LMFDB - Embedded newform 832.2.p.a.753.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(337,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("832.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.959512576.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 81 $ x^8 + 7*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 208)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			753.2
Root			$-0.819051 + 1.52616i$ of defining polynomial
Character	$\chi$	$=$	832.753
Dual form			832.2.p.a.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.15831 + 2.15831i) q^{3} +(0.707107 - 0.707107i) q^{5} -0.223888 q^{7} -6.31662i q^{9} +(1.41421 - 1.41421i) q^{11} +(1.34521 + 3.34521i) q^{13} +3.05231i q^{15} +3.00000 q^{17} +(4.46653 + 4.46653i) q^{19} +(0.483219 - 0.483219i) q^{21} -6.31662i q^{23} +4.00000i q^{25} +(7.15831 + 7.15831i) q^{27} +(0.316625 - 0.316625i) q^{29} -4.24264i q^{31} +6.10463i q^{33} +(-0.158312 + 0.158312i) q^{35} +(-6.58785 + 6.58785i) q^{37} +(-10.1234 - 4.31662i) q^{39} +(5.47494 + 5.47494i) q^{43} +(-4.46653 - 4.46653i) q^{45} +10.5712i q^{47} -6.94987 q^{49} +(-6.47494 + 6.47494i) q^{51} +(3.63325 + 3.63325i) q^{53} -2.00000i q^{55} -19.2803 q^{57} +(-7.74273 + 7.74273i) q^{59} +(4.00000 - 4.00000i) q^{61} +1.41421i q^{63} +(3.31662 + 1.41421i) q^{65} +(-4.69042 - 4.69042i) q^{67} +(13.6332 + 13.6332i) q^{69} +0.671663 q^{71} +3.79487 q^{73} +(-8.63325 - 8.63325i) q^{75} +(-0.316625 + 0.316625i) q^{77} +10.9499 q^{79} -11.9499 q^{81} +(11.9854 + 11.9854i) q^{83} +(2.12132 - 2.12132i) q^{85} +1.36675i q^{87} +14.0712 q^{89} +(-0.301175 - 0.748950i) q^{91} +(9.15694 + 9.15694i) q^{93} +6.31662 q^{95} +8.48528i q^{97} +(-8.93306 - 8.93306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{13} + 24 q^{17} + 44 q^{27} - 24 q^{29} + 12 q^{35} + 4 q^{43} + 24 q^{49} - 12 q^{51} - 24 q^{53} + 32 q^{61} + 56 q^{69} - 16 q^{75} + 24 q^{77} + 8 q^{79} - 16 q^{81} - 44 q^{91}+ \cdots + 24 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^13 + 24 * q^17 + 44 * q^27 - 24 * q^29 + 12 * q^35 + 4 * q^43 + 24 * q^49 - 12 * q^51 - 24 * q^53 + 32 * q^61 + 56 * q^69 - 16 * q^75 + 24 * q^77 + 8 * q^79 - 16 * q^81 - 44 * q^91 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.15831	+	2.15831i	−1.24610	+	1.24610i	−0.288675	+	0.957427i	$0.593215\pi$
$3$	−2.15831	+	2.15831i	−1.24610	+	1.24610i	−0.957427	+	0.288675i	$0.906785\pi$
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i	−0.531089	−	0.847316i	$-0.678217\pi$
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i	0.847316	+	0.531089i	$0.178217\pi$
$6$		0			0
$7$	−0.223888			−0.0846215			−0.0423108	−	0.999104i	$-0.513472\pi$
$7$	−0.223888			−0.0846215			−0.0423108	+	0.999104i	$0.513472\pi$
$8$		0			0
$9$		−	6.31662i		−	2.10554i
$10$		0			0
$11$	1.41421	−	1.41421i	0.426401	−	0.426401i	−0.460999	−	0.887401i	$-0.652509\pi$
$11$	1.41421	−	1.41421i	0.426401	−	0.426401i	0.887401	+	0.460999i	$0.152509\pi$
$12$		0			0
$13$	1.34521	+	3.34521i	0.373094	+	0.927794i
$13$	1.34521	+	3.34521i	0.373094	+	0.927794i
$14$		0			0
$15$			3.05231i			0.788104i
$16$		0			0
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	4.46653	+	4.46653i	1.02469	+	1.02469i	0.999687	+	0.0250045i	$0.00796001\pi$
$19$	4.46653	+	4.46653i	1.02469	+	1.02469i	0.0250045	+	0.999687i	$0.492040\pi$
$20$		0			0
$21$	0.483219	−	0.483219i	0.105447	−	0.105447i
$22$		0			0
$23$		−	6.31662i		−	1.31711i	−0.752534	−	0.658554i	$-0.771169\pi$
$23$		−	6.31662i		−	1.31711i	0.752534	−	0.658554i	$-0.228831\pi$
$24$		0			0
$25$			4.00000i			0.800000i
$26$		0			0
$27$	7.15831	+	7.15831i	1.37762	+	1.37762i
$28$		0			0
$29$	0.316625	−	0.316625i	0.0587957	−	0.0587957i	−0.677098	−	0.735893i	$-0.736762\pi$
$29$	0.316625	−	0.316625i	0.0587957	−	0.0587957i	0.735893	+	0.677098i	$0.236762\pi$
$30$		0			0
$31$		−	4.24264i		−	0.762001i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$		−	4.24264i		−	0.762001i	0.924575	−	0.381000i	$-0.124420\pi$
$32$		0			0
$33$			6.10463i			1.06268i
$34$		0			0
$35$	−0.158312	+	0.158312i	−0.0267597	+	0.0267597i
$36$		0			0
$37$	−6.58785	+	6.58785i	−1.08304	+	1.08304i	−0.0868108	+	0.996225i	$0.527668\pi$
$37$	−6.58785	+	6.58785i	−1.08304	+	1.08304i	−0.996225	+	0.0868108i	$0.972332\pi$
$38$		0			0
$39$	−10.1234	−	4.31662i	−1.62104	−	0.691213i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	5.47494	+	5.47494i	0.834920	+	0.834920i	0.988185	−	0.153265i	$-0.0489788\pi$
$43$	5.47494	+	5.47494i	0.834920	+	0.834920i	−0.153265	+	0.988185i	$0.548979\pi$
$44$		0			0
$45$	−4.46653	−	4.46653i	−0.665831	−	0.665831i
$46$		0			0
$47$			10.5712i			1.54196i	0.636858	+	0.770981i	$0.280234\pi$
$47$			10.5712i			1.54196i	−0.636858	+	0.770981i	$0.719766\pi$
$48$		0			0
$49$	−6.94987			−0.992839
$50$		0			0
$51$	−6.47494	+	6.47494i	−0.906673	+	0.906673i
$52$		0			0
$53$	3.63325	+	3.63325i	0.499065	+	0.499065i	0.911147	−	0.412082i	$-0.135198\pi$
$53$	3.63325	+	3.63325i	0.499065	+	0.499065i	−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$		−	2.00000i		−	0.269680i
$56$		0			0
$57$	−19.2803			−2.55374
$58$		0			0
$59$	−7.74273	+	7.74273i	−1.00802	+	1.00802i	−0.00805004	+	0.999968i	$0.502562\pi$
$59$	−7.74273	+	7.74273i	−1.00802	+	1.00802i	−0.999968	+	0.00805004i	$0.997438\pi$
$60$		0			0
$61$	4.00000	−	4.00000i	0.512148	−	0.512148i	−0.403036	−	0.915184i	$-0.632045\pi$
$61$	4.00000	−	4.00000i	0.512148	−	0.512148i	0.915184	+	0.403036i	$0.132045\pi$
$62$		0			0
$63$			1.41421i			0.178174i
$64$		0			0
$65$	3.31662	+	1.41421i	0.411377	+	0.175412i
$66$		0			0
$67$	−4.69042	−	4.69042i	−0.573025	−	0.573025i	0.359947	−	0.932973i	$-0.382795\pi$
$67$	−4.69042	−	4.69042i	−0.573025	−	0.573025i	−0.932973	+	0.359947i	$0.882795\pi$
$68$		0			0
$69$	13.6332	+	13.6332i	1.64125	+	1.64125i
$70$		0			0
$71$	0.671663			0.0797117			0.0398558	−	0.999205i	$-0.487310\pi$
$71$	0.671663			0.0797117			0.0398558	+	0.999205i	$0.487310\pi$
$72$		0			0
$73$	3.79487			0.444155			0.222078	−	0.975029i	$-0.428716\pi$
$73$	3.79487			0.444155			0.222078	+	0.975029i	$0.428716\pi$
$74$		0			0
$75$	−8.63325	−	8.63325i	−0.996882	−	0.996882i
$76$		0			0
$77$	−0.316625	+	0.316625i	−0.0360827	+	0.0360827i
$78$		0			0
$79$	10.9499			1.23196			0.615979	−	0.787763i	$-0.288761\pi$
$79$	10.9499			1.23196			0.615979	+	0.787763i	$0.288761\pi$
$80$		0			0
$81$	−11.9499			−1.32776
$82$		0			0
$83$	11.9854	+	11.9854i	1.31557	+	1.31557i	0.917247	+	0.398318i	$0.130406\pi$
$83$	11.9854	+	11.9854i	1.31557	+	1.31557i	0.398318	+	0.917247i	$0.369594\pi$
$84$		0			0
$85$	2.12132	−	2.12132i	0.230089	−	0.230089i
$86$		0			0
$87$			1.36675i			0.146531i
$88$		0			0
$89$	14.0712			1.49155			0.745775	−	0.666198i	$-0.232080\pi$
$89$	14.0712			1.49155			0.745775	+	0.666198i	$0.232080\pi$
$90$		0			0
$91$	−0.301175	−	0.748950i	−0.0315717	−	0.0785113i
$92$		0			0
$93$	9.15694	+	9.15694i	0.949531	+	0.949531i
$94$		0			0
$95$	6.31662			0.648072
$96$		0			0
$97$			8.48528i			0.861550i	0.902459	+	0.430775i	$0.141760\pi$
$97$			8.48528i			0.861550i	−0.902459	+	0.430775i	$0.858240\pi$
$98$		0			0
$99$	−8.93306	−	8.93306i	−0.897806	−	0.897806i
$100$		0			0
$101$	−6.31662	−	6.31662i	−0.628528	−	0.628528i	0.319170	−	0.947698i	$-0.396596\pi$
$101$	−6.31662	−	6.31662i	−0.628528	−	0.628528i	−0.947698	+	0.319170i	$0.896596\pi$
$102$		0			0
$103$		−	0.949874i		−	0.0935939i	−0.998904	−	0.0467970i	$-0.985099\pi$
$103$		−	0.949874i		−	0.0935939i	0.998904	−	0.0467970i	$-0.0149014\pi$
$104$		0			0
$105$		−	0.683375i		−	0.0666906i
$106$		0			0
$107$	−9.63325	−	9.63325i	−0.931281	−	0.931281i	0.0665047	−	0.997786i	$-0.478815\pi$
$107$	−9.63325	−	9.63325i	−0.931281	−	0.931281i	−0.997786	+	0.0665047i	$0.978815\pi$
$108$		0			0
$109$	−2.34521	−	2.34521i	−0.224630	−	0.224630i	0.585815	−	0.810445i	$-0.300775\pi$
$109$	−2.34521	−	2.34521i	−0.224630	−	0.224630i	−0.810445	+	0.585815i	$0.800775\pi$
$110$		0			0
$111$		−	28.4373i		−	2.69915i
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−4.46653	−	4.46653i	−0.416506	−	0.416506i
$116$		0			0
$117$	21.1304	−	8.49717i	1.95351	−	0.785564i
$118$		0			0
$119$	−0.671663			−0.0615712
$120$		0			0
$121$			7.00000i			0.636364i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.36396	+	6.36396i	0.569210	+	0.569210i
$126$		0			0
$127$	−2.94987			−0.261759			−0.130880	−	0.991398i	$-0.541780\pi$
$127$	−2.94987			−0.261759			−0.130880	+	0.991398i	$0.541780\pi$
$128$		0			0
$129$	−23.6332			−2.08079
$130$		0			0
$131$	−2.84169	+	2.84169i	−0.248279	+	0.248279i	−0.820264	−	0.571985i	$-0.806174\pi$
$131$	−2.84169	+	2.84169i	−0.248279	+	0.248279i	0.571985	+	0.820264i	$0.306174\pi$
$132$		0			0
$133$	−1.00000	−	1.00000i	−0.0867110	−	0.0867110i
$134$		0			0
$135$	10.1234			0.871282
$136$		0			0
$137$	14.0712			1.20219			0.601094	−	0.799178i	$-0.294732\pi$
$137$	14.0712			1.20219			0.601094	+	0.799178i	$0.294732\pi$
$138$		0			0
$139$	2.47494	+	2.47494i	0.209921	+	0.209921i	0.804234	−	0.594313i	$-0.202576\pi$
$139$	2.47494	+	2.47494i	0.209921	+	0.209921i	−0.594313	+	0.804234i	$0.702576\pi$
$140$		0			0
$141$	−22.8159	−	22.8159i	−1.92144	−	1.92144i
$142$		0			0
$143$	6.63325	+	2.82843i	0.554700	+	0.236525i
$144$		0			0
$145$		−	0.447775i		−	0.0371857i
$146$		0			0
$147$	15.0000	−	15.0000i	1.23718	−	1.23718i
$148$		0			0
$149$	7.07107	−	7.07107i	0.579284	−	0.579284i	−0.355422	−	0.934706i	$-0.615663\pi$
$149$	7.07107	−	7.07107i	0.579284	−	0.579284i	0.934706	+	0.355422i	$0.115663\pi$
$150$		0			0
$151$	−4.46653			−0.363481			−0.181740	−	0.983347i	$-0.558173\pi$
$151$	−4.46653			−0.363481			−0.181740	+	0.983347i	$0.558173\pi$
$152$		0			0
$153$		−	18.9499i		−	1.53201i
$154$		0			0
$155$	−3.00000	−	3.00000i	−0.240966	−	0.240966i
$156$		0			0
$157$	7.94987	−	7.94987i	0.634469	−	0.634469i	−0.314717	−	0.949186i	$-0.601909\pi$
$157$	7.94987	−	7.94987i	0.634469	−	0.634469i	0.949186	+	0.314717i	$0.101909\pi$
$158$		0			0
$159$	−15.6834			−1.24377
$160$		0			0
$161$			1.41421i			0.111456i
$162$		0			0
$163$	8.70917	+	8.70917i	0.682155	+	0.682155i	0.960485	−	0.278331i	$-0.0897811\pi$
$163$	8.70917	+	8.70917i	0.682155	+	0.682155i	−0.278331	+	0.960485i	$0.589781\pi$
$164$		0			0
$165$	4.31662	+	4.31662i	0.336049	+	0.336049i
$166$		0			0
$167$	14.0712			1.08887			0.544433	−	0.838804i	$-0.316745\pi$
$167$	14.0712			1.08887			0.544433	+	0.838804i	$0.316745\pi$
$168$		0			0
$169$	−9.38083	+	9.00000i	−0.721602	+	0.692308i
$170$		0			0
$171$	28.2134	−	28.2134i	2.15753	−	2.15753i
$172$		0			0
$173$	15.3166	−	15.3166i	1.16450	−	1.16450i	0.181022	−	0.983479i	$-0.442059\pi$
$173$	15.3166	−	15.3166i	1.16450	−	1.16450i	0.983479	−	0.181022i	$-0.0579407\pi$
$174$		0			0
$175$		−	0.895550i		−	0.0676972i
$176$		0			0
$177$		−	33.4225i		−	2.51219i
$178$		0			0
$179$	−6.79156	+	6.79156i	−0.507625	+	0.507625i	−0.913797	−	0.406172i	$-0.866864\pi$
$179$	−6.79156	+	6.79156i	−0.507625	+	0.507625i	0.406172	+	0.913797i	$0.366864\pi$
$180$		0			0
$181$	−17.9499	−	17.9499i	−1.33420	−	1.33420i	−0.901570	−	0.432634i	$-0.857584\pi$
$181$	−17.9499	−	17.9499i	−1.33420	−	1.33420i	−0.432634	−	0.901570i	$-0.642416\pi$
$182$		0			0
$183$			17.2665i			1.27638i
$184$		0			0
$185$			9.31662i			0.684972i
$186$		0			0
$187$	4.24264	−	4.24264i	0.310253	−	0.310253i
$188$		0			0
$189$	−1.60266	−	1.60266i	−0.116576	−	0.116576i
$190$		0			0
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$		0			0
$193$			12.7279i			0.916176i	0.888907	+	0.458088i	$0.151466\pi$
$193$			12.7279i			0.916176i	−0.888907	+	0.458088i	$0.848534\pi$
$194$		0			0
$195$	−10.2106	+	4.10600i	−0.731198	+	0.294037i
$196$		0			0
$197$	−2.86387	+	2.86387i	−0.204042	+	0.204042i	−0.801729	−	0.597687i	$-0.796087\pi$
$197$	−2.86387	+	2.86387i	−0.204042	+	0.204042i	0.597687	+	0.801729i	$0.296087\pi$
$198$		0			0
$199$		−	18.0000i		−	1.27599i	−0.770042	−	0.637993i	$-0.779765\pi$
$199$		−	18.0000i		−	1.27599i	0.770042	−	0.637993i	$-0.220235\pi$
$200$		0			0
$201$	20.2468			1.42810
$202$		0			0
$203$	−0.0708883	+	0.0708883i	−0.00497539	+	0.00497539i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−39.8997			−2.77322
$208$		0			0
$209$	12.6332			0.873860
$210$		0			0
$211$	−6.52506	+	6.52506i	−0.449204	+	0.449204i	−0.895090	−	0.445886i	$-0.852889\pi$
$211$	−6.52506	+	6.52506i	−0.449204	+	0.449204i	0.445886	+	0.895090i	$0.352889\pi$
$212$		0			0
$213$	−1.44966	+	1.44966i	−0.0993289	+	0.0993289i
$214$		0			0
$215$	7.74273			0.528050
$216$		0			0
$217$			0.949874i			0.0644817i
$218$		0			0
$219$	−8.19051	+	8.19051i	−0.553463	+	0.553463i
$220$		0			0
$221$	4.03562	+	10.0356i	0.271465	+	0.675069i
$222$		0			0
$223$			23.2282i			1.55547i	0.628589	+	0.777737i	$0.283633\pi$
$223$			23.2282i			1.55547i	−0.628589	+	0.777737i	$0.716367\pi$
$224$		0			0
$225$	25.2665			1.68443
$226$		0			0
$227$	−1.41421	−	1.41421i	−0.0938647	−	0.0938647i	0.658615	−	0.752480i	$-0.271143\pi$
$227$	−1.41421	−	1.41421i	−0.0938647	−	0.0938647i	−0.752480	+	0.658615i	$0.771143\pi$
$228$		0			0
$229$	−1.67355	+	1.67355i	−0.110591	+	0.110591i	−0.760237	−	0.649646i	$-0.774917\pi$
$229$	−1.67355	+	1.67355i	−0.110591	+	0.110591i	0.649646	+	0.760237i	$0.274917\pi$
$230$		0			0
$231$		−	1.36675i		−	0.0899256i
$232$		0			0
$233$		−	22.5831i		−	1.47947i	−0.672899	−	0.739735i	$-0.734951\pi$
$233$		−	22.5831i		−	1.47947i	0.672899	−	0.739735i	$-0.265049\pi$
$234$		0			0
$235$	7.47494	+	7.47494i	0.487611	+	0.487611i
$236$		0			0
$237$	−23.6332	+	23.6332i	−1.53514	+	1.53514i
$238$		0			0
$239$		−	11.9854i		−	0.775269i	−0.921813	−	0.387635i	$-0.873292\pi$
$239$		−	11.9854i		−	0.775269i	0.921813	−	0.387635i	$-0.126708\pi$
$240$		0			0
$241$		−	12.7279i		−	0.819878i	−0.912113	−	0.409939i	$-0.865550\pi$
$241$		−	12.7279i		−	0.819878i	0.912113	−	0.409939i	$-0.134450\pi$
$242$		0			0
$243$	4.31662	−	4.31662i	0.276912	−	0.276912i
$244$		0			0
$245$	−4.91430	+	4.91430i	−0.313963	+	0.313963i
$246$		0			0
$247$	−8.93306	+	20.9499i	−0.568397	+	1.33301i
$248$		0			0
$249$	−51.7364			−3.27866
$250$		0			0
$251$	−3.63325	−	3.63325i	−0.229329	−	0.229329i	0.583084	−	0.812412i	$-0.301846\pi$
$251$	−3.63325	−	3.63325i	−0.229329	−	0.229329i	−0.812412	+	0.583084i	$0.801846\pi$
$252$		0			0
$253$	−8.93306	−	8.93306i	−0.561616	−	0.561616i
$254$		0			0
$255$			9.15694i			0.573430i
$256$		0			0
$257$	15.0000			0.935674			0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000			0.935674			0.467837	+	0.883815i	$0.345033\pi$
$258$		0			0
$259$	1.47494	−	1.47494i	0.0916481	−	0.0916481i
$260$		0			0
$261$	−2.00000	−	2.00000i	−0.123797	−	0.123797i
$262$		0			0
$263$			0.633250i			0.0390478i	0.999809	+	0.0195239i	$0.00621505\pi$
$263$			0.633250i			0.0390478i	−0.999809	+	0.0195239i	$0.993785\pi$
$264$		0			0
$265$	5.13819			0.315637
$266$		0			0
$267$	−30.3701	+	30.3701i	−1.85862	+	1.85862i
$268$		0			0
$269$	−12.6332	+	12.6332i	−0.770263	+	0.770263i	−0.978152	−	0.207889i	$-0.933341\pi$
$269$	−12.6332	+	12.6332i	−0.770263	+	0.770263i	0.207889	+	0.978152i	$0.433341\pi$
$270$		0			0
$271$		−	23.2282i		−	1.41101i	−0.708704	−	0.705506i	$-0.750720\pi$
$271$		−	23.2282i		−	1.41101i	0.708704	−	0.705506i	$-0.249280\pi$
$272$		0			0
$273$	2.26650	+	0.966438i	0.137175	+	0.0584915i
$274$		0			0
$275$	5.65685	+	5.65685i	0.341121	+	0.341121i
$276$		0			0
$277$	−14.9499	−	14.9499i	−0.898251	−	0.898251i	0.0970305	−	0.995281i	$-0.469066\pi$
$277$	−14.9499	−	14.9499i	−0.898251	−	0.898251i	−0.995281	+	0.0970305i	$0.969066\pi$
$278$		0			0
$279$	−26.7992			−1.60442
$280$		0			0
$281$	−12.7279			−0.759284			−0.379642	−	0.925133i	$-0.623953\pi$
$281$	−12.7279			−0.759284			−0.379642	+	0.925133i	$0.623953\pi$
$282$		0			0
$283$	11.0000	+	11.0000i	0.653882	+	0.653882i	0.953926	−	0.300043i	$-0.0970012\pi$
$283$	11.0000	+	11.0000i	0.653882	+	0.653882i	−0.300043	+	0.953926i	$0.597001\pi$
$284$		0			0
$285$	−13.6332	+	13.6332i	−0.807564	+	0.807564i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$	−18.3139	−	18.3139i	−1.07358	−	1.07358i
$292$		0			0
$293$	−12.6925	+	12.6925i	−0.741502	+	0.741502i	−0.972867	−	0.231365i	$-0.925681\pi$
$293$	−12.6925	+	12.6925i	−0.741502	+	0.741502i	0.231365	+	0.972867i	$0.425681\pi$
$294$		0			0
$295$			10.9499i			0.637526i
$296$		0			0
$297$	20.2468			1.17484
$298$		0			0
$299$	21.1304	−	8.49717i	1.22200	−	0.491404i
$300$		0			0
$301$	−1.22577	−	1.22577i	−0.0706522	−	0.0706522i
$302$		0			0
$303$	27.2665			1.56642
$304$		0			0
$305$		−	5.65685i		−	0.323911i
$306$		0			0
$307$	−12.5040	−	12.5040i	−0.713643	−	0.713643i	0.253652	−	0.967295i	$-0.418368\pi$
$307$	−12.5040	−	12.5040i	−0.713643	−	0.713643i	−0.967295	+	0.253652i	$0.918368\pi$
$308$		0			0
$309$	2.05013	+	2.05013i	0.116628	+	0.116628i
$310$		0			0
$311$		−	18.3166i		−	1.03864i	−0.854580	−	0.519320i	$-0.826185\pi$
$311$		−	18.3166i		−	1.03864i	0.854580	−	0.519320i	$-0.173815\pi$
$312$		0			0
$313$			9.94987i			0.562400i	0.959649	+	0.281200i	$0.0907325\pi$
$313$			9.94987i			0.562400i	−0.959649	+	0.281200i	$0.909268\pi$
$314$		0			0
$315$	1.00000	+	1.00000i	0.0563436	+	0.0563436i
$316$		0			0
$317$	15.4855	+	15.4855i	0.869750	+	0.869750i	0.992445	−	0.122694i	$-0.0391535\pi$
$317$	15.4855	+	15.4855i	0.869750	+	0.869750i	−0.122694	+	0.992445i	$0.539153\pi$
$318$		0			0
$319$		−	0.895550i		−	0.0501412i
$320$		0			0
$321$	41.5831			2.32094
$322$		0			0
$323$	13.3996	+	13.3996i	0.745573	+	0.745573i
$324$		0			0
$325$	−13.3808	+	5.38083i	−0.742235	+	0.298475i
$326$		0			0
$327$	10.1234			0.559824
$328$		0			0
$329$		−	2.36675i		−	0.130483i
$330$		0			0
$331$	−5.36208	+	5.36208i	−0.294726	+	0.294726i	−0.838944	−	0.544218i	$-0.816827\pi$
$331$	−5.36208	+	5.36208i	−0.294726	+	0.294726i	0.544218	+	0.838944i	$0.316827\pi$
$332$		0			0
$333$	41.6130	+	41.6130i	2.28038	+	2.28038i
$334$		0			0
$335$	−6.63325			−0.362413
$336$		0			0
$337$	5.94987			0.324110			0.162055	−	0.986782i	$-0.448188\pi$
$337$	5.94987			0.324110			0.162055	+	0.986782i	$0.448188\pi$
$338$		0			0
$339$	12.9499	−	12.9499i	0.703341	−	0.703341i
$340$		0			0
$341$	−6.00000	−	6.00000i	−0.324918	−	0.324918i
$342$		0			0
$343$	3.12320			0.168637
$344$		0			0
$345$	19.2803			1.03802
$346$		0			0
$347$	5.84169	+	5.84169i	0.313598	+	0.313598i	0.846302	−	0.532704i	$-0.178824\pi$
$347$	5.84169	+	5.84169i	0.313598	+	0.313598i	−0.532704	+	0.846302i	$0.678824\pi$
$348$		0			0
$349$	−3.01687	−	3.01687i	−0.161489	−	0.161489i	0.621737	−	0.783226i	$-0.286427\pi$
$349$	−3.01687	−	3.01687i	−0.161489	−	0.161489i	−0.783226	+	0.621737i	$0.786427\pi$
$350$		0			0
$351$	−14.3166	+	33.5755i	−0.764165	+	1.79213i
$352$		0			0
$353$		−	11.2428i		−	0.598395i	−0.954191	−	0.299197i	$-0.903281\pi$
$353$		−	11.2428i		−	0.598395i	0.954191	−	0.299197i	$-0.0967189\pi$
$354$		0			0
$355$	0.474937	−	0.474937i	0.0252070	−	0.0252070i
$356$		0			0
$357$	1.44966	−	1.44966i	0.0767240	−	0.0767240i
$358$		0			0
$359$	12.7279			0.671754			0.335877	−	0.941906i	$-0.390967\pi$
$359$	12.7279			0.671754			0.335877	+	0.941906i	$0.390967\pi$
$360$		0			0
$361$			20.8997i			1.09999i
$362$		0			0
$363$	−15.1082	−	15.1082i	−0.792974	−	0.792974i
$364$		0			0
$365$	2.68338	−	2.68338i	0.140454	−	0.140454i
$366$		0			0
$367$	−27.8997			−1.45636			−0.728178	−	0.685389i	$-0.759632\pi$
$367$	−27.8997			−1.45636			−0.728178	+	0.685389i	$0.759632\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.813439	−	0.813439i	−0.0422317	−	0.0422317i
$372$		0			0
$373$	−2.94987	−	2.94987i	−0.152739	−	0.152739i	0.626601	−	0.779340i	$-0.284445\pi$
$373$	−2.94987	−	2.94987i	−0.152739	−	0.152739i	−0.779340	+	0.626601i	$0.784445\pi$
$374$		0			0
$375$	−27.4708			−1.41859
$376$		0			0
$377$	1.48510	+	0.633250i	0.0764866	+	0.0326140i
$378$		0			0
$379$	17.1945	−	17.1945i	0.883220	−	0.883220i	−0.110641	−	0.993860i	$-0.535290\pi$
$379$	17.1945	−	17.1945i	0.883220	−	0.883220i	0.993860	+	0.110641i	$0.0352903\pi$
$380$		0			0
$381$	6.36675	−	6.36675i	0.326179	−	0.326179i
$382$		0			0
$383$			2.08588i			0.106583i	0.998579	+	0.0532916i	$0.0169713\pi$
$383$			2.08588i			0.106583i	−0.998579	+	0.0532916i	$0.983029\pi$
$384$		0			0
$385$			0.447775i			0.0228207i
$386$		0			0
$387$	34.5831	−	34.5831i	1.75796	−	1.75796i
$388$		0			0
$389$	−3.31662	−	3.31662i	−0.168160	−	0.168160i	0.618010	−	0.786170i	$-0.287939\pi$
$389$	−3.31662	−	3.31662i	−0.168160	−	0.168160i	−0.786170	+	0.618010i	$0.787939\pi$
$390$		0			0
$391$		−	18.9499i		−	0.958336i
$392$		0			0
$393$		−	12.2665i		−	0.618763i
$394$		0			0
$395$	7.74273	−	7.74273i	0.389579	−	0.389579i
$396$		0			0
$397$	−27.6947	−	27.6947i	−1.38996	−	1.38996i	−0.825379	−	0.564579i	$-0.809038\pi$
$397$	−27.6947	−	27.6947i	−1.38996	−	1.38996i	−0.564579	−	0.825379i	$-0.690962\pi$
$398$		0			0
$399$	4.31662			0.216102
$400$		0			0
$401$			26.7283i			1.33475i	0.744723	+	0.667373i	$0.232581\pi$
$401$			26.7283i			1.33475i	−0.744723	+	0.667373i	$0.767419\pi$
$402$		0			0
$403$	14.1925	−	5.70723i	0.706980	−	0.284298i
$404$		0			0
$405$	−8.44984	+	8.44984i	−0.419876	+	0.419876i
$406$		0			0
$407$			18.6332i			0.923616i
$408$		0			0
$409$	30.5940			1.51278			0.756389	−	0.654122i	$-0.226962\pi$
$409$	30.5940			1.51278			0.756389	+	0.654122i	$0.226962\pi$
$410$		0			0
$411$	−30.3701	+	30.3701i	−1.49805	+	1.49805i
$412$		0			0
$413$	1.73350	−	1.73350i	0.0853000	−	0.0853000i
$414$		0			0
$415$	16.9499			0.832037
$416$		0			0
$417$	−10.6834			−0.523167
$418$		0			0
$419$	−5.84169	+	5.84169i	−0.285385	+	0.285385i	−0.835252	−	0.549867i	$-0.814678\pi$
$419$	−5.84169	+	5.84169i	−0.285385	+	0.285385i	0.549867	+	0.835252i	$0.314678\pi$
$420$		0			0
$421$	−15.7448	+	15.7448i	−0.767354	+	0.767354i	−0.977640	−	0.210286i	$-0.932561\pi$
$421$	−15.7448	+	15.7448i	−0.767354	+	0.767354i	0.210286	+	0.977640i	$0.432561\pi$
$422$		0			0
$423$	66.7740			3.24666
$424$		0			0
$425$			12.0000i			0.582086i
$426$		0			0
$427$	−0.895550	+	0.895550i	−0.0433387	+	0.0433387i
$428$		0			0
$429$	−20.4213	+	8.21200i	−0.985947	+	0.396479i
$430$		0			0
$431$			6.32852i			0.304834i	0.988316	+	0.152417i	$0.0487057\pi$
$431$			6.32852i			0.304834i	−0.988316	+	0.152417i	$0.951294\pi$
$432$		0			0
$433$	10.0501			0.482978			0.241489	−	0.970404i	$-0.422364\pi$
$433$	10.0501			0.482978			0.241489	+	0.970404i	$0.422364\pi$
$434$		0			0
$435$	0.966438	+	0.966438i	0.0463372	+	0.0463372i
$436$		0			0
$437$	28.2134	−	28.2134i	1.34963	−	1.34963i
$438$		0			0
$439$		−	0.949874i		−	0.0453350i	−0.999743	−	0.0226675i	$-0.992784\pi$
$439$		−	0.949874i		−	0.0453350i	0.999743	−	0.0226675i	$-0.00721591\pi$
$440$		0			0
$441$			43.8997i			2.09046i
$442$		0			0
$443$	−22.1082	−	22.1082i	−1.05039	−	1.05039i	−0.998661	−	0.0517306i	$-0.983526\pi$
$443$	−22.1082	−	22.1082i	−1.05039	−	1.05039i	−0.0517306	−	0.998661i	$-0.516474\pi$
$444$		0			0
$445$	9.94987	−	9.94987i	0.471669	−	0.471669i
$446$		0			0
$447$			30.5231i			1.44370i
$448$		0			0
$449$		−	4.31353i		−	0.203568i	−0.994807	−	0.101784i	$-0.967545\pi$
$449$		−	4.31353i		−	0.203568i	0.994807	−	0.101784i	$-0.0324551\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	9.64016	−	9.64016i	0.452934	−	0.452934i
$454$		0			0
$455$	−0.742551	−	0.316625i	−0.0348113	−	0.0148436i
$456$		0			0
$457$	−14.5190			−0.679171			−0.339586	−	0.940575i	$-0.610287\pi$
$457$	−14.5190			−0.679171			−0.339586	+	0.940575i	$0.610287\pi$
$458$		0			0
$459$	21.4749	+	21.4749i	1.00236	+	1.00236i
$460$		0			0
$461$	−4.27808	−	4.27808i	−0.199250	−	0.199250i	0.600428	−	0.799679i	$-0.294997\pi$
$461$	−4.27808	−	4.27808i	−0.199250	−	0.199250i	−0.799679	+	0.600428i	$0.794997\pi$
$462$		0			0
$463$		−	12.7279i		−	0.591517i	−0.955263	−	0.295758i	$-0.904428\pi$
$463$		−	12.7279i		−	0.591517i	0.955263	−	0.295758i	$-0.0955723\pi$
$464$		0			0
$465$	12.9499			0.600536
$466$		0			0
$467$	3.63325	−	3.63325i	0.168127	−	0.168127i	−0.618029	−	0.786155i	$-0.712068\pi$
$467$	3.63325	−	3.63325i	0.168127	−	0.168127i	0.786155	+	0.618029i	$0.212068\pi$
$468$		0			0
$469$	1.05013	+	1.05013i	0.0484903	+	0.0484903i
$470$		0			0
$471$			34.3166i			1.58123i
$472$		0			0
$473$	15.4855			0.712022
$474$		0			0
$475$	−17.8661	+	17.8661i	−0.819753	+	0.819753i
$476$		0			0
$477$	22.9499	−	22.9499i	1.05080	−	1.05080i
$478$		0			0
$479$		−	16.2280i		−	0.741477i	−0.928737	−	0.370738i	$-0.879105\pi$
$479$		−	16.2280i		−	0.741477i	0.928737	−	0.370738i	$-0.120895\pi$
$480$		0			0
$481$	−30.8997	−	13.1757i	−1.40891	−	0.600760i
$482$		0			0
$483$	−3.05231	−	3.05231i	−0.138885	−	0.138885i
$484$		0			0
$485$	6.00000	+	6.00000i	0.272446	+	0.272446i
$486$		0			0
$487$	−29.2507			−1.32548			−0.662738	−	0.748851i	$-0.730606\pi$
$487$	−29.2507			−1.32548			−0.662738	+	0.748851i	$0.730606\pi$
$488$		0			0
$489$	−37.5942			−1.70007
$490$		0			0
$491$	−21.1583	−	21.1583i	−0.954861	−	0.954861i	0.0441631	−	0.999024i	$-0.485938\pi$
$491$	−21.1583	−	21.1583i	−0.954861	−	0.954861i	−0.999024	+	0.0441631i	$0.985938\pi$
$492$		0			0
$493$	0.949874	−	0.949874i	0.0427802	−	0.0427802i
$494$		0			0
$495$	−12.6332			−0.567822
$496$		0			0
$497$	−0.150377			−0.00674533
$498$		0			0
$499$	−17.4183	−	17.4183i	−0.779752	−	0.779752i	0.200037	−	0.979788i	$-0.435894\pi$
$499$	−17.4183	−	17.4183i	−0.779752	−	0.779752i	−0.979788	+	0.200037i	$0.935894\pi$
$500$		0			0
$501$	−30.3701	+	30.3701i	−1.35684	+	1.35684i
$502$		0			0
$503$		−	10.4169i		−	0.464466i	−0.972660	−	0.232233i	$-0.925397\pi$
$503$		−	10.4169i		−	0.464466i	0.972660	−	0.232233i	$-0.0746031\pi$
$504$		0			0
$505$	−8.93306			−0.397516
$506$		0			0
$507$	0.821953	−	39.6716i	0.0365042	−	1.76188i
$508$		0			0
$509$	5.65685	+	5.65685i	0.250736	+	0.250736i	0.821272	−	0.570537i	$-0.193265\pi$
$509$	5.65685	+	5.65685i	0.250736	+	0.250736i	−0.570537	+	0.821272i	$0.693265\pi$
$510$		0			0
$511$	−0.849623			−0.0375851
$512$		0			0
$513$			63.9456i			2.82327i
$514$		0			0
$515$	−0.671663	−	0.671663i	−0.0295970	−	0.0295970i
$516$		0			0
$517$	14.9499	+	14.9499i	0.657495	+	0.657495i
$518$		0			0
$519$			66.1161i			2.90218i
$520$		0			0
$521$			7.41688i			0.324939i	0.986714	+	0.162470i	$0.0519459\pi$
$521$			7.41688i			0.324939i	−0.986714	+	0.162470i	$0.948054\pi$
$522$		0			0
$523$	−0.0501256	−	0.0501256i	−0.00219184	−	0.00219184i	0.706010	−	0.708202i	$-0.250493\pi$
$523$	−0.0501256	−	0.0501256i	−0.00219184	−	0.00219184i	−0.708202	+	0.706010i	$0.750493\pi$
$524$		0			0
$525$	1.93288	+	1.93288i	0.0843577	+	0.0843577i
$526$		0			0
$527$		−	12.7279i		−	0.554437i
$528$		0			0
$529$	−16.8997			−0.734772
$530$		0			0
$531$	48.9079	+	48.9079i	2.12242	+	2.12242i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−13.6235			−0.588994
$536$		0			0
$537$		−	29.3166i		−	1.26511i
$538$		0			0
$539$	−9.82861	+	9.82861i	−0.423348	+	0.423348i
$540$		0			0
$541$	14.6254	+	14.6254i	0.628793	+	0.628793i	0.947764	−	0.318971i	$-0.103337\pi$
$541$	14.6254	+	14.6254i	0.628793	+	0.628793i	−0.318971	+	0.947764i	$0.603337\pi$
$542$		0			0
$543$	77.4829			3.32511
$544$		0			0
$545$	−3.31662			−0.142069
$546$		0			0
$547$	−5.42481	+	5.42481i	−0.231948	+	0.231948i	−0.813505	−	0.581557i	$-0.802444\pi$
$547$	−5.42481	+	5.42481i	−0.231948	+	0.231948i	0.581557	+	0.813505i	$0.302444\pi$
$548$		0			0
$549$	−25.2665	−	25.2665i	−1.07835	−	1.07835i
$550$		0			0
$551$	2.82843			0.120495
$552$		0			0
$553$	−2.45154			−0.104250
$554$		0			0
$555$	−20.1082	−	20.1082i	−0.853545	−	0.853545i
$556$		0			0
$557$	−8.52073	−	8.52073i	−0.361035	−	0.361035i	0.503159	−	0.864194i	$-0.332171\pi$
$557$	−8.52073	−	8.52073i	−0.361035	−	0.361035i	−0.864194	+	0.503159i	$0.832171\pi$
$558$		0			0
$559$	−10.9499	+	25.6797i	−0.463130	+	1.08614i
$560$		0			0
$561$			18.3139i			0.773213i
$562$		0			0
$563$	24.1583	−	24.1583i	1.01815	−	1.01815i	0.0183193	−	0.999832i	$-0.494168\pi$
$563$	24.1583	−	24.1583i	1.01815	−	1.01815i	0.999832	−	0.0183193i	$-0.00583154\pi$
$564$		0			0
$565$	−4.24264	+	4.24264i	−0.178489	+	0.178489i
$566$		0			0
$567$	2.67543			0.112357
$568$		0			0
$569$		−	21.6332i		−	0.906913i	−0.891278	−	0.453457i	$-0.850191\pi$
$569$		−	21.6332i		−	0.906913i	0.891278	−	0.453457i	$-0.149809\pi$
$570$		0			0
$571$	21.4248	+	21.4248i	0.896600	+	0.896600i	0.995134	−	0.0985333i	$-0.0314151\pi$
$571$	21.4248	+	21.4248i	0.896600	+	0.896600i	−0.0985333	+	0.995134i	$0.531415\pi$
$572$		0			0
$573$	−38.8496	+	38.8496i	−1.62297	+	1.62297i
$574$		0			0
$575$	25.2665			1.05369
$576$		0			0
$577$		−	29.6985i		−	1.23636i	−0.786035	−	0.618182i	$-0.787869\pi$
$577$		−	29.6985i		−	1.23636i	0.786035	−	0.618182i	$-0.212131\pi$
$578$		0			0
$579$	−27.4708	−	27.4708i	−1.14165	−	1.14165i
$580$		0			0
$581$	−2.68338	−	2.68338i	−0.111325	−	0.111325i
$582$		0			0
$583$	10.2764			0.425604
$584$		0			0
$585$	8.93306	−	20.9499i	0.369336	−	0.866171i
$586$		0			0
$587$	−10.6420	+	10.6420i	−0.439244	+	0.439244i	−0.891758	−	0.452513i	$-0.850527\pi$
$587$	−10.6420	+	10.6420i	−0.439244	+	0.439244i	0.452513	+	0.891758i	$0.350527\pi$
$588$		0			0
$589$	18.9499	−	18.9499i	0.780816	−	0.780816i
$590$		0			0
$591$		−	12.3623i		−	0.508515i
$592$		0			0
$593$		−	4.31353i		−	0.177135i	−0.996070	−	0.0885677i	$-0.971771\pi$
$593$		−	4.31353i		−	0.177135i	0.996070	−	0.0885677i	$-0.0282290\pi$
$594$		0			0
$595$	−0.474937	+	0.474937i	−0.0194705	+	0.0194705i
$596$		0			0
$597$	38.8496	+	38.8496i	1.59001	+	1.59001i
$598$		0			0
$599$			11.6834i			0.477370i	0.971097	+	0.238685i	$0.0767163\pi$
$599$			11.6834i			0.477370i	−0.971097	+	0.238685i	$0.923284\pi$
$600$		0			0
$601$			28.8997i			1.17885i	0.807825	+	0.589423i	$0.200645\pi$
$601$			28.8997i			1.17885i	−0.807825	+	0.589423i	$0.799355\pi$
$602$		0			0
$603$	−29.6276	+	29.6276i	−1.20653	+	1.20653i
$604$		0			0
$605$	4.94975	+	4.94975i	0.201236	+	0.201236i
$606$		0			0
$607$	−32.9499			−1.33739			−0.668697	−	0.743535i	$-0.733148\pi$
$607$	−32.9499			−1.33739			−0.668697	+	0.743535i	$0.733148\pi$
$608$		0			0
$609$		−	0.305998i		−	0.0123997i
$610$		0			0
$611$	−35.3627	+	14.2204i	−1.43062	+	0.575296i
$612$		0			0
$613$	27.2469	−	27.2469i	1.10049	−	1.10049i	0.106143	−	0.994351i	$-0.466150\pi$
$613$	27.2469	−	27.2469i	1.10049	−	1.10049i	0.994351	−	0.106143i	$-0.0338501\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.34333			0.0540802			0.0270401	−	0.999634i	$-0.491392\pi$
$617$	1.34333			0.0540802			0.0270401	+	0.999634i	$0.491392\pi$
$618$		0			0
$619$	5.13819	−	5.13819i	0.206521	−	0.206521i	−0.596266	−	0.802787i	$-0.703350\pi$
$619$	5.13819	−	5.13819i	0.206521	−	0.206521i	0.802787	+	0.596266i	$0.203350\pi$
$620$		0			0
$621$	45.2164	−	45.2164i	1.81447	−	1.81447i
$622$		0			0
$623$	−3.15038			−0.126217
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	−27.2665	+	27.2665i	−1.08892	+	1.08892i
$628$		0			0
$629$	−19.7635	+	19.7635i	−0.788024	+	0.788024i
$630$		0			0
$631$	−5.80985			−0.231287			−0.115643	−	0.993291i	$-0.536893\pi$
$631$	−5.80985			−0.231287			−0.115643	+	0.993291i	$0.536893\pi$
$632$		0			0
$633$		−	28.1662i		−	1.11951i
$634$		0			0
$635$	−2.08588	+	2.08588i	−0.0827755	+	0.0827755i
$636$		0			0
$637$	−9.34903	−	23.2488i	−0.370422	−	0.921150i
$638$		0			0
$639$		−	4.24264i		−	0.167836i
$640$		0			0
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$		0			0
$643$	−8.93306	−	8.93306i	−0.352285	−	0.352285i	0.508674	−	0.860959i	$-0.330136\pi$
$643$	−8.93306	−	8.93306i	−0.352285	−	0.352285i	−0.860959	+	0.508674i	$0.830136\pi$
$644$		0			0
$645$	−16.7112	+	16.7112i	−0.658004	+	0.658004i
$646$		0			0
$647$			19.5831i			0.769892i	0.922939	+	0.384946i	$0.125780\pi$
$647$			19.5831i			0.769892i	−0.922939	+	0.384946i	$0.874220\pi$
$648$		0			0
$649$			21.8997i			0.859640i
$650$		0			0
$651$	−2.05013	−	2.05013i	−0.0803508	−	0.0803508i
$652$		0			0
$653$	−13.5831	+	13.5831i	−0.531549	+	0.531549i	−0.921033	−	0.389484i	$-0.872653\pi$
$653$	−13.5831	+	13.5831i	−0.531549	+	0.531549i	0.389484	+	0.921033i	$0.372653\pi$
$654$		0			0
$655$			4.01875i			0.157026i
$656$		0			0
$657$		−	23.9707i		−	0.935188i
$658$		0			0
$659$	8.68338	−	8.68338i	0.338256	−	0.338256i	−0.517454	−	0.855711i	$-0.673120\pi$
$659$	8.68338	−	8.68338i	0.338256	−	0.338256i	0.855711	+	0.517454i	$0.173120\pi$
$660$		0			0
$661$	17.4183	−	17.4183i	0.677495	−	0.677495i	−0.281938	−	0.959433i	$-0.590977\pi$
$661$	17.4183	−	17.4183i	0.677495	−	0.677495i	0.959433	+	0.281938i	$0.0909772\pi$
$662$		0			0
$663$	−30.3701	−	12.9499i	−1.17948	−	0.502931i
$664$		0			0
$665$	−1.41421			−0.0548408
$666$		0			0
$667$	−2.00000	−	2.00000i	−0.0774403	−	0.0774403i
$668$		0			0
$669$	−50.1337	−	50.1337i	−1.93828	−	1.93828i
$670$		0			0
$671$		−	11.3137i		−	0.436761i
$672$		0			0
$673$	18.8997			0.728532			0.364266	−	0.931295i	$-0.381320\pi$
$673$	18.8997			0.728532			0.364266	+	0.931295i	$0.381320\pi$
$674$		0			0
$675$	−28.6332	+	28.6332i	−1.10209	+	1.10209i
$676$		0			0
$677$	8.68338	+	8.68338i	0.333729	+	0.333729i	0.854001	−	0.520272i	$-0.174169\pi$
$677$	8.68338	+	8.68338i	0.333729	+	0.333729i	−0.520272	+	0.854001i	$0.674169\pi$
$678$		0			0
$679$		−	1.89975i		−	0.0729057i
$680$		0			0
$681$	6.10463			0.233930
$682$		0			0
$683$	10.5712	−	10.5712i	0.404494	−	0.404494i	−0.475319	−	0.879813i	$-0.657667\pi$
$683$	10.5712	−	10.5712i	0.404494	−	0.404494i	0.879813	+	0.475319i	$0.157667\pi$
$684$		0			0
$685$	9.94987	−	9.94987i	0.380165	−	0.380165i
$686$		0			0
$687$		−	7.22407i		−	0.275615i
$688$		0			0
$689$	−7.26650	+	17.0415i	−0.276832	+	0.649228i
$690$		0			0
$691$	−3.34709	−	3.34709i	−0.127329	−	0.127329i	0.640570	−	0.767900i	$-0.278698\pi$
$691$	−3.34709	−	3.34709i	−0.127329	−	0.127329i	−0.767900	+	0.640570i	$0.778698\pi$
$692$		0			0
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$		0			0
$695$	3.50009			0.132766
$696$		0			0
$697$		0			0
$698$		0			0
$699$	48.7414	+	48.7414i	1.84357	+	1.84357i
$700$		0			0
$701$	11.2164	−	11.2164i	0.423637	−	0.423637i	−0.462817	−	0.886454i	$-0.653161\pi$
$701$	11.2164	−	11.2164i	0.423637	−	0.423637i	0.886454	+	0.462817i	$0.153161\pi$
$702$		0			0
$703$	−58.8496			−2.21956
$704$		0			0
$705$	−32.2665			−1.21523
$706$		0			0
$707$	1.41421	+	1.41421i	0.0531870	+	0.0531870i
$708$		0			0
$709$	3.34709	−	3.34709i	0.125703	−	0.125703i	−0.641457	−	0.767159i	$-0.721670\pi$
$709$	3.34709	−	3.34709i	0.125703	−	0.125703i	0.767159	+	0.641457i	$0.221670\pi$
$710$		0			0
$711$		−	69.1662i		−	2.59394i
$712$		0			0
$713$	−26.7992			−1.00364
$714$		0			0
$715$	6.69042	−	2.69042i	0.250207	−	0.100616i
$716$		0			0
$717$	25.8682	+	25.8682i	0.966065	+	0.966065i
$718$		0			0
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$			0.212665i			0.00792006i
$722$		0			0
$723$	27.4708	+	27.4708i	1.02165	+	1.02165i
$724$		0			0
$725$	1.26650	+	1.26650i	0.0470366	+	0.0470366i
$726$		0			0
$727$		−	37.8997i		−	1.40562i	−0.711376	−	0.702812i	$-0.751928\pi$
$727$		−	37.8997i		−	1.40562i	0.711376	−	0.702812i	$-0.248072\pi$
$728$		0			0
$729$		−	17.2164i		−	0.637643i
$730$		0			0
$731$	16.4248	+	16.4248i	0.607494	+	0.607494i
$732$		0			0
$733$	6.81174	+	6.81174i	0.251597	+	0.251597i	0.821625	−	0.570028i	$-0.193068\pi$
$733$	6.81174	+	6.81174i	0.251597	+	0.251597i	−0.570028	+	0.821625i	$0.693068\pi$
$734$		0			0
$735$		−	21.2132i		−	0.782461i
$736$		0			0
$737$	−13.2665			−0.488678
$738$		0			0
$739$	−18.7617	−	18.7617i	−0.690159	−	0.690159i	0.272108	−	0.962267i	$-0.412279\pi$
$739$	−18.7617	−	18.7617i	−0.690159	−	0.690159i	−0.962267	+	0.272108i	$0.912279\pi$
$740$		0			0
$741$	−25.9360	−	64.4967i	−0.952784	−	2.36935i
$742$		0			0
$743$	−12.0563			−0.442301			−0.221151	−	0.975240i	$-0.570981\pi$
$743$	−12.0563			−0.442301			−0.221151	+	0.975240i	$0.570981\pi$
$744$		0			0
$745$		−	10.0000i		−	0.366372i
$746$		0			0
$747$	75.7071	−	75.7071i	2.76998	−	2.76998i
$748$		0			0
$749$	2.15676	+	2.15676i	0.0788065	+	0.0788065i
$750$		0			0
$751$	−15.8997			−0.580190			−0.290095	−	0.956998i	$-0.593687\pi$
$751$	−15.8997			−0.580190			−0.290095	+	0.956998i	$0.593687\pi$
$752$		0			0
$753$	15.6834			0.571534
$754$		0			0
$755$	−3.15831	+	3.15831i	−0.114943	+	0.114943i
$756$		0			0
$757$	20.8997	+	20.8997i	0.759614	+	0.759614i	0.976252	−	0.216638i	$-0.0695091\pi$
$757$	20.8997	+	20.8997i	0.759614	+	0.759614i	−0.216638	+	0.976252i	$0.569509\pi$
$758$		0			0
$759$	38.5607			1.39966
$760$		0			0
$761$	12.7279			0.461387			0.230693	−	0.973026i	$-0.425901\pi$
$761$	12.7279			0.461387			0.230693	+	0.973026i	$0.425901\pi$
$762$		0			0
$763$	0.525063	+	0.525063i	0.0190086	+	0.0190086i
$764$		0			0
$765$	−13.3996	−	13.3996i	−0.484463	−	0.484463i
$766$		0			0
$767$	−36.3166	−	15.4855i	−1.31132	−	0.559148i
$768$		0			0
$769$		−	25.4558i		−	0.917961i	−0.888446	−	0.458981i	$-0.848215\pi$
$769$		−	25.4558i		−	0.917961i	0.888446	−	0.458981i	$-0.151785\pi$
$770$		0			0
$771$	−32.3747	+	32.3747i	−1.16595	+	1.16595i
$772$		0			0
$773$	23.2636	−	23.2636i	0.836735	−	0.836735i	−0.151693	−	0.988428i	$-0.548472\pi$
$773$	23.2636	−	23.2636i	0.836735	−	0.836735i	0.988428	+	0.151693i	$0.0484725\pi$
$774$		0			0
$775$	16.9706			0.609601
$776$		0			0
$777$			6.36675i			0.228406i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	0.949874	−	0.949874i	0.0339892	−	0.0339892i
$782$		0			0
$783$	4.53300			0.161996
$784$		0			0
$785$		−	11.2428i		−	0.401273i
$786$		0			0
$787$	25.0081	+	25.0081i	0.891441	+	0.891441i	0.994659	−	0.103217i	$-0.0329137\pi$
$787$	25.0081	+	25.0081i	0.891441	+	0.891441i	−0.103217	+	0.994659i	$0.532914\pi$
$788$		0			0
$789$	−1.36675	−	1.36675i	−0.0486576	−	0.0486576i
$790$		0			0
$791$	1.34333			0.0477631
$792$		0			0
$793$	18.7617	+	8.00000i	0.666246	+	0.284088i
$794$		0			0
$795$	−11.0898	+	11.0898i	−0.393315	+	0.393315i
$796$		0			0
$797$	−34.5831	+	34.5831i	−1.22500	+	1.22500i	−0.259164	+	0.965833i	$0.583447\pi$
$797$	−34.5831	+	34.5831i	−1.22500	+	1.22500i	−0.965833	+	0.259164i	$0.916553\pi$
$798$		0			0
$799$			31.7135i			1.12194i
$800$		0			0
$801$		−	88.8828i		−	3.14052i
$802$		0			0
$803$	5.36675	−	5.36675i	0.189389	−	0.189389i
$804$		0			0
$805$	1.00000	+	1.00000i	0.0352454	+	0.0352454i
$806$		0			0
$807$		−	54.5330i		−	1.91965i
$808$		0			0
$809$		−	22.5831i		−	0.793980i	−0.917823	−	0.396990i	$-0.870055\pi$
$809$		−	22.5831i		−	0.793980i	0.917823	−	0.396990i	$-0.129945\pi$
$810$		0			0
$811$	27.6947	−	27.6947i	0.972493	−	0.972493i	−0.0271385	−	0.999632i	$-0.508640\pi$
$811$	27.6947	−	27.6947i	0.972493	−	0.972493i	0.999632	+	0.0271385i	$0.00863953\pi$
$812$		0			0
$813$	50.1337	+	50.1337i	1.75827	+	1.75827i
$814$		0			0
$815$	12.3166			0.431433
$816$		0			0
$817$			48.9079i			1.71107i
$818$		0			0
$819$	−4.73084	+	1.90241i	−0.165309	+	0.0664756i
$820$		0			0
$821$	17.6777	−	17.6777i	0.616955	−	0.616955i	−0.327794	−	0.944749i	$-0.606305\pi$
$821$	17.6777	−	17.6777i	0.616955	−	0.616955i	0.944749	+	0.327794i	$0.106305\pi$
$822$		0			0
$823$		−	18.9499i		−	0.660551i	−0.943885	−	0.330276i	$-0.892858\pi$
$823$		−	18.9499i		−	0.660551i	0.943885	−	0.330276i	$-0.107142\pi$
$824$		0			0
$825$	−24.4185			−0.850144
$826$		0			0
$827$	−3.50009	+	3.50009i	−0.121710	+	0.121710i	−0.765338	−	0.643628i	$-0.777428\pi$
$827$	−3.50009	+	3.50009i	−0.121710	+	0.121710i	0.643628	+	0.765338i	$0.277428\pi$
$828$		0			0
$829$	−8.00000	+	8.00000i	−0.277851	+	0.277851i	−0.832251	−	0.554399i	$-0.812948\pi$
$829$	−8.00000	+	8.00000i	−0.277851	+	0.277851i	0.554399	+	0.832251i	$0.312948\pi$
$830$		0			0
$831$	64.5330			2.23862
$832$		0			0
$833$	−20.8496			−0.722397
$834$		0			0
$835$	9.94987	−	9.94987i	0.344330	−	0.344330i
$836$		0			0
$837$	30.3701	−	30.3701i	1.04975	−	1.04975i
$838$		0			0
$839$	−15.4146			−0.532170			−0.266085	−	0.963950i	$-0.585730\pi$
$839$	−15.4146			−0.532170			−0.266085	+	0.963950i	$0.585730\pi$
$840$		0			0
$841$			28.7995i			0.993086i
$842$		0			0
$843$	27.4708	−	27.4708i	0.946146	−	0.946146i
$844$		0			0
$845$	−0.269289	+	12.9972i	−0.00926381	+	0.447118i
$846$		0			0
$847$		−	1.56721i		−	0.0538501i
$848$		0			0
$849$	−47.4829			−1.62961
$850$		0			0
$851$	41.6130	+	41.6130i	1.42647	+	1.42647i
$852$		0			0
$853$	−19.9874	+	19.9874i	−0.684357	+	0.684357i	−0.960979	−	0.276622i	$-0.910785\pi$
$853$	−19.9874	+	19.9874i	−0.684357	+	0.684357i	0.276622	+	0.960979i	$0.410785\pi$
$854$		0			0
$855$		−	39.8997i		−	1.36454i
$856$		0			0
$857$		−	36.6332i		−	1.25137i	−0.780077	−	0.625684i	$-0.784820\pi$
$857$		−	36.6332i		−	1.25137i	0.780077	−	0.625684i	$-0.215180\pi$
$858$		0			0
$859$	−25.9499	−	25.9499i	−0.885398	−	0.885398i	0.108679	−	0.994077i	$-0.465338\pi$
$859$	−25.9499	−	25.9499i	−0.885398	−	0.885398i	−0.994077	+	0.108679i	$0.965338\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	20.4707i		−	0.696829i	−0.937341	−	0.348415i	$-0.886720\pi$
$863$		−	20.4707i		−	0.696829i	0.937341	−	0.348415i	$-0.113280\pi$
$864$		0			0
$865$		−	21.6610i		−	0.736495i
$866$		0			0
$867$	17.2665	−	17.2665i	0.586401	−	0.586401i
$868$		0			0
$869$	15.4855	−	15.4855i	0.525308	−	0.525308i
$870$		0			0
$871$	9.38083	−	22.0000i	0.317857	−	0.745442i
$872$		0			0
$873$	53.5983			1.81403
$874$		0			0
$875$	−1.42481	−	1.42481i	−0.0481674	−	0.0481674i
$876$		0			0
$877$	−1.67355	−	1.67355i	−0.0565116	−	0.0565116i	0.678286	−	0.734798i	$-0.262723\pi$
$877$	−1.67355	−	1.67355i	−0.0565116	−	0.0565116i	−0.734798	+	0.678286i	$0.762723\pi$
$878$		0			0
$879$		−	54.7887i		−	1.84798i
$880$		0			0
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$		0			0
$883$	−1.47494	+	1.47494i	−0.0496356	+	0.0496356i	−0.731489	−	0.681853i	$-0.761174\pi$
$883$	−1.47494	+	1.47494i	−0.0496356	+	0.0496356i	0.681853	+	0.731489i	$0.261174\pi$
$884$		0			0
$885$	−23.6332	−	23.6332i	−0.794423	−	0.794423i
$886$		0			0
$887$		−	39.1662i		−	1.31507i	−0.753422	−	0.657537i	$-0.771598\pi$
$887$		−	39.1662i		−	1.31507i	0.753422	−	0.657537i	$-0.228402\pi$
$888$		0			0
$889$	0.660440			0.0221505
$890$		0			0
$891$	−16.8997	+	16.8997i	−0.566160	+	0.566160i
$892$		0			0
$893$	−47.2164	+	47.2164i	−1.58004	+	1.58004i
$894$		0			0
$895$			9.60472i			0.321050i
$896$		0			0
$897$	−27.2665	+	63.9456i	−0.910402	+	2.13508i
$898$		0			0
$899$	−1.34333	−	1.34333i	−0.0448024	−	0.0448024i
$900$		0			0
$901$	10.8997	+	10.8997i	0.363123	+	0.363123i
$902$		0			0
$903$	5.29119			0.176080
$904$		0			0
$905$	−25.3850			−0.843824
$906$		0			0
$907$	25.3747	+	25.3747i	0.842553	+	0.842553i	0.989190	−	0.146638i	$-0.0468451\pi$
$907$	25.3747	+	25.3747i	0.842553	+	0.842553i	−0.146638	+	0.989190i	$0.546845\pi$
$908$		0			0
$909$	−39.8997	+	39.8997i	−1.32339	+	1.32339i
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	33.8997			1.12192
$914$		0			0
$915$	12.2093	+	12.2093i	0.403626	+	0.403626i
$916$		0			0
$917$	0.636218	−	0.636218i	0.0210098	−	0.0210098i
$918$		0			0
$919$			36.0000i			1.18753i	0.804638	+	0.593765i	$0.202359\pi$
$919$			36.0000i			1.18753i	−0.804638	+	0.593765i	$0.797641\pi$
$920$		0			0
$921$	53.9752			1.77854
$922$		0			0
$923$	0.903526	+	2.24685i	0.0297399	+	0.0739560i
$924$		0			0
$925$	−26.3514	−	26.3514i	−0.866429	−	0.866429i
$926$		0			0
$927$	−6.00000			−0.197066
$928$		0			0
$929$		−	25.3141i		−	0.830528i	−0.909701	−	0.415264i	$-0.863689\pi$
$929$		−	25.3141i		−	0.830528i	0.909701	−	0.415264i	$-0.136311\pi$
$930$		0			0
$931$	−31.0418	−	31.0418i	−1.01735	−	1.01735i
$932$		0			0
$933$	39.5330	+	39.5330i	1.29425	+	1.29425i
$934$		0			0
$935$		−	6.00000i		−	0.196221i
$936$		0			0
$937$		−	16.1003i		−	0.525972i	−0.964800	−	0.262986i	$-0.915293\pi$
$937$		−	16.1003i		−	0.525972i	0.964800	−	0.262986i	$-0.0847074\pi$
$938$		0			0
$939$	−21.4749	−	21.4749i	−0.700808	−	0.700808i
$940$		0			0
$941$	−16.1217	−	16.1217i	−0.525552	−	0.525552i	0.393691	−	0.919243i	$-0.371198\pi$
$941$	−16.1217	−	16.1217i	−0.525552	−	0.525552i	−0.919243	+	0.393691i	$0.871198\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−2.26650			−0.0737292
$946$		0			0
$947$	−40.9413	−	40.9413i	−1.33041	−	1.33041i	−0.904998	−	0.425415i	$-0.860128\pi$
$947$	−40.9413	−	40.9413i	−1.33041	−	1.33041i	−0.425415	−	0.904998i	$-0.639872\pi$
$948$		0			0
$949$	5.10488	+	12.6946i	0.165712	+	0.412085i
$950$		0			0
$951$	−66.8449			−2.16760
$952$		0			0
$953$		−	49.4327i		−	1.60128i	−0.599143	−	0.800642i	$-0.704492\pi$
$953$		−	49.4327i		−	1.60128i	0.599143	−	0.800642i	$-0.295508\pi$
$954$		0			0
$955$	12.7279	−	12.7279i	0.411866	−	0.411866i
$956$		0			0
$957$	1.93288	+	1.93288i	0.0624810	+	0.0624810i
$958$		0			0
$959$	−3.15038			−0.101731
$960$		0			0
$961$	13.0000			0.419355
$962$		0			0
$963$	−60.8496	+	60.8496i	−1.96085	+	1.96085i
$964$		0			0
$965$	9.00000	+	9.00000i	0.289720	+	0.289720i
$966$		0			0
$967$	−7.36584			−0.236870			−0.118435	−	0.992962i	$-0.537788\pi$
$967$	−7.36584			−0.236870			−0.118435	+	0.992962i	$0.537788\pi$
$968$		0			0
$969$	−57.8410			−1.85812
$970$		0			0
$971$	15.7916	+	15.7916i	0.506775	+	0.506775i	0.913535	−	0.406760i	$-0.133341\pi$
$971$	15.7916	+	15.7916i	0.506775	+	0.506775i	−0.406760	+	0.913535i	$0.633341\pi$
$972$		0			0
$973$	−0.554108	−	0.554108i	−0.0177639	−	0.0177639i
$974$		0			0
$975$	17.2665	−	40.4935i	0.552971	−	1.29683i
$976$		0			0
$977$			9.97038i			0.318981i	0.987199	+	0.159490i	$0.0509851\pi$
$977$			9.97038i			0.318981i	−0.987199	+	0.159490i	$0.949015\pi$
$978$		0			0
$979$	19.8997	−	19.8997i	0.635999	−	0.635999i
$980$		0			0
$981$	−14.8138	+	14.8138i	−0.472968	+	0.472968i
$982$		0			0
$983$	51.5834			1.64525			0.822627	−	0.568582i	$-0.192508\pi$
$983$	51.5834			1.64525			0.822627	+	0.568582i	$0.192508\pi$
$984$		0			0
$985$			4.05013i			0.129048i
$986$		0			0
$987$	5.10819	+	5.10819i	0.162595	+	0.162595i
$988$		0			0
$989$	34.5831	−	34.5831i	1.09968	−	1.09968i
$990$		0			0
$991$	−20.9499			−0.665495			−0.332747	−	0.943016i	$-0.607976\pi$
$991$	−20.9499			−0.665495			−0.332747	+	0.943016i	$0.607976\pi$
$992$		0			0
$993$		−	23.1461i		−	0.734519i
$994$		0			0
$995$	−12.7279	−	12.7279i	−0.403502	−	0.403502i
$996$		0			0
$997$	40.9499	+	40.9499i	1.29690	+	1.29690i	0.930433	+	0.366463i	$0.119431\pi$
$997$	40.9499	+	40.9499i	1.29690	+	1.29690i	0.366463	+	0.930433i	$0.380569\pi$
$998$		0			0
$999$	−94.3158			−2.98402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.p.a.753.2		8
4.3	odd	2		208.2.p.a.181.4	yes	8
13.12	even	2	inner	832.2.p.a.753.1		8
16.3	odd	4		208.2.p.a.77.4	yes	8
16.13	even	4	inner	832.2.p.a.337.1		8
52.51	odd	2		208.2.p.a.181.2	yes	8
208.51	odd	4		208.2.p.a.77.2	✓	8
208.77	even	4	inner	832.2.p.a.337.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.p.a.77.2	✓	8	208.51	odd	4
208.2.p.a.77.4	yes	8	16.3	odd	4
208.2.p.a.181.2	yes	8	52.51	odd	2
208.2.p.a.181.4	yes	8	4.3	odd	2
832.2.p.a.337.1		8	16.13	even	4	inner
832.2.p.a.337.2		8	208.77	even	4	inner
832.2.p.a.753.1		8	13.12	even	2	inner
832.2.p.a.753.2		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.15831 + 2.15831i) q^{3} +(0.707107 - 0.707107i) q^{5} -0.223888 q^{7} -6.31662i q^{9} +(1.41421 - 1.41421i) q^{11} +(1.34521 + 3.34521i) q^{13} +3.05231i q^{15} +3.00000 q^{17} +(4.46653 + 4.46653i) q^{19} +(0.483219 - 0.483219i) q^{21} -6.31662i q^{23} +4.00000i q^{25} +(7.15831 + 7.15831i) q^{27} +(0.316625 - 0.316625i) q^{29} -4.24264i q^{31} +6.10463i q^{33} +(-0.158312 + 0.158312i) q^{35} +(-6.58785 + 6.58785i) q^{37} +(-10.1234 - 4.31662i) q^{39} +(5.47494 + 5.47494i) q^{43} +(-4.46653 - 4.46653i) q^{45} +10.5712i q^{47} -6.94987 q^{49} +(-6.47494 + 6.47494i) q^{51} +(3.63325 + 3.63325i) q^{53} -2.00000i q^{55} -19.2803 q^{57} +(-7.74273 + 7.74273i) q^{59} +(4.00000 - 4.00000i) q^{61} +1.41421i q^{63} +(3.31662 + 1.41421i) q^{65} +(-4.69042 - 4.69042i) q^{67} +(13.6332 + 13.6332i) q^{69} +0.671663 q^{71} +3.79487 q^{73} +(-8.63325 - 8.63325i) q^{75} +(-0.316625 + 0.316625i) q^{77} +10.9499 q^{79} -11.9499 q^{81} +(11.9854 + 11.9854i) q^{83} +(2.12132 - 2.12132i) q^{85} +1.36675i q^{87} +14.0712 q^{89} +(-0.301175 - 0.748950i) q^{91} +(9.15694 + 9.15694i) q^{93} +6.31662 q^{95} +8.48528i q^{97} +(-8.93306 - 8.93306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{13} + 24 q^{17} + 44 q^{27} - 24 q^{29} + 12 q^{35} + 4 q^{43} + 24 q^{49} - 12 q^{51} - 24 q^{53} + 32 q^{61} + 56 q^{69} - 16 q^{75} + 24 q^{77} + 8 q^{79} - 16 q^{81} - 44 q^{91}+ \cdots + 24 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^13 + 24 * q^17 + 44 * q^27 - 24 * q^29 + 12 * q^35 + 4 * q^43 + 24 * q^49 - 12 * q^51 - 24 * q^53 + 32 * q^61 + 56 * q^69 - 16 * q^75 + 24 * q^77 + 8 * q^79 - 16 * q^81 - 44 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more