LMFDB - Embedded newform 441.2.o.e.293.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(146,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.146"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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			293.19
Character	$\chi$	$=$	441.293
Dual form			441.2.o.e.146.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61855 - 0.934468i) q^{2} +(-1.01272 + 1.40514i) q^{3} +(0.746462 - 1.29291i) q^{4} +(-1.25287 + 2.17003i) q^{5} +(-0.326074 + 3.22063i) q^{6} +0.947692i q^{8} +(-0.948811 - 2.84601i) q^{9} +4.68306i q^{10} +(-4.85803 + 2.80479i) q^{11} +(1.06076 + 2.35823i) q^{12} +(-0.384312 - 0.221883i) q^{13} +(-1.78039 - 3.95807i) q^{15} +(2.37851 + 4.11970i) q^{16} -3.07770 q^{17} +(-4.19520 - 3.71976i) q^{18} -2.57419i q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(6.83476 + 3.94605i) q^{23} +(-1.33164 - 0.959743i) q^{24} +(-0.639351 - 1.10739i) q^{25} -0.829370 q^{26} +(4.95990 + 1.54899i) q^{27} +(2.71041 - 1.56485i) q^{29} +(-6.58033 - 4.74261i) q^{30} +(9.06457 + 5.23343i) q^{31} +(6.05802 + 3.49760i) q^{32} +(0.978704 - 9.66665i) q^{33} +(-4.98140 + 2.87601i) q^{34} +(-4.38788 - 0.897709i) q^{36} -1.41634 q^{37} +(-2.40550 - 4.16645i) q^{38} +(0.700975 - 0.315306i) q^{39} +(-2.05652 - 1.18733i) q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +8.37467i q^{44} +(7.36465 + 1.50672i) q^{45} +14.7498 q^{46} +(1.07190 + 1.85659i) q^{47} +(-8.19750 - 0.829960i) q^{48} +(-2.06964 - 1.19491i) q^{50} +(3.11684 - 4.32458i) q^{51} +(-0.573749 + 0.331254i) q^{52} +4.85412i q^{53} +(9.47532 - 2.12776i) q^{54} -14.0561i q^{55} +(3.61709 + 2.60693i) q^{57} +(2.92461 - 5.06558i) q^{58} +(3.65496 - 6.33057i) q^{59} +(-6.44642 - 0.652671i) q^{60} +(-7.40950 + 4.27788i) q^{61} +19.5619 q^{62} +3.55953 q^{64} +(0.962984 - 0.555979i) q^{65} +(-7.44910 - 16.5605i) q^{66} +(0.934442 - 1.61850i) q^{67} +(-2.29739 + 3.97919i) q^{68} +(-12.4664 + 5.60753i) q^{69} +2.95338i q^{71} +(2.69714 - 0.899181i) q^{72} -8.51943i q^{73} +(-2.29241 + 1.32352i) q^{74} +(2.20351 + 0.223096i) q^{75} +(-3.32820 - 1.92154i) q^{76} +(0.839916 - 1.16538i) q^{78} +(0.287130 + 0.497324i) q^{79} -11.9198 q^{80} +(-7.19951 + 5.40065i) q^{81} +6.15497i q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(-15.3981 - 8.89008i) q^{86} +(-0.546041 + 5.39324i) q^{87} +(-2.65807 - 4.60392i) q^{88} +7.57858 q^{89} +(13.3280 - 4.44334i) q^{90} +(10.2038 - 5.89115i) q^{92} +(-16.5335 + 7.43697i) q^{93} +(3.46984 + 2.00332i) q^{94} +(5.58607 + 3.22512i) q^{95} +(-11.0497 + 4.97026i) q^{96} +(3.22662 - 1.86289i) q^{97} +(12.5918 + 11.1648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.61855	−	0.934468i	1.14449	−	0.660769i	0.196948	−	0.980414i	$-0.436897\pi$
$2$	1.61855	−	0.934468i	1.14449	−	0.660769i	0.947537	+	0.319645i	$0.103564\pi$
$3$	−1.01272	+	1.40514i	−0.584692	+	0.811255i
$3$	−1.01272	+	1.40514i	−0.584692	+	0.811255i
$4$	0.746462	−	1.29291i	0.373231	−	0.646455i
$5$	−1.25287	+	2.17003i	−0.560299	+	0.970467i	0.437171	+	0.899378i	$0.355980\pi$
$5$	−1.25287	+	2.17003i	−0.560299	+	0.970467i	−0.997470	+	0.0710881i	$0.977353\pi$
$6$	−0.326074	+	3.22063i	−0.133119	+	1.31482i
$7$		0			0
$7$		0			0
$8$			0.947692i			0.335060i
$9$	−0.948811	−	2.84601i	−0.316270	−	0.948669i
$10$			4.68306i			1.48091i
$11$	−4.85803	+	2.80479i	−1.46475	+	0.845675i	−0.999225	−	0.0393590i	$-0.987468\pi$
$11$	−4.85803	+	2.80479i	−1.46475	+	0.845675i	−0.465527	+	0.885034i	$0.654135\pi$
$12$	1.06076	+	2.35823i	0.306215	+	0.680763i
$13$	−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
$16$	2.37851	+	4.11970i	0.594628	+	1.02993i
$17$	−3.07770			−0.746451			−0.373226	−	0.927741i	$-0.621748\pi$
$17$	−3.07770			−0.746451			−0.373226	+	0.927741i	$0.621748\pi$
$18$	−4.19520	−	3.71976i	−0.988818	−	0.876756i
$19$		−	2.57419i		−	0.590560i	−0.955411	−	0.295280i	$-0.904587\pi$
$19$		−	2.57419i		−	0.590560i	0.955411	−	0.295280i	$-0.0954130\pi$
$20$	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	$-0.0257395\pi$
$23$	6.83476	+	3.94605i	1.42515	+	0.822808i	0.428413	+	0.903583i	$0.359073\pi$
$24$	−1.33164	−	0.959743i	−0.271819	−	0.195907i
$25$	−0.639351	−	1.10739i	−0.127870	−	0.221478i
$26$	−0.829370			−0.162653
$27$	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	$0.239483\pi$
$30$	−6.58033	−	4.74261i	−1.20140	−	0.865878i
$31$	9.06457	+	5.23343i	1.62805	+	0.939952i	0.984675	+	0.174397i	$0.0557975\pi$
$31$	9.06457	+	5.23343i	1.62805	+	0.939952i	0.643370	+	0.765556i	$0.277536\pi$
$32$	6.05802	+	3.49760i	1.07092	+	0.618294i
$33$	0.978704	−	9.66665i	0.170370	−	1.68275i
$34$	−4.98140	+	2.87601i	−0.854303	+	0.493232i
$35$		0			0
$36$	−4.38788	−	0.897709i	−0.731314	−	0.149618i
$37$	−1.41634			−0.232844			−0.116422	−	0.993200i	$-0.537143\pi$
$37$	−1.41634			−0.232844			−0.116422	+	0.993200i	$0.537143\pi$
$38$	−2.40550	−	4.16645i	−0.390224	−	0.675887i
$39$	0.700975	−	0.315306i	0.112246	−	0.0504894i
$40$	−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	$-0.425011\pi$
$44$			8.37467i			1.26253i
$45$	7.36465	+	1.50672i	1.09786	+	0.224609i
$46$	14.7498			2.17474
$47$	1.07190	+	1.85659i	0.156353	+	0.270811i	0.933551	−	0.358445i	$-0.116693\pi$
$47$	1.07190	+	1.85659i	0.156353	+	0.270811i	−0.777198	+	0.629256i	$0.783360\pi$
$48$	−8.19750	−	0.829960i	−1.18321	−	0.119794i
$49$		0			0
$50$	−2.06964	−	1.19491i	−0.292691	−	0.168985i
$51$	3.11684	−	4.32458i	0.436444	−	0.605563i
$52$	−0.573749	+	0.331254i	−0.0795647	+	0.0459367i
$53$			4.85412i			0.666764i	0.942792	+	0.333382i	$0.108190\pi$
$53$			4.85412i			0.666764i	−0.942792	+	0.333382i	$0.891810\pi$
$54$	9.47532	−	2.12776i	1.28943	−	0.289551i
$55$		−	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
$59$	3.65496	−	6.33057i	0.475835	−	0.824170i	−0.523782	−	0.851852i	$-0.675479\pi$
$59$	3.65496	−	6.33057i	0.475835	−	0.824170i	0.999617	+	0.0276824i	$0.00881270\pi$
$60$	−6.44642	−	0.652671i	−0.832230	−	0.0842595i
$61$	−7.40950	+	4.27788i	−0.948690	+	0.547726i	−0.892674	−	0.450704i	$-0.851173\pi$
$61$	−7.40950	+	4.27788i	−0.948690	+	0.547726i	−0.0560160	+	0.998430i	$0.517840\pi$
$62$	19.5619			2.48437
$63$		0			0
$64$	3.55953			0.444941
$65$	0.962984	−	0.555979i	0.119443	−	0.0689607i
$66$	−7.44910	−	16.5605i	−0.916920	−	2.03845i
$67$	0.934442	−	1.61850i	0.114160	−	0.197731i	−0.803284	−	0.595597i	$-0.796916\pi$
$67$	0.934442	−	1.61850i	0.114160	−	0.197731i	0.917444	+	0.397865i	$0.130249\pi$
$68$	−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	$0.943926\pi$
$72$	2.69714	−	0.899181i	0.317861	−	0.105969i
$73$		−	8.51943i		−	0.997124i	−0.866854	−	0.498562i	$-0.833862\pi$
$73$		−	8.51943i		−	0.997124i	0.866854	−	0.498562i	$-0.166138\pi$
$74$	−2.29241	+	1.32352i	−0.266487	+	0.153856i
$75$	2.20351	+	0.223096i	0.254440	+	0.0257609i
$76$	−3.32820	−	1.92154i	−0.381771	−	0.220415i
$77$		0			0
$78$	0.839916	−	1.16538i	0.0951018	−	0.131953i
$79$	0.287130	+	0.497324i	0.0323047	+	0.0559533i	0.881726	−	0.471762i	$-0.156382\pi$
$79$	0.287130	+	0.497324i	0.0323047	+	0.0559533i	−0.849421	+	0.527716i	$0.823049\pi$
$80$	−11.9198			−1.33268
$81$	−7.19951	+	5.40065i	−0.799946	+	0.600072i
$82$			6.15497i			0.679702i
$83$	−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
$87$	−0.546041	+	5.39324i	−0.0585417	+	0.578216i
$88$	−2.65807	−	4.60392i	−0.283352	−	0.490779i
$89$	7.57858			0.803328			0.401664	−	0.915787i	$-0.368432\pi$
$89$	7.57858			0.803328			0.401664	+	0.915787i	$0.368432\pi$
$90$	13.3280	−	4.44334i	1.40490	−	0.468369i
$91$		0			0
$92$	10.2038	−	5.89115i	1.06382	−	0.614195i
$93$	−16.5335	+	7.43697i	−1.71445	+	0.771178i
$94$	3.46984	+	2.00332i	0.357887	+	0.206626i
$95$	5.58607	+	3.22512i	0.573119	+	0.330890i
$96$	−11.0497	+	4.97026i	−1.12775	+	0.507275i
$97$	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
$100$	−1.90901			−0.190901
$101$	3.76725	+	6.52506i	0.374855	+	0.649268i	0.990305	−	0.138908i	$-0.0443592\pi$
$101$	3.76725	+	6.52506i	0.374855	+	0.649268i	−0.615450	+	0.788176i	$0.711026\pi$
$102$	1.00356	−	9.91212i	0.0993670	−	0.981447i
$103$	12.4045	+	7.16173i	1.22225	+	0.705666i	0.965397	−	0.260784i	$-0.0839812\pi$
$103$	12.4045	+	7.16173i	1.22225	+	0.705666i	0.256853	+	0.966451i	$0.417315\pi$
$104$	0.210276	−	0.364210i	0.0206193	−	0.0357137i
$105$		0			0
$106$	4.53602	+	7.85662i	0.440577	+	0.763102i
$107$			13.4866i			1.30380i	0.758305	+	0.651900i	$0.226028\pi$
$107$			13.4866i			1.30380i	−0.758305	+	0.651900i	$0.773972\pi$
$108$	5.70509	−	5.25645i	0.548972	−	0.505802i
$109$	−0.918695			−0.0879950			−0.0439975	−	0.999032i	$-0.514009\pi$
$109$	−0.918695			−0.0879950			−0.0439975	+	0.999032i	$0.514009\pi$
$110$	−13.1350	−	22.7504i	−1.25237	−	2.16917i
$111$	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	$0.595113\pi$
$114$	8.29052	+	0.839377i	0.776478	+	0.0786149i
$115$	−17.1261	+	9.88775i	−1.59702	+	0.922037i
$116$		−	4.67242i		−	0.433823i
$117$	−0.266840	+	1.30428i	−0.0246694	+	0.120581i
$118$		−	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
$122$	−7.99508	+	13.8479i	−0.723841	+	1.25373i
$123$	−2.33997	−	5.20211i	−0.210988	−	0.469059i
$124$	13.5327	−	7.81312i	1.21527	−	0.701639i
$125$	−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	$0.393929\pi$
$128$	−6.35477	+	3.66893i	−0.561688	+	0.324291i
$129$	16.3941	+	1.65983i	1.44342	+	0.146139i
$130$	1.03909	−	1.79976i	0.0911342	−	0.157849i
$131$	−3.93150	+	6.80955i	−0.343497	+	0.594953i	−0.985079	−	0.172100i	$-0.944945\pi$
$131$	−3.93150	+	6.80955i	−0.343497	+	0.594953i	0.641583	+	0.767054i	$0.278278\pi$
$132$	−11.7675	−	8.48116i	−1.02423	−	0.738191i
$133$		0			0
$134$		−	3.49283i		−	0.301734i
$135$	−9.57545	+	8.82246i	−0.824124	+	0.759316i
$136$		−	2.91671i		−	0.250106i
$137$	−10.0198	+	5.78491i	−0.856046	+	0.494238i	−0.862686	−	0.505740i	$-0.831220\pi$
$137$	−10.0198	+	5.78491i	−0.856046	+	0.494238i	0.00664016	+	0.999978i	$0.497886\pi$
$138$	−14.9374	+	20.7255i	−1.27156	+	1.76427i
$139$	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
$142$	2.75984	+	4.78018i	0.231600	+	0.401144i
$143$	2.48933			0.208169
$144$	9.46795	−	10.6781i	0.788996	−	0.889841i
$145$			7.84221i			0.651260i
$146$	−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	$-0.556370\pi$
$149$	−13.6315	−	7.87012i	−1.11673	−	0.644746i	−0.940565	+	0.339615i	$0.889703\pi$
$150$	3.77496	−	1.69802i	0.308225	−	0.138643i
$151$	0.991353	+	1.71707i	0.0806752	+	0.139734i	0.903540	−	0.428503i	$-0.140959\pi$
$151$	0.991353	+	1.71707i	0.0806752	+	0.139734i	−0.822865	+	0.568237i	$0.807626\pi$
$152$	2.43954			0.197873
$153$	2.92015	+	8.75915i	0.236081	+	0.708135i
$154$		0			0
$155$	−22.7134	+	13.1136i	−1.82438	+	1.05331i
$156$	0.115588	−	1.14166i	0.00925445	−	0.0914061i
$157$	−7.26790	−	4.19612i	−0.580041	−	0.334887i	0.181108	−	0.983463i	$-0.442031\pi$
$157$	−7.26790	−	4.19612i	−0.580041	−	0.334887i	−0.761150	+	0.648576i	$0.775365\pi$
$158$	0.929468	+	0.536628i	0.0739445	+	0.0426919i
$159$	−6.82069	−	4.91584i	−0.540916	−	0.389852i
$160$	−15.1798	+	8.76405i	−1.20007	+	0.692859i
$161$		0			0
$162$	−6.60602	+	15.4689i	−0.519018	+	1.21535i
$163$	−1.07411			−0.0841306			−0.0420653	−	0.999115i	$-0.513394\pi$
$163$	−1.07411			−0.0841306			−0.0420653	+	0.999115i	$0.513394\pi$
$164$	2.45832	+	4.25794i	0.191963	+	0.332489i
$165$	19.7507	+	14.2348i	1.53759	+	1.10818i
$166$	−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
$170$		−	14.4130i		−	1.10543i
$171$	−7.32617	+	2.44242i	−0.560246	+	0.186777i
$172$	−14.2030			−1.08297
$173$	0.501744	+	0.869046i	0.0381469	+	0.0660723i	0.884468	−	0.466600i	$-0.154521\pi$
$173$	0.501744	+	0.869046i	0.0381469	+	0.0660723i	−0.846322	+	0.532672i	$0.821188\pi$
$174$	4.15602	+	9.23947i	0.315067	+	0.700442i
$175$		0			0
$176$	−23.1098	−	13.3424i	−1.74197	−	1.00572i
$177$	5.19387	+	11.5468i	0.390395	+	0.867909i
$178$	12.2663	−	7.08195i	0.919398	−	0.530814i
$179$		−	1.47539i		−	0.110276i	−0.998479	−	0.0551379i	$-0.982440\pi$
$179$		−	1.47539i		−	0.110276i	0.998479	−	0.0551379i	$-0.0175599\pi$
$180$	7.44549	−	8.39713i	0.554954	−	0.625885i
$181$			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
$185$	1.77448	−	3.07349i	0.130462	−	0.225967i
$186$	−19.8107	+	27.4871i	−1.45259	+	2.01545i
$187$	14.9516	−	8.63229i	1.09337	−	0.631255i
$188$	3.20054			0.233423
$189$		0			0
$190$	12.0551			0.874568
$191$	11.4521	−	6.61187i	0.828644	−	0.478418i	−0.0247439	−	0.999694i	$-0.507877\pi$
$191$	11.4521	−	6.61187i	0.828644	−	0.478418i	0.853388	+	0.521276i	$0.174544\pi$
$192$	−3.60479	+	5.00162i	−0.260153	+	0.360961i
$193$	0.777855	−	1.34728i	0.0559912	−	0.0969796i	−0.836671	−	0.547705i	$-0.815501\pi$
$193$	0.777855	−	1.34728i	0.0559912	−	0.0969796i	0.892662	+	0.450726i	$0.148835\pi$
$194$	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	$0.943439\pi$
$198$	30.8135	+	6.30408i	2.18982	+	0.448012i
$199$		−	11.1922i		−	0.793394i	−0.917950	−	0.396697i	$-0.870156\pi$
$199$		−	11.1922i		−	0.793394i	0.917950	−	0.396697i	$-0.129844\pi$
$200$	1.04946	−	0.605908i	0.0742083	−	0.0428442i
$201$	1.32789	+	2.95210i	0.0936620	+	0.208225i
$202$	12.1949	+	7.04074i	0.858032	+	0.495385i
$203$		0			0
$204$	−3.26470	−	7.25793i	−0.228575	−	0.508157i
$205$	−4.12606	−	7.14655i	−0.288177	−	0.499137i
$206$	26.7696			1.86513
$207$	4.74559	−	23.1958i	0.329841	−	1.61222i
$208$		−	2.11100i		−	0.146372i
$209$	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
$213$	−4.14990	−	2.99093i	−0.284346	−	0.204935i
$214$	12.6028	+	21.8287i	0.861511	+	1.49218i
$215$	23.8383			1.62576
$216$	−1.46796	+	4.70046i	−0.0998824	+	0.319826i
$217$		0			0
$218$	−1.48695	+	0.858492i	−0.100709	+	0.0581444i
$219$	11.9710	+	8.62776i	0.808922	+	0.583010i
$220$	−18.1733	−	10.4923i	−1.22524	−	0.707394i
$221$	1.18280	+	0.682888i	0.0795635	+	0.0459360i
$222$	0.461830	−	4.56149i	0.0309960	−	0.306147i
$223$	−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
$226$	8.85695			0.589156
$227$	−7.33494	−	12.7045i	−0.486837	−	0.843227i	0.513048	−	0.858360i	$-0.328516\pi$
$227$	−7.33494	−	12.7045i	−0.486837	−	0.843227i	−0.999885	+	0.0151329i	$0.995183\pi$
$228$	6.07054	−	2.73060i	0.402031	−	0.180838i
$229$	2.92550	+	1.68904i	0.193322	+	0.111615i	0.593537	−	0.804807i	$-0.297731\pi$
$229$	2.92550	+	1.68904i	0.193322	+	0.111615i	−0.400215	+	0.916421i	$0.631064\pi$
$230$	−18.4796	+	32.0076i	−1.21851	+	2.11052i
$231$		0			0
$232$	1.48300	+	2.56863i	0.0973637	+	0.168639i
$233$			4.88009i			0.319706i	0.987141	+	0.159853i	$0.0511020\pi$
$233$			4.88009i			0.319706i	−0.987141	+	0.159853i	$0.948898\pi$
$234$	0.786915	+	2.36039i	0.0514423	+	0.154304i
$235$	−5.37180			−0.350418
$236$	−5.45657	−	9.45106i	−0.355193	−	0.615212i
$237$	−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	$0.496739\pi$
$240$	12.0714	−	16.7490i	0.779207	−	1.08114i
$241$	−0.666305	+	0.384691i	−0.0429205	+	0.0247801i	−0.521307	−	0.853369i	$-0.674555\pi$
$241$	−0.666305	+	0.384691i	−0.0429205	+	0.0247801i	0.478386	+	0.878150i	$0.341222\pi$
$242$		−	38.2521i		−	2.45894i
$243$	−0.297576	−	15.5856i	−0.0190895	−	0.999818i
$244$			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
$248$	−4.95968	+	8.59042i	−0.314940	+	0.545492i
$249$	14.5966	+	1.47784i	0.925020	+	0.0936541i
$250$	−15.0923	+	8.71353i	−0.954519	+	0.551092i
$251$	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
$254$	11.9327	−	6.88933i	0.748722	−	0.432275i
$255$	5.47949	+	12.1818i	0.343139	+	0.762851i
$256$	−10.4165	+	18.0420i	−0.651033	+	1.12762i
$257$	−14.4917	+	25.1004i	−0.903969	+	1.56572i	−0.0816738	+	0.996659i	$0.526027\pi$
$257$	−14.4917	+	25.1004i	−0.903969	+	1.56572i	−0.822295	+	0.569061i	$0.807307\pi$
$258$	28.0856	−	12.6332i	1.74853	−	0.786511i
$259$		0			0
$260$		−	1.66007i		−	0.102953i
$261$	−7.02525	−	6.22908i	−0.434852	−	0.385571i
$262$			14.6954i			0.907887i
$263$	11.8643	−	6.84988i	0.731586	−	0.422381i	−0.0874160	−	0.996172i	$-0.527861\pi$
$263$	11.8643	−	6.84988i	0.731586	−	0.422381i	0.819002	+	0.573790i	$0.194528\pi$
$264$	9.16100	+	0.927510i	0.563821	+	0.0570843i
$265$	−10.5336	−	6.08156i	−0.647072	−	0.373587i
$266$		0			0
$267$	−7.67496	+	10.6489i	−0.469700	+	0.651704i
$268$	−1.39505	−	2.41630i	−0.0852163	−	0.147599i
$269$	10.4795			0.638944			0.319472	−	0.947596i	$-0.396494\pi$
$269$	10.4795			0.638944			0.319472	+	0.947596i	$0.396494\pi$
$270$	−7.25401	+	23.2275i	−0.441465	+	1.41358i
$271$		−	6.54607i		−	0.397646i	−0.980035	−	0.198823i	$-0.936288\pi$
$271$		−	6.54607i		−	0.397646i	0.980035	−	0.198823i	$-0.0637118\pi$
$272$	−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
$276$	−2.05566	+	20.3038i	−0.123736	+	1.22214i
$277$	−11.2156	−	19.4261i	−0.673883	−	1.16720i	−0.976794	−	0.214181i	$-0.931292\pi$
$277$	−11.2156	−	19.4261i	−0.673883	−	1.16720i	0.302911	−	0.953019i	$-0.402041\pi$
$278$	36.6311			2.19699
$279$	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	$0.101071\pi$
$282$	−6.32890	+	2.84681i	−0.376880	+	0.169525i
$283$	16.4296	+	9.48563i	0.976638	+	0.563862i	0.901254	−	0.433292i	$-0.142648\pi$
$283$	16.4296	+	9.48563i	0.976638	+	0.563862i	0.0753848	+	0.997155i	$0.475981\pi$
$284$	3.81845	+	2.20459i	0.226584	+	0.130818i
$285$	−10.1888	+	4.58306i	−0.603535	+	0.271477i
$286$	4.02910	−	2.32620i	0.238246	−	0.137551i
$287$		0			0
$288$	4.20627	−	20.5597i	0.247857	−	1.21149i
$289$	−7.52777			−0.442810
$290$	7.32830	+	12.6930i	0.430333	+	0.745358i
$291$	−0.650038	+	6.42042i	−0.0381059	+	0.376372i
$292$	−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
$296$		−	1.34225i		−	0.0780167i
$297$	−28.4399	+	6.38642i	−1.65025	+	0.370578i
$298$	−29.4175			−1.70411
$299$	−1.75112	−	3.03303i	−0.101270	−	0.175405i
$300$	1.93328	−	2.68241i	0.111618	−	0.154869i
$301$		0			0
$302$	3.20910	+	1.85278i	0.184663	+	0.106615i
$303$	−12.9837	−	1.31455i	−0.745897	−	0.0755187i
$304$	10.6049	−	6.12275i	0.608233	−	0.351164i
$305$		−	21.4385i		−	1.22756i
$306$	12.9116	+	11.4483i	0.738105	+	0.654456i
$307$			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
$311$	6.64294	−	11.5059i	0.376687	−	0.652441i	−0.613891	−	0.789391i	$-0.710397\pi$
$311$	6.64294	−	11.5059i	0.376687	−	0.652441i	0.990578	+	0.136950i	$0.0437300\pi$
$312$	0.298813	+	0.664308i	0.0169170	+	0.0376090i
$313$	−27.3227	+	15.7748i	−1.54437	+	0.891643i	−0.545815	+	0.837905i	$0.683780\pi$
$313$	−27.3227	+	15.7748i	−1.54437	+	0.891643i	−0.998555	+	0.0537372i	$0.982887\pi$
$314$	−15.6846			−0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$	17.3819	−	10.0354i	0.976264	−	0.563646i	0.0751236	−	0.997174i	$-0.476065\pi$
$317$	17.3819	−	10.0354i	0.976264	−	0.563646i	0.901140	+	0.433528i	$0.142732\pi$
$318$	−15.6333	−	1.58280i	−0.876672	−	0.0887591i
$319$	−8.77816	+	15.2042i	−0.491483	+	0.851273i
$320$	−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
$324$	1.60839	+	13.3397i	0.0893549	+	0.741095i
$325$			0.567444i			0.0314761i
$326$	−1.73849	+	1.00372i	−0.0962862	+	0.0555909i
$327$	0.930378	−	1.29089i	0.0514500	−	0.0713864i
$328$	−2.70289	−	1.56052i	−0.149242	−	0.0861651i
$329$		0			0
$330$	45.2695	+	4.58333i	2.49200	+	0.252304i
$331$	−0.623957	−	1.08073i	−0.0342958	−	0.0594020i	0.848368	−	0.529407i	$-0.177585\pi$
$331$	−0.623957	−	1.08073i	−0.0342958	−	0.0594020i	−0.882664	+	0.470005i	$0.844252\pi$
$332$	−12.6457			−0.694023
$333$	1.34384	+	4.03090i	0.0736417	+	0.220892i
$334$		−	14.9414i		−	0.817559i
$335$	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
$339$	−7.48581	+	3.36720i	−0.406573	+	0.182881i
$340$	−5.75664	−	9.97079i	−0.312198	−	0.540742i
$341$	−58.7146			−3.17958
$342$	−9.57538	+	10.7992i	−0.517777	+	0.583956i
$343$		0			0
$344$	7.80798	−	4.50794i	0.420978	−	0.243052i
$345$	3.45024	−	34.0780i	0.185755	−	1.83470i
$346$	1.62419	+	0.937727i	0.0873171	+	0.0504125i
$347$	−23.4411	−	13.5337i	−1.25838	−	0.726529i	−0.285624	−	0.958342i	$-0.592201\pi$
$347$	−23.4411	−	13.5337i	−1.25838	−	0.726529i	−0.972760	+	0.231813i	$0.925534\pi$
$348$	6.56538	+	4.73183i	0.351941	+	0.253653i
$349$	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
$352$	−39.2401			−2.09150
$353$	1.26256	+	2.18682i	0.0671992	+	0.116392i	0.897667	−	0.440674i	$-0.145260\pi$
$353$	1.26256	+	2.18682i	0.0671992	+	0.116392i	−0.830468	+	0.557066i	$0.811927\pi$
$354$	19.1966	+	13.8355i	1.02029	+	0.735348i
$355$	−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
$359$			7.26762i			0.383570i	0.981437	+	0.191785i	$0.0614277\pi$
$359$			7.26762i			0.383570i	−0.981437	+	0.191785i	$0.938572\pi$
$360$	−1.42791	+	6.97942i	−0.0752573	+	0.367848i
$361$	12.3735			0.651239
$362$	14.0581	+	24.3494i	0.738880	+	1.27978i
$363$	14.5425	+	32.3303i	0.763285	+	1.69690i
$364$		0			0
$365$	18.4874	+	10.6737i	0.967675	+	0.558688i
$366$	−11.3614	−	25.2582i	−0.593871	−	1.32027i
$367$	−11.6714	+	6.73848i	−0.609242	+	0.351746i	−0.772669	−	0.634809i	$-0.781079\pi$
$367$	−11.6714	+	6.73848i	−0.609242	+	0.351746i	0.163427	+	0.986555i	$0.447745\pi$
$368$			37.5429i			1.95706i
$369$	9.67940	+	1.98029i	0.503889	+	0.103090i
$370$		−	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	0.375121	+	0.926976i	$0.377601\pi$
$373$	−11.8820	+	20.5801i	−0.615224	+	1.06560i	−0.990345	+	0.138624i	$0.955732\pi$
$374$	16.1332	−	27.9435i	0.834228	−	1.44492i
$375$	9.44316	−	13.1023i	0.487642	−	0.676600i
$376$	−1.75947	+	1.01583i	−0.0907379	+	0.0523875i
$377$	−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	$0.316449\pi$
$380$	8.33958	−	4.81486i	0.427812	−	0.246997i
$381$	−7.46621	+	10.3593i	−0.382505	+	0.530723i
$382$	12.3572	−	21.4032i	0.632248	−	1.09509i
$383$	6.47930	−	11.2225i	0.331077	−	0.573442i	−0.651646	−	0.758523i	$-0.725921\pi$
$383$	6.47930	−	11.2225i	0.331077	−	0.573442i	0.982723	+	0.185081i	$0.0592547\pi$
$384$	1.28024	−	12.6449i	0.0653319	−	0.645282i
$385$		0			0
$386$		−	2.90752i		−	0.147989i
$387$	−18.9348	+	21.3550i	−0.962511	+	1.08553i
$388$		−	5.56231i		−	0.282384i
$389$	9.48037	−	5.47350i	0.480674	−	0.277517i	−0.240023	−	0.970767i	$-0.577155\pi$
$389$	9.48037	−	5.47350i	0.480674	−	0.277517i	0.720697	+	0.693250i	$0.243822\pi$
$390$	1.47660	+	3.28271i	0.0747705	+	0.166226i
$391$	−21.0353	−	12.1447i	−1.06380	−	0.614186i
$392$		0			0
$393$	−5.58685	−	12.4204i	−0.281819	−	0.626528i
$394$	4.63669	+	8.03098i	0.233593	+	0.404595i
$395$	−1.43894			−0.0724011
$396$	23.8344	−	7.94598i	1.19772	−	0.399301i
$397$		−	29.8901i		−	1.50014i	−0.661358	−	0.750071i	$-0.730019\pi$
$397$		−	29.8901i		−	1.50014i	0.661358	−	0.750071i	$-0.269981\pi$
$398$	−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	$-0.174234\pi$
$401$	16.6233	+	9.59744i	0.830126	+	0.479273i	−0.0237698	+	0.999717i	$0.507567\pi$
$402$	4.90789	+	3.53724i	0.244783	+	0.176422i
$403$	−2.32242	−	4.02254i	−0.115688	−	0.200377i
$404$	11.2484			0.559630
$405$	−2.69953	−	22.3894i	−0.134141	−	1.11254i
$406$		0			0
$407$	6.88060	−	3.97252i	0.341059	−	0.196910i
$408$	4.09837	+	2.95380i	0.202900	+	0.146235i
$409$	−24.9737	−	14.4186i	−1.23487	−	0.712953i	−0.266830	−	0.963744i	$-0.585976\pi$
$409$	−24.9737	−	14.4186i	−1.23487	−	0.712953i	−0.968041	+	0.250790i	$0.919309\pi$
$410$	−13.3565	−	7.71135i	−0.659628	−	0.380837i
$411$	2.01859	−	19.9376i	0.0995698	−	0.983449i
$412$	18.5190	−	10.6919i	0.912363	−	0.526753i
$413$		0			0
$414$	−13.9948	−	41.9781i	−0.687807	−	2.06311i
$415$	21.2246			1.04188
$416$	−1.55211	−	2.68834i	−0.0760986	−	0.131807i
$417$	−30.9602	+	13.9263i	−1.51613	+	0.681972i
$418$	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	$0.620702\pi$
$422$		−	28.7079i		−	1.39748i
$423$	4.26683	−	4.81219i	0.207460	−	0.233977i
$424$	−4.60021			−0.223406
$425$	1.96773	+	3.40821i	0.0954490	+	0.165322i
$426$	−9.51173	−	0.963020i	−0.460845	−	0.0466585i
$427$		0			0
$428$	17.4370	+	10.0673i	0.842849	+	0.486619i
$429$	−2.52099	+	3.49785i	−0.121715	+	0.168878i
$430$	38.5834	−	22.2762i	1.86066	−	1.07425i
$431$		−	10.8434i		−	0.522308i	−0.965297	−	0.261154i	$-0.915897\pi$
$431$		−	10.8434i		−	0.522308i	0.965297	−	0.261154i	$-0.0841031\pi$
$432$	5.41581	+	24.1176i	0.260568	+	1.16036i
$433$		−	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
$437$	10.1579	−	17.5940i	0.485918	−	0.841634i
$438$	27.4379	+	2.77796i	1.31103	+	0.132736i
$439$	27.6736	−	15.9773i	1.32079	−	0.762557i	0.336933	−	0.941529i	$-0.390611\pi$
$439$	27.6736	−	15.9773i	1.32079	−	0.762557i	0.983854	+	0.178972i	$0.0572772\pi$
$440$	13.3208			0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$	21.4748	−	12.3985i	1.02030	−	0.589068i	0.106107	−	0.994355i	$-0.466162\pi$
$443$	21.4748	−	12.3985i	1.02030	−	0.589068i	0.914190	+	0.405286i	$0.132828\pi$
$444$	−1.50239	−	3.34005i	−0.0713004	−	0.158512i
$445$	−9.49496	+	16.4458i	−0.450104	+	0.779603i
$446$	−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	$-0.105346\pi$
$450$	−1.43702	+	7.02395i	−0.0677416	+	0.331112i
$451$		−	18.4740i		−	0.869906i
$452$	6.12715	−	3.53751i	0.288197	−	0.166390i
$453$	−3.41668	−	0.345923i	−0.160530	−	0.0162529i
$454$	−23.7439	−	13.7085i	−1.11436	−	0.643374i
$455$		0			0
$456$	−2.47056	+	3.42789i	−0.115695	+	0.160525i
$457$	−13.6554	−	23.6518i	−0.638771	−	1.10638i	−0.985703	−	0.168494i	$-0.946110\pi$
$457$	−13.6554	−	23.6518i	−0.638771	−	1.10638i	0.346931	−	0.937890i	$-0.387224\pi$
$458$	6.31340			0.295006
$459$	−15.2651	−	4.76732i	−0.712513	−	0.222520i
$460$			29.5233i			1.37653i
$461$	−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
$465$	4.57587	−	45.1958i	0.212201	−	2.09590i
$466$	4.56029	+	7.89866i	0.211251	+	0.365898i
$467$	15.9048			0.735988			0.367994	−	0.929828i	$-0.380045\pi$
$467$	15.9048			0.735988			0.367994	+	0.929828i	$0.380045\pi$
$468$	1.48713	+	1.31860i	0.0687427	+	0.0609521i
$469$		0			0
$470$	−8.69451	+	5.01978i	−0.401048	+	0.231545i
$471$	13.2564	−	5.96290i	0.610824	−	0.274756i
$472$	5.99943	+	3.46377i	0.276146	+	0.159433i
$473$	46.2169	+	26.6834i	2.12506	+	1.22690i
$474$	−1.69532	+	0.762576i	−0.0778687	+	0.0350263i
$475$	−2.85063	+	1.64581i	−0.130796	+	0.0755151i
$476$		0			0
$477$	13.8149	−	4.60564i	0.632539	−	0.210878i
$478$	29.4042			1.34492
$479$	−6.92685	−	11.9976i	−0.316496	−	0.548187i	0.663259	−	0.748390i	$-0.269173\pi$
$479$	−6.92685	−	11.9976i	−0.316496	−	0.548187i	−0.979754	+	0.200204i	$0.935840\pi$
$480$	3.05813	−	30.2051i	0.139584	−	1.37867i
$481$	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
$485$			9.33582i			0.423918i
$486$	−15.0459	−	24.9480i	−0.682496	−	1.13166i
$487$	28.7987			1.30499			0.652496	−	0.757792i	$-0.273722\pi$
$487$	28.7987			1.30499			0.652496	+	0.757792i	$0.273722\pi$
$488$	−4.05411	−	7.02193i	−0.183521	−	0.317868i
$489$	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	$-0.672138\pi$
$492$	−8.47257	−	0.857809i	−0.381973	−	0.0386730i
$493$	−8.34181	+	4.81615i	−0.375696	+	0.216908i
$494$			2.13496i			0.0960562i
$495$	−40.0038	+	13.3366i	−1.79803	+	0.599435i
$496$			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	−0.824617	−	0.565691i	$-0.808609\pi$
$499$	1.73333	−	3.00222i	0.0775946	−	0.134398i	0.902212	+	0.431294i	$0.141943\pi$
$500$	−6.96045	+	12.0558i	−0.311281	+	0.539154i
$501$	5.68038	+	12.6283i	0.253780	+	0.564193i
$502$	1.85395	−	1.07038i	0.0827458	−	0.0477733i
$503$	−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
$506$	−71.6552	+	41.3701i	−3.18546	+	1.83913i
$507$	22.0628	+	2.23376i	0.979842	+	0.0992046i
$508$	5.50326	−	9.53193i	0.244168	−	0.422911i
$509$	17.9062	−	31.0144i	0.793678	−	1.37469i	−0.129997	−	0.991514i	$-0.541497\pi$
$509$	17.9062	−	31.0144i	0.793678	−	1.37469i	0.923675	−	0.383176i	$-0.125170\pi$
$510$	20.2523	+	14.5963i	0.896786	+	0.646336i
$511$		0			0
$512$			24.2599i			1.07215i
$513$	3.98740	−	12.7677i	0.176048	−	0.563709i
$514$			54.1682i			2.38926i
$515$	−31.0823	+	17.9454i	−1.36965	+	0.790768i
$516$	14.3836	−	19.9571i	0.633201	−	0.878561i
$517$	−10.4147	−	6.01291i	−0.458036	−	0.264447i
$518$		0			0
$519$	−1.72925	−	0.175079i	−0.0759057	−	0.00768511i
$520$	0.526897	+	0.912612i	0.0231060	+	0.0400207i
$521$	−26.9216			−1.17946			−0.589729	−	0.807601i	$-0.700766\pi$
$521$	−26.9216			−1.17946			−0.589729	+	0.807601i	$0.700766\pi$
$522$	−17.1916	−	3.51719i	−0.752455	−	0.153943i
$523$		−	9.03185i		−	0.394935i	−0.980309	−	0.197468i	$-0.936728\pi$
$523$		−	9.03185i		−	0.394935i	0.980309	−	0.197468i	$-0.0632717\pi$
$524$	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
$528$	42.1516	−	18.9603i	1.83441	−	0.825140i
$529$	19.6426	+	34.0220i	0.854026	+	1.47922i
$530$	−22.7321			−0.987420
$531$	−21.4847	−	4.39552i	−0.932357	−	0.190749i
$532$		0			0
$533$	1.26565	−	0.730726i	0.0548216	−	0.0316513i
$534$	−2.47118	+	24.4078i	−0.106938	+	1.05623i
$535$	−29.2664	−	16.8969i	−1.26530	−	0.730518i
$536$	1.53384	+	0.885563i	0.0662518	+	0.0382505i
$537$	2.07312	+	1.49415i	0.0894619	+	0.0644774i
$538$	16.9615	−	9.79273i	0.731262	−	0.422195i
$539$		0			0
$540$	4.25893	+	18.9658i	0.183275	+	0.816159i
$541$	11.3358			0.487366			0.243683	−	0.969855i	$-0.421644\pi$
$541$	11.3358			0.487366			0.243683	+	0.969855i	$0.421644\pi$
$542$	−6.11710	−	10.5951i	−0.262752	−	0.455100i
$543$	−21.1389	−	15.2353i	−0.907155	−	0.653810i
$544$	−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	$0.521367\pi$
$548$			17.2729i			0.737861i
$549$	19.2051	+	17.0286i	0.819653	+	0.726763i
$550$	13.4058			0.571627
$551$	−4.02823	−	6.97711i	−0.171609	−	0.297235i
$552$	−5.31421	−	11.8143i	−0.226188	−	0.502850i
$553$		0			0
$554$	−36.3061	−	20.9613i	−1.54250	−	0.890562i
$555$	2.52162	+	5.60596i	0.107037	+	0.237960i
$556$	25.3410	−	14.6306i	1.07470	−	0.620478i
$557$		−	7.26499i		−	0.307827i	−0.988084	−	0.153914i	$-0.950812\pi$
$557$		−	7.26499i		−	0.307827i	0.988084	−	0.153914i	$-0.0491878\pi$
$558$	−18.5606	−	55.6733i	−0.785731	−	2.35684i
$559$			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
$563$	−11.5409	+	19.9894i	−0.486390	+	0.842453i	−0.999878	−	0.0156446i	$-0.995020\pi$
$563$	−11.5409	+	19.9894i	−0.486390	+	0.842453i	0.513487	+	0.858097i	$0.328353\pi$
$564$	−3.24123	+	4.49719i	−0.136481	+	0.189366i
$565$	−10.2838	+	5.93738i	−0.432644	+	0.249787i
$566$	35.4561			1.49033
$567$		0			0
$568$	−2.79889			−0.117439
$569$	−15.5482	+	8.97677i	−0.651815	+	0.376326i	−0.789151	−	0.614199i	$-0.789479\pi$
$569$	−15.5482	+	8.97677i	−0.651815	+	0.376326i	0.137336	+	0.990525i	$0.456146\pi$
$570$	−12.2084	+	16.9390i	−0.511353	+	0.709498i
$571$	7.04234	−	12.1977i	0.294713	−	0.510457i	−0.680205	−	0.733022i	$-0.738109\pi$
$571$	7.04234	−	12.1977i	0.294713	−	0.510457i	0.974918	+	0.222564i	$0.0714427\pi$
$572$	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
$576$	−3.37732	−	10.1304i	−0.140722	−	0.422102i
$577$			30.0675i			1.25172i	0.779934	+	0.625862i	$0.215253\pi$
$577$			30.0675i			1.25172i	−0.779934	+	0.625862i	$0.784747\pi$
$578$	−12.1841	+	7.03447i	−0.506790	+	0.292595i
$579$	1.10537	+	2.45741i	0.0459376	+	0.102126i
$580$	10.1393	+	5.85392i	0.421011	+	0.243071i
$581$		0			0
$582$	4.94756	+	10.9992i	0.205083	+	0.455931i
$583$	−13.6148	−	23.5815i	−0.563866	−	0.976644i
$584$	8.07379			0.334096
$585$	−2.49601	−	2.21314i	−0.103197	−	0.0915021i
$586$			16.4891i			0.681158i
$587$	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
$591$	−6.97207	−	5.02494i	−0.286793	−	0.206699i
$592$	−3.36877	−	5.83489i	−0.138456	−	0.239812i
$593$	−2.04317			−0.0839028			−0.0419514	−	0.999120i	$-0.513357\pi$
$593$	−2.04317			−0.0839028			−0.0419514	+	0.999120i	$0.513357\pi$
$594$	−40.0635	+	36.9130i	−1.64382	+	1.51456i
$595$		0			0
$596$	−20.3507	+	11.7495i	−0.833598	+	0.481278i
$597$	15.7266	+	11.3345i	0.643645	+	0.463891i
$598$	−5.66854	−	3.27273i	−0.231804	−	0.133832i
$599$	−15.7873	−	9.11478i	−0.645050	−	0.372420i	0.141507	−	0.989937i	$-0.454805\pi$
$599$	−15.7873	−	9.11478i	−0.645050	−	0.372420i	−0.786557	+	0.617517i	$0.788139\pi$
$600$	−0.211426	+	2.08825i	−0.00863143	+	0.0852525i
$601$	−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
$604$	2.96003			0.120442
$605$	25.6428	+	44.4146i	1.04253	+	1.80571i
$606$	−22.2432	+	10.0052i	−0.903568	+	0.406435i
$607$	17.1730	+	9.91482i	0.697030	+	0.402430i	0.806240	−	0.591588i	$-0.201499\pi$
$607$	17.1730	+	9.91482i	0.697030	+	0.402430i	−0.109211	+	0.994019i	$0.534832\pi$
$608$	9.00349	−	15.5945i	0.365140	−	0.632440i
$609$		0			0
$610$	−20.0336	−	34.6991i	−0.811135	−	1.40493i
$611$		−	0.951346i		−	0.0384873i
$612$	13.5046	+	2.76288i	0.545891	+	0.111683i
$613$	−12.6882			−0.512473			−0.256237	−	0.966614i	$-0.582483\pi$
$613$	−12.6882			−0.512473			−0.256237	+	0.966614i	$0.582483\pi$
$614$	26.8690	+	46.5385i	1.08435	+	1.87814i
$615$	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	$0.634261\pi$
$618$	−27.1100	+	37.6150i	−1.09053	+	1.51310i
$619$	0.231999	−	0.133945i	0.00932485	−	0.00538370i	−0.495330	−	0.868705i	$-0.664953\pi$
$619$	0.231999	−	0.133945i	0.00932485	−	0.00538370i	0.504655	+	0.863321i	$0.331620\pi$
$620$			39.1552i			1.57251i
$621$	27.7873	+	30.1590i	1.11507	+	1.21024i
$622$		−	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
$626$	−29.4820	+	51.0644i	−1.17834	+	2.04094i
$627$	−24.8838	−	2.51937i	−0.993763	−	0.100614i
$628$	−10.8504	+	6.26449i	−0.432979	+	0.249981i
$629$	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	$0.228994\pi$
$632$	−0.471310	+	0.272111i	−0.0187477	+	0.0108240i
$633$	10.9140	+	24.2636i	0.433794	+	0.964391i
$634$	18.7556	−	32.4856i	0.744880	−	1.29017i
$635$	−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
$639$	8.40533	−	2.80220i	0.332510	−	0.110853i
$640$		−	18.3867i		−	0.726799i
$641$	29.7991	−	17.2045i	1.17699	−	0.679537i	0.221676	−	0.975120i	$-0.428847\pi$
$641$	29.7991	−	17.2045i	1.17699	−	0.679537i	0.955317	+	0.295583i	$0.0955140\pi$
$642$	−43.4354	−	4.39764i	−1.71426	−	0.173561i
$643$	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
$646$	7.40341	+	12.8231i	0.291283	+	0.504517i
$647$	−19.6436			−0.772271			−0.386136	−	0.922442i	$-0.626190\pi$
$647$	−19.6436			−0.772271			−0.386136	+	0.922442i	$0.626190\pi$
$648$	−5.11815	−	6.82292i	−0.201060	−	0.268030i
$649$			41.0055i			1.60961i
$650$	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	$-0.313356\pi$
$653$	2.77600	+	1.60272i	0.108633	+	0.0627194i	−0.444699	+	0.895680i	$0.646689\pi$
$654$	0.299563	−	2.95878i	0.0117138	−	0.115697i
$655$	−9.85129	−	17.0629i	−0.384922	−	0.666704i
$656$	−15.6663			−0.611666
$657$	−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	$0.517345\pi$
$660$	33.1475	−	14.9101i	1.29027	−	0.580377i
$661$	28.0490	+	16.1941i	1.09098	+	0.629878i	0.933837	−	0.357698i	$-0.116438\pi$
$661$	28.0490	+	16.1941i	1.09098	+	0.629878i	0.157143	+	0.987576i	$0.449772\pi$
$662$	−2.01981	−	1.16614i	−0.0785020	−	0.0453232i
$663$	−2.15739	+	0.970418i	−0.0837860	+	0.0376879i
$664$	6.95189	−	4.01367i	0.269785	−	0.155761i
$665$		0			0
$666$	5.94181	+	5.26843i	0.230240	+	0.204148i
$667$	24.7000			0.956386
$668$	−5.96768	−	10.3363i	−0.230897	−	0.399925i
$669$	0.557735	−	5.50874i	0.0215633	−	0.212980i
$670$	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	$0.963412\pi$
$674$		−	24.6231i		−	0.948445i
$675$	−1.45579	−	6.48289i	−0.0560332	−	0.249527i
$676$	−19.1140			−0.735155
$677$	−25.1655	−	43.5880i	−0.967190	−	1.67522i	−0.703612	−	0.710585i	$-0.748431\pi$
$677$	−25.1655	−	43.5880i	−0.967190	−	1.67522i	−0.263578	−	0.964638i	$-0.584903\pi$
$678$	−8.96958	+	12.4452i	−0.344475	+	0.477956i
$679$		0			0
$680$	6.32935	+	3.65425i	0.242719	+	0.140134i
$681$	25.2798	+	2.55946i	0.968722	+	0.0980787i
$682$	−95.0324	+	54.8670i	−3.63898	+	2.10097i
$683$			13.7445i			0.525920i	0.964807	+	0.262960i	$0.0846987\pi$
$683$			13.7445i			0.525920i	−0.964807	+	0.262960i	$0.915301\pi$
$684$	−2.31087	+	11.2953i	−0.0883585	+	0.431885i
$685$		−	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
$689$	1.07705	−	1.86550i	0.0410321	−	0.0710698i
$690$	−26.2604	−	58.3809i	−0.999716	−	2.22252i
$691$	25.4328	−	14.6837i	0.967511	−	0.558593i	0.0690343	−	0.997614i	$-0.478008\pi$
$691$	25.4328	−	14.6837i	0.967511	−	0.558593i	0.898476	+	0.439022i	$0.144675\pi$
$692$	1.49813			0.0569504
$693$		0			0
$694$	−50.5874			−1.92027
$695$	−42.5325	+	24.5562i	−1.61335	+	0.931468i
$696$	−5.11113	−	0.517479i	−0.193737	−	0.0196150i
$697$	5.06789	−	8.77784i	0.191960	−	0.332484i
$698$	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	$-0.314374\pi$
$702$	−4.11359	−	1.28469i	−0.155258	−	0.0484873i
$703$			3.64592i			0.137508i
$704$	−17.2923	+	9.98371i	−0.651728	+	0.376275i
$705$	5.44011	−	7.54811i	0.204886	−	0.284278i
$706$	4.08702	+	2.35964i	0.153817	+	0.0888063i
$707$		0			0
$708$	18.8060	+	1.90402i	0.706772	+	0.0715575i
$709$	5.66629	+	9.81430i	0.212802	+	0.368584i	0.952590	−	0.304256i	$-0.0984077\pi$
$709$	5.66629	+	9.81430i	0.212802	+	0.368584i	−0.739788	+	0.672840i	$0.765074\pi$
$710$	−13.8308			−0.519062
$711$	1.14296	−	1.28904i	0.0428642	−	0.0483428i
$712$			7.18216i			0.269163i
$713$	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
$717$	−24.8522	+	11.1788i	−0.928121	+	0.417479i
$718$	6.79136	+	11.7630i	0.253451	+	0.438991i
$719$	−36.1294			−1.34740			−0.673700	−	0.739005i	$-0.735296\pi$
$719$	−36.1294			−1.34740			−0.673700	+	0.739005i	$0.735296\pi$
$720$	11.3097	+	33.9240i	0.421487	+	1.26427i
$721$		0			0
$722$	20.0271	−	11.5627i	0.745333	−	0.430318i
$723$	0.134234	−	1.32583i	0.00499223	−	0.0493082i
$724$	19.4505	+	11.2298i	0.722874	+	0.417351i
$725$	−3.46580	−	2.00098i	−0.128717	−	0.0743146i
$726$	53.7494	+	38.7385i	1.99483	+	1.43772i
$727$	−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
$730$	39.8970			1.47665
$731$	14.6399	+	25.3570i	0.541475	+	0.937862i
$732$	−17.9479	−	12.9355i	−0.663375	−	0.478111i
$733$	41.4391	+	23.9249i	1.53059	+	0.883685i	0.999335	+	0.0364726i	$0.0116122\pi$
$733$	41.4391	+	23.9249i	1.53059	+	0.883685i	0.531253	+	0.847213i	$0.321721\pi$
$734$	−12.5938	+	21.8131i	−0.464846	+	0.805136i
$735$		0			0
$736$	27.6034	+	47.8105i	1.01747	+	1.76232i
$737$			10.4836i			0.386170i
$738$	17.5171	−	5.83990i	0.644812	−	0.214970i
$739$	15.3483			0.564597			0.282299	−	0.959327i	$-0.408903\pi$
$739$	15.3483			0.564597			0.282299	+	0.959327i	$0.408903\pi$
$740$	−2.64917	−	4.58849i	−0.0973853	−	0.168676i
$741$	−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	$0.401441\pi$
$744$	−7.04795	−	15.6687i	−0.258391	−	0.574442i
$745$	34.1568	−	19.7204i	1.25141	−	0.722501i
$746$			44.4132i			1.62608i
$747$	−16.8587	+	19.0135i	−0.616829	+	0.695669i
$748$		−	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	0.371463	+	0.928448i	$0.378856\pi$
$751$	−16.9449	+	29.3494i	−0.618327	+	1.07097i	−0.989791	+	0.142527i	$0.954477\pi$
$752$	−5.09906	+	8.83183i	−0.185944	+	0.322064i
$753$	−1.16001	+	1.60950i	−0.0422730	+	0.0586534i
$754$	−2.24793	+	1.29784i	−0.0818647	+	0.0472646i
$755$	−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	$0.533220\pi$
$758$	34.3589	−	19.8371i	1.24797	−	0.720517i
$759$	44.8343	−	62.2072i	1.62738	−	2.25798i
$760$	−3.05642	+	5.29387i	−0.110868	+	0.192029i
$761$	13.2666	−	22.9784i	0.480914	−	0.832968i	−0.518846	−	0.854868i	$-0.673638\pi$
$761$	13.2666	−	22.9784i	0.480914	−	0.832968i	0.999760	+	0.0218999i	$0.00697151\pi$
$762$	−2.40397	+	23.7439i	−0.0870865	+	0.860152i
$763$		0			0
$764$		−	19.7420i		−	0.714242i
$765$	−22.6662	−	4.63723i	−0.819498	−	0.167659i
$766$		−	24.2188i		−	0.875061i
$767$	−2.80929	+	1.62194i	−0.101438	+	0.0585650i
$768$	−14.8024	−	32.9080i	−0.534136	−	1.18747i
$769$	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
$772$	−1.16128	−	2.01139i	−0.0417953	−	0.0723916i
$773$	−22.6017			−0.812927			−0.406464	−	0.913667i	$-0.633238\pi$
$773$	−22.6017			−0.812927			−0.406464	+	0.913667i	$0.633238\pi$
$774$	−10.6914	+	52.2580i	−0.384293	+	1.87838i
$775$		−	13.3840i		−	0.480768i
$776$	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
$780$	2.33262	+	1.68118i	0.0835213	+	0.0601959i
$781$	−8.28359	−	14.3476i	−0.296410	−	0.513398i
$782$	−45.3955			−1.62334
$783$	15.8673	−	3.56313i	0.567051	−	0.127336i
$784$		0			0
$785$	18.2114	−	10.5144i	0.649993	−	0.375274i
$786$	−20.6491	−	14.8823i	−0.736528	−	0.530835i
$787$	22.6864	+	13.0980i	0.808683	+	0.466893i	0.846498	−	0.532391i	$-0.178707\pi$
$787$	22.6864	+	13.0980i	0.808683	+	0.466893i	−0.0378153	+	0.999285i	$0.512040\pi$
$788$	6.41523	+	3.70383i	0.228533	+	0.131944i
$789$	−2.39020	+	23.6080i	−0.0850934	+	0.840466i
$790$	−2.32900	+	1.34465i	−0.0828620	+	0.0478404i
$791$		0			0
$792$	−10.5808	+	11.9331i	−0.375971	+	0.424026i
$793$	3.79675			0.134827
$794$	−27.9314	−	48.3785i	−0.991247	−	1.71689i
$795$	19.2129	−	8.64220i	0.681413	−	0.306507i
$796$	−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
$800$		−	8.94478i		−	0.316246i
$801$	−7.19065	−	21.5687i	−0.254069	−	0.762093i
$802$	35.8740			1.26676
$803$	23.8952	+	41.3877i	0.843242	+	1.46054i
$804$	4.80802	+	0.486790i	0.169566	+	0.0171678i
$805$		0			0
$806$	−7.51788	−	4.34045i	−0.264806	−	0.152886i
$807$	−10.6127	+	14.7251i	−0.373586	+	0.518347i
$808$	−6.18375	+	3.57019i	−0.217543	+	0.125599i
$809$			26.4887i			0.931292i	0.884971	+	0.465646i	$0.154178\pi$
$809$			26.4887i			0.931292i	−0.884971	+	0.465646i	$0.845822\pi$
$810$	−25.2915	−	33.7157i	−0.888654	−	1.18465i
$811$			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
$815$	1.34571	−	2.33084i	0.0471383	−	0.0816459i
$816$	25.2294	+	2.55437i	0.883207	+	0.0894207i
$817$	−21.2086	+	12.2448i	−0.741996	+	0.428391i
$818$	−53.8949			−1.88439
$819$		0			0
$820$	−12.3198			−0.430226
$821$	−11.7493	+	6.78346i	−0.410053	+	0.236744i	−0.690813	−	0.723034i	$-0.742747\pi$
$821$	−11.7493	+	6.78346i	−0.410053	+	0.236744i	0.280759	+	0.959778i	$0.409414\pi$
$822$	−15.3639	−	34.1562i	−0.535877	−	1.19134i
$823$	−7.34857	+	12.7281i	−0.256155	+	0.443674i	−0.965209	−	0.261481i	$-0.915789\pi$
$823$	−7.34857	+	12.7281i	−0.256155	+	0.443674i	0.709053	+	0.705155i	$0.249122\pi$
$824$	−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	$-0.251642\pi$
$828$	−26.4477	−	23.4504i	−0.919122	−	0.814959i
$829$		−	20.4600i		−	0.710605i	−0.934751	−	0.355302i	$-0.884378\pi$
$829$		−	20.4600i		−	0.710605i	0.934751	−	0.355302i	$-0.115622\pi$
$830$	34.3530	−	19.8337i	1.19241	−	0.688439i
$831$	38.6545	+	3.91360i	1.34091	+	0.135761i
$832$	−1.36797	−	0.789798i	−0.0474258	−	0.0273813i
$833$		0			0
$834$	−37.0969	+	51.4717i	−1.28456	+	1.78232i
$835$	10.0162	+	17.3486i	0.346625	+	0.600372i
$836$	21.5580			0.745599
$837$	36.8529	+	39.9982i	1.27382	+	1.38254i
$838$		−	18.9282i		−	0.653865i
$839$	−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
$843$	−3.89931	+	38.5134i	−0.134299	+	1.32647i
$844$	−11.4661	−	19.8598i	−0.394678	−	0.683602i
$845$	32.0811			1.10362
$846$	2.40922	−	11.7760i	0.0828308	−	0.404866i
$847$		0			0
$848$	−19.9975	+	11.5456i	−0.686718	+	0.396477i
$849$	−29.9671	+	13.4796i	−1.02847	+	0.462617i
$850$	6.36973	+	3.67756i	0.218480	+	0.126139i
$851$	−9.68031	−	5.58893i	−0.331837	−	0.191586i
$852$	−6.96475	+	3.13282i	−0.238608	+	0.107329i
$853$	−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
$856$	−12.7812			−0.436851
$857$	−9.16200	−	15.8691i	−0.312968	−	0.542077i	0.666035	−	0.745920i	$-0.267990\pi$
$857$	−9.16200	−	15.8691i	−0.312968	−	0.542077i	−0.979003	+	0.203844i	$0.934657\pi$
$858$	−0.811707	+	8.01722i	−0.0277112	+	0.273704i
$859$	−33.4579	−	19.3169i	−1.14157	−	0.659085i	−0.194750	−	0.980853i	$-0.562390\pi$
$859$	−33.4579	−	19.3169i	−1.14157	−	0.659085i	−0.946819	+	0.321768i	$0.895723\pi$
$860$	17.7944	−	30.8208i	0.606784	−	1.05098i
$861$		0			0
$862$	−10.1328	−	17.5505i	−0.345125	−	0.597774i
$863$			16.7000i			0.568475i	0.958754	+	0.284238i	$0.0917405\pi$
$863$			16.7000i			0.568475i	−0.958754	+	0.284238i	$0.908260\pi$
$864$	24.6294	+	26.7315i	0.837910	+	0.909426i
$865$	−2.51447			−0.0854947
$866$	−12.1966	−	21.1251i	−0.414456	−	0.717859i
$867$	7.62350	−	10.5775i	0.258908	−	0.359232i
$868$		0			0
$869$	−2.78978	−	1.61068i	−0.0946367	−	0.0546385i
$870$	−25.2569	−	2.55714i	−0.856288	−	0.0866952i
$871$	−0.718235	+	0.414673i	−0.0243365	+	0.0140507i
$872$		−	0.870640i		−	0.0294836i
$873$	−8.36326	−	7.41546i	−0.283053	−	0.250975i
$874$		−	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	0.430953	+	0.902374i	$0.358177\pi$
$877$	−16.7617	+	29.0321i	−0.566002	+	0.980345i	−0.996956	+	0.0779707i	$0.975156\pi$
$878$	29.8606	−	51.7201i	1.00775	−	1.74547i
$879$	−6.26876	−	13.9364i	−0.211440	−	0.470063i
$880$	57.9070	−	33.4326i	1.95204	−	1.12701i
$881$	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	$0.722277\pi$
$884$	1.76583	−	1.01950i	0.0593912	−	0.0342895i
$885$	−31.5641	−	3.19572i	−1.06101	−	0.107423i
$886$	23.1719	−	40.1350i	0.778476	−	1.34836i
$887$	−17.5914	+	30.4692i	−0.590662	+	1.02306i	0.403481	+	0.914988i	$0.367800\pi$
$887$	−17.5914	+	30.4692i	−0.590662	+	1.02306i	−0.994143	+	0.108069i	$0.965533\pi$
$888$	1.88604	+	1.35932i	0.0632915	+	0.0456157i
$889$		0			0
$890$			35.4910i			1.18966i
$891$	19.8278	−	46.4296i	0.664257	−	1.55545i
$892$			4.77248i			0.159794i
$893$	4.77921	−	2.75928i	0.159930	−	0.0923358i
$894$	29.7916	−	41.3356i	0.996380	−	1.38247i
$895$	3.20164	+	1.84847i	0.107019	+	0.0617875i
$896$		0			0
$897$	6.03521	+	0.611037i	0.201510	+	0.0204019i
$898$	−12.8685	−	22.2890i	−0.429429	−	0.743792i
$899$	32.7582			1.09255
$900$	1.81129	+	5.43305i	0.0603762	+	0.181102i
$901$		−	14.9395i		−	0.497707i
$902$	−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
$906$	−5.85331	+	2.63289i	−0.194463	+	0.0874718i
$907$	21.2977	+	36.8887i	0.707179	+	1.22487i	0.965899	+	0.258918i	$0.0833660\pi$
$907$	21.2977	+	36.8887i	0.707179	+	1.22487i	−0.258720	+	0.965952i	$0.583301\pi$
$908$	−21.9010			−0.726811
$909$	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	$0.646430\pi$
$912$	−2.13648	+	21.1019i	−0.0707458	+	0.698755i
$913$	41.1496	+	23.7577i	1.36185	+	0.786265i
$914$	−44.2037	−	25.5210i	−1.46213	−	0.844160i
$915$	30.1239	+	21.7111i	0.995866	+	0.717746i
$916$	4.36754	−	2.52160i	0.144308	−	0.0833161i
$917$		0			0
$918$	−29.1622	+	6.54860i	−0.962495	+	0.216136i
$919$	−58.6972			−1.93624			−0.968121	−	0.250481i	$-0.919411\pi$
$919$	−58.6972			−1.93624			−0.968121	+	0.250481i	$0.919411\pi$
$920$	−9.37054	−	16.2303i	−0.308938	−	0.535096i
$921$	−40.4023	−	29.1189i	−1.33130	−	0.959501i
$922$	−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
$926$			45.7315i			1.50283i
$927$	8.61282	−	42.0984i	0.282882	−	1.38269i
$928$	21.8929			0.718670
$929$	7.19115	+	12.4554i	0.235934	+	0.408650i	0.959544	−	0.281560i	$-0.0908518\pi$
$929$	7.19115	+	12.4554i	0.235934	+	0.408650i	−0.723610	+	0.690209i	$0.757518\pi$
$930$	−34.8278	−	77.4275i	−1.14205	−	2.53895i
$931$		0			0
$932$	6.30952	+	3.64281i	0.206675	+	0.119324i
$933$	9.43995	+	20.9865i	0.309050	+	0.687066i
$934$	25.7427	−	14.8626i	0.842327	−	0.486318i
$935$			43.2604i			1.41477i
$936$	−1.23606	−	0.252882i	−0.0404017	−	0.00826572i
$937$		−	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
$941$	7.44400	−	12.8934i	0.242667	−	0.420312i	−0.718806	−	0.695211i	$-0.755311\pi$
$941$	7.44400	−	12.8934i	0.242667	−	0.420312i	0.961473	+	0.274899i	$0.0886443\pi$
$942$	15.8840	−	22.0390i	0.517530	−	0.718068i
$943$	−22.5089	+	12.9955i	−0.732990	+	0.423192i
$944$	34.7734			1.13178
$945$		0			0
$946$	99.7390			3.24280
$947$	36.3343	−	20.9776i	1.18071	−	0.681681i	0.224528	−	0.974468i	$-0.427916\pi$
$947$	36.3343	−	20.9776i	1.18071	−	0.681681i	0.956178	+	0.292787i	$0.0945827\pi$
$948$	−0.868230	+	1.20466i	−0.0281988	+	0.0391256i
$949$	−1.89031	+	3.27412i	−0.0613622	+	0.106282i
$950$	−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	$0.927284\pi$
$954$	18.0562	−	20.3640i	0.584590	−	0.659308i
$955$			33.1352i			1.07223i
$956$	20.3415	−	11.7442i	0.657892	−	0.379834i
$957$	−12.4742	−	27.7321i	−0.403234	−	0.896450i
$958$	−22.4228	−	12.9458i	−0.724449	−	0.418261i
$959$		0			0
$960$	−6.33733	−	14.0889i	−0.204537	−	0.454716i
$961$	39.2776	+	68.0309i	1.26702	+	2.19454i
$962$	1.17467			0.0378728
$963$	38.3830	−	12.7963i	1.23688	−	0.412354i
$964$			1.14863i			0.0369949i
$965$	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
$969$	−11.1323	−	8.02333i	−0.357621	−	0.257747i
$970$	8.72403	+	15.1105i	0.280112	+	0.485168i
$971$	43.3737			1.39193			0.695965	−	0.718076i	$-0.254977\pi$
$971$	43.3737			1.39193			0.695965	+	0.718076i	$0.254977\pi$
$972$	−20.3729	−	11.2493i	−0.653462	−	0.360823i
$973$		0			0
$974$	46.6120	−	26.9114i	1.49354	−	0.862298i
$975$	−0.797336	−	0.574660i	−0.0255352	−	0.0184038i
$976$	−35.2472	−	20.3500i	−1.12824	−	0.651387i
$977$	−10.4210	−	6.01657i	−0.333397	−	0.192487i	0.323951	−	0.946074i	$-0.394989\pi$
$977$	−10.4210	−	6.01657i	−0.333397	−	0.192487i	−0.657348	+	0.753587i	$0.728322\pi$
$978$	0.350238	−	3.45930i	0.0111994	−	0.110616i
$979$	−36.8170	+	21.2563i	−1.17668	+	0.679355i
$980$		0			0
$981$	0.871668	+	2.61461i	0.0278302	+	0.0834782i
$982$	−72.4304			−2.31135
$983$	−3.14829	−	5.45300i	−0.100415	−	0.173924i	0.811441	−	0.584435i	$-0.198684\pi$
$983$	−3.14829	−	5.45300i	−0.100415	−	0.173924i	−0.911856	+	0.410511i	$0.865350\pi$
$984$	4.93000	−	2.21757i	0.157163	−	0.0706936i
$985$	−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
$989$		−	75.0816i		−	2.38745i
$990$	−52.2853	+	58.9681i	−1.66174	+	1.87413i
$991$	33.5627			1.06616			0.533078	−	0.846066i	$-0.321035\pi$
$991$	33.5627			1.06616			0.533078	+	0.846066i	$0.321035\pi$
$992$	36.6089	+	63.4085i	1.16233	+	2.01322i
$993$	2.15046	+	0.217724i	0.0682427	+	0.00690926i
$994$		0			0
$995$	24.2874	+	14.0223i	0.769963	+	0.444538i
$996$	12.8065	−	17.7689i	0.405790	−	0.563030i
$997$	9.74838	−	5.62823i	0.308734	−	0.178248i	−0.337626	−	0.941280i	$-0.609624\pi$
$997$	9.74838	−	5.62823i	0.308734	−	0.178248i	0.646360	+	0.763033i	$0.276290\pi$
$998$		−	6.47898i		−	0.205088i
$999$	−7.02489	−	2.19389i	−0.222258	−	0.0694116i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.61855 - 0.934468i) q^{2} +(-1.01272 + 1.40514i) q^{3} +(0.746462 - 1.29291i) q^{4} +(-1.25287 + 2.17003i) q^{5} +(-0.326074 + 3.22063i) q^{6} +0.947692i q^{8} +(-0.948811 - 2.84601i) q^{9} +4.68306i q^{10} +(-4.85803 + 2.80479i) q^{11} +(1.06076 + 2.35823i) q^{12} +(-0.384312 - 0.221883i) q^{13} +(-1.78039 - 3.95807i) q^{15} +(2.37851 + 4.11970i) q^{16} -3.07770 q^{17} +(-4.19520 - 3.71976i) q^{18} -2.57419i q^{19} +(1.87044 + 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(6.83476 + 3.94605i) q^{23} +(-1.33164 - 0.959743i) q^{24} +(-0.639351 - 1.10739i) q^{25} -0.829370 q^{26} +(4.95990 + 1.54899i) q^{27} +(2.71041 - 1.56485i) q^{29} +(-6.58033 - 4.74261i) q^{30} +(9.06457 + 5.23343i) q^{31} +(6.05802 + 3.49760i) q^{32} +(0.978704 - 9.66665i) q^{33} +(-4.98140 + 2.87601i) q^{34} +(-4.38788 - 0.897709i) q^{36} -1.41634 q^{37} +(-2.40550 - 4.16645i) q^{38} +(0.700975 - 0.315306i) q^{39} +(-2.05652 - 1.18733i) q^{40} +(-1.64665 + 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +8.37467i q^{44} +(7.36465 + 1.50672i) q^{45} +14.7498 q^{46} +(1.07190 + 1.85659i) q^{47} +(-8.19750 - 0.829960i) q^{48} +(-2.06964 - 1.19491i) q^{50} +(3.11684 - 4.32458i) q^{51} +(-0.573749 + 0.331254i) q^{52} +4.85412i q^{53} +(9.47532 - 2.12776i) q^{54} -14.0561i q^{55} +(3.61709 + 2.60693i) q^{57} +(2.92461 - 5.06558i) q^{58} +(3.65496 - 6.33057i) q^{59} +(-6.44642 - 0.652671i) q^{60} +(-7.40950 + 4.27788i) q^{61} +19.5619 q^{62} +3.55953 q^{64} +(0.962984 - 0.555979i) q^{65} +(-7.44910 - 16.5605i) q^{66} +(0.934442 - 1.61850i) q^{67} +(-2.29739 + 3.97919i) q^{68} +(-12.4664 + 5.60753i) q^{69} +2.95338i q^{71} +(2.69714 - 0.899181i) q^{72} -8.51943i q^{73} +(-2.29241 + 1.32352i) q^{74} +(2.20351 + 0.223096i) q^{75} +(-3.32820 - 1.92154i) q^{76} +(0.839916 - 1.16538i) q^{78} +(0.287130 + 0.497324i) q^{79} -11.9198 q^{80} +(-7.19951 + 5.40065i) q^{81} +6.15497i q^{82} +(-4.23521 - 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(-15.3981 - 8.89008i) q^{86} +(-0.546041 + 5.39324i) q^{87} +(-2.65807 - 4.60392i) q^{88} +7.57858 q^{89} +(13.3280 - 4.44334i) q^{90} +(10.2038 - 5.89115i) q^{92} +(-16.5335 + 7.43697i) q^{93} +(3.46984 + 2.00332i) q^{94} +(5.58607 + 3.22512i) q^{95} +(-11.0497 + 4.97026i) q^{96} +(3.22662 - 1.86289i) q^{97} +(12.5918 + 11.1648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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