LMFDB - Embedded newform 882.2.bl.a.395.3

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			395.3
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.3

$q$-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	−0.192414	−	0.981314i	$-0.561632\pi$
$5$	−2.63004	−	1.79313i	−1.17619	−	0.801912i	−0.983776	+	0.179401i	$0.942584\pi$
$6$		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	$-0.851588\pi$
$11$	−0.571086	−	3.78891i	−0.172189	−	1.14240i	0.721072	−	0.692860i	$-0.243650\pi$
$12$		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	0.777932	−	0.628349i	$-0.216269\pi$
$17$	4.39823	+	1.35668i	1.06673	+	0.329042i	0.288796	+	0.957391i	$0.406745\pi$
$18$		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	$0.0467472\pi$
$23$	1.21969	+	3.95414i	0.254323	+	0.824496i	−0.734912	+	0.678162i	$0.762777\pi$
$24$		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	−0.414331	−	0.910126i	$-0.635984\pi$
$29$	−2.11497	+	0.482729i	−0.392741	+	0.0896405i	0.0215900	+	0.999767i	$0.493127\pi$
$30$		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	−0.602246	−	0.798310i	$-0.705727\pi$
$41$	−2.26412	+	1.09034i	−0.353596	+	0.170283i	0.248650	+	0.968593i	$0.420013\pi$
$42$		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	$0.244642\pi$
$47$	−1.92561	+	4.90638i	−0.280880	+	0.715670i	−0.999789	+	0.0205654i	$0.993453\pi$
$48$		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	−0.517024	−	0.855971i	$-0.672960\pi$
$53$	2.73142	−	2.94378i	0.375190	−	0.404359i	0.892214	+	0.451612i	$0.149151\pi$
$54$		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	−0.854098	−	0.520111i	$-0.825890\pi$
$59$	−5.23837	+	3.57146i	−0.681978	+	0.464965i	0.172121	+	0.985076i	$0.444938\pi$
$60$		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	−0.352520	−	0.935804i	$-0.614675\pi$
$71$	−9.06789	−	2.06969i	−1.07616	−	0.245627i	−0.723640	+	0.690178i	$0.757532\pi$
$72$		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	−0.949506	−	0.313749i	$-0.898415\pi$
$83$	−3.93879	+	4.93909i	−0.432338	+	0.542135i	0.517168	+	0.855884i	$0.326986\pi$
$84$		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	0.963984	−	0.265959i	$-0.0856886\pi$
$89$	17.0448	+	2.56910i	1.80675	+	0.272324i	0.842764	+	0.538283i	$0.180927\pi$
$90$		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	$-0.858733\pi$
$101$	0.541771	−	7.22943i	0.0539082	−	0.719355i	0.957033	−	0.289978i	$-0.0936480\pi$
$102$		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	−0.998779	−	0.0494083i	$-0.984266\pi$
$107$	−0.308353	+	2.04579i	−0.0298096	+	0.197774i	0.968969	+	0.247182i	$0.0795045\pi$
$108$		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	0.439794	−	0.898099i	$-0.355051\pi$
$113$	−3.59218	−	2.86467i	−0.337924	−	0.269485i	−0.777718	+	0.628613i	$0.783623\pi$
$114$		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	0.999575	−	0.0291564i	$-0.00928208\pi$
$131$	0.0780458	+	1.04145i	0.00681889	+	0.0909918i	−0.992756	+	0.120148i	$0.961663\pi$
$132$		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	$0.0453793\pi$
$137$	8.90119	+	13.0556i	0.760480	+	1.11542i	−0.229375	+	0.973338i	$0.573668\pi$
$138$		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	−0.147271	−	0.989096i	$-0.547049\pi$
$149$	−11.3275	−	4.44571i	−0.927985	−	0.364207i	−0.780714	+	0.624889i	$0.785144\pi$
$150$		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	$0.173595\pi$
$167$	4.00265	+	17.5368i	0.309734	+	1.35703i	−0.545203	+	0.838304i	$0.683548\pi$
$168$		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	0.0603962	−	0.998174i	$-0.480764\pi$
$173$	8.84653	−	2.72879i	0.672590	−	0.207466i	0.612193	+	0.790708i	$0.290287\pi$
$174$		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	$0.306566\pi$
$179$	−4.86002	+	15.7558i	−0.363255	+	1.17764i	−0.934229	+	0.356675i	$0.883910\pi$
$180$		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	$0.639777\pi$
$191$	−15.3734	+	22.5486i	−1.11238	+	1.63156i	−0.687234	+	0.726436i	$0.741175\pi$
$192$		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	$-0.747778\pi$
$197$		−	19.9875i		−	1.42405i	0.702153	−	0.712026i	$-0.252222\pi$
$198$		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	−0.982318	−	0.187222i	$-0.940052\pi$
$227$	−4.95719	+	8.58610i	−0.329020	+	0.569880i	0.653298	+	0.757101i	$0.273385\pi$
$228$		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	0.976658	−	0.214800i	$-0.0689099\pi$
$233$	10.5243	+	11.3426i	0.689473	+	0.743075i	−0.287185	+	0.957875i	$0.592719\pi$
$234$		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	$-0.521832\pi$
$239$	11.6595	−	24.2112i	0.754189	−	1.56609i	0.822724	−	0.568441i	$-0.192453\pi$
$240$		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	0.918784	−	0.394760i	$-0.129172\pi$
$251$	18.7423	+	9.02580i	1.18300	+	0.569703i	0.264217	+	0.964463i	$0.414886\pi$
$252$		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	−0.846900	−	0.531753i	$-0.821534\pi$
$257$	−6.09062	+	5.65127i	−0.379922	+	0.352517i	0.466977	+	0.884269i	$0.345343\pi$
$258$		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	0.143909	−	0.989591i	$-0.454033\pi$
$263$	−10.3977	−	6.00309i	−0.641147	−	0.370166i	−0.785056	+	0.619425i	$0.787366\pi$
$264$		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	0.947289	−	0.320380i	$-0.103811\pi$
$269$	0.573435	+	1.46109i	0.0349630	+	0.0890842i	−0.912326	+	0.409465i	$0.865716\pi$
$270$		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	−0.786399	−	0.617719i	$-0.788057\pi$
$281$	−6.02057	+	4.80124i	−0.359157	+	0.286418i	0.427242	+	0.904138i	$0.359485\pi$
$282$		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	$-0.489482\pi$
$293$	1.13101			0.0660742			0.0330371	+	0.999454i	$0.489482\pi$
$294$		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	0.881670	−	0.471866i	$-0.156419\pi$
$311$	23.7075	+	7.31279i	1.34433	+	0.414670i	0.462658	+	0.886537i	$0.346896\pi$
$312$		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	0.942566	−	0.334019i	$-0.108405\pi$
$317$	−0.434041	−	1.40713i	−0.0243781	−	0.0790320i	−0.966944	+	0.254987i	$0.917929\pi$
$318$		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	$0.595215\pi$
$347$	−22.8301	+	24.6050i	−1.22559	+	1.32087i	−0.930900	+	0.365274i	$0.880975\pi$
$348$		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	−0.291691	−	0.956513i	$-0.594218\pi$
$353$	9.24639	−	6.30408i	0.492135	−	0.335532i	0.783826	+	0.620980i	$0.213265\pi$
$354$		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	0.678099	−	0.734971i	$-0.262804\pi$
$359$	27.6283	−	2.07045i	1.45817	−	0.109274i	0.780067	+	0.625696i	$0.215185\pi$
$360$		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	0.270082	−	0.962837i	$-0.412949\pi$
$383$	4.78229	+	0.720814i	0.244363	+	0.0368319i	−0.0257184	+	0.999669i	$0.508187\pi$
$384$		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	0.523054	−	0.852299i	$-0.324792\pi$
$389$	18.0119	+	1.34980i	0.913238	+	0.0684377i	0.390184	+	0.920737i	$0.372412\pi$
$390$		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	$-0.695865\pi$
$401$	4.30632	−	28.5706i	0.215048	−	1.42675i	0.792275	−	0.610164i	$-0.208896\pi$
$402$		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	$-0.663560\pi$
$419$	6.73810	−	29.5215i	0.329178	−	1.44222i	0.820701	−	0.571357i	$-0.193583\pi$
$420$		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	$0.161499\pi$
$431$	20.9058	+	30.6632i	1.00700	+	1.47700i	0.132971	+	0.991120i	$0.457548\pi$
$432$		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	0.758881	−	0.651229i	$-0.225746\pi$
$443$	18.3583	+	7.20512i	0.872231	+	0.342326i	0.113351	+	0.993555i	$0.463842\pi$
$444$		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	0.864946	−	0.501865i	$-0.167353\pi$
$449$	−1.41362	−	2.93542i	−0.0667131	−	0.138531i	−0.931659	+	0.363334i	$0.881638\pi$
$450$		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	$0.116812\pi$
$461$	5.32719	+	23.3400i	0.248112	+	1.08705i	−0.685305	+	0.728256i	$0.740331\pi$
$462$		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	−0.629764	−	0.776787i	$-0.716848\pi$
$467$	−15.3977	+	4.74956i	−0.712520	+	0.219783i	−0.0827560	+	0.996570i	$0.526372\pi$
$468$		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	−0.660269	−	0.751029i	$-0.729558\pi$
$479$	−23.4145	+	3.52917i	−1.06984	+	0.161252i	−0.409566	+	0.912281i	$0.634320\pi$
$480$		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	$0.0473440\pi$
$491$			6.56725i			0.296376i	−0.988959	+	0.148188i	$0.952656\pi$
$492$		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	0.864775	−	0.502159i	$-0.167461\pi$
$503$	4.09923	+	5.14027i	0.182776	+	0.229194i	−0.682000	+	0.731353i	$0.738889\pi$
$504$		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	0.768367	−	0.640010i	$-0.221070\pi$
$509$	−3.83721	−	6.64624i	−0.170081	−	0.294589i	−0.938448	+	0.345420i	$0.887736\pi$
$510$		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	$0.422881\pi$
$521$	−16.4520	+	28.4957i	−0.720776	+	1.24842i	−0.960689	+	0.277626i	$0.910453\pi$
$522$		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	0.574741	−	0.818335i	$-0.305103\pi$
$557$	3.62068	+	2.09040i	0.153413	+	0.0885730i	−0.421328	+	0.906908i	$0.638436\pi$
$558$		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	0.939239	−	0.343264i	$-0.111533\pi$
$563$	0.409276	+	1.04282i	0.0172489	+	0.0439496i	−0.921990	+	0.387214i	$0.873437\pi$
$564$		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	−0.515382	−	0.856960i	$-0.672350\pi$
$569$	−0.737652	+	0.425883i	−0.0309240	+	0.0178540i	0.484458	+	0.874814i	$0.339017\pi$
$570$		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	$-0.633041\pi$
$587$	−19.6682			−0.811795			−0.405897	+	0.913919i	$0.633041\pi$
$588$		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	$0.0507046\pi$
$593$	36.4229	+	24.8327i	1.49571	+	1.01976i	0.508371	+	0.861138i	$0.330248\pi$
$594$		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	$0.0224372\pi$
$599$	1.59271	+	10.5670i	0.0650766	+	0.431755i	−0.932440	+	0.361324i	$0.882325\pi$
$600$		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	−0.929780	−	0.368117i	$-0.880003\pi$
$617$	−39.9360	+	9.11513i	−1.60776	+	0.366961i	−0.677983	+	0.735078i	$0.737146\pi$
$618$		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	−0.125122	−	0.992141i	$-0.539932\pi$
$641$	22.1177	−	23.8372i	0.873595	−	0.941512i	0.998718	+	0.0506294i	$0.0161227\pi$
$642$		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	−0.996477	−	0.0838609i	$-0.973275\pi$
$647$	−32.6211	+	22.2407i	−1.28247	+	0.874372i	−0.285990	+	0.958233i	$0.592322\pi$
$648$		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	0.248824	−	0.968549i	$-0.419956\pi$
$653$	16.3346	−	1.22411i	0.639224	−	0.0479032i	0.390400	+	0.920645i	$0.372337\pi$
$654$		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	0.399985	−	0.916522i	$-0.369015\pi$
$659$	9.31074	+	2.12512i	0.362695	+	0.0827828i	−0.0372899	+	0.999304i	$0.511872\pi$
$660$		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	−0.353598	−	0.935398i	$-0.615042\pi$
$677$	−25.1658	−	3.79313i	−0.967199	−	0.145782i	−0.613601	+	0.789616i	$0.710280\pi$
$678$		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	0.109073	−	0.994034i	$-0.465212\pi$
$683$	1.79735	+	0.134693i	0.0687739	+	0.00515389i	−0.0402987	+	0.999188i	$0.512831\pi$
$684$		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	$0.00575570\pi$
$701$	32.8294	+	26.1806i	1.23995	+	0.988826i	0.240112	+	0.970745i	$0.422816\pi$
$702$		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	0.997293	−	0.0735318i	$-0.0234270\pi$
$719$	0.00481569	+	0.0642609i	0.000179595	+	0.00239653i	−0.997113	+	0.0759283i	$0.975808\pi$
$720$		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	0.930593	−	0.366055i	$-0.119292\pi$
$743$	1.74955	+	3.63299i	0.0641849	+	0.133281i	−0.866408	+	0.499336i	$0.833577\pi$
$744$		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	−0.611975	−	0.790877i	$-0.709625\pi$
$761$	−18.5406	+	5.71901i	−0.672095	+	0.207314i	−0.0601202	+	0.998191i	$0.519148\pi$
$762$		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	−0.622301	−	0.782778i	$-0.713802\pi$
$773$	−27.4200	+	4.13289i	−0.986227	+	0.148650i	−0.363926	+	0.931428i	$0.618564\pi$
$774$		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	0.321180	−	0.947018i	$-0.395921\pi$
$797$	−19.0155	−	23.8447i	−0.673564	−	0.844622i	−0.994744	+	0.102396i	$0.967349\pi$
$798$		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	−0.993014	−	0.118001i	$-0.962351\pi$
$809$	−46.6658	+	18.3150i	−1.64068	+	0.643921i	−0.647670	+	0.761921i	$0.724256\pi$
$810$		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	0.134562	−	0.990905i	$-0.457037\pi$
$821$	−24.7456	−	26.6694i	−0.863628	−	0.930770i	−0.998190	+	0.0601354i	$0.980847\pi$
$822$		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	$-0.665797\pi$
$827$	14.1139	−	29.3077i	0.490787	−	1.01913i	0.988420	−	0.151742i	$-0.0484884\pi$
$828$		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	0.301639	−	0.953422i	$-0.402466\pi$
$839$	−7.40670	−	3.56688i	−0.255708	−	0.123142i	−0.557347	+	0.830280i	$0.688181\pi$
$840$		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	0.874377	−	0.485247i	$-0.161270\pi$
$857$	−2.82904	−	7.20827i	−0.0966381	−	0.246230i	−0.971015	+	0.239017i	$0.923175\pi$
$858$		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	−0.787111	−	0.616812i	$-0.788424\pi$
$863$	−18.9919	+	10.9650i	−0.646491	+	0.373252i	0.140620	+	0.990064i	$0.455091\pi$
$864$		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	$-0.464485\pi$
$881$	6.60971			0.222687			0.111343	+	0.993782i	$0.464485\pi$
$882$		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	−0.108660	−	0.994079i	$-0.534656\pi$
$887$	−31.9781	−	21.8023i	−1.07372	−	0.732050i	−0.965060	+	0.262029i	$0.915608\pi$
$888$		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	−0.974527	−	0.224271i	$-0.928000\pi$
$911$	−52.9779	+	12.0919i	−1.75524	+	0.400621i	−0.780711	+	0.624893i	$0.785143\pi$
$912$		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	−0.940579	−	0.339575i	$-0.889717\pi$
$929$	−0.613141	+	1.56226i	−0.0201165	+	0.0512560i	0.920463	+	0.390831i	$0.127812\pi$
$930$		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	0.291248	−	0.956648i	$-0.405930\pi$
$941$	39.5156	−	26.9413i	1.28817	−	0.878260i	0.996923	+	0.0783875i	$0.0249771\pi$
$942$		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	−0.333282	−	0.942827i	$-0.608156\pi$
$947$	−16.0736	+	1.20455i	−0.522321	+	0.0391426i	−0.189039	+	0.981970i	$0.560537\pi$
$948$		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	−0.147615	−	0.989045i	$-0.547160\pi$
$953$	−21.9102	−	5.00086i	−0.709741	−	0.161994i	−0.562127	+	0.827051i	$0.690017\pi$
$954$		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	0.356368	−	0.934346i	$-0.384015\pi$
$971$	13.1343	+	1.97968i	0.421501	+	0.0635310i	0.0651325	+	0.997877i	$0.479253\pi$
$972$		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	0.879616	−	0.475685i	$-0.157800\pi$
$977$	52.4652	+	3.93172i	1.67851	+	0.125787i	0.798894	+	0.601472i	$0.205419\pi$
$978$		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	$-0.720685\pi$
$983$	3.37032	−	44.9738i	0.107496	−	1.43444i	0.746576	−	0.665300i	$-0.231696\pi$
$984$		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.395.3	✓	240
3.2	odd	2	inner	882.2.bl.a.395.18	yes	240
49.33	odd	42	inner	882.2.bl.a.719.18	yes	240
147.131	even	42	inner	882.2.bl.a.719.3	yes	240

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

Groups

Database

Properties

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