5.54207	−	13.3797i	0.204701	−	0.494192i	−0.787872	−	0.615838i	$-0.788817\pi$
$733$	5.54207	−	13.3797i	0.204701	−	0.494192i	0.992573	+	0.121646i	$0.0388174\pi$
$734$	2.57726	−	16.8986i	0.0951284	−	0.623740i
$735$		0			0
$736$	−0.582731	−	20.3231i	−0.0214797	−	0.749121i
$737$	−1.90301			−0.0700984
$738$		0			0
$739$	10.6843	−	25.7941i	0.393027	−	0.948851i	−0.596250	−	0.802799i	$-0.703343\pi$
$739$	10.6843	−	25.7941i	0.393027	−	0.948851i	0.989277	−	0.146052i	$-0.0466567\pi$
$740$	−0.201580	+	0.105639i	−0.00741023	+	0.00388336i
$741$		0			0
$742$	13.3046	+	8.04852i	0.488428	+	0.295471i
$743$	−7.48429	+	7.48429i	−0.274572	+	0.274572i	−0.830938	−	0.556366i	$-0.812195\pi$
$743$	−7.48429	+	7.48429i	−0.274572	+	0.274572i	0.556366	+	0.830938i	$0.312195\pi$
$744$		0			0
$745$	0.275282	+	0.275282i	0.0100856	+	0.0100856i
$746$	−6.19793	−	25.1794i	−0.226923	−	0.921885i
$747$		0			0
$748$	−10.3360	+	0.932826i	−0.377923	+	0.0341075i
$749$	−17.0879	−	7.07804i	−0.624378	−	0.258626i
$750$		0			0
$751$			26.4441i			0.964959i	0.875907	+	0.482480i	$0.160264\pi$
$751$			26.4441i			0.964959i	−0.875907	+	0.482480i	$0.839736\pi$
$752$	−17.0325	+	24.6108i	−0.621111	+	0.897464i
$753$		0			0
$754$	−4.31832	+	3.17543i	−0.157264	+	0.115642i
$755$	−0.125669	−	0.0520538i	−0.00457356	−	0.00189443i
$756$		0			0
$757$	−17.2384	−	41.6171i	−0.626539	−	1.51260i	−0.843896	−	0.536507i	$-0.819744\pi$
$757$	−17.2384	−	41.6171i	−0.626539	−	1.51260i	0.217357	−	0.976092i	$-0.430256\pi$
$758$	−26.4549	+	6.51189i	−0.960885	+	0.236523i
$759$		0			0
$760$	−0.415992	−	0.203024i	−0.0150896	−	0.00736444i
$761$	−14.3062	+	14.3062i	−0.518599	+	0.518599i	−0.917147	−	0.398549i	$-0.869514\pi$
$761$	−14.3062	+	14.3062i	−0.518599	+	0.518599i	0.398549	+	0.917147i	$0.369514\pi$
$762$		0			0
$763$	−21.7953	+	9.02790i	−0.789042	+	0.326832i
$764$	−21.6105	−	6.74872i	−0.781839	−	0.244160i
$765$		0			0
$766$	28.6412	+	4.36816i	1.03485	+	0.157828i
$767$	−2.63384			−0.0951026
$768$		0			0
$769$	−15.8743			−0.572442			−0.286221	−	0.958164i	$-0.592399\pi$
$769$	−15.8743			−0.572442			−0.286221	+	0.958164i	$0.592399\pi$
$770$	−0.176243	−	0.0268793i	−0.00635134	−	0.000968661i
$771$		0			0
$772$	−15.8577	−	4.95221i	−0.570732	−	0.178234i
$773$	5.28904	−	2.19079i	0.190234	−	0.0787973i	−0.285533	−	0.958369i	$-0.592171\pi$
$773$	5.28904	−	2.19079i	0.190234	−	0.0787973i	0.475767	+	0.879572i	$0.342171\pi$
$774$		0			0
$775$	−29.2050	+	29.2050i	−1.04908	+	1.04908i
$776$	31.4237	+	15.3362i	1.12804	+	0.550538i
$777$		0			0
$778$	−25.5045	+	6.27795i	−0.914381	+	0.225075i
$779$	13.5472	+	32.7059i	0.485380	+	1.17181i
$780$		0			0
$781$	39.4482	+	16.3400i	1.41157	+	0.584691i
$782$	−7.70608	+	5.66658i	−0.275569	+	0.202636i
$783$		0			0
$784$	−3.56994	+	5.15832i	−0.127498	+	0.184226i
$785$			0.0679636i			0.00242573i
$786$		0			0
$787$	6.79611	+	2.81504i	0.242255	+	0.100345i	0.500508	−	0.865732i	$-0.333147\pi$
$787$	6.79611	+	2.81504i	0.242255	+	0.100345i	−0.258252	+	0.966077i	$0.583147\pi$
$788$	−12.1965	+	1.10074i	−0.434484	+	0.0392121i
$789$		0			0
$790$	−0.0158753	−	0.0644941i	−0.000564816	−	0.00229460i
$791$	−9.95488	−	9.95488i	−0.353955	−	0.353955i
$792$		0			0
$793$	0.220259	−	0.220259i	0.00782162	−	0.00782162i
$794$	9.69998	+	5.86793i	0.344239	+	0.208245i
$795$		0			0
$796$	13.3152	−	6.97788i	0.471944	−	0.247324i
$797$	4.32560	−	10.4429i	0.153220	−	0.369907i	−0.828567	−	0.559890i	$-0.810843\pi$
$797$	4.32560	−	10.4429i	0.153220	−	0.369907i	0.981787	+	0.189983i	$0.0608433\pi$
$798$		0			0
$799$	14.0809			0.498147
$800$	28.2705	−	0.810606i	0.999512	−	0.0286593i
$801$		0			0
$802$	1.85129	−	12.1386i	0.0653713	−	0.428629i
$803$	2.01594	−	4.86691i	0.0711409	−	0.171749i
$804$		0			0
$805$	−0.151810	+	0.0628816i	−0.00535058	+	0.00221628i
$806$	6.70223	+	4.05446i	0.236076	+	0.142812i
$807$		0			0
$808$	−27.5726	−	1.69345i	−0.970002	−	0.0595752i
$809$	28.0585	+	28.0585i	0.986485	+	0.986485i	0.999910	−	0.0134249i	$-0.00427342\pi$
$809$	28.0585	+	28.0585i	0.986485	+	0.986485i	−0.0134249	+	0.999910i	$0.504273\pi$
$810$		0			0
$811$	−10.2570	−	24.7626i	−0.360172	−	0.869532i	−0.995274	−	0.0971038i	$-0.969042\pi$
$811$	−10.2570	−	24.7626i	−0.360172	−	0.869532i	0.635102	−	0.772428i	$-0.280958\pi$
$812$	−2.36842	−	26.2430i	−0.0831153	−	0.920947i
$813$		0			0
$814$	−13.4007	−	18.2239i	−0.469695	−	0.638747i
$815$		−	0.480053i		−	0.0168155i
$816$		0			0
$817$		−	32.4319i		−	1.13465i
$818$	27.7135	−	20.3788i	0.968981	−	0.712529i
$819$		0			0
$820$	0.127820	+	0.106659i	0.00446368	+	0.00372468i
$821$	8.80031	+	21.2458i	0.307133	+	0.741485i	0.999795	+	0.0202229i	$0.00643758\pi$
$821$	8.80031	+	21.2458i	0.307133	+	0.741485i	−0.692662	+	0.721262i	$0.743562\pi$
$822$		0			0
$823$	−27.3171	−	27.3171i	−0.952215	−	0.952215i	0.0466941	−	0.998909i	$-0.485131\pi$
$823$	−27.3171	−	27.3171i	−0.952215	−	0.952215i	−0.998909	+	0.0466941i	$0.985131\pi$
$824$	−21.4159	+	7.36799i	−0.746057	+	0.256676i
$825$		0			0
$826$	6.70167	−	11.0782i	0.233181	−	0.385460i
$827$	4.85757	−	2.01207i	0.168914	−	0.0699665i	−0.296624	−	0.954994i	$-0.595861\pi$
$827$	4.85757	−	2.01207i	0.168914	−	0.0699665i	0.465538	+	0.885028i	$0.345861\pi$
$828$		0			0
$829$	16.4173	−	39.6350i	0.570198	−	1.37658i	−0.331188	−	0.943565i	$-0.607450\pi$
$829$	16.4173	−	39.6350i	0.570198	−	1.37658i	0.901387	−	0.433015i	$-0.142550\pi$
$830$	−0.406102	−	0.0619358i	−0.0140960	−	0.00214982i
$831$		0			0
$832$	−1.43080	−	5.16949i	−0.0496040	−	0.179220i
$833$	2.95130			0.102257
$834$		0			0
$835$	0.0821614	−	0.198355i	0.00284331	−	0.00686436i
$836$	13.7149	−	43.9172i	0.474339	−	1.51891i
$837$		0			0
$838$	−23.1238	+	38.2248i	−0.798799	+	1.32045i
$839$	6.03752	−	6.03752i	0.208438	−	0.208438i	−0.595165	−	0.803603i	$-0.702913\pi$
$839$	6.03752	−	6.03752i	0.208438	−	0.208438i	0.803603	+	0.595165i	$0.202913\pi$
$840$		0			0
$841$	−2.09020	−	2.09020i	−0.0720760	−	0.0720760i
$842$	−14.3722	+	3.53773i	−0.495299	+	0.121918i
$843$		0			0
$844$	9.92632	+	8.28294i	0.341678	+	0.285110i
$845$	−0.227455	−	0.0942151i	−0.00782470	−	0.00324110i
$846$		0			0
$847$			7.91649i			0.272014i
$848$	−3.98345	+	18.4459i	−0.136792	+	0.633434i
$849$		0			0
$850$	−7.88248	−	10.7195i	−0.270367	−	0.367677i
$851$	−19.2619	−	7.97853i	−0.660289	−	0.273500i
$852$		0			0
$853$	−12.4550	−	30.0690i	−0.426451	−	1.02954i	−0.980404	−	0.196996i	$-0.936881\pi$
$853$	−12.4550	−	30.0690i	−0.426451	−	1.02954i	0.553953	−	0.832548i	$-0.313119\pi$
$854$	0.365993	+	1.48687i	0.0125240	+	0.0508795i
$855$		0			0
$856$	1.37602	−	22.4044i	0.0470315	−	0.765765i
$857$	−31.9567	+	31.9567i	−1.09162	+	1.09162i	−0.0962632	+	0.995356i	$0.530689\pi$
$857$	−31.9567	+	31.9567i	−1.09162	+	1.09162i	−0.995356	+	0.0962632i	$0.969311\pi$
$858$		0			0
$859$	−38.5141	+	15.9531i	−1.31409	+	0.544312i	−0.926074	−	0.377343i	$-0.876838\pi$
$859$	−38.5141	+	15.9531i	−1.31409	+	0.544312i	−0.388011	+	0.921655i	$0.626838\pi$
$860$	−0.0707938	−	0.135089i	−0.00241405	−	0.00460649i
$861$		0			0
$862$	5.61415	−	36.8110i	0.191219	−	1.25379i
$863$	27.5858			0.939033			0.469516	−	0.882924i	$-0.344428\pi$
$863$	27.5858			0.939033			0.469516	+	0.882924i	$0.344428\pi$
$864$		0			0
$865$	0.158747			0.00539758
$866$	−2.86800	+	18.8050i	−0.0974587	+	0.639020i
$867$		0			0
$868$	−34.1069	+	17.8738i	−1.15766	+	0.606678i
$869$	6.09919	−	2.52637i	0.206901	−	0.0857011i
$870$		0			0
$871$	−0.327200	+	0.327200i	−0.0110868	+	0.0110868i
$872$	−18.9655	−	21.4476i	−0.642252	−	0.726306i
$873$		0			0
$874$	−10.1356	−	41.1763i	−0.342841	−	1.39281i
$875$	−0.174949	−	0.422365i	−0.00591437	−	0.0142785i
$876$		0			0
$877$	14.1124	+	5.84554i	0.476541	+	0.197390i	0.608008	−	0.793931i	$-0.291969\pi$
$877$	14.1124	+	5.84554i	0.476541	+	0.197390i	−0.131467	+	0.991321i	$0.541969\pi$
$878$	20.8716	+	28.3836i	0.704381	+	0.957900i
$879$		0			0
$880$	−0.0387377	−	0.212866i	−0.00130585	−	0.00717571i
$881$			38.6400i			1.30181i	0.759157	+	0.650907i	$0.225611\pi$
$881$			38.6400i			1.30181i	−0.759157	+	0.650907i	$0.774389\pi$
$882$		0			0
$883$	−8.72441	−	3.61377i	−0.293600	−	0.121613i	0.231022	−	0.972949i	$-0.425793\pi$
$883$	−8.72441	−	3.61377i	−0.293600	−	0.121613i	−0.524621	+	0.851336i	$0.675793\pi$
$884$	−1.61677	+	1.93755i	−0.0543778	+	0.0651667i
$885$		0			0
$886$	22.0845	−	5.43611i	0.741942	−	0.182630i
$887$	8.66180	+	8.66180i	0.290835	+	0.290835i	0.837410	−	0.546575i	$-0.184069\pi$
$887$	8.66180	+	8.66180i	0.290835	+	0.290835i	−0.546575	+	0.837410i	$0.684069\pi$
$888$		0			0
$889$	−14.1638	+	14.1638i	−0.475037	+	0.475037i
$890$	0.0579001	−	0.0957118i	0.00194082	−	0.00320827i
$891$		0			0
$892$	16.2115	+	5.06267i	0.542800	+	0.169511i
$893$	−23.8889	+	57.6729i	−0.799412	+	1.92995i
$894$		0			0
$895$	−0.387402			−0.0129494
$896$	25.3839	+	7.13541i	0.848018	+	0.238377i
$897$		0			0
$898$	−47.1046	−	7.18405i	−1.57190	−	0.239735i
$899$	−17.8711	+	43.1447i	−0.596036	+	1.43896i
$900$		0			0
$901$	8.20236	−	3.39753i	0.273260	−	0.113188i
$902$	−8.56465	+	14.1578i	−0.285172	+	0.471403i
$903$		0			0
$904$	7.49369	−	15.3544i	0.249237	−	0.510681i
$905$	−0.288929	−	0.288929i	−0.00960432	−	0.00960432i
$906$		0			0
$907$	−8.42556	−	20.3411i	−0.279766	−	0.675415i	0.720063	−	0.693909i	$-0.244113\pi$
$907$	−8.42556	−	20.3411i	−0.279766	−	0.675415i	−0.999829	+	0.0184938i	$0.994113\pi$
$908$	−3.96343	+	4.74980i	−0.131531	+	0.157628i
$909$		0			0
$910$	−0.0349243	+	0.0256812i	−0.00115773	+	0.000851324i
$911$		−	17.8498i		−	0.591390i	−0.955282	−	0.295695i	$-0.904449\pi$
$911$		−	17.8498i		−	0.591390i	0.955282	−	0.295695i	$-0.0955513\pi$
$912$		0			0
$913$		−	40.8312i		−	1.35131i
$914$	−26.3223	−	35.7961i	−0.870663	−	1.18403i
$915$		0			0
$916$	−46.6565	+	4.21074i	−1.54157	+	0.139127i
$917$	11.7035	+	28.2548i	0.386484	+	0.933054i
$918$		0			0
$919$	−24.9064	−	24.9064i	−0.821585	−	0.821585i	0.164750	−	0.986335i	$-0.447318\pi$
$919$	−24.9064	−	24.9064i	−0.821585	−	0.821585i	−0.986335	+	0.164750i	$0.947318\pi$
$920$	−0.132099	−	0.149388i	−0.00435518	−	0.00492516i
$921$		0			0
$922$	36.3375	+	21.9821i	1.19671	+	0.723941i
$923$	9.59211	−	3.97318i	0.315728	−	0.130779i
$924$		0			0
$925$	11.0985	−	26.7942i	0.364917	−	0.880988i
$926$	5.58985	−	36.6517i	0.183694	−	1.20445i
$927$		0			0
$928$	29.1809	−	13.0792i	0.957911	−	0.429345i
$929$	31.2255			1.02447			0.512237	−	0.858844i	$-0.328817\pi$
$929$	31.2255			1.02447			0.512237	+	0.858844i	$0.328817\pi$
$930$		0			0
$931$	−5.00702	+	12.0880i	−0.164098	+	0.396169i
$932$	−22.2067	−	42.3749i	−0.727406	−	1.38804i
$933$		0			0
$934$	−9.42478	−	5.70145i	−0.308388	−	0.186557i
$935$	−0.0719767	+	0.0719767i	−0.00235389	+	0.00235389i
$936$		0			0
$937$	38.3410	+	38.3410i	1.25255	+	1.25255i	0.954575	+	0.297970i	$0.0963096\pi$
$937$	38.3410	+	38.3410i	1.25255	+	1.25255i	0.297970	+	0.954575i	$0.403690\pi$
$938$	−0.543692	−	2.20878i	−0.0177522	−	0.0721191i
$939$		0			0
$940$	0.0263865	+	0.292371i	0.000860631	+	0.00953610i
$941$	36.2709	+	15.0239i	1.18240	+	0.489765i	0.885272	−	0.465074i	$-0.153972\pi$
$941$	36.2709	+	15.0239i	1.18240	+	0.489765i	0.297125	+	0.954839i	$0.403972\pi$
$942$		0			0
$943$			15.2508i			0.496635i
$944$	15.3591	+	3.31685i	0.499897	+	0.107954i
$945$		0			0
$946$	12.2127	−	8.98049i	0.397070	−	0.291981i
$947$	47.9330	+	19.8545i	1.55761	+	0.645185i	0.984673	−	0.174411i	$-0.0558021\pi$
$947$	47.9330	+	19.8545i	1.55761	+	0.645185i	0.572942	+	0.819596i	$0.305802\pi$
$948$		0			0
$949$	−0.490189	−	1.18342i	−0.0159122	−	0.0384155i
$950$	57.2782	−	14.0991i	1.85835	−	0.457435i
$951$		0			0
$952$	−4.03572	−	11.7303i	−0.130798	−	0.380180i
$953$	32.1529	−	32.1529i	1.04154	−	1.04154i	0.0424364	−	0.999099i	$-0.486488\pi$
$953$	32.1529	−	32.1529i	1.04154	−	1.04154i	0.999099	−	0.0424364i	$-0.0135120\pi$
$954$		0			0
$955$	−0.205153	+	0.0849772i	−0.00663860	+	0.00274980i
$956$	−4.63352	+	14.8373i	−0.149859	+	0.479872i
$957$		0			0
$958$	−36.2244	−	5.52468i	−1.17036	−	0.178494i
$959$	23.6343			0.763193
$960$		0			0
$961$	37.2452			1.20146
$962$	−5.43747	−	0.829284i	−0.175311	−	0.0267372i
$963$		0			0
$964$	8.91309	−	28.5411i	0.287071	−	0.919248i
$965$	−0.150541	+	0.0623562i	−0.00484609	+	0.00200732i
$966$		0			0
$967$	−14.1431	+	14.1431i	−0.454811	+	0.454811i	−0.896948	−	0.442136i	$-0.854221\pi$
$967$	−14.1431	+	14.1431i	−0.454811	+	0.454811i	0.442136	+	0.896948i	$0.354221\pi$
$968$	−9.08485	+	3.12558i	−0.291998	+	0.100460i
$969$		0			0
$970$	0.333018	−	0.0819727i	0.0106926	−	0.00263198i
$971$	13.6967	+	33.0668i	0.439549	+	1.06116i	0.976105	+	0.217300i	$0.0697249\pi$
$971$	13.6967	+	33.0668i	0.439549	+	1.06116i	−0.536556	+	0.843864i	$0.680275\pi$
$972$		0			0
$973$	−20.0193	−	8.29226i	−0.641789	−	0.265838i
$974$	28.6740	−	21.0851i	0.918774	−	0.675610i
$975$		0			0
$976$	−1.56180	+	1.00705i	−0.0499921	+	0.0322349i
$977$			57.3860i			1.83594i	0.396649	+	0.917970i	$0.370173\pi$
$977$			57.3860i			1.83594i	−0.396649	+	0.917970i	$0.629827\pi$
$978$		0			0
$979$	10.2722	+	4.25487i	0.328300	+	0.135986i
$980$	0.00553049	+	0.0612798i	0.000176665	+	0.00195751i
$981$		0			0
$982$	13.5819	+	55.1773i	0.433417	+	1.76078i
$983$	11.2266	+	11.2266i	0.358072	+	0.358072i	0.863102	−	0.505030i	$-0.168519\pi$
$983$	11.2266	+	11.2266i	0.358072	+	0.358072i	−0.505030	+	0.863102i	$0.668519\pi$
$984$		0			0
$985$	−0.0849326	+	0.0849326i	−0.00270618	+	0.00270618i
$986$	−12.8724	−	7.78706i	−0.409940	−	0.247990i
$987$		0			0
$988$	−5.19292	−	9.90913i	−0.165209	−	0.315251i
$989$	5.34681	−	12.9083i	0.170019	−	0.410461i
$990$		0			0
$991$	11.5414			0.366624			0.183312	−	0.983055i	$-0.441318\pi$
$991$	11.5414			0.366624			0.183312	+	0.983055i	$0.441318\pi$
$992$	−33.9778	−	32.0836i	−1.07880	−	1.01866i
$993$		0			0
$994$	−7.69501	+	50.4548i	−0.244071	+	1.60033i
$995$	0.0564249	−	0.136222i	0.00178879	−	0.00431852i
$996$		0			0
$997$	40.9760	−	16.9728i	1.29772	−	0.537535i	0.376445	−	0.926439i	$-0.377146\pi$
$997$	40.9760	−	16.9728i	1.29772	−	0.537535i	0.921278	+	0.388904i	$0.127146\pi$
$998$	29.9076	+	18.0924i	0.946709	+	0.572705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.1	✓	128
3.2	odd	2	inner	864.2.v.a.109.32	yes	128
32.5	even	8	inner	864.2.v.a.325.1	yes	128
96.5	odd	8	inner	864.2.v.a.325.32	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.1	✓	128	1.1	even	1	trivial
864.2.v.a.109.32	yes	128	3.2	odd	2	inner
864.2.v.a.325.1	yes	128	32.5	even	8	inner
864.2.v.a.325.32	yes	128	96.5	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39805 - 0.213220i) q^{2} +(1.90907 + 0.596184i) q^{4} +(0.0181233 - 0.00750691i) q^{5} +(-1.64798 + 1.64798i) q^{7} +(-2.54186 - 1.24055i) q^{8} +O(q^{10})\)	\(q+(-1.39805 - 0.213220i) q^{2} +(1.90907 + 0.596184i) q^{4} +(0.0181233 - 0.00750691i) q^{5} +(-1.64798 + 1.64798i) q^{7} +(-2.54186 - 1.24055i) q^{8} +(-0.0269378 + 0.00663076i) q^{10} +(-1.05521 - 2.54750i) q^{11} +(-0.619443 - 0.256582i) q^{13} +(2.65534 - 1.95258i) q^{14} +(3.28913 + 2.27632i) q^{16} -1.88186i q^{17} +(7.70774 + 3.19265i) q^{19} +(0.0390742 - 0.00352644i) q^{20} +(0.932055 + 3.78652i) q^{22} +(2.54144 + 2.54144i) q^{23} +(-3.53526 + 3.53526i) q^{25} +(0.811303 + 0.490791i) q^{26} +(-4.12863 + 2.16362i) q^{28} +(-2.16330 + 5.22266i) q^{29} +8.26107 q^{31} +(-4.11300 - 3.88371i) q^{32} +(-0.401250 + 2.63092i) q^{34} +(-0.0174956 + 0.0422381i) q^{35} +(-5.35925 + 2.21987i) q^{37} +(-10.0951 - 6.10693i) q^{38} +(-0.0553795 - 0.00340128i) q^{40} +(3.00044 + 3.00044i) q^{41} +(-1.48765 - 3.59150i) q^{43} +(-0.495695 - 5.49247i) q^{44} +(-3.01116 - 4.09494i) q^{46} +7.48247i q^{47} +1.56829i q^{49} +(5.69625 - 4.18868i) q^{50} +(-1.02959 - 0.859136i) q^{52} +(1.80541 + 4.35866i) q^{53} +(-0.0382477 - 0.0382477i) q^{55} +(6.23334 - 2.14454i) q^{56} +(4.13797 - 6.84027i) q^{58} +(3.62927 - 1.50329i) q^{59} +(-0.177788 + 0.429218i) q^{61} +(-11.5494 - 1.76143i) q^{62} +(4.92209 + 6.30659i) q^{64} -0.0131525 q^{65} +(0.264108 - 0.637614i) q^{67} +(1.12193 - 3.59260i) q^{68} +(0.0334657 - 0.0553205i) q^{70} +(-10.9496 + 10.9496i) q^{71} +(1.35090 + 1.35090i) q^{73} +(7.96581 - 1.96079i) q^{74} +(12.8112 + 10.6902i) q^{76} +(5.93722 + 2.45928i) q^{77} +2.39418i q^{79} +(0.0766979 + 0.0165632i) q^{80} +(-3.55500 - 4.83450i) q^{82} +(13.6807 + 5.66672i) q^{83} +(-0.0141269 - 0.0341054i) q^{85} +(1.31402 + 5.33829i) q^{86} +(-0.478101 + 7.78443i) q^{88} +(-2.85123 + 2.85123i) q^{89} +(1.44368 - 0.597990i) q^{91} +(3.33663 + 6.36696i) q^{92} +(1.59541 - 10.4608i) q^{94} +0.163656 q^{95} -12.3625 q^{97} +(0.334392 - 2.19255i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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