LMFDB - Embedded newform 441.2.bb.d.163.4

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			163.4
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.d.46.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.887059 + 2.26019i) q^{2} +(-2.85548 + 2.64950i) q^{4} +(-1.29033 + 0.879733i) q^{5} +(-2.25101 + 1.39030i) q^{7} +(-4.14619 - 1.99670i) q^{8} +O(q^{10})$	\(q+(0.887059 + 2.26019i) q^{2} +(-2.85548 + 2.64950i) q^{4} +(-1.29033 + 0.879733i) q^{5} +(-2.25101 + 1.39030i) q^{7} +(-4.14619 - 1.99670i) q^{8} +(-3.13296 - 2.13602i) q^{10} +(-3.02851 - 0.456475i) q^{11} +(2.18151 - 2.73553i) q^{13} +(-5.13913 - 3.85444i) q^{14} +(0.252808 - 3.37349i) q^{16} +(5.24271 - 1.61716i) q^{17} +(-3.92472 + 6.79781i) q^{19} +(1.35366 - 5.93079i) q^{20} +(-1.65475 - 7.24993i) q^{22} +(-1.80345 - 0.556289i) q^{23} +(-0.935681 + 2.38408i) q^{25} +(8.11794 + 2.50405i) q^{26} +(2.74413 - 9.93403i) q^{28} +(-0.641717 + 2.81155i) q^{29} +(-0.836206 - 1.44835i) q^{31} +(-0.945969 + 0.291793i) q^{32} +(8.30568 + 10.4150i) q^{34} +(1.68146 - 3.77424i) q^{35} +(1.09883 + 1.01957i) q^{37} +(-18.8458 - 2.84055i) q^{38} +(7.10652 - 1.07114i) q^{40} +(3.40817 + 1.64129i) q^{41} +(-4.49511 + 2.16473i) q^{43} +(9.85729 - 6.72058i) q^{44} +(-0.342443 - 4.56959i) q^{46} +(2.38176 + 6.06861i) q^{47} +(3.13413 - 6.25917i) q^{49} -6.21847 q^{50} +(1.01852 + 13.5912i) q^{52} +(-0.167306 + 0.155237i) q^{53} +(4.30936 - 2.07528i) q^{55} +(12.1091 - 1.26985i) q^{56} +(-6.92387 + 1.04361i) q^{58} +(8.09633 + 5.51998i) q^{59} +(7.98095 + 7.40524i) q^{61} +(2.53178 - 3.17476i) q^{62} +(-5.71710 - 7.16902i) q^{64} +(-0.408337 + 5.44888i) q^{65} +(2.81315 + 4.87252i) q^{67} +(-10.6858 + 18.5083i) q^{68} +(10.0221 + 0.452446i) q^{70} +(0.747726 + 3.27600i) q^{71} +(0.199459 - 0.508213i) q^{73} +(-1.32969 + 3.38798i) q^{74} +(-6.80384 - 29.8096i) q^{76} +(7.45186 - 3.18301i) q^{77} +(2.69999 - 4.67652i) q^{79} +(2.64156 + 4.57532i) q^{80} +(-0.686374 + 9.15903i) q^{82} +(1.69135 + 2.12089i) q^{83} +(-5.34216 + 6.69885i) q^{85} +(-8.88013 - 8.23955i) q^{86} +(11.6453 + 7.93966i) q^{88} +(-1.08665 + 0.163786i) q^{89} +(-1.10740 + 9.19067i) q^{91} +(6.62359 - 3.18975i) q^{92} +(-11.6035 + 10.7664i) q^{94} +(-0.916072 - 12.2241i) q^{95} -4.43145 q^{97} +(16.9271 + 1.53147i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.887059	+	2.26019i	0.627246	+	1.59820i	0.791083	+	0.611708i	$0.209517\pi$
$2$	0.887059	+	2.26019i	0.627246	+	1.59820i	−0.163838	+	0.986487i	$0.552387\pi$
$3$		0			0
$3$		0			0
$4$	−2.85548	+	2.64950i	−1.42774	+	1.32475i
$5$	−1.29033	+	0.879733i	−0.577054	+	0.393428i	−0.816384	−	0.577510i	$-0.804025\pi$
$5$	−1.29033	+	0.879733i	−0.577054	+	0.393428i	0.239330	+	0.970938i	$0.423072\pi$
$6$		0			0
$7$	−2.25101	+	1.39030i	−0.850803	+	0.525484i
$7$	−2.25101	+	1.39030i	−0.850803	+	0.525484i
$8$	−4.14619	−	1.99670i	−1.46590	−	0.705940i
$9$		0			0
$10$	−3.13296	−	2.13602i	−0.990730	−	0.675468i
$11$	−3.02851	−	0.456475i	−0.913131	−	0.137632i	−0.324361	−	0.945933i	$-0.605149\pi$
$11$	−3.02851	−	0.456475i	−0.913131	−	0.137632i	−0.588770	+	0.808301i	$0.700387\pi$
$12$		0			0
$13$	2.18151	−	2.73553i	0.605042	−	0.758699i	−0.381112	−	0.924529i	$-0.624459\pi$
$13$	2.18151	−	2.73553i	0.605042	−	0.758699i	0.986154	+	0.165830i	$0.0530302\pi$
$14$	−5.13913	−	3.85444i	−1.37349	−	1.03014i
$15$		0			0
$16$	0.252808	−	3.37349i	0.0632020	−	0.843372i
$17$	5.24271	−	1.61716i	1.27154	−	0.392219i	0.415722	−	0.909492i	$-0.363529\pi$
$17$	5.24271	−	1.61716i	1.27154	−	0.392219i	0.855821	+	0.517273i	$0.173053\pi$
$18$		0			0
$19$	−3.92472	+	6.79781i	−0.900392	+	1.55953i	−0.0734066	+	0.997302i	$0.523387\pi$
$19$	−3.92472	+	6.79781i	−0.900392	+	1.55953i	−0.826986	+	0.562223i	$0.809946\pi$
$20$	1.35366	−	5.93079i	0.302688	−	1.32616i
$21$		0			0
$22$	−1.65475	−	7.24993i	−0.352794	−	1.54569i
$23$	−1.80345	−	0.556289i	−0.376044	−	0.115994i	0.100971	−	0.994889i	$-0.467805\pi$
$23$	−1.80345	−	0.556289i	−0.376044	−	0.115994i	−0.477015	+	0.878895i	$0.658281\pi$
$24$		0			0
$25$	−0.935681	+	2.38408i	−0.187136	+	0.476815i
$26$	8.11794	+	2.50405i	1.59206	+	0.491085i
$27$		0			0
$28$	2.74413	−	9.93403i	0.518591	−	1.87736i
$29$	−0.641717	+	2.81155i	−0.119164	+	0.522091i	0.879747	+	0.475441i	$0.157712\pi$
$29$	−0.641717	+	2.81155i	−0.119164	+	0.522091i	−0.998911	+	0.0466497i	$0.985146\pi$
$30$		0			0
$31$	−0.836206	−	1.44835i	−0.150187	−	0.260131i	0.781109	−	0.624395i	$-0.214654\pi$
$31$	−0.836206	−	1.44835i	−0.150187	−	0.260131i	−0.931296	+	0.364263i	$0.881321\pi$
$32$	−0.945969	+	0.291793i	−0.167225	+	0.0515822i
$33$		0			0
$34$	8.30568	+	10.4150i	1.42441	+	1.78616i
$35$	1.68146	−	3.77424i	0.284219	−	0.637963i
$36$		0			0
$37$	1.09883	+	1.01957i	0.180647	+	0.167616i	0.765313	−	0.643658i	$-0.222584\pi$
$37$	1.09883	+	1.01957i	0.180647	+	0.167616i	−0.584666	+	0.811274i	$0.698775\pi$
$38$	−18.8458	−	2.84055i	−3.05719	−	0.460798i
$39$		0			0
$40$	7.10652	−	1.07114i	1.12364	−	0.169361i
$41$	3.40817	+	1.64129i	0.532267	+	0.256326i	0.680656	−	0.732603i	$-0.261695\pi$
$41$	3.40817	+	1.64129i	0.532267	+	0.256326i	−0.148390	+	0.988929i	$0.547409\pi$
$42$		0			0
$43$	−4.49511	+	2.16473i	−0.685498	+	0.330118i	−0.744010	−	0.668168i	$-0.767079\pi$
$43$	−4.49511	+	2.16473i	−0.685498	+	0.330118i	0.0585124	+	0.998287i	$0.481364\pi$
$44$	9.85729	−	6.72058i	1.48604	−	1.01317i
$45$		0			0
$46$	−0.342443	−	4.56959i	−0.0504905	−	0.673749i
$47$	2.38176	+	6.06861i	0.347415	+	0.885198i	0.992629	+	0.121196i	$0.0386731\pi$
$47$	2.38176	+	6.06861i	0.347415	+	0.885198i	−0.645214	+	0.764002i	$0.723232\pi$
$48$		0			0
$49$	3.13413	−	6.25917i	0.447733	−	0.894168i
$50$	−6.21847			−0.879424
$51$		0			0
$52$	1.01852	+	13.5912i	0.141243	+	1.88475i
$53$	−0.167306	+	0.155237i	−0.0229812	+	0.0213235i	−0.691580	−	0.722300i	$-0.743085\pi$
$53$	−0.167306	+	0.155237i	−0.0229812	+	0.0213235i	0.668599	+	0.743624i	$0.266894\pi$
$54$		0			0
$55$	4.30936	−	2.07528i	0.581074	−	0.279830i
$56$	12.1091	−	1.26985i	1.61815	−	0.169691i
$57$		0			0
$58$	−6.92387	+	1.04361i	−0.909149	+	0.137032i
$59$	8.09633	+	5.51998i	1.05405	+	0.718641i	0.960868	−	0.277008i	$-0.0893429\pi$
$59$	8.09633	+	5.51998i	1.05405	+	0.718641i	0.0931846	+	0.995649i	$0.470295\pi$
$60$		0			0
$61$	7.98095	+	7.40524i	1.02186	+	0.948144i	0.998669	−	0.0515868i	$-0.0164279\pi$
$61$	7.98095	+	7.40524i	1.02186	+	0.948144i	0.0231881	+	0.999731i	$0.492618\pi$
$62$	2.53178	−	3.17476i	0.321537	−	0.403194i
$63$		0			0
$64$	−5.71710	−	7.16902i	−0.714638	−	0.896128i
$65$	−0.408337	+	5.44888i	−0.0506480	+	0.675851i
$66$		0			0
$67$	2.81315	+	4.87252i	0.343681	+	0.595273i	0.985113	−	0.171907i	$-0.0549927\pi$
$67$	2.81315	+	4.87252i	0.343681	+	0.595273i	−0.641432	+	0.767180i	$0.721659\pi$
$68$	−10.6858	+	18.5083i	−1.29584	+	2.24446i
$69$		0			0
$70$	10.0221	+	0.452446i	1.19786	+	0.0540776i
$71$	0.747726	+	3.27600i	0.0887387	+	0.388790i	0.999720	−	0.0236578i	$-0.00753120\pi$
$71$	0.747726	+	3.27600i	0.0887387	+	0.388790i	−0.910981	+	0.412447i	$0.864674\pi$
$72$		0			0
$73$	0.199459	−	0.508213i	0.0233449	−	0.0594818i	−0.918726	−	0.394895i	$-0.870781\pi$
$73$	0.199459	−	0.508213i	0.0233449	−	0.0594818i	0.942071	+	0.335414i	$0.108876\pi$
$74$	−1.32969	+	3.38798i	−0.154573	+	0.393845i
$75$		0			0
$76$	−6.80384	−	29.8096i	−0.780454	−	3.41939i
$77$	7.45186	−	3.18301i	0.849218	−	0.362738i
$78$		0			0
$79$	2.69999	−	4.67652i	0.303773	−	0.526150i	−0.673215	−	0.739447i	$-0.735087\pi$
$79$	2.69999	−	4.67652i	0.303773	−	0.526150i	0.976987	+	0.213297i	$0.0684204\pi$
$80$	2.64156	+	4.57532i	0.295336	+	0.511536i
$81$		0			0
$82$	−0.686374	+	9.15903i	−0.0757974	+	1.01145i
$83$	1.69135	+	2.12089i	0.185650	+	0.232798i	0.865943	−	0.500142i	$-0.166719\pi$
$83$	1.69135	+	2.12089i	0.185650	+	0.232798i	−0.680293	+	0.732940i	$0.738148\pi$
$84$		0			0
$85$	−5.34216	+	6.69885i	−0.579438	+	0.726593i
$86$	−8.88013	−	8.23955i	−0.957569	−	0.888494i
$87$		0			0
$88$	11.6453	+	7.93966i	1.24140	+	0.846371i
$89$	−1.08665	+	0.163786i	−0.115185	+	0.0173613i	−0.206382	−	0.978472i	$-0.566169\pi$
$89$	−1.08665	+	0.163786i	−0.115185	+	0.0173613i	0.0911969	+	0.995833i	$0.470931\pi$
$90$		0			0
$91$	−1.10740	+	9.19067i	−0.116088	+	0.963444i
$92$	6.62359	−	3.18975i	0.690557	−	0.332555i
$93$		0			0
$94$	−11.6035	+	10.7664i	−1.19681	+	1.11047i
$95$	−0.916072	−	12.2241i	−0.0939870	−	1.25417i
$96$		0			0
$97$	−4.43145			−0.449946			−0.224973	−	0.974365i	$-0.572229\pi$
$97$	−4.43145			−0.449946			−0.224973	+	0.974365i	$0.572229\pi$
$98$	16.9271	+	1.53147i	1.70989	+	0.154702i
$99$		0			0
$100$	−3.64479	−	9.28677i	−0.364479	−	0.928677i
$101$	−0.401220	−	5.35391i	−0.0399229	−	0.532734i	−0.980932	−	0.194352i	$-0.937739\pi$
$101$	−0.401220	−	5.35391i	−0.0399229	−	0.532734i	0.941009	−	0.338382i	$-0.109880\pi$
$102$		0			0
$103$	8.65734	−	5.90247i	0.853033	−	0.581588i	−0.0559442	−	0.998434i	$-0.517817\pi$
$103$	8.65734	−	5.90247i	0.853033	−	0.581588i	0.908977	+	0.416846i	$0.136865\pi$
$104$	−14.5070	+	6.98620i	−1.42253	+	0.685053i
$105$		0			0
$106$	−0.499276	−	0.240439i	−0.0484940	−	0.0233535i
$107$	0.961563	−	0.144932i	0.0929578	−	0.0140111i	−0.102399	−	0.994743i	$-0.532652\pi$
$107$	0.961563	−	0.144932i	0.0929578	−	0.0140111i	0.195356	+	0.980732i	$0.437414\pi$
$108$		0			0
$109$	−15.9723	−	2.40744i	−1.52987	−	0.230591i	−0.670488	−	0.741920i	$-0.733915\pi$
$109$	−15.9723	−	2.40744i	−1.52987	−	0.230591i	−0.859385	+	0.511329i	$0.829153\pi$
$110$	8.51318	+	7.89907i	0.811700	+	0.753147i
$111$		0			0
$112$	4.12109	+	7.94525i	0.389406	+	0.750755i
$113$	−11.3219	−	14.1972i	−1.06507	−	1.33556i	−0.939145	−	0.343522i	$-0.888380\pi$
$113$	−11.3219	−	14.1972i	−1.06507	−	1.33556i	−0.125929	−	0.992039i	$-0.540191\pi$
$114$		0			0
$115$	2.81643	−	0.868753i	0.262633	−	0.0810116i
$116$	−5.61678	−	9.72854i	−0.521505	−	0.903273i
$117$		0			0
$118$	−5.29429	+	23.1958i	−0.487379	+	2.13535i
$119$	−9.55306	+	10.9292i	−0.875728	+	1.00188i
$120$		0			0
$121$	−1.54778	−	0.477428i	−0.140708	−	0.0434026i
$122$	−9.65768	+	24.6074i	−0.874365	+	2.22785i
$123$		0			0
$124$	6.22517	+	1.92021i	0.559037	+	0.172440i
$125$	−2.62756	−	11.5121i	−0.235016	−	1.02967i
$126$		0			0
$127$	0.791401	−	3.46735i	0.0702255	−	0.307678i	−0.927601	−	0.373572i	$-0.878133\pi$
$127$	0.791401	−	3.46735i	0.0702255	−	0.307678i	0.997827	+	0.0658943i	$0.0209900\pi$
$128$	10.1420	−	17.5664i	0.896434	−	1.55267i
$129$		0			0
$130$	−12.6777	+	3.91056i	−1.11191	+	0.342979i
$131$	0.536820	−	7.16336i	0.0469022	−	0.625866i	−0.923380	−	0.383888i	$-0.874585\pi$
$131$	0.536820	−	7.16336i	0.0469022	−	0.625866i	0.970282	−	0.241978i	$-0.0777961\pi$
$132$		0			0
$133$	−0.616406	−	20.7585i	−0.0534492	−	1.79999i
$134$	−8.51739	+	10.6805i	−0.735791	+	0.922652i
$135$		0			0
$136$	−24.9662	−	3.76305i	−2.14084	−	0.322679i
$137$	15.1102	+	10.3019i	1.29095	+	0.880153i	0.997130	−	0.0757083i	$-0.0241218\pi$
$137$	15.1102	+	10.3019i	1.29095	+	0.880153i	0.293818	+	0.955861i	$0.405074\pi$
$138$		0			0
$139$	10.2297	+	4.92634i	0.867668	+	0.417847i	0.814105	−	0.580717i	$-0.197228\pi$
$139$	10.2297	+	4.92634i	0.867668	+	0.417847i	0.0535632	+	0.998564i	$0.482942\pi$
$140$	5.19846	+	15.2323i	0.439350	+	1.28736i
$141$		0			0
$142$	−6.74110	+	4.59601i	−0.565701	+	0.385688i
$143$	−7.85543	+	7.28878i	−0.656904	+	0.609518i
$144$		0			0
$145$	−1.64538	−	4.19236i	−0.136642	−	0.348157i
$146$	1.32559			0.109707
$147$		0			0
$148$	−5.83903			−0.479965
$149$	4.48775	+	11.4346i	0.367651	+	0.936759i	0.988280	+	0.152655i	$0.0487822\pi$
$149$	4.48775	+	11.4346i	0.367651	+	0.936759i	−0.620629	+	0.784105i	$0.713123\pi$
$150$		0			0
$151$	9.78902	−	9.08288i	0.796619	−	0.739154i	−0.172696	−	0.984975i	$-0.555248\pi$
$151$	9.78902	−	9.08288i	0.796619	−	0.739154i	0.969315	+	0.245821i	$0.0790575\pi$
$152$	29.8458	−	20.3485i	2.42082	−	1.65048i
$153$		0			0
$154$	13.8045	+	14.0191i	1.11239	+	1.12969i
$155$	2.35314	+	1.13321i	0.189009	+	0.0910220i
$156$		0			0
$157$	13.8526	+	9.44455i	1.10556	+	0.753757i	0.971458	−	0.237211i	$-0.0762333\pi$
$157$	13.8526	+	9.44455i	1.10556	+	0.753757i	0.134100	+	0.990968i	$0.457186\pi$
$158$	12.9649	+	1.95414i	1.03143	+	0.155463i
$159$		0			0
$160$	0.963913	−	1.20871i	0.0762040	−	0.0955568i
$161$	4.83299	−	1.25512i	0.380893	−	0.0989170i
$162$		0			0
$163$	−0.389128	+	5.19256i	−0.0304789	+	0.406713i	0.961009	+	0.276516i	$0.0891799\pi$
$163$	−0.389128	+	5.19256i	−0.0304789	+	0.406713i	−0.991488	+	0.130197i	$0.958439\pi$
$164$	−14.0805	+	4.34327i	−1.09951	+	0.339153i
$165$		0			0
$166$	−3.29328	+	5.70413i	−0.255608	+	0.442727i
$167$	−1.81512	+	7.95258i	−0.140459	+	0.615389i	0.854870	+	0.518842i	$0.173637\pi$
$167$	−1.81512	+	7.95258i	−0.140459	+	0.615389i	−0.995328	+	0.0965467i	$0.969220\pi$
$168$		0			0
$169$	0.168647	+	0.738893i	0.0129729	+	0.0568379i
$170$	−19.8795	−	6.13201i	−1.52469	−	0.470304i
$171$		0			0
$172$	7.10024	−	18.0911i	0.541389	−	1.37944i
$173$	−3.40089	−	1.04904i	−0.258565	−	0.0797567i	0.162763	−	0.986665i	$-0.447960\pi$
$173$	−3.40089	−	1.04904i	−0.258565	−	0.0797567i	−0.421328	+	0.906909i	$0.638436\pi$
$174$		0			0
$175$	−1.20835	−	6.66747i	−0.0913428	−	0.504013i
$176$	−2.30554	+	10.1012i	−0.173787	+	0.761410i
$177$		0			0
$178$	−1.33411	−	2.31075i	−0.0999958	−	0.173198i
$179$	−5.08069	+	1.56718i	−0.379748	+	0.117137i	−0.478752	−	0.877950i	$-0.658911\pi$
$179$	−5.08069	+	1.56718i	−0.379748	+	0.117137i	0.0990036	+	0.995087i	$0.468434\pi$
$180$		0			0
$181$	0.536308	+	0.672509i	0.0398635	+	0.0499872i	0.801364	−	0.598178i	$-0.204108\pi$
$181$	0.536308	+	0.672509i	0.0398635	+	0.0499872i	−0.761500	+	0.648165i	$0.775537\pi$
$182$	−21.7550	+	5.64972i	−1.61259	+	0.418785i
$183$		0			0
$184$	6.36668	+	5.90742i	0.469358	+	0.435501i
$185$	−2.31480	−	0.348900i	−0.170188	−	0.0256517i
$186$		0			0
$187$	−16.6158	+	2.50443i	−1.21507	+	0.183142i
$188$	−22.8798	−	11.0184i	−1.66868	−	0.803596i
$189$		0			0
$190$	26.8162	−	12.9140i	1.94546	−	0.936882i
$191$	0.667483	−	0.455082i	0.0482974	−	0.0329286i	−0.538931	−	0.842350i	$-0.681172\pi$
$191$	0.667483	−	0.455082i	0.0482974	−	0.0329286i	0.587228	+	0.809421i	$0.300219\pi$
$192$		0			0
$193$	0.219031	+	2.92277i	0.0157662	+	0.210386i	0.999523	+	0.0308796i	$0.00983086\pi$
$193$	0.219031	+	2.92277i	0.0157662	+	0.210386i	−0.983757	+	0.179506i	$0.942550\pi$
$194$	−3.93096	−	10.0159i	−0.282226	−	0.719101i
$195$		0			0
$196$	7.63423	+	26.1768i	0.545302	+	1.86977i
$197$	22.8205			1.62589			0.812946	−	0.582339i	$-0.197862\pi$
$197$	22.8205			1.62589			0.812946	+	0.582339i	$0.197862\pi$
$198$		0			0
$199$	−1.92636	−	25.7055i	−0.136556	−	1.82221i	−0.473619	−	0.880730i	$-0.657053\pi$
$199$	−1.92636	−	25.7055i	−0.136556	−	1.82221i	0.337064	−	0.941482i	$-0.390566\pi$
$200$	8.63979	−	8.01656i	0.610926	−	0.566856i
$201$		0			0
$202$	11.7450	−	5.65607i	0.826372	−	0.397960i
$203$	−2.46438	−	7.22101i	−0.172966	−	0.506816i
$204$		0			0
$205$	−5.84156	+	0.880474i	−0.407992	+	0.0614949i
$206$	21.0203	+	14.3314i	1.46455	+	0.998515i
$207$		0			0
$208$	−8.67677	−	8.05086i	−0.601625	−	0.558227i
$209$	14.9891	−	18.7957i	1.03682	−	1.30013i
$210$		0			0
$211$	0.226187	+	0.283629i	0.0155713	+	0.0195258i	0.789556	−	0.613678i	$-0.210311\pi$
$211$	0.226187	+	0.283629i	0.0155713	+	0.0195258i	−0.773985	+	0.633204i	$0.781739\pi$
$212$	0.0664380	−	0.886554i	0.00456298	−	0.0608888i
$213$		0			0
$214$	1.18054	+	2.04475i	0.0806999	+	0.139776i
$215$	3.89579	−	6.74771i	0.265691	−	0.460190i
$216$		0			0
$217$	3.89595	+	2.09768i	0.264475	+	0.142400i
$218$	−8.72714	−	38.2361i	−0.591076	−	2.58967i
$219$		0			0
$220$	−6.80684	+	17.3436i	−0.458917	+	1.16930i
$221$	7.01323	−	17.8694i	0.471761	−	1.20203i
$222$		0			0
$223$	0.117341	+	0.514107i	0.00785777	+	0.0344271i	0.978705	−	0.205273i	$-0.0658081\pi$
$223$	0.117341	+	0.514107i	0.00785777	+	0.0344271i	−0.970847	+	0.239700i	$0.922951\pi$
$224$	1.72371	−	1.97201i	0.115170	−	0.131761i
$225$		0			0
$226$	22.0452	−	38.1834i	1.46642	−	2.53992i
$227$	−4.39549	−	7.61320i	−0.291739	−	0.505306i	0.682482	−	0.730902i	$-0.260900\pi$
$227$	−4.39549	−	7.61320i	−0.291739	−	0.505306i	−0.974221	+	0.225596i	$0.927567\pi$
$228$		0			0
$229$	0.595911	−	7.95188i	0.0393789	−	0.525475i	−0.942280	−	0.334827i	$-0.891322\pi$
$229$	0.595911	−	7.95188i	0.0393789	−	0.525475i	0.981658	−	0.190648i	$-0.0610589\pi$
$230$	4.46188	+	5.59502i	0.294208	+	0.368925i
$231$		0			0
$232$	8.27449	−	10.3759i	0.543247	−	0.681210i
$233$	11.5194	+	10.6885i	0.754664	+	0.700226i	0.960475	−	0.278366i	$-0.0897928\pi$
$233$	11.5194	+	10.6885i	0.754664	+	0.700226i	−0.205811	+	0.978592i	$0.565983\pi$
$234$		0			0
$235$	−8.41201	−	5.73521i	−0.548739	−	0.374124i
$236$	−37.7441	+	5.68901i	−2.45693	+	0.370323i
$237$		0			0
$238$	−33.1762	−	11.8969i	−2.15049	−	0.771162i
$239$	−11.2136	+	5.40021i	−0.725351	+	0.349310i	−0.759854	−	0.650094i	$-0.774729\pi$
$239$	−11.2136	+	5.40021i	−0.725351	+	0.349310i	0.0345030	+	0.999405i	$0.489015\pi$
$240$		0			0
$241$	14.0646	−	13.0501i	0.905981	−	0.840628i	−0.0817722	−	0.996651i	$-0.526058\pi$
$241$	14.0646	−	13.0501i	0.905981	−	0.840628i	0.987753	+	0.156023i	$0.0498675\pi$
$242$	−0.293898	−	3.92179i	−0.0188925	−	0.252103i
$243$		0			0
$244$	−42.4096			−2.71500
$245$	1.46234	+	10.8336i	0.0934253	+	0.692133i
$246$		0			0
$247$	10.0338	+	25.5657i	0.638435	+	1.62671i
$248$	0.575146	+	7.67479i	0.0365218	+	0.487350i
$249$		0			0
$250$	23.6887	−	16.1507i	1.49820	−	1.02146i
$251$	−24.2589	+	11.6825i	−1.53121	+	0.737390i	−0.994337	−	0.106275i	$-0.966108\pi$
$251$	−24.2589	+	11.6825i	−1.53121	+	0.737390i	−0.536870	+	0.843665i	$0.680393\pi$
$252$		0			0
$253$	5.20782	+	2.50796i	0.327413	+	0.157674i
$254$	8.53889	−	1.28703i	0.535778	−	0.0807555i
$255$		0			0
$256$	30.5658	+	4.60706i	1.91036	+	0.287941i
$257$	−12.7855	−	11.8632i	−0.797537	−	0.740007i	0.171961	−	0.985104i	$-0.444990\pi$
$257$	−12.7855	−	11.8632i	−0.797537	−	0.740007i	−0.969499	+	0.245097i	$0.921180\pi$
$258$		0			0
$259$	−3.89099	−	0.767352i	−0.241774	−	0.0476810i
$260$	−13.2708	−	16.6411i	−0.823021	−	1.03204i
$261$		0			0
$262$	16.6668	−	5.14101i	1.02968	−	0.317613i
$263$	1.47151	+	2.54873i	0.0907370	+	0.157161i	0.907821	−	0.419357i	$-0.137744\pi$
$263$	1.47151	+	2.54873i	0.0907370	+	0.157161i	−0.817084	+	0.576518i	$0.804411\pi$
$264$		0			0
$265$	0.0793128	−	0.347492i	0.00487214	−	0.0213463i
$266$	46.3714	−	19.8072i	2.84321	−	1.21446i
$267$		0			0
$268$	−20.9426	−	6.45995i	−1.27928	−	0.394604i
$269$	7.87136	−	20.0559i	0.479925	−	1.22283i	−0.461962	−	0.886900i	$-0.652854\pi$
$269$	7.87136	−	20.0559i	0.479925	−	1.22283i	0.941887	−	0.335930i	$-0.109051\pi$
$270$		0			0
$271$	−21.5633	−	6.65138i	−1.30987	−	0.404043i	−0.440303	−	0.897849i	$-0.645129\pi$
$271$	−21.5633	−	6.65138i	−1.30987	−	0.404043i	−0.869572	+	0.493806i	$0.835605\pi$
$272$	−4.13007	−	18.0950i	−0.250422	−	1.09717i
$273$		0			0
$274$	−9.88071	+	43.2902i	−0.596916	+	2.61526i
$275$	3.92199	−	6.79309i	0.236505	−	0.409639i
$276$		0			0
$277$	20.9756	−	6.47013i	1.26030	−	0.388752i	0.408570	−	0.912727i	$-0.366028\pi$
$277$	20.9756	−	6.47013i	1.26030	−	0.388752i	0.851734	+	0.523975i	$0.175551\pi$
$278$	−2.06016	+	27.4909i	−0.123560	+	1.64880i
$279$		0			0
$280$	−14.5077	+	12.2913i	−0.866999	+	0.734548i
$281$	−16.1430	+	20.2426i	−0.963008	+	1.20757i	0.0151866	+	0.999885i	$0.495166\pi$
$281$	−16.1430	+	20.2426i	−0.963008	+	1.20757i	−0.978195	+	0.207689i	$0.933406\pi$
$282$		0			0
$283$	−1.82000	−	0.274321i	−0.108188	−	0.0163067i	0.0947252	−	0.995503i	$-0.469803\pi$
$283$	−1.82000	−	0.274321i	−0.108188	−	0.0163067i	−0.202913	+	0.979197i	$0.565041\pi$
$284$	−10.8149	−	7.37346i	−0.641745	−	0.437534i
$285$		0			0
$286$	−23.4422	−	11.2892i	−1.38617	−	0.667544i
$287$	−9.95372	+	1.04382i	−0.587549	+	0.0616146i
$288$		0			0
$289$	10.8247	−	7.38015i	0.636747	−	0.434127i
$290$	8.01599	−	7.43775i	0.470715	−	0.436760i
$291$		0			0
$292$	0.776958	+	1.97966i	0.0454680	+	0.115851i
$293$	0.517582			0.0302375			0.0151187	−	0.999886i	$-0.495187\pi$
$293$	0.517582			0.0302375			0.0151187	+	0.999886i	$0.495187\pi$
$294$		0			0
$295$	−15.3031			−0.890978
$296$	−2.52019	−	6.42135i	−0.146483	−	0.373233i
$297$		0			0
$298$	−21.8635	+	20.2863i	−1.26652	+	1.17516i
$299$	−5.45598	+	3.71982i	−0.315528	+	0.215123i
$300$		0			0
$301$	7.10893	−	11.1224i	0.409752	−	0.641084i
$302$	29.2125	+	14.0680i	1.68099	+	0.809521i
$303$		0			0
$304$	21.9401	+	14.9585i	1.25835	+	0.857931i
$305$	−16.8127	−	2.53411i	−0.962693	−	0.145103i
$306$		0			0
$307$	−4.57770	+	5.74025i	−0.261263	+	0.327614i	−0.895110	−	0.445845i	$-0.852903\pi$
$307$	−4.57770	+	5.74025i	−0.261263	+	0.327614i	0.633847	+	0.773458i	$0.281475\pi$
$308$	−12.8453	+	28.8327i	−0.731926	+	1.64290i
$309$		0			0
$310$	−0.473902	+	6.32378i	−0.0269158	+	0.359167i
$311$	25.7482	−	7.94225i	1.46004	−	0.450364i	0.539828	−	0.841775i	$-0.318489\pi$
$311$	25.7482	−	7.94225i	1.46004	−	0.450364i	0.920216	+	0.391411i	$0.128013\pi$
$312$		0			0
$313$	−14.1348	+	24.4821i	−0.798944	+	1.38381i	0.121361	+	0.992608i	$0.461274\pi$
$313$	−14.1348	+	24.4821i	−0.798944	+	1.38381i	−0.920304	+	0.391203i	$0.872059\pi$
$314$	−9.05839	+	39.6874i	−0.511194	+	2.23969i
$315$		0			0
$316$	4.68066	+	20.5073i	0.263308	+	1.15363i
$317$	0.132966	+	0.0410147i	0.00746813	+	0.00230361i	0.298487	−	0.954414i	$-0.403518\pi$
$317$	0.132966	+	0.0410147i	0.00746813	+	0.00230361i	−0.291019	+	0.956717i	$0.593994\pi$
$318$		0			0
$319$	3.22685	−	8.22187i	0.180669	−	0.460337i
$320$	13.6838	+	4.22089i	0.764946	+	0.235955i
$321$		0			0
$322$	7.12395	+	9.81011i	0.397002	+	0.546696i
$323$	−9.58299	+	41.9858i	−0.533212	+	2.33615i
$324$		0			0
$325$	4.48051	+	7.76047i	0.248534	+	0.430473i
$326$	−12.0813	+	3.72660i	−0.669124	+	0.206397i
$327$		0			0
$328$	−10.8538	−	13.6102i	−0.599298	−	0.751496i
$329$	−13.7986	−	10.3492i	−0.760739	−	0.570569i
$330$		0			0
$331$	23.5887	+	21.8871i	1.29655	+	1.20303i	0.965794	+	0.259311i	$0.0834953\pi$
$331$	23.5887	+	21.8871i	1.29655	+	1.20303i	0.330759	+	0.943715i	$0.392695\pi$
$332$	−10.4489	−	1.57492i	−0.573459	−	0.0864350i
$333$		0			0
$334$	−19.5845	+	2.95188i	−1.07161	+	0.161520i
$335$	−7.91641	−	3.81234i	−0.432520	−	0.208291i
$336$		0			0
$337$	−24.6230	+	11.8578i	−1.34130	+	0.645936i	−0.960386	−	0.278674i	$-0.910105\pi$
$337$	−24.6230	+	11.8578i	−1.34130	+	0.645936i	−0.380915	+	0.924610i	$0.624391\pi$
$338$	−1.52044	+	1.03662i	−0.0827009	+	0.0563845i
$339$		0			0
$340$	−2.49418	−	33.2825i	−0.135266	−	1.80500i
$341$	1.87132	+	4.76805i	0.101338	+	0.258205i
$342$		0			0
$343$	1.64717	+	18.4469i	0.0889386	+	0.996037i
$344$	22.9599			1.23791
$345$		0			0
$346$	−0.645771	−	8.61721i	−0.0347169	−	0.463264i
$347$	−14.0797	+	13.0641i	−0.755840	+	0.701317i	−0.960735	−	0.277467i	$-0.910505\pi$
$347$	−14.0797	+	13.0641i	−0.755840	+	0.701317i	0.204895	+	0.978784i	$0.434315\pi$
$348$		0			0
$349$	11.1837	−	5.38581i	0.598652	−	0.288296i	−0.109913	−	0.993941i	$-0.535057\pi$
$349$	11.1837	−	5.38581i	0.598652	−	0.288296i	0.708565	+	0.705645i	$0.249343\pi$
$350$	13.9979	−	8.64554i	0.748217	−	0.462124i
$351$		0			0
$352$	2.99807	−	0.451887i	0.159798	−	0.0240857i
$353$	−4.03933	−	2.75397i	−0.214992	−	0.146579i	0.451036	−	0.892506i	$-0.351055\pi$
$353$	−4.03933	−	2.75397i	−0.214992	−	0.146579i	−0.666028	+	0.745927i	$0.732007\pi$
$354$		0			0
$355$	−3.84682	−	3.56933i	−0.204168	−	0.189440i
$356$	2.66896	−	3.34677i	0.141454	−	0.177378i
$357$		0			0
$358$	−8.04900	−	10.0931i	−0.425403	−	0.533438i
$359$	1.42400	−	19.0020i	0.0751559	−	1.00289i	−0.824380	−	0.566037i	$-0.808476\pi$
$359$	1.42400	−	19.0020i	0.0751559	−	1.00289i	0.899535	−	0.436848i	$-0.143905\pi$
$360$		0			0
$361$	−21.3068	−	36.9045i	−1.12141	−	1.94234i
$362$	−1.04426	+	1.80871i	−0.0548852	+	0.0950639i
$363$		0			0
$364$	−21.1885	−	29.1778i	−1.11058	−	1.52933i
$365$	0.189724	+	0.831233i	0.00993058	+	0.0435087i
$366$		0			0
$367$	−5.36555	+	13.6712i	−0.280080	+	0.713631i	0.719733	+	0.694251i	$0.244264\pi$
$367$	−5.36555	+	13.6712i	−0.280080	+	0.713631i	−0.999812	+	0.0193798i	$0.993831\pi$
$368$	−2.33256	+	5.94327i	−0.121593	+	0.309814i
$369$		0			0
$370$	−1.26479	−	5.54139i	−0.0657531	−	0.288083i
$371$	0.160782	−	0.582047i	0.00834737	−	0.0302184i
$372$		0			0
$373$	−6.15258	+	10.6566i	−0.318568	+	0.551777i	−0.980190	−	0.198062i	$-0.936535\pi$
$373$	−6.15258	+	10.6566i	−0.318568	+	0.551777i	0.661621	+	0.749838i	$0.269869\pi$
$374$	−20.3997	−	35.3333i	−1.05484	−	1.82704i
$375$		0			0
$376$	2.24199	−	29.9173i	0.115622	−	1.54287i
$377$	6.29115	+	7.88885i	0.324011	+	0.406297i
$378$		0			0
$379$	−14.3952	+	18.0510i	−0.739433	+	0.927220i	−0.999261	−	0.0384349i	$-0.987763\pi$
$379$	−14.3952	+	18.0510i	−0.739433	+	0.927220i	0.259828	+	0.965655i	$0.416334\pi$
$380$	35.0036	+	32.4786i	1.79565	+	1.66612i
$381$		0			0
$382$	1.62067	+	1.10495i	0.0829207	+	0.0565343i
$383$	22.4348	−	3.38150i	1.14636	−	0.172787i	0.451733	−	0.892153i	$-0.350806\pi$
$383$	22.4348	−	3.38150i	1.14636	−	0.172787i	0.694631	+	0.719367i	$0.255568\pi$
$384$		0			0
$385$	−6.81517	+	10.6628i	−0.347333	+	0.543426i
$386$	−6.41172	+	3.08772i	−0.326348	+	0.157161i
$387$		0			0
$388$	12.6539	−	11.7411i	0.642406	−	0.596065i
$389$	−0.561877	−	7.49773i	−0.0284883	−	0.380150i	−0.993165	−	0.116715i	$-0.962764\pi$
$389$	−0.561877	−	7.49773i	−0.0284883	−	0.380150i	0.964677	−	0.263435i	$-0.0848555\pi$
$390$		0			0
$391$	−10.3545			−0.523652
$392$	−25.4924	+	19.6938i	−1.28756	+	0.994687i
$393$		0			0
$394$	20.2431	+	51.5786i	1.01983	+	2.59849i
$395$	0.630207	+	8.40953i	0.0317092	+	0.423129i
$396$		0			0
$397$	−2.52948	+	1.72457i	−0.126951	+	0.0865538i	−0.625131	−	0.780520i	$-0.714954\pi$
$397$	−2.52948	+	1.72457i	−0.126951	+	0.0865538i	0.498180	+	0.867074i	$0.334002\pi$
$398$	56.3904	−	27.1562i	2.82660	−	1.36122i
$399$		0			0
$400$	7.80610	+	3.75922i	0.390305	+	0.187961i
$401$	5.20235	−	0.784128i	0.259793	−	0.0391575i	−0.0178542	−	0.999841i	$-0.505683\pi$
$401$	5.20235	−	0.784128i	0.259793	−	0.0391575i	0.277647	+	0.960683i	$0.410445\pi$
$402$		0			0
$403$	−5.78620	−	0.872129i	−0.288231	−	0.0434438i
$404$	15.3309	+	14.2250i	0.762739	+	0.707718i
$405$		0			0
$406$	14.1348	−	11.9754i	0.701498	−	0.594331i
$407$	−2.86242	−	3.58936i	−0.141885	−	0.177918i
$408$		0			0
$409$	22.6139	−	6.97546i	1.11818	−	0.344914i	0.320054	−	0.947399i	$-0.396299\pi$
$409$	22.6139	−	6.97546i	1.11818	−	0.344914i	0.798130	+	0.602485i	$0.205823\pi$
$410$	−7.17185	−	12.4220i	−0.354192	−	0.613479i
$411$		0			0
$412$	−9.08227	+	39.7920i	−0.447451	+	1.96041i
$413$	−25.8994	−	1.16923i	−1.27443	−	0.0575340i
$414$		0			0
$415$	−4.04822	−	1.24871i	−0.198719	−	0.0612968i
$416$	−1.26543	+	3.22427i	−0.0620430	+	0.158083i
$417$		0			0
$418$	55.7781	+	17.2053i	2.72820	+	0.841537i
$419$	−5.29762	−	23.2104i	−0.258806	−	1.13390i	−0.922530	−	0.385924i	$-0.873883\pi$
$419$	−5.29762	−	23.2104i	−0.258806	−	1.13390i	0.663725	−	0.747977i	$-0.268975\pi$
$420$		0			0
$421$	1.74637	−	7.65135i	0.0851129	−	0.372904i	−0.914376	−	0.404866i	$-0.867318\pi$
$421$	1.74637	−	7.65135i	0.0851129	−	0.372904i	0.999489	+	0.0319615i	$0.0101754\pi$
$422$	−0.440415	+	0.762821i	−0.0214391	+	0.0371335i
$423$		0			0
$424$	1.00364	−	0.309583i	0.0487413	−	0.0150347i
$425$	−1.05007	+	14.0122i	−0.0509357	+	0.679689i
$426$		0			0
$427$	−28.2608	−	5.57338i	−1.36763	−	0.269715i
$428$	−2.36173	+	2.96151i	−0.114158	+	0.143150i
$429$		0			0
$430$	18.7069	+	2.81961i	0.902127	+	0.135974i
$431$	−14.7612	−	10.0640i	−0.711021	−	0.484766i	0.152997	−	0.988227i	$-0.451107\pi$
$431$	−14.7612	−	10.0640i	−0.711021	−	0.484766i	−0.864018	+	0.503461i	$0.832060\pi$
$432$		0			0
$433$	30.6192	+	14.7454i	1.47147	+	0.708620i	0.986171	−	0.165730i	$-0.0529981\pi$
$433$	30.6192	+	14.7454i	1.47147	+	0.708620i	0.485294	+	0.874351i	$0.338712\pi$
$434$	−1.28521	+	10.6664i	−0.0616923	+	0.512002i
$435$		0			0
$436$	51.9872	−	35.4443i	2.48974	−	1.69747i
$437$	10.8596	−	10.0762i	0.519483	−	0.482010i
$438$		0			0
$439$	2.62428	+	6.68655i	0.125250	+	0.319132i	0.979721	−	0.200368i	$-0.0642137\pi$
$439$	2.62428	+	6.68655i	0.125250	+	0.319132i	−0.854471	+	0.519499i	$0.826118\pi$
$440$	−22.0111			−1.04934
$441$		0			0
$442$	46.6094			2.21699
$443$	14.6438	+	37.3119i	0.695750	+	1.77274i	0.632255	+	0.774761i	$0.282130\pi$
$443$	14.6438	+	37.3119i	0.695750	+	1.77274i	0.0634957	+	0.997982i	$0.479775\pi$
$444$		0			0
$445$	1.25805	−	1.16730i	0.0596373	−	0.0553353i
$446$	−1.05789	+	0.721257i	−0.0500925	+	0.0341525i
$447$		0			0
$448$	22.8364	+	8.18907i	1.07892	+	0.386897i
$449$	−14.2446	−	6.85983i	−0.672243	−	0.323735i	0.0664376	−	0.997791i	$-0.478837\pi$
$449$	−14.2446	−	6.85983i	−0.672243	−	0.323735i	−0.738681	+	0.674055i	$0.764551\pi$
$450$		0			0
$451$	−9.57247	−	6.52640i	−0.450750	−	0.307316i
$452$	69.9449	+	10.5425i	3.28993	+	0.495878i
$453$		0			0
$454$	13.3082	−	16.6880i	0.624586	−	0.783206i
$455$	−6.65641	−	12.8332i	−0.312057	−	0.601631i
$456$		0			0
$457$	0.179876	−	2.40027i	0.00841423	−	0.112280i	−0.991415	−	0.130752i	$-0.958261\pi$
$457$	0.179876	−	2.40027i	0.00841423	−	0.112280i	0.999829	+	0.0184716i	$0.00588001\pi$
$458$	18.5014	−	5.70692i	0.864512	−	0.266667i
$459$		0			0
$460$	−5.74049	+	9.94283i	−0.267652	+	0.463587i
$461$	−2.89680	+	12.6917i	−0.134917	+	0.591111i	0.861590	+	0.507605i	$0.169469\pi$
$461$	−2.89680	+	12.6917i	−0.134917	+	0.591111i	−0.996507	+	0.0835064i	$0.973388\pi$
$462$		0			0
$463$	−3.54715	−	15.5411i	−0.164850	−	0.722254i	−0.988003	−	0.154435i	$-0.950644\pi$
$463$	−3.54715	−	15.5411i	−0.164850	−	0.722254i	0.823153	−	0.567819i	$-0.192213\pi$
$464$	9.32248	+	2.87561i	0.432785	+	0.133497i
$465$		0			0
$466$	−13.9396	+	35.5174i	−0.645738	+	1.64531i
$467$	−11.2621	−	3.47390i	−0.521149	−	0.160753i	0.0230101	−	0.999735i	$-0.492675\pi$
$467$	−11.2621	−	3.47390i	−0.521149	−	0.160753i	−0.544159	+	0.838982i	$0.683151\pi$
$468$		0			0
$469$	−13.1067	−	7.05699i	−0.605212	−	0.325861i
$470$	5.50072	−	24.1002i	0.253729	−	1.11166i
$471$		0			0
$472$	−22.5472	−	39.0528i	−1.03782	−	1.79755i
$473$	14.6016	−	4.50401i	0.671384	−	0.207094i
$474$		0			0
$475$	−12.5342	−	15.7174i	−0.575109	−	0.721164i
$476$	−1.67828	−	56.5189i	−0.0769239	−	2.59054i
$477$		0			0
$478$	−22.1527	−	20.5547i	−1.01324	−	0.940149i
$479$	8.15738	+	1.22953i	0.372720	+	0.0561785i	0.332732	−	0.943022i	$-0.392030\pi$
$479$	8.15738	+	1.22953i	0.372720	+	0.0561785i	0.0399887	+	0.999200i	$0.487268\pi$
$480$		0			0
$481$	5.18616	−	0.781689i	0.236469	−	0.0356419i
$482$	41.9717	+	20.2125i	1.91176	+	0.920655i
$483$		0			0
$484$	5.68462	−	2.73757i	0.258392	−	0.124435i
$485$	5.71804	−	3.89849i	0.259643	−	0.177021i
$486$		0			0
$487$	1.51006	+	20.1504i	0.0684276	+	0.913102i	0.920767	+	0.390113i	$0.127564\pi$
$487$	1.51006	+	20.1504i	0.0684276	+	0.913102i	−0.852339	+	0.522989i	$0.824817\pi$
$488$	−18.3045	−	46.6391i	−0.828606	−	2.11125i
$489$		0			0
$490$	−23.1888	+	12.9152i	−1.04756	+	0.583449i
$491$	−0.606258			−0.0273600			−0.0136800	−	0.999906i	$-0.504355\pi$
$491$	−0.606258			−0.0273600			−0.0136800	+	0.999906i	$0.504355\pi$
$492$		0			0
$493$	1.18239	+	15.7779i	0.0532521	+	0.710600i
$494$	−48.8827	+	45.3565i	−2.19934	+	2.04069i
$495$		0			0
$496$	−5.09739	+	2.45477i	−0.228880	+	0.110223i
$497$	−6.23777	−	6.33476i	−0.279802	−	0.284153i
$498$		0			0
$499$	−1.60727	+	0.242258i	−0.0719515	+	0.0108449i	−0.184919	−	0.982754i	$-0.559202\pi$
$499$	−1.60727	+	0.242258i	−0.0719515	+	0.0108449i	0.112968	+	0.993599i	$0.463964\pi$
$500$	38.0042	+	25.9108i	1.69960	+	1.15877i
$501$		0			0
$502$	−47.9236	−	44.4666i	−2.13894	−	1.98464i
$503$	−13.4583	+	16.8762i	−0.600076	+	0.752472i	−0.985390	−	0.170314i	$-0.945522\pi$
$503$	−13.4583	+	16.8762i	−0.600076	+	0.752472i	0.385314	+	0.922786i	$0.374093\pi$
$504$		0			0
$505$	5.22772	+	6.55535i	0.232631	+	0.291709i
$506$	−1.04881	+	13.9954i	−0.0466252	+	0.622170i
$507$		0			0
$508$	6.92692	+	11.9978i	0.307332	+	0.532315i
$509$	−9.20544	+	15.9443i	−0.408024	+	0.706718i	−0.994668	−	0.103127i	$-0.967115\pi$
$509$	−9.20544	+	15.9443i	−0.408024	+	0.706718i	0.586644	+	0.809845i	$0.300449\pi$
$510$		0			0
$511$	0.257584	+	1.42130i	0.0113948	+	0.0628747i
$512$	7.67365	+	33.6205i	0.339131	+	1.48583i
$513$		0			0
$514$	15.4716	−	39.4210i	0.682423	−	1.73879i
$515$	−5.97823	+	15.2323i	−0.263432	+	0.671215i
$516$		0			0
$517$	−4.44301	−	19.4661i	−0.195403	−	0.856117i
$518$	−1.71717	−	9.47506i	−0.0754483	−	0.416310i
$519$		0			0
$520$	12.5728	−	21.7768i	0.551355	−	0.954975i
$521$	17.2503	+	29.8784i	0.755749	+	1.30900i	0.945001	+	0.327067i	$0.106060\pi$
$521$	17.2503	+	29.8784i	0.755749	+	1.30900i	−0.189252	+	0.981928i	$0.560606\pi$
$522$		0			0
$523$	−0.840750	+	11.2190i	−0.0367634	+	0.490574i	0.948184	+	0.317721i	$0.102918\pi$
$523$	−0.840750	+	11.2190i	−0.0367634	+	0.490574i	−0.984948	+	0.172853i	$0.944701\pi$
$524$	17.4464	+	21.8771i	0.762151	+	0.955708i
$525$		0			0
$526$	−4.45529	+	5.58676i	−0.194260	+	0.243594i
$527$	−6.72620	−	6.24100i	−0.292998	−	0.271862i
$528$		0			0
$529$	−16.0605	−	10.9499i	−0.698284	−	0.476082i
$530$	0.855753	−	0.128984i	0.0371715	−	0.00560271i
$531$		0			0
$532$	56.7598	+	57.6424i	2.46085	+	2.49911i
$533$	11.9247	−	5.74266i	0.516518	−	0.248742i
$534$		0			0
$535$	−1.11323	+	1.03293i	−0.0481293	+	0.0446574i
$536$	−1.93490	−	25.8194i	−0.0835749	−	1.11523i
$537$		0			0
$538$	52.3125			2.25535
$539$	−12.3489	+	17.5253i	−0.531905	+	0.754869i
$540$		0			0
$541$	3.99294	+	10.1739i	0.171670	+	0.437408i	0.990652	−	0.136411i	$-0.0435567\pi$
$541$	3.99294	+	10.1739i	0.171670	+	0.437408i	−0.818982	+	0.573819i	$0.805461\pi$
$542$	−4.09449	−	54.6372i	−0.175874	−	2.34687i
$543$		0			0
$544$	−4.48756	+	3.05957i	−0.192403	+	0.131178i
$545$	22.7275	−	10.9450i	0.973540	−	0.468832i
$546$		0			0
$547$	29.8603	+	14.3800i	1.27673	+	0.614843i	0.944549	−	0.328371i	$-0.106500\pi$
$547$	29.8603	+	14.3800i	1.27673	+	0.614843i	0.332186	+	0.943214i	$0.392214\pi$
$548$	−70.4417	+	10.6174i	−3.00912	+	0.453552i
$549$		0			0
$550$	18.8327	+	2.83857i	0.803029	+	0.121037i
$551$	−16.5938	−	15.3968i	−0.706920	−	0.655926i
$552$		0			0
$553$	0.424054	+	14.2807i	0.0180326	+	0.607278i
$554$	33.2304	+	41.6695i	1.41182	+	1.77037i
$555$		0			0
$556$	−42.2629	+	13.0364i	−1.79235	+	0.552866i
$557$	−18.6828	−	32.3596i	−0.791617	−	1.37112i	−0.924965	−	0.380051i	$-0.875906\pi$
$557$	−18.6828	−	32.3596i	−0.791617	−	1.37112i	0.133349	−	0.991069i	$-0.457427\pi$
$558$		0			0
$559$	−3.88445	+	17.0189i	−0.164295	+	0.719822i
$560$	−12.3073	−	6.62654i	−0.520077	−	0.280022i
$561$		0			0
$562$	−60.0719	−	18.5297i	−2.53398	−	0.781630i
$563$	−4.92060	+	12.5375i	−0.207379	+	0.528392i	−0.996285	−	0.0861217i	$-0.972553\pi$
$563$	−4.92060	+	12.5375i	−0.207379	+	0.528392i	0.788906	+	0.614514i	$0.210648\pi$
$564$		0			0
$565$	27.0987	+	8.35885i	1.14005	+	0.351660i
$566$	−0.994431	−	4.35689i	−0.0417990	−	0.183134i
$567$		0			0
$568$	3.44098	−	15.0759i	0.144380	−	0.632571i
$569$	−17.8445	+	30.9075i	−0.748078	+	1.29571i	0.200664	+	0.979660i	$0.435690\pi$
$569$	−17.8445	+	30.9075i	−0.748078	+	1.29571i	−0.948743	+	0.316050i	$0.897643\pi$
$570$		0			0
$571$	−17.8289	+	5.49950i	−0.746118	+	0.230147i	−0.644423	−	0.764669i	$-0.722903\pi$
$571$	−17.8289	+	5.49950i	−0.746118	+	0.230147i	−0.101694	+	0.994816i	$0.532426\pi$
$572$	3.11943	−	41.6259i	0.130430	−	1.74047i
$573$		0			0
$574$	−11.1888	−	21.5714i	−0.467010	−	0.900371i
$575$	3.01369	−	3.77904i	0.125679	−	0.157597i
$576$		0			0
$577$	5.86518	+	0.884034i	0.244171	+	0.0368028i	0.269987	−	0.962864i	$-0.412981\pi$
$577$	5.86518	+	0.884034i	0.244171	+	0.0368028i	−0.0258166	+	0.999667i	$0.508219\pi$
$578$	26.2827	+	17.9192i	1.09322	+	0.745342i
$579$		0			0
$580$	15.8060	+	7.61178i	0.656309	+	0.316062i
$581$	−6.75593	−	2.42266i	−0.280283	−	0.100509i
$582$		0			0
$583$	0.577550	−	0.393767i	0.0239197	−	0.0163082i
$584$	−1.84174	+	1.70889i	−0.0762119	+	0.0707143i
$585$		0			0
$586$	0.459126	+	1.16983i	0.0189663	+	0.0483254i
$587$	−17.4677			−0.720968			−0.360484	−	0.932765i	$-0.617389\pi$
$587$	−17.4677			−0.720968			−0.360484	+	0.932765i	$0.617389\pi$
$588$		0			0
$589$	13.1275			0.540909
$590$	−13.5747	−	34.5878i	−0.558862	−	1.42396i
$591$		0			0
$592$	3.71729	−	3.44914i	0.152780	−	0.141759i
$593$	20.6716	−	14.0937i	0.848883	−	0.578758i	−0.0588694	−	0.998266i	$-0.518750\pi$
$593$	20.6716	−	14.0937i	0.848883	−	0.578758i	0.907752	+	0.419507i	$0.137797\pi$
$594$		0			0
$595$	2.71185	−	22.5064i	0.111175	−	0.922673i
$596$	−43.1106	−	20.7610i	−1.76588	−	0.850403i
$597$		0			0
$598$	−13.2473	−	9.03185i	−0.541722	−	0.369340i
$599$	45.0102	+	6.78420i	1.83907	+	0.277195i	0.974346	−	0.225055i	$-0.0722560\pi$
$599$	45.0102	+	6.78420i	1.83907	+	0.277195i	0.864723	+	0.502250i	$0.167494\pi$
$600$		0			0
$601$	−20.1667	+	25.2882i	−0.822616	+	1.03153i	0.176271	+	0.984342i	$0.443597\pi$
$601$	−20.1667	+	25.2882i	−0.822616	+	1.03153i	−0.998886	+	0.0471855i	$0.984975\pi$
$602$	31.4448	+	6.20130i	1.28159	+	0.252746i
$603$		0			0
$604$	−3.88727	+	51.8720i	−0.158171	+	2.11064i
$605$	2.41716	−	0.745596i	0.0982717	−	0.0303128i
$606$		0			0
$607$	22.1531	−	38.3702i	0.899165	−	1.55740i	0.0706009	−	0.997505i	$-0.477508\pi$
$607$	22.1531	−	38.3702i	0.899165	−	1.55740i	0.828564	−	0.559894i	$-0.189158\pi$
$608$	1.72911	−	7.57572i	0.0701247	−	0.307236i
$609$		0			0
$610$	−9.18630	−	40.2478i	−0.371942	−	1.62959i
$611$	21.7967	+	6.72339i	0.881800	+	0.271999i
$612$		0			0
$613$	−5.01654	+	12.7819i	−0.202616	+	0.516257i	−0.995677	−	0.0928852i	$-0.970391\pi$
$613$	−5.01654	+	12.7819i	−0.202616	+	0.516257i	0.793061	+	0.609143i	$0.208486\pi$
$614$	−17.0347	−	5.25452i	−0.687467	−	0.212055i
$615$		0			0
$616$	−37.2523	−	1.68176i	−1.50094	−	0.0677600i
$617$	5.21414	−	22.8446i	0.209913	−	0.919691i	−0.754710	−	0.656059i	$-0.772222\pi$
$617$	5.21414	−	22.8446i	0.209913	−	0.919691i	0.964623	−	0.263632i	$-0.0849204\pi$
$618$		0			0
$619$	0.000120145	0	0.000208098i	4.82905e−6	0	8.36415e-6i	0.866028	−	0.499996i	$-0.166665\pi$
$619$	0.000120145	0	0.000208098i	4.82905e−6	0	8.36415e-6i	−0.866023	+	0.500004i	$0.833332\pi$
$620$	−9.72181	+	2.99878i	−0.390437	+	0.120434i
$621$		0			0
$622$	40.7911	+	51.1505i	1.63558	+	2.05095i
$623$	2.21835	−	1.87945i	0.0888764	−	0.0752988i
$624$		0			0
$625$	4.13082	+	3.83284i	0.165233	+	0.153314i
$626$	−67.8726	−	10.2302i	−2.71274	−	0.408879i
$627$		0			0
$628$	−64.5792	+	9.73374i	−2.57699	+	0.388419i
$629$	7.40965	+	3.56830i	0.295442	+	0.142277i
$630$		0			0
$631$	−11.4086	+	5.49411i	−0.454171	+	0.218717i	−0.646961	−	0.762523i	$-0.723961\pi$
$631$	−11.4086	+	5.49411i	−0.454171	+	0.218717i	0.192790	+	0.981240i	$0.438246\pi$
$632$	−20.5323	+	13.9987i	−0.816730	+	0.556837i
$633$		0			0
$634$	0.0252480	+	0.336911i	0.00100273	+	0.0133805i
$635$	2.02918	+	5.17025i	0.0805254	+	0.205175i
$636$		0			0
$637$	−10.2850	−	22.2279i	−0.407507	−	0.880703i
$638$	21.4454			0.849032
$639$		0			0
$640$	2.36725	+	31.5888i	0.0935738	+	1.24866i
$641$	27.1957	−	25.2339i	1.07417	−	0.996680i	0.0741658	−	0.997246i	$-0.476371\pi$
$641$	27.1957	−	25.2339i	1.07417	−	0.996680i	1.00000		0.000565897i	$0.000180131\pi$
$642$		0			0
$643$	13.3581	−	6.43294i	0.526793	−	0.253690i	−0.151532	−	0.988452i	$-0.548421\pi$
$643$	13.3581	−	6.43294i	0.526793	−	0.253690i	0.678325	+	0.734762i	$0.262706\pi$
$644$	−10.4751	+	16.3890i	−0.412776	+	0.645816i
$645$		0			0
$646$	−103.397	+	15.5845i	−4.06809	+	0.613165i
$647$	−30.8898	−	21.0603i	−1.21440	−	0.827967i	−0.225171	−	0.974319i	$-0.572294\pi$
$647$	−30.8898	−	21.0603i	−1.21440	−	0.827967i	−0.989233	+	0.146353i	$0.953247\pi$
$648$		0			0
$649$	−22.0001	−	20.4131i	−0.863579	−	0.801284i
$650$	−13.5657	+	17.0108i	−0.532089	+	0.667218i
$651$		0			0
$652$	−12.6465	−	15.8582i	−0.495276	−	0.621057i
$653$	0.164562	−	2.19593i	0.00643982	−	0.0859334i	−0.993058	−	0.117627i	$-0.962471\pi$
$653$	0.164562	−	2.19593i	0.00643982	−	0.0859334i	0.999498	+	0.0316940i	$0.0100902\pi$
$654$		0			0
$655$	5.60917	+	9.71537i	0.219168	+	0.379611i
$656$	6.39847	−	11.0825i	0.249818	−	0.432698i
$657$		0			0
$658$	11.1510	−	40.3677i	0.434710	−	1.57370i
$659$	−2.18801	−	9.58632i	−0.0852329	−	0.373430i	0.914265	−	0.405117i	$-0.132769\pi$
$659$	−2.18801	−	9.58632i	−0.0852329	−	0.373430i	−0.999498	+	0.0316870i	$0.989912\pi$
$660$		0			0
$661$	6.73280	−	17.1549i	0.261876	−	0.667248i	−0.738097	−	0.674695i	$-0.764275\pi$
$661$	6.73280	−	17.1549i	0.261876	−	0.667248i	0.999972	+	0.00744696i	$0.00237046\pi$
$662$	−28.5445	+	72.7302i	−1.10941	+	2.82674i
$663$		0			0
$664$	−2.77789	−	12.1707i	−0.107803	−	0.472316i
$665$	19.0573	+	26.2431i	0.739011	+	1.01766i
$666$		0			0
$667$	2.72133	−	4.71349i	0.105370	−	0.182507i
$668$	−15.8873	−	27.5176i	−0.614698	−	1.06469i
$669$		0			0
$670$	1.59429	−	21.2744i	0.0615929	−	0.821901i
$671$	−20.7901	−	26.0700i	−0.802593	−	1.00642i
$672$		0			0
$673$	−7.25364	+	9.09577i	−0.279607	+	0.350616i	−0.901727	−	0.432306i	$-0.857700\pi$
$673$	−7.25364	+	9.09577i	−0.279607	+	0.350616i	0.622120	+	0.782922i	$0.286272\pi$
$674$	−48.6430	−	45.1341i	−1.87366	−	1.73850i
$675$		0			0
$676$	−2.43927	−	1.66306i	−0.0938179	−	0.0639640i
$677$	−42.8688	+	6.46142i	−1.64758	+	0.248333i	−0.906230	−	0.422786i	$-0.861052\pi$
$677$	−42.8688	+	6.46142i	−1.64758	+	0.248333i	−0.741350	+	0.671118i	$0.765814\pi$
$678$		0			0
$679$	9.97526	−	6.16105i	0.382815	−	0.236439i
$680$	35.5252	−	17.1080i	1.36233	−	0.656063i
$681$		0			0
$682$	−9.11673	+	8.45909i	−0.349098	+	0.323915i
$683$	1.92390	+	25.6727i	0.0736161	+	0.982339i	0.904661	+	0.426133i	$0.140124\pi$
$683$	1.92390	+	25.6727i	0.0736161	+	0.982339i	−0.831044	+	0.556206i	$0.812257\pi$
$684$		0			0
$685$	−28.5600			−1.09122
$686$	−40.2323	+	20.0864i	−1.53608	+	0.766901i
$687$		0			0
$688$	6.16629	+	15.7115i	0.235088	+	0.598993i
$689$	0.0596761	+	0.796322i	0.00227348	+	0.0303374i
$690$		0			0
$691$	20.4454	−	13.9394i	0.777779	−	0.530281i	−0.108131	−	0.994137i	$-0.534487\pi$
$691$	20.4454	−	13.9394i	0.777779	−	0.530281i	0.885911	+	0.463856i	$0.153534\pi$
$692$	12.4906	−	6.01515i	0.474821	−	0.228662i
$693$		0			0
$694$	−42.0169	−	20.2343i	−1.59494	−	0.768083i
$695$	−17.5335	+	2.64275i	−0.665084	+	0.100245i
$696$		0			0
$697$	20.5223	+	3.09323i	0.777336	+	0.117165i
$698$	22.0936	+	20.4999i	0.836255	+	0.775931i
$699$		0			0
$700$	21.1159	+	15.8373i	0.798105	+	0.598593i
$701$	1.39315	+	1.74696i	0.0526186	+	0.0659817i	0.807444	−	0.589944i	$-0.200850\pi$
$701$	1.39315	+	1.74696i	0.0526186	+	0.0659817i	−0.754826	+	0.655925i	$0.772279\pi$
$702$		0			0
$703$	−11.2434	+	3.46814i	−0.424054	+	0.130803i
$704$	14.0418	+	24.3212i	0.529222	+	0.916639i
$705$		0			0
$706$	2.64137	−	11.5726i	0.0994093	−	0.435541i
$707$	8.34670	+	11.4939i	0.313910	+	0.432273i
$708$		0			0
$709$	−32.9177	−	10.1538i	−1.23625	−	0.381332i	−0.393342	−	0.919392i	$-0.628681\pi$
$709$	−32.9177	−	10.1538i	−1.23625	−	0.381332i	−0.842906	+	0.538060i	$0.819157\pi$
$710$	4.65500	−	11.8607i	0.174699	−	0.445126i
$711$		0			0
$712$	4.83249	+	1.49063i	0.181105	+	0.0558635i
$713$	0.702349	+	3.07719i	0.0263032	+	0.115242i
$714$		0			0
$715$	3.72393	−	16.3156i	0.139267	−	0.610169i
$716$	10.3555	−	17.9363i	0.387005	−	0.670312i
$717$		0			0
$718$	44.2112	−	13.6374i	1.64995	−	0.508942i
$719$	2.29424	−	30.6145i	0.0855608	−	1.14173i	−0.774856	−	0.632138i	$-0.782177\pi$
$719$	2.29424	−	30.6145i	0.0855608	−	1.14173i	0.860416	−	0.509592i	$-0.170203\pi$
$720$		0			0
$721$	−11.2816	+	25.3229i	−0.420148	+	0.943072i
$722$	64.5108	−	80.8940i	2.40084	−	3.01056i
$723$		0			0
$724$	−3.31323	−	0.499389i	−0.123135	−	0.0185596i
$725$	−6.10250	−	4.16061i	−0.226641	−	0.154521i
$726$		0			0
$727$	−7.12939	−	3.43333i	−0.264414	−	0.127335i	0.296980	−	0.954884i	$-0.404021\pi$
$727$	−7.12939	−	3.43333i	−0.264414	−	0.127335i	−0.561394	+	0.827548i	$0.689735\pi$
$728$	22.9425	−	35.8951i	0.850306	−	1.33036i
$729$		0			0
$730$	−1.71045	+	1.16616i	−0.0633066	+	0.0431617i
$731$	−20.0658	+	18.6184i	−0.742161	+	0.688625i
$732$		0			0
$733$	19.1171	+	48.7096i	0.706107	+	1.79913i	0.592445	+	0.805611i	$0.298163\pi$
$733$	19.1171	+	48.7096i	0.706107	+	1.79913i	0.113662	+	0.993520i	$0.463742\pi$
$734$	−35.6591			−1.31620
$735$		0			0
$736$	1.86832			0.0688674
$737$	−6.29548	−	16.0406i	−0.231897	−	0.590864i
$738$		0			0
$739$	−9.89033	+	9.17688i	−0.363822	+	0.337577i	−0.840808	−	0.541334i	$-0.817920\pi$
$739$	−9.89033	+	9.17688i	−0.363822	+	0.337577i	0.476986	+	0.878911i	$0.341729\pi$
$740$	7.53428	−	5.13679i	0.276966	−	0.188832i
$741$		0			0
$742$	1.45816	−	0.152913i	0.0535307	−	0.00561361i
$743$	3.45639	+	1.66451i	0.126802	+	0.0610649i	0.496209	−	0.868203i	$-0.334725\pi$
$743$	3.45639	+	1.66451i	0.126802	+	0.0610649i	−0.369407	+	0.929268i	$0.620439\pi$
$744$		0			0
$745$	−15.8501	−	10.8064i	−0.580702	−	0.395916i
$746$	−29.5436	−	4.45298i	−1.08167	−	0.163035i
$747$		0			0
$748$	40.8106	−	51.1749i	1.49218	−	1.87114i
$749$	−1.96299	+	1.66311i	−0.0717262	+	0.0607686i
$750$		0			0
$751$	1.89910	−	25.3417i	0.0692992	−	0.924733i	−0.848885	−	0.528578i	$-0.822725\pi$
$751$	1.89910	−	25.3417i	0.0692992	−	0.924733i	0.918184	−	0.396155i	$-0.129656\pi$
$752$	21.0745	−	6.50063i	0.768509	−	0.237054i
$753$		0			0
$754$	−12.2497	+	21.2171i	−0.446107	+	0.772680i
$755$	−4.64056	+	20.3316i	−0.168887	+	0.739944i
$756$		0			0
$757$	−7.11850	−	31.1882i	−0.258726	−	1.13355i	−0.922615	−	0.385722i	$-0.873952\pi$
$757$	−7.11850	−	31.1882i	−0.258726	−	1.13355i	0.663889	−	0.747831i	$-0.268905\pi$
$758$	−53.5682	−	16.5236i	−1.94569	−	0.600164i
$759$		0			0
$760$	−20.6097	+	52.5127i	−0.747593	+	1.90484i
$761$	43.2549	+	13.3424i	1.56799	+	0.483660i	0.952513	−	0.304497i	$-0.0984883\pi$
$761$	43.2549	+	13.3424i	1.56799	+	0.483660i	0.615474	+	0.788157i	$0.288964\pi$
$762$		0			0
$763$	39.3011	−	16.7872i	1.42279	−	0.607737i
$764$	−0.700245	+	3.06797i	−0.0253340	+	0.110995i
$765$		0			0
$766$	27.5438	+	47.7073i	0.995198	+	1.72373i
$767$	32.7623	−	10.1058i	1.18298	−	0.364900i
$768$		0			0
$769$	−2.57459	−	3.22843i	−0.0928420	−	0.116420i	0.733240	−	0.679969i	$-0.238007\pi$
$769$	−2.57459	−	3.22843i	−0.0928420	−	0.116420i	−0.826083	+	0.563549i	$0.809436\pi$
$770$	−30.1454	−	5.94505i	−1.08636	−	0.214245i
$771$		0			0
$772$	−8.36931	−	7.76559i	−0.301218	−	0.279490i
$773$	52.9663	+	7.98338i	1.90506	+	0.287142i	0.992544	−	0.121889i	$-0.0388952\pi$
$773$	52.9663	+	7.98338i	1.90506	+	0.287142i	0.912520	+	0.409031i	$0.134133\pi$
$774$		0			0
$775$	4.23540	−	0.638384i	0.152140	−	0.0229314i
$776$	18.3736	+	8.84828i	0.659575	+	0.317635i
$777$		0			0
$778$	16.4479	−	7.92088i	0.589685	−	0.283977i
$779$	−24.5333	+	16.7265i	−0.878996	+	0.599289i
$780$		0			0
$781$	−0.769085	−	10.2627i	−0.0275200	−	0.367229i
$782$	−9.18509	−	23.4032i	−0.328458	−	0.836898i
$783$		0			0
$784$	−20.3229	−	12.1553i	−0.725818	−	0.434118i
$785$	−26.1831			−0.934516
$786$		0			0
$787$	0.668564	+	8.92137i	0.0238317	+	0.318013i	0.996361	+	0.0852323i	$0.0271632\pi$
$787$	0.668564	+	8.92137i	0.0238317	+	0.318013i	−0.972529	+	0.232780i	$0.925218\pi$
$788$	−65.1634	+	60.4628i	−2.32135	+	2.15390i
$789$		0			0
$790$	−18.4481	+	8.88414i	−0.656354	+	0.316083i
$791$	45.2241	+	16.2173i	1.60798	+	0.576620i
$792$		0			0
$793$	37.6678	−	5.67751i	1.33762	−	0.201614i
$794$	−6.14166	−	4.18731i	−0.217959	−	0.148602i
$795$		0			0
$796$	73.6072	+	68.2975i	2.60894	+	2.42074i
$797$	−16.8342	+	21.1094i	−0.596298	+	0.747734i	−0.984796	−	0.173716i	$-0.944423\pi$
$797$	−16.8342	+	21.1094i	−0.596298	+	0.747734i	0.388498	+	0.921450i	$0.372994\pi$
$798$		0			0
$799$	22.3008	+	27.9643i	0.788944	+	0.989305i
$800$	0.189469	−	2.52829i	0.00669874	−	0.0893884i
$801$		0			0
$802$	6.38707	+	11.0627i	0.225535	+	0.390639i
$803$	−0.836050	+	1.44808i	−0.0295036	+	0.0511017i
$804$		0			0
$805$	−5.13199	+	5.87126i	−0.180879	+	0.206935i
$806$	−3.16152	−	13.8515i	−0.111360	−	0.487899i
$807$		0			0
$808$	−9.02662	+	22.9995i	−0.317555	+	0.809118i
$809$	14.2134	−	36.2153i	0.499718	−	1.27326i	−0.429278	−	0.903172i	$-0.641232\pi$
$809$	14.2134	−	36.2153i	0.499718	−	1.27326i	0.928996	−	0.370089i	$-0.120673\pi$
$810$		0			0
$811$	−2.39549	−	10.4953i	−0.0841170	−	0.368541i	0.915297	−	0.402780i	$-0.131956\pi$
$811$	−2.39549	−	10.4953i	−0.0841170	−	0.368541i	−0.999414	+	0.0342397i	$0.989099\pi$
$812$	26.1690	+	14.0901i	0.918353	+	0.494465i
$813$		0			0
$814$	5.57350	−	9.65358i	0.195351	−	0.338358i
$815$	−4.06596	−	7.04245i	−0.142424	−	0.246686i
$816$		0			0
$817$	2.92661	−	39.0529i	0.102389	−	1.36629i
$818$	35.8257	+	44.9240i	1.25262	+	1.57073i
$819$		0			0
$820$	14.3476	−	17.9914i	0.501042	−	0.628286i
$821$	11.4717	+	10.6442i	0.400364	+	0.371484i	0.854502	−	0.519448i	$-0.173862\pi$
$821$	11.4717	+	10.6442i	0.400364	+	0.371484i	−0.454138	+	0.890931i	$0.650053\pi$
$822$		0			0
$823$	18.7886	+	12.8098i	0.654929	+	0.446523i	0.844653	−	0.535314i	$-0.179807\pi$
$823$	18.7886	+	12.8098i	0.654929	+	0.446523i	−0.189724	+	0.981838i	$0.560759\pi$
$824$	−47.6804	+	7.18667i	−1.66103	+	0.250360i
$825$		0			0
$826$	−20.3316	−	59.5747i	−0.707427	−	2.07287i
$827$	22.1483	−	10.6661i	0.770172	−	0.370895i	−0.00716936	−	0.999974i	$-0.502282\pi$
$827$	22.1483	−	10.6661i	0.770172	−	0.370895i	0.777341	+	0.629079i	$0.216568\pi$
$828$		0			0
$829$	−29.1178	+	27.0173i	−1.01130	+	0.938351i	−0.998103	−	0.0615616i	$-0.980392\pi$
$829$	−29.1178	+	27.0173i	−1.01130	+	0.938351i	−0.0131989	+	0.999913i	$0.504201\pi$
$830$	−0.768688	−	10.2574i	−0.0266816	−	0.356041i
$831$		0			0
$832$	−32.0830			−1.11228
$833$	6.30922	−	37.8834i	0.218602	−	1.31258i
$834$		0			0
$835$	−4.65403	−	11.8583i	−0.161059	−	0.410373i
$836$	6.99819	+	93.3844i	0.242038	+	3.22977i
$837$		0			0
$838$	47.7606	−	32.5626i	1.64986	−	1.12486i
$839$	29.5194	−	14.2158i	1.01912	−	0.490784i	0.151738	−	0.988421i	$-0.451513\pi$
$839$	29.5194	−	14.2158i	1.01912	−	0.490784i	0.867386	+	0.497637i	$0.165799\pi$
$840$		0			0
$841$	18.6351	+	8.97419i	0.642590	+	0.309455i
$842$	18.8426	−	2.84007i	0.649361	−	0.0978754i
$843$		0			0
$844$	−1.39735	−	0.210616i	−0.0480987	−	0.00724971i
$845$	−0.867639	−	0.805052i	−0.0298477	−	0.0276946i
$846$		0			0
$847$	4.14785	−	1.07719i	0.142522	−	0.0370126i
$848$	0.481395	+	0.603650i	0.0165312	+	0.0207294i
$849$		0			0
$850$	−32.6016	+	10.0563i	−1.11823	+	0.344927i
$851$	−1.41451	−	2.45000i	−0.0484887	−	0.0839849i
$852$		0			0
$853$	5.56733	−	24.3921i	0.190622	−	0.835169i	−0.785659	−	0.618660i	$-0.787676\pi$
$853$	5.56733	−	24.3921i	0.190622	−	0.835169i	0.976281	−	0.216509i	$-0.0694670\pi$
$854$	−12.4721	−	68.8186i	−0.426785	−	2.35492i
$855$		0			0
$856$	−4.27621	−	1.31904i	−0.146158	−	0.0450837i
$857$	3.21483	−	8.19124i	0.109816	−	0.279808i	−0.865392	−	0.501095i	$-0.832931\pi$
$857$	3.21483	−	8.19124i	0.109816	−	0.279808i	0.975209	+	0.221288i	$0.0710259\pi$
$858$		0			0
$859$	23.9914	+	7.40037i	0.818576	+	0.252497i	0.675637	−	0.737234i	$-0.263869\pi$
$859$	23.9914	+	7.40037i	0.818576	+	0.252497i	0.142939	+	0.989732i	$0.454345\pi$
$860$	6.75369	+	29.5899i	0.230299	+	1.00901i
$861$		0			0
$862$	9.65251	−	42.2904i	0.328766	−	1.44042i
$863$	18.6063	−	32.2271i	0.633367	−	1.09702i	−0.353491	−	0.935438i	$-0.615006\pi$
$863$	18.6063	−	32.2271i	0.633367	−	1.09702i	0.986859	−	0.161587i	$-0.0516611\pi$
$864$		0			0
$865$	5.31115	−	1.63827i	0.180584	−	0.0557029i
$866$	−6.16643	+	82.2853i	−0.209544	+	2.79617i
$867$		0			0
$868$	−16.6826	+	4.33244i	−0.566245	+	0.147053i
$869$	−10.3117	+	12.9304i	−0.349799	+	0.438634i
$870$		0			0
$871$	19.4658	+	2.93400i	0.659575	+	0.0994149i
$872$	61.4174	+	41.8737i	2.07986	+	1.41802i
$873$		0			0
$874$	32.4072	+	15.6065i	1.09619	+	0.527897i
$875$	21.9199	+	22.2608i	0.741029	+	0.752551i
$876$		0			0
$877$	−13.0301	+	8.88376i	−0.439995	+	0.299983i	−0.762982	−	0.646420i	$-0.776265\pi$
$877$	−13.0301	+	8.88376i	−0.439995	+	0.299983i	0.322987	+	0.946403i	$0.395313\pi$
$878$	−12.7850	+	11.8627i	−0.431472	+	0.400348i
$879$		0			0
$880$	−5.91148	−	15.0622i	−0.199276	−	0.507747i
$881$	−3.91548			−0.131916			−0.0659579	−	0.997822i	$-0.521010\pi$
$881$	−3.91548			−0.131916			−0.0659579	+	0.997822i	$0.521010\pi$
$882$		0			0
$883$	−13.4565			−0.452848			−0.226424	−	0.974029i	$-0.572703\pi$
$883$	−13.4565			−0.452848			−0.226424	+	0.974029i	$0.572703\pi$
$884$	27.3189	+	69.6073i	0.918833	+	2.34115i
$885$		0			0
$886$	−71.3421	+	66.1958i	−2.39678	+	2.22389i
$887$	16.0707	−	10.9568i	0.539603	−	0.367895i	−0.262639	−	0.964894i	$-0.584593\pi$
$887$	16.0707	−	10.9568i	0.539603	−	0.367895i	0.802242	+	0.596999i	$0.203641\pi$
$888$		0			0
$889$	3.03921	+	8.90534i	0.101932	+	0.298676i
$890$	3.75428	+	1.80797i	0.125844	+	0.0606032i
$891$		0			0
$892$	−1.69719	−	1.15713i	−0.0568261	−	0.0387434i
$893$	−50.6010	−	7.62688i	−1.69330	−	0.255224i
$894$		0			0
$895$	5.17706	−	6.49183i	0.173050	−	0.216998i
$896$	1.59287	+	53.6427i	0.0532142	+	1.79208i
$897$		0			0
$898$	2.86873	−	38.2805i	0.0957307	−	1.27744i
$899$	4.60871	−	1.42160i	0.153709	−	0.0474130i
$900$		0			0
$901$	−0.626092	+	1.08442i	−0.0208582	+	0.0361274i
$902$	6.25956	−	27.4249i	0.208420	−	0.913150i
$903$		0			0
$904$	18.5952	+	81.4707i	0.618466	+	2.70968i
$905$	−1.28364	−	0.395952i	−0.0426698	−	0.0131619i
$906$		0			0
$907$	6.32639	−	16.1194i	0.210064	−	0.535235i	−0.786543	−	0.617535i	$-0.788131\pi$
$907$	6.32639	−	16.1194i	0.210064	−	0.535235i	0.996608	+	0.0822999i	$0.0262265\pi$
$908$	32.7224	+	10.0935i	1.08593	+	0.334965i
$909$		0			0
$910$	23.1009	−	26.4286i	0.765787	−	0.876099i
$911$	8.25765	−	36.1791i	0.273588	−	1.19867i	−0.632155	−	0.774842i	$-0.717829\pi$
$911$	8.25765	−	36.1791i	0.273588	−	1.19867i	0.905743	−	0.423827i	$-0.139313\pi$
$912$		0			0
$913$	−4.15415	−	7.19520i	−0.137482	−	0.238126i
$914$	5.58463	−	1.72263i	0.184723	−	0.0569796i
$915$		0			0
$916$	19.3669	+	24.2853i	0.639900	+	0.802409i
$917$	8.75084	+	16.8712i	0.288978	+	0.557135i
$918$		0			0
$919$	−34.6921	−	32.1895i	−1.14439	−	1.06183i	−0.997354	−	0.0727030i	$-0.976837\pi$
$919$	−34.6921	−	32.1895i	−1.14439	−	1.06183i	−0.147032	−	0.989132i	$-0.546972\pi$
$920$	−13.4121	−	2.02155i	−0.442183	−	0.0666484i
$921$		0			0
$922$	−31.2553	+	4.71097i	−1.02934	+	0.155148i
$923$	10.5928	+	5.10121i	0.348665	+	0.167908i
$924$		0			0
$925$	−3.45888	+	1.66571i	−0.113727	+	0.0547682i
$926$	31.9792	−	21.8031i	1.05090	−	0.716493i
$927$		0			0
$928$	−0.213344	−	2.84688i	−0.00700337	−	0.0934535i
$929$	−21.0524	−	53.6407i	−0.690708	−	1.75989i	−0.649029	−	0.760764i	$-0.724825\pi$
$929$	−21.0524	−	53.6407i	−0.690708	−	1.75989i	−0.0416787	−	0.999131i	$-0.513271\pi$
$930$		0			0
$931$	30.2481	+	45.8707i	0.991342	+	1.50335i
$932$	−61.2127			−2.00509
$933$		0			0
$934$	−2.13848	−	28.5361i	−0.0699734	−	0.933730i
$935$	19.2366	−	17.8490i	0.629105	−	0.583725i
$936$		0			0
$937$	31.1081	−	14.9809i	1.01626	−	0.489404i	0.149833	−	0.988711i	$-0.452126\pi$
$937$	31.1081	−	14.9809i	1.01626	−	0.489404i	0.866425	+	0.499307i	$0.166412\pi$
$938$	4.32370	−	35.8836i	0.141174	−	1.17164i
$939$		0			0
$940$	39.2158	−	5.91083i	1.27908	−	0.192790i
$941$	0.952295	+	0.649264i	0.0310439	+	0.0211654i	0.578743	−	0.815510i	$-0.303544\pi$
$941$	0.952295	+	0.649264i	0.0310439	+	0.0211654i	−0.547699	+	0.836676i	$0.684496\pi$
$942$		0			0
$943$	−5.23342	−	4.85590i	−0.170423	−	0.158130i
$944$	20.6684	−	25.9174i	0.672699	−	0.843538i
$945$		0			0
$946$	23.1324	+	29.0071i	0.752100	+	0.943104i
$947$	−0.0225062	+	0.300325i	−0.000731355	+	0.00975925i	−0.997558	−	0.0698496i	$-0.977748\pi$
$947$	−0.0225062	+	0.300325i	−0.000731355	+	0.00975925i	0.996826	+	0.0796088i	$0.0253671\pi$
$948$		0			0
$949$	−0.955109	−	1.65430i	−0.0310041	−	0.0537008i
$950$	24.4057	−	42.2720i	0.791827	−	1.37148i
$951$		0			0
$952$	61.4311	−	26.2399i	1.99099	−	0.850440i
$953$	8.03373	+	35.1981i	0.260238	+	1.14018i	0.920994	+	0.389577i	$0.127379\pi$
$953$	8.03373	+	35.1981i	0.260238	+	1.14018i	−0.660756	+	0.750601i	$0.729764\pi$
$954$		0			0
$955$	−0.460923	+	1.17441i	−0.0149151	+	0.0380031i
$956$	17.7125	−	45.1307i	0.572863	−	1.45963i
$957$		0			0
$958$	4.45711	+	19.5279i	0.144003	+	0.630918i
$959$	−48.3359	−	2.18213i	−1.56085	−	0.0704646i
$960$		0			0
$961$	14.1015	−	24.4245i	0.454888	−	0.787889i
$962$	6.36720	+	11.0283i	0.205287	+	0.355567i
$963$		0			0
$964$	−5.58513	+	74.5283i	−0.179885	+	2.40040i
$965$	−2.85388	−	3.57865i	−0.0918696	−	0.115201i
$966$		0			0
$967$	14.3783	−	18.0298i	0.462374	−	0.579799i	−0.494911	−	0.868944i	$-0.664799\pi$
$967$	14.3783	−	18.0298i	0.462374	−	0.579799i	0.957285	+	0.289144i	$0.0933708\pi$
$968$	5.46413	+	5.06997i	0.175624	+	0.162955i
$969$		0			0
$970$	13.8836	+	9.46566i	0.445775	+	0.303924i
$971$	−8.62105	+	1.29941i	−0.276663	+	0.0417002i	−0.285908	−	0.958257i	$-0.592295\pi$
$971$	−8.62105	+	1.29941i	−0.276663	+	0.0417002i	0.00924539	+	0.999957i	$0.497057\pi$
$972$		0			0
$973$	−29.8762	+	3.13303i	−0.957787	+	0.100440i
$974$	−44.2042	+	21.2876i	−1.41640	+	0.682100i
$975$		0			0
$976$	26.9991	−	25.0515i	0.864222	−	0.801880i
$977$	3.71338	+	49.5516i	0.118802	+	1.58530i	0.664483	+	0.747304i	$0.268652\pi$
$977$	3.71338	+	49.5516i	0.118802	+	1.58530i	−0.545681	+	0.837993i	$0.683729\pi$
$978$		0			0
$979$	3.36570			0.107568
$980$	−32.8793	−	27.0607i	−1.05029	−	0.864421i
$981$		0			0
$982$	−0.537787	−	1.37026i	−0.0171615	−	0.0437267i
$983$	1.58600	+	21.1638i	0.0505857	+	0.675019i	0.963644	+	0.267190i	$0.0860951\pi$
$983$	1.58600	+	21.1638i	0.0505857	+	0.675019i	−0.913058	+	0.407829i	$0.866286\pi$
$984$		0			0
$985$	−29.4460	+	20.0759i	−0.938227	+	0.639672i
$986$	−34.6121	+	16.6683i	−1.10227	+	0.530828i
$987$		0			0
$988$	−96.3875	−	46.4178i	−3.06650	−	1.47675i
$989$	9.31090	−	1.40339i	0.296069	−	0.0446253i
$990$		0			0
$991$	42.7961	+	6.45048i	1.35946	+	0.204906i	0.787977	−	0.615705i	$-0.211129\pi$
$991$	42.7961	+	6.45048i	1.35946	+	0.204906i	0.571487	+	0.820611i	$0.306367\pi$
$992$	1.21364	+	1.12610i	0.0385332	+	0.0357536i
$993$		0			0
$994$	8.78449	−	19.7178i	0.278627	−	0.625412i
$995$	25.0996	+	31.4739i	0.795710	+	0.997789i
$996$		0			0
$997$	30.0995	−	9.28445i	0.953259	−	0.294042i	0.221159	−	0.975238i	$-0.429016\pi$
$997$	30.0995	−	9.28445i	0.953259	−	0.294042i	0.732101	+	0.681196i	$0.238540\pi$
$998$	−1.97330	−	3.41785i	−0.0624636	−	0.108190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.163.4		48
3.2	odd	2		49.2.g.a.16.1	✓	48
12.11	even	2		784.2.bg.c.65.2		48
21.2	odd	6		343.2.e.d.295.1		48
21.5	even	6		343.2.e.c.295.1		48
21.11	odd	6		343.2.g.i.165.4		48
21.17	even	6		343.2.g.h.165.4		48
21.20	even	2		343.2.g.g.226.1		48
49.46	even	21	inner	441.2.bb.d.46.4		48
147.5	even	42		343.2.e.c.50.1		48
147.8	odd	14		343.2.g.i.79.4		48
147.41	even	14		343.2.g.h.79.4		48
147.44	odd	42		343.2.e.d.50.1		48
147.86	odd	42		2401.2.a.h.1.3		24
147.95	odd	42		49.2.g.a.46.1	yes	48
147.101	even	42		343.2.g.g.214.1		48
147.110	even	42		2401.2.a.i.1.3		24
588.95	even	42		784.2.bg.c.193.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.16.1	✓	48	3.2	odd	2
49.2.g.a.46.1	yes	48	147.95	odd	42
343.2.e.c.50.1		48	147.5	even	42
343.2.e.c.295.1		48	21.5	even	6
343.2.e.d.50.1		48	147.44	odd	42
343.2.e.d.295.1		48	21.2	odd	6
343.2.g.g.214.1		48	147.101	even	42
343.2.g.g.226.1		48	21.20	even	2
343.2.g.h.79.4		48	147.41	even	14
343.2.g.h.165.4		48	21.17	even	6
343.2.g.i.79.4		48	147.8	odd	14
343.2.g.i.165.4		48	21.11	odd	6
441.2.bb.d.46.4		48	49.46	even	21	inner
441.2.bb.d.163.4		48	1.1	even	1	trivial
784.2.bg.c.65.2		48	12.11	even	2
784.2.bg.c.193.2		48	588.95	even	42
2401.2.a.h.1.3		24	147.86	odd	42
2401.2.a.i.1.3		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)

\(f(q)\)	\(=\)	\(q+(0.887059 + 2.26019i) q^{2} +(-2.85548 + 2.64950i) q^{4} +(-1.29033 + 0.879733i) q^{5} +(-2.25101 + 1.39030i) q^{7} +(-4.14619 - 1.99670i) q^{8} +O(q^{10})\)	\(q+(0.887059 + 2.26019i) q^{2} +(-2.85548 + 2.64950i) q^{4} +(-1.29033 + 0.879733i) q^{5} +(-2.25101 + 1.39030i) q^{7} +(-4.14619 - 1.99670i) q^{8} +(-3.13296 - 2.13602i) q^{10} +(-3.02851 - 0.456475i) q^{11} +(2.18151 - 2.73553i) q^{13} +(-5.13913 - 3.85444i) q^{14} +(0.252808 - 3.37349i) q^{16} +(5.24271 - 1.61716i) q^{17} +(-3.92472 + 6.79781i) q^{19} +(1.35366 - 5.93079i) q^{20} +(-1.65475 - 7.24993i) q^{22} +(-1.80345 - 0.556289i) q^{23} +(-0.935681 + 2.38408i) q^{25} +(8.11794 + 2.50405i) q^{26} +(2.74413 - 9.93403i) q^{28} +(-0.641717 + 2.81155i) q^{29} +(-0.836206 - 1.44835i) q^{31} +(-0.945969 + 0.291793i) q^{32} +(8.30568 + 10.4150i) q^{34} +(1.68146 - 3.77424i) q^{35} +(1.09883 + 1.01957i) q^{37} +(-18.8458 - 2.84055i) q^{38} +(7.10652 - 1.07114i) q^{40} +(3.40817 + 1.64129i) q^{41} +(-4.49511 + 2.16473i) q^{43} +(9.85729 - 6.72058i) q^{44} +(-0.342443 - 4.56959i) q^{46} +(2.38176 + 6.06861i) q^{47} +(3.13413 - 6.25917i) q^{49} -6.21847 q^{50} +(1.01852 + 13.5912i) q^{52} +(-0.167306 + 0.155237i) q^{53} +(4.30936 - 2.07528i) q^{55} +(12.1091 - 1.26985i) q^{56} +(-6.92387 + 1.04361i) q^{58} +(8.09633 + 5.51998i) q^{59} +(7.98095 + 7.40524i) q^{61} +(2.53178 - 3.17476i) q^{62} +(-5.71710 - 7.16902i) q^{64} +(-0.408337 + 5.44888i) q^{65} +(2.81315 + 4.87252i) q^{67} +(-10.6858 + 18.5083i) q^{68} +(10.0221 + 0.452446i) q^{70} +(0.747726 + 3.27600i) q^{71} +(0.199459 - 0.508213i) q^{73} +(-1.32969 + 3.38798i) q^{74} +(-6.80384 - 29.8096i) q^{76} +(7.45186 - 3.18301i) q^{77} +(2.69999 - 4.67652i) q^{79} +(2.64156 + 4.57532i) q^{80} +(-0.686374 + 9.15903i) q^{82} +(1.69135 + 2.12089i) q^{83} +(-5.34216 + 6.69885i) q^{85} +(-8.88013 - 8.23955i) q^{86} +(11.6453 + 7.93966i) q^{88} +(-1.08665 + 0.163786i) q^{89} +(-1.10740 + 9.19067i) q^{91} +(6.62359 - 3.18975i) q^{92} +(-11.6035 + 10.7664i) q^{94} +(-0.916072 - 12.2241i) q^{95} -4.43145 q^{97} +(16.9271 + 1.53147i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 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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