LMFDB - Embedded newform 980.2.k.i.687.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(687,980)] 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("980.687"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			687.11
Character	$\chi$	$=$	980.687
Dual form			980.2.k.i.883.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.284821 + 1.38524i) q^{2} +(-2.22691 - 2.22691i) q^{3} +(-1.83775 + 0.789089i) q^{4} +(-2.19495 + 0.426822i) q^{5} +(2.45053 - 3.71907i) q^{6} +(-1.61650 - 2.32097i) q^{8} +6.91829i q^{9} +(-1.21642 - 2.91896i) q^{10} +3.97534i q^{11} +(5.84975 + 2.33529i) q^{12} +(-2.52606 + 2.52606i) q^{13} +(5.83847 + 3.93748i) q^{15} +(2.75468 - 2.90030i) q^{16} +(-0.757926 - 0.757926i) q^{17} +(-9.58346 + 1.97048i) q^{18} -1.31625 q^{19} +(3.69698 - 2.51641i) q^{20} +(-5.50679 + 1.13226i) q^{22} +(-3.67551 - 3.67551i) q^{23} +(-1.56879 + 8.76842i) q^{24} +(4.63565 - 1.87371i) q^{25} +(-4.21866 - 2.77971i) q^{26} +(8.72570 - 8.72570i) q^{27} -4.50936i q^{29} +(-3.79141 + 9.20913i) q^{30} +2.57510i q^{31} +(4.80219 + 2.98981i) q^{32} +(8.85275 - 8.85275i) q^{33} +(0.834032 - 1.26578i) q^{34} +(-5.45915 - 12.7141i) q^{36} +(-5.34011 - 5.34011i) q^{37} +(-0.374896 - 1.82332i) q^{38} +11.2506 q^{39} +(4.53880 + 4.40447i) q^{40} +11.3180 q^{41} +(1.77452 + 1.77452i) q^{43} +(-3.13690 - 7.30570i) q^{44} +(-2.95288 - 15.1853i) q^{45} +(4.04458 - 6.13831i) q^{46} +(4.83434 - 4.83434i) q^{47} +(-12.5932 + 0.324292i) q^{48} +(3.91586 + 5.88779i) q^{50} +3.37567i q^{51} +(2.64899 - 6.63556i) q^{52} +(5.91829 - 5.91829i) q^{53} +(14.5724 + 9.60188i) q^{54} +(-1.69676 - 8.72570i) q^{55} +(2.93118 + 2.93118i) q^{57} +(6.24652 - 1.28436i) q^{58} -8.34518 q^{59} +(-13.8367 - 2.62904i) q^{60} -1.34720 q^{61} +(-3.56712 + 0.733444i) q^{62} +(-2.77382 + 7.50373i) q^{64} +(4.46640 - 6.62276i) q^{65} +(14.7846 + 9.74169i) q^{66} +(-3.89961 + 3.89961i) q^{67} +(1.99095 + 0.794810i) q^{68} +16.3701i q^{69} -3.47330i q^{71} +(16.0572 - 11.1835i) q^{72} +(-1.70729 + 1.70729i) q^{73} +(5.87634 - 8.91829i) q^{74} +(-14.4958 - 6.15059i) q^{75} +(2.41895 - 1.03864i) q^{76} +(3.20442 + 15.5848i) q^{78} +3.45140 q^{79} +(-4.80848 + 7.54179i) q^{80} -18.1079 q^{81} +(3.22360 + 15.6780i) q^{82} +(8.37751 + 8.37751i) q^{83} +(1.98711 + 1.34011i) q^{85} +(-1.95270 + 2.96354i) q^{86} +(-10.0419 + 10.0419i) q^{87} +(9.22666 - 6.42616i) q^{88} -9.41924i q^{89} +(20.1942 - 8.41554i) q^{90} +(9.65498 + 3.85438i) q^{92} +(5.73453 - 5.73453i) q^{93} +(8.07362 + 5.31978i) q^{94} +(2.88911 - 0.561805i) q^{95} +(-4.03602 - 17.3521i) q^{96} +(-9.04418 - 9.04418i) q^{97} -27.5026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 8 q^{8} + 8 q^{16} - 40 q^{18} - 36 q^{22} + 32 q^{25} - 36 q^{30} + 16 q^{32} - 88 q^{36} - 48 q^{37} + 28 q^{50} + 16 q^{53} - 16 q^{57} + 36 q^{58} - 80 q^{60} + 64 q^{65} + 56 q^{72}+ \cdots + 32 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 8 * q^8 + 8 * q^16 - 40 * q^18 - 36 * q^22 + 32 * q^25 - 36 * q^30 + 16 * q^32 - 88 * q^36 - 48 * q^37 + 28 * q^50 + 16 * q^53 - 16 * q^57 + 36 * q^58 - 80 * q^60 + 64 * q^65 + 56 * q^72 + 28 * q^78 + 56 * q^86 + 88 * q^88 + 136 * q^92 + 32 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.284821	+	1.38524i	0.201399	+	0.979509i
$2$	0.284821	+	1.38524i	0.201399	+	0.979509i
$3$	−2.22691	−	2.22691i	−1.28571	−	1.28571i	−0.937368	−	0.348342i	$-0.886745\pi$
$3$	−2.22691	−	2.22691i	−1.28571	−	1.28571i	−0.348342	−	0.937368i	$-0.613255\pi$
$4$	−1.83775	+	0.789089i	−0.918877	+	0.394544i
$5$	−2.19495	+	0.426822i	−0.981613	+	0.190881i
$5$	−2.19495	+	0.426822i	−0.981613	+	0.190881i
$6$	2.45053	−	3.71907i	1.00042	−	1.51830i
$7$		0			0
$7$		0			0
$8$	−1.61650	−	2.32097i	−0.571521	−	0.820588i
$9$			6.91829i			2.30610i
$10$	−1.21642	−	2.91896i	−0.384665	−	0.923056i
$11$			3.97534i			1.19861i	0.800520	+	0.599306i	$0.204557\pi$
$11$			3.97534i			1.19861i	−0.800520	+	0.599306i	$0.795443\pi$
$12$	5.84975	+	2.33529i	1.68868	+	0.674139i
$13$	−2.52606	+	2.52606i	−0.700602	+	0.700602i	−0.964540	−	0.263937i	$-0.914979\pi$
$13$	−2.52606	+	2.52606i	−0.700602	+	0.700602i	0.263937	+	0.964540i	$0.414979\pi$
$14$		0			0
$15$	5.83847	+	3.93748i	1.50749	+	1.01665i
$16$	2.75468	−	2.90030i	0.688669	−	0.725075i
$17$	−0.757926	−	0.757926i	−0.183824	−	0.183824i	0.609196	−	0.793020i	$-0.291492\pi$
$17$	−0.757926	−	0.757926i	−0.183824	−	0.183824i	−0.793020	+	0.609196i	$0.791492\pi$
$18$	−9.58346	+	1.97048i	−2.25884	+	0.464446i
$19$	−1.31625			−0.301969			−0.150984	−	0.988536i	$-0.548244\pi$
$19$	−1.31625			−0.301969			−0.150984	+	0.988536i	$0.548244\pi$
$20$	3.69698	−	2.51641i	0.826671	−	0.562686i
$21$		0			0
$22$	−5.50679	+	1.13226i	−1.17405	+	0.241399i
$23$	−3.67551	−	3.67551i	−0.766396	−	0.766396i	0.211074	−	0.977470i	$-0.432304\pi$
$23$	−3.67551	−	3.67551i	−0.766396	−	0.766396i	−0.977470	+	0.211074i	$0.932304\pi$
$24$	−1.56879	+	8.76842i	−0.320228	+	1.78985i
$25$	4.63565	−	1.87371i	0.927129	−	0.374742i
$26$	−4.21866	−	2.77971i	−0.827347	−	0.545146i
$27$	8.72570	−	8.72570i	1.67926	−	1.67926i
$28$		0			0
$29$		−	4.50936i		−	0.837366i	−0.908132	−	0.418683i	$-0.862492\pi$
$29$		−	4.50936i		−	0.837366i	0.908132	−	0.418683i	$-0.137508\pi$
$30$	−3.79141	+	9.20913i	−0.692214	+	1.68135i
$31$			2.57510i			0.462502i	0.972894	+	0.231251i	$0.0742819\pi$
$31$			2.57510i			0.462502i	−0.972894	+	0.231251i	$0.925718\pi$
$32$	4.80219	+	2.98981i	0.848915	+	0.528529i
$33$	8.85275	−	8.85275i	1.54107	−	1.54107i
$34$	0.834032	−	1.26578i	0.143035	−	0.217079i
$35$		0			0
$36$	−5.45915	−	12.7141i	−0.909858	−	2.11902i
$37$	−5.34011	−	5.34011i	−0.877909	−	0.877909i	0.115409	−	0.993318i	$-0.463182\pi$
$37$	−5.34011	−	5.34011i	−0.877909	−	0.877909i	−0.993318	+	0.115409i	$0.963182\pi$
$38$	−0.374896	−	1.82332i	−0.0608162	−	0.295781i
$39$	11.2506			1.80154
$40$	4.53880	+	4.40447i	0.717647	+	0.696407i
$41$	11.3180			1.76757			0.883784	−	0.467894i	$-0.154987\pi$
$41$	11.3180			1.76757			0.883784	+	0.467894i	$0.154987\pi$
$42$		0			0
$43$	1.77452	+	1.77452i	0.270611	+	0.270611i	0.829346	−	0.558735i	$-0.188713\pi$
$43$	1.77452	+	1.77452i	0.270611	+	0.270611i	−0.558735	+	0.829346i	$0.688713\pi$
$44$	−3.13690	−	7.30570i	−0.472905	−	1.10138i
$45$	−2.95288	−	15.1853i	−0.440189	−	2.26370i
$46$	4.04458	−	6.13831i	0.596341	−	0.905044i
$47$	4.83434	−	4.83434i	0.705161	−	0.705161i	−0.260353	−	0.965514i	$-0.583839\pi$
$47$	4.83434	−	4.83434i	0.705161	−	0.705161i	0.965514	+	0.260353i	$0.0838388\pi$
$48$	−12.5932	+	0.324292i	−1.81766	+	0.0468075i
$49$		0			0
$50$	3.91586	+	5.88779i	0.553786	+	0.832659i
$51$			3.37567i			0.472689i
$52$	2.64899	−	6.63556i	0.367349	−	0.920186i
$53$	5.91829	−	5.91829i	0.812940	−	0.812940i	−0.172134	−	0.985074i	$-0.555066\pi$
$53$	5.91829	−	5.91829i	0.812940	−	0.812940i	0.985074	+	0.172134i	$0.0550662\pi$
$54$	14.5724	+	9.60188i	1.98305	+	1.30665i
$55$	−1.69676	−	8.72570i	−0.228792	−	1.17657i
$56$		0			0
$57$	2.93118	+	2.93118i	0.388244	+	0.388244i
$58$	6.24652	−	1.28436i	0.820208	−	0.168645i
$59$	−8.34518			−1.08645			−0.543225	−	0.839587i	$-0.682797\pi$
$59$	−8.34518			−1.08645			−0.543225	+	0.839587i	$0.682797\pi$
$60$	−13.8367	−	2.62904i	−1.78631	−	0.339408i
$61$	−1.34720			−0.172492			−0.0862458	−	0.996274i	$-0.527487\pi$
$61$	−1.34720			−0.172492			−0.0862458	+	0.996274i	$0.527487\pi$
$62$	−3.56712	+	0.733444i	−0.453025	+	0.0931475i
$63$		0			0
$64$	−2.77382	+	7.50373i	−0.346728	+	0.937966i
$65$	4.46640	−	6.62276i	0.553989	−	0.821452i
$66$	14.7846	+	9.74169i	1.81986	+	1.19912i
$67$	−3.89961	+	3.89961i	−0.476413	+	0.476413i	−0.903983	−	0.427569i	$-0.859370\pi$
$67$	−3.89961	+	3.89961i	−0.476413	+	0.476413i	0.427569	+	0.903983i	$0.359370\pi$
$68$	1.99095	+	0.794810i	0.241438	+	0.0963849i
$69$			16.3701i			1.97073i
$70$		0			0
$71$		−	3.47330i		−	0.412205i	−0.978530	−	0.206102i	$-0.933922\pi$
$71$		−	3.47330i		−	0.412205i	0.978530	−	0.206102i	$-0.0660780\pi$
$72$	16.0572	−	11.1835i	1.89235	−	1.31798i
$73$	−1.70729	+	1.70729i	−0.199823	+	0.199823i	−0.799924	−	0.600101i	$-0.795127\pi$
$73$	−1.70729	+	1.70729i	−0.199823	+	0.199823i	0.600101	+	0.799924i	$0.295127\pi$
$74$	5.87634	−	8.91829i	0.683110	−	1.03673i
$75$	−14.4958	−	6.15059i	−1.67383	−	0.710209i
$76$	2.41895	−	1.03864i	0.277472	−	0.119140i
$77$		0			0
$78$	3.20442	+	15.5848i	0.362829	+	1.76463i
$79$	3.45140			0.388313			0.194157	−	0.980971i	$-0.437803\pi$
$79$	3.45140			0.388313			0.194157	+	0.980971i	$0.437803\pi$
$80$	−4.80848	+	7.54179i	−0.537604	+	0.843197i
$81$	−18.1079			−2.01199
$82$	3.22360	+	15.6780i	0.355987	+	1.73135i
$83$	8.37751	+	8.37751i	0.919551	+	0.919551i	0.996997	−	0.0774458i	$-0.0246765\pi$
$83$	8.37751	+	8.37751i	0.919551	+	0.919551i	−0.0774458	+	0.996997i	$0.524676\pi$
$84$		0			0
$85$	1.98711	+	1.34011i	0.215533	+	0.145356i
$86$	−1.95270	+	2.96354i	−0.210565	+	0.319567i
$87$	−10.0419	+	10.0419i	−1.07661	+	1.07661i
$88$	9.22666	−	6.42616i	0.983565	−	0.685031i
$89$		−	9.41924i		−	0.998437i	−0.866476	−	0.499219i	$-0.833620\pi$
$89$		−	9.41924i		−	0.998437i	0.866476	−	0.499219i	$-0.166380\pi$
$90$	20.1942	−	8.41554i	2.12866	−	0.887076i
$91$		0			0
$92$	9.65498	+	3.85438i	1.00660	+	0.401846i
$93$	5.73453	−	5.73453i	0.594643	−	0.594643i
$94$	8.07362	+	5.31978i	0.832731	+	0.548693i
$95$	2.88911	−	0.561805i	0.296417	−	0.0576400i
$96$	−4.03602	−	17.3521i	−0.411924	−	1.77099i
$97$	−9.04418	−	9.04418i	−0.918298	−	0.918298i	0.0786079	−	0.996906i	$-0.474952\pi$
$97$	−9.04418	−	9.04418i	−0.918298	−	0.918298i	−0.996906	+	0.0786079i	$0.974952\pi$
$98$		0			0
$99$	−27.5026			−2.76411
$100$	−7.04065	+	7.10135i	−0.704065	+	0.710135i
$101$	10.2729			1.02219			0.511095	−	0.859524i	$-0.329240\pi$
$101$	10.2729			1.02219			0.511095	+	0.859524i	$0.329240\pi$
$102$	−4.67610	+	0.961463i	−0.463003	+	0.0951990i
$103$	2.95562	+	2.95562i	0.291226	+	0.291226i	0.837564	−	0.546339i	$-0.183979\pi$
$103$	2.95562	+	2.95562i	0.291226	+	0.291226i	−0.546339	+	0.837564i	$0.683979\pi$
$104$	9.94629	+	1.77953i	0.975314	+	0.174497i
$105$		0			0
$106$	9.88388	+	6.51257i	0.960007	+	0.632557i
$107$	11.2506	−	11.2506i	1.08764	−	1.08764i	0.0918679	−	0.995771i	$-0.470716\pi$
$107$	11.2506	−	11.2506i	1.08764	−	1.08764i	0.995771	−	0.0918679i	$-0.0292837\pi$
$108$	−9.15033	+	22.9210i	−0.880491	+	2.20558i
$109$			2.98548i			0.285958i	0.989726	+	0.142979i	$0.0456681\pi$
$109$			2.98548i			0.285958i	−0.989726	+	0.142979i	$0.954332\pi$
$110$	11.6039	−	4.83568i	1.10639	−	0.461064i
$111$			23.7839i			2.25747i
$112$		0			0
$113$	−0.407307	+	0.407307i	−0.0383162	+	0.0383162i	−0.726005	−	0.687689i	$-0.758625\pi$
$113$	−0.407307	+	0.407307i	−0.0383162	+	0.0383162i	0.687689	+	0.726005i	$0.258625\pi$
$114$	−3.22551	+	4.89523i	−0.302097	+	0.458481i
$115$	9.63636	+	6.49878i	0.898595	+	0.606015i
$116$	3.55828	+	8.28709i	0.330378	+	0.769437i
$117$	−17.4760	−	17.4760i	−1.61566	−	1.61566i
$118$	−2.37688	−	11.5600i	−0.218810	−	1.06419i
$119$		0			0
$120$	−0.299139	−	19.9159i	−0.0273076	−	1.81806i
$121$	−4.80335			−0.436669
$122$	−0.383712	−	1.86619i	−0.0347396	−	0.168957i
$123$	−25.2041	−	25.2041i	−2.27258	−	2.27258i
$124$	−2.03198	−	4.73241i	−0.182478	−	0.424983i
$125$	−9.37529	+	6.09130i	−0.838551	+	0.544823i
$126$		0			0
$127$	10.3756	−	10.3756i	0.920687	−	0.920687i	−0.0763907	−	0.997078i	$-0.524340\pi$
$127$	10.3756	−	10.3756i	0.920687	−	0.920687i	0.997078	+	0.0763907i	$0.0243396\pi$
$128$	−11.1845	−	1.70518i	−0.988577	−	0.150718i
$129$		−	7.90338i		−	0.695854i
$130$	10.4462	+	4.30072i	0.916193	+	0.377198i
$131$			9.85999i			0.861471i	0.902478	+	0.430736i	$0.141746\pi$
$131$			9.85999i			0.861471i	−0.902478	+	0.430736i	$0.858254\pi$
$132$	−9.28357	+	23.2548i	−0.808031	+	2.02407i
$133$		0			0
$134$	−6.51257	−	4.29119i	−0.562600	−	0.370702i
$135$	−15.4282	+	22.8768i	−1.32785	+	1.96892i
$136$	−0.533934	+	2.98432i	−0.0457845	+	0.255903i
$137$	11.4148	+	11.4148i	0.975229	+	0.975229i	0.999701	−	0.0244719i	$-0.00779042\pi$
$137$	11.4148	+	11.4148i	0.975229	+	0.975229i	−0.0244719	+	0.999701i	$0.507790\pi$
$138$	−22.6764	+	4.66254i	−1.93034	+	0.396902i
$139$	−9.10621			−0.772379			−0.386189	−	0.922420i	$-0.626209\pi$
$139$	−9.10621			−0.772379			−0.386189	+	0.922420i	$0.626209\pi$
$140$		0			0
$141$	−21.5313			−1.81326
$142$	4.81133	−	0.989269i	0.403758	−	0.0830176i
$143$	−10.0419	−	10.0419i	−0.839750	−	0.839750i
$144$	20.0651	+	19.0577i	1.67209	+	1.58814i
$145$	1.92469	+	9.89783i	0.159837	+	0.821970i
$146$	−2.85127	−	1.87872i	−0.235973	−	0.155484i
$147$		0			0
$148$	14.0276	+	5.59999i	1.15306	+	0.460316i
$149$			1.97422i			0.161735i	0.996725	+	0.0808674i	$0.0257690\pi$
$149$			1.97422i			0.161735i	−0.996725	+	0.0808674i	$0.974231\pi$
$150$	4.39131	−	21.8319i	0.358549	−	1.78257i
$151$			8.62995i			0.702296i	0.936320	+	0.351148i	$0.114209\pi$
$151$			8.62995i			0.702296i	−0.936320	+	0.351148i	$0.885791\pi$
$152$	2.12773	+	3.05498i	0.172581	+	0.247792i
$153$	5.24355	−	5.24355i	0.423916	−	0.423916i
$154$		0			0
$155$	−1.09911	−	5.65223i	−0.0882827	−	0.453998i
$156$	−20.6759	+	8.87774i	−1.65540	+	0.710788i
$157$	−11.2102	−	11.2102i	−0.894668	−	0.894668i	0.100290	−	0.994958i	$-0.468023\pi$
$157$	−11.2102	−	11.2102i	−0.894668	−	0.894668i	−0.994958	+	0.100290i	$0.968023\pi$
$158$	0.983033	+	4.78101i	0.0782059	+	0.380356i
$159$	−26.3590			−2.09041
$160$	−11.8167	−	4.51281i	−0.934193	−	0.356769i
$161$		0			0
$162$	−5.15751	−	25.0837i	−0.405212	−	1.97076i
$163$	4.92560	+	4.92560i	0.385802	+	0.385802i	0.873187	−	0.487385i	$-0.162049\pi$
$163$	4.92560	+	4.92560i	0.385802	+	0.385802i	−0.487385	+	0.873187i	$0.662049\pi$
$164$	−20.7996	+	8.93088i	−1.62418	+	0.697384i
$165$	−15.6528	+	23.2099i	−1.21857	+	1.80689i
$166$	−9.21873	+	13.9909i	−0.715512	+	1.08591i
$167$	11.9207	−	11.9207i	0.922449	−	0.922449i	−0.0747528	−	0.997202i	$-0.523817\pi$
$167$	11.9207	−	11.9207i	0.922449	−	0.922449i	0.997202	+	0.0747528i	$0.0238168\pi$
$168$		0			0
$169$			0.238064i			0.0183127i
$170$	−1.29040	+	3.13431i	−0.0989692	+	0.240391i
$171$		−	9.10621i		−	0.696369i
$172$	−4.66137	−	1.86087i	−0.355426	−	0.141890i
$173$	−0.156561	+	0.156561i	−0.0119031	+	0.0119031i	−0.713033	−	0.701130i	$-0.752679\pi$
$173$	−0.156561	+	0.156561i	−0.0119031	+	0.0119031i	0.701130	+	0.713033i	$0.252679\pi$
$174$	−16.7706	−	11.0503i	−1.27138	−	0.837721i
$175$		0			0
$176$	11.5297	+	10.9508i	0.869083	+	0.825447i
$177$	18.5840	+	18.5840i	1.39686	+	1.39686i
$178$	13.0479	−	2.68280i	0.977978	−	0.201084i
$179$	−20.4045			−1.52511			−0.762553	−	0.646926i	$-0.776054\pi$
$179$	−20.4045			−1.52511			−0.762553	+	0.646926i	$0.776054\pi$
$180$	17.4092	+	25.5768i	1.29761	+	1.90638i
$181$	13.1697			0.978898			0.489449	−	0.872032i	$-0.337198\pi$
$181$	13.1697			0.978898			0.489449	+	0.872032i	$0.337198\pi$
$182$		0			0
$183$	3.00010	+	3.00010i	0.221774	+	0.221774i
$184$	−2.58928	+	14.4722i	−0.190884	+	1.06691i
$185$	14.0006	+	9.44202i	1.02934	+	0.694191i
$186$	9.57699	+	6.31036i	0.702219	+	0.462698i
$187$	3.01302	−	3.01302i	0.220334	−	0.220334i
$188$	−5.06960	+	12.6991i	−0.369739	+	0.926174i
$189$		0			0
$190$	1.60111	+	3.84208i	0.116157	+	0.278734i
$191$		−	12.1033i		−	0.875761i	−0.899033	−	0.437880i	$-0.855729\pi$
$191$		−	12.1033i		−	0.875761i	0.899033	−	0.437880i	$-0.144271\pi$
$192$	22.8872	−	10.5331i	1.65174	−	0.760160i
$193$	0.496468	−	0.496468i	0.0357366	−	0.0357366i	−0.689013	−	0.724749i	$-0.741956\pi$
$193$	0.496468	−	0.496468i	0.0357366	−	0.0357366i	0.724749	+	0.689013i	$0.241956\pi$
$194$	9.95235	−	15.1043i	0.714537	−	1.08443i
$195$	−24.6946	+	4.80202i	−1.76842	+	0.343880i
$196$		0			0
$197$	−1.16924	−	1.16924i	−0.0833051	−	0.0833051i	0.664226	−	0.747531i	$-0.268761\pi$
$197$	−1.16924	−	1.16924i	−0.0833051	−	0.0833051i	−0.747531	+	0.664226i	$0.768761\pi$
$198$	−7.83332	−	38.0975i	−0.556690	−	2.70747i
$199$	17.4514			1.23710			0.618548	−	0.785747i	$-0.287721\pi$
$199$	17.4514			1.23710			0.618548	+	0.785747i	$0.287721\pi$
$200$	−11.8424	−	7.73034i	−0.837382	−	0.546618i
$201$	17.3682			1.22506
$202$	2.92593	+	14.2304i	0.205868	+	1.00124i
$203$		0			0
$204$	−2.66370	−	6.20365i	−0.186497	−	0.434343i
$205$	−24.8424	+	4.83076i	−1.73507	+	0.337395i
$206$	−3.25240	+	4.93605i	−0.226606	+	0.343911i
$207$	25.4282	−	25.4282i	1.76738	−	1.76738i
$208$	0.367854	+	14.2848i	0.0255061	+	0.990473i
$209$		−	5.23255i		−	0.361943i
$210$		0			0
$211$		−	6.32503i		−	0.435433i	−0.976012	−	0.217717i	$-0.930139\pi$
$211$		−	6.32503i		−	0.435433i	0.976012	−	0.217717i	$-0.0698608\pi$
$212$	−6.20630	+	15.5464i	−0.426251	+	1.06773i
$213$	−7.73473	+	7.73473i	−0.529975	+	0.529975i
$214$	18.7892	+	12.3803i	1.28440	+	0.846303i
$215$	−4.65238	−	3.13758i	−0.317290	−	0.213981i
$216$	−34.3572	−	6.14697i	−2.33771	−	0.418248i
$217$		0			0
$218$	−4.13560	+	0.850329i	−0.280098	+	0.0575916i
$219$	7.60397			0.513829
$220$	10.0036	+	14.6968i	0.674441	+	0.990857i
$221$	3.82913			0.257575
$222$	−32.9464	+	6.77417i	−2.21121	+	0.454653i
$223$	1.13429	+	1.13429i	0.0759578	+	0.0759578i	0.744065	−	0.668107i	$-0.232895\pi$
$223$	1.13429	+	1.13429i	0.0759578	+	0.0759578i	−0.668107	+	0.744065i	$0.732895\pi$
$224$		0			0
$225$	12.9629	+	32.0707i	0.864191	+	2.13805i
$226$	−0.680226	−	0.448207i	−0.0452480	−	0.0298143i
$227$	3.54317	−	3.54317i	0.235168	−	0.235168i	−0.579678	−	0.814846i	$-0.696822\pi$
$227$	3.54317	−	3.54317i	0.235168	−	0.235168i	0.814846	+	0.579678i	$0.196822\pi$
$228$	−7.69974	−	3.07382i	−0.509928	−	0.203569i
$229$		−	10.3185i		−	0.681863i	−0.940088	−	0.340931i	$-0.889258\pi$
$229$		−	10.3185i		−	0.681863i	0.940088	−	0.340931i	$-0.110742\pi$
$230$	−6.25770	+	15.1996i	−0.412621	+	1.00223i
$231$		0			0
$232$	−10.4661	+	7.28940i	−0.687132	+	0.478572i
$233$	−9.03323	+	9.03323i	−0.591786	+	0.591786i	−0.938114	−	0.346327i	$-0.887429\pi$
$233$	−9.03323	+	9.03323i	−0.591786	+	0.591786i	0.346327	+	0.938114i	$0.387429\pi$
$234$	19.2308	−	29.1859i	1.25716	−	1.90794i
$235$	−8.54775	+	12.6746i	−0.557594	+	0.826797i
$236$	15.3364	−	6.58509i	0.998314	−	0.428653i
$237$	−7.68598	−	7.68598i	−0.499258	−	0.499258i
$238$		0			0
$239$	19.1256			1.23713			0.618565	−	0.785733i	$-0.287714\pi$
$239$	19.1256			1.23713			0.618565	+	0.785733i	$0.287714\pi$
$240$	27.5030	−	6.08684i	1.77531	−	0.392904i
$241$	−14.1582			−0.912012			−0.456006	−	0.889977i	$-0.650720\pi$
$241$	−14.1582			−0.912012			−0.456006	+	0.889977i	$0.650720\pi$
$242$	−1.36810	−	6.65378i	−0.0879446	−	0.427721i
$243$	14.1476	+	14.1476i	0.907568	+	0.907568i
$244$	2.47583	−	1.06306i	0.158499	−	0.0680556i
$245$		0			0
$246$	27.7350	−	42.0923i	1.76832	−	2.68371i
$247$	3.32493	−	3.32493i	0.211560	−	0.211560i
$248$	5.97674	−	4.16267i	0.379524	−	0.264330i
$249$		−	37.3120i		−	2.36455i
$250$	−11.1082	−	11.2520i	−0.702542	−	0.711642i
$251$		−	8.70910i		−	0.549714i	−0.961485	−	0.274857i	$-0.911370\pi$
$251$		−	8.70910i		−	0.549714i	0.961485	−	0.274857i	$-0.0886305\pi$
$252$		0			0
$253$	14.6114	−	14.6114i	0.918611	−	0.918611i
$254$	17.3279	+	11.4175i	1.08725	+	0.716396i
$255$	−1.44081	−	7.40944i	−0.0902271	−	0.463997i
$256$	−0.823500	−	15.9788i	−0.0514687	−	0.998675i
$257$	4.22126	+	4.22126i	0.263315	+	0.263315i	0.826399	−	0.563084i	$-0.190385\pi$
$257$	4.22126	+	4.22126i	0.263315	+	0.263315i	−0.563084	+	0.826399i	$0.690385\pi$
$258$	10.9480	−	2.25105i	0.681596	−	0.140144i
$259$		0			0
$260$	−2.98220	+	15.6954i	−0.184949	+	0.973387i
$261$	31.1970			1.93105
$262$	−13.6584	+	2.80833i	−0.843819	+	0.173499i
$263$	11.1749	+	11.1749i	0.689073	+	0.689073i	0.962027	−	0.272954i	$-0.0880006\pi$
$263$	11.1749	+	11.1749i	0.689073	+	0.689073i	−0.272954	+	0.962027i	$0.588001\pi$
$264$	−34.8575	−	6.23647i	−2.14533	−	0.383828i
$265$	−10.4643	+	15.5164i	−0.642818	+	0.953167i
$266$		0			0
$267$	−20.9758	+	20.9758i	−1.28370	+	1.28370i
$268$	4.08939	−	10.2437i	0.249799	−	0.625731i
$269$		−	7.99592i		−	0.487520i	−0.969836	−	0.243760i	$-0.921619\pi$
$269$		−	7.99592i		−	0.487520i	0.969836	−	0.243760i	$-0.0783809\pi$
$270$	−36.0841	−	14.8559i	−2.19601	−	0.904099i
$271$			30.0591i			1.82596i	0.408004	+	0.912980i	$0.366225\pi$
$271$			30.0591i			1.82596i	−0.408004	+	0.912980i	$0.633775\pi$
$272$	−4.28606	+	0.110372i	−0.259880	+	0.00669229i
$273$		0			0
$274$	−12.5610	+	19.0633i	−0.758835	+	1.15166i
$275$	7.44864	+	18.4283i	0.449170	+	1.11127i
$276$	−12.9174	−	30.0842i	−0.777539	−	1.81085i
$277$	−1.74742	−	1.74742i	−0.104992	−	0.104992i	0.652659	−	0.757652i	$-0.273653\pi$
$277$	−1.74742	−	1.74742i	−0.104992	−	0.104992i	−0.757652	+	0.652659i	$0.773653\pi$
$278$	−2.59364	−	12.6142i	−0.155556	−	0.756552i
$279$	−17.8153			−1.06657
$280$		0			0
$281$	−2.85110			−0.170082			−0.0850411	−	0.996377i	$-0.527102\pi$
$281$	−2.85110			−0.170082			−0.0850411	+	0.996377i	$0.527102\pi$
$282$	−6.13258	−	29.8259i	−0.365190	−	1.77611i
$283$	6.11827	+	6.11827i	0.363693	+	0.363693i	0.865171	−	0.501477i	$-0.167210\pi$
$283$	6.11827	+	6.11827i	0.363693	+	0.363693i	−0.501477	+	0.865171i	$0.667210\pi$
$284$	2.74074	+	6.38307i	0.162633	+	0.378765i
$285$	−7.68489	−	5.18271i	−0.455214	−	0.306997i
$286$	11.0503	−	16.7706i	0.653418	−	0.991667i
$287$		0			0
$288$	−20.6844	+	33.2230i	−1.21884	+	1.95768i
$289$		−	15.8511i		−	0.932417i
$290$	−13.1626	+	5.48526i	−0.772936	+	0.322106i
$291$			40.2812i			2.36133i
$292$	1.79037	−	4.48478i	0.104774	−	0.262452i
$293$	16.5266	−	16.5266i	0.965497	−	0.965497i	−0.0339277	−	0.999424i	$-0.510802\pi$
$293$	16.5266	−	16.5266i	0.965497	−	0.965497i	0.999424	+	0.0339277i	$0.0108016\pi$
$294$		0			0
$295$	18.3173	−	3.56191i	1.06647	−	0.207382i
$296$	−3.76194	+	21.0266i	−0.218658	+	1.22214i
$297$	34.6876	+	34.6876i	2.01278	+	2.01278i
$298$	−2.73477	+	0.562301i	−0.158421	+	0.0325732i
$299$	18.5691			1.07388
$300$	31.4930	−	0.135178i	1.81825	−	0.00780451i
$301$		0			0
$302$	−11.9545	+	2.45799i	−0.687905	+	0.141442i
$303$	−22.8768	−	22.8768i	−1.31424	−	1.31424i
$304$	−3.62585	+	3.81753i	−0.207957	+	0.218950i
$305$	2.95705	−	0.575016i	0.169320	−	0.0329253i
$306$	8.75703	+	5.77008i	0.500606	+	0.329853i
$307$	−15.0259	+	15.0259i	−0.857575	+	0.857575i	−0.991052	−	0.133477i	$-0.957386\pi$
$307$	−15.0259	+	15.0259i	−0.857575	+	0.857575i	0.133477	+	0.991052i	$0.457386\pi$
$308$		0			0
$309$		−	13.1638i		−	0.748863i
$310$	7.51662	−	3.13240i	0.426915	−	0.177909i
$311$		−	28.1731i		−	1.59755i	−0.601629	−	0.798776i	$-0.705481\pi$
$311$		−	28.1731i		−	1.59755i	0.601629	−	0.798776i	$-0.294519\pi$
$312$	−18.1867	−	26.1124i	−1.02962	−	1.47832i
$313$	−18.1503	+	18.1503i	−1.02592	+	1.02592i	−0.0262603	+	0.999655i	$0.508360\pi$
$313$	−18.1503	+	18.1503i	−1.02592	+	1.02592i	−0.999655	+	0.0262603i	$0.991640\pi$
$314$	12.3358	−	18.7216i	0.696150	−	1.05652i
$315$		0			0
$316$	−6.34283	+	2.72346i	−0.356812	+	0.153207i
$317$	−18.5985	−	18.5985i	−1.04460	−	1.04460i	−0.998958	−	0.0456388i	$-0.985468\pi$
$317$	−18.5985	−	18.5985i	−1.04460	−	1.04460i	−0.0456388	−	0.998958i	$-0.514532\pi$
$318$	−7.50762	−	36.5135i	−0.421006	−	2.04757i
$319$	17.9262			1.00368
$320$	2.88566	−	17.6543i	0.161313	−	0.986903i
$321$	−50.1083			−2.79678
$322$		0			0
$323$	0.997621	+	0.997621i	0.0555091	+	0.0555091i
$324$	33.2778	−	14.2887i	1.84877	−	0.793818i
$325$	−6.97681	+	16.4430i	−0.387004	+	0.912094i
$326$	−5.42019	+	8.22602i	−0.300197	+	0.455597i
$327$	6.64842	−	6.64842i	0.367658	−	0.367658i
$328$	−18.2955	−	26.2687i	−1.01020	−	1.45044i
$329$		0			0
$330$	−36.6095	−	15.0722i	−2.01528	−	0.829695i
$331$		−	17.2022i		−	0.945519i	−0.881192	−	0.472759i	$-0.843258\pi$
$331$		−	17.2022i		−	0.945519i	0.881192	−	0.472759i	$-0.156742\pi$
$332$	−22.0064	−	8.78520i	−1.20776	−	0.482150i
$333$	36.9445	−	36.9445i	2.02454	−	2.02454i
$334$	19.9082	+	13.1177i	1.08933	+	0.717767i
$335$	6.89503	−	10.2239i	0.376715	−	0.558592i
$336$		0			0
$337$	−12.9038	−	12.9038i	−0.702913	−	0.702913i	0.262121	−	0.965035i	$-0.415578\pi$
$337$	−12.9038	−	12.9038i	−0.702913	−	0.702913i	−0.965035	+	0.262121i	$0.915578\pi$
$338$	−0.329775	+	0.0678058i	−0.0179374	+	0.00368815i
$339$	1.81408			0.0985271
$340$	−4.70929	−	0.894790i	−0.255397	−	0.0485268i
$341$	−10.2369			−0.554360
$342$	12.6142	−	2.59364i	0.682100	−	0.140248i
$343$		0			0
$344$	1.25009	−	6.98711i	0.0674002	−	0.376720i
$345$	−6.98711	−	35.9316i	−0.376173	−	1.93449i
$346$	−0.261466	−	0.172282i	−0.0140565	−	0.00926196i
$347$	13.3538	−	13.3538i	0.716871	−	0.716871i	−0.251092	−	0.967963i	$-0.580790\pi$
$347$	13.3538	−	13.3538i	0.716871	−	0.716871i	0.967963	+	0.251092i	$0.0807897\pi$
$348$	10.5306	−	26.3786i	0.564501	−	1.41404i
$349$		−	22.9263i		−	1.22721i	−0.789611	−	0.613607i	$-0.789718\pi$
$349$		−	22.9263i		−	1.22721i	0.789611	−	0.613607i	$-0.210282\pi$
$350$		0			0
$351$			44.0832i			2.35299i
$352$	−11.8855	+	19.0904i	−0.633500	+	1.01752i
$353$	21.1578	−	21.1578i	1.12612	−	1.12612i	0.135315	−	0.990803i	$-0.456795\pi$
$353$	21.1578	−	21.1578i	1.12612	−	1.12612i	0.990803	−	0.135315i	$-0.0432045\pi$
$354$	−20.4501	+	31.0363i	−1.08691	+	1.64956i
$355$	1.48248	+	7.62373i	0.0786819	+	0.404625i
$356$	7.43261	+	17.3102i	0.393928	+	0.917441i
$357$		0			0
$358$	−5.81164	−	28.2651i	−0.307155	−	1.49385i
$359$	8.55036			0.451271			0.225635	−	0.974212i	$-0.427554\pi$
$359$	8.55036			0.451271			0.225635	+	0.974212i	$0.427554\pi$
$360$	−30.4714	+	31.4007i	−1.60598	+	1.65496i
$361$	−17.2675			−0.908815
$362$	3.75102	+	18.2432i	0.197149	+	0.958840i
$363$	10.6967	+	10.6967i	0.561429	+	0.561429i
$364$		0			0
$365$	3.01871	−	4.47613i	0.158007	−	0.234291i
$366$	−3.30136	+	5.01034i	−0.172565	+	0.261895i
$367$	3.70939	−	3.70939i	0.193629	−	0.193629i	−0.603633	−	0.797262i	$-0.706281\pi$
$367$	3.70939	−	3.70939i	0.193629	−	0.193629i	0.797262	+	0.603633i	$0.206281\pi$
$368$	−20.7849	+	0.535241i	−1.08349	+	0.0279014i
$369$			78.3009i			4.07618i
$370$	−9.09176	+	22.0834i	−0.472658	+	1.14806i
$371$		0			0
$372$	−6.01360	+	15.0637i	−0.311791	+	0.781017i
$373$	−2.18376	+	2.18376i	−0.113071	+	0.113071i	−0.761378	−	0.648308i	$-0.775477\pi$
$373$	−2.18376	+	2.18376i	−0.113071	+	0.113071i	0.648308	+	0.761378i	$0.275477\pi$
$374$	5.03191	+	3.31557i	0.260194	+	0.171444i
$375$	34.4428	+	7.31315i	1.77862	+	0.377649i
$376$	−19.0351	−	3.40564i	−0.981661	−	0.175632i
$377$	11.3909	+	11.3909i	0.586661	+	0.586661i
$378$		0			0
$379$	−17.0070			−0.873589			−0.436794	−	0.899561i	$-0.643886\pi$
$379$	−17.0070			−0.873589			−0.436794	+	0.899561i	$0.643886\pi$
$380$	−4.86616	+	3.31222i	−0.249629	+	0.169914i
$381$	−46.2112			−2.36747
$382$	16.7659	−	3.44726i	0.857816	−	0.176377i
$383$	−19.2727	−	19.2727i	−0.984790	−	0.984790i	0.0150963	−	0.999886i	$-0.495195\pi$
$383$	−19.2727	−	19.2727i	−0.984790	−	0.984790i	−0.999886	+	0.0150963i	$0.995195\pi$
$384$	21.1096	+	28.7041i	1.07724	+	1.46480i
$385$		0			0
$386$	0.829130	+	0.546320i	0.0422016	+	0.0278070i
$387$	−12.2766	+	12.2766i	−0.624055	+	0.624055i
$388$	23.7576	+	9.48432i	1.20611	+	0.481493i
$389$			12.6470i			0.641228i	0.947210	+	0.320614i	$0.103889\pi$
$389$			12.6470i			0.641228i	−0.947210	+	0.320614i	$0.896111\pi$
$390$	−13.6855	−	32.8401i	−0.692991	−	1.66292i
$391$			5.57153i			0.281764i
$392$		0			0
$393$	21.9573	−	21.9573i	1.10760	−	1.10760i
$394$	1.28665	−	1.95270i	0.0648206	−	0.0983757i
$395$	−7.57567	+	1.47314i	−0.381173	+	0.0741215i
$396$	50.5430	−	21.7020i	2.53988	−	1.09057i
$397$	8.57768	+	8.57768i	0.430501	+	0.430501i	0.888799	−	0.458297i	$-0.151541\pi$
$397$	8.57768	+	8.57768i	0.430501	+	0.430501i	−0.458297	+	0.888799i	$0.651541\pi$
$398$	4.97053	+	24.1743i	0.249150	+	1.21175i
$399$		0			0
$400$	7.33539	−	18.6062i	0.366769	−	0.930312i
$401$	−14.2568			−0.711949			−0.355975	−	0.934496i	$-0.615851\pi$
$401$	−14.2568			−0.711949			−0.355975	+	0.934496i	$0.615851\pi$
$402$	4.94683	+	24.0590i	0.246725	+	1.19996i
$403$	−6.50486	−	6.50486i	−0.324030	−	0.324030i
$404$	−18.8790	+	8.10621i	−0.939267	+	0.403299i
$405$	39.7459	−	7.72884i	1.97499	−	0.384049i
$406$		0			0
$407$	21.2288	−	21.2288i	1.05227	−	1.05227i
$408$	7.83484	−	5.45679i	0.387882	−	0.270151i
$409$			29.8999i			1.47845i	0.673456	+	0.739227i	$0.264809\pi$
$409$			29.8999i			1.47845i	−0.673456	+	0.739227i	$0.735191\pi$
$410$	−13.7674	−	33.0367i	−0.679922	−	1.63157i
$411$		−	50.8394i		−	2.50772i
$412$	−7.76394	−	3.09945i	−0.382502	−	0.152699i
$413$		0			0
$414$	42.4666	+	27.9816i	2.08712	+	1.37522i
$415$	−21.9639	−	14.8125i	−1.07817	−	0.727119i
$416$	−19.6830	+	4.57818i	−0.965041	+	0.224464i
$417$	20.2787	+	20.2787i	0.993054	+	0.993054i
$418$	7.24831	−	1.49034i	0.354527	−	0.0728950i
$419$	37.6505			1.83935			0.919674	−	0.392684i	$-0.128453\pi$
$419$	37.6505			1.83935			0.919674	+	0.392684i	$0.128453\pi$
$420$		0			0
$421$	−8.37171			−0.408012			−0.204006	−	0.978970i	$-0.565396\pi$
$421$	−8.37171			−0.408012			−0.204006	+	0.978970i	$0.565396\pi$
$422$	8.76166	−	1.80150i	0.426511	−	0.0876958i
$423$	33.4454	+	33.4454i	1.62617	+	1.62617i
$424$	−23.3031	−	4.16924i	−1.13170	−	0.202476i
$425$	−4.93361	−	2.09334i	−0.239315	−	0.101542i
$426$	−12.9174	−	8.51141i	−0.625852	−	0.412379i
$427$		0			0
$428$	−11.7981	+	29.5536i	−0.570285	+	1.42853i
$429$			44.7251i			2.15935i
$430$	3.02118	−	7.33829i	0.145694	−	0.353884i
$431$			4.97943i			0.239851i	0.992783	+	0.119925i	$0.0382656\pi$
$431$			4.97943i			0.239851i	−0.992783	+	0.119925i	$0.961734\pi$
$432$	−1.27067	−	49.3436i	−0.0611351	−	2.37405i
$433$	−2.70541	+	2.70541i	−0.130014	+	0.130014i	−0.769119	−	0.639106i	$-0.779305\pi$
$433$	−2.70541	+	2.70541i	−0.130014	+	0.130014i	0.639106	+	0.769119i	$0.279305\pi$
$434$		0			0
$435$	17.7555	−	26.3277i	0.851310	−	1.26232i
$436$	−2.35581	−	5.48659i	−0.112823	−	0.262760i
$437$	4.83789	+	4.83789i	0.231428	+	0.231428i
$438$	2.16577	+	10.5333i	0.103485	+	0.503300i
$439$	37.5353			1.79146			0.895731	−	0.444597i	$-0.146653\pi$
$439$	37.5353			1.79146			0.895731	+	0.444597i	$0.146653\pi$
$440$	−17.5093	+	18.0433i	−0.834722	+	0.860179i
$441$		0			0
$442$	1.09062	+	5.30425i	0.0518754	+	0.252297i
$443$	−8.97407	−	8.97407i	−0.426371	−	0.426371i	0.461019	−	0.887390i	$-0.347484\pi$
$443$	−8.97407	−	8.97407i	−0.426371	−	0.426371i	−0.887390	+	0.461019i	$0.847484\pi$
$444$	−18.7676	−	43.7090i	−0.890673	−	2.07434i
$445$	4.02034	+	20.6748i	0.190582	+	0.980079i
$446$	−1.24819	+	1.89433i	−0.0591035	+	0.0896992i
$447$	4.39643	−	4.39643i	0.207944	−	0.207944i
$448$		0			0
$449$		−	25.1638i		−	1.18755i	−0.804630	−	0.593777i	$-0.797636\pi$
$449$		−	25.1638i		−	1.18755i	0.804630	−	0.593777i	$-0.202364\pi$
$450$	−40.7334	+	27.0911i	−1.92019	+	1.27708i
$451$			44.9928i			2.11863i
$452$	0.427129	−	1.06993i	0.0200904	−	0.0503254i
$453$	19.2182	−	19.2182i	0.902948	−	0.902948i
$454$	5.91729	+	3.89895i	0.277712	+	0.182987i
$455$		0			0
$456$	2.06492	−	11.5414i	0.0966987	−	0.540478i
$457$	19.2326	+	19.2326i	0.899664	+	0.899664i	0.995406	−	0.0957418i	$-0.0305223\pi$
$457$	19.2326	+	19.2326i	0.899664	+	0.899664i	−0.0957418	+	0.995406i	$0.530522\pi$
$458$	14.2935	−	2.93891i	0.667891	−	0.137326i
$459$	−13.2269			−0.617377
$460$	−22.8374	−	4.33922i	−1.06480	−	0.202317i
$461$	20.0052			0.931737			0.465868	−	0.884854i	$-0.345742\pi$
$461$	20.0052			0.931737			0.465868	+	0.884854i	$0.345742\pi$
$462$		0			0
$463$	−10.1515	−	10.1515i	−0.471781	−	0.471781i	0.430710	−	0.902491i	$-0.358263\pi$
$463$	−10.1515	−	10.1515i	−0.471781	−	0.471781i	−0.902491	+	0.430710i	$0.858263\pi$
$464$	−13.0785	−	12.4218i	−0.607154	−	0.576669i
$465$	−10.1394	+	15.0347i	−0.470204	+	0.697216i
$466$	−15.0860	−	9.94029i	−0.698845	−	0.460475i
$467$	2.92329	−	2.92329i	0.135274	−	0.135274i	−0.636228	−	0.771501i	$-0.719506\pi$
$467$	2.92329	−	2.92329i	0.135274	−	0.135274i	0.771501	+	0.636228i	$0.219506\pi$
$468$	45.9067	+	18.3265i	2.12204	+	0.847141i
$469$		0			0
$470$	−19.9918	−	8.23066i	−0.922154	−	0.379652i
$471$			49.9281i			2.30057i
$472$	13.4900	+	19.3689i	0.620929	+	0.891528i
$473$	−7.05431	+	7.05431i	−0.324357	+	0.324357i
$474$	8.45776	−	12.8360i	0.388478	−	0.589578i
$475$	−6.10167	+	2.46627i	−0.279964	+	0.113160i
$476$		0			0
$477$	40.9445	+	40.9445i	1.87472	+	1.87472i
$478$	5.44737	+	26.4934i	0.249157	+	1.21178i
$479$	9.32897			0.426252			0.213126	−	0.977025i	$-0.431636\pi$
$479$	9.32897			0.426252			0.213126	+	0.977025i	$0.431636\pi$
$480$	16.2651	+	36.3644i	0.742399	+	1.65980i
$481$	26.9789			1.23013
$482$	−4.03256	−	19.6125i	−0.183678	−	0.893324i
$483$		0			0
$484$	8.82738	−	3.79027i	0.401245	−	0.172285i
$485$	23.7118	+	15.9913i	1.07670	+	0.726128i
$486$	−15.5682	+	23.6273i	−0.706188	+	1.07175i
$487$	−20.5026	+	20.5026i	−0.929063	+	0.929063i	−0.997645	−	0.0685824i	$-0.978152\pi$
$487$	−20.5026	+	20.5026i	−0.929063	+	0.929063i	0.0685824	+	0.997645i	$0.478152\pi$
$488$	2.17776	+	3.12682i	0.0985825	+	0.141544i
$489$		−	21.9378i		−	0.992060i
$490$		0			0
$491$			28.1818i			1.27183i	0.771760	+	0.635914i	$0.219377\pi$
$491$			28.1818i			1.27183i	−0.771760	+	0.635914i	$0.780623\pi$
$492$	66.2073	+	26.4307i	2.98485	+	1.19159i
$493$	−3.41776	+	3.41776i	−0.153928	+	0.153928i
$494$	5.55282	+	3.65880i	0.249833	+	0.164617i
$495$	60.3669	−	11.7387i	2.71329	−	0.527616i
$496$	7.46858	+	7.09358i	0.335349	+	0.318511i
$497$		0			0
$498$	51.6859	−	10.6272i	2.31610	−	0.476218i
$499$	31.0735			1.39104			0.695521	−	0.718506i	$-0.255174\pi$
$499$	31.0735			1.39104			0.695521	+	0.718506i	$0.255174\pi$
$500$	12.4229	−	18.5923i	0.555569	−	0.831471i
$501$	−53.0926			−2.37200
$502$	12.0642	−	2.48054i	0.538450	−	0.110712i
$503$	−28.6110	−	28.6110i	−1.27570	−	1.27570i	−0.943049	−	0.332654i	$-0.892056\pi$
$503$	−28.6110	−	28.6110i	−1.27570	−	1.27570i	−0.332654	−	0.943049i	$-0.607944\pi$
$504$		0			0
$505$	−22.5485	+	4.38469i	−1.00340	+	0.195116i
$506$	24.4019	+	16.0786i	1.08480	+	0.714781i
$507$	0.530149	−	0.530149i	0.0235447	−	0.0235447i
$508$	−10.8805	+	27.2551i	−0.482746	+	1.20925i
$509$		−	12.2524i		−	0.543076i	−0.962428	−	0.271538i	$-0.912468\pi$
$509$		−	12.2524i		−	0.543076i	0.962428	−	0.271538i	$-0.0875323\pi$
$510$	9.85345	−	4.10623i	0.436318	−	0.181827i
$511$		0			0
$512$	21.8998	−	5.69184i	0.967845	−	0.251546i
$513$	−11.4852	+	11.4852i	−0.507084	+	0.507084i
$514$	−4.64513	+	7.04974i	−0.204888	+	0.310951i
$515$	−7.74896	−	5.22592i	−0.341460	−	0.230282i
$516$	6.23647	+	14.5245i	0.274545	+	0.639404i
$517$	19.2182	+	19.2182i	0.845214	+	0.845214i
$518$		0			0
$519$	0.697297			0.0306080
$520$	−22.5912	+	0.339323i	−0.990690	+	0.0148803i
$521$	35.5672			1.55823			0.779115	−	0.626881i	$-0.215669\pi$
$521$	35.5672			1.55823			0.779115	+	0.626881i	$0.215669\pi$
$522$	8.88558	+	43.2152i	0.388911	+	1.89148i
$523$	8.12155	+	8.12155i	0.355131	+	0.355131i	0.862014	−	0.506884i	$-0.169203\pi$
$523$	8.12155	+	8.12155i	0.355131	+	0.355131i	−0.506884	+	0.862014i	$0.669203\pi$
$524$	−7.78040	−	18.1202i	−0.339889	−	0.791586i
$525$		0			0
$526$	−12.2970	+	18.6627i	−0.536175	+	0.813733i
$527$	1.95174	−	1.95174i	0.0850190	−	0.0850190i
$528$	−1.28917	−	50.0621i	−0.0561040	−	2.17867i
$529$			4.01871i			0.174727i
$530$	−24.4744	−	10.0761i	−1.06310	−	0.437679i
$531$		−	57.7344i		−	2.50546i
$532$		0			0
$533$	−28.5898	+	28.5898i	−1.23836	+	1.23836i
$534$	−35.0308	−	23.0821i	−1.51593	−	0.998860i
$535$	−19.8926	+	29.4966i	−0.860032	+	1.27525i
$536$	15.3546	+	2.74715i	0.663219	+	0.118659i
$537$	45.4391	+	45.4391i	1.96084	+	1.96084i
$538$	11.0762	−	2.27741i	0.477530	−	0.0981860i
$539$		0			0
$540$	10.3014	−	54.2162i	0.443300	−	2.33309i
$541$	12.8511			0.552512			0.276256	−	0.961084i	$-0.410906\pi$
$541$	12.8511			0.552512			0.276256	+	0.961084i	$0.410906\pi$
$542$	−41.6389	+	8.56147i	−1.78854	+	0.367747i
$543$	−29.3278	−	29.3278i	−1.25858	−	1.25858i
$544$	−1.37365	−	5.90576i	−0.0588948	−	0.253207i
$545$	−1.27427	−	6.55300i	−0.0545838	−	0.280700i
$546$		0			0
$547$	−1.19674	+	1.19674i	−0.0511688	+	0.0511688i	−0.732228	−	0.681059i	$-0.761520\pi$
$547$	−1.19674	+	1.19674i	−0.0511688	+	0.0511688i	0.681059	+	0.732228i	$0.261520\pi$
$548$	−29.9848	−	11.9703i	−1.28089	−	0.511344i
$549$		−	9.32034i		−	0.397782i
$550$	−23.4060	+	15.5669i	−0.998034	+	0.663774i
$551$			5.93545i			0.252858i
$552$	37.9945	−	26.4623i	1.61715	−	1.12631i
$553$		0			0
$554$	1.92289	−	2.91829i	0.0816956	−	0.123986i
$555$	−10.1515	−	52.2047i	−0.430908	−	2.21596i
$556$	16.7350	−	7.18561i	0.709721	−	0.304738i
$557$	−11.7507	−	11.7507i	−0.497892	−	0.497892i	0.412889	−	0.910781i	$-0.364520\pi$
$557$	−11.7507	−	11.7507i	−0.497892	−	0.497892i	−0.910781	+	0.412889i	$0.864520\pi$
$558$	−5.07418	−	24.6784i	−0.214807	−	1.04472i
$559$	−8.96505			−0.379181
$560$		0			0
$561$	−13.4195			−0.566570
$562$	−0.812053	−	3.94944i	−0.0342544	−	0.166597i
$563$	−26.3267	−	26.3267i	−1.10954	−	1.10954i	−0.993211	−	0.116328i	$-0.962888\pi$
$563$	−26.3267	−	26.3267i	−1.10954	−	1.10954i	−0.116328	−	0.993211i	$-0.537112\pi$
$564$	39.5693	−	16.9901i	1.66617	−	0.715413i
$565$	0.720173	−	1.06787i	0.0302979	−	0.0449256i
$566$	−6.73263	+	10.2179i	−0.282993	+	0.429488i
$567$		0			0
$568$	−8.06143	+	5.61460i	−0.338250	+	0.235583i
$569$			16.4567i			0.689900i	0.938621	+	0.344950i	$0.112104\pi$
$569$			16.4567i			0.689900i	−0.938621	+	0.344950i	$0.887896\pi$
$570$	4.99045	−	12.1215i	0.209027	−	0.507715i
$571$		−	44.7495i		−	1.87271i	−0.351054	−	0.936355i	$-0.614177\pi$
$571$		−	44.7495i		−	1.87271i	0.351054	−	0.936355i	$-0.385823\pi$
$572$	26.3786	+	10.5306i	1.10295	+	0.440308i
$573$	−26.9529	+	26.9529i	−1.12597	+	1.12597i
$574$		0			0
$575$	−23.9252	−	10.1515i	−0.997749	−	0.423347i
$576$	−51.9130	−	19.1901i	−2.16304	−	0.799588i
$577$	−9.68360	−	9.68360i	−0.403134	−	0.403134i	0.476202	−	0.879336i	$-0.342013\pi$
$577$	−9.68360	−	9.68360i	−0.403134	−	0.403134i	−0.879336	+	0.476202i	$0.842013\pi$
$578$	21.9575	−	4.51473i	0.913312	−	0.187788i
$579$	−2.21118			−0.0918936
$580$	−11.3474	−	16.6710i	−0.471174	−	0.692226i
$581$		0			0
$582$	−55.7990	+	11.4729i	−2.31294	+	0.475569i
$583$	23.5272	+	23.5272i	0.974399	+	0.974399i
$584$	6.72241	+	1.20273i	0.278175	+	0.0497693i
$585$	45.8182	+	30.8999i	1.89435	+	1.27755i
$586$	27.6004	+	18.1861i	1.14016	+	0.751263i
$587$	−24.5126	+	24.5126i	−1.01175	+	1.01175i	−0.0118150	+	0.999930i	$0.503761\pi$
$587$	−24.5126	+	24.5126i	−1.01175	+	1.01175i	−0.999930	+	0.0118150i	$0.996239\pi$
$588$		0			0
$589$		−	3.38948i		−	0.139661i
$590$	10.1512	+	24.3593i	0.417920	+	1.00285i
$591$			5.20761i			0.214212i
$592$	−30.1982	+	0.777648i	−1.24114	+	0.0319611i
$593$	−32.3651	+	32.3651i	−1.32908	+	1.32908i	−0.422898	+	0.906177i	$0.638987\pi$
$593$	−32.3651	+	32.3651i	−1.32908	+	1.32908i	−0.906177	+	0.422898i	$0.861013\pi$
$594$	−38.1708	+	57.9303i	−1.56617	+	2.37691i
$595$		0			0
$596$	−1.55784	−	3.62814i	−0.0638115	−	0.148614i
$597$	−38.8627	−	38.8627i	−1.59055	−	1.59055i
$598$	5.28887	+	25.7226i	0.216278	+	1.05187i
$599$	−31.2069			−1.27508			−0.637540	−	0.770417i	$-0.720048\pi$
$599$	−31.2069			−1.27508			−0.637540	+	0.770417i	$0.720048\pi$
$600$	9.15714	+	43.5868i	0.373838	+	1.77942i
$601$	−3.84939			−0.157020			−0.0785099	−	0.996913i	$-0.525016\pi$
$601$	−3.84939			−0.157020			−0.0785099	+	0.996913i	$0.525016\pi$
$602$		0			0
$603$	−26.9786	−	26.9786i	−1.09866	−	1.09866i
$604$	−6.80980	−	15.8597i	−0.277087	−	0.645323i
$605$	10.5431	−	2.05018i	0.428640	−	0.0833516i
$606$	25.1740	−	38.2056i	1.02262	−	1.55200i
$607$	4.07331	−	4.07331i	0.165331	−	0.165331i	−0.619593	−	0.784923i	$-0.712702\pi$
$607$	4.07331	−	4.07331i	0.165331	−	0.165331i	0.784923	+	0.619593i	$0.212702\pi$
$608$	−6.32089	−	3.93534i	−0.256346	−	0.159599i
$609$		0			0
$610$	1.63876	+	3.93243i	0.0663515	+	0.159219i
$611$			24.4236i			0.988075i
$612$	−5.49873	+	13.7740i	−0.222273	+	0.556780i
$613$	14.3977	−	14.3977i	0.581517	−	0.581517i	−0.353803	−	0.935320i	$-0.615112\pi$
$613$	14.3977	−	14.3977i	0.581517	−	0.581517i	0.935320	+	0.353803i	$0.115112\pi$
$614$	−25.0941	−	16.5347i	−1.01272	−	0.667288i
$615$	66.0796	+	44.5642i	2.66459	+	1.79700i
$616$		0			0
$617$	−5.54965	−	5.54965i	−0.223420	−	0.223420i	0.586517	−	0.809937i	$-0.300499\pi$
$617$	−5.54965	−	5.54965i	−0.223420	−	0.223420i	−0.809937	+	0.586517i	$0.800499\pi$
$618$	18.2350	−	3.74933i	0.733518	−	0.150820i
$619$	5.04224			0.202665			0.101332	−	0.994853i	$-0.467689\pi$
$619$	5.04224			0.202665			0.101332	+	0.994853i	$0.467689\pi$
$620$	6.48001	+	9.52012i	0.260243	+	0.382337i
$621$	−64.1427			−2.57396
$622$	39.0264	−	8.02430i	1.56482	−	0.321745i
$623$		0			0
$624$	30.9919	−	32.6302i	1.24067	−	1.30625i
$625$	17.9784	−	17.3717i	0.719137	−	0.694868i
$626$	−30.3120	−	19.9728i	−1.21151	−	0.798275i
$627$	−11.6524	+	11.6524i	−0.465354	+	0.465354i
$628$	29.4473	+	11.7557i	1.17508	+	0.469103i
$629$			8.09482i			0.322762i
$630$		0			0
$631$		−	22.4036i		−	0.891874i	−0.895064	−	0.445937i	$-0.852870\pi$
$631$		−	22.4036i		−	0.891874i	0.895064	−	0.445937i	$-0.147130\pi$
$632$	−5.57921	−	8.01061i	−0.221929	−	0.318645i
$633$	−14.0853	+	14.0853i	−0.559840	+	0.559840i
$634$	20.4661	−	31.0606i	0.812811	−	1.23357i
$635$	−18.3455	+	27.2025i	−0.728017	+	1.07950i
$636$	48.4414	−	20.7996i	1.92083	−	0.824759i
$637$		0			0
$638$	5.10577	+	24.8321i	0.202139	+	0.983111i
$639$	24.0293			0.950584
$640$	25.2772	−	1.03099i	0.999169	−	0.0407535i
$641$	−43.1195			−1.70312			−0.851559	−	0.524258i	$-0.824343\pi$
$641$	−43.1195			−1.70312			−0.851559	+	0.524258i	$0.824343\pi$
$642$	−14.2719	−	69.4119i	−0.563268	−	2.73947i
$643$	−1.10922	−	1.10922i	−0.0437432	−	0.0437432i	0.684897	−	0.728640i	$-0.259847\pi$
$643$	−1.10922	−	1.10922i	−0.0437432	−	0.0437432i	−0.728640	+	0.684897i	$0.759847\pi$
$644$		0			0
$645$	3.37334	+	17.3476i	0.132825	+	0.683060i
$646$	−1.09780	+	1.66608i	−0.0431922	+	0.0655512i
$647$	23.8413	−	23.8413i	0.937300	−	0.937300i	−0.0608472	−	0.998147i	$-0.519380\pi$
$647$	23.8413	−	23.8413i	0.937300	−	0.937300i	0.998147	+	0.0608472i	$0.0193802\pi$
$648$	29.2715	+	42.0279i	1.14989	+	1.65101i
$649$		−	33.1750i		−	1.30223i
$650$	−24.7646	−	4.98120i	−0.971347	−	0.195379i
$651$		0			0
$652$	−12.9388	−	5.16530i	−0.506721	−	0.202289i
$653$	27.2099	−	27.2099i	1.06481	−	1.06481i	0.0670574	−	0.997749i	$-0.478639\pi$
$653$	27.2099	−	27.2099i	1.06481	−	1.06481i	0.997749	−	0.0670574i	$-0.0213611\pi$
$654$	11.1032	+	7.31601i	0.434171	+	0.286079i
$655$	−4.20846	−	21.6422i	−0.164438	−	0.845631i
$656$	31.1773	−	32.8255i	1.21727	−	1.28162i
$657$	−11.8115	−	11.8115i	−0.460811	−	0.460811i
$658$		0			0
$659$	12.4757			0.485985			0.242993	−	0.970028i	$-0.421871\pi$
$659$	12.4757			0.485985			0.242993	+	0.970028i	$0.421871\pi$
$660$	10.4513	−	55.0056i	0.406818	−	2.14109i
$661$	6.62593			0.257719			0.128859	−	0.991663i	$-0.458868\pi$
$661$	6.62593			0.257719			0.128859	+	0.991663i	$0.458868\pi$
$662$	23.8291	−	4.89955i	0.926144	−	0.190427i
$663$	−8.52714	−	8.52714i	−0.331167	−	0.331167i
$664$	5.90168	−	32.9862i	0.229030	−	1.28011i
$665$		0			0
$666$	61.6993	+	40.6542i	2.39080	+	1.57532i
$667$	−16.5742	+	16.5742i	−0.641754	+	0.641754i
$668$	−12.5008	+	31.3137i	−0.483670	+	1.21156i
$669$		−	5.05194i		−	0.195319i
$670$	16.1264	+	6.63925i	0.623016	+	0.256497i
$671$		−	5.35559i		−	0.206750i
$672$		0			0
$673$	−27.7823	+	27.7823i	−1.07093	+	1.07093i	−0.0736433	+	0.997285i	$0.523463\pi$
$673$	−27.7823	+	27.7823i	−1.07093	+	1.07093i	−0.997285	+	0.0736433i	$0.976537\pi$
$674$	14.1995	−	21.5500i	0.546944	−	0.830076i
$675$	24.0998	−	56.7987i	0.927602	−	2.18618i
$676$	−0.187854	−	0.437504i	−0.00722515	−	0.0168271i
$677$	−12.4726	−	12.4726i	−0.479363	−	0.479363i	0.425565	−	0.904928i	$-0.360075\pi$
$677$	−12.4726	−	12.4726i	−0.479363	−	0.479363i	−0.904928	+	0.425565i	$0.860075\pi$
$678$	0.516687	+	2.51292i	0.0198433	+	0.0965082i
$679$		0			0
$680$	−0.101812	−	6.77833i	−0.00390429	−	0.259937i
$681$	−15.7806			−0.604716
$682$	−2.91569	−	14.1805i	−0.111648	−	0.543001i
$683$	−3.84838	−	3.84838i	−0.147254	−	0.147254i	0.629636	−	0.776890i	$-0.283204\pi$
$683$	−3.84838	−	3.84838i	−0.147254	−	0.147254i	−0.776890	+	0.629636i	$0.783204\pi$
$684$	7.18561	+	16.7350i	0.274749	+	0.639878i
$685$	−29.9269	−	20.1828i	−1.14345	−	0.771145i
$686$		0			0
$687$	−22.9783	+	22.9783i	−0.876677	+	0.876677i
$688$	10.0348	−	0.258412i	0.382575	−	0.00985185i
$689$			29.8999i			1.13909i
$690$	47.7836	−	19.9129i	1.81909	−	0.758070i
$691$		−	37.0043i		−	1.40771i	−0.710344	−	0.703854i	$-0.751461\pi$
$691$		−	37.0043i		−	1.40771i	0.710344	−	0.703854i	$-0.248539\pi$
$692$	0.164180	−	0.411262i	0.00624120	−	0.0156338i
$693$		0			0
$694$	22.3016	+	14.6947i	0.846559	+	0.557805i
$695$	19.9877	−	3.88673i	0.758177	−	0.147432i
$696$	39.5399	+	7.07422i	1.49876	+	0.268148i
$697$	−8.57818	−	8.57818i	−0.324922	−	0.324922i
$698$	31.7583	−	6.52988i	1.20207	−	0.247160i
$699$	40.2324			1.52173
$700$		0			0
$701$	−29.4765			−1.11331			−0.556656	−	0.830743i	$-0.687916\pi$
$701$	−29.4765			−1.11331			−0.556656	+	0.830743i	$0.687916\pi$
$702$	−61.0656	+	12.5558i	−2.30477	+	0.473889i
$703$	7.02893	+	7.02893i	0.265101	+	0.265101i
$704$	−29.8299	−	11.0269i	−1.12426	−	0.415592i
$705$	47.2603	−	9.19005i	1.77992	−	0.346117i
$706$	35.3348	+	23.2824i	1.32984	+	0.876244i
$707$		0			0
$708$	−48.8172	−	19.4884i	−1.83466	−	0.732419i
$709$		−	18.1193i		−	0.680485i	−0.940338	−	0.340243i	$-0.889491\pi$
$709$		−	18.1193i		−	0.680485i	0.940338	−	0.340243i	$-0.110509\pi$
$710$	−10.1384	+	4.22498i	−0.380488	+	0.158561i
$711$			23.8778i			0.895488i
$712$	−21.8618	+	15.2262i	−0.819305	+	0.570628i
$713$	9.46481	−	9.46481i	0.354460	−	0.354460i
$714$		0			0
$715$	26.3277	+	17.7555i	0.984602	+	0.664017i
$716$	37.4985	−	16.1010i	1.40138	−	0.601722i
$717$	−42.5910	−	42.5910i	−1.59059	−	1.59059i
$718$	2.43532	+	11.8443i	0.0908855	+	0.442024i
$719$	−9.32897			−0.347912			−0.173956	−	0.984753i	$-0.555655\pi$
$719$	−9.32897			−0.347912			−0.173956	+	0.984753i	$0.555655\pi$
$720$	−52.1763	−	33.2664i	−1.94449	−	1.23977i
$721$		0			0
$722$	−4.91814	−	23.9195i	−0.183034	−	0.890193i
$723$	31.5292	+	31.5292i	1.17258	+	1.17258i
$724$	−24.2027	+	10.3921i	−0.899487	+	0.386219i
$725$	−8.44923	−	20.9038i	−0.313796	−	0.776347i
$726$	−11.7708	+	17.8640i	−0.436854	+	0.662996i
$727$	−11.9373	+	11.9373i	−0.442729	+	0.442729i	−0.892928	−	0.450199i	$-0.851353\pi$
$727$	−11.9373	+	11.9373i	−0.442729	+	0.442729i	0.450199	+	0.892928i	$0.351353\pi$
$728$		0			0
$729$		−	8.68729i		−	0.321751i
$730$	7.06028	+	2.90673i	0.261313	+	0.107583i
$731$		−	2.68990i		−	0.0994896i
$732$	−7.88080	−	3.14610i	−0.291283	−	0.116283i
$733$	−32.0769	+	32.0769i	−1.18479	+	1.18479i	−0.206296	+	0.978490i	$0.566141\pi$
$733$	−32.0769	+	32.0769i	−1.18479	+	1.18479i	−0.978490	+	0.206296i	$0.933859\pi$
$734$	6.19490	+	4.08187i	0.228658	+	0.150665i
$735$		0			0
$736$	−6.66142	−	28.6396i	−0.245543	−	1.05567i
$737$	−15.5023	−	15.5023i	−0.571034	−	0.571034i
$738$	−108.465	+	22.3018i	−3.99266	+	0.820939i
$739$	23.9754			0.881951			0.440975	−	0.897519i	$-0.354633\pi$
$739$	23.9754			0.881951			0.440975	+	0.897519i	$0.354633\pi$
$740$	−33.1802	−	6.30441i	−1.21973	−	0.231755i
$741$	−14.8087			−0.544009
$742$		0			0
$743$	−26.3785	−	26.3785i	−0.967733	−	0.967733i	0.0317628	−	0.999495i	$-0.489888\pi$
$743$	−26.3785	−	26.3785i	−0.967733	−	0.967733i	−0.999495	+	0.0317628i	$0.989888\pi$
$744$	−22.5796	−	4.03979i	−0.827808	−	0.148106i
$745$	−0.842643	−	4.33333i	−0.0308720	−	0.158761i
$746$	−3.64700	−	2.40304i	−0.133526	−	0.0879815i
$747$	−57.9580	+	57.9580i	−2.12057	+	2.12057i
$748$	−3.15964	+	7.91472i	−0.115528	+	0.289391i
$749$		0			0
$750$	−0.320402	+	49.7943i	−0.0116994	+	1.81823i
$751$		−	52.3306i		−	1.90957i	−0.297293	−	0.954786i	$-0.596084\pi$
$751$		−	52.3306i		−	1.90957i	0.297293	−	0.954786i	$-0.403916\pi$
$752$	−0.703995	−	27.3381i	−0.0256721	−	0.996918i
$753$	−19.3944	+	19.3944i	−0.706772	+	0.706772i
$754$	−12.5347	+	19.0234i	−0.456487	+	0.692793i
$755$	−3.68346	−	18.9424i	−0.134055	−	0.689383i
$756$		0			0
$757$	23.8139	+	23.8139i	0.865530	+	0.865530i	0.991974	−	0.126444i	$-0.0403563\pi$
$757$	23.8139	+	23.8139i	0.865530	+	0.865530i	−0.126444	+	0.991974i	$0.540356\pi$
$758$	−4.84394	−	23.5586i	−0.175940	−	0.855688i
$759$	−65.0767			−2.36213
$760$	−5.97420	−	5.79739i	−0.216707	−	0.210293i
$761$	18.8709			0.684069			0.342034	−	0.939687i	$-0.388884\pi$
$761$	18.8709			0.684069			0.342034	+	0.939687i	$0.388884\pi$
$762$	−13.1619	−	64.0134i	−0.476807	−	2.31896i
$763$		0			0
$764$	9.55054	+	22.2428i	0.345526	+	0.804716i
$765$	−9.27129	+	13.7474i	−0.335204	+	0.497039i
$766$	21.2080	−	32.1865i	0.766275	−	1.16295i
$767$	21.0804	−	21.0804i	0.761170	−	0.761170i
$768$	−33.7495	+	37.4173i	−1.21783	+	1.35018i
$769$			12.2463i			0.441614i	0.975318	+	0.220807i	$0.0708691\pi$
$769$			12.2463i			0.441614i	−0.975318	+	0.220807i	$0.929131\pi$
$770$		0			0
$771$		−	18.8008i		−	0.677093i
$772$	−0.520629	+	1.30414i	−0.0187378	+	0.0469371i
$773$	3.04379	−	3.04379i	0.109478	−	0.109478i	−0.650246	−	0.759724i	$-0.725334\pi$
$773$	3.04379	−	3.04379i	0.109478	−	0.109478i	0.759724	+	0.650246i	$0.225334\pi$
$774$	−20.5026	−	13.5094i	−0.736952	−	0.485584i
$775$	4.82500	+	11.9373i	0.173319	+	0.428799i
$776$	−6.37133	+	35.6113i	−0.228718	+	1.27837i
$777$		0			0
$778$	−17.5191	+	3.60213i	−0.628089	+	0.129143i
$779$	−14.8973			−0.533751
$780$	41.5934	−	28.3112i	1.48928	−	1.01370i
$781$	13.8076			0.494073
$782$	−7.71787	+	1.58689i	−0.275991	+	0.0567470i
$783$	−39.3473	−	39.3473i	−1.40616	−	1.40616i
$784$		0			0
$785$	29.3905	+	19.8210i	1.04899	+	0.707443i
$786$	36.6700	+	24.1622i	1.30798	+	0.861836i
$787$	2.98794	−	2.98794i	0.106509	−	0.106509i	−0.651844	−	0.758353i	$-0.726004\pi$
$787$	2.98794	−	2.98794i	0.106509	−	0.106509i	0.758353	+	0.651844i	$0.226004\pi$
$788$	3.07142	+	1.22614i	0.109415	+	0.0436796i
$789$		−	49.7711i		−	1.77190i
$790$	−4.19835	−	10.0745i	−0.149371	−	0.358435i
$791$		0			0
$792$	44.4581	+	63.8327i	1.57975	+	2.26820i
$793$	3.40311	−	3.40311i	0.120848	−	0.120848i
$794$	−9.43900	+	14.3252i	−0.334978	+	0.508383i
$795$	57.8569	−	11.2506i	2.05197	−	0.399019i
$796$	−32.0714	+	13.7707i	−1.13674	+	0.488089i
$797$	35.3989	+	35.3989i	1.25389	+	1.25389i	0.953960	+	0.299933i	$0.0969644\pi$
$797$	35.3989	+	35.3989i	1.25389	+	1.25389i	0.299933	+	0.953960i	$0.403036\pi$
$798$		0			0
$799$	−7.32815			−0.259251
$800$	27.8633	+	4.86178i	0.985116	+	0.171890i
$801$	65.1650			2.30249
$802$	−4.06063	−	19.7490i	−0.143386	−	0.697361i
$803$	−6.78706	−	6.78706i	−0.239510	−	0.239510i
$804$	−31.9185	+	13.7050i	−1.12568	+	0.483340i
$805$		0			0
$806$	7.15804	−	10.8635i	0.252131	−	0.382650i
$807$	−17.8062	+	17.8062i	−0.626809	+	0.626809i
$808$	−16.6062	−	23.8431i	−0.584203	−	0.838796i
$809$		−	28.9112i		−	1.01646i	−0.861220	−	0.508232i	$-0.830299\pi$
$809$		−	28.9112i		−	1.01646i	0.861220	−	0.508232i	$-0.169701\pi$
$810$	22.0268	+	52.8561i	0.773941	+	1.85718i
$811$		−	23.9566i		−	0.841229i	−0.907240	−	0.420614i	$-0.861815\pi$
$811$		−	23.9566i		−	0.841229i	0.907240	−	0.420614i	$-0.138185\pi$
$812$		0			0
$813$	66.9390	−	66.9390i	2.34765	−	2.34765i
$814$	35.4533	+	23.3605i	1.24264	+	0.818783i
$815$	−12.9138	−	8.70910i	−0.452351	−	0.305067i
$816$	9.79047	+	9.29889i	0.342735	+	0.325526i
$817$	−2.33571	−	2.33571i	−0.0817161	−	0.0817161i
$818$	−41.4184	+	8.51612i	−1.44816	+	0.297759i
$819$		0			0
$820$	41.8423	−	28.4806i	1.46120	−	0.994586i
$821$	35.6774			1.24515			0.622574	−	0.782561i	$-0.286087\pi$
$821$	35.6774			1.24515			0.622574	+	0.782561i	$0.286087\pi$
$822$	70.4245	−	14.4801i	2.45634	−	0.505053i
$823$	9.32078	+	9.32078i	0.324902	+	0.324902i	0.850644	−	0.525742i	$-0.176212\pi$
$823$	9.32078	+	9.32078i	0.324902	+	0.324902i	−0.525742	+	0.850644i	$0.676212\pi$
$824$	2.08214	−	11.6377i	0.0725346	−	0.405418i
$825$	24.4507	−	57.6257i	0.851265	−	2.00627i
$826$		0			0
$827$	6.42266	−	6.42266i	0.223338	−	0.223338i	−0.586565	−	0.809902i	$-0.699520\pi$
$827$	6.42266	−	6.42266i	0.223338	−	0.223338i	0.809902	+	0.586565i	$0.199520\pi$
$828$	−26.6657	+	66.7960i	−0.926697	+	2.32132i
$829$		−	18.7374i		−	0.650777i	−0.945580	−	0.325388i	$-0.894505\pi$
$829$		−	18.7374i		−	0.650777i	0.945580	−	0.325388i	$-0.105495\pi$
$830$	14.2630	−	34.6442i	0.495078	−	1.20252i
$831$			7.78271i			0.269979i
$832$	−11.9480	−	25.9617i	−0.414223	−	0.900059i
$833$		0			0
$834$	−22.3150	+	33.8666i	−0.772706	+	1.17271i
$835$	−21.0773	+	31.2533i	−0.729411	+	1.08157i
$836$	4.12895	+	9.61614i	0.142803	+	0.332581i
$837$	22.4696	+	22.4696i	0.776662	+	0.776662i
$838$	10.7237	+	52.1548i	0.370443	+	1.80166i
$839$	−50.3921			−1.73973			−0.869864	−	0.493291i	$-0.835794\pi$
$839$	−50.3921			−1.73973			−0.869864	+	0.493291i	$0.835794\pi$
$840$		0			0
$841$	8.66571			0.298818
$842$	−2.38444	−	11.5968i	−0.0821733	−	0.399652i
$843$	6.34915	+	6.34915i	0.218676	+	0.218676i
$844$	4.99101	+	11.6238i	0.171798	+	0.400109i
$845$	−0.101611	−	0.522541i	−0.00349553	−	0.0179759i
$846$	−36.8038	+	55.8557i	−1.26534	+	1.92036i
$847$		0			0
$848$	−0.861844	−	33.4678i	−0.0295958	−	1.14929i
$849$		−	27.2497i		−	0.935208i
$850$	1.49458	−	7.43044i	0.0512635	−	0.254862i
$851$			39.2553i			1.34565i
$852$	8.11115	−	20.3179i	0.277883	−	0.696081i
$853$	−12.0652	+	12.0652i	−0.413104	+	0.413104i	−0.882818	−	0.469714i	$-0.844357\pi$
$853$	−12.0652	+	12.0652i	−0.413104	+	0.413104i	0.469714	+	0.882818i	$0.344357\pi$
$854$		0			0
$855$	3.88673	+	19.9877i	0.132923	+	0.683565i
$856$	−44.2991	−	7.92570i	−1.51411	−	0.270895i
$857$	−14.5411	−	14.5411i	−0.496715	−	0.496715i	0.413699	−	0.910414i	$-0.364237\pi$
$857$	−14.5411	−	14.5411i	−0.496715	−	0.496715i	−0.910414	+	0.413699i	$0.864237\pi$
$858$	−61.9548	+	12.7387i	−2.11510	+	0.434891i
$859$	43.6765			1.49022			0.745112	−	0.666939i	$-0.232396\pi$
$859$	43.6765			1.49022			0.745112	+	0.666939i	$0.232396\pi$
$860$	11.0258	+	2.09495i	0.375975	+	0.0714372i
$861$		0			0
$862$	−6.89769	+	1.41825i	−0.234936	+	0.0483057i
$863$	−18.0484	−	18.0484i	−0.614373	−	0.614373i	0.329709	−	0.944083i	$-0.393049\pi$
$863$	−18.0484	−	18.0484i	−0.614373	−	0.614373i	−0.944083	+	0.329709i	$0.893049\pi$
$864$	67.9906	−	15.8143i	2.31309	−	0.538013i
$865$	0.276821	−	0.410469i	0.00941220	−	0.0139564i
$866$	−4.51818	−	2.97707i	−0.153534	−	0.101165i
$867$	−35.2990	+	35.2990i	−1.19882	+	1.19882i
$868$		0			0
$869$			13.7205i			0.465437i
$870$	41.5272	+	17.0968i	1.40791	+	0.579637i
$871$		−	19.7013i		−	0.667553i
$872$	6.92923	−	4.82605i	0.234653	−	0.163431i
$873$	62.5703	−	62.5703i	2.11768	−	2.11768i
$874$	−5.32368	+	8.07955i	−0.180076	+	0.273295i
$875$		0			0
$876$	−13.9742	+	6.00021i	−0.472145	+	0.202728i
$877$	36.5704	+	36.5704i	1.23489	+	1.23489i	0.962062	+	0.272832i	$0.0879603\pi$
$877$	36.5704	+	36.5704i	1.23489	+	1.23489i	0.272832	+	0.962062i	$0.412040\pi$
$878$	10.6908	+	51.9952i	0.360799	+	1.75475i
$879$	−73.6068			−2.48270
$880$	−29.9812	−	19.1154i	−1.01067	−	0.644378i
$881$	29.9298			1.00836			0.504181	−	0.863598i	$-0.331795\pi$
$881$	29.9298			1.00836			0.504181	+	0.863598i	$0.331795\pi$
$882$		0			0
$883$	22.0057	+	22.0057i	0.740550	+	0.740550i	0.972684	−	0.232134i	$-0.0745707\pi$
$883$	22.0057	+	22.0057i	0.740550	+	0.740550i	−0.232134	+	0.972684i	$0.574571\pi$
$884$	−7.03700	+	3.02152i	−0.236680	+	0.101625i
$885$	−48.7231	−	32.8590i	−1.63781	−	1.10454i
$886$	9.87519	−	14.9872i	0.331763	−	0.503505i
$887$	−34.0844	+	34.0844i	−1.14444	+	1.14444i	−0.156812	+	0.987628i	$0.550122\pi$
$887$	−34.0844	+	34.0844i	−1.14444	+	1.14444i	−0.987628	+	0.156812i	$0.949878\pi$
$888$	55.2019	−	38.4469i	1.85245	−	1.29019i
$889$		0			0
$890$	−27.4944	+	11.4577i	−0.921613	+	0.384064i
$891$		−	71.9850i		−	2.41159i
$892$	−2.97960	−	1.18949i	−0.0997645	−	0.0398271i
$893$	−6.36321	+	6.36321i	−0.212937	+	0.212937i
$894$	7.34228	+	4.83789i	0.245563	+	0.161803i
$895$	44.7870	−	8.70910i	1.49706	−	0.291113i
$896$		0			0
$897$	−41.3518	−	41.3518i	−1.38070	−	1.38070i
$898$	34.8578	−	7.16719i	1.16322	−	0.239172i
$899$	11.6121			0.387284
$900$	−49.1292	−	48.7093i	−1.63764	−	1.62364i
$901$	−8.97125			−0.298876
$902$	−62.3256	+	12.8149i	−2.07522	+	0.426689i
$903$		0			0
$904$	1.60376	+	0.286935i	0.0533404	+	0.00954330i
$905$	−28.9069	+	5.62113i	−0.960899	+	0.186853i
$906$	32.0954	+	21.1479i	1.06630	+	0.702593i
$907$	5.69988	−	5.69988i	0.189262	−	0.189262i	−0.606115	−	0.795377i	$-0.707273\pi$
$907$	5.69988	−	5.69988i	0.189262	−	0.189262i	0.795377	+	0.606115i	$0.207273\pi$
$908$	−3.71559	+	9.30734i	−0.123306	+	0.308875i
$909$			71.0708i			2.35727i
$910$		0			0
$911$			15.9014i			0.526836i	0.964682	+	0.263418i	$0.0848498\pi$
$911$			15.9014i			0.526836i	−0.964682	+	0.263418i	$0.915150\pi$
$912$	16.5758	−	0.426849i	0.548878	−	0.0141344i
$913$	−33.3035	+	33.3035i	−1.10218	+	1.10218i
$914$	−21.1639	+	32.1196i	−0.700038	+	1.06242i
$915$	−7.86560	−	5.30458i	−0.260029	−	0.175364i
$916$	8.14218	+	18.9628i	0.269025	+	0.626548i
$917$		0			0
$918$	−3.76729	−	18.3223i	−0.124339	−	0.604727i
$919$	−45.3593			−1.49626			−0.748132	−	0.663550i	$-0.769049\pi$
$919$	−45.3593			−1.49626			−0.748132	+	0.663550i	$0.769049\pi$
$920$	−0.493728	−	32.8710i	−0.0162777	−	1.08373i
$921$	66.9229			2.20518
$922$	5.69792	+	27.7120i	0.187651	+	0.912645i
$923$	8.77375	+	8.77375i	0.288792	+	0.288792i
$924$		0			0
$925$	−34.7607	−	14.7490i	−1.14292	−	0.484946i
$926$	11.1709	−	16.9536i	0.367098	−	0.557130i
$927$	−20.4478	+	20.4478i	−0.671594	+	0.671594i
$928$	13.4821	−	21.6548i	0.442572	−	0.710853i
$929$		−	38.5886i		−	1.26605i	−0.774132	−	0.633025i	$-0.781813\pi$
$929$		−	38.5886i		−	1.26605i	0.774132	−	0.633025i	$-0.218187\pi$
$930$	−23.7145	−	9.76328i	−0.777628	−	0.320150i
$931$		0			0
$932$	9.47283	−	23.7289i	0.310293	−	0.777265i
$933$	−62.7391	+	62.7391i	−2.05399	+	2.05399i
$934$	4.88206	+	3.21683i	0.159746	+	0.105258i
$935$	−5.32741	+	7.89945i	−0.174225	+	0.258340i
$936$	−12.3113	+	68.8114i	−0.402407	+	2.24917i
$937$	−15.2293	−	15.2293i	−0.497519	−	0.497519i	0.413146	−	0.910665i	$-0.364430\pi$
$937$	−15.2293	−	15.2293i	−0.497519	−	0.497519i	−0.910665	+	0.413146i	$0.864430\pi$
$938$		0			0
$939$	80.8383			2.63806
$940$	5.70731	−	30.0377i	0.186152	−	0.979720i
$941$	47.4153			1.54570			0.772848	−	0.634591i	$-0.218832\pi$
$941$	47.4153			1.54570			0.772848	+	0.634591i	$0.218832\pi$
$942$	−69.1622	+	14.2206i	−2.25343	+	0.463332i
$943$	−41.5993	−	41.5993i	−1.35466	−	1.35466i
$944$	−22.9883	+	24.2035i	−0.748205	+	0.787758i
$945$		0			0
$946$	−11.7811	−	7.76266i	−0.383036	−	0.252386i
$947$	−24.9331	+	24.9331i	−0.810218	+	0.810218i	−0.984666	−	0.174448i	$-0.944186\pi$
$947$	−24.9331	+	24.9331i	−0.810218	+	0.810218i	0.174448	+	0.984666i	$0.444186\pi$
$948$	20.1899	+	8.06002i	0.655736	+	0.261777i
$949$		−	8.62542i		−	0.279993i
$950$	−5.15426	−	7.74981i	−0.167226	−	0.251437i
$951$			82.8346i			2.68610i
$952$		0			0
$953$	34.4409	−	34.4409i	1.11565	−	1.11565i	0.123279	−	0.992372i	$-0.460659\pi$
$953$	34.4409	−	34.4409i	1.11565	−	1.11565i	0.992372	−	0.123279i	$-0.0393409\pi$
$954$	−45.0559	+	68.3796i	−1.45874	+	2.21387i
$955$	5.16594	+	26.5661i	0.167166	+	0.859658i
$956$	−35.1481	+	15.0918i	−1.13677	+	0.488103i
$957$	−39.9202	−	39.9202i	−1.29044	−	1.29044i
$958$	2.65709	+	12.9228i	0.0858467	+	0.417518i
$959$		0			0
$960$	−45.7406	+	32.8884i	−1.47627	+	1.06147i
$961$	24.3688			0.786092
$962$	7.68415	+	37.3721i	0.247747	+	1.20492i
$963$	77.8351	+	77.8351i	2.50820	+	2.50820i
$964$	26.0193	−	11.1721i	0.838026	−	0.359829i
$965$	−0.877821	+	1.30163i	−0.0282581	+	0.0419009i
$966$		0			0
$967$	−28.3737	+	28.3737i	−0.912437	+	0.912437i	−0.996464	−	0.0840261i	$-0.973222\pi$
$967$	−28.3737	+	28.3737i	−0.912437	+	0.912437i	0.0840261	+	0.996464i	$0.473222\pi$
$968$	7.76465	+	11.1485i	0.249565	+	0.358325i
$969$		−	4.44323i		−	0.142737i
$970$	−15.3981	+	37.4011i	−0.494403	+	1.20088i
$971$		−	7.25895i		−	0.232951i	−0.993194	−	0.116475i	$-0.962840\pi$
$971$		−	7.25895i		−	0.232951i	0.993194	−	0.116475i	$-0.0371596\pi$
$972$	−37.1635	−	14.8361i	−1.19202	−	0.475867i
$973$		0			0
$974$	−34.2406	−	22.5614i	−1.09714	−	0.722913i
$975$	52.1539	−	21.0804i	1.67026	−	0.675113i
$976$	−3.71111	+	3.90729i	−0.118790	+	0.125069i
$977$	8.42927	+	8.42927i	0.269676	+	0.269676i	0.828970	−	0.559293i	$-0.188927\pi$
$977$	8.42927	+	8.42927i	0.269676	+	0.269676i	−0.559293	+	0.828970i	$0.688927\pi$
$978$	30.3890	−	6.24834i	0.971732	−	0.199800i
$979$	37.4447			1.19674
$980$		0			0
$981$	−20.6545			−0.659446
$982$	−39.0385	+	8.02679i	−1.24577	+	0.256145i
$983$	−13.3708	−	13.3708i	−0.426463	−	0.426463i	0.460959	−	0.887422i	$-0.347506\pi$
$983$	−13.3708	−	13.3708i	−0.426463	−	0.426463i	−0.887422	+	0.460959i	$0.847506\pi$
$984$	−17.7555	+	99.2407i	−0.566024	+	3.16368i
$985$	3.06549	+	2.06738i	0.0976747	+	0.0658721i
$986$	−5.70785	−	3.76095i	−0.181775	−	0.119773i
$987$		0			0
$988$	−3.48673	+	8.73406i	−0.110928	+	0.277867i
$989$		−	13.0445i		−	0.414791i
$990$	33.4546	+	80.2789i	1.06326	+	2.55143i
$991$		−	22.0788i		−	0.701356i	−0.936496	−	0.350678i	$-0.885951\pi$
$991$		−	22.0788i		−	0.701356i	0.936496	−	0.350678i	$-0.114049\pi$
$992$	−7.69907	+	12.3661i	−0.244446	+	0.392625i
$993$	−38.3078	+	38.3078i	−1.21566	+	1.21566i
$994$		0			0
$995$	−38.3050	+	7.44864i	−1.21435	+	0.236138i
$996$	29.4425	+	68.5702i	0.932920	+	2.17273i
$997$	−21.1080	−	21.1080i	−0.668497	−	0.668497i	0.288871	−	0.957368i	$-0.406720\pi$
$997$	−21.1080	−	21.1080i	−0.668497	−	0.668497i	−0.957368	+	0.288871i	$0.906720\pi$
$998$	8.85039	+	43.0441i	0.280154	+	1.36254i
$999$	−93.1924			−2.94848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.i.687.11	✓	32
4.3	odd	2	inner	980.2.k.i.687.16	yes	32
5.3	odd	4	inner	980.2.k.i.883.16	yes	32
7.2	even	3		980.2.x.j.67.14		64
7.3	odd	6		980.2.x.j.667.2		64
7.4	even	3		980.2.x.j.667.1		64
7.5	odd	6		980.2.x.j.67.13		64
7.6	odd	2	inner	980.2.k.i.687.12	yes	32
20.3	even	4	inner	980.2.k.i.883.11	yes	32
28.3	even	6		980.2.x.j.667.3		64
28.11	odd	6		980.2.x.j.667.4		64
28.19	even	6		980.2.x.j.67.8		64
28.23	odd	6		980.2.x.j.67.7		64
28.27	even	2	inner	980.2.k.i.687.15	yes	32
35.3	even	12		980.2.x.j.863.8		64
35.13	even	4	inner	980.2.k.i.883.15	yes	32
35.18	odd	12		980.2.x.j.863.7		64
35.23	odd	12		980.2.x.j.263.4		64
35.33	even	12		980.2.x.j.263.3		64
140.3	odd	12		980.2.x.j.863.13		64
140.23	even	12		980.2.x.j.263.1		64
140.83	odd	4	inner	980.2.k.i.883.12	yes	32
140.103	odd	12		980.2.x.j.263.2		64
140.123	even	12		980.2.x.j.863.14		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.i.687.11	✓	32	1.1	even	1	trivial
980.2.k.i.687.12	yes	32	7.6	odd	2	inner
980.2.k.i.687.15	yes	32	28.27	even	2	inner
980.2.k.i.687.16	yes	32	4.3	odd	2	inner
980.2.k.i.883.11	yes	32	20.3	even	4	inner
980.2.k.i.883.12	yes	32	140.83	odd	4	inner
980.2.k.i.883.15	yes	32	35.13	even	4	inner
980.2.k.i.883.16	yes	32	5.3	odd	4	inner
980.2.x.j.67.7		64	28.23	odd	6
980.2.x.j.67.8		64	28.19	even	6
980.2.x.j.67.13		64	7.5	odd	6
980.2.x.j.67.14		64	7.2	even	3
980.2.x.j.263.1		64	140.23	even	12
980.2.x.j.263.2		64	140.103	odd	12
980.2.x.j.263.3		64	35.33	even	12
980.2.x.j.263.4		64	35.23	odd	12
980.2.x.j.667.1		64	7.4	even	3
980.2.x.j.667.2		64	7.3	odd	6
980.2.x.j.667.3		64	28.3	even	6
980.2.x.j.667.4		64	28.11	odd	6
980.2.x.j.863.7		64	35.18	odd	12
980.2.x.j.863.8		64	35.3	even	12
980.2.x.j.863.13		64	140.3	odd	12
980.2.x.j.863.14		64	140.123	even	12

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.284821 + 1.38524i) q^{2} +(-2.22691 - 2.22691i) q^{3} +(-1.83775 + 0.789089i) q^{4} +(-2.19495 + 0.426822i) q^{5} +(2.45053 - 3.71907i) q^{6} +(-1.61650 - 2.32097i) q^{8} +6.91829i q^{9} +(-1.21642 - 2.91896i) q^{10} +3.97534i q^{11} +(5.84975 + 2.33529i) q^{12} +(-2.52606 + 2.52606i) q^{13} +(5.83847 + 3.93748i) q^{15} +(2.75468 - 2.90030i) q^{16} +(-0.757926 - 0.757926i) q^{17} +(-9.58346 + 1.97048i) q^{18} -1.31625 q^{19} +(3.69698 - 2.51641i) q^{20} +(-5.50679 + 1.13226i) q^{22} +(-3.67551 - 3.67551i) q^{23} +(-1.56879 + 8.76842i) q^{24} +(4.63565 - 1.87371i) q^{25} +(-4.21866 - 2.77971i) q^{26} +(8.72570 - 8.72570i) q^{27} -4.50936i q^{29} +(-3.79141 + 9.20913i) q^{30} +2.57510i q^{31} +(4.80219 + 2.98981i) q^{32} +(8.85275 - 8.85275i) q^{33} +(0.834032 - 1.26578i) q^{34} +(-5.45915 - 12.7141i) q^{36} +(-5.34011 - 5.34011i) q^{37} +(-0.374896 - 1.82332i) q^{38} +11.2506 q^{39} +(4.53880 + 4.40447i) q^{40} +11.3180 q^{41} +(1.77452 + 1.77452i) q^{43} +(-3.13690 - 7.30570i) q^{44} +(-2.95288 - 15.1853i) q^{45} +(4.04458 - 6.13831i) q^{46} +(4.83434 - 4.83434i) q^{47} +(-12.5932 + 0.324292i) q^{48} +(3.91586 + 5.88779i) q^{50} +3.37567i q^{51} +(2.64899 - 6.63556i) q^{52} +(5.91829 - 5.91829i) q^{53} +(14.5724 + 9.60188i) q^{54} +(-1.69676 - 8.72570i) q^{55} +(2.93118 + 2.93118i) q^{57} +(6.24652 - 1.28436i) q^{58} -8.34518 q^{59} +(-13.8367 - 2.62904i) q^{60} -1.34720 q^{61} +(-3.56712 + 0.733444i) q^{62} +(-2.77382 + 7.50373i) q^{64} +(4.46640 - 6.62276i) q^{65} +(14.7846 + 9.74169i) q^{66} +(-3.89961 + 3.89961i) q^{67} +(1.99095 + 0.794810i) q^{68} +16.3701i q^{69} -3.47330i q^{71} +(16.0572 - 11.1835i) q^{72} +(-1.70729 + 1.70729i) q^{73} +(5.87634 - 8.91829i) q^{74} +(-14.4958 - 6.15059i) q^{75} +(2.41895 - 1.03864i) q^{76} +(3.20442 + 15.5848i) q^{78} +3.45140 q^{79} +(-4.80848 + 7.54179i) q^{80} -18.1079 q^{81} +(3.22360 + 15.6780i) q^{82} +(8.37751 + 8.37751i) q^{83} +(1.98711 + 1.34011i) q^{85} +(-1.95270 + 2.96354i) q^{86} +(-10.0419 + 10.0419i) q^{87} +(9.22666 - 6.42616i) q^{88} -9.41924i q^{89} +(20.1942 - 8.41554i) q^{90} +(9.65498 + 3.85438i) q^{92} +(5.73453 - 5.73453i) q^{93} +(8.07362 + 5.31978i) q^{94} +(2.88911 - 0.561805i) q^{95} +(-4.03602 - 17.3521i) q^{96} +(-9.04418 - 9.04418i) q^{97} -27.5026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 8 q^{8} + 8 q^{16} - 40 q^{18} - 36 q^{22} + 32 q^{25} - 36 q^{30} + 16 q^{32} - 88 q^{36} - 48 q^{37} + 28 q^{50} + 16 q^{53} - 16 q^{57} + 36 q^{58} - 80 q^{60} + 64 q^{65} + 56 q^{72}+ \cdots + 32 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 8 * q^8 + 8 * q^16 - 40 * q^18 - 36 * q^22 + 32 * q^25 - 36 * q^30 + 16 * q^32 - 88 * q^36 - 48 * q^37 + 28 * q^50 + 16 * q^53 - 16 * q^57 + 36 * q^58 - 80 * q^60 + 64 * q^65 + 56 * q^72 + 28 * q^78 + 56 * q^86 + 88 * q^88 + 136 * q^92 + 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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