LMFDB - Embedded newform 882.2.bl.a.395.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(17,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("882.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.18
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(2.63004 + 1.79313i) q^{5} +(-2.53890 + 0.744299i) q^{7} +(0.433884 + 0.900969i) q^{8} +O(q^{10})$	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(2.63004 + 1.79313i) q^{5} +(-2.53890 + 0.744299i) q^{7} +(0.433884 + 0.900969i) q^{8} +(1.79313 + 2.63004i) q^{10} +(0.571086 + 3.78891i) q^{11} +(-5.36836 + 4.28112i) q^{13} +(-2.63532 - 0.234717i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-4.39823 - 1.35668i) q^{17} +(4.57611 - 2.64202i) q^{19} +(0.708317 + 3.10334i) q^{20} +(-0.852634 + 3.73564i) q^{22} +(-1.21969 - 3.95414i) q^{23} +(1.87509 + 4.77764i) q^{25} +(-6.56133 + 2.02390i) q^{26} +(-2.36740 - 1.18128i) q^{28} +(2.11497 - 0.482729i) q^{29} +(4.71405 + 2.72166i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-3.59855 - 2.86975i) q^{34} +(-8.01204 - 2.59505i) q^{35} +(2.28232 - 2.11768i) q^{37} +(5.22502 - 0.787544i) q^{38} +(-0.474424 + 3.14759i) q^{40} +(2.26412 - 1.09034i) q^{41} +(7.68742 + 3.70206i) q^{43} +(-2.15848 + 3.16590i) q^{44} +(0.309232 - 4.12641i) q^{46} +(1.92561 - 4.90638i) q^{47} +(5.89204 - 3.77940i) q^{49} +5.13243i q^{50} +(-6.84718 - 0.513126i) q^{52} +(-2.73142 + 2.94378i) q^{53} +(-5.29203 + 10.9890i) q^{55} +(-1.77218 - 1.96453i) q^{56} +(2.14513 + 0.323327i) q^{58} +(5.23837 - 3.57146i) q^{59} +(4.87224 + 5.25102i) q^{61} +(3.39385 + 4.25576i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-21.7956 + 1.63335i) q^{65} +(1.99581 - 3.45685i) q^{67} +(-2.30136 - 3.98607i) q^{68} +(-6.51012 - 5.34279i) q^{70} +(9.06789 + 2.06969i) q^{71} +(-10.9744 + 4.30713i) q^{73} +(2.89823 - 1.13747i) q^{74} +(5.15155 + 1.17581i) q^{76} +(-4.27001 - 9.19460i) q^{77} +(3.29241 + 5.70262i) q^{79} +(-1.59157 + 2.75669i) q^{80} +(2.50596 - 0.187796i) q^{82} +(3.93879 - 4.93909i) q^{83} +(-9.13483 - 11.4547i) q^{85} +(5.80350 + 6.25468i) q^{86} +(-3.16590 + 2.15848i) q^{88} +(-17.0448 - 2.56910i) q^{89} +(10.4433 - 14.8650i) q^{91} +(1.79540 - 3.72819i) q^{92} +(3.58501 - 3.86372i) q^{94} +(16.7728 + 1.25695i) q^{95} +10.9117i q^{97} +(6.86551 - 1.36554i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) $ 240 * q - 20 * q^4 - 4 * q^7	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	2.63004	+	1.79313i	1.17619	+	0.801912i	0.983776	−	0.179401i	$-0.0574161\pi$
$5$	2.63004	+	1.79313i	1.17619	+	0.801912i	0.192414	+	0.981314i	$0.438368\pi$
$6$		0			0
$7$	−2.53890	+	0.744299i	−0.959614	+	0.281318i
$7$	−2.53890	+	0.744299i	−0.959614	+	0.281318i
$8$	0.433884	+	0.900969i	0.153401	+	0.318541i
$9$		0			0
$10$	1.79313	+	2.63004i	0.567038	+	0.831692i
$11$	0.571086	+	3.78891i	0.172189	+	1.14240i	0.893261	+	0.449538i	$0.148412\pi$
$11$	0.571086	+	3.78891i	0.172189	+	1.14240i	−0.721072	+	0.692860i	$0.756350\pi$
$12$		0			0
$13$	−5.36836	+	4.28112i	−1.48891	+	1.18737i	−0.553989	+	0.832524i	$0.686895\pi$
$13$	−5.36836	+	4.28112i	−1.48891	+	1.18737i	−0.934925	+	0.354845i	$0.884534\pi$
$14$	−2.63532	−	0.234717i	−0.704319	−	0.0627307i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−4.39823	−	1.35668i	−1.06673	−	0.329042i	−0.288796	−	0.957391i	$-0.593255\pi$
$17$	−4.39823	−	1.35668i	−1.06673	−	0.329042i	−0.777932	+	0.628349i	$0.783731\pi$
$18$		0			0
$19$	4.57611	−	2.64202i	1.04983	−	0.606120i	0.127229	−	0.991873i	$-0.459392\pi$
$19$	4.57611	−	2.64202i	1.04983	−	0.606120i	0.922602	+	0.385753i	$0.126058\pi$
$20$	0.708317	+	3.10334i	0.158384	+	0.693928i
$21$		0			0
$22$	−0.852634	+	3.73564i	−0.181782	+	0.796440i
$23$	−1.21969	−	3.95414i	−0.254323	−	0.824496i	−0.989235	−	0.146333i	$-0.953253\pi$
$23$	−1.21969	−	3.95414i	−0.254323	−	0.824496i	0.734912	−	0.678162i	$-0.237223\pi$
$24$		0			0
$25$	1.87509	+	4.77764i	0.375017	+	0.955529i
$26$	−6.56133	+	2.02390i	−1.28678	+	0.396920i
$27$		0			0
$28$	−2.36740	−	1.18128i	−0.447396	−	0.223241i
$29$	2.11497	−	0.482729i	0.392741	−	0.0896405i	−0.0215900	−	0.999767i	$-0.506873\pi$
$29$	2.11497	−	0.482729i	0.392741	−	0.0896405i	0.414331	+	0.910126i	$0.364016\pi$
$30$		0			0
$31$	4.71405	+	2.72166i	0.846669	+	0.488824i	0.859525	−	0.511093i	$-0.170759\pi$
$31$	4.71405	+	2.72166i	0.846669	+	0.488824i	−0.0128568	+	0.999917i	$0.504093\pi$
$32$	−0.294755	+	0.955573i	−0.0521058	+	0.168923i
$33$		0			0
$34$	−3.59855	−	2.86975i	−0.617146	−	0.492158i
$35$	−8.01204	−	2.59505i	−1.35428	−	0.438643i
$36$		0			0
$37$	2.28232	−	2.11768i	0.375211	−	0.348145i	−0.469915	−	0.882712i	$-0.655716\pi$
$37$	2.28232	−	2.11768i	0.375211	−	0.348145i	0.845126	+	0.534566i	$0.179525\pi$
$38$	5.22502	−	0.787544i	0.847610	−	0.127757i
$39$		0			0
$40$	−0.474424	+	3.14759i	−0.0750129	+	0.497678i
$41$	2.26412	−	1.09034i	0.353596	−	0.170283i	−0.248650	−	0.968593i	$-0.579987\pi$
$41$	2.26412	−	1.09034i	0.353596	−	0.170283i	0.602246	+	0.798310i	$0.294273\pi$
$42$		0			0
$43$	7.68742	+	3.70206i	1.17232	+	0.564560i	0.915665	−	0.401943i	$-0.131665\pi$
$43$	7.68742	+	3.70206i	1.17232	+	0.564560i	0.256656	+	0.966503i	$0.417379\pi$
$44$	−2.15848	+	3.16590i	−0.325402	+	0.477278i
$45$		0			0
$46$	0.309232	−	4.12641i	0.0455937	−	0.608406i
$47$	1.92561	−	4.90638i	0.280880	−	0.715670i	−0.718909	−	0.695104i	$-0.755358\pi$
$47$	1.92561	−	4.90638i	0.280880	−	0.715670i	0.999789	−	0.0205654i	$-0.00654663\pi$
$48$		0			0
$49$	5.89204	−	3.77940i	0.841720	−	0.539915i
$50$			5.13243i			0.725835i
$51$		0			0
$52$	−6.84718	−	0.513126i	−0.949534	−	0.0711577i
$53$	−2.73142	+	2.94378i	−0.375190	+	0.404359i	−0.892214	−	0.451612i	$-0.850849\pi$
$53$	−2.73142	+	2.94378i	−0.375190	+	0.404359i	0.517024	+	0.855971i	$0.327040\pi$
$54$		0			0
$55$	−5.29203	+	10.9890i	−0.713577	+	1.48176i
$56$	−1.77218	−	1.96453i	−0.236817	−	0.262522i
$57$		0			0
$58$	2.14513	+	0.323327i	0.281670	+	0.0424549i
$59$	5.23837	−	3.57146i	0.681978	−	0.464965i	−0.172121	−	0.985076i	$-0.555062\pi$
$59$	5.23837	−	3.57146i	0.681978	−	0.464965i	0.854098	+	0.520111i	$0.174110\pi$
$60$		0			0
$61$	4.87224	+	5.25102i	0.623826	+	0.672324i	0.963342	−	0.268276i	$-0.0864538\pi$
$61$	4.87224	+	5.25102i	0.623826	+	0.672324i	−0.339516	+	0.940600i	$0.610263\pi$
$62$	3.39385	+	4.25576i	0.431020	+	0.540482i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−21.7956	+	1.63335i	−2.70341	+	0.202593i
$66$		0			0
$67$	1.99581	−	3.45685i	0.243827	−	0.422321i	−0.717974	−	0.696070i	$-0.754930\pi$
$67$	1.99581	−	3.45685i	0.243827	−	0.422321i	0.961801	+	0.273749i	$0.0882637\pi$
$68$	−2.30136	−	3.98607i	−0.279081	−	0.483382i
$69$		0			0
$70$	−6.51012	−	5.34279i	−0.778108	−	0.638585i
$71$	9.06789	+	2.06969i	1.07616	+	0.245627i	0.723640	−	0.690178i	$-0.242468\pi$
$71$	9.06789	+	2.06969i	1.07616	+	0.245627i	0.352520	+	0.935804i	$0.385325\pi$
$72$		0			0
$73$	−10.9744	+	4.30713i	−1.28445	+	0.504111i	−0.906693	−	0.421791i	$-0.861401\pi$
$73$	−10.9744	+	4.30713i	−1.28445	+	0.504111i	−0.377762	+	0.925903i	$0.623306\pi$
$74$	2.89823	−	1.13747i	0.336912	−	0.132228i
$75$		0			0
$76$	5.15155	+	1.17581i	0.590924	+	0.134874i
$77$	−4.27001	−	9.19460i	−0.486613	−	1.04782i
$78$		0			0
$79$	3.29241	+	5.70262i	0.370425	+	0.641595i	0.989631	−	0.143634i	$-0.0458787\pi$
$79$	3.29241	+	5.70262i	0.370425	+	0.641595i	−0.619206	+	0.785229i	$0.712545\pi$
$80$	−1.59157	+	2.75669i	−0.177943	+	0.308207i
$81$		0			0
$82$	2.50596	−	0.187796i	0.276737	−	0.0207385i
$83$	3.93879	−	4.93909i	0.432338	−	0.542135i	−0.517168	−	0.855884i	$-0.673014\pi$
$83$	3.93879	−	4.93909i	0.432338	−	0.542135i	0.949506	+	0.313749i	$0.101585\pi$
$84$		0			0
$85$	−9.13483	−	11.4547i	−0.990812	−	1.24244i
$86$	5.80350	+	6.25468i	0.625807	+	0.674460i
$87$		0			0
$88$	−3.16590	+	2.15848i	−0.337486	+	0.230094i
$89$	−17.0448	−	2.56910i	−1.80675	−	0.272324i	−0.842764	−	0.538283i	$-0.819073\pi$
$89$	−17.0448	−	2.56910i	−1.80675	−	0.272324i	−0.963984	+	0.265959i	$0.914311\pi$
$90$		0			0
$91$	10.4433	−	14.8650i	1.09475	−	1.55828i
$92$	1.79540	−	3.72819i	0.187184	−	0.388691i
$93$		0			0
$94$	3.58501	−	3.86372i	0.369765	−	0.398512i
$95$	16.7728	+	1.25695i	1.72086	+	0.128960i
$96$		0			0
$97$			10.9117i			1.10791i	0.832546	+	0.553956i	$0.186882\pi$
$97$			10.9117i			1.10791i	−0.832546	+	0.553956i	$0.813118\pi$
$98$	6.86551	−	1.36554i	0.693522	−	0.137941i
$99$		0			0
$100$	−1.87509	+	4.77764i	−0.187509	+	0.477764i
$101$	−0.541771	+	7.22943i	−0.0539082	+	0.719355i	0.903125	+	0.429377i	$0.141267\pi$
$101$	−0.541771	+	7.22943i	−0.0539082	+	0.719355i	−0.957033	+	0.289978i	$0.906352\pi$
$102$		0			0
$103$	−0.626622	+	0.919085i	−0.0617429	+	0.0905602i	−0.855869	−	0.517193i	$-0.826977\pi$
$103$	−0.626622	+	0.919085i	−0.0617429	+	0.0905602i	0.794126	+	0.607754i	$0.207929\pi$
$104$	−6.18640	−	2.97921i	−0.606626	−	0.292136i
$105$		0			0
$106$	−3.61809	+	1.74238i	−0.351420	+	0.169235i
$107$	0.308353	−	2.04579i	0.0298096	−	0.197774i	−0.968969	−	0.247182i	$-0.920495\pi$
$107$	0.308353	−	2.04579i	0.0298096	−	0.197774i	0.998779	+	0.0494083i	$0.0157335\pi$
$108$		0			0
$109$	19.0485	−	2.87110i	1.82451	−	0.275001i	0.854748	−	0.519043i	$-0.173712\pi$
$109$	19.0485	−	2.87110i	1.82451	−	0.275001i	0.969765	+	0.244042i	$0.0784734\pi$
$110$	−8.94095	+	8.29598i	−0.852486	+	0.790991i
$111$		0			0
$112$	−0.931950	−	2.47618i	−0.0880610	−	0.233977i
$113$	3.59218	+	2.86467i	0.337924	+	0.269485i	0.777718	−	0.628613i	$-0.216377\pi$
$113$	3.59218	+	2.86467i	0.337924	+	0.269485i	−0.439794	+	0.898099i	$0.644949\pi$
$114$		0			0
$115$	3.88246	−	12.5866i	0.362041	−	1.17371i
$116$	1.87872	+	1.08468i	0.174435	+	0.100710i
$117$		0			0
$118$	6.18106	−	1.41079i	0.569013	−	0.129873i
$119$	12.1764	+	0.170865i	1.11621	+	0.0156632i
$120$		0			0
$121$	−3.51838	+	1.08528i	−0.319852	+	0.0986614i
$122$	2.61702	+	6.66807i	0.236934	+	0.603698i
$123$		0			0
$124$	1.60445	+	5.20149i	0.144084	+	0.467107i
$125$	−0.0938011	+	0.410970i	−0.00838983	+	0.0367582i
$126$		0			0
$127$	2.07225	+	9.07913i	0.183883	+	0.805643i	0.979759	+	0.200183i	$0.0641536\pi$
$127$	2.07225	+	9.07913i	0.183883	+	0.805643i	−0.795876	+	0.605460i	$0.792989\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−20.8857	−	6.44238i	−1.83180	−	0.565034i
$131$	−0.0780458	−	1.04145i	−0.00681889	−	0.0909918i	0.992756	−	0.120148i	$-0.0383370\pi$
$131$	−0.0780458	−	1.04145i	−0.00681889	−	0.0909918i	−0.999575	+	0.0291564i	$0.990718\pi$
$132$		0			0
$133$	−9.65184	+	10.1138i	−0.836920	+	0.876979i
$134$	3.12078	−	2.48874i	0.269594	−	0.214994i
$135$		0			0
$136$	−0.686000	−	4.55131i	−0.0588240	−	0.390272i
$137$	−8.90119	−	13.0556i	−0.760480	−	1.11542i	−0.989855	−	0.142081i	$-0.954621\pi$
$137$	−8.90119	−	13.0556i	−0.760480	−	1.11542i	0.229375	−	0.973338i	$-0.426332\pi$
$138$		0			0
$139$	6.89784	+	14.3235i	0.585067	+	1.21490i	0.957926	+	0.287016i	$0.0926632\pi$
$139$	6.89784	+	14.3235i	0.585067	+	1.21490i	−0.372859	+	0.927888i	$0.621623\pi$
$140$	−4.10816	−	7.35187i	−0.347203	−	0.621347i
$141$		0			0
$142$	7.68492	+	5.23949i	0.644904	+	0.439688i
$143$	−19.2866	−	17.8953i	−1.61282	−	1.49648i
$144$		0			0
$145$	6.42806	+	2.52283i	0.533821	+	0.209509i
$146$	−11.7893			−0.975693
$147$		0			0
$148$	3.11345			0.255924
$149$	11.3275	+	4.44571i	0.927985	+	0.364207i	0.780714	−	0.624889i	$-0.214856\pi$
$149$	11.3275	+	4.44571i	0.927985	+	0.364207i	0.147271	+	0.989096i	$0.452951\pi$
$150$		0			0
$151$	−7.20545	−	6.68568i	−0.586371	−	0.544073i	0.330217	−	0.943905i	$-0.392878\pi$
$151$	−7.20545	−	6.68568i	−0.586371	−	0.544073i	−0.916589	+	0.399832i	$0.869069\pi$
$152$	4.36587	+	2.97660i	0.354119	+	0.241434i
$153$		0			0
$154$	−0.615674	−	10.1190i	−0.0496124	−	0.815414i
$155$	7.51785	+	15.6110i	0.603848	+	1.25390i
$156$		0			0
$157$	−1.29765	−	1.90331i	−0.103564	−	0.151900i	0.770959	−	0.636885i	$-0.219778\pi$
$157$	−1.29765	−	1.90331i	−0.103564	−	0.151900i	−0.874523	+	0.484985i	$0.838825\pi$
$158$	0.981417	+	6.51128i	0.0780773	+	0.518009i
$159$		0			0
$160$	−2.48868	+	1.98466i	−0.196748	+	0.156901i
$161$	6.03974	+	9.13136i	0.475998	+	0.719652i
$162$		0			0
$163$	−0.972051	−	12.9711i	−0.0761369	−	1.01598i	−0.896185	−	0.443681i	$-0.853672\pi$
$163$	−0.972051	−	12.9711i	−0.0761369	−	1.01598i	0.820048	−	0.572295i	$-0.193947\pi$
$164$	2.40134	+	0.740715i	0.187513	+	0.0578401i
$165$		0			0
$166$	5.47097	−	3.15866i	0.424629	−	0.245160i
$167$	−4.00265	−	17.5368i	−0.309734	−	1.35703i	−0.854938	−	0.518731i	$-0.826405\pi$
$167$	−4.00265	−	17.5368i	−0.309734	−	1.35703i	0.545203	−	0.838304i	$-0.316452\pi$
$168$		0			0
$169$	7.59847	−	33.2911i	0.584498	−	2.56085i
$170$	−4.31850	−	14.0002i	−0.331214	−	1.07377i
$171$		0			0
$172$	3.11723	+	7.94258i	0.237687	+	0.605616i
$173$	−8.84653	+	2.72879i	−0.672590	+	0.207466i	−0.612193	−	0.790708i	$-0.709713\pi$
$173$	−8.84653	+	2.72879i	−0.672590	+	0.207466i	−0.0603962	+	0.998174i	$0.519236\pi$
$174$		0			0
$175$	−8.31665	−	10.7343i	−0.628680	−	0.811440i
$176$	−3.73564	+	0.852634i	−0.281584	+	0.0642697i
$177$		0			0
$178$	−14.9280	−	8.61868i	−1.11890	−	0.645997i
$179$	4.86002	−	15.7558i	0.363255	−	1.17764i	−0.570974	−	0.820968i	$-0.693434\pi$
$179$	4.86002	−	15.7558i	0.363255	−	1.17764i	0.934229	−	0.356675i	$-0.116090\pi$
$180$		0			0
$181$	−19.7498	−	15.7499i	−1.46799	−	1.17068i	−0.948738	−	0.316065i	$-0.897638\pi$
$181$	−19.7498	−	15.7499i	−1.46799	−	1.17068i	−0.519254	−	0.854620i	$-0.673790\pi$
$182$	15.1522	−	10.0221i	1.12315	−	0.742886i
$183$		0			0
$184$	3.03335	−	2.81454i	0.223622	−	0.207491i
$185$	9.79988	−	1.47709i	0.720501	−	0.108598i
$186$		0			0
$187$	2.62855	−	17.4393i	0.192218	−	1.27529i
$188$	4.74876	−	2.28688i	0.346339	−	0.166788i
$189$		0			0
$190$	15.1542	+	7.29786i	1.09940	+	0.529443i
$191$	15.3734	−	22.5486i	1.11238	−	1.63156i	0.425145	−	0.905125i	$-0.360223\pi$
$191$	15.3734	−	22.5486i	1.11238	−	1.63156i	0.687234	−	0.726436i	$-0.258825\pi$
$192$		0			0
$193$	1.60543	−	21.4230i	0.115562	−	1.54206i	−0.574615	−	0.818424i	$-0.694848\pi$
$193$	1.60543	−	21.4230i	0.115562	−	1.54206i	0.690177	−	0.723641i	$-0.257533\pi$
$194$	−3.98648	+	10.1574i	−0.286213	+	0.729258i
$195$		0			0
$196$	6.88982	+	1.23711i	0.492130	+	0.0883648i
$197$			19.9875i			1.42405i	0.702153	+	0.712026i	$0.252222\pi$
$197$			19.9875i			1.42405i	−0.702153	+	0.712026i	$0.747778\pi$
$198$		0			0
$199$	−23.1959	−	1.73829i	−1.64432	−	0.123224i	−0.779867	−	0.625946i	$-0.784713\pi$
$199$	−23.1959	−	1.73829i	−1.64432	−	0.123224i	−0.864448	+	0.502721i	$0.832332\pi$
$200$	−3.49094	+	3.76234i	−0.246847	+	0.266037i
$201$		0			0
$202$	−3.14553	+	6.53176i	−0.221319	+	0.459573i
$203$	−5.01041	+	2.79977i	−0.351662	+	0.196506i
$204$		0			0
$205$	7.90985	+	1.19222i	0.552448	+	0.0832682i
$206$	−0.919085	+	0.626622i	−0.0640357	+	0.0436588i
$207$		0			0
$208$	−4.67033	−	5.03342i	−0.323829	−	0.349005i
$209$	12.6237	+	15.8296i	0.873200	+	1.09496i
$210$		0			0
$211$	−7.89761	+	9.90329i	−0.543694	+	0.681771i	−0.975450	−	0.220220i	$-0.929323\pi$
$211$	−7.89761	+	9.90329i	−0.543694	+	0.681771i	0.431756	+	0.901990i	$0.357894\pi$
$212$	−4.00455	+	0.300100i	−0.275034	+	0.0206109i
$213$		0			0
$214$	1.03445	−	1.79172i	0.0707134	−	0.122479i
$215$	13.5799	+	23.5211i	0.926143	+	1.60413i
$216$		0			0
$217$	−13.9942	−	3.40136i	−0.949991	−	0.230899i
$218$	18.7807	+	4.28656i	1.27199	+	0.290323i
$219$		0			0
$220$	−11.3538	+	4.45602i	−0.765470	+	0.300425i
$221$	29.4194	−	11.5462i	1.97896	−	0.776685i
$222$		0			0
$223$	−4.57894	−	1.04511i	−0.306628	−	0.0699859i	0.0664382	−	0.997791i	$-0.478836\pi$
$223$	−4.57894	−	1.04511i	−0.306628	−	0.0699859i	−0.373066	+	0.927805i	$0.621694\pi$
$224$	0.0371227	−	2.64549i	0.00248036	−	0.176759i
$225$		0			0
$226$	2.29728	+	3.97901i	0.152813	+	0.264680i
$227$	4.95719	−	8.58610i	0.329020	−	0.569880i	−0.653298	−	0.757101i	$-0.726615\pi$
$227$	4.95719	−	8.58610i	0.329020	−	0.569880i	0.982318	+	0.187222i	$0.0599483\pi$
$228$		0			0
$229$	−10.3910	+	0.778697i	−0.686656	+	0.0514577i	−0.413489	−	0.910509i	$-0.635690\pi$
$229$	−10.3910	+	0.778697i	−0.686656	+	0.0514577i	−0.273167	+	0.961967i	$0.588071\pi$
$230$	8.21248	−	10.2981i	0.541515	−	0.679039i
$231$		0			0
$232$	1.35258	+	1.69608i	0.0888010	+	0.111353i
$233$	−10.5243	−	11.3426i	−0.689473	−	0.743075i	0.287185	−	0.957875i	$-0.407281\pi$
$233$	−10.5243	−	11.3426i	−0.689473	−	0.743075i	−0.976658	+	0.214800i	$0.931090\pi$
$234$		0			0
$235$	13.8622	−	9.45111i	0.904272	−	0.616522i
$236$	6.26921	+	0.944931i	0.408091	+	0.0615098i
$237$		0			0
$238$	11.2723	+	4.60761i	0.730675	+	0.298667i
$239$	−11.6595	+	24.2112i	−0.754189	+	1.56609i	0.0685348	+	0.997649i	$0.478168\pi$
$239$	−11.6595	+	24.2112i	−0.754189	+	1.56609i	−0.822724	+	0.568441i	$0.807547\pi$
$240$		0			0
$241$	−16.7810	+	18.0857i	−1.08096	+	1.16500i	−0.0954423	+	0.995435i	$0.530427\pi$
$241$	−16.7810	+	18.0857i	−1.08096	+	1.16500i	−0.985519	+	0.169564i	$0.945764\pi$
$242$	−3.67166	−	0.275153i	−0.236023	−	0.0176875i
$243$		0			0
$244$			7.16323i			0.458579i
$245$	22.2733	+	0.625219i	1.42299	+	0.0399438i
$246$		0			0
$247$	−13.2554	+	33.7742i	−0.843420	+	2.14900i
$248$	−0.406780	+	5.42810i	−0.0258305	+	0.344685i
$249$		0			0
$250$	−0.237461	+	0.348291i	−0.0150184	+	0.0220279i
$251$	−18.7423	−	9.02580i	−1.18300	−	0.569703i	−0.264217	−	0.964463i	$-0.585114\pi$
$251$	−18.7423	−	9.02580i	−1.18300	−	0.569703i	−0.918784	+	0.394760i	$0.870828\pi$
$252$		0			0
$253$	14.2853	−	6.87945i	0.898111	−	0.432507i
$254$	−1.38797	+	9.20860i	−0.0870892	+	0.577799i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	6.09062	−	5.65127i	0.379922	−	0.352517i	−0.466977	−	0.884269i	$-0.654657\pi$
$257$	6.09062	−	5.65127i	0.379922	−	0.352517i	0.846900	+	0.531753i	$0.178466\pi$
$258$		0			0
$259$	−4.21840	+	7.07532i	−0.262118	+	0.439639i
$260$	−17.0883	−	13.6274i	−1.05977	−	0.845138i
$261$		0			0
$262$	0.307833	−	0.997970i	0.0190180	−	0.0616548i
$263$	10.3977	+	6.00309i	0.641147	+	0.370166i	0.785056	−	0.619425i	$-0.212634\pi$
$263$	10.3977	+	6.00309i	0.641147	+	0.370166i	−0.143909	+	0.989591i	$0.545967\pi$
$264$		0			0
$265$	−12.4623	+	2.84445i	−0.765555	+	0.174733i
$266$	−12.6796	+	5.88847i	−0.777438	+	0.361045i
$267$		0			0
$268$	3.81429	−	1.17655i	0.232995	−	0.0718694i
$269$	−0.573435	−	1.46109i	−0.0349630	−	0.0890842i	0.912326	−	0.409465i	$-0.134284\pi$
$269$	−0.573435	−	1.46109i	−0.0349630	−	0.0890842i	−0.947289	+	0.320380i	$0.896189\pi$
$270$		0			0
$271$	5.30735	+	17.2060i	0.322398	+	1.04519i	0.961208	+	0.275825i	$0.0889510\pi$
$271$	5.30735	+	17.2060i	0.322398	+	1.04519i	−0.638810	+	0.769365i	$0.720573\pi$
$272$	1.02420	−	4.48732i	0.0621013	−	0.272084i
$273$		0			0
$274$	−3.51612	−	15.4051i	−0.212417	−	0.930658i
$275$	−17.0312	+	9.83297i	−1.02702	+	0.592951i
$276$		0			0
$277$	31.3329	+	9.66493i	1.88261	+	0.580709i	0.992049	+	0.125853i	$0.0401668\pi$
$277$	31.3329	+	9.66493i	1.88261	+	0.580709i	0.890565	+	0.454856i	$0.150309\pi$
$278$	1.18805	+	15.8534i	0.0712545	+	0.950826i
$279$		0			0
$280$	−1.13824	−	8.34454i	−0.0680226	−	0.498682i
$281$	6.02057	−	4.80124i	0.359157	−	0.286418i	−0.427242	−	0.904138i	$-0.640515\pi$
$281$	6.02057	−	4.80124i	0.359157	−	0.286418i	0.786399	+	0.617719i	$0.211943\pi$
$282$		0			0
$283$	1.54926	+	10.2786i	0.0920937	+	0.611002i	0.986502	+	0.163750i	$0.0523590\pi$
$283$	1.54926	+	10.2786i	0.0920937	+	0.611002i	−0.894408	+	0.447252i	$0.852403\pi$
$284$	5.23949	+	7.68492i	0.310906	+	0.456016i
$285$		0			0
$286$	−11.4155	−	23.7044i	−0.675010	−	1.40167i
$287$	−4.93684	+	4.45345i	−0.291412	+	0.262879i
$288$		0			0
$289$	3.45782	+	2.35750i	0.203401	+	0.138677i
$290$	5.06202	+	4.69687i	0.297252	+	0.275810i
$291$		0			0
$292$	−10.9744	−	4.30713i	−0.642227	−	0.252056i
$293$	−1.13101			−0.0660742			−0.0330371	−	0.999454i	$-0.510518\pi$
$293$	−1.13101			−0.0660742			−0.0330371	+	0.999454i	$0.510518\pi$
$294$		0			0
$295$	20.1812			1.17500
$296$	2.89823	+	1.13747i	0.168456	+	0.0661142i
$297$		0			0
$298$	8.92027	+	8.27680i	0.516737	+	0.479462i
$299$	23.4759	+	16.0056i	1.35765	+	0.925627i
$300$		0			0
$301$	−22.2730	−	3.67744i	−1.28380	−	0.211964i
$302$	−4.26481	−	8.85597i	−0.245412	−	0.509604i
$303$		0			0
$304$	2.97660	+	4.36587i	0.170720	+	0.250400i
$305$	3.39841	+	22.5470i	0.194592	+	1.29103i
$306$		0			0
$307$	3.83448	−	3.05789i	0.218845	−	0.174523i	−0.507931	−	0.861398i	$-0.669589\pi$
$307$	3.83448	−	3.05789i	0.218845	−	0.174523i	0.726776	+	0.686875i	$0.241018\pi$
$308$	3.12378	−	9.64446i	0.177994	−	0.549544i
$309$		0			0
$310$	1.29484	+	17.2784i	0.0735419	+	0.981349i
$311$	−23.7075	−	7.31279i	−1.34433	−	0.414670i	−0.462658	−	0.886537i	$-0.653104\pi$
$311$	−23.7075	−	7.31279i	−1.34433	−	0.414670i	−0.881670	+	0.471866i	$0.843581\pi$
$312$		0			0
$313$	8.46261	−	4.88589i	0.478335	−	0.276167i	−0.241387	−	0.970429i	$-0.577602\pi$
$313$	8.46261	−	4.88589i	0.478335	−	0.276167i	0.719722	+	0.694262i	$0.244269\pi$
$314$	−0.512595	−	2.24582i	−0.0289274	−	0.126739i
$315$		0			0
$316$	−1.46526	+	6.41973i	−0.0824274	+	0.361138i
$317$	0.434041	+	1.40713i	0.0243781	+	0.0790320i	0.966944	−	0.254987i	$-0.0820712\pi$
$317$	0.434041	+	1.40713i	0.0243781	+	0.0790320i	−0.942566	+	0.334019i	$0.891595\pi$
$318$		0			0
$319$	3.03685	+	7.73776i	0.170031	+	0.433231i
$320$	−3.04173	+	0.938249i	−0.170038	+	0.0524497i
$321$		0			0
$322$	2.28617	+	10.7067i	0.127403	+	0.596662i
$323$	−23.7111	+	5.41191i	−1.31932	+	0.301127i
$324$		0			0
$325$	−30.5198	−	17.6206i	−1.69293	−	0.977416i
$326$	3.83402	−	12.4296i	0.212347	−	0.688412i
$327$		0			0
$328$	1.96473	+	1.56682i	0.108484	+	0.0865131i
$329$	−1.23713	+	13.8901i	−0.0682051	+	0.765784i
$330$		0			0
$331$	4.89425	−	4.54120i	0.269012	−	0.249607i	−0.534119	−	0.845409i	$-0.679356\pi$
$331$	4.89425	−	4.54120i	0.269012	−	0.249607i	0.803131	+	0.595803i	$0.203166\pi$
$332$	6.24677	−	0.941549i	0.342836	−	0.0516742i
$333$		0			0
$334$	2.68093	−	17.7868i	0.146694	−	0.973252i
$335$	11.4476	−	5.51290i	0.625452	−	0.301202i
$336$		0			0
$337$	−10.1312	−	4.87891i	−0.551879	−	0.265771i	0.137094	−	0.990558i	$-0.456224\pi$
$337$	−10.1312	−	4.87891i	−0.551879	−	0.265771i	−0.688973	+	0.724787i	$0.741938\pi$
$338$	19.2358	−	28.2138i	1.04629	−	1.53463i
$339$		0			0
$340$	1.09488	−	14.6102i	0.0593782	−	0.792347i
$341$	−7.61998	+	19.4154i	−0.412645	+	1.05140i
$342$		0			0
$343$	−12.1463	+	13.9810i	−0.655839	+	0.754901i
$344$			8.53239i			0.460036i
$345$		0			0
$346$	−9.23195	−	0.691839i	−0.496313	−	0.0371935i
$347$	22.8301	−	24.6050i	1.22559	−	1.32087i	0.294687	−	0.955594i	$-0.404785\pi$
$347$	22.8301	−	24.6050i	1.22559	−	1.32087i	0.930900	−	0.365274i	$-0.119025\pi$
$348$		0			0
$349$	2.18725	−	4.54187i	0.117081	−	0.243121i	−0.834190	−	0.551477i	$-0.814065\pi$
$349$	2.18725	−	4.54187i	0.117081	−	0.243121i	0.951271	+	0.308356i	$0.0997788\pi$
$350$	−3.82006	−	13.0307i	−0.204191	−	0.696522i
$351$		0			0
$352$	−3.78891	−	0.571086i	−0.201949	−	0.0304390i
$353$	−9.24639	+	6.30408i	−0.492135	+	0.335532i	−0.783826	−	0.620980i	$-0.786735\pi$
$353$	−9.24639	+	6.30408i	−0.492135	+	0.335532i	0.291691	+	0.956513i	$0.405782\pi$
$354$		0			0
$355$	20.1377	+	21.7033i	1.06880	+	1.15189i
$356$	−10.7473	−	13.4767i	−0.569607	−	0.714264i
$357$		0			0
$358$	10.2803	−	12.8911i	0.543331	−	0.681315i
$359$	−27.6283	+	2.07045i	−1.45817	+	0.109274i	−0.780067	−	0.625696i	$-0.784815\pi$
$359$	−27.6283	+	2.07045i	−1.45817	+	0.109274i	−0.678099	+	0.734971i	$0.737196\pi$
$360$		0			0
$361$	4.46051	−	7.72583i	0.234764	−	0.406623i
$362$	−12.6305	−	21.8766i	−0.663843	−	1.14981i
$363$		0			0
$364$	17.7662	−	3.79358i	0.931204	−	0.198837i
$365$	−36.5863	−	8.35059i	−1.91502	−	0.437090i
$366$		0			0
$367$	30.3449	−	11.9095i	1.58399	−	0.621671i	0.600019	−	0.799986i	$-0.295160\pi$
$367$	30.3449	−	11.9095i	1.58399	−	0.621671i	0.983974	+	0.178314i	$0.0570644\pi$
$368$	3.85194	−	1.51177i	0.200796	−	0.0788067i
$369$		0			0
$370$	9.66209	+	2.20531i	0.502308	+	0.114649i
$371$	4.74377	−	9.50695i	0.246284	−	0.493576i
$372$		0			0
$373$	14.7601	+	25.5653i	0.764251	+	1.32372i	0.940642	+	0.339401i	$0.110224\pi$
$373$	14.7601	+	25.5653i	0.764251	+	1.32372i	−0.176391	+	0.984320i	$0.556442\pi$
$374$	8.81813	−	15.2734i	0.455974	−	0.789771i
$375$		0			0
$376$	5.25599	−	0.393882i	0.271057	−	0.0203129i
$377$	−9.28731	+	11.6459i	−0.478321	+	0.599795i
$378$		0			0
$379$	−1.55041	−	1.94415i	−0.0796391	−	0.0998643i	0.740416	−	0.672149i	$-0.234629\pi$
$379$	−1.55041	−	1.94415i	−0.0796391	−	0.0998643i	−0.820055	+	0.572285i	$0.806057\pi$
$380$	11.4404	+	12.3298i	0.586881	+	0.632507i
$381$		0			0
$382$	22.5486	−	15.3734i	1.15369	−	0.786571i
$383$	−4.78229	−	0.720814i	−0.244363	−	0.0368319i	0.0257184	−	0.999669i	$-0.491813\pi$
$383$	−4.78229	−	0.720814i	−0.244363	−	0.0368319i	−0.270082	+	0.962837i	$0.587051\pi$
$384$		0			0
$385$	5.25683	−	31.8389i	0.267913	−	1.62266i
$386$	9.32117	−	19.3556i	0.474435	−	0.985175i
$387$		0			0
$388$	−7.42182	+	7.99882i	−0.376786	+	0.406079i
$389$	−18.0119	−	1.34980i	−0.913238	−	0.0684377i	−0.390184	−	0.920737i	$-0.627588\pi$
$389$	−18.0119	−	1.34980i	−0.913238	−	0.0684377i	−0.523054	+	0.852299i	$0.675208\pi$
$390$		0			0
$391$			19.0460i			0.963196i
$392$	5.96158	+	3.66872i	0.301105	+	0.185298i
$393$		0			0
$394$	−7.30227	+	18.6059i	−0.367883	+	0.937350i
$395$	−1.56638	+	20.9019i	−0.0788130	+	1.05169i
$396$		0			0
$397$	−9.30762	+	13.6518i	−0.467136	+	0.685163i	−0.985438	−	0.170035i	$-0.945612\pi$
$397$	−9.30762	+	13.6518i	−0.467136	+	0.685163i	0.518302	+	0.855198i	$0.326564\pi$
$398$	−20.9574	−	10.0926i	−1.05050	−	0.505894i
$399$		0			0
$400$	−4.62416	+	2.22688i	−0.231208	+	0.111344i
$401$	−4.30632	+	28.5706i	−0.215048	+	1.42675i	0.577228	+	0.816583i	$0.304135\pi$
$401$	−4.30632	+	28.5706i	−0.215048	+	1.42675i	−0.792275	+	0.610164i	$0.791104\pi$
$402$		0			0
$403$	−36.9585	+	5.57059i	−1.84103	+	0.277491i
$404$	−5.31441	+	4.93105i	−0.264402	+	0.245329i
$405$		0			0
$406$	−5.68693	+	0.775725i	−0.282238	+	0.0384986i
$407$	9.32711	+	7.43812i	0.462328	+	0.368694i
$408$		0			0
$409$	8.08344	−	26.2059i	0.399700	−	1.29580i	−0.502536	−	0.864556i	$-0.667600\pi$
$409$	8.08344	−	26.2059i	0.399700	−	1.29580i	0.902237	−	0.431241i	$-0.141924\pi$
$410$	6.92751	+	3.99960i	0.342125	+	0.197526i
$411$		0			0
$412$	−1.08448	+	0.247526i	−0.0534287	+	0.0121947i
$413$	−10.6415	+	12.9665i	−0.523633	+	0.638040i
$414$		0			0
$415$	19.2156	−	5.92723i	0.943257	−	0.290956i
$416$	−2.50857	−	6.39174i	−0.122993	−	0.313381i
$417$		0			0
$418$	5.96787	+	19.3473i	0.291898	+	0.946310i
$419$	−6.73810	+	29.5215i	−0.329178	+	1.44222i	0.491524	+	0.870864i	$0.336440\pi$
$419$	−6.73810	+	29.5215i	−0.329178	+	1.44222i	−0.820701	+	0.571357i	$0.806417\pi$
$420$		0			0
$421$	0.603089	+	2.64231i	0.0293928	+	0.128778i	0.987496	−	0.157646i	$-0.0503905\pi$
$421$	0.603089	+	2.64231i	0.0293928	+	0.128778i	−0.958103	+	0.286424i	$0.907533\pi$
$422$	−10.9698	+	6.33339i	−0.533999	+	0.308305i
$423$		0			0
$424$	−3.83737	−	1.18367i	−0.186359	−	0.0574842i
$425$	−1.76536	−	23.5571i	−0.0856324	−	1.14269i
$426$		0			0
$427$	−16.2785	−	9.70543i	−0.787770	−	0.469679i
$428$	1.61753	−	1.28993i	0.0781861	−	0.0623514i
$429$		0			0
$430$	4.04797	+	26.8565i	0.195210	+	1.29514i
$431$	−20.9058	−	30.6632i	−1.00700	−	1.47700i	−0.874028	−	0.485876i	$-0.838501\pi$
$431$	−20.9058	−	30.6632i	−1.00700	−	1.47700i	−0.132971	−	0.991120i	$-0.542452\pi$
$432$		0			0
$433$	9.11048	+	18.9181i	0.437822	+	0.909147i	0.996798	+	0.0799627i	$0.0254801\pi$
$433$	9.11048	+	18.9181i	0.437822	+	0.909147i	−0.558976	+	0.829184i	$0.688806\pi$
$434$	−11.7842	−	8.27891i	−0.565660	−	0.397400i
$435$		0			0
$436$	15.9164	+	10.8516i	0.762255	+	0.519697i
$437$	−16.0283	−	14.8721i	−0.766740	−	0.711431i
$438$		0			0
$439$	19.5712	+	7.68113i	0.934083	+	0.366600i	0.783072	−	0.621932i	$-0.213652\pi$
$439$	19.5712	+	7.68113i	0.934083	+	0.366600i	0.151011	+	0.988532i	$0.451747\pi$
$440$	−12.1969			−0.581463
$441$		0			0
$442$	31.6040			1.50325
$443$	−18.3583	−	7.20512i	−0.872231	−	0.342326i	−0.113351	−	0.993555i	$-0.536158\pi$
$443$	−18.3583	−	7.20512i	−0.872231	−	0.342326i	−0.758881	+	0.651229i	$0.774254\pi$
$444$		0			0
$445$	−40.2219	−	37.3204i	−1.90670	−	1.76916i
$446$	−3.88059	−	2.64574i	−0.183751	−	0.125279i
$447$		0			0
$448$	1.00106	−	2.44906i	0.0472958	−	0.115707i
$449$	1.41362	+	2.93542i	0.0667131	+	0.138531i	0.931659	−	0.363334i	$-0.118362\pi$
$449$	1.41362	+	2.93542i	0.0667131	+	0.138531i	−0.864946	+	0.501865i	$0.832647\pi$
$450$		0			0
$451$	5.42421	+	7.95586i	0.255416	+	0.374627i
$452$	0.684785	+	4.54325i	0.0322096	+	0.213697i
$453$		0			0
$454$	7.75137	−	6.18151i	0.363790	−	0.290113i
$455$	54.1212	−	20.3694i	2.53724	−	0.954930i
$456$		0			0
$457$	0.962484	+	12.8435i	0.0450231	+	0.600792i	0.973394	+	0.229137i	$0.0735904\pi$
$457$	0.962484	+	12.8435i	0.0450231	+	0.600792i	−0.928371	+	0.371655i	$0.878791\pi$
$458$	−9.95719	−	3.07139i	−0.465269	−	0.143516i
$459$		0			0
$460$	11.4071	−	6.58590i	0.531860	−	0.307069i
$461$	−5.32719	−	23.3400i	−0.248112	−	1.08705i	−0.933417	−	0.358794i	$-0.883188\pi$
$461$	−5.32719	−	23.3400i	−0.248112	−	1.08705i	0.685305	−	0.728256i	$-0.259669\pi$
$462$		0			0
$463$	−4.23600	+	18.5591i	−0.196864	+	0.862516i	0.775926	+	0.630824i	$0.217283\pi$
$463$	−4.23600	+	18.5591i	−0.196864	+	0.862516i	−0.972789	+	0.231691i	$0.925574\pi$
$464$	0.639431	+	2.07298i	0.0296848	+	0.0962359i
$465$		0			0
$466$	−5.65294	−	14.4035i	−0.261867	−	0.667227i
$467$	15.3977	−	4.74956i	0.712520	−	0.219783i	0.0827560	−	0.996570i	$-0.473628\pi$
$467$	15.3977	−	4.74956i	0.712520	−	0.219783i	0.629764	+	0.776787i	$0.283152\pi$
$468$		0			0
$469$	−2.49424	+	10.2621i	−0.115173	+	0.473859i
$470$	16.3569	−	3.73335i	0.754486	−	0.172207i
$471$		0			0
$472$	5.49062	+	3.17001i	0.252726	+	0.145912i
$473$	−9.63660	+	31.2411i	−0.443092	+	1.43647i
$474$		0			0
$475$	21.2032	+	16.9090i	0.972870	+	0.775838i
$476$	8.80975	+	8.40734i	0.403794	+	0.385350i
$477$		0			0
$478$	−19.6988	+	18.2778i	−0.901004	+	0.836009i
$479$	23.4145	−	3.52917i	1.06984	−	0.161252i	0.409566	−	0.912281i	$-0.365680\pi$
$479$	23.4145	−	3.52917i	1.06984	−	0.161252i	0.660269	+	0.751029i	$0.270442\pi$
$480$		0			0
$481$	−3.18625	+	21.1394i	−0.145280	+	0.963872i
$482$	−22.2285	+	10.7047i	−1.01248	+	0.487584i
$483$		0			0
$484$	−3.31733	−	1.59754i	−0.150788	−	0.0726155i
$485$	−19.5661	+	28.6981i	−0.888449	+	1.30311i
$486$		0			0
$487$	−1.21676	+	16.2365i	−0.0551367	+	0.735748i	0.899300	+	0.437333i	$0.144077\pi$
$487$	−1.21676	+	16.2365i	−0.0551367	+	0.735748i	−0.954436	+	0.298415i	$0.903542\pi$
$488$	−2.61702	+	6.66807i	−0.118467	+	0.301849i
$489$		0			0
$490$	20.5052	+	8.71934i	0.926329	+	0.393899i
$491$		−	6.56725i		−	0.296376i	−0.988959	−	0.148188i	$-0.952656\pi$
$491$		−	6.56725i		−	0.296376i	0.988959	−	0.148188i	$-0.0473440\pi$
$492$		0			0
$493$	−9.95705	−	0.746178i	−0.448443	−	0.0336062i
$494$	−24.6782	+	26.5967i	−1.11032	+	1.19664i
$495$		0			0
$496$	−2.36177	+	4.90426i	−0.106046	+	0.220208i
$497$	−24.5629	+	1.49449i	−1.10180	+	0.0670370i
$498$		0			0
$499$	−41.6585	−	6.27900i	−1.86489	−	0.281087i	−0.882835	−	0.469684i	$-0.844368\pi$
$499$	−41.6585	−	6.27900i	−1.86489	−	0.281087i	−0.982055	+	0.188597i	$0.939606\pi$
$500$	−0.348291	+	0.237461i	−0.0155761	+	0.0106196i
$501$		0			0
$502$	−14.1492	−	15.2492i	−0.631509	−	0.680605i
$503$	−4.09923	−	5.14027i	−0.182776	−	0.229194i	0.682000	−	0.731353i	$-0.261111\pi$
$503$	−4.09923	−	5.14027i	−0.182776	−	0.229194i	−0.864775	+	0.502159i	$0.832539\pi$
$504$		0			0
$505$	−14.3882	+	18.0422i	−0.640266	+	0.802869i
$506$	15.8112	−	1.18488i	0.702893	−	0.0526745i
$507$		0			0
$508$	−4.65631	+	8.06496i	−0.206590	+	0.357825i
$509$	3.83721	+	6.64624i	0.170081	+	0.294589i	0.938448	−	0.345420i	$-0.112264\pi$
$509$	3.83721	+	6.64624i	0.170081	+	0.294589i	−0.768367	+	0.640010i	$0.778930\pi$
$510$		0			0
$511$	24.6571	−	19.1036i	1.09077	−	0.845093i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$		0			0
$514$	7.73424	−	3.03547i	0.341143	−	0.133889i
$515$	−3.29608	+	1.29362i	−0.145243	+	0.0570036i
$516$		0			0
$517$	19.6895	+	4.49401i	0.865944	+	0.197646i
$518$	−6.51170	+	5.04507i	−0.286108	+	0.221668i
$519$		0			0
$520$	−10.9284	−	18.9285i	−0.479240	−	0.830068i
$521$	16.4520	−	28.4957i	0.720776	−	1.24842i	−0.239914	−	0.970794i	$-0.577119\pi$
$521$	16.4520	−	28.4957i	0.720776	−	1.24842i	0.960689	−	0.277626i	$-0.0895475\pi$
$522$		0			0
$523$	11.4606	−	0.858851i	0.501136	−	0.0375549i	0.178235	−	0.983988i	$-0.442961\pi$
$523$	11.4606	−	0.858851i	0.501136	−	0.0375549i	0.322900	+	0.946433i	$0.395342\pi$
$524$	0.651153	−	0.816520i	0.0284458	−	0.0356699i
$525$		0			0
$526$	7.48573	+	9.38681i	0.326393	+	0.409284i
$527$	−17.0411	−	18.3659i	−0.742321	−	0.800032i
$528$		0			0
$529$	4.85590	−	3.31070i	0.211126	−	0.143943i
$530$	−12.6400	−	1.90518i	−0.549049	−	0.0827558i
$531$		0			0
$532$	−13.9544	+	0.849033i	−0.605002	+	0.0368102i
$533$	−7.48671	+	15.5463i	−0.324286	+	0.673386i
$534$		0			0
$535$	4.47934	−	4.82758i	0.193659	−	0.208715i
$536$	3.98046	+	0.298295i	0.171930	+	0.0128844i
$537$		0			0
$538$		−	1.56959i		−	0.0676698i
$539$	17.6847	+	20.1660i	0.761732	+	0.868612i
$540$		0			0
$541$	2.85801	−	7.28208i	0.122875	−	0.313081i	−0.856179	−	0.516679i	$-0.827168\pi$
$541$	2.85801	−	7.28208i	0.122875	−	0.313081i	0.979055	+	0.203598i	$0.0652634\pi$
$542$	−1.34559	+	17.9556i	−0.0577979	+	0.771259i
$543$		0			0
$544$	2.59280	−	3.80294i	0.111166	−	0.163050i
$545$	55.2465	+	26.6053i	2.36650	+	1.13965i
$546$		0			0
$547$	−6.71446	+	3.23351i	−0.287090	+	0.138255i	−0.571886	−	0.820333i	$-0.693788\pi$
$547$	−6.71446	+	3.23351i	−0.287090	+	0.138255i	0.284797	+	0.958588i	$0.408074\pi$
$548$	2.35506	−	15.6248i	0.100603	−	0.667459i
$549$		0			0
$550$	−19.4463	+	2.93106i	−0.829193	+	0.124981i
$551$	8.40297	−	7.79681i	0.357978	−	0.332155i
$552$		0			0
$553$	−12.6036	−	12.0279i	−0.535958	−	0.511477i
$554$	25.6360	+	20.4440i	1.08917	+	0.868584i
$555$		0			0
$556$	−4.68598	+	15.1916i	−0.198730	+	0.644267i
$557$	−3.62068	−	2.09040i	−0.153413	−	0.0885730i	0.421328	−	0.906908i	$-0.361564\pi$
$557$	−3.62068	−	2.09040i	−0.153413	−	0.0885730i	−0.574741	+	0.818335i	$0.694897\pi$
$558$		0			0
$559$	−57.1178	+	13.0368i	−2.41582	+	0.551396i
$560$	1.98905	−	8.18356i	0.0840527	−	0.345819i
$561$		0			0
$562$	7.35848	−	2.26979i	0.310399	−	0.0957454i
$563$	−0.409276	−	1.04282i	−0.0172489	−	0.0439496i	0.921990	−	0.387214i	$-0.126563\pi$
$563$	−0.409276	−	1.04282i	−0.0172489	−	0.0439496i	−0.939239	+	0.343264i	$0.888467\pi$
$564$		0			0
$565$	4.31085	+	13.9754i	0.181359	+	0.587951i
$566$	−2.31305	+	10.1341i	−0.0972246	+	0.425969i
$567$		0			0
$568$	2.06969	+	9.06789i	0.0868421	+	0.380480i
$569$	0.737652	−	0.425883i	0.0309240	−	0.0178540i	−0.484458	−	0.874814i	$-0.660983\pi$
$569$	0.737652	−	0.425883i	0.0309240	−	0.0178540i	0.515382	+	0.856960i	$0.327650\pi$
$570$		0			0
$571$	7.07465	+	2.18224i	0.296065	+	0.0913239i	0.439229	−	0.898375i	$-0.355252\pi$
$571$	7.07465	+	2.18224i	0.296065	+	0.0913239i	−0.143164	+	0.989699i	$0.545728\pi$
$572$	−1.96615	−	26.2364i	−0.0822087	−	1.09700i
$573$		0			0
$574$	−6.22260	+	2.34197i	−0.259726	+	0.0977521i
$575$	16.6044	−	13.2416i	0.692453	−	0.552213i
$576$		0			0
$577$	−1.60302	−	10.6353i	−0.0667346	−	0.442755i	−0.997099	−	0.0761184i	$-0.975747\pi$
$577$	−1.60302	−	10.6353i	−0.0667346	−	0.442755i	0.930364	−	0.366637i	$-0.119491\pi$
$578$	2.35750	+	3.45782i	0.0980592	+	0.143826i
$579$		0			0
$580$	2.99614	+	6.22155i	0.124408	+	0.258336i
$581$	−6.32404	+	15.4715i	−0.262365	+	0.641865i
$582$		0			0
$583$	−12.7136	−	8.66796i	−0.526542	−	0.358990i
$584$	−8.64220	−	8.01879i	−0.357617	−	0.331820i
$585$		0			0
$586$	−1.05283	−	0.413204i	−0.0434918	−	0.0170693i
$587$	19.6682			0.811795			0.405897	−	0.913919i	$-0.366959\pi$
$587$	19.6682			0.811795			0.405897	+	0.913919i	$0.366959\pi$
$588$		0			0
$589$	28.7627			1.18515
$590$	18.7862	+	7.37303i	0.773414	+	0.303543i
$591$		0			0
$592$	2.28232	+	2.11768i	0.0938028	+	0.0870363i
$593$	−36.4229	−	24.8327i	−1.49571	−	1.01976i	−0.987340	−	0.158620i	$-0.949295\pi$
$593$	−36.4229	−	24.8327i	−1.49571	−	1.01976i	−0.508371	−	0.861138i	$-0.669752\pi$
$594$		0			0
$595$	31.7182	+	22.2833i	1.30032	+	0.913528i
$596$	5.27979	+	10.9636i	0.216269	+	0.449086i
$597$		0			0
$598$	16.0056	+	23.4759i	0.654517	+	0.960001i
$599$	−1.59271	−	10.5670i	−0.0650766	−	0.431755i	−0.997517	−	0.0704303i	$-0.977563\pi$
$599$	−1.59271	−	10.5670i	−0.0650766	−	0.431755i	0.932440	−	0.361324i	$-0.117675\pi$
$600$		0			0
$601$	−18.8606	+	15.0409i	−0.769342	+	0.613530i	−0.927474	−	0.373888i	$-0.878024\pi$
$601$	−18.8606	+	15.0409i	−0.769342	+	0.613530i	0.158132	+	0.987418i	$0.449453\pi$
$602$	−19.3899	−	11.5605i	−0.790272	−	0.471170i
$603$		0			0
$604$	−0.734551	−	9.80190i	−0.0298885	−	0.398834i
$605$	−11.1995	−	3.45459i	−0.455325	−	0.140449i
$606$		0			0
$607$	−1.47567	+	0.851978i	−0.0598956	+	0.0345807i	−0.529649	−	0.848217i	$-0.677676\pi$
$607$	−1.47567	+	0.851978i	−0.0598956	+	0.0345807i	0.469753	+	0.882798i	$0.344343\pi$
$608$	1.17581	+	5.15155i	0.0476853	+	0.208923i
$609$		0			0
$610$	−5.07384	+	22.2299i	−0.205434	+	0.900064i
$611$	10.6674	+	34.5830i	0.431559	+	1.39908i
$612$		0			0
$613$	−1.29641	−	3.30321i	−0.0523617	−	0.133415i	0.902300	−	0.431109i	$-0.141878\pi$
$613$	−1.29641	−	3.30321i	−0.0523617	−	0.133415i	−0.954661	+	0.297694i	$0.903782\pi$
$614$	4.68659	−	1.44562i	0.189135	−	0.0583405i
$615$		0			0
$616$	6.43136	−	7.83653i	0.259127	−	0.315743i
$617$	39.9360	−	9.11513i	1.60776	−	0.366961i	0.677983	−	0.735078i	$-0.262854\pi$
$617$	39.9360	−	9.11513i	1.60776	−	0.366961i	0.929780	+	0.368117i	$0.119997\pi$
$618$		0			0
$619$	−2.29789	−	1.32668i	−0.0923598	−	0.0533240i	0.453109	−	0.891455i	$-0.350315\pi$
$619$	−2.29789	−	1.32668i	−0.0923598	−	0.0533240i	−0.545469	+	0.838131i	$0.683648\pi$
$620$	−5.10719	+	16.5571i	−0.205110	+	0.664949i
$621$		0			0
$622$	−19.3970	−	15.4686i	−0.777750	−	0.620235i
$623$	45.1873	−	6.16377i	1.81039	−	0.246946i
$624$		0			0
$625$	17.8281	−	16.5420i	0.713122	−	0.661681i
$626$	9.66264	−	1.45641i	0.386197	−	0.0582098i
$627$		0			0
$628$	0.343331	−	2.27785i	0.0137004	−	0.0908962i
$629$	−12.9112	+	6.21770i	−0.514803	+	0.247916i
$630$		0			0
$631$	19.9521	+	9.60842i	0.794280	+	0.382505i	0.786598	−	0.617465i	$-0.211840\pi$
$631$	19.9521	+	9.60842i	0.794280	+	0.382505i	0.00768200	+	0.999970i	$0.497555\pi$
$632$	−3.70936	+	5.44064i	−0.147551	+	0.216417i
$633$		0			0
$634$	−0.110044	+	1.46843i	−0.00437039	+	0.0583188i
$635$	−10.8300	+	27.5943i	−0.429774	+	1.09505i
$636$		0			0
$637$	−15.4505	+	45.5137i	−0.612170	+	1.80332i
$638$			8.31236i			0.329089i
$639$		0			0
$640$	−3.17425	−	0.237877i	−0.125473	−	0.00940291i
$641$	−22.1177	+	23.8372i	−0.873595	+	0.941512i	−0.998718	−	0.0506294i	$-0.983877\pi$
$641$	−22.1177	+	23.8372i	−0.873595	+	0.941512i	0.125122	+	0.992141i	$0.460068\pi$
$642$		0			0
$643$	12.2631	−	25.4645i	0.483608	−	1.00422i	−0.506280	−	0.862369i	$-0.668980\pi$
$643$	12.2631	−	25.4645i	0.483608	−	1.00422i	0.989888	−	0.141853i	$-0.0453059\pi$
$644$	−1.78346	+	10.8018i	−0.0702782	+	0.425652i
$645$		0			0
$646$	−24.0493	−	3.62485i	−0.946206	−	0.142618i
$647$	32.6211	−	22.2407i	1.28247	−	0.874372i	0.285990	−	0.958233i	$-0.407678\pi$
$647$	32.6211	−	22.2407i	1.28247	−	0.874372i	0.996477	+	0.0838609i	$0.0267251\pi$
$648$		0			0
$649$	16.5235	+	17.8081i	0.648604	+	0.699029i
$650$	−21.9725	−	27.5527i	−0.861834	−	1.08071i
$651$		0			0
$652$	8.11004	−	10.1697i	0.317614	−	0.398275i
$653$	−16.3346	+	1.22411i	−0.639224	+	0.0479032i	−0.390400	−	0.920645i	$-0.627663\pi$
$653$	−16.3346	+	1.22411i	−0.639224	+	0.0479032i	−0.248824	+	0.968549i	$0.580044\pi$
$654$		0			0
$655$	1.66219	−	2.87900i	0.0649471	−	0.112492i
$656$	1.25649	+	2.17631i	0.0490578	+	0.0849705i
$657$		0			0
$658$	−6.22622	+	12.4779i	−0.242723	+	0.486440i
$659$	−9.31074	−	2.12512i	−0.362695	−	0.0827828i	0.0372899	−	0.999304i	$-0.488128\pi$
$659$	−9.31074	−	2.12512i	−0.362695	−	0.0827828i	−0.399985	+	0.916522i	$0.630985\pi$
$660$		0			0
$661$	8.28279	−	3.25076i	0.322163	−	0.126440i	−0.198748	−	0.980051i	$-0.563687\pi$
$661$	8.28279	−	3.25076i	0.322163	−	0.126440i	0.520911	+	0.853611i	$0.325592\pi$
$662$	6.21501	−	2.43921i	0.241553	−	0.0948027i
$663$		0			0
$664$	6.15894	+	1.40574i	0.239013	+	0.0545532i
$665$	−43.5201	+	9.29272i	−1.68764	+	0.360356i
$666$		0			0
$667$	−4.48839	−	7.77412i	−0.173791	−	0.301015i
$668$	8.99387	−	15.5778i	0.347983	−	0.602725i
$669$		0			0
$670$	12.6704	−	0.949515i	0.489500	−	0.0366830i
$671$	−17.1132	+	21.4592i	−0.660647	+	0.828425i
$672$		0			0
$673$	−13.8290	−	17.3411i	−0.533071	−	0.668449i	0.440256	−	0.897872i	$-0.354888\pi$
$673$	−13.8290	−	17.3411i	−0.533071	−	0.668449i	−0.973327	+	0.229423i	$0.926316\pi$
$674$	−7.64836	−	8.24297i	−0.294604	−	0.317507i
$675$		0			0
$676$	28.2138	−	19.2358i	1.08514	−	0.739839i
$677$	25.1658	+	3.79313i	0.967199	+	0.145782i	0.613601	−	0.789616i	$-0.289720\pi$
$677$	25.1658	+	3.79313i	0.967199	+	0.145782i	0.353598	+	0.935398i	$0.384958\pi$
$678$		0			0
$679$	−8.12154	−	27.7037i	−0.311676	−	1.06317i
$680$	6.35689	−	13.2002i	0.243776	−	0.506205i
$681$		0			0
$682$	−14.1865	+	15.2894i	−0.543229	+	0.585461i
$683$	−1.79735	−	0.134693i	−0.0687739	−	0.00515389i	0.0402987	−	0.999188i	$-0.487169\pi$
$683$	−1.79735	−	0.134693i	−0.0687739	−	0.00515389i	−0.109073	+	0.994034i	$0.534788\pi$
$684$		0			0
$685$		−	50.2979i		−	1.92178i
$686$	−16.4145	+	8.57697i	−0.626708	+	0.327470i
$687$		0			0
$688$	−3.11723	+	7.94258i	−0.118843	+	0.302808i
$689$	2.06060	−	27.4968i	0.0785026	−	1.04754i
$690$		0			0
$691$	7.49818	−	10.9978i	0.285244	−	0.418376i	−0.656697	−	0.754155i	$-0.728047\pi$
$691$	7.49818	−	10.9978i	0.285244	−	0.418376i	0.941941	+	0.335778i	$0.108999\pi$
$692$	−8.34102	−	4.01682i	−0.317078	−	0.152697i
$693$		0			0
$694$	30.2412	−	14.5634i	1.14794	−	0.552819i
$695$	−7.54233	+	50.0401i	−0.286097	+	1.89813i
$696$		0			0
$697$	−11.4374	+	1.72391i	−0.433221	+	0.0652976i
$698$	3.69538	−	3.42881i	0.139872	−	0.129783i
$699$		0			0
$700$	1.20467	−	13.5256i	0.0455321	−	0.511219i
$701$	−32.8294	−	26.1806i	−1.23995	−	0.988826i	−0.999837	−	0.0180811i	$-0.994244\pi$
$701$	−32.8294	−	26.1806i	−1.23995	−	0.988826i	−0.240112	−	0.970745i	$-0.577184\pi$
$702$		0			0
$703$	4.84919	−	15.7207i	0.182891	−	0.592917i
$704$	−3.31835	−	1.91585i	−0.125065	−	0.0722064i
$705$		0			0
$706$	−10.9104	+	2.49022i	−0.410617	+	0.0937206i
$707$	−4.00535	−	18.7581i	−0.150637	−	0.705469i
$708$		0			0
$709$	19.2726	−	5.94482i	0.723799	−	0.223262i	0.0891009	−	0.996023i	$-0.471601\pi$
$709$	19.2726	−	5.94482i	0.723799	−	0.223262i	0.634698	+	0.772760i	$0.281124\pi$
$710$	10.8166	+	27.5601i	0.405938	+	1.03431i
$711$		0			0
$712$	−5.08080	−	16.4716i	−0.190411	−	0.617298i
$713$	5.01214	−	21.9596i	0.187706	−	0.822394i
$714$		0			0
$715$	−18.6358	−	81.6487i	−0.696939	−	3.05349i
$716$	14.2793	−	8.24416i	0.533643	−	0.308099i
$717$		0			0
$718$	−26.4749	−	8.16642i	−0.988034	−	0.304768i
$719$	−0.00481569	−	0.0642609i	−0.000179595	−	0.00239653i	0.997113	−	0.0759283i	$-0.0241920\pi$
$719$	−0.00481569	−	0.0642609i	−0.000179595	−	0.00239653i	−0.997293	+	0.0735318i	$0.976573\pi$
$720$		0			0
$721$	0.906857	−	2.79986i	0.0337731	−	0.104272i
$722$	6.97473	−	5.56216i	0.259573	−	0.207002i
$723$		0			0
$724$	−3.76495	−	24.9788i	−0.139923	−	0.928330i
$725$	6.27206	+	9.19943i	0.232939	+	0.341658i
$726$		0			0
$727$	6.44241	+	13.3778i	0.238936	+	0.496156i	0.985610	−	0.169034i	$-0.0540649\pi$
$727$	6.44241	+	13.3778i	0.238936	+	0.496156i	−0.746674	+	0.665190i	$0.768351\pi$
$728$	17.9241	+	2.95940i	0.664311	+	0.109683i
$729$		0			0
$730$	−31.0064	−	21.1398i	−1.14760	−	0.782420i
$731$	−28.7885	−	26.7119i	−1.06478	−	0.987974i
$732$		0			0
$733$	−20.1336	−	7.90185i	−0.743651	−	0.291861i	−0.0368951	−	0.999319i	$-0.511747\pi$
$733$	−20.1336	−	7.90185i	−0.743651	−	0.291861i	−0.706756	+	0.707458i	$0.749842\pi$
$734$	32.5983			1.20323
$735$		0			0
$736$	4.13798			0.152528
$737$	14.2375	+	5.58779i	0.524444	+	0.205829i
$738$		0			0
$739$	32.3281	+	29.9961i	1.18921	+	1.10343i	0.992409	+	0.122982i	$0.0392457\pi$
$739$	32.3281	+	29.9961i	1.18921	+	1.10343i	0.196801	+	0.980444i	$0.436945\pi$
$740$	8.18850	+	5.58282i	0.301015	+	0.205229i
$741$		0			0
$742$	7.88913	−	7.11668i	0.289619	−	0.261261i
$743$	−1.74955	−	3.63299i	−0.0641849	−	0.133281i	0.866408	−	0.499336i	$-0.166423\pi$
$743$	−1.74955	−	3.63299i	−0.0641849	−	0.133281i	−0.930593	+	0.366055i	$0.880708\pi$
$744$		0			0
$745$	21.8200	+	32.0041i	0.799424	+	1.17254i
$746$	4.39977	+	29.1906i	0.161087	+	1.06874i
$747$		0			0
$748$	13.7886	−	10.9960i	0.504160	−	0.402054i
$749$	0.739799	+	5.42356i	0.0270317	+	0.198172i
$750$		0			0
$751$	−2.27082	−	30.3019i	−0.0828632	−	1.10573i	−0.871344	−	0.490673i	$-0.836751\pi$
$751$	−2.27082	−	30.3019i	−0.0828632	−	1.10573i	0.788480	−	0.615060i	$-0.210868\pi$
$752$	5.03657	+	1.55358i	0.183665	+	0.0566531i
$753$		0			0
$754$	−12.9000	+	7.44784i	−0.469792	+	0.271234i
$755$	−6.96232	−	30.5039i	−0.253385	−	1.11015i
$756$		0			0
$757$	−0.942046	+	4.12737i	−0.0342392	+	0.150012i	−0.989158	−	0.146855i	$-0.953085\pi$
$757$	−0.942046	+	4.12737i	−0.0342392	+	0.150012i	0.954919	+	0.296867i	$0.0959419\pi$
$758$	−0.732957	−	2.37619i	−0.0266222	−	0.0863070i
$759$		0			0
$760$	6.14499	+	15.6572i	0.222902	+	0.567945i
$761$	18.5406	−	5.71901i	0.672095	−	0.207314i	0.0601202	−	0.998191i	$-0.480852\pi$
$761$	18.5406	−	5.71901i	0.672095	−	0.207314i	0.611975	+	0.790877i	$0.290375\pi$
$762$		0			0
$763$	−46.2252	+	21.4672i	−1.67347	+	0.777164i
$764$	26.6065	−	6.07275i	0.962588	−	0.219704i
$765$		0			0
$766$	−4.18836	−	2.41815i	−0.151332	−	0.0873714i
$767$	−12.8316	+	41.5990i	−0.463322	+	1.50205i
$768$		0			0
$769$	23.1969	+	18.4989i	0.836502	+	0.667088i	0.945022	−	0.327006i	$-0.106040\pi$
$769$	23.1969	+	18.4989i	0.836502	+	0.667088i	−0.108521	+	0.994094i	$0.534611\pi$
$770$	16.5255	−	27.7174i	0.595537	−	0.998866i
$771$		0			0
$772$	15.7482	−	14.6122i	0.566791	−	0.525906i
$773$	27.4200	−	4.13289i	0.986227	−	0.148650i	0.363926	−	0.931428i	$-0.381436\pi$
$773$	27.4200	−	4.13289i	0.986227	−	0.148650i	0.622301	+	0.782778i	$0.286198\pi$
$774$		0			0
$775$	−4.16386	+	27.6254i	−0.149570	+	0.992334i
$776$	−9.83107	+	4.73440i	−0.352915	+	0.169955i
$777$		0			0
$778$	−16.2736	−	7.83697i	−0.583438	−	0.280969i
$779$	7.48015	−	10.9714i	0.268004	−	0.393090i
$780$		0			0
$781$	−2.66331	+	35.5394i	−0.0953006	+	1.27170i
$782$	−6.95827	+	17.7294i	−0.248827	+	0.634001i
$783$		0			0
$784$	4.20915	+	5.59313i	0.150327	+	0.199755i
$785$		−	7.33264i		−	0.261713i
$786$		0			0
$787$	25.4864	+	1.90994i	0.908491	+	0.0680820i	0.520772	−	0.853696i	$-0.325644\pi$
$787$	25.4864	+	1.90994i	0.908491	+	0.0680820i	0.387719	+	0.921778i	$0.373263\pi$
$788$	−13.5950	+	14.6519i	−0.484301	+	0.521952i
$789$		0			0
$790$	−9.09440	+	18.8847i	−0.323564	+	0.671888i
$791$	−11.2524	−	4.59945i	−0.400088	−	0.163538i
$792$		0			0
$793$	−48.6362	−	7.33072i	−1.72712	−	0.260322i
$794$	−13.6518	+	9.30762i	−0.484483	+	0.330315i
$795$		0			0
$796$	−15.8215	−	17.0515i	−0.560777	−	0.604374i
$797$	19.0155	+	23.8447i	0.673564	+	0.844622i	0.994744	−	0.102396i	$-0.0326508\pi$
$797$	19.0155	+	23.8447i	0.673564	+	0.844622i	−0.321180	+	0.947018i	$0.604079\pi$
$798$		0			0
$799$	−15.1257	+	18.9670i	−0.535108	+	0.671004i
$800$	−5.11808	+	0.383547i	−0.180951	+	0.0135604i
$801$		0			0
$802$	−14.4467	+	25.0223i	−0.510129	+	0.883569i
$803$	−22.5866	−	39.1212i	−0.797065	−	1.38056i
$804$		0			0
$805$	−0.488973	+	34.8459i	−0.0172340	+	1.22816i
$806$	−36.4388	−	8.31692i	−1.28350	−	0.292951i
$807$		0			0
$808$	−6.74856	+	2.64861i	−0.237413	+	0.0931779i
$809$	46.6658	−	18.3150i	1.64068	−	0.643921i	0.647670	−	0.761921i	$-0.275744\pi$
$809$	46.6658	−	18.3150i	1.64068	−	0.643921i	0.993014	+	0.118001i	$0.0376485\pi$
$810$		0			0
$811$	−38.2658	−	8.73393i	−1.34370	−	0.306690i	−0.510600	−	0.859818i	$-0.670577\pi$
$811$	−38.2658	−	8.73393i	−1.34370	−	0.306690i	−0.833096	+	0.553129i	$0.813434\pi$
$812$	−5.57722	−	1.35557i	−0.195722	−	0.0475711i
$813$		0			0
$814$	5.96491	+	10.3315i	0.209070	+	0.362120i
$815$	20.7024	−	35.8576i	0.725173	−	1.25604i
$816$		0			0
$817$	44.9594	−	3.36924i	1.57293	−	0.117875i
$818$	17.0987	−	21.4411i	0.597844	−	0.749672i
$819$		0			0
$820$	4.98742	+	6.25402i	0.174168	+	0.218400i
$821$	24.7456	+	26.6694i	0.863628	+	0.930770i	0.998190	−	0.0601354i	$-0.0191532\pi$
$821$	24.7456	+	26.6694i	0.863628	+	0.930770i	−0.134562	+	0.990905i	$0.542963\pi$
$822$		0			0
$823$	2.75060	−	1.87533i	0.0958800	−	0.0653699i	−0.514431	−	0.857532i	$-0.671997\pi$
$823$	2.75060	−	1.87533i	0.0958800	−	0.0653699i	0.610311	+	0.792162i	$0.291044\pi$
$824$	−1.09995	−	0.165791i	−0.0383185	−	0.00577559i
$825$		0			0
$826$	−14.6431	+	8.18241i	−0.509497	+	0.284702i
$827$	−14.1139	+	29.3077i	−0.490787	+	1.01913i	0.497633	+	0.867388i	$0.334203\pi$
$827$	−14.1139	+	29.3077i	−0.490787	+	1.01913i	−0.988420	+	0.151742i	$0.951512\pi$
$828$		0			0
$829$	0.560832	−	0.604433i	0.0194785	−	0.0209928i	−0.723237	−	0.690599i	$-0.757347\pi$
$829$	0.560832	−	0.604433i	0.0194785	−	0.0209928i	0.742716	+	0.669607i	$0.233537\pi$
$830$	20.0528	+	1.50275i	0.696041	+	0.0521611i
$831$		0			0
$832$		−	6.86638i		−	0.238049i
$833$	−31.0420	+	8.62911i	−1.07554	+	0.298981i
$834$		0			0
$835$	20.9186	−	53.2996i	0.723917	−	1.84451i
$836$	−1.51305	+	20.1902i	−0.0523299	+	0.698294i
$837$		0			0
$838$	−17.0577	+	25.0191i	−0.589250	+	0.864271i
$839$	7.40670	+	3.56688i	0.255708	+	0.123142i	0.557347	−	0.830280i	$-0.311819\pi$
$839$	7.40670	+	3.56688i	0.255708	+	0.123142i	−0.301639	+	0.953422i	$0.597534\pi$
$840$		0			0
$841$	−21.8880	+	10.5407i	−0.754759	+	0.363473i
$842$	−0.403943	+	2.67999i	−0.0139208	+	0.0923585i
$843$		0			0
$844$	−12.5253	+	1.88789i	−0.431139	+	0.0649837i
$845$	79.6796	−	73.9318i	2.74106	−	2.54333i
$846$		0			0
$847$	8.12504	−	5.37413i	0.279180	−	0.184657i
$848$	−3.13966	−	2.50380i	−0.107816	−	0.0859808i
$849$		0			0
$850$	6.96304	−	22.5736i	0.238830	−	0.774268i
$851$	−11.1573	−	6.44170i	−0.382469	−	0.220819i
$852$		0			0
$853$	−40.0941	+	9.15121i	−1.37280	+	0.313332i	−0.844421	−	0.535680i	$-0.820055\pi$
$853$	−40.0941	+	9.15121i	−1.37280	+	0.313332i	−0.528374	+	0.849012i	$0.677198\pi$
$854$	−11.6074	−	14.9817i	−0.397197	−	0.512664i
$855$		0			0
$856$	1.97698	−	0.609817i	0.0675718	−	0.0208431i
$857$	2.82904	+	7.20827i	0.0966381	+	0.246230i	0.971015	−	0.239017i	$-0.0768251\pi$
$857$	2.82904	+	7.20827i	0.0966381	+	0.246230i	−0.874377	+	0.485247i	$0.838730\pi$
$858$		0			0
$859$	−12.8455	−	41.6441i	−0.438282	−	1.42088i	−0.858200	−	0.513315i	$-0.828417\pi$
$859$	−12.8455	−	41.6441i	−0.438282	−	1.42088i	0.419918	−	0.907562i	$-0.362059\pi$
$860$	−6.04364	+	26.4789i	−0.206086	+	0.902923i
$861$		0			0
$862$	−8.25816	−	36.1814i	−0.281274	−	1.23234i
$863$	18.9919	−	10.9650i	0.646491	−	0.373252i	−0.140620	−	0.990064i	$-0.544909\pi$
$863$	18.9919	−	10.9650i	0.646491	−	0.373252i	0.787111	+	0.616812i	$0.211576\pi$
$864$		0			0
$865$	−28.1598	−	8.68616i	−0.957463	−	0.295338i
$866$	1.56915	+	20.9388i	0.0533218	+	0.711530i
$867$		0			0
$868$	−7.94499	−	12.0119i	−0.269671	−	0.407710i
$869$	−19.7265	+	15.7313i	−0.669174	+	0.533649i
$870$		0			0
$871$	4.08496	+	27.1019i	0.138413	+	0.918313i
$872$	10.8516	+	15.9164i	0.367481	+	0.538996i
$873$		0			0
$874$	−9.48697	−	19.6999i	−0.320901	−	0.666359i
$875$	−0.0677323	−	1.11323i	−0.00228977	−	0.0376339i
$876$		0			0
$877$	27.9301	+	19.0424i	0.943132	+	0.643016i	0.934126	−	0.356943i	$-0.116181\pi$
$877$	27.9301	+	19.0424i	0.943132	+	0.643016i	0.00900563	+	0.999959i	$0.497133\pi$
$878$	15.4121	+	14.3003i	0.520133	+	0.482613i
$879$		0			0
$880$	−11.3538	−	4.45602i	−0.382735	−	0.150212i
$881$	−6.60971			−0.222687			−0.111343	−	0.993782i	$-0.535515\pi$
$881$	−6.60971			−0.222687			−0.111343	+	0.993782i	$0.535515\pi$
$882$		0			0
$883$	−19.5618			−0.658308			−0.329154	−	0.944276i	$-0.606763\pi$
$883$	−19.5618			−0.658308			−0.329154	+	0.944276i	$0.606763\pi$
$884$	29.4194	+	11.5462i	0.989480	+	0.388342i
$885$		0			0
$886$	−14.4570	−	13.4141i	−0.485692	−	0.450656i
$887$	31.9781	+	21.8023i	1.07372	+	0.732050i	0.965060	−	0.262029i	$-0.0843916\pi$
$887$	31.9781	+	21.8023i	1.07372	+	0.732050i	0.108660	+	0.994079i	$0.465344\pi$
$888$		0			0
$889$	−12.0188	−	21.5086i	−0.403099	−	0.721377i
$890$	−23.8068	−	49.4353i	−0.798005	−	1.65708i
$891$		0			0
$892$	−2.64574	−	3.88059i	−0.0885859	−	0.129932i
$893$	−4.15093	−	27.5397i	−0.138906	−	0.921579i
$894$		0			0
$895$	41.0342	−	32.7237i	1.37162	−	1.09383i
$896$	1.82660	−	1.91403i	0.0610225	−	0.0639433i
$897$		0			0
$898$	0.243476	+	3.24896i	0.00812490	+	0.108419i
$899$	11.2839	+	3.48063i	0.376340	+	0.116085i
$900$		0			0
$901$	16.0072	−	9.24175i	0.533277	−	0.307887i
$902$	2.14266	+	9.38759i	0.0713426	+	0.312573i
$903$		0			0
$904$	−1.02239	+	4.47937i	−0.0340041	+	0.148982i
$905$	−23.7011	−	76.8370i	−0.787850	−	2.55415i
$906$		0			0
$907$	0.228612	+	0.582495i	0.00759095	+	0.0193414i	0.934619	−	0.355651i	$-0.115741\pi$
$907$	0.228612	+	0.582495i	0.00759095	+	0.0193414i	−0.927028	+	0.374992i	$0.877645\pi$
$908$	9.47391	−	2.92231i	0.314403	−	0.0969804i
$909$		0			0
$910$	57.8217	+	0.811380i	1.91677	+	0.0268970i
$911$	52.9779	−	12.0919i	1.75524	−	0.400621i	0.780711	−	0.624893i	$-0.214857\pi$
$911$	52.9779	−	12.0919i	1.75524	−	0.400621i	0.974527	+	0.224271i	$0.0720002\pi$
$912$		0			0
$913$	20.9631	+	12.1031i	0.693778	+	0.400553i
$914$	−3.79629	+	12.3073i	−0.125570	+	0.407088i
$915$		0			0
$916$	−8.14678	−	6.49684i	−0.269177	−	0.214662i
$917$	0.973299	+	2.58605i	0.0321412	+	0.0853987i
$918$		0			0
$919$	1.89849	−	1.76154i	0.0626255	−	0.0581079i	−0.648239	−	0.761437i	$-0.724494\pi$
$919$	1.89849	−	1.76154i	0.0626255	−	0.0581079i	0.710865	+	0.703329i	$0.248304\pi$
$920$	13.0247	−	1.96316i	0.429411	−	0.0647233i
$921$		0			0
$922$	3.56810	−	23.6728i	0.117509	−	0.779622i
$923$	−57.5402	+	27.7099i	−1.89396	+	0.912083i
$924$		0			0
$925$	14.3971	+	6.93327i	0.473373	+	0.227965i
$926$	−10.7236	+	15.7286i	−0.352399	+	0.516874i
$927$		0			0
$928$	−0.162117	+	2.16330i	−0.00532174	+	0.0710137i
$929$	0.613141	−	1.56226i	0.0201165	−	0.0512560i	−0.920463	−	0.390831i	$-0.872188\pi$
$929$	0.613141	−	1.56226i	0.0201165	−	0.0512560i	0.940579	+	0.339575i	$0.110283\pi$
$930$		0			0
$931$	16.9774	−	32.8618i	0.556411	−	1.07700i
$932$		−	15.4731i		−	0.506837i
$933$		0			0
$934$	16.0685	+	1.20417i	0.525778	+	0.0394016i
$935$	38.1841	−	41.1527i	1.24875	−	1.34584i
$936$		0			0
$937$	8.49169	−	17.6332i	0.277411	−	0.576051i	−0.714984	−	0.699141i	$-0.753566\pi$
$937$	8.49169	−	17.6332i	0.277411	−	0.576051i	0.992396	+	0.123090i	$0.0392804\pi$
$938$	−6.07098	+	8.64145i	−0.198225	+	0.282153i
$939$		0			0
$940$	16.5901	+	2.50056i	0.541110	+	0.0815592i
$941$	−39.5156	+	26.9413i	−1.28817	+	0.878260i	−0.996923	−	0.0783875i	$-0.975023\pi$
$941$	−39.5156	+	26.9413i	−1.28817	+	0.878260i	−0.291248	+	0.956648i	$0.594070\pi$
$942$		0			0
$943$	−7.07290	−	7.62277i	−0.230325	−	0.248232i
$944$	3.95294	+	4.95683i	0.128657	+	0.161331i
$945$		0			0
$946$	−20.3841	+	25.5609i	−0.662745	+	0.831056i
$947$	16.0736	−	1.20455i	0.522321	−	0.0391426i	0.189039	−	0.981970i	$-0.439463\pi$
$947$	16.0736	−	1.20455i	0.522321	−	0.0391426i	0.333282	+	0.942827i	$0.391844\pi$
$948$		0			0
$949$	40.4751	−	70.1049i	1.31388	−	2.27570i
$950$	13.5600	+	23.4865i	0.439943	+	0.762004i
$951$		0			0
$952$	5.12922	+	11.0447i	0.166239	+	0.357962i
$953$	21.9102	+	5.00086i	0.709741	+	0.161994i	0.562127	−	0.827051i	$-0.309983\pi$
$953$	21.9102	+	5.00086i	0.709741	+	0.161994i	0.147615	+	0.989045i	$0.452840\pi$
$954$		0			0
$955$	80.8653	−	31.7373i	2.61674	−	1.02699i
$956$	−25.0148	+	9.81758i	−0.809036	+	0.317523i
$957$		0			0
$958$	23.0853	+	5.26906i	0.745852	+	0.170236i
$959$	32.3165	+	26.5218i	1.04356	+	0.856435i
$960$		0			0
$961$	−0.685146	−	1.18671i	−0.0221015	−	0.0382809i
$962$	−10.6891	+	18.5140i	−0.344630	+	0.596916i
$963$		0			0
$964$	−24.6027	+	1.84372i	−0.792401	+	0.0593822i
$965$	42.6367	−	53.4647i	1.37252	−	1.72109i
$966$		0			0
$967$	−3.36079	−	4.21429i	−0.108076	−	0.135522i	0.724852	−	0.688905i	$-0.241908\pi$
$967$	−3.36079	−	4.21429i	−0.108076	−	0.135522i	−0.832927	+	0.553382i	$0.813337\pi$
$968$	−2.50437	−	2.69906i	−0.0804934	−	0.0867512i
$969$		0			0
$970$	−28.6981	+	19.5661i	−0.921441	+	0.628228i
$971$	−13.1343	−	1.97968i	−0.421501	−	0.0635310i	−0.0651325	−	0.997877i	$-0.520747\pi$
$971$	−13.1343	−	1.97968i	−0.421501	−	0.0635310i	−0.356368	+	0.934346i	$0.615985\pi$
$972$		0			0
$973$	−28.1739	−	31.2319i	−0.903213	−	1.00125i
$974$	−7.06453	+	14.6696i	−0.226362	+	0.470046i
$975$		0			0
$976$	−4.87224	+	5.25102i	−0.155956	+	0.168081i
$977$	−52.4652	−	3.93172i	−1.67851	−	0.125787i	−0.798894	−	0.601472i	$-0.794581\pi$
$977$	−52.4652	−	3.93172i	−1.67851	−	0.125787i	−0.879616	+	0.475685i	$0.842200\pi$
$978$		0			0
$979$		−	66.0485i		−	2.11092i
$980$	15.9022	+	15.6080i	0.507977	+	0.498579i
$981$		0			0
$982$	2.39929	−	6.11328i	0.0765643	−	0.195083i
$983$	−3.37032	+	44.9738i	−0.107496	+	1.43444i	0.639080	+	0.769141i	$0.279315\pi$
$983$	−3.37032	+	44.9738i	−0.107496	+	1.43444i	−0.746576	+	0.665300i	$0.768304\pi$
$984$		0			0
$985$	−35.8403	+	52.5680i	−1.14197	+	1.67496i
$986$	−8.99615	−	4.33232i	−0.286496	−	0.137969i
$987$		0			0
$988$	−32.6891	+	15.7423i	−1.03998	+	0.500828i
$989$	5.26221	−	34.9125i	0.167329	−	1.11015i
$990$		0			0
$991$	9.55779	−	1.44061i	0.303613	−	0.0457624i	0.00453126	−	0.999990i	$-0.498558\pi$
$991$	9.55779	−	1.44061i	0.303613	−	0.0457624i	0.299082	+	0.954227i	$0.403320\pi$
$992$	−3.99023	+	3.70240i	−0.126690	+	0.117551i
$993$		0			0
$994$	−23.4110	−	7.58267i	−0.742552	−	0.240508i
$995$	−57.8892	−	46.1651i	−1.83521	−	1.46353i
$996$		0			0
$997$	14.0889	−	45.6751i	0.446200	−	1.44654i	−0.401398	−	0.915904i	$-0.631475\pi$
$997$	14.0889	−	45.6751i	0.446200	−	1.44654i	0.847597	−	0.530640i	$-0.178048\pi$
$998$	−36.4848	−	21.0645i	−1.15491	−	0.666785i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.18	yes	240
3.2	odd	2	inner	882.2.bl.a.395.3	✓	240
49.33	odd	42	inner	882.2.bl.a.719.3	yes	240
147.131	even	42	inner	882.2.bl.a.719.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.3	✓	240	3.2	odd	2	inner
882.2.bl.a.395.18	yes	240	1.1	even	1	trivial
882.2.bl.a.719.3	yes	240	49.33	odd	42	inner
882.2.bl.a.719.18	yes	240	147.131	even	42	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(2.63004 + 1.79313i) q^{5} +(-2.53890 + 0.744299i) q^{7} +(0.433884 + 0.900969i) q^{8} +O(q^{10})\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(2.63004 + 1.79313i) q^{5} +(-2.53890 + 0.744299i) q^{7} +(0.433884 + 0.900969i) q^{8} +(1.79313 + 2.63004i) q^{10} +(0.571086 + 3.78891i) q^{11} +(-5.36836 + 4.28112i) q^{13} +(-2.63532 - 0.234717i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-4.39823 - 1.35668i) q^{17} +(4.57611 - 2.64202i) q^{19} +(0.708317 + 3.10334i) q^{20} +(-0.852634 + 3.73564i) q^{22} +(-1.21969 - 3.95414i) q^{23} +(1.87509 + 4.77764i) q^{25} +(-6.56133 + 2.02390i) q^{26} +(-2.36740 - 1.18128i) q^{28} +(2.11497 - 0.482729i) q^{29} +(4.71405 + 2.72166i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-3.59855 - 2.86975i) q^{34} +(-8.01204 - 2.59505i) q^{35} +(2.28232 - 2.11768i) q^{37} +(5.22502 - 0.787544i) q^{38} +(-0.474424 + 3.14759i) q^{40} +(2.26412 - 1.09034i) q^{41} +(7.68742 + 3.70206i) q^{43} +(-2.15848 + 3.16590i) q^{44} +(0.309232 - 4.12641i) q^{46} +(1.92561 - 4.90638i) q^{47} +(5.89204 - 3.77940i) q^{49} +5.13243i q^{50} +(-6.84718 - 0.513126i) q^{52} +(-2.73142 + 2.94378i) q^{53} +(-5.29203 + 10.9890i) q^{55} +(-1.77218 - 1.96453i) q^{56} +(2.14513 + 0.323327i) q^{58} +(5.23837 - 3.57146i) q^{59} +(4.87224 + 5.25102i) q^{61} +(3.39385 + 4.25576i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-21.7956 + 1.63335i) q^{65} +(1.99581 - 3.45685i) q^{67} +(-2.30136 - 3.98607i) q^{68} +(-6.51012 - 5.34279i) q^{70} +(9.06789 + 2.06969i) q^{71} +(-10.9744 + 4.30713i) q^{73} +(2.89823 - 1.13747i) q^{74} +(5.15155 + 1.17581i) q^{76} +(-4.27001 - 9.19460i) q^{77} +(3.29241 + 5.70262i) q^{79} +(-1.59157 + 2.75669i) q^{80} +(2.50596 - 0.187796i) q^{82} +(3.93879 - 4.93909i) q^{83} +(-9.13483 - 11.4547i) q^{85} +(5.80350 + 6.25468i) q^{86} +(-3.16590 + 2.15848i) q^{88} +(-17.0448 - 2.56910i) q^{89} +(10.4433 - 14.8650i) q^{91} +(1.79540 - 3.72819i) q^{92} +(3.58501 - 3.86372i) q^{94} +(16.7728 + 1.25695i) q^{95} +10.9117i q^{97} +(6.86551 - 1.36554i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) \) 240 * q - 20 * q^4 - 4 * q^7	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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