LMFDB - Embedded newform 648.2.t.a.613.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			613.4
Character	$\chi$	$=$	648.613
Dual form			648.2.t.a.37.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30848 + 0.536554i) q^{2} +(1.42422 - 1.40414i) q^{4} +(-1.34230 + 3.68793i) q^{5} +(-0.499959 + 2.83541i) q^{7} +(-1.11016 + 2.60145i) q^{8} +(-0.222412 - 5.54579i) q^{10} +(0.996019 + 2.73654i) q^{11} +(2.55767 + 3.04812i) q^{13} +(-0.867166 - 3.97832i) q^{14} +(0.0567986 - 3.99960i) q^{16} +(-2.48745 - 4.30839i) q^{17} +(-1.78004 - 1.02771i) q^{19} +(3.26664 + 7.13719i) q^{20} +(-2.77157 - 3.04628i) q^{22} +(-0.165146 - 0.936587i) q^{23} +(-7.96887 - 6.68667i) q^{25} +(-4.98214 - 2.61606i) q^{26} +(3.26925 + 4.74025i) q^{28} +(5.18495 - 6.17919i) q^{29} +(0.331534 + 1.88022i) q^{31} +(2.07168 + 5.26385i) q^{32} +(5.56646 + 4.30278i) q^{34} +(-9.78570 - 5.64977i) q^{35} +(-8.31066 + 4.79816i) q^{37} +(2.88056 + 0.389641i) q^{38} +(-8.10381 - 7.58612i) q^{40} +(-0.581151 + 0.487644i) q^{41} +(2.14125 + 5.88303i) q^{43} +(5.26103 + 2.49888i) q^{44} +(0.718619 + 1.13689i) q^{46} +(-0.932102 + 5.28621i) q^{47} +(-1.21172 - 0.441031i) q^{49} +(14.0148 + 4.47362i) q^{50} +(7.92266 + 0.749861i) q^{52} -3.54207i q^{53} -11.4291 q^{55} +(-6.82113 - 4.44837i) q^{56} +(-3.46892 + 10.8673i) q^{58} +(-2.13303 + 5.86045i) q^{59} +(3.22446 + 0.568559i) q^{61} +(-1.44265 - 2.28234i) q^{62} +(-5.53509 - 5.77605i) q^{64} +(-14.6744 + 5.34105i) q^{65} +(-4.40861 - 5.25398i) q^{67} +(-9.59225 - 2.64337i) q^{68} +(15.8358 + 2.14204i) q^{70} +(-3.83709 - 6.64603i) q^{71} +(3.46824 - 6.00718i) q^{73} +(8.29983 - 10.7374i) q^{74} +(-3.97821 + 1.03574i) q^{76} +(-8.25717 + 1.45596i) q^{77} +(0.205269 + 0.172241i) q^{79} +(14.6740 + 5.57812i) q^{80} +(0.498775 - 0.949889i) q^{82} +(-7.91149 + 9.42855i) q^{83} +(19.2280 - 3.39041i) q^{85} +(-5.95834 - 6.54891i) q^{86} +(-8.22471 - 0.446904i) q^{88} +(4.11349 - 7.12477i) q^{89} +(-9.92138 + 5.72811i) q^{91} +(-1.55030 - 1.10202i) q^{92} +(-1.61671 - 7.41700i) q^{94} +(6.17946 - 5.18518i) q^{95} +(5.06123 - 1.84214i) q^{97} +(1.82215 - 0.0730766i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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 $

$2$	−1.30848	+	0.536554i	−0.925232	+	0.379401i
$2$	−1.30848	+	0.536554i	−0.925232	+	0.379401i
$3$		0			0
$3$		0			0
$4$	1.42422	−	1.40414i	0.712109	−	0.702069i
$5$	−1.34230	+	3.68793i	−0.600294	+	1.64929i	0.150386	+	0.988627i	$0.451948\pi$
$5$	−1.34230	+	3.68793i	−0.600294	+	1.64929i	−0.750679	+	0.660667i	$0.770274\pi$
$6$		0			0
$7$	−0.499959	+	2.83541i	−0.188967	+	1.07168i	0.731786	+	0.681535i	$0.238687\pi$
$7$	−0.499959	+	2.83541i	−0.188967	+	1.07168i	−0.920752	+	0.390148i	$0.872424\pi$
$8$	−1.11016	+	2.60145i	−0.392501	+	0.919752i
$9$		0			0
$10$	−0.222412	−	5.54579i	−0.0703329	−	1.75373i
$11$	0.996019	+	2.73654i	0.300311	+	0.825098i	0.994446	+	0.105252i	$0.0335650\pi$
$11$	0.996019	+	2.73654i	0.300311	+	0.825098i	−0.694135	+	0.719845i	$0.744213\pi$
$12$		0			0
$13$	2.55767	+	3.04812i	0.709371	+	0.845396i	0.993552	−	0.113375i	$-0.0361661\pi$
$13$	2.55767	+	3.04812i	0.709371	+	0.845396i	−0.284181	+	0.958771i	$0.591722\pi$
$14$	−0.867166	−	3.97832i	−0.231760	−	1.06325i
$15$		0			0
$16$	0.0567986	−	3.99960i	0.0141996	−	0.999899i
$17$	−2.48745	−	4.30839i	−0.603296	−	1.04494i	−0.992318	−	0.123711i	$-0.960520\pi$
$17$	−2.48745	−	4.30839i	−0.603296	−	1.04494i	0.389022	−	0.921228i	$-0.372813\pi$
$18$		0			0
$19$	−1.78004	−	1.02771i	−0.408369	−	0.235772i	0.281720	−	0.959497i	$-0.409095\pi$
$19$	−1.78004	−	1.02771i	−0.408369	−	0.235772i	−0.690089	+	0.723725i	$0.742429\pi$
$20$	3.26664	+	7.13719i	0.730442	+	1.59593i
$21$		0			0
$22$	−2.77157	−	3.04628i	−0.590900	−	0.649469i
$23$	−0.165146	−	0.936587i	−0.0344352	−	0.195292i	0.962737	−	0.270438i	$-0.0871687\pi$
$23$	−0.165146	−	0.936587i	−0.0344352	−	0.195292i	−0.997173	+	0.0751465i	$0.976058\pi$
$24$		0			0
$25$	−7.96887	−	6.68667i	−1.59377	−	1.33733i
$26$	−4.98214	−	2.61606i	−0.977077	−	0.513051i
$27$		0			0
$28$	3.26925	+	4.74025i	0.617830	+	0.895823i
$29$	5.18495	−	6.17919i	0.962821	−	1.14745i	−0.0261974	−	0.999657i	$-0.508340\pi$
$29$	5.18495	−	6.17919i	0.962821	−	1.14745i	0.989019	−	0.147789i	$-0.0472157\pi$
$30$		0			0
$31$	0.331534	+	1.88022i	0.0595453	+	0.337698i	0.999998	−	0.00222778i	$-0.000709125\pi$
$31$	0.331534	+	1.88022i	0.0595453	+	0.337698i	−0.940452	+	0.339926i	$0.889598\pi$
$32$	2.07168	+	5.26385i	0.366225	+	0.930526i
$33$		0			0
$34$	5.56646	+	4.30278i	0.954640	+	0.737920i
$35$	−9.78570	−	5.64977i	−1.65408	−	0.954986i
$36$		0			0
$37$	−8.31066	+	4.79816i	−1.36626	+	0.788813i	−0.990449	−	0.137881i	$-0.955971\pi$
$37$	−8.31066	+	4.79816i	−1.36626	+	0.788813i	−0.375816	+	0.926694i	$0.622637\pi$
$38$	2.88056	+	0.389641i	0.467289	+	0.0632082i
$39$		0			0
$40$	−8.10381	−	7.58612i	−1.28132	−	1.19947i
$41$	−0.581151	+	0.487644i	−0.0907605	+	0.0761571i	−0.687039	−	0.726621i	$-0.741090\pi$
$41$	−0.581151	+	0.487644i	−0.0907605	+	0.0761571i	0.596278	+	0.802778i	$0.296645\pi$
$42$		0			0
$43$	2.14125	+	5.88303i	0.326537	+	0.897154i	0.988981	+	0.148042i	$0.0472972\pi$
$43$	2.14125	+	5.88303i	0.326537	+	0.897154i	−0.662444	+	0.749112i	$0.730481\pi$
$44$	5.26103	+	2.49888i	0.793129	+	0.376721i
$45$		0			0
$46$	0.718619	+	1.13689i	0.105955	+	0.167626i
$47$	−0.932102	+	5.28621i	−0.135961	+	0.771073i	0.838225	+	0.545325i	$0.183594\pi$
$47$	−0.932102	+	5.28621i	−0.135961	+	0.771073i	−0.974186	+	0.225748i	$0.927517\pi$
$48$		0			0
$49$	−1.21172	−	0.441031i	−0.173103	−	0.0630044i
$50$	14.0148	+	4.47362i	1.98200	+	0.632666i
$51$		0			0
$52$	7.92266	+	0.749861i	1.09868	+	0.103987i
$53$		−	3.54207i		−	0.486541i	−0.969959	−	0.243270i	$-0.921780\pi$
$53$		−	3.54207i		−	0.486541i	0.969959	−	0.243270i	$-0.0782202\pi$
$54$		0			0
$55$	−11.4291			−1.54110
$56$	−6.82113	−	4.44837i	−0.911513	−	0.594439i
$57$		0			0
$58$	−3.46892	+	10.8673i	−0.455491	+	1.42695i
$59$	−2.13303	+	5.86045i	−0.277697	+	0.762966i	0.719926	+	0.694051i	$0.244176\pi$
$59$	−2.13303	+	5.86045i	−0.277697	+	0.762966i	−0.997623	+	0.0689146i	$0.978046\pi$
$60$		0			0
$61$	3.22446	+	0.568559i	0.412849	+	0.0727965i	0.376215	−	0.926532i	$-0.377225\pi$
$61$	3.22446	+	0.568559i	0.412849	+	0.0727965i	0.0366341	+	0.999329i	$0.488336\pi$
$62$	−1.44265	−	2.28234i	−0.183216	−	0.289858i
$63$		0			0
$64$	−5.53509	−	5.77605i	−0.691886	−	0.722007i
$65$	−14.6744	+	5.34105i	−1.82014	+	0.662476i
$66$		0			0
$67$	−4.40861	−	5.25398i	−0.538598	−	0.641876i	0.426275	−	0.904594i	$-0.359826\pi$
$67$	−4.40861	−	5.25398i	−0.538598	−	0.641876i	−0.964873	+	0.262718i	$0.915381\pi$
$68$	−9.59225	−	2.64337i	−1.16323	−	0.320556i
$69$		0			0
$70$	15.8358	+	2.14204i	1.89274	+	0.256022i
$71$	−3.83709	−	6.64603i	−0.455378	−	0.788738i	0.543332	−	0.839518i	$-0.317163\pi$
$71$	−3.83709	−	6.64603i	−0.455378	−	0.788738i	−0.998710	+	0.0507798i	$0.983829\pi$
$72$		0			0
$73$	3.46824	−	6.00718i	0.405927	−	0.703087i	−0.588502	−	0.808496i	$-0.700282\pi$
$73$	3.46824	−	6.00718i	0.405927	−	0.703087i	0.994429	+	0.105409i	$0.0336153\pi$
$74$	8.29983	−	10.7374i	0.964835	−	1.24820i
$75$		0			0
$76$	−3.97821	+	1.03574i	−0.456332	+	0.118808i
$77$	−8.25717	+	1.45596i	−0.940992	+	0.165922i
$78$		0			0
$79$	0.205269	+	0.172241i	0.0230945	+	0.0193786i	0.654262	−	0.756268i	$-0.272979\pi$
$79$	0.205269	+	0.172241i	0.0230945	+	0.0193786i	−0.631167	+	0.775647i	$0.717424\pi$
$80$	14.6740	+	5.57812i	1.64060	+	0.623653i
$81$		0			0
$82$	0.498775	−	0.949889i	0.0550805	−	0.104898i
$83$	−7.91149	+	9.42855i	−0.868399	+	1.03492i	0.130655	+	0.991428i	$0.458292\pi$
$83$	−7.91149	+	9.42855i	−0.868399	+	1.03492i	−0.999054	+	0.0434896i	$0.986152\pi$
$84$		0			0
$85$	19.2280	−	3.39041i	2.08557	−	0.367742i
$86$	−5.95834	−	6.54891i	−0.642504	−	0.706187i
$87$		0			0
$88$	−8.22471	−	0.446904i	−0.876757	−	0.0476401i
$89$	4.11349	−	7.12477i	0.436029	−	0.755224i	−0.561350	−	0.827578i	$-0.689718\pi$
$89$	4.11349	−	7.12477i	0.436029	−	0.755224i	0.997379	+	0.0723541i	$0.0230512\pi$
$90$		0			0
$91$	−9.92138	+	5.72811i	−1.04004	+	0.600469i
$92$	−1.55030	−	1.10202i	−0.161630	−	0.114893i
$93$		0			0
$94$	−1.61671	−	7.41700i	−0.166751	−	0.765005i
$95$	6.17946	−	5.18518i	0.633999	−	0.531988i
$96$		0			0
$97$	5.06123	−	1.84214i	0.513891	−	0.187041i	−0.0720406	−	0.997402i	$-0.522951\pi$
$97$	5.06123	−	1.84214i	0.513891	−	0.187041i	0.585931	+	0.810361i	$0.300729\pi$
$98$	1.82215	−	0.0730766i	0.184065	−	0.00738186i
$99$		0			0
$100$	−20.7384	+	1.66609i	−2.07384	+	0.166609i
$101$	−3.98336	−	0.702375i	−0.396360	−	0.0698889i	−0.0280840	−	0.999606i	$-0.508941\pi$
$101$	−3.98336	−	0.702375i	−0.396360	−	0.0698889i	−0.368276	+	0.929717i	$0.620052\pi$
$102$		0			0
$103$	1.07241	+	0.390325i	0.105668	+	0.0384599i	0.394313	−	0.918976i	$-0.370983\pi$
$103$	1.07241	+	0.390325i	0.105668	+	0.0384599i	−0.288645	+	0.957436i	$0.593205\pi$
$104$	−10.7690	+	3.26976i	−1.05598	+	0.320627i
$105$		0			0
$106$	1.90051	+	4.63471i	0.184594	+	0.450163i
$107$			4.87553i			0.471335i	0.971834	+	0.235667i	$0.0757276\pi$
$107$			4.87553i			0.471335i	−0.971834	+	0.235667i	$0.924272\pi$
$108$		0			0
$109$		−	2.52010i		−	0.241382i	−0.992690	−	0.120691i	$-0.961489\pi$
$109$		−	2.52010i		−	0.241382i	0.992690	−	0.120691i	$-0.0385111\pi$
$110$	14.9547	−	6.13235i	1.42588	−	0.584697i
$111$		0			0
$112$	11.3121	+	2.16068i	1.06889	+	0.204165i
$113$	6.79620	+	2.47361i	0.639332	+	0.232698i	0.641288	−	0.767300i	$-0.278400\pi$
$113$	6.79620	+	2.47361i	0.639332	+	0.232698i	−0.00195583	+	0.999998i	$0.500623\pi$
$114$		0			0
$115$	3.67575	+	0.648133i	0.342765	+	0.0604387i
$116$	−1.29192	−	16.0809i	−0.119951	−	1.49307i
$117$		0			0
$118$	−0.353432	−	8.81275i	−0.0325361	−	0.811279i
$119$	13.4597	−	4.89892i	1.23385	−	0.449083i
$120$		0			0
$121$	1.92989	−	1.61937i	0.175445	−	0.147216i
$122$	−4.52419	+	0.986151i	−0.409601	+	0.0892819i
$123$		0			0
$124$	3.11227	+	2.21233i	0.279490	+	0.198673i
$125$	18.3625	−	10.6016i	1.64239	−	0.948236i
$126$		0			0
$127$	−2.38507	+	4.13106i	−0.211641	+	0.366573i	−0.952228	−	0.305387i	$-0.901214\pi$
$127$	−2.38507	+	4.13106i	−0.211641	+	0.366573i	0.740587	+	0.671960i	$0.234547\pi$
$128$	10.3417	+	4.58795i	0.914086	+	0.405522i
$129$		0			0
$130$	16.3354	−	14.8623i	1.43271	−	1.30351i
$131$	−3.45051	+	0.608417i	−0.301472	+	0.0531577i	−0.322338	−	0.946625i	$-0.604469\pi$
$131$	−3.45051	+	0.608417i	−0.301472	+	0.0531577i	0.0208660	+	0.999782i	$0.493358\pi$
$132$		0			0
$133$	3.80391	−	4.53333i	0.329841	−	0.393089i
$134$	8.58761	+	4.50925i	0.741857	+	0.389540i
$135$		0			0
$136$	13.9695	−	1.68798i	1.19788	−	0.144743i
$137$	12.6574	+	10.6208i	1.08140	+	0.907400i	0.996036	−	0.0889501i	$-0.0283512\pi$
$137$	12.6574	+	10.6208i	1.08140	+	0.907400i	0.0853611	+	0.996350i	$0.472796\pi$
$138$		0			0
$139$	−19.5648	+	3.44981i	−1.65947	+	0.292609i	−0.923268	−	0.384157i	$-0.874492\pi$
$139$	−19.5648	+	3.44981i	−1.65947	+	0.292609i	−0.736199	+	0.676765i	$0.763381\pi$
$140$	−21.8700	+	5.69394i	−1.84836	+	0.481226i
$141$		0			0
$142$	8.58669	+	6.63736i	0.720579	+	0.556995i
$143$	−5.79380	+	10.0352i	−0.484502	+	0.839182i
$144$		0			0
$145$	15.8287	+	27.4161i	1.31450	+	2.27678i
$146$	−1.31494	+	9.72115i	−0.108825	+	0.804528i
$147$		0			0
$148$	−5.09892	+	18.5029i	−0.419129	+	1.52093i
$149$	7.39950	+	8.81838i	0.606190	+	0.722429i	0.978630	−	0.205627i	$-0.0659233\pi$
$149$	7.39950	+	8.81838i	0.606190	+	0.722429i	−0.372440	+	0.928056i	$0.621479\pi$
$150$		0			0
$151$	−3.42462	+	1.24646i	−0.278692	+	0.101436i	−0.477585	−	0.878586i	$-0.658488\pi$
$151$	−3.42462	+	1.24646i	−0.278692	+	0.101436i	0.198893	+	0.980021i	$0.436265\pi$
$152$	4.64966	−	3.48977i	0.377137	−	0.283058i
$153$		0			0
$154$	10.0231	−	6.33551i	0.807685	−	0.510530i
$155$	−7.37916	−	1.30114i	−0.592708	−	0.104510i
$156$		0			0
$157$	−5.00630	+	13.7547i	−0.399546	+	1.09774i	0.562960	+	0.826484i	$0.309662\pi$
$157$	−5.00630	+	13.7547i	−0.399546	+	1.09774i	−0.962506	+	0.271259i	$0.912560\pi$
$158$	−0.361005	−	0.115235i	−0.0287201	−	0.00916762i
$159$		0			0
$160$	−22.1935	+	0.574566i	−1.75455	+	0.0454234i
$161$	2.73817			0.215798
$162$		0			0
$163$			5.93891i			0.465171i	0.972576	+	0.232586i	$0.0747186\pi$
$163$			5.93891i			0.465171i	−0.972576	+	0.232586i	$0.925281\pi$
$164$	−0.142968	+	1.51053i	−0.0111639	+	0.117952i
$165$		0			0
$166$	5.29307	−	16.5820i	0.410822	−	1.28701i
$167$	18.7096	+	6.80974i	1.44779	+	0.526953i	0.941974	−	0.335687i	$-0.108968\pi$
$167$	18.7096	+	6.80974i	1.44779	+	0.526953i	0.505818	+	0.862640i	$0.331191\pi$
$168$		0			0
$169$	−0.491897	+	2.78968i	−0.0378382	+	0.214591i
$170$	−23.3402	+	14.7531i	−1.79011	+	1.13151i
$171$		0			0
$172$	11.3102	+	5.37212i	0.862394	+	0.409620i
$173$	3.76876	+	10.3546i	0.286534	+	0.787245i	0.996545	+	0.0830547i	$0.0264676\pi$
$173$	3.76876	+	10.3546i	0.286534	+	0.787245i	−0.710011	+	0.704190i	$0.751310\pi$
$174$		0			0
$175$	22.9435	−	19.2519i	1.73437	−	1.45531i
$176$	11.0016	−	3.82824i	0.829279	−	0.288565i
$177$		0			0
$178$	−1.55957	+	11.5297i	−0.116895	+	0.864188i
$179$	3.66363	−	2.11520i	0.273832	−	0.158097i	−0.356796	−	0.934182i	$-0.616131\pi$
$179$	3.66363	−	2.11520i	0.273832	−	0.158097i	0.630628	+	0.776085i	$0.282797\pi$
$180$		0			0
$181$	16.4676	+	9.50759i	1.22403	+	0.706694i	0.965775	−	0.259383i	$-0.0835192\pi$
$181$	16.4676	+	9.50759i	1.22403	+	0.706694i	0.258255	+	0.966077i	$0.416853\pi$
$182$	9.90845	−	12.8185i	0.734463	−	0.950168i
$183$		0			0
$184$	2.61982	+	0.610144i	0.193136	+	0.0449804i
$185$	−6.53992	−	37.0897i	−0.480825	−	2.72689i
$186$		0			0
$187$	9.31254	−	11.0983i	0.681000	−	0.811585i
$188$	6.09505	+	8.83752i	0.444527	+	0.644542i
$189$		0			0
$190$	−5.30354	+	10.1003i	−0.384759	+	0.732753i
$191$	−6.22796	−	5.22588i	−0.450639	−	0.378131i	0.389034	−	0.921224i	$-0.372809\pi$
$191$	−6.22796	−	5.22588i	−0.450639	−	0.378131i	−0.839673	+	0.543092i	$0.817253\pi$
$192$		0			0
$193$	−2.29037	−	12.9893i	−0.164864	−	0.934993i	−0.949204	−	0.314661i	$-0.898109\pi$
$193$	−2.29037	−	12.9893i	−0.164864	−	0.934993i	0.784340	−	0.620332i	$-0.213002\pi$
$194$	−5.63410	+	5.12602i	−0.404505	+	0.368027i
$195$		0			0
$196$	−2.34503	+	1.07330i	−0.167502	+	0.0766643i
$197$	−5.35211	−	3.09004i	−0.381322	−	0.220156i	0.297071	−	0.954855i	$-0.403990\pi$
$197$	−5.35211	−	3.09004i	−0.381322	−	0.220156i	−0.678393	+	0.734699i	$0.737323\pi$
$198$		0			0
$199$	4.43708	+	7.68525i	0.314537	+	0.544793i	0.979339	−	0.202226i	$-0.0648176\pi$
$199$	4.43708	+	7.68525i	0.314537	+	0.544793i	−0.664802	+	0.747019i	$0.731484\pi$
$200$	26.2418	−	13.3073i	1.85557	−	0.940971i
$201$		0			0
$202$	5.58900	−	1.21825i	0.393241	−	0.0857159i
$203$	14.9282	+	17.7908i	1.04776	+	1.24867i
$204$		0			0
$205$	−1.01832	−	2.79781i	−0.0711225	−	0.195407i
$206$	−1.61265	+	0.0646749i	−0.112359	+	0.00450612i
$207$		0			0
$208$	12.3365	−	10.0565i	0.855383	−	0.697295i
$209$	1.03941	−	5.89477i	0.0718972	−	0.407750i
$210$		0			0
$211$	6.04444	−	16.6070i	0.416116	−	1.14327i	−0.537767	−	0.843093i	$-0.680732\pi$
$211$	6.04444	−	16.6070i	0.416116	−	1.14327i	0.953884	−	0.300177i	$-0.0970457\pi$
$212$	−4.97355	−	5.04468i	−0.341585	−	0.346470i
$213$		0			0
$214$	−2.61598	−	6.37951i	−0.178825	−	0.436094i
$215$	−24.5704			−1.67569
$216$		0			0
$217$	−5.49695			−0.373157
$218$	1.35217	+	3.29750i	0.0915807	+	0.223335i
$219$		0			0
$220$	−16.2776	+	16.0481i	−1.09743	+	1.08196i
$221$	6.77040	−	18.6015i	0.455426	−	1.25127i
$222$		0			0
$223$	−4.05080	+	22.9732i	−0.271262	+	1.53840i	0.479330	+	0.877635i	$0.340880\pi$
$223$	−4.05080	+	22.9732i	−0.271262	+	1.53840i	−0.750592	+	0.660767i	$0.770231\pi$
$224$	−15.9609	+	3.24235i	−1.06643	+	0.216639i
$225$		0			0
$226$	−10.2199	+	0.409865i	−0.679817	+	0.0272638i
$227$	−8.48739	−	23.3189i	−0.563328	−	1.54773i	−0.814726	−	0.579846i	$-0.803113\pi$
$227$	−8.48739	−	23.3189i	−0.563328	−	1.54773i	0.251398	−	0.967884i	$-0.419110\pi$
$228$		0			0
$229$	−3.58229	−	4.26921i	−0.236724	−	0.282117i	0.634583	−	0.772855i	$-0.281172\pi$
$229$	−3.58229	−	4.26921i	−0.236724	−	0.282117i	−0.871307	+	0.490738i	$0.836727\pi$
$230$	−5.15738	+	1.12417i	−0.340068	+	0.0741256i
$231$		0			0
$232$	10.3187	+	20.3483i	0.677457	+	1.33593i
$233$	3.32571	+	5.76031i	0.217875	+	0.377370i	0.954158	−	0.299303i	$-0.0967542\pi$
$233$	3.32571	+	5.76031i	0.217875	+	0.377370i	−0.736283	+	0.676673i	$0.763421\pi$
$234$		0			0
$235$	−18.2440	−	10.5332i	−1.19011	−	0.687110i
$236$	5.19097	+	11.3416i	0.337904	+	0.738277i
$237$		0			0
$238$	−14.9831	+	13.6320i	−0.971211	+	0.883629i
$239$	4.54329	+	25.7663i	0.293881	+	1.66668i	0.671717	+	0.740808i	$0.265557\pi$
$239$	4.54329	+	25.7663i	0.293881	+	1.66668i	−0.377836	+	0.925872i	$0.623332\pi$
$240$		0			0
$241$	−19.2391	−	16.1435i	−1.23930	−	1.03989i	−0.997579	−	0.0695464i	$-0.977845\pi$
$241$	−19.2391	−	16.1435i	−1.23930	−	1.03989i	−0.241718	−	0.970347i	$-0.577711\pi$
$242$	−1.65634	+	3.15440i	−0.106473	+	0.202773i
$243$		0			0
$244$	5.39067	−	3.71783i	0.345102	−	0.238010i
$245$	3.25299	−	3.87676i	0.207826	−	0.247677i
$246$		0			0
$247$	−1.42019	−	8.05431i	−0.0903647	−	0.512484i
$248$	−5.25936	−	1.22488i	−0.333970	−	0.0777799i
$249$		0			0
$250$	−18.3386	+	23.7244i	−1.15983	+	1.50046i
$251$	25.2441	+	14.5747i	1.59339	+	0.919945i	0.992719	+	0.120450i	$0.0384337\pi$
$251$	25.2441	+	14.5747i	1.59339	+	0.919945i	0.600672	+	0.799495i	$0.294900\pi$
$252$		0			0
$253$	2.39852	−	1.38479i	0.150794	−	0.0870608i
$254$	0.904268	−	6.68512i	0.0567388	−	0.419462i
$255$		0			0
$256$	−15.9935	−	0.454343i	−0.999597	−	0.0283964i
$257$	5.42626	−	4.55318i	0.338481	−	0.284019i	−0.457664	−	0.889125i	$-0.651314\pi$
$257$	5.42626	−	4.55318i	0.338481	−	0.284019i	0.796145	+	0.605106i	$0.206869\pi$
$258$		0			0
$259$	−9.44975	−	25.9630i	−0.587179	−	1.61326i
$260$	−13.4000	+	28.2117i	−0.831034	+	1.74962i
$261$		0			0
$262$	4.18845	−	2.64748i	0.258764	−	0.163562i
$263$	−1.99223	+	11.2985i	−0.122846	+	0.696695i	0.859718	+	0.510770i	$0.170639\pi$
$263$	−1.99223	+	11.2985i	−0.122846	+	0.696695i	−0.982564	+	0.185926i	$0.940472\pi$
$264$		0			0
$265$	13.0629	+	4.75451i	0.802449	+	0.292067i
$266$	−2.54495	+	7.97276i	−0.156041	+	0.488841i
$267$		0			0
$268$	−13.6561	−	1.29252i	−0.834182	−	0.0789533i
$269$		−	15.1820i		−	0.925661i	−0.886447	−	0.462831i	$-0.846834\pi$
$269$		−	15.1820i		−	0.925661i	0.886447	−	0.462831i	$-0.153166\pi$
$270$		0			0
$271$	13.2808			0.806753			0.403376	−	0.915034i	$-0.367837\pi$
$271$	13.2808			0.806753			0.403376	+	0.915034i	$0.367837\pi$
$272$	−17.3731	+	9.70410i	−1.05340	+	0.588397i
$273$		0			0
$274$	−22.2606	−	7.10572i	−1.34481	−	0.429272i
$275$	10.3612	−	28.4672i	0.624804	−	1.71664i
$276$		0			0
$277$	−2.53413	−	0.446836i	−0.152261	−	0.0268478i	0.0969979	−	0.995285i	$-0.469076\pi$
$277$	−2.53413	−	0.446836i	−0.152261	−	0.0268478i	−0.249259	+	0.968437i	$0.580187\pi$
$278$	23.7491	−	15.0116i	1.42438	−	0.900335i
$279$		0			0
$280$	25.5613	−	19.1848i	1.52758	−	1.14651i
$281$	−25.4277	+	9.25491i	−1.51689	+	0.552102i	−0.960368	−	0.278734i	$-0.910085\pi$
$281$	−25.4277	+	9.25491i	−1.51689	+	0.552102i	−0.556518	+	0.830835i	$0.687863\pi$
$282$		0			0
$283$	17.1845	+	20.4797i	1.02151	+	1.21739i	0.975851	+	0.218436i	$0.0700955\pi$
$283$	17.1845	+	20.4797i	1.02151	+	1.21739i	0.0456626	+	0.998957i	$0.485460\pi$
$284$	−14.7968	−	4.07760i	−0.878028	−	0.241961i
$285$		0			0
$286$	2.19664	−	16.2395i	0.129890	−	0.960259i
$287$	−1.09212	−	1.89160i	−0.0644656	−	0.111658i
$288$		0			0
$289$	−3.87484	+	6.71142i	−0.227932	+	0.394789i
$290$	−35.4217	−	27.3803i	−2.08003	−	1.60783i
$291$		0			0
$292$	−3.49536	−	13.4254i	−0.204550	−	0.785663i
$293$	−17.3330	+	3.05628i	−1.01261	+	0.178550i	−0.655245	−	0.755416i	$-0.727435\pi$
$293$	−17.3330	+	3.05628i	−1.01261	+	0.178550i	−0.357361	+	0.933966i	$0.616323\pi$
$294$		0			0
$295$	−18.7498	−	15.7329i	−1.09166	−	0.916007i
$296$	−3.25602	−	26.9465i	−0.189252	−	1.56623i
$297$		0			0
$298$	−14.4136	−	7.56840i	−0.834957	−	0.438426i
$299$	2.43244	−	2.89887i	0.140672	−	0.167646i
$300$		0			0
$301$	−17.7513	+	3.13004i	−1.02317	+	0.180412i
$302$	3.81224	−	3.46846i	0.219370	−	0.199587i
$303$		0			0
$304$	−4.21152	+	7.06107i	−0.241547	+	0.404980i
$305$	−6.42499	+	11.1284i	−0.367894	+	0.637211i
$306$		0			0
$307$	10.1962	−	5.88676i	0.581926	−	0.335975i	−0.179972	−	0.983672i	$-0.557601\pi$
$307$	10.1962	−	5.88676i	0.581926	−	0.335975i	0.761898	+	0.647696i	$0.224268\pi$
$308$	−9.71565	+	13.6678i	−0.553600	+	0.778796i
$309$		0			0
$310$	10.3536	−	2.25680i	0.588044	−	0.128178i
$311$	−26.0496	+	21.8582i	−1.47714	+	1.23947i	−0.567965	+	0.823053i	$0.692269\pi$
$311$	−26.0496	+	21.8582i	−1.47714	+	1.23947i	−0.909175	+	0.416414i	$0.863287\pi$
$312$		0			0
$313$	6.64081	−	2.41706i	0.375361	−	0.136620i	−0.147449	−	0.989070i	$-0.547106\pi$
$313$	6.64081	−	2.41706i	0.375361	−	0.136620i	0.522809	+	0.852450i	$0.324884\pi$
$314$	−0.829518	−	20.6838i	−0.0468124	−	1.16726i
$315$		0			0
$316$	0.534197	−	0.0429166i	0.0300509	−	0.00241425i
$317$	5.34112	+	0.941783i	0.299987	+	0.0528958i	0.321616	−	0.946870i	$-0.395774\pi$
$317$	5.34112	+	0.941783i	0.299987	+	0.0528958i	−0.0216287	+	0.999766i	$0.506885\pi$
$318$		0			0
$319$	22.0739	+	8.03424i	1.23590	+	0.449831i
$320$	28.7314	−	12.6599i	1.60614	−	0.707707i
$321$		0			0
$322$	−3.58283	+	1.46918i	−0.199663	+	0.0818741i
$323$			10.2255i			0.568961i
$324$		0			0
$325$		−	41.3924i		−	2.29604i
$326$	−3.18655	−	7.77092i	−0.176486	−	0.430391i
$327$		0			0
$328$	−0.623410	−	2.05320i	−0.0344220	−	0.113369i
$329$	−14.5225	−	5.28577i	−0.800654	−	0.291414i
$330$		0			0
$331$	−5.34260	−	0.942044i	−0.293656	−	0.0517794i	0.0248795	−	0.999690i	$-0.492080\pi$
$331$	−5.34260	−	0.942044i	−0.293656	−	0.0517794i	−0.318535	+	0.947911i	$0.603191\pi$
$332$	1.97128	+	24.5371i	0.108188	+	1.34665i
$333$		0			0
$334$	−28.1348	+	1.12834i	−1.53947	+	0.0617400i
$335$	25.2940	−	9.20627i	1.38196	−	0.502992i
$336$		0			0
$337$	−22.3325	+	18.7392i	−1.21653	+	1.02079i	−0.217528	+	0.976054i	$0.569799\pi$
$337$	−22.3325	+	18.7392i	−1.21653	+	1.02079i	−0.998999	+	0.0447328i	$0.985756\pi$
$338$	−0.853182	−	3.91416i	−0.0464070	−	0.212902i
$339$		0			0
$340$	22.6242	−	31.8274i	1.22697	−	1.72608i
$341$	−4.81509	+	2.77999i	−0.260752	+	0.150545i
$342$		0			0
$343$	−8.22070	+	14.2387i	−0.443876	+	0.768816i
$344$	−17.6816	−	0.960757i	−0.953325	−	0.0518006i
$345$		0			0
$346$	−10.4871	−	11.5266i	−0.563792	−	0.619673i
$347$	−17.1238	+	3.01939i	−0.919255	+	0.162089i	−0.613203	−	0.789925i	$-0.710119\pi$
$347$	−17.1238	+	3.01939i	−0.919255	+	0.162089i	−0.306052	+	0.952015i	$0.599008\pi$
$348$		0			0
$349$	−3.38478	+	4.03383i	−0.181183	+	0.215926i	−0.848990	−	0.528409i	$-0.822789\pi$
$349$	−3.38478	+	4.03383i	−0.181183	+	0.215926i	0.667807	+	0.744335i	$0.267233\pi$
$350$	−19.6914	+	37.5011i	−1.05255	+	2.00452i
$351$		0			0
$352$	−12.3413	+	10.9121i	−0.657794	+	0.581619i
$353$	7.22029	+	6.05854i	0.384297	+	0.322463i	0.814387	−	0.580323i	$-0.197074\pi$
$353$	7.22029	+	6.05854i	0.384297	+	0.322463i	−0.430090	+	0.902786i	$0.641518\pi$
$354$		0			0
$355$	29.6606	−	5.22997i	1.57422	−	0.277578i
$356$	−4.14565	−	15.9231i	−0.219719	−	0.843925i
$357$		0			0
$358$	−3.65885	+	4.73342i	−0.193376	+	0.250169i
$359$	8.12377	−	14.0708i	0.428756	−	0.742628i	−0.568007	−	0.823024i	$-0.692285\pi$
$359$	8.12377	−	14.0708i	0.428756	−	0.742628i	0.996763	+	0.0803962i	$0.0256186\pi$
$360$		0			0
$361$	−7.38764	−	12.7958i	−0.388823	−	0.673461i
$362$	−26.6488	−	3.60468i	−1.40063	−	0.189458i
$363$		0			0
$364$	−6.08717	+	22.0891i	−0.319054	+	1.15778i
$365$	17.4986	+	20.8541i	0.915921	+	1.09155i
$366$		0			0
$367$	12.0315	−	4.37912i	0.628042	−	0.228588i	−0.00833711	−	0.999965i	$-0.502654\pi$
$367$	12.0315	−	4.37912i	0.628042	−	0.228588i	0.636379	+	0.771377i	$0.280432\pi$
$368$	−3.75535	+	0.607319i	−0.195761	+	0.0316587i
$369$		0			0
$370$	28.4580	+	45.0220i	1.47946	+	2.34058i
$371$	10.0432	+	1.77089i	0.521417	+	0.0919400i
$372$		0			0
$373$	2.16442	−	5.94669i	0.112069	−	0.307908i	−0.870961	−	0.491353i	$-0.836503\pi$
$373$	2.16442	−	5.94669i	0.112069	−	0.307908i	0.983030	+	0.183445i	$0.0587248\pi$
$374$	−6.23042	+	19.5185i	−0.322167	+	1.00928i
$375$		0			0
$376$	−12.7170	−	8.29336i	−0.655831	−	0.427697i
$377$	32.0963			1.65304
$378$		0			0
$379$			28.5066i			1.46428i	0.681152	+	0.732142i	$0.261479\pi$
$379$			28.5066i			1.46428i	−0.681152	+	0.732142i	$0.738521\pi$
$380$	1.52020	−	16.0616i	0.0779844	−	0.823945i
$381$		0			0
$382$	10.9531	+	3.49630i	0.560410	+	0.178886i
$383$	29.5410	+	10.7521i	1.50948	+	0.549405i	0.958494	−	0.285112i	$-0.0920308\pi$
$383$	29.5410	+	10.7521i	1.50948	+	0.549405i	0.550983	+	0.834517i	$0.314253\pi$
$384$		0			0
$385$	5.71409	−	32.4062i	0.291217	−	1.65157i
$386$	9.96638	+	15.7673i	0.507275	+	0.802536i
$387$		0			0
$388$	4.62169	−	9.73028i	0.234631	−	0.493980i
$389$	1.34416	+	3.69306i	0.0681518	+	0.187246i	0.969093	−	0.246696i	$-0.0793448\pi$
$389$	1.34416	+	3.69306i	0.0681518	+	0.187246i	−0.900941	+	0.433941i	$0.857123\pi$
$390$		0			0
$391$	−3.62440	+	3.04123i	−0.183294	+	0.153802i
$392$	2.49253	−	2.66262i	0.125892	−	0.134483i
$393$		0			0
$394$	8.66108	+	1.17155i	0.436339	+	0.0590217i
$395$	−0.910744	+	0.525818i	−0.0458245	+	0.0264568i
$396$		0			0
$397$	−17.9961	−	10.3901i	−0.903200	−	0.521463i	−0.0249629	−	0.999688i	$-0.507947\pi$
$397$	−17.9961	−	10.3901i	−0.903200	−	0.521463i	−0.878237	+	0.478226i	$0.841280\pi$
$398$	−9.92937	−	7.67523i	−0.497715	−	0.384725i
$399$		0			0
$400$	−27.1966	+	31.4925i	−1.35983	+	1.57462i
$401$	4.02373	+	22.8197i	0.200935	+	1.13956i	0.903709	+	0.428147i	$0.140834\pi$
$401$	4.02373	+	22.8197i	0.200935	+	1.13956i	−0.702774	+	0.711413i	$0.748055\pi$
$402$		0			0
$403$	−4.88319	+	5.81955i	−0.243249	+	0.289893i
$404$	−6.65941	+	4.59285i	−0.331318	+	0.228503i
$405$		0			0
$406$	−29.0790	−	15.2690i	−1.44316	−	0.757788i
$407$	−21.4079	−	17.9634i	−1.06115	−	0.890412i
$408$		0			0
$409$	5.07096	+	28.7589i	0.250743	+	1.42203i	0.806768	+	0.590868i	$0.201215\pi$
$409$	5.07096	+	28.7589i	0.250743	+	1.42203i	−0.556025	+	0.831165i	$0.687674\pi$
$410$	2.83362	+	3.11448i	0.139943	+	0.153813i
$411$		0			0
$412$	2.07542	−	0.949901i	0.102248	−	0.0467983i
$413$	−15.5503	−	8.97799i	−0.765182	−	0.441778i
$414$		0			0
$415$	−24.1523	−	41.8330i	−1.18559	−	2.05350i
$416$	−10.7462	+	19.7779i	−0.526873	+	0.969694i
$417$		0			0
$418$	1.80282	+	8.27086i	0.0881790	+	0.404541i
$419$	8.33906	+	9.93810i	0.407390	+	0.485508i	0.930258	−	0.366905i	$-0.119583\pi$
$419$	8.33906	+	9.93810i	0.407390	+	0.485508i	−0.522869	+	0.852413i	$0.675138\pi$
$420$		0			0
$421$	1.49536	+	4.10848i	0.0728795	+	0.200235i	0.970784	−	0.239956i	$-0.0771330\pi$
$421$	1.49536	+	4.10848i	0.0728795	+	0.200235i	−0.897904	+	0.440191i	$0.854911\pi$
$422$	1.00153	+	24.9730i	0.0487539	+	1.21567i
$423$		0			0
$424$	9.21452	+	3.93227i	0.447497	+	0.190968i
$425$	−8.98665	+	50.9658i	−0.435916	+	2.47220i
$426$		0			0
$427$	−3.22419	+	8.85839i	−0.156030	+	0.428688i
$428$	6.84591	+	6.94382i	0.330909	+	0.335642i
$429$		0			0
$430$	32.1498	−	13.1834i	1.55040	−	0.635759i
$431$	−1.15854			−0.0558051			−0.0279025	−	0.999611i	$-0.508883\pi$
$431$	−1.15854			−0.0558051			−0.0279025	+	0.999611i	$0.508883\pi$
$432$		0			0
$433$	37.7498			1.81414			0.907069	−	0.420982i	$-0.138314\pi$
$433$	37.7498			1.81414			0.907069	+	0.420982i	$0.138314\pi$
$434$	7.19263	−	2.94941i	0.345257	−	0.141576i
$435$		0			0
$436$	−3.53857	−	3.58918i	−0.169467	−	0.171891i
$437$	−0.668571	+	1.83688i	−0.0319821	+	0.0878701i
$438$		0			0
$439$	−4.69964	+	26.6530i	−0.224301	+	1.27208i	0.639715	+	0.768612i	$0.279052\pi$
$439$	−4.69964	+	26.6530i	−0.224301	+	1.27208i	−0.864016	+	0.503464i	$0.832059\pi$
$440$	12.6882	−	29.7323i	0.604885	−	1.41743i
$441$		0			0
$442$	1.12182	+	27.9723i	0.0533596	+	1.33051i
$443$	−10.3614	−	28.4677i	−0.492285	−	1.35254i	−0.898584	−	0.438802i	$-0.855403\pi$
$443$	−10.3614	−	28.4677i	−0.492285	−	1.35254i	0.406299	−	0.913740i	$-0.366819\pi$
$444$		0			0
$445$	20.7542	+	24.7338i	0.983841	+	1.17250i
$446$	−7.02601	−	32.2334i	−0.332691	−	1.52630i
$447$		0			0
$448$	19.1448	−	12.8064i	0.904506	−	0.605047i
$449$	1.70434	+	2.95201i	0.0804330	+	0.139314i	0.903436	−	0.428723i	$-0.141036\pi$
$449$	1.70434	+	2.95201i	0.0804330	+	0.139314i	−0.823003	+	0.568037i	$0.807703\pi$
$450$		0			0
$451$	−1.91329	−	1.10464i	−0.0900934	−	0.0520155i
$452$	13.1526	−	6.01982i	0.618644	−	0.283149i
$453$		0			0
$454$	23.6174	+	25.9583i	1.10842	+	1.21828i
$455$	−7.80745	−	44.2782i	−0.366019	−	2.07580i
$456$		0			0
$457$	7.27754	+	6.10658i	0.340429	+	0.285654i	0.796933	−	0.604068i	$-0.206454\pi$
$457$	7.27754	+	6.10658i	0.340429	+	0.285654i	−0.456504	+	0.889721i	$0.650899\pi$
$458$	6.97800	+	3.66406i	0.326060	+	0.171210i
$459$		0			0
$460$	6.14514	−	4.23817i	0.286518	−	0.197606i
$461$	−19.8885	+	23.7021i	−0.926298	+	1.10392i	0.0680433	+	0.997682i	$0.478324\pi$
$461$	−19.8885	+	23.7021i	−0.926298	+	1.10392i	−0.994341	+	0.106236i	$0.966120\pi$
$462$		0			0
$463$	−4.27095	−	24.2217i	−0.198488	−	1.12568i	−0.907364	−	0.420347i	$-0.861908\pi$
$463$	−4.27095	−	24.2217i	−0.198488	−	1.12568i	0.708876	−	0.705333i	$-0.249203\pi$
$464$	−24.4198	−	21.0887i	−1.13366	−	0.979018i
$465$		0			0
$466$	−7.44233	−	5.75280i	−0.344759	−	0.266493i
$467$	−0.849394	−	0.490398i	−0.0393052	−	0.0226929i	0.480219	−	0.877149i	$-0.340557\pi$
$467$	−0.849394	−	0.490398i	−0.0393052	−	0.0226929i	−0.519524	+	0.854456i	$0.673891\pi$
$468$		0			0
$469$	17.1013	−	9.87344i	0.789665	−	0.455913i
$470$	29.5235	+	3.99352i	1.36182	+	0.184207i
$471$		0			0
$472$	−12.8777	−	12.0550i	−0.592743	−	0.554877i
$473$	−13.9664	+	11.7192i	−0.642177	+	0.538851i
$474$		0			0
$475$	7.31297	+	20.0922i	0.335542	+	0.921894i
$476$	12.2908	−	25.8764i	0.563346	−	1.18604i
$477$		0			0
$478$	−19.7698	−	31.2768i	−0.904248	−	1.43057i
$479$	1.26087	−	7.15074i	0.0576105	−	0.326726i	−0.942358	−	0.334605i	$-0.891397\pi$
$479$	1.26087	−	7.15074i	0.0576105	−	0.326726i	0.999969	+	0.00787960i	$0.00250818\pi$
$480$		0			0
$481$	−35.8813	−	13.0597i	−1.63605	−	0.595473i
$482$	33.8357	+	10.8006i	1.54117	+	0.491952i
$483$		0			0
$484$	0.474769	−	5.01618i	0.0215804	−	0.228008i
$485$			21.1382i			0.959836i
$486$		0			0
$487$	0.153837			0.00697103			0.00348552	−	0.999994i	$-0.498891\pi$
$487$	0.153837			0.00697103			0.00348552	+	0.999994i	$0.498891\pi$
$488$	−5.05874	+	7.75707i	−0.228999	+	0.351146i
$489$		0			0
$490$	−2.17636	+	6.81805i	−0.0983181	+	0.308008i
$491$	7.10851	−	19.5305i	0.320802	−	0.881398i	−0.669543	−	0.742774i	$-0.733510\pi$
$491$	7.10851	−	19.5305i	0.320802	−	0.881398i	0.990345	−	0.138624i	$-0.0442679\pi$
$492$		0			0
$493$	−39.5197	−	6.96839i	−1.77988	−	0.313840i
$494$	6.17986	+	9.77686i	0.278045	+	0.439882i
$495$		0			0
$496$	7.53897	−	1.21921i	0.338510	−	0.0547441i
$497$	20.7626	−	7.55696i	0.931329	−	0.338976i
$498$		0			0
$499$	−12.0312	−	14.3382i	−0.538588	−	0.641865i	0.426282	−	0.904590i	$-0.359823\pi$
$499$	−12.0312	−	14.3382i	−0.538588	−	0.641865i	−0.964871	+	0.262726i	$0.915379\pi$
$500$	11.2661	−	40.8825i	0.503837	−	1.82832i
$501$		0			0
$502$	−40.8514	−	5.52579i	−1.82329	−	0.246628i
$503$	−15.2553	−	26.4230i	−0.680200	−	1.17814i	−0.974919	−	0.222558i	$-0.928559\pi$
$503$	−15.2553	−	26.4230i	−0.680200	−	1.17814i	0.294719	−	0.955584i	$-0.404774\pi$
$504$		0			0
$505$	7.93717	−	13.7476i	0.353200	−	0.611760i
$506$	−2.39539	+	3.09890i	−0.106488	+	0.137763i
$507$		0			0
$508$	2.40372	+	9.23250i	0.106648	+	0.409626i
$509$	25.1247	−	4.43017i	1.11363	−	0.196364i	0.413590	−	0.910463i	$-0.364275\pi$
$509$	25.1247	−	4.43017i	1.11363	−	0.196364i	0.700044	+	0.714099i	$0.253164\pi$
$510$		0			0
$511$	15.2988	+	12.8372i	0.676779	+	0.567885i
$512$	21.1710	−	7.98691i	0.935633	−	0.352975i
$513$		0			0
$514$	−4.65711	+	8.86921i	−0.205416	+	0.391204i
$515$	−2.87899	+	3.43104i	−0.126863	+	0.151190i
$516$		0			0
$517$	−15.3943	+	2.71443i	−0.677041	+	0.119381i
$518$	26.2953	+	28.9016i	1.15535	+	1.26987i
$519$		0			0
$520$	2.39648	−	44.1042i	0.105092	−	1.93410i
$521$	8.58140	−	14.8634i	0.375958	−	0.651178i	−0.614512	−	0.788908i	$-0.710647\pi$
$521$	8.58140	−	14.8634i	0.375958	−	0.651178i	0.990470	+	0.137729i	$0.0439803\pi$
$522$		0			0
$523$	35.9656	−	20.7647i	1.57266	−	0.907978i	0.576824	−	0.816869i	$-0.304292\pi$
$523$	35.9656	−	20.7647i	1.57266	−	0.907978i	0.995841	−	0.0911099i	$-0.0290415\pi$
$524$	−4.05997	+	5.71150i	−0.177361	+	0.249508i
$525$		0			0
$526$	−3.45547	−	15.8528i	−0.150666	−	0.691213i
$527$	7.27607	−	6.10535i	0.316950	−	0.265953i
$528$		0			0
$529$	20.7630	−	7.55712i	0.902739	−	0.328570i
$530$	−19.6436	+	0.787799i	−0.853262	+	0.0342198i
$531$		0			0
$532$	−0.947808	−	11.7977i	−0.0410927	−	0.511494i
$533$	−2.97279	−	0.524183i	−0.128766	−	0.0227049i
$534$		0			0
$535$	−17.9806	−	6.54441i	−0.777370	−	0.282939i
$536$	18.5622	−	5.63603i	0.801767	−	0.243439i
$537$		0			0
$538$	8.14595	+	19.8652i	0.351197	+	0.856452i
$539$		−	3.75520i		−	0.161748i
$540$		0			0
$541$		−	11.2309i		−	0.482852i	−0.970419	−	0.241426i	$-0.922385\pi$
$541$		−	11.2309i		−	0.482852i	0.970419	−	0.241426i	$-0.0776152\pi$
$542$	−17.3776	+	7.12589i	−0.746434	+	0.306083i
$543$		0			0
$544$	17.5255	−	22.0192i	0.751401	−	0.944065i
$545$	9.29398	+	3.38273i	0.398110	+	0.144900i
$546$		0			0
$547$	19.8704	+	3.50369i	0.849599	+	0.149807i	0.581462	−	0.813574i	$-0.302481\pi$
$547$	19.8704	+	3.50369i	0.849599	+	0.149807i	0.268137	+	0.963381i	$0.413592\pi$
$548$	32.9401	−	2.64636i	1.40713	−	0.113047i
$549$		0			0
$550$	1.71680	+	42.8080i	0.0732046	+	1.82534i
$551$	−15.5798	+	5.67059i	−0.663722	+	0.241575i
$552$		0			0
$553$	−0.590998	+	0.495906i	−0.0251318	+	0.0210881i
$554$	3.55560	−	0.775026i	0.151063	−	0.0329277i
$555$		0			0
$556$	−23.0206	+	32.3850i	−0.976290	+	1.37343i
$557$	−26.7781	+	15.4604i	−1.13463	+	0.655076i	−0.945094	−	0.326798i	$-0.894030\pi$
$557$	−26.7781	+	15.4604i	−1.13463	+	0.655076i	−0.189532	+	0.981875i	$0.560697\pi$
$558$		0			0
$559$	−12.4556	+	21.5737i	−0.526814	+	0.912469i
$560$	−23.1526	+	38.8179i	−0.978377	+	1.64036i
$561$		0			0
$562$	28.3057	−	25.7531i	1.19400	−	1.08633i
$563$	20.3052	−	3.58035i	0.855761	−	0.150894i	0.271479	−	0.962444i	$-0.412487\pi$
$563$	20.3052	−	3.58035i	0.855761	−	0.150894i	0.584282	+	0.811551i	$0.301376\pi$
$564$		0			0
$565$	−18.2450	+	21.7436i	−0.767575	+	0.914760i
$566$	−33.4740	−	17.5768i	−1.40702	−	0.738808i
$567$		0			0
$568$	21.5491	−	2.60383i	0.904180	−	0.109254i
$569$	3.82688	+	3.21114i	0.160431	+	0.134618i	0.719469	−	0.694524i	$-0.244385\pi$
$569$	3.82688	+	3.21114i	0.160431	+	0.134618i	−0.559038	+	0.829142i	$0.688829\pi$
$570$		0			0
$571$	7.54047	−	1.32959i	0.315559	−	0.0556415i	−0.0136257	−	0.999907i	$-0.504337\pi$
$571$	7.54047	−	1.32959i	0.315559	−	0.0556415i	0.329184	+	0.944266i	$0.393226\pi$
$572$	5.83910	+	22.4276i	0.244145	+	0.937743i
$573$		0			0
$574$	2.44395	+	1.88913i	0.102009	+	0.0788509i
$575$	−4.94663	+	8.56781i	−0.206289	+	0.357303i
$576$		0			0
$577$	6.53703	+	11.3225i	0.272140	+	0.471361i	0.969410	−	0.245449i	$-0.0789352\pi$
$577$	6.53703	+	11.3225i	0.272140	+	0.471361i	−0.697269	+	0.716809i	$0.745602\pi$
$578$	1.46909	−	10.8608i	0.0611062	−	0.451749i
$579$		0			0
$580$	61.0394	+	16.8209i	2.53452	+	0.698448i
$581$	−22.7783	−	27.1462i	−0.945005	−	1.12621i
$582$		0			0
$583$	9.69302	−	3.52797i	0.401444	−	0.146114i
$584$	11.7771	+	15.6914i	0.487338	+	0.649314i
$585$		0			0
$586$	21.0400	−	13.2992i	0.869154	−	0.549384i
$587$	−20.2706	−	3.57425i	−0.836657	−	0.147525i	−0.261126	−	0.965305i	$-0.584094\pi$
$587$	−20.2706	−	3.57425i	−0.836657	−	0.147525i	−0.575532	+	0.817780i	$0.695205\pi$
$588$		0			0
$589$	1.34217	−	3.68759i	0.0553033	−	0.151945i
$590$	32.9752	+	10.5259i	1.35757	+	0.433344i
$591$		0			0
$592$	18.7187	+	33.5118i	0.769333	+	1.37733i
$593$	−35.4674			−1.45647			−0.728237	−	0.685326i	$-0.759660\pi$
$593$	−35.4674			−1.45647			−0.728237	+	0.685326i	$0.759660\pi$
$594$		0			0
$595$			56.2142i			2.30456i
$596$	22.9207	+	2.16939i	0.938869	+	0.0888617i
$597$		0			0
$598$	−1.62739	+	5.09824i	−0.0665489	+	0.208482i
$599$	−4.95171	−	1.80227i	−0.202321	−	0.0736389i	0.238872	−	0.971051i	$-0.423222\pi$
$599$	−4.95171	−	1.80227i	−0.202321	−	0.0736389i	−0.441193	+	0.897412i	$0.645445\pi$
$600$		0			0
$601$	−6.16086	+	34.9400i	−0.251307	+	1.42523i	0.554071	+	0.832469i	$0.313074\pi$
$601$	−6.16086	+	34.9400i	−0.251307	+	1.42523i	−0.805378	+	0.592762i	$0.798038\pi$
$602$	21.5478	−	13.6201i	0.878221	−	0.555115i
$603$		0			0
$604$	−3.12721	+	6.58387i	−0.127244	+	0.267894i
$605$	3.38165	+	9.29100i	0.137484	+	0.377733i
$606$		0			0
$607$	−6.68660	+	5.61072i	−0.271401	+	0.227732i	−0.768322	−	0.640063i	$-0.778908\pi$
$607$	−6.68660	+	5.61072i	−0.271401	+	0.227732i	0.496922	+	0.867795i	$0.334464\pi$
$608$	1.72202	−	11.4990i	0.0698371	−	0.466344i
$609$		0			0
$610$	2.43595	−	18.0086i	0.0986287	−	0.729147i
$611$	−18.4970	+	10.6793i	−0.748309	+	0.432036i
$612$		0			0
$613$	28.4795	+	16.4426i	1.15028	+	0.664112i	0.948954	−	0.315414i	$-0.102143\pi$
$613$	28.4795	+	16.4426i	1.15028	+	0.664112i	0.201321	+	0.979525i	$0.435477\pi$
$614$	−10.1829	+	13.1735i	−0.410947	+	0.531639i
$615$		0			0
$616$	5.37917	−	23.0970i	0.216733	−	0.930603i
$617$	−5.77150	−	32.7318i	−0.232352	−	1.31773i	−0.848119	−	0.529805i	$-0.822265\pi$
$617$	−5.77150	−	32.7318i	−0.232352	−	1.31773i	0.615767	−	0.787928i	$-0.288846\pi$
$618$		0			0
$619$	22.6481	−	26.9910i	0.910305	−	1.08486i	−0.0857667	−	0.996315i	$-0.527334\pi$
$619$	22.6481	−	26.9910i	0.910305	−	1.08486i	0.996072	−	0.0885446i	$-0.0282216\pi$
$620$	−12.3365	+	8.50823i	−0.495446	+	0.341699i
$621$		0			0
$622$	22.3572	−	42.5780i	0.896442	−	1.70722i
$623$	18.1451	+	15.2255i	0.726966	+	0.609997i
$624$		0			0
$625$	5.41806	+	30.7273i	0.216722	+	1.22909i
$626$	−7.39246	+	6.72582i	−0.295462	+	0.268818i
$627$		0			0
$628$	12.1834	+	26.6192i	0.486171	+	1.06222i
$629$	41.3448	+	23.8704i	1.64852	+	0.951775i
$630$		0			0
$631$	−20.3613	−	35.2667i	−0.810569	−	1.40395i	−0.912466	−	0.409152i	$-0.865825\pi$
$631$	−20.3613	−	35.2667i	−0.810569	−	1.40395i	0.101898	−	0.994795i	$-0.467509\pi$
$632$	−0.675957	+	0.342781i	−0.0268881	+	0.0136351i
$633$		0			0
$634$	−7.49404	+	1.63350i	−0.297626	+	0.0648746i
$635$	−12.0336	−	14.3411i	−0.477539	−	0.569109i
$636$		0			0
$637$	−1.75488	−	4.82149i	−0.0695308	−	0.191034i
$638$	−33.1940	+	1.33123i	−1.31416	+	0.0527040i
$639$		0			0
$640$	−30.8017	+	31.9811i	−1.21754	+	1.26416i
$641$	8.76821	−	49.7270i	0.346323	−	1.96410i	0.0995006	−	0.995038i	$-0.468275\pi$
$641$	8.76821	−	49.7270i	0.346323	−	1.96410i	0.246823	−	0.969061i	$-0.420613\pi$
$642$		0			0
$643$	−15.1261	+	41.5587i	−0.596517	+	1.63892i	0.161645	+	0.986849i	$0.448320\pi$
$643$	−15.1261	+	41.5587i	−0.596517	+	1.63892i	−0.758162	+	0.652067i	$0.773902\pi$
$644$	3.89976	−	3.84477i	0.153672	−	0.151505i
$645$		0			0
$646$	−5.48653	−	13.3798i	−0.215865	−	0.526421i
$647$	−2.96214			−0.116454			−0.0582268	−	0.998303i	$-0.518545\pi$
$647$	−2.96214			−0.116454			−0.0582268	+	0.998303i	$0.518545\pi$
$648$		0			0
$649$	−18.1619			−0.712917
$650$	22.2093	+	54.1609i	0.871119	+	2.12437i
$651$		0			0
$652$	8.33904	+	8.45830i	0.326582	+	0.331253i
$653$	−0.829258	+	2.27837i	−0.0324514	+	0.0891594i	−0.954860	−	0.297055i	$-0.903995\pi$
$653$	−0.829258	+	2.27837i	−0.0324514	+	0.0891594i	0.922409	+	0.386215i	$0.126218\pi$
$654$		0			0
$655$	2.38780	−	13.5419i	0.0932992	−	0.529126i
$656$	1.91737	+	2.35207i	0.0748607	+	0.0918328i
$657$		0			0
$658$	21.8385	−	0.875826i	0.851354	−	0.0341433i
$659$	14.7728	+	40.5879i	0.575466	+	1.58108i	0.795738	+	0.605641i	$0.207083\pi$
$659$	14.7728	+	40.5879i	0.575466	+	1.58108i	−0.220272	+	0.975438i	$0.570695\pi$
$660$		0			0
$661$	−11.3612	−	13.5398i	−0.441901	−	0.526637i	0.498415	−	0.866938i	$-0.333915\pi$
$661$	−11.3612	−	13.5398i	−0.441901	−	0.526637i	−0.940317	+	0.340301i	$0.889471\pi$
$662$	7.49612	−	1.63395i	0.291345	−	0.0635053i
$663$		0			0
$664$	−15.7449	−	31.0485i	−0.611020	−	1.20492i
$665$	11.6126	+	20.1137i	0.450318	+	0.779974i
$666$		0			0
$667$	−6.64362	−	3.83570i	−0.257242	−	0.148519i
$668$	36.2084	−	16.5723i	1.40094	−	0.641201i
$669$		0			0
$670$	−28.1569	+	25.6178i	−1.08780	+	0.989702i
$671$	1.65574	+	9.39015i	0.0639190	+	0.362503i
$672$		0			0
$673$	1.22568	+	1.02847i	0.0472465	+	0.0396445i	0.666105	−	0.745858i	$-0.267960\pi$
$673$	1.22568	+	1.02847i	0.0472465	+	0.0396445i	−0.618859	+	0.785502i	$0.712405\pi$
$674$	19.1669	−	36.5023i	0.738282	−	1.40602i
$675$		0			0
$676$	3.21653	+	4.66381i	0.123713	+	0.179377i
$677$	4.41092	−	5.25673i	0.169526	−	0.202033i	−0.674592	−	0.738191i	$-0.735680\pi$
$677$	4.41092	−	5.25673i	0.169526	−	0.202033i	0.844118	+	0.536158i	$0.180125\pi$
$678$		0			0
$679$	2.69280	+	15.2717i	0.103340	+	0.586072i
$680$	−12.5261	+	53.7845i	−0.480356	+	2.06254i
$681$		0			0
$682$	4.80881	−	6.22111i	0.184139	−	0.238219i
$683$	−4.11971	−	2.37852i	−0.157636	−	0.0910113i	0.419107	−	0.907937i	$-0.362343\pi$
$683$	−4.11971	−	2.37852i	−0.157636	−	0.0910113i	−0.576743	+	0.816926i	$0.695677\pi$
$684$		0			0
$685$	−56.1590	+	32.4234i	−2.14573	+	1.23884i
$686$	3.11677	−	23.0418i	0.118999	−	0.879741i
$687$		0			0
$688$	23.6514	−	8.22999i	0.901701	−	0.313765i
$689$	10.7966	−	9.05946i	0.411320	−	0.345138i
$690$		0			0
$691$	4.35017	+	11.9520i	0.165488	+	0.454675i	0.994523	−	0.104523i	$-0.0333315\pi$
$691$	4.35017	+	11.9520i	0.165488	+	0.454675i	−0.829034	+	0.559198i	$0.811109\pi$
$692$	19.9068	+	9.45535i	0.756743	+	0.359438i
$693$		0			0
$694$	20.7860	−	13.1387i	0.789027	−	0.498737i
$695$	13.5392	−	76.7844i	0.513570	−	2.91260i
$696$		0			0
$697$	3.54655	+	1.29084i	0.134335	+	0.0488939i
$698$	2.26454	−	7.09429i	0.0857141	−	0.268523i
$699$		0			0
$700$	5.64429	−	59.6348i	0.213334	−	2.25398i
$701$		−	12.2688i		−	0.463386i	−0.972789	−	0.231693i	$-0.925573\pi$
$701$		−	12.2688i		−	0.463386i	0.972789	−	0.231693i	$-0.0744265\pi$
$702$		0			0
$703$	19.7244			0.743921
$704$	10.2933	−	20.9000i	0.387945	−	0.787700i
$705$		0			0
$706$	−12.6983	−	4.05338i	−0.477907	−	0.152551i
$707$	3.98304	−	10.9433i	0.149797	−	0.411565i
$708$		0			0
$709$	−25.9792	−	4.58083i	−0.975668	−	0.172037i	−0.336988	−	0.941509i	$-0.609408\pi$
$709$	−25.9792	−	4.58083i	−0.975668	−	0.172037i	−0.638680	+	0.769473i	$0.720519\pi$
$710$	−36.0041	+	22.7578i	−1.35121	+	0.854086i
$711$		0			0
$712$	13.9681	+	18.6107i	0.523477	+	0.697465i
$713$	1.70624	−	0.621021i	0.0638993	−	0.0232574i
$714$		0			0
$715$	−29.2320	−	34.8373i	−1.09321	−	1.30284i
$716$	2.24778	−	8.15674i	0.0840036	−	0.304832i
$717$		0			0
$718$	−3.08002	+	22.7701i	−0.114945	+	0.849774i
$719$	15.9411	+	27.6108i	0.594502	+	1.02971i	0.993617	+	0.112807i	$0.0359841\pi$
$719$	15.9411	+	27.6108i	0.594502	+	1.02971i	−0.399115	+	0.916901i	$0.630683\pi$
$720$		0			0
$721$	−1.64289	+	2.84557i	−0.0611845	+	0.105975i
$722$	16.5322	+	12.7791i	0.615264	+	0.475588i
$723$		0			0
$724$	36.8035	−	9.58192i	1.36779	−	0.356109i
$725$	−82.6364	+	14.5710i	−3.06904	+	0.541154i
$726$		0			0
$727$	30.8679	+	25.9013i	1.14483	+	0.960625i	0.999586	−	0.0287706i	$-0.00915924\pi$
$727$	30.8679	+	25.9013i	1.14483	+	0.960625i	0.145243	+	0.989396i	$0.453604\pi$
$728$	−3.88708	−	32.1691i	−0.144065	−	1.19227i
$729$		0			0
$730$	−34.0859	−	17.8981i	−1.26158	−	0.662438i
$731$	20.0202	−	23.8591i	0.740473	−	0.882461i
$732$		0			0
$733$	−0.103428	+	0.0182371i	−0.00382018	+	0.000673601i	−0.175558	−	0.984469i	$-0.556173\pi$
$733$	−0.103428	+	0.0182371i	−0.00382018	+	0.000673601i	0.171738	+	0.985143i	$0.445062\pi$
$734$	−13.3934	+	12.1856i	−0.494358	+	0.449777i
$735$		0			0
$736$	4.58793	−	2.80961i	0.169113	−	0.103564i
$737$	9.98667	−	17.2974i	0.367864	−	0.637158i
$738$		0			0
$739$	26.3545	−	15.2158i	0.969466	−	0.559722i	0.0703928	−	0.997519i	$-0.477575\pi$
$739$	26.3545	−	15.2158i	0.969466	−	0.559722i	0.899074	+	0.437798i	$0.144241\pi$
$740$	−61.3933	−	43.6410i	−2.25686	−	1.60427i
$741$		0			0
$742$	−14.0915	+	3.07156i	−0.517314	+	0.112761i
$743$	−12.9183	+	10.8397i	−0.473926	+	0.397671i	−0.848224	−	0.529637i	$-0.822328\pi$
$743$	−12.9183	+	10.8397i	−0.473926	+	0.397671i	0.374298	+	0.927308i	$0.377884\pi$
$744$		0			0
$745$	−42.4539	+	15.4520i	−1.55539	+	0.566116i
$746$	0.358633	+	8.94243i	0.0131305	+	0.327406i
$747$		0			0
$748$	−2.32037	−	28.8824i	−0.0848412	−	1.05605i
$749$	−13.8241	−	2.43756i	−0.505122	−	0.0890666i
$750$		0			0
$751$	14.6848	+	5.34482i	0.535855	+	0.195035i	0.595751	−	0.803169i	$-0.296855\pi$
$751$	14.6848	+	5.34482i	0.535855	+	0.195035i	−0.0598958	+	0.998205i	$0.519077\pi$
$752$	21.0898	+	4.02828i	0.769065	+	0.146896i
$753$		0			0
$754$	−41.9972	+	17.2214i	−1.52945	+	0.627167i
$755$		−	14.3029i		−	0.520536i
$756$		0			0
$757$			27.3201i			0.992967i	0.868046	+	0.496484i	$0.165376\pi$
$757$			27.3201i			0.992967i	−0.868046	+	0.496484i	$0.834624\pi$
$758$	−15.2953	−	37.3002i	−0.555551	−	1.35480i
$759$		0			0
$760$	6.62880	+	21.8319i	0.240452	+	0.791928i
$761$	14.1817	+	5.16172i	0.514086	+	0.187112i	0.586019	−	0.810297i	$-0.300694\pi$
$761$	14.1817	+	5.16172i	0.514086	+	0.187112i	−0.0719327	+	0.997409i	$0.522917\pi$
$762$		0			0
$763$	7.14552	+	1.25995i	0.258685	+	0.0456132i
$764$	−16.2078	+	1.30211i	−0.586379	+	0.0471088i
$765$		0			0
$766$	−44.4228	+	1.78156i	−1.60506	+	0.0643705i
$767$	−23.3189	+	8.48740i	−0.841998	+	0.306462i
$768$		0			0
$769$	−11.4199	+	9.58242i	−0.411811	+	0.345551i	−0.825038	−	0.565077i	$-0.808846\pi$
$769$	−11.4199	+	9.58242i	−0.411811	+	0.345551i	0.413226	+	0.910628i	$0.364402\pi$
$770$	9.91095	+	45.4687i	0.357166	+	1.63858i
$771$		0			0
$772$	−21.5008	−	15.2837i	−0.773831	−	0.550071i
$773$	−27.9615	+	16.1436i	−1.00571	+	0.580644i	−0.909931	−	0.414759i	$-0.863866\pi$
$773$	−27.9615	+	16.1436i	−1.00571	+	0.580644i	−0.0957742	+	0.995403i	$0.530533\pi$
$774$		0			0
$775$	9.93049	−	17.2001i	0.356714	−	0.617846i
$776$	−0.826549	+	15.2116i	−0.0296714	+	0.546065i
$777$		0			0
$778$	−3.74033	−	4.11106i	−0.134097	−	0.147389i
$779$	1.53563	−	0.270772i	0.0550195	−	0.00970143i
$780$		0			0
$781$	14.3653	−	17.1199i	0.514031	−	0.612598i
$782$	3.11065	−	5.92406i	0.111237	−	0.211844i
$783$		0			0
$784$	−1.83277	+	4.82135i	−0.0654561	+	0.172191i
$785$	−44.0064	−	36.9258i	−1.57066	−	1.31794i
$786$		0			0
$787$	−39.6718	+	6.99522i	−1.41415	+	0.249353i	−0.827944	−	0.560811i	$-0.810490\pi$
$787$	−39.6718	+	6.99522i	−1.41415	+	0.249353i	−0.586204	+	0.810163i	$0.699378\pi$
$788$	−11.9614	+	3.11420i	−0.426108	+	0.110939i
$789$		0			0
$790$	0.909556	−	1.17668i	0.0323606	−	0.0418645i
$791$	−10.4115	+	18.0333i	−0.370191	+	0.641189i
$792$		0			0
$793$	6.51408	+	11.2827i	0.231322	+	0.400661i
$794$	29.1223	+	3.93926i	1.03351	+	0.139799i
$795$		0			0
$796$	17.1105	+	4.71521i	0.606467	+	0.167126i
$797$	2.35451	+	2.80599i	0.0834009	+	0.0993934i	0.806131	−	0.591737i	$-0.201558\pi$
$797$	2.35451	+	2.80599i	0.0834009	+	0.0993934i	−0.722730	+	0.691130i	$0.757113\pi$
$798$		0			0
$799$	25.0936	−	9.13334i	0.887749	−	0.323114i
$800$	18.6887	−	55.7996i	0.660745	−	1.97281i
$801$		0			0
$802$	−17.5090	−	27.7001i	−0.618263	−	0.978123i
$803$	19.8933	+	3.50773i	0.702020	+	0.123785i
$804$		0			0
$805$	−3.67544	+	10.0982i	−0.129542	+	0.355915i
$806$	3.26702	−	10.2348i	0.115076	−	0.360507i
$807$		0			0
$808$	6.24937	−	9.58278i	0.219852	−	0.337121i
$809$	41.2691			1.45094			0.725472	−	0.688252i	$-0.241622\pi$
$809$	41.2691			1.45094			0.725472	+	0.688252i	$0.241622\pi$
$810$		0			0
$811$		−	25.6578i		−	0.900966i	−0.892785	−	0.450483i	$-0.851252\pi$
$811$		−	25.6578i		−	0.900966i	0.892785	−	0.450483i	$-0.148748\pi$
$812$	46.2418	+	4.37668i	1.62277	+	0.153591i
$813$		0			0
$814$	37.6501	+	12.0181i	1.31964	+	0.421236i
$815$	−21.9023	−	7.97178i	−0.767204	−	0.279239i
$816$		0			0
$817$	2.23452	−	12.6726i	0.0781761	−	0.443359i
$818$	−22.0659	−	34.9094i	−0.771517	−	1.22058i
$819$		0			0
$820$	−5.37882	−	2.55483i	−0.187836	−	0.0892186i
$821$	−8.61194	−	23.6611i	−0.300559	−	0.825778i	−0.994403	−	0.105653i	$-0.966307\pi$
$821$	−8.61194	−	23.6611i	−0.300559	−	0.825778i	0.693844	−	0.720125i	$-0.255916\pi$
$822$		0			0
$823$	10.3916	−	8.71956i	0.362227	−	0.303945i	−0.443450	−	0.896299i	$-0.646246\pi$
$823$	10.3916	−	8.71956i	0.362227	−	0.303945i	0.805678	+	0.592354i	$0.201801\pi$
$824$	−2.20596	+	2.35650i	−0.0768482	+	0.0820924i
$825$		0			0
$826$	25.1644	+	3.40388i	0.875582	+	0.118436i
$827$	9.62668	−	5.55796i	0.334752	−	0.193269i	−0.323197	−	0.946332i	$-0.604758\pi$
$827$	9.62668	−	5.55796i	0.334752	−	0.193269i	0.657949	+	0.753062i	$0.271424\pi$
$828$		0			0
$829$	26.4493	+	15.2705i	0.918621	+	0.530366i	0.883195	−	0.469006i	$-0.155388\pi$
$829$	26.4493	+	15.2705i	0.918621	+	0.530366i	0.0354262	+	0.999372i	$0.488721\pi$
$830$	54.0483	+	41.7784i	1.87605	+	1.45015i
$831$		0			0
$832$	3.44914	−	31.6449i	0.119577	−	1.09709i
$833$	1.11397	+	6.31762i	0.0385967	+	0.218893i
$834$		0			0
$835$	−50.2277	+	59.8590i	−1.73820	+	2.07151i
$836$	−6.79672	−	9.85491i	−0.235069	−	0.340839i
$837$		0			0
$838$	−16.2438	−	8.52941i	−0.561132	−	0.294644i
$839$	3.67221	+	3.08135i	0.126779	+	0.106380i	0.703972	−	0.710227i	$-0.251408\pi$
$839$	3.67221	+	3.08135i	0.126779	+	0.106380i	−0.577194	+	0.816607i	$0.695852\pi$
$840$		0			0
$841$	−6.26281	−	35.5181i	−0.215959	−	1.22476i
$842$	−4.16107	−	4.57350i	−0.143400	−	0.157613i
$843$		0			0
$844$	−14.7098	−	32.1392i	−0.506334	−	1.10628i
$845$	−9.62790	−	5.55867i	−0.331210	−	0.191224i
$846$		0			0
$847$	3.62672	+	6.28165i	0.124615	+	0.215840i
$848$	−14.1669	−	0.201185i	−0.486492	−	0.00690870i
$849$		0			0
$850$	−15.5871	−	71.5093i	−0.534634	−	2.45275i
$851$	5.86637	+	6.99127i	0.201097	+	0.239657i
$852$		0			0
$853$	−7.52367	−	20.6711i	−0.257605	−	0.707765i	−0.999314	−	0.0370424i	$-0.988206\pi$
$853$	−7.52367	−	20.6711i	−0.257605	−	0.707765i	0.741708	−	0.670723i	$-0.234016\pi$
$854$	−0.534232	−	13.3209i	−0.0182811	−	0.455833i
$855$		0			0
$856$	−12.6834	−	5.41262i	−0.433511	−	0.184999i
$857$	1.54554	−	8.76520i	0.0527947	−	0.299414i	−0.946965	−	0.321337i	$-0.895868\pi$
$857$	1.54554	−	8.76520i	0.0527947	−	0.299414i	0.999760	+	0.0219232i	$0.00697894\pi$
$858$		0			0
$859$	7.12897	−	19.5867i	0.243237	−	0.668289i	−0.756658	−	0.653811i	$-0.773169\pi$
$859$	7.12897	−	19.5867i	0.243237	−	0.668289i	0.999895	−	0.0144780i	$-0.00460866\pi$
$860$	−34.9937	+	34.5003i	−1.19327	+	1.17645i
$861$		0			0
$862$	1.51593	−	0.621621i	0.0516326	−	0.0211725i
$863$	21.4666			0.730731			0.365365	−	0.930864i	$-0.380944\pi$
$863$	21.4666			0.730731			0.365365	+	0.930864i	$0.380944\pi$
$864$		0			0
$865$	−43.2459			−1.47040
$866$	−49.3947	+	20.2548i	−1.67850	+	0.688286i
$867$		0			0
$868$	−7.82886	+	7.71847i	−0.265729	+	0.261982i
$869$	−0.266892	+	0.733280i	−0.00905370	+	0.0248748i
$870$		0			0
$871$	4.73896	−	26.8760i	0.160573	−	0.910657i
$872$	6.55593	+	2.79772i	0.222012	+	0.0947428i
$873$		0			0
$874$	−0.110779	−	2.76224i	−0.00374715	−	0.0934343i
$875$	20.8794	+	57.3655i	0.705851	+	1.93931i
$876$		0			0
$877$	−0.176559	−	0.210415i	−0.00596198	−	0.00710521i	0.763055	−	0.646333i	$-0.223698\pi$
$877$	−0.176559	−	0.210415i	−0.00596198	−	0.00710521i	−0.769017	+	0.639228i	$0.779254\pi$
$878$	−8.15140	−	37.3964i	−0.275096	−	1.26207i
$879$		0			0
$880$	−0.649158	+	45.7119i	−0.0218831	+	1.54095i
$881$	11.9250	+	20.6547i	0.401763	+	0.695873i	0.993939	−	0.109935i	$-0.0350643\pi$
$881$	11.9250	+	20.6547i	0.401763	+	0.695873i	−0.592176	+	0.805809i	$0.701731\pi$
$882$		0			0
$883$	−4.93626	−	2.84995i	−0.166118	−	0.0959085i	0.414636	−	0.909987i	$-0.363909\pi$
$883$	−4.93626	−	2.84995i	−0.166118	−	0.0959085i	−0.580754	+	0.814079i	$0.697242\pi$
$884$	−16.4765	−	35.9992i	−0.554166	−	1.21078i
$885$		0			0
$886$	28.8321	+	31.6899i	0.968634	+	1.06464i
$887$	2.98032	+	16.9022i	0.100069	+	0.567521i	0.993076	+	0.117477i	$0.0374806\pi$
$887$	2.98032	+	16.9022i	0.100069	+	0.567521i	−0.893006	+	0.450044i	$0.851408\pi$
$888$		0			0
$889$	−10.5208	−	8.82801i	−0.352857	−	0.296082i
$890$	−40.4274	−	21.2279i	−1.35513	−	0.711561i
$891$		0			0
$892$	26.4883	+	38.4068i	0.886895	+	1.28595i
$893$	7.09185	−	8.45174i	0.237320	−	0.282827i
$894$		0			0
$895$	2.88302	+	16.3504i	0.0963689	+	0.546535i
$896$	−18.1791	+	27.0291i	−0.607322	+	0.902980i
$897$		0			0
$898$	−3.81401	−	2.94816i	−0.127275	−	0.0983814i
$899$	13.3372	+	7.70026i	0.444822	+	0.256818i
$900$		0			0
$901$	−15.2606	+	8.81073i	−0.508405	+	0.293528i
$902$	3.09620	+	0.418810i	0.103092	+	0.0139448i
$903$		0			0
$904$	−13.9798	+	14.9339i	−0.464963	+	0.496693i
$905$	−57.1678	+	47.9695i	−1.90032	+	1.59456i
$906$		0			0
$907$	14.9621	+	41.1081i	0.496809	+	1.36497i	0.894342	+	0.447383i	$0.147644\pi$
$907$	14.9621	+	41.1081i	0.496809	+	1.36497i	−0.397533	+	0.917588i	$0.630134\pi$
$908$	−44.8308	−	21.2938i	−1.48776	−	0.706658i
$909$		0			0
$910$	33.9735	+	53.7479i	1.12621	+	1.78173i
$911$	−0.448255	+	2.54218i	−0.0148514	+	0.0842262i	−0.991333	−	0.131376i	$-0.958060\pi$
$911$	−0.448255	+	2.54218i	−0.0148514	+	0.0842262i	0.976481	+	0.215602i	$0.0691715\pi$
$912$		0			0
$913$	−33.6816	−	12.2591i	−1.11470	−	0.405717i
$914$	−12.7990	−	4.08552i	−0.423353	−	0.135137i
$915$		0			0
$916$	−11.0965	−	1.05026i	−0.366639	−	0.0347015i
$917$		−	10.0878i		−	0.333127i
$918$		0			0
$919$	−59.9068			−1.97614			−0.988071	−	0.153998i	$-0.950785\pi$
$919$	−59.9068			−1.97614			−0.988071	+	0.153998i	$0.950785\pi$
$920$	−5.76675	+	8.84274i	−0.190124	+	0.291537i
$921$		0			0
$922$	13.3061	−	41.6849i	0.438212	−	1.37282i
$923$	10.4439	−	28.6943i	0.343764	−	0.944483i
$924$		0			0
$925$	98.3103	+	17.3348i	3.23242	+	0.569963i
$926$	18.5847	+	29.4020i	0.610732	+	0.966209i
$927$		0			0
$928$	43.2679	+	14.4915i	1.42034	+	0.475707i
$929$	30.1626	−	10.9783i	0.989604	−	0.360186i	0.204037	−	0.978963i	$-0.434594\pi$
$929$	30.1626	−	10.9783i	0.989604	−	0.360186i	0.785567	+	0.618777i	$0.212371\pi$
$930$		0			0
$931$	1.70366	+	2.03035i	0.0558354	+	0.0665420i
$932$	12.8248	+	3.53418i	0.420090	+	0.115766i
$933$		0			0
$934$	1.37454	+	0.185928i	0.0449762	+	0.00608374i
$935$	28.4294	+	49.2412i	0.929741	+	1.61036i
$936$		0			0
$937$	8.40875	−	14.5644i	0.274702	−	0.475797i	−0.695358	−	0.718663i	$-0.744754\pi$
$937$	8.40875	−	14.5644i	0.274702	−	0.475797i	0.970060	+	0.242866i	$0.0780875\pi$
$938$	−17.0790	+	22.0949i	−0.557649	+	0.721425i
$939$		0			0
$940$	−40.7736	+	10.6155i	−1.32989	+	0.346241i
$941$	−20.4427	+	3.60459i	−0.666412	+	0.117506i	−0.496613	−	0.867972i	$-0.665423\pi$
$941$	−20.4427	+	3.60459i	−0.666412	+	0.117506i	−0.169799	+	0.985479i	$0.554312\pi$
$942$		0			0
$943$	0.552695	+	0.463766i	0.0179982	+	0.0151023i
$944$	23.3183	+	8.86412i	0.758946	+	0.288503i
$945$		0			0
$946$	11.9867	−	22.8281i	0.389722	−	0.742205i
$947$	−11.7887	+	14.0493i	−0.383082	+	0.456540i	−0.922785	−	0.385316i	$-0.874092\pi$
$947$	−11.7887	+	14.0493i	−0.383082	+	0.456540i	0.539702	+	0.841856i	$0.318537\pi$
$948$		0			0
$949$	27.1812	−	4.79278i	0.882340	−	0.155580i
$950$	−20.3494	−	22.3664i	−0.660222	−	0.725661i
$951$		0			0
$952$	−2.19810	+	40.4533i	−0.0712407	+	1.31110i
$953$	−1.73534	+	3.00570i	−0.0562133	+	0.0973643i	−0.892763	−	0.450527i	$-0.851236\pi$
$953$	−1.73534	+	3.00570i	−0.0562133	+	0.0973643i	0.836549	+	0.547892i	$0.184569\pi$
$954$		0			0
$955$	27.6325	−	15.9536i	0.894166	−	0.516247i
$956$	42.6500	+	30.3174i	1.37940	+	0.980534i
$957$		0			0
$958$	2.18694	+	10.0331i	0.0706570	+	0.324154i
$959$	−36.4426	+	30.5790i	−1.17679	+	0.987447i
$960$		0			0
$961$	25.7051	−	9.35591i	0.829198	−	0.301803i
$962$	53.9571	−	2.16393i	1.73965	−	0.0697680i
$963$		0			0
$964$	−50.0683	+	4.02241i	−1.61259	+	0.129553i
$965$	50.9782	+	8.98883i	1.64105	+	0.289361i
$966$		0			0
$967$	−29.0536	−	10.5747i	−0.934301	−	0.340058i	−0.170388	−	0.985377i	$-0.554502\pi$
$967$	−29.0536	−	10.5747i	−0.934301	−	0.340058i	−0.763913	+	0.645319i	$0.776724\pi$
$968$	2.07023	+	6.81829i	0.0665396	+	0.219148i
$969$		0			0
$970$	−11.3418	−	27.6588i	−0.364163	−	0.888071i
$971$			0.278968i			0.00895249i	0.999990	+	0.00447625i	$0.00142484\pi$
$971$			0.278968i			0.00895249i	−0.999990	+	0.00447625i	$0.998575\pi$
$972$		0			0
$973$		−	57.1990i		−	1.83372i
$974$	−0.201292	+	0.0825420i	−0.00644982	+	0.00264482i
$975$		0			0
$976$	2.45715	−	12.8642i	0.0786515	−	0.411774i
$977$	−20.1241	−	7.32457i	−0.643827	−	0.234334i	−0.000588326	−	1.00000i	$-0.500187\pi$
$977$	−20.1241	−	7.32457i	−0.643827	−	0.234334i	−0.643238	+	0.765666i	$0.722409\pi$
$978$		0			0
$979$	23.5943	+	4.16032i	0.754078	+	0.132964i
$980$	−0.810535	−	10.0890i	−0.0258916	−	0.322281i
$981$		0			0
$982$	1.17784	+	29.3692i	0.0375865	+	0.937210i
$983$	5.52983	−	2.01269i	0.176374	−	0.0641950i	−0.252324	−	0.967643i	$-0.581195\pi$
$983$	5.52983	−	2.01269i	0.176374	−	0.0641950i	0.428698	+	0.903448i	$0.358973\pi$
$984$		0			0
$985$	18.5800	−	15.5905i	0.592008	−	0.496753i
$986$	55.4495	−	12.0865i	1.76587	−	0.384912i
$987$		0			0
$988$	−13.3320	−	9.47696i	−0.424148	−	0.301502i
$989$	5.15636	−	2.97702i	0.163963	−	0.0946639i
$990$		0			0
$991$	17.5543	−	30.4049i	0.557631	−	0.965845i	−0.440063	−	0.897967i	$-0.645044\pi$
$991$	17.5543	−	30.4049i	0.557631	−	0.965845i	0.997694	−	0.0678778i	$-0.0216228\pi$
$992$	−9.21038	+	5.64037i	−0.292430	+	0.179082i
$993$		0			0
$994$	−23.1126	+	21.0284i	−0.733088	+	0.666979i
$995$	−34.2986	+	6.04777i	−1.08734	+	0.191727i
$996$		0			0
$997$	−16.1819	+	19.2848i	−0.512485	+	0.610756i	−0.958787	−	0.284127i	$-0.908296\pi$
$997$	−16.1819	+	19.2848i	−0.512485	+	0.610756i	0.446302	+	0.894883i	$0.352741\pi$
$998$	23.4357	+	12.3058i	0.741844	+	0.389533i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.613.4		204
3.2	odd	2		216.2.t.a.205.31	yes	204
8.5	even	2	inner	648.2.t.a.613.18		204
12.11	even	2		864.2.bf.a.529.28		204
24.5	odd	2		216.2.t.a.205.17	yes	204
24.11	even	2		864.2.bf.a.529.7		204
27.5	odd	18		216.2.t.a.157.17	✓	204
27.22	even	9	inner	648.2.t.a.37.18		204
108.59	even	18		864.2.bf.a.49.7		204
216.5	odd	18		216.2.t.a.157.31	yes	204
216.59	even	18		864.2.bf.a.49.28		204
216.157	even	18	inner	648.2.t.a.37.4		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.17	✓	204	27.5	odd	18
216.2.t.a.157.31	yes	204	216.5	odd	18
216.2.t.a.205.17	yes	204	24.5	odd	2
216.2.t.a.205.31	yes	204	3.2	odd	2
648.2.t.a.37.4		204	216.157	even	18	inner
648.2.t.a.37.18		204	27.22	even	9	inner
648.2.t.a.613.4		204	1.1	even	1	trivial
648.2.t.a.613.18		204	8.5	even	2	inner
864.2.bf.a.49.7		204	108.59	even	18
864.2.bf.a.49.28		204	216.59	even	18
864.2.bf.a.529.7		204	24.11	even	2
864.2.bf.a.529.28		204	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30848 + 0.536554i) q^{2} +(1.42422 - 1.40414i) q^{4} +(-1.34230 + 3.68793i) q^{5} +(-0.499959 + 2.83541i) q^{7} +(-1.11016 + 2.60145i) q^{8} +(-0.222412 - 5.54579i) q^{10} +(0.996019 + 2.73654i) q^{11} +(2.55767 + 3.04812i) q^{13} +(-0.867166 - 3.97832i) q^{14} +(0.0567986 - 3.99960i) q^{16} +(-2.48745 - 4.30839i) q^{17} +(-1.78004 - 1.02771i) q^{19} +(3.26664 + 7.13719i) q^{20} +(-2.77157 - 3.04628i) q^{22} +(-0.165146 - 0.936587i) q^{23} +(-7.96887 - 6.68667i) q^{25} +(-4.98214 - 2.61606i) q^{26} +(3.26925 + 4.74025i) q^{28} +(5.18495 - 6.17919i) q^{29} +(0.331534 + 1.88022i) q^{31} +(2.07168 + 5.26385i) q^{32} +(5.56646 + 4.30278i) q^{34} +(-9.78570 - 5.64977i) q^{35} +(-8.31066 + 4.79816i) q^{37} +(2.88056 + 0.389641i) q^{38} +(-8.10381 - 7.58612i) q^{40} +(-0.581151 + 0.487644i) q^{41} +(2.14125 + 5.88303i) q^{43} +(5.26103 + 2.49888i) q^{44} +(0.718619 + 1.13689i) q^{46} +(-0.932102 + 5.28621i) q^{47} +(-1.21172 - 0.441031i) q^{49} +(14.0148 + 4.47362i) q^{50} +(7.92266 + 0.749861i) q^{52} -3.54207i q^{53} -11.4291 q^{55} +(-6.82113 - 4.44837i) q^{56} +(-3.46892 + 10.8673i) q^{58} +(-2.13303 + 5.86045i) q^{59} +(3.22446 + 0.568559i) q^{61} +(-1.44265 - 2.28234i) q^{62} +(-5.53509 - 5.77605i) q^{64} +(-14.6744 + 5.34105i) q^{65} +(-4.40861 - 5.25398i) q^{67} +(-9.59225 - 2.64337i) q^{68} +(15.8358 + 2.14204i) q^{70} +(-3.83709 - 6.64603i) q^{71} +(3.46824 - 6.00718i) q^{73} +(8.29983 - 10.7374i) q^{74} +(-3.97821 + 1.03574i) q^{76} +(-8.25717 + 1.45596i) q^{77} +(0.205269 + 0.172241i) q^{79} +(14.6740 + 5.57812i) q^{80} +(0.498775 - 0.949889i) q^{82} +(-7.91149 + 9.42855i) q^{83} +(19.2280 - 3.39041i) q^{85} +(-5.95834 - 6.54891i) q^{86} +(-8.22471 - 0.446904i) q^{88} +(4.11349 - 7.12477i) q^{89} +(-9.92138 + 5.72811i) q^{91} +(-1.55030 - 1.10202i) q^{92} +(-1.61671 - 7.41700i) q^{94} +(6.17946 - 5.18518i) q^{95} +(5.06123 - 1.84214i) q^{97} +(1.82215 - 0.0730766i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more