LMFDB - Embedded newform 855.2.dl.a.352.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,12,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			352.7
Character	$\chi$	$=$	855.352
Dual form			855.2.dl.a.838.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.51450 + 1.06046i) q^{2} +(0.485079 + 1.33274i) q^{4} +(-0.762040 + 2.10221i) q^{5} +(-4.38823 + 1.17582i) q^{7} +(0.278366 - 1.03888i) q^{8} +(-3.38342 + 2.37568i) q^{10} +(0.761040 + 1.31816i) q^{11} +(-0.0120870 - 0.138155i) q^{13} +(-7.89287 - 2.87277i) q^{14} +(3.69620 - 3.10148i) q^{16} +(-2.90701 + 4.15164i) q^{17} +(-4.14601 + 1.34559i) q^{19} +(-3.17136 + 0.00413488i) q^{20} +(-0.245266 + 2.80340i) q^{22} +(-3.12809 + 6.70821i) q^{23} +(-3.83859 - 3.20394i) q^{25} +(0.128202 - 0.222052i) q^{26} +(-3.69571 - 5.27802i) q^{28} +(0.346487 - 1.96502i) q^{29} +(-1.08369 - 0.625668i) q^{31} +(6.74402 - 0.590025i) q^{32} +(-8.80531 + 3.20487i) q^{34} +(0.872178 - 10.1210i) q^{35} +(2.05676 - 2.05676i) q^{37} +(-7.70606 - 2.35879i) q^{38} +(1.97181 + 1.37685i) q^{40} +(-1.05100 - 1.25253i) q^{41} +(-0.801514 + 0.373752i) q^{43} +(-1.38761 + 1.65368i) q^{44} +(-11.8513 + 6.84234i) q^{46} +(2.02502 - 1.41793i) q^{47} +(11.8118 - 6.81954i) q^{49} +(-2.41588 - 8.92303i) q^{50} +(0.178262 - 0.0831248i) q^{52} +(10.1702 + 4.74246i) q^{53} +(-3.35100 + 0.595377i) q^{55} +4.88613i q^{56} +(2.60859 - 2.60859i) q^{58} +(1.86831 + 10.5957i) q^{59} +(-2.79178 + 1.01612i) q^{61} +(-0.977745 - 2.09678i) q^{62} +(2.48226 + 1.43314i) q^{64} +(0.299641 + 0.0798700i) q^{65} +(8.15144 + 11.6415i) q^{67} +(-6.94321 - 1.86043i) q^{68} +(12.0538 - 14.4033i) q^{70} +(1.79203 - 4.92356i) q^{71} +(-0.526410 + 6.01690i) q^{73} +(5.29607 - 0.933839i) q^{74} +(-3.80447 - 4.87285i) q^{76} +(-4.88954 - 4.88954i) q^{77} +(4.43572 - 3.72201i) q^{79} +(3.70331 + 10.1336i) q^{80} +(-0.263472 - 3.01150i) q^{82} +(0.122763 + 0.458159i) q^{83} +(-6.51237 - 9.27487i) q^{85} +(-1.61024 - 0.283929i) q^{86} +(1.58125 - 0.423695i) q^{88} +(-1.43212 - 1.20169i) q^{89} +(0.215486 + 0.592042i) q^{91} +(-10.4577 - 0.914930i) q^{92} +4.57054 q^{94} +(0.330711 - 9.74118i) q^{95} +(-0.975134 - 0.682796i) q^{97} +(25.1208 + 2.19778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	1.51450	+	1.06046i	1.07091	+	0.749860i	0.969526	−	0.244988i	$-0.0787839\pi$
$2$	1.51450	+	1.06046i	1.07091	+	0.749860i	0.101384	+	0.994847i	$0.467673\pi$
$3$		0			0
$3$		0			0
$4$	0.485079	+	1.33274i	0.242540	+	0.666372i
$5$	−0.762040	+	2.10221i	−0.340795	+	0.940138i
$5$	−0.762040	+	2.10221i	−0.340795	+	0.940138i
$6$		0			0
$7$	−4.38823	+	1.17582i	−1.65859	+	0.444419i	−0.962001	−	0.273048i	$-0.911968\pi$
$7$	−4.38823	+	1.17582i	−1.65859	+	0.444419i	−0.696593	+	0.717466i	$0.745302\pi$
$8$	0.278366	−	1.03888i	0.0984172	−	0.367298i
$9$		0			0
$10$	−3.38342	+	2.37568i	−1.06993	+	0.751255i
$11$	0.761040	+	1.31816i	0.229462	+	0.397440i	0.957649	−	0.287939i	$-0.0929699\pi$
$11$	0.761040	+	1.31816i	0.229462	+	0.397440i	−0.728187	+	0.685379i	$0.759637\pi$
$12$		0			0
$13$	−0.0120870	−	0.138155i	−0.00335232	−	0.0383172i	0.994334	−	0.106298i	$-0.0338998\pi$
$13$	−0.0120870	−	0.138155i	−0.00335232	−	0.0383172i	−0.997687	+	0.0679810i	$0.978344\pi$
$14$	−7.89287	−	2.87277i	−2.10946	−	0.767780i
$15$		0			0
$16$	3.69620	−	3.10148i	0.924050	−	0.775370i
$17$	−2.90701	+	4.15164i	−0.705054	+	1.00692i	0.293645	+	0.955915i	$0.405132\pi$
$17$	−2.90701	+	4.15164i	−0.705054	+	1.00692i	−0.998698	+	0.0510063i	$0.983757\pi$
$18$		0			0
$19$	−4.14601	+	1.34559i	−0.951160	+	0.308699i
$19$	−4.14601	+	1.34559i	−0.951160	+	0.308699i
$20$	−3.17136	+	0.00413488i	−0.709138	+	0.000924588i
$21$		0			0
$22$	−0.245266	+	2.80340i	−0.0522909	+	0.597687i
$23$	−3.12809	+	6.70821i	−0.652252	+	1.39876i	0.250297	+	0.968169i	$0.419472\pi$
$23$	−3.12809	+	6.70821i	−0.652252	+	1.39876i	−0.902548	+	0.430589i	$0.858306\pi$
$24$		0			0
$25$	−3.83859	−	3.20394i	−0.767718	−	0.640788i
$26$	0.128202	−	0.222052i	0.0251425	−	0.0435481i
$27$		0			0
$28$	−3.69571	−	5.27802i	−0.698423	−	0.997452i
$29$	0.346487	−	1.96502i	0.0643410	−	0.364896i	−0.935589	−	0.353090i	$-0.885131\pi$
$29$	0.346487	−	1.96502i	0.0643410	−	0.364896i	0.999930	−	0.0118058i	$-0.00375798\pi$
$30$		0			0
$31$	−1.08369	−	0.625668i	−0.194636	−	0.112373i	0.399515	−	0.916727i	$-0.369179\pi$
$31$	−1.08369	−	0.625668i	−0.194636	−	0.112373i	−0.594151	+	0.804353i	$0.702512\pi$
$32$	6.74402	−	0.590025i	1.19218	−	0.104303i
$33$		0			0
$34$	−8.80531	+	3.20487i	−1.51010	+	0.549631i
$35$	0.872178	−	10.1210i	0.147425	−	1.71076i
$36$		0			0
$37$	2.05676	−	2.05676i	0.338129	−	0.338129i	−0.517534	−	0.855663i	$-0.673150\pi$
$37$	2.05676	−	2.05676i	0.338129	−	0.338129i	0.855663	+	0.517534i	$0.173150\pi$
$38$	−7.70606	−	2.35879i	−1.25009	−	0.382647i
$39$		0			0
$40$	1.97181	+	1.37685i	0.311771	+	0.217699i
$41$	−1.05100	−	1.25253i	−0.164138	−	0.195613i	0.677706	−	0.735333i	$-0.262974\pi$
$41$	−1.05100	−	1.25253i	−0.164138	−	0.195613i	−0.841844	+	0.539721i	$0.818530\pi$
$42$		0			0
$43$	−0.801514	+	0.373752i	−0.122230	+	0.0569966i	−0.482771	−	0.875747i	$-0.660370\pi$
$43$	−0.801514	+	0.373752i	−0.122230	+	0.0569966i	0.360541	+	0.932743i	$0.382592\pi$
$44$	−1.38761	+	1.65368i	−0.209190	+	0.249302i
$45$		0			0
$46$	−11.8513	+	6.84234i	−1.74738	+	1.00885i
$47$	2.02502	−	1.41793i	0.295379	−	0.206827i	−0.416488	−	0.909141i	$-0.636739\pi$
$47$	2.02502	−	1.41793i	0.295379	−	0.206827i	0.711866	+	0.702315i	$0.247850\pi$
$48$		0			0
$49$	11.8118	−	6.81954i	1.68740	−	0.974220i
$50$	−2.41588	−	8.92303i	−0.341656	−	1.26191i
$51$		0			0
$52$	0.178262	−	0.0831248i	0.0247205	−	0.0115273i
$53$	10.1702	+	4.74246i	1.39699	+	0.651427i	0.967784	−	0.251780i	$-0.0810160\pi$
$53$	10.1702	+	4.74246i	1.39699	+	0.651427i	0.429205	+	0.903207i	$0.358794\pi$
$54$		0			0
$55$	−3.35100	+	0.595377i	−0.451848	+	0.0802806i
$56$			4.88613i			0.652936i
$57$		0			0
$58$	2.60859	−	2.60859i	0.342524	−	0.342524i
$59$	1.86831	+	10.5957i	0.243233	+	1.37944i	0.824561	+	0.565773i	$0.191422\pi$
$59$	1.86831	+	10.5957i	0.243233	+	1.37944i	−0.581328	+	0.813669i	$0.697467\pi$
$60$		0			0
$61$	−2.79178	+	1.01612i	−0.357451	+	0.130101i	−0.514502	−	0.857489i	$-0.672023\pi$
$61$	−2.79178	+	1.01612i	−0.357451	+	0.130101i	0.157052	+	0.987590i	$0.449801\pi$
$62$	−0.977745	−	2.09678i	−0.124174	−	0.266292i
$63$		0			0
$64$	2.48226	+	1.43314i	0.310283	+	0.179142i
$65$	0.299641	+	0.0798700i	0.0371659	+	0.00990666i
$66$		0			0
$67$	8.15144	+	11.6415i	0.995857	+	1.42223i	0.904530	+	0.426411i	$0.140222\pi$
$67$	8.15144	+	11.6415i	0.995857	+	1.42223i	0.0913279	+	0.995821i	$0.470889\pi$
$68$	−6.94321	−	1.86043i	−0.841988	−	0.225610i
$69$		0			0
$70$	12.0538	−	14.4033i	1.44071	−	1.72152i
$71$	1.79203	−	4.92356i	0.212675	−	0.584319i	−0.786784	−	0.617229i	$-0.788255\pi$
$71$	1.79203	−	4.92356i	0.212675	−	0.584319i	0.999458	+	0.0329100i	$0.0104775\pi$
$72$		0			0
$73$	−0.526410	+	6.01690i	−0.0616117	+	0.704225i	0.901085	+	0.433642i	$0.142772\pi$
$73$	−0.526410	+	6.01690i	−0.0616117	+	0.704225i	−0.962697	+	0.270582i	$0.912784\pi$
$74$	5.29607	−	0.933839i	0.615655	−	0.108557i
$75$		0			0
$76$	−3.80447	−	4.87285i	−0.436403	−	0.558955i
$77$	−4.88954	−	4.88954i	−0.557215	−	0.557215i
$78$		0			0
$79$	4.43572	−	3.72201i	0.499058	−	0.418759i	−0.358201	−	0.933644i	$-0.616610\pi$
$79$	4.43572	−	3.72201i	0.499058	−	0.418759i	0.857259	+	0.514885i	$0.172165\pi$
$80$	3.70331	+	10.1336i	0.414043	+	1.13298i
$81$		0			0
$82$	−0.263472	−	3.01150i	−0.0290956	−	0.332564i
$83$	0.122763	+	0.458159i	0.0134750	+	0.0502895i	0.972336	−	0.233587i	$-0.0750462\pi$
$83$	0.122763	+	0.458159i	0.0134750	+	0.0502895i	−0.958861	+	0.283876i	$0.908380\pi$
$84$		0			0
$85$	−6.51237	−	9.27487i	−0.706366	−	1.00600i
$86$	−1.61024	−	0.283929i	−0.173636	−	0.0306168i
$87$		0			0
$88$	1.58125	−	0.423695i	0.168562	−	0.0451661i
$89$	−1.43212	−	1.20169i	−0.151805	−	0.127379i	0.563722	−	0.825964i	$-0.309369\pi$
$89$	−1.43212	−	1.20169i	−0.151805	−	0.127379i	−0.715527	+	0.698585i	$0.753813\pi$
$90$		0			0
$91$	0.215486	+	0.592042i	0.0225890	+	0.0620628i
$92$	−10.4577	−	0.914930i	−1.09029	−	0.0953881i
$93$		0			0
$94$	4.57054			0.471415
$95$	0.330711	−	9.74118i	0.0339302	−	0.999424i
$96$		0			0
$97$	−0.975134	−	0.682796i	−0.0990098	−	0.0693274i	0.523023	−	0.852318i	$-0.324804\pi$
$97$	−0.975134	−	0.682796i	−0.0990098	−	0.0693274i	−0.622033	+	0.782991i	$0.713693\pi$
$98$	25.1208	+	2.19778i	2.53758	+	0.222010i
$99$		0			0
$100$	2.40801	−	6.67003i	0.240801	−	0.667003i
$101$	0.589039	+	0.494263i	0.0586116	+	0.0491810i	0.671623	−	0.740893i	$-0.265598\pi$
$101$	0.589039	+	0.494263i	0.0586116	+	0.0491810i	−0.613011	+	0.790074i	$0.710042\pi$
$102$		0			0
$103$	−1.02732	+	3.83402i	−0.101225	+	0.377777i	−0.997890	−	0.0649337i	$-0.979316\pi$
$103$	−1.02732	+	3.83402i	−0.101225	+	0.377777i	0.896665	+	0.442711i	$0.145983\pi$
$104$	−0.146890	−	0.0259007i	−0.0144038	−	0.00253977i
$105$		0			0
$106$	10.3736	+	17.9676i	1.00757	+	1.74517i
$107$	3.91983	+	14.6290i	0.378944	+	1.41424i	0.847496	+	0.530802i	$0.178109\pi$
$107$	3.91983	+	14.6290i	0.378944	+	1.41424i	−0.468552	+	0.883436i	$0.655224\pi$
$108$		0			0
$109$	8.35240	+	3.04003i	0.800015	+	0.291182i	0.709493	−	0.704713i	$-0.248924\pi$
$109$	8.35240	+	3.04003i	0.800015	+	0.291182i	0.0905223	+	0.995894i	$0.471146\pi$
$110$	−5.70644	−	2.65191i	−0.544088	−	0.252849i
$111$		0			0
$112$	−12.5730	+	17.9561i	−1.18803	+	1.69669i
$113$	3.03272	+	3.03272i	0.285294	+	0.285294i	0.835216	−	0.549922i	$-0.185342\pi$
$113$	3.03272	+	3.03272i	0.285294	+	0.285294i	−0.549922	+	0.835216i	$0.685342\pi$
$114$		0			0
$115$	−11.7183	−	11.6878i	−1.09274	−	1.08990i
$116$	2.78695	−	0.491414i	0.258762	−	0.0456267i
$117$		0			0
$118$	−8.40679	+	18.0284i	−0.773907	+	1.65965i
$119$	7.87503	−	21.6365i	0.721903	−	1.98341i
$120$		0			0
$121$	4.34164	−	7.51993i	0.394694	−	0.683630i
$122$	−5.30570	−	1.42166i	−0.480355	−	0.128711i
$123$		0			0
$124$	0.308181	−	1.74778i	0.0276754	−	0.156955i
$125$	9.66052	−	5.62800i	0.864063	−	0.503384i
$126$		0			0
$127$	−13.3493	+	1.16792i	−1.18456	+	0.103636i	−0.662360	−	0.749186i	$-0.730445\pi$
$127$	−13.3493	+	1.16792i	−1.18456	+	0.103636i	−0.522202	+	0.852822i	$0.674889\pi$
$128$	−3.48247	−	7.46818i	−0.307810	−	0.660100i
$129$		0			0
$130$	0.369106	+	0.438721i	0.0323728	+	0.0384784i
$131$	1.85946	+	10.5455i	0.162462	+	0.921369i	0.951643	+	0.307207i	$0.0993945\pi$
$131$	1.85946	+	10.5455i	0.162462	+	0.921369i	−0.789180	+	0.614161i	$0.789494\pi$
$132$		0			0
$133$	16.6115	−	10.7797i	1.44040	−	0.934720i
$134$			26.2753i			2.26984i
$135$		0			0
$136$	3.50383	+	4.17570i	0.300451	+	0.358063i
$137$	−18.9179	−	8.82158i	−1.61627	−	0.753679i	−0.616828	−	0.787098i	$-0.711582\pi$
$137$	−18.9179	−	8.82158i	−1.61627	−	0.753679i	−0.999441	+	0.0334197i	$0.989360\pi$
$138$		0			0
$139$	−4.32307	+	5.15204i	−0.366678	+	0.436990i	−0.917562	−	0.397592i	$-0.869846\pi$
$139$	−4.32307	+	5.15204i	−0.366678	+	0.436990i	0.550884	+	0.834582i	$0.314291\pi$
$140$	13.9118	−	3.74710i	1.17576	−	0.316688i
$141$		0			0
$142$	7.93526	−	5.55633i	0.665913	−	0.466277i
$143$	0.172911	−	0.121074i	0.0144596	−	0.0101247i
$144$		0			0
$145$	3.86686	+	2.22582i	0.321125	+	0.184844i
$146$	−7.17794	+	8.55433i	−0.594050	+	0.707961i
$147$		0			0
$148$	3.73883	+	1.74344i	0.307330	+	0.143310i
$149$	5.56213	+	6.62869i	0.455668	+	0.543043i	0.944144	−	0.329534i	$-0.106892\pi$
$149$	5.56213	+	6.62869i	0.455668	+	0.543043i	−0.488476	+	0.872577i	$0.662447\pi$
$150$		0			0
$151$		−	10.4228i		−	0.848193i	−0.905617	−	0.424097i	$-0.860592\pi$
$151$		−	10.4228i		−	0.848193i	0.905617	−	0.424097i	$-0.139408\pi$
$152$	0.243792	+	4.68175i	0.0197742	+	0.379740i
$153$		0			0
$154$	−2.22002	−	12.5904i	−0.178894	−	1.01456i
$155$	2.14110	−	1.80136i	0.171977	−	0.144689i
$156$		0			0
$157$	−6.88494	−	14.7648i	−0.549478	−	1.17836i	−0.963405	−	0.268049i	$-0.913621\pi$
$157$	−6.88494	−	14.7648i	−0.549478	−	1.17836i	0.413927	−	0.910310i	$-0.364157\pi$
$158$	10.6649	−	0.933061i	0.848457	−	0.0742304i
$159$		0			0
$160$	−3.89885	+	14.6270i	−0.308231	+	1.15636i
$161$	5.83910	−	33.1152i	0.460186	−	2.60984i
$162$		0			0
$163$	−5.73737	−	1.53732i	−0.449386	−	0.120413i	0.0270262	−	0.999635i	$-0.491396\pi$
$163$	−5.73737	−	1.53732i	−0.449386	−	0.120413i	−0.476412	+	0.879222i	$0.658063\pi$
$164$	1.15949	−	2.00829i	0.0905407	−	0.156821i
$165$		0			0
$166$	−0.299935	+	0.824066i	−0.0232795	+	0.0639599i
$167$	−6.31154	+	13.5351i	−0.488402	+	1.04738i	0.495490	+	0.868614i	$0.334989\pi$
$167$	−6.31154	+	13.5351i	−0.488402	+	1.04738i	−0.983891	+	0.178767i	$0.942789\pi$
$168$		0			0
$169$	12.7836	−	2.25409i	0.983351	−	0.173391i
$170$	−0.0273188	−	20.9529i	−0.00209525	−	1.60701i
$171$		0			0
$172$	−0.886914	−	0.886914i	−0.0676265	−	0.0676265i
$173$	7.88448	−	11.2602i	0.599446	−	0.856098i	−0.398692	−	0.917085i	$-0.630536\pi$
$173$	7.88448	−	11.2602i	0.599446	−	0.856098i	0.998139	+	0.0609868i	$0.0194248\pi$
$174$		0			0
$175$	20.6119	+	9.54611i	1.55811	+	0.721618i
$176$	6.90120	+	2.51183i	0.520198	+	0.189336i
$177$		0			0
$178$	−0.894595	−	3.33867i	−0.0670527	−	0.250244i
$179$	2.00568	+	3.47394i	0.149912	+	0.259654i	0.931195	−	0.364523i	$-0.118768\pi$
$179$	2.00568	+	3.47394i	0.149912	+	0.259654i	−0.781283	+	0.624177i	$0.785434\pi$
$180$		0			0
$181$	−22.2392	−	3.92137i	−1.65303	−	0.291473i	−0.732096	−	0.681202i	$-0.761458\pi$
$181$	−22.2392	−	3.92137i	−1.65303	−	0.291473i	−0.920930	+	0.389729i	$0.872569\pi$
$182$	−0.301485	+	1.12516i	−0.0223476	+	0.0834023i
$183$		0			0
$184$	6.09824	+	5.11703i	0.449568	+	0.377232i
$185$	2.75641	+	5.89107i	0.202655	+	0.433120i
$186$		0			0
$187$	−7.68488	−	0.672340i	−0.561974	−	0.0491664i
$188$	2.87203	+	2.01102i	0.209465	+	0.146669i
$189$		0			0
$190$	10.8310	−	14.4023i	0.785764	−	1.04485i
$191$	−12.6937			−0.918482			−0.459241	−	0.888312i	$-0.651879\pi$
$191$	−12.6937			−0.918482			−0.459241	+	0.888312i	$0.651879\pi$
$192$		0			0
$193$	14.8711	+	1.30105i	1.07045	+	0.0936519i	0.608731	−	0.793376i	$-0.291679\pi$
$193$	14.8711	+	1.30105i	1.07045	+	0.0936519i	0.461715	+	0.887028i	$0.347234\pi$
$194$	−0.752757	−	2.06818i	−0.0540448	−	0.148487i
$195$		0			0
$196$	14.8184	+	12.4341i	1.05845	+	0.888149i
$197$	−6.10369	+	1.63548i	−0.434870	+	0.116523i	−0.469611	−	0.882873i	$-0.655606\pi$
$197$	−6.10369	+	1.63548i	−0.434870	+	0.116523i	0.0347415	+	0.999396i	$0.488939\pi$
$198$		0			0
$199$	12.5304	+	2.20944i	0.888254	+	0.156623i	0.599114	−	0.800664i	$-0.295520\pi$
$199$	12.5304	+	2.20944i	0.888254	+	0.156623i	0.289140	+	0.957287i	$0.406631\pi$
$200$	−4.39703	+	3.09595i	−0.310917	+	0.218917i
$201$		0			0
$202$	0.367951	+	1.37321i	0.0258890	+	0.0966189i
$203$	0.790056	+	9.03038i	0.0554510	+	0.633808i
$204$		0			0
$205$	3.43399	−	1.25494i	0.239840	−	0.0876490i
$206$	−5.62170	+	4.71717i	−0.391683	+	0.328661i
$207$		0			0
$208$	−0.473160	−	0.473160i	−0.0328077	−	0.0328077i
$209$	−4.92898	−	4.44106i	−0.340945	−	0.307194i
$210$		0			0
$211$	16.9039	−	2.98061i	1.16371	−	0.205193i	0.441756	−	0.897135i	$-0.354356\pi$
$211$	16.9039	−	2.98061i	1.16371	−	0.205193i	0.721953	+	0.691942i	$0.243245\pi$
$212$	−1.38712	+	15.8548i	−0.0952675	+	1.08891i
$213$		0			0
$214$	−9.57692	+	26.3124i	−0.654665	+	1.79868i
$215$	−0.174920	−	1.96977i	−0.0119295	−	0.134337i
$216$		0			0
$217$	5.49114	+	1.47135i	0.372763	+	0.0998816i
$218$	9.42585	+	13.4615i	0.638399	+	0.911728i
$219$		0			0
$220$	−2.41898	−	4.17722i	−0.163088	−	0.281628i
$221$	0.608705	+	0.351436i	0.0409460	+	0.0236402i
$222$		0			0
$223$	−7.93699	−	17.0209i	−0.531500	−	1.13981i	−0.970452	−	0.241295i	$-0.922428\pi$
$223$	−7.93699	−	17.0209i	−0.531500	−	1.13981i	0.438952	−	0.898511i	$-0.355350\pi$
$224$	−28.9005	+	10.5189i	−1.93100	+	0.702825i
$225$		0			0
$226$	1.37696	+	7.80913i	0.0915940	+	0.519456i
$227$	−0.0653385	+	0.0653385i	−0.00433667	+	0.00433667i	−0.709272	−	0.704935i	$-0.750976\pi$
$227$	−0.0653385	+	0.0653385i	−0.00433667	+	0.00433667i	0.704935	+	0.709272i	$0.250976\pi$
$228$		0			0
$229$		−	10.2958i		−	0.680367i	−0.940359	−	0.340184i	$-0.889511\pi$
$229$		−	10.2958i		−	0.680367i	0.940359	−	0.340184i	$-0.110489\pi$
$230$	−5.35290	−	30.1280i	−0.352959	−	1.98658i
$231$		0			0
$232$	−1.94497	−	0.906952i	−0.127693	−	0.0595443i
$233$	−19.6455	+	9.16084i	−1.28702	+	0.600146i	−0.941103	−	0.338119i	$-0.890209\pi$
$233$	−19.6455	+	9.16084i	−1.28702	+	0.600146i	−0.345915	+	0.938266i	$0.612431\pi$
$234$		0			0
$235$	1.43765	+	5.33753i	0.0937819	+	0.348182i
$236$	−13.2151	+	7.62973i	−0.860229	+	0.496653i
$237$		0			0
$238$	34.8713	−	24.4172i	2.26037	−	1.58273i
$239$	−8.88903	+	5.13208i	−0.574984	+	0.331967i	−0.759137	−	0.650931i	$-0.774379\pi$
$239$	−8.88903	+	5.13208i	−0.574984	+	0.331967i	0.184154	+	0.982897i	$0.441046\pi$
$240$		0			0
$241$	−12.7247	+	15.1647i	−0.819672	+	0.976847i	−0.999977	−	0.00676413i	$-0.997847\pi$
$241$	−12.7247	+	15.1647i	−0.819672	+	0.976847i	0.180306	+	0.983611i	$0.442291\pi$
$242$	14.5500	−	6.78477i	0.935309	−	0.436142i
$243$		0			0
$244$	−2.70847	−	3.22783i	−0.173392	−	0.206640i
$245$	5.33506	+	30.0277i	0.340845	+	1.91840i
$246$		0			0
$247$	0.236012	+	0.556526i	0.0150171	+	0.0354109i
$248$	−0.951653	+	0.951653i	−0.0604300	+	0.0604300i
$249$		0			0
$250$	20.5991	+	1.72103i	1.30280	+	0.108847i
$251$	−5.76397	+	2.09791i	−0.363819	+	0.132419i	−0.517460	−	0.855708i	$-0.673122\pi$
$251$	−5.76397	+	2.09791i	−0.363819	+	0.132419i	0.153641	+	0.988127i	$0.450900\pi$
$252$		0			0
$253$	−11.2231	+	0.981894i	−0.705590	+	0.0617311i
$254$	−21.4560	−	12.3877i	−1.34627	−	0.777270i
$255$		0			0
$256$	3.64098	−	20.6490i	0.227561	−	1.29056i
$257$	13.3449	+	19.0585i	0.832430	+	1.18883i	0.979845	+	0.199759i	$0.0640159\pi$
$257$	13.3449	+	19.0585i	0.832430	+	1.18883i	−0.147415	+	0.989075i	$0.547095\pi$
$258$		0			0
$259$	−6.60714	+	11.4439i	−0.410548	+	0.711090i
$260$	0.0389034	+	0.438088i	0.00241269	+	0.0271691i
$261$		0			0
$262$	−8.36700	+	17.9431i	−0.516915	+	1.10853i
$263$	−1.09837	+	12.5544i	−0.0677285	+	0.774140i	0.884058	+	0.467378i	$0.154801\pi$
$263$	−1.09837	+	12.5544i	−0.0677285	+	0.774140i	−0.951786	+	0.306762i	$0.900754\pi$
$264$		0			0
$265$	−17.7198	+	17.7660i	−1.08852	+	1.09136i
$266$	36.5895	+	1.28997i	2.24344	+	0.0790930i
$267$		0			0
$268$	−11.5610	+	16.5108i	−0.706201	+	1.00856i
$269$	13.4512	−	11.2869i	0.820136	−	0.688176i	−0.132868	−	0.991134i	$-0.542419\pi$
$269$	13.4512	−	11.2869i	0.820136	−	0.688176i	0.953004	+	0.302958i	$0.0979742\pi$
$270$		0			0
$271$	−15.7503	−	5.73264i	−0.956762	−	0.348233i	−0.183998	−	0.982927i	$-0.558904\pi$
$271$	−15.7503	−	5.73264i	−0.956762	−	0.348233i	−0.772764	+	0.634694i	$0.781126\pi$
$272$	2.13134	+	24.3613i	0.129231	+	1.47712i
$273$		0			0
$274$	−19.2962	−	33.4220i	−1.16573	−	2.01910i
$275$	1.30198	−	7.49820i	0.0785126	−	0.452159i
$276$		0			0
$277$	−7.79634	+	29.0963i	−0.468437	+	1.74823i	0.176800	+	0.984247i	$0.443425\pi$
$277$	−7.79634	+	29.0963i	−0.468437	+	1.74823i	−0.645237	+	0.763982i	$0.723241\pi$
$278$	−12.0108	+	3.21829i	−0.720361	+	0.193020i
$279$		0			0
$280$	−10.2717	−	3.72343i	−0.613850	−	0.222517i
$281$	−9.59450	−	26.3607i	−0.572360	−	1.57255i	−0.800764	−	0.598980i	$-0.795573\pi$
$281$	−9.59450	−	26.3607i	−0.572360	−	1.57255i	0.228404	−	0.973566i	$-0.426649\pi$
$282$		0			0
$283$	16.0049	+	11.2068i	0.951394	+	0.666173i	0.942648	−	0.333789i	$-0.108327\pi$
$283$	16.0049	+	11.2068i	0.951394	+	0.666173i	0.00874584	+	0.999962i	$0.497216\pi$
$284$	7.43112			0.440956
$285$		0			0
$286$	0.390268			0.0230770
$287$	6.08478	+	4.26061i	0.359173	+	0.251496i
$288$		0			0
$289$	−2.97107	−	8.16296i	−0.174769	−	0.480174i
$290$	3.49595	+	7.47165i	0.205289	+	0.438750i
$291$		0			0
$292$	−8.27434	+	2.21710i	−0.484219	+	0.129746i
$293$	1.45003	−	5.41159i	0.0847117	−	0.316148i	−0.910548	−	0.413404i	$-0.864340\pi$
$293$	1.45003	−	5.41159i	0.0847117	−	0.316148i	0.995259	+	0.0972556i	$0.0310064\pi$
$294$		0			0
$295$	−23.6981	−	4.14677i	−1.37976	−	0.241434i
$296$	−1.56418	−	2.70925i	−0.0909164	−	0.157472i
$297$		0			0
$298$	1.39436	+	15.9376i	0.0807728	+	0.923238i
$299$	0.964579	+	0.351078i	0.0557831	+	0.0203034i
$300$		0			0
$301$	3.07776	−	2.58254i	0.177399	−	0.148855i
$302$	11.0530	−	15.7853i	0.636026	−	0.908339i
$303$		0			0
$304$	−11.1512	+	17.8323i	−0.639563	+	1.02275i
$305$	−0.00866158	−	6.64324i	−0.000495961	−	0.380391i
$306$		0			0
$307$	1.42367	−	16.2726i	0.0812529	−	0.928725i	−0.840720	−	0.541470i	$-0.817868\pi$
$307$	1.42367	−	16.2726i	0.0812529	−	0.928725i	0.921973	−	0.387255i	$-0.126577\pi$
$308$	4.14469	−	8.88832i	0.236166	−	0.506459i
$309$		0			0
$310$	5.15296	−	0.457596i	0.292669	−	0.0259897i
$311$	−0.890255	+	1.54197i	−0.0504817	+	0.0874369i	−0.890162	−	0.455644i	$-0.849409\pi$
$311$	−0.890255	+	1.54197i	−0.0504817	+	0.0874369i	0.839680	+	0.543081i	$0.182742\pi$
$312$		0			0
$313$	2.51948	+	3.59819i	0.142409	+	0.203382i	0.884020	−	0.467449i	$-0.154827\pi$
$313$	2.51948	+	3.59819i	0.142409	+	0.203382i	−0.741611	+	0.670830i	$0.765938\pi$
$314$	5.23029	−	29.6624i	0.295162	−	1.67395i
$315$		0			0
$316$	7.11217	+	4.10622i	0.400091	+	0.230993i
$317$	9.14589	−	0.800161i	0.513684	−	0.0449415i	0.172633	−	0.984986i	$-0.444773\pi$
$317$	9.14589	−	0.800161i	0.513684	−	0.0449415i	0.341051	+	0.940045i	$0.389217\pi$
$318$		0			0
$319$	2.85391	−	1.03874i	0.159788	−	0.0581581i
$320$	−4.90434	+	4.12614i	−0.274161	+	0.230658i
$321$		0			0
$322$	43.9607	−	43.9607i	2.44983	−	2.44983i
$323$	6.46609	−	21.1244i	0.359783	−	1.17539i
$324$		0			0
$325$	−0.396242	+	0.569045i	−0.0219796	+	0.0315649i
$326$	−7.05896	−	8.41254i	−0.390959	−	0.465927i
$327$		0			0
$328$	−1.59379	+	0.743195i	−0.0880021	+	0.0410361i
$329$	−7.21899	+	8.60326i	−0.397996	+	0.474313i
$330$		0			0
$331$	9.85862	−	5.69188i	0.541879	−	0.312854i	−0.203961	−	0.978979i	$-0.565382\pi$
$331$	9.85862	−	5.69188i	0.541879	−	0.312854i	0.745840	+	0.666125i	$0.232048\pi$
$332$	−0.551059	+	0.385856i	−0.0302433	+	0.0211766i
$333$		0			0
$334$	−23.9123	+	13.8058i	−1.30842	+	0.755418i
$335$	−30.6846	+	8.26480i	−1.67648	+	0.451554i
$336$		0			0
$337$	14.1389	−	6.59306i	0.770193	−	0.359147i	0.00252652	−	0.999997i	$-0.499196\pi$
$337$	14.1389	−	6.59306i	0.770193	−	0.359147i	0.767666	+	0.640850i	$0.221418\pi$
$338$	21.7510	+	10.1427i	1.18310	+	0.551688i
$339$		0			0
$340$	9.20202	−	13.1784i	0.499049	−	0.714698i
$341$		−	1.90463i		−	0.103142i
$342$		0			0
$343$	−21.3274	+	21.3274i	−1.15157	+	1.15157i
$344$	0.165168	+	0.936712i	0.00890524	+	0.0505041i
$345$		0			0
$346$	23.8820	−	8.69235i	1.28391	−	0.467304i
$347$	−5.93804	−	12.7342i	−0.318770	−	0.683606i	0.679998	−	0.733214i	$-0.261981\pi$
$347$	−5.93804	−	12.7342i	−0.318770	−	0.683606i	−0.998769	+	0.0496082i	$0.984203\pi$
$348$		0			0
$349$	−20.6061	−	11.8969i	−1.10302	−	0.636829i	−0.166007	−	0.986125i	$-0.553087\pi$
$349$	−20.6061	−	11.8969i	−1.10302	−	0.636829i	−0.937012	+	0.349296i	$0.886421\pi$
$350$	21.0933	+	36.3156i	1.12748	+	1.94115i
$351$		0			0
$352$	5.91022	+	8.44066i	0.315016	+	0.449889i
$353$	12.3909	+	3.32012i	0.659499	+	0.176712i	0.573020	−	0.819542i	$-0.305772\pi$
$353$	12.3909	+	3.32012i	0.659499	+	0.176712i	0.0864789	+	0.996254i	$0.472438\pi$
$354$		0			0
$355$	8.98477	+	7.51917i	0.476862	+	0.399076i
$356$	0.906858	−	2.49157i	0.0480634	−	0.132053i
$357$		0			0
$358$	−0.646385	+	7.38821i	−0.0341625	+	0.390479i
$359$	−1.62390	+	0.286337i	−0.0857062	+	0.0151123i	−0.216337	−	0.976319i	$-0.569411\pi$
$359$	−1.62390	+	0.286337i	−0.0857062	+	0.0151123i	0.130631	+	0.991431i	$0.458300\pi$
$360$		0			0
$361$	15.3788	−	11.1576i	0.809409	−	0.587245i
$362$	−29.5227	−	29.5227i	−1.55168	−	1.55168i
$363$		0			0
$364$	−0.684513	+	0.574375i	−0.0358782	+	0.0301054i
$365$	−12.2476	−	5.69174i	−0.641071	−	0.297919i
$366$		0			0
$367$	1.54633	+	17.6746i	0.0807176	+	0.922606i	0.923310	+	0.384055i	$0.125473\pi$
$367$	1.54633	+	17.6746i	0.0807176	+	0.922606i	−0.842593	+	0.538551i	$0.818972\pi$
$368$	9.24333	+	34.4966i	0.481842	+	1.79826i
$369$		0			0
$370$	−2.07269	+	11.8451i	−0.107754	+	0.615796i
$371$	−50.2056	−	8.85260i	−2.60654	−	0.459604i
$372$		0			0
$373$	−12.5757	+	3.36965i	−0.651145	+	0.174474i	−0.569246	−	0.822167i	$-0.692765\pi$
$373$	−12.5757	+	3.36965i	−0.651145	+	0.174474i	−0.0818983	+	0.996641i	$0.526098\pi$
$374$	−10.9257	−	9.16778i	−0.564956	−	0.474054i
$375$		0			0
$376$	−0.909359	−	2.49844i	−0.0468966	−	0.128847i
$377$	−0.275665	−	0.0241176i	−0.0141975	−	0.00124212i
$378$		0			0
$379$	19.2818			0.990442			0.495221	−	0.868767i	$-0.335087\pi$
$379$	19.2818			0.990442			0.495221	+	0.868767i	$0.335087\pi$
$380$	13.1429	−	4.28449i	0.674218	−	0.219790i
$381$		0			0
$382$	−19.2245	−	13.4612i	−0.983612	−	0.688733i
$383$	−14.9442	−	1.30745i	−0.763612	−	0.0668074i	−0.301305	−	0.953528i	$-0.597422\pi$
$383$	−14.9442	−	1.30745i	−0.763612	−	0.0668074i	−0.462306	+	0.886720i	$0.652978\pi$
$384$		0			0
$385$	14.0049	−	6.55282i	0.713754	−	0.333963i
$386$	21.1425	+	17.7407i	1.07613	+	0.902977i
$387$		0			0
$388$	0.436975	−	1.63081i	0.0221841	−	0.0827921i
$389$	−13.3902	−	2.36105i	−0.678909	−	0.119710i	−0.176448	−	0.984310i	$-0.556461\pi$
$389$	−13.3902	−	2.36105i	−0.678909	−	0.119710i	−0.502461	+	0.864600i	$0.667572\pi$
$390$		0			0
$391$	−18.7567	−	32.4875i	−0.948566	−	1.64297i
$392$	−3.79666	−	14.1693i	−0.191760	−	0.715658i
$393$		0			0
$394$	−10.9784	−	3.99580i	−0.553082	−	0.201306i
$395$	4.44426	+	12.1612i	0.223615	+	0.611894i
$396$		0			0
$397$	2.68829	−	3.83927i	0.134921	−	0.192687i	−0.746006	−	0.665939i	$-0.768031\pi$
$397$	2.68829	−	3.83927i	0.134921	−	0.192687i	0.880927	+	0.473252i	$0.156920\pi$
$398$	16.6342	+	16.6342i	0.833795	+	0.833795i
$399$		0			0
$400$	−24.1251	+	0.0629097i	−1.20626	+	0.00314549i
$401$	29.5512	−	5.21067i	1.47572	−	0.260209i	0.622851	−	0.782340i	$-0.285974\pi$
$401$	29.5512	−	5.21067i	1.47572	−	0.260209i	0.852865	+	0.522132i	$0.174863\pi$
$402$		0			0
$403$	−0.0733404	+	0.157279i	−0.00365335	+	0.00783463i
$404$	−0.372995	+	1.02480i	−0.0185572	+	0.0509855i
$405$		0			0
$406$	−8.37983	+	14.5143i	−0.415884	+	0.720333i
$407$	4.27641	+	1.14586i	0.211974	+	0.0567982i
$408$		0			0
$409$	−5.94508	+	33.7162i	−0.293965	+	1.66716i	0.377414	+	0.926045i	$0.376813\pi$
$409$	−5.94508	+	33.7162i	−0.293965	+	1.66716i	−0.671379	+	0.741114i	$0.734298\pi$
$410$	6.53158	+	1.74101i	0.322572	+	0.0859823i
$411$		0			0
$412$	−5.60810	+	0.490645i	−0.276291	+	0.0241723i
$413$	−20.6572	−	44.2995i	−1.01647	−	2.17984i
$414$		0			0
$415$	−1.05670	−	0.0910609i	−0.0518713	−	0.00447001i
$416$	−0.163029	−	0.924586i	−0.00799317	−	0.0453315i
$417$		0			0
$418$	−2.75535	−	11.9530i	−0.134769	−	0.584638i
$419$		−	7.01480i		−	0.342696i	−0.985211	−	0.171348i	$-0.945188\pi$
$419$		−	7.01480i		−	0.342696i	0.985211	−	0.171348i	$-0.0548122\pi$
$420$		0			0
$421$	−2.21994	−	2.64562i	−0.108193	−	0.128939i	0.709230	−	0.704977i	$-0.249043\pi$
$421$	−2.21994	−	2.64562i	−0.108193	−	0.128939i	−0.817423	+	0.576037i	$0.804598\pi$
$422$	28.7616	+	13.4118i	1.40009	+	0.652875i
$423$		0			0
$424$	7.75787	−	9.24547i	0.376755	−	0.449000i
$425$	24.4604	−	6.62256i	1.18651	−	0.321242i
$426$		0			0
$427$	11.0562	−	7.74162i	0.535046	−	0.374643i
$428$	−17.5953	+	12.3203i	−0.850500	+	0.595526i
$429$		0			0
$430$	1.82394	−	3.16870i	0.0879584	−	0.152808i
$431$	6.73534	−	8.02687i	0.324430	−	0.386641i	−0.579035	−	0.815303i	$-0.696571\pi$
$431$	6.73534	−	8.02687i	0.324430	−	0.386641i	0.903465	+	0.428662i	$0.141015\pi$
$432$		0			0
$433$	21.5929	+	10.0690i	1.03769	+	0.483883i	0.865357	−	0.501156i	$-0.167092\pi$
$433$	21.5929	+	10.0690i	1.03769	+	0.483883i	0.172333	+	0.985039i	$0.444869\pi$
$434$	6.75601	+	8.05150i	0.324299	+	0.386484i
$435$		0			0
$436$			12.6063i			0.603731i
$437$	3.94259	−	32.0214i	0.188600	−	1.53179i
$438$		0			0
$439$	0.100282	+	0.568729i	0.00478621	+	0.0271439i	0.987107	−	0.160060i	$-0.0511687\pi$
$439$	0.100282	+	0.568729i	0.00478621	+	0.0271439i	−0.982321	+	0.187204i	$0.940058\pi$
$440$	−0.314280	+	3.64700i	−0.0149827	+	0.173864i
$441$		0			0
$442$	0.549197	+	1.17776i	0.0261227	+	0.0560202i
$443$	8.46505	−	0.740596i	0.402187	−	0.0351868i	0.115732	−	0.993281i	$-0.463079\pi$
$443$	8.46505	−	0.740596i	0.402187	−	0.0351868i	0.286455	+	0.958094i	$0.407523\pi$
$444$		0			0
$445$	3.61755	−	2.09489i	0.171488	−	0.0993072i
$446$	6.02950	−	34.1950i	0.285505	−	1.61918i
$447$		0			0
$448$	−12.5778	−	3.37022i	−0.594247	−	0.159228i
$449$	−4.27636	+	7.40687i	−0.201814	+	0.349552i	−0.949113	−	0.314936i	$-0.898017\pi$
$449$	−4.27636	+	7.40687i	−0.201814	+	0.349552i	0.747299	+	0.664488i	$0.231350\pi$
$450$		0			0
$451$	0.851185	−	2.33861i	0.0400807	−	0.110121i
$452$	−2.57073	+	5.51295i	−0.120917	+	0.259308i
$453$		0			0
$454$	−0.168244	+	0.0296659i	−0.00789608	+	0.00139229i
$455$	−1.40881	+	0.00183683i	−0.0660458	+	8.61118e-5i
$456$		0			0
$457$	1.00342	+	1.00342i	0.0469379	+	0.0469379i	0.730186	−	0.683248i	$-0.239433\pi$
$457$	1.00342	+	1.00342i	0.0469379	+	0.0469379i	−0.683248	+	0.730186i	$0.739433\pi$
$458$	10.9183	−	15.5930i	0.510180	−	0.728612i
$459$		0			0
$460$	9.89256	−	21.2871i	0.461243	−	0.992516i
$461$	0.708319	+	0.257807i	0.0329897	+	0.0120073i	0.358462	−	0.933544i	$-0.383301\pi$
$461$	0.708319	+	0.257807i	0.0329897	+	0.0120073i	−0.325473	+	0.945551i	$0.605523\pi$
$462$		0			0
$463$	−5.65758	−	21.1144i	−0.262930	−	0.981269i	−0.963505	−	0.267690i	$-0.913740\pi$
$463$	−5.65758	−	21.1144i	−0.262930	−	0.981269i	0.700575	−	0.713579i	$-0.252927\pi$
$464$	−4.81380	−	8.33774i	−0.223475	−	0.387070i
$465$		0			0
$466$	−39.4677	−	6.95922i	−1.82831	−	0.322380i
$467$	0.811663	−	3.02917i	0.0375593	−	0.140173i	−0.944600	−	0.328223i	$-0.893550\pi$
$467$	0.811663	−	3.02917i	0.0375593	−	0.140173i	0.982159	+	0.188050i	$0.0602168\pi$
$468$		0			0
$469$	−49.4587	−	41.5008i	−2.28379	−	1.91633i
$470$	−3.48293	+	9.60824i	−0.160656	+	0.443195i
$471$		0			0
$472$	11.5277	+	1.00854i	0.530605	+	0.0464219i
$473$	−1.10265	−	0.772083i	−0.0506999	−	0.0355004i
$474$		0			0
$475$	20.2260	+	8.11840i	0.928033	+	0.372498i
$476$	32.6559			1.49678
$477$		0			0
$478$	−18.9048	−	1.65395i	−0.864684	−	0.0756501i
$479$	9.80127	+	26.9288i	0.447831	+	1.23041i	0.934230	+	0.356670i	$0.116088\pi$
$479$	9.80127	+	26.9288i	0.447831	+	1.23041i	−0.486399	+	0.873737i	$0.661690\pi$
$480$		0			0
$481$	−0.309011	−	0.259291i	−0.0140897	−	0.0118226i
$482$	−35.3532	+	9.47285i	−1.61029	+	0.431477i
$483$		0			0
$484$	12.1282	+	2.13853i	0.551281	+	0.0972058i
$485$	2.17847	−	1.52962i	0.0989193	−	0.0694565i
$486$		0			0
$487$	−2.52061	−	9.40703i	−0.114220	−	0.426273i	0.885008	−	0.465576i	$-0.154153\pi$
$487$	−2.52061	−	9.40703i	−0.114220	−	0.426273i	−0.999227	+	0.0393029i	$0.987486\pi$
$488$	0.278491	+	3.18316i	0.0126067	+	0.144095i
$489$		0			0
$490$	−23.7632	+	51.1344i	−1.07351	+	2.31002i
$491$	−6.63665	+	5.56881i	−0.299508	+	0.251317i	−0.780139	−	0.625606i	$-0.784852\pi$
$491$	−6.63665	+	5.56881i	−0.299508	+	0.251317i	0.480631	+	0.876923i	$0.340407\pi$
$492$		0			0
$493$	7.15084	+	7.15084i	0.322057	+	0.322057i
$494$	−0.232735	+	1.09314i	−0.0104713	+	0.0491826i
$495$		0			0
$496$	−5.94602	+	1.04844i	−0.266984	+	0.0470765i
$497$	−2.07460	+	23.7128i	−0.0930586	+	1.06366i
$498$		0			0
$499$	−0.511920	+	1.40649i	−0.0229167	+	0.0629631i	−0.950623	−	0.310347i	$-0.899555\pi$
$499$	−0.511920	+	1.40649i	−0.0229167	+	0.0629631i	0.927707	+	0.373310i	$0.121777\pi$
$500$	12.1868	+	10.1450i	0.545010	+	0.453697i
$501$		0			0
$502$	−10.9543	−	2.93519i	−0.488913	−	0.131004i
$503$	4.54411	+	6.48967i	0.202612	+	0.289360i	0.907580	−	0.419879i	$-0.137928\pi$
$503$	4.54411	+	6.48967i	0.202612	+	0.289360i	−0.704968	+	0.709239i	$0.749039\pi$
$504$		0			0
$505$	−1.48792	+	0.861638i	−0.0662114	+	0.0383424i
$506$	−18.0386	−	10.4146i	−0.801913	−	0.462985i
$507$		0			0
$508$	−8.03202	−	17.2247i	−0.356363	−	0.764223i
$509$	31.2055	−	11.3579i	1.38316	−	0.503430i	0.460026	−	0.887905i	$-0.347840\pi$
$509$	31.2055	−	11.3579i	1.38316	−	0.503430i	0.923135	+	0.384476i	$0.125618\pi$
$510$		0			0
$511$	−4.76479	−	27.0225i	−0.210782	−	1.19540i
$512$	15.7583	−	15.7583i	0.696424	−	0.696424i
$513$		0			0
$514$			43.0157i			1.89734i
$515$	−7.27706	−	5.08132i	−0.320665	−	0.223910i
$516$		0			0
$517$	3.41018	+	1.59019i	0.149979	+	0.0699366i
$518$	−22.1423	+	10.3251i	−0.972877	+	0.453660i
$519$		0			0
$520$	0.166385	−	0.289057i	0.00729646	−	0.0126760i
$521$	−26.1470	+	15.0960i	−1.14552	+	0.661367i	−0.947792	−	0.318890i	$-0.896690\pi$
$521$	−26.1470	+	15.0960i	−1.14552	+	0.661367i	−0.197729	+	0.980257i	$0.563357\pi$
$522$		0			0
$523$	6.98083	−	4.88803i	0.305250	−	0.213739i	−0.410907	−	0.911677i	$-0.634788\pi$
$523$	6.98083	−	4.88803i	0.305250	−	0.213739i	0.716158	+	0.697939i	$0.245899\pi$
$524$	−13.1525	+	7.59362i	−0.574571	+	0.331729i
$525$		0			0
$526$	−14.9770	+	17.8489i	−0.653028	+	0.778248i
$527$	5.74784	−	2.68026i	0.250380	−	0.116754i
$528$		0			0
$529$	−20.4310	−	24.3487i	−0.888304	−	1.05864i
$530$	−45.6768	+	8.11546i	−1.98407	+	0.352513i
$531$		0			0
$532$	22.4245	+	16.9098i	0.972225	+	0.733133i
$533$	−0.160340	+	0.160340i	−0.00694508	+	0.00694508i
$534$		0			0
$535$	−33.7403	−	2.90757i	−1.45872	−	0.125705i
$536$	14.3631	−	5.22775i	0.620392	−	0.225804i
$537$		0			0
$538$	32.3412	−	2.82949i	1.39433	−	0.121988i
$539$	17.9785	+	10.3799i	0.774389	+	0.447094i
$540$		0			0
$541$	3.84885	−	21.8279i	0.165475	−	0.938454i	−0.783099	−	0.621897i	$-0.786362\pi$
$541$	3.84885	−	21.8279i	0.165475	−	0.938454i	0.948574	−	0.316557i	$-0.102527\pi$
$542$	−17.7745	−	25.3846i	−0.763481	−	1.09036i
$543$		0			0
$544$	−17.1554	+	29.7139i	−0.735530	+	1.27397i
$545$	−12.7556	+	15.2419i	−0.546392	+	0.652891i
$546$		0			0
$547$	−13.3830	+	28.6999i	−0.572216	+	1.22712i	0.380928	+	0.924605i	$0.375604\pi$
$547$	−13.3830	+	28.6999i	−0.572216	+	1.22712i	−0.953144	+	0.302516i	$0.902173\pi$
$548$	2.58021	−	29.4920i	0.110221	−	1.25983i
$549$		0			0
$550$	9.92341	−	9.97530i	0.423136	−	0.425348i
$551$	1.20758	+	8.61324i	0.0514446	+	0.366936i
$552$		0			0
$553$	−15.0885	+	21.5487i	−0.641630	+	0.916342i
$554$	−42.6631	+	35.7986i	−1.81258	+	1.52094i
$555$		0			0
$556$	−8.96338	−	3.26240i	−0.380132	−	0.138357i
$557$	0.0223538	+	0.255505i	0.000947162	+	0.0108261i	0.996654	−	0.0817414i	$-0.0260482\pi$
$557$	0.0223538	+	0.255505i	0.000947162	+	0.0108261i	−0.995706	+	0.0925675i	$0.970493\pi$
$558$		0			0
$559$	0.0613234	+	0.106215i	0.00259370	+	0.00449243i
$560$	−28.1663	−	40.1143i	−1.19025	−	1.69514i
$561$		0			0
$562$	13.4237	−	50.0978i	0.566243	−	2.11325i
$563$	5.15121	−	1.38026i	0.217097	−	0.0581711i	−0.148631	−	0.988893i	$-0.547487\pi$
$563$	5.15121	−	1.38026i	0.217097	−	0.0581711i	0.365728	+	0.930722i	$0.380820\pi$
$564$		0			0
$565$	−8.68648	+	4.06437i	−0.365443	+	0.170989i
$566$	12.3550	+	33.9452i	0.519321	+	1.42682i
$567$		0			0
$568$	−4.61612	−	3.23224i	−0.193688	−	0.135622i
$569$	−20.8877			−0.875659			−0.437830	−	0.899058i	$-0.644253\pi$
$569$	−20.8877			−0.875659			−0.437830	+	0.899058i	$0.644253\pi$
$570$		0			0
$571$	−14.0563			−0.588237			−0.294118	−	0.955769i	$-0.595026\pi$
$571$	−14.0563			−0.588237			−0.294118	+	0.955769i	$0.595026\pi$
$572$	0.245236	+	0.171716i	0.0102538	+	0.00717982i
$573$		0			0
$574$	4.69716	+	12.9053i	0.196056	+	0.538659i
$575$	33.5001	−	15.7279i	1.39705	−	0.655897i
$576$		0			0
$577$	26.6223	−	7.13342i	1.10830	−	0.296968i	0.342160	−	0.939642i	$-0.388841\pi$
$577$	26.6223	−	7.13342i	1.10830	−	0.296968i	0.766140	+	0.642673i	$0.222175\pi$
$578$	4.15682	−	15.5135i	0.172901	−	0.645275i
$579$		0			0
$580$	−1.09071	+	6.23324i	−0.0452893	+	0.258821i
$581$	−1.07743	−	1.86616i	−0.0446992	−	0.0774212i
$582$		0			0
$583$	1.48864	+	17.0152i	0.0616531	+	0.704698i
$584$	6.10427	+	2.22177i	0.252597	+	0.0919376i
$585$		0			0
$586$	7.93484	−	6.65812i	0.327785	−	0.275045i
$587$	−9.44733	+	13.4922i	−0.389933	+	0.556882i	−0.965343	−	0.260983i	$-0.915953\pi$
$587$	−9.44733	+	13.4922i	−0.389933	+	0.556882i	0.575410	+	0.817865i	$0.304842\pi$
$588$		0			0
$589$	5.33487	+	1.13583i	0.219820	+	0.0468009i
$590$	−31.4932	−	31.4112i	−1.29656	−	1.29318i
$591$		0			0
$592$	1.22319	−	13.9812i	0.0502730	−	0.574623i
$593$	−8.02791	+	17.2159i	−0.329667	+	0.706972i	−0.999364	−	0.0356619i	$-0.988646\pi$
$593$	−8.02791	+	17.2159i	−0.329667	+	0.706972i	0.669697	+	0.742634i	$0.266424\pi$
$594$		0			0
$595$	39.4834	+	33.0428i	1.61866	+	1.35462i
$596$	−6.13628	+	10.6283i	−0.251352	+	0.435354i
$597$		0			0
$598$	1.08855	+	1.55461i	0.0445140	+	0.0635726i
$599$	−6.72471	+	38.1377i	−0.274764	+	1.55826i	0.464946	+	0.885339i	$0.346074\pi$
$599$	−6.72471	+	38.1377i	−0.274764	+	1.55826i	−0.739710	+	0.672926i	$0.765037\pi$
$600$		0			0
$601$	24.2204	+	13.9836i	0.987970	+	0.570405i	0.904667	−	0.426120i	$-0.140120\pi$
$601$	24.2204	+	13.9836i	0.987970	+	0.570405i	0.0833031	+	0.996524i	$0.473453\pi$
$602$	7.39994	−	0.647411i	0.301599	−	0.0263865i
$603$		0			0
$604$	13.8909	−	5.05587i	0.565213	−	0.205721i
$605$	12.5000	+	14.8575i	0.508197	+	0.604044i
$606$		0			0
$607$	−31.1811	+	31.1811i	−1.26560	+	1.26560i	−0.317263	+	0.948338i	$0.602764\pi$
$607$	−31.1811	+	31.1811i	−1.26560	+	1.26560i	−0.948338	+	0.317263i	$0.897236\pi$
$608$	−27.1668	+	11.5209i	−1.10176	+	0.467235i
$609$		0			0
$610$	7.03178	−	10.0703i	0.284708	−	0.407736i
$611$	−0.220370	−	0.262627i	−0.00891522	−	0.0106247i
$612$		0			0
$613$	13.2254	−	6.16710i	0.534169	−	0.249087i	−0.136766	−	0.990603i	$-0.543671\pi$
$613$	13.2254	−	6.16710i	0.534169	−	0.249087i	0.670935	+	0.741516i	$0.265893\pi$
$614$	19.4126	−	23.1350i	0.783428	−	0.933653i
$615$		0			0
$616$	−6.44070	+	3.71854i	−0.259503	+	0.149824i
$617$	5.03505	−	3.52558i	0.202704	−	0.141935i	−0.467817	−	0.883825i	$-0.654960\pi$
$617$	5.03505	−	3.52558i	0.202704	−	0.141935i	0.670521	+	0.741891i	$0.266071\pi$
$618$		0			0
$619$	19.4464	−	11.2274i	0.781618	−	0.451268i	−0.0553852	−	0.998465i	$-0.517639\pi$
$619$	19.4464	−	11.2274i	0.781618	−	0.451268i	0.837003	+	0.547198i	$0.184305\pi$
$620$	3.43936	+	1.97974i	0.138128	+	0.0795082i
$621$		0			0
$622$	−2.98348	+	1.39122i	−0.119627	+	0.0557829i
$623$	7.69746	+	3.58938i	0.308392	+	0.143806i
$624$		0			0
$625$	4.46955	+	24.5972i	0.178782	+	0.983889i
$626$			8.12126i			0.324591i
$627$		0			0
$628$	16.3380	−	16.3380i	0.651956	−	0.651956i
$629$	2.55990	+	14.5179i	0.102070	+	0.578868i
$630$		0			0
$631$	12.9935	−	4.72926i	0.517264	−	0.188269i	−0.0701787	−	0.997534i	$-0.522357\pi$
$631$	12.9935	−	4.72926i	0.517264	−	0.188269i	0.587443	+	0.809266i	$0.300135\pi$
$632$	−2.63196	−	5.64425i	−0.104694	−	0.224516i
$633$		0			0
$634$	14.7000	+	8.48702i	0.583810	+	0.337063i
$635$	7.71752	−	28.9531i	0.306260	−	1.14897i
$636$		0			0
$637$	−1.08492	−	1.54943i	−0.0429861	−	0.0613905i
$638$	5.42377	+	1.45330i	0.214729	+	0.0575365i
$639$		0			0
$640$	18.3535	−	1.62984i	0.725485	−	0.0644250i
$641$	−10.3038	+	28.3093i	−0.406974	+	1.11815i	0.551799	+	0.833977i	$0.313942\pi$
$641$	−10.3038	+	28.3093i	−0.406974	+	1.11815i	−0.958773	+	0.284174i	$0.908281\pi$
$642$		0			0
$643$	−2.23293	+	25.5226i	−0.0880584	+	1.00651i	0.815702	+	0.578473i	$0.196351\pi$
$643$	−2.23293	+	25.5226i	−0.0880584	+	1.00651i	−0.903760	+	0.428039i	$0.859205\pi$
$644$	46.9665	−	8.28147i	1.85074	−	0.326336i
$645$		0			0
$646$	32.1945	−	25.1358i	1.26667	−	0.988953i
$647$	5.87443	+	5.87443i	0.230948	+	0.230948i	0.813088	−	0.582141i	$-0.197785\pi$
$647$	5.87443	+	5.87443i	0.230948	+	0.230948i	−0.582141	+	0.813088i	$0.697785\pi$
$648$		0			0
$649$	−12.5450	+	10.5265i	−0.492433	+	0.413200i
$650$	−1.20356	+	0.441617i	−0.0472074	+	0.0173216i
$651$		0			0
$652$	−0.734220	−	8.39218i	−0.0287543	−	0.328663i
$653$	−1.41293	−	5.27313i	−0.0552922	−	0.206353i	0.932753	−	0.360515i	$-0.117399\pi$
$653$	−1.41293	−	5.27313i	−0.0552922	−	0.206353i	−0.988046	+	0.154162i	$0.950732\pi$
$654$		0			0
$655$	−23.5860	−	4.12714i	−0.921580	−	0.161261i
$656$	−7.76940	−	1.36995i	−0.303344	−	0.0534878i
$657$		0			0
$658$	−20.0566	+	5.37414i	−0.781886	+	0.209506i
$659$	−22.7331	−	19.0754i	−0.885557	−	0.743071i	0.0817569	−	0.996652i	$-0.473947\pi$
$659$	−22.7331	−	19.0754i	−0.885557	−	0.743071i	−0.967314	+	0.253582i	$0.918391\pi$
$660$		0			0
$661$	8.70685	+	23.9219i	0.338657	+	0.930454i	0.985776	+	0.168064i	$0.0537516\pi$
$661$	8.70685	+	23.9219i	0.338657	+	0.930454i	−0.647119	+	0.762389i	$0.724026\pi$
$662$	20.9669	+	1.83436i	0.814900	+	0.0712945i
$663$		0			0
$664$	0.510143			0.0197974
$665$	10.0027	+	43.1354i	0.387886	+	1.67272i
$666$		0			0
$667$	12.0980	+	8.47108i	0.468435	+	0.328001i
$668$	−21.1005	−	1.84605i	−0.816402	−	0.0714259i
$669$		0			0
$670$	−55.2362	−	20.0228i	−2.13396	−	0.773548i
$671$	−3.46407	−	2.90670i	−0.133729	−	0.112212i
$672$		0			0
$673$	10.0188	−	37.3907i	0.386197	−	1.44131i	−0.450075	−	0.892991i	$-0.648603\pi$
$673$	10.0188	−	37.3907i	0.386197	−	1.44131i	0.836272	−	0.548315i	$-0.184731\pi$
$674$	28.4049	+	5.00855i	1.09412	+	0.192922i
$675$		0			0
$676$	9.20516	+	15.9438i	0.354045	+	0.613224i
$677$	3.50187	+	13.0692i	0.134588	+	0.502289i	0.999999	+	0.00122697i	$0.000390556\pi$
$677$	3.50187	+	13.0692i	0.134588	+	0.502289i	−0.865411	+	0.501062i	$0.832943\pi$
$678$		0			0
$679$	5.08195	+	1.84968i	0.195027	+	0.0709842i
$680$	−11.4483	+	4.18374i	−0.439021	+	0.160439i
$681$		0			0
$682$	2.01979	−	2.88456i	0.0773418	−	0.110456i
$683$	−8.52271	−	8.52271i	−0.326112	−	0.326112i	0.524994	−	0.851106i	$-0.324068\pi$
$683$	−8.52271	−	8.52271i	−0.326112	−	0.326112i	−0.851106	+	0.524994i	$0.824068\pi$
$684$		0			0
$685$	32.9611	−	33.0471i	1.25938	−	1.26267i
$686$	−54.9172	+	9.68339i	−2.09675	+	0.369714i
$687$		0			0
$688$	−1.80337	+	3.86734i	−0.0687528	+	0.147441i
$689$	0.532265	−	1.46239i	0.0202777	−	0.0557125i
$690$		0			0
$691$	−26.0866	+	45.1834i	−0.992383	+	1.71886i	−0.389504	+	0.921025i	$0.627354\pi$
$691$	−26.0866	+	45.1834i	−0.992383	+	1.71886i	−0.602878	+	0.797833i	$0.705980\pi$
$692$	18.8316	+	5.04591i	0.715869	+	0.191817i
$693$		0			0
$694$	4.51095	−	25.5829i	0.171233	−	0.971113i
$695$	−7.53632	−	13.0141i	−0.285869	−	0.493652i
$696$		0			0
$697$	8.25533	−	0.722248i	0.312693	−	0.0273571i
$698$	−18.5916	−	39.8698i	−0.703703	−	1.50910i
$699$		0			0
$700$	−2.72414	+	32.1010i	−0.102963	+	1.21330i
$701$	4.07872	+	23.1316i	0.154051	+	0.873668i	0.959648	+	0.281204i	$0.0907337\pi$
$701$	4.07872	+	23.1316i	0.154051	+	0.873668i	−0.805597	+	0.592464i	$0.798155\pi$
$702$		0			0
$703$	−5.75979	+	11.2949i	−0.217234	+	0.425995i
$704$			4.36270i			0.164425i
$705$		0			0
$706$	15.2450	+	18.1683i	0.573755	+	0.683774i
$707$	−3.16600	−	1.47633i	−0.119070	−	0.0555232i
$708$		0			0
$709$	−8.49230	+	10.1207i	−0.318935	+	0.380092i	−0.901564	−	0.432647i	$-0.857580\pi$
$709$	−8.49230	+	10.1207i	−0.318935	+	0.380092i	0.582629	+	0.812739i	$0.302024\pi$
$710$	5.63360	+	20.9158i	0.211425	+	0.784954i
$711$		0			0
$712$	−1.64706	+	1.15329i	−0.0617264	+	0.0432213i
$713$	7.58698	−	5.31246i	0.284135	−	0.198953i
$714$		0			0
$715$	0.122757	+	0.455759i	0.00459087	+	0.0170444i
$716$	−3.65696	+	4.35819i	−0.136667	+	0.162873i
$717$		0			0
$718$	−2.76304	−	1.28843i	−0.103116	−	0.0480837i
$719$	−30.9997	−	36.9440i	−1.15609	−	1.37778i	−0.913092	−	0.407753i	$-0.866313\pi$
$719$	−30.9997	−	36.9440i	−1.15609	−	1.37778i	−0.243001	−	0.970026i	$-0.578132\pi$
$720$		0			0
$721$		−	18.0325i		−	0.671565i
$722$	35.1234	−	0.589612i	1.30716	−	0.0219431i
$723$		0			0
$724$	−5.56159	−	31.5413i	−0.206695	−	1.17222i
$725$	−7.62584	+	6.43280i	−0.283217	+	0.238908i
$726$		0			0
$727$	−2.41835	−	5.18618i	−0.0896918	−	0.192345i	0.856345	−	0.516404i	$-0.172730\pi$
$727$	−2.41835	−	5.18618i	−0.0896918	−	0.192345i	−0.946037	+	0.324060i	$0.894952\pi$
$728$	0.675041	−	0.0590585i	0.0250187	−	0.00218885i
$729$		0			0
$730$	−12.5131	−	21.6083i	−0.463132	−	0.799758i
$731$	0.778324	−	4.41410i	0.0287874	−	0.163261i
$732$		0			0
$733$	14.5096	+	3.88782i	0.535923	+	0.143600i	0.516622	−	0.856214i	$-0.327189\pi$
$733$	14.5096	+	3.88782i	0.535923	+	0.143600i	0.0193008	+	0.999814i	$0.493856\pi$
$734$	−16.4013	+	28.4079i	−0.605384	+	1.04856i
$735$		0			0
$736$	−17.1379	+	47.0859i	−0.631710	+	1.73561i
$737$	−9.14175	+	19.6045i	−0.336741	+	0.722142i
$738$		0			0
$739$	−37.0848	+	6.53906i	−1.36419	+	0.240543i	−0.807347	−	0.590077i	$-0.799098\pi$
$739$	−37.0848	+	6.53906i	−1.36419	+	0.240543i	−0.556840	+	0.830620i	$0.687986\pi$
$740$	−6.51422	+	6.53123i	−0.239468	+	0.240093i
$741$		0			0
$742$	−66.6483	−	66.6483i	−2.44674	−	2.44674i
$743$	−3.84433	+	5.49028i	−0.141035	+	0.201419i	−0.883455	−	0.468516i	$-0.844789\pi$
$743$	−3.84433	+	5.49028i	−0.141035	+	0.201419i	0.742420	+	0.669934i	$0.233678\pi$
$744$		0			0
$745$	−18.1735	+	6.64145i	−0.665825	+	0.243324i
$746$	−22.6192	−	8.23272i	−0.828148	−	0.301421i
$747$		0			0
$748$	−2.83172	−	10.5681i	−0.103538	−	0.386409i
$749$	−34.4022	−	59.5863i	−1.25703	−	2.17724i
$750$		0			0
$751$	16.8825	+	2.97683i	0.616050	+	0.108626i	0.472960	−	0.881084i	$-0.343185\pi$
$751$	16.8825	+	2.97683i	0.616050	+	0.108626i	0.143089	+	0.989710i	$0.454296\pi$
$752$	3.08718	−	11.5215i	0.112578	−	0.420146i
$753$		0			0
$754$	−0.391918	−	0.328858i	−0.0142728	−	0.0119763i
$755$	21.9109	+	7.94257i	0.797419	+	0.289060i
$756$		0			0
$757$	6.62372	+	0.579501i	0.240743	+	0.0210623i	0.206889	−	0.978364i	$-0.433666\pi$
$757$	6.62372	+	0.579501i	0.240743	+	0.0210623i	0.0338545	+	0.999427i	$0.489222\pi$
$758$	29.2023	+	20.4477i	1.06067	+	0.742692i
$759$		0			0
$760$	−10.0278	−	3.05518i	−0.363747	−	0.110823i
$761$	46.7690			1.69538			0.847688	−	0.530495i	$-0.177994\pi$
$761$	46.7690			1.69538			0.847688	+	0.530495i	$0.177994\pi$
$762$		0			0
$763$	−40.2268	−	3.51938i	−1.45631	−	0.127410i
$764$	−6.15744	−	16.9174i	−0.222768	−	0.612051i
$765$		0			0
$766$	−21.2464	−	17.8278i	−0.767664	−	0.644146i
$767$	1.44126	−	0.386185i	0.0520410	−	0.0139443i
$768$		0			0
$769$	48.7943	+	8.60376i	1.75957	+	0.310259i	0.957813	−	0.287392i	$-0.0927883\pi$
$769$	48.7943	+	8.60376i	1.75957	+	0.310259i	0.801756	+	0.597652i	$0.203899\pi$
$770$	28.1593	+	4.92740i	1.01479	+	0.177571i
$771$		0			0
$772$	5.47970	+	20.4505i	0.197219	+	0.736030i
$773$	−1.24000	−	14.1733i	−0.0445998	−	0.509778i	−0.985334	−	0.170634i	$-0.945418\pi$
$773$	−1.24000	−	14.1733i	−0.0445998	−	0.509778i	0.940735	−	0.339144i	$-0.110137\pi$
$774$		0			0
$775$	2.15523	+	5.87376i	0.0774183	+	0.210992i
$776$	−0.980784	+	0.822975i	−0.0352081	+	0.0295431i
$777$		0			0
$778$	−17.7756	−	17.7756i	−0.637285	−	0.637285i
$779$	6.04284	+	3.77880i	0.216507	+	0.135389i
$780$		0			0
$781$	7.85385	−	1.38484i	0.281033	−	0.0495536i
$782$	6.04485	−	69.0930i	0.216163	−	2.47076i
$783$		0			0
$784$	22.5081	−	61.8404i	0.803860	−	2.20859i
$785$	36.2853	−	3.22223i	1.29508	−	0.115006i
$786$		0			0
$787$	−20.5663	−	5.51072i	−0.733110	−	0.196436i	−0.127096	−	0.991890i	$-0.540566\pi$
$787$	−20.5663	−	5.51072i	−0.733110	−	0.196436i	−0.606014	+	0.795454i	$0.707232\pi$
$788$	−5.14045	−	7.34132i	−0.183121	−	0.261524i
$789$		0			0
$790$	−6.16562	+	23.1310i	−0.219363	+	0.822964i
$791$	−16.8742	−	9.74233i	−0.599978	−	0.346397i
$792$		0			0
$793$	0.174126	+	0.373415i	0.00618341	+	0.0132604i
$794$	8.14280	−	2.96374i	0.288977	−	0.105179i
$795$		0			0
$796$	3.13360	+	17.7715i	0.111068	+	0.629895i
$797$	−2.03401	+	2.03401i	−0.0720484	+	0.0720484i	−0.742213	−	0.670164i	$-0.766224\pi$
$797$	−2.03401	+	2.03401i	−0.0720484	+	0.0720484i	0.670164	+	0.742213i	$0.266224\pi$
$798$		0			0
$799$			12.5291i			0.443247i
$800$	−27.7779	−	19.3426i	−0.982098	−	0.683863i
$801$		0			0
$802$	50.2809	+	23.4464i	1.77548	+	0.827920i
$803$	−8.33186	+	3.88521i	−0.294025	+	0.137106i
$804$		0			0
$805$	65.1656	+	37.5101i	2.29678	+	1.32206i
$806$	−0.277862	+	0.160424i	−0.00978728	+	0.00565069i
$807$		0			0
$808$	0.677446	−	0.474353i	0.0238325	−	0.0166877i
$809$	8.61084	−	4.97147i	0.302741	−	0.174788i	−0.340932	−	0.940088i	$-0.610743\pi$
$809$	8.61084	−	4.97147i	0.302741	−	0.174788i	0.643674	+	0.765300i	$0.277409\pi$
$810$		0			0
$811$	4.70296	−	5.60477i	0.165143	−	0.196810i	−0.677126	−	0.735867i	$-0.736775\pi$
$811$	4.70296	−	5.60477i	0.165143	−	0.196810i	0.842269	+	0.539057i	$0.181219\pi$
$812$	−11.6520	+	5.43339i	−0.408903	+	0.190675i
$813$		0			0
$814$	5.26147	+	6.27038i	0.184414	+	0.219777i
$815$	7.60389	−	10.8897i	0.266353	−	0.381449i
$816$		0			0
$817$	2.82017	−	2.62809i	0.0986651	−	0.0919451i
$818$	−44.7585	+	44.7585i	−1.56495	+	1.56495i
$819$		0			0
$820$	3.33828	+	3.96789i	0.116578	+	0.138565i
$821$	42.9758	−	15.6419i	1.49986	−	0.545906i	0.543839	−	0.839190i	$-0.316970\pi$
$821$	42.9758	−	15.6419i	1.49986	−	0.545906i	0.956025	+	0.293284i	$0.0947481\pi$
$822$		0			0
$823$	50.0561	−	4.37934i	1.74485	−	0.152654i	0.830348	−	0.557245i	$-0.188142\pi$
$823$	50.0561	−	4.37934i	1.74485	−	0.152654i	0.914498	+	0.404591i	$0.132586\pi$
$824$	3.69709	+	2.13452i	0.128794	+	0.0743595i
$825$		0			0
$826$	15.6927	−	88.9976i	0.546018	−	3.09662i
$827$	28.0454	+	40.0530i	0.975234	+	1.39278i	0.918954	+	0.394364i	$0.129035\pi$
$827$	28.0454	+	40.0530i	0.975234	+	1.39278i	0.0562800	+	0.998415i	$0.482076\pi$
$828$		0			0
$829$	17.1185	−	29.6501i	0.594549	−	1.02979i	−0.399061	−	0.916924i	$-0.630664\pi$
$829$	17.1185	−	29.6501i	0.594549	−	1.02979i	0.993610	−	0.112865i	$-0.0360028\pi$
$830$	−1.50380	−	1.25850i	−0.0521976	−	0.0436831i
$831$		0			0
$832$	0.167991	−	0.360259i	0.00582405	−	0.0124897i
$833$	−6.02472	+	68.8628i	−0.208744	+	2.38596i
$834$		0			0
$835$	−23.6441	−	23.5825i	−0.818237	−	0.816107i
$836$	3.52785	−	8.72334i	0.122013	−	0.301703i
$837$		0			0
$838$	7.43893	−	10.6239i	0.256974	−	0.366996i
$839$	20.4137	−	17.1291i	0.704758	−	0.591362i	−0.218365	−	0.975867i	$-0.570072\pi$
$839$	20.4137	−	17.1291i	0.704758	−	0.591362i	0.923123	+	0.384505i	$0.125628\pi$
$840$		0			0
$841$	23.5098	+	8.55687i	0.810683	+	0.295065i
$842$	−0.556510	−	6.36093i	−0.0191786	−	0.219212i
$843$		0			0
$844$	12.1721	+	21.0827i	0.418981	+	0.725696i
$845$	−5.00302	+	28.5915i	−0.172109	+	0.983576i
$846$		0			0
$847$	−10.2100	+	38.1042i	−0.350819	+	1.30927i
$848$	52.2998	−	14.0137i	1.79598	−	0.481232i
$849$		0			0
$850$	44.0682	+	15.9095i	1.51153	+	0.545691i
$851$	7.36344	+	20.2309i	0.252415	+	0.693506i
$852$		0			0
$853$	12.6145	+	8.83275i	0.431911	+	0.302427i	0.769241	−	0.638959i	$-0.220635\pi$
$853$	12.6145	+	8.83275i	0.431911	+	0.302427i	−0.337329	+	0.941387i	$0.609524\pi$
$854$	24.9542			0.853916
$855$		0			0
$856$	16.2888			0.556741
$857$	28.7532	+	20.1332i	0.982191	+	0.687737i	0.950164	−	0.311750i	$-0.100915\pi$
$857$	28.7532	+	20.1332i	0.982191	+	0.687737i	0.0320266	+	0.999487i	$0.489804\pi$
$858$		0			0
$859$	13.2030	+	36.2749i	0.450480	+	1.23768i	0.932387	+	0.361462i	$0.117722\pi$
$859$	13.2030	+	36.2749i	0.450480	+	1.23768i	−0.481907	+	0.876223i	$0.660056\pi$
$860$	2.54034	−	1.18862i	0.0866250	−	0.0405315i
$861$		0			0
$862$	18.7128	−	5.01409i	0.637362	−	0.170781i
$863$	8.56232	−	31.9550i	0.291465	−	1.08776i	−0.652520	−	0.757772i	$-0.726288\pi$
$863$	8.56232	−	31.9550i	0.291465	−	1.08776i	0.943985	−	0.329989i	$-0.107045\pi$
$864$		0			0
$865$	17.6631	+	25.1556i	0.600562	+	0.855316i
$866$	22.0247	+	38.1479i	0.748429	+	1.29632i
$867$		0			0
$868$	0.702710	+	8.03201i	0.0238515	+	0.272624i
$869$	8.28198	+	3.01439i	0.280947	+	0.102256i
$870$		0			0
$871$	1.50980	−	1.26687i	0.0511575	−	0.0429263i
$872$	5.48323	−	7.83086i	0.185686	−	0.265187i
$873$		0			0
$874$	39.9285	−	44.3153i	1.35060	−	1.49899i
$875$	−35.7750	+	36.0560i	−1.20942	+	1.21891i
$876$		0			0
$877$	3.04056	−	34.7538i	0.102672	−	1.17355i	−0.753709	−	0.657208i	$-0.771737\pi$
$877$	3.04056	−	34.7538i	0.102672	−	1.17355i	0.856382	−	0.516343i	$-0.172707\pi$
$878$	−0.451238	+	0.967683i	−0.0152285	+	0.0326577i
$879$		0			0
$880$	−10.5394	+	12.5937i	−0.355283	+	0.424533i
$881$	4.01849	−	6.96024i	0.135387	−	0.234496i	−0.790359	−	0.612645i	$-0.790106\pi$
$881$	4.01849	−	6.96024i	0.135387	−	0.234496i	0.925745	+	0.378148i	$0.123439\pi$
$882$		0			0
$883$	−3.73014	−	5.32719i	−0.125529	−	0.179274i	0.751468	−	0.659769i	$-0.229346\pi$
$883$	−3.73014	−	5.32719i	−0.125529	−	0.179274i	−0.876997	+	0.480495i	$0.840457\pi$
$884$	−0.173104	+	0.981724i	−0.00582213	+	0.0330189i
$885$		0			0
$886$	13.6057	+	7.85523i	0.457091	+	0.263902i
$887$	−47.7217	+	4.17511i	−1.60234	+	0.140186i	−0.852967	−	0.521965i	$-0.825199\pi$
$887$	−47.7217	+	4.17511i	−1.60234	+	0.140186i	−0.749370	+	0.662151i	$0.769644\pi$
$888$		0			0
$889$	57.2066	−	20.8215i	1.91865	−	0.698331i
$890$	7.70031	+	0.663575i	0.258115	+	0.0222431i
$891$		0			0
$892$	18.8345	−	18.8345i	0.630625	−	0.630625i
$893$	−6.48778	+	8.60359i	−0.217105	+	0.287908i
$894$		0			0
$895$	−8.83136	+	1.56908i	−0.295200	+	0.0524487i
$896$	24.0631	+	28.6773i	0.803892	+	0.958041i
$897$		0			0
$898$	−14.3312	+	6.68276i	−0.478239	+	0.223007i
$899$	−1.60494	+	1.91269i	−0.0535276	+	0.0637918i
$900$		0			0
$901$	−49.2540	+	28.4368i	−1.64089	+	0.947367i
$902$	3.76913	−	2.63917i	0.125498	−	0.0878747i
$903$		0			0
$904$	3.99483	−	2.30641i	0.132866	−	0.0767102i
$905$	25.1907	−	43.7632i	0.837367	−	1.45474i
$906$		0			0
$907$	−24.9537	+	11.6361i	−0.828574	+	0.386370i	−0.790167	−	0.612892i	$-0.790006\pi$
$907$	−24.9537	+	11.6361i	−0.828574	+	0.386370i	−0.0384071	+	0.999262i	$0.512228\pi$
$908$	−0.118774	−	0.0553852i	−0.00394165	−	0.00183802i
$909$		0			0
$910$	−2.13558	−	1.49120i	−0.0707938	−	0.0494329i
$911$		−	50.4735i		−	1.67226i	−0.548529	−	0.836132i	$-0.684812\pi$
$911$		−	50.4735i		−	1.67226i	0.548529	−	0.836132i	$-0.315188\pi$
$912$		0			0
$913$	−0.510499	+	0.510499i	−0.0168951	+	0.0168951i
$914$	0.455586	+	2.58376i	0.0150694	+	0.0854631i
$915$		0			0
$916$	13.7217	−	4.99429i	0.453378	−	0.165016i
$917$	−20.5594	−	44.0898i	−0.678932	−	1.45598i
$918$		0			0
$919$	22.3948	+	12.9296i	0.738736	+	0.426510i	0.821610	−	0.570050i	$-0.193076\pi$
$919$	22.3948	+	12.9296i	0.738736	+	0.426510i	−0.0828733	+	0.996560i	$0.526410\pi$
$920$	−15.4042	+	8.92041i	−0.507861	+	0.294097i
$921$		0			0
$922$	0.799352	+	1.14159i	0.0263252	+	0.0375964i
$923$	−0.701873	−	0.188066i	−0.0231024	−	0.00619027i
$924$		0			0
$925$	−14.4848	+	1.30532i	−0.476257	+	0.0429188i
$926$	13.8226	−	37.9773i	0.454239	−	1.24801i
$927$		0			0
$928$	1.17730	−	13.4566i	0.0386467	−	0.441734i
$929$	49.5361	−	8.73454i	1.62523	−	0.286571i	0.714516	−	0.699619i	$-0.246647\pi$
$929$	49.5361	−	8.73454i	1.62523	−	0.286571i	0.910709	+	0.413048i	$0.135536\pi$
$930$		0			0
$931$	−39.7955	+	44.1677i	−1.30424	+	1.44754i
$932$	−21.7387	−	21.7387i	−0.712074	−	0.712074i
$933$		0			0
$934$	4.44157	−	3.72692i	0.145333	−	0.121949i
$935$	7.26959	−	15.6429i	0.237741	−	0.511577i
$936$		0			0
$937$	2.94620	+	33.6752i	0.0962482	+	1.10012i	0.878688	+	0.477396i	$0.158419\pi$
$937$	2.94620	+	33.6752i	0.0962482	+	1.10012i	−0.782440	+	0.622726i	$0.786025\pi$
$938$	−30.8950	−	115.302i	−1.00876	−	3.76474i
$939$		0			0
$940$	−6.41619	+	4.50515i	−0.209273	+	0.146942i
$941$	20.3861	+	3.59461i	0.664567	+	0.117181i	0.495748	−	0.868466i	$-0.334894\pi$
$941$	20.3861	+	3.59461i	0.664567	+	0.117181i	0.168818	+	0.985647i	$0.446005\pi$
$942$		0			0
$943$	11.6899	−	3.13229i	0.380674	−	0.102001i
$944$	39.7680	+	33.3693i	1.29434	+	1.08608i
$945$		0			0
$946$	−0.851193	−	2.33863i	−0.0276747	−	0.0760355i
$947$	36.6021	+	3.20227i	1.18941	+	0.104060i	0.664625	−	0.747177i	$-0.268591\pi$
$947$	36.6021	+	3.20227i	1.18941	+	0.104060i	0.524782	+	0.851237i	$0.324147\pi$
$948$		0			0
$949$	0.837625			0.0271905
$950$	22.0230	+	33.7442i	0.714520	+	1.09481i
$951$		0			0
$952$	−20.2855	−	14.2040i	−0.657455	−	0.460355i
$953$	13.6473	+	1.19399i	0.442080	+	0.0386770i	0.306023	−	0.952024i	$-0.401001\pi$
$953$	13.6473	+	1.19399i	0.442080	+	0.0386770i	0.136057	+	0.990701i	$0.456557\pi$
$954$		0			0
$955$	9.67309	−	26.6848i	0.313014	−	0.863500i
$956$	−11.1516	−	9.35734i	−0.360670	−	0.302638i
$957$		0			0
$958$	−13.7129	+	51.1774i	−0.443045	+	1.65347i
$959$	93.3888	+	16.4670i	3.01568	+	0.531746i
$960$		0			0
$961$	−14.7171	−	25.4907i	−0.474744	−	0.822282i
$962$	−0.193028	−	0.720389i	−0.00622346	−	0.0232263i
$963$		0			0
$964$	−26.3832	−	9.60271i	−0.849746	−	0.309282i
$965$	−14.0675	+	30.2708i	−0.452848	+	0.974451i
$966$		0			0
$967$	−0.179322	+	0.256099i	−0.00576661	+	0.00823557i	−0.822025	−	0.569451i	$-0.807156\pi$
$967$	−0.179322	+	0.256099i	−0.00576661	+	0.00823557i	0.816258	+	0.577687i	$0.196045\pi$
$968$	−6.60371	−	6.60371i	−0.212251	−	0.212251i
$969$		0			0
$970$	4.92139	−	0.00641660i	0.158016	−	0.000206025i
$971$	38.3652	−	6.76482i	1.23120	−	0.217093i	0.480058	−	0.877237i	$-0.340616\pi$
$971$	38.3652	−	6.76482i	1.23120	−	0.217093i	0.751140	+	0.660143i	$0.229504\pi$
$972$		0			0
$973$	12.9127	−	27.6915i	0.413963	−	0.887748i
$974$	6.15835	−	16.9199i	0.197326	−	0.542149i
$975$		0			0
$976$	−7.16748	+	12.4144i	−0.229425	+	0.397376i
$977$	−16.1368	−	4.32385i	−0.516262	−	0.138332i	−0.00872521	−	0.999962i	$-0.502777\pi$
$977$	−16.1368	−	4.32385i	−0.516262	−	0.138332i	−0.507537	+	0.861630i	$0.669444\pi$
$978$		0			0
$979$	0.494122	−	2.80231i	0.0157922	−	0.0895621i
$980$	−37.4313	+	21.6761i	−1.19570	+	0.692417i
$981$		0			0
$982$	−15.9567	+	1.39603i	−0.509199	+	0.0445491i
$983$	9.25970	+	19.8575i	0.295338	+	0.633355i	0.996851	−	0.0793022i	$-0.0252692\pi$
$983$	9.25970	+	19.8575i	0.295338	+	0.633355i	−0.701512	+	0.712657i	$0.747491\pi$
$984$		0			0
$985$	1.21313	−	14.0775i	0.0386536	−	0.448548i
$986$	3.24673	+	18.4131i	0.103397	+	0.586393i
$987$		0			0
$988$	−0.627223	+	0.584503i	−0.0199546	+	0.0185955i
$989$		−	6.54585i		−	0.208146i
$990$		0			0
$991$	20.3243	+	24.2215i	0.645622	+	0.769422i	0.985247	−	0.171139i	$-0.0547446\pi$
$991$	20.3243	+	24.2215i	0.645622	+	0.769422i	−0.339625	+	0.940561i	$0.610300\pi$
$992$	−7.67757	−	3.58011i	−0.243763	−	0.113669i
$993$		0			0
$994$	−28.2885	+	33.7129i	−0.897256	+	1.06931i
$995$	−14.1934	+	24.6578i	−0.449959	+	0.781705i
$996$		0			0
$997$	28.7750	−	20.1485i	0.911314	−	0.638109i	−0.0209919	−	0.999780i	$-0.506682\pi$
$997$	28.7750	−	20.1485i	0.911314	−	0.638109i	0.932306	+	0.361671i	$0.117794\pi$
$998$	−2.26683	+	1.58725i	−0.0717553	+	0.0502436i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.352.7		96
3.2	odd	2		95.2.r.a.67.2	yes	96
5.3	odd	4	inner	855.2.dl.a.523.7		96
15.2	even	4		475.2.bb.b.143.7		96
15.8	even	4		95.2.r.a.48.2	yes	96
15.14	odd	2		475.2.bb.b.257.7		96
19.2	odd	18	inner	855.2.dl.a.667.7		96
57.2	even	18		95.2.r.a.2.2	✓	96
95.78	even	36	inner	855.2.dl.a.838.7		96
285.2	odd	36		475.2.bb.b.268.7		96
285.59	even	18		475.2.bb.b.382.7		96
285.173	odd	36		95.2.r.a.78.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.2	✓	96	57.2	even	18
95.2.r.a.48.2	yes	96	15.8	even	4
95.2.r.a.67.2	yes	96	3.2	odd	2
95.2.r.a.78.2	yes	96	285.173	odd	36
475.2.bb.b.143.7		96	15.2	even	4
475.2.bb.b.257.7		96	15.14	odd	2
475.2.bb.b.268.7		96	285.2	odd	36
475.2.bb.b.382.7		96	285.59	even	18
855.2.dl.a.352.7		96	1.1	even	1	trivial
855.2.dl.a.523.7		96	5.3	odd	4	inner
855.2.dl.a.667.7		96	19.2	odd	18	inner
855.2.dl.a.838.7		96	95.78	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51450 + 1.06046i) q^{2} +(0.485079 + 1.33274i) q^{4} +(-0.762040 + 2.10221i) q^{5} +(-4.38823 + 1.17582i) q^{7} +(0.278366 - 1.03888i) q^{8} +(-3.38342 + 2.37568i) q^{10} +(0.761040 + 1.31816i) q^{11} +(-0.0120870 - 0.138155i) q^{13} +(-7.89287 - 2.87277i) q^{14} +(3.69620 - 3.10148i) q^{16} +(-2.90701 + 4.15164i) q^{17} +(-4.14601 + 1.34559i) q^{19} +(-3.17136 + 0.00413488i) q^{20} +(-0.245266 + 2.80340i) q^{22} +(-3.12809 + 6.70821i) q^{23} +(-3.83859 - 3.20394i) q^{25} +(0.128202 - 0.222052i) q^{26} +(-3.69571 - 5.27802i) q^{28} +(0.346487 - 1.96502i) q^{29} +(-1.08369 - 0.625668i) q^{31} +(6.74402 - 0.590025i) q^{32} +(-8.80531 + 3.20487i) q^{34} +(0.872178 - 10.1210i) q^{35} +(2.05676 - 2.05676i) q^{37} +(-7.70606 - 2.35879i) q^{38} +(1.97181 + 1.37685i) q^{40} +(-1.05100 - 1.25253i) q^{41} +(-0.801514 + 0.373752i) q^{43} +(-1.38761 + 1.65368i) q^{44} +(-11.8513 + 6.84234i) q^{46} +(2.02502 - 1.41793i) q^{47} +(11.8118 - 6.81954i) q^{49} +(-2.41588 - 8.92303i) q^{50} +(0.178262 - 0.0831248i) q^{52} +(10.1702 + 4.74246i) q^{53} +(-3.35100 + 0.595377i) q^{55} +4.88613i q^{56} +(2.60859 - 2.60859i) q^{58} +(1.86831 + 10.5957i) q^{59} +(-2.79178 + 1.01612i) q^{61} +(-0.977745 - 2.09678i) q^{62} +(2.48226 + 1.43314i) q^{64} +(0.299641 + 0.0798700i) q^{65} +(8.15144 + 11.6415i) q^{67} +(-6.94321 - 1.86043i) q^{68} +(12.0538 - 14.4033i) q^{70} +(1.79203 - 4.92356i) q^{71} +(-0.526410 + 6.01690i) q^{73} +(5.29607 - 0.933839i) q^{74} +(-3.80447 - 4.87285i) q^{76} +(-4.88954 - 4.88954i) q^{77} +(4.43572 - 3.72201i) q^{79} +(3.70331 + 10.1336i) q^{80} +(-0.263472 - 3.01150i) q^{82} +(0.122763 + 0.458159i) q^{83} +(-6.51237 - 9.27487i) q^{85} +(-1.61024 - 0.283929i) q^{86} +(1.58125 - 0.423695i) q^{88} +(-1.43212 - 1.20169i) q^{89} +(0.215486 + 0.592042i) q^{91} +(-10.4577 - 0.914930i) q^{92} +4.57054 q^{94} +(0.330711 - 9.74118i) q^{95} +(-0.975134 - 0.682796i) q^{97} +(25.1208 + 2.19778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more