LMFDB - Embedded newform 441.2.bb.d.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.3
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.d.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.354207 + 0.902506i) q^{2} +(0.777050 - 0.720997i) q^{4} +(0.605902 - 0.413097i) q^{5} +(-0.310399 - 2.62748i) q^{7} +(2.67297 + 1.28723i) q^{8} +O(q^{10})$	\(q+(0.354207 + 0.902506i) q^{2} +(0.777050 - 0.720997i) q^{4} +(0.605902 - 0.413097i) q^{5} +(-0.310399 - 2.62748i) q^{7} +(2.67297 + 1.28723i) q^{8} +(0.587437 + 0.400508i) q^{10} +(-1.30775 - 0.197112i) q^{11} +(-0.696197 + 0.873004i) q^{13} +(2.26137 - 1.21081i) q^{14} +(-0.0565197 + 0.754203i) q^{16} +(5.89890 - 1.81957i) q^{17} +(2.99610 - 5.18940i) q^{19} +(0.172974 - 0.757850i) q^{20} +(-0.285321 - 1.25007i) q^{22} +(-5.13778 - 1.58479i) q^{23} +(-1.63024 + 4.15378i) q^{25} +(-1.03449 - 0.319098i) q^{26} +(-2.13560 - 1.81789i) q^{28} +(-0.529674 + 2.32065i) q^{29} +(3.15709 + 5.46824i) q^{31} +(4.96923 - 1.53281i) q^{32} +(3.73161 + 4.67929i) q^{34} +(-1.27348 - 1.46377i) q^{35} +(4.10810 + 3.81176i) q^{37} +(5.74471 + 0.865875i) q^{38} +(2.15131 - 0.324257i) q^{40} +(0.798221 + 0.384403i) q^{41} +(-5.17256 + 2.49098i) q^{43} +(-1.15831 + 0.789719i) q^{44} +(-0.389553 - 5.19822i) q^{46} +(0.440505 + 1.12239i) q^{47} +(-6.80731 + 1.63113i) q^{49} -4.32625 q^{50} +(0.0884530 + 1.18032i) q^{52} +(-6.99227 + 6.48788i) q^{53} +(-0.873796 + 0.420798i) q^{55} +(2.55249 - 7.42272i) q^{56} +(-2.28202 + 0.343959i) q^{58} +(-0.392674 - 0.267721i) q^{59} +(-2.56745 - 2.38225i) q^{61} +(-3.81686 + 4.78619i) q^{62} +(4.08662 + 5.12446i) q^{64} +(-0.0611921 + 0.816551i) q^{65} +(-2.53523 - 4.39115i) q^{67} +(3.27183 - 5.66698i) q^{68} +(0.869987 - 1.66780i) q^{70} +(2.06601 + 9.05180i) q^{71} +(1.19973 - 3.05687i) q^{73} +(-1.98501 + 5.05773i) q^{74} +(-1.41342 - 6.19260i) q^{76} +(-0.111983 + 3.49728i) q^{77} +(0.509557 - 0.882579i) q^{79} +(0.277313 + 0.480321i) q^{80} +(-0.0641901 + 0.856558i) q^{82} +(-4.13385 - 5.18369i) q^{83} +(2.82250 - 3.53930i) q^{85} +(-4.08028 - 3.78595i) q^{86} +(-3.24185 - 2.21025i) q^{88} +(-3.59885 + 0.542439i) q^{89} +(2.50990 + 1.55827i) q^{91} +(-5.13494 + 2.47286i) q^{92} +(-0.856932 + 0.795117i) q^{94} +(-0.328382 - 4.38195i) q^{95} -14.7267 q^{97} +(-3.88331 - 5.56587i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	0.354207	+	0.902506i	0.250463	+	0.638168i	0.999709	−	0.0241232i	$-0.00767939\pi$
$2$	0.354207	+	0.902506i	0.250463	+	0.638168i	−0.749246	+	0.662291i	$0.769584\pi$
$3$		0			0
$3$		0			0
$4$	0.777050	−	0.720997i	0.388525	−	0.360498i
$5$	0.605902	−	0.413097i	0.270968	−	0.184743i	−0.420211	−	0.907426i	$-0.638044\pi$
$5$	0.605902	−	0.413097i	0.270968	−	0.184743i	0.691179	+	0.722684i	$0.257092\pi$
$6$		0			0
$7$	−0.310399	−	2.62748i	−0.117320	−	0.993094i
$7$	−0.310399	−	2.62748i	−0.117320	−	0.993094i
$8$	2.67297	+	1.28723i	0.945036	+	0.455105i
$9$		0			0
$10$	0.587437	+	0.400508i	0.185764	+	0.126652i
$11$	−1.30775	−	0.197112i	−0.394302	−	0.0594315i	−0.0511011	−	0.998693i	$-0.516273\pi$
$11$	−1.30775	−	0.197112i	−0.394302	−	0.0594315i	−0.343201	+	0.939262i	$0.611511\pi$
$12$		0			0
$13$	−0.696197	+	0.873004i	−0.193090	+	0.242128i	−0.868947	−	0.494906i	$-0.835203\pi$
$13$	−0.696197	+	0.873004i	−0.193090	+	0.242128i	0.675856	+	0.737033i	$0.263774\pi$
$14$	2.26137	−	1.21081i	0.604377	−	0.323603i
$15$		0			0
$16$	−0.0565197	+	0.754203i	−0.0141299	+	0.188551i
$17$	5.89890	−	1.81957i	1.43069	−	0.441310i	0.519919	−	0.854216i	$-0.325962\pi$
$17$	5.89890	−	1.81957i	1.43069	−	0.441310i	0.910774	+	0.412905i	$0.135486\pi$
$18$		0			0
$19$	2.99610	−	5.18940i	0.687353	−	1.19053i	−0.285338	−	0.958427i	$-0.592106\pi$
$19$	2.99610	−	5.18940i	0.687353	−	1.19053i	0.972691	−	0.232103i	$-0.0745607\pi$
$20$	0.172974	−	0.757850i	0.0386782	−	0.169460i
$21$		0			0
$22$	−0.285321	−	1.25007i	−0.0608306	−	0.266516i
$23$	−5.13778	−	1.58479i	−1.07130	−	0.330452i	−0.291558	−	0.956553i	$-0.594174\pi$
$23$	−5.13778	−	1.58479i	−1.07130	−	0.330452i	−0.779742	+	0.626101i	$0.784650\pi$
$24$		0			0
$25$	−1.63024	+	4.15378i	−0.326047	+	0.830755i
$26$	−1.03449	−	0.319098i	−0.202880	−	0.0625802i
$27$		0			0
$28$	−2.13560	−	1.81789i	−0.403590	−	0.343548i
$29$	−0.529674	+	2.32065i	−0.0983579	+	0.430934i	−0.999999	−	0.00155131i	$-0.999506\pi$
$29$	−0.529674	+	2.32065i	−0.0983579	+	0.430934i	0.901641	+	0.432486i	$0.142363\pi$
$30$		0			0
$31$	3.15709	+	5.46824i	0.567030	+	0.982125i	0.996858	+	0.0792143i	$0.0252411\pi$
$31$	3.15709	+	5.46824i	0.567030	+	0.982125i	−0.429827	+	0.902911i	$0.641426\pi$
$32$	4.96923	−	1.53281i	0.878445	−	0.270964i
$33$		0			0
$34$	3.73161	+	4.67929i	0.639965	+	0.802491i
$35$	−1.27348	−	1.46377i	−0.215257	−	0.247422i
$36$		0			0
$37$	4.10810	+	3.81176i	0.675367	+	0.626649i	0.941391	−	0.337318i	$-0.109520\pi$
$37$	4.10810	+	3.81176i	0.675367	+	0.626649i	−0.266024	+	0.963966i	$0.585710\pi$
$38$	5.74471	+	0.865875i	0.931915	+	0.140464i
$39$		0			0
$40$	2.15131	−	0.324257i	0.340151	−	0.0512696i
$41$	0.798221	+	0.384403i	0.124661	+	0.0600337i	0.495175	−	0.868793i	$-0.335104\pi$
$41$	0.798221	+	0.384403i	0.124661	+	0.0600337i	−0.370514	+	0.928827i	$0.620818\pi$
$42$		0			0
$43$	−5.17256	+	2.49098i	−0.788809	+	0.379870i	−0.784507	−	0.620121i	$-0.787084\pi$
$43$	−5.17256	+	2.49098i	−0.788809	+	0.379870i	−0.00430211	+	0.999991i	$0.501369\pi$
$44$	−1.15831	+	0.789719i	−0.174621	+	0.119055i
$45$		0			0
$46$	−0.389553	−	5.19822i	−0.0574364	−	0.766435i
$47$	0.440505	+	1.12239i	0.0642543	+	0.163717i	0.959395	−	0.282067i	$-0.0910201\pi$
$47$	0.440505	+	1.12239i	0.0642543	+	0.163717i	−0.895140	+	0.445784i	$0.852925\pi$
$48$		0			0
$49$	−6.80731	+	1.63113i	−0.972472	+	0.233019i
$50$	−4.32625			−0.611824
$51$		0			0
$52$	0.0884530	+	1.18032i	0.0122662	+	0.163681i
$53$	−6.99227	+	6.48788i	−0.960463	+	0.891179i	−0.994123	−	0.108254i	$-0.965474\pi$
$53$	−6.99227	+	6.48788i	−0.960463	+	0.891179i	0.0336606	+	0.999433i	$0.489283\pi$
$54$		0			0
$55$	−0.873796	+	0.420798i	−0.117823	+	0.0567404i
$56$	2.55249	−	7.42272i	0.341091	−	0.991903i
$57$		0			0
$58$	−2.28202	+	0.343959i	−0.299643	+	0.0451640i
$59$	−0.392674	−	0.267721i	−0.0511218	−	0.0348543i	0.537490	−	0.843270i	$-0.319373\pi$
$59$	−0.392674	−	0.267721i	−0.0511218	−	0.0348543i	−0.588611	+	0.808416i	$0.700325\pi$
$60$		0			0
$61$	−2.56745	−	2.38225i	−0.328729	−	0.305016i	0.498490	−	0.866895i	$-0.333888\pi$
$61$	−2.56745	−	2.38225i	−0.328729	−	0.305016i	−0.827219	+	0.561880i	$0.810078\pi$
$62$	−3.81686	+	4.78619i	−0.484741	+	0.607846i
$63$		0			0
$64$	4.08662	+	5.12446i	0.510827	+	0.640557i
$65$	−0.0611921	+	0.816551i	−0.00758994	+	0.101281i
$66$		0			0
$67$	−2.53523	−	4.39115i	−0.309728	−	0.536465i	0.668575	−	0.743645i	$-0.266905\pi$
$67$	−2.53523	−	4.39115i	−0.309728	−	0.536465i	−0.978303	+	0.207180i	$0.933571\pi$
$68$	3.27183	−	5.66698i	0.396768	−	0.687222i
$69$		0			0
$70$	0.869987	−	1.66780i	0.103983	−	0.199340i
$71$	2.06601	+	9.05180i	0.245191	+	1.07425i	0.936217	+	0.351422i	$0.114302\pi$
$71$	2.06601	+	9.05180i	0.245191	+	1.07425i	−0.691026	+	0.722830i	$0.742841\pi$
$72$		0			0
$73$	1.19973	−	3.05687i	0.140418	−	0.357780i	−0.843314	−	0.537421i	$-0.819399\pi$
$73$	1.19973	−	3.05687i	0.140418	−	0.357780i	0.983732	+	0.179641i	$0.0574938\pi$
$74$	−1.98501	+	5.05773i	−0.230753	+	0.587950i
$75$		0			0
$76$	−1.41342	−	6.19260i	−0.162131	−	0.710340i
$77$	−0.111983	+	3.49728i	−0.0127617	+	0.398551i
$78$		0			0
$79$	0.509557	−	0.882579i	0.0573297	−	0.0992979i	−0.835936	−	0.548827i	$-0.815075\pi$
$79$	0.509557	−	0.882579i	0.0573297	−	0.0992979i	0.893266	+	0.449529i	$0.148408\pi$
$80$	0.277313	+	0.480321i	0.0310046	+	0.0537015i
$81$		0			0
$82$	−0.0641901	+	0.856558i	−0.00708861	+	0.0945910i
$83$	−4.13385	−	5.18369i	−0.453749	−	0.568984i	0.501359	−	0.865239i	$-0.332833\pi$
$83$	−4.13385	−	5.18369i	−0.453749	−	0.568984i	−0.955109	+	0.296255i	$0.904262\pi$
$84$		0			0
$85$	2.82250	−	3.53930i	0.306143	−	0.383891i
$86$	−4.08028	−	3.78595i	−0.439988	−	0.408249i
$87$		0			0
$88$	−3.24185	−	2.21025i	−0.345582	−	0.235614i
$89$	−3.59885	+	0.542439i	−0.381477	+	0.0574984i	−0.336982	−	0.941511i	$-0.609406\pi$
$89$	−3.59885	+	0.542439i	−0.381477	+	0.0574984i	−0.0444953	+	0.999010i	$0.514168\pi$
$90$		0			0
$91$	2.50990	+	1.55827i	0.263109	+	0.163351i
$92$	−5.13494	+	2.47286i	−0.535354	+	0.257813i
$93$		0			0
$94$	−0.856932	+	0.795117i	−0.0883858	+	0.0820100i
$95$	−0.328382	−	4.38195i	−0.0336912	−	0.449578i
$96$		0			0
$97$	−14.7267			−1.49527			−0.747636	−	0.664109i	$-0.768811\pi$
$97$	−14.7267			−1.49527			−0.747636	+	0.664109i	$0.768811\pi$
$98$	−3.88331	−	5.56587i	−0.392273	−	0.562238i
$99$		0			0
$100$	1.72808	+	4.40309i	0.172808	+	0.440309i
$101$	0.328936	+	4.38934i	0.0327303	+	0.436756i	0.989364	+	0.145462i	$0.0464668\pi$
$101$	0.328936	+	4.38934i	0.0327303	+	0.436756i	−0.956634	+	0.291294i	$0.905914\pi$
$102$		0			0
$103$	5.50872	−	3.75578i	0.542791	−	0.370068i	−0.260668	−	0.965428i	$-0.583943\pi$
$103$	5.50872	−	3.75578i	0.542791	−	0.370068i	0.803459	+	0.595360i	$0.202991\pi$
$104$	−2.98467	+	1.43734i	−0.292671	+	0.140943i
$105$		0			0
$106$	−8.33207	−	4.01251i	−0.809282	−	0.389730i
$107$	−13.0554	+	1.96778i	−1.26211	+	0.190232i	−0.745800	−	0.666170i	$-0.767932\pi$
$107$	−13.0554	+	1.96778i	−1.26211	+	0.190232i	−0.516309	+	0.856402i	$0.672694\pi$
$108$		0			0
$109$	8.27777	+	1.24767i	0.792866	+	0.119505i	0.532973	−	0.846132i	$-0.321075\pi$
$109$	8.27777	+	1.24767i	0.792866	+	0.119505i	0.259893	+	0.965637i	$0.416313\pi$
$110$	−0.689277	−	0.639556i	−0.0657200	−	0.0609793i
$111$		0			0
$112$	1.99920	−	0.0855991i	0.188906	−	0.00808835i
$113$	5.57830	+	6.99497i	0.524762	+	0.658031i	0.971613	−	0.236578i	$-0.0760257\pi$
$113$	5.57830	+	6.99497i	0.524762	+	0.658031i	−0.446850	+	0.894609i	$0.647454\pi$
$114$		0			0
$115$	−3.76766	+	1.16217i	−0.351336	+	0.108373i
$116$	1.26160	+	2.18515i	0.117137	+	0.202887i
$117$		0			0
$118$	0.102531	−	0.449219i	0.00943878	−	0.0413540i
$119$	−6.61189	−	14.9344i	−0.606111	−	1.36904i
$120$		0			0
$121$	−8.83994	−	2.72676i	−0.803631	−	0.247887i
$122$	1.24058	−	3.16095i	0.112317	−	0.286179i
$123$		0			0
$124$	6.39580	+	1.97284i	0.574360	+	0.177167i
$125$	1.54405	+	6.76492i	0.138104	+	0.605073i
$126$		0			0
$127$	−1.12111	+	4.91191i	−0.0994826	+	0.435862i	0.900517	+	0.434821i	$0.143188\pi$
$127$	−1.12111	+	4.91191i	−0.0994826	+	0.435862i	−0.999999	+	0.00104074i	$0.999669\pi$
$128$	2.02292	−	3.50381i	0.178803	−	0.309696i
$129$		0			0
$130$	−0.758617	+	0.234002i	−0.0665351	+	0.0205234i
$131$	0.850330	−	11.3469i	0.0742937	−	0.991380i	−0.828132	−	0.560534i	$-0.810596\pi$
$131$	0.850330	−	11.3469i	0.0742937	−	0.991380i	0.902425	−	0.430846i	$-0.141785\pi$
$132$		0			0
$133$	−14.5650	−	6.26142i	−1.26295	−	0.542934i
$134$	3.06504	−	3.84344i	0.264779	−	0.332023i
$135$		0			0
$136$	18.1098	+	2.72961i	1.55290	+	0.234062i
$137$	−6.14396	−	4.18888i	−0.524914	−	0.357880i	0.271687	−	0.962386i	$-0.412418\pi$
$137$	−6.14396	−	4.18888i	−0.524914	−	0.357880i	−0.796601	+	0.604506i	$0.793371\pi$
$138$		0			0
$139$	8.54606	+	4.11557i	0.724868	+	0.349078i	0.759663	−	0.650317i	$-0.225364\pi$
$139$	8.54606	+	4.11557i	0.724868	+	0.349078i	−0.0347957	+	0.999394i	$0.511078\pi$
$140$	−2.04493	−	0.219251i	−0.172828	−	0.0185301i
$141$		0			0
$142$	−7.43751	+	5.07081i	−0.624142	+	0.425533i
$143$	1.08253	−	1.00444i	0.0905259	−	0.0839958i
$144$		0			0
$145$	0.637724	+	1.62489i	0.0529601	+	0.134940i
$146$	3.18380			0.263493
$147$		0			0
$148$	5.94046			0.488303
$149$	−3.70002	−	9.42750i	−0.303117	−	0.772331i	−0.998555	−	0.0537439i	$-0.982885\pi$
$149$	−3.70002	−	9.42750i	−0.303117	−	0.772331i	0.695437	−	0.718587i	$-0.255211\pi$
$150$		0			0
$151$	−4.14923	+	3.84992i	−0.337660	+	0.313302i	−0.830717	−	0.556694i	$-0.812070\pi$
$151$	−4.14923	+	3.84992i	−0.337660	+	0.313302i	0.493058	+	0.869996i	$0.335879\pi$
$152$	14.6884	−	10.0144i	1.19139	−	0.812276i
$153$		0			0
$154$	−3.19598	+	1.13770i	−0.257539	+	0.0916781i
$155$	4.17180	+	2.00903i	0.335087	+	0.161369i
$156$		0			0
$157$	2.35121	+	1.60303i	0.187647	+	0.127936i	0.653500	−	0.756927i	$-0.273300\pi$
$157$	2.35121	+	1.60303i	0.187647	+	0.127936i	−0.465853	+	0.884862i	$0.654252\pi$
$158$	0.977022	+	0.147262i	0.0777277	+	0.0117156i
$159$		0			0
$160$	2.37767	−	2.98150i	0.187971	−	0.235709i
$161$	−2.56926	+	13.9913i	−0.202486	+	1.10267i
$162$		0			0
$163$	1.23174	−	16.4365i	0.0964776	−	1.28740i	−0.713380	−	0.700777i	$-0.752837\pi$
$163$	1.23174	−	16.4365i	0.0964776	−	1.28740i	0.809858	−	0.586626i	$-0.199544\pi$
$164$	0.897411	−	0.276815i	0.0700760	−	0.0216156i
$165$		0			0
$166$	3.21407	−	5.56693i	0.249460	−	0.432077i
$167$	−5.43239	+	23.8009i	−0.420371	+	1.84177i	0.109908	+	0.993942i	$0.464944\pi$
$167$	−5.43239	+	23.8009i	−0.420371	+	1.84177i	−0.530279	+	0.847823i	$0.677913\pi$
$168$		0			0
$169$	2.61533	+	11.4585i	0.201179	+	0.881423i
$170$	4.19399	+	1.29367i	0.321664	+	0.0992202i
$171$		0			0
$172$	−2.22335	+	5.66501i	−0.169529	+	0.431953i
$173$	18.9634	+	5.84942i	1.44176	+	0.444723i	0.914362	−	0.404897i	$-0.132693\pi$
$173$	18.9634	+	5.84942i	1.44176	+	0.444723i	0.527395	+	0.849620i	$0.323169\pi$
$174$		0			0
$175$	11.4200	+	2.99409i	0.863270	+	0.226332i
$176$	0.222576	−	0.975169i	0.0167773	−	0.0735061i
$177$		0			0
$178$	−1.76429	−	3.05585i	−0.132239	−	0.229045i
$179$	−7.59859	+	2.34385i	−0.567945	+	0.175188i	−0.565412	−	0.824809i	$-0.691283\pi$
$179$	−7.59859	+	2.34385i	−0.567945	+	0.175188i	−0.00253361	+	0.999997i	$0.500806\pi$
$180$		0			0
$181$	3.03369	+	3.80413i	0.225492	+	0.282758i	0.881689	−	0.471832i	$-0.156407\pi$
$181$	3.03369	+	3.80413i	0.225492	+	0.282758i	−0.656196	+	0.754590i	$0.727836\pi$
$182$	−0.517319	+	2.81715i	−0.0383462	+	0.208821i
$183$		0			0
$184$	−11.6931	−	10.8496i	−0.862027	−	0.799844i
$185$	4.06373	+	0.612508i	0.298771	+	0.0450325i
$186$		0			0
$187$	−8.07295	+	1.21680i	−0.590353	+	0.0889814i
$188$	1.15153	+	0.554549i	0.0839842	+	0.0404446i
$189$		0			0
$190$	3.83842	−	1.84849i	0.278468	−	0.134103i
$191$	13.5906	−	9.26589i	0.983379	−	0.670457i	0.0389738	−	0.999240i	$-0.487591\pi$
$191$	13.5906	−	9.26589i	0.983379	−	0.670457i	0.944405	+	0.328784i	$0.106639\pi$
$192$		0			0
$193$	1.77164	+	23.6409i	0.127525	+	1.70171i	0.583823	+	0.811881i	$0.301556\pi$
$193$	1.77164	+	23.6409i	0.127525	+	1.70171i	−0.456298	+	0.889827i	$0.650825\pi$
$194$	−5.21632	−	13.2910i	−0.374510	−	0.954235i
$195$		0			0
$196$	−4.11357	+	6.17552i	−0.293827	+	0.441108i
$197$	6.19181			0.441148			0.220574	−	0.975370i	$-0.429207\pi$
$197$	6.19181			0.441148			0.220574	+	0.975370i	$0.429207\pi$
$198$		0			0
$199$	−0.965516	−	12.8839i	−0.0684436	−	0.913317i	−0.920720	−	0.390224i	$-0.872397\pi$
$199$	−0.965516	−	12.8839i	−0.0684436	−	0.913317i	0.852276	−	0.523092i	$-0.175222\pi$
$200$	−9.70444	+	9.00441i	−0.686208	+	0.636708i
$201$		0			0
$202$	−3.84490	+	1.85160i	−0.270526	+	0.130278i
$203$	6.26188	+	0.671380i	0.439498	+	0.0471216i
$204$		0			0
$205$	0.642439	−	0.0968321i	0.0448699	−	0.00676305i
$206$	5.34085	+	3.64133i	0.372115	+	0.253703i
$207$		0			0
$208$	−0.619073	−	0.574416i	−0.0429250	−	0.0398286i
$209$	−4.94105	+	6.19588i	−0.341780	+	0.428578i
$210$		0			0
$211$	6.98276	+	8.75610i	0.480713	+	0.602795i	0.961758	−	0.273901i	$-0.0883140\pi$
$211$	6.98276	+	8.75610i	0.480713	+	0.602795i	−0.481045	+	0.876696i	$0.659743\pi$
$212$	−0.755602	+	10.0828i	−0.0518950	+	0.692490i
$213$		0			0
$214$	−6.40023	−	11.0855i	−0.437511	−	0.757791i
$215$	−2.10505	+	3.64606i	−0.143563	+	0.248659i
$216$		0			0
$217$	13.3877	−	9.99253i	0.908819	−	0.678337i
$218$	1.80602	+	7.91267i	0.122319	+	0.535914i
$219$		0			0
$220$	−0.375589	+	0.956984i	−0.0253222	+	0.0645199i
$221$	−2.51831	+	6.41654i	−0.169400	+	0.431623i
$222$		0			0
$223$	0.535149	+	2.34464i	0.0358362	+	0.157009i	0.989680	−	0.143294i	$-0.0457694\pi$
$223$	0.535149	+	2.34464i	0.0358362	+	0.157009i	−0.953844	+	0.300303i	$0.902912\pi$
$224$	−5.56986	−	12.5808i	−0.372152	−	0.840589i
$225$		0			0
$226$	−4.33712	+	7.51212i	−0.288501	+	0.499699i
$227$	0.234888	+	0.406839i	0.0155901	+	0.0270028i	0.873715	−	0.486438i	$-0.161704\pi$
$227$	0.234888	+	0.406839i	0.0155901	+	0.0270028i	−0.858125	+	0.513441i	$0.828371\pi$
$228$		0			0
$229$	0.630488	−	8.41327i	0.0416638	−	0.555965i	−0.936843	−	0.349750i	$-0.886266\pi$
$229$	0.630488	−	8.41327i	0.0416638	−	0.555965i	0.978507	−	0.206215i	$-0.0661145\pi$
$230$	−2.38340	−	2.98869i	−0.157157	−	0.197068i
$231$		0			0
$232$	−4.40302	+	5.52121i	−0.289072	+	0.362485i
$233$	−3.33255	−	3.09215i	−0.218322	−	0.202574i	0.563428	−	0.826165i	$-0.309482\pi$
$233$	−3.33255	−	3.09215i	−0.218322	−	0.202574i	−0.781750	+	0.623592i	$0.785673\pi$
$234$		0			0
$235$	0.730558	+	0.498086i	0.0476564	+	0.0324916i
$236$	−0.498153	+	0.0750845i	−0.0324270	+	0.00488758i
$237$		0			0
$238$	11.1364	−	11.2572i	0.721869	−	0.729694i
$239$	26.7126	−	12.8641i	1.72789	−	0.832109i	0.740846	−	0.671674i	$-0.234425\pi$
$239$	26.7126	−	12.8641i	1.72789	−	0.832109i	0.987046	−	0.160435i	$-0.0512897\pi$
$240$		0			0
$241$	3.75064	−	3.48008i	0.241600	−	0.224172i	−0.550074	−	0.835116i	$-0.685400\pi$
$241$	3.75064	−	3.48008i	0.241600	−	0.224172i	0.791674	+	0.610944i	$0.209210\pi$
$242$	−0.670255	−	8.94394i	−0.0430857	−	0.574938i
$243$		0			0
$244$	−3.71263			−0.237677
$245$	−3.45074	+	3.80038i	−0.220460	+	0.242798i
$246$		0			0
$247$	2.44449	+	6.22845i	0.155539	+	0.396307i
$248$	1.39990	+	18.6803i	0.0888936	+	1.18620i
$249$		0			0
$250$	−5.55847	+	3.78970i	−0.351549	+	0.239682i
$251$	18.0281	−	8.68186i	1.13792	−	0.547994i	0.232537	−	0.972587i	$-0.425297\pi$
$251$	18.0281	−	8.68186i	1.13792	−	0.547994i	0.905384	+	0.424593i	$0.139583\pi$
$252$		0			0
$253$	6.40655	+	3.08523i	0.402776	+	0.193967i
$254$	−4.83014	+	0.728026i	−0.303070	+	0.0456804i
$255$		0			0
$256$	16.8412	+	2.53840i	1.05257	+	0.158650i
$257$	7.18712	+	6.66867i	0.448320	+	0.415980i	0.871752	−	0.489948i	$-0.162984\pi$
$257$	7.18712	+	6.66867i	0.448320	+	0.415980i	−0.423432	+	0.905928i	$0.639175\pi$
$258$		0			0
$259$	8.74017	−	11.9771i	0.543088	−	0.744221i
$260$	0.541182	+	0.678620i	0.0335627	+	0.0420862i
$261$		0			0
$262$	10.5418	−	3.25172i	0.651275	−	0.200892i
$263$	−8.63988	−	14.9647i	−0.532758	−	0.922764i	−0.999268	−	0.0382482i	$-0.987822\pi$
$263$	−8.63988	−	14.9647i	−0.532758	−	0.922764i	0.466510	−	0.884516i	$-0.345511\pi$
$264$		0			0
$265$	−1.55651	+	6.81951i	−0.0956155	+	0.418919i
$266$	0.491921	−	15.3629i	0.0301616	−	0.941958i
$267$		0			0
$268$	−5.13601	−	1.58425i	−0.313732	−	0.0967734i
$269$	4.40829	−	11.2321i	0.268778	−	0.684835i	−0.731218	−	0.682143i	$-0.761048\pi$
$269$	4.40829	−	11.2321i	0.268778	−	0.684835i	0.999996	−	0.00269177i	$-0.000856817\pi$
$270$		0			0
$271$	8.32784	+	2.56880i	0.505880	+	0.156043i	0.537182	−	0.843467i	$-0.319489\pi$
$271$	8.32784	+	2.56880i	0.505880	+	0.156043i	−0.0313014	+	0.999510i	$0.509965\pi$
$272$	1.03892	+	4.55181i	0.0629938	+	0.275994i
$273$		0			0
$274$	1.60425	−	7.02869i	0.0969164	−	0.424619i
$275$	2.95070	−	5.11077i	0.177934	−	0.308191i
$276$		0			0
$277$	−21.6749	+	6.68583i	−1.30232	+	0.401712i	−0.866885	−	0.498508i	$-0.833881\pi$
$277$	−21.6749	+	6.68583i	−1.30232	+	0.401712i	−0.435434	+	0.900220i	$0.643405\pi$
$278$	−0.687244	+	9.17064i	−0.0412182	+	0.550018i
$279$		0			0
$280$	−1.51974	−	5.55187i	−0.0908220	−	0.331788i
$281$	−9.27960	+	11.6363i	−0.553575	+	0.694161i	−0.977355	−	0.211604i	$-0.932131\pi$
$281$	−9.27960	+	11.6363i	−0.553575	+	0.694161i	0.423781	+	0.905765i	$0.360703\pi$
$282$		0			0
$283$	−27.1913	−	4.09843i	−1.61636	−	0.243627i	−0.722300	−	0.691580i	$-0.756915\pi$
$283$	−27.1913	−	4.09843i	−1.61636	−	0.243627i	−0.894057	+	0.447953i	$0.852153\pi$
$284$	8.13172	+	5.54411i	0.482529	+	0.328982i
$285$		0			0
$286$	1.28996	+	0.621211i	0.0762768	+	0.0367330i
$287$	0.762245	−	2.21663i	0.0449939	−	0.130843i
$288$		0			0
$289$	17.4401	−	11.8905i	1.02589	−	0.699439i
$290$	−1.24059	+	1.15110i	−0.0728499	+	0.0675949i
$291$		0			0
$292$	−1.27174	−	3.24035i	−0.0744231	−	0.189627i
$293$	1.76427			0.103070			0.0515348	−	0.998671i	$-0.483589\pi$
$293$	1.76427			0.103070			0.0515348	+	0.998671i	$0.483589\pi$
$294$		0			0
$295$	−0.348517			−0.0202914
$296$	6.07418	+	15.4768i	0.353055	+	0.899569i
$297$		0			0
$298$	7.19780	−	6.67858i	0.416957	−	0.386880i
$299$	4.96044	−	3.38197i	0.286869	−	0.195584i
$300$		0			0
$301$	8.15055	+	12.8176i	0.469790	+	0.738795i
$302$	−4.94427	−	2.38103i	−0.284511	−	0.137013i
$303$		0			0
$304$	3.74452	+	2.55297i	0.214763	+	0.146423i
$305$	−2.53972	−	0.382802i	−0.145424	−	0.0219192i
$306$		0			0
$307$	2.40192	−	3.01191i	0.137085	−	0.171899i	−0.708550	−	0.705660i	$-0.750651\pi$
$307$	2.40192	−	3.01191i	0.137085	−	0.171899i	0.845635	+	0.533761i	$0.179222\pi$
$308$	2.43451	+	2.79830i	0.138719	+	0.159448i
$309$		0			0
$310$	−0.335482	+	4.47669i	−0.0190541	+	0.254259i
$311$	7.89454	−	2.43514i	0.447658	−	0.138084i	−0.0627260	−	0.998031i	$-0.519979\pi$
$311$	7.89454	−	2.43514i	0.447658	−	0.138084i	0.510384	+	0.859947i	$0.329503\pi$
$312$		0			0
$313$	−14.2747	+	24.7245i	−0.806854	+	1.39751i	0.108179	+	0.994131i	$0.465498\pi$
$313$	−14.2747	+	24.7245i	−0.806854	+	1.39751i	−0.915033	+	0.403380i	$0.867835\pi$
$314$	−0.613926	+	2.68979i	−0.0346459	+	0.151793i
$315$		0			0
$316$	−0.240385	−	1.05320i	−0.0135227	−	0.0592469i
$317$	−5.85456	−	1.80589i	−0.328825	−	0.101429i	0.125947	−	0.992037i	$-0.459803\pi$
$317$	−5.85456	−	1.80589i	−0.328825	−	0.101429i	−0.454772	+	0.890608i	$0.650279\pi$
$318$		0			0
$319$	1.15011	−	2.93043i	0.0643938	−	0.164073i
$320$	4.59299	+	1.41675i	0.256756	+	0.0791987i
$321$		0			0
$322$	−13.5373	+	2.63706i	−0.754404	+	0.146958i
$323$	8.23123	−	36.0634i	0.457998	−	2.00662i
$324$		0			0
$325$	−2.49130	−	4.31505i	−0.138192	−	0.239356i
$326$	15.2703	−	4.71027i	0.845744	−	0.260877i
$327$		0			0
$328$	1.63880	+	2.05499i	0.0904877	+	0.113468i
$329$	2.81232	−	1.50581i	0.155048	−	0.0830178i
$330$		0			0
$331$	1.28167	+	1.18922i	0.0704472	+	0.0653654i	0.714611	−	0.699522i	$-0.246604\pi$
$331$	1.28167	+	1.18922i	0.0704472	+	0.0653654i	−0.644163	+	0.764888i	$0.722794\pi$
$332$	−6.94963	−	1.04749i	−0.381411	−	0.0574884i
$333$		0			0
$334$	−23.4046	+	3.52768i	−1.28064	+	0.193026i
$335$	−3.35007	−	1.61331i	−0.183034	−	0.0881446i
$336$		0			0
$337$	−2.46216	+	1.18571i	−0.134122	+	0.0645900i	−0.499741	−	0.866175i	$-0.666572\pi$
$337$	−2.46216	+	1.18571i	−0.134122	+	0.0645900i	0.365619	+	0.930765i	$0.380857\pi$
$338$	−9.41499	+	6.41903i	−0.512108	+	0.349149i
$339$		0			0
$340$	−0.358603	−	4.78522i	−0.0194480	−	0.259515i
$341$	−3.05084	−	7.77340i	−0.165212	−	0.420953i
$342$		0			0
$343$	6.39875	+	17.3798i	0.345500	+	0.938419i
$344$	−17.0326			−0.918334
$345$		0			0
$346$	1.43783	+	19.1865i	0.0772980	+	1.03147i
$347$	−23.9175	+	22.1922i	−1.28396	+	1.19134i	−0.313634	+	0.949544i	$0.601547\pi$
$347$	−23.9175	+	22.1922i	−1.28396	+	1.19134i	−0.970327	+	0.241798i	$0.922263\pi$
$348$		0			0
$349$	19.2153	−	9.25361i	1.02857	−	0.495335i	0.158034	−	0.987434i	$-0.449485\pi$
$349$	19.2153	−	9.25361i	1.02857	−	0.495335i	0.870539	+	0.492099i	$0.163770\pi$
$350$	1.34286	+	11.3671i	0.0717790	+	0.607599i
$351$		0			0
$352$	−6.80066	+	1.02503i	−0.362476	+	0.0546345i
$353$	−12.5084	−	8.52807i	−0.665754	−	0.453904i	0.182703	−	0.983168i	$-0.441515\pi$
$353$	−12.5084	−	8.52807i	−0.665754	−	0.453904i	−0.848457	+	0.529265i	$0.822468\pi$
$354$		0			0
$355$	4.99107	+	4.63104i	0.264899	+	0.245790i
$356$	−2.40539	+	3.01626i	−0.127485	+	0.159861i
$357$		0			0
$358$	−4.80682	−	6.02756i	−0.254048	−	0.318567i
$359$	1.36484	−	18.2125i	0.0720334	−	0.961218i	−0.837728	−	0.546087i	$-0.816117\pi$
$359$	1.36484	−	18.2125i	0.0720334	−	0.961218i	0.909762	−	0.415131i	$-0.136264\pi$
$360$		0			0
$361$	−8.45325	−	14.6415i	−0.444908	−	0.770603i
$362$	−2.35869	+	4.08537i	−0.123970	+	0.214722i
$363$		0			0
$364$	3.07382	−	0.598779i	0.161112	−	0.0313846i
$365$	−0.535863	−	2.34777i	−0.0280484	−	0.122888i
$366$		0			0
$367$	10.4929	−	26.7356i	0.547727	−	1.39558i	−0.342263	−	0.939604i	$-0.611193\pi$
$367$	10.4929	−	26.7356i	0.547727	−	1.39558i	0.889990	−	0.455980i	$-0.150711\pi$
$368$	1.48564	−	3.78535i	0.0774444	−	0.197325i
$369$		0			0
$370$	0.886610	+	3.88449i	0.0460927	+	0.201945i
$371$	19.2172	+	16.3582i	0.997706	+	0.849277i
$372$		0			0
$373$	17.9437	−	31.0793i	0.929087	−	1.60923i	0.144235	−	0.989543i	$-0.453928\pi$
$373$	17.9437	−	31.0793i	0.929087	−	1.60923i	0.784852	−	0.619683i	$-0.212739\pi$
$374$	−3.95767	−	6.85489i	−0.204646	−	0.354458i
$375$		0			0
$376$	−0.267320	+	3.56714i	−0.0137860	+	0.183961i
$377$	−1.65718	−	2.07804i	−0.0853491	−	0.107024i
$378$		0			0
$379$	9.52620	−	11.9455i	0.489328	−	0.613598i	−0.474457	−	0.880279i	$-0.657356\pi$
$379$	9.52620	−	11.9455i	0.489328	−	0.613598i	0.963785	+	0.266681i	$0.0859270\pi$
$380$	−3.41454	−	3.16823i	−0.175162	−	0.162527i
$381$		0			0
$382$	13.1764	+	8.98352i	0.674164	+	0.459637i
$383$	−29.1858	+	4.39904i	−1.49132	+	0.224781i	−0.843549	−	0.537052i	$-0.819538\pi$
$383$	−29.1858	+	4.39904i	−1.49132	+	0.224781i	−0.647773	+	0.761833i	$0.724300\pi$
$384$		0			0
$385$	1.37686	+	2.16527i	0.0701714	+	0.110352i
$386$	−20.7085	+	9.97269i	−1.05404	+	0.507597i
$387$		0			0
$388$	−11.4434	+	10.6179i	−0.580950	+	0.539043i
$389$	−2.15361	−	28.7379i	−0.109192	−	1.45707i	−0.735516	−	0.677507i	$-0.763060\pi$
$389$	−2.15361	−	28.7379i	−0.109192	−	1.45707i	0.626324	−	0.779563i	$-0.284559\pi$
$390$		0			0
$391$	−33.1909			−1.67853
$392$	−20.2953	−	4.40262i	−1.02507	−	0.222366i
$393$		0			0
$394$	2.19319	+	5.58815i	0.110491	+	0.281527i
$395$	−0.0558490	−	0.745253i	−0.00281007	−	0.0374977i
$396$		0			0
$397$	11.4823	−	7.82848i	0.576278	−	0.392900i	−0.239816	−	0.970818i	$-0.577087\pi$
$397$	11.4823	−	7.82848i	0.576278	−	0.392900i	0.816095	+	0.577918i	$0.196135\pi$
$398$	11.2858	−	5.43496i	0.565707	−	0.272430i
$399$		0			0
$400$	−3.04065	−	1.46430i	−0.152032	−	0.0732150i
$401$	16.1953	−	2.44105i	0.808755	−	0.121900i	0.268368	−	0.963317i	$-0.413516\pi$
$401$	16.1953	−	2.44105i	0.808755	−	0.121900i	0.540387	+	0.841416i	$0.318278\pi$
$402$		0			0
$403$	−6.97175	−	1.05082i	−0.347288	−	0.0523452i
$404$	3.42030	+	3.17358i	0.170166	+	0.157891i
$405$		0			0
$406$	1.61208	+	5.88919i	0.0800061	+	0.292276i
$407$	−4.62103	−	5.79459i	−0.229056	−	0.287227i
$408$		0			0
$409$	−15.6130	+	4.81598i	−0.772014	+	0.238135i	−0.655643	−	0.755071i	$-0.727602\pi$
$409$	−15.6130	+	4.81598i	−0.772014	+	0.238135i	−0.116371	+	0.993206i	$0.537126\pi$
$410$	0.314948	+	0.545507i	0.0155542	+	0.0269407i
$411$		0			0
$412$	1.57264	−	6.89020i	0.0774786	−	0.339456i
$413$	−0.581545	+	1.11484i	−0.0286160	+	0.0548579i
$414$		0			0
$415$	−4.64607	−	1.43312i	−0.228067	−	0.0703493i
$416$	−2.12142	+	5.40529i	−0.104011	+	0.265016i
$417$		0			0
$418$	−7.34198	−	2.26470i	−0.359108	−	0.110770i
$419$	−3.36310	−	14.7347i	−0.164298	−	0.719837i	−0.988208	−	0.153117i	$-0.951069\pi$
$419$	−3.36310	−	14.7347i	−0.164298	−	0.719837i	0.823910	−	0.566721i	$-0.191788\pi$
$420$		0			0
$421$	1.56331	−	6.84933i	0.0761913	−	0.333816i	−0.922439	−	0.386144i	$-0.873807\pi$
$421$	1.56331	−	6.84933i	0.0761913	−	0.333816i	0.998630	+	0.0523278i	$0.0166641\pi$
$422$	−5.42909	+	9.40346i	−0.264284	+	0.457753i
$423$		0			0
$424$	−27.0415	+	8.34120i	−1.31325	+	0.405085i
$425$	−2.05852	+	27.4690i	−0.0998529	+	1.33244i
$426$		0			0
$427$	−5.46238	+	7.48538i	−0.264343	+	0.362243i
$428$	−8.72590	+	10.9419i	−0.421782	+	0.528898i
$429$		0			0
$430$	−4.03621	−	0.608361i	−0.194644	−	0.0293378i
$431$	12.5785	+	8.57589i	0.605886	+	0.413086i	0.827032	−	0.562155i	$-0.190027\pi$
$431$	12.5785	+	8.57589i	0.605886	+	0.413086i	−0.221146	+	0.975241i	$0.570980\pi$
$432$		0			0
$433$	6.45680	+	3.10943i	0.310294	+	0.149430i	0.582549	−	0.812795i	$-0.302055\pi$
$433$	6.45680	+	3.10943i	0.310294	+	0.149430i	−0.272255	+	0.962225i	$0.587770\pi$
$434$	13.7604	+	8.54309i	0.660518	+	0.410081i
$435$		0			0
$436$	7.33181	−	4.99874i	0.351130	−	0.239396i
$437$	−23.6174	+	21.9138i	−1.12977	+	1.04828i
$438$		0			0
$439$	0.923286	+	2.35249i	0.0440660	+	0.112278i	0.951212	−	0.308537i	$-0.0998393\pi$
$439$	0.923286	+	2.35249i	0.0440660	+	0.112278i	−0.907146	+	0.420815i	$0.861744\pi$
$440$	−2.87729			−0.137169
$441$		0			0
$442$	−6.68297			−0.317876
$443$	1.15467	+	2.94206i	0.0548602	+	0.139781i	0.955676	−	0.294419i	$-0.0951261\pi$
$443$	1.15467	+	2.94206i	0.0548602	+	0.139781i	−0.900816	+	0.434201i	$0.857031\pi$
$444$		0			0
$445$	−1.95647	+	1.81534i	−0.0927455	+	0.0860553i
$446$	−1.92650	+	1.31347i	−0.0912224	+	0.0621944i
$447$		0			0
$448$	12.1959	−	12.3281i	0.576204	−	0.582450i
$449$	16.8409	+	8.11014i	0.794771	+	0.382741i	0.786785	−	0.617227i	$-0.211744\pi$
$449$	16.8409	+	8.11014i	0.794771	+	0.382741i	0.00798535	+	0.999968i	$0.497458\pi$
$450$		0			0
$451$	−0.968104	−	0.660042i	−0.0455863	−	0.0310802i
$452$	9.37797	+	1.41350i	0.441102	+	0.0664855i
$453$		0			0
$454$	−0.283975	+	0.356093i	−0.0133276	+	0.0167123i
$455$	2.16447	−	0.0926754i	0.101472	−	0.00434469i
$456$		0			0
$457$	−1.40015	+	18.6837i	−0.0654963	+	0.873988i	0.863607	+	0.504166i	$0.168200\pi$
$457$	−1.40015	+	18.6837i	−0.0654963	+	0.873988i	−0.929103	+	0.369821i	$0.879419\pi$
$458$	7.81635	−	2.41103i	0.365234	−	0.112660i
$459$		0			0
$460$	−2.08974	+	3.61953i	−0.0974346	+	0.168762i
$461$	−1.58855	+	6.95990i	−0.0739862	+	0.324155i	−0.998354	−	0.0573470i	$-0.981736\pi$
$461$	−1.58855	+	6.95990i	−0.0739862	+	0.324155i	0.924368	+	0.381502i	$0.124593\pi$
$462$		0			0
$463$	−8.12461	−	35.5962i	−0.377583	−	1.65430i	−0.704843	−	0.709364i	$-0.748982\pi$
$463$	−8.12461	−	35.5962i	−0.377583	−	1.65430i	0.327260	−	0.944934i	$-0.393875\pi$
$464$	−1.72030	−	0.530644i	−0.0798631	−	0.0246345i
$465$		0			0
$466$	1.61027	−	4.10291i	0.0745944	−	0.190064i
$467$	−39.8324	−	12.2867i	−1.84322	−	0.568559i	−0.999495	−	0.0317884i	$-0.989880\pi$
$467$	−39.8324	−	12.2867i	−1.84322	−	0.568559i	−0.843728	−	0.536771i	$-0.819644\pi$
$468$		0			0
$469$	−10.7507	+	8.02428i	−0.496423	+	0.370527i
$470$	−0.190757	+	0.835759i	−0.00879894	+	0.0385507i
$471$		0			0
$472$	−0.704986	−	1.22107i	−0.0324496	−	0.0562043i
$473$	7.25543	−	2.23800i	0.333605	−	0.102904i
$474$		0			0
$475$	16.6713	+	20.9051i	0.764930	+	0.959191i
$476$	−15.9055	−	6.83765i	−0.729025	−	0.313403i
$477$		0			0
$478$	21.0717	+	19.5517i	0.963798	+	0.894274i
$479$	−7.81738	−	1.17828i	−0.357185	−	0.0538370i	−0.0320014	−	0.999488i	$-0.510188\pi$
$479$	−7.81738	−	1.17828i	−0.357185	−	0.0538370i	−0.325184	+	0.945651i	$0.605426\pi$
$480$		0			0
$481$	−6.18772	+	0.932649i	−0.282136	+	0.0425251i
$482$	4.46930	+	2.15230i	0.203571	+	0.0980346i
$483$		0			0
$484$	−8.83506	+	4.25474i	−0.401594	+	0.193397i
$485$	−8.92295	+	6.08356i	−0.405170	+	0.276240i
$486$		0			0
$487$	−1.84295	−	24.5925i	−0.0835122	−	1.11439i	−0.868767	−	0.495220i	$-0.835087\pi$
$487$	−1.84295	−	24.5925i	−0.0835122	−	1.11439i	0.785255	−	0.619172i	$-0.212532\pi$
$488$	−3.79621	−	9.67258i	−0.171846	−	0.437857i
$489$		0			0
$490$	−4.65215	−	1.76819i	−0.210163	−	0.0798788i
$491$	−9.78275			−0.441489			−0.220745	−	0.975332i	$-0.570849\pi$
$491$	−9.78275			−0.441489			−0.220745	+	0.975332i	$0.570849\pi$
$492$		0			0
$493$	1.09810	+	14.6531i	0.0494557	+	0.659941i
$494$	−4.75536	+	4.41233i	−0.213954	+	0.198520i
$495$		0			0
$496$	−4.30260	+	2.07202i	−0.193192	+	0.0930366i
$497$	23.1421	−	8.23808i	1.03807	−	0.369528i
$498$		0			0
$499$	−36.2150	+	5.45853i	−1.62121	+	0.244357i	−0.895960	−	0.444134i	$-0.853511\pi$
$499$	−36.2150	+	5.45853i	−1.62121	+	0.244357i	−0.725245	+	0.688491i	$0.758273\pi$
$500$	6.07729	+	4.14343i	0.271785	+	0.185300i
$501$		0			0
$502$	14.2211	+	13.1953i	0.634719	+	0.588933i
$503$	−2.68292	+	3.36428i	−0.119626	+	0.150006i	−0.838038	−	0.545611i	$-0.816298\pi$
$503$	−2.68292	+	3.36428i	−0.119626	+	0.150006i	0.718413	+	0.695617i	$0.244869\pi$
$504$		0			0
$505$	2.01253	+	2.52363i	0.0895563	+	0.112300i
$506$	−0.515192	+	6.87476i	−0.0229031	+	0.305621i
$507$		0			0
$508$	2.67031	+	4.62512i	0.118476	+	0.205207i
$509$	−16.9704	+	29.3935i	−0.752198	+	1.30284i	0.194557	+	0.980891i	$0.437673\pi$
$509$	−16.9704	+	29.3935i	−0.752198	+	1.30284i	−0.946755	+	0.321954i	$0.895660\pi$
$510$		0			0
$511$	−8.40427	−	2.20343i	−0.371783	−	0.0974739i
$512$	1.87378	+	8.20956i	0.0828101	+	0.362815i
$513$		0			0
$514$	−3.47279	+	8.84851i	−0.153178	+	0.390291i
$515$	1.78624	−	4.55127i	0.0787113	−	0.200553i
$516$		0			0
$517$	−0.354835	−	1.55463i	−0.0156056	−	0.0683727i
$518$	13.9052	+	3.64567i	0.610961	+	0.160182i
$519$		0			0
$520$	−1.21466	+	2.10385i	−0.0532662	+	0.0922597i
$521$	−22.2446	−	38.5288i	−0.974555	−	1.68798i	−0.681395	−	0.731916i	$-0.738626\pi$
$521$	−22.2446	−	38.5288i	−0.974555	−	1.68798i	−0.293161	−	0.956063i	$-0.594707\pi$
$522$		0			0
$523$	0.487773	−	6.50888i	0.0213288	−	0.284614i	−0.976333	−	0.216272i	$-0.930610\pi$
$523$	0.487773	−	6.50888i	0.0213288	−	0.284614i	0.997662	−	0.0683416i	$-0.0217708\pi$
$524$	−7.52030	−	9.43016i	−0.328526	−	0.411958i
$525$		0			0
$526$	10.4454	−	13.0982i	0.455443	−	0.571107i
$527$	28.5732	+	26.5121i	1.24467	+	1.15488i
$528$		0			0
$529$	4.88167	+	3.32827i	0.212246	+	0.144707i
$530$	−6.70597	+	1.01076i	−0.291289	+	0.0439047i
$531$		0			0
$532$	−15.8322	+	5.63591i	−0.686414	+	0.244348i
$533$	−0.891304	+	0.429230i	−0.0386067	+	0.0185920i
$534$		0			0
$535$	−7.09738	+	6.58541i	−0.306846	+	0.284712i
$536$	−1.12416	−	15.0008i	−0.0485562	−	0.647937i
$537$		0			0
$538$	11.6985			0.504359
$539$	9.22378	−	0.791315i	0.397296	−	0.0340844i
$540$		0			0
$541$	8.98067	+	22.8824i	0.386109	+	0.983790i	0.983349	+	0.181727i	$0.0581689\pi$
$541$	8.98067	+	22.8824i	0.386109	+	0.983790i	−0.597240	+	0.802063i	$0.703736\pi$
$542$	0.631427	+	8.42581i	0.0271221	+	0.361920i
$543$		0			0
$544$	26.5240	−	18.0837i	1.13721	−	0.775333i
$545$	5.53093	−	2.66355i	0.236919	−	0.114094i
$546$		0			0
$547$	0.390071	+	0.187849i	0.0166783	+	0.00803182i	0.442204	−	0.896914i	$-0.354197\pi$
$547$	0.390071	+	0.187849i	0.0166783	+	0.00803182i	−0.425526	+	0.904946i	$0.639911\pi$
$548$	−7.79433	+	1.17481i	−0.332957	+	0.0501852i
$549$		0			0
$550$	5.65766	+	0.852755i	0.241243	+	0.0363616i
$551$	10.4558	+	9.70160i	0.445434	+	0.413302i
$552$		0			0
$553$	−2.47712	−	1.06490i	−0.105338	−	0.0452842i
$554$	−13.7114	−	17.1936i	−0.582542	−	0.730485i
$555$		0			0
$556$	9.60803	−	2.96368i	0.407471	−	0.125688i
$557$	14.7530	+	25.5529i	0.625104	+	1.08271i	0.988521	+	0.151085i	$0.0482766\pi$
$557$	14.7530	+	25.5529i	0.625104	+	1.08271i	−0.363417	+	0.931626i	$0.618390\pi$
$558$		0			0
$559$	1.42649	−	6.24988i	0.0603343	−	0.264342i
$560$	1.17596	−	0.877726i	0.0496932	−	0.0370907i
$561$		0			0
$562$	−13.7887	−	4.25325i	−0.581641	−	0.179413i
$563$	16.0259	−	40.8334i	0.675413	−	1.72092i	−0.0174436	−	0.999848i	$-0.505553\pi$
$563$	16.0259	−	40.8334i	0.675413	−	1.72092i	0.692856	−	0.721076i	$-0.256352\pi$
$564$		0			0
$565$	6.26950	+	1.93389i	0.263760	+	0.0813592i
$566$	−5.93251	−	25.9920i	−0.249362	−	1.09253i
$567$		0			0
$568$	−6.12939	+	26.8546i	−0.257183	+	1.12679i
$569$	18.8824	−	32.7053i	0.791593	−	1.37108i	−0.133387	−	0.991064i	$-0.542585\pi$
$569$	18.8824	−	32.7053i	0.791593	−	1.37108i	0.924980	−	0.380015i	$-0.124081\pi$
$570$		0			0
$571$	20.5360	−	6.33452i	0.859405	−	0.265091i	0.166430	−	0.986053i	$-0.446776\pi$
$571$	20.5360	−	6.33452i	0.859405	−	0.265091i	0.692975	+	0.720962i	$0.256300\pi$
$572$	0.116981	−	1.56100i	0.00489123	−	0.0652689i
$573$		0			0
$574$	2.27051	−	0.0972160i	0.0947694	−	0.00405772i
$575$	14.9587	−	18.7576i	0.623820	−	0.782245i
$576$		0			0
$577$	−7.91340	−	1.19275i	−0.329439	−	0.0496550i	−0.0177598	−	0.999842i	$-0.505653\pi$
$577$	−7.91340	−	1.19275i	−0.329439	−	0.0496550i	−0.311679	+	0.950187i	$0.600891\pi$
$578$	16.9086	+	11.5281i	0.703306	+	0.479506i
$579$		0			0
$580$	1.66709	+	0.802826i	0.0692220	+	0.0333356i
$581$	−12.3369	+	12.4706i	−0.511821	+	0.517369i
$582$		0			0
$583$	10.4230	−	7.10628i	0.431676	−	0.294312i
$584$	7.14175	−	6.62658i	0.295528	−	0.274210i
$585$		0			0
$586$	0.624917	+	1.59226i	0.0258151	+	0.0657758i
$587$	−23.2048			−0.957765			−0.478882	−	0.877879i	$-0.658958\pi$
$587$	−23.2048			−0.957765			−0.478882	+	0.877879i	$0.658958\pi$
$588$		0			0
$589$	37.8359			1.55900
$590$	−0.123447	−	0.314538i	−0.00508224	−	0.0129493i
$591$		0			0
$592$	−3.10702	+	2.88290i	−0.127698	+	0.118486i
$593$	34.6741	−	23.6404i	1.42390	−	0.970796i	0.426084	−	0.904683i	$-0.359893\pi$
$593$	34.6741	−	23.6404i	1.42390	−	0.970796i	0.997812	−	0.0661128i	$-0.0210597\pi$
$594$		0			0
$595$	−10.1755	−	6.31746i	−0.417156	−	0.258991i
$596$	−9.67229	−	4.65793i	−0.396193	−	0.190796i
$597$		0			0
$598$	4.80927	+	3.27890i	0.196666	+	0.134084i
$599$	40.2574	+	6.06782i	1.64487	+	0.247924i	0.905182	−	0.425024i	$-0.139734\pi$
$599$	40.2574	+	6.06782i	1.64487	+	0.247924i	0.739689	+	0.672949i	$0.234973\pi$
$600$		0			0
$601$	11.8350	−	14.8406i	0.482759	−	0.605360i	−0.479485	−	0.877550i	$-0.659176\pi$
$601$	11.8350	−	14.8406i	0.482759	−	0.605360i	0.962244	+	0.272190i	$0.0877478\pi$
$602$	−8.68099	+	11.8960i	−0.353811	+	0.484845i
$603$		0			0
$604$	−0.448376	+	5.98316i	−0.0182442	+	0.243451i
$605$	−6.48255	+	1.99960i	−0.263553	+	0.0812954i
$606$		0			0
$607$	−7.30343	+	12.6499i	−0.296437	+	0.513444i	−0.975318	−	0.220804i	$-0.929132\pi$
$607$	−7.30343	+	12.6499i	−0.296437	+	0.513444i	0.678881	+	0.734248i	$0.262465\pi$
$608$	6.93399	−	30.3798i	0.281210	−	1.23206i
$609$		0			0
$610$	−0.554108	−	2.42771i	−0.0224352	−	0.0982950i
$611$	−1.28653	−	0.396841i	−0.0520473	−	0.0160545i
$612$		0			0
$613$	2.37674	−	6.05584i	0.0959957	−	0.244593i	−0.874807	−	0.484471i	$-0.839012\pi$
$613$	2.37674	−	6.05584i	0.0959957	−	0.244593i	0.970803	+	0.239878i	$0.0771074\pi$
$614$	3.56904	+	1.10090i	0.144035	+	0.0444288i
$615$		0			0
$616$	−4.80113	+	9.20395i	−0.193443	+	0.370838i
$617$	−8.86369	+	38.8344i	−0.356839	+	1.56341i	0.404178	+	0.914680i	$0.367558\pi$
$617$	−8.86369	+	38.8344i	−0.356839	+	1.56341i	−0.761017	+	0.648732i	$0.775299\pi$
$618$		0			0
$619$	−11.3318	−	19.6273i	−0.455463	−	0.788886i	0.543251	−	0.839570i	$-0.317193\pi$
$619$	−11.3318	−	19.6273i	−0.455463	−	0.788886i	−0.998715	+	0.0506844i	$0.983860\pi$
$620$	4.69020	−	1.44674i	0.188363	−	0.0581023i
$621$		0			0
$622$	4.99404	+	6.26232i	0.200243	+	0.251096i
$623$	2.54233	+	9.28753i	0.101856	+	0.372097i
$624$		0			0
$625$	−12.6251	−	11.7144i	−0.505005	−	0.468576i
$626$	−27.3702	−	4.12540i	−1.09393	−	0.164884i
$627$		0			0
$628$	2.98279	−	0.449583i	0.119026	−	0.0179403i
$629$	31.1690	+	15.0102i	1.24279	+	0.598496i
$630$		0			0
$631$	−13.7573	+	6.62518i	−0.547670	+	0.263744i	−0.687193	−	0.726475i	$-0.741157\pi$
$631$	−13.7573	+	6.62518i	−0.547670	+	0.263744i	0.139523	+	0.990219i	$0.455443\pi$
$632$	2.49811	−	1.70318i	0.0993696	−	0.0677490i
$633$		0			0
$634$	−0.443900	−	5.92343i	−0.0176295	−	0.235250i
$635$	1.34981	+	3.43927i	0.0535657	+	0.136483i
$636$		0			0
$637$	3.31524	−	7.07839i	0.131355	−	0.280456i
$638$	3.05211			0.120834
$639$		0			0
$640$	−0.221718	−	2.95863i	−0.00876419	−	0.116950i
$641$	5.22195	−	4.84526i	0.206254	−	0.191376i	−0.570281	−	0.821450i	$-0.693166\pi$
$641$	5.22195	−	4.84526i	0.206254	−	0.191376i	0.776536	+	0.630073i	$0.216975\pi$
$642$		0			0
$643$	−20.0496	+	9.65540i	−0.790681	+	0.380772i	−0.785223	−	0.619213i	$-0.787452\pi$
$643$	−20.0496	+	9.65540i	−0.790681	+	0.380772i	−0.00545784	+	0.999985i	$0.501737\pi$
$644$	8.09126	+	12.7244i	0.318840	+	0.501411i
$645$		0			0
$646$	35.4630	−	5.34518i	1.39527	−	0.210303i
$647$	33.2203	+	22.6492i	1.30602	+	0.890432i	0.998138	−	0.0609916i	$-0.0194263\pi$
$647$	33.2203	+	22.6492i	1.30602	+	0.890432i	0.307885	+	0.951423i	$0.400379\pi$
$648$		0			0
$649$	0.460749	+	0.427513i	0.0180860	+	0.0167813i
$650$	3.01192	−	3.77683i	0.118137	−	0.148140i
$651$		0			0
$652$	−10.8935	−	13.6600i	−0.426623	−	0.534968i
$653$	0.194264	−	2.59228i	0.00760215	−	0.101444i	−0.992112	−	0.125355i	$-0.959993\pi$
$653$	0.194264	−	2.59228i	0.00760215	−	0.101444i	0.999714	+	0.0239115i	$0.00761200\pi$
$654$		0			0
$655$	−4.17214	−	7.22635i	−0.163019	−	0.282357i
$656$	−0.335033	+	0.580294i	−0.0130808	+	0.0226567i
$657$		0			0
$658$	2.35514	+	2.00477i	0.0918131	+	0.0781540i
$659$	−3.98807	−	17.4729i	−0.155353	−	0.680646i	−0.991276	−	0.131800i	$-0.957924\pi$
$659$	−3.98807	−	17.4729i	−0.155353	−	0.680646i	0.835923	−	0.548846i	$-0.184933\pi$
$660$		0			0
$661$	−3.63099	+	9.25162i	−0.141229	+	0.359846i	−0.983935	−	0.178529i	$-0.942866\pi$
$661$	−3.63099	+	9.25162i	−0.141229	+	0.359846i	0.842705	+	0.538375i	$0.180962\pi$
$662$	−0.619299	+	1.57795i	−0.0240698	+	0.0613287i
$663$		0			0
$664$	−4.37704	−	19.1770i	−0.169862	−	0.744214i
$665$	−11.4116	+	2.22297i	−0.442521	+	0.0862030i
$666$		0			0
$667$	6.39910	−	11.0836i	0.247774	−	0.429157i
$668$	12.9391	+	22.4112i	0.500629	+	0.867115i
$669$		0			0
$670$	0.269401	−	3.59491i	0.0104079	−	0.138883i
$671$	2.88802	+	3.62147i	0.111491	+	0.139805i
$672$		0			0
$673$	−6.53275	+	8.19181i	−0.251819	+	0.315771i	−0.891633	−	0.452759i	$-0.850440\pi$
$673$	−6.53275	+	8.19181i	−0.251819	+	0.315771i	0.639814	+	0.768530i	$0.279011\pi$
$674$	−1.94223	−	1.80213i	−0.0748119	−	0.0694153i
$675$		0			0
$676$	10.2938	+	7.01818i	0.395915	+	0.269930i
$677$	−43.4082	+	6.54274i	−1.66831	+	0.251458i	−0.914194	−	0.405278i	$-0.867175\pi$
$677$	−43.4082	+	6.54274i	−1.66831	+	0.251458i	−0.754121	+	0.656736i	$0.771937\pi$
$678$		0			0
$679$	4.57115	+	38.6942i	0.175425	+	1.48495i
$680$	12.1003	−	5.82721i	0.464026	−	0.223463i
$681$		0			0
$682$	5.93491	−	5.50680i	0.227260	−	0.210866i
$683$	−2.19850	−	29.3369i	−0.0841231	−	1.12255i	−0.866312	−	0.499504i	$-0.833516\pi$
$683$	−2.19850	−	29.3369i	−0.0841231	−	1.12255i	0.782189	−	0.623042i	$-0.214103\pi$
$684$		0			0
$685$	−5.45305			−0.208350
$686$	−13.4189	+	11.9309i	−0.512334	+	0.455526i
$687$		0			0
$688$	−1.58635	−	4.04195i	−0.0604790	−	0.154098i
$689$	−0.795943	−	10.6211i	−0.0303230	−	0.404633i
$690$		0			0
$691$	15.6930	−	10.6993i	0.596990	−	0.407021i	−0.226779	−	0.973946i	$-0.572820\pi$
$691$	15.6930	−	10.6993i	0.596990	−	0.407021i	0.823769	+	0.566926i	$0.191867\pi$
$692$	18.9529	−	9.12723i	0.720481	−	0.346965i
$693$		0			0
$694$	−28.5004	−	13.7251i	−1.08186	−	0.520997i
$695$	6.87820	−	1.03672i	0.260905	−	0.0393251i
$696$		0			0
$697$	5.40807	+	0.815136i	0.204845	+	0.0308755i
$698$	15.1577	+	14.0642i	0.573726	+	0.532340i
$699$		0			0
$700$	11.0326	−	5.90722i	0.416994	−	0.223272i
$701$	−1.24452	−	1.56058i	−0.0470049	−	0.0589423i	0.757773	−	0.652518i	$-0.226287\pi$
$701$	−1.24452	−	1.56058i	−0.0470049	−	0.0589423i	−0.804778	+	0.593576i	$0.797716\pi$
$702$		0			0
$703$	32.0890	−	9.89815i	1.21026	−	0.373316i
$704$	−4.33419	−	7.50704i	−0.163351	−	0.282932i
$705$		0			0
$706$	3.26607	−	14.3096i	0.122920	−	0.538549i
$707$	11.4308	−	2.22672i	0.429900	−	0.0837443i
$708$		0			0
$709$	35.5484	+	10.9652i	1.33505	+	0.411808i	0.878437	−	0.477858i	$-0.158587\pi$
$709$	35.5484	+	10.9652i	1.33505	+	0.411808i	0.456612	+	0.889666i	$0.349063\pi$
$710$	−2.41167	+	6.14482i	−0.0905082	+	0.230611i
$711$		0			0
$712$	−10.3178	−	3.18263i	−0.386677	−	0.119274i
$713$	−7.55439	−	33.0979i	−0.282914	−	1.23953i
$714$		0			0
$715$	0.240976	−	1.05578i	0.00901199	−	0.0394841i
$716$	−4.21457	+	7.29985i	−0.157506	+	0.272808i
$717$		0			0
$718$	16.9203	−	5.21923i	0.631461	−	0.194780i
$719$	−2.07091	+	27.6344i	−0.0772321	+	1.03059i	0.815132	+	0.579275i	$0.196664\pi$
$719$	−2.07091	+	27.6344i	−0.0772321	+	1.03059i	−0.892364	+	0.451316i	$0.850955\pi$
$720$		0			0
$721$	−11.5781	−	13.3083i	−0.431193	−	0.495626i
$722$	10.2198	−	12.8152i	0.380342	−	0.476933i
$723$		0			0
$724$	5.10009	+	0.768715i	0.189543	+	0.0285691i
$725$	−8.77597	−	5.98336i	−0.325932	−	0.222216i
$726$		0			0
$727$	37.5072	+	18.0625i	1.39107	+	0.669902i	0.971328	−	0.237743i	$-0.0764077\pi$
$727$	37.5072	+	18.0625i	1.39107	+	0.669902i	0.419738	+	0.907645i	$0.362122\pi$
$728$	4.70302	+	7.39601i	0.174306	+	0.274114i
$729$		0			0
$730$	1.92907	−	1.31522i	0.0713981	−	0.0486784i
$731$	−25.9799	+	24.1058i	−0.960902	+	0.891587i
$732$		0			0
$733$	−13.6419	−	34.7591i	−0.503876	−	1.28385i	−0.926071	−	0.377350i	$-0.876835\pi$
$733$	−13.6419	−	34.7591i	−0.503876	−	1.28385i	0.422195	−	0.906505i	$-0.361260\pi$
$734$	27.8457			1.02780
$735$		0			0
$736$	−27.9600			−1.03062
$737$	2.44991	+	6.24226i	0.0902435	+	0.229937i
$738$		0			0
$739$	−10.3705	+	9.62244i	−0.381486	+	0.353967i	−0.847486	−	0.530817i	$-0.821885\pi$
$739$	−10.3705	+	9.62244i	−0.381486	+	0.353967i	0.466000	+	0.884785i	$0.345695\pi$
$740$	3.59934	−	2.45399i	0.132314	−	0.0902103i
$741$		0			0
$742$	−7.95654	+	23.1378i	−0.292094	+	0.849416i
$743$	−15.7580	−	7.58866i	−0.578106	−	0.278401i	0.121895	−	0.992543i	$-0.461103\pi$
$743$	−15.7580	−	7.58866i	−0.578106	−	0.278401i	−0.700001	+	0.714142i	$0.746817\pi$
$744$		0			0
$745$	−6.13632	−	4.18367i	−0.224817	−	0.153278i
$746$	34.4051	+	5.18573i	1.25966	+	0.189863i
$747$		0			0
$748$	−5.39577	+	6.76609i	−0.197289	+	0.247393i
$749$	9.22266	+	33.6919i	0.336989	+	1.23107i
$750$		0			0
$751$	−0.405109	+	5.40580i	−0.0147826	+	0.197260i	0.984923	+	0.172994i	$0.0553441\pi$
$751$	−0.405109	+	5.40580i	−0.0147826	+	0.197260i	−0.999706	+	0.0242666i	$0.992275\pi$
$752$	−0.871406	+	0.268793i	−0.0317769	+	0.00980187i
$753$		0			0
$754$	1.28846	−	2.23167i	0.0469228	−	0.0812727i
$755$	−0.923635	+	4.04671i	−0.0336145	+	0.147275i
$756$		0			0
$757$	0.389200	+	1.70520i	0.0141457	+	0.0619765i	0.981508	−	0.191420i	$-0.0613093\pi$
$757$	0.389200	+	1.70520i	0.0141457	+	0.0619765i	−0.967362	+	0.253397i	$0.918452\pi$
$758$	14.1551	+	4.36627i	0.514137	+	0.158590i
$759$		0			0
$760$	4.76283	−	12.1355i	0.172766	−	0.440201i
$761$	19.9120	+	6.14204i	0.721810	+	0.222649i	0.633829	−	0.773473i	$-0.281482\pi$
$761$	19.9120	+	6.14204i	0.721810	+	0.222649i	0.0879809	+	0.996122i	$0.471959\pi$
$762$		0			0
$763$	0.708828	−	22.1369i	0.0256613	−	0.801411i
$764$	3.87987	−	16.9988i	0.140369	−	0.614996i
$765$		0			0
$766$	−14.3080	−	24.7821i	−0.516968	−	0.895415i
$767$	0.507100	−	0.156420i	0.0183103	−	0.00564798i
$768$		0			0
$769$	−24.7924	−	31.0887i	−0.894036	−	1.12109i	−0.992043	−	0.125900i	$-0.959818\pi$
$769$	−24.7924	−	31.0887i	−0.894036	−	1.12109i	0.0980071	−	0.995186i	$-0.468753\pi$
$770$	−1.46647	+	2.00958i	−0.0528479	+	0.0724202i
$771$		0			0
$772$	18.4216	+	17.0928i	0.663010	+	0.615183i
$773$	−41.5987	−	6.27000i	−1.49620	−	0.225516i	−0.650637	−	0.759389i	$-0.725498\pi$
$773$	−41.5987	−	6.27000i	−1.49620	−	0.225516i	−0.845565	+	0.533873i	$0.820736\pi$
$774$		0			0
$775$	−27.8607	+	4.19932i	−1.00078	+	0.150844i
$776$	−39.3640	−	18.9567i	−1.41309	−	0.680506i
$777$		0			0
$778$	25.1733	−	12.1228i	0.902507	−	0.434624i
$779$	4.38637	−	2.99058i	0.157158	−	0.107149i
$780$		0			0
$781$	−0.917617	−	12.2447i	−0.0328349	−	0.438151i
$782$	−11.7564	−	29.9549i	−0.420410	−	1.07119i
$783$		0			0
$784$	−0.845458	−	5.22628i	−0.0301949	−	0.186653i
$785$	2.08681			0.0744814
$786$		0			0
$787$	3.41215	+	45.5320i	0.121630	+	1.62304i	0.640340	+	0.768092i	$0.278793\pi$
$787$	3.41215	+	45.5320i	0.121630	+	1.62304i	−0.518710	+	0.854950i	$0.673588\pi$
$788$	4.81135	−	4.46428i	0.171397	−	0.159033i
$789$		0			0
$790$	0.652813	−	0.314378i	0.0232260	−	0.0111851i
$791$	16.6476	−	16.8281i	0.591922	−	0.598339i
$792$		0			0
$793$	3.86717	−	0.582881i	0.137327	−	0.0206987i
$794$	11.1324	+	7.58991i	0.395072	+	0.269356i
$795$		0			0
$796$	−10.0395	−	9.31531i	−0.355841	−	0.330172i
$797$	22.9601	−	28.7910i	0.813288	−	1.01983i	−0.186017	−	0.982546i	$-0.559558\pi$
$797$	22.9601	−	28.7910i	0.813288	−	1.01983i	0.999305	−	0.0372839i	$-0.0118706\pi$
$798$		0			0
$799$	4.64076	+	5.81933i	0.164178	+	0.205873i
$800$	−1.73410	+	23.1399i	−0.0613096	+	0.818120i
$801$		0			0
$802$	7.93956	+	13.7517i	0.280356	+	0.485590i
$803$	−2.17150	+	3.76115i	−0.0766305	+	0.132728i
$804$		0			0
$805$	4.22305	+	9.53872i	0.148843	+	0.336196i
$806$	−1.52107	−	6.66426i	−0.0535775	−	0.234739i
$807$		0			0
$808$	−4.77087	+	12.1560i	−0.167839	+	0.427646i
$809$	−13.4508	+	34.2720i	−0.472904	+	1.20494i	0.473165	+	0.880974i	$0.343112\pi$
$809$	−13.4508	+	34.2720i	−0.472904	+	1.20494i	−0.946069	+	0.323966i	$0.894984\pi$
$810$		0			0
$811$	−9.14959	−	40.0870i	−0.321286	−	1.40764i	−0.835268	−	0.549844i	$-0.814687\pi$
$811$	−9.14959	−	40.0870i	−0.321286	−	1.40764i	0.513982	−	0.857801i	$-0.328170\pi$
$812$	5.34985	−	3.99310i	0.187743	−	0.140130i
$813$		0			0
$814$	3.59285	−	6.22299i	0.125929	−	0.218116i
$815$	−6.04354	−	10.4677i	−0.211696	−	0.366668i
$816$		0			0
$817$	−2.57086	+	34.3057i	−0.0899430	+	1.20021i
$818$	−9.87669	−	12.3850i	−0.345331	−	0.433031i
$819$		0			0
$820$	0.429392	−	0.538440i	0.0149950	−	0.0188031i
$821$	20.2999	+	18.8356i	0.708473	+	0.657366i	0.949721	−	0.313097i	$-0.101366\pi$
$821$	20.2999	+	18.8356i	0.708473	+	0.657366i	−0.241249	+	0.970463i	$0.577557\pi$
$822$		0			0
$823$	41.2923	+	28.1526i	1.43936	+	0.981337i	0.996398	+	0.0847958i	$0.0270238\pi$
$823$	41.2923	+	28.1526i	1.43936	+	0.981337i	0.442959	+	0.896542i	$0.353929\pi$
$824$	19.5592	−	2.94807i	0.681377	−	0.102701i
$825$		0			0
$826$	−1.21214	−	0.129962i	−0.0421758	−	0.00452196i
$827$	−19.9768	+	9.62033i	−0.694662	+	0.334531i	−0.747677	−	0.664062i	$-0.768831\pi$
$827$	−19.9768	+	9.62033i	−0.694662	+	0.334531i	0.0530156	+	0.998594i	$0.483117\pi$
$828$		0			0
$829$	−26.1507	+	24.2643i	−0.908250	+	0.842733i	−0.988059	−	0.154077i	$-0.950759\pi$
$829$	−26.1507	+	24.2643i	−0.908250	+	0.842733i	0.0798089	+	0.996810i	$0.474569\pi$
$830$	−0.352271	−	4.70073i	−0.0122275	−	0.163165i
$831$		0			0
$832$	−7.31876			−0.253732
$833$	−37.1876	+	22.0082i	−1.28848	+	0.762541i
$834$		0			0
$835$	6.54056	+	16.6651i	0.226346	+	0.576719i
$836$	0.627768	+	8.37699i	0.0217118	+	0.289724i
$837$		0			0
$838$	12.1069	−	8.25436i	0.418227	−	0.285142i
$839$	−23.4080	+	11.2727i	−0.808135	+	0.389177i	−0.791869	−	0.610690i	$-0.790892\pi$
$839$	−23.4080	+	11.2727i	−0.808135	+	0.389177i	−0.0162656	+	0.999868i	$0.505178\pi$
$840$		0			0
$841$	21.0232	+	10.1243i	0.724939	+	0.349112i
$842$	6.73530	−	1.01518i	0.232114	−	0.0349855i
$843$		0			0
$844$	11.7391	+	1.76938i	0.404076	+	0.0609046i
$845$	6.31810	+	5.86234i	0.217349	+	0.201671i
$846$		0			0
$847$	−4.42060	+	24.0731i	−0.151894	+	0.827163i
$848$	−4.49798	−	5.64028i	−0.154461	−	0.193688i
$849$		0			0
$850$	−25.5201	+	7.87191i	−0.875332	+	0.270004i
$851$	−15.0656	−	26.0944i	−0.516443	−	0.894506i
$852$		0			0
$853$	−0.746687	+	3.27145i	−0.0255661	+	0.112012i	−0.986101	−	0.166147i	$-0.946867\pi$
$853$	−0.746687	+	3.27145i	−0.0255661	+	0.112012i	0.960535	+	0.278160i	$0.0897244\pi$
$854$	−8.69042	−	2.27845i	−0.297380	−	0.0779670i
$855$		0			0
$856$	−37.4295	−	11.5455i	−1.27931	−	0.394616i
$857$	−4.62926	+	11.7952i	−0.158132	+	0.402915i	−0.987879	−	0.155225i	$-0.950390\pi$
$857$	−4.62926	+	11.7952i	−0.158132	+	0.402915i	0.829747	+	0.558140i	$0.188485\pi$
$858$		0			0
$859$	10.9627	+	3.38155i	0.374044	+	0.115377i	0.476076	−	0.879404i	$-0.342059\pi$
$859$	10.9627	+	3.38155i	0.374044	+	0.115377i	−0.102033	+	0.994781i	$0.532535\pi$
$860$	0.993065	+	4.35090i	0.0338632	+	0.148365i
$861$		0			0
$862$	−3.28438	+	14.3898i	−0.111867	+	0.490120i
$863$	−21.5486	+	37.3233i	−0.733524	+	1.27050i	0.221843	+	0.975082i	$0.428793\pi$
$863$	−21.5486	+	37.3233i	−0.733524	+	1.27050i	−0.955368	+	0.295419i	$0.904541\pi$
$864$		0			0
$865$	13.9063	−	4.28953i	0.472829	−	0.145848i
$866$	−0.519233	+	6.92868i	−0.0176443	+	0.235446i
$867$		0			0
$868$	3.19836	−	17.4172i	0.108559	−	0.591179i
$869$	−0.840341	+	1.05375i	−0.0285066	+	0.0357462i
$870$		0			0
$871$	5.59851	+	0.843840i	0.189698	+	0.0285924i
$872$	20.5201	+	13.9904i	0.694900	+	0.473775i
$873$		0			0
$874$	−28.1428	−	13.5528i	−0.951944	−	0.458432i
$875$	17.2954	−	6.15678i	0.584692	−	0.208137i
$876$		0			0
$877$	−27.8263	+	18.9716i	−0.939627	+	0.640627i	−0.933202	−	0.359353i	$-0.882997\pi$
$877$	−27.8263	+	18.9716i	−0.939627	+	0.640627i	−0.00642476	+	0.999979i	$0.502045\pi$
$878$	−1.79611	+	1.66654i	−0.0606156	+	0.0562431i
$879$		0			0
$880$	−0.267980	−	0.682802i	−0.00903361	−	0.0230173i
$881$	−9.12231			−0.307339			−0.153669	−	0.988122i	$-0.549109\pi$
$881$	−9.12231			−0.307339			−0.153669	+	0.988122i	$0.549109\pi$
$882$		0			0
$883$	−36.8992			−1.24176			−0.620879	−	0.783907i	$-0.713224\pi$
$883$	−36.8992			−1.24176			−0.620879	+	0.783907i	$0.713224\pi$
$884$	2.66945	+	6.80166i	0.0897835	+	0.228765i
$885$		0			0
$886$	−2.24623	+	2.08420i	−0.0754637	+	0.0700200i
$887$	7.33354	−	4.99993i	0.246236	−	0.167881i	−0.433913	−	0.900955i	$-0.642867\pi$
$887$	7.33354	−	4.99993i	0.246236	−	0.167881i	0.680149	+	0.733074i	$0.261915\pi$
$888$		0			0
$889$	13.2540	+	1.42105i	0.444523	+	0.0476605i
$890$	−2.33135	−	1.12272i	−0.0781470	−	0.0376336i
$891$		0			0
$892$	2.10632	+	1.43606i	0.0705247	+	0.0480829i
$893$	7.14432	+	1.07683i	0.239076	+	0.0360349i
$894$		0			0
$895$	−3.63576	+	4.55910i	−0.121530	+	0.152394i
$896$	−9.83410	−	4.22762i	−0.328534	−	0.141235i
$897$		0			0
$898$	−1.35428	+	18.0717i	−0.0451931	+	0.603060i
$899$	−14.3621	+	4.43013i	−0.479003	+	0.147753i
$900$		0			0
$901$	−29.4416	+	50.9943i	−0.980841	+	1.69887i
$902$	0.252782	−	1.10751i	0.00841673	−	0.0368761i
$903$		0			0
$904$	5.90646	+	25.8779i	0.196446	+	0.860685i
$905$	3.40959	+	1.05172i	0.113339	+	0.0349603i
$906$		0			0
$907$	10.3851	−	26.4608i	0.344832	−	0.878618i	−0.648275	−	0.761406i	$-0.724509\pi$
$907$	10.3851	−	26.4608i	0.344832	−	0.878618i	0.993107	−	0.117212i	$-0.0373956\pi$
$908$	0.475849	+	0.146780i	0.0157916	+	0.00487107i
$909$		0			0
$910$	0.850310	+	1.92062i	0.0281875	+	0.0636679i
$911$	−0.179717	+	0.787391i	−0.00595429	+	0.0260874i	−0.977818	−	0.209457i	$-0.932830\pi$
$911$	−0.179717	+	0.787391i	−0.00595429	+	0.0260874i	0.971864	+	0.235545i	$0.0756874\pi$
$912$		0			0
$913$	4.38429	+	7.59381i	0.145099	+	0.251318i
$914$	−17.3581	+	5.35427i	−0.574155	+	0.177104i
$915$		0			0
$916$	−5.57602	−	6.99211i	−0.184237	−	0.231026i
$917$	−30.0776	+	1.28782i	−0.993250	+	0.0425277i
$918$		0			0
$919$	−4.94529	−	4.58855i	−0.163130	−	0.151362i	0.594384	−	0.804181i	$-0.297396\pi$
$919$	−4.94529	−	4.58855i	−0.163130	−	0.151362i	−0.757514	+	0.652819i	$0.773586\pi$
$920$	−11.5668	−	1.74342i	−0.381346	−	0.0574787i
$921$		0			0
$922$	−6.84403	+	1.03157i	−0.225396	+	0.0339730i
$923$	−9.34061	−	4.49820i	−0.307450	−	0.148060i
$924$		0			0
$925$	−22.5304	+	10.8500i	−0.740793	+	0.356747i
$926$	29.2480	−	19.9410i	0.961150	−	0.655301i
$927$		0			0
$928$	0.925036	+	12.3437i	0.0303658	+	0.405203i
$929$	−13.3276	−	33.9582i	−0.437265	−	1.11413i	−0.964423	−	0.264365i	$-0.914838\pi$
$929$	−13.3276	−	33.9582i	−0.437265	−	1.11413i	0.527158	−	0.849767i	$-0.323258\pi$
$930$		0			0
$931$	−11.9308	+	40.2129i	−0.391016	+	1.31792i
$932$	−4.81899			−0.157851
$933$		0			0
$934$	−3.02014	−	40.3010i	−0.0988221	−	1.31869i
$935$	−4.38876	+	4.07217i	−0.143528	+	0.133174i
$936$		0			0
$937$	11.5520	−	5.56317i	0.377389	−	0.181741i	−0.235567	−	0.971858i	$-0.575695\pi$
$937$	11.5520	−	5.56317i	0.377389	−	0.181741i	0.612956	+	0.790117i	$0.289980\pi$
$938$	−11.0500	−	6.86034i	−0.360794	−	0.223998i
$939$		0			0
$940$	0.926798	−	0.139692i	0.0302288	−	0.00455626i
$941$	−16.7869	−	11.4451i	−0.547239	−	0.373101i	0.257915	−	0.966168i	$-0.416965\pi$
$941$	−16.7869	−	11.4451i	−0.547239	−	0.373101i	−0.805153	+	0.593067i	$0.797917\pi$
$942$		0			0
$943$	−3.49188	−	3.23999i	−0.113711	−	0.105509i
$944$	0.224109	−	0.281024i	0.00729414	−	0.00914656i
$945$		0			0
$946$	4.58974	+	5.75535i	0.149225	+	0.187123i
$947$	2.23752	−	29.8577i	0.0727097	−	0.970244i	−0.834893	−	0.550413i	$-0.814470\pi$
$947$	2.23752	−	29.8577i	0.0727097	−	0.970244i	0.907602	−	0.419831i	$-0.137911\pi$
$948$		0			0
$949$	1.83341	+	3.17556i	0.0595150	+	0.103083i
$950$	−12.9619	+	22.4506i	−0.420539	+	0.728395i
$951$		0			0
$952$	1.55075	−	48.4303i	0.0502599	−	1.56964i
$953$	−4.67686	−	20.4907i	−0.151498	−	0.663758i	−0.992450	−	0.122648i	$-0.960861\pi$
$953$	−4.67686	−	20.4907i	−0.151498	−	0.663758i	0.840952	−	0.541110i	$-0.181996\pi$
$954$		0			0
$955$	4.40684	−	11.2284i	0.142602	−	0.363344i
$956$	11.4820	−	29.2557i	0.371355	−	0.946198i
$957$		0			0
$958$	−1.70557	−	7.47259i	−0.0551045	−	0.241428i
$959$	−9.09912	+	17.4433i	−0.293826	+	0.563275i
$960$		0			0
$961$	−4.43445	+	7.68070i	−0.143047	+	0.247764i
$962$	−3.03346	−	5.25410i	−0.0978026	−	0.169399i
$963$		0			0
$964$	0.405303	−	5.40839i	0.0130539	−	0.174193i
$965$	10.8394	+	13.5922i	0.348933	+	0.437548i
$966$		0			0
$967$	−13.2742	+	16.6454i	−0.426871	+	0.535279i	−0.948030	−	0.318180i	$-0.896928\pi$
$967$	−13.2742	+	16.6454i	−0.426871	+	0.535279i	0.521160	+	0.853459i	$0.325500\pi$
$968$	−20.1189	−	18.6676i	−0.646645	−	0.599999i
$969$		0			0
$970$	−8.65103	−	5.89817i	−0.277768	−	0.189379i
$971$	−45.9891	+	6.93175i	−1.47586	+	0.222450i	−0.837141	−	0.546988i	$-0.815774\pi$
$971$	−45.9891	+	6.93175i	−1.47586	+	0.222450i	−0.638721	+	0.769438i	$0.720536\pi$
$972$		0			0
$973$	8.16089	−	23.7321i	0.261626	−	0.760816i
$974$	21.5421	−	10.3741i	0.690253	−	0.332408i
$975$		0			0
$976$	1.94181	−	1.80174i	0.0621558	−	0.0576722i
$977$	−2.75876	−	36.8131i	−0.0882606	−	1.17776i	−0.848890	−	0.528569i	$-0.822729\pi$
$977$	−2.75876	−	36.8131i	−0.0882606	−	1.17776i	0.760630	−	0.649186i	$-0.224890\pi$
$978$		0			0
$979$	4.81332			0.153834
$980$	0.0586646	+	5.44106i	0.00187397	+	0.173808i
$981$		0			0
$982$	−3.46512	−	8.82899i	−0.110577	−	0.281744i
$983$	2.13587	+	28.5012i	0.0681237	+	0.909048i	0.921656	+	0.388008i	$0.126837\pi$
$983$	2.13587	+	28.5012i	0.0681237	+	0.909048i	−0.853532	+	0.521040i	$0.825544\pi$
$984$		0			0
$985$	3.75163	−	2.55782i	0.119537	−	0.0814989i
$986$	−12.8355	+	6.18126i	−0.408766	+	0.196852i
$987$		0			0
$988$	6.39018	+	3.07735i	0.203299	+	0.0979036i
$989$	30.5232	−	4.60063i	0.970580	−	0.146291i
$990$		0			0
$991$	−0.577517	−	0.0870467i	−0.0183454	−	0.00276513i	0.139863	−	0.990171i	$-0.455334\pi$
$991$	−0.577517	−	0.0870467i	−0.0183454	−	0.00276513i	−0.158209	+	0.987406i	$0.550572\pi$
$992$	24.0701	+	22.3338i	0.764226	+	0.709098i
$993$		0			0
$994$	15.6320	+	17.9679i	0.495818	+	0.569908i
$995$	−5.90731	−	7.40754i	−0.187274	−	0.234835i
$996$		0			0
$997$	58.3437	−	17.9966i	1.84776	−	0.569959i	0.848600	−	0.529034i	$-0.177446\pi$
$997$	58.3437	−	17.9966i	1.84776	−	0.569959i	0.999162	−	0.0409249i	$-0.0130304\pi$
$998$	−17.7540	−	30.7508i	−0.561992	−	0.973399i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.163.3		48
3.2	odd	2		49.2.g.a.16.2	✓	48
12.11	even	2		784.2.bg.c.65.1		48
21.2	odd	6		343.2.e.d.295.3		48
21.5	even	6		343.2.e.c.295.3		48
21.11	odd	6		343.2.g.i.165.3		48
21.17	even	6		343.2.g.h.165.3		48
21.20	even	2		343.2.g.g.226.2		48
49.46	even	21	inner	441.2.bb.d.46.3		48
147.5	even	42		343.2.e.c.50.3		48
147.8	odd	14		343.2.g.i.79.3		48
147.41	even	14		343.2.g.h.79.3		48
147.44	odd	42		343.2.e.d.50.3		48
147.86	odd	42		2401.2.a.h.1.10		24
147.95	odd	42		49.2.g.a.46.2	yes	48
147.101	even	42		343.2.g.g.214.2		48
147.110	even	42		2401.2.a.i.1.10		24
588.95	even	42		784.2.bg.c.193.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.16.2	✓	48	3.2	odd	2
49.2.g.a.46.2	yes	48	147.95	odd	42
343.2.e.c.50.3		48	147.5	even	42
343.2.e.c.295.3		48	21.5	even	6
343.2.e.d.50.3		48	147.44	odd	42
343.2.e.d.295.3		48	21.2	odd	6
343.2.g.g.214.2		48	147.101	even	42
343.2.g.g.226.2		48	21.20	even	2
343.2.g.h.79.3		48	147.41	even	14
343.2.g.h.165.3		48	21.17	even	6
343.2.g.i.79.3		48	147.8	odd	14
343.2.g.i.165.3		48	21.11	odd	6
441.2.bb.d.46.3		48	49.46	even	21	inner
441.2.bb.d.163.3		48	1.1	even	1	trivial
784.2.bg.c.65.1		48	12.11	even	2
784.2.bg.c.193.1		48	588.95	even	42
2401.2.a.h.1.10		24	147.86	odd	42
2401.2.a.i.1.10		24	147.110	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.354207 + 0.902506i) q^{2} +(0.777050 - 0.720997i) q^{4} +(0.605902 - 0.413097i) q^{5} +(-0.310399 - 2.62748i) q^{7} +(2.67297 + 1.28723i) q^{8} +O(q^{10})\)	\(q+(0.354207 + 0.902506i) q^{2} +(0.777050 - 0.720997i) q^{4} +(0.605902 - 0.413097i) q^{5} +(-0.310399 - 2.62748i) q^{7} +(2.67297 + 1.28723i) q^{8} +(0.587437 + 0.400508i) q^{10} +(-1.30775 - 0.197112i) q^{11} +(-0.696197 + 0.873004i) q^{13} +(2.26137 - 1.21081i) q^{14} +(-0.0565197 + 0.754203i) q^{16} +(5.89890 - 1.81957i) q^{17} +(2.99610 - 5.18940i) q^{19} +(0.172974 - 0.757850i) q^{20} +(-0.285321 - 1.25007i) q^{22} +(-5.13778 - 1.58479i) q^{23} +(-1.63024 + 4.15378i) q^{25} +(-1.03449 - 0.319098i) q^{26} +(-2.13560 - 1.81789i) q^{28} +(-0.529674 + 2.32065i) q^{29} +(3.15709 + 5.46824i) q^{31} +(4.96923 - 1.53281i) q^{32} +(3.73161 + 4.67929i) q^{34} +(-1.27348 - 1.46377i) q^{35} +(4.10810 + 3.81176i) q^{37} +(5.74471 + 0.865875i) q^{38} +(2.15131 - 0.324257i) q^{40} +(0.798221 + 0.384403i) q^{41} +(-5.17256 + 2.49098i) q^{43} +(-1.15831 + 0.789719i) q^{44} +(-0.389553 - 5.19822i) q^{46} +(0.440505 + 1.12239i) q^{47} +(-6.80731 + 1.63113i) q^{49} -4.32625 q^{50} +(0.0884530 + 1.18032i) q^{52} +(-6.99227 + 6.48788i) q^{53} +(-0.873796 + 0.420798i) q^{55} +(2.55249 - 7.42272i) q^{56} +(-2.28202 + 0.343959i) q^{58} +(-0.392674 - 0.267721i) q^{59} +(-2.56745 - 2.38225i) q^{61} +(-3.81686 + 4.78619i) q^{62} +(4.08662 + 5.12446i) q^{64} +(-0.0611921 + 0.816551i) q^{65} +(-2.53523 - 4.39115i) q^{67} +(3.27183 - 5.66698i) q^{68} +(0.869987 - 1.66780i) q^{70} +(2.06601 + 9.05180i) q^{71} +(1.19973 - 3.05687i) q^{73} +(-1.98501 + 5.05773i) q^{74} +(-1.41342 - 6.19260i) q^{76} +(-0.111983 + 3.49728i) q^{77} +(0.509557 - 0.882579i) q^{79} +(0.277313 + 0.480321i) q^{80} +(-0.0641901 + 0.856558i) q^{82} +(-4.13385 - 5.18369i) q^{83} +(2.82250 - 3.53930i) q^{85} +(-4.08028 - 3.78595i) q^{86} +(-3.24185 - 2.21025i) q^{88} +(-3.59885 + 0.542439i) q^{89} +(2.50990 + 1.55827i) q^{91} +(-5.13494 + 2.47286i) q^{92} +(-0.856932 + 0.795117i) q^{94} +(-0.328382 - 4.38195i) q^{95} -14.7267 q^{97} +(-3.88331 - 5.56587i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

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