LMFDB - Embedded newform 396.2.w.a.71.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(71,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 4]))

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

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

chi := DirichletCharacter("396.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			71.7
Character	$\chi$	$=$	396.71
Dual form			396.2.w.a.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.961537 + 1.03704i) q^{2} +(-0.150891 - 1.99430i) q^{4} +(-3.05406 - 0.992323i) q^{5} +(1.53508 + 2.11286i) q^{7} +(2.21325 + 1.76111i) q^{8} +O(q^{10})$	\(q+(-0.961537 + 1.03704i) q^{2} +(-0.150891 - 1.99430i) q^{4} +(-3.05406 - 0.992323i) q^{5} +(1.53508 + 2.11286i) q^{7} +(2.21325 + 1.76111i) q^{8} +(3.96566 - 2.21301i) q^{10} +(-1.44061 - 2.98741i) q^{11} +(0.510980 + 1.57264i) q^{13} +(-3.66715 - 0.439656i) q^{14} +(-3.95446 + 0.601846i) q^{16} +(6.92800 + 2.25104i) q^{17} +(4.52170 - 6.22358i) q^{19} +(-1.51816 + 6.24044i) q^{20} +(4.48326 + 1.37854i) q^{22} +7.73311 q^{23} +(4.29747 + 3.12229i) q^{25} +(-2.12221 - 0.982242i) q^{26} +(3.98204 - 3.38023i) q^{28} +(2.59390 + 3.57020i) q^{29} +(0.800604 - 0.260132i) q^{31} +(3.17823 - 4.67962i) q^{32} +(-8.99595 + 5.02013i) q^{34} +(-2.59159 - 7.97609i) q^{35} +(-2.62566 + 1.90766i) q^{37} +(2.10630 + 10.6734i) q^{38} +(-5.01180 - 7.57480i) q^{40} +(-3.38435 + 4.65816i) q^{41} -4.30942i q^{43} +(-5.74042 + 3.32378i) q^{44} +(-7.43567 + 8.01952i) q^{46} +(-1.82404 - 1.32524i) q^{47} +(0.0554224 - 0.170573i) q^{49} +(-7.37011 + 1.45443i) q^{50} +(3.05920 - 1.25634i) q^{52} +(5.63776 - 1.83182i) q^{53} +(1.43522 + 10.5533i) q^{55} +(-0.323464 + 7.37974i) q^{56} +(-6.19657 - 0.742909i) q^{58} +(0.425469 - 0.309122i) q^{59} +(-1.35376 + 4.16644i) q^{61} +(-0.500044 + 1.08038i) q^{62} +(1.79696 + 7.79557i) q^{64} -5.30997i q^{65} +4.09015i q^{67} +(3.44388 - 14.1562i) q^{68} +(10.7634 + 4.98173i) q^{70} +(2.71519 - 8.35649i) q^{71} +(-2.01619 + 1.46485i) q^{73} +(0.546363 - 4.55719i) q^{74} +(-13.0940 - 8.07853i) q^{76} +(4.10053 - 7.62973i) q^{77} +(4.59951 - 1.49447i) q^{79} +(12.6744 + 2.08603i) q^{80} +(-1.57650 - 7.98869i) q^{82} +(-0.154218 + 0.474633i) q^{83} +(-18.9247 - 13.7496i) q^{85} +(4.46903 + 4.14367i) q^{86} +(2.07275 - 9.14897i) q^{88} -11.8056i q^{89} +(-2.53836 + 3.49375i) q^{91} +(-1.16686 - 15.4221i) q^{92} +(3.12820 - 0.617326i) q^{94} +(-19.9853 + 14.5202i) q^{95} +(-2.43497 - 7.49407i) q^{97} +(0.123599 + 0.221487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{10} + 32 q^{16} + 60 q^{22} + 8 q^{25} - 12 q^{28} + 24 q^{34} + 16 q^{40} - 40 q^{46} + 40 q^{49} - 32 q^{52} - 80 q^{58} - 72 q^{64} - 48 q^{70} - 24 q^{73} - 136 q^{76} - 132 q^{82} - 48 q^{85} - 64 q^{88} - 80 q^{94} - 80 q^{97}+O(q^{100}) $ 96 * q - 16 * q^10 + 32 * q^16 + 60 * q^22 + 8 * q^25 - 12 * q^28 + 24 * q^34 + 16 * q^40 - 40 * q^46 + 40 * q^49 - 32 * q^52 - 80 * q^58 - 72 * q^64 - 48 * q^70 - 24 * q^73 - 136 * q^76 - 132 * q^82 - 48 * q^85 - 64 * q^88 - 80 * q^94 - 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.961537	+	1.03704i	−0.679910	+	0.733296i
$2$	−0.961537	+	1.03704i	−0.679910	+	0.733296i
$3$		0			0
$3$		0			0
$4$	−0.150891	−	1.99430i	−0.0754457	−	0.997150i
$5$	−3.05406	−	0.992323i	−1.36582	−	0.443780i	−0.467835	−	0.883816i	$-0.654966\pi$
$5$	−3.05406	−	0.992323i	−1.36582	−	0.443780i	−0.897980	+	0.440036i	$0.854966\pi$
$6$		0			0
$7$	1.53508	+	2.11286i	0.580206	+	0.798586i	0.993718	−	0.111913i	$-0.0356979\pi$
$7$	1.53508	+	2.11286i	0.580206	+	0.798586i	−0.413512	+	0.910499i	$0.635698\pi$
$8$	2.21325	+	1.76111i	0.782502	+	0.622648i
$9$		0			0
$10$	3.96566	−	2.21301i	1.25405	−	0.699816i
$11$	−1.44061	−	2.98741i	−0.434360	−	0.900739i
$11$	−1.44061	−	2.98741i	−0.434360	−	0.900739i
$12$		0			0
$13$	0.510980	+	1.57264i	0.141720	+	0.436171i	0.996575	−	0.0826976i	$-0.0263536\pi$
$13$	0.510980	+	1.57264i	0.141720	+	0.436171i	−0.854854	+	0.518868i	$0.826354\pi$
$14$	−3.66715	−	0.439656i	−0.980088	−	0.117503i
$15$		0			0
$16$	−3.95446	+	0.601846i	−0.988616	+	0.150461i
$17$	6.92800	+	2.25104i	1.68029	+	0.545958i	0.984967	−	0.172742i	$-0.0552628\pi$
$17$	6.92800	+	2.25104i	1.68029	+	0.545958i	0.695320	+	0.718701i	$0.255263\pi$
$18$		0			0
$19$	4.52170	−	6.22358i	1.03735	−	1.42779i	0.138064	−	0.990423i	$-0.455912\pi$
$19$	4.52170	−	6.22358i	1.03735	−	1.42779i	0.899284	−	0.437364i	$-0.144088\pi$
$20$	−1.51816	+	6.24044i	−0.339470	+	1.39540i
$21$		0			0
$22$	4.48326	+	1.37854i	0.955834	+	0.293907i
$23$	7.73311			1.61246			0.806232	−	0.591599i	$-0.201503\pi$
$23$	7.73311			1.61246			0.806232	+	0.591599i	$0.201503\pi$
$24$		0			0
$25$	4.29747	+	3.12229i	0.859493	+	0.624458i
$26$	−2.12221	−	0.982242i	−0.416199	−	0.192634i
$27$		0			0
$28$	3.98204	−	3.38023i	0.752535	−	0.638803i
$29$	2.59390	+	3.57020i	0.481676	+	0.662970i	0.978826	−	0.204695i	$-0.0656201\pi$
$29$	2.59390	+	3.57020i	0.481676	+	0.662970i	−0.497150	+	0.867665i	$0.665620\pi$
$30$		0			0
$31$	0.800604	−	0.260132i	0.143793	−	0.0467211i	−0.236236	−	0.971696i	$-0.575914\pi$
$31$	0.800604	−	0.260132i	0.143793	−	0.0467211i	0.380029	+	0.924975i	$0.375914\pi$
$32$	3.17823	−	4.67962i	0.561837	−	0.827248i
$33$		0			0
$34$	−8.99595	+	5.02013i	−1.54279	+	0.860945i
$35$	−2.59159	−	7.97609i	−0.438058	−	1.34820i
$36$		0			0
$37$	−2.62566	+	1.90766i	−0.431656	+	0.313617i	−0.782311	−	0.622888i	$-0.785959\pi$
$37$	−2.62566	+	1.90766i	−0.431656	+	0.313617i	0.350655	+	0.936505i	$0.385959\pi$
$38$	2.10630	+	10.6734i	0.341688	+	1.73145i
$39$		0			0
$40$	−5.01180	−	7.57480i	−0.792435	−	1.19768i
$41$	−3.38435	+	4.65816i	−0.528547	+	0.727482i	−0.986908	−	0.161284i	$-0.948437\pi$
$41$	−3.38435	+	4.65816i	−0.528547	+	0.727482i	0.458361	+	0.888766i	$0.348437\pi$
$42$		0			0
$43$		−	4.30942i		−	0.657180i	−0.944473	−	0.328590i	$-0.893427\pi$
$43$		−	4.30942i		−	0.657180i	0.944473	−	0.328590i	$-0.106573\pi$
$44$	−5.74042	+	3.32378i	−0.865401	+	0.501079i
$45$		0			0
$46$	−7.43567	+	8.01952i	−1.09633	+	1.18241i
$47$	−1.82404	−	1.32524i	−0.266063	−	0.193306i	0.446753	−	0.894658i	$-0.352580\pi$
$47$	−1.82404	−	1.32524i	−0.266063	−	0.193306i	−0.712816	+	0.701351i	$0.752580\pi$
$48$		0			0
$49$	0.0554224	−	0.170573i	0.00791748	−	0.0243675i
$50$	−7.37011	+	1.45443i	−1.04229	+	0.205688i
$51$		0			0
$52$	3.05920	−	1.25634i	0.424235	−	0.174224i
$53$	5.63776	−	1.83182i	0.774406	−	0.251620i	0.104956	−	0.994477i	$-0.466530\pi$
$53$	5.63776	−	1.83182i	0.774406	−	0.251620i	0.669450	+	0.742857i	$0.266530\pi$
$54$		0			0
$55$	1.43522	+	10.5533i	0.193525	+	1.42300i
$56$	−0.323464	+	7.37974i	−0.0432248	+	0.986159i
$57$		0			0
$58$	−6.19657	−	0.742909i	−0.813649	−	0.0975487i
$59$	0.425469	−	0.309122i	0.0553914	−	0.0402442i	−0.559745	−	0.828665i	$-0.689101\pi$
$59$	0.425469	−	0.309122i	0.0553914	−	0.0402442i	0.615136	+	0.788421i	$0.289101\pi$
$60$		0			0
$61$	−1.35376	+	4.16644i	−0.173331	+	0.533458i	−0.999553	−	0.0298861i	$-0.990486\pi$
$61$	−1.35376	+	4.16644i	−0.173331	+	0.533458i	0.826222	+	0.563344i	$0.190486\pi$
$62$	−0.500044	+	1.08038i	−0.0635057	+	0.137209i
$63$		0			0
$64$	1.79696	+	7.79557i	0.224619	+	0.974447i
$65$		−	5.30997i		−	0.658621i
$66$		0			0
$67$			4.09015i			0.499692i	0.968286	+	0.249846i	$0.0803799\pi$
$67$			4.09015i			0.499692i	−0.968286	+	0.249846i	$0.919620\pi$
$68$	3.44388	−	14.1562i	0.417632	−	1.71669i
$69$		0			0
$70$	10.7634	+	4.98173i	1.28647	+	0.595431i
$71$	2.71519	−	8.35649i	0.322233	−	0.991732i	−0.650441	−	0.759557i	$-0.725416\pi$
$71$	2.71519	−	8.35649i	0.322233	−	0.991732i	0.972674	−	0.232175i	$-0.0745843\pi$
$72$		0			0
$73$	−2.01619	+	1.46485i	−0.235977	+	0.171447i	−0.699489	−	0.714643i	$-0.746589\pi$
$73$	−2.01619	+	1.46485i	−0.235977	+	0.171447i	0.463512	+	0.886091i	$0.346589\pi$
$74$	0.546363	−	4.55719i	0.0635135	−	0.529763i
$75$		0			0
$76$	−13.0940	−	8.07853i	−1.50198	−	0.926671i
$77$	4.10053	−	7.62973i	0.467299	−	0.869489i
$78$		0			0
$79$	4.59951	−	1.49447i	0.517485	−	0.168141i	−0.0386186	−	0.999254i	$-0.512296\pi$
$79$	4.59951	−	1.49447i	0.517485	−	0.168141i	0.556104	+	0.831113i	$0.312296\pi$
$80$	12.6744	+	2.08603i	1.41704	+	0.233226i
$81$		0			0
$82$	−1.57650	−	7.98869i	−0.174096	−	0.882203i
$83$	−0.154218	+	0.474633i	−0.0169276	+	0.0520978i	−0.959164	−	0.282852i	$-0.908719\pi$
$83$	−0.154218	+	0.474633i	−0.0169276	+	0.0520978i	0.942236	+	0.334950i	$0.108719\pi$
$84$		0			0
$85$	−18.9247	−	13.7496i	−2.05268	−	1.49136i
$86$	4.46903	+	4.14367i	0.481907	+	0.446823i
$87$		0			0
$88$	2.07275	−	9.14897i	0.220955	−	0.975284i
$89$		−	11.8056i		−	1.25139i	−0.780068	−	0.625695i	$-0.784816\pi$
$89$		−	11.8056i		−	1.25139i	0.780068	−	0.625695i	$-0.215184\pi$
$90$		0			0
$91$	−2.53836	+	3.49375i	−0.266092	+	0.366245i
$92$	−1.16686	−	15.4221i	−0.121654	−	1.60787i
$93$		0			0
$94$	3.12820	−	0.617326i	0.322650	−	0.0636723i
$95$	−19.9853	+	14.5202i	−2.05045	+	1.48974i
$96$		0			0
$97$	−2.43497	−	7.49407i	−0.247234	−	0.760907i	−0.995261	−	0.0972393i	$-0.968999\pi$
$97$	−2.43497	−	7.49407i	−0.247234	−	0.760907i	0.748027	−	0.663668i	$-0.231001\pi$
$98$	0.123599	+	0.221487i	0.0124854	+	0.0223736i
$99$		0			0
$100$	5.57833	−	9.04156i	0.557833	−	0.904156i
$101$	−4.92146	+	1.59908i	−0.489704	+	0.159114i	−0.543452	−	0.839440i	$-0.682883\pi$
$101$	−4.92146	+	1.59908i	−0.489704	+	0.159114i	0.0537484	+	0.998555i	$0.482883\pi$
$102$		0			0
$103$	9.20341	+	12.6674i	0.906839	+	1.24816i	0.968235	+	0.250043i	$0.0804447\pi$
$103$	9.20341	+	12.6674i	0.906839	+	1.24816i	−0.0613962	+	0.998113i	$0.519555\pi$
$104$	−1.63866	+	4.38053i	−0.160684	+	0.429546i
$105$		0			0
$106$	−3.52125	+	7.60793i	−0.342014	+	0.738947i
$107$	−6.78678	−	4.93088i	−0.656102	−	0.476686i	0.209242	−	0.977864i	$-0.432900\pi$
$107$	−6.78678	−	4.93088i	−0.656102	−	0.476686i	−0.865344	+	0.501178i	$0.832900\pi$
$108$		0			0
$109$	13.0022			1.24539			0.622694	−	0.782465i	$-0.286038\pi$
$109$	13.0022			1.24539			0.622694	+	0.782465i	$0.286038\pi$
$110$	−12.3242	−	8.65899i	−1.17506	−	0.825603i
$111$		0			0
$112$	−7.34204	−	7.43134i	−0.693758	−	0.702196i
$113$	−7.02673	+	9.67147i	−0.661020	+	0.909815i	−0.999515	−	0.0311528i	$-0.990082\pi$
$113$	−7.02673	+	9.67147i	−0.661020	+	0.909815i	0.338495	+	0.940968i	$0.390082\pi$
$114$		0			0
$115$	−23.6173	−	7.67374i	−2.20233	−	0.715580i
$116$	6.72866	−	5.71174i	0.624740	−	0.530321i
$117$		0			0
$118$	−0.0885342	+	0.738460i	−0.00815024	+	0.0679807i
$119$	5.87891	+	18.0934i	0.538919	+	1.65862i
$120$		0			0
$121$	−6.84929	+	8.60740i	−0.622662	+	0.782491i
$122$	−3.01906	−	5.41009i	−0.273333	−	0.489806i
$123$		0			0
$124$	−0.639586	−	1.55739i	−0.0574365	−	0.139858i
$125$	−0.588827	−	0.810451i	−0.0526663	−	0.0724889i
$126$		0			0
$127$	−12.9692	−	4.21394i	−1.15083	−	0.373927i	−0.329373	−	0.944200i	$-0.606837\pi$
$127$	−12.9692	−	4.21394i	−1.15083	−	0.373927i	−0.821455	+	0.570273i	$0.806837\pi$
$128$	−9.81214	−	5.63223i	−0.867279	−	0.497823i
$129$		0			0
$130$	5.50664	+	5.10574i	0.482964	+	0.447803i
$131$	18.6625			1.63055			0.815275	−	0.579074i	$-0.196586\pi$
$131$	18.6625			1.63055			0.815275	+	0.579074i	$0.196586\pi$
$132$		0			0
$133$	20.0907			1.74209
$134$	−4.24164	−	3.93283i	−0.366422	−	0.339745i
$135$		0			0
$136$	11.3691	+	17.1831i	0.974888	+	1.47344i
$137$	−11.1269	−	3.61535i	−0.950635	−	0.308880i	−0.207661	−	0.978201i	$-0.566585\pi$
$137$	−11.1269	−	3.61535i	−0.950635	−	0.308880i	−0.742973	+	0.669321i	$0.766585\pi$
$138$		0			0
$139$	−4.84927	−	6.67444i	−0.411309	−	0.566119i	0.552228	−	0.833693i	$-0.313778\pi$
$139$	−4.84927	−	6.67444i	−0.411309	−	0.566119i	−0.963537	+	0.267574i	$0.913778\pi$
$140$	−15.5157	+	6.37193i	−1.31131	+	0.538526i
$141$		0			0
$142$	6.05523	+	10.8508i	0.508144	+	0.910581i
$143$	3.96199	−	3.79206i	0.331318	−	0.317108i
$144$		0			0
$145$	−4.37913	−	13.4776i	−0.363667	−	1.11925i
$146$	0.419540	−	3.49937i	0.0347214	−	0.289610i
$147$		0			0
$148$	4.20063	+	4.94851i	0.345289	+	0.406765i
$149$	−9.09641	−	2.95560i	−0.745207	−	0.242132i	−0.0882892	−	0.996095i	$-0.528140\pi$
$149$	−9.09641	−	2.95560i	−0.745207	−	0.242132i	−0.656917	+	0.753963i	$0.728140\pi$
$150$		0			0
$151$	10.0650	−	13.8532i	0.819075	−	1.12736i	−0.170785	−	0.985308i	$-0.554630\pi$
$151$	10.0650	−	13.8532i	0.819075	−	1.12736i	0.989859	−	0.142051i	$-0.0453697\pi$
$152$	20.9681	−	5.81112i	1.70074	−	0.471344i
$153$		0			0
$154$	3.96950	+	11.5887i	0.319871	+	0.933842i
$155$	−2.70322			−0.217128
$156$		0			0
$157$	0.208184	+	0.151255i	0.0166149	+	0.0120715i	0.596062	−	0.802939i	$-0.296731\pi$
$157$	0.208184	+	0.151255i	0.0166149	+	0.0120715i	−0.579447	+	0.815010i	$0.696731\pi$
$158$	−2.87278	+	6.20685i	−0.228546	+	0.493790i
$159$		0			0
$160$	−14.3502	+	11.1380i	−1.13448	+	0.880536i
$161$	11.8710	+	16.3390i	0.935562	+	1.28769i
$162$		0			0
$163$	4.80438	−	1.56104i	0.376308	−	0.122270i	−0.114755	−	0.993394i	$-0.536608\pi$
$163$	4.80438	−	1.56104i	0.376308	−	0.122270i	0.491063	+	0.871124i	$0.336608\pi$
$164$	9.80043	+	6.04653i	0.765285	+	0.472155i
$165$		0			0
$166$	−0.343926	−	0.616307i	−0.0266938	−	0.0478347i
$167$	3.15832	+	9.72031i	0.244398	+	0.752180i	0.995735	+	0.0922611i	$0.0294095\pi$
$167$	3.15832	+	9.72031i	0.244398	+	0.752180i	−0.751337	+	0.659919i	$0.770591\pi$
$168$		0			0
$169$	8.30514	−	6.03404i	0.638857	−	0.464157i
$170$	32.4557	−	6.40487i	2.48924	−	0.491231i
$171$		0			0
$172$	−8.59427	+	0.650255i	−0.655307	+	0.0495814i
$173$	−0.991909	+	1.36525i	−0.0754135	+	0.103798i	−0.845057	−	0.534676i	$-0.820434\pi$
$173$	−0.991909	+	1.36525i	−0.0754135	+	0.103798i	0.769644	+	0.638473i	$0.220434\pi$
$174$		0			0
$175$			13.8729i			1.04869i
$176$	7.49480	+	10.9466i	0.564942	+	0.825131i
$177$		0			0
$178$	12.2428	+	11.3515i	0.917638	+	0.850831i
$179$	4.46528	+	3.24422i	0.333751	+	0.242484i	0.742021	−	0.670377i	$-0.233868\pi$
$179$	4.46528	+	3.24422i	0.333751	+	0.242484i	−0.408270	+	0.912861i	$0.633868\pi$
$180$		0			0
$181$	−7.57701	+	23.3196i	−0.563195	+	1.73333i	0.110061	+	0.993925i	$0.464895\pi$
$181$	−7.57701	+	23.3196i	−0.563195	+	1.73333i	−0.673256	+	0.739410i	$0.735105\pi$
$182$	−1.18242	−	5.99175i	−0.0876470	−	0.444138i
$183$		0			0
$184$	17.1153	+	13.6189i	1.26176	+	1.00400i
$185$	9.91193	−	3.22058i	0.728739	−	0.236782i
$186$		0			0
$187$	−3.25574	−	23.9397i	−0.238084	−	1.75064i
$188$	−2.36770	+	3.83765i	−0.172682	+	0.279889i
$189$		0			0
$190$	4.15866	−	34.6872i	0.301701	−	2.51647i
$191$	−6.94603	+	5.04659i	−0.502597	+	0.365158i	−0.810008	−	0.586419i	$-0.800537\pi$
$191$	−6.94603	+	5.04659i	−0.502597	+	0.365158i	0.307411	+	0.951577i	$0.400537\pi$
$192$		0			0
$193$	−0.642645	+	1.97786i	−0.0462586	+	0.142369i	−0.971518	−	0.236965i	$-0.923847\pi$
$193$	−0.642645	+	1.97786i	−0.0462586	+	0.142369i	0.925259	+	0.379335i	$0.123847\pi$
$194$	10.1129	+	4.68067i	0.726067	+	0.336053i
$195$		0			0
$196$	−0.348536	−	0.0847909i	−0.0248954	−	0.00605649i
$197$			14.1317i			1.00685i	0.864040	+	0.503423i	$0.167926\pi$
$197$			14.1317i			1.00685i	−0.864040	+	0.503423i	$0.832074\pi$
$198$		0			0
$199$			10.2051i			0.723417i	0.932291	+	0.361709i	$0.117806\pi$
$199$			10.2051i			0.723417i	−0.932291	+	0.361709i	$0.882194\pi$
$200$	4.01266	+	14.4787i	0.283738	+	1.02380i
$201$		0			0
$202$	3.07387	−	6.64131i	0.216276	−	0.467281i
$203$	−3.56148	+	10.9611i	−0.249967	+	0.769319i
$204$		0			0
$205$	14.9584	−	10.8679i	1.04474	−	0.759047i
$206$	−21.9860	−	2.63591i	−1.53184	−	0.183652i
$207$		0			0
$208$	−2.96714	−	5.91140i	−0.205734	−	0.409882i
$209$	−25.1064	−	4.54243i	−1.73665	−	0.314206i
$210$		0			0
$211$	−21.2998	+	6.92071i	−1.46634	+	0.476441i	−0.929999	−	0.367562i	$-0.880192\pi$
$211$	−21.2998	+	6.92071i	−1.46634	+	0.476441i	−0.536337	+	0.844004i	$0.680192\pi$
$212$	−4.50388	−	10.9670i	−0.309328	−	0.753215i
$213$		0			0
$214$	11.6392	−	2.29691i	0.795642	−	0.157014i
$215$	−4.27633	+	13.1612i	−0.291644	+	0.897587i
$216$		0			0
$217$	1.77862	+	1.29224i	0.120740	+	0.0877229i
$218$	−12.5021	+	13.4838i	−0.846752	+	0.913238i
$219$		0			0
$220$	20.8298	−	4.45467i	1.40435	−	0.300333i
$221$			12.0455i			0.810265i
$222$		0			0
$223$	2.77535	−	3.81994i	0.185851	−	0.255802i	−0.705917	−	0.708294i	$-0.749465\pi$
$223$	2.77535	−	3.81994i	0.185851	−	0.255802i	0.891768	+	0.452492i	$0.149465\pi$
$224$	14.7662	−	0.468455i	0.986610	−	0.0313000i
$225$		0			0
$226$	−3.27320	−	16.5865i	−0.217730	−	1.10332i
$227$	9.96023	−	7.23653i	0.661083	−	0.480305i	−0.205945	−	0.978564i	$-0.566027\pi$
$227$	9.96023	−	7.23653i	0.661083	−	0.480305i	0.867029	+	0.498258i	$0.166027\pi$
$228$		0			0
$229$	3.69623	+	11.3758i	0.244253	+	0.751735i	0.995758	+	0.0920073i	$0.0293283\pi$
$229$	3.69623	+	11.3758i	0.244253	+	0.751735i	−0.751505	+	0.659728i	$0.770672\pi$
$230$	30.6669	−	17.1135i	2.02212	−	1.12843i
$231$		0			0
$232$	−0.546574	+	12.4699i	−0.0358843	+	0.818690i
$233$	10.8337	−	3.52008i	0.709738	−	0.230608i	0.0681696	−	0.997674i	$-0.478284\pi$
$233$	10.8337	−	3.52008i	0.709738	−	0.230608i	0.641568	+	0.767066i	$0.278284\pi$
$234$		0			0
$235$	4.25565	+	5.85739i	0.277608	+	0.382094i
$236$	−0.680681	−	0.801870i	−0.0443086	−	0.0521973i
$237$		0			0
$238$	−24.4163	−	11.3009i	−1.58268	−	0.732526i
$239$	−9.67933	−	7.03245i	−0.626104	−	0.454891i	0.228944	−	0.973440i	$-0.426473\pi$
$239$	−9.67933	−	7.03245i	−0.626104	−	0.454891i	−0.855048	+	0.518548i	$0.826473\pi$
$240$		0			0
$241$	−2.73544			−0.176205			−0.0881027	−	0.996111i	$-0.528080\pi$
$241$	−2.73544			−0.176205			−0.0881027	+	0.996111i	$0.528080\pi$
$242$	−2.34034	−	15.3793i	−0.150443	−	0.988619i
$243$		0			0
$244$	8.51341	+	2.07112i	0.545015	+	0.132590i
$245$	−0.338526	+	0.465941i	−0.0216276	+	0.0297679i
$246$		0			0
$247$	12.0979	+	3.93085i	0.769772	+	0.250114i
$248$	2.23006	+	0.834218i	0.141609	+	0.0529729i
$249$		0			0
$250$	1.40665	+	0.168643i	0.0889641	+	0.0106659i
$251$	7.98875	+	24.5868i	0.504245	+	1.55191i	0.802035	+	0.597276i	$0.203750\pi$
$251$	7.98875	+	24.5868i	0.504245	+	1.55191i	−0.297790	+	0.954631i	$0.596250\pi$
$252$		0			0
$253$	−11.1404	−	23.1020i	−0.700390	−	1.45241i
$254$	16.8404	−	9.39765i	1.05666	−	0.589661i
$255$		0			0
$256$	15.2756	−	4.75995i	0.954723	−	0.297497i
$257$	−8.32386	−	11.4568i	−0.519228	−	0.714656i	0.466213	−	0.884672i	$-0.345618\pi$
$257$	−8.32386	−	11.4568i	−0.519228	−	0.714656i	−0.985441	+	0.170016i	$0.945618\pi$
$258$		0			0
$259$	−8.06121	−	2.61925i	−0.500899	−	0.162752i
$260$	−10.5897	+	0.801230i	−0.656744	+	0.0496902i
$261$		0			0
$262$	−17.9447	+	19.3537i	−1.10863	+	1.19568i
$263$	−8.31515			−0.512734			−0.256367	−	0.966580i	$-0.582526\pi$
$263$	−8.31515			−0.512734			−0.256367	+	0.966580i	$0.582526\pi$
$264$		0			0
$265$	−19.0358			−1.16936
$266$	−19.3180	+	20.8348i	−1.18446	+	1.27747i
$267$		0			0
$268$	8.15699	−	0.617169i	0.498267	−	0.0376996i
$269$	−9.66319	−	3.13976i	−0.589175	−	0.191435i	−0.000768420	−	1.00000i	$-0.500245\pi$
$269$	−9.66319	−	3.13976i	−0.589175	−	0.191435i	−0.588407	+	0.808565i	$0.700245\pi$
$270$		0			0
$271$	3.02380	+	4.16191i	0.183683	+	0.252818i	0.890922	−	0.454157i	$-0.150059\pi$
$271$	3.02380	+	4.16191i	0.183683	+	0.252818i	−0.707239	+	0.706975i	$0.750059\pi$
$272$	−28.7513	−	4.73208i	−1.74330	−	0.286925i
$273$		0			0
$274$	14.4482	−	8.06271i	0.872846	−	0.487086i
$275$	3.13661	−	17.3363i	0.189144	−	1.04542i
$276$		0			0
$277$	−2.89941	−	8.92346i	−0.174209	−	0.536159i	0.825388	−	0.564566i	$-0.190956\pi$
$277$	−2.89941	−	8.92346i	−0.174209	−	0.536159i	−0.999596	+	0.0284072i	$0.990956\pi$
$278$	11.5844	+	1.38886i	0.694786	+	0.0832982i
$279$		0			0
$280$	8.31096	−	22.2172i	0.496675	−	1.32773i
$281$	−0.267460	−	0.0869029i	−0.0159553	−	0.00518419i	0.301028	−	0.953615i	$-0.402670\pi$
$281$	−0.267460	−	0.0869029i	−0.0159553	−	0.00518419i	−0.316984	+	0.948431i	$0.602670\pi$
$282$		0			0
$283$	5.12092	−	7.04834i	0.304407	−	0.418980i	−0.629220	−	0.777227i	$-0.716625\pi$
$283$	5.12092	−	7.04834i	0.304407	−	0.418980i	0.933627	+	0.358247i	$0.116625\pi$
$284$	−17.0750	−	4.15397i	−1.01322	−	0.246493i
$285$		0			0
$286$	0.122908	+	7.75494i	0.00726773	+	0.458559i
$287$	−15.0373			−0.887623
$288$		0			0
$289$	29.1767	+	21.1981i	1.71628	+	1.24695i
$290$	18.1875	+	8.41788i	1.06800	+	0.494315i
$291$		0			0
$292$	3.22557	+	3.79985i	0.188762	+	0.222369i
$293$	1.31949	+	1.81612i	0.0770855	+	0.106099i	0.845819	−	0.533471i	$-0.179113\pi$
$293$	1.31949	+	1.81612i	0.0770855	+	0.106099i	−0.768733	+	0.639570i	$0.779113\pi$
$294$		0			0
$295$	−1.60616	+	0.521872i	−0.0935140	+	0.0303845i
$296$	−9.17085	−	0.401971i	−0.533045	−	0.0233641i
$297$		0			0
$298$	11.8116	−	6.59139i	0.684228	−	0.381829i
$299$	3.95146	+	12.1614i	0.228519	+	0.703309i
$300$		0			0
$301$	9.10519	−	6.61531i	0.524815	−	0.381300i
$302$	4.68847	+	23.7581i	0.269791	+	1.36713i
$303$		0			0
$304$	−14.1352	+	27.3323i	−0.810712	+	1.56761i
$305$	8.26891	−	11.3812i	0.473476	−	0.651684i
$306$		0			0
$307$			15.2327i			0.869378i	0.900581	+	0.434689i	$0.143142\pi$
$307$			15.2327i			0.869378i	−0.900581	+	0.434689i	$0.856858\pi$
$308$	−15.8347	−	7.02643i	−0.902266	−	0.400368i
$309$		0			0
$310$	2.59925	−	2.80334i	0.147628	−	0.159219i
$311$	−23.4849	−	17.0628i	−1.33171	−	0.967543i	−0.999706	−	0.0242642i	$-0.992276\pi$
$311$	−23.4849	−	17.0628i	−1.33171	−	0.967543i	−0.332003	−	0.943278i	$-0.607724\pi$
$312$		0			0
$313$	−9.12814	+	28.0935i	−0.515953	+	1.58794i	0.265588	+	0.964087i	$0.414434\pi$
$313$	−9.12814	+	28.0935i	−0.515953	+	1.58794i	−0.781541	+	0.623853i	$0.785566\pi$
$314$	−0.357034	+	0.0704578i	−0.0201486	+	0.00397616i
$315$		0			0
$316$	−3.67445	−	8.94729i	−0.206704	−	0.503325i
$317$	13.3011	−	4.32180i	0.747066	−	0.242736i	0.0893475	−	0.996001i	$-0.471522\pi$
$317$	13.3011	−	4.32180i	0.747066	−	0.242736i	0.657718	+	0.753264i	$0.271522\pi$
$318$		0			0
$319$	6.92887	−	12.8923i	0.387942	−	0.721832i
$320$	2.24772	−	25.5913i	0.125651	−	1.43060i
$321$		0			0
$322$	−28.3585	−	3.39991i	−1.58036	−	0.189470i
$323$	45.3359	−	32.9384i	2.52255	−	1.83274i
$324$		0			0
$325$	−2.71431	+	8.35377i	−0.150563	+	0.463384i
$326$	−3.00074	+	6.48332i	−0.166196	+	0.359078i
$327$		0			0
$328$	−15.6940	+	4.34944i	−0.866554	+	0.240158i
$329$		−	5.88829i		−	0.324632i
$330$		0			0
$331$		−	11.9855i		−	0.658782i	−0.944194	−	0.329391i	$-0.893157\pi$
$331$		−	11.9855i		−	0.658782i	0.944194	−	0.329391i	$-0.106843\pi$
$332$	0.969831	+	0.235938i	0.0532264	+	0.0129488i
$333$		0			0
$334$	−13.1172	−	6.07115i	−0.717739	−	0.332198i
$335$	4.05875	−	12.4916i	0.221753	−	0.682486i
$336$		0			0
$337$	23.4660	−	17.0491i	1.27828	−	0.928722i	0.278776	−	0.960356i	$-0.410071\pi$
$337$	23.4660	−	17.0491i	1.27828	−	0.928722i	0.999500	+	0.0316342i	$0.0100711\pi$
$338$	−1.72818	+	14.4147i	−0.0940008	+	0.784056i
$339$		0			0
$340$	−24.5653	+	39.8163i	−1.33224	+	2.15934i
$341$	−1.93048	−	2.01699i	−0.104541	−	0.109226i
$342$		0			0
$343$	17.8322	−	5.79403i	0.962847	−	0.312848i
$344$	7.58938	−	9.53782i	0.409192	−	0.514245i
$345$		0			0
$346$	−0.462053	−	2.34138i	−0.0248401	−	0.125873i
$347$	9.81451	−	30.2060i	0.526871	−	1.62154i	−0.233716	−	0.972305i	$-0.575089\pi$
$347$	9.81451	−	30.2060i	0.526871	−	1.62154i	0.760587	−	0.649236i	$-0.224911\pi$
$348$		0			0
$349$	−17.3395	−	12.5979i	−0.928161	−	0.674349i	0.0173806	−	0.999849i	$-0.494467\pi$
$349$	−17.3395	−	12.5979i	−0.928161	−	0.674349i	−0.945542	+	0.325500i	$0.894467\pi$
$350$	−14.3867	−	13.3393i	−0.769003	−	0.713017i
$351$		0			0
$352$	−18.5586	−	2.75317i	−0.989174	−	0.146745i
$353$			4.44069i			0.236354i	0.992993	+	0.118177i	$0.0377051\pi$
$353$			4.44069i			0.236354i	−0.992993	+	0.118177i	$0.962295\pi$
$354$		0			0
$355$	−16.5847	+	22.8268i	−0.880222	+	1.21152i
$356$	−23.5439	+	1.78136i	−1.24782	+	0.0944120i
$357$		0			0
$358$	−7.65791	+	1.51123i	−0.404733	+	0.0798708i
$359$	−18.6058	+	13.5179i	−0.981974	+	0.713446i	−0.958149	−	0.286270i	$-0.907585\pi$
$359$	−18.6058	+	13.5179i	−0.981974	+	0.713446i	−0.0238253	+	0.999716i	$0.507585\pi$
$360$		0			0
$361$	−12.4159	−	38.2122i	−0.653469	−	2.01117i
$362$	−16.8977	−	30.2803i	−0.888126	−	1.59150i
$363$		0			0
$364$	7.35061	+	4.53507i	0.385277	+	0.237702i
$365$	7.61115	−	2.47301i	0.398386	−	0.129443i
$366$		0			0
$367$	−4.67897	−	6.44004i	−0.244240	−	0.336168i	0.669244	−	0.743043i	$-0.266618\pi$
$367$	−4.67897	−	6.44004i	−0.244240	−	0.336168i	−0.913484	+	0.406876i	$0.866618\pi$
$368$	−30.5803	+	4.65414i	−1.59411	+	0.242614i
$369$		0			0
$370$	−6.19083	+	13.3757i	−0.321846	+	0.695372i
$371$	12.5248	+	9.09979i	0.650255	+	0.472438i
$372$		0			0
$373$	16.6258			0.860850			0.430425	−	0.902626i	$-0.358364\pi$
$373$	16.6258			0.860850			0.430425	+	0.902626i	$0.358364\pi$
$374$	27.9569	+	19.6426i	1.44561	+	1.01569i
$375$		0			0
$376$	−1.70315	−	6.14543i	−0.0878334	−	0.316926i
$377$	−4.28919	+	5.90357i	−0.220905	+	0.304049i
$378$		0			0
$379$	−19.5257	−	6.34428i	−1.00297	−	0.325884i	−0.238916	−	0.971040i	$-0.576792\pi$
$379$	−19.5257	−	6.34428i	−1.00297	−	0.325884i	−0.764050	+	0.645157i	$0.776792\pi$
$380$	31.9732	+	37.6657i	1.64019	+	1.93221i
$381$		0			0
$382$	1.44537	−	12.0558i	0.0739517	−	0.616827i
$383$	−1.91568	−	5.89586i	−0.0978868	−	0.301265i	0.890108	−	0.455749i	$-0.150628\pi$
$383$	−1.91568	−	5.89586i	−0.0978868	−	0.301265i	−0.987995	+	0.154484i	$0.950628\pi$
$384$		0			0
$385$	−20.0944	+	19.2326i	−1.02411	+	0.980183i
$386$	−1.43319	−	2.56823i	−0.0729472	−	0.130720i
$387$		0			0
$388$	−14.5780	+	5.98685i	−0.740086	+	0.303936i
$389$	−6.80943	−	9.37238i	−0.345252	−	0.475198i	0.600714	−	0.799464i	$-0.294883\pi$
$389$	−6.80943	−	9.37238i	−0.345252	−	0.475198i	−0.945966	+	0.324265i	$0.894883\pi$
$390$		0			0
$391$	53.5750	+	17.4076i	2.70940	+	0.880338i
$392$	0.423061	−	0.279915i	0.0213678	−	0.0141378i
$393$		0			0
$394$	−14.6551	−	13.5882i	−0.738316	−	0.684564i
$395$	−15.5301			−0.781407
$396$		0			0
$397$	−28.2616			−1.41841			−0.709204	−	0.705003i	$-0.750945\pi$
$397$	−28.2616			−1.41841			−0.709204	+	0.705003i	$0.750945\pi$
$398$	−10.5830	−	9.81254i	−0.530479	−	0.491858i
$399$		0			0
$400$	−18.8733	−	9.76058i	−0.943665	−	0.488029i
$401$	27.6117	+	8.97159i	1.37886	+	0.448020i	0.902296	−	0.431118i	$-0.141881\pi$
$401$	27.6117	+	8.97159i	1.37886	+	0.448020i	0.476568	+	0.879138i	$0.341881\pi$
$402$		0			0
$403$	0.818186	+	1.12614i	0.0407567	+	0.0560968i
$404$	3.93165	+	9.57358i	0.195607	+	0.476304i
$405$		0			0
$406$	−7.94258	−	14.2329i	−0.394184	−	0.706367i
$407$	9.48151	+	5.09575i	0.469981	+	0.252587i
$408$		0			0
$409$	4.73574	+	14.5751i	0.234167	+	0.720692i	0.997231	+	0.0743691i	$0.0236943\pi$
$409$	4.73574	+	14.5751i	0.234167	+	0.720692i	−0.763064	+	0.646323i	$0.776306\pi$
$410$	−3.11263	+	25.9623i	−0.153722	+	1.28219i
$411$		0			0
$412$	23.8739	−	20.2658i	1.17618	−	0.998422i
$413$	1.30626	+	0.424430i	0.0642769	+	0.0208848i
$414$		0			0
$415$	0.941979	−	1.29652i	0.0462399	−	0.0636438i
$416$	8.98335	+	2.60700i	0.440445	+	0.127819i
$417$		0			0
$418$	28.8514	−	21.6686i	1.41117	−	1.05984i
$419$	−10.7786			−0.526569			−0.263284	−	0.964718i	$-0.584806\pi$
$419$	−10.7786			−0.526569			−0.263284	+	0.964718i	$0.584806\pi$
$420$		0			0
$421$	−2.99097	−	2.17306i	−0.145771	−	0.105909i	0.512510	−	0.858681i	$-0.328716\pi$
$421$	−2.99097	−	2.17306i	−0.145771	−	0.105909i	−0.658280	+	0.752773i	$0.728716\pi$
$422$	13.3035	−	28.7432i	0.647603	−	1.39920i
$423$		0			0
$424$	15.7038	+	5.87446i	0.762644	+	0.285289i
$425$	22.7444	+	31.3050i	1.10327	+	1.51852i
$426$		0			0
$427$	−10.8812	+	3.53553i	−0.526580	+	0.171096i
$428$	−8.80959	+	14.2789i	−0.425828	+	0.690196i
$429$		0			0
$430$	−9.53680	−	17.0897i	−0.459905	−	0.824139i
$431$	−6.64794	−	20.4602i	−0.320220	−	0.985535i	−0.973552	−	0.228464i	$-0.926630\pi$
$431$	−6.64794	−	20.4602i	−0.320220	−	0.985535i	0.653332	−	0.757071i	$-0.273370\pi$
$432$		0			0
$433$	−29.2991	+	21.2870i	−1.40802	+	1.02299i	−0.414419	+	0.910086i	$0.636015\pi$
$433$	−29.2991	+	21.2870i	−1.40802	+	1.02299i	−0.993606	+	0.112903i	$0.963985\pi$
$434$	−3.05031	+	0.601953i	−0.146419	+	0.0288947i
$435$		0			0
$436$	−1.96193	−	25.9304i	−0.0939592	−	1.24184i
$437$	34.9668	−	48.1276i	1.67269	−	2.30226i
$438$		0			0
$439$			3.85233i			0.183862i	0.995765	+	0.0919309i	$0.0293039\pi$
$439$			3.85233i			0.183862i	−0.995765	+	0.0919309i	$0.970696\pi$
$440$	−15.4090	+	25.8846i	−0.734596	+	1.23400i
$441$		0			0
$442$	−12.4916	−	11.5822i	−0.594164	−	0.550907i
$443$	−19.5842	−	14.2287i	−0.930471	−	0.676027i	0.0156368	−	0.999878i	$-0.495022\pi$
$443$	−19.5842	−	14.2287i	−0.930471	−	0.676027i	−0.946108	+	0.323851i	$0.895022\pi$
$444$		0			0
$445$	−11.7149	+	36.0549i	−0.555342	+	1.70917i
$446$	1.29282	+	6.55116i	0.0612168	+	0.310207i
$447$		0			0
$448$	−13.7125	+	15.7636i	−0.647853	+	0.744758i
$449$	9.09170	−	2.95407i	0.429064	−	0.139411i	−0.0865206	−	0.996250i	$-0.527575\pi$
$449$	9.09170	−	2.95407i	0.429064	−	0.139411i	0.515584	+	0.856839i	$0.327575\pi$
$450$		0			0
$451$	18.7914	+	3.39987i	0.884851	+	0.160093i
$452$	20.3481	+	12.5541i	0.957093	+	0.590494i
$453$		0			0
$454$	−2.07258	+	17.2873i	−0.0972711	+	0.811334i
$455$	11.2192	−	8.15124i	0.525965	−	0.382136i
$456$		0			0
$457$	10.6501	−	32.7775i	0.498188	−	1.53327i	−0.313740	−	0.949509i	$-0.601582\pi$
$457$	10.6501	−	32.7775i	0.498188	−	1.53327i	0.811928	−	0.583757i	$-0.198418\pi$
$458$	−15.3512	−	7.10515i	−0.717314	−	0.332002i
$459$		0			0
$460$	−11.7401	+	48.2580i	−0.547384	+	2.25004i
$461$			4.81433i			0.224226i	0.993695	+	0.112113i	$0.0357618\pi$
$461$			4.81433i			0.224226i	−0.993695	+	0.112113i	$0.964238\pi$
$462$		0			0
$463$			20.9971i			0.975816i	0.872895	+	0.487908i	$0.162240\pi$
$463$			20.9971i			0.975816i	−0.872895	+	0.487908i	$0.837760\pi$
$464$	−12.4062	−	12.5571i	−0.575944	−	0.582949i
$465$		0			0
$466$	−6.76654	+	14.6196i	−0.313454	+	0.677240i
$467$	0.766301	−	2.35843i	0.0354602	−	0.109135i	−0.931760	−	0.363076i	$-0.881727\pi$
$467$	0.766301	−	2.35843i	0.0354602	−	0.109135i	0.967220	+	0.253940i	$0.0817267\pi$
$468$		0			0
$469$	−8.64191	+	6.27872i	−0.399047	+	0.289924i
$470$	−10.1663	−	1.21884i	−0.468936	−	0.0562210i
$471$		0			0
$472$	1.48607	+	0.0651365i	0.0684019	+	0.00299815i
$473$	−12.8740	+	6.20819i	−0.591948	+	0.285453i
$474$		0			0
$475$	38.8637	−	12.6276i	1.78319	−	0.579393i
$476$	35.1966	−	14.4544i	1.61323	−	0.662519i
$477$		0			0
$478$	16.5999	−	3.27587i	0.759264	−	0.149835i
$479$	−5.53685	+	17.0407i	−0.252985	+	0.778608i	0.741235	+	0.671246i	$0.234240\pi$
$479$	−5.53685	+	17.0407i	−0.252985	+	0.778608i	−0.994220	+	0.107362i	$0.965760\pi$
$480$		0			0
$481$	−4.34171	−	3.15443i	−0.197965	−	0.143830i
$482$	2.63023	−	2.83676i	0.119804	−	0.129211i
$483$		0			0
$484$	18.1992	+	12.3607i	0.827238	+	0.561852i
$485$			25.3036i			1.14898i
$486$		0			0
$487$	−16.8613	+	23.2076i	−0.764058	+	1.05164i	0.232808	+	0.972523i	$0.425209\pi$
$487$	−16.8613	+	23.2076i	−0.764058	+	1.05164i	−0.996866	+	0.0791127i	$0.974791\pi$
$488$	−10.3338	+	6.83726i	−0.467789	+	0.309508i
$489$		0			0
$490$	−0.157693	−	0.799084i	−0.00712383	−	0.0360989i
$491$	−0.903596	+	0.656501i	−0.0407787	+	0.0296275i	−0.607988	−	0.793946i	$-0.708023\pi$
$491$	−0.903596	+	0.656501i	−0.0407787	+	0.0296275i	0.567209	+	0.823574i	$0.308023\pi$
$492$		0			0
$493$	9.93389	+	30.5734i	0.447400	+	1.37695i
$494$	−15.7090	+	8.76633i	−0.706783	+	0.394416i
$495$		0			0
$496$	−3.00940	+	1.51052i	−0.135126	+	0.0678245i
$497$	21.8241	−	7.09108i	0.978945	−	0.318079i
$498$		0			0
$499$	−23.8786	−	32.8661i	−1.06895	−	1.47129i	−0.871132	−	0.491048i	$-0.836614\pi$
$499$	−23.8786	−	32.8661i	−1.06895	−	1.47129i	−0.197820	−	0.980238i	$-0.563386\pi$
$500$	−1.52743	+	1.29659i	−0.0683089	+	0.0579851i
$501$		0			0
$502$	−33.1789	−	15.3565i	−1.48085	−	0.685396i
$503$	3.94158	+	2.86373i	0.175746	+	0.127687i	0.672181	−	0.740387i	$-0.265358\pi$
$503$	3.94158	+	2.86373i	0.175746	+	0.127687i	−0.496434	+	0.868074i	$0.665358\pi$
$504$		0			0
$505$	16.6172			0.739457
$506$	34.6695	+	10.6604i	1.54125	+	0.473914i
$507$		0			0
$508$	−6.44692	+	26.5003i	−0.286036	+	1.17576i
$509$	−23.7338	+	32.6668i	−1.05198	+	1.44793i	−0.164904	+	0.986310i	$0.552731\pi$
$509$	−23.7338	+	32.6668i	−1.05198	+	1.44793i	−0.887078	+	0.461620i	$0.847269\pi$
$510$		0			0
$511$	−6.19003	−	2.01126i	−0.273831	−	0.0889730i
$512$	−9.75178	+	20.4182i	−0.430972	+	0.902365i
$513$		0			0
$514$	19.8848	+	2.38400i	0.877083	+	0.105154i
$515$	−15.5376	−	47.8197i	−0.684667	−	2.10719i
$516$		0			0
$517$	−1.33132	+	7.35831i	−0.0585512	+	0.323618i
$518$	10.4674	−	5.84127i	0.459912	−	0.256651i
$519$		0			0
$520$	9.35147	−	11.7523i	0.410089	−	0.515372i
$521$	−6.10412	−	8.40159i	−0.267426	−	0.368081i	0.654093	−	0.756415i	$-0.273051\pi$
$521$	−6.10412	−	8.40159i	−0.267426	−	0.368081i	−0.921519	+	0.388334i	$0.873051\pi$
$522$		0			0
$523$	8.78990	+	2.85601i	0.384355	+	0.124885i	0.494820	−	0.868995i	$-0.335234\pi$
$523$	8.78990	+	2.85601i	0.384355	+	0.124885i	−0.110465	+	0.993880i	$0.535234\pi$
$524$	−2.81601	−	37.2186i	−0.123018	−	1.62590i
$525$		0			0
$526$	7.99533	−	8.62312i	0.348613	−	0.375986i
$527$	6.13215			0.267121
$528$		0			0
$529$	36.8009			1.60004
$530$	18.3036	−	19.7408i	0.795058	−	0.857486i
$531$		0			0
$532$	−3.03152	−	40.0669i	−0.131433	−	1.73712i
$533$	−9.05492	−	2.94212i	−0.392212	−	0.127437i
$534$		0			0
$535$	15.8342	+	21.7939i	0.684571	+	0.942231i
$536$	−7.20322	+	9.05253i	−0.311132	+	0.391010i
$537$		0			0
$538$	12.5476	−	7.00209i	0.540964	−	0.301881i
$539$	−0.589413	+	0.0801589i	−0.0253878	+	0.00345269i
$540$		0			0
$541$	0.333016	+	1.02492i	0.0143175	+	0.0440647i	0.957960	−	0.286902i	$-0.0926253\pi$
$541$	0.333016	+	1.02492i	0.0143175	+	0.0440647i	−0.943643	+	0.330966i	$0.892625\pi$
$542$	−7.22356	−	0.866035i	−0.310278	−	0.0371994i
$543$		0			0
$544$	32.5528	−	25.2661i	1.39569	−	1.08327i
$545$	−39.7095	−	12.9024i	−1.70097	−	0.552679i
$546$		0			0
$547$	−9.24809	+	12.7289i	−0.395420	+	0.544248i	−0.959587	−	0.281412i	$-0.909197\pi$
$547$	−9.24809	+	12.7289i	−0.395420	+	0.544248i	0.564167	+	0.825660i	$0.309197\pi$
$548$	−5.53113	+	22.7359i	−0.236278	+	0.971229i
$549$		0			0
$550$	14.9624	+	19.9223i	0.638000	+	0.849489i
$551$	33.9483			1.44625
$552$		0			0
$553$	10.2182	+	7.42398i	0.434523	+	0.315700i
$554$	12.0419	+	5.57345i	0.511609	+	0.236793i
$555$		0			0
$556$	−12.5791	+	10.6780i	−0.533474	+	0.452848i
$557$	−21.3220	−	29.3473i	−0.903443	−	1.24348i	−0.969357	−	0.245658i	$-0.920996\pi$
$557$	−21.3220	−	29.3473i	−0.903443	−	1.24348i	0.0659132	−	0.997825i	$-0.479004\pi$
$558$		0			0
$559$	6.77714	−	2.20203i	0.286643	−	0.0931358i
$560$	15.0487	+	29.9814i	0.635924	+	1.26695i
$561$		0			0
$562$	0.347294	−	0.193805i	0.0146497	−	0.00817518i
$563$	4.63610	+	14.2684i	0.195388	+	0.601343i	0.999972	+	0.00750368i	$0.00238852\pi$
$563$	4.63610	+	14.2684i	0.195388	+	0.601343i	−0.804584	+	0.593839i	$0.797611\pi$
$564$		0			0
$565$	31.0573	−	22.5644i	1.30659	−	0.949292i
$566$	2.38543	+	12.0878i	0.100267	+	0.508089i
$567$		0			0
$568$	20.7261	−	13.7132i	0.869648	−	0.575395i
$569$	−11.6551	+	16.0419i	−0.488608	+	0.672512i	−0.980131	−	0.198353i	$-0.936441\pi$
$569$	−11.6551	+	16.0419i	−0.488608	+	0.672512i	0.491522	+	0.870865i	$0.336441\pi$
$570$		0			0
$571$			2.33790i			0.0978382i	0.998803	+	0.0489191i	$0.0155776\pi$
$571$			2.33790i			0.0978382i	−0.998803	+	0.0489191i	$0.984422\pi$
$572$	−8.16034	−	7.32921i	−0.341201	−	0.306449i
$573$		0			0
$574$	14.4589	−	15.5942i	0.603503	−	0.650890i
$575$	33.2328	+	24.1450i	1.38590	+	1.00692i
$576$		0			0
$577$	7.93861	−	24.4325i	0.330489	−	1.01714i	−0.638413	−	0.769694i	$-0.720409\pi$
$577$	7.93861	−	24.4325i	0.330489	−	1.01714i	0.968902	−	0.247446i	$-0.0795912\pi$
$578$	−50.0377	+	9.87453i	−2.08129	+	0.410726i
$579$		0			0
$580$	−26.2176	+	10.7670i	−1.08863	+	0.447074i
$581$	−1.23957	+	0.402761i	−0.0514260	+	0.0167093i
$582$		0			0
$583$	−13.5942	−	14.2034i	−0.563015	−	0.588244i
$584$	−7.04209	−	0.308665i	−0.291404	−	0.0127726i
$585$		0			0
$586$	−3.15213	−	0.377910i	−0.130213	−	0.0156113i
$587$	−29.2731	+	21.2681i	−1.20823	+	0.877829i	−0.995069	−	0.0991880i	$-0.968375\pi$
$587$	−29.2731	+	21.2681i	−1.20823	+	0.877829i	−0.213160	+	0.977017i	$0.568375\pi$
$588$		0			0
$589$	2.00114	−	6.15886i	0.0824554	−	0.253772i
$590$	1.00318	−	2.16744i	0.0413002	−	0.0892322i
$591$		0			0
$592$	9.23497	−	9.12400i	0.379555	−	0.374994i
$593$			3.87813i			0.159256i	0.996825	+	0.0796279i	$0.0253732\pi$
$593$			3.87813i			0.159256i	−0.996825	+	0.0796279i	$0.974627\pi$
$594$		0			0
$595$		−	61.0921i		−	2.50453i
$596$	−4.52178	+	18.5869i	−0.185220	+	0.761351i
$597$		0			0
$598$	−16.4113	−	7.59579i	−0.671106	−	0.310615i
$599$	−11.9898	+	36.9007i	−0.489888	+	1.50772i	0.334887	+	0.942258i	$0.391302\pi$
$599$	−11.9898	+	36.9007i	−0.489888	+	1.50772i	−0.824775	+	0.565462i	$0.808698\pi$
$600$		0			0
$601$	19.8976	−	14.4564i	0.811638	−	0.589690i	−0.102667	−	0.994716i	$-0.532738\pi$
$601$	19.8976	−	14.4564i	0.811638	−	0.589690i	0.914305	+	0.405026i	$0.132738\pi$
$602$	−1.89466	+	15.8033i	−0.0772207	+	0.644094i
$603$		0			0
$604$	−29.1462	−	17.9822i	−1.18594	−	0.731686i
$605$	29.4594	−	19.4908i	1.19770	−	0.792412i
$606$		0			0
$607$	0.263693	−	0.0856789i	0.0107030	−	0.00347760i	−0.303661	−	0.952780i	$-0.598209\pi$
$607$	0.263693	−	0.0856789i	0.0107030	−	0.00347760i	0.314364	+	0.949303i	$0.398209\pi$
$608$	−14.7530	−	40.9398i	−0.598314	−	1.66033i
$609$		0			0
$610$	3.85184	+	19.5186i	0.155956	+	0.790285i
$611$	1.15207	−	3.54572i	0.0466079	−	0.143444i
$612$		0			0
$613$	−21.2743	−	15.4567i	−0.859262	−	0.624290i	0.0684220	−	0.997656i	$-0.478204\pi$
$613$	−21.2743	−	15.4567i	−0.859262	−	0.624290i	−0.927684	+	0.373366i	$0.878204\pi$
$614$	−15.7969	−	14.6468i	−0.637511	−	0.591098i
$615$		0			0
$616$	22.5123	−	9.66500i	0.907047	−	0.389414i
$617$			11.2077i			0.451204i	0.974220	+	0.225602i	$0.0724348\pi$
$617$			11.2077i			0.451204i	−0.974220	+	0.225602i	$0.927565\pi$
$618$		0			0
$619$	25.8996	−	35.6478i	1.04099	−	1.43280i	0.144630	−	0.989486i	$-0.453801\pi$
$619$	25.8996	−	35.6478i	1.04099	−	1.43280i	0.896364	−	0.443319i	$-0.146199\pi$
$620$	0.407894	+	5.39104i	0.0163814	+	0.216509i
$621$		0			0
$622$	40.2764	−	7.94822i	1.61494	−	0.318695i
$623$	24.9435	−	18.1225i	0.999341	−	0.726064i
$624$		0			0
$625$	−7.21335	−	22.2004i	−0.288534	−	0.888016i
$626$	−20.3570	−	36.4792i	−0.813628	−	1.45800i
$627$		0			0
$628$	0.270234	−	0.438005i	0.0107835	−	0.0174783i
$629$	−22.4848	+	7.30575i	−0.896528	+	0.291299i
$630$		0			0
$631$	−11.5187	−	15.8541i	−0.458553	−	0.631144i	0.515655	−	0.856796i	$-0.327549\pi$
$631$	−11.5187	−	15.8541i	−0.458553	−	0.631144i	−0.974208	+	0.225653i	$0.927549\pi$
$632$	12.8118	+	4.79262i	0.509626	+	0.190640i
$633$		0			0
$634$	−8.30767	+	17.9493i	−0.329940	+	0.712859i
$635$	35.4270	+	25.7392i	1.40588	+	1.02143i
$636$		0			0
$637$	0.296568			0.0117505
$638$	6.70746	+	19.5820i	0.265551	+	0.775257i
$639$		0			0
$640$	24.3778	+	26.9379i	0.963618	+	1.06482i
$641$	−2.01773	+	2.77716i	−0.0796955	+	0.109691i	−0.847004	−	0.531587i	$-0.821596\pi$
$641$	−2.01773	+	2.77716i	−0.0796955	+	0.109691i	0.767308	+	0.641279i	$0.221596\pi$
$642$		0			0
$643$	−10.5758	−	3.43629i	−0.417069	−	0.135514i	0.0929627	−	0.995670i	$-0.470366\pi$
$643$	−10.5758	−	3.43629i	−0.417069	−	0.135514i	−0.510032	+	0.860156i	$0.670366\pi$
$644$	30.7936	−	26.1397i	1.21344	−	1.03005i
$645$		0			0
$646$	−9.43376	+	78.6865i	−0.371166	+	3.09588i
$647$	−2.85127	−	8.77532i	−0.112095	−	0.344993i	0.879235	−	0.476388i	$-0.158054\pi$
$647$	−2.85127	−	8.77532i	−0.112095	−	0.344993i	−0.991330	+	0.131395i	$0.958054\pi$
$648$		0			0
$649$	−1.53641	−	0.825730i	−0.0603094	−	0.0324127i
$650$	−6.05327	−	10.8473i	−0.237429	−	0.425466i
$651$		0			0
$652$	−3.83812	−	9.34583i	−0.150312	−	0.366011i
$653$	17.7133	+	24.3802i	0.693173	+	0.954071i	0.999997	+	0.00230508i	$0.000733730\pi$
$653$	17.7133	+	24.3802i	0.693173	+	0.954071i	−0.306824	+	0.951766i	$0.599266\pi$
$654$		0			0
$655$	−56.9963	−	18.5192i	−2.22703	−	0.723606i
$656$	10.5798	−	20.4574i	0.413072	−	0.798726i
$657$		0			0
$658$	6.10637	+	5.66181i	0.238051	+	0.220720i
$659$	−40.8066			−1.58960			−0.794800	−	0.606872i	$-0.792424\pi$
$659$	−40.8066			−1.58960			−0.794800	+	0.606872i	$0.792424\pi$
$660$		0			0
$661$	17.6629			0.687009			0.343504	−	0.939151i	$-0.388386\pi$
$661$	17.6629			0.687009			0.343504	+	0.939151i	$0.388386\pi$
$662$	12.4294	+	11.5245i	0.483082	+	0.447912i
$663$		0			0
$664$	−1.17721	+	0.778887i	−0.0456844	+	0.0302267i
$665$	−61.3582	−	19.9365i	−2.37937	−	0.773104i
$666$		0			0
$667$	20.0589	+	27.6088i	0.776685	+	1.06902i
$668$	18.9086	−	7.76535i	0.731598	−	0.300450i
$669$		0			0
$670$	9.05156	+	16.2202i	0.349692	+	0.626640i
$671$	14.3971	−	1.95798i	0.555795	−	0.0755869i
$672$		0			0
$673$	2.64993	+	8.15563i	0.102147	+	0.314376i	0.989050	−	0.147579i	$-0.0471480\pi$
$673$	2.64993	+	8.15563i	0.102147	+	0.314376i	−0.886903	+	0.461955i	$0.847148\pi$
$674$	−4.88295	+	40.7285i	−0.188084	+	1.56880i
$675$		0			0
$676$	−13.2869	−	15.6525i	−0.511033	−	0.602017i
$677$	36.1794	+	11.7554i	1.39049	+	0.451797i	0.906103	−	0.423057i	$-0.139043\pi$
$677$	36.1794	+	11.7554i	1.39049	+	0.451797i	0.484386	+	0.874855i	$0.339043\pi$
$678$		0			0
$679$	12.0960	−	16.6488i	0.464203	−	0.638921i
$680$	−17.6705	−	63.7600i	−0.677634	−	2.44508i
$681$		0			0
$682$	3.94792	−	0.0625708i	0.151174	−	0.00239596i
$683$	10.2224			0.391148			0.195574	−	0.980689i	$-0.437343\pi$
$683$	10.2224			0.391148			0.195574	+	0.980689i	$0.437343\pi$
$684$		0			0
$685$	30.3946	+	22.0829i	1.16132	+	0.843746i
$686$	−11.1377	+	24.0638i	−0.425239	+	0.918760i
$687$		0			0
$688$	2.59360	+	17.0414i	0.0988803	+	0.649699i
$689$	5.76156	+	7.93011i	0.219498	+	0.302113i
$690$		0			0
$691$	−22.0670	+	7.17001i	−0.839469	+	0.272760i	−0.697028	−	0.717043i	$-0.745495\pi$
$691$	−22.0670	+	7.17001i	−0.839469	+	0.272760i	−0.142440	+	0.989803i	$0.545495\pi$
$692$	2.87238	+	1.77216i	0.109192	+	0.0673674i
$693$		0			0
$694$	21.8877	+	39.2222i	0.830845	+	1.48885i
$695$	8.18673	+	25.1962i	0.310540	+	0.955745i
$696$		0			0
$697$	−33.9325	+	24.6534i	−1.28528	+	0.933814i
$698$	29.7370	−	5.86836i	1.12556	−	0.222121i
$699$		0			0
$700$	27.6667	−	2.09330i	1.04570	−	0.0791195i
$701$	−9.52810	+	13.1143i	−0.359871	+	0.495320i	−0.950113	−	0.311906i	$-0.899033\pi$
$701$	−9.52810	+	13.1143i	−0.359871	+	0.495320i	0.590242	+	0.807227i	$0.299033\pi$
$702$		0			0
$703$			24.9669i			0.941643i
$704$	20.6999	−	16.5986i	0.780157	−	0.625584i
$705$		0			0
$706$	−4.60516	−	4.26989i	−0.173318	−	0.160700i
$707$	−10.9335	−	7.94364i	−0.411196	−	0.298751i
$708$		0			0
$709$	−1.18129	+	3.63565i	−0.0443645	+	0.136540i	−0.970785	−	0.239950i	$-0.922869\pi$
$709$	−1.18129	+	3.63565i	−0.0443645	+	0.136540i	0.926421	+	0.376490i	$0.122869\pi$
$710$	−7.72549	−	39.1478i	−0.289933	−	1.46919i
$711$		0			0
$712$	20.7910	−	26.1287i	0.779175	−	0.979215i
$713$	6.19116	−	2.01163i	0.231861	−	0.0753361i
$714$		0			0
$715$	−15.8631	+	7.64960i	−0.593246	+	0.286079i
$716$	5.79617	−	9.39464i	0.216613	−	0.351094i
$717$		0			0
$718$	3.87160	−	32.2928i	0.144487	−	1.20516i
$719$	−30.8537	+	22.4165i	−1.15065	+	0.835994i	−0.988567	−	0.150783i	$-0.951820\pi$
$719$	−30.8537	+	22.4165i	−1.15065	+	0.835994i	−0.162081	+	0.986778i	$0.551820\pi$
$720$		0			0
$721$	−12.6365	+	38.8910i	−0.470606	+	1.44838i
$722$	51.5658	+	23.8667i	1.91908	+	0.888228i
$723$		0			0
$724$	47.6496	+	11.5921i	1.77089	+	0.430817i
$725$			23.4418i			0.870605i
$726$		0			0
$727$			32.7492i			1.21460i	0.794473	+	0.607300i	$0.207747\pi$
$727$			32.7492i			1.21460i	−0.794473	+	0.607300i	$0.792253\pi$
$728$	−11.7709	+	3.26221i	−0.436259	+	0.120906i
$729$		0			0
$730$	−4.75380	+	10.2709i	−0.175946	+	0.380145i
$731$	9.70069	−	29.8556i	0.358793	−	1.10425i
$732$		0			0
$733$	6.69143	−	4.86161i	0.247154	−	0.179568i	−0.457311	−	0.889307i	$-0.651187\pi$
$733$	6.69143	−	4.86161i	0.247154	−	0.179568i	0.704464	+	0.709739i	$0.251187\pi$
$734$	11.1776	+	1.34008i	0.412571	+	0.0494634i
$735$		0			0
$736$	24.5776	−	36.1880i	0.905942	−	1.33391i
$737$	12.2190	−	5.89231i	0.450092	−	0.217046i
$738$		0			0
$739$	−9.78747	+	3.18014i	−0.360038	+	0.116983i	−0.483450	−	0.875372i	$-0.660616\pi$
$739$	−9.78747	+	3.18014i	−0.360038	+	0.116983i	0.123412	+	0.992356i	$0.460616\pi$
$740$	−7.91843	−	19.2814i	−0.291087	−	0.708798i
$741$		0			0
$742$	−21.4799	+	4.23888i	−0.788551	+	0.155614i
$743$	−4.52332	+	13.9214i	−0.165945	+	0.510725i	−0.999105	−	0.0423070i	$-0.986529\pi$
$743$	−4.52332	+	13.9214i	−0.165945	+	0.510725i	0.833160	+	0.553032i	$0.186529\pi$
$744$		0			0
$745$	24.8480	+	18.0531i	0.910361	+	0.661416i
$746$	−15.9863	+	17.2415i	−0.585300	+	0.631258i
$747$		0			0
$748$	−47.2516	+	10.1052i	−1.72769	+	0.369484i
$749$		−	21.9088i		−	0.800530i
$750$		0			0
$751$	−16.3876	+	22.5555i	−0.597991	+	0.823063i	−0.995522	−	0.0945249i	$-0.969867\pi$
$751$	−16.3876	+	22.5555i	−0.597991	+	0.823063i	0.397532	+	0.917588i	$0.369867\pi$
$752$	8.01068	+	4.14283i	0.292119	+	0.151073i
$753$		0			0
$754$	−1.99800	−	10.1246i	−0.0727628	−	0.368715i
$755$	−44.4858	+	32.3208i	−1.61900	+	1.17628i
$756$		0			0
$757$	−11.4986	−	35.3889i	−0.417922	−	1.28623i	−0.909611	−	0.415461i	$-0.863620\pi$
$757$	−11.4986	−	35.3889i	−0.417922	−	1.28623i	0.491689	−	0.870771i	$-0.336380\pi$
$758$	25.3539	−	14.1486i	0.920896	−	0.513900i
$759$		0			0
$760$	−69.8042	−	3.05962i	−2.53206	−	0.110984i
$761$	8.00209	−	2.60004i	0.290076	−	0.0942513i	−0.160365	−	0.987058i	$-0.551267\pi$
$761$	8.00209	−	2.60004i	0.290076	−	0.0942513i	0.450440	+	0.892807i	$0.351267\pi$
$762$		0			0
$763$	19.9595	+	27.4719i	0.722582	+	0.994549i
$764$	11.1125	+	13.0910i	0.402036	+	0.473615i
$765$		0			0
$766$	7.95623	+	3.68246i	0.287470	+	0.133053i
$767$	0.703542	+	0.511153i	0.0254034	+	0.0184567i
$768$		0			0
$769$	−48.9221			−1.76418			−0.882089	−	0.471084i	$-0.843863\pi$
$769$	−48.9221			−1.76418			−0.882089	+	0.471084i	$0.843863\pi$
$770$	−0.623366	−	39.3315i	−0.0224646	−	1.41741i
$771$		0			0
$772$	4.04141	+	0.983185i	0.145454	+	0.0353856i
$773$	2.69781	−	3.71322i	0.0970336	−	0.133555i	−0.757740	−	0.652557i	$-0.773696\pi$
$773$	2.69781	−	3.71322i	0.0970336	−	0.133555i	0.854773	+	0.519002i	$0.173696\pi$
$774$		0			0
$775$	4.25278	+	1.38181i	0.152764	+	0.0496361i
$776$	7.80871	−	20.8745i	0.280316	−	0.749351i
$777$		0			0
$778$	16.2670	+	1.95026i	0.583201	+	0.0699202i
$779$	13.6874	+	42.1256i	0.490403	+	1.50930i
$780$		0			0
$781$	−28.8758	+	3.92705i	−1.03326	+	0.140521i
$782$	−69.5666	+	38.8212i	−2.48770	+	1.38824i
$783$		0			0
$784$	−0.116507	+	0.707879i	−0.00416098	+	0.0252814i
$785$	−0.485713	−	0.668527i	−0.0173358	−	0.0238607i
$786$		0			0
$787$	−25.4341	−	8.26403i	−0.906626	−	0.294581i	−0.181657	−	0.983362i	$-0.558146\pi$
$787$	−25.4341	−	8.26403i	−0.906626	−	0.294581i	−0.724969	+	0.688781i	$0.758146\pi$
$788$	28.1829	−	2.13236i	1.00398	−	0.0759622i
$789$		0			0
$790$	14.9328	−	16.1053i	0.531286	−	0.573002i
$791$	−31.2211			−1.11009
$792$		0			0
$793$	−7.24404			−0.257243
$794$	27.1746	−	29.3083i	0.964389	−	1.04011i
$795$		0			0
$796$	20.3519	−	1.53986i	0.721356	−	0.0545788i
$797$	−23.9640	−	7.78637i	−0.848848	−	0.275808i	−0.147885	−	0.989005i	$-0.547246\pi$
$797$	−23.9640	−	7.78637i	−0.848848	−	0.275808i	−0.700964	+	0.713197i	$0.747246\pi$
$798$		0			0
$799$	−9.65376	−	13.2873i	−0.341525	−	0.470069i
$800$	28.2695	−	10.1872i	0.999477	−	0.360170i
$801$		0			0
$802$	−35.8536	+	20.0079i	−1.26603	+	0.706502i
$803$	7.28064	+	3.91292i	0.256928	+	0.138084i
$804$		0			0
$805$	−20.0410	−	61.6799i	−0.706353	−	2.17393i
$806$	−1.95456	−	0.234333i	−0.0688465	−	0.00825403i
$807$		0			0
$808$	−13.7086	−	5.12809i	−0.482267	−	0.180406i
$809$	15.3691	+	4.99373i	0.540349	+	0.175570i	0.566461	−	0.824089i	$-0.308312\pi$
$809$	15.3691	+	4.99373i	0.540349	+	0.175570i	−0.0261111	+	0.999659i	$0.508312\pi$
$810$		0			0
$811$	−17.0838	+	23.5138i	−0.599893	+	0.825683i	−0.995699	−	0.0926520i	$-0.970466\pi$
$811$	−17.0838	+	23.5138i	−0.599893	+	0.825683i	0.395805	+	0.918335i	$0.370466\pi$
$812$	22.3971	+	5.44872i	0.785985	+	0.191213i
$813$		0			0
$814$	−14.4013	+	4.93292i	−0.504766	+	0.172899i
$815$	−16.2219			−0.568229
$816$		0			0
$817$	−26.8200	−	19.4859i	−0.938314	−	0.681725i
$818$	−19.6685	−	9.10337i	−0.687693	−	0.318292i
$819$		0			0
$820$	−23.9310	−	28.1916i	−0.835705	−	0.984495i
$821$	−27.6887	−	38.1103i	−0.966343	−	1.33006i	−0.943873	−	0.330310i	$-0.892847\pi$
$821$	−27.6887	−	38.1103i	−0.966343	−	1.33006i	−0.0224706	−	0.999748i	$-0.507153\pi$
$822$		0			0
$823$	36.3221	−	11.8018i	1.26611	−	0.411384i	0.402442	−	0.915445i	$-0.368161\pi$
$823$	36.3221	−	11.8018i	1.26611	−	0.411384i	0.863668	+	0.504061i	$0.168161\pi$
$824$	−1.93929	+	44.2444i	−0.0675585	+	1.54133i
$825$		0			0
$826$	−1.69617	+	0.946536i	−0.0590172	+	0.0329342i
$827$	4.59530	+	14.1429i	0.159794	+	0.491796i	0.998615	−	0.0526113i	$-0.0167544\pi$
$827$	4.59530	+	14.1429i	0.159794	+	0.491796i	−0.838821	+	0.544408i	$0.816754\pi$
$828$		0			0
$829$	23.1323	−	16.8066i	0.803419	−	0.583718i	−0.108497	−	0.994097i	$-0.534604\pi$
$829$	23.1323	−	16.8066i	0.803419	−	0.583718i	0.911915	+	0.410379i	$0.134604\pi$
$830$	0.438794	+	2.22352i	0.0152308	+	0.0771796i
$831$		0			0
$832$	−11.3414	+	6.80934i	−0.393192	+	0.236071i
$833$	0.767933	−	1.05697i	0.0266073	−	0.0366218i
$834$		0			0
$835$		−	32.8204i		−	1.13580i
$836$	−5.27062	+	50.7551i	−0.182288	+	1.75540i
$837$		0			0
$838$	10.3640	−	11.1778i	0.358019	−	0.386131i
$839$	8.94942	+	6.50214i	0.308968	+	0.224479i	0.731454	−	0.681891i	$-0.238842\pi$
$839$	8.94942	+	6.50214i	0.308968	+	0.224479i	−0.422485	+	0.906370i	$0.638842\pi$
$840$		0			0
$841$	2.94348	−	9.05911i	0.101499	−	0.312383i
$842$	5.12947	−	1.01226i	0.176773	−	0.0348848i
$843$		0			0
$844$	17.0159	+	41.4338i	0.585712	+	1.42621i
$845$	−31.3521	+	10.1869i	−1.07854	+	0.350440i
$846$		0			0
$847$	−28.7004	−	1.25852i	−0.986158	−	0.0432432i
$848$	−21.1918	+	10.6369i	−0.727731	+	0.365273i
$849$		0			0
$850$	−54.3341	−	6.51413i	−1.86364	−	0.223433i
$851$	−20.3045	+	14.7521i	−0.696030	+	0.505696i
$852$		0			0
$853$	−8.72137	+	26.8416i	−0.298614	+	0.919039i	0.683370	+	0.730073i	$0.260514\pi$
$853$	−8.72137	+	26.8416i	−0.298614	+	0.919039i	−0.981983	+	0.188967i	$0.939486\pi$
$854$	6.79624	−	14.6838i	0.232563	−	0.502469i
$855$		0			0
$856$	−6.33699	−	22.8656i	−0.216594	−	0.781529i
$857$			15.1734i			0.518313i	0.965835	+	0.259156i	$0.0834445\pi$
$857$			15.1734i			0.518313i	−0.965835	+	0.259156i	$0.916555\pi$
$858$		0			0
$859$			37.2957i			1.27251i	0.771478	+	0.636256i	$0.219518\pi$
$859$			37.2957i			1.27251i	−0.771478	+	0.636256i	$0.780482\pi$
$860$	26.8926	+	6.54238i	0.917032	+	0.223093i
$861$		0			0
$862$	27.6103	+	12.7791i	0.940410	+	0.435259i
$863$	16.2673	−	50.0656i	0.553745	−	1.70425i	−0.145489	−	0.989360i	$-0.546475\pi$
$863$	16.2673	−	50.0656i	0.553745	−	1.70425i	0.699234	−	0.714893i	$-0.253525\pi$
$864$		0			0
$865$	4.38411	−	3.18524i	0.149064	−	0.108302i
$866$	6.09673	−	50.8525i	0.207175	−	1.72804i
$867$		0			0
$868$	2.30874	−	3.74208i	0.0783636	−	0.127014i
$869$	−11.0907	−	11.5877i	−0.376226	−	0.393085i
$870$		0			0
$871$	−6.43232	+	2.08999i	−0.217951	+	0.0708165i
$872$	28.7772	+	22.8984i	0.974519	+	0.775438i
$873$		0			0
$874$	16.2883	+	82.5383i	0.550959	+	2.79190i
$875$	0.808470	−	2.48822i	0.0273313	−	0.0841171i
$876$		0			0
$877$	−12.8696	−	9.35029i	−0.434575	−	0.315737i	0.348901	−	0.937160i	$-0.386555\pi$
$877$	−12.8696	−	9.35029i	−0.434575	−	0.315737i	−0.783475	+	0.621423i	$0.786555\pi$
$878$	−3.99501	−	3.70416i	−0.134825	−	0.125009i
$879$		0			0
$880$	−12.0270	−	40.8688i	−0.405430	−	1.37769i
$881$		−	58.3208i		−	1.96488i	−0.186585	−	0.982439i	$-0.559742\pi$
$881$		−	58.3208i		−	1.96488i	0.186585	−	0.982439i	$-0.440258\pi$
$882$		0			0
$883$	−1.97571	+	2.71932i	−0.0664878	+	0.0915126i	−0.840966	−	0.541088i	$-0.818013\pi$
$883$	−1.97571	+	2.71932i	−0.0664878	+	0.0915126i	0.774478	+	0.632601i	$0.218013\pi$
$884$	24.0222	−	1.81756i	0.807956	−	0.0611310i
$885$		0			0
$886$	33.5866	−	6.62805i	1.12836	−	0.222674i
$887$	41.0526	−	29.8264i	1.37841	−	1.00147i	0.381383	−	0.924417i	$-0.375448\pi$
$887$	41.0526	−	29.8264i	1.37841	−	1.00147i	0.997027	−	0.0770562i	$-0.0245521\pi$
$888$		0			0
$889$	−11.0053	−	33.8708i	−0.369105	−	1.13599i
$890$	−26.1259	−	46.8170i	−0.875742	−	1.56931i
$891$		0			0
$892$	−8.03689	−	4.95849i	−0.269095	−	0.166022i
$893$	−16.4955	+	5.35971i	−0.552001	+	0.179356i
$894$		0			0
$895$	−10.4179	−	14.3390i	−0.348232	−	0.479301i
$896$	−3.16234	−	29.3776i	−0.105646	−	0.981436i
$897$		0			0
$898$	−5.67853	+	12.2689i	−0.189495	+	0.409418i
$899$	3.00542	+	2.18356i	0.100236	+	0.0728259i
$900$		0			0
$901$	43.1819			1.43860
$902$	−21.5944	+	16.2183i	−0.719015	+	0.540009i
$903$		0			0
$904$	−32.5845	+	9.03051i	−1.08374	+	0.300350i
$905$	46.2812	−	63.7006i	1.53844	−	2.11748i
$906$		0			0
$907$	54.6953	+	17.7716i	1.81613	+	0.590096i	0.999924	+	0.0123330i	$0.00392580\pi$
$907$	54.6953	+	17.7716i	1.81613	+	0.590096i	0.816205	+	0.577763i	$0.196074\pi$
$908$	−15.9347	−	18.7717i	−0.528812	−	0.622962i
$909$		0			0
$910$	−2.33456	+	19.4725i	−0.0773900	+	0.645506i
$911$	−6.75728	−	20.7968i	−0.223879	−	0.689028i	−0.998403	−	0.0564841i	$-0.982011\pi$
$911$	−6.75728	−	20.7968i	−0.223879	−	0.689028i	0.774525	−	0.632543i	$-0.217989\pi$
$912$		0			0
$913$	1.64009	−	0.223049i	0.0542792	−	0.00738185i
$914$	23.7510	+	42.5613i	0.785615	+	1.40780i
$915$		0			0
$916$	22.1291	−	9.08790i	0.731164	−	0.300273i
$917$	28.6485	+	39.4312i	0.946056	+	1.30213i
$918$		0			0
$919$	−13.8559	−	4.50206i	−0.457064	−	0.148509i	0.0714309	−	0.997446i	$-0.477243\pi$
$919$	−13.8559	−	4.50206i	−0.457064	−	0.148509i	−0.528495	+	0.848936i	$0.677243\pi$
$920$	−38.7568	−	58.5767i	−1.27777	−	1.93122i
$921$		0			0
$922$	−4.99264	−	4.62916i	−0.164424	−	0.152453i
$923$	14.5291			0.478231
$924$		0			0
$925$	−17.2399			−0.566846
$926$	−21.7747	−	20.1895i	−0.715562	−	0.663467i
$927$		0			0
$928$	24.9512	−	0.791572i	0.819064	−	0.0259846i
$929$	0.0709540	+	0.0230544i	0.00232793	+	0.000756389i	0.310181	−	0.950678i	$-0.399610\pi$
$929$	0.0709540	+	0.0230544i	0.00232793	+	0.000756389i	−0.307853	+	0.951434i	$0.599610\pi$
$930$		0			0
$931$	−0.810969	−	1.11620i	−0.0265784	−	0.0365821i
$932$	−8.65480	−	21.0745i	−0.283497	−	0.690317i
$933$		0			0
$934$	1.70895	+	3.06240i	0.0559187	+	0.100205i
$935$	−13.8127	+	76.3439i	−0.451722	+	2.49671i
$936$		0			0
$937$	12.9123	+	39.7401i	0.421828	+	1.29825i	0.905999	+	0.423280i	$0.139121\pi$
$937$	12.9123	+	39.7401i	0.421828	+	1.29825i	−0.484171	+	0.874973i	$0.660879\pi$
$938$	1.79826	−	14.9992i	0.0587153	−	0.489742i
$939$		0			0
$940$	11.0393	−	9.37086i	0.360061	−	0.305644i
$941$	13.4909	+	4.38346i	0.439791	+	0.142897i	0.520539	−	0.853838i	$-0.325731\pi$
$941$	13.4909	+	4.38346i	0.439791	+	0.142897i	−0.0807482	+	0.996735i	$0.525731\pi$
$942$		0			0
$943$	−26.1715	+	36.0220i	−0.852263	+	1.17304i
$944$	−1.49646	+	1.47848i	−0.0487056	+	0.0481203i
$945$		0			0
$946$	5.94073	−	19.3202i	0.193150	−	0.628155i
$947$	−35.0211			−1.13803			−0.569016	−	0.822327i	$-0.692676\pi$
$947$	−35.0211			−1.13803			−0.569016	+	0.822327i	$0.692676\pi$
$948$		0			0
$949$	−3.33390	−	2.42222i	−0.108223	−	0.0786286i
$950$	−24.2736	+	52.4450i	−0.787540	+	1.70154i
$951$		0			0
$952$	−18.8531	+	50.3987i	−0.611032	+	1.63343i
$953$	27.4295	+	37.7535i	0.888530	+	1.22296i	0.973985	+	0.226615i	$0.0727658\pi$
$953$	27.4295	+	37.7535i	0.888530	+	1.22296i	−0.0854545	+	0.996342i	$0.527234\pi$
$954$		0			0
$955$	26.2214	−	8.51985i	0.848505	−	0.275696i
$956$	−12.5643	+	20.3646i	−0.406358	+	0.658639i
$957$		0			0
$958$	−12.3479	−	22.1272i	−0.398943	−	0.714896i
$959$	−9.44198	−	29.0594i	−0.304897	−	0.938377i
$960$		0			0
$961$	−24.5062	+	17.8048i	−0.790523	+	0.574349i
$962$	7.44598	−	1.46940i	0.240068	−	0.0473755i
$963$		0			0
$964$	0.412755	+	5.45530i	0.0132940	+	0.175703i
$965$	3.92535	−	5.40278i	0.126361	−	0.173922i
$966$		0			0
$967$		−	56.5676i		−	1.81909i	−0.415605	−	0.909545i	$-0.636430\pi$
$967$		−	56.5676i		−	1.81909i	0.415605	−	0.909545i	$-0.363570\pi$
$968$	−30.3178	+	6.98795i	−0.974451	+	0.224601i
$969$		0			0
$970$	−26.2407	−	24.3303i	−0.842539	−	0.781200i
$971$	26.6504	+	19.3627i	0.855253	+	0.621378i	0.926589	−	0.376075i	$-0.122726\pi$
$971$	26.6504	+	19.3627i	0.855253	+	0.621378i	−0.0713364	+	0.997452i	$0.522726\pi$
$972$		0			0
$973$	6.65813	−	20.4916i	0.213450	−	0.656932i
$974$	−7.85435	−	39.8007i	−0.251670	−	1.27530i
$975$		0			0
$976$	2.84584	−	17.2908i	0.0910930	−	0.553465i
$977$	−36.6271	+	11.9009i	−1.17180	+	0.380742i	−0.829316	−	0.558779i	$-0.811270\pi$
$977$	−36.6271	+	11.9009i	−1.17180	+	0.380742i	−0.342489	+	0.939522i	$0.611270\pi$
$978$		0			0
$979$	−35.2682	+	17.0072i	−1.12718	+	0.543554i
$980$	0.980307	+	0.604816i	0.0313148	+	0.0193201i
$981$		0			0
$982$	0.188026	−	1.56831i	0.00600014	−	0.0500469i
$983$	−12.7755	+	9.28197i	−0.407476	+	0.296049i	−0.772579	−	0.634918i	$-0.781034\pi$
$983$	−12.7755	+	9.28197i	−0.407476	+	0.296049i	0.365103	+	0.930967i	$0.381034\pi$
$984$		0			0
$985$	14.0233	−	43.1591i	0.446818	−	1.37516i
$986$	−41.2575	−	19.0956i	−1.31391	−	0.608128i
$987$		0			0
$988$	6.01383	−	24.7200i	0.191325	−	0.786448i
$989$		−	33.3252i		−	1.05968i
$990$		0			0
$991$		−	33.3931i		−	1.06077i	−0.847758	−	0.530383i	$-0.822048\pi$
$991$		−	33.3931i		−	1.06077i	0.847758	−	0.530383i	$-0.177952\pi$
$992$	1.32718	−	4.57328i	0.0421381	−	0.145202i
$993$		0			0
$994$	−13.6310	+	29.4507i	−0.432348	+	0.934121i
$995$	10.1267	−	31.1668i	0.321038	−	0.988054i
$996$		0			0
$997$	−21.3970	+	15.5458i	−0.677650	+	0.492341i	−0.872577	−	0.488476i	$-0.837553\pi$
$997$	−21.3970	+	15.5458i	−0.677650	+	0.492341i	0.194927	+	0.980818i	$0.437553\pi$
$998$	57.0435	+	6.83896i	1.80568	+	0.216484i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.w.a.71.7	yes	96
3.2	odd	2	inner	396.2.w.a.71.18	yes	96
4.3	odd	2	inner	396.2.w.a.71.3	✓	96
11.9	even	5	inner	396.2.w.a.251.22	yes	96
12.11	even	2	inner	396.2.w.a.71.22	yes	96
33.20	odd	10	inner	396.2.w.a.251.3	yes	96
44.31	odd	10	inner	396.2.w.a.251.18	yes	96
132.119	even	10	inner	396.2.w.a.251.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.w.a.71.3	✓	96	4.3	odd	2	inner
396.2.w.a.71.7	yes	96	1.1	even	1	trivial
396.2.w.a.71.18	yes	96	3.2	odd	2	inner
396.2.w.a.71.22	yes	96	12.11	even	2	inner
396.2.w.a.251.3	yes	96	33.20	odd	10	inner
396.2.w.a.251.7	yes	96	132.119	even	10	inner
396.2.w.a.251.18	yes	96	44.31	odd	10	inner
396.2.w.a.251.22	yes	96	11.9	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.961537 + 1.03704i) q^{2} +(-0.150891 - 1.99430i) q^{4} +(-3.05406 - 0.992323i) q^{5} +(1.53508 + 2.11286i) q^{7} +(2.21325 + 1.76111i) q^{8} +O(q^{10})\)	\(q+(-0.961537 + 1.03704i) q^{2} +(-0.150891 - 1.99430i) q^{4} +(-3.05406 - 0.992323i) q^{5} +(1.53508 + 2.11286i) q^{7} +(2.21325 + 1.76111i) q^{8} +(3.96566 - 2.21301i) q^{10} +(-1.44061 - 2.98741i) q^{11} +(0.510980 + 1.57264i) q^{13} +(-3.66715 - 0.439656i) q^{14} +(-3.95446 + 0.601846i) q^{16} +(6.92800 + 2.25104i) q^{17} +(4.52170 - 6.22358i) q^{19} +(-1.51816 + 6.24044i) q^{20} +(4.48326 + 1.37854i) q^{22} +7.73311 q^{23} +(4.29747 + 3.12229i) q^{25} +(-2.12221 - 0.982242i) q^{26} +(3.98204 - 3.38023i) q^{28} +(2.59390 + 3.57020i) q^{29} +(0.800604 - 0.260132i) q^{31} +(3.17823 - 4.67962i) q^{32} +(-8.99595 + 5.02013i) q^{34} +(-2.59159 - 7.97609i) q^{35} +(-2.62566 + 1.90766i) q^{37} +(2.10630 + 10.6734i) q^{38} +(-5.01180 - 7.57480i) q^{40} +(-3.38435 + 4.65816i) q^{41} -4.30942i q^{43} +(-5.74042 + 3.32378i) q^{44} +(-7.43567 + 8.01952i) q^{46} +(-1.82404 - 1.32524i) q^{47} +(0.0554224 - 0.170573i) q^{49} +(-7.37011 + 1.45443i) q^{50} +(3.05920 - 1.25634i) q^{52} +(5.63776 - 1.83182i) q^{53} +(1.43522 + 10.5533i) q^{55} +(-0.323464 + 7.37974i) q^{56} +(-6.19657 - 0.742909i) q^{58} +(0.425469 - 0.309122i) q^{59} +(-1.35376 + 4.16644i) q^{61} +(-0.500044 + 1.08038i) q^{62} +(1.79696 + 7.79557i) q^{64} -5.30997i q^{65} +4.09015i q^{67} +(3.44388 - 14.1562i) q^{68} +(10.7634 + 4.98173i) q^{70} +(2.71519 - 8.35649i) q^{71} +(-2.01619 + 1.46485i) q^{73} +(0.546363 - 4.55719i) q^{74} +(-13.0940 - 8.07853i) q^{76} +(4.10053 - 7.62973i) q^{77} +(4.59951 - 1.49447i) q^{79} +(12.6744 + 2.08603i) q^{80} +(-1.57650 - 7.98869i) q^{82} +(-0.154218 + 0.474633i) q^{83} +(-18.9247 - 13.7496i) q^{85} +(4.46903 + 4.14367i) q^{86} +(2.07275 - 9.14897i) q^{88} -11.8056i q^{89} +(-2.53836 + 3.49375i) q^{91} +(-1.16686 - 15.4221i) q^{92} +(3.12820 - 0.617326i) q^{94} +(-19.9853 + 14.5202i) q^{95} +(-2.43497 - 7.49407i) q^{97} +(0.123599 + 0.221487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{10} + 32 q^{16} + 60 q^{22} + 8 q^{25} - 12 q^{28} + 24 q^{34} + 16 q^{40} - 40 q^{46} + 40 q^{49} - 32 q^{52} - 80 q^{58} - 72 q^{64} - 48 q^{70} - 24 q^{73} - 136 q^{76} - 132 q^{82} - 48 q^{85} - 64 q^{88} - 80 q^{94} - 80 q^{97}+O(q^{100}) \) 96 * q - 16 * q^10 + 32 * q^16 + 60 * q^22 + 8 * q^25 - 12 * q^28 + 24 * q^34 + 16 * q^40 - 40 * q^46 + 40 * q^49 - 32 * q^52 - 80 * q^58 - 72 * q^64 - 48 * q^70 - 24 * q^73 - 136 * q^76 - 132 * q^82 - 48 * q^85 - 64 * q^88 - 80 * q^94 - 80 * q^97

Introduction

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