LMFDB - Embedded newform 441.2.i.d.68.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(68,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.20
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.86894i q^{2} +(1.72324 + 0.174470i) q^{3} -1.49292 q^{4} +(-1.25287 - 2.17003i) q^{5} +(-0.326074 + 3.22063i) q^{6} +0.947692i q^{8} +(2.93912 + 0.601309i) q^{9} +(4.05565 - 2.34153i) q^{10} +(4.85803 + 2.80479i) q^{11} +(-2.57267 - 0.260471i) q^{12} +(-0.384312 - 0.221883i) q^{13} +(-1.78039 - 3.95807i) q^{15} -4.75703 q^{16} +(1.53885 + 2.66536i) q^{17} +(-1.12381 + 5.49303i) q^{18} +(2.22932 + 1.28710i) q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(-0.165344 + 1.63310i) q^{24} +(-0.639351 + 1.10739i) q^{25} +(0.414685 - 0.718255i) q^{26} +(4.95990 + 1.54899i) q^{27} +(2.71041 - 1.56485i) q^{29} +(7.39739 - 3.32743i) q^{30} -10.4669i q^{31} -6.99520i q^{32} +(7.88221 + 5.68091i) q^{33} +(-4.98140 + 2.87601i) q^{34} +(-4.38788 - 0.897709i) q^{36} +(0.708168 - 1.22658i) q^{37} +(-2.40550 + 4.16645i) q^{38} +(-0.623551 - 0.449409i) q^{39} +(2.05652 - 1.18733i) q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(-7.25268 - 4.18733i) q^{44} +(-2.37747 - 7.13134i) q^{45} +(-7.37492 - 12.7737i) q^{46} -2.14380 q^{47} +(-8.19750 - 0.829960i) q^{48} +(-2.06964 - 1.19491i) q^{50} +(2.18678 + 4.86155i) q^{51} +(0.573749 + 0.331254i) q^{52} +(4.20379 - 2.42706i) q^{53} +(-2.89496 + 9.26974i) q^{54} -14.0561i q^{55} +(3.61709 + 2.60693i) q^{57} +(2.92461 + 5.06558i) q^{58} -7.30991 q^{59} +(2.65798 + 5.90910i) q^{60} -8.55576i q^{61} +19.5619 q^{62} +3.55953 q^{64} +1.11196i q^{65} +(-10.6173 + 14.7314i) q^{66} -1.86888 q^{67} +(-2.29739 - 3.97919i) q^{68} +(-12.4664 + 5.60753i) q^{69} +2.95338i q^{71} +(-0.569856 + 2.78538i) q^{72} +(-7.37804 + 4.25971i) q^{73} +(2.29241 + 1.32352i) q^{74} +(-1.29496 + 1.79675i) q^{75} +(-3.32820 - 1.92154i) q^{76} +(0.839916 - 1.16538i) q^{78} -0.574261 q^{79} +(5.95992 + 10.3229i) q^{80} +(8.27686 + 3.53464i) q^{81} +(-5.33036 - 3.07748i) q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(4.94370 - 2.22373i) q^{87} +(-2.65807 + 4.60392i) q^{88} +(-3.78929 + 6.56325i) q^{89} +(13.3280 - 4.44334i) q^{90} +(10.2038 - 5.89115i) q^{92} +(1.82616 - 18.0369i) q^{93} -4.00663i q^{94} -6.45024i q^{95} +(1.22045 - 12.0544i) q^{96} +(3.22662 - 1.86289i) q^{97} +(12.5918 + 11.1648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.86894i			1.32154i	0.750589	+	0.660769i	$0.229770\pi$
$2$			1.86894i			1.32154i	−0.750589	+	0.660769i	$0.770230\pi$
$3$	1.72324	+	0.174470i	0.994914	+	0.100730i
$3$	1.72324	+	0.174470i	0.994914	+	0.100730i
$4$	−1.49292			−0.746462
$5$	−1.25287	−	2.17003i	−0.560299	−	0.970467i	−0.997470	−	0.0710881i	$-0.977353\pi$
$5$	−1.25287	−	2.17003i	−0.560299	−	0.970467i	0.437171	−	0.899378i	$-0.355980\pi$
$6$	−0.326074	+	3.22063i	−0.133119	+	1.31482i
$7$		0			0
$7$		0			0
$8$			0.947692i			0.335060i
$9$	2.93912	+	0.601309i	0.979707	+	0.200436i
$10$	4.05565	−	2.34153i	1.28251	−	0.740457i
$11$	4.85803	+	2.80479i	1.46475	+	0.845675i	0.999225	−	0.0393590i	$-0.0125316\pi$
$11$	4.85803	+	2.80479i	1.46475	+	0.845675i	0.465527	+	0.885034i	$0.345865\pi$
$12$	−2.57267	−	0.260471i	−0.742666	−	0.0751915i
$13$	−0.384312	−	0.221883i	−0.106589	−	0.0615392i	0.445758	−	0.895154i	$-0.352934\pi$
$13$	−0.384312	−	0.221883i	−0.106589	−	0.0615392i	−0.552347	+	0.833614i	$0.686268\pi$
$14$		0			0
$15$	−1.78039	−	3.95807i	−0.459694	−	1.02197i
$16$	−4.75703			−1.18926
$17$	1.53885	+	2.66536i	0.373226	+	0.646446i	0.990060	−	0.140647i	$-0.0449184\pi$
$17$	1.53885	+	2.66536i	0.373226	+	0.646446i	−0.616834	+	0.787093i	$0.711585\pi$
$18$	−1.12381	+	5.49303i	−0.264884	+	1.29472i
$19$	2.22932	+	1.28710i	0.511440	+	0.295280i	0.733425	−	0.679770i	$-0.237920\pi$
$19$	2.22932	+	1.28710i	0.511440	+	0.295280i	−0.221985	+	0.975050i	$0.571254\pi$
$20$	1.87044	+	3.23969i	0.418242	+	0.724417i
$21$		0			0
$22$	−5.24197	+	9.07935i	−1.11759	+	1.93572i
$23$	−6.83476	+	3.94605i	−1.42515	+	0.822808i	−0.996732	−	0.0807749i	$-0.974261\pi$
$23$	−6.83476	+	3.94605i	−1.42515	+	0.822808i	−0.428413	+	0.903583i	$0.640927\pi$
$24$	−0.165344	+	1.63310i	−0.0337507	+	0.333355i
$25$	−0.639351	+	1.10739i	−0.127870	+	0.221478i
$26$	0.414685	−	0.718255i	0.0813264	−	0.140861i
$27$	4.95990	+	1.54899i	0.954534	+	0.298103i
$28$		0			0
$29$	2.71041	−	1.56485i	0.503310	−	0.290586i	−0.226770	−	0.973948i	$-0.572816\pi$
$29$	2.71041	−	1.56485i	0.503310	−	0.290586i	0.730079	+	0.683362i	$0.239483\pi$
$30$	7.39739	−	3.32743i	1.35057	−	0.607503i
$31$		−	10.4669i		−	1.87990i	−0.341306	−	0.939952i	$-0.610869\pi$
$31$		−	10.4669i		−	1.87990i	0.341306	−	0.939952i	$-0.389131\pi$
$32$		−	6.99520i		−	1.23659i
$33$	7.88221	+	5.68091i	1.37212	+	0.988919i
$34$	−4.98140	+	2.87601i	−0.854303	+	0.493232i
$35$		0			0
$36$	−4.38788	−	0.897709i	−0.731314	−	0.149618i
$37$	0.708168	−	1.22658i	0.116422	−	0.201649i	−0.801925	−	0.597424i	$-0.796191\pi$
$37$	0.708168	−	1.22658i	0.116422	−	0.201649i	0.918347	+	0.395775i	$0.129524\pi$
$38$	−2.40550	+	4.16645i	−0.390224	+	0.675887i
$39$	−0.623551	−	0.449409i	−0.0998480	−	0.0719630i
$40$	2.05652	−	1.18733i	0.325164	−	0.187734i
$41$	−1.64665	+	2.85208i	−0.257163	+	0.445420i	−0.965481	−	0.260474i	$-0.916121\pi$
$41$	−1.64665	+	2.85208i	−0.257163	+	0.445420i	0.708318	+	0.705894i	$0.249455\pi$
$42$		0			0
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	−0.958810	−	0.284049i	$-0.908322\pi$
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	0.233411	−	0.972378i	$-0.425011\pi$
$44$	−7.25268	−	4.18733i	−1.09338	−	0.631264i
$45$	−2.37747	−	7.13134i	−0.354412	−	1.06308i
$46$	−7.37492	−	12.7737i	−1.08737	−	1.88338i
$47$	−2.14380			−0.312706			−0.156353	−	0.987701i	$-0.549974\pi$
$47$	−2.14380			−0.312706			−0.156353	+	0.987701i	$0.549974\pi$
$48$	−8.19750	−	0.829960i	−1.18321	−	0.119794i
$49$		0			0
$50$	−2.06964	−	1.19491i	−0.292691	−	0.168985i
$51$	2.18678	+	4.86155i	0.306211	+	0.680753i
$52$	0.573749	+	0.331254i	0.0795647	+	0.0459367i
$53$	4.20379	−	2.42706i	0.577435	−	0.333382i	−0.182678	−	0.983173i	$-0.558477\pi$
$53$	4.20379	−	2.42706i	0.577435	−	0.333382i	0.760113	+	0.649791i	$0.225143\pi$
$54$	−2.89496	+	9.26974i	−0.393955	+	1.26145i
$55$		−	14.0561i		−	1.89532i
$56$		0			0
$57$	3.61709	+	2.60693i	0.479095	+	0.345296i
$58$	2.92461	+	5.06558i	0.384020	+	0.665143i
$59$	−7.30991			−0.951669			−0.475835	−	0.879535i	$-0.657854\pi$
$59$	−7.30991			−0.951669			−0.475835	+	0.879535i	$0.657854\pi$
$60$	2.65798	+	5.90910i	0.343144	+	0.762862i
$61$		−	8.55576i		−	1.09545i	−0.836658	−	0.547726i	$-0.815494\pi$
$61$		−	8.55576i		−	1.09545i	0.836658	−	0.547726i	$-0.184506\pi$
$62$	19.5619			2.48437
$63$		0			0
$64$	3.55953			0.444941
$65$			1.11196i			0.137921i
$66$	−10.6173	+	14.7314i	−1.30689	+	1.81330i
$67$	−1.86888			−0.228321			−0.114160	−	0.993462i	$-0.536418\pi$
$67$	−1.86888			−0.228321			−0.114160	+	0.993462i	$0.536418\pi$
$68$	−2.29739	−	3.97919i	−0.278599	−	0.482548i
$69$	−12.4664	+	5.60753i	−1.50078	+	0.675067i
$70$		0			0
$71$			2.95338i			0.350501i	0.984524	+	0.175251i	$0.0560736\pi$
$71$			2.95338i			0.350501i	−0.984524	+	0.175251i	$0.943926\pi$
$72$	−0.569856	+	2.78538i	−0.0671581	+	0.328260i
$73$	−7.37804	+	4.25971i	−0.863534	+	0.498562i	−0.865194	−	0.501437i	$-0.832805\pi$
$73$	−7.37804	+	4.25971i	−0.863534	+	0.498562i	0.00165984	+	0.999999i	$0.499472\pi$
$74$	2.29241	+	1.32352i	0.266487	+	0.153856i
$75$	−1.29496	+	1.79675i	−0.149529	+	0.207471i
$76$	−3.32820	−	1.92154i	−0.381771	−	0.220415i
$77$		0			0
$78$	0.839916	−	1.16538i	0.0951018	−	0.131953i
$79$	−0.574261			−0.0646094			−0.0323047	−	0.999478i	$-0.510285\pi$
$79$	−0.574261			−0.0646094			−0.0323047	+	0.999478i	$0.510285\pi$
$80$	5.95992	+	10.3229i	0.666339	+	1.15413i
$81$	8.27686	+	3.53464i	0.919651	+	0.392738i
$82$	−5.33036	−	3.07748i	−0.588639	−	0.339851i
$83$	−4.23521	−	7.33560i	−0.464875	−	0.805186i	0.534321	−	0.845281i	$-0.320567\pi$
$83$	−4.23521	−	7.33560i	−0.464875	−	0.805186i	−0.999196	+	0.0400951i	$0.987234\pi$
$84$		0			0
$85$	3.85595	−	6.67870i	0.418236	−	0.724406i
$86$	15.3981	−	8.89008i	1.66042	−	0.958642i
$87$	4.94370	−	2.22373i	0.530021	−	0.238409i
$88$	−2.65807	+	4.60392i	−0.283352	+	0.490779i
$89$	−3.78929	+	6.56325i	−0.401664	+	0.695703i	−0.993927	−	0.110042i	$-0.964901\pi$
$89$	−3.78929	+	6.56325i	−0.401664	+	0.695703i	0.592263	+	0.805745i	$0.298235\pi$
$90$	13.3280	−	4.44334i	1.40490	−	0.468369i
$91$		0			0
$92$	10.2038	−	5.89115i	1.06382	−	0.614195i
$93$	1.82616	−	18.0369i	0.189364	−	1.87034i
$94$		−	4.00663i		−	0.413252i
$95$		−	6.45024i		−	0.661781i
$96$	1.22045	−	12.0544i	0.124562	−	1.23030i
$97$	3.22662	−	1.86289i	0.327614	−	0.189148i	−0.327167	−	0.944966i	$-0.606094\pi$
$97$	3.22662	−	1.86289i	0.327614	−	0.189148i	0.654781	+	0.755818i	$0.272761\pi$
$98$		0			0
$99$	12.5918	+	11.1648i	1.26552	+	1.12210i
$100$	0.954503	−	1.65325i	0.0954503	−	0.165325i
$101$	3.76725	−	6.52506i	0.374855	−	0.649268i	−0.615450	−	0.788176i	$-0.711026\pi$
$101$	3.76725	−	6.52506i	0.374855	−	0.649268i	0.990305	+	0.138908i	$0.0443592\pi$
$102$	−9.08593	+	4.08696i	−0.899641	+	0.404669i
$103$	−12.4045	+	7.16173i	−1.22225	+	0.705666i	−0.965397	−	0.260784i	$-0.916019\pi$
$103$	−12.4045	+	7.16173i	−1.22225	+	0.705666i	−0.256853	+	0.966451i	$0.582685\pi$
$104$	0.210276	−	0.364210i	0.0206193	−	0.0357137i
$105$		0			0
$106$	4.53602	+	7.85662i	0.440577	+	0.763102i
$107$	−11.6798	−	6.74331i	−1.12912	−	0.651900i	−0.185410	−	0.982661i	$-0.559361\pi$
$107$	−11.6798	−	6.74331i	−1.12912	−	0.651900i	−0.943715	+	0.330761i	$0.892695\pi$
$108$	−7.40476	−	2.31252i	−0.712523	−	0.222523i
$109$	0.459348	+	0.795613i	0.0439975	+	0.0762059i	0.887186	−	0.461413i	$-0.152657\pi$
$109$	0.459348	+	0.795613i	0.0439975	+	0.0762059i	−0.843188	+	0.537619i	$0.819324\pi$
$110$	26.2700			2.50474
$111$	1.43435	−	1.99014i	0.136142	−	0.188896i
$112$		0			0
$113$	4.10412	+	2.36952i	0.386083	+	0.222905i	0.680462	−	0.732784i	$-0.261779\pi$
$113$	4.10412	+	2.36952i	0.386083	+	0.222905i	−0.294378	+	0.955689i	$0.595113\pi$
$114$	−4.87218	+	6.76011i	−0.456321	+	0.633142i
$115$	17.1261	+	9.88775i	1.59702	+	0.922037i
$116$	−4.04643	+	2.33621i	−0.375702	+	0.216912i
$117$	−0.996120	−	0.883231i	−0.0920913	−	0.0816547i
$118$		−	13.6618i		−	1.25767i
$119$		0			0
$120$	3.75103	−	1.68726i	0.342421	−	0.154025i
$121$	10.2337	+	17.7252i	0.930332	+	1.61138i
$122$	15.9902			1.44768
$123$	−3.33518	+	4.62753i	−0.300723	+	0.417250i
$124$			15.6262i			1.40328i
$125$	−9.32458			−0.834016
$126$		0			0
$127$	7.37245			0.654200			0.327100	−	0.944990i	$-0.393929\pi$
$127$	7.37245			0.654200			0.327100	+	0.944990i	$0.393929\pi$
$128$		−	7.33786i		−	0.648581i
$129$	−6.75959	−	15.0276i	−0.595148	−	1.32311i
$130$	−2.07818			−0.182268
$131$	−3.93150	−	6.80955i	−0.343497	−	0.594953i	0.641583	−	0.767054i	$-0.278278\pi$
$131$	−3.93150	−	6.80955i	−0.343497	−	0.594953i	−0.985079	+	0.172100i	$0.944945\pi$
$132$	−11.7675	−	8.48116i	−1.02423	−	0.738191i
$133$		0			0
$134$		−	3.49283i		−	0.301734i
$135$	−2.85275	−	12.7038i	−0.245525	−	1.09337i
$136$	−2.52594	+	1.45835i	−0.216598	+	0.125053i
$137$	10.0198	+	5.78491i	0.856046	+	0.494238i	0.862686	−	0.505740i	$-0.168780\pi$
$137$	10.0198	+	5.78491i	0.856046	+	0.494238i	−0.00664016	+	0.999978i	$0.502114\pi$
$138$	−10.4801	−	23.2989i	−0.892127	−	1.98334i
$139$	16.9741	+	9.79999i	1.43972	+	0.831224i	0.997830	−	0.0658437i	$-0.0209739\pi$
$139$	16.9741	+	9.79999i	1.43972	+	0.831224i	0.441893	+	0.897068i	$0.354307\pi$
$140$		0			0
$141$	−3.69429	−	0.374030i	−0.311115	−	0.0314990i
$142$	−5.51968			−0.463201
$143$	−1.24467	−	2.15583i	−0.104084	−	0.180279i
$144$	−13.9815	−	2.86044i	−1.16512	−	0.238370i
$145$	−6.79156	−	3.92111i	−0.564008	−	0.325630i
$146$	−7.96114	−	13.7891i	−0.658868	−	1.14119i
$147$		0			0
$148$	−1.05724	+	1.83120i	−0.0869047	+	0.150523i
$149$	13.6315	−	7.87012i	1.11673	−	0.644746i	0.176167	−	0.984360i	$-0.443630\pi$
$149$	13.6315	−	7.87012i	1.11673	−	0.644746i	0.940565	+	0.339615i	$0.110297\pi$
$150$	−3.35801	−	2.42020i	−0.274181	−	0.197609i
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	−0.822865	−	0.568237i	$-0.807626\pi$
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	0.903540	+	0.428503i	$0.140959\pi$
$152$	−1.21977	+	2.11270i	−0.0989364	+	0.171363i
$153$	2.92015	+	8.75915i	0.236081	+	0.708135i
$154$		0			0
$155$	−22.7134	+	13.1136i	−1.82438	+	1.05331i
$156$	0.930914	+	0.670933i	0.0745328	+	0.0537176i
$157$			8.39224i			0.669774i	0.942258	+	0.334887i	$0.108698\pi$
$157$			8.39224i			0.669774i	−0.942258	+	0.334887i	$0.891302\pi$
$158$		−	1.07326i		−	0.0853837i
$159$	7.66759	−	3.44897i	0.608080	−	0.273521i
$160$	−15.1798	+	8.76405i	−1.20007	+	0.692859i
$161$		0			0
$162$	−6.60602	+	15.4689i	−0.519018	+	1.21535i
$163$	0.537054	−	0.930204i	0.0420653	−	0.0728592i	−0.844226	−	0.535987i	$-0.819940\pi$
$163$	0.537054	−	0.930204i	0.0420653	−	0.0728592i	0.886291	+	0.463128i	$0.153273\pi$
$164$	2.45832	−	4.25794i	0.191963	−	0.332489i
$165$	2.45237	−	24.2220i	0.190917	−	1.88568i
$166$	13.7098	−	7.91534i	1.06408	−	0.614349i
$167$	3.99731	−	6.92354i	0.309321	−	0.535760i	−0.668893	−	0.743359i	$-0.733232\pi$
$167$	3.99731	−	6.92354i	0.309321	−	0.535760i	0.978214	+	0.207599i	$0.0665649\pi$
$168$		0			0
$169$	−6.40154	−	11.0878i	−0.492426	−	0.852907i
$170$	12.4821	+	7.20652i	0.957330	+	0.552715i
$171$	5.77828	+	5.12344i	0.441876	+	0.391799i
$172$	7.10148	+	12.3001i	0.541483	+	0.937875i
$173$	−1.00349			−0.0762938			−0.0381469	−	0.999272i	$-0.512145\pi$
$173$	−1.00349			−0.0762938			−0.0381469	+	0.999272i	$0.512145\pi$
$174$	4.15602	+	9.23947i	0.315067	+	0.700442i
$175$		0			0
$176$	−23.1098	−	13.3424i	−1.74197	−	1.00572i
$177$	−12.5967	−	1.27536i	−0.946829	−	0.0958621i
$178$	−12.2663	−	7.08195i	−0.919398	−	0.530814i
$179$	−1.27773	+	0.737695i	−0.0955017	+	0.0551379i	−0.546990	−	0.837139i	$-0.684227\pi$
$179$	−1.27773	+	0.737695i	−0.0955017	+	0.0551379i	0.451489	+	0.892277i	$0.350893\pi$
$180$	3.54938	+	10.6465i	0.264555	+	0.793547i
$181$			15.0440i			1.11821i	0.829096	+	0.559106i	$0.188855\pi$
$181$			15.0440i			1.11821i	−0.829096	+	0.559106i	$0.811145\pi$
$182$		0			0
$183$	1.49273	−	14.7436i	0.110345	−	1.08988i
$184$	−3.73964	−	6.47724i	−0.275690	−	0.477509i
$185$	−3.54896			−0.260925
$186$	33.7099	+	3.41297i	2.47173	+	0.250251i
$187$			17.2646i			1.26251i
$188$	3.20054			0.233423
$189$		0			0
$190$	12.0551			0.874568
$191$			13.2237i			0.956836i	0.878132	+	0.478418i	$0.158790\pi$
$191$			13.2237i			0.956836i	−0.878132	+	0.478418i	$0.841210\pi$
$192$	6.13392	+	0.621032i	0.442678	+	0.0448191i
$193$	−1.55571			−0.111982			−0.0559912	−	0.998431i	$-0.517832\pi$
$193$	−1.55571			−0.111982			−0.0559912	+	0.998431i	$0.517832\pi$
$194$	3.48163	+	6.03035i	0.249966	+	0.432954i
$195$	−0.194004	+	1.91617i	−0.0138929	+	0.137220i
$196$		0			0
$197$			4.96185i			0.353517i	0.984254	+	0.176759i	$0.0565612\pi$
$197$			4.96185i			0.353517i	−0.984254	+	0.176759i	$0.943439\pi$
$198$	−20.8663	+	23.5333i	−1.48290	+	1.67244i
$199$	−9.69273	+	5.59610i	−0.687100	+	0.396697i	−0.802525	−	0.596619i	$-0.796510\pi$
$199$	−9.69273	+	5.59610i	−0.687100	+	0.396697i	0.115425	+	0.993316i	$0.463177\pi$
$200$	−1.04946	−	0.605908i	−0.0742083	−	0.0428442i
$201$	−3.22054	−	0.326065i	−0.227159	−	0.0229988i
$202$	12.1949	+	7.04074i	0.858032	+	0.495385i
$203$		0			0
$204$	−3.26470	−	7.25793i	−0.228575	−	0.508157i
$205$	8.25213			0.576354
$206$	−13.3848	−	23.1832i	−0.932565	−	1.61525i
$207$	−22.4610	+	7.48811i	−1.56115	+	0.520460i
$208$	1.82818	+	1.05550i	0.126762	+	0.0731859i
$209$	7.22006	+	12.5055i	0.499422	+	0.865024i
$210$		0			0
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	−0.470708	−	0.882289i	$-0.656001\pi$
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	0.999439	−	0.0334999i	$-0.0106654\pi$
$212$	−6.27594	+	3.62342i	−0.431033	+	0.248857i
$213$	−0.515277	+	5.08938i	−0.0353062	+	0.348719i
$214$	12.6028	−	21.8287i	0.861511	−	1.49218i
$215$	−11.9192	+	20.6446i	−0.812880	+	1.40795i
$216$	−1.46796	+	4.70046i	−0.0998824	+	0.319826i
$217$		0			0
$218$	−1.48695	+	0.858492i	−0.100709	+	0.0581444i
$219$	−13.4573	+	6.05327i	−0.909363	+	0.409042i
$220$			20.9847i			1.41479i
$221$		−	1.36578i		−	0.0918721i
$222$	3.71945	+	2.68070i	0.249633	+	0.179917i
$223$	−2.76845	+	1.59837i	−0.185389	+	0.107034i	−0.589822	−	0.807533i	$-0.700802\pi$
$223$	−2.76845	+	1.59837i	−0.185389	+	0.107034i	0.404433	+	0.914568i	$0.367469\pi$
$224$		0			0
$225$	−2.54501	+	2.87030i	−0.169668	+	0.191353i
$226$	−4.42848	+	7.67035i	−0.294578	+	0.510224i
$227$	−7.33494	+	12.7045i	−0.486837	+	0.843227i	−0.999885	−	0.0151329i	$-0.995183\pi$
$227$	−7.33494	+	12.7045i	−0.486837	+	0.843227i	0.513048	+	0.858360i	$0.328516\pi$
$228$	−5.40004	−	3.89194i	−0.357626	−	0.257750i
$229$	−2.92550	+	1.68904i	−0.193322	+	0.111615i	−0.593537	−	0.804807i	$-0.702269\pi$
$229$	−2.92550	+	1.68904i	−0.193322	+	0.111615i	0.400215	+	0.916421i	$0.368936\pi$
$230$	−18.4796	+	32.0076i	−1.21851	+	2.11052i
$231$		0			0
$232$	1.48300	+	2.56863i	0.0973637	+	0.168639i
$233$	−4.22628	−	2.44005i	−0.276873	−	0.159853i	0.355134	−	0.934815i	$-0.384435\pi$
$233$	−4.22628	−	2.44005i	−0.276873	−	0.159853i	−0.632007	+	0.774963i	$0.717769\pi$
$234$	1.65070	−	1.86168i	0.107910	−	0.121702i
$235$	2.68590	+	4.65211i	0.175209	+	0.303470i
$236$	10.9131			0.710385
$237$	−0.989589	−	0.100191i	−0.0642807	−	0.00650813i
$238$		0			0
$239$	13.6253	+	7.86657i	0.881347	+	0.508846i	0.871102	−	0.491101i	$-0.163406\pi$
$239$	13.6253	+	7.86657i	0.881347	+	0.508846i	0.0102448	+	0.999948i	$0.496739\pi$
$240$	8.46934	+	18.8286i	0.546694	+	1.21538i
$241$	0.666305	+	0.384691i	0.0429205	+	0.0247801i	0.521307	−	0.853369i	$-0.325445\pi$
$241$	0.666305	+	0.384691i	0.0429205	+	0.0247801i	−0.478386	+	0.878150i	$0.658778\pi$
$242$	−33.1273	+	19.1260i	−2.12950	+	1.22947i
$243$	13.6463	+	7.53510i	0.875412	+	0.483377i
$244$			12.7731i			0.817714i
$245$		0			0
$246$	−8.64856	−	6.23323i	−0.551412	−	0.397416i
$247$	−0.571169	−	0.989293i	−0.0363426	−	0.0629472i
$248$	9.91936			0.629880
$249$	−6.01844	−	13.3799i	−0.381403	−	0.847918i
$250$		−	17.4271i		−	1.10218i
$251$	1.14544			0.0722996			0.0361498	−	0.999346i	$-0.488491\pi$
$251$	1.14544			0.0722996			0.0361498	+	0.999346i	$0.488491\pi$
$252$		0			0
$253$	−44.2713			−2.78331
$254$			13.7787i			0.864549i
$255$	7.80996	−	10.8363i	0.489079	−	0.678593i
$256$	20.8331			1.30207
$257$	−14.4917	−	25.1004i	−0.903969	−	1.56572i	−0.822295	−	0.569061i	$-0.807307\pi$
$257$	−14.4917	−	25.1004i	−0.903969	−	1.56572i	−0.0816738	−	0.996659i	$-0.526027\pi$
$258$	28.0856	−	12.6332i	1.74853	−	0.786511i
$259$		0			0
$260$		−	1.66007i		−	0.102953i
$261$	8.90717	−	2.96950i	0.551340	−	0.183808i
$262$	12.7266	−	7.34772i	0.786254	−	0.453944i
$263$	−11.8643	−	6.84988i	−0.731586	−	0.422381i	0.0874160	−	0.996172i	$-0.472139\pi$
$263$	−11.8643	−	6.84988i	−0.731586	−	0.422381i	−0.819002	+	0.573790i	$0.805472\pi$
$264$	−5.38375	+	7.46991i	−0.331347	+	0.459741i
$265$	−10.5336	−	6.08156i	−0.647072	−	0.373587i
$266$		0			0
$267$	−7.67496	+	10.6489i	−0.469700	+	0.651704i
$268$	2.79010			0.170433
$269$	−5.23973	−	9.07548i	−0.319472	−	0.553342i	0.660906	−	0.750469i	$-0.270172\pi$
$269$	−5.23973	−	9.07548i	−0.319472	−	0.553342i	−0.980378	+	0.197127i	$0.936839\pi$
$270$	23.7426	−	5.33160i	1.44493	−	0.324471i
$271$	5.66907	+	3.27304i	0.344371	+	0.198823i	0.662203	−	0.749324i	$-0.269621\pi$
$271$	5.66907	+	3.27304i	0.344371	+	0.198823i	−0.317832	+	0.948147i	$0.602955\pi$
$272$	−7.32034	−	12.6792i	−0.443861	−	0.768790i
$273$		0			0
$274$	−10.8116	+	18.7263i	−0.653155	+	1.13130i
$275$	−6.21198	+	3.58649i	−0.374596	+	0.216273i
$276$	18.6114	−	8.37162i	1.12027	−	0.503912i
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	0.302911	+	0.953019i	$0.402041\pi$
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	−0.976794	+	0.214181i	$0.931292\pi$
$278$	−18.3156	+	31.7235i	−1.09849	+	1.90265i
$279$	6.29382	−	30.7634i	0.376801	−	1.84176i
$280$		0			0
$281$	19.3552	−	11.1747i	1.15463	−	0.666627i	0.204621	−	0.978841i	$-0.434404\pi$
$281$	19.3552	−	11.1747i	1.15463	−	0.666627i	0.950012	+	0.312214i	$0.101071\pi$
$282$	0.699038	−	6.90439i	0.0416271	−	0.411151i
$283$		−	18.9713i		−	1.12772i	−0.825869	−	0.563862i	$-0.809315\pi$
$283$		−	18.9713i		−	1.12772i	0.825869	−	0.563862i	$-0.190685\pi$
$284$		−	4.40917i		−	0.261636i
$285$	1.12538	−	11.1153i	0.0666615	−	0.658415i
$286$	4.02910	−	2.32620i	0.238246	−	0.137551i
$287$		0			0
$288$	4.20627	−	20.5597i	0.247857	−	1.21149i
$289$	3.76389	−	6.51924i	0.221405	−	0.383485i
$290$	7.32830	−	12.6930i	0.430333	−	0.745358i
$291$	5.88527	−	2.64726i	0.345000	−	0.155185i
$292$	11.0149	−	6.35943i	0.644596	−	0.372158i
$293$	−4.41136	+	7.64069i	−0.257714	+	0.446374i	−0.965629	−	0.259924i	$-0.916303\pi$
$293$	−4.41136	+	7.64069i	−0.257714	+	0.446374i	0.707915	+	0.706298i	$0.249636\pi$
$294$		0			0
$295$	9.15835	+	15.8627i	0.533220	+	0.923563i
$296$	1.16242	+	0.671125i	0.0675644	+	0.0390083i
$297$	19.7508	+	21.4365i	1.14606	+	1.24387i
$298$	14.7088	+	25.4763i	0.852056	+	1.47580i
$299$	3.50224			0.202540
$300$	1.93328	−	2.68241i	0.111618	−	0.154869i
$301$		0			0
$302$	3.20910	+	1.85278i	0.184663	+	0.106615i
$303$	7.63030	−	10.5870i	0.438349	−	0.608206i
$304$	−10.6049	−	6.12275i	−0.608233	−	0.351164i
$305$	−18.5662	+	10.7192i	−1.06310	+	0.613781i
$306$	−16.3703	+	5.45758i	−0.935828	+	0.311989i
$307$			28.7533i			1.64104i	0.571620	+	0.820519i	$0.306315\pi$
$307$			28.7533i			1.64104i	−0.571620	+	0.820519i	$0.693685\pi$
$308$		0			0
$309$	−22.6254	+	10.1772i	−1.28712	+	0.578959i
$310$	−24.5085	−	42.4499i	−1.39199	−	2.41099i
$311$	−13.2859			−0.753373			−0.376687	−	0.926341i	$-0.622937\pi$
$311$	−13.2859			−0.753373			−0.376687	+	0.926341i	$0.622937\pi$
$312$	0.425901	−	0.590934i	0.0241119	−	0.0334550i
$313$		−	31.5495i		−	1.78329i	−0.452740	−	0.891643i	$-0.649553\pi$
$313$		−	31.5495i		−	1.78329i	0.452740	−	0.891643i	$-0.350447\pi$
$314$	−15.6846			−0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$			20.0709i			1.12729i	0.826016	+	0.563646i	$0.190602\pi$
$317$			20.0709i			1.12729i	−0.826016	+	0.563646i	$0.809398\pi$
$318$	6.44591	+	14.3302i	0.361469	+	0.803600i
$319$	17.5563			0.982965
$320$	−4.45961	−	7.72428i	−0.249300	−	0.431800i
$321$	−18.9505	−	13.6581i	−1.05772	−	0.762322i
$322$		0			0
$323$			7.92259i			0.440824i
$324$	−12.3567	−	5.27695i	−0.686484	−	0.293164i
$325$	0.491421	−	0.283722i	0.0272591	−	0.0157381i
$326$	1.73849	+	1.00372i	0.0962862	+	0.0555909i
$327$	0.652756	+	1.45118i	0.0360975	+	0.0802502i
$328$	−2.70289	−	1.56052i	−0.149242	−	0.0861651i
$329$		0			0
$330$	45.2695	+	4.58333i	2.49200	+	0.252304i
$331$	1.24791			0.0685915			0.0342958	−	0.999412i	$-0.489081\pi$
$331$	1.24791			0.0685915			0.0342958	+	0.999412i	$0.489081\pi$
$332$	6.32285	+	10.9515i	0.347011	+	0.601041i
$333$	2.81895	−	3.17925i	0.154477	−	0.174222i
$334$	12.9397	+	7.47072i	0.708027	+	0.408780i
$335$	2.34146	+	4.05553i	0.127928	+	0.221577i
$336$		0			0
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	−0.628926	−	0.777465i	$-0.716505\pi$
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	0.987768	+	0.155933i	$0.0498385\pi$
$338$	20.7224	−	11.9641i	1.12715	−	0.650759i
$339$	6.65898	+	4.79930i	0.361666	+	0.260662i
$340$	−5.75664	+	9.97079i	−0.312198	+	0.540742i
$341$	29.3573	−	50.8484i	1.58979	−	2.75359i
$342$	−9.57538	+	10.7992i	−0.517777	+	0.583956i
$343$		0			0
$344$	7.80798	−	4.50794i	0.420978	−	0.243052i
$345$	27.7873	+	20.0270i	1.49602	+	1.07822i
$346$		−	1.87545i		−	0.100825i
$347$			27.0675i			1.45306i	0.687136	+	0.726529i	$0.258868\pi$
$347$			27.0675i			1.45306i	−0.687136	+	0.726529i	$0.741132\pi$
$348$	−7.38058	+	3.31987i	−0.395640	+	0.177964i
$349$	30.3413	−	17.5176i	1.62413	−	0.937694i	0.638336	−	0.769758i	$-0.279623\pi$
$349$	30.3413	−	17.5176i	1.62413	−	0.937694i	0.985798	−	0.167936i	$-0.0537101\pi$
$350$		0			0
$351$	−1.56246	−	1.69581i	−0.0833978	−	0.0905158i
$352$	19.6200	−	33.9829i	1.04575	−	1.81129i
$353$	1.26256	−	2.18682i	0.0671992	−	0.116392i	−0.830468	−	0.557066i	$-0.811927\pi$
$353$	1.26256	−	2.18682i	0.0671992	−	0.116392i	0.897667	+	0.440674i	$0.145260\pi$
$354$	2.38357	−	23.5425i	0.126685	−	1.25127i
$355$	6.40892	−	3.70019i	0.340150	−	0.196386i
$356$	5.65713	−	9.79843i	0.299827	−	0.519316i
$357$		0			0
$358$	−1.37871	−	2.38799i	−0.0728669	−	0.126209i
$359$	−6.29395	−	3.63381i	−0.332182	−	0.191785i	0.324628	−	0.945842i	$-0.394761\pi$
$359$	−6.29395	−	3.63381i	−0.332182	−	0.191785i	−0.656809	+	0.754057i	$0.728094\pi$
$360$	6.75831	−	2.25311i	0.356194	−	0.118749i
$361$	−6.18677	−	10.7158i	−0.325619	−	0.563989i
$362$	−28.1163			−1.47776
$363$	14.5425	+	32.3303i	0.763285	+	1.69690i
$364$		0			0
$365$	18.4874	+	10.6737i	0.967675	+	0.558688i
$366$	27.5549	+	2.78981i	1.44032	+	0.145826i
$367$	11.6714	+	6.73848i	0.609242	+	0.351746i	0.772669	−	0.634809i	$-0.218921\pi$
$367$	11.6714	+	6.73848i	0.609242	+	0.351746i	−0.163427	+	0.986555i	$0.552255\pi$
$368$	32.5131	−	18.7715i	1.69486	−	0.978530i
$369$	−6.55468	+	7.39246i	−0.341223	+	0.384836i
$370$		−	6.63278i		−	0.344822i
$371$		0			0
$372$	−2.72632	+	26.9278i	−0.141353	+	1.39614i
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	−0.990345	−	0.138624i	$-0.955732\pi$
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	0.375121	−	0.926976i	$-0.377601\pi$
$374$	−32.2664			−1.66846
$375$	−16.0685	−	1.62686i	−0.829774	−	0.0840108i
$376$		−	2.03166i		−	0.104775i
$377$	−1.38886			−0.0715297
$378$		0			0
$379$	21.2283			1.09042			0.545211	−	0.838299i	$-0.316449\pi$
$379$	21.2283			1.09042			0.545211	+	0.838299i	$0.316449\pi$
$380$			9.62972i			0.493994i
$381$	12.7045	+	1.28627i	0.650872	+	0.0658978i
$382$	−24.7143			−1.26450
$383$	6.47930	+	11.2225i	0.331077	+	0.573442i	0.982723	−	0.185081i	$-0.0592547\pi$
$383$	6.47930	+	11.2225i	0.331077	+	0.573442i	−0.651646	+	0.758523i	$0.725921\pi$
$384$	1.28024	−	12.6449i	0.0653319	−	0.645282i
$385$		0			0
$386$		−	2.90752i		−	0.147989i
$387$	−9.02653	−	27.0755i	−0.458844	−	1.37633i
$388$	−4.81710	+	2.78116i	−0.244551	+	0.141192i
$389$	−9.48037	−	5.47350i	−0.480674	−	0.277517i	0.240023	−	0.970767i	$-0.422845\pi$
$389$	−9.48037	−	5.47350i	−0.480674	−	0.277517i	−0.720697	+	0.693250i	$0.756178\pi$
$390$	−3.58121	−	0.362581i	−0.181341	−	0.0183600i
$391$	−21.0353	−	12.1447i	−1.06380	−	0.614186i
$392$		0			0
$393$	−5.58685	−	12.4204i	−0.281819	−	0.626528i
$394$	−9.27338			−0.467186
$395$	0.719472	+	1.24616i	0.0362006	+	0.0627012i
$396$	−18.7986	−	16.6682i	−0.944665	−	0.837607i
$397$	25.8856	+	14.9451i	1.29916	+	0.750071i	0.980259	−	0.197717i	$-0.0633528\pi$
$397$	25.8856	+	14.9451i	1.29916	+	0.750071i	0.318901	+	0.947788i	$0.396686\pi$
$398$	−10.4588	−	18.1151i	−0.524250	−	0.908028i
$399$		0			0
$400$	3.04141	−	5.26788i	0.152071	−	0.263394i
$401$	−16.6233	+	9.59744i	−0.830126	+	0.479273i	−0.853896	−	0.520444i	$-0.825766\pi$
$401$	−16.6233	+	9.59744i	−0.830126	+	0.479273i	0.0237698	+	0.999717i	$0.492433\pi$
$402$	0.609395	−	6.01898i	0.0303938	−	0.300200i
$403$	−2.32242	+	4.02254i	−0.115688	+	0.200377i
$404$	−5.62421	+	9.74142i	−0.279815	+	0.484654i
$405$	−2.69953	−	22.3894i	−0.134141	−	1.11254i
$406$		0			0
$407$	6.88060	−	3.97252i	0.341059	−	0.196910i
$408$	−4.60725	+	2.07239i	−0.228093	+	0.102599i
$409$			28.8372i			1.42591i	0.701212	+	0.712953i	$0.252643\pi$
$409$			28.8372i			1.42591i	−0.701212	+	0.712953i	$0.747357\pi$
$410$			15.4227i			0.761673i
$411$	16.2572	+	11.7170i	0.801907	+	0.577955i
$412$	18.5190	−	10.6919i	0.912363	−	0.526753i
$413$		0			0
$414$	−13.9948	−	41.9781i	−0.687807	−	2.06311i
$415$	−10.6123	+	18.3811i	−0.520938	+	0.902290i
$416$	−1.55211	+	2.68834i	−0.0760986	+	0.131807i
$417$	27.5406	+	19.8492i	1.34867	+	0.972020i
$418$	−23.3720	+	13.4938i	−1.14316	+	0.660005i
$419$	5.06390	−	8.77094i	0.247388	−	0.428488i	−0.715412	−	0.698702i	$-0.753761\pi$
$419$	5.06390	−	8.77094i	0.247388	−	0.428488i	0.962800	+	0.270214i	$0.0870945\pi$
$420$		0			0
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	0.989592	+	0.143902i	$0.0459651\pi$
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	−0.370173	+	0.928963i	$0.620702\pi$
$422$	24.8617	+	14.3539i	1.21025	+	0.698738i
$423$	−6.30089	−	1.28909i	−0.306360	−	0.0626776i
$424$	2.30010	+	3.98390i	0.111703	+	0.193475i
$425$	−3.93546			−0.190898
$426$	−9.51173	−	0.963020i	−0.460845	−	0.0466585i
$427$		0			0
$428$	17.4370	+	10.0673i	0.842849	+	0.486619i
$429$	−1.76873	−	3.93217i	−0.0853953	−	0.189847i
$430$	−38.5834	−	22.2762i	−1.86066	−	1.07425i
$431$	−9.39066	+	5.42170i	−0.452332	+	0.261154i	−0.708815	−	0.705395i	$-0.750770\pi$
$431$	−9.39066	+	5.42170i	−0.452332	+	0.261154i	0.256482	+	0.966549i	$0.417436\pi$
$432$	−23.5944	−	7.36858i	−1.13519	−	0.354521i
$433$		−	13.0519i		−	0.627233i	−0.949550	−	0.313616i	$-0.898459\pi$
$433$		−	13.0519i		−	0.627233i	0.949550	−	0.313616i	$-0.101541\pi$
$434$		0			0
$435$	−11.0194	−	7.94194i	−0.528338	−	0.380787i
$436$	−0.685771	−	1.18779i	−0.0328425	−	0.0568849i
$437$	−20.3158			−0.971835
$438$	−11.3132	−	25.1509i	−0.540564	−	1.20176i
$439$			31.9547i			1.52511i	0.646922	+	0.762557i	$0.276056\pi$
$439$			31.9547i			1.52511i	−0.646922	+	0.762557i	$0.723944\pi$
$440$	13.3208			0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$			24.7969i			1.17814i	0.808083	+	0.589068i	$0.200505\pi$
$443$			24.7969i			1.17814i	−0.808083	+	0.589068i	$0.799495\pi$
$444$	−2.14137	+	2.97113i	−0.101625	+	0.141004i
$445$	18.9899			0.900208
$446$	−2.98724	−	5.17406i	−0.141450	−	0.244999i
$447$	24.8634	−	11.1838i	1.17600	−	0.528977i
$448$		0			0
$449$		−	13.7710i		−	0.649892i	−0.945733	−	0.324946i	$-0.894654\pi$
$449$		−	13.7710i		−	0.649892i	0.945733	−	0.324946i	$-0.105346\pi$
$450$	−5.36441	−	4.75647i	−0.252881	−	0.224222i
$451$	−15.9989	+	9.23700i	−0.753361	+	0.434953i
$452$	−6.12715	−	3.53751i	−0.288197	−	0.166390i
$453$	2.00792	−	2.78597i	0.0943403	−	0.130896i
$454$	−23.7439	−	13.7085i	−1.11436	−	0.643374i
$455$		0			0
$456$	−2.47056	+	3.42789i	−0.115695	+	0.160525i
$457$	27.3107			1.27754			0.638771	−	0.769397i	$-0.279443\pi$
$457$	27.3107			1.27754			0.638771	+	0.769397i	$0.279443\pi$
$458$	−3.15670	−	5.46757i	−0.147503	−	0.255483i
$459$	3.50392	+	15.6036i	0.163549	+	0.728314i
$460$	−25.5680	−	14.7617i	−1.19211	−	0.688266i
$461$	−5.51822	−	9.55784i	−0.257009	−	0.445153i	0.708430	−	0.705781i	$-0.249404\pi$
$461$	−5.51822	−	9.55784i	−0.257009	−	0.445153i	−0.965439	+	0.260628i	$0.916070\pi$
$462$		0			0
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	0.428115	+	0.903724i	$0.359178\pi$
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	−0.996706	+	0.0811042i	$0.974155\pi$
$464$	−12.8935	+	7.44405i	−0.598564	+	0.345581i
$465$	−41.4286	+	18.6351i	−1.92121	+	0.864180i
$466$	4.56029	−	7.89866i	0.211251	−	0.365898i
$467$	−7.95241	+	13.7740i	−0.367994	+	0.637384i	−0.989252	−	0.146222i	$-0.953289\pi$
$467$	−7.95241	+	13.7740i	−0.367994	+	0.637384i	0.621258	+	0.783606i	$0.286622\pi$
$468$	1.48713	+	1.31860i	0.0687427	+	0.0609521i
$469$		0			0
$470$	−8.69451	+	5.01978i	−0.401048	+	0.231545i
$471$	−1.46420	+	14.4619i	−0.0674667	+	0.666367i
$472$		−	6.92754i		−	0.318866i
$473$		−	53.3667i		−	2.45380i
$474$	0.187251	−	1.84948i	0.00860074	−	0.0849494i
$475$	−2.85063	+	1.64581i	−0.130796	+	0.0755151i
$476$		0			0
$477$	13.8149	−	4.60564i	0.632539	−	0.210878i
$478$	−14.7021	+	25.4648i	−0.672459	+	1.16473i
$479$	−6.92685	+	11.9976i	−0.316496	+	0.548187i	−0.979754	−	0.200204i	$-0.935840\pi$
$479$	−6.92685	+	11.9976i	−0.316496	+	0.548187i	0.663259	+	0.748390i	$0.269173\pi$
$480$	−27.6875	+	12.4542i	−1.26376	+	0.568452i
$481$	−0.544315	+	0.314261i	−0.0248186	+	0.0143290i
$482$	−0.718964	+	1.24528i	−0.0327479	+	0.0567210i
$483$		0			0
$484$	−15.2781	−	26.4624i	−0.694458	−	1.20284i
$485$	−8.08506	−	4.66791i	−0.367123	−	0.211959i
$486$	−14.0826	+	25.5041i	−0.638801	+	1.15689i
$487$	−14.3993	−	24.9404i	−0.652496	−	1.13016i	−0.982515	−	0.186182i	$-0.940389\pi$
$487$	−14.3993	−	24.9404i	−0.652496	−	1.13016i	0.330020	−	0.943974i	$-0.392945\pi$
$488$	8.10822			0.367042
$489$	1.08777	−	1.50927i	0.0491905	−	0.0682514i
$490$		0			0
$491$	−33.5627	−	19.3774i	−1.51466	−	0.874492i	−0.999852	−	0.0171884i	$-0.994528\pi$
$491$	−33.5627	−	19.3774i	−1.51466	−	0.874492i	−0.514812	−	0.857303i	$-0.672138\pi$
$492$	4.97917	−	6.90855i	0.224478	−	0.311462i
$493$	8.34181	+	4.81615i	0.375696	+	0.216908i
$494$	1.84893	−	1.06748i	0.0831872	−	0.0480281i
$495$	8.45206	−	41.3126i	0.379892	−	1.85686i
$496$			49.7911i			2.23569i
$497$		0			0
$498$	25.0062	−	11.2481i	1.12056	−	0.504039i
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	0.902212	−	0.431294i	$-0.141943\pi$
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	−0.824617	+	0.565691i	$0.808609\pi$
$500$	13.9209			0.622561
$501$	8.09628	−	11.2335i	0.361715	−	0.501877i
$502$			2.14076i			0.0955467i
$503$	−28.2202			−1.25828			−0.629138	−	0.777293i	$-0.716592\pi$
$503$	−28.2202			−1.25828			−0.629138	+	0.777293i	$0.716592\pi$
$504$		0			0
$505$	−18.8794			−0.840124
$506$		−	82.7403i		−	3.67825i
$507$	−9.09690	−	20.2238i	−0.404008	−	0.898171i
$508$	−11.0065			−0.488335
$509$	17.9062	+	31.0144i	0.793678	+	1.37469i	0.923675	+	0.383176i	$0.125170\pi$
$509$	17.9062	+	31.0144i	0.793678	+	1.37469i	−0.129997	+	0.991514i	$0.541497\pi$
$510$	20.2523	+	14.5963i	0.896786	+	0.646336i
$511$		0			0
$512$			24.2599i			1.07215i
$513$	9.06349	+	9.83706i	0.400163	+	0.434317i
$514$	46.9111	−	27.0841i	2.06916	−	1.19463i
$515$	31.0823	+	17.9454i	1.36965	+	0.790768i
$516$	10.0916	+	22.4351i	0.444256	+	0.987649i
$517$	−10.4147	−	6.01291i	−0.458036	−	0.264447i
$518$		0			0
$519$	−1.72925	−	0.175079i	−0.0759057	−	0.00768511i
$520$	−1.05379			−0.0462119
$521$	13.4608	+	23.3148i	0.589729	+	1.02144i	0.994268	+	0.106920i	$0.0340989\pi$
$521$	13.4608	+	23.3148i	0.589729	+	1.02144i	−0.404538	+	0.914521i	$0.632568\pi$
$522$	5.54981	+	16.6469i	0.242909	+	0.728617i
$523$	7.82181	+	4.51593i	0.342024	+	0.197468i	0.661167	−	0.750239i	$-0.270062\pi$
$523$	7.82181	+	4.51593i	0.342024	+	0.197468i	−0.319143	+	0.947707i	$0.603395\pi$
$524$	5.86943	+	10.1662i	0.256407	+	0.444110i
$525$		0			0
$526$	12.8020	−	22.1737i	0.558193	−	0.966819i
$527$	27.8980	−	16.1069i	1.21526	−	0.701629i
$528$	−37.4959	−	27.0242i	−1.63180	−	1.17608i
$529$	19.6426	−	34.0220i	0.854026	−	1.47922i
$530$	11.3661	−	19.6866i	0.493710	−	0.855131i
$531$	−21.4847	−	4.39552i	−0.932357	−	0.190749i
$532$		0			0
$533$	1.26565	−	0.730726i	0.0548216	−	0.0316513i
$534$	−19.9022	−	14.3440i	−0.861252	−	0.620726i
$535$			33.7939i			1.46104i
$536$		−	1.77113i		−	0.0765010i
$537$	−2.33054	+	1.04830i	−0.100570	+	0.0452376i
$538$	16.9615	−	9.79273i	0.731262	−	0.422195i
$539$		0			0
$540$	4.25893	+	18.9658i	0.183275	+	0.816159i
$541$	−5.66792	+	9.81713i	−0.243683	+	0.422071i	−0.961760	−	0.273892i	$-0.911689\pi$
$541$	−5.66792	+	9.81713i	−0.243683	+	0.422071i	0.718078	+	0.695963i	$0.245022\pi$
$542$	−6.11710	+	10.5951i	−0.262752	+	0.455100i
$543$	−2.62473	+	25.9244i	−0.112638	+	1.11252i
$544$	18.6447	−	10.7646i	0.799387	−	0.461526i
$545$	1.15100	−	1.99360i	0.0493035	−	0.0853962i
$546$		0			0
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	0.897613	+	0.440784i	$0.145300\pi$
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	−0.0670762	+	0.997748i	$0.521367\pi$
$548$	−14.9587	−	8.63644i	−0.639006	−	0.368930i
$549$	5.14465	−	25.1464i	0.219568	−	1.07322i
$550$	−6.70292	−	11.6098i	−0.285813	−	0.495043i
$551$	8.05647			0.343217
$552$	−5.31421	−	11.8143i	−0.226188	−	0.502850i
$553$		0			0
$554$	−36.3061	−	20.9613i	−1.54250	−	0.890562i
$555$	−6.11572	−	0.619188i	−0.259598	−	0.0262831i
$556$	−25.3410	−	14.6306i	−1.07470	−	0.620478i
$557$	−6.29167	+	3.63249i	−0.266586	+	0.153914i	−0.627335	−	0.778749i	$-0.715854\pi$
$557$	−6.29167	+	3.63249i	−0.266586	+	0.153914i	0.360749	+	0.932663i	$0.382521\pi$
$558$	57.4948	+	11.7628i	2.43395	+	0.497957i
$559$			4.22177i			0.178562i
$560$		0			0
$561$	−3.01216	+	29.7510i	−0.127173	+	1.25609i
$562$	20.8848	+	36.1736i	0.880973	+	1.52589i
$563$	23.0818			0.972780			0.486390	−	0.873742i	$-0.338313\pi$
$563$	23.0818			0.972780			0.486390	+	0.873742i	$0.338313\pi$
$564$	5.51529	+	0.558399i	0.232236	+	0.0235128i
$565$		−	11.8748i		−	0.499575i
$566$	35.4561			1.49033
$567$		0			0
$568$	−2.79889			−0.117439
$569$		−	17.9535i		−	0.752651i	−0.926487	−	0.376326i	$-0.877187\pi$
$569$		−	17.9535i		−	0.752651i	0.926487	−	0.376326i	$-0.122813\pi$
$570$	20.7738	+	2.10326i	0.870120	+	0.0880957i
$571$	−14.0847			−0.589425			−0.294713	−	0.955586i	$-0.595224\pi$
$571$	−14.0847			−0.589425			−0.294713	+	0.955586i	$0.595224\pi$
$572$	1.85819	+	3.21849i	0.0776950	+	0.134572i
$573$	−2.30715	+	22.7877i	−0.0963826	+	0.951969i
$574$		0			0
$575$		−	10.0916i		−	0.420851i
$576$	10.4619	+	2.14038i	0.435912	+	0.0891823i
$577$	26.0392	−	15.0337i	1.08403	−	0.625862i	0.152046	−	0.988373i	$-0.451414\pi$
$577$	26.0392	−	15.0337i	1.08403	−	0.625862i	0.931979	+	0.362511i	$0.118081\pi$
$578$	12.1841	+	7.03447i	0.506790	+	0.292595i
$579$	−2.68086	−	0.271425i	−0.111413	−	0.0112800i
$580$	10.1393	+	5.85392i	0.421011	+	0.243071i
$581$		0			0
$582$	4.94756	+	10.9992i	0.205083	+	0.455931i
$583$	27.2295			1.12773
$584$	−4.03690	−	6.99211i	−0.167048	−	0.289336i
$585$	−0.668631	+	3.26818i	−0.0276445	+	0.135123i
$586$	−14.2800	−	8.24455i	−0.589900	−	0.340579i
$587$	18.0979	+	31.3465i	0.746981	+	1.29381i	0.949264	+	0.314481i	$0.101831\pi$
$587$	18.0979	+	31.3465i	0.746981	+	1.29381i	−0.202283	+	0.979327i	$0.564836\pi$
$588$		0			0
$589$	13.4719	−	23.3339i	0.555098	−	0.961459i
$590$	−29.6464	+	17.1164i	−1.22052	+	0.704670i
$591$	−0.865695	+	8.55046i	−0.0356099	+	0.351719i
$592$	−3.36877	+	5.83489i	−0.138456	+	0.239812i
$593$	1.02158	−	1.76943i	0.0419514	−	0.0726620i	−0.844287	−	0.535891i	$-0.819976\pi$
$593$	1.02158	−	1.76943i	0.0419514	−	0.0726620i	0.886239	+	0.463229i	$0.153309\pi$
$594$	−40.0635	+	36.9130i	−1.64382	+	1.51456i
$595$		0			0
$596$	−20.3507	+	11.7495i	−0.833598	+	0.481278i
$597$	−17.6793	+	7.95234i	−0.723564	+	0.325468i
$598$			6.54547i			0.267664i
$599$			18.2296i			0.744840i	0.928064	+	0.372420i	$0.121472\pi$
$599$			18.2296i			0.744840i	−0.928064	+	0.372420i	$0.878528\pi$
$600$	−1.70277	−	1.22723i	−0.0695151	−	0.0501013i
$601$	−32.1713	+	18.5741i	−1.31230	+	0.757654i	−0.982476	−	0.186390i	$-0.940321\pi$
$601$	−32.1713	+	18.5741i	−1.31230	+	0.757654i	−0.329820	+	0.944044i	$0.606988\pi$
$602$		0			0
$603$	−5.49287	−	1.12378i	−0.223687	−	0.0457637i
$604$	−1.48002	+	2.56346i	−0.0602210	+	0.104306i
$605$	25.6428	−	44.4146i	1.04253	−	1.80571i
$606$	19.7864	+	14.2606i	0.803768	+	0.579295i
$607$	−17.1730	+	9.91482i	−0.697030	+	0.402430i	−0.806240	−	0.591588i	$-0.798501\pi$
$607$	−17.1730	+	9.91482i	−0.697030	+	0.402430i	0.109211	+	0.994019i	$0.465168\pi$
$608$	9.00349	−	15.5945i	0.365140	−	0.632440i
$609$		0			0
$610$	−20.0336	−	34.6991i	−0.811135	−	1.40493i
$611$	0.823890	+	0.475673i	0.0333310	+	0.0192437i
$612$	−4.35957	−	13.0768i	−0.176225	−	0.528596i
$613$	6.34412	+	10.9883i	0.256237	+	0.443815i	0.965231	−	0.261400i	$-0.0841840\pi$
$613$	6.34412	+	10.9883i	0.256237	+	0.443815i	−0.708994	+	0.705214i	$0.750851\pi$
$614$	−53.7381			−2.16869
$615$	14.2204	+	1.43975i	0.573422	+	0.0580564i
$616$		0			0
$617$	4.37247	+	2.52445i	0.176029	+	0.101630i	0.585426	−	0.810726i	$-0.300927\pi$
$617$	4.37247	+	2.52445i	0.176029	+	0.101630i	−0.409397	+	0.912357i	$0.634261\pi$
$618$	−19.0205	−	42.2855i	−0.765116	−	1.70097i
$619$	−0.231999	−	0.133945i	−0.00932485	−	0.00538370i	0.495330	−	0.868705i	$-0.335047\pi$
$619$	−0.231999	−	0.133945i	−0.00932485	−	0.00538370i	−0.504655	+	0.863321i	$0.668380\pi$
$620$	33.9094	−	19.5776i	1.36183	−	0.786255i
$621$	−40.0121	+	8.98505i	−1.60563	+	0.360558i
$622$		−	24.8305i		−	0.995611i
$623$		0			0
$624$	2.96625	+	2.13785i	0.118745	+	0.0855824i
$625$	14.8792	+	25.7716i	0.595169	+	1.03086i
$626$	58.9641			2.35668
$627$	10.2601	+	22.8097i	0.409747	+	0.910931i
$628$		−	12.5290i		−	0.499961i
$629$	4.35905			0.173807
$630$		0			0
$631$	37.7899			1.50439			0.752197	−	0.658938i	$-0.228994\pi$
$631$	37.7899			1.50439			0.752197	+	0.658938i	$0.228994\pi$
$632$		−	0.544222i		−	0.0216480i
$633$	15.5559	−	21.5836i	0.618290	−	0.857872i
$634$	−37.5112			−1.48976
$635$	−9.23671	−	15.9984i	−0.366547	−	0.634879i
$636$	−11.4471	+	5.14905i	−0.453908	+	0.204173i
$637$		0			0
$638$			32.8117i			1.29903i
$639$	−1.77589	+	8.68033i	−0.0702532	+	0.343389i
$640$	−15.9234	+	9.19336i	−0.629426	+	0.363400i
$641$	−29.7991	−	17.2045i	−1.17699	−	0.679537i	−0.221676	−	0.975120i	$-0.571153\pi$
$641$	−29.7991	−	17.2045i	−1.17699	−	0.679537i	−0.955317	+	0.295583i	$0.904486\pi$
$642$	25.5262	−	35.4173i	1.00744	−	1.39781i
$643$	0.676278	+	0.390449i	0.0266698	+	0.0153978i	0.513276	−	0.858224i	$-0.328432\pi$
$643$	0.676278	+	0.390449i	0.0266698	+	0.0153978i	−0.486606	+	0.873622i	$0.661765\pi$
$644$		0			0
$645$	−24.1415	+	33.4961i	−0.950569	+	1.31891i
$646$	−14.8068			−0.582566
$647$	9.82182	+	17.0119i	0.386136	+	0.668807i	0.991926	−	0.126818i	$-0.0404763\pi$
$647$	9.82182	+	17.0119i	0.386136	+	0.668807i	−0.605790	+	0.795624i	$0.707143\pi$
$648$	−3.34975	+	7.84391i	−0.131591	+	0.308138i
$649$	−35.5118	−	20.5027i	−1.39396	−	0.804803i
$650$	0.530259	+	0.918435i	0.0207985	+	0.0360240i
$651$		0			0
$652$	−0.801781	+	1.38872i	−0.0314001	+	0.0543867i
$653$	−2.77600	+	1.60272i	−0.108633	+	0.0627194i	−0.553332	−	0.832961i	$-0.686644\pi$
$653$	−2.77600	+	1.60272i	−0.108633	+	0.0627194i	0.444699	+	0.895680i	$0.353311\pi$
$654$	−2.71216	+	1.21996i	−0.106054	+	0.0477042i
$655$	−9.85129	+	17.0629i	−0.384922	+	0.666704i
$656$	7.83315	−	13.5674i	0.305833	−	0.529719i
$657$	−24.2464	+	8.08333i	−0.945940	+	0.315361i
$658$		0			0
$659$	−24.2959	+	14.0273i	−0.946435	+	0.546425i	−0.891972	−	0.452091i	$-0.850678\pi$
$659$	−24.2959	+	14.0273i	−0.946435	+	0.546425i	−0.0544636	+	0.998516i	$0.517345\pi$
$660$	−3.66121	+	36.1617i	−0.142512	+	1.40759i
$661$		−	32.3882i		−	1.25976i	−0.776694	−	0.629878i	$-0.783105\pi$
$661$		−	32.3882i		−	1.25976i	0.776694	−	0.629878i	$-0.216895\pi$
$662$			2.33227i			0.0906463i
$663$	0.238287	−	2.35356i	0.00925432	−	0.0914048i
$664$	6.95189	−	4.01367i	0.269785	−	0.155761i
$665$		0			0
$666$	5.94181	+	5.26843i	0.230240	+	0.204148i
$667$	−12.3500	+	21.3908i	−0.478193	+	0.828255i
$668$	−5.96768	+	10.3363i	−0.230897	+	0.399925i
$669$	−5.04957	+	2.27136i	−0.195228	+	0.0878157i
$670$	−7.57953	+	4.37605i	−0.292823	+	0.169061i
$671$	23.9971	−	41.5641i	0.926397	−	1.60457i
$672$		0			0
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	0.596026	−	0.802965i	$-0.296745\pi$
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	−0.993401	+	0.114692i	$0.963412\pi$
$674$	21.3242	+	12.3115i	0.821378	+	0.474223i
$675$	−4.88645	+	4.50219i	−0.188080	+	0.173289i
$676$	9.55701	+	16.5532i	0.367577	+	0.636663i
$677$	50.3311			1.93438			0.967190	−	0.254053i	$-0.0817639\pi$
$677$	50.3311			1.93438			0.967190	+	0.254053i	$0.0817639\pi$
$678$	−8.96958	+	12.4452i	−0.344475	+	0.477956i
$679$		0			0
$680$	6.32935	+	3.65425i	0.242719	+	0.140134i
$681$	−14.8564	+	20.6132i	−0.569300	+	0.789899i
$682$	95.0324	+	54.8670i	3.63898	+	2.10097i
$683$	11.9031	−	6.87227i	0.455460	−	0.262960i	−0.254673	−	0.967027i	$-0.581968\pi$
$683$	11.9031	−	6.87227i	0.455460	−	0.262960i	0.710133	+	0.704067i	$0.248635\pi$
$684$	−8.62654	−	7.64891i	−0.329844	−	0.292463i
$685$		−	28.9909i		−	1.10769i
$686$		0			0
$687$	−5.33602	+	2.40020i	−0.203582	+	0.0915735i
$688$	22.6280	+	39.1929i	0.862685	+	1.49421i
$689$	−2.15409			−0.0820643
$690$	−37.4291	+	51.9326i	−1.42490	+	1.97704i
$691$			29.3673i			1.11719i	0.829442	+	0.558593i	$0.188658\pi$
$691$			29.3673i			1.11719i	−0.829442	+	0.558593i	$0.811342\pi$
$692$	1.49813			0.0569504
$693$		0			0
$694$	−50.5874			−1.92027
$695$		−	49.1123i		−	1.86294i
$696$	2.10742	+	4.68511i	0.0798814	+	0.177589i
$697$	−10.1358			−0.383920
$698$	32.7392	+	56.7060i	1.23920	+	2.14635i
$699$	−6.85719	−	4.94215i	−0.259363	−	0.186929i
$700$		0			0
$701$		−	44.2011i		−	1.66945i	−0.550666	−	0.834726i	$-0.685626\pi$
$701$		−	44.2011i		−	1.66945i	0.550666	−	0.834726i	$-0.314374\pi$
$702$	3.16937	−	2.92013i	0.119620	−	0.110213i
$703$	3.15746	−	1.82296i	0.119086	−	0.0687542i
$704$	17.2923	+	9.98371i	0.651728	+	0.376275i
$705$	3.81680	+	8.48532i	0.143749	+	0.319576i
$706$	4.08702	+	2.35964i	0.153817	+	0.0888063i
$707$		0			0
$708$	18.8060	+	1.90402i	0.706772	+	0.0715575i
$709$	−11.3326			−0.425604			−0.212802	−	0.977095i	$-0.568259\pi$
$709$	−11.3326			−0.425604			−0.212802	+	0.977095i	$0.568259\pi$
$710$	6.91542	+	11.9779i	0.259531	+	0.449521i
$711$	−1.68782	−	0.345308i	−0.0632982	−	0.0129501i
$712$	−6.21994	−	3.59108i	−0.233102	−	0.134581i
$713$	41.3028	+	71.5385i	1.54680	+	2.67914i
$714$		0			0
$715$	−3.11881	+	5.40193i	−0.116637	+	0.202021i
$716$	1.90755	−	1.10132i	0.0712884	−	0.0411584i
$717$	22.1072	+	15.9332i	0.825608	+	0.595036i
$718$	6.79136	−	11.7630i	0.253451	−	0.438991i
$719$	18.0647	−	31.2890i	0.673700	−	1.16688i	−0.303147	−	0.952944i	$-0.598037\pi$
$719$	18.0647	−	31.2890i	0.673700	−	1.16688i	0.976847	−	0.213939i	$-0.0686294\pi$
$720$	11.3097	+	33.9240i	0.421487	+	1.26427i
$721$		0			0
$722$	20.0271	−	11.5627i	0.745333	−	0.430318i
$723$	1.08109	+	0.779166i	0.0402061	+	0.0289775i
$724$		−	22.4596i		−	0.834703i
$725$			4.00197i			0.148629i
$726$	−60.4232	+	27.1791i	−2.24252	+	1.00871i
$727$	−6.20547	+	3.58273i	−0.230148	+	0.132876i	−0.610640	−	0.791908i	$-0.709088\pi$
$727$	−6.20547	+	3.58273i	−0.230148	+	0.132876i	0.380492	+	0.924784i	$0.375755\pi$
$728$		0			0
$729$	22.2013	+	15.3657i	0.822269	+	0.569099i
$730$	−19.9485	+	34.5518i	−0.738327	+	1.27882i
$731$	14.6399	−	25.3570i	0.541475	−	0.937862i
$732$	−2.22853	+	22.0111i	−0.0823687	+	0.813555i
$733$	−41.4391	+	23.9249i	−1.53059	+	0.883685i	−0.531253	+	0.847213i	$0.678279\pi$
$733$	−41.4391	+	23.9249i	−1.53059	+	0.883685i	−0.999335	+	0.0364726i	$0.988388\pi$
$734$	−12.5938	+	21.8131i	−0.464846	+	0.805136i
$735$		0			0
$736$	27.6034	+	47.8105i	1.01747	+	1.76232i
$737$	−9.07910	−	5.24182i	−0.334433	−	0.193085i
$738$	−13.8160	−	12.2503i	−0.508575	−	0.450939i
$739$	−7.67416	−	13.2920i	−0.282299	−	0.488956i	0.689652	−	0.724141i	$-0.257764\pi$
$739$	−7.67416	−	13.2920i	−0.282299	−	0.488956i	−0.971951	+	0.235185i	$0.924430\pi$
$740$	5.29833			0.194771
$741$	−0.811659	−	1.80444i	−0.0298170	−	0.0662879i
$742$		0			0
$743$	34.9422	+	20.1739i	1.28191	+	0.740109i	0.977197	−	0.212337i	$-0.0681073\pi$
$743$	34.9422	+	20.1739i	1.28191	+	0.740109i	0.304709	+	0.952445i	$0.401441\pi$
$744$	17.0935	+	1.73063i	0.626677	+	0.0634481i
$745$	−34.1568	−	19.7204i	−1.25141	−	0.722501i
$746$	38.4630	−	22.2066i	1.40823	−	0.813042i
$747$	−8.03683	−	24.1069i	−0.294052	−	0.882024i
$748$		−	25.7747i		−	0.942417i
$749$		0			0
$750$	3.04050	−	30.0310i	0.111023	−	1.09658i
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	−0.989791	−	0.142527i	$-0.954477\pi$
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	0.371463	−	0.928448i	$-0.378856\pi$
$752$	10.1981			0.371887
$753$	1.97387	+	0.199846i	0.0719319	+	0.00728277i
$754$		−	2.59568i		−	0.0945293i
$755$	−4.96814			−0.180809
$756$		0			0
$757$	−5.73237			−0.208346			−0.104173	−	0.994559i	$-0.533220\pi$
$757$	−5.73237			−0.208346			−0.104173	+	0.994559i	$0.533220\pi$
$758$			39.6743i			1.44103i
$759$	−76.2901	−	7.72403i	−2.76916	−	0.280364i
$760$	6.11284			0.221736
$761$	13.2666	+	22.9784i	0.480914	+	0.832968i	0.999760	−	0.0218999i	$-0.00697151\pi$
$761$	13.2666	+	22.9784i	0.480914	+	0.832968i	−0.518846	+	0.854868i	$0.673638\pi$
$762$	−2.40397	+	23.7439i	−0.0870865	+	0.860152i
$763$		0			0
$764$		−	19.7420i		−	0.714242i
$765$	15.3490	−	17.3109i	0.554946	−	0.625876i
$766$	−20.9741	+	12.1094i	−0.757825	+	0.437531i
$767$	2.80929	+	1.62194i	0.101438	+	0.0585650i
$768$	35.9004	+	3.63475i	1.29544	+	0.131158i
$769$	23.3944	+	13.5068i	0.843623	+	0.487066i	0.858494	−	0.512823i	$-0.171400\pi$
$769$	23.3944	+	13.5068i	0.843623	+	0.487066i	−0.0148711	+	0.999889i	$0.504734\pi$
$770$		0			0
$771$	−20.5935	−	45.7824i	−0.741655	−	1.64881i
$772$	2.32256			0.0835906
$773$	11.3009	+	19.5737i	0.406464	+	0.704016i	0.994491	−	0.104826i	$-0.0334284\pi$
$773$	11.3009	+	19.5737i	0.406464	+	0.704016i	−0.588027	+	0.808841i	$0.700095\pi$
$774$	50.6024	−	16.8700i	1.81887	−	0.606380i
$775$	11.5909	+	6.69201i	0.416357	+	0.240384i
$776$	1.76545	+	3.05784i	0.0633758	+	0.109770i
$777$		0			0
$778$	10.2296	−	17.7182i	0.366750	−	0.635229i
$779$	−7.34180	+	4.23879i	−0.263047	+	0.151870i
$780$	0.289633	−	2.86070i	0.0103705	−	0.102430i
$781$	−8.28359	+	14.3476i	−0.296410	+	0.513398i
$782$	22.6978	−	39.3137i	0.811670	−	1.40585i
$783$	15.8673	−	3.56313i	0.567051	−	0.127336i
$784$		0			0
$785$	18.2114	−	10.5144i	0.649993	−	0.375274i
$786$	23.2130	−	10.4415i	0.827980	−	0.372435i
$787$		−	26.1960i		−	0.933787i	−0.884314	−	0.466893i	$-0.845373\pi$
$787$		−	26.1960i		−	0.933787i	0.884314	−	0.466893i	$-0.154627\pi$
$788$		−	7.40767i		−	0.263887i
$789$	−19.2500	−	13.8740i	−0.685318	−	0.493926i
$790$	−2.32900	+	1.34465i	−0.0828620	+	0.0478404i
$791$		0			0
$792$	−10.5808	+	11.9331i	−0.375971	+	0.424026i
$793$	−1.89838	+	3.28808i	−0.0674133	+	0.116763i
$794$	−27.9314	+	48.3785i	−0.991247	+	1.71689i
$795$	−17.0908	−	12.3178i	−0.606150	−	0.436867i
$796$	14.4705	−	8.35456i	0.512894	−	0.296120i
$797$	−5.96560	+	10.3327i	−0.211312	+	0.366004i	−0.952126	−	0.305707i	$-0.901107\pi$
$797$	−5.96560	+	10.3327i	−0.211312	+	0.366004i	0.740813	+	0.671711i	$0.234440\pi$
$798$		0			0
$799$	−3.29899	−	5.71402i	−0.116710	−	0.202147i
$800$	7.74640	+	4.47239i	0.273877	+	0.158123i
$801$	−15.0837	+	17.0116i	−0.532957	+	0.601077i
$802$	−17.9370	−	31.0678i	−0.633378	−	1.09704i
$803$	−47.7904			−1.68648
$804$	4.80802	+	0.486790i	0.169566	+	0.0171678i
$805$		0			0
$806$	−7.51788	−	4.34045i	−0.264806	−	0.152886i
$807$	−7.44592	−	16.5534i	−0.262109	−	0.582708i
$808$	6.18375	+	3.57019i	0.217543	+	0.125599i
$809$	22.9399	−	13.2443i	0.806522	−	0.465646i	−0.0392244	−	0.999230i	$-0.512489\pi$
$809$	22.9399	−	13.2443i	0.806522	−	0.465646i	0.845747	+	0.533585i	$0.179155\pi$
$810$	41.8445	−	5.04525i	1.47026	−	0.177272i
$811$			13.7419i			0.482544i	0.970458	+	0.241272i	$0.0775646\pi$
$811$			13.7419i			0.482544i	−0.970458	+	0.241272i	$0.922435\pi$
$812$		0			0
$813$	9.19812	+	6.62932i	0.322592	+	0.232500i
$814$	7.42439	+	12.8594i	0.260225	+	0.450722i
$815$	−2.69143			−0.0942766
$816$	−10.4026	−	23.1265i	−0.364163	−	0.809590i
$817$		−	24.4896i		−	0.856783i
$818$	−53.8949			−1.88439
$819$		0			0
$820$	−12.3198			−0.430226
$821$		−	13.5669i		−	0.473489i	−0.971572	−	0.236744i	$-0.923920\pi$
$821$		−	13.5669i		−	0.473489i	0.971572	−	0.236744i	$-0.0760804\pi$
$822$	−21.8982	+	30.3836i	−0.763789	+	1.05975i
$823$	14.6971			0.512310			0.256155	−	0.966636i	$-0.417544\pi$
$823$	14.6971			0.512310			0.256155	+	0.966636i	$0.417544\pi$
$824$	−6.78711	−	11.7556i	−0.236440	−	0.409527i
$825$	−11.3305	+	5.09658i	−0.394476	+	0.177440i
$826$		0			0
$827$		−	40.8787i		−	1.42149i	−0.703449	−	0.710746i	$-0.748358\pi$
$827$		−	40.8787i		−	1.42149i	0.703449	−	0.710746i	$-0.251642\pi$
$828$	33.5325	−	11.1792i	1.16534	−	0.388504i
$829$	−17.7189	+	10.2300i	−0.615402	+	0.355302i	−0.775077	−	0.631867i	$-0.782289\pi$
$829$	−17.7189	+	10.2300i	−0.615402	+	0.355302i	0.159675	+	0.987170i	$0.448955\pi$
$830$	−34.3530	−	19.8337i	−1.19241	−	0.688439i
$831$	−22.7165	+	31.5190i	−0.788028	+	1.09338i
$832$	−1.36797	−	0.789798i	−0.0474258	−	0.0273813i
$833$		0			0
$834$	−37.0969	+	51.4717i	−1.28456	+	1.78232i
$835$	−20.0324			−0.693249
$836$	−10.7790	−	18.6698i	−0.372800	−	0.645708i
$837$	16.2131	−	51.9146i	0.560406	−	1.79443i
$838$	16.3923	+	9.46412i	0.566264	+	0.326932i
$839$	−27.3475	−	47.3673i	−0.944141	−	1.63530i	−0.757462	−	0.652880i	$-0.773561\pi$
$839$	−27.3475	−	47.3673i	−0.944141	−	1.63530i	−0.186680	−	0.982421i	$-0.559773\pi$
$840$		0			0
$841$	−9.60247	+	16.6320i	−0.331120	+	0.573516i
$842$	−41.1416	+	23.7531i	−1.41783	+	0.818586i
$843$	35.3033	−	15.8798i	1.21591	−	0.546930i
$844$	−11.4661	+	19.8598i	−0.394678	+	0.683602i
$845$	−16.0405	+	27.7830i	−0.551812	+	0.955766i
$846$	2.40922	−	11.7760i	0.0828308	−	0.404866i
$847$		0			0
$848$	−19.9975	+	11.5456i	−0.686718	+	0.396477i
$849$	3.30992	−	32.6921i	0.113596	−	1.12199i
$850$		−	7.35513i		−	0.252279i
$851$			11.1779i			0.383172i
$852$	0.769269	−	7.59806i	0.0263547	−	0.260305i
$853$	−11.0684	+	6.39037i	−0.378976	+	0.218802i	−0.677373	−	0.735640i	$-0.736882\pi$
$853$	−11.0684	+	6.39037i	−0.378976	+	0.218802i	0.298396	+	0.954442i	$0.403548\pi$
$854$		0			0
$855$	3.87859	−	18.9580i	0.132645	−	0.648351i
$856$	6.39058	−	11.0688i	0.218426	−	0.378324i
$857$	−9.16200	+	15.8691i	−0.312968	+	0.542077i	−0.979003	−	0.203844i	$-0.934657\pi$
$857$	−9.16200	+	15.8691i	−0.312968	+	0.542077i	0.666035	+	0.745920i	$0.267990\pi$
$858$	7.34897	−	3.30565i	0.250890	−	0.112853i
$859$	33.4579	−	19.3169i	1.14157	−	0.659085i	0.194750	−	0.980853i	$-0.437610\pi$
$859$	33.4579	−	19.3169i	1.14157	−	0.659085i	0.946819	+	0.321768i	$0.104277\pi$
$860$	17.7944	−	30.8208i	0.606784	−	1.05098i
$861$		0			0
$862$	−10.1328	−	17.5505i	−0.345125	−	0.597774i
$863$	−14.4626	−	8.35001i	−0.492314	−	0.284238i	0.233220	−	0.972424i	$-0.425074\pi$
$863$	−14.4626	−	8.35001i	−0.492314	−	0.284238i	−0.725534	+	0.688186i	$0.758407\pi$
$864$	10.8355	−	34.6955i	0.368631	−	1.18036i
$865$	1.25724	+	2.17760i	0.0427473	+	0.0740405i
$866$	24.3931			0.828912
$867$	7.62350	−	10.5775i	0.258908	−	0.359232i
$868$		0			0
$869$	−2.78978	−	1.61068i	−0.0946367	−	0.0546385i
$870$	14.8430	−	20.5945i	0.503224	−	0.698219i
$871$	0.718235	+	0.414673i	0.0243365	+	0.0140507i
$872$	−0.753996	+	0.435320i	−0.0255335	+	0.0147418i
$873$	10.6036	−	3.53506i	0.358878	−	0.119644i
$874$		−	37.9689i		−	1.28432i
$875$		0			0
$876$	20.0908	−	9.03707i	0.678805	−	0.305334i
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	−0.996956	−	0.0779707i	$-0.975156\pi$
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	0.430953	−	0.902374i	$-0.358177\pi$
$878$	−59.7213			−2.01549
$879$	−8.93491	+	12.3971i	−0.301367	+	0.418144i
$880$			66.8652i			2.25403i
$881$	28.6657			0.965771			0.482885	−	0.875684i	$-0.339589\pi$
$881$	28.6657			0.965771			0.482885	+	0.875684i	$0.339589\pi$
$882$		0			0
$883$	−38.2091			−1.28584			−0.642919	−	0.765935i	$-0.722277\pi$
$883$	−38.2091			−1.28584			−0.642919	+	0.765935i	$0.722277\pi$
$884$			2.03900i			0.0685790i
$885$	13.0145	+	28.9332i	0.437476	+	0.972577i
$886$	−46.3439			−1.55695
$887$	−17.5914	−	30.4692i	−0.590662	−	1.02306i	−0.994143	−	0.108069i	$-0.965533\pi$
$887$	−17.5914	−	30.4692i	−0.590662	−	1.02306i	0.403481	−	0.914988i	$-0.367800\pi$
$888$	1.88604	+	1.35932i	0.0632915	+	0.0456157i
$889$		0			0
$890$			35.4910i			1.18966i
$891$	30.2953	+	40.3862i	1.01493	+	1.35299i
$892$	4.13309	−	2.38624i	0.138386	−	0.0798972i
$893$	−4.77921	−	2.75928i	−0.159930	−	0.0923358i
$894$	20.9019	+	46.4681i	0.699063	+	1.55413i
$895$	3.20164	+	1.84847i	0.107019	+	0.0617875i
$896$		0			0
$897$	6.03521	+	0.611037i	0.201510	+	0.0204019i
$898$	25.7371			0.858857
$899$	−16.3791	−	28.3695i	−0.546274	−	0.946174i
$900$	3.79951	−	4.28514i	0.126650	−	0.142838i
$901$	12.9380	+	7.46975i	0.431027	+	0.248854i
$902$	−17.2634	−	29.9010i	−0.574807	−	0.995595i
$903$		0			0
$904$	−2.24557	+	3.88944i	−0.0746866	+	0.129361i
$905$	32.6459	−	18.8481i	1.08519	−	0.626533i
$906$	5.20680	+	3.75267i	0.172984	+	0.124674i
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	−0.258720	−	0.965952i	$-0.583301\pi$
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	0.965899	−	0.258918i	$-0.0833660\pi$
$908$	10.9505	−	18.9669i	0.363406	−	0.629437i
$909$	14.9960	−	16.9127i	0.497385	−	0.560958i
$910$		0			0
$911$	−43.5221	+	25.1275i	−1.44195	+	0.832510i	−0.997980	−	0.0635313i	$-0.979764\pi$
$911$	−43.5221	+	25.1275i	−1.44195	+	0.832510i	−0.443970	+	0.896042i	$0.646430\pi$
$912$	−17.2066	−	12.4012i	−0.569767	−	0.410645i
$913$		−	47.5154i		−	1.57253i
$914$			51.0420i			1.68832i
$915$	−33.8643	+	15.2326i	−1.11952	+	0.503573i
$916$	4.36754	−	2.52160i	0.144308	−	0.0833161i
$917$		0			0
$918$	−29.1622	+	6.54860i	−0.962495	+	0.216136i
$919$	29.3486	−	50.8333i	0.968121	−	1.67684i	0.267137	−	0.963658i	$-0.413922\pi$
$919$	29.3486	−	50.8333i	0.968121	−	1.67684i	0.700984	−	0.713177i	$-0.252744\pi$
$920$	−9.37054	+	16.2303i	−0.308938	+	0.535096i
$921$	−5.01660	+	49.5489i	−0.165302	+	1.63269i
$922$	17.8630	−	10.3132i	0.588287	−	0.339647i
$923$	0.655304	−	1.13502i	0.0215696	−	0.0373596i
$924$		0			0
$925$	0.905536	+	1.56843i	0.0297738	+	0.0515698i
$926$	−39.6046	−	22.8657i	−1.30149	−	0.751415i
$927$	−40.7647	+	13.5903i	−1.33889	+	0.446363i
$928$	−10.9465	−	18.9598i	−0.359335	−	0.622387i
$929$	−14.3823			−0.471868			−0.235934	−	0.971769i	$-0.575815\pi$
$929$	−14.3823			−0.471868			−0.235934	+	0.971769i	$0.575815\pi$
$930$	−34.8278	−	77.4275i	−1.14205	−	2.53895i
$931$		0			0
$932$	6.30952	+	3.64281i	0.206675	+	0.119324i
$933$	−22.8948	−	2.31799i	−0.749542	−	0.0758877i
$934$	−25.7427	−	14.8626i	−0.842327	−	0.486318i
$935$	37.4646	−	21.6302i	1.22522	−	0.707384i
$936$	0.837030	−	0.944015i	0.0273592	−	0.0308561i
$937$		−	44.2981i		−	1.44716i	−0.690243	−	0.723578i	$-0.742496\pi$
$937$		−	44.2981i		−	1.44716i	0.690243	−	0.723578i	$-0.257504\pi$
$938$		0			0
$939$	5.50446	−	54.3675i	0.179631	−	1.77422i
$940$	−4.00985	−	6.94526i	−0.130787	−	0.226529i
$941$	−14.8880			−0.485335			−0.242667	−	0.970110i	$-0.578022\pi$
$941$	−14.8880			−0.485335			−0.242667	+	0.970110i	$0.578022\pi$
$942$	−27.0283	−	2.73649i	−0.880630	−	0.0891598i
$943$		−	25.9910i		−	0.846384i
$944$	34.7734			1.13178
$945$		0			0
$946$	99.7390			3.24280
$947$			41.9552i			1.36336i	0.731650	+	0.681681i	$0.238751\pi$
$947$			41.9552i			1.36336i	−0.731650	+	0.681681i	$0.761249\pi$
$948$	1.47738	+	0.149578i	0.0479832	+	0.00485808i
$949$	3.78063			0.122724
$950$	−3.07592	−	5.32765i	−0.0997960	−	0.172852i
$951$	−3.50177	+	34.5869i	−0.113553	+	1.12156i
$952$		0			0
$953$			13.9821i			0.452926i	0.974020	+	0.226463i	$0.0727162\pi$
$953$			13.9821i			0.452926i	−0.974020	+	0.226463i	$0.927284\pi$
$954$	8.60765	+	25.8191i	0.278683	+	0.835924i
$955$	28.6959	−	16.5676i	0.928578	−	0.536115i
$956$	−20.3415	−	11.7442i	−0.657892	−	0.379834i
$957$	30.2538	+	3.06306i	0.977966	+	0.0990146i
$958$	−22.4228	−	12.9458i	−0.724449	−	0.418261i
$959$		0			0
$960$	−6.33733	−	14.0889i	−0.204537	−	0.454716i
$961$	−78.5553			−2.53404
$962$	−0.587333	−	1.01729i	−0.0189364	−	0.0327988i
$963$	−30.2734	−	26.8425i	−0.975546	−	0.864989i
$964$	−0.994743	−	0.574315i	−0.0320385	−	0.0184974i
$965$	1.94910	+	3.37593i	0.0627436	+	0.108675i
$966$		0			0
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	−0.989911	−	0.141690i	$-0.954746\pi$
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	0.617662	+	0.786443i	$0.288080\pi$
$968$	−16.7980	+	9.69835i	−0.539909	+	0.311717i
$969$	−1.38226	+	13.6525i	−0.0444045	+	0.438582i
$970$	8.72403	−	15.1105i	0.280112	−	0.485168i
$971$	−21.6869	+	37.5628i	−0.695965	+	1.20545i	0.273890	+	0.961761i	$0.411690\pi$
$971$	−21.6869	+	37.5628i	−0.695965	+	1.20545i	−0.969854	+	0.243685i	$0.921644\pi$
$972$	−20.3729	−	11.2493i	−0.653462	−	0.360823i
$973$		0			0
$974$	46.6120	−	26.9114i	1.49354	−	0.862298i
$975$	0.896338	−	0.403183i	0.0287058	−	0.0129122i
$976$			40.7000i			1.30277i
$977$			12.0331i			0.384974i	0.981300	+	0.192487i	$0.0616553\pi$
$977$			12.0331i			0.384974i	−0.981300	+	0.192487i	$0.938345\pi$
$978$	2.82072	+	2.03297i	0.0901968	+	0.0650071i
$979$	−36.8170	+	21.2563i	−1.17668	+	0.679355i
$980$		0			0
$981$	0.871668	+	2.61461i	0.0278302	+	0.0834782i
$982$	36.2152	−	62.7266i	1.15567	−	2.00169i
$983$	−3.14829	+	5.45300i	−0.100415	+	0.173924i	−0.911856	−	0.410511i	$-0.865350\pi$
$983$	−3.14829	+	5.45300i	−0.100415	+	0.173924i	0.811441	+	0.584435i	$0.198684\pi$
$984$	−4.38547	−	3.16072i	−0.139804	−	0.100760i
$985$	10.7674	−	6.21654i	0.343077	−	0.198075i
$986$	−9.00108	+	15.5903i	−0.286653	+	0.496497i
$987$		0			0
$988$	0.852712	+	1.47694i	0.0271284	+	0.0469877i
$989$	65.0225	+	37.5408i	2.06760	+	1.19373i
$990$	77.2106	+	15.7964i	2.45391	+	0.502041i
$991$	−16.7814	−	29.0662i	−0.533078	−	0.923317i	−0.999254	−	0.0386256i	$-0.987702\pi$
$991$	−16.7814	−	29.0662i	−0.533078	−	0.923317i	0.466176	−	0.884692i	$-0.345631\pi$
$992$	−73.2178			−2.32467
$993$	2.15046	+	0.217724i	0.0682427	+	0.00690926i
$994$		0			0
$995$	24.2874	+	14.0223i	0.769963	+	0.444538i
$996$	8.98508	+	19.9752i	0.284703	+	0.632939i
$997$	−9.74838	−	5.62823i	−0.308734	−	0.178248i	0.337626	−	0.941280i	$-0.390376\pi$
$997$	−9.74838	−	5.62823i	−0.308734	−	0.178248i	−0.646360	+	0.763033i	$0.723710\pi$
$998$	−5.61096	+	3.23949i	−0.177612	+	0.102544i
$999$	5.41241	−	4.98679i	0.171241	−	0.157775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.20		48
3.2	odd	2		1323.2.i.d.1097.7		48
7.2	even	3		441.2.o.e.293.19	yes	48
7.3	odd	6		441.2.s.d.374.6		48
7.4	even	3		441.2.s.d.374.5		48
7.5	odd	6		441.2.o.e.293.20	yes	48
7.6	odd	2	inner	441.2.i.d.68.19		48
9.2	odd	6		441.2.s.d.362.6		48
9.7	even	3		1323.2.s.d.656.20		48
21.2	odd	6		1323.2.o.e.881.6		48
21.5	even	6		1323.2.o.e.881.5		48
21.11	odd	6		1323.2.s.d.962.19		48
21.17	even	6		1323.2.s.d.962.20		48
21.20	even	2		1323.2.i.d.1097.22		48
63.2	odd	6		441.2.o.e.146.20	yes	48
63.11	odd	6	inner	441.2.i.d.227.5		48
63.16	even	3		1323.2.o.e.440.5		48
63.20	even	6		441.2.s.d.362.5		48
63.25	even	3		1323.2.i.d.521.22		48
63.34	odd	6		1323.2.s.d.656.19		48
63.38	even	6	inner	441.2.i.d.227.6		48
63.47	even	6		441.2.o.e.146.19	✓	48
63.52	odd	6		1323.2.i.d.521.7		48
63.61	odd	6		1323.2.o.e.440.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.19		48	7.6	odd	2	inner
441.2.i.d.68.20		48	1.1	even	1	trivial
441.2.i.d.227.5		48	63.11	odd	6	inner
441.2.i.d.227.6		48	63.38	even	6	inner
441.2.o.e.146.19	✓	48	63.47	even	6
441.2.o.e.146.20	yes	48	63.2	odd	6
441.2.o.e.293.19	yes	48	7.2	even	3
441.2.o.e.293.20	yes	48	7.5	odd	6
441.2.s.d.362.5		48	63.20	even	6
441.2.s.d.362.6		48	9.2	odd	6
441.2.s.d.374.5		48	7.4	even	3
441.2.s.d.374.6		48	7.3	odd	6
1323.2.i.d.521.7		48	63.52	odd	6
1323.2.i.d.521.22		48	63.25	even	3
1323.2.i.d.1097.7		48	3.2	odd	2
1323.2.i.d.1097.22		48	21.20	even	2
1323.2.o.e.440.5		48	63.16	even	3
1323.2.o.e.440.6		48	63.61	odd	6
1323.2.o.e.881.5		48	21.5	even	6
1323.2.o.e.881.6		48	21.2	odd	6
1323.2.s.d.656.19		48	63.34	odd	6
1323.2.s.d.656.20		48	9.7	even	3
1323.2.s.d.962.19		48	21.11	odd	6
1323.2.s.d.962.20		48	21.17	even	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.86894i q^{2} +(1.72324 + 0.174470i) q^{3} -1.49292 q^{4} +(-1.25287 - 2.17003i) q^{5} +(-0.326074 + 3.22063i) q^{6} +0.947692i q^{8} +(2.93912 + 0.601309i) q^{9} +(4.05565 - 2.34153i) q^{10} +(4.85803 + 2.80479i) q^{11} +(-2.57267 - 0.260471i) q^{12} +(-0.384312 - 0.221883i) q^{13} +(-1.78039 - 3.95807i) q^{15} -4.75703 q^{16} +(1.53885 + 2.66536i) q^{17} +(-1.12381 + 5.49303i) q^{18} +(2.22932 + 1.28710i) q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(-0.165344 + 1.63310i) q^{24} +(-0.639351 + 1.10739i) q^{25} +(0.414685 - 0.718255i) q^{26} +(4.95990 + 1.54899i) q^{27} +(2.71041 - 1.56485i) q^{29} +(7.39739 - 3.32743i) q^{30} -10.4669i q^{31} -6.99520i q^{32} +(7.88221 + 5.68091i) q^{33} +(-4.98140 + 2.87601i) q^{34} +(-4.38788 - 0.897709i) q^{36} +(0.708168 - 1.22658i) q^{37} +(-2.40550 + 4.16645i) q^{38} +(-0.623551 - 0.449409i) q^{39} +(2.05652 - 1.18733i) q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(-7.25268 - 4.18733i) q^{44} +(-2.37747 - 7.13134i) q^{45} +(-7.37492 - 12.7737i) q^{46} -2.14380 q^{47} +(-8.19750 - 0.829960i) q^{48} +(-2.06964 - 1.19491i) q^{50} +(2.18678 + 4.86155i) q^{51} +(0.573749 + 0.331254i) q^{52} +(4.20379 - 2.42706i) q^{53} +(-2.89496 + 9.26974i) q^{54} -14.0561i q^{55} +(3.61709 + 2.60693i) q^{57} +(2.92461 + 5.06558i) q^{58} -7.30991 q^{59} +(2.65798 + 5.90910i) q^{60} -8.55576i q^{61} +19.5619 q^{62} +3.55953 q^{64} +1.11196i q^{65} +(-10.6173 + 14.7314i) q^{66} -1.86888 q^{67} +(-2.29739 - 3.97919i) q^{68} +(-12.4664 + 5.60753i) q^{69} +2.95338i q^{71} +(-0.569856 + 2.78538i) q^{72} +(-7.37804 + 4.25971i) q^{73} +(2.29241 + 1.32352i) q^{74} +(-1.29496 + 1.79675i) q^{75} +(-3.32820 - 1.92154i) q^{76} +(0.839916 - 1.16538i) q^{78} -0.574261 q^{79} +(5.95992 + 10.3229i) q^{80} +(8.27686 + 3.53464i) q^{81} +(-5.33036 - 3.07748i) q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(4.94370 - 2.22373i) q^{87} +(-2.65807 + 4.60392i) q^{88} +(-3.78929 + 6.56325i) q^{89} +(13.3280 - 4.44334i) q^{90} +(10.2038 - 5.89115i) q^{92} +(1.82616 - 18.0369i) q^{93} -4.00663i q^{94} -6.45024i q^{95} +(1.22045 - 12.0544i) q^{96} +(3.22662 - 1.86289i) q^{97} +(12.5918 + 11.1648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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