LMFDB - Embedded newform 2070.2.j.j.737.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, degree $2$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 $ x^20 - 20x^18 + 187x^16 - 1012x^14 + 3533x^12 - 7896x^10 + 10837x^8 - 5668x^6 - 4125x^4 + 8700*x^2 + 3721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.9
Root			$2.39613 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.j.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24750 + 1.85573i) q^{5} +(-3.35392 - 3.35392i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24750 + 1.85573i) q^{5} +(-3.35392 - 3.35392i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.19432 + 0.430087i) q^{10} +4.58406i q^{11} +(0.617014 - 0.617014i) q^{13} -4.74316 q^{14} -1.00000 q^{16} +(-4.58406 + 4.58406i) q^{17} -3.62266i q^{19} +(1.85573 - 1.24750i) q^{20} +(3.24142 + 3.24142i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.88749 + 4.63005i) q^{25} -0.872590i q^{26} +(-3.35392 + 3.35392i) q^{28} -9.41018 q^{29} -3.77499 q^{31} +(-0.707107 + 0.707107i) q^{32} +6.48283i q^{34} +(2.03997 - 10.4080i) q^{35} +(-4.79894 - 4.79894i) q^{37} +(-2.56161 - 2.56161i) q^{38} +(0.430087 - 2.19432i) q^{40} -2.87751i q^{41} +(-0.112507 + 0.112507i) q^{43} +4.58406 q^{44} +1.00000 q^{46} +(-7.28725 + 7.28725i) q^{47} +15.4976i q^{49} +(1.93928 + 4.60860i) q^{50} +(-0.617014 - 0.617014i) q^{52} +(5.77255 + 5.77255i) q^{53} +(-8.50679 + 5.71861i) q^{55} +4.74316i q^{56} +(-6.65400 + 6.65400i) q^{58} +10.6992 q^{59} +12.7541 q^{61} +(-2.66932 + 2.66932i) q^{62} +1.00000i q^{64} +(1.91474 + 0.375289i) q^{65} +(-7.73517 - 7.73517i) q^{67} +(4.58406 + 4.58406i) q^{68} +(-5.91709 - 8.80205i) q^{70} +5.53162i q^{71} +(-8.22311 + 8.22311i) q^{73} -6.78672 q^{74} -3.62266 q^{76} +(15.3746 - 15.3746i) q^{77} +5.17939i q^{79} +(-1.24750 - 1.85573i) q^{80} +(-2.03471 - 2.03471i) q^{82} +(-4.85886 - 4.85886i) q^{83} +(-14.2254 - 2.78818i) q^{85} +0.159108i q^{86} +(3.24142 - 3.24142i) q^{88} -9.90748 q^{89} -4.13884 q^{91} +(0.707107 - 0.707107i) q^{92} +10.3057i q^{94} +(6.72269 - 4.51927i) q^{95} +(-5.11076 - 5.11076i) q^{97} +(10.9585 + 10.9585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{7}+O(q^{10}) $ 20 * q - 16 * q^7	$ 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) $ 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.24750	+	1.85573i	0.557898	+	0.829909i
$5$	1.24750	+	1.85573i	0.557898	+	0.829909i
$6$		0			0
$7$	−3.35392	−	3.35392i	−1.26766	−	1.26766i	−0.947292	−	0.320373i	$-0.896192\pi$
$7$	−3.35392	−	3.35392i	−1.26766	−	1.26766i	−0.320373	−	0.947292i	$-0.603808\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.19432	+	0.430087i	0.693904	+	0.136005i
$11$			4.58406i			1.38215i	0.722785	+	0.691073i	$0.242861\pi$
$11$			4.58406i			1.38215i	−0.722785	+	0.691073i	$0.757139\pi$
$12$		0			0
$13$	0.617014	−	0.617014i	0.171129	−	0.171129i	−0.616346	−	0.787475i	$-0.711388\pi$
$13$	0.617014	−	0.617014i	0.171129	−	0.171129i	0.787475	+	0.616346i	$0.211388\pi$
$14$	−4.74316			−1.26766
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.58406	+	4.58406i	−1.11180	+	1.11180i	−0.118890	+	0.992907i	$0.537933\pi$
$17$	−4.58406	+	4.58406i	−1.11180	+	1.11180i	−0.992907	+	0.118890i	$0.962067\pi$
$18$		0			0
$19$		−	3.62266i		−	0.831095i	−0.909571	−	0.415548i	$-0.863590\pi$
$19$		−	3.62266i		−	0.831095i	0.909571	−	0.415548i	$-0.136410\pi$
$20$	1.85573	−	1.24750i	0.414955	−	0.278949i
$21$		0			0
$22$	3.24142	+	3.24142i	0.691073	+	0.691073i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−1.88749	+	4.63005i	−0.377499	+	0.926010i
$26$		−	0.872590i		−	0.171129i
$27$		0			0
$28$	−3.35392	+	3.35392i	−0.633832	+	0.633832i
$29$	−9.41018			−1.74743			−0.873713	−	0.486441i	$-0.838295\pi$
$29$	−9.41018			−1.74743			−0.873713	+	0.486441i	$0.838295\pi$
$30$		0			0
$31$	−3.77499			−0.678008			−0.339004	−	0.940785i	$-0.610090\pi$
$31$	−3.77499			−0.678008			−0.339004	+	0.940785i	$0.610090\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			6.48283i			1.11180i
$35$	2.03997	−	10.4080i	0.344818	−	1.75927i
$36$		0			0
$37$	−4.79894	−	4.79894i	−0.788941	−	0.788941i	0.192380	−	0.981321i	$-0.438379\pi$
$37$	−4.79894	−	4.79894i	−0.788941	−	0.788941i	−0.981321	+	0.192380i	$0.938379\pi$
$38$	−2.56161	−	2.56161i	−0.415548	−	0.415548i
$39$		0			0
$40$	0.430087	−	2.19432i	0.0680027	−	0.346952i
$41$		−	2.87751i		−	0.449392i	−0.974429	−	0.224696i	$-0.927861\pi$
$41$		−	2.87751i		−	0.449392i	0.974429	−	0.224696i	$-0.0721389\pi$
$42$		0			0
$43$	−0.112507	+	0.112507i	−0.0171571	+	0.0171571i	−0.715633	−	0.698476i	$-0.753862\pi$
$43$	−0.112507	+	0.112507i	−0.0171571	+	0.0171571i	0.698476	+	0.715633i	$0.253862\pi$
$44$	4.58406			0.691073
$45$		0			0
$46$	1.00000			0.147442
$47$	−7.28725	+	7.28725i	−1.06295	+	1.06295i	−0.0650740	+	0.997880i	$0.520728\pi$
$47$	−7.28725	+	7.28725i	−1.06295	+	1.06295i	−0.997880	+	0.0650740i	$0.979272\pi$
$48$		0			0
$49$			15.4976i			2.21394i
$50$	1.93928	+	4.60860i	0.274256	+	0.651754i
$51$		0			0
$52$	−0.617014	−	0.617014i	−0.0855644	−	0.0855644i
$53$	5.77255	+	5.77255i	0.792921	+	0.792921i	0.981968	−	0.189047i	$-0.0605399\pi$
$53$	5.77255	+	5.77255i	0.792921	+	0.792921i	−0.189047	+	0.981968i	$0.560540\pi$
$54$		0			0
$55$	−8.50679	+	5.71861i	−1.14705	+	0.771097i
$56$			4.74316i			0.633832i
$57$		0			0
$58$	−6.65400	+	6.65400i	−0.873713	+	0.873713i
$59$	10.6992			1.39291			0.696456	−	0.717600i	$-0.254759\pi$
$59$	10.6992			1.39291			0.696456	+	0.717600i	$0.254759\pi$
$60$		0			0
$61$	12.7541			1.63300			0.816501	−	0.577345i	$-0.195911\pi$
$61$	12.7541			1.63300			0.816501	+	0.577345i	$0.195911\pi$
$62$	−2.66932	+	2.66932i	−0.339004	+	0.339004i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.91474	+	0.375289i	0.237494	+	0.0465489i
$66$		0			0
$67$	−7.73517	−	7.73517i	−0.945001	−	0.945001i	0.0535633	−	0.998564i	$-0.482942\pi$
$67$	−7.73517	−	7.73517i	−0.945001	−	0.945001i	−0.998564	+	0.0535633i	$0.982942\pi$
$68$	4.58406	+	4.58406i	0.555899	+	0.555899i
$69$		0			0
$70$	−5.91709	−	8.80205i	−0.707228	−	1.05205i
$71$			5.53162i			0.656482i	0.944594	+	0.328241i	$0.106456\pi$
$71$			5.53162i			0.656482i	−0.944594	+	0.328241i	$0.893544\pi$
$72$		0			0
$73$	−8.22311	+	8.22311i	−0.962443	+	0.962443i	−0.999320	−	0.0368773i	$-0.988259\pi$
$73$	−8.22311	+	8.22311i	−0.962443	+	0.962443i	0.0368773	+	0.999320i	$0.488259\pi$
$74$	−6.78672			−0.788941
$75$		0			0
$76$	−3.62266			−0.415548
$77$	15.3746	−	15.3746i	1.75210	−	1.75210i
$78$		0			0
$79$			5.17939i			0.582727i	0.956612	+	0.291363i	$0.0941089\pi$
$79$			5.17939i			0.582727i	−0.956612	+	0.291363i	$0.905891\pi$
$80$	−1.24750	−	1.85573i	−0.139475	−	0.207477i
$81$		0			0
$82$	−2.03471	−	2.03471i	−0.224696	−	0.224696i
$83$	−4.85886	−	4.85886i	−0.533329	−	0.533329i	0.388232	−	0.921562i	$-0.373086\pi$
$83$	−4.85886	−	4.85886i	−0.533329	−	0.533329i	−0.921562	+	0.388232i	$0.873086\pi$
$84$		0			0
$85$	−14.2254	−	2.78818i	−1.54296	−	0.302421i
$86$			0.159108i			0.0171571i
$87$		0			0
$88$	3.24142	−	3.24142i	0.345536	−	0.345536i
$89$	−9.90748			−1.05019			−0.525095	−	0.851043i	$-0.675970\pi$
$89$	−9.90748			−1.05019			−0.525095	+	0.851043i	$0.675970\pi$
$90$		0			0
$91$	−4.13884			−0.433868
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$			10.3057i			1.06295i
$95$	6.72269	−	4.51927i	0.689734	−	0.463667i
$96$		0			0
$97$	−5.11076	−	5.11076i	−0.518920	−	0.518920i	0.398325	−	0.917244i	$-0.369592\pi$
$97$	−5.11076	−	5.11076i	−0.518920	−	0.518920i	−0.917244	+	0.398325i	$0.869592\pi$
$98$	10.9585	+	10.9585i	1.10697	+	1.10697i
$99$		0			0
$100$	4.63005	+	1.88749i	0.463005	+	0.188749i
$101$			16.0003i			1.59209i	0.605235	+	0.796047i	$0.293079\pi$
$101$			16.0003i			1.59209i	−0.605235	+	0.796047i	$0.706921\pi$
$102$		0			0
$103$	−1.07427	+	1.07427i	−0.105851	+	0.105851i	−0.758049	−	0.652198i	$-0.773847\pi$
$103$	−1.07427	+	1.07427i	−0.105851	+	0.105851i	0.652198	+	0.758049i	$0.273847\pi$
$104$	−0.872590			−0.0855644
$105$		0			0
$106$	8.16362			0.792921
$107$	12.6877	−	12.6877i	1.22657	−	1.22657i	0.261316	−	0.965253i	$-0.415843\pi$
$107$	12.6877	−	12.6877i	1.22657	−	1.22657i	0.965253	−	0.261316i	$-0.0841566\pi$
$108$		0			0
$109$			13.5680i			1.29958i	0.760113	+	0.649790i	$0.225143\pi$
$109$			13.5680i			1.29958i	−0.760113	+	0.649790i	$0.774857\pi$
$110$	−1.97154	+	10.0589i	−0.187979	+	0.959076i
$111$		0			0
$112$	3.35392	+	3.35392i	0.316916	+	0.316916i
$113$	−14.7943	−	14.7943i	−1.39173	−	1.39173i	−0.821446	−	0.570286i	$-0.806832\pi$
$113$	−14.7943	−	14.7943i	−1.39173	−	1.39173i	−0.570286	−	0.821446i	$-0.693168\pi$
$114$		0			0
$115$	−0.430087	+	2.19432i	−0.0401058	+	0.204621i
$116$			9.41018i			0.873713i
$117$		0			0
$118$	7.56545	−	7.56545i	0.696456	−	0.696456i
$119$	30.7492			2.81877
$120$		0			0
$121$	−10.0136			−0.910325
$122$	9.01854	−	9.01854i	0.816501	−	0.816501i
$123$		0			0
$124$			3.77499i			0.339004i
$125$	−10.9468	+	2.27330i	−0.979110	+	0.203330i
$126$		0			0
$127$	3.16025	+	3.16025i	0.280427	+	0.280427i	0.833279	−	0.552852i	$-0.186461\pi$
$127$	3.16025	+	3.16025i	0.280427	+	0.280427i	−0.552852	+	0.833279i	$0.686461\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	1.61929	−	1.08855i	0.142021	−	0.0954725i
$131$		−	6.64247i		−	0.580355i	−0.956973	−	0.290177i	$-0.906286\pi$
$131$		−	6.64247i		−	0.580355i	0.956973	−	0.290177i	$-0.0937143\pi$
$132$		0			0
$133$	−12.1501	+	12.1501i	−1.05355	+	1.05355i
$134$	−10.9392			−0.945001
$135$		0			0
$136$	6.48283			0.555899
$137$	−16.1594	+	16.1594i	−1.38059	+	1.38059i	−0.537034	+	0.843561i	$0.680455\pi$
$137$	−16.1594	+	16.1594i	−1.38059	+	1.38059i	−0.843561	+	0.537034i	$0.819545\pi$
$138$		0			0
$139$			2.42364i			0.205570i	0.994704	+	0.102785i	$0.0327754\pi$
$139$			2.42364i			0.205570i	−0.994704	+	0.102785i	$0.967225\pi$
$140$	−10.4080	−	2.03997i	−0.879637	−	0.172409i
$141$		0			0
$142$	3.91145	+	3.91145i	0.328241	+	0.328241i
$143$	2.82843	+	2.82843i	0.236525	+	0.236525i
$144$		0			0
$145$	−11.7392	−	17.4628i	−0.974887	−	1.45021i
$146$			11.6292i			0.962443i
$147$		0			0
$148$	−4.79894	+	4.79894i	−0.394470	+	0.394470i
$149$	−0.534398			−0.0437796			−0.0218898	−	0.999760i	$-0.506968\pi$
$149$	−0.534398			−0.0437796			−0.0218898	+	0.999760i	$0.506968\pi$
$150$		0			0
$151$	9.17424			0.746589			0.373295	−	0.927713i	$-0.378228\pi$
$151$	9.17424			0.746589			0.373295	+	0.927713i	$0.378228\pi$
$152$	−2.56161	+	2.56161i	−0.207774	+	0.207774i
$153$		0			0
$154$		−	21.7429i		−	1.75210i
$155$	−4.70929	−	7.00537i	−0.378259	−	0.562685i
$156$		0			0
$157$	−14.5091	−	14.5091i	−1.15795	−	1.15795i	−0.984916	−	0.173034i	$-0.944643\pi$
$157$	−14.5091	−	14.5091i	−1.15795	−	1.15795i	−0.173034	−	0.984916i	$-0.555357\pi$
$158$	3.66238	+	3.66238i	0.291363	+	0.291363i
$159$		0			0
$160$	−2.19432	−	0.430087i	−0.173476	−	0.0340013i
$161$		−	4.74316i		−	0.373814i
$162$		0			0
$163$	1.48056	−	1.48056i	0.115966	−	0.115966i	−0.646742	−	0.762708i	$-0.723869\pi$
$163$	1.48056	−	1.48056i	0.115966	−	0.115966i	0.762708	+	0.646742i	$0.223869\pi$
$164$	−2.87751			−0.224696
$165$		0			0
$166$	−6.87147			−0.533329
$167$	3.15709	−	3.15709i	0.244303	−	0.244303i	−0.574324	−	0.818628i	$-0.694735\pi$
$167$	3.15709	−	3.15709i	0.244303	−	0.244303i	0.818628	+	0.574324i	$0.194735\pi$
$168$		0			0
$169$			12.2386i			0.941430i
$170$	−12.0304	+	8.08733i	−0.922691	+	0.620270i
$171$		0			0
$172$	0.112507	+	0.112507i	0.00857855	+	0.00857855i
$173$	0.166335	+	0.166335i	0.0126462	+	0.0126462i	0.713402	−	0.700755i	$-0.247154\pi$
$173$	0.166335	+	0.166335i	0.0126462	+	0.0126462i	−0.700755	+	0.713402i	$0.747154\pi$
$174$		0			0
$175$	21.8593	−	9.19833i	1.65241	−	0.695328i
$176$		−	4.58406i		−	0.345536i
$177$		0			0
$178$	−7.00565	+	7.00565i	−0.525095	+	0.525095i
$179$	−13.3617			−0.998698			−0.499349	−	0.866401i	$-0.666427\pi$
$179$	−13.3617			−0.998698			−0.499349	+	0.866401i	$0.666427\pi$
$180$		0			0
$181$	12.6397			0.939503			0.469751	−	0.882799i	$-0.344344\pi$
$181$	12.6397			0.939503			0.469751	+	0.882799i	$0.344344\pi$
$182$	−2.92660	+	2.92660i	−0.216934	+	0.216934i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	2.91888	−	14.8922i	0.214600	−	1.09490i
$186$		0			0
$187$	−21.0136	−	21.0136i	−1.53666	−	1.53666i
$188$	7.28725	+	7.28725i	0.531477	+	0.531477i
$189$		0			0
$190$	1.55806	−	7.94927i	0.113033	−	0.576700i
$191$		−	19.6699i		−	1.42327i	−0.702551	−	0.711634i	$-0.747956\pi$
$191$		−	19.6699i		−	1.42327i	0.702551	−	0.711634i	$-0.252044\pi$
$192$		0			0
$193$	2.51717	−	2.51717i	0.181190	−	0.181190i	−0.610684	−	0.791874i	$-0.709106\pi$
$193$	2.51717	−	2.51717i	0.181190	−	0.181190i	0.791874	+	0.610684i	$0.209106\pi$
$194$	−7.22771			−0.518920
$195$		0			0
$196$	15.4976			1.10697
$197$	10.8642	−	10.8642i	0.774043	−	0.774043i	−0.204768	−	0.978811i	$-0.565644\pi$
$197$	10.8642	−	10.8642i	0.774043	−	0.774043i	0.978811	+	0.204768i	$0.0656440\pi$
$198$		0			0
$199$		−	8.66450i		−	0.614210i	−0.951676	−	0.307105i	$-0.900640\pi$
$199$		−	8.66450i		−	0.614210i	0.951676	−	0.307105i	$-0.0993603\pi$
$200$	4.60860	−	1.93928i	0.325877	−	0.137128i
$201$		0			0
$202$	11.3139	+	11.3139i	0.796047	+	0.796047i
$203$	31.5610	+	31.5610i	2.21515	+	2.21515i
$204$		0			0
$205$	5.33990	−	3.58969i	0.372955	−	0.250715i
$206$			1.51925i			0.105851i
$207$		0			0
$208$	−0.617014	+	0.617014i	−0.0427822	+	0.0427822i
$209$	16.6065			1.14869
$210$		0			0
$211$	6.41849			0.441867			0.220934	−	0.975289i	$-0.429090\pi$
$211$	6.41849			0.441867			0.220934	+	0.975289i	$0.429090\pi$
$212$	5.77255	−	5.77255i	0.396460	−	0.396460i
$213$		0			0
$214$		−	17.9432i		−	1.22657i
$215$	−0.349134	−	0.0684304i	−0.0238108	−	0.00466692i
$216$		0			0
$217$	12.6610	+	12.6610i	0.859486	+	0.859486i
$218$	9.59404	+	9.59404i	0.649790	+	0.649790i
$219$		0			0
$220$	5.71861	+	8.50679i	0.385548	+	0.573527i
$221$			5.65685i			0.380521i
$222$		0			0
$223$	19.4403	−	19.4403i	1.30182	−	1.30182i	0.374652	−	0.927165i	$-0.377762\pi$
$223$	19.4403	−	19.4403i	1.30182	−	1.30182i	0.927165	−	0.374652i	$-0.122238\pi$
$224$	4.74316			0.316916
$225$		0			0
$226$	−20.9223			−1.39173
$227$	−5.88580	+	5.88580i	−0.390654	+	0.390654i	−0.874921	−	0.484266i	$-0.839087\pi$
$227$	−5.88580	+	5.88580i	−0.390654	+	0.390654i	0.484266	+	0.874921i	$0.339087\pi$
$228$		0			0
$229$			9.40113i			0.621244i	0.950533	+	0.310622i	$0.100537\pi$
$229$			9.40113i			0.621244i	−0.950533	+	0.310622i	$0.899463\pi$
$230$	1.24750	+	1.85573i	0.0822576	+	0.122363i
$231$		0			0
$232$	6.65400	+	6.65400i	0.436857	+	0.436857i
$233$	14.3252	+	14.3252i	0.938475	+	0.938475i	0.998214	−	0.0597388i	$-0.0190268\pi$
$233$	14.3252	+	14.3252i	0.938475	+	0.938475i	−0.0597388	+	0.998214i	$0.519027\pi$
$234$		0			0
$235$	−22.6140	−	4.43236i	−1.47518	−	0.289135i
$236$		−	10.6992i		−	0.696456i
$237$		0			0
$238$	21.7429	−	21.7429i	1.40939	−	1.40939i
$239$	−10.5062			−0.679588			−0.339794	−	0.940500i	$-0.610357\pi$
$239$	−10.5062			−0.679588			−0.339794	+	0.940500i	$0.610357\pi$
$240$		0			0
$241$	−15.9827			−1.02954			−0.514769	−	0.857329i	$-0.672122\pi$
$241$	−15.9827			−1.02954			−0.514769	+	0.857329i	$0.672122\pi$
$242$	−7.08067	+	7.08067i	−0.455162	+	0.455162i
$243$		0			0
$244$		−	12.7541i		−	0.816501i
$245$	−28.7594	+	19.3333i	−1.83737	+	1.23516i
$246$		0			0
$247$	−2.23523	−	2.23523i	−0.142224	−	0.142224i
$248$	2.66932	+	2.66932i	0.169502	+	0.169502i
$249$		0			0
$250$	−6.13308	+	9.34801i	−0.387890	+	0.591220i
$251$		−	12.9871i		−	0.819741i	−0.912144	−	0.409870i	$-0.865574\pi$
$251$		−	12.9871i		−	0.819741i	0.912144	−	0.409870i	$-0.134426\pi$
$252$		0			0
$253$	−3.24142	+	3.24142i	−0.203786	+	0.203786i
$254$	4.46927			0.280427
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.1470	−	19.1470i	1.19436	−	1.19436i	0.218524	−	0.975831i	$-0.429876\pi$
$257$	19.1470	−	19.1470i	1.19436	−	1.19436i	0.975831	−	0.218524i	$-0.0701243\pi$
$258$		0			0
$259$			32.1906i			2.00022i
$260$	0.375289	−	1.91474i	0.0232745	−	0.118747i
$261$		0			0
$262$	−4.69693	−	4.69693i	−0.290177	−	0.290177i
$263$	17.5398	+	17.5398i	1.08155	+	1.08155i	0.996365	+	0.0851843i	$0.0271479\pi$
$263$	17.5398	+	17.5398i	1.08155	+	1.08155i	0.0851843	+	0.996365i	$0.472852\pi$
$264$		0			0
$265$	−3.51107	+	17.9136i	−0.215683	+	1.10042i
$266$			17.1829i			1.05355i
$267$		0			0
$268$	−7.73517	+	7.73517i	−0.472501	+	0.472501i
$269$	−4.11149			−0.250682			−0.125341	−	0.992114i	$-0.540003\pi$
$269$	−4.11149			−0.250682			−0.125341	+	0.992114i	$0.540003\pi$
$270$		0			0
$271$	11.4111			0.693177			0.346589	−	0.938017i	$-0.387340\pi$
$271$	11.4111			0.693177			0.346589	+	0.938017i	$0.387340\pi$
$272$	4.58406	−	4.58406i	0.277949	−	0.277949i
$273$		0			0
$274$			22.8529i			1.38059i
$275$	−21.2244	−	8.65238i	−1.27988	−	0.521758i
$276$		0			0
$277$	5.37950	+	5.37950i	0.323223	+	0.323223i	0.850002	−	0.526779i	$-0.176601\pi$
$277$	5.37950	+	5.37950i	0.323223	+	0.323223i	−0.526779	+	0.850002i	$0.676601\pi$
$278$	1.71377	+	1.71377i	0.102785	+	0.102785i
$279$		0			0
$280$	−8.80205	+	5.91709i	−0.526023	+	0.353614i
$281$			8.01236i			0.477977i	0.971022	+	0.238989i	$0.0768158\pi$
$281$			8.01236i			0.477977i	−0.971022	+	0.238989i	$0.923184\pi$
$282$		0			0
$283$	9.85249	−	9.85249i	0.585670	−	0.585670i	−0.350786	−	0.936456i	$-0.614086\pi$
$283$	9.85249	−	9.85249i	0.585670	−	0.585670i	0.936456	+	0.350786i	$0.114086\pi$
$284$	5.53162			0.328241
$285$		0			0
$286$	4.00000			0.236525
$287$	−9.65096	+	9.65096i	−0.569678	+	0.569678i
$288$		0			0
$289$		−	25.0271i		−	1.47219i
$290$	−20.6489	−	4.04719i	−1.21255	−	0.237659i
$291$		0			0
$292$	8.22311	+	8.22311i	0.481221	+	0.481221i
$293$	−8.42167	−	8.42167i	−0.491999	−	0.491999i	0.416936	−	0.908936i	$-0.363104\pi$
$293$	−8.42167	−	8.42167i	−0.491999	−	0.491999i	−0.908936	+	0.416936i	$0.863104\pi$
$294$		0			0
$295$	13.3472	+	19.8548i	0.777103	+	1.15599i
$296$			6.78672i			0.394470i
$297$		0			0
$298$	−0.377876	+	0.377876i	−0.0218898	+	0.0218898i
$299$	0.872590			0.0504632
$300$		0			0
$301$	0.754678			0.0434989
$302$	6.48717	−	6.48717i	0.373295	−	0.373295i
$303$		0			0
$304$			3.62266i			0.207774i
$305$	15.9108	+	23.6683i	0.911049	+	1.35524i
$306$		0			0
$307$	8.95438	+	8.95438i	0.511053	+	0.511053i	0.914849	−	0.403796i	$-0.132309\pi$
$307$	8.95438	+	8.95438i	0.511053	+	0.511053i	−0.403796	+	0.914849i	$0.632309\pi$
$308$	−15.3746	−	15.3746i	−0.876048	−	0.876048i
$309$		0			0
$310$	−8.28352	−	1.62357i	−0.470472	−	0.0922127i
$311$			12.1323i			0.687959i	0.938977	+	0.343979i	$0.111775\pi$
$311$			12.1323i			0.687959i	−0.938977	+	0.343979i	$0.888225\pi$
$312$		0			0
$313$	1.12554	−	1.12554i	0.0636195	−	0.0636195i	−0.674581	−	0.738201i	$-0.735676\pi$
$313$	1.12554	−	1.12554i	0.0636195	−	0.0636195i	0.738201	+	0.674581i	$0.235676\pi$
$314$	−20.5189			−1.15795
$315$		0			0
$316$	5.17939			0.291363
$317$	5.77845	−	5.77845i	0.324550	−	0.324550i	−0.525960	−	0.850510i	$-0.676294\pi$
$317$	5.77845	−	5.77845i	0.324550	−	0.324550i	0.850510	+	0.525960i	$0.176294\pi$
$318$		0			0
$319$		−	43.1368i		−	2.41520i
$320$	−1.85573	+	1.24750i	−0.103739	+	0.0697373i
$321$		0			0
$322$	−3.35392	−	3.35392i	−0.186907	−	0.186907i
$323$	16.6065	+	16.6065i	0.924009	+	0.924009i
$324$		0			0
$325$	1.69220	+	4.02142i	0.0938662	+	0.223068i
$326$		−	2.09382i		−	0.115966i
$327$		0			0
$328$	−2.03471	+	2.03471i	−0.112348	+	0.112348i
$329$	48.8818			2.69494
$330$		0			0
$331$	−19.3193			−1.06188			−0.530942	−	0.847408i	$-0.678162\pi$
$331$	−19.3193			−1.06188			−0.530942	+	0.847408i	$0.678162\pi$
$332$	−4.85886	+	4.85886i	−0.266665	+	0.266665i
$333$		0			0
$334$		−	4.46481i		−	0.244303i
$335$	4.70480	−	24.0040i	0.257051	−	1.31148i
$336$		0			0
$337$	−10.1233	−	10.1233i	−0.551449	−	0.551449i	0.375410	−	0.926859i	$-0.377502\pi$
$337$	−10.1233	−	10.1233i	−0.551449	−	0.551449i	−0.926859	+	0.375410i	$0.877502\pi$
$338$	8.65399	+	8.65399i	0.470715	+	0.470715i
$339$		0			0
$340$	−2.78818	+	14.2254i	−0.151210	+	0.771480i
$341$		−	17.3048i		−	0.937105i
$342$		0			0
$343$	28.5004	−	28.5004i	1.53887	−	1.53887i
$344$	0.159108			0.00857855
$345$		0			0
$346$	0.235233			0.0126462
$347$	−3.24353	+	3.24353i	−0.174122	+	0.174122i	−0.788788	−	0.614666i	$-0.789291\pi$
$347$	−3.24353	+	3.24353i	−0.174122	+	0.174122i	0.614666	+	0.788788i	$0.289291\pi$
$348$		0			0
$349$		−	8.62789i		−	0.461841i	−0.972973	−	0.230920i	$-0.925826\pi$
$349$		−	8.62789i		−	0.461841i	0.972973	−	0.230920i	$-0.0741737\pi$
$350$	8.95269	−	21.9611i	0.478542	−	1.17387i
$351$		0			0
$352$	−3.24142	−	3.24142i	−0.172768	−	0.172768i
$353$	−13.7208	−	13.7208i	−0.730282	−	0.730282i	0.240393	−	0.970676i	$-0.422724\pi$
$353$	−13.7208	−	13.7208i	−0.730282	−	0.730282i	−0.970676	+	0.240393i	$0.922724\pi$
$354$		0			0
$355$	−10.2652	+	6.90069i	−0.544821	+	0.366251i
$356$			9.90748i			0.525095i
$357$		0			0
$358$	−9.44813	+	9.44813i	−0.499349	+	0.499349i
$359$	−5.92095			−0.312496			−0.156248	−	0.987718i	$-0.549940\pi$
$359$	−5.92095			−0.312496			−0.156248	+	0.987718i	$0.549940\pi$
$360$		0			0
$361$	5.87633			0.309280
$362$	8.93763	−	8.93763i	0.469751	−	0.469751i
$363$		0			0
$364$			4.13884i			0.216934i
$365$	−25.5182	−	5.00158i	−1.33569	−	0.261795i
$366$		0			0
$367$	4.88238	+	4.88238i	0.254858	+	0.254858i	0.822959	−	0.568101i	$-0.192322\pi$
$367$	4.88238	+	4.88238i	0.254858	+	0.254858i	−0.568101	+	0.822959i	$0.692322\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	−8.46643	−	12.5944i	−0.440149	−	0.654749i
$371$		−	38.7214i		−	2.01031i
$372$		0			0
$373$	11.7431	−	11.7431i	0.608034	−	0.608034i	−0.334398	−	0.942432i	$-0.608533\pi$
$373$	11.7431	−	11.7431i	0.608034	−	0.608034i	0.942432	+	0.334398i	$0.108533\pi$
$374$	−29.7177			−1.53666
$375$		0			0
$376$	10.3057			0.531477
$377$	−5.80621	+	5.80621i	−0.299035	+	0.299035i
$378$		0			0
$379$		−	19.0351i		−	0.977768i	−0.872349	−	0.488884i	$-0.837404\pi$
$379$		−	19.0351i		−	0.977768i	0.872349	−	0.488884i	$-0.162596\pi$
$380$	−4.51927	−	6.72269i	−0.231833	−	0.344867i
$381$		0			0
$382$	−13.9088	−	13.9088i	−0.711634	−	0.711634i
$383$	2.59703	+	2.59703i	0.132702	+	0.132702i	0.770338	−	0.637636i	$-0.220087\pi$
$383$	2.59703	+	2.59703i	0.132702	+	0.132702i	−0.637636	+	0.770338i	$0.720087\pi$
$384$		0			0
$385$	47.7109	+	9.35135i	2.43157	+	0.476589i
$386$		−	3.55981i		−	0.181190i
$387$		0			0
$388$	−5.11076	+	5.11076i	−0.259460	+	0.259460i
$389$	−3.53140			−0.179049			−0.0895245	−	0.995985i	$-0.528535\pi$
$389$	−3.53140			−0.179049			−0.0895245	+	0.995985i	$0.528535\pi$
$390$		0			0
$391$	−6.48283			−0.327851
$392$	10.9585	−	10.9585i	0.553486	−	0.553486i
$393$		0			0
$394$		−	15.3643i		−	0.774043i
$395$	−9.61156	+	6.46128i	−0.483610	+	0.325102i
$396$		0			0
$397$	−1.92046	−	1.92046i	−0.0963851	−	0.0963851i	0.657270	−	0.753655i	$-0.271711\pi$
$397$	−1.92046	−	1.92046i	−0.0963851	−	0.0963851i	−0.753655	+	0.657270i	$0.771711\pi$
$398$	−6.12673	−	6.12673i	−0.307105	−	0.307105i
$399$		0			0
$400$	1.88749	−	4.63005i	0.0943747	−	0.231503i
$401$		−	24.8466i		−	1.24078i	−0.784294	−	0.620390i	$-0.786974\pi$
$401$		−	24.8466i		−	1.24078i	0.784294	−	0.620390i	$-0.213026\pi$
$402$		0			0
$403$	−2.32922	+	2.32922i	−0.116027	+	0.116027i
$404$	16.0003			0.796047
$405$		0			0
$406$	44.6340			2.21515
$407$	21.9986	−	21.9986i	1.09043	−	1.09043i
$408$		0			0
$409$			25.5928i			1.26548i	0.774363	+	0.632741i	$0.218070\pi$
$409$			25.5928i			1.26548i	−0.774363	+	0.632741i	$0.781930\pi$
$410$	1.23758	−	6.31417i	0.0611197	−	0.311835i
$411$		0			0
$412$	1.07427	+	1.07427i	0.0529256	+	0.0529256i
$413$	−35.8842	−	35.8842i	−1.76574	−	1.76574i
$414$		0			0
$415$	2.95533	−	15.0782i	0.145071	−	0.740159i
$416$			0.872590i			0.0427822i
$417$		0			0
$418$	11.7426	−	11.7426i	0.574347	−	0.574347i
$419$	1.35104			0.0660025			0.0330013	−	0.999455i	$-0.489493\pi$
$419$	1.35104			0.0660025			0.0330013	+	0.999455i	$0.489493\pi$
$420$		0			0
$421$	1.78681			0.0870839			0.0435420	−	0.999052i	$-0.486136\pi$
$421$	1.78681			0.0870839			0.0435420	+	0.999052i	$0.486136\pi$
$422$	4.53856	−	4.53856i	0.220934	−	0.220934i
$423$		0			0
$424$		−	8.16362i		−	0.396460i
$425$	−12.5720	−	29.8768i	−0.609833	−	1.44924i
$426$		0			0
$427$	−42.7764	−	42.7764i	−2.07010	−	2.07010i
$428$	−12.6877	−	12.6877i	−0.613285	−	0.613285i
$429$		0			0
$430$	−0.295263	+	0.198488i	−0.0142388	+	0.00957192i
$431$			6.65145i			0.320389i	0.987085	+	0.160195i	$0.0512122\pi$
$431$			6.65145i			0.320389i	−0.987085	+	0.160195i	$0.948788\pi$
$432$		0			0
$433$	−15.5503	+	15.5503i	−0.747298	+	0.747298i	−0.973971	−	0.226673i	$-0.927215\pi$
$433$	−15.5503	+	15.5503i	−0.747298	+	0.747298i	0.226673	+	0.973971i	$0.427215\pi$
$434$	17.9054			0.859486
$435$		0			0
$436$	13.5680			0.649790
$437$	2.56161	−	2.56161i	0.122538	−	0.122538i
$438$		0			0
$439$			21.3909i			1.02093i	0.859898	+	0.510466i	$0.170527\pi$
$439$			21.3909i			1.02093i	−0.859898	+	0.510466i	$0.829473\pi$
$440$	10.0589	+	1.97154i	0.479538	+	0.0939896i
$441$		0			0
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	−4.92225	−	4.92225i	−0.233863	−	0.233863i	0.580440	−	0.814303i	$-0.302881\pi$
$443$	−4.92225	−	4.92225i	−0.233863	−	0.233863i	−0.814303	+	0.580440i	$0.802881\pi$
$444$		0			0
$445$	−12.3596	−	18.3856i	−0.585900	−	0.871563i
$446$		−	27.4927i		−	1.30182i
$447$		0			0
$448$	3.35392	−	3.35392i	0.158458	−	0.158458i
$449$	−32.6184			−1.53936			−0.769680	−	0.638430i	$-0.779584\pi$
$449$	−32.6184			−1.53936			−0.769680	+	0.638430i	$0.779584\pi$
$450$		0			0
$451$	13.1907			0.621125
$452$	−14.7943	+	14.7943i	−0.695866	+	0.695866i
$453$		0			0
$454$			8.32377i			0.390654i
$455$	−5.16319	−	7.68058i	−0.242054	−	0.360071i
$456$		0			0
$457$	8.04165	+	8.04165i	0.376172	+	0.376172i	0.869719	−	0.493547i	$-0.164300\pi$
$457$	8.04165	+	8.04165i	0.376172	+	0.376172i	−0.493547	+	0.869719i	$0.664300\pi$
$458$	6.64760	+	6.64760i	0.310622	+	0.310622i
$459$		0			0
$460$	2.19432	+	0.430087i	0.102311	+	0.0200529i
$461$			31.4171i			1.46324i	0.681712	+	0.731621i	$0.261236\pi$
$461$			31.4171i			1.46324i	−0.681712	+	0.731621i	$0.738764\pi$
$462$		0			0
$463$	−17.9273	+	17.9273i	−0.833152	+	0.833152i	−0.987947	−	0.154794i	$-0.950528\pi$
$463$	−17.9273	+	17.9273i	−0.833152	+	0.833152i	0.154794	+	0.987947i	$0.450528\pi$
$464$	9.41018			0.436857
$465$		0			0
$466$	20.2589			0.938475
$467$	−12.2455	+	12.2455i	−0.566652	+	0.566652i	−0.931189	−	0.364537i	$-0.881227\pi$
$467$	−12.2455	+	12.2455i	−0.566652	+	0.566652i	0.364537	+	0.931189i	$0.381227\pi$
$468$		0			0
$469$			51.8863i			2.39589i
$470$	−19.1247	+	12.8564i	−0.882156	+	0.593021i
$471$		0			0
$472$	−7.56545	−	7.56545i	−0.348228	−	0.348228i
$473$	−0.515737	−	0.515737i	−0.0237136	−	0.0237136i
$474$		0			0
$475$	16.7731	+	6.83775i	0.769603	+	0.313737i
$476$		−	30.7492i		−	1.40939i
$477$		0			0
$478$	−7.42899	+	7.42899i	−0.339794	+	0.339794i
$479$	−6.96659			−0.318312			−0.159156	−	0.987253i	$-0.550877\pi$
$479$	−6.96659			−0.318312			−0.159156	+	0.987253i	$0.550877\pi$
$480$		0			0
$481$	−5.92203			−0.270021
$482$	−11.3015	+	11.3015i	−0.514769	+	0.514769i
$483$		0			0
$484$			10.0136i			0.455162i
$485$	3.10854	−	15.8599i	0.141152	−	0.720160i
$486$		0			0
$487$	−1.93296	−	1.93296i	−0.0875907	−	0.0875907i	0.661954	−	0.749545i	$-0.269727\pi$
$487$	−1.93296	−	1.93296i	−0.0875907	−	0.0875907i	−0.749545	+	0.661954i	$0.769727\pi$
$488$	−9.01854	−	9.01854i	−0.408250	−	0.408250i
$489$		0			0
$490$	−6.66532	+	34.0067i	−0.301108	+	1.53626i
$491$		−	1.43735i		−	0.0648669i	−0.999474	−	0.0324334i	$-0.989674\pi$
$491$		−	1.43735i		−	0.0648669i	0.999474	−	0.0324334i	$-0.0103257\pi$
$492$		0			0
$493$	43.1368	−	43.1368i	1.94278	−	1.94278i
$494$	−3.16110			−0.142224
$495$		0			0
$496$	3.77499			0.169502
$497$	18.5526	−	18.5526i	0.832199	−	0.832199i
$498$		0			0
$499$		−	37.3155i		−	1.67047i	−0.549892	−	0.835236i	$-0.685331\pi$
$499$		−	37.3155i		−	1.67047i	0.549892	−	0.835236i	$-0.314669\pi$
$500$	2.27330	+	10.9468i	0.101665	+	0.489555i
$501$		0			0
$502$	−9.18329	−	9.18329i	−0.409870	−	0.409870i
$503$	−18.4498	−	18.4498i	−0.822637	−	0.822637i	0.163848	−	0.986486i	$-0.447609\pi$
$503$	−18.4498	−	18.4498i	−0.822637	−	0.822637i	−0.986486	+	0.163848i	$0.947609\pi$
$504$		0			0
$505$	−29.6924	+	19.9604i	−1.32129	+	0.888226i
$506$			4.58406i			0.203786i
$507$		0			0
$508$	3.16025	−	3.16025i	0.140214	−	0.140214i
$509$	−17.6141			−0.780732			−0.390366	−	0.920660i	$-0.627652\pi$
$509$	−17.6141			−0.780732			−0.390366	+	0.920660i	$0.627652\pi$
$510$		0			0
$511$	55.1594			2.44011
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	27.0779i		−	1.19436i
$515$	−3.33371	−	0.653409i	−0.146901	−	0.0287926i
$516$		0			0
$517$	−33.4052	−	33.4052i	−1.46916	−	1.46916i
$518$	22.7622	+	22.7622i	1.00011	+	1.00011i
$519$		0			0
$520$	−1.08855	−	1.61929i	−0.0477363	−	0.0710107i
$521$		−	3.68194i		−	0.161309i	−0.996742	−	0.0806544i	$-0.974299\pi$
$521$		−	3.68194i		−	0.161309i	0.996742	−	0.0806544i	$-0.0257010\pi$
$522$		0			0
$523$	−5.11130	+	5.11130i	−0.223502	+	0.223502i	−0.809971	−	0.586470i	$-0.800517\pi$
$523$	−5.11130	+	5.11130i	−0.223502	+	0.223502i	0.586470	+	0.809971i	$0.300517\pi$
$524$	−6.64247			−0.290177
$525$		0			0
$526$	24.8050			1.08155
$527$	17.3048	−	17.3048i	0.753807	−	0.753807i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	10.1841	+	15.1495i	0.442369	+	0.658052i
$531$		0			0
$532$	12.1501	+	12.1501i	0.526775	+	0.526775i
$533$	−1.77547	−	1.77547i	−0.0769040	−	0.0769040i
$534$		0			0
$535$	39.3730	+	7.71712i	1.70224	+	0.333640i
$536$			10.9392i			0.472501i
$537$		0			0
$538$	−2.90727	+	2.90727i	−0.125341	+	0.125341i
$539$	−71.0419			−3.05999
$540$		0			0
$541$	18.4492			0.793193			0.396596	−	0.917993i	$-0.370191\pi$
$541$	18.4492			0.793193			0.396596	+	0.917993i	$0.370191\pi$
$542$	8.06889	−	8.06889i	0.346589	−	0.346589i
$543$		0			0
$544$		−	6.48283i		−	0.277949i
$545$	−25.1786	+	16.9261i	−1.07853	+	0.725034i
$546$		0			0
$547$	−8.23631	−	8.23631i	−0.352159	−	0.352159i	0.508753	−	0.860912i	$-0.330107\pi$
$547$	−8.23631	−	8.23631i	−0.352159	−	0.352159i	−0.860912	+	0.508753i	$0.830107\pi$
$548$	16.1594	+	16.1594i	0.690297	+	0.690297i
$549$		0			0
$550$	−21.1261	+	8.88977i	−0.900819	+	0.379061i
$551$			34.0899i			1.45228i
$552$		0			0
$553$	17.3713	−	17.3713i	0.738702	−	0.738702i
$554$	7.60776			0.323223
$555$		0			0
$556$	2.42364			0.102785
$557$	0.269342	−	0.269342i	0.0114124	−	0.0114124i	−0.701378	−	0.712790i	$-0.747431\pi$
$557$	0.269342	−	0.269342i	0.0114124	−	0.0114124i	0.712790	+	0.701378i	$0.247431\pi$
$558$		0			0
$559$			0.138836i			0.00587215i
$560$	−2.03997	+	10.4080i	−0.0862046	+	0.439819i
$561$		0			0
$562$	5.66559	+	5.66559i	0.238989	+	0.238989i
$563$	7.23585	+	7.23585i	0.304955	+	0.304955i	0.842949	−	0.537994i	$-0.180818\pi$
$563$	7.23585	+	7.23585i	0.304955	+	0.304955i	−0.537994	+	0.842949i	$0.680818\pi$
$564$		0			0
$565$	8.99842	−	45.9102i	0.378566	−	1.93146i
$566$		−	13.9335i		−	0.585670i
$567$		0			0
$568$	3.91145	−	3.91145i	0.164121	−	0.164121i
$569$	4.72832			0.198221			0.0991106	−	0.995076i	$-0.468400\pi$
$569$	4.72832			0.198221			0.0991106	+	0.995076i	$0.468400\pi$
$570$		0			0
$571$	15.2588			0.638561			0.319281	−	0.947660i	$-0.396559\pi$
$571$	15.2588			0.638561			0.319281	+	0.947660i	$0.396559\pi$
$572$	2.82843	−	2.82843i	0.118262	−	0.118262i
$573$		0			0
$574$			13.6485i			0.569678i
$575$	−4.60860	+	1.93928i	−0.192192	+	0.0808736i
$576$		0			0
$577$	2.58537	+	2.58537i	0.107631	+	0.107631i	0.758871	−	0.651241i	$-0.225751\pi$
$577$	2.58537	+	2.58537i	0.107631	+	0.107631i	−0.651241	+	0.758871i	$0.725751\pi$
$578$	−17.6969	−	17.6969i	−0.736093	−	0.736093i
$579$		0			0
$580$	−17.4628	+	11.7392i	−0.725103	+	0.487443i
$581$			32.5925i			1.35217i
$582$		0			0
$583$	−26.4617	+	26.4617i	−1.09593	+	1.09593i
$584$	11.6292			0.481221
$585$		0			0
$586$	−11.9100			−0.491999
$587$	−9.23950	+	9.23950i	−0.381355	+	0.381355i	−0.871590	−	0.490235i	$-0.836911\pi$
$587$	−9.23950	+	9.23950i	−0.381355	+	0.381355i	0.490235	+	0.871590i	$0.336911\pi$
$588$		0			0
$589$			13.6755i			0.563489i
$590$	23.4773	+	4.60157i	0.966547	+	0.189444i
$591$		0			0
$592$	4.79894	+	4.79894i	0.197235	+	0.197235i
$593$	3.91515	+	3.91515i	0.160776	+	0.160776i	0.782910	−	0.622134i	$-0.213734\pi$
$593$	3.91515	+	3.91515i	0.160776	+	0.160776i	−0.622134	+	0.782910i	$0.713734\pi$
$594$		0			0
$595$	38.3595	+	57.0622i	1.57259	+	2.33932i
$596$			0.534398i			0.0218898i
$597$		0			0
$598$	0.617014	−	0.617014i	0.0252316	−	0.0252316i
$599$	16.4553			0.672345			0.336173	−	0.941800i	$-0.390867\pi$
$599$	16.4553			0.672345			0.336173	+	0.941800i	$0.390867\pi$
$600$		0			0
$601$	−6.67663			−0.272345			−0.136173	−	0.990685i	$-0.543480\pi$
$601$	−6.67663			−0.272345			−0.136173	+	0.990685i	$0.543480\pi$
$602$	0.533638	−	0.533638i	0.0217494	−	0.0217494i
$603$		0			0
$604$		−	9.17424i		−	0.373295i
$605$	−12.4919	−	18.5825i	−0.507869	−	0.755487i
$606$		0			0
$607$	20.2192	+	20.2192i	0.820673	+	0.820673i	0.986204	−	0.165532i	$-0.0529341\pi$
$607$	20.2192	+	20.2192i	0.820673	+	0.820673i	−0.165532	+	0.986204i	$0.552934\pi$
$608$	2.56161	+	2.56161i	0.103887	+	0.103887i
$609$		0			0
$610$	27.9866	+	5.48539i	1.13315	+	0.222097i
$611$			8.99267i			0.363804i
$612$		0			0
$613$	−22.9688	+	22.9688i	−0.927700	+	0.927700i	−0.997557	−	0.0698567i	$-0.977746\pi$
$613$	−22.9688	+	22.9688i	−0.927700	+	0.927700i	0.0698567	+	0.997557i	$0.477746\pi$
$614$	12.6634			0.511053
$615$		0			0
$616$	−21.7429			−0.876048
$617$	13.6903	−	13.6903i	0.551152	−	0.551152i	−0.375621	−	0.926773i	$-0.622571\pi$
$617$	13.6903	−	13.6903i	0.551152	−	0.551152i	0.926773	+	0.375621i	$0.122571\pi$
$618$		0			0
$619$			30.1917i			1.21351i	0.794891	+	0.606753i	$0.207528\pi$
$619$			30.1917i			1.21351i	−0.794891	+	0.606753i	$0.792472\pi$
$620$	−7.00537	+	4.70929i	−0.281342	+	0.189130i
$621$		0			0
$622$	8.57882	+	8.57882i	0.343979	+	0.343979i
$623$	33.2289	+	33.2289i	1.33129	+	1.33129i
$624$		0			0
$625$	−17.8747	−	17.4784i	−0.714990	−	0.699135i
$626$		−	1.59176i		−	0.0636195i
$627$		0			0
$628$	−14.5091	+	14.5091i	−0.578975	+	0.578975i
$629$	43.9972			1.75428
$630$		0			0
$631$	−25.8404			−1.02869			−0.514345	−	0.857583i	$-0.671965\pi$
$631$	−25.8404			−1.02869			−0.514345	+	0.857583i	$0.671965\pi$
$632$	3.66238	−	3.66238i	0.145682	−	0.145682i
$633$		0			0
$634$		−	8.17196i		−	0.324550i
$635$	−1.92217	+	9.80700i	−0.0762792	+	0.389179i
$636$		0			0
$637$	9.56224	+	9.56224i	0.378870	+	0.378870i
$638$	−30.5023	−	30.5023i	−1.20760	−	1.20760i
$639$		0			0
$640$	−0.430087	+	2.19432i	−0.0170007	+	0.0867380i
$641$		−	7.46962i		−	0.295032i	−0.989060	−	0.147516i	$-0.952872\pi$
$641$		−	7.46962i		−	0.295032i	0.989060	−	0.147516i	$-0.0471278\pi$
$642$		0			0
$643$	−7.31470	+	7.31470i	−0.288464	+	0.288464i	−0.836472	−	0.548009i	$-0.815386\pi$
$643$	−7.31470	+	7.31470i	−0.288464	+	0.288464i	0.548009	+	0.836472i	$0.315386\pi$
$644$	−4.74316			−0.186907
$645$		0			0
$646$	23.4851			0.924009
$647$	−10.5271	+	10.5271i	−0.413862	+	0.413862i	−0.883082	−	0.469219i	$-0.844535\pi$
$647$	−10.5271	+	10.5271i	−0.413862	+	0.413862i	0.469219	+	0.883082i	$0.344535\pi$
$648$		0			0
$649$			49.0456i			1.92521i
$650$	4.04013	+	1.64701i	0.158467	+	0.0646009i
$651$		0			0
$652$	−1.48056	−	1.48056i	−0.0579830	−	0.0579830i
$653$	−6.61949	−	6.61949i	−0.259041	−	0.259041i	0.565623	−	0.824664i	$-0.308636\pi$
$653$	−6.61949	−	6.61949i	−0.259041	−	0.259041i	−0.824664	+	0.565623i	$0.808636\pi$
$654$		0			0
$655$	12.3266	−	8.28647i	0.481642	−	0.323779i
$656$			2.87751i			0.112348i
$657$		0			0
$658$	34.5646	−	34.5646i	1.34747	−	1.34747i
$659$	34.5381			1.34541			0.672706	−	0.739910i	$-0.265132\pi$
$659$	34.5381			1.34541			0.672706	+	0.739910i	$0.265132\pi$
$660$		0			0
$661$	37.4325			1.45596			0.727978	−	0.685600i	$-0.240460\pi$
$661$	37.4325			1.45596			0.727978	+	0.685600i	$0.240460\pi$
$662$	−13.6608	+	13.6608i	−0.530942	+	0.530942i
$663$		0			0
$664$			6.87147i			0.266665i
$665$	−37.7047	−	7.39013i	−1.46212	−	0.286577i
$666$		0			0
$667$	−6.65400	−	6.65400i	−0.257644	−	0.257644i
$668$	−3.15709	−	3.15709i	−0.122152	−	0.122152i
$669$		0			0
$670$	−13.6466	−	20.3002i	−0.527215	−	0.784265i
$671$			58.4657i			2.25704i
$672$		0			0
$673$	30.7218	−	30.7218i	1.18424	−	1.18424i	0.205603	−	0.978636i	$-0.434084\pi$
$673$	30.7218	−	30.7218i	1.18424	−	1.18424i	0.978636	−	0.205603i	$-0.0659155\pi$
$674$	−14.3165			−0.551449
$675$		0			0
$676$	12.2386			0.470715
$677$	−16.3990	+	16.3990i	−0.630264	+	0.630264i	−0.948134	−	0.317870i	$-0.897032\pi$
$677$	−16.3990	+	16.3990i	−0.630264	+	0.630264i	0.317870	+	0.948134i	$0.397032\pi$
$678$		0			0
$679$			34.2822i			1.31563i
$680$	8.08733	+	12.0304i	0.310135	+	0.461345i
$681$		0			0
$682$	−12.2363	−	12.2363i	−0.468552	−	0.468552i
$683$	0.960087	+	0.960087i	0.0367367	+	0.0367367i	0.725237	−	0.688500i	$-0.241730\pi$
$683$	0.960087	+	0.960087i	0.0367367	+	0.0367367i	−0.688500	+	0.725237i	$0.741730\pi$
$684$		0			0
$685$	−50.1465	−	9.82873i	−1.91600	−	0.375537i
$686$		−	40.3056i		−	1.53887i
$687$		0			0
$688$	0.112507	−	0.112507i	0.00428928	−	0.00428928i
$689$	7.12349			0.271383
$690$		0			0
$691$	−30.3351			−1.15400			−0.577001	−	0.816743i	$-0.695777\pi$
$691$	−30.3351			−1.15400			−0.577001	+	0.816743i	$0.695777\pi$
$692$	0.166335	−	0.166335i	0.00632310	−	0.00632310i
$693$		0			0
$694$			4.58704i			0.174122i
$695$	−4.49762	+	3.02348i	−0.170605	+	0.114687i
$696$		0			0
$697$	13.1907	+	13.1907i	0.499633	+	0.499633i
$698$	−6.10084	−	6.10084i	−0.230920	−	0.230920i
$699$		0			0
$700$	−9.19833	−	21.8593i	−0.347664	−	0.826206i
$701$			37.4086i			1.41290i	0.707762	+	0.706451i	$0.249705\pi$
$701$			37.4086i			1.41290i	−0.707762	+	0.706451i	$0.750295\pi$
$702$		0			0
$703$	−17.3849	+	17.3849i	−0.655685	+	0.655685i
$704$	−4.58406			−0.172768
$705$		0			0
$706$	−19.4041			−0.730282
$707$	53.6639	−	53.6639i	2.01824	−	2.01824i
$708$		0			0
$709$			7.58637i			0.284912i	0.989801	+	0.142456i	$0.0454999\pi$
$709$			7.58637i			0.284912i	−0.989801	+	0.142456i	$0.954500\pi$
$710$	−2.37908	+	12.1381i	−0.0892852	+	0.455536i
$711$		0			0
$712$	7.00565	+	7.00565i	0.262548	+	0.262548i
$713$	−2.66932	−	2.66932i	−0.0999668	−	0.0999668i
$714$		0			0
$715$	−1.72035	+	8.77727i	−0.0643373	+	0.328251i
$716$			13.3617i			0.499349i
$717$		0			0
$718$	−4.18674	+	4.18674i	−0.156248	+	0.156248i
$719$	−14.2310			−0.530728			−0.265364	−	0.964148i	$-0.585492\pi$
$719$	−14.2310			−0.530728			−0.265364	+	0.964148i	$0.585492\pi$
$720$		0			0
$721$	7.20605			0.268367
$722$	4.15519	−	4.15519i	0.154640	−	0.154640i
$723$		0			0
$724$		−	12.6397i		−	0.469751i
$725$	17.7617	−	43.5696i	0.659651	−	1.61813i
$726$		0			0
$727$	−24.2813	−	24.2813i	−0.900544	−	0.900544i	0.0949388	−	0.995483i	$-0.469734\pi$
$727$	−24.2813	−	24.2813i	−0.900544	−	0.900544i	−0.995483	+	0.0949388i	$0.969734\pi$
$728$	2.92660	+	2.92660i	0.108467	+	0.108467i
$729$		0			0
$730$	−21.5808	+	14.5075i	−0.798740	+	0.536945i
$731$		−	1.03147i		−	0.0381504i
$732$		0			0
$733$	−14.8762	+	14.8762i	−0.549464	+	0.549464i	−0.926286	−	0.376821i	$-0.877017\pi$
$733$	−14.8762	+	14.8762i	−0.549464	+	0.549464i	0.376821	+	0.926286i	$0.377017\pi$
$734$	6.90473			0.254858
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	35.4584	−	35.4584i	1.30613	−	1.30613i
$738$		0			0
$739$			0.965670i			0.0355227i	0.999842	+	0.0177614i	$0.00565392\pi$
$739$			0.965670i			0.0355227i	−0.999842	+	0.0177614i	$0.994346\pi$
$740$	−14.8922	−	2.91888i	−0.547449	−	0.107300i
$741$		0			0
$742$	−27.3802	−	27.3802i	−1.00516	−	1.00516i
$743$	21.0170	+	21.0170i	0.771038	+	0.771038i	0.978288	−	0.207250i	$-0.0664513\pi$
$743$	21.0170	+	21.0170i	0.771038	+	0.771038i	−0.207250	+	0.978288i	$0.566451\pi$
$744$		0			0
$745$	−0.666661	−	0.991700i	−0.0244246	−	0.0363331i
$746$		−	16.6072i		−	0.608034i
$747$		0			0
$748$	−21.0136	+	21.0136i	−0.768332	+	0.768332i
$749$	−85.1074			−3.10976
$750$		0			0
$751$	−39.2791			−1.43332			−0.716658	−	0.697425i	$-0.754329\pi$
$751$	−39.2791			−1.43332			−0.716658	+	0.697425i	$0.754329\pi$
$752$	7.28725	−	7.28725i	0.265739	−	0.265739i
$753$		0			0
$754$			8.21123i			0.299035i
$755$	11.4449	+	17.0249i	0.416521	+	0.619601i
$756$		0			0
$757$	2.01623	+	2.01623i	0.0732810	+	0.0732810i	0.742797	−	0.669516i	$-0.233499\pi$
$757$	2.01623	+	2.01623i	0.0732810	+	0.0732810i	−0.669516	+	0.742797i	$0.733499\pi$
$758$	−13.4599	−	13.4599i	−0.488884	−	0.488884i
$759$		0			0
$760$	−7.94927	−	1.55806i	−0.288350	−	0.0565167i
$761$		−	14.2222i		−	0.515554i	−0.966204	−	0.257777i	$-0.917010\pi$
$761$		−	14.2222i		−	0.515554i	0.966204	−	0.257777i	$-0.0829899\pi$
$762$		0			0
$763$	45.5061	−	45.5061i	1.64743	−	1.64743i
$764$	−19.6699			−0.711634
$765$		0			0
$766$	3.67276			0.132702
$767$	6.60153	−	6.60153i	0.238367	−	0.238367i
$768$		0			0
$769$			9.82745i			0.354387i	0.984176	+	0.177193i	$0.0567018\pi$
$769$			9.82745i			0.354387i	−0.984176	+	0.177193i	$0.943298\pi$
$770$	40.3491	−	27.1243i	1.45408	−	0.977491i
$771$		0			0
$772$	−2.51717	−	2.51717i	−0.0905948	−	0.0905948i
$773$	11.4044	+	11.4044i	0.410189	+	0.410189i	0.881804	−	0.471615i	$-0.156329\pi$
$773$	11.4044	+	11.4044i	0.410189	+	0.410189i	−0.471615	+	0.881804i	$0.656329\pi$
$774$		0			0
$775$	7.12526	−	17.4784i	0.255947	−	0.627842i
$776$			7.22771i			0.259460i
$777$		0			0
$778$	−2.49708	+	2.49708i	−0.0895245	+	0.0895245i
$779$	−10.4243			−0.373488
$780$		0			0
$781$	−25.3573			−0.907354
$782$	−4.58406	+	4.58406i	−0.163926	+	0.163926i
$783$		0			0
$784$		−	15.4976i		−	0.553486i
$785$	8.82492	−	45.0250i	0.314975	−	1.60701i
$786$		0			0
$787$	17.7658	+	17.7658i	0.633282	+	0.633282i	0.948890	−	0.315607i	$-0.102208\pi$
$787$	17.7658	+	17.7658i	0.633282	+	0.633282i	−0.315607	+	0.948890i	$0.602208\pi$
$788$	−10.8642	−	10.8642i	−0.387021	−	0.387021i
$789$		0			0
$790$	−2.22759	+	11.3652i	−0.0792540	+	0.404356i
$791$			99.2380i			3.52850i
$792$		0			0
$793$	7.86949	−	7.86949i	0.279454	−	0.279454i
$794$	−2.71594			−0.0963851
$795$		0			0
$796$	−8.66450			−0.307105
$797$	1.05869	−	1.05869i	0.0375007	−	0.0375007i	−0.688108	−	0.725608i	$-0.741558\pi$
$797$	1.05869	−	1.05869i	0.0375007	−	0.0375007i	0.725608	+	0.688108i	$0.241558\pi$
$798$		0			0
$799$		−	66.8103i		−	2.36358i
$800$	−1.93928	−	4.60860i	−0.0685639	−	0.162939i
$801$		0			0
$802$	−17.5692	−	17.5692i	−0.620390	−	0.620390i
$803$	−37.6952	−	37.6952i	−1.33024	−	1.33024i
$804$		0			0
$805$	8.80205	−	5.91709i	0.310231	−	0.208550i
$806$			3.29401i			0.116027i
$807$		0			0
$808$	11.3139	−	11.3139i	0.398023	−	0.398023i
$809$	−3.06839			−0.107879			−0.0539395	−	0.998544i	$-0.517178\pi$
$809$	−3.06839			−0.107879			−0.0539395	+	0.998544i	$0.517178\pi$
$810$		0			0
$811$	−12.2398			−0.429797			−0.214899	−	0.976636i	$-0.568942\pi$
$811$	−12.2398			−0.429797			−0.214899	+	0.976636i	$0.568942\pi$
$812$	31.5610	−	31.5610i	1.10758	−	1.10758i
$813$		0			0
$814$		−	31.1107i		−	1.09043i
$815$	4.59451	+	0.900525i	0.160939	+	0.0315440i
$816$		0			0
$817$	0.407573	+	0.407573i	0.0142592	+	0.0142592i
$818$	18.0968	+	18.0968i	0.632741	+	0.632741i
$819$		0			0
$820$	−3.58969	−	5.33990i	−0.125358	−	0.186477i
$821$			47.5972i			1.66115i	0.556905	+	0.830576i	$0.311989\pi$
$821$			47.5972i			1.66115i	−0.556905	+	0.830576i	$0.688011\pi$
$822$		0			0
$823$	27.9530	−	27.9530i	0.974380	−	0.974380i	−0.0252998	−	0.999680i	$-0.508054\pi$
$823$	27.9530	−	27.9530i	0.974380	−	0.974380i	0.999680	+	0.0252998i	$0.00805404\pi$
$824$	1.51925			0.0529256
$825$		0			0
$826$	−50.7479			−1.76574
$827$	−21.0957	+	21.0957i	−0.733571	+	0.733571i	−0.971325	−	0.237754i	$-0.923589\pi$
$827$	−21.0957	+	21.0957i	−0.733571	+	0.733571i	0.237754	+	0.971325i	$0.423589\pi$
$828$		0			0
$829$			20.1668i			0.700422i	0.936671	+	0.350211i	$0.113890\pi$
$829$			20.1668i			0.700422i	−0.936671	+	0.350211i	$0.886110\pi$
$830$	−8.57215	−	12.7516i	−0.297544	−	0.442615i
$831$		0			0
$832$	0.617014	+	0.617014i	0.0213911	+	0.0213911i
$833$	−71.0419	−	71.0419i	−2.46146	−	2.46146i
$834$		0			0
$835$	9.79720	+	1.92025i	0.339046	+	0.0664531i
$836$		−	16.6065i		−	0.574347i
$837$		0			0
$838$	0.955328	−	0.955328i	0.0330013	−	0.0330013i
$839$	24.6123			0.849710			0.424855	−	0.905262i	$-0.360325\pi$
$839$	24.6123			0.849710			0.424855	+	0.905262i	$0.360325\pi$
$840$		0			0
$841$	59.5515			2.05350
$842$	1.26347	−	1.26347i	0.0435420	−	0.0435420i
$843$		0			0
$844$		−	6.41849i		−	0.220934i
$845$	−22.7116	+	15.2676i	−0.781301	+	0.525222i
$846$		0			0
$847$	33.5848	+	33.5848i	1.15399	+	1.15399i
$848$	−5.77255	−	5.77255i	−0.198230	−	0.198230i
$849$		0			0
$850$	−30.0159	−	12.2363i	−1.02954	−	0.419702i
$851$		−	6.78672i		−	0.232646i
$852$		0			0
$853$	2.63960	−	2.63960i	0.0903783	−	0.0903783i	−0.660472	−	0.750850i	$-0.729644\pi$
$853$	2.63960	−	2.63960i	0.0903783	−	0.0903783i	0.750850	+	0.660472i	$0.229644\pi$
$854$	−60.4950			−2.07010
$855$		0			0
$856$	−17.9432			−0.613285
$857$	10.5437	−	10.5437i	0.360166	−	0.360166i	−0.503708	−	0.863874i	$-0.668031\pi$
$857$	10.5437	−	10.5437i	0.360166	−	0.360166i	0.863874	+	0.503708i	$0.168031\pi$
$858$		0			0
$859$			32.8276i			1.12006i	0.828471	+	0.560031i	$0.189211\pi$
$859$			32.8276i			1.12006i	−0.828471	+	0.560031i	$0.810789\pi$
$860$	−0.0684304	+	0.349134i	−0.00233346	+	0.0119054i
$861$		0			0
$862$	4.70329	+	4.70329i	0.160195	+	0.160195i
$863$	14.9043	+	14.9043i	0.507350	+	0.507350i	0.913712	−	0.406362i	$-0.133203\pi$
$863$	14.9043	+	14.9043i	0.507350	+	0.507350i	−0.406362	+	0.913712i	$0.633203\pi$
$864$		0			0
$865$	−0.101171	+	0.516175i	−0.00343990	+	0.0175505i
$866$			21.9914i			0.747298i
$867$		0			0
$868$	12.6610	−	12.6610i	0.429743	−	0.429743i
$869$	−23.7426			−0.805413
$870$		0			0
$871$	−9.54541			−0.323434
$872$	9.59404	−	9.59404i	0.324895	−	0.324895i
$873$		0			0
$874$		−	3.62266i		−	0.122538i
$875$	44.3392	+	29.0902i	1.49894	+	0.983429i
$876$		0			0
$877$	26.2655	+	26.2655i	0.886921	+	0.886921i	0.994226	−	0.107305i	$-0.0342221\pi$
$877$	26.2655	+	26.2655i	0.886921	+	0.886921i	−0.107305	+	0.994226i	$0.534222\pi$
$878$	15.1256	+	15.1256i	0.510466	+	0.510466i
$879$		0			0
$880$	8.50679	−	5.71861i	0.286764	−	0.192774i
$881$		−	9.32927i		−	0.314311i	−0.987574	−	0.157156i	$-0.949768\pi$
$881$		−	9.32927i		−	0.314311i	0.987574	−	0.157156i	$-0.0502324\pi$
$882$		0			0
$883$	−19.2827	+	19.2827i	−0.648914	+	0.648914i	−0.952731	−	0.303816i	$-0.901739\pi$
$883$	−19.2827	+	19.2827i	−0.648914	+	0.648914i	0.303816	+	0.952731i	$0.401739\pi$
$884$	5.65685			0.190261
$885$		0			0
$886$	−6.96111			−0.233863
$887$	−24.8216	+	24.8216i	−0.833427	+	0.833427i	−0.987984	−	0.154557i	$-0.950605\pi$
$887$	−24.8216	+	24.8216i	−0.833427	+	0.833427i	0.154557	+	0.987984i	$0.450605\pi$
$888$		0			0
$889$		−	21.1985i		−	0.710975i
$890$	−21.7402	−	4.26108i	−0.728732	−	0.142832i
$891$		0			0
$892$	−19.4403	−	19.4403i	−0.650909	−	0.650909i
$893$	26.3992	+	26.3992i	0.883417	+	0.883417i
$894$		0			0
$895$	−16.6687	−	24.7957i	−0.557172	−	0.828829i
$896$		−	4.74316i		−	0.158458i
$897$		0			0
$898$	−23.0647	+	23.0647i	−0.769680	+	0.769680i
$899$	35.5233			1.18477
$900$		0			0
$901$	−52.9234			−1.76313
$902$	9.32722	−	9.32722i	0.310563	−	0.310563i
$903$		0			0
$904$			20.9223i			0.695866i
$905$	15.7680	+	23.4560i	0.524147	+	0.779702i
$906$		0			0
$907$	−30.7963	−	30.7963i	−1.02258	−	1.02258i	−0.999739	−	0.0228367i	$-0.992730\pi$
$907$	−30.7963	−	30.7963i	−1.02258	−	1.02258i	−0.0228367	−	0.999739i	$-0.507270\pi$
$908$	5.88580	+	5.88580i	0.195327	+	0.195327i
$909$		0			0
$910$	−9.08192	−	1.78006i	−0.301063	−	0.0590084i
$911$			36.9538i			1.22433i	0.790729	+	0.612167i	$0.209702\pi$
$911$			36.9538i			1.22433i	−0.790729	+	0.612167i	$0.790298\pi$
$912$		0			0
$913$	22.2733	−	22.2733i	0.737139	−	0.737139i
$914$	11.3726			0.376172
$915$		0			0
$916$	9.40113			0.310622
$917$	−22.2783	+	22.2783i	−0.735695	+	0.735695i
$918$		0			0
$919$		−	42.0681i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$919$		−	42.0681i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$920$	1.85573	−	1.24750i	0.0611817	−	0.0411288i
$921$		0			0
$922$	22.2153	+	22.2153i	0.731621	+	0.731621i
$923$	3.41309	+	3.41309i	0.112343	+	0.112343i
$924$		0			0
$925$	31.2773	−	13.1614i	1.02839	−	0.432743i
$926$			25.3530i			0.833152i
$927$		0			0
$928$	6.65400	−	6.65400i	0.218428	−	0.218428i
$929$	7.89076			0.258887			0.129444	−	0.991587i	$-0.458681\pi$
$929$	7.89076			0.258887			0.129444	+	0.991587i	$0.458681\pi$
$930$		0			0
$931$	56.1426			1.84000
$932$	14.3252	−	14.3252i	0.469238	−	0.469238i
$933$		0			0
$934$			17.3177i			0.566652i
$935$	12.7812	−	65.2100i	0.417989	−	2.13260i
$936$		0			0
$937$	−7.81347	−	7.81347i	−0.255255	−	0.255255i	0.567866	−	0.823121i	$-0.307769\pi$
$937$	−7.81347	−	7.81347i	−0.255255	−	0.255255i	−0.823121	+	0.567866i	$0.807769\pi$
$938$	36.6892	+	36.6892i	1.19794	+	1.19794i
$939$		0			0
$940$	−4.43236	+	22.6140i	−0.144568	+	0.737588i
$941$			50.6075i			1.64976i	0.565310	+	0.824879i	$0.308757\pi$
$941$			50.6075i			1.64976i	−0.565310	+	0.824879i	$0.691243\pi$
$942$		0			0
$943$	2.03471	−	2.03471i	0.0662592	−	0.0662592i
$944$	−10.6992			−0.348228
$945$		0			0
$946$	−0.729362			−0.0237136
$947$	14.6295	−	14.6295i	0.475394	−	0.475394i	−0.428261	−	0.903655i	$-0.640874\pi$
$947$	14.6295	−	14.6295i	0.475394	−	0.475394i	0.903655	+	0.428261i	$0.140874\pi$
$948$		0			0
$949$			10.1476i			0.329403i
$950$	16.6954	−	7.02536i	0.541670	−	0.227933i
$951$		0			0
$952$	−21.7429	−	21.7429i	−0.704693	−	0.704693i
$953$	−9.57293	−	9.57293i	−0.310098	−	0.310098i	0.534850	−	0.844947i	$-0.320368\pi$
$953$	−9.57293	−	9.57293i	−0.310098	−	0.310098i	−0.844947	+	0.534850i	$0.820368\pi$
$954$		0			0
$955$	36.5022	−	24.5382i	1.18118	−	0.794039i
$956$			10.5062i			0.339794i
$957$		0			0
$958$	−4.92613	+	4.92613i	−0.159156	+	0.159156i
$959$	108.395			3.50026
$960$		0			0
$961$	−16.7495			−0.540306
$962$	−4.18750	+	4.18750i	−0.135011	+	0.135011i
$963$		0			0
$964$			15.9827i			0.514769i
$965$	7.81135	+	1.53103i	0.251456	+	0.0492855i
$966$		0			0
$967$	5.33350	+	5.33350i	0.171514	+	0.171514i	0.787644	−	0.616130i	$-0.211301\pi$
$967$	5.33350	+	5.33350i	0.171514	+	0.171514i	−0.616130	+	0.787644i	$0.711301\pi$
$968$	7.08067	+	7.08067i	0.227581	+	0.227581i
$969$		0			0
$970$	−9.01656	−	13.4127i	−0.289504	−	0.430656i
$971$			37.0228i			1.18812i	0.804422	+	0.594059i	$0.202475\pi$
$971$			37.0228i			1.18812i	−0.804422	+	0.594059i	$0.797525\pi$
$972$		0			0
$973$	8.12869	−	8.12869i	0.260594	−	0.260594i
$974$	−2.73362			−0.0875907
$975$		0			0
$976$	−12.7541			−0.408250
$977$	−27.2225	+	27.2225i	−0.870926	+	0.870926i	−0.992573	−	0.121648i	$-0.961182\pi$
$977$	−27.2225	+	27.2225i	−0.870926	+	0.870926i	0.121648	+	0.992573i	$0.461182\pi$
$978$		0			0
$979$		−	45.4165i		−	1.45152i
$980$	19.3333	+	28.7594i	0.617578	+	0.918687i
$981$		0			0
$982$	−1.01636	−	1.01636i	−0.0324334	−	0.0324334i
$983$	14.2627	+	14.2627i	0.454910	+	0.454910i	0.896980	−	0.442070i	$-0.145756\pi$
$983$	14.2627	+	14.2627i	0.454910	+	0.454910i	−0.442070	+	0.896980i	$0.645756\pi$
$984$		0			0
$985$	33.7142	+	6.60799i	1.07422	+	0.210548i
$986$		−	61.0046i		−	1.94278i
$987$		0			0
$988$	−2.23523	+	2.23523i	−0.0711122	+	0.0711122i
$989$	−0.159108			−0.00505935
$990$		0			0
$991$	−17.0715			−0.542293			−0.271146	−	0.962538i	$-0.587403\pi$
$991$	−17.0715			−0.542293			−0.271146	+	0.962538i	$0.587403\pi$
$992$	2.66932	−	2.66932i	0.0847510	−	0.0847510i
$993$		0			0
$994$		−	26.2374i		−	0.832199i
$995$	16.0790	−	10.8090i	0.509739	−	0.342667i
$996$		0			0
$997$	−11.1693	−	11.1693i	−0.353734	−	0.353734i	0.507763	−	0.861497i	$-0.330473\pi$
$997$	−11.1693	−	11.1693i	−0.353734	−	0.353734i	−0.861497	+	0.507763i	$0.830473\pi$
$998$	−26.3860	−	26.3860i	−0.835236	−	0.835236i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.j.737.9	yes	20
3.2	odd	2	inner	2070.2.j.j.737.2	yes	20
5.3	odd	4	inner	2070.2.j.j.323.2	✓	20
15.8	even	4	inner	2070.2.j.j.323.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.j.323.2	✓	20	5.3	odd	4	inner
2070.2.j.j.323.9	yes	20	15.8	even	4	inner
2070.2.j.j.737.2	yes	20	3.2	odd	2	inner
2070.2.j.j.737.9	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24750 + 1.85573i) q^{5} +(-3.35392 - 3.35392i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24750 + 1.85573i) q^{5} +(-3.35392 - 3.35392i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.19432 + 0.430087i) q^{10} +4.58406i q^{11} +(0.617014 - 0.617014i) q^{13} -4.74316 q^{14} -1.00000 q^{16} +(-4.58406 + 4.58406i) q^{17} -3.62266i q^{19} +(1.85573 - 1.24750i) q^{20} +(3.24142 + 3.24142i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.88749 + 4.63005i) q^{25} -0.872590i q^{26} +(-3.35392 + 3.35392i) q^{28} -9.41018 q^{29} -3.77499 q^{31} +(-0.707107 + 0.707107i) q^{32} +6.48283i q^{34} +(2.03997 - 10.4080i) q^{35} +(-4.79894 - 4.79894i) q^{37} +(-2.56161 - 2.56161i) q^{38} +(0.430087 - 2.19432i) q^{40} -2.87751i q^{41} +(-0.112507 + 0.112507i) q^{43} +4.58406 q^{44} +1.00000 q^{46} +(-7.28725 + 7.28725i) q^{47} +15.4976i q^{49} +(1.93928 + 4.60860i) q^{50} +(-0.617014 - 0.617014i) q^{52} +(5.77255 + 5.77255i) q^{53} +(-8.50679 + 5.71861i) q^{55} +4.74316i q^{56} +(-6.65400 + 6.65400i) q^{58} +10.6992 q^{59} +12.7541 q^{61} +(-2.66932 + 2.66932i) q^{62} +1.00000i q^{64} +(1.91474 + 0.375289i) q^{65} +(-7.73517 - 7.73517i) q^{67} +(4.58406 + 4.58406i) q^{68} +(-5.91709 - 8.80205i) q^{70} +5.53162i q^{71} +(-8.22311 + 8.22311i) q^{73} -6.78672 q^{74} -3.62266 q^{76} +(15.3746 - 15.3746i) q^{77} +5.17939i q^{79} +(-1.24750 - 1.85573i) q^{80} +(-2.03471 - 2.03471i) q^{82} +(-4.85886 - 4.85886i) q^{83} +(-14.2254 - 2.78818i) q^{85} +0.159108i q^{86} +(3.24142 - 3.24142i) q^{88} -9.90748 q^{89} -4.13884 q^{91} +(0.707107 - 0.707107i) q^{92} +10.3057i q^{94} +(6.72269 - 4.51927i) q^{95} +(-5.11076 - 5.11076i) q^{97} +(10.9585 + 10.9585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{7}+O(q^{10}) \) 20 * q - 16 * q^7	\( 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) \) 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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