LMFDB - Embedded newform 882.2.bl.a.395.12

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			395.12
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.38675 - 1.62726i) q^{5} +(-1.53151 + 2.15742i) q^{7} +(0.433884 + 0.900969i) q^{8} +O(q^{10})$	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.38675 - 1.62726i) q^{5} +(-1.53151 + 2.15742i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-1.62726 - 2.38675i) q^{10} +(-0.328853 - 2.18179i) q^{11} +(-1.90048 + 1.51558i) q^{13} +(-2.21384 + 1.44876i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-1.54987 - 0.478073i) q^{17} +(-5.96225 + 3.44230i) q^{19} +(-0.642794 - 2.81626i) q^{20} +(0.490979 - 2.15112i) q^{22} +(0.270954 + 0.878413i) q^{23} +(1.22189 + 3.11333i) q^{25} +(-2.32282 + 0.716494i) q^{26} +(-2.59010 + 0.539808i) q^{28} +(-3.46478 + 0.790814i) q^{29} +(-7.19671 - 4.15502i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-1.26808 - 1.01126i) q^{34} +(7.16601 - 2.65705i) q^{35} +(-2.79305 + 2.59157i) q^{37} +(-6.80771 + 1.02610i) q^{38} +(0.430537 - 2.85642i) q^{40} +(1.04356 - 0.502552i) q^{41} +(-0.507888 - 0.244586i) q^{43} +(1.24293 - 1.82304i) q^{44} +(-0.0686958 + 0.916682i) q^{46} +(-2.28364 + 5.81862i) q^{47} +(-2.30893 - 6.60824i) q^{49} +3.34452i q^{50} +(-2.42401 - 0.181655i) q^{52} +(6.70669 - 7.22810i) q^{53} +(-2.76545 + 5.74252i) q^{55} +(-2.60827 - 0.443776i) q^{56} +(-3.51419 - 0.529679i) q^{58} +(-4.53118 + 3.08931i) q^{59} +(4.79525 + 5.16805i) q^{61} +(-5.18123 - 6.49705i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(7.00222 - 0.524744i) q^{65} +(-1.18486 + 2.05224i) q^{67} +(-0.810966 - 1.40463i) q^{68} +(7.64138 + 0.144658i) q^{70} +(-3.34620 - 0.763749i) q^{71} +(9.86161 - 3.87040i) q^{73} +(-3.54679 + 1.39201i) q^{74} +(-6.71200 - 1.53197i) q^{76} +(5.21069 + 2.63197i) q^{77} +(8.54125 + 14.7939i) q^{79} +(1.44434 - 2.50168i) q^{80} +(1.15503 - 0.0865573i) q^{82} +(7.46549 - 9.36143i) q^{83} +(2.92121 + 3.66308i) q^{85} +(-0.383422 - 0.413231i) q^{86} +(1.82304 - 1.24293i) q^{88} +(-7.83109 - 1.18035i) q^{89} +(-0.359138 - 6.42128i) q^{91} +(-0.398849 + 0.828218i) q^{92} +(-4.25156 + 4.58209i) q^{94} +(19.8319 + 1.48619i) q^{95} +9.32506i q^{97} +(0.264938 - 6.99498i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.38675	−	1.62726i	−1.06739	−	0.727731i	−0.103656	−	0.994613i	$-0.533054\pi$
$5$	−2.38675	−	1.62726i	−1.06739	−	0.727731i	−0.963729	+	0.266882i	$0.914007\pi$
$6$		0			0
$7$	−1.53151	+	2.15742i	−0.578858	+	0.815429i
$7$	−1.53151	+	2.15742i	−0.578858	+	0.815429i
$8$	0.433884	+	0.900969i	0.153401	+	0.318541i
$9$		0			0
$10$	−1.62726	−	2.38675i	−0.514584	−	0.754755i
$11$	−0.328853	−	2.18179i	−0.0991528	−	0.657836i	−0.982100	−	0.188363i	$-0.939682\pi$
$11$	−0.328853	−	2.18179i	−0.0991528	−	0.657836i	0.882947	−	0.469473i	$-0.155556\pi$
$12$		0			0
$13$	−1.90048	+	1.51558i	−0.527099	+	0.420348i	−0.850547	−	0.525898i	$-0.823729\pi$
$13$	−1.90048	+	1.51558i	−0.527099	+	0.420348i	0.323448	+	0.946246i	$0.395158\pi$
$14$	−2.21384	+	1.44876i	−0.591674	+	0.387198i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−1.54987	−	0.478073i	−0.375900	−	0.115950i	0.101048	−	0.994882i	$-0.467781\pi$
$17$	−1.54987	−	0.478073i	−0.375900	−	0.115950i	−0.476947	+	0.878932i	$0.658257\pi$
$18$		0			0
$19$	−5.96225	+	3.44230i	−1.36783	+	0.789719i	−0.990651	−	0.136420i	$-0.956440\pi$
$19$	−5.96225	+	3.44230i	−1.36783	+	0.789719i	−0.377182	+	0.926139i	$0.623107\pi$
$20$	−0.642794	−	2.81626i	−0.143733	−	0.629736i
$21$		0			0
$22$	0.490979	−	2.15112i	0.104677	−	0.458620i
$23$	0.270954	+	0.878413i	0.0564979	+	0.183162i	0.979423	−	0.201818i	$-0.0646848\pi$
$23$	0.270954	+	0.878413i	0.0564979	+	0.183162i	−0.922925	+	0.384979i	$0.874209\pi$
$24$		0			0
$25$	1.22189	+	3.11333i	0.244378	+	0.622665i
$26$	−2.32282	+	0.716494i	−0.455542	+	0.140516i
$27$		0			0
$28$	−2.59010	+	0.539808i	−0.489483	+	0.102014i
$29$	−3.46478	+	0.790814i	−0.643394	+	0.146850i	−0.531755	−	0.846898i	$-0.678467\pi$
$29$	−3.46478	+	0.790814i	−0.643394	+	0.146850i	−0.111639	+	0.993749i	$0.535610\pi$
$30$		0			0
$31$	−7.19671	−	4.15502i	−1.29257	−	0.746264i	−0.313459	−	0.949602i	$-0.601488\pi$
$31$	−7.19671	−	4.15502i	−1.29257	−	0.746264i	−0.979109	+	0.203338i	$0.934821\pi$
$32$	−0.294755	+	0.955573i	−0.0521058	+	0.168923i
$33$		0			0
$34$	−1.26808	−	1.01126i	−0.217473	−	0.173429i
$35$	7.16601	−	2.65705i	1.21128	−	0.449124i
$36$		0			0
$37$	−2.79305	+	2.59157i	−0.459175	+	0.426052i	−0.875540	−	0.483145i	$-0.839494\pi$
$37$	−2.79305	+	2.59157i	−0.459175	+	0.426052i	0.416365	+	0.909198i	$0.363304\pi$
$38$	−6.80771	+	1.02610i	−1.10436	+	0.166455i
$39$		0			0
$40$	0.430537	−	2.85642i	0.0680738	−	0.451640i
$41$	1.04356	−	0.502552i	0.162977	−	0.0784855i	−0.350617	−	0.936519i	$-0.614028\pi$
$41$	1.04356	−	0.502552i	0.162977	−	0.0784855i	0.513594	+	0.858033i	$0.328314\pi$
$42$		0			0
$43$	−0.507888	−	0.244586i	−0.0774521	−	0.0372990i	0.394757	−	0.918786i	$-0.370829\pi$
$43$	−0.507888	−	0.244586i	−0.0774521	−	0.0372990i	−0.472209	+	0.881487i	$0.656543\pi$
$44$	1.24293	−	1.82304i	0.187379	−	0.274834i
$45$		0			0
$46$	−0.0686958	+	0.916682i	−0.0101286	+	0.135157i
$47$	−2.28364	+	5.81862i	−0.333103	+	0.848733i	0.661965	+	0.749535i	$0.269723\pi$
$47$	−2.28364	+	5.81862i	−0.333103	+	0.848733i	−0.995068	+	0.0991977i	$0.968372\pi$
$48$		0			0
$49$	−2.30893	−	6.60824i	−0.329847	−	0.944034i
$50$			3.34452i			0.472987i
$51$		0			0
$52$	−2.42401	−	0.181655i	−0.336150	−	0.0251910i
$53$	6.70669	−	7.22810i	0.921235	−	0.992855i	−0.0787568	−	0.996894i	$-0.525095\pi$
$53$	6.70669	−	7.22810i	0.921235	−	0.992855i	0.999992	+	0.00403857i	$0.00128552\pi$
$54$		0			0
$55$	−2.76545	+	5.74252i	−0.372893	+	0.774321i
$56$	−2.60827	−	0.443776i	−0.348544	−	0.0593021i
$57$		0			0
$58$	−3.51419	−	0.529679i	−0.461436	−	0.0695503i
$59$	−4.53118	+	3.08931i	−0.589909	+	0.402193i	−0.821158	−	0.570701i	$-0.806671\pi$
$59$	−4.53118	+	3.08931i	−0.589909	+	0.402193i	0.231248	+	0.972895i	$0.425719\pi$
$60$		0			0
$61$	4.79525	+	5.16805i	0.613969	+	0.661701i	0.961127	−	0.276105i	$-0.0890438\pi$
$61$	4.79525	+	5.16805i	0.613969	+	0.661701i	−0.347158	+	0.937807i	$0.612853\pi$
$62$	−5.18123	−	6.49705i	−0.658017	−	0.825127i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	7.00222	−	0.524744i	0.868518	−	0.0650864i
$66$		0			0
$67$	−1.18486	+	2.05224i	−0.144754	+	0.250722i	−0.929281	−	0.369373i	$-0.879572\pi$
$67$	−1.18486	+	2.05224i	−0.144754	+	0.250722i	0.784527	+	0.620095i	$0.212906\pi$
$68$	−0.810966	−	1.40463i	−0.0983441	−	0.170337i
$69$		0			0
$70$	7.64138	+	0.144658i	0.913320	+	0.0172900i
$71$	−3.34620	−	0.763749i	−0.397121	−	0.0906404i	0.0192962	−	0.999814i	$-0.493857\pi$
$71$	−3.34620	−	0.763749i	−0.397121	−	0.0906404i	−0.416418	+	0.909173i	$0.636715\pi$
$72$		0			0
$73$	9.86161	−	3.87040i	1.15421	−	0.452996i	0.290449	−	0.956890i	$-0.406195\pi$
$73$	9.86161	−	3.87040i	1.15421	−	0.452996i	0.863765	+	0.503895i	$0.168100\pi$
$74$	−3.54679	+	1.39201i	−0.412306	+	0.161818i
$75$		0			0
$76$	−6.71200	−	1.53197i	−0.769919	−	0.175729i
$77$	5.21069	+	2.63197i	0.593813	+	0.299941i
$78$		0			0
$79$	8.54125	+	14.7939i	0.960965	+	1.66444i	0.720085	+	0.693886i	$0.244103\pi$
$79$	8.54125	+	14.7939i	0.960965	+	1.66444i	0.240881	+	0.970555i	$0.422564\pi$
$80$	1.44434	−	2.50168i	0.161483	−	0.279696i
$81$		0			0
$82$	1.15503	−	0.0865573i	0.127551	−	0.00955865i
$83$	7.46549	−	9.36143i	0.819444	−	1.02755i	−0.179596	−	0.983740i	$-0.557479\pi$
$83$	7.46549	−	9.36143i	0.819444	−	1.02755i	0.999040	−	0.0438099i	$-0.0139496\pi$
$84$		0			0
$85$	2.92121	+	3.66308i	0.316850	+	0.397317i
$86$	−0.383422	−	0.413231i	−0.0413455	−	0.0445598i
$87$		0			0
$88$	1.82304	−	1.24293i	0.194337	−	0.132497i
$89$	−7.83109	−	1.18035i	−0.830094	−	0.125117i	−0.279769	−	0.960067i	$-0.590258\pi$
$89$	−7.83109	−	1.18035i	−0.830094	−	0.125117i	−0.550325	+	0.834951i	$0.685496\pi$
$90$		0			0
$91$	−0.359138	−	6.42128i	−0.0376479	−	0.673133i
$92$	−0.398849	+	0.828218i	−0.0415828	+	0.0863477i
$93$		0			0
$94$	−4.25156	+	4.58209i	−0.438515	+	0.472607i
$95$	19.8319	+	1.48619i	2.03471	+	0.152480i
$96$		0			0
$97$			9.32506i			0.946816i	0.880843	+	0.473408i	$0.156976\pi$
$97$			9.32506i			0.946816i	−0.880843	+	0.473408i	$0.843024\pi$
$98$	0.264938	−	6.99498i	0.0267628	−	0.706600i
$99$		0			0
$100$	−1.22189	+	3.11333i	−0.122189	+	0.311333i
$101$	0.340104	−	4.53837i	0.0338416	−	0.451585i	−0.954384	−	0.298582i	$-0.903486\pi$
$101$	0.340104	−	4.53837i	0.0338416	−	0.451585i	0.988226	−	0.153003i	$-0.0488945\pi$
$102$		0			0
$103$	−6.38286	+	9.36194i	−0.628922	+	0.922459i	−0.999981	−	0.00615006i	$-0.998042\pi$
$103$	−6.38286	+	9.36194i	−0.628922	+	0.922459i	0.371059	+	0.928609i	$0.378995\pi$
$104$	−2.19008	−	1.05469i	−0.214755	−	0.103421i
$105$		0			0
$106$	8.88380	−	4.27821i	0.862871	−	0.415537i
$107$	2.54863	−	16.9090i	0.246385	−	1.63466i	−0.433368	−	0.901217i	$-0.642675\pi$
$107$	2.54863	−	16.9090i	0.246385	−	1.63466i	0.679753	−	0.733441i	$-0.262087\pi$
$108$		0			0
$109$	9.81632	−	1.47957i	0.940233	−	0.141717i	0.338996	−	0.940788i	$-0.389913\pi$
$109$	9.81632	−	1.47957i	0.940233	−	0.141717i	0.601237	+	0.799071i	$0.294675\pi$
$110$	−4.67226	+	4.33523i	−0.445483	+	0.413348i
$111$		0			0
$112$	−2.26584	−	1.36601i	−0.214102	−	0.129076i
$113$	−5.06070	−	4.03578i	−0.476071	−	0.379654i	0.355855	−	0.934541i	$-0.384190\pi$
$113$	−5.06070	−	4.03578i	−0.476071	−	0.379654i	−0.831925	+	0.554888i	$0.812761\pi$
$114$		0			0
$115$	0.782703	−	2.53746i	0.0729874	−	0.236619i
$116$	−3.07775	−	1.77694i	−0.285762	−	0.164985i
$117$		0			0
$118$	−5.34661	+	1.22033i	−0.492195	+	0.112340i
$119$	3.40506	−	2.61156i	0.312141	−	0.239401i
$120$		0			0
$121$	5.85922	−	1.80733i	0.532656	−	0.164303i
$122$	2.57567	+	6.56271i	0.233190	+	0.594159i
$123$		0			0
$124$	−2.44943	−	7.94085i	−0.219965	−	0.713110i
$125$	−1.06413	+	4.66226i	−0.0951788	+	0.417006i
$126$		0			0
$127$	−2.52230	−	11.0509i	−0.223818	−	0.980611i	−0.954574	−	0.297973i	$-0.903690\pi$
$127$	−2.52230	−	11.0509i	−0.223818	−	0.980611i	0.730756	−	0.682639i	$-0.239168\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	6.70989	+	2.06973i	0.588496	+	0.181527i
$131$	−0.120961	−	1.61411i	−0.0105684	−	0.141025i	0.989423	−	0.145056i	$-0.0463361\pi$
$131$	−0.120961	−	1.61411i	−0.0105684	−	0.141025i	−0.999992	+	0.00403039i	$0.998717\pi$
$132$		0			0
$133$	1.70476	−	18.1350i	0.147822	−	1.57251i
$134$	−1.85273	+	1.47750i	−0.160051	+	0.127637i
$135$		0			0
$136$	−0.241736	−	1.60382i	−0.0207287	−	0.137526i
$137$	5.93678	+	8.70766i	0.507213	+	0.743946i	0.991378	−	0.131031i	$-0.0418288\pi$
$137$	5.93678	+	8.70766i	0.507213	+	0.743946i	−0.484165	+	0.874977i	$0.660876\pi$
$138$		0			0
$139$	−3.62648	−	7.53047i	−0.307594	−	0.638726i	0.688671	−	0.725074i	$-0.258195\pi$
$139$	−3.62648	−	7.53047i	−0.307594	−	0.638726i	−0.996265	+	0.0863480i	$0.972480\pi$
$140$	7.06031	+	2.92637i	0.596705	+	0.247323i
$141$		0			0
$142$	−2.83586	−	1.93346i	−0.237980	−	0.162252i
$143$	3.93167	+	3.64806i	0.328783	+	0.305066i
$144$		0			0
$145$	9.55641	+	3.75061i	0.793617	+	0.311472i
$146$	10.5939			0.876760
$147$		0			0
$148$	−3.81017			−0.313194
$149$	−19.7693	−	7.75889i	−1.61957	−	0.635633i	−0.629598	−	0.776921i	$-0.716780\pi$
$149$	−19.7693	−	7.75889i	−1.61957	−	0.635633i	−0.989968	+	0.141288i	$0.954876\pi$
$150$		0			0
$151$	10.1747	+	9.44079i	0.828009	+	0.768280i	0.975317	−	0.220810i	$-0.0708702\pi$
$151$	10.1747	+	9.44079i	0.828009	+	0.768280i	−0.147307	+	0.989091i	$0.547061\pi$
$152$	−5.68833	−	3.87824i	−0.461385	−	0.314567i
$153$		0			0
$154$	3.88893	+	4.35372i	0.313379	+	0.350832i
$155$	10.4154	+	21.6279i	0.836588	+	1.73719i
$156$		0			0
$157$	−10.5016	−	15.4031i	−0.838123	−	1.22930i	−0.971217	−	0.238197i	$-0.923444\pi$
$157$	−10.5016	−	15.4031i	−0.838123	−	1.22930i	0.133094	−	0.991103i	$-0.457509\pi$
$158$	2.54601	+	16.8917i	0.202550	+	1.34383i
$159$		0			0
$160$	2.25847	−	1.80107i	0.178548	−	0.142387i
$161$	−2.31008	−	0.760738i	−0.182060	−	0.0599546i
$162$		0			0
$163$	1.52653	+	20.3701i	0.119567	+	1.59551i	0.658116	+	0.752916i	$0.271354\pi$
$163$	1.52653	+	20.3701i	0.119567	+	1.59551i	−0.538549	+	0.842594i	$0.681027\pi$
$164$	1.10681	+	0.341405i	0.0864271	+	0.0266592i
$165$		0			0
$166$	10.3695	−	5.98686i	0.804833	−	0.464670i
$167$	2.32091	+	10.1686i	0.179598	+	0.786868i	0.981816	+	0.189837i	$0.0607960\pi$
$167$	2.32091	+	10.1686i	0.179598	+	0.786868i	−0.802218	+	0.597031i	$0.796347\pi$
$168$		0			0
$169$	−1.57793	+	6.91338i	−0.121379	+	0.531798i
$170$	1.38100	+	4.47710i	0.105918	+	0.343378i
$171$		0			0
$172$	−0.205947	−	0.524745i	−0.0157033	−	0.0400115i
$173$	−8.09800	+	2.49790i	−0.615679	+	0.189912i	−0.586881	−	0.809673i	$-0.699644\pi$
$173$	−8.09800	+	2.49790i	−0.615679	+	0.189912i	−0.0287985	+	0.999585i	$0.509168\pi$
$174$		0			0
$175$	−8.58810	−	2.13197i	−0.649199	−	0.161162i
$176$	2.15112	−	0.490979i	0.162147	−	0.0370089i
$177$		0			0
$178$	−6.85853	−	3.95977i	−0.514068	−	0.296797i
$179$	−4.54937	+	14.7487i	−0.340036	+	1.10237i	0.610568	+	0.791964i	$0.290941\pi$
$179$	−4.54937	+	14.7487i	−0.340036	+	1.10237i	−0.950604	+	0.310406i	$0.899535\pi$
$180$		0			0
$181$	−11.6926	−	9.32455i	−0.869105	−	0.693088i	0.0837588	−	0.996486i	$-0.473307\pi$
$181$	−11.6926	−	9.32455i	−0.869105	−	0.693088i	−0.952864	+	0.303398i	$0.901879\pi$
$182$	2.01165	−	6.10861i	0.149113	−	0.452800i
$183$		0			0
$184$	−0.673860	+	0.625250i	−0.0496776	+	0.0460941i
$185$	10.8835	−	1.64042i	0.800168	−	0.120606i
$186$		0			0
$187$	−0.533376	+	3.53872i	−0.0390043	+	0.258777i
$188$	−5.63169	+	2.71208i	−0.410733	+	0.197799i
$189$		0			0
$190$	17.9180	+	8.62886i	1.29991	+	0.626003i
$191$	−12.0798	+	17.7178i	−0.874063	+	1.28202i	0.0842932	+	0.996441i	$0.473137\pi$
$191$	−12.0798	+	17.7178i	−0.874063	+	1.28202i	−0.958357	+	0.285574i	$0.907816\pi$
$192$		0			0
$193$	0.940672	−	12.5524i	0.0677110	−	0.903541i	−0.855143	−	0.518392i	$-0.826531\pi$
$193$	0.940672	−	12.5524i	0.0677110	−	0.903541i	0.922854	−	0.385149i	$-0.125850\pi$
$194$	−3.40683	+	8.68045i	−0.244596	+	0.623220i
$195$		0			0
$196$	2.80218	−	6.41465i	0.200156	−	0.458190i
$197$			9.06267i			0.645689i	0.946452	+	0.322844i	$0.104639\pi$
$197$			9.06267i			0.645689i	−0.946452	+	0.322844i	$0.895361\pi$
$198$		0			0
$199$	8.90305	+	0.667191i	0.631120	+	0.0472959i	0.386450	−	0.922310i	$-0.373701\pi$
$199$	8.90305	+	0.667191i	0.631120	+	0.0472959i	0.244670	+	0.969606i	$0.421320\pi$
$200$	−2.27485	+	2.45171i	−0.160856	+	0.173362i
$201$		0			0
$202$	1.97465	−	4.10040i	0.138936	−	0.288503i
$203$	3.60024	−	8.68613i	0.252687	−	0.609647i
$204$		0			0
$205$	−3.30850	−	0.498676i	−0.231075	−	0.0348290i
$206$	−9.36194	+	6.38286i	−0.652277	+	0.444715i
$207$		0			0
$208$	−1.65337	−	1.78191i	−0.114641	−	0.123553i
$209$	9.47110	+	11.8764i	0.655130	+	0.821507i
$210$		0			0
$211$	−1.65883	+	2.08011i	−0.114199	+	0.143201i	−0.835645	−	0.549269i	$-0.814906\pi$
$211$	−1.65883	+	2.08011i	−0.114199	+	0.143201i	0.721447	+	0.692470i	$0.243478\pi$
$212$	9.83271	−	0.736860i	0.675313	−	0.0506077i
$213$		0			0
$214$	8.55002	−	14.8091i	0.584467	−	1.01233i
$215$	0.814195	+	1.41023i	0.0555276	+	0.0961767i
$216$		0			0
$217$	19.9860	−	9.16286i	1.35674	−	0.622015i
$218$	9.67830	+	2.20901i	0.655497	+	0.149613i
$219$		0			0
$220$	−5.93312	+	2.32858i	−0.400011	+	0.156993i
$221$	3.67007	−	1.44040i	0.246876	−	0.0968915i
$222$		0			0
$223$	0.979634	+	0.223595i	0.0656012	+	0.0149730i	0.255196	−	0.966889i	$-0.417860\pi$
$223$	0.979634	+	0.223595i	0.0656012	+	0.0149730i	−0.189594	+	0.981863i	$0.560717\pi$
$224$	−1.61015	−	2.09938i	−0.107583	−	0.140271i
$225$		0			0
$226$	−3.23644	−	5.60568i	−0.215285	−	0.372884i
$227$	14.3011	−	24.7702i	0.949196	−	1.64406i	0.202073	−	0.979371i	$-0.435232\pi$
$227$	14.3011	−	24.7702i	0.949196	−	1.64406i	0.747124	−	0.664685i	$-0.231434\pi$
$228$		0			0
$229$	27.1801	−	2.03686i	1.79611	−	0.134600i	0.865569	−	0.500790i	$-0.166957\pi$
$229$	27.1801	−	2.03686i	1.79611	−	0.134600i	0.930540	+	0.366190i	$0.119338\pi$
$230$	1.65564	−	2.07610i	0.109169	−	0.136894i
$231$		0			0
$232$	−2.21581	−	2.77854i	−0.145475	−	0.182420i
$233$	−17.5818	−	18.9487i	−1.15182	−	1.24137i	−0.965931	−	0.258801i	$-0.916673\pi$
$233$	−17.5818	−	18.9487i	−1.15182	−	1.24137i	−0.185893	−	0.982570i	$-0.559518\pi$
$234$		0			0
$235$	14.9189	−	10.1715i	0.973199	−	0.663516i
$236$	−5.42285	−	0.817363i	−0.352998	−	0.0532058i
$237$		0			0
$238$	4.12379	−	1.18702i	0.267305	−	0.0769432i
$239$	−12.4119	+	25.7735i	−0.802857	+	1.66715i	−0.0595252	+	0.998227i	$0.518959\pi$
$239$	−12.4119	+	25.7735i	−0.802857	+	1.66715i	−0.743332	+	0.668923i	$0.766756\pi$
$240$		0			0
$241$	−10.2543	+	11.0515i	−0.660538	+	0.711891i	−0.971103	−	0.238662i	$-0.923291\pi$
$241$	−10.2543	+	11.0515i	−0.660538	+	0.711891i	0.310565	+	0.950552i	$0.399482\pi$
$242$	6.11448	+	0.458217i	0.393054	+	0.0294553i
$243$		0			0
$244$			7.05005i			0.451333i
$245$	−5.24247	+	19.5294i	−0.334929	+	1.24769i
$246$		0			0
$247$	6.11405	−	15.5783i	0.389027	−	0.991226i
$248$	0.621010	−	8.28681i	0.0394342	−	0.526213i
$249$		0			0
$250$	−2.69389	+	3.95121i	−0.170376	+	0.249896i
$251$	−0.388521	−	0.187102i	−0.0245232	−	0.0118098i	0.421582	−	0.906790i	$-0.361475\pi$
$251$	−0.388521	−	0.187102i	−0.0245232	−	0.0118098i	−0.446105	+	0.894981i	$0.647189\pi$
$252$		0			0
$253$	1.82741	−	0.880035i	0.114888	−	0.0553273i
$254$	1.68941	−	11.2085i	0.106003	−	0.703285i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	11.3266	−	10.5095i	0.706531	−	0.655565i	−0.242716	−	0.970097i	$-0.578038\pi$
$257$	11.3266	−	10.5095i	0.706531	−	0.655565i	0.949247	+	0.314533i	$0.101848\pi$
$258$		0			0
$259$	−1.31352	−	9.99482i	−0.0816181	−	0.621048i
$260$	5.48990	+	4.37805i	0.340469	+	0.271515i
$261$		0			0
$262$	0.477101	−	1.54672i	0.0294754	−	0.0955569i
$263$	3.00757	+	1.73642i	0.185455	+	0.107072i	0.589853	−	0.807511i	$-0.299186\pi$
$263$	3.00757	+	1.73642i	0.185455	+	0.107072i	−0.404398	+	0.914583i	$0.632519\pi$
$264$		0			0
$265$	−27.7691	+	6.33812i	−1.70584	+	0.389348i
$266$	8.21238	−	16.2586i	0.503534	−	0.996878i
$267$		0			0
$268$	−2.26445	+	0.698489i	−0.138323	+	0.0426670i
$269$	−5.05049	−	12.8684i	−0.307934	−	0.784602i	−0.998138	−	0.0609881i	$-0.980575\pi$
$269$	−5.05049	−	12.8684i	−0.307934	−	0.784602i	0.690205	−	0.723614i	$-0.257520\pi$
$270$		0			0
$271$	4.26138	+	13.8150i	0.258860	+	0.839204i	0.987948	+	0.154784i	$0.0494682\pi$
$271$	4.26138	+	13.8150i	0.258860	+	0.839204i	−0.729088	+	0.684420i	$0.760056\pi$
$272$	0.360914	−	1.58127i	0.0218836	−	0.0958784i
$273$		0			0
$274$	2.34513	+	10.2747i	0.141674	+	0.620716i
$275$	6.39082	−	3.68974i	0.385381	−	0.222500i
$276$		0			0
$277$	−26.9887	−	8.32493i	−1.62160	−	0.500196i	−0.654813	−	0.755791i	$-0.727253\pi$
$277$	−26.9887	−	8.32493i	−1.62160	−	0.500196i	−0.966784	+	0.255595i	$0.917729\pi$
$278$	−0.624609	−	8.33482i	−0.0374615	−	0.499889i
$279$		0			0
$280$	5.50314	+	5.30350i	0.328875	+	0.316945i
$281$	−8.99124	+	7.17028i	−0.536372	+	0.427743i	−0.853847	−	0.520524i	$-0.825737\pi$
$281$	−8.99124	+	7.17028i	−0.536372	+	0.427743i	0.317475	+	0.948267i	$0.397165\pi$
$282$		0			0
$283$	−3.49644	−	23.1973i	−0.207842	−	1.37894i	−0.812735	−	0.582633i	$-0.802023\pi$
$283$	−3.49644	−	23.1973i	−0.207842	−	1.37894i	0.604894	−	0.796306i	$-0.293216\pi$
$284$	−1.93346	−	2.83586i	−0.114730	−	0.168278i
$285$		0			0
$286$	2.32711	+	4.83228i	0.137605	+	0.285739i
$287$	−0.514011	+	3.02107i	−0.0303411	+	0.178328i
$288$		0			0
$289$	−11.8725	−	8.09454i	−0.698383	−	0.476149i
$290$	7.52556	+	6.98270i	0.441916	+	0.410038i
$291$		0			0
$292$	9.86161	+	3.87040i	0.577107	+	0.226498i
$293$	−15.2997			−0.893819			−0.446909	−	0.894579i	$-0.647475\pi$
$293$	−15.2997			−0.893819			−0.446909	+	0.894579i	$0.647475\pi$
$294$		0			0
$295$	15.8419			0.922349
$296$	−3.54679	−	1.39201i	−0.206153	−	0.0809091i
$297$		0			0
$298$	−15.5681	−	14.4451i	−0.901836	−	0.836782i
$299$	−1.84625	−	1.25875i	−0.106772	−	0.0727956i
$300$		0			0
$301$	1.30551	−	0.721141i	0.0752484	−	0.0415659i
$302$	6.02230	+	12.5054i	0.346544	+	0.719607i
$303$		0			0
$304$	−3.87824	−	5.68833i	−0.222432	−	0.326248i
$305$	−3.03530	−	20.1379i	−0.173801	−	1.15309i
$306$		0			0
$307$	−10.5332	+	8.39991i	−0.601159	+	0.479408i	−0.876150	−	0.482039i	$-0.839897\pi$
$307$	−10.5332	+	8.39991i	−0.601159	+	0.479408i	0.274991	+	0.961447i	$0.411325\pi$
$308$	2.02951	+	5.47354i	0.115642	+	0.311884i
$309$		0			0
$310$	1.79391	+	23.9380i	0.101887	+	1.35959i
$311$	22.5086	+	6.94297i	1.27634	+	0.393700i	0.857559	−	0.514386i	$-0.171980\pi$
$311$	22.5086	+	6.94297i	1.27634	+	0.393700i	0.418785	+	0.908086i	$0.362456\pi$
$312$		0			0
$313$	4.73189	−	2.73196i	0.267462	−	0.154419i	−0.360272	−	0.932847i	$-0.617316\pi$
$313$	4.73189	−	2.73196i	0.267462	−	0.154419i	0.627734	+	0.778428i	$0.283983\pi$
$314$	−4.14833	−	18.1750i	−0.234104	−	1.02568i
$315$		0			0
$316$	−3.80121	+	16.6542i	−0.213835	+	0.936872i
$317$	4.05840	+	13.1570i	0.227943	+	0.738972i	0.995220	+	0.0976567i	$0.0311347\pi$
$317$	4.05840	+	13.1570i	0.227943	+	0.738972i	−0.767278	+	0.641315i	$0.778389\pi$
$318$		0			0
$319$	2.86479	+	7.29938i	0.160398	+	0.408687i
$320$	2.76035	−	0.851456i	0.154308	−	0.0475978i
$321$		0			0
$322$	−1.87246	−	1.55212i	−0.104348	−	0.0864961i
$323$	10.8864	−	2.48475i	0.605736	−	0.138255i
$324$		0			0
$325$	−7.04069	−	4.06495i	−0.390547	−	0.225483i
$326$	−6.02103	+	19.5197i	−0.333474	+	1.08110i
$327$		0			0
$328$	0.905568	+	0.722167i	0.0500016	+	0.0398750i
$329$	−9.05578	−	13.8381i	−0.499262	−	0.762917i
$330$		0			0
$331$	−1.72926	+	1.60452i	−0.0950487	+	0.0881923i	−0.726266	−	0.687414i	$-0.758746\pi$
$331$	−1.72926	+	1.60452i	−0.0950487	+	0.0881923i	0.631217	+	0.775606i	$0.282556\pi$
$332$	11.8400	−	1.78459i	0.649803	−	0.0979421i
$333$		0			0
$334$	−1.55452	+	10.3136i	−0.0850597	+	0.564335i
$335$	6.16750	−	2.97011i	0.336966	−	0.162274i
$336$		0			0
$337$	24.8098	+	11.9478i	1.35148	+	0.650837i	0.962719	−	0.270503i	$-0.0871901\pi$
$337$	24.8098	+	11.9478i	1.35148	+	0.650837i	0.388757	+	0.921340i	$0.372904\pi$
$338$	−3.99460	+	5.85900i	−0.217277	+	0.318687i
$339$		0			0
$340$	−0.350130	+	4.67215i	−0.0189884	+	0.253383i
$341$	−6.69875	+	17.0681i	−0.362757	+	0.924291i
$342$		0			0
$343$	17.7929	+	5.13927i	0.960727	+	0.277495i
$344$		−	0.563713i		−	0.0303933i
$345$		0			0
$346$	−8.45080	−	0.633300i	−0.454318	−	0.0340464i
$347$	−4.30125	+	4.63565i	−0.230903	+	0.248855i	−0.837866	−	0.545876i	$-0.816197\pi$
$347$	−4.30125	+	4.63565i	−0.230903	+	0.248855i	0.606963	+	0.794730i	$0.292388\pi$
$348$		0			0
$349$	−14.2203	+	29.5287i	−0.761194	+	1.58063i	0.0520040	+	0.998647i	$0.483439\pi$
$349$	−14.2203	+	29.5287i	−0.761194	+	1.58063i	−0.813198	+	0.581988i	$0.802275\pi$
$350$	−7.21554	−	5.12218i	−0.385687	−	0.273792i
$351$		0			0
$352$	2.18179	+	0.328853i	0.116290	+	0.0175279i
$353$	−25.7717	+	17.5709i	−1.37169	+	0.935203i	−0.371714	+	0.928347i	$0.621230\pi$
$353$	−25.7717	+	17.5709i	−1.37169	+	0.935203i	−0.999977	+	0.00685549i	$0.997818\pi$
$354$		0			0
$355$	6.74373	+	7.26801i	0.357920	+	0.385746i
$356$	−4.93776	−	6.19175i	−0.261700	−	0.328162i
$357$		0			0
$358$	−9.62320	+	12.0671i	−0.508602	+	0.637766i
$359$	−33.5255	+	2.51239i	−1.76941	+	0.132599i	−0.919185	−	0.393826i	$-0.871151\pi$
$359$	−33.5255	+	2.51239i	−1.76941	+	0.132599i	−0.850222	+	0.526425i	$0.823532\pi$
$360$		0			0
$361$	14.1989	−	24.5933i	0.747312	−	1.29438i
$362$	−7.47771	−	12.9518i	−0.393020	−	0.680730i
$363$		0			0
$364$	4.10431	−	4.95141i	0.215124	−	0.259524i
$365$	−29.8353	−	6.80971i	−1.56165	−	0.356437i
$366$		0			0
$367$	−3.87006	+	1.51889i	−0.202016	+	0.0792853i	−0.464192	−	0.885735i	$-0.653655\pi$
$367$	−3.87006	+	1.51889i	−0.202016	+	0.0792853i	0.262176	+	0.965020i	$0.415560\pi$
$368$	−0.855708	+	0.335841i	−0.0446069	+	0.0175069i
$369$		0			0
$370$	10.7304	+	2.44915i	0.557849	+	0.127325i
$371$	5.32265	+	25.5391i	0.276338	+	1.32592i
$372$		0			0
$373$	−10.9954	−	19.0446i	−0.569321	−	0.986093i	−0.996633	−	0.0819889i	$-0.973873\pi$
$373$	−10.9954	−	19.0446i	−0.569321	−	0.986093i	0.427312	−	0.904104i	$-0.359461\pi$
$374$	−1.78935	+	3.09924i	−0.0925249	+	0.160258i
$375$		0			0
$376$	−6.23323	+	0.467116i	−0.321454	+	0.0240897i
$377$	5.38621	−	6.75410i	0.277404	−	0.347854i
$378$		0			0
$379$	−1.33280	−	1.67128i	−0.0684615	−	0.0858480i	0.746422	−	0.665473i	$-0.231770\pi$
$379$	−1.33280	−	1.67128i	−0.0684615	−	0.0858480i	−0.814883	+	0.579625i	$0.803199\pi$
$380$	13.5269	+	14.5786i	0.693917	+	0.747865i
$381$		0			0
$382$	−17.7178	+	12.0798i	−0.906522	+	0.618056i
$383$	2.21136	+	0.333309i	0.112995	+	0.0170313i	0.205296	−	0.978700i	$-0.434184\pi$
$383$	2.21136	+	0.333309i	0.112995	+	0.0170313i	−0.0923012	+	0.995731i	$0.529422\pi$
$384$		0			0
$385$	−8.15370	−	14.7610i	−0.415551	−	0.752289i
$386$	5.46155	−	11.3410i	0.277986	−	0.577243i
$387$		0			0
$388$	−6.34265	+	6.83575i	−0.321999	+	0.347033i
$389$	7.18426	+	0.538386i	0.364256	+	0.0272972i	0.255601	−	0.966782i	$-0.417727\pi$
$389$	7.18426	+	0.538386i	0.364256	+	0.0272972i	0.108655	+	0.994080i	$0.465346\pi$
$390$		0			0
$391$		−	1.49096i		−	0.0754013i
$392$	4.95201	−	4.94748i	0.250114	−	0.249886i
$393$		0			0
$394$	−3.31097	+	8.43620i	−0.166804	+	0.425010i
$395$	3.68763	−	49.2080i	0.185545	−	2.47592i
$396$		0			0
$397$	−14.2445	+	20.8929i	−0.714912	+	1.04858i	0.281127	+	0.959671i	$0.409292\pi$
$397$	−14.2445	+	20.8929i	−0.714912	+	1.04858i	−0.996039	+	0.0889132i	$0.971661\pi$
$398$	8.04386	+	3.87372i	0.403202	+	0.194172i
$399$		0			0
$400$	−3.01331	+	1.45113i	−0.150665	+	0.0725567i
$401$	3.27574	−	21.7331i	0.163582	−	1.08530i	−0.744839	−	0.667244i	$-0.767474\pi$
$401$	3.27574	−	21.7331i	0.163582	−	1.08530i	0.908422	−	0.418055i	$-0.137288\pi$
$402$		0			0
$403$	19.9745	−	3.01067i	0.995001	−	0.149972i
$404$	3.33619	−	3.09553i	0.165982	−	0.154009i
$405$		0			0
$406$	6.52477	−	6.77038i	0.323819	−	0.336008i
$407$	6.57279	+	5.24162i	0.325801	+	0.259818i
$408$		0			0
$409$	1.00386	−	3.25445i	0.0496379	−	0.160922i	−0.927360	−	0.374170i	$-0.877928\pi$
$409$	1.00386	−	3.25445i	0.0496379	−	0.160922i	0.976998	+	0.213247i	$0.0684040\pi$
$410$	−2.89761	−	1.67293i	−0.143103	−	0.0826203i
$411$		0			0
$412$	−11.0467	+	2.52134i	−0.544232	+	0.124217i
$413$	0.274630	−	14.5070i	0.0135137	−	0.713842i
$414$		0			0
$415$	−33.0517	+	10.1951i	−1.62244	+	0.500457i
$416$	−0.888074	−	2.26278i	−0.0435414	−	0.110942i
$417$		0			0
$418$	4.47747	+	14.5156i	0.219000	+	0.709981i
$419$	−5.02232	+	22.0042i	−0.245357	+	1.07498i	0.690704	+	0.723138i	$0.257301\pi$
$419$	−5.02232	+	22.0042i	−0.245357	+	1.07498i	−0.936060	+	0.351840i	$0.885556\pi$
$420$		0			0
$421$	−6.26712	−	27.4580i	−0.305441	−	1.33822i	−0.861786	−	0.507272i	$-0.830654\pi$
$421$	−6.26712	−	27.4580i	−0.305441	−	1.33822i	0.556345	−	0.830951i	$-0.312203\pi$
$422$	−2.30412	+	1.33028i	−0.112163	+	0.0647571i
$423$		0			0
$424$	9.42221	+	2.90637i	0.457583	+	0.141146i
$425$	−0.405380	−	5.40942i	−0.0196638	−	0.262395i
$426$		0			0
$427$	−18.4937	+	2.43043i	−0.894971	+	0.117617i
$428$	13.3693	−	10.6617i	0.646232	−	0.515353i
$429$		0			0
$430$	0.242699	+	1.61020i	0.0117040	+	0.0776509i
$431$	6.66859	+	9.78102i	0.321214	+	0.471135i	0.952553	−	0.304372i	$-0.0984466\pi$
$431$	6.66859	+	9.78102i	0.321214	+	0.471135i	−0.631339	+	0.775507i	$0.717494\pi$
$432$		0			0
$433$	−6.51552	−	13.5296i	−0.313116	−	0.650192i	0.683714	−	0.729750i	$-0.260364\pi$
$433$	−6.51552	−	13.5296i	−0.313116	−	0.650192i	−0.996830	+	0.0795577i	$0.974649\pi$
$434$	21.9520	−	1.22776i	1.05373	−	0.0589345i
$435$		0			0
$436$	8.20224	+	5.59219i	0.392816	+	0.267817i
$437$	−4.63926	−	4.30460i	−0.221926	−	0.205917i
$438$		0			0
$439$	−12.3769	−	4.85758i	−0.590717	−	0.231840i	0.0511044	−	0.998693i	$-0.483726\pi$
$439$	−12.3769	−	4.85758i	−0.590717	−	0.231840i	−0.641822	+	0.766854i	$0.721821\pi$
$440$	−6.37371			−0.303855
$441$		0			0
$442$	3.94261			0.187531
$443$	−34.7595	−	13.6421i	−1.65147	−	0.648155i	−0.657071	−	0.753829i	$-0.728205\pi$
$443$	−34.7595	−	13.6421i	−1.65147	−	0.648155i	−0.994401	+	0.105674i	$0.966300\pi$
$444$		0			0
$445$	16.7701	+	15.5604i	0.794979	+	0.737633i
$446$	0.830227	+	0.566039i	0.0393124	+	0.0268027i
$447$		0			0
$448$	−0.731856	−	2.54252i	−0.0345770	−	0.120123i
$449$	−15.4411	−	32.0637i	−0.728709	−	1.51318i	−0.853554	−	0.521004i	$-0.825558\pi$
$449$	−15.4411	−	32.0637i	−0.728709	−	1.51318i	0.124845	−	0.992176i	$-0.460157\pi$
$450$		0			0
$451$	−1.43964	−	2.11157i	−0.0677902	−	0.0994299i
$452$	−0.964733	−	6.40058i	−0.0453772	−	0.301058i
$453$		0			0
$454$	22.3621	−	17.8332i	1.04950	−	0.836951i
$455$	−9.59190	+	15.9104i	−0.449675	+	0.745890i
$456$		0			0
$457$	2.20373	+	29.4067i	0.103086	+	1.37559i	0.773593	+	0.633683i	$0.218458\pi$
$457$	2.20373	+	29.4067i	0.103086	+	1.37559i	−0.670507	+	0.741904i	$0.733923\pi$
$458$	26.0454	+	8.03393i	1.21702	+	0.375401i
$459$		0			0
$460$	2.29967	−	1.32772i	0.107223	−	0.0619051i
$461$	−6.45020	−	28.2602i	−0.300416	−	1.31621i	−0.869502	−	0.493930i	$-0.835560\pi$
$461$	−6.45020	−	28.2602i	−0.300416	−	1.31621i	0.569086	−	0.822278i	$-0.307297\pi$
$462$		0			0
$463$	−0.731933	+	3.20681i	−0.0340158	+	0.149033i	−0.989084	−	0.147354i	$-0.952925\pi$
$463$	−0.731933	+	3.20681i	−0.0340158	+	0.149033i	0.955068	+	0.296386i	$0.0957816\pi$
$464$	−1.04753	−	3.39599i	−0.0486302	−	0.157655i
$465$		0			0
$466$	−9.44372	−	24.0622i	−0.437472	−	1.11466i
$467$	−0.750691	+	0.231557i	−0.0347378	+	0.0107152i	−0.312075	−	0.950057i	$-0.601024\pi$
$467$	−0.750691	+	0.231557i	−0.0347378	+	0.0107152i	0.277338	+	0.960773i	$0.410548\pi$
$468$		0			0
$469$	−2.61292	−	5.69929i	−0.120653	−	0.263169i
$470$	17.6036	−	4.01791i	0.811995	−	0.185333i
$471$		0			0
$472$	−4.74937	−	2.74205i	−0.218608	−	0.126213i
$473$	−0.366616	+	1.18854i	−0.0168570	+	0.0546491i
$474$		0			0
$475$	−18.0022	−	14.3563i	−0.825999	−	0.658712i
$476$	4.27239	+	0.401622i	0.195825	+	0.0184083i
$477$		0			0
$478$	−20.9700	+	19.4573i	−0.959146	+	0.889957i
$479$	6.76616	−	1.01983i	0.309154	−	0.0465974i	0.00736689	−	0.999973i	$-0.497655\pi$
$479$	6.76616	−	1.01983i	0.309154	−	0.0465974i	0.301787	+	0.953375i	$0.402417\pi$
$480$		0			0
$481$	1.38040	−	9.15835i	0.0629408	−	0.417585i
$482$	−13.5830	+	6.54125i	−0.618690	+	0.297946i
$483$		0			0
$484$	5.52441	+	2.66041i	0.251109	+	0.120928i
$485$	15.1743	−	22.2566i	0.689028	−	1.01062i
$486$		0			0
$487$	−2.07419	+	27.6781i	−0.0939905	+	1.25422i	0.728344	+	0.685212i	$0.240290\pi$
$487$	−2.07419	+	27.6781i	−0.0939905	+	1.25422i	−0.822335	+	0.569004i	$0.807329\pi$
$488$	−2.57567	+	6.56271i	−0.116595	+	0.297080i
$489$		0			0
$490$	−12.0150	+	16.2641i	−0.542781	+	0.734739i
$491$			8.22726i			0.371291i	0.982617	+	0.185646i	$0.0594376\pi$
$491$			8.22726i			0.371291i	−0.982617	+	0.185646i	$0.940562\pi$
$492$		0			0
$493$	5.74804	+	0.430756i	0.258879	+	0.0194003i
$494$	11.3828	−	12.2678i	0.512137	−	0.551952i
$495$		0			0
$496$	3.60559	−	7.48709i	0.161896	−	0.336180i
$497$	6.77249	−	6.04948i	0.303788	−	0.271356i
$498$		0			0
$499$	17.5730	+	2.64870i	0.786675	+	0.118572i	0.530081	−	0.847947i	$-0.322162\pi$
$499$	17.5730	+	2.64870i	0.786675	+	0.118572i	0.256594	+	0.966519i	$0.417400\pi$
$500$	−3.95121	+	2.69389i	−0.176703	+	0.120474i
$501$		0			0
$502$	−0.293308	−	0.316111i	−0.0130910	−	0.0141087i
$503$	2.46327	+	3.08884i	0.109832	+	0.137724i	0.833709	−	0.552204i	$-0.186213\pi$
$503$	2.46327	+	3.08884i	0.109832	+	0.137724i	−0.723877	+	0.689929i	$0.757642\pi$
$504$		0			0
$505$	−8.19684	+	10.2785i	−0.364754	+	0.457388i
$506$	2.02260	−	0.151573i	0.0899156	−	0.00673825i
$507$		0			0
$508$	5.66756	−	9.81651i	0.251457	−	0.435537i
$509$	11.1990	+	19.3972i	0.496385	+	0.859765i	0.999991	−	0.00416876i	$-0.00132696\pi$
$509$	11.1990	+	19.3972i	0.496385	+	0.859765i	−0.503606	+	0.863934i	$0.667994\pi$
$510$		0			0
$511$	−6.75312	+	27.2032i	−0.298740	+	1.20340i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$		0			0
$514$	14.3831	−	5.64497i	0.634413	−	0.248989i
$515$	30.4685	−	11.9580i	1.34260	−	0.526933i
$516$		0			0
$517$	13.4460	+	3.06896i	0.591355	+	0.134973i
$518$	2.42880	−	9.78380i	0.106715	−	0.429876i
$519$		0			0
$520$	3.51093	+	6.08110i	0.153964	+	0.266674i
$521$	6.15804	−	10.6660i	0.269789	−	0.467288i	−0.699018	−	0.715104i	$-0.746379\pi$
$521$	6.15804	−	10.6660i	0.269789	−	0.467288i	0.968807	+	0.247816i	$0.0797128\pi$
$522$		0			0
$523$	−29.9702	+	2.24596i	−1.31051	+	0.0982088i	−0.711585	−	0.702600i	$-0.752022\pi$
$523$	−29.9702	+	2.24596i	−1.31051	+	0.0982088i	−0.598920	+	0.800809i	$0.704403\pi$
$524$	1.00920	−	1.26550i	0.0440872	−	0.0552836i
$525$		0			0
$526$	2.16528	+	2.71518i	0.0944109	+	0.118388i
$527$	9.16759	+	9.88031i	0.399346	+	0.430393i
$528$		0			0
$529$	18.3053	−	12.4803i	0.795883	−	0.542624i
$530$	−28.1651	−	4.24521i	−1.22342	−	0.184400i
$531$		0			0
$532$	13.5846	−	12.1344i	0.588968	−	0.526092i
$533$	−1.22161	+	2.53670i	−0.0529138	+	0.109877i
$534$		0			0
$535$	−33.5983	+	36.2103i	−1.45258	+	1.56551i
$536$	−2.36310	−	0.177090i	−0.102070	−	0.00764912i
$537$		0			0
$538$		−	13.8240i		−	0.595997i
$539$	−13.6585	+	7.21075i	−0.588314	+	0.310589i
$540$		0			0
$541$	−0.948212	+	2.41600i	−0.0407668	+	0.103872i	−0.949807	−	0.312836i	$-0.898721\pi$
$541$	−0.948212	+	2.41600i	−0.0407668	+	0.103872i	0.909040	+	0.416708i	$0.136816\pi$
$542$	−1.08040	+	14.4169i	−0.0464071	+	0.619260i
$543$		0			0
$544$	0.913667	−	1.34010i	0.0391731	−	0.0574564i
$545$	−25.8367	−	12.4423i	−1.10672	−	0.532970i
$546$		0			0
$547$	9.80963	−	4.72407i	0.419430	−	0.201987i	−0.212251	−	0.977215i	$-0.568080\pi$
$547$	9.80963	−	4.72407i	0.419430	−	0.201987i	0.631681	+	0.775228i	$0.282365\pi$
$548$	−1.57074	+	10.4212i	−0.0670988	+	0.445172i
$549$		0			0
$550$	7.29706	−	1.09985i	0.311148	−	0.0468979i
$551$	17.9357	−	16.6419i	0.764085	−	0.708967i
$552$		0			0
$553$	−44.9977	−	4.22996i	−1.91349	−	0.179876i
$554$	−22.0817	−	17.6096i	−0.938161	−	0.748158i
$555$		0			0
$556$	2.46362	−	7.98686i	0.104481	−	0.338718i
$557$	−40.6865	−	23.4904i	−1.72394	−	0.995318i	−0.910297	−	0.413955i	$-0.864147\pi$
$557$	−40.6865	−	23.4904i	−1.72394	−	0.995318i	−0.813644	−	0.581363i	$-0.802520\pi$
$558$		0			0
$559$	1.33592	−	0.304916i	0.0565035	−	0.0128966i
$560$	3.18514	+	6.94741i	0.134597	+	0.293582i
$561$		0			0
$562$	−10.9893	+	3.38975i	−0.463556	+	0.142988i
$563$	−12.4397	−	31.6959i	−0.524272	−	1.33582i	−0.910534	−	0.413433i	$-0.864329\pi$
$563$	−12.4397	−	31.6959i	−0.524272	−	1.33582i	0.386263	−	0.922389i	$-0.373766\pi$
$564$		0			0
$565$	5.51137	+	17.8674i	0.231865	+	0.751689i
$566$	5.22020	−	22.8712i	0.219421	−	0.961348i
$567$		0			0
$568$	−0.763749	−	3.34620i	−0.0320462	−	0.140404i
$569$	−20.0233	+	11.5604i	−0.839419	+	0.484639i	−0.857067	−	0.515206i	$-0.827716\pi$
$569$	−20.0233	+	11.5604i	−0.839419	+	0.484639i	0.0176479	+	0.999844i	$0.494382\pi$
$570$		0			0
$571$	−11.8276	−	3.64833i	−0.494969	−	0.152678i	0.0372136	−	0.999307i	$-0.488152\pi$
$571$	−11.8276	−	3.64833i	−0.494969	−	0.152678i	−0.532183	+	0.846630i	$0.678628\pi$
$572$	0.400810	+	5.34843i	0.0167587	+	0.223629i
$573$		0			0
$574$	−1.58220	+	2.62444i	−0.0660397	+	0.109542i
$575$	−2.40371	+	1.91689i	−0.100242	+	0.0799400i
$576$		0			0
$577$	−0.696374	−	4.62014i	−0.0289904	−	0.192339i	0.969648	−	0.244505i	$-0.0786255\pi$
$577$	−0.696374	−	4.62014i	−0.0289904	−	0.192339i	−0.998638	+	0.0521663i	$0.983387\pi$
$578$	−8.09454	−	11.8725i	−0.336688	−	0.493831i
$579$		0			0
$580$	4.45428	+	9.24940i	0.184954	+	0.384061i
$581$	8.76304	+	30.4434i	0.363552	+	1.26300i
$582$		0			0
$583$	−17.9757	−	12.2556i	−0.744479	−	0.507577i
$584$	7.76590	+	7.20570i	0.321355	+	0.298174i
$585$		0			0
$586$	−14.2421	−	5.58961i	−0.588336	−	0.230905i
$587$	5.99609			0.247485			0.123743	−	0.992314i	$-0.460510\pi$
$587$	5.99609			0.247485			0.123743	+	0.992314i	$0.460510\pi$
$588$		0			0
$589$	57.2114			2.35736
$590$	14.7468	+	5.78768i	0.607115	+	0.238275i
$591$		0			0
$592$	−2.79305	−	2.59157i	−0.114794	−	0.106513i
$593$	30.3298	+	20.6785i	1.24550	+	0.849166i	0.992963	−	0.118422i	$-0.0377836\pi$
$593$	30.3298	+	20.6785i	1.24550	+	0.849166i	0.252534	+	0.967588i	$0.418736\pi$
$594$		0			0
$595$	−12.3767	+	0.692220i	−0.507394	+	0.0283782i
$596$	−9.21456	−	19.1342i	−0.377443	−	0.783768i
$597$		0			0
$598$	−1.25875	−	1.84625i	−0.0514743	−	0.0754989i
$599$	6.80576	+	45.1533i	0.278076	+	1.84491i	0.495213	+	0.868772i	$0.335090\pi$
$599$	6.80576	+	45.1533i	0.278076	+	1.84491i	−0.217137	+	0.976141i	$0.569672\pi$
$600$		0			0
$601$	−10.8950	+	8.68849i	−0.444417	+	0.354411i	−0.819986	−	0.572384i	$-0.806019\pi$
$601$	−10.8950	+	8.68849i	−0.444417	+	0.354411i	0.375569	+	0.926795i	$0.377447\pi$
$602$	1.47873	−	0.194334i	0.0602685	−	0.00792047i
$603$		0			0
$604$	1.03725	+	13.8412i	0.0422052	+	0.563189i
$605$	−16.9255	−	5.22081i	−0.688118	−	0.212256i
$606$		0			0
$607$	−8.93876	+	5.16080i	−0.362813	+	0.209470i	−0.670314	−	0.742077i	$-0.733841\pi$
$607$	−8.93876	+	5.16080i	−0.362813	+	0.209470i	0.307501	+	0.951548i	$0.400507\pi$
$608$	−1.53197	−	6.71200i	−0.0621296	−	0.272207i
$609$		0			0
$610$	4.53173	−	19.8548i	0.183484	−	0.803897i
$611$	−4.47859	−	14.5192i	−0.181184	−	0.587385i
$612$		0			0
$613$	−1.93898	−	4.94044i	−0.0783147	−	0.199543i	0.886354	−	0.463008i	$-0.153230\pi$
$613$	−1.93898	−	4.94044i	−0.0783147	−	0.199543i	−0.964669	+	0.263465i	$0.915135\pi$
$614$	−12.8739	+	3.97106i	−0.519547	+	0.160259i
$615$		0			0
$616$	−0.110493	+	5.83664i	−0.00445189	+	0.235165i
$617$	−10.7670	+	2.45750i	−0.433464	+	0.0989354i	−0.433685	−	0.901065i	$-0.642787\pi$
$617$	−10.7670	+	2.45750i	−0.433464	+	0.0989354i	0.000220713		1.00000i	$0.499930\pi$
$618$		0			0
$619$	12.9000	+	7.44781i	0.518494	+	0.299353i	0.736318	−	0.676635i	$-0.236563\pi$
$619$	12.9000	+	7.44781i	0.518494	+	0.299353i	−0.217824	+	0.975988i	$0.569896\pi$
$620$	−7.07564	+	22.9386i	−0.284164	+	0.921238i
$621$		0			0
$622$	18.4161	+	14.6863i	0.738417	+	0.588868i
$623$	14.5399	−	15.0872i	0.582530	−	0.604458i
$624$		0			0
$625$	22.3850	−	20.7703i	0.895402	−	0.830812i
$626$	5.40289	−	0.814354i	0.215943	−	0.0325481i
$627$		0			0
$628$	2.77851	−	18.4342i	0.110875	−	0.735605i
$629$	5.56784	−	2.68133i	0.222004	−	0.106912i
$630$		0			0
$631$	−23.4614	−	11.2984i	−0.933982	−	0.449782i	−0.0959397	−	0.995387i	$-0.530586\pi$
$631$	−23.4614	−	11.2984i	−0.933982	−	0.449782i	−0.838042	+	0.545605i	$0.816300\pi$
$632$	−9.62291	+	14.1142i	−0.382779	+	0.561434i
$633$		0			0
$634$	−1.02894	+	13.7302i	−0.0408644	+	0.545297i
$635$	−11.9626	+	30.4802i	−0.474721	+	1.20957i
$636$		0			0
$637$	14.4034	+	9.05947i	0.570685	+	0.358949i
$638$			7.84143i			0.310445i
$639$		0			0
$640$	2.88061	+	0.215872i	0.113866	+	0.00853309i
$641$	−6.01746	+	6.48528i	−0.237676	+	0.256153i	−0.840614	−	0.541634i	$-0.817806\pi$
$641$	−6.01746	+	6.48528i	−0.237676	+	0.256153i	0.602939	+	0.797787i	$0.293996\pi$
$642$		0			0
$643$	7.76728	−	16.1289i	0.306311	−	0.636062i	−0.689816	−	0.723985i	$-0.742309\pi$
$643$	7.76728	−	16.1289i	0.306311	−	0.636062i	0.996127	+	0.0879226i	$0.0280228\pi$
$644$	−1.17597	−	2.12891i	−0.0463398	−	0.0838909i
$645$		0			0
$646$	11.0416	+	1.66426i	0.434428	+	0.0654795i
$647$	−26.1690	+	17.8417i	−1.02881	+	0.701430i	−0.955232	−	0.295859i	$-0.904394\pi$
$647$	−26.1690	+	17.8417i	−1.02881	+	0.701430i	−0.0735779	+	0.997289i	$0.523442\pi$
$648$		0			0
$649$	8.23032	+	8.87017i	0.323068	+	0.348185i
$650$	−5.06891	−	6.35621i	−0.198819	−	0.249311i
$651$		0			0
$652$	−12.7362	+	15.9707i	−0.498787	+	0.625459i
$653$	46.5483	−	3.48832i	1.82158	−	0.136508i	0.880359	−	0.474307i	$-0.157301\pi$
$653$	46.5483	−	3.48832i	1.82158	−	0.136508i	0.941218	+	0.337799i	$0.109682\pi$
$654$		0			0
$655$	−2.33787	+	4.04930i	−0.0913479	+	0.158219i
$656$	0.579133	+	1.00309i	0.0226113	+	0.0391640i
$657$		0			0
$658$	−3.37418	−	16.1899i	−0.131539	−	0.631150i
$659$	−6.41994	−	1.46531i	−0.250085	−	0.0570804i	0.0956404	−	0.995416i	$-0.469510\pi$
$659$	−6.41994	−	1.46531i	−0.250085	−	0.0570804i	−0.345726	+	0.938336i	$0.612367\pi$
$660$		0			0
$661$	19.2811	−	7.56727i	0.749947	−	0.294333i	0.0405843	−	0.999176i	$-0.487078\pi$
$661$	19.2811	−	7.56727i	0.749947	−	0.294333i	0.709363	+	0.704844i	$0.248983\pi$
$662$	−2.19592	+	0.861835i	−0.0853468	+	0.0334962i
$663$		0			0
$664$	11.6735	+	2.66440i	0.453020	+	0.103399i
$665$	−33.5791	+	40.5096i	−1.30214	+	1.57089i
$666$		0			0
$667$	−1.63346	−	2.82923i	−0.0632478	−	0.109548i
$668$	−5.21504	+	9.03272i	−0.201776	+	0.349486i
$669$		0			0
$670$	6.82626	−	0.511558i	0.263722	−	0.0197632i
$671$	9.69869	−	12.1618i	0.374414	−	0.469500i
$672$		0			0
$673$	−3.89279	−	4.88141i	−0.150056	−	0.188164i	0.701122	−	0.713041i	$-0.252683\pi$
$673$	−3.89279	−	4.88141i	−0.150056	−	0.188164i	−0.851178	+	0.524877i	$0.824111\pi$
$674$	18.7298	+	20.1859i	0.721444	+	0.777532i
$675$		0			0
$676$	−5.85900	+	3.99460i	−0.225346	+	0.153638i
$677$	24.4692	+	3.68814i	0.940428	+	0.141747i	0.601327	−	0.799003i	$-0.294639\pi$
$677$	24.4692	+	3.68814i	0.940428	+	0.141747i	0.339101	+	0.940750i	$0.389877\pi$
$678$		0			0
$679$	−20.1181	−	14.2815i	−0.772061	−	0.548072i
$680$	−2.03286	+	4.22127i	−0.0779565	+	0.161878i
$681$		0			0
$682$	−12.4714	+	13.4409i	−0.477554	+	0.514680i
$683$	4.98131	+	0.373298i	0.190605	+	0.0142838i	0.169690	−	0.985497i	$-0.445723\pi$
$683$	4.98131	+	0.373298i	0.190605	+	0.0142838i	0.0209142	+	0.999781i	$0.493342\pi$
$684$		0			0
$685$		−	30.4436i		−	1.16319i
$686$	14.6854	+	11.2845i	0.560690	+	0.430844i
$687$		0			0
$688$	0.205947	−	0.524745i	0.00785167	−	0.0200057i
$689$	−1.79117	+	23.9014i	−0.0682380	+	0.910572i
$690$		0			0
$691$	−0.811774	+	1.19065i	−0.0308813	+	0.0452946i	−0.841369	−	0.540461i	$-0.818250\pi$
$691$	−0.811774	+	1.19065i	−0.0308813	+	0.0452946i	0.810488	+	0.585756i	$0.199202\pi$
$692$	−7.63526	−	3.67695i	−0.290249	−	0.139777i
$693$		0			0
$694$	−5.69751	+	2.74378i	−0.216275	+	0.104152i
$695$	−3.59851	+	23.8745i	−0.136499	+	0.905613i
$696$		0			0
$697$	−1.85764	+	0.279995i	−0.0703633	+	0.0106056i
$698$	−24.0253	+	22.2922i	−0.909372	+	0.843774i
$699$		0			0
$700$	−4.84541	−	7.40424i	−0.183139	−	0.279854i
$701$	−22.9620	−	18.3116i	−0.867265	−	0.691620i	0.0851691	−	0.996367i	$-0.472857\pi$
$701$	−22.9620	−	18.3116i	−0.867265	−	0.691620i	−0.952434	+	0.304746i	$0.901428\pi$
$702$		0			0
$703$	7.73188	−	25.0661i	0.291613	−	0.945388i
$704$	1.91083	+	1.10322i	0.0720172	+	0.0415791i
$705$		0			0
$706$	−30.4096	+	6.94079i	−1.14448	+	0.261220i
$707$	9.27031	+	7.68433i	0.348646	+	0.288999i
$708$		0			0
$709$	10.2245	−	3.15386i	0.383991	−	0.118446i	−0.0967488	−	0.995309i	$-0.530844\pi$
$709$	10.2245	−	3.15386i	0.383991	−	0.118446i	0.480740	+	0.876863i	$0.340368\pi$
$710$	3.62226	+	9.22936i	0.135941	+	0.346372i
$711$		0			0
$712$	−2.33433	−	7.56770i	−0.0874826	−	0.283612i
$713$	1.69984	−	7.44750i	0.0636596	−	0.278911i
$714$		0			0
$715$	−3.44758	−	15.1048i	−0.128932	−	0.564889i
$716$	−13.3666	+	7.71720i	−0.499533	+	0.288405i
$717$		0			0
$718$	−32.1259	−	9.90951i	−1.19893	−	0.369820i
$719$	1.35449	+	18.0744i	0.0505139	+	0.674061i	0.963780	+	0.266698i	$0.0859326\pi$
$719$	1.35449	+	18.0744i	0.0505139	+	0.674061i	−0.913266	+	0.407363i	$0.866448\pi$
$720$		0			0
$721$	−10.4222	−	28.1085i	−0.388143	−	1.04681i
$722$	22.2023	−	17.7058i	0.826285	−	0.658940i
$723$		0			0
$724$	−2.22899	−	14.7884i	−0.0828397	−	0.549606i
$725$	−6.69564	−	9.82071i	−0.248670	−	0.364732i
$726$		0			0
$727$	15.7402	+	32.6849i	0.583773	+	1.21222i	0.958503	+	0.285083i	$0.0920213\pi$
$727$	15.7402	+	32.6849i	0.583773	+	1.21222i	−0.374730	+	0.927134i	$0.622264\pi$
$728$	5.62955	−	3.10966i	0.208645	−	0.115252i
$729$		0			0
$730$	−25.2850	−	17.2390i	−0.935841	−	0.638045i
$731$	0.670232	+	0.621884i	0.0247894	+	0.0230012i
$732$		0			0
$733$	1.15885	+	0.454815i	0.0428031	+	0.0167990i	0.386646	−	0.922228i	$-0.373634\pi$
$733$	1.15885	+	0.454815i	0.0428031	+	0.0167990i	−0.343843	+	0.939027i	$0.611729\pi$
$734$	−4.15745			−0.153454
$735$		0			0
$736$	−0.919252			−0.0338841
$737$	4.86722	+	1.91024i	0.179286	+	0.0703647i
$738$		0			0
$739$	23.8144	+	22.0965i	0.876027	+	0.812834i	0.983412	−	0.181383i	$-0.0580574\pi$
$739$	23.8144	+	22.0965i	0.876027	+	0.812834i	−0.107386	+	0.994217i	$0.534248\pi$
$740$	9.09391	+	6.20013i	0.334299	+	0.227921i
$741$		0			0
$742$	−4.37576	+	25.7183i	−0.160639	+	0.944147i
$743$	−4.46963	−	9.28128i	−0.163975	−	0.340497i	0.802750	−	0.596316i	$-0.203369\pi$
$743$	−4.46963	−	9.28128i	−0.163975	−	0.340497i	−0.966725	+	0.255819i	$0.917655\pi$
$744$		0			0
$745$	34.5587	+	50.6883i	1.26613	+	1.85707i
$746$	−3.27756	−	21.7452i	−0.120000	−	0.796149i
$747$		0			0
$748$	−2.79793	+	2.23128i	−0.102303	+	0.0815836i
$749$	32.5767	+	31.3949i	1.19033	+	1.14714i
$750$		0			0
$751$	−1.82292	−	24.3251i	−0.0665191	−	0.887636i	−0.926255	−	0.376897i	$-0.876991\pi$
$751$	−1.82292	−	24.3251i	−0.0665191	−	0.887636i	0.859736	−	0.510739i	$-0.170628\pi$
$752$	−5.97300	−	1.84243i	−0.217813	−	0.0671864i
$753$		0			0
$754$	7.48143	−	4.31941i	0.272458	−	0.157304i
$755$	−8.92197	−	39.0897i	−0.324704	−	1.42262i
$756$		0			0
$757$	4.57454	−	20.0424i	0.166264	−	0.728452i	−0.821204	−	0.570635i	$-0.806697\pi$
$757$	4.57454	−	20.0424i	0.166264	−	0.728452i	0.987468	−	0.157817i	$-0.0504456\pi$
$758$	−0.630084	−	2.04268i	−0.0228857	−	0.0741935i
$759$		0			0
$760$	7.26572	+	18.5127i	0.263555	+	0.671528i
$761$	8.53133	−	2.63157i	0.309260	−	0.0953942i	−0.136240	−	0.990676i	$-0.543502\pi$
$761$	8.53133	−	2.63157i	0.309260	−	0.0953942i	0.445501	+	0.895282i	$0.353026\pi$
$762$		0			0
$763$	−11.8418	+	23.4439i	−0.428701	+	0.848727i
$764$	−20.9063	+	4.77172i	−0.756363	+	0.172635i
$765$		0			0
$766$	1.93672	+	1.11817i	0.0699767	+	0.0404011i
$767$	3.92933	−	12.7386i	0.141880	−	0.459963i
$768$		0			0
$769$	−22.7614	−	18.1516i	−0.820798	−	0.654565i	0.120285	−	0.992739i	$-0.461619\pi$
$769$	−22.7614	−	18.1516i	−0.820798	−	0.654565i	−0.941083	+	0.338175i	$0.890190\pi$
$770$	−2.19727	−	16.7195i	−0.0791842	−	0.602529i
$771$		0			0
$772$	9.22735	−	8.56173i	0.332100	−	0.308144i
$773$	−3.89537	+	0.587132i	−0.140107	+	0.0211177i	−0.218721	−	0.975787i	$-0.570188\pi$
$773$	−3.89537	+	0.587132i	−0.140107	+	0.0211177i	0.0786145	+	0.996905i	$0.474950\pi$
$774$		0			0
$775$	4.14235	−	27.4827i	0.148798	−	0.987207i
$776$	−8.40159	+	4.04599i	−0.301599	+	0.145243i
$777$		0			0
$778$	6.49094	+	3.12587i	0.232712	+	0.112068i
$779$	−4.49203	+	6.58860i	−0.160944	+	0.236061i
$780$		0			0
$781$	−0.565936	+	7.55189i	−0.0202508	+	0.270228i
$782$	0.544711	−	1.38790i	0.0194788	−	0.0496312i
$783$		0			0
$784$	6.41722	−	2.79631i	0.229186	−	0.0998682i
$785$			53.8521i			1.92207i
$786$		0			0
$787$	18.9430	+	1.41958i	0.675245	+	0.0506026i	0.407939	−	0.913009i	$-0.366248\pi$
$787$	18.9430	+	1.41958i	0.675245	+	0.0506026i	0.267306	+	0.963612i	$0.413867\pi$
$788$	−6.16418	+	6.64341i	−0.219590	+	0.236662i
$789$		0			0
$790$	21.4104	−	44.4592i	0.761749	−	1.58179i
$791$	16.4574	−	4.73722i	0.585158	−	0.168436i
$792$		0			0
$793$	−16.9459	−	2.55419i	−0.601767	−	0.0907018i
$794$	−20.8929	+	14.2445i	−0.741461	+	0.505519i
$795$		0			0
$796$	6.07259	+	6.54470i	0.215237	+	0.231971i
$797$	20.8228	+	26.1109i	0.737580	+	0.924896i	0.999189	−	0.0402782i	$-0.0128244\pi$
$797$	20.8228	+	26.1109i	0.737580	+	0.924896i	−0.261609	+	0.965174i	$0.584253\pi$
$798$		0			0
$799$	6.32108	−	7.92638i	0.223624	−	0.280415i
$800$	−3.33517	+	0.249936i	−0.117916	+	0.00883658i
$801$		0			0
$802$	10.9893	−	19.0340i	0.388045	−	0.672114i
$803$	−11.6874	−	20.2432i	−0.412440	−	0.714368i
$804$		0			0
$805$	4.27565	+	5.57477i	0.150697	+	0.196485i
$806$	19.6937	+	4.49495i	0.693680	+	0.158328i
$807$		0			0
$808$	4.23650	−	1.66270i	0.149039	−	0.0584937i
$809$	5.62977	−	2.20952i	0.197932	−	0.0776827i	−0.264304	−	0.964439i	$-0.585142\pi$
$809$	5.62977	−	2.20952i	0.197932	−	0.0776827i	0.462237	+	0.886757i	$0.347047\pi$
$810$		0			0
$811$	31.8646	+	7.27290i	1.11892	+	0.255386i	0.741696	−	0.670736i	$-0.234022\pi$
$811$	31.8646	+	7.27290i	1.11892	+	0.255386i	0.377223	+	0.926122i	$0.376879\pi$
$812$	8.54723	−	3.91860i	0.299949	−	0.137516i
$813$		0			0
$814$	4.20345	+	7.28060i	0.147331	+	0.255185i
$815$	29.5040	−	51.1024i	1.03348	−	1.79004i
$816$		0			0
$817$	3.87009	−	0.290023i	0.135397	−	0.0101466i
$818$	2.12346	−	2.66273i	0.0742449	−	0.0931001i
$819$		0			0
$820$	−2.08611	−	2.61590i	−0.0728503	−	0.0913513i
$821$	23.6513	+	25.4900i	0.825434	+	0.889607i	0.995396	−	0.0958438i	$-0.0305549\pi$
$821$	23.6513	+	25.4900i	0.825434	+	0.889607i	−0.169962	+	0.985451i	$0.554364\pi$
$822$		0			0
$823$	10.9948	−	7.49613i	0.383255	−	0.261299i	−0.356333	−	0.934359i	$-0.615973\pi$
$823$	10.9948	−	7.49613i	0.383255	−	0.261299i	0.739588	+	0.673060i	$0.235021\pi$
$824$	−11.2042	−	1.68877i	−0.390318	−	0.0588310i
$825$		0			0
$826$	5.55564	−	13.4038i	0.193305	−	0.466379i
$827$	11.5348	−	23.9522i	0.401103	−	0.832899i	−0.598394	−	0.801202i	$-0.704194\pi$
$827$	11.5348	−	23.9522i	0.401103	−	0.832899i	0.999498	−	0.0316975i	$-0.0100913\pi$
$828$		0			0
$829$	−0.432672	+	0.466309i	−0.0150273	+	0.0161956i	−0.740521	−	0.672033i	$-0.765421\pi$
$829$	−0.432672	+	0.466309i	−0.0150273	+	0.0161956i	0.725493	+	0.688229i	$0.241612\pi$
$830$	−34.4916	−	2.58479i	−1.19722	−	0.0897194i
$831$		0			0
$832$		−	2.43081i		−	0.0842732i
$833$	0.419332	+	11.3458i	0.0145290	+	0.393108i
$834$		0			0
$835$	11.0075	−	28.0465i	0.380929	−	0.970591i
$836$	−1.13518	+	15.1480i	−0.0392612	+	0.523904i
$837$		0			0
$838$	−12.7142	+	18.6483i	−0.439205	+	0.644195i
$839$	−4.31941	−	2.08012i	−0.149123	−	0.0718137i	0.357834	−	0.933785i	$-0.383515\pi$
$839$	−4.31941	−	2.08012i	−0.149123	−	0.0718137i	−0.506957	+	0.861971i	$0.669230\pi$
$840$		0			0
$841$	−14.7488	+	7.10264i	−0.508579	+	0.244919i
$842$	4.19765	−	27.8496i	0.144661	−	0.959761i
$843$		0			0
$844$	−2.63085	+	0.396537i	−0.0905575	+	0.0136494i
$845$	15.0160	−	13.9328i	0.516565	−	0.479302i
$846$		0			0
$847$	−5.07430	+	15.4088i	−0.174355	+	0.529451i
$848$	7.70908	+	6.14778i	0.264731	+	0.211116i
$849$		0			0
$850$	1.59892	−	5.18359i	0.0548427	−	0.177796i
$851$	−3.03326	−	1.75125i	−0.103979	−	0.0600322i
$852$		0			0
$853$	23.4549	−	5.35343i	0.803081	−	0.183298i	0.198770	−	0.980046i	$-0.436305\pi$
$853$	23.4549	−	5.35343i	0.803081	−	0.183298i	0.604311	+	0.796748i	$0.293448\pi$
$854$	−18.1032	−	4.49406i	−0.619479	−	0.153784i
$855$		0			0
$856$	16.3403	−	5.04032i	0.558501	−	0.172275i
$857$	14.5463	+	37.0634i	0.496893	+	1.26606i	0.930940	+	0.365172i	$0.118990\pi$
$857$	14.5463	+	37.0634i	0.496893	+	1.26606i	−0.434048	+	0.900890i	$0.642915\pi$
$858$		0			0
$859$	3.96915	+	12.8677i	0.135426	+	0.439039i	0.997729	−	0.0673524i	$-0.0214552\pi$
$859$	3.96915	+	12.8677i	0.135426	+	0.439039i	−0.862304	+	0.506392i	$0.830979\pi$
$860$	−0.362351	+	1.58756i	−0.0123561	+	0.0541354i
$861$		0			0
$862$	2.63420	+	11.5412i	0.0897213	+	0.393095i
$863$	7.99328	−	4.61492i	0.272095	−	0.157094i	−0.357745	−	0.933819i	$-0.616454\pi$
$863$	7.99328	−	4.61492i	0.272095	−	0.157094i	0.629839	+	0.776726i	$0.283121\pi$
$864$		0			0
$865$	23.3926	+	7.21566i	0.795372	+	0.245340i
$866$	−1.12220	−	14.9748i	−0.0381340	−	0.508863i
$867$		0			0
$868$	20.8831	+	6.87708i	0.708818	+	0.233423i
$869$	29.4684	−	23.5002i	0.999646	−	0.797191i
$870$		0			0
$871$	−0.858537	−	5.69602i	−0.0290904	−	0.193002i
$872$	5.59219	+	8.20224i	0.189375	+	0.277763i
$873$		0			0
$874$	−2.74592	−	5.70196i	−0.0928820	−	0.192872i
$875$	−8.42874	−	9.43610i	−0.284943	−	0.318998i
$876$		0			0
$877$	10.9955	+	7.49662i	0.371293	+	0.253143i	0.734563	−	0.678541i	$-0.237387\pi$
$877$	10.9955	+	7.49662i	0.371293	+	0.253143i	−0.363270	+	0.931684i	$0.618340\pi$
$878$	−9.74666	−	9.04358i	−0.328934	−	0.305206i
$879$		0			0
$880$	−5.93312	−	2.32858i	−0.200005	−	0.0784964i
$881$	25.2528			0.850788			0.425394	−	0.905008i	$-0.360136\pi$
$881$	25.2528			0.850788			0.425394	+	0.905008i	$0.360136\pi$
$882$		0			0
$883$	45.1695			1.52007			0.760037	−	0.649880i	$-0.225181\pi$
$883$	45.1695			1.52007			0.760037	+	0.649880i	$0.225181\pi$
$884$	3.67007	+	1.44040i	0.123438	+	0.0484458i
$885$		0			0
$886$	−27.3727	−	25.3981i	−0.919602	−	0.853266i
$887$	28.5418	+	19.4595i	0.958339	+	0.653385i	0.938083	−	0.346410i	$-0.112599\pi$
$887$	28.5418	+	19.4595i	0.958339	+	0.653385i	0.0202560	+	0.999795i	$0.493552\pi$
$888$		0			0
$889$	27.7044	+	11.4830i	0.929177	+	0.385127i
$890$	9.92600	+	20.6116i	0.332720	+	0.690901i
$891$		0			0
$892$	0.566039	+	0.830227i	0.0189524	+	0.0277981i
$893$	−6.41384	−	42.5530i	−0.214631	−	1.42398i
$894$		0			0
$895$	34.8581	−	27.7984i	1.16518	−	0.929199i
$896$	0.247619	−	2.63414i	0.00827238	−	0.0880004i
$897$		0			0
$898$	−2.65950	−	35.4885i	−0.0887486	−	1.18427i
$899$	28.2209	+	8.70499i	0.941219	+	0.290328i
$900$		0			0
$901$	−13.8501	+	7.99635i	−0.461413	+	0.266397i
$902$	−0.568684	−	2.49157i	−0.0189351	−	0.0829601i
$903$		0			0
$904$	1.44035	−	6.31059i	0.0479054	−	0.209887i
$905$	12.7339	+	41.2822i	0.423288	+	1.37227i
$906$		0			0
$907$	5.50874	+	14.0360i	0.182915	+	0.466059i	0.992692	−	0.120679i	$-0.0385071\pi$
$907$	5.50874	+	14.0360i	0.182915	+	0.466059i	−0.809777	+	0.586738i	$0.800412\pi$
$908$	27.3314	−	8.43063i	0.907026	−	0.279780i
$909$		0			0
$910$	−14.7416	+	11.3062i	−0.488678	+	0.374798i
$911$	45.3971	−	10.3616i	1.50407	−	0.343295i	0.610429	−	0.792071i	$-0.290997\pi$
$911$	45.3971	−	10.3616i	1.50407	−	0.343295i	0.893644	+	0.448776i	$0.148140\pi$
$912$		0			0
$913$	−22.8798	−	13.2096i	−0.757210	−	0.437175i
$914$	−8.69208	+	28.1790i	−0.287508	+	0.932079i
$915$		0			0
$916$	21.3098	+	16.9940i	0.704096	+	0.561498i
$917$	3.66756	+	2.21107i	0.121114	+	0.0730158i
$918$		0			0
$919$	21.7532	−	20.1840i	0.717571	−	0.665809i	−0.234350	−	0.972152i	$-0.575296\pi$
$919$	21.7532	−	20.1840i	0.717571	−	0.665809i	0.951921	+	0.306344i	$0.0991056\pi$
$920$	2.62577	−	0.395772i	0.0865692	−	0.0130482i
$921$		0			0
$922$	4.32028	−	28.6632i	0.142281	−	0.943972i
$923$	7.51693	−	3.61996i	0.247423	−	0.119153i
$924$		0			0
$925$	−11.4812	−	5.52907i	−0.377500	−	0.181795i
$926$	−1.85292	+	2.71773i	−0.0608906	+	0.0893101i
$927$		0			0
$928$	0.265582	−	3.54395i	0.00871816	−	0.116336i
$929$	11.9753	−	30.5125i	0.392896	−	1.00108i	−0.588399	−	0.808571i	$-0.700241\pi$
$929$	11.9753	−	30.5125i	0.392896	−	1.00108i	0.981295	−	0.192512i	$-0.0616634\pi$
$930$		0			0
$931$	36.5140	+	31.4519i	1.19670	+	1.03079i
$932$		−	25.8491i		−	0.846714i
$933$		0			0
$934$	−0.783396	−	0.0587074i	−0.0256335	−	0.00192096i
$935$	7.03144	−	7.57809i	0.229953	−	0.247830i
$936$		0			0
$937$	−19.7208	+	40.9506i	−0.644249	+	1.33780i	0.281464	+	0.959572i	$0.409180\pi$
$937$	−19.7208	+	40.9506i	−0.644249	+	1.33780i	−0.925713	+	0.378226i	$0.876534\pi$
$938$	−0.350114	−	6.25993i	−0.0114316	−	0.204394i
$939$		0			0
$940$	17.8547	+	2.69116i	0.582355	+	0.0877759i
$941$	18.6220	−	12.6963i	0.607060	−	0.413887i	−0.220401	−	0.975409i	$-0.570737\pi$
$941$	18.6220	−	12.6963i	0.607060	−	0.413887i	0.827461	+	0.561523i	$0.189784\pi$
$942$		0			0
$943$	0.724206	+	0.780508i	0.0235834	+	0.0254168i
$944$	−3.41928	−	4.28765i	−0.111288	−	0.139551i
$945$		0			0
$946$	−0.775495	+	0.972440i	−0.0252135	+	0.0316167i
$947$	−35.4916	+	2.65972i	−1.15332	+	0.0864294i	−0.637628	−	0.770344i	$-0.720084\pi$
$947$	−35.4916	+	2.65972i	−1.15332	+	0.0864294i	−0.515693	+	0.856774i	$0.672465\pi$
$948$		0			0
$949$	−12.8759	+	22.3017i	−0.417970	+	0.723945i
$950$	−11.5129	−	19.9409i	−0.373527	−	0.646967i
$951$		0			0
$952$	3.83033	+	1.93474i	0.124142	+	0.0627053i
$953$	−1.38869	−	0.316960i	−0.0449842	−	0.0102673i	0.199970	−	0.979802i	$-0.435916\pi$
$953$	−1.38869	−	0.316960i	−0.0449842	−	0.0102673i	−0.244954	+	0.969535i	$0.578773\pi$
$954$		0			0
$955$	57.6628	−	22.6310i	1.86592	−	0.732322i
$956$	−26.6290	+	10.4511i	−0.861243	+	0.338013i
$957$		0			0
$958$	6.67103	+	1.52262i	0.215531	+	0.0491936i
$959$	−27.8784	−	0.527763i	−0.900239	−	0.0170423i
$960$		0			0
$961$	19.0284	+	32.9582i	0.613820	+	1.06317i
$962$	4.63090	−	8.02095i	0.149306	−	0.258606i
$963$		0			0
$964$	−15.0339	+	1.12663i	−0.484209	+	0.0362864i
$965$	−22.6711	+	28.4287i	−0.729808	+	0.915151i
$966$		0			0
$967$	−35.7858	−	44.8739i	−1.15079	−	1.44305i	−0.876500	−	0.481401i	$-0.840128\pi$
$967$	−35.7858	−	44.8739i	−1.15079	−	1.44305i	−0.274292	−	0.961646i	$-0.588443\pi$
$968$	4.17057	+	4.49480i	0.134047	+	0.144468i
$969$		0			0
$970$	22.2566	−	15.1743i	0.714615	−	0.487216i
$971$	−12.0028	−	1.80914i	−0.385189	−	0.0580579i	−0.0464066	−	0.998923i	$-0.514777\pi$
$971$	−12.0028	−	1.80914i	−0.385189	−	0.0580579i	−0.338783	+	0.940865i	$0.610015\pi$
$972$		0			0
$973$	21.8004	+	3.70917i	0.698889	+	0.118910i
$974$	−12.0428	+	25.0071i	−0.385875	+	0.801278i
$975$		0			0
$976$	−4.79525	+	5.16805i	−0.153492	+	0.165425i
$977$	46.2334	+	3.46471i	1.47914	+	0.110846i	0.789697	−	0.613496i	$-0.210238\pi$
$977$	46.2334	+	3.46471i	1.47914	+	0.110846i	0.689440	+	0.724343i	$0.257857\pi$
$978$		0			0
$979$			17.4740i			0.558471i
$980$	−17.1264	+	10.7503i	−0.547082	+	0.343405i
$981$		0			0
$982$	−3.00576	+	7.65854i	−0.0959175	+	0.244394i
$983$	−1.64512	+	21.9527i	−0.0524713	+	0.700181i	0.907494	+	0.420064i	$0.137992\pi$
$983$	−1.64512	+	21.9527i	−0.0524713	+	0.700181i	−0.959966	+	0.280117i	$0.909627\pi$
$984$		0			0
$985$	14.7473	−	21.6303i	0.469888	−	0.689199i
$986$	5.19333	+	2.50097i	0.165389	+	0.0796472i
$987$		0			0
$988$	15.0779	−	7.26112i	0.479691	−	0.231007i
$989$	0.0772328	−	0.512406i	0.00245586	−	0.0162936i
$990$		0			0
$991$	−57.6911	+	8.69554i	−1.83262	+	0.276223i	−0.972335	−	0.233592i	$-0.924952\pi$
$991$	−57.6911	+	8.69554i	−1.83262	+	0.276223i	−0.860284	+	0.509815i	$0.829714\pi$
$992$	6.09169	−	5.65227i	0.193411	−	0.179460i
$993$		0			0
$994$	8.51445	−	3.15703i	0.270062	−	0.100135i
$995$	−20.1636	−	16.0800i	−0.639230	−	0.509769i
$996$		0			0
$997$	1.46738	−	4.75712i	0.0464723	−	0.150660i	−0.929363	−	0.369168i	$-0.879643\pi$
$997$	1.46738	−	4.75712i	0.0464723	−	0.150660i	0.975835	+	0.218508i	$0.0701190\pi$
$998$	15.3905	+	8.88574i	0.487179	+	0.281273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.12	yes	240
3.2	odd	2	inner	882.2.bl.a.395.9	✓	240
49.33	odd	42	inner	882.2.bl.a.719.9	yes	240
147.131	even	42	inner	882.2.bl.a.719.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.9	✓	240	3.2	odd	2	inner
882.2.bl.a.395.12	yes	240	1.1	even	1	trivial
882.2.bl.a.719.9	yes	240	49.33	odd	42	inner
882.2.bl.a.719.12	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)

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.38675 - 1.62726i) q^{5} +(-1.53151 + 2.15742i) q^{7} +(0.433884 + 0.900969i) q^{8} +O(q^{10})\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.38675 - 1.62726i) q^{5} +(-1.53151 + 2.15742i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-1.62726 - 2.38675i) q^{10} +(-0.328853 - 2.18179i) q^{11} +(-1.90048 + 1.51558i) q^{13} +(-2.21384 + 1.44876i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-1.54987 - 0.478073i) q^{17} +(-5.96225 + 3.44230i) q^{19} +(-0.642794 - 2.81626i) q^{20} +(0.490979 - 2.15112i) q^{22} +(0.270954 + 0.878413i) q^{23} +(1.22189 + 3.11333i) q^{25} +(-2.32282 + 0.716494i) q^{26} +(-2.59010 + 0.539808i) q^{28} +(-3.46478 + 0.790814i) q^{29} +(-7.19671 - 4.15502i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-1.26808 - 1.01126i) q^{34} +(7.16601 - 2.65705i) q^{35} +(-2.79305 + 2.59157i) q^{37} +(-6.80771 + 1.02610i) q^{38} +(0.430537 - 2.85642i) q^{40} +(1.04356 - 0.502552i) q^{41} +(-0.507888 - 0.244586i) q^{43} +(1.24293 - 1.82304i) q^{44} +(-0.0686958 + 0.916682i) q^{46} +(-2.28364 + 5.81862i) q^{47} +(-2.30893 - 6.60824i) q^{49} +3.34452i q^{50} +(-2.42401 - 0.181655i) q^{52} +(6.70669 - 7.22810i) q^{53} +(-2.76545 + 5.74252i) q^{55} +(-2.60827 - 0.443776i) q^{56} +(-3.51419 - 0.529679i) q^{58} +(-4.53118 + 3.08931i) q^{59} +(4.79525 + 5.16805i) q^{61} +(-5.18123 - 6.49705i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(7.00222 - 0.524744i) q^{65} +(-1.18486 + 2.05224i) q^{67} +(-0.810966 - 1.40463i) q^{68} +(7.64138 + 0.144658i) q^{70} +(-3.34620 - 0.763749i) q^{71} +(9.86161 - 3.87040i) q^{73} +(-3.54679 + 1.39201i) q^{74} +(-6.71200 - 1.53197i) q^{76} +(5.21069 + 2.63197i) q^{77} +(8.54125 + 14.7939i) q^{79} +(1.44434 - 2.50168i) q^{80} +(1.15503 - 0.0865573i) q^{82} +(7.46549 - 9.36143i) q^{83} +(2.92121 + 3.66308i) q^{85} +(-0.383422 - 0.413231i) q^{86} +(1.82304 - 1.24293i) q^{88} +(-7.83109 - 1.18035i) q^{89} +(-0.359138 - 6.42128i) q^{91} +(-0.398849 + 0.828218i) q^{92} +(-4.25156 + 4.58209i) q^{94} +(19.8319 + 1.48619i) q^{95} +9.32506i q^{97} +(0.264938 - 6.99498i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) \) 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

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Database

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