LMFDB - Embedded newform 980.2.x.m.67.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.5
Character	$\chi$	$=$	980.67
Dual form			980.2.x.m.863.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05431 + 0.942570i) q^{2} +(1.20413 - 0.322645i) q^{3} +(0.223125 - 1.98751i) q^{4} +(-2.09885 - 0.771256i) q^{5} +(-0.965404 + 1.47514i) q^{6} +(1.63813 + 2.30576i) q^{8} +(-1.25225 + 0.722989i) q^{9} +(2.93979 - 1.16517i) q^{10} +(0.824629 + 0.476100i) q^{11} +(-0.372591 - 2.46521i) q^{12} +(3.15680 - 3.15680i) q^{13} +(-2.77612 - 0.251508i) q^{15} +(-3.90043 - 0.886929i) q^{16} +(-2.56885 + 0.688322i) q^{17} +(0.638792 - 1.94259i) q^{18} +(-1.99048 - 3.44760i) q^{19} +(-2.00119 + 3.99941i) q^{20} +(-1.31817 + 0.275315i) q^{22} +(-0.141582 + 0.528392i) q^{23} +(2.71646 + 2.24790i) q^{24} +(3.81033 + 3.23750i) q^{25} +(-0.352732 + 6.30375i) q^{26} +(-3.91905 + 3.91905i) q^{27} -7.23080i q^{29} +(3.16395 - 2.35152i) q^{30} +(-3.41863 - 1.97375i) q^{31} +(4.94824 - 2.74133i) q^{32} +(1.14657 + 0.307222i) q^{33} +(2.05957 - 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(0.269180 - 1.00460i) q^{37} +(5.34818 + 1.75867i) q^{38} +(2.78267 - 4.81972i) q^{39} +(-1.65985 - 6.10286i) q^{40} -3.71449 q^{41} +(-8.73324 - 8.73324i) q^{43} +(1.13025 - 1.53273i) q^{44} +(3.18590 - 0.551635i) q^{45} +(-0.348775 - 0.690538i) q^{46} +(-3.09794 - 0.830089i) q^{47} +(-4.98278 + 0.190479i) q^{48} +(-7.06882 + 0.178182i) q^{50} +(-2.87114 + 1.65765i) q^{51} +(-5.56983 - 6.97856i) q^{52} +(-0.760768 - 2.83923i) q^{53} +(0.437903 - 7.82586i) q^{54} +(-1.36358 - 1.63526i) q^{55} +(-3.50914 - 3.50914i) q^{57} +(6.81553 + 7.62348i) q^{58} +(-6.30084 + 10.9134i) q^{59} +(-1.11930 + 5.46147i) q^{60} +(-3.01183 - 5.21665i) q^{61} +(5.46468 - 1.14136i) q^{62} +(-2.63307 + 7.55427i) q^{64} +(-9.06036 + 4.19095i) q^{65} +(-1.49841 + 0.756815i) q^{66} +(-3.85605 - 14.3910i) q^{67} +(0.794874 + 5.25921i) q^{68} +0.681932i q^{69} +7.60710i q^{71} +(-3.71839 - 1.70305i) q^{72} +(-3.80964 - 14.2178i) q^{73} +(0.663102 + 1.31287i) q^{74} +(5.63268 + 2.66898i) q^{75} +(-7.29629 + 3.18685i) q^{76} +(1.60914 + 7.70432i) q^{78} +(5.34864 + 9.26412i) q^{79} +(7.50236 + 4.86976i) q^{80} +(-1.28561 + 2.22674i) q^{81} +(3.91621 - 3.50117i) q^{82} +(-5.72446 - 5.72446i) q^{83} +(5.92250 + 0.536560i) q^{85} +(17.4392 + 0.975826i) q^{86} +(-2.33298 - 8.70680i) q^{87} +(0.253076 + 2.68131i) q^{88} +(1.83403 - 1.05888i) q^{89} +(-2.83896 + 3.58452i) q^{90} +(1.01860 + 0.399294i) q^{92} +(-4.75329 - 1.27364i) q^{93} +(4.04859 - 2.04485i) q^{94} +(1.51872 + 8.77117i) q^{95} +(5.07384 - 4.89744i) q^{96} +(3.08588 + 3.08588i) q^{97} -1.37686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.05431	+	0.942570i	−0.745507	+	0.666497i
$2$	−1.05431	+	0.942570i	−0.745507	+	0.666497i
$3$	1.20413	−	0.322645i	0.695203	−	0.186279i	0.106122	−	0.994353i	$-0.466157\pi$
$3$	1.20413	−	0.322645i	0.695203	−	0.186279i	0.589081	+	0.808074i	$0.299490\pi$
$4$	0.223125	−	1.98751i	0.111563	−	0.993757i
$5$	−2.09885	−	0.771256i	−0.938633	−	0.344916i
$5$	−2.09885	−	0.771256i	−0.938633	−	0.344916i
$6$	−0.965404	+	1.47514i	−0.394125	+	0.602224i
$7$		0			0
$7$		0			0
$8$	1.63813	+	2.30576i	0.579166	+	0.815210i
$9$	−1.25225	+	0.722989i	−0.417418	+	0.240996i
$10$	2.93979	−	1.16517i	0.929644	−	0.368459i
$11$	0.824629	+	0.476100i	0.248635	+	0.143549i	0.619139	−	0.785281i	$-0.287482\pi$
$11$	0.824629	+	0.476100i	0.248635	+	0.143549i	−0.370504	+	0.928831i	$0.620815\pi$
$12$	−0.372591	−	2.46521i	−0.107558	−	0.711645i
$13$	3.15680	−	3.15680i	0.875540	−	0.875540i	−0.117529	−	0.993069i	$-0.537497\pi$
$13$	3.15680	−	3.15680i	0.875540	−	0.875540i	0.993069	+	0.117529i	$0.0374974\pi$
$14$		0			0
$15$	−2.77612	−	0.251508i	−0.716792	−	0.0649391i
$16$	−3.90043	−	0.886929i	−0.975108	−	0.221732i
$17$	−2.56885	+	0.688322i	−0.623038	+	0.166943i	−0.556508	−	0.830842i	$-0.687859\pi$
$17$	−2.56885	+	0.688322i	−0.623038	+	0.166943i	−0.0665295	+	0.997784i	$0.521193\pi$
$18$	0.638792	−	1.94259i	0.150565	−	0.457872i
$19$	−1.99048	−	3.44760i	−0.456646	−	0.790935i	0.542135	−	0.840292i	$-0.317616\pi$
$19$	−1.99048	−	3.44760i	−0.456646	−	0.790935i	−0.998781	+	0.0493567i	$0.984283\pi$
$20$	−2.00119	+	3.99941i	−0.447479	+	0.894294i
$21$		0			0
$22$	−1.31817	+	0.275315i	−0.281034	+	0.0586973i
$23$	−0.141582	+	0.528392i	−0.0295219	+	0.110177i	−0.979115	−	0.203309i	$-0.934830\pi$
$23$	−0.141582	+	0.528392i	−0.0295219	+	0.110177i	0.949593	+	0.313486i	$0.101497\pi$
$24$	2.71646	+	2.24790i	0.554495	+	0.458850i
$25$	3.81033	+	3.23750i	0.762066	+	0.647500i
$26$	−0.352732	+	6.30375i	−0.0691765	+	1.23627i
$27$	−3.91905	+	3.91905i	−0.754222	+	0.754222i
$28$		0			0
$29$		−	7.23080i		−	1.34273i	−0.741129	−	0.671363i	$-0.765709\pi$
$29$		−	7.23080i		−	1.34273i	0.741129	−	0.671363i	$-0.234291\pi$
$30$	3.16395	−	2.35152i	0.577655	−	0.429327i
$31$	−3.41863	−	1.97375i	−0.614004	−	0.354495i	0.160527	−	0.987031i	$-0.448681\pi$
$31$	−3.41863	−	1.97375i	−0.614004	−	0.354495i	−0.774531	+	0.632536i	$0.782014\pi$
$32$	4.94824	−	2.74133i	0.874734	−	0.484604i
$33$	1.14657	+	0.307222i	0.199592	+	0.0534805i
$34$	2.05957	−	3.14702i	0.353213	−	0.539710i
$35$		0			0
$36$	1.15754	+	2.65019i	0.192924	+	0.441698i
$37$	0.269180	−	1.00460i	0.0442530	−	0.165154i	−0.940263	−	0.340449i	$-0.889421\pi$
$37$	0.269180	−	1.00460i	0.0442530	−	0.165154i	0.984516	+	0.175294i	$0.0560877\pi$
$38$	5.34818	+	1.75867i	0.867589	+	0.285294i
$39$	2.78267	−	4.81972i	0.445584	−	0.771773i
$40$	−1.65985	−	6.10286i	−0.262446	−	0.964947i
$41$	−3.71449			−0.580106			−0.290053	−	0.957011i	$-0.593673\pi$
$41$	−3.71449			−0.580106			−0.290053	+	0.957011i	$0.593673\pi$
$42$		0			0
$43$	−8.73324	−	8.73324i	−1.33181	−	1.33181i	−0.903754	−	0.428052i	$-0.859200\pi$
$43$	−8.73324	−	8.73324i	−1.33181	−	1.33181i	−0.428052	−	0.903754i	$-0.640800\pi$
$44$	1.13025	−	1.53273i	0.170392	−	0.231068i
$45$	3.18590	−	0.551635i	0.474926	−	0.0822329i
$46$	−0.348775	−	0.690538i	−0.0514241	−	0.101814i
$47$	−3.09794	−	0.830089i	−0.451880	−	0.121081i	0.0256988	−	0.999670i	$-0.491819\pi$
$47$	−3.09794	−	0.830089i	−0.451880	−	0.121081i	−0.477579	+	0.878589i	$0.658486\pi$
$48$	−4.98278	+	0.190479i	−0.719202	+	0.0274933i
$49$		0			0
$50$	−7.06882	+	0.178182i	−0.999682	+	0.0251987i
$51$	−2.87114	+	1.65765i	−0.402040	+	0.232118i
$52$	−5.56983	−	6.97856i	−0.772397	−	0.967752i
$53$	−0.760768	−	2.83923i	−0.104500	−	0.389998i	0.893788	−	0.448489i	$-0.148038\pi$
$53$	−0.760768	−	2.83923i	−0.104500	−	0.389998i	−0.998288	+	0.0584914i	$0.981371\pi$
$54$	0.437903	−	7.82586i	0.0595911	−	1.06496i
$55$	−1.36358	−	1.63526i	−0.183864	−	0.220498i
$56$		0			0
$57$	−3.50914	−	3.50914i	−0.464797	−	0.464797i
$58$	6.81553	+	7.62348i	0.894923	+	1.00101i
$59$	−6.30084	+	10.9134i	−0.820300	+	1.42080i	0.0851594	+	0.996367i	$0.472860\pi$
$59$	−6.30084	+	10.9134i	−0.820300	+	1.42080i	−0.905459	+	0.424433i	$0.860473\pi$
$60$	−1.11930	+	5.46147i	−0.144501	+	0.705072i
$61$	−3.01183	−	5.21665i	−0.385626	−	0.667923i	0.606230	−	0.795289i	$-0.292681\pi$
$61$	−3.01183	−	5.21665i	−0.385626	−	0.667923i	−0.991856	+	0.127366i	$0.959348\pi$
$62$	5.46468	−	1.14136i	0.694015	−	0.144953i
$63$		0			0
$64$	−2.63307	+	7.55427i	−0.329134	+	0.944283i
$65$	−9.06036	+	4.19095i	−1.12380	+	0.519823i
$66$	−1.49841	+	0.756815i	−0.184442	+	0.0931574i
$67$	−3.85605	−	14.3910i	−0.471092	−	1.75814i	−0.635858	−	0.771806i	$-0.719353\pi$
$67$	−3.85605	−	14.3910i	−0.471092	−	1.75814i	0.164766	−	0.986333i	$-0.447313\pi$
$68$	0.794874	+	5.25921i	0.0963927	+	0.637773i
$69$			0.681932i			0.0820949i
$70$		0			0
$71$			7.60710i			0.902797i	0.892322	+	0.451399i	$0.149075\pi$
$71$			7.60710i			0.902797i	−0.892322	+	0.451399i	$0.850925\pi$
$72$	−3.71839	−	1.70305i	−0.438216	−	0.200706i
$73$	−3.80964	−	14.2178i	−0.445885	−	1.66406i	−0.713590	−	0.700564i	$-0.752932\pi$
$73$	−3.80964	−	14.2178i	−0.445885	−	1.66406i	0.267705	−	0.963501i	$-0.413735\pi$
$74$	0.663102	+	1.31287i	0.0770841	+	0.152618i
$75$	5.63268	+	2.66898i	0.650406	+	0.308187i
$76$	−7.29629	+	3.18685i	−0.836942	+	0.365557i
$77$		0			0
$78$	1.60914	+	7.70432i	0.182199	+	0.872343i
$79$	5.34864	+	9.26412i	0.601769	+	1.04230i	0.992553	+	0.121813i	$0.0388707\pi$
$79$	5.34864	+	9.26412i	0.601769	+	1.04230i	−0.390784	+	0.920483i	$0.627796\pi$
$80$	7.50236	+	4.86976i	0.838790	+	0.544456i
$81$	−1.28561	+	2.22674i	−0.142846	+	0.247416i
$82$	3.91621	−	3.50117i	0.432473	−	0.386639i
$83$	−5.72446	−	5.72446i	−0.628341	−	0.628341i	0.319309	−	0.947651i	$-0.396549\pi$
$83$	−5.72446	−	5.72446i	−0.628341	−	0.628341i	−0.947651	+	0.319309i	$0.896549\pi$
$84$		0			0
$85$	5.92250	+	0.536560i	0.642386	+	0.0581981i
$86$	17.4392	+	0.975826i	1.88052	+	0.105226i
$87$	−2.33298	−	8.70680i	−0.250122	−	0.933467i
$88$	0.253076	+	2.68131i	0.0269780	+	0.285828i
$89$	1.83403	−	1.05888i	0.194407	−	0.112241i	−0.399637	−	0.916673i	$-0.630864\pi$
$89$	1.83403	−	1.05888i	0.194407	−	0.112241i	0.594044	+	0.804433i	$0.297531\pi$
$90$	−2.83896	+	3.58452i	−0.299253	+	0.377842i
$91$		0			0
$92$	1.01860	+	0.399294i	0.106196	+	0.0416293i
$93$	−4.75329	−	1.27364i	−0.492893	−	0.132070i
$94$	4.04859	−	2.04485i	0.417580	−	0.210910i
$95$	1.51872	+	8.77117i	0.155817	+	0.899903i
$96$	5.07384	−	4.89744i	0.517846	−	0.499843i
$97$	3.08588	+	3.08588i	0.313324	+	0.313324i	0.846196	−	0.532872i	$-0.178887\pi$
$97$	3.08588	+	3.08588i	0.313324	+	0.313324i	−0.532872	+	0.846196i	$0.678887\pi$
$98$		0			0
$99$	−1.37686			−0.138379
$100$	7.28476	−	6.85072i	0.728476	−	0.685072i
$101$	−0.715074	+	1.23854i	−0.0711525	+	0.123240i	−0.899407	−	0.437113i	$-0.856001\pi$
$101$	−0.715074	+	1.23854i	−0.0711525	+	0.123240i	0.828254	+	0.560353i	$0.189334\pi$
$102$	1.46461	−	4.45393i	0.145018	−	0.441004i
$103$	−2.63366	+	9.82894i	−0.259502	+	0.968474i	0.706028	+	0.708183i	$0.250485\pi$
$103$	−2.63366	+	9.82894i	−0.259502	+	0.968474i	−0.965530	+	0.260291i	$0.916182\pi$
$104$	12.4501	+	2.10758i	1.22083	+	0.206666i
$105$		0			0
$106$	3.47825	+	2.27634i	0.337838	+	0.221097i
$107$	−0.0388547	−	0.0104111i	−0.00375622	−	0.00100648i	0.256940	−	0.966427i	$-0.417286\pi$
$107$	−0.0388547	−	0.0104111i	−0.00375622	−	0.00100648i	−0.260697	+	0.965421i	$0.583952\pi$
$108$	6.91473	+	8.66361i	0.665371	+	0.833656i
$109$	5.44983	+	3.14646i	0.521999	+	0.301376i	0.737752	−	0.675072i	$-0.235887\pi$
$109$	5.44983	+	3.14646i	0.521999	+	0.301376i	−0.215753	+	0.976448i	$0.569221\pi$
$110$	2.97897	+	0.438801i	0.284034	+	0.0418381i
$111$		−	1.29651i		−	0.123059i
$112$		0			0
$113$	10.8513	−	10.8513i	1.02081	−	1.02081i	0.0210265	−	0.999779i	$-0.493307\pi$
$113$	10.8513	−	10.8513i	1.02081	−	1.02081i	0.999779	−	0.0210265i	$-0.00669344\pi$
$114$	7.00732	+	0.392101i	0.656295	+	0.0367236i
$115$	0.704685	−	0.999818i	0.0657122	−	0.0932335i
$116$	−14.3713	−	1.61337i	−1.33434	−	0.149798i
$117$	−1.67078	+	6.23545i	−0.154464	+	0.576468i
$118$	−3.64360	−	17.4450i	−0.335420	−	1.60595i
$119$		0			0
$120$	−3.96773	−	6.81308i	−0.362202	−	0.621946i
$121$	−5.04666	−	8.74107i	−0.458787	−	0.794643i
$122$	8.09245	+	2.66108i	0.732656	+	0.240923i
$123$	−4.47272	+	1.19846i	−0.403292	+	0.108062i
$124$	−4.68563	+	6.35419i	−0.420782	+	0.570623i
$125$	−5.50036	−	9.73376i	−0.491967	−	0.870614i
$126$		0			0
$127$	−1.22418	+	1.22418i	−0.108629	+	0.108629i	−0.759332	−	0.650703i	$-0.774474\pi$
$127$	−1.22418	+	1.22418i	−0.108629	+	0.108629i	0.650703	+	0.759332i	$0.274474\pi$
$128$	−4.34436	−	10.4464i	−0.383991	−	0.923337i
$129$	−13.3337	−	7.69820i	−1.17396	−	0.677788i
$130$	5.60214	−	12.9586i	0.491340	−	1.13654i
$131$	1.12982	−	0.652300i	0.0987126	−	0.0569918i	−0.449831	−	0.893114i	$-0.648516\pi$
$131$	1.12982	−	0.652300i	0.0987126	−	0.0569918i	0.548544	+	0.836122i	$0.315182\pi$
$132$	0.866437	−	2.21027i	0.0754137	−	0.192380i
$133$		0			0
$134$	17.6300	+	11.5379i	1.52300	+	0.996724i
$135$	11.2481	−	5.20290i	0.968081	−	0.447794i
$136$	−5.79522	−	4.79560i	−0.496936	−	0.411219i
$137$	−1.12037	+	0.300203i	−0.0957198	+	0.0256480i	−0.306361	−	0.951915i	$-0.599111\pi$
$137$	−1.12037	+	0.300203i	−0.0957198	+	0.0256480i	0.210641	+	0.977563i	$0.432445\pi$
$138$	−0.642768	−	0.718965i	−0.0547161	−	0.0612024i
$139$	17.4513			1.48020			0.740099	−	0.672498i	$-0.234779\pi$
$139$	17.4513			1.48020			0.740099	+	0.672498i	$0.234779\pi$
$140$		0			0
$141$	−3.99813			−0.336704
$142$	−7.17023	−	8.02022i	−0.601712	−	0.673042i
$143$	4.10614	−	1.10024i	0.343373	−	0.0920065i
$144$	5.52556	−	1.70931i	0.460464	−	0.142442i
$145$	−5.57680	+	15.1763i	−0.463128	+	1.26033i
$146$	17.4178	+	11.3990i	1.44151	+	0.943392i
$147$		0			0
$148$	−1.93659	−	0.759151i	−0.159186	−	0.0624018i
$149$	9.70894	−	5.60546i	0.795387	−	0.459217i	−0.0464684	−	0.998920i	$-0.514797\pi$
$149$	9.70894	−	5.60546i	0.795387	−	0.459217i	0.841856	+	0.539703i	$0.181463\pi$
$150$	−8.45427	+	2.49527i	−0.690289	+	0.203738i
$151$	13.0081	+	7.51022i	1.05858	+	0.611173i	0.925040	−	0.379870i	$-0.124031\pi$
$151$	13.0081	+	7.51022i	1.05858	+	0.611173i	0.133543	+	0.991043i	$0.457365\pi$
$152$	4.68870	−	10.2372i	0.380304	−	0.830345i
$153$	2.71920	−	2.71920i	0.219835	−	0.219835i
$154$		0			0
$155$	5.65292	+	6.77924i	0.454054	+	0.544521i
$156$	−8.95839	−	6.60600i	−0.717245	−	0.528903i
$157$	7.27171	−	1.94845i	0.580345	−	0.155503i	0.0433084	−	0.999062i	$-0.486210\pi$
$157$	7.27171	−	1.94845i	0.580345	−	0.155503i	0.537037	+	0.843559i	$0.319544\pi$
$158$	−14.3712	−	4.72576i	−1.14331	−	0.375961i
$159$	−1.83212	−	3.17333i	−0.145297	−	0.251662i
$160$	−12.4999	+	1.93728i	−0.988202	+	0.153155i
$161$		0			0
$162$	−0.743432	−	3.55944i	−0.0584095	−	0.279656i
$163$	−1.72089	+	6.42243i	−0.134790	+	0.503044i	0.865208	+	0.501412i	$0.167186\pi$
$163$	−1.72089	+	6.42243i	−0.134790	+	0.503044i	−0.999999	+	0.00163153i	$0.999481\pi$
$164$	−0.828796	+	7.38261i	−0.0647181	+	0.576485i
$165$	−2.16953	−	1.52911i	−0.168897	−	0.119041i
$166$	11.4310	+	0.639635i	0.887221	+	0.0496453i
$167$	5.93258	−	5.93258i	0.459077	−	0.459077i	−0.439276	−	0.898352i	$-0.644765\pi$
$167$	5.93258	−	5.93258i	0.459077	−	0.459077i	0.898352	+	0.439276i	$0.144765\pi$
$168$		0			0
$169$		−	6.93083i		−	0.533141i
$170$	−6.74988	+	5.01667i	−0.517692	+	0.384761i
$171$	4.98516	+	2.87818i	0.381225	+	0.220100i
$172$	−19.3060	+	15.4088i	−1.47207	+	1.17491i
$173$	−2.13818	−	0.572923i	−0.162563	−	0.0435585i	0.176620	−	0.984279i	$-0.443484\pi$
$173$	−2.13818	−	0.572923i	−0.162563	−	0.0435585i	−0.339182	+	0.940721i	$0.610150\pi$
$174$	10.6664	+	6.98064i	0.808621	+	0.529201i
$175$		0			0
$176$	−2.79414	−	2.58838i	−0.210616	−	0.195106i
$177$	−4.06587	+	15.1740i	−0.305610	+	1.14055i
$178$	−0.935563	+	2.84508i	−0.0701234	+	0.213248i
$179$	−8.23493	+	14.2633i	−0.615507	+	1.06609i	0.374788	+	0.927111i	$0.377716\pi$
$179$	−8.23493	+	14.2633i	−0.615507	+	1.06609i	−0.990295	+	0.138980i	$0.955618\pi$
$180$	−0.385530	−	6.45510i	−0.0287357	−	0.481135i
$181$	5.97636			0.444219			0.222110	−	0.975022i	$-0.428706\pi$
$181$	5.97636			0.444219			0.222110	+	0.975022i	$0.428706\pi$
$182$		0			0
$183$	−5.30976	−	5.30976i	−0.392508	−	0.392508i
$184$	−1.45027	+	0.539119i	−0.106916	+	0.0397444i
$185$	−1.33977	+	1.90089i	−0.0985018	+	0.139756i
$186$	6.21192	−	3.13750i	0.455480	−	0.230052i
$187$	−2.44606	−	0.655419i	−0.178873	−	0.0479290i
$188$	−2.34104	+	5.97198i	−0.170738	+	0.435551i
$189$		0			0
$190$	−9.86863	−	7.81600i	−0.715946	−	0.567032i
$191$	−6.96830	+	4.02315i	−0.504209	+	0.291105i	−0.730450	−	0.682966i	$-0.760690\pi$
$191$	−6.96830	+	4.02315i	−0.504209	+	0.291105i	0.226241	+	0.974071i	$0.427356\pi$
$192$	−0.733203	+	9.94585i	−0.0529144	+	0.717780i
$193$	−3.76831	−	14.0635i	−0.271249	−	1.01231i	−0.958314	−	0.285718i	$-0.907768\pi$
$193$	−3.76831	−	14.0635i	−0.271249	−	1.01231i	0.687065	−	0.726596i	$-0.258899\pi$
$194$	−6.16213	−	0.344807i	−0.442415	−	0.0247557i
$195$	−9.55764	+	7.96972i	−0.684437	+	0.570723i
$196$		0			0
$197$	16.4919	+	16.4919i	1.17500	+	1.17500i	0.981001	+	0.194001i	$0.0621465\pi$
$197$	16.4919	+	16.4919i	1.17500	+	1.17500i	0.194001	+	0.981001i	$0.437854\pi$
$198$	1.45163	−	1.29778i	0.103163	−	0.0922295i
$199$	−4.82793	+	8.36222i	−0.342243	+	0.592782i	−0.984849	−	0.173415i	$-0.944520\pi$
$199$	−4.82793	+	8.36222i	−0.342243	+	0.592782i	0.642606	+	0.766197i	$0.277853\pi$
$200$	−1.22309	+	14.0891i	−0.0864857	+	0.996253i
$201$	−9.28636	−	16.0844i	−0.655009	−	1.13451i
$202$	−0.413507	−	1.97981i	−0.0290943	−	0.139299i
$203$		0			0
$204$	2.65399	+	6.07630i	0.185816	+	0.425426i
$205$	7.79615	+	2.86482i	0.544507	+	0.200088i
$206$	−6.48778	−	12.8451i	−0.452025	−	0.894962i
$207$	−0.204725	−	0.764042i	−0.0142293	−	0.0531046i
$208$	−15.1128	+	9.51304i	−1.04788	+	0.659610i
$209$		−	3.79066i		−	0.262205i
$210$		0			0
$211$		−	10.4344i		−	0.718333i	−0.933274	−	0.359166i	$-0.883061\pi$
$211$		−	10.4344i		−	0.718333i	0.933274	−	0.359166i	$-0.116939\pi$
$212$	−5.81275	+	0.878535i	−0.399221	+	0.0603381i
$213$	2.45439	+	9.15992i	0.168172	+	0.627628i
$214$	0.0507779	−	0.0256468i	0.00347111	−	0.00175318i
$215$	11.5942	+	25.0653i	0.790716	+	1.70944i
$216$	−15.4563	−	2.61649i	−1.05167	−	0.178029i
$217$		0			0
$218$	−8.71155	+	1.81951i	−0.590020	+	0.123233i
$219$	−9.17459	−	15.8909i	−0.619961	−	1.07380i
$220$	−3.55435	+	2.34526i	−0.239634	+	0.158117i
$221$	−5.93647	+	10.2823i	−0.399330	+	0.691660i
$222$	1.22205	+	1.36692i	0.0820187	+	0.0917416i
$223$	−10.7262	−	10.7262i	−0.718279	−	0.718279i	0.249973	−	0.968253i	$-0.419578\pi$
$223$	−10.7262	−	10.7262i	−0.718279	−	0.718279i	−0.968253	+	0.249973i	$0.919578\pi$
$224$		0			0
$225$	−7.11217	−	1.29934i	−0.474145	−	0.0866230i
$226$	−1.21249	+	21.6687i	−0.0806539	+	1.44138i
$227$	2.59397	+	9.68083i	0.172168	+	0.642539i	0.997017	+	0.0771860i	$0.0245935\pi$
$227$	2.59397	+	9.68083i	0.172168	+	0.642539i	−0.824849	+	0.565353i	$0.808740\pi$
$228$	−7.75744	+	6.19149i	−0.513749	+	0.410041i
$229$	14.7989	−	8.54416i	0.977940	−	0.564614i	0.0762921	−	0.997086i	$-0.475692\pi$
$229$	14.7989	−	8.54416i	0.977940	−	0.564614i	0.901647	+	0.432472i	$0.142359\pi$
$230$	0.199444	+	1.71833i	0.0131510	+	0.113303i
$231$		0			0
$232$	16.6725	−	11.8450i	1.09460	−	0.777661i
$233$	1.81156	+	0.485407i	0.118680	+	0.0318001i	0.317670	−	0.948201i	$-0.397100\pi$
$233$	1.81156	+	0.485407i	0.118680	+	0.0318001i	−0.198990	+	0.980001i	$0.563766\pi$
$234$	−4.11583	−	8.14891i	−0.269060	−	0.532711i
$235$	5.86188	+	4.13153i	0.382387	+	0.269512i
$236$	20.2846	+	14.9581i	1.32042	+	0.973687i
$237$	9.42947	+	9.42947i	0.612510	+	0.612510i
$238$		0			0
$239$	15.2182			0.984385			0.492193	−	0.870486i	$-0.336196\pi$
$239$	15.2182			0.984385			0.492193	+	0.870486i	$0.336196\pi$
$240$	10.6050	+	3.44321i	0.684550	+	0.222258i
$241$	−6.58780	+	11.4104i	−0.424357	+	0.735008i	−0.996360	−	0.0852432i	$-0.972833\pi$
$241$	−6.58780	+	11.4104i	−0.424357	+	0.735008i	0.572003	+	0.820252i	$0.306167\pi$
$242$	13.5598	+	4.45894i	0.871656	+	0.286632i
$243$	3.47383	−	12.9645i	0.222846	−	0.831673i
$244$	−11.0402	+	4.82210i	−0.706775	+	0.308703i
$245$		0			0
$246$	3.58599	−	5.47940i	0.228634	−	0.349354i
$247$	−17.1670	−	4.59987i	−1.09231	−	0.292683i
$248$	−1.04917	−	11.1158i	−0.0666222	−	0.705854i
$249$	−8.73995	−	5.04601i	−0.553872	−	0.319778i
$250$	14.9738	+	5.07790i	0.947027	+	0.321154i
$251$			14.7048i			0.928161i	0.885793	+	0.464080i	$0.153615\pi$
$251$			14.7048i			0.928161i	−0.885793	+	0.464080i	$0.846385\pi$
$252$		0			0
$253$	−0.368320	+	0.368320i	−0.0231561	+	0.0231561i
$254$	0.136786	−	2.44454i	0.00858275	−	0.153384i
$255$	7.30457	−	1.26478i	0.457430	−	0.0792035i
$256$	14.4267	+	6.91881i	0.901670	+	0.432426i
$257$	−3.42109	+	12.7677i	−0.213402	+	0.796426i	0.773321	+	0.634014i	$0.218594\pi$
$257$	−3.42109	+	12.7677i	−0.213402	+	0.796426i	−0.986723	+	0.162412i	$0.948073\pi$
$258$	21.3139	−	4.45165i	1.32694	−	0.277148i
$259$		0			0
$260$	6.30798	+	18.9427i	0.391204	+	1.17478i
$261$	5.22778	+	9.05478i	0.323592	+	0.560477i
$262$	−0.576336	+	1.75266i	−0.0356061	+	0.108279i
$263$	−10.2083	+	2.73529i	−0.629468	+	0.168665i	−0.559428	−	0.828879i	$-0.688979\pi$
$263$	−10.2083	+	2.73529i	−0.629468	+	0.168665i	−0.0700398	+	0.997544i	$0.522313\pi$
$264$	1.16985	+	3.14698i	0.0719991	+	0.193683i
$265$	−0.593033	+	6.54585i	−0.0364298	+	0.402108i
$266$		0			0
$267$	1.86676	−	1.86676i	0.114244	−	0.114244i
$268$	−29.4627	+	4.45297i	−1.79972	+	0.272009i
$269$	10.5625	+	6.09826i	0.644007	+	0.371818i	0.786156	−	0.618027i	$-0.212068\pi$
$269$	10.5625	+	6.09826i	0.644007	+	0.371818i	−0.142149	+	0.989845i	$0.545401\pi$
$270$	−6.95484	+	16.0876i	−0.423258	+	0.979058i
$271$	−5.70012	+	3.29096i	−0.346257	+	0.199912i	−0.663036	−	0.748588i	$-0.730732\pi$
$271$	−5.70012	+	3.29096i	−0.346257	+	0.199912i	0.316778	+	0.948500i	$0.397399\pi$
$272$	10.6301	−	0.406362i	0.644546	−	0.0246393i
$273$		0			0
$274$	0.898253	−	1.37253i	0.0542655	−	0.0829178i
$275$	1.60073	+	4.48383i	0.0965278	+	0.270385i
$276$	1.35535	+	0.152156i	0.0815824	+	0.00915872i
$277$	3.96687	−	1.06292i	0.238346	−	0.0638646i	−0.137669	−	0.990478i	$-0.543961\pi$
$277$	3.96687	−	1.06292i	0.238346	−	0.0638646i	0.376015	+	0.926614i	$0.377294\pi$
$278$	−18.3990	+	16.4490i	−1.10350	+	0.986548i
$279$	5.70799			0.341728
$280$		0			0
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	4.21526	−	3.76852i	0.251015	−	0.224412i
$283$	−18.8626	+	5.05423i	−1.12127	+	0.300443i	−0.771396	−	0.636355i	$-0.780441\pi$
$283$	−18.8626	+	5.05423i	−1.12127	+	0.300443i	−0.349872	+	0.936798i	$0.613775\pi$
$284$	15.1192	+	1.69734i	0.897161	+	0.100718i
$285$	4.65870	+	10.0716i	0.275958	+	0.596590i
$286$	−3.29208	+	5.03032i	−0.194665	+	0.297449i
$287$		0			0
$288$	−4.21450	+	7.01036i	−0.248342	+	0.413090i
$289$	−8.59722	+	4.96361i	−0.505719	+	0.291977i
$290$	−8.42511	−	21.2570i	−0.494739	−	1.24826i
$291$	4.71144	+	2.72015i	0.276190	+	0.159458i
$292$	−29.1081	+	4.39938i	−1.70342	+	0.257454i
$293$	−12.6859	+	12.6859i	−0.741121	+	0.741121i	−0.972794	−	0.231673i	$-0.925580\pi$
$293$	−12.6859	+	12.6859i	−0.741121	+	0.741121i	0.231673	+	0.972794i	$0.425580\pi$
$294$		0			0
$295$	21.6415	−	18.0460i	1.26002	−	1.05068i
$296$	2.75731	−	1.02499i	0.160265	−	0.0595764i
$297$	−5.09762	+	1.36590i	−0.295794	+	0.0792577i
$298$	−4.95266	+	15.0612i	−0.286900	+	0.872473i
$299$	1.22108	+	2.11498i	0.0706170	+	0.122312i
$300$	6.56143	−	10.5995i	0.378824	−	0.611964i
$301$		0			0
$302$	−20.7934	+	4.34295i	−1.19653	+	0.249909i
$303$	−0.461430	+	1.72208i	−0.0265085	+	0.0989309i
$304$	4.70593	+	15.2126i	0.269904	+	0.872500i
$305$	2.29801	+	13.2718i	0.131584	+	0.759944i
$306$	−0.303836	+	5.42991i	−0.0173691	+	0.310407i
$307$	9.98091	−	9.98091i	0.569640	−	0.569640i	−0.362387	−	0.932028i	$-0.618038\pi$
$307$	9.98091	−	9.98091i	0.569640	−	0.569640i	0.932028	+	0.362387i	$0.118038\pi$
$308$		0			0
$309$			12.6850i			0.721626i
$310$	−12.3498	−	1.81912i	−0.701422	−	0.103319i
$311$	12.0711	+	6.96926i	0.684490	+	0.395190i	0.801544	−	0.597935i	$-0.204012\pi$
$311$	12.0711	+	6.96926i	0.684490	+	0.395190i	−0.117055	+	0.993125i	$0.537345\pi$
$312$	15.6715	−	1.47916i	0.887224	−	0.0837409i
$313$	4.74109	+	1.27037i	0.267982	+	0.0718056i	0.390308	−	0.920684i	$-0.372369\pi$
$313$	4.74109	+	1.27037i	0.267982	+	0.0718056i	−0.122326	+	0.992490i	$0.539035\pi$
$314$	−5.83006	+	8.90835i	−0.329009	+	0.502727i
$315$		0			0
$316$	19.6060	−	8.56345i	1.10292	−	0.481732i
$317$	8.90414	−	33.2307i	0.500106	−	1.86642i	0.000794747	−	1.00000i	$-0.499747\pi$
$317$	8.90414	−	33.2307i	0.500106	−	1.86642i	0.499312	−	0.866423i	$-0.333586\pi$
$318$	4.92271	+	1.61876i	0.276052	+	0.0907756i
$319$	3.44258	−	5.96272i	0.192747	−	0.333848i
$320$	11.3527	−	13.8245i	0.634634	−	0.772812i
$321$	−0.0501451			−0.00279883
$322$		0			0
$323$	7.48630	+	7.48630i	0.416549	+	0.416549i
$324$	4.13883	+	3.05201i	0.229935	+	0.169556i
$325$	22.2486	−	1.80831i	1.23413	−	0.100307i
$326$	−4.23925	−	8.39327i	−0.234790	−	0.464860i
$327$	7.57748	+	2.03038i	0.419035	+	0.112280i
$328$	−6.08482	−	8.56473i	−0.335978	−	0.472908i
$329$		0			0
$330$	3.72864	−	0.432778i	0.205255	−	0.0238237i
$331$	11.2201	−	6.47792i	0.616712	−	0.356059i	−0.158876	−	0.987299i	$-0.550787\pi$
$331$	11.2201	−	6.47792i	0.616712	−	0.356059i	0.775588	+	0.631240i	$0.217454\pi$
$332$	−12.6547	+	10.1002i	−0.694518	+	0.554320i
$333$	0.389229	+	1.45262i	0.0213296	+	0.0796032i
$334$	−0.662889	+	11.8466i	−0.0362717	+	0.648219i
$335$	−3.00587	+	33.1785i	−0.164228	+	1.81274i
$336$		0			0
$337$	7.43071	+	7.43071i	0.404776	+	0.404776i	0.879912	−	0.475136i	$-0.157601\pi$
$337$	7.43071	+	7.43071i	0.404776	+	0.404776i	−0.475136	+	0.879912i	$0.657601\pi$
$338$	6.53279	+	7.30722i	0.355337	+	0.397461i
$339$	9.56524	−	16.5675i	0.519513	−	0.899822i
$340$	2.38788	−	11.6513i	0.129501	−	0.631883i
$341$	−1.87940	−	3.25522i	−0.101775	−	0.176280i
$342$	−7.96877	+	1.66437i	−0.430902	+	0.0899989i
$343$		0			0
$344$	5.83059	−	34.4429i	0.314364	−	1.85704i
$345$	0.525944	−	1.43127i	0.0283159	−	0.0770571i
$346$	2.79431	−	1.41134i	0.150223	−	0.0758743i
$347$	2.37153	+	8.85066i	0.127310	+	0.475128i	0.999911	−	0.0133050i	$-0.00423525\pi$
$347$	2.37153	+	8.85066i	0.127310	+	0.475128i	−0.872601	+	0.488433i	$0.837569\pi$
$348$	−17.8254	+	2.69413i	−0.955544	+	0.144420i
$349$			19.9513i			1.06797i	0.845495	+	0.533984i	$0.179306\pi$
$349$			19.9513i			1.06797i	−0.845495	+	0.533984i	$0.820694\pi$
$350$		0			0
$351$			24.7434i			1.32070i
$352$	5.38561	+	0.0952748i	0.287054	+	0.00507817i
$353$	−0.641552	−	2.39430i	−0.0341464	−	0.127436i	0.946749	−	0.321973i	$-0.104346\pi$
$353$	−0.641552	−	2.39430i	−0.0341464	−	0.127436i	−0.980895	+	0.194537i	$0.937679\pi$
$354$	−10.0159	−	19.8305i	−0.532340	−	1.05398i
$355$	5.86703	−	15.9662i	0.311389	−	0.847396i
$356$	−1.69532	−	3.88142i	−0.0898516	−	0.205715i
$357$		0			0
$358$	−4.76203	−	22.7999i	−0.251681	−	1.20501i
$359$	−7.94645	−	13.7637i	−0.419398	−	0.726418i	0.576481	−	0.817110i	$-0.304425\pi$
$359$	−7.94645	−	13.7637i	−0.419398	−	0.726418i	−0.995879	+	0.0906921i	$0.971092\pi$
$360$	6.49085	+	6.44227i	0.342098	+	0.339537i
$361$	1.57601	−	2.72973i	0.0829481	−	0.143670i
$362$	−6.30091	+	5.63313i	−0.331169	+	0.296071i
$363$	−8.89708	−	8.89708i	−0.466976	−	0.466976i
$364$		0			0
$365$	−2.96969	+	32.7792i	−0.155441	+	1.71574i
$366$	10.6029	+	0.593297i	0.554224	+	0.0310121i
$367$	−2.78634	−	10.3988i	−0.145446	−	0.542812i	−0.999735	−	0.0230136i	$-0.992674\pi$
$367$	−2.78634	−	10.3988i	−0.145446	−	0.542812i	0.854289	−	0.519798i	$-0.173993\pi$
$368$	1.02088	−	1.93538i	0.0532169	−	0.100889i
$369$	4.65148	−	2.68553i	0.242147	−	0.139803i
$370$	−0.379189	−	3.26694i	−0.0197131	−	0.169840i
$371$		0			0
$372$	−3.59195	+	9.16305i	−0.186234	+	0.475082i
$373$	14.2618	+	3.82144i	0.738448	+	0.197867i	0.608388	−	0.793640i	$-0.291816\pi$
$373$	14.2618	+	3.82144i	0.738448	+	0.197867i	0.130060	+	0.991506i	$0.458483\pi$
$374$	3.19667	−	1.61457i	0.165296	−	0.0834873i
$375$	−9.76368	−	9.94602i	−0.504194	−	0.513610i
$376$	−3.16083	−	8.50289i	−0.163007	−	0.438503i
$377$	−22.8262	−	22.8262i	−1.17561	−	1.17561i
$378$		0			0
$379$	−26.4563			−1.35897			−0.679483	−	0.733691i	$-0.737796\pi$
$379$	−26.4563			−1.35897			−0.679483	+	0.733691i	$0.737796\pi$
$380$	17.7717	−	1.06141i	0.911668	−	0.0544492i
$381$	−1.07909	+	1.86905i	−0.0552837	+	0.0957542i
$382$	3.55463	−	10.8097i	0.181871	−	0.553075i
$383$	7.60437	−	28.3799i	0.388565	−	1.45015i	−0.443904	−	0.896074i	$-0.646407\pi$
$383$	7.60437	−	28.3799i	0.388565	−	1.45015i	0.832470	−	0.554071i	$-0.186926\pi$
$384$	−8.60163	−	11.1771i	−0.438950	−	0.570377i
$385$		0			0
$386$	17.2288	+	11.2754i	0.876922	+	0.573901i
$387$	17.2503	+	4.62219i	0.876880	+	0.234959i
$388$	6.82177	−	5.44470i	0.346323	−	0.276413i
$389$	−8.09963	−	4.67632i	−0.410667	−	0.237099i	0.280409	−	0.959881i	$-0.409530\pi$
$389$	−8.09963	−	4.67632i	−0.410667	−	0.237099i	−0.691076	+	0.722782i	$0.742863\pi$
$390$	2.56467	−	17.4113i	0.129867	−	0.881654i
$391$		−	1.45481i		−	0.0735731i
$392$		0			0
$393$	1.14998	−	1.14998i	0.0580090	−	0.0580090i
$394$	−32.9324	−	1.84276i	−1.65911	−	0.0928370i
$395$	−4.08098	−	23.5692i	−0.205336	−	1.18589i
$396$	−0.307212	+	2.73653i	−0.0154380	+	0.137516i
$397$	4.59912	−	17.1641i	0.230823	−	0.861443i	−0.749164	−	0.662384i	$-0.769545\pi$
$397$	4.59912	−	17.1641i	0.230823	−	0.861443i	0.979987	−	0.199059i	$-0.0637886\pi$
$398$	−2.79186	−	13.3670i	−0.139943	−	0.670028i
$399$		0			0
$400$	−11.9905	−	16.0071i	−0.599524	−	0.800357i
$401$	−3.07671	−	5.32902i	−0.153644	−	0.266118i	0.778921	−	0.627122i	$-0.215767\pi$
$401$	−3.07671	−	5.32902i	−0.153644	−	0.266118i	−0.932564	+	0.361004i	$0.882434\pi$
$402$	24.9514	+	8.20490i	1.24446	+	0.409223i
$403$	−17.0227	+	4.56121i	−0.847960	+	0.227210i
$404$	2.30207	+	1.69757i	0.114532	+	0.0844573i
$405$	4.41569	−	3.68206i	0.219417	−	0.182963i
$406$		0			0
$407$	0.700261	−	0.700261i	0.0347107	−	0.0347107i
$408$	−8.52545	−	3.90471i	−0.422073	−	0.193312i
$409$	−5.66917	−	3.27310i	−0.280322	−	0.161844i	0.353247	−	0.935530i	$-0.385078\pi$
$409$	−5.66917	−	3.27310i	−0.280322	−	0.161844i	−0.633569	+	0.773686i	$0.718411\pi$
$410$	−10.9198	+	4.32801i	−0.539292	+	0.213745i
$411$	−1.25221	+	0.722965i	−0.0617670	+	0.0356612i
$412$	18.9475	+	7.42751i	0.933478	+	0.365927i
$413$		0			0
$414$	0.936005	+	0.612568i	0.0460022	+	0.0301061i
$415$	7.59975	+	16.4298i	0.373057	+	0.806508i
$416$	6.96678	−	24.2745i	0.341575	−	1.19015i
$417$	21.0136	−	5.63057i	1.02904	−	0.275730i
$418$	3.57296	+	3.99652i	0.174759	+	0.195476i
$419$	17.7908			0.869139			0.434569	−	0.900638i	$-0.356901\pi$
$419$	17.7908			0.869139			0.434569	+	0.900638i	$0.356901\pi$
$420$		0			0
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	9.83513	+	11.0010i	0.478767	+	0.535522i
$423$	4.47954	−	1.20029i	0.217803	−	0.0583601i
$424$	5.30034	−	6.40517i	0.257407	−	0.311062i
$425$	−12.0166	−	5.69392i	−0.582891	−	0.276196i
$426$	−11.2215	−	7.34393i	−0.543686	−	0.355815i
$427$		0			0
$428$	−0.0293616	+	0.0749013i	−0.00141925	+	0.00362049i
$429$	4.58934	−	2.64965i	0.221575	−	0.127926i
$430$	−35.8496	−	15.4982i	−1.72882	−	0.747389i
$431$	−13.1055	−	7.56644i	−0.631268	−	0.364463i	0.149975	−	0.988690i	$-0.452081\pi$
$431$	−13.1055	−	7.56644i	−0.631268	−	0.364463i	−0.781243	+	0.624227i	$0.785414\pi$
$432$	18.7619	−	11.8101i	0.902683	−	0.568212i
$433$	5.45382	−	5.45382i	0.262094	−	0.262094i	−0.563811	−	0.825904i	$-0.690665\pi$
$433$	5.45382	−	5.45382i	0.262094	−	0.262094i	0.825904	+	0.563811i	$0.190665\pi$
$434$		0			0
$435$	−1.81860	+	20.0736i	−0.0871953	+	0.962454i
$436$	7.46963	−	10.1296i	0.357730	−	0.485118i
$437$	2.10350	−	0.563632i	0.100624	−	0.0269622i
$438$	24.6511	+	8.10614i	1.17787	+	0.387327i
$439$	−12.8732	−	22.2970i	−0.614402	−	1.06418i	−0.990489	−	0.137592i	$-0.956064\pi$
$439$	−12.8732	−	22.2970i	−0.614402	−	1.06418i	0.376087	−	0.926585i	$-0.377270\pi$
$440$	1.53681	−	5.82285i	0.0732644	−	0.277593i
$441$		0			0
$442$	−3.43289	−	16.4362i	−0.163286	−	0.781790i
$443$	4.47481	−	16.7002i	0.212605	−	0.793452i	−0.774391	−	0.632707i	$-0.781944\pi$
$443$	4.47481	−	16.7002i	0.212605	−	0.793452i	0.986996	−	0.160745i	$-0.0513897\pi$
$444$	−2.57683	−	0.289284i	−0.122291	−	0.0137288i
$445$	−4.66601	+	0.807916i	−0.221190	+	0.0382989i
$446$	21.4189	+	1.19851i	1.01421	+	0.0567513i
$447$	9.88223	−	9.88223i	0.467413	−	0.467413i
$448$		0			0
$449$		−	11.0999i		−	0.523839i	−0.965090	−	0.261919i	$-0.915645\pi$
$449$		−	11.0999i		−	0.523839i	0.965090	−	0.261919i	$-0.0843555\pi$
$450$	8.72313	−	5.33381i	0.411212	−	0.251438i
$451$	−3.06308	−	1.76847i	−0.144235	−	0.0832739i
$452$	−19.1459	−	23.9883i	−0.900549	−	1.12832i
$453$	18.0865	+	4.84627i	0.849779	+	0.227698i
$454$	−11.8597	−	7.76157i	−0.556603	−	0.364268i
$455$		0			0
$456$	2.34281	−	13.8397i	0.109712	−	0.648101i
$457$	−5.49672	+	20.5140i	−0.257126	+	0.959606i	0.709770	+	0.704434i	$0.248799\pi$
$457$	−5.49672	+	20.5140i	−0.257126	+	0.959606i	−0.966896	+	0.255172i	$0.917868\pi$
$458$	−7.54913	+	22.9572i	−0.352748	+	1.07272i
$459$	7.36989	−	12.7650i	0.343997	−	0.595821i
$460$	−1.82992	−	1.62366i	−0.0853205	−	0.0757033i
$461$	8.61652			0.401311			0.200656	−	0.979662i	$-0.435693\pi$
$461$	8.61652			0.401311			0.200656	+	0.979662i	$0.435693\pi$
$462$		0			0
$463$	−1.63340	−	1.63340i	−0.0759103	−	0.0759103i	0.668132	−	0.744043i	$-0.267094\pi$
$463$	−1.63340	−	1.63340i	−0.0759103	−	0.0759103i	−0.744043	+	0.668132i	$0.767094\pi$
$464$	−6.41320	+	28.2032i	−0.297725	+	1.30930i
$465$	8.99413	+	6.33918i	0.417093	+	0.293972i
$466$	−2.36747	+	1.19576i	−0.109671	+	0.0553924i
$467$	−24.6125	−	6.59489i	−1.13893	−	0.305175i	−0.360409	−	0.932794i	$-0.617363\pi$
$467$	−24.6125	−	6.59489i	−1.13893	−	0.305175i	−0.778521	+	0.627619i	$0.784030\pi$
$468$	12.0203	+	4.71199i	0.555637	+	0.217812i
$469$		0			0
$470$	−10.0745	+	1.16933i	−0.464701	+	0.0539372i
$471$	8.12741	−	4.69236i	0.374491	−	0.216213i
$472$	−35.4852	+	3.34928i	−1.63334	+	0.154163i
$473$	−3.04379	−	11.3596i	−0.139953	−	0.522313i
$474$	−18.8295	−	1.05362i	−0.864867	−	0.0483944i
$475$	3.57726	−	19.5807i	0.164136	−	0.898423i
$476$		0			0
$477$	3.00540	+	3.00540i	0.137608	+	0.137608i
$478$	−16.0447	+	14.3442i	−0.733867	+	0.656090i
$479$	4.63924	−	8.03541i	0.211972	−	0.367147i	−0.740359	−	0.672211i	$-0.765345\pi$
$479$	4.63924	−	8.03541i	0.211972	−	0.367147i	0.952332	+	0.305064i	$0.0986780\pi$
$480$	−14.4264	+	6.36575i	−0.658472	+	0.290556i
$481$	−2.32156	−	4.02106i	−0.105854	−	0.183345i
$482$	−3.80954	−	18.2395i	−0.173520	−	0.830787i
$483$		0			0
$484$	−18.4990	+	8.07996i	−0.840865	+	0.367271i
$485$	−4.09679	−	8.85680i	−0.186026	−	0.402167i
$486$	8.55746	+	16.9429i	0.388174	+	0.768544i
$487$	−4.60932	−	17.2022i	−0.208868	−	0.779506i	−0.988236	−	0.152939i	$-0.951126\pi$
$487$	−4.60932	−	17.2022i	−0.208868	−	0.779506i	0.779368	−	0.626567i	$-0.215541\pi$
$488$	7.09457	−	15.4901i	0.321156	−	0.701204i
$489$			8.28866i			0.374826i
$490$		0			0
$491$		−	2.49970i		−	0.112810i	−0.998408	−	0.0564049i	$-0.982036\pi$
$491$		−	2.49970i		−	0.112810i	0.998408	−	0.0564049i	$-0.0179638\pi$
$492$	1.38398	+	9.15701i	0.0623949	+	0.412830i
$493$	4.97711	+	18.5748i	0.224158	+	0.836569i
$494$	22.4349	−	11.3314i	1.00940	−	0.509823i
$495$	2.88982	+	1.06191i	0.129888	+	0.0477293i
$496$	11.5836	+	10.7305i	0.520117	+	0.481816i
$497$		0			0
$498$	13.9708	−	2.91797i	0.626047	−	0.130757i
$499$	−3.26199	−	5.64993i	−0.146027	−	0.252926i	0.783729	−	0.621103i	$-0.213315\pi$
$499$	−3.26199	−	5.64993i	−0.146027	−	0.252926i	−0.929756	+	0.368178i	$0.879982\pi$
$500$	−20.5733	+	8.76020i	−0.920064	+	0.391768i
$501$	5.22947	−	9.05770i	0.233635	−	0.404668i
$502$	−13.8603	−	15.5034i	−0.618617	−	0.691951i
$503$	14.6078	+	14.6078i	0.651327	+	0.651327i	0.953313	−	0.301985i	$-0.0976493\pi$
$503$	14.6078	+	14.6078i	0.651327	+	0.651327i	−0.301985	+	0.953313i	$0.597649\pi$
$504$		0			0
$505$	2.45607	−	2.04801i	0.109294	−	0.0911353i
$506$	0.0411550	−	0.735489i	0.00182956	−	0.0326965i
$507$	−2.23620	−	8.34561i	−0.0993131	−	0.370641i
$508$	2.15993	+	2.70623i	0.0958316	+	0.120069i
$509$	29.8459	−	17.2316i	1.32290	−	0.763775i	0.338708	−	0.940892i	$-0.390010\pi$
$509$	29.8459	−	17.2316i	1.32290	−	0.763775i	0.984190	+	0.177116i	$0.0566769\pi$
$510$	−6.50911	+	8.21853i	−0.288228	+	0.363922i
$511$		0			0
$512$	−21.7316	+	6.30364i	−0.960412	+	0.278584i
$513$	21.3121	+	5.71056i	0.940953	+	0.252128i
$514$	−8.42755	−	16.6857i	−0.371723	−	0.735973i
$515$	13.1083	−	18.5982i	0.577620	−	0.819536i
$516$	−18.2754	+	24.7832i	−0.804528	+	1.09102i
$517$	−2.15944	−	2.15944i	−0.0949721	−	0.0949721i
$518$		0			0
$519$	−2.75949			−0.121128
$520$	−24.5054	−	14.0257i	−1.07463	−	0.615068i
$521$	−16.9526	+	29.3627i	−0.742705	+	1.28640i	0.208555	+	0.978011i	$0.433124\pi$
$521$	−16.9526	+	29.3627i	−0.742705	+	1.28640i	−0.951259	+	0.308392i	$0.900209\pi$
$522$	−14.0465	−	4.61897i	−0.614796	−	0.202167i
$523$	−4.77618	+	17.8250i	−0.208848	+	0.779431i	0.779394	+	0.626534i	$0.215527\pi$
$523$	−4.77618	+	17.8250i	−0.208848	+	0.779431i	−0.988242	+	0.152897i	$0.951140\pi$
$524$	−1.04437	−	2.39107i	−0.0456233	−	0.104455i
$525$		0			0
$526$	8.18443	−	12.5058i	0.356858	−	0.545280i
$527$	10.1405	+	2.71715i	0.441728	+	0.118361i
$528$	−4.19963	−	2.21522i	−0.182765	−	0.0964053i
$529$	19.6594	+	11.3504i	0.854758	+	0.493495i
$530$	−5.54468	−	7.46031i	−0.240846	−	0.324055i
$531$		−	18.2217i		−	0.790756i
$532$		0			0
$533$	−11.7259	+	11.7259i	−0.507906	+	0.507906i
$534$	−0.208587	+	3.72769i	−0.00902643	+	0.161313i
$535$	0.0735205	+	0.0518182i	0.00317857	+	0.00224030i
$536$	26.8655	−	32.4654i	1.16041	−	1.40229i
$537$	−5.31392	+	19.8318i	−0.229312	+	0.855806i
$538$	−16.8842	+	3.52645i	−0.727928	+	0.152036i
$539$		0			0
$540$	−7.83111	−	23.5166i	−0.336997	−	1.01199i
$541$	−1.59149	−	2.75655i	−0.0684236	−	0.118513i	0.829784	−	0.558085i	$-0.188464\pi$
$541$	−1.59149	−	2.75655i	−0.0684236	−	0.118513i	−0.898208	+	0.439572i	$0.855130\pi$
$542$	2.90771	−	8.84244i	0.124897	−	0.379815i
$543$	7.19630	−	1.92824i	0.308823	−	0.0827488i
$544$	−10.8244	+	10.4481i	−0.464092	+	0.447957i
$545$	−9.01164	−	10.8072i	−0.386016	−	0.462928i
$546$		0			0
$547$	15.6791	−	15.6791i	0.670391	−	0.670391i	−0.287415	−	0.957806i	$-0.592796\pi$
$547$	15.6791	−	15.6791i	0.670391	−	0.670391i	0.957806	+	0.287415i	$0.0927960\pi$
$548$	0.346674	+	2.29374i	0.0148092	+	0.0979836i
$549$	7.54315	+	4.35504i	0.321934	+	0.185869i
$550$	−5.91398	−	3.21853i	−0.252173	−	0.137239i
$551$	−24.9289	+	14.3927i	−1.06201	+	0.613151i
$552$	−1.57237	+	1.11709i	−0.0669246	+	0.0475466i
$553$		0			0
$554$	−3.18042	+	4.85969i	−0.135123	+	0.206469i
$555$	−0.999942	+	2.72118i	−0.0424452	+	0.115508i
$556$	3.89382	−	34.6847i	0.165135	−	1.47096i
$557$	−20.6171	+	5.52434i	−0.873575	+	0.234074i	−0.667633	−	0.744491i	$-0.732692\pi$
$557$	−20.6171	+	5.52434i	−0.873575	+	0.234074i	−0.205942	+	0.978564i	$0.566026\pi$
$558$	−6.01797	+	5.38017i	−0.254761	+	0.227761i
$559$	−55.1382			−2.33210
$560$		0			0
$561$	−3.15683			−0.133282
$562$	34.0302	−	30.4236i	1.43548	−	1.28334i
$563$	13.1487	−	3.52319i	0.554153	−	0.148485i	0.0291340	−	0.999576i	$-0.490725\pi$
$563$	13.1487	−	3.52319i	0.554153	−	0.148485i	0.525019	+	0.851091i	$0.324058\pi$
$564$	−0.892084	+	7.94635i	−0.0375635	+	0.334602i
$565$	−31.1444	+	14.4061i	−1.31025	+	0.606070i
$566$	15.1231	−	23.1081i	0.635669	−	0.971305i
$567$		0			0
$568$	−17.5402	+	12.4614i	−0.735969	+	0.522869i
$569$	20.3421	−	11.7445i	0.852787	−	0.492357i	−0.00880335	−	0.999961i	$-0.502802\pi$
$569$	20.3421	−	11.7445i	0.852787	−	0.492357i	0.861590	+	0.507605i	$0.169469\pi$
$570$	−14.4049	−	6.22740i	−0.603354	−	0.260837i
$571$	23.4830	+	13.5579i	0.982734	+	0.567382i	0.903094	−	0.429442i	$-0.141290\pi$
$571$	23.4830	+	13.5579i	0.982734	+	0.567382i	0.0796395	+	0.996824i	$0.474623\pi$
$572$	−1.27056	−	8.40651i	−0.0531246	−	0.351494i
$573$	−7.09267	+	7.09267i	−0.296301	+	0.296301i
$574$		0			0
$575$	−2.25014	+	1.55497i	−0.0938374	+	0.0648469i
$576$	−2.16438	−	11.3635i	−0.0901826	−	0.473480i
$577$	26.9522	−	7.22183i	1.12204	−	0.300649i	0.350329	−	0.936627i	$-0.386070\pi$
$577$	26.9522	−	7.22183i	1.12204	−	0.300649i	0.771707	+	0.635978i	$0.219403\pi$
$578$	4.38556	−	13.3366i	0.182415	−	0.554731i
$579$	−9.07505	−	15.7184i	−0.377146	−	0.653236i
$580$	28.9189	+	14.4702i	1.20079	+	0.600842i
$581$		0			0
$582$	−7.53124	+	1.57299i	−0.312180	+	0.0652024i
$583$	0.724403	−	2.70351i	0.0300017	−	0.111968i
$584$	26.5421	−	32.0747i	1.09832	−	1.32726i
$585$	8.31585	−	11.7987i	0.343818	−	0.487815i
$586$	1.41749	−	25.3323i	0.0585560	−	1.04647i
$587$	−22.8296	+	22.8296i	−0.942280	+	0.942280i	−0.998423	−	0.0561427i	$-0.982120\pi$
$587$	−22.8296	+	22.8296i	−0.942280	+	0.942280i	0.0561427	+	0.998423i	$0.482120\pi$
$588$		0			0
$589$			15.7148i			0.647516i
$590$	−5.80723	+	39.4246i	−0.239080	+	1.62309i
$591$	25.1794	+	14.5374i	1.03574	+	0.597987i
$592$	−1.94092	+	3.67961i	−0.0797715	+	0.151231i
$593$	36.8872	+	9.88391i	1.51478	+	0.405883i	0.918019	−	0.396537i	$-0.129788\pi$
$593$	36.8872	+	9.88391i	1.51478	+	0.405883i	0.596759	+	0.802421i	$0.296455\pi$
$594$	4.08700	−	6.24494i	0.167691	−	0.256233i
$595$		0			0
$596$	−8.97462	−	20.5474i	−0.367615	−	0.841653i
$597$	−3.11542	+	11.6269i	−0.127506	+	0.475857i
$598$	−3.28091	−	1.07888i	−0.134166	−	0.0441186i
$599$	14.4801	−	25.0802i	0.591640	−	1.02475i	−0.402372	−	0.915476i	$-0.631814\pi$
$599$	14.4801	−	25.0802i	0.591640	−	1.02475i	0.994012	−	0.109274i	$-0.0348526\pi$
$600$	3.07303	+	17.3598i	0.125456	+	0.708709i
$601$	8.88262			0.362330			0.181165	−	0.983453i	$-0.442013\pi$
$601$	8.88262			0.362330			0.181165	+	0.983453i	$0.442013\pi$
$602$		0			0
$603$	15.2333	+	15.2333i	0.620347	+	0.620347i
$604$	17.8291	−	24.1780i	0.725456	−	0.983791i
$605$	3.85057	+	22.2384i	0.156548	+	0.904121i
$606$	−1.13669	−	2.25053i	−0.0461749	−	0.0914215i
$607$	44.3709	+	11.8891i	1.80096	+	0.482565i	0.994127	−	0.108218i	$-0.0345145\pi$
$607$	44.3709	+	11.8891i	1.80096	+	0.482565i	0.806830	+	0.590783i	$0.201181\pi$
$608$	−19.3004	−	11.6030i	−0.782734	−	0.470565i
$609$		0			0
$610$	−14.9324	−	11.8266i	−0.604597	−	0.478844i
$611$	−12.4000	+	7.15915i	−0.501651	+	0.289628i
$612$	−4.79773	−	6.01118i	−0.193937	−	0.242988i
$613$	0.0600047	+	0.223941i	0.00242357	+	0.00904487i	0.967127	−	0.254294i	$-0.0818430\pi$
$613$	0.0600047	+	0.223941i	0.00242357	+	0.00904487i	−0.964703	+	0.263339i	$0.915176\pi$
$614$	−1.11524	+	19.9306i	−0.0450073	+	0.804335i
$615$	10.3119	+	0.934224i	0.415815	+	0.0376716i
$616$		0			0
$617$	−27.1038	−	27.1038i	−1.09116	−	1.09116i	−0.995405	−	0.0957517i	$-0.969475\pi$
$617$	−27.1038	−	27.1038i	−1.09116	−	1.09116i	−0.0957517	−	0.995405i	$-0.530525\pi$
$618$	−11.9565	−	13.3739i	−0.480962	−	0.537978i
$619$	7.14970	−	12.3836i	0.287371	−	0.497741i	−0.685811	−	0.727780i	$-0.740552\pi$
$619$	7.14970	−	12.3836i	0.287371	−	0.497741i	0.973181	+	0.230039i	$0.0738855\pi$
$620$	14.7351	−	9.72265i	0.591778	−	0.390471i
$621$	−1.51593	−	2.62566i	−0.0608320	−	0.105364i
$622$	−19.2957	+	4.03012i	−0.773685	+	0.161593i
$623$		0			0
$624$	−15.1284	+	16.3310i	−0.605619	+	0.653762i
$625$	4.03719	+	24.6719i	0.161488	+	0.986875i
$626$	−6.19597	+	3.12944i	−0.247641	+	0.125078i
$627$	−1.22304	−	4.56444i	−0.0488434	−	0.182286i
$628$	−2.25007	−	14.8874i	−0.0897875	−	0.594071i
$629$			2.76594i			0.110285i
$630$		0			0
$631$			30.7128i			1.22266i	0.791377	+	0.611328i	$0.209364\pi$
$631$			30.7128i			1.22266i	−0.791377	+	0.611328i	$0.790636\pi$
$632$	−12.5991	+	27.5085i	−0.501165	+	1.09423i
$633$	−3.36660	−	12.5643i	−0.133810	−	0.499387i
$634$	21.9346	+	43.4281i	0.871132	+	1.72475i
$635$	3.51353	−	1.62521i	0.139430	−	0.0644946i
$636$	−6.71584	+	2.93332i	−0.266300	+	0.116314i
$637$		0			0
$638$	1.99075	+	9.53141i	0.0788144	+	0.377352i
$639$	−5.49985	−	9.52602i	−0.217571	−	0.376843i
$640$	1.06133	+	25.2759i	0.0419528	+	0.999120i
$641$	−20.7752	+	35.9837i	−0.820572	+	1.42127i	0.0846851	+	0.996408i	$0.473012\pi$
$641$	−20.7752	+	35.9837i	−0.820572	+	1.42127i	−0.905257	+	0.424864i	$0.860322\pi$
$642$	0.0528683	−	0.0472652i	0.00208655	−	0.00186541i
$643$	12.5692	+	12.5692i	0.495681	+	0.495681i	0.910090	−	0.414410i	$-0.136012\pi$
$643$	12.5692	+	12.5692i	0.495681	+	0.495681i	−0.414410	+	0.910090i	$0.636012\pi$
$644$		0			0
$645$	22.0481	+	26.4410i	0.868142	+	1.04111i
$646$	−14.9492	−	0.836497i	−0.588169	−	0.0329115i
$647$	9.22084	+	34.4127i	0.362509	+	1.35290i	0.870767	+	0.491696i	$0.163623\pi$
$647$	9.22084	+	34.4127i	0.362509	+	1.35290i	−0.508258	+	0.861205i	$0.669710\pi$
$648$	−7.24033	+	0.683380i	−0.284427	+	0.0268457i
$649$	−10.3917	+	5.99966i	−0.407910	+	0.235507i
$650$	−21.7524	+	22.8774i	−0.853200	+	0.897325i
$651$		0			0
$652$	12.3807	+	4.85329i	0.484866	+	0.190070i
$653$	−12.7132	−	3.40648i	−0.497505	−	0.133306i	0.00133684	−	0.999999i	$-0.499574\pi$
$653$	−12.7132	−	3.40648i	−0.497505	−	0.133306i	−0.498842	+	0.866693i	$0.666241\pi$
$654$	−9.90276	+	5.00166i	−0.387229	+	0.195580i
$655$	−2.87441	+	0.497701i	−0.112312	+	0.0194468i
$656$	14.4881	+	3.29449i	0.565666	+	0.128628i
$657$	15.0499	+	15.0499i	0.587153	+	0.587153i
$658$		0			0
$659$	−10.3786			−0.404294			−0.202147	−	0.979355i	$-0.564792\pi$
$659$	−10.3786			−0.404294			−0.202147	+	0.979355i	$0.564792\pi$
$660$	−3.52321	+	3.97078i	−0.137141	+	0.154563i
$661$	11.5282	−	19.9675i	0.448397	−	0.776646i	−0.549885	−	0.835240i	$-0.685329\pi$
$661$	11.5282	−	19.9675i	0.448397	−	0.776646i	0.998282	+	0.0585946i	$0.0186619\pi$
$662$	−5.72352	+	17.4054i	−0.222451	+	0.676481i
$663$	−3.83074	+	14.2965i	−0.148774	+	0.555231i
$664$	3.82184	−	22.5767i	0.148316	−	0.876144i
$665$		0			0
$666$	−1.77956	−	1.16463i	−0.0689567	−	0.0451286i
$667$	3.82069	+	1.02375i	0.147938	+	0.0396398i
$668$	−10.4674	−	13.1148i	−0.404995	−	0.507427i
$669$	−16.3765	−	9.45496i	−0.633151	−	0.365550i
$670$	−28.1039	−	37.8136i	−1.08575	−	1.46087i
$671$		−	5.73573i		−	0.221425i
$672$		0			0
$673$	27.9624	−	27.9624i	1.07787	−	1.07787i	0.0811716	−	0.996700i	$-0.474134\pi$
$673$	27.9624	−	27.9624i	1.07787	−	1.07787i	0.996700	−	0.0811716i	$-0.0258662\pi$
$674$	−14.8382	−	0.830285i	−0.571546	−	0.0319814i
$675$	−27.6208	+	2.24494i	−1.06312	+	0.0864079i
$676$	−13.7751	−	1.54644i	−0.529813	−	0.0594786i
$677$	8.86132	−	33.0709i	0.340568	−	1.27102i	−0.557137	−	0.830421i	$-0.688100\pi$
$677$	8.86132	−	33.0709i	0.340568	−	1.27102i	0.897705	−	0.440597i	$-0.145233\pi$
$678$	5.53131	+	26.4831i	0.212429	+	1.01708i
$679$		0			0
$680$	8.46464	+	14.5348i	0.324604	+	0.557385i
$681$	6.24694	+	10.8200i	0.239383	+	0.414624i
$682$	5.04973	+	1.66053i	0.193364	+	0.0635850i
$683$	1.86138	−	0.498756i	0.0712239	−	0.0190844i	−0.223031	−	0.974811i	$-0.571595\pi$
$683$	1.86138	−	0.498756i	0.0712239	−	0.0190844i	0.294255	+	0.955727i	$0.404928\pi$
$684$	6.83274	−	9.26588i	0.261256	−	0.354290i
$685$	2.58302	+	0.234014i	0.0986922	+	0.00894120i
$686$		0			0
$687$	15.0630	−	15.0630i	0.574691	−	0.574691i
$688$	26.3176	+	41.8091i	1.00335	+	1.59396i
$689$	−11.3645	−	6.56128i	−0.432952	−	0.249965i
$690$	0.794566	+	2.00474i	0.0302486	+	0.0763191i
$691$	−30.8812	+	17.8293i	−1.17478	+	0.678257i	−0.954800	−	0.297248i	$-0.903931\pi$
$691$	−30.8812	+	17.8293i	−1.17478	+	0.678257i	−0.219976	+	0.975505i	$0.570598\pi$
$692$	−1.61577	+	4.12182i	−0.0614225	+	0.156688i
$693$		0			0
$694$	−10.8427	−	7.09598i	−0.411582	−	0.269360i
$695$	−36.6276	−	13.4594i	−1.38936	−	0.510544i
$696$	16.2541	−	19.6422i	0.616109	−	0.744534i
$697$	9.54198	−	2.55677i	0.361428	−	0.0968444i
$698$	−18.8055	−	21.0348i	−0.711797	−	0.796177i
$699$	2.33797			0.0884301
$700$		0			0
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	−23.3223	−	26.0871i	−0.880245	−	0.984594i
$703$	−3.99924	+	1.07159i	−0.150834	+	0.0404159i
$704$	−5.76789	+	4.97586i	−0.217385	+	0.187535i
$705$	8.39147	+	3.08359i	0.316041	+	0.116135i
$706$	2.93319	+	1.91962i	0.110392	+	0.0722460i
$707$		0			0
$708$	29.2514	+	11.4667i	1.09934	+	0.430944i
$709$	7.92917	−	4.57791i	0.297786	−	0.171927i	−0.343662	−	0.939093i	$-0.611667\pi$
$709$	7.92917	−	4.57791i	0.297786	−	0.171927i	0.641448	+	0.767167i	$0.278334\pi$
$710$	8.86357	+	22.3633i	0.332644	+	0.839280i
$711$	−13.3957	−	7.73401i	−0.502378	−	0.290048i
$712$	5.44589	+	2.49425i	0.204093	+	0.0934762i
$713$	1.52693	−	1.52693i	0.0571839	−	0.0571839i
$714$		0			0
$715$	−9.46674	−	0.857657i	−0.354036	−	0.0320745i
$716$	26.5111	+	19.5495i	0.990767	+	0.730601i
$717$	18.3247	−	4.91009i	0.684348	−	0.183370i
$718$	21.3512	+	7.02104i	0.796820	+	0.262023i
$719$	−6.67322	−	11.5584i	−0.248869	−	0.431054i	0.714343	−	0.699796i	$-0.246726\pi$
$719$	−6.67322	−	11.5584i	−0.248869	−	0.431054i	−0.963212	+	0.268742i	$0.913392\pi$
$720$	−12.9156	−	0.674050i	−0.481337	−	0.0251203i
$721$		0			0
$722$	0.911364	+	4.36348i	0.0339175	+	0.162392i
$723$	−4.25104	+	15.8651i	−0.158098	+	0.590029i
$724$	1.33348	−	11.8781i	0.0495582	−	0.441446i
$725$	23.4097	−	27.5517i	0.869414	−	1.02324i
$726$	17.7664	+	0.994134i	0.659372	+	0.0368958i
$727$	6.15934	−	6.15934i	0.228437	−	0.228437i	−0.583602	−	0.812040i	$-0.698357\pi$
$727$	6.15934	−	6.15934i	0.228437	−	0.228437i	0.812040	+	0.583602i	$0.198357\pi$
$728$		0			0
$729$		−	24.4454i		−	0.905384i
$730$	−27.7657	−	37.3584i	−1.02765	−	1.38270i
$731$	28.4457	+	16.4231i	1.05210	+	0.607431i
$732$	−11.7380	+	9.36848i	−0.433847	+	0.346269i
$733$	9.92223	+	2.65865i	0.366486	+	0.0981996i	0.437362	−	0.899286i	$-0.355913\pi$
$733$	9.92223	+	2.65865i	0.366486	+	0.0981996i	−0.0708761	+	0.997485i	$0.522580\pi$
$734$	12.7392	+	8.33717i	0.470213	+	0.307731i
$735$		0			0
$736$	0.747914	+	3.00273i	0.0275685	+	0.110682i
$737$	3.67173	−	13.7031i	0.135250	−	0.504760i
$738$	−2.37279	+	7.21572i	−0.0873435	+	0.265614i
$739$	−21.8583	+	37.8597i	−0.804070	+	1.39269i	0.112847	+	0.993612i	$0.464003\pi$
$739$	−21.8583	+	37.8597i	−0.804070	+	1.39269i	−0.916917	+	0.399078i	$0.869330\pi$
$740$	3.47910	+	3.08695i	0.127894	+	0.113478i
$741$	−22.1553			−0.813897
$742$		0			0
$743$	−26.0186	−	26.0186i	−0.954529	−	0.954529i	0.0444813	−	0.999010i	$-0.485836\pi$
$743$	−26.0186	−	26.0186i	−0.954529	−	0.954529i	−0.999010	+	0.0444813i	$0.985836\pi$
$744$	−4.84979	−	13.0463i	−0.177802	−	0.478302i
$745$	−24.7008	+	4.27693i	−0.904969	+	0.156694i
$746$	−18.6383	+	9.41377i	−0.682396	+	0.344663i
$747$	11.3072	+	3.02975i	0.413709	+	0.110853i
$748$	−1.84843	+	4.71534i	−0.0675854	+	0.172410i
$749$		0			0
$750$	19.6687	+	1.28321i	0.718201	+	0.0468562i
$751$	−7.30460	+	4.21731i	−0.266548	+	0.153892i	−0.627318	−	0.778763i	$-0.715847\pi$
$751$	−7.30460	+	4.21731i	−0.266548	+	0.153892i	0.360770	+	0.932655i	$0.382514\pi$
$752$	11.3471	+	5.98535i	0.413784	+	0.218263i
$753$	4.74444	+	17.7065i	0.172897	+	0.645260i
$754$	45.5811	+	2.55053i	1.65997	+	0.0928850i
$755$	−21.5097	−	25.7954i	−0.782818	−	0.938790i
$756$		0			0
$757$	3.33081	+	3.33081i	0.121060	+	0.121060i	0.765041	−	0.643981i	$-0.222718\pi$
$757$	3.33081	+	3.33081i	0.121060	+	0.121060i	−0.643981	+	0.765041i	$0.722718\pi$
$758$	27.8930	−	24.9369i	1.01312	−	0.905748i
$759$	−0.324667	+	0.562340i	−0.0117847	+	0.0204117i
$760$	−17.7364	+	17.8701i	−0.643365	+	0.648217i
$761$	−17.2317	−	29.8462i	−0.624649	−	1.08192i	−0.988609	−	0.150509i	$-0.951909\pi$
$761$	−17.2317	−	29.8462i	−0.624649	−	1.08192i	0.363959	−	0.931415i	$-0.381425\pi$
$762$	−0.624010	−	2.98767i	−0.0226055	−	0.108232i
$763$		0			0
$764$	6.44127	+	14.7473i	0.233037	+	0.533537i
$765$	−7.80440	+	3.60999i	−0.282169	+	0.130520i
$766$	18.7327	+	37.0888i	0.676840	+	1.34007i
$767$	14.5609	+	54.3419i	0.525763	+	1.96217i
$768$	19.6039	+	3.67642i	0.707396	+	0.132661i
$769$		−	18.7498i		−	0.676135i	−0.941122	−	0.338067i	$-0.890227\pi$
$769$		−	18.7498i		−	0.676135i	0.941122	−	0.338067i	$-0.109773\pi$
$770$		0			0
$771$			16.4777i			0.593431i
$772$	−28.7922	+	4.35164i	−1.03626	+	0.156619i
$773$	−11.5075	−	42.9466i	−0.413896	−	1.54468i	−0.787036	−	0.616907i	$-0.788386\pi$
$773$	−11.5075	−	42.9466i	−0.413896	−	1.54468i	0.373140	−	0.927775i	$-0.378281\pi$
$774$	−22.5438	+	11.3864i	−0.810320	+	0.409274i
$775$	−6.63610	−	18.5884i	−0.238376	−	0.667716i
$776$	−2.06023	+	12.1704i	−0.0739581	+	0.436891i
$777$		0			0
$778$	12.9472	−	2.70418i	0.464181	−	0.0969497i
$779$	7.39361	+	12.8061i	0.264903	+	0.458826i
$780$	13.7074	+	20.7742i	0.490803	+	0.743835i
$781$	−3.62174	+	6.27304i	−0.129596	+	0.224467i
$782$	1.37126	+	1.53382i	0.0490363	+	0.0548493i
$783$	28.3379	+	28.3379i	1.01271	+	1.01271i
$784$		0			0
$785$	−16.7650	−	1.51885i	−0.598367	−	0.0542102i
$786$	−0.128496	+	2.29637i	−0.00458329	+	0.0819089i
$787$	−0.279451	−	1.04293i	−0.00996136	−	0.0371763i	0.960766	−	0.277359i	$-0.0894592\pi$
$787$	−0.279451	−	1.04293i	−0.00996136	−	0.0371763i	−0.970728	+	0.240183i	$0.922793\pi$
$788$	36.4577	−	29.0982i	1.29875	−	1.03658i
$789$	−11.4095	+	6.58729i	−0.406189	+	0.234514i
$790$	26.5182	+	21.0025i	0.943474	+	0.747236i
$791$		0			0
$792$	−2.25547	−	3.17471i	−0.0801447	−	0.112808i
$793$	−25.9757	−	6.96017i	−0.922424	−	0.247163i
$794$	11.3295	+	22.4312i	0.402069	+	0.796055i
$795$	1.39790	+	8.07338i	0.0495783	+	0.286333i
$796$	15.5428	+	11.4614i	0.550900	+	0.406239i
$797$	13.9414	+	13.9414i	0.493829	+	0.493829i	0.909510	−	0.415681i	$-0.136457\pi$
$797$	13.9414	+	13.9414i	0.493829	+	0.493829i	−0.415681	+	0.909510i	$0.636457\pi$
$798$		0			0
$799$	8.52950			0.301752
$800$	27.7295	+	5.57456i	0.980385	+	0.197090i
$801$	−1.53111	+	2.65196i	−0.0540992	+	0.0937025i
$802$	8.26676	+	2.71841i	0.291910	+	0.0959902i
$803$	3.62754	−	13.5382i	0.128013	−	0.477751i
$804$	−34.0401	+	14.8679i	−1.20050	+	0.524352i
$805$		0			0
$806$	13.6479	−	20.8540i	0.480726	−	0.734550i
$807$	14.6862	+	3.93515i	0.516978	+	0.138524i
$808$	−4.02717	+	0.380106i	−0.141675	+	0.0133721i
$809$	−4.37439	−	2.52555i	−0.153795	−	0.0887937i	0.421127	−	0.907001i	$-0.361635\pi$
$809$	−4.37439	−	2.52555i	−0.153795	−	0.0887937i	−0.574923	+	0.818208i	$0.694968\pi$
$810$	−1.18489	+	8.04411i	−0.0416329	+	0.282641i
$811$			21.1629i			0.743131i	0.928407	+	0.371565i	$0.121179\pi$
$811$			21.1629i			0.743131i	−0.928407	+	0.371565i	$0.878821\pi$
$812$		0			0
$813$	−5.80185	+	5.80185i	−0.203480	+	0.203480i
$814$	−0.0782451	+	1.39833i	−0.00274249	+	0.0490116i
$815$	8.56522	−	12.1525i	0.300027	−	0.425682i
$816$	12.6689	−	3.91907i	0.443501	−	0.137195i
$817$	−12.7255	+	47.4920i	−0.445207	+	1.66154i
$818$	9.06216	−	1.89274i	0.316851	−	0.0661781i
$819$		0			0
$820$	7.43340	−	14.8558i	0.259586	−	0.518786i
$821$	−21.3620	−	37.0001i	−0.745540	−	1.29131i	−0.949942	−	0.312426i	$-0.898858\pi$
$821$	−21.3620	−	37.0001i	−0.745540	−	1.29131i	0.204402	−	0.978887i	$-0.434475\pi$
$822$	0.638770	−	1.94252i	0.0222797	−	0.0677533i
$823$	−4.61152	+	1.23565i	−0.160748	+	0.0430722i	−0.338295	−	0.941040i	$-0.609850\pi$
$823$	−4.61152	+	1.23565i	−0.160748	+	0.0430722i	0.177548	+	0.984112i	$0.443184\pi$
$824$	−26.9775	+	10.0285i	−0.939804	+	0.349359i
$825$	3.37417	+	4.88263i	0.117474	+	0.169992i
$826$		0			0
$827$	6.21884	−	6.21884i	0.216250	−	0.216250i	−0.590666	−	0.806916i	$-0.701135\pi$
$827$	6.21884	−	6.21884i	0.216250	−	0.216250i	0.806916	+	0.590666i	$0.201135\pi$
$828$	−1.56422	+	0.236416i	−0.0543606	+	0.00821602i
$829$	−33.7077	−	19.4612i	−1.17072	−	0.675915i	−0.216869	−	0.976201i	$-0.569585\pi$
$829$	−33.7077	−	19.4612i	−1.17072	−	0.675915i	−0.953849	+	0.300286i	$0.902918\pi$
$830$	−23.4987	−	10.1588i	−0.815652	−	0.352616i
$831$	4.43367	−	2.55978i	0.153802	−	0.0887978i
$832$	15.5353	+	32.1594i	0.538588	+	1.11493i
$833$		0			0
$834$	−16.8475	+	25.7431i	−0.583383	+	0.891410i
$835$	−17.0271	+	7.87605i	−0.589248	+	0.272562i
$836$	−7.53399	−	0.845791i	−0.260568	−	0.0292523i
$837$	21.1330	−	5.66257i	0.730464	−	0.195727i
$838$	−18.7570	+	16.7691i	−0.647949	+	0.579279i
$839$	−15.0742			−0.520418			−0.260209	−	0.965552i	$-0.583791\pi$
$839$	−15.0742			−0.520418			−0.260209	+	0.965552i	$0.583791\pi$
$840$		0			0
$841$	−23.2844			−0.802910
$842$	17.3621	−	15.5220i	0.598337	−	0.534925i
$843$	−38.8660	+	10.4141i	−1.33862	+	0.358681i
$844$	−20.7385	−	2.32817i	−0.713848	−	0.0801390i
$845$	−5.34545	+	14.5468i	−0.183889	+	0.500424i
$846$	−3.59146	+	5.48776i	−0.123477	+	0.188673i
$847$		0			0
$848$	0.449132	+	11.7489i	0.0154233	+	0.403461i
$849$	−21.0823	+	12.1719i	−0.723543	+	0.417738i
$850$	18.0361	−	5.32335i	0.618633	−	0.182589i
$851$	0.492709	+	0.284465i	0.0168898	+	0.00975135i
$852$	18.7531	−	2.83434i	0.642471	−	0.0971028i
$853$	14.0097	−	14.0097i	0.479684	−	0.479684i	−0.425346	−	0.905031i	$-0.639848\pi$
$853$	14.0097	−	14.0097i	0.479684	−	0.479684i	0.905031	+	0.425346i	$0.139848\pi$
$854$		0			0
$855$	−8.24327	−	9.88570i	−0.281914	−	0.338084i
$856$	−0.0396435	−	0.106644i	−0.00135499	−	0.00364503i
$857$	−34.4324	+	9.22615i	−1.17619	+	0.315159i	−0.793414	−	0.608682i	$-0.791698\pi$
$857$	−34.4324	+	9.22615i	−1.17619	+	0.315159i	−0.382776	+	0.923841i	$0.625032\pi$
$858$	−2.34108	+	7.11932i	−0.0799233	+	0.243049i
$859$	26.2004	+	45.3805i	0.893947	+	1.54836i	0.835103	+	0.550094i	$0.185408\pi$
$859$	26.2004	+	45.3805i	0.893947	+	1.54836i	0.0588442	+	0.998267i	$0.481258\pi$
$860$	52.4046	−	17.4509i	1.78698	−	0.595071i
$861$		0			0
$862$	20.9491	−	4.37546i	0.713528	−	0.149029i
$863$	1.36585	−	5.09743i	0.0464941	−	0.173518i	−0.938775	−	0.344532i	$-0.888038\pi$
$863$	1.36585	−	5.09743i	0.0464941	−	0.173518i	0.985269	+	0.171014i	$0.0547042\pi$
$864$	−8.64899	+	30.1358i	−0.294245	+	1.02524i
$865$	4.04584	+	2.85156i	0.137563	+	0.0969559i
$866$	−0.609393	+	10.8906i	−0.0207080	+	0.370077i
$867$	−8.75067	+	8.75067i	−0.297188	+	0.297188i
$868$		0			0
$869$			10.1859i			0.345535i
$870$	−17.0034	−	22.8779i	−0.576469	−	0.775632i
$871$	−57.6023	−	33.2567i	−1.95178	−	1.12686i
$872$	1.67254	+	17.7203i	0.0566392	+	0.600085i
$873$	−6.09536	−	1.63325i	−0.206297	−	0.0552771i
$874$	−1.68647	+	2.57694i	−0.0570458	+	0.0871662i
$875$		0			0
$876$	−33.6304	+	14.6890i	−1.13627	+	0.496295i
$877$	−2.89005	+	10.7858i	−0.0975901	+	0.364211i	−0.997399	−	0.0720722i	$-0.977039\pi$
$877$	−2.89005	+	10.7858i	−0.0975901	+	0.364211i	0.899809	+	0.436283i	$0.143705\pi$
$878$	34.5887	+	11.3740i	1.16731	+	0.383854i
$879$	−11.1824	+	19.3685i	−0.377174	+	0.653285i
$880$	3.86817	+	7.58761i	0.130396	+	0.255778i
$881$	−22.0701			−0.743561			−0.371781	−	0.928321i	$-0.621253\pi$
$881$	−22.0701			−0.743561			−0.371781	+	0.928321i	$0.621253\pi$
$882$		0			0
$883$	−5.32169	−	5.32169i	−0.179089	−	0.179089i	0.611869	−	0.790959i	$-0.290418\pi$
$883$	−5.32169	−	5.32169i	−0.179089	−	0.179089i	−0.790959	+	0.611869i	$0.790418\pi$
$884$	19.1116	+	14.0930i	0.642792	+	0.474000i
$885$	20.2367	−	28.7122i	0.680250	−	0.965149i
$886$	11.0233	+	21.8250i	0.370335	+	0.733225i
$887$	−4.89193	−	1.31079i	−0.164255	−	0.0440120i	0.175754	−	0.984434i	$-0.443764\pi$
$887$	−4.89193	−	1.31079i	−0.164255	−	0.0440120i	−0.340009	+	0.940422i	$0.610430\pi$
$888$	2.98944	−	2.12385i	0.100319	−	0.0712718i
$889$		0			0
$890$	4.15789	−	5.24983i	0.139373	−	0.175975i
$891$	−2.12030	+	1.22416i	−0.0710327	+	0.0410108i
$892$	−23.7118	+	18.9252i	−0.793929	+	0.633662i
$893$	3.30454	+	12.3327i	0.110582	+	0.412699i
$894$	−1.10421	+	19.7336i	−0.0369303	+	0.659990i
$895$	28.2845	−	23.5853i	0.945448	−	0.788369i
$896$		0			0
$897$	2.15273	+	2.15273i	0.0718774	+	0.0718774i
$898$	10.4625	+	11.7028i	0.349137	+	0.390526i
$899$	−14.2718	+	24.7194i	−0.475990	+	0.824439i
$900$	−4.16937	+	13.8456i	−0.138979	+	0.461521i
$901$	3.90860	+	6.76989i	0.130214	+	0.225538i
$902$	4.89633	−	1.02265i	0.163030	−	0.0340507i
$903$		0			0
$904$	42.7964	+	7.24469i	1.42339	+	0.240955i
$905$	−12.5435	−	4.60930i	−0.416959	−	0.153218i
$906$	−23.6367	+	11.9384i	−0.785277	+	0.396625i
$907$	−0.876735	−	3.27202i	−0.0291115	−	0.108646i	0.949841	−	0.312732i	$-0.101244\pi$
$907$	−0.876735	−	3.27202i	−0.0291115	−	0.108646i	−0.978953	+	0.204087i	$0.934578\pi$
$908$	19.8196	−	2.99552i	0.657736	−	0.0994098i
$909$		−	2.06796i		−	0.0685899i
$910$		0			0
$911$		−	31.5983i		−	1.04690i	−0.852057	−	0.523449i	$-0.824645\pi$
$911$		−	31.5983i		−	1.04690i	0.852057	−	0.523449i	$-0.175355\pi$
$912$	10.5748	+	16.7995i	0.350166	+	0.556287i
$913$	−1.99514	−	7.44597i	−0.0660295	−	0.246426i
$914$	−13.5407	−	26.8091i	−0.447886	−	0.886767i
$915$	7.04919	+	15.2396i	0.233039	+	0.503804i
$916$	−13.6796	−	31.3195i	−0.451988	−	1.03482i
$917$		0			0
$918$	4.26180	+	20.4049i	0.140660	+	0.673462i
$919$	23.1351	+	40.0712i	0.763157	+	1.32183i	0.941215	+	0.337807i	$0.109685\pi$
$919$	23.1351	+	40.0712i	0.763157	+	1.32183i	−0.178058	+	0.984020i	$0.556982\pi$
$920$	3.45971	−	0.0129957i	0.114063	−	0.000428455i
$921$	8.79800	−	15.2386i	0.289904	−	0.502128i
$922$	−9.08446	+	8.12167i	−0.299181	+	0.267473i
$923$	24.0141	+	24.0141i	0.790435	+	0.790435i
$924$		0			0
$925$	4.27804	−	2.95637i	0.140661	−	0.0972047i
$926$	3.26169	+	0.182511i	0.107186	+	0.00599768i
$927$	−3.80821	−	14.2124i	−0.125078	−	0.466797i
$928$	−19.8220	−	35.7797i	−0.650689	−	1.17453i
$929$	−37.0594	+	21.3962i	−1.21588	+	0.701987i	−0.964034	−	0.265780i	$-0.914370\pi$
$929$	−37.0594	+	21.3962i	−1.21588	+	0.701987i	−0.251844	+	0.967768i	$0.581037\pi$
$930$	−15.4577	+	1.79415i	−0.506877	+	0.0588326i
$931$		0			0
$932$	1.36896	−	3.49220i	0.0448418	−	0.114391i
$933$	16.7837	+	4.49719i	0.549475	+	0.147231i
$934$	32.1652	−	16.2459i	1.05248	−	0.531583i
$935$	4.62841	+	3.26216i	0.151365	+	0.106684i
$936$	−17.1144	+	6.36204i	−0.559402	+	0.207950i
$937$	−18.9957	−	18.9957i	−0.620561	−	0.620561i	0.325114	−	0.945675i	$-0.394597\pi$
$937$	−18.9957	−	18.9957i	−0.620561	−	0.620561i	−0.945675	+	0.325114i	$0.894597\pi$
$938$		0			0
$939$	6.11875			0.199678
$940$	9.51942	−	10.7287i	0.310489	−	0.349933i
$941$	−10.8404	+	18.7762i	−0.353388	+	0.612086i	−0.986841	−	0.161696i	$-0.948304\pi$
$941$	−10.8404	+	18.7762i	−0.353388	+	0.612086i	0.633453	+	0.773781i	$0.281637\pi$
$942$	−4.14590	+	12.6078i	−0.135081	+	0.410785i
$943$	0.525906	−	1.96271i	0.0171258	−	0.0639145i
$944$	34.2554	−	36.9785i	1.11492	−	1.20355i
$945$		0			0
$946$	13.9163	+	9.10749i	0.452457	+	0.296110i
$947$	−14.8363	−	3.97536i	−0.482114	−	0.129182i	0.00957300	−	0.999954i	$-0.496953\pi$
$947$	−14.8363	−	3.97536i	−0.482114	−	0.129182i	−0.491687	+	0.870772i	$0.663619\pi$
$948$	20.8452	−	16.6373i	0.677019	−	0.540353i
$949$	−56.9090	−	32.8564i	−1.84735	−	1.06657i
$950$	14.6846	+	24.0158i	0.476432	+	0.779177i
$951$		−	42.8869i		−	1.39070i
$952$		0			0
$953$	22.0087	−	22.0087i	0.712931	−	0.712931i	−0.254216	−	0.967147i	$-0.581817\pi$
$953$	22.0087	−	22.0087i	0.712931	−	0.712931i	0.967147	+	0.254216i	$0.0818174\pi$
$954$	−6.00141	−	0.335815i	−0.194303	−	0.0108724i
$955$	17.7283	−	3.06964i	0.573674	−	0.0993311i
$956$	3.39557	−	30.2465i	0.109821	−	0.978240i
$957$	2.22146	−	8.29061i	0.0718096	−	0.267997i
$958$	2.68274	+	12.8446i	0.0866755	+	0.414990i
$959$		0			0
$960$	9.20968	−	20.3093i	0.297241	−	0.655481i
$961$	−7.70864	−	13.3518i	−0.248666	−	0.430702i
$962$	6.23777	+	2.05120i	0.201114	+	0.0661333i
$963$	0.0561830	−	0.0150542i	0.00181047	−	0.000485114i
$964$	21.2084	+	15.6393i	0.683078	+	0.503708i
$965$	−2.93747	+	32.4235i	−0.0945604	+	1.04375i
$966$		0			0
$967$	−16.9281	+	16.9281i	−0.544372	+	0.544372i	−0.924807	−	0.380435i	$-0.875774\pi$
$967$	−16.9281	+	16.9281i	−0.544372	+	0.544372i	0.380435	+	0.924807i	$0.375774\pi$
$968$	11.8877	−	25.9554i	0.382086	−	0.834238i
$969$	11.4299	+	6.59904i	0.367180	+	0.211992i
$970$	12.6674	+	5.47628i	0.406727	+	0.175833i
$971$	32.1198	−	18.5444i	1.03077	−	0.595118i	0.113568	−	0.993530i	$-0.463772\pi$
$971$	32.1198	−	18.5444i	1.03077	−	0.595118i	0.917206	+	0.398412i	$0.130439\pi$
$972$	−24.9920	−	9.79698i	−0.801620	−	0.314238i
$973$		0			0
$974$	21.0739	+	13.7918i	0.675251	+	0.441918i
$975$	26.2067	−	9.35584i	0.839287	−	0.299627i
$976$	7.12065	+	23.0185i	0.227926	+	0.736803i
$977$	−22.5762	+	6.04928i	−0.722277	+	0.193534i	−0.601188	−	0.799108i	$-0.705306\pi$
$977$	−22.5762	+	6.04928i	−0.722277	+	0.193534i	−0.121090	+	0.992642i	$0.538639\pi$
$978$	−7.81264	−	8.73879i	−0.249821	−	0.279436i
$979$	2.01652			0.0644484
$980$		0			0
$981$	−9.09942			−0.290522
$982$	2.35614	+	2.63545i	0.0751875	+	0.0841006i
$983$	−19.2069	+	5.14648i	−0.612606	+	0.164147i	−0.551764	−	0.834000i	$-0.686045\pi$
$983$	−19.2069	+	5.14648i	−0.612606	+	0.164147i	−0.0608417	+	0.998147i	$0.519378\pi$
$984$	−10.0903	−	8.34979i	−0.321666	−	0.266182i
$985$	−21.8946	−	47.3336i	−0.697619	−	1.50817i
$986$	−22.7555	−	14.8923i	−0.724682	−	0.474268i
$987$		0			0
$988$	−12.9727	+	33.0932i	−0.412716	+	1.05284i
$989$	5.85104	−	3.37810i	0.186052	−	0.107417i
$990$	−4.04768	+	1.60427i	−0.128644	+	0.0509872i
$991$	−19.5362	−	11.2792i	−0.620586	−	0.358296i	0.156511	−	0.987676i	$-0.449975\pi$
$991$	−19.5362	−	11.2792i	−0.620586	−	0.358296i	−0.777097	+	0.629380i	$0.783309\pi$
$992$	−22.3269	−	0.394977i	−0.708880	−	0.0125405i
$993$	11.4204	−	11.4204i	0.362414	−	0.362414i
$994$		0			0
$995$	16.5825	−	13.8275i	0.525701	−	0.438360i
$996$	−11.9791	+	16.2449i	−0.379573	+	0.514739i
$997$	16.6372	−	4.45792i	0.526905	−	0.141184i	0.0144466	−	0.999896i	$-0.495401\pi$
$997$	16.6372	−	4.45792i	0.526905	−	0.141184i	0.512459	+	0.858712i	$0.328735\pi$
$998$	8.76459	+	2.88211i	0.277438	+	0.0912315i
$999$	2.88213	+	4.99199i	0.0911865	+	0.157940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.67.5		72
4.3	odd	2	inner	980.2.x.m.67.11		72
5.3	odd	4	inner	980.2.x.m.263.14		72
7.2	even	3	inner	980.2.x.m.667.17		72
7.3	odd	6		980.2.k.k.687.8		36
7.4	even	3		980.2.k.j.687.8		36
7.5	odd	6		140.2.w.b.107.17	yes	72
7.6	odd	2		140.2.w.b.67.5	yes	72
20.3	even	4	inner	980.2.x.m.263.17		72
28.3	even	6		980.2.k.k.687.1		36
28.11	odd	6		980.2.k.j.687.1		36
28.19	even	6		140.2.w.b.107.14	yes	72
28.23	odd	6	inner	980.2.x.m.667.14		72
28.27	even	2		140.2.w.b.67.11	yes	72
35.3	even	12		980.2.k.k.883.1		36
35.12	even	12		700.2.be.e.443.8		72
35.13	even	4		140.2.w.b.123.14	yes	72
35.18	odd	12		980.2.k.j.883.1		36
35.19	odd	6		700.2.be.e.107.2		72
35.23	odd	12	inner	980.2.x.m.863.11		72
35.27	even	4		700.2.be.e.543.5		72
35.33	even	12		140.2.w.b.23.11	yes	72
35.34	odd	2		700.2.be.e.207.14		72
140.3	odd	12		980.2.k.k.883.8		36
140.19	even	6		700.2.be.e.107.5		72
140.23	even	12	inner	980.2.x.m.863.5		72
140.27	odd	4		700.2.be.e.543.2		72
140.47	odd	12		700.2.be.e.443.14		72
140.83	odd	4		140.2.w.b.123.17	yes	72
140.103	odd	12		140.2.w.b.23.5	✓	72
140.123	even	12		980.2.k.j.883.8		36
140.139	even	2		700.2.be.e.207.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	140.103	odd	12
140.2.w.b.23.11	yes	72	35.33	even	12
140.2.w.b.67.5	yes	72	7.6	odd	2
140.2.w.b.67.11	yes	72	28.27	even	2
140.2.w.b.107.14	yes	72	28.19	even	6
140.2.w.b.107.17	yes	72	7.5	odd	6
140.2.w.b.123.14	yes	72	35.13	even	4
140.2.w.b.123.17	yes	72	140.83	odd	4
700.2.be.e.107.2		72	35.19	odd	6
700.2.be.e.107.5		72	140.19	even	6
700.2.be.e.207.8		72	140.139	even	2
700.2.be.e.207.14		72	35.34	odd	2
700.2.be.e.443.8		72	35.12	even	12
700.2.be.e.443.14		72	140.47	odd	12
700.2.be.e.543.2		72	140.27	odd	4
700.2.be.e.543.5		72	35.27	even	4
980.2.k.j.687.1		36	28.11	odd	6
980.2.k.j.687.8		36	7.4	even	3
980.2.k.j.883.1		36	35.18	odd	12
980.2.k.j.883.8		36	140.123	even	12
980.2.k.k.687.1		36	28.3	even	6
980.2.k.k.687.8		36	7.3	odd	6
980.2.k.k.883.1		36	35.3	even	12
980.2.k.k.883.8		36	140.3	odd	12
980.2.x.m.67.5		72	1.1	even	1	trivial
980.2.x.m.67.11		72	4.3	odd	2	inner
980.2.x.m.263.14		72	5.3	odd	4	inner
980.2.x.m.263.17		72	20.3	even	4	inner
980.2.x.m.667.14		72	28.23	odd	6	inner
980.2.x.m.667.17		72	7.2	even	3	inner
980.2.x.m.863.5		72	140.23	even	12	inner
980.2.x.m.863.11		72	35.23	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05431 + 0.942570i) q^{2} +(1.20413 - 0.322645i) q^{3} +(0.223125 - 1.98751i) q^{4} +(-2.09885 - 0.771256i) q^{5} +(-0.965404 + 1.47514i) q^{6} +(1.63813 + 2.30576i) q^{8} +(-1.25225 + 0.722989i) q^{9} +(2.93979 - 1.16517i) q^{10} +(0.824629 + 0.476100i) q^{11} +(-0.372591 - 2.46521i) q^{12} +(3.15680 - 3.15680i) q^{13} +(-2.77612 - 0.251508i) q^{15} +(-3.90043 - 0.886929i) q^{16} +(-2.56885 + 0.688322i) q^{17} +(0.638792 - 1.94259i) q^{18} +(-1.99048 - 3.44760i) q^{19} +(-2.00119 + 3.99941i) q^{20} +(-1.31817 + 0.275315i) q^{22} +(-0.141582 + 0.528392i) q^{23} +(2.71646 + 2.24790i) q^{24} +(3.81033 + 3.23750i) q^{25} +(-0.352732 + 6.30375i) q^{26} +(-3.91905 + 3.91905i) q^{27} -7.23080i q^{29} +(3.16395 - 2.35152i) q^{30} +(-3.41863 - 1.97375i) q^{31} +(4.94824 - 2.74133i) q^{32} +(1.14657 + 0.307222i) q^{33} +(2.05957 - 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(0.269180 - 1.00460i) q^{37} +(5.34818 + 1.75867i) q^{38} +(2.78267 - 4.81972i) q^{39} +(-1.65985 - 6.10286i) q^{40} -3.71449 q^{41} +(-8.73324 - 8.73324i) q^{43} +(1.13025 - 1.53273i) q^{44} +(3.18590 - 0.551635i) q^{45} +(-0.348775 - 0.690538i) q^{46} +(-3.09794 - 0.830089i) q^{47} +(-4.98278 + 0.190479i) q^{48} +(-7.06882 + 0.178182i) q^{50} +(-2.87114 + 1.65765i) q^{51} +(-5.56983 - 6.97856i) q^{52} +(-0.760768 - 2.83923i) q^{53} +(0.437903 - 7.82586i) q^{54} +(-1.36358 - 1.63526i) q^{55} +(-3.50914 - 3.50914i) q^{57} +(6.81553 + 7.62348i) q^{58} +(-6.30084 + 10.9134i) q^{59} +(-1.11930 + 5.46147i) q^{60} +(-3.01183 - 5.21665i) q^{61} +(5.46468 - 1.14136i) q^{62} +(-2.63307 + 7.55427i) q^{64} +(-9.06036 + 4.19095i) q^{65} +(-1.49841 + 0.756815i) q^{66} +(-3.85605 - 14.3910i) q^{67} +(0.794874 + 5.25921i) q^{68} +0.681932i q^{69} +7.60710i q^{71} +(-3.71839 - 1.70305i) q^{72} +(-3.80964 - 14.2178i) q^{73} +(0.663102 + 1.31287i) q^{74} +(5.63268 + 2.66898i) q^{75} +(-7.29629 + 3.18685i) q^{76} +(1.60914 + 7.70432i) q^{78} +(5.34864 + 9.26412i) q^{79} +(7.50236 + 4.86976i) q^{80} +(-1.28561 + 2.22674i) q^{81} +(3.91621 - 3.50117i) q^{82} +(-5.72446 - 5.72446i) q^{83} +(5.92250 + 0.536560i) q^{85} +(17.4392 + 0.975826i) q^{86} +(-2.33298 - 8.70680i) q^{87} +(0.253076 + 2.68131i) q^{88} +(1.83403 - 1.05888i) q^{89} +(-2.83896 + 3.58452i) q^{90} +(1.01860 + 0.399294i) q^{92} +(-4.75329 - 1.27364i) q^{93} +(4.04859 - 2.04485i) q^{94} +(1.51872 + 8.77117i) q^{95} +(5.07384 - 4.89744i) q^{96} +(3.08588 + 3.08588i) q^{97} -1.37686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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