LMFDB - Embedded newform 990.2.n.i.631.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.2769390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + 21x^{4} + 75x^{3} - 198x^{2} - 87x + 841 $ x^8 - x^7 - 2x^6 + 5x^5 + 21x^4 + 75x^3 - 198x^2 - 87x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.2
Root			$-1.07877 + 2.33544i$ of defining polynomial
Character	$\chi$	$=$	990.631
Dual form			990.2.n.i.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.57877 + 4.85894i) q^{7} +(0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(-1.45132 + 2.98223i) q^{11} +(-1.07877 - 0.783769i) q^{13} +(1.57877 - 4.85894i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.627445 - 0.455866i) q^{17} +(-0.0242693 + 0.0746932i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(2.92705 - 1.55961i) q^{22} -6.64849 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.412052 + 1.26816i) q^{26} +(-4.13326 + 3.00299i) q^{28} +(0.623850 + 1.92001i) q^{29} +(-6.86933 - 4.99086i) q^{31} +1.00000 q^{32} -0.775565 q^{34} +(-4.13326 - 3.00299i) q^{35} +(-1.21539 - 3.74060i) q^{37} +(0.0635378 - 0.0461629i) q^{38} +(0.309017 + 0.951057i) q^{40} +(3.67612 - 11.3139i) q^{41} -6.01163 q^{43} +(-3.28475 - 0.458729i) q^{44} +(5.37874 + 3.90788i) q^{46} +(-2.03009 + 6.24796i) q^{47} +(-15.4537 + 11.2278i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(0.412052 - 1.26816i) q^{52} +(8.36933 + 6.08067i) q^{53} +(-0.578765 - 3.26574i) q^{55} +5.10899 q^{56} +(0.623850 - 1.92001i) q^{58} +(1.64590 + 5.06555i) q^{59} +(3.03046 - 2.20175i) q^{61} +(2.62385 + 8.07538i) q^{62} +(-0.809017 - 0.587785i) q^{64} +1.33343 q^{65} +0.588036 q^{67} +(0.627445 + 0.455866i) q^{68} +(1.57877 + 4.85894i) q^{70} +(-1.87292 + 1.36076i) q^{71} +(3.38197 + 10.4086i) q^{73} +(-1.21539 + 3.74060i) q^{74} -0.0785371 q^{76} +(-16.7818 - 2.34364i) q^{77} +(-9.97251 - 7.24545i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-9.62422 + 6.99241i) q^{82} +(-6.47214 + 4.70228i) q^{83} +(-0.239663 + 0.737606i) q^{85} +(4.86351 + 3.53355i) q^{86} +(2.38778 + 2.30185i) q^{88} +9.67821 q^{89} +(2.10517 - 6.47904i) q^{91} +(-2.05450 - 6.32309i) q^{92} +(5.31483 - 3.86145i) q^{94} +(-0.0242693 - 0.0746932i) q^{95} +(10.8846 + 7.90809i) q^{97} +19.1018 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8} + 8 q^{10} - 10 q^{11} + q^{13} + 3 q^{14} - 2 q^{16} - 3 q^{17} - 12 q^{19} - 2 q^{20} + 10 q^{22} - 2 q^{25} + q^{26} - 2 q^{28} - 27 q^{29} - 6 q^{31}+ \cdots + 62 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8 + 8 * q^10 - 10 * q^11 + q^13 + 3 * q^14 - 2 * q^16 - 3 * q^17 - 12 * q^19 - 2 * q^20 + 10 * q^22 - 2 * q^25 + q^26 - 2 * q^28 - 27 * q^29 - 6 * q^31 + 8 * q^32 + 22 * q^34 - 2 * q^35 - 4 * q^37 + 13 * q^38 - 2 * q^40 + 23 * q^41 - 2 * q^43 - 10 * q^44 - 5 * q^46 - 5 * q^47 - 53 * q^49 - 2 * q^50 + q^52 + 18 * q^53 + 5 * q^55 - 2 * q^56 - 27 * q^58 + 40 * q^59 - 20 * q^61 - 11 * q^62 - 2 * q^64 - 4 * q^65 + 18 * q^67 - 3 * q^68 + 3 * q^70 + 10 * q^71 + 36 * q^73 - 4 * q^74 - 2 * q^76 - 50 * q^77 - 11 * q^79 - 2 * q^80 - 12 * q^82 - 16 * q^83 - 8 * q^85 + 13 * q^86 + 5 * q^88 + 46 * q^89 - 39 * q^91 + 5 * q^92 + 15 * q^94 - 12 * q^95 + 16 * q^97 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	1.57877	+	4.85894i	0.596717	+	1.83651i	0.545986	+	0.837795i	$0.316155\pi$
$7$	1.57877	+	4.85894i	0.596717	+	1.83651i	0.0507316	+	0.998712i	$0.483845\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	1.00000			0.316228
$11$	−1.45132	+	2.98223i	−0.437590	+	0.899175i
$11$	−1.45132	+	2.98223i	−0.437590	+	0.899175i
$12$		0			0
$13$	−1.07877	−	0.783769i	−0.299196	−	0.217378i	0.428051	−	0.903755i	$-0.359200\pi$
$13$	−1.07877	−	0.783769i	−0.299196	−	0.217378i	−0.727247	+	0.686376i	$0.759200\pi$
$14$	1.57877	−	4.85894i	0.421943	−	1.29861i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.627445	−	0.455866i	0.152178	−	0.110564i	−0.509091	−	0.860713i	$-0.670018\pi$
$17$	0.627445	−	0.455866i	0.152178	−	0.110564i	0.661269	+	0.750149i	$0.270018\pi$
$18$		0			0
$19$	−0.0242693	+	0.0746932i	−0.00556776	+	0.0171358i	−0.953802	−	0.300437i	$-0.902868\pi$
$19$	−0.0242693	+	0.0746932i	−0.00556776	+	0.0171358i	0.948234	+	0.317572i	$0.102868\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$		0			0
$22$	2.92705	−	1.55961i	0.624049	−	0.332509i
$23$	−6.64849			−1.38631			−0.693153	−	0.720791i	$-0.743779\pi$
$23$	−6.64849			−1.38631			−0.693153	+	0.720791i	$0.743779\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.412052	+	1.26816i	0.0808100	+	0.248708i
$27$		0			0
$28$	−4.13326	+	3.00299i	−0.781113	+	0.567512i
$29$	0.623850	+	1.92001i	0.115846	+	0.356538i	0.992123	−	0.125271i	$-0.0399800\pi$
$29$	0.623850	+	1.92001i	0.115846	+	0.356538i	−0.876276	+	0.481809i	$0.839980\pi$
$30$		0			0
$31$	−6.86933	−	4.99086i	−1.23377	−	0.896385i	−0.236601	−	0.971607i	$-0.576033\pi$
$31$	−6.86933	−	4.99086i	−1.23377	−	0.896385i	−0.997167	+	0.0752219i	$0.976033\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.775565			−0.133008
$35$	−4.13326	−	3.00299i	−0.698649	−	0.507598i
$36$		0			0
$37$	−1.21539	−	3.74060i	−0.199809	−	0.614950i	−0.999887	−	0.0150533i	$-0.995208\pi$
$37$	−1.21539	−	3.74060i	−0.199809	−	0.614950i	0.800077	−	0.599897i	$-0.204792\pi$
$38$	0.0635378	−	0.0461629i	0.0103072	−	0.00748862i
$39$		0			0
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	3.67612	−	11.3139i	0.574114	−	1.76694i	−0.0650614	−	0.997881i	$-0.520724\pi$
$41$	3.67612	−	11.3139i	0.574114	−	1.76694i	0.639176	−	0.769061i	$-0.279276\pi$
$42$		0			0
$43$	−6.01163			−0.916765			−0.458383	−	0.888755i	$-0.651571\pi$
$43$	−6.01163			−0.916765			−0.458383	+	0.888755i	$0.651571\pi$
$44$	−3.28475	−	0.458729i	−0.495194	−	0.0691560i
$45$		0			0
$46$	5.37874	+	3.90788i	0.793052	+	0.576186i
$47$	−2.03009	+	6.24796i	−0.296118	+	0.911359i	0.686725	+	0.726917i	$0.259048\pi$
$47$	−2.03009	+	6.24796i	−0.296118	+	0.911359i	−0.982843	+	0.184442i	$0.940952\pi$
$48$		0			0
$49$	−15.4537	+	11.2278i	−2.20767	+	1.60397i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$		0			0
$52$	0.412052	−	1.26816i	0.0571413	−	0.175863i
$53$	8.36933	+	6.08067i	1.14962	+	0.835245i	0.988430	−	0.151679i	$-0.0484681\pi$
$53$	8.36933	+	6.08067i	1.14962	+	0.835245i	0.161186	+	0.986924i	$0.448468\pi$
$54$		0			0
$55$	−0.578765	−	3.26574i	−0.0780407	−	0.440352i
$56$	5.10899			0.682718
$57$		0			0
$58$	0.623850	−	1.92001i	0.0819156	−	0.252110i
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	0.999204	+	0.0398899i	$0.0127007\pi$
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	−0.784926	+	0.619589i	$0.787299\pi$
$60$		0			0
$61$	3.03046	−	2.20175i	0.388010	−	0.281906i	−0.376630	−	0.926364i	$-0.622917\pi$
$61$	3.03046	−	2.20175i	0.388010	−	0.281906i	0.764640	+	0.644458i	$0.222917\pi$
$62$	2.62385	+	8.07538i	0.333229	+	1.02557i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.33343			0.165391
$66$		0			0
$67$	0.588036			0.0718400			0.0359200	−	0.999355i	$-0.488564\pi$
$67$	0.588036			0.0718400			0.0359200	+	0.999355i	$0.488564\pi$
$68$	0.627445	+	0.455866i	0.0760889	+	0.0552818i
$69$		0			0
$70$	1.57877	+	4.85894i	0.188699	+	0.580754i
$71$	−1.87292	+	1.36076i	−0.222275	+	0.161492i	−0.693350	−	0.720601i	$-0.743866\pi$
$71$	−1.87292	+	1.36076i	−0.222275	+	0.161492i	0.471075	+	0.882093i	$0.343866\pi$
$72$		0			0
$73$	3.38197	+	10.4086i	0.395829	+	1.21824i	0.928314	+	0.371797i	$0.121258\pi$
$73$	3.38197	+	10.4086i	0.395829	+	1.21824i	−0.532485	+	0.846440i	$0.678742\pi$
$74$	−1.21539	+	3.74060i	−0.141287	+	0.434836i
$75$		0			0
$76$	−0.0785371			−0.00900882
$77$	−16.7818	−	2.34364i	−1.91246	−	0.267083i
$78$		0			0
$79$	−9.97251	−	7.24545i	−1.12199	−	0.815177i	−0.137484	−	0.990504i	$-0.543902\pi$
$79$	−9.97251	−	7.24545i	−1.12199	−	0.815177i	−0.984510	+	0.175327i	$0.943902\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$		0			0
$82$	−9.62422	+	6.99241i	−1.06282	+	0.772182i
$83$	−6.47214	+	4.70228i	−0.710409	+	0.516143i	−0.883306	−	0.468798i	$-0.844687\pi$
$83$	−6.47214	+	4.70228i	−0.710409	+	0.516143i	0.172896	+	0.984940i	$0.444687\pi$
$84$		0			0
$85$	−0.239663	+	0.737606i	−0.0259951	+	0.0800046i
$86$	4.86351	+	3.53355i	0.524446	+	0.381032i
$87$		0			0
$88$	2.38778	+	2.30185i	0.254538	+	0.245378i
$89$	9.67821			1.02589			0.512944	−	0.858422i	$-0.328555\pi$
$89$	9.67821			1.02589			0.512944	+	0.858422i	$0.328555\pi$
$90$		0			0
$91$	2.10517	−	6.47904i	0.220682	−	0.679188i
$92$	−2.05450	−	6.32309i	−0.214196	−	0.659228i
$93$		0			0
$94$	5.31483	−	3.86145i	0.548183	−	0.398278i
$95$	−0.0242693	−	0.0746932i	−0.00248998	−	0.00766336i
$96$		0			0
$97$	10.8846	+	7.90809i	1.10516	+	0.802945i	0.981895	−	0.189429i	$-0.0606635\pi$
$97$	10.8846	+	7.90809i	1.10516	+	0.802945i	0.123265	+	0.992374i	$0.460664\pi$
$98$	19.1018			1.92957
$99$		0			0
$100$	1.00000			0.100000
$101$	−8.60862	−	6.25453i	−0.856590	−	0.622349i	0.0703651	−	0.997521i	$-0.477584\pi$
$101$	−8.60862	−	6.25453i	−0.856590	−	0.622349i	−0.926955	+	0.375172i	$0.877584\pi$
$102$		0			0
$103$	5.16326	+	15.8909i	0.508751	+	1.56577i	0.794372	+	0.607432i	$0.207800\pi$
$103$	5.16326	+	15.8909i	0.508751	+	1.56577i	−0.285620	+	0.958343i	$0.592200\pi$
$104$	−1.07877	+	0.783769i	−0.105782	+	0.0768549i
$105$		0			0
$106$	−3.19680	−	9.83874i	−0.310501	−	0.955623i
$107$	−5.42360	+	16.6921i	−0.524319	+	1.61369i	0.241340	+	0.970441i	$0.422413\pi$
$107$	−5.42360	+	16.6921i	−0.524319	+	1.61369i	−0.765659	+	0.643247i	$0.777587\pi$
$108$		0			0
$109$	−8.94427			−0.856706			−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427			−0.856706			−0.428353	+	0.903612i	$0.640906\pi$
$110$	−1.45132	+	2.98223i	−0.138378	+	0.284344i
$111$		0			0
$112$	−4.13326	−	3.00299i	−0.390557	−	0.283756i
$113$	1.76975	−	5.44673i	0.166484	−	0.512385i	−0.832659	−	0.553787i	$-0.813182\pi$
$113$	1.76975	−	5.44673i	0.166484	−	0.512385i	0.999143	+	0.0414017i	$0.0131823\pi$
$114$		0			0
$115$	5.37874	−	3.90788i	0.501570	−	0.364412i
$116$	−1.63326	+	1.18663i	−0.151645	+	0.110176i
$117$		0			0
$118$	1.64590	−	5.06555i	0.151517	−	0.466322i
$119$	3.20561	+	2.32901i	0.293858	+	0.213500i
$120$		0			0
$121$	−6.78734	−	8.65633i	−0.617031	−	0.786939i
$122$	−3.74585			−0.339133
$123$		0			0
$124$	2.62385	−	8.07538i	0.235629	−	0.725191i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	5.63303	−	4.09264i	0.499851	−	0.363163i	−0.309109	−	0.951027i	$-0.600031\pi$
$127$	5.63303	−	4.09264i	0.499851	−	0.363163i	0.808960	+	0.587864i	$0.200031\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−1.07877	−	0.783769i	−0.0946140	−	0.0687411i
$131$	2.19916			0.192142			0.0960709	−	0.995374i	$-0.469372\pi$
$131$	2.19916			0.192142			0.0960709	+	0.995374i	$0.469372\pi$
$132$		0			0
$133$	−0.401245			−0.0347924
$134$	−0.475731	−	0.345639i	−0.0410969	−	0.0298586i
$135$		0			0
$136$	−0.239663	−	0.737606i	−0.0205509	−	0.0632492i
$137$	−1.76034	+	1.27896i	−0.150396	+	0.109269i	−0.660438	−	0.750880i	$-0.729630\pi$
$137$	−1.76034	+	1.27896i	−0.150396	+	0.109269i	0.510043	+	0.860149i	$0.329630\pi$
$138$		0			0
$139$	3.18517	+	9.80293i	0.270162	+	0.831474i	0.990459	+	0.137808i	$0.0440057\pi$
$139$	3.18517	+	9.80293i	0.270162	+	0.831474i	−0.720297	+	0.693666i	$0.755994\pi$
$140$	1.57877	−	4.85894i	0.133430	−	0.410655i
$141$		0			0
$142$	2.31506			0.194276
$143$	3.90301	−	2.07962i	0.326386	−	0.173907i
$144$		0			0
$145$	−1.63326	−	1.18663i	−0.135635	−	0.0985446i
$146$	3.38197	−	10.4086i	0.279893	−	0.861424i
$147$		0			0
$148$	3.18194	−	2.31182i	0.261554	−	0.190030i
$149$	−12.3356	+	8.96237i	−1.01058	+	0.734226i	−0.964330	−	0.264704i	$-0.914726\pi$
$149$	−12.3356	+	8.96237i	−1.01058	+	0.734226i	−0.0462460	+	0.998930i	$0.514726\pi$
$150$		0			0
$151$	2.03000	−	6.24769i	0.165199	−	0.508430i	−0.833852	−	0.551988i	$-0.813869\pi$
$151$	2.03000	−	6.24769i	0.165199	−	0.508430i	0.999051	+	0.0435581i	$0.0138694\pi$
$152$	0.0635378	+	0.0461629i	0.00515360	+	0.00374431i
$153$		0			0
$154$	12.1992	+	11.7601i	0.983037	+	0.947657i
$155$	8.49096			0.682010
$156$		0			0
$157$	−2.87638	+	8.85258i	−0.229560	+	0.706513i	0.768237	+	0.640166i	$0.221134\pi$
$157$	−2.87638	+	8.85258i	−0.229560	+	0.706513i	−0.997797	+	0.0663469i	$0.978866\pi$
$158$	3.80916	+	11.7234i	0.303040	+	0.932662i
$159$		0			0
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	−10.4964	−	32.3046i	−0.827233	−	2.54596i
$162$		0			0
$163$	15.1300	+	10.9926i	1.18508	+	0.861008i	0.992735	−	0.120320i	$-0.0383921\pi$
$163$	15.1300	+	10.9926i	1.18508	+	0.861008i	0.192341	+	0.981328i	$0.438392\pi$
$164$	11.8962			0.928936
$165$		0			0
$166$	8.00000			0.620920
$167$	−1.92123	−	1.39586i	−0.148670	−	0.108015i	0.510964	−	0.859602i	$-0.329289\pi$
$167$	−1.92123	−	1.39586i	−0.148670	−	0.108015i	−0.659634	+	0.751587i	$0.729289\pi$
$168$		0			0
$169$	−3.46778	−	10.6727i	−0.266752	−	0.820979i
$170$	0.627445	−	0.455866i	0.0481228	−	0.0349633i
$171$		0			0
$172$	−1.85770	−	5.71740i	−0.141648	−	0.435948i
$173$	−0.900560	+	2.77164i	−0.0684683	+	0.210724i	−0.979436	−	0.201753i	$-0.935336\pi$
$173$	−0.900560	+	2.77164i	−0.0684683	+	0.210724i	0.910968	+	0.412477i	$0.135336\pi$
$174$		0			0
$175$	5.10899			0.386204
$176$	−0.578765	−	3.26574i	−0.0436261	−	0.246164i
$177$		0			0
$178$	−7.82983	−	5.68871i	−0.586871	−	0.426387i
$179$	−0.482779	+	1.48584i	−0.0360846	+	0.111057i	−0.967476	−	0.252961i	$-0.918595\pi$
$179$	−0.482779	+	1.48584i	−0.0360846	+	0.111057i	0.931392	+	0.364018i	$0.118595\pi$
$180$		0			0
$181$	−14.9443	+	10.8576i	−1.11080	+	0.807043i	−0.982789	−	0.184730i	$-0.940859\pi$
$181$	−14.9443	+	10.8576i	−1.11080	+	0.807043i	−0.128010	+	0.991773i	$0.540859\pi$
$182$	−5.51140	+	4.00427i	−0.408532	+	0.296816i
$183$		0			0
$184$	−2.05450	+	6.32309i	−0.151459	+	0.466144i
$185$	3.18194	+	2.31182i	0.233941	+	0.169968i
$186$		0			0
$187$	0.448870	+	2.53279i	0.0328246	+	0.185216i
$188$	−6.56950			−0.479130
$189$		0			0
$190$	−0.0242693	+	0.0746932i	−0.00176068	+	0.00541881i
$191$	−6.40523	−	19.7133i	−0.463466	−	1.42640i	−0.860901	−	0.508772i	$-0.830100\pi$
$191$	−6.40523	−	19.7133i	−0.463466	−	1.42640i	0.397435	−	0.917630i	$-0.369900\pi$
$192$		0			0
$193$	−1.10899	+	0.805730i	−0.0798270	+	0.0579977i	−0.626983	−	0.779033i	$-0.715710\pi$
$193$	−1.10899	+	0.805730i	−0.0798270	+	0.0579977i	0.547156	+	0.837031i	$0.315710\pi$
$194$	−4.15753	−	12.7956i	−0.298493	−	0.918668i
$195$		0			0
$196$	−15.4537	−	11.2278i	−1.10383	−	0.801983i
$197$	5.01135			0.357044			0.178522	−	0.983936i	$-0.442868\pi$
$197$	5.01135			0.357044			0.178522	+	0.983936i	$0.442868\pi$
$198$		0			0
$199$	23.3086			1.65230			0.826152	−	0.563448i	$-0.190525\pi$
$199$	23.3086			1.65230			0.826152	+	0.563448i	$0.190525\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$		0			0
$202$	3.28820	+	10.1200i	0.231357	+	0.712044i
$203$	−8.34432	+	6.06250i	−0.585657	+	0.425504i
$204$		0			0
$205$	3.67612	+	11.3139i	0.256752	+	0.790200i
$206$	5.16326	−	15.8909i	0.359741	−	1.10717i
$207$		0			0
$208$	1.33343			0.0924566
$209$	−0.187529	−	0.180780i	−0.0129717	−	0.0125048i
$210$		0			0
$211$	16.2484	+	11.8052i	1.11859	+	0.812702i	0.983995	−	0.178199i	$-0.0570269\pi$
$211$	16.2484	+	11.8052i	1.11859	+	0.812702i	0.134594	+	0.990901i	$0.457027\pi$
$212$	−3.19680	+	9.83874i	−0.219557	+	0.675727i
$213$		0			0
$214$	14.1992	−	10.3163i	0.970635	−	0.705207i
$215$	4.86351	−	3.53355i	0.331689	−	0.240986i
$216$		0			0
$217$	13.4052	−	41.2571i	0.910006	−	2.80071i
$218$	7.23607	+	5.25731i	0.490088	+	0.356070i
$219$		0			0
$220$	2.92705	−	1.55961i	0.197342	−	0.105149i
$221$	−1.03416			−0.0695651
$222$		0			0
$223$	2.81483	−	8.66317i	0.188495	−	0.580129i	−0.811496	−	0.584358i	$-0.801346\pi$
$223$	2.81483	−	8.66317i	0.188495	−	0.580129i	0.999991	+	0.00422962i	$0.00134633\pi$
$224$	1.57877	+	4.85894i	0.105486	+	0.324652i
$225$		0			0
$226$	−4.63326	+	3.36626i	−0.308200	+	0.223920i
$227$	−6.39360	−	19.6775i	−0.424358	−	1.30604i	−0.903608	−	0.428361i	$-0.859091\pi$
$227$	−6.39360	−	19.6775i	−0.424358	−	1.30604i	0.479250	−	0.877679i	$-0.340909\pi$
$228$		0			0
$229$	−8.88456	−	6.45501i	−0.587108	−	0.426559i	0.254172	−	0.967159i	$-0.418197\pi$
$229$	−8.88456	−	6.45501i	−0.587108	−	0.426559i	−0.841280	+	0.540600i	$0.818197\pi$
$230$	−6.64849			−0.438388
$231$		0			0
$232$	2.01882			0.132542
$233$	−2.39719	−	1.74166i	−0.157045	−	0.114100i	0.506487	−	0.862247i	$-0.330944\pi$
$233$	−2.39719	−	1.74166i	−0.157045	−	0.114100i	−0.663533	+	0.748147i	$0.730944\pi$
$234$		0			0
$235$	−2.03009	−	6.24796i	−0.132428	−	0.407572i
$236$	−4.30902	+	3.13068i	−0.280493	+	0.203790i
$237$		0			0
$238$	−1.22444	−	3.76842i	−0.0793683	−	0.244271i
$239$	−2.64821	+	8.15034i	−0.171298	+	0.527202i	−0.999445	−	0.0333094i	$-0.989395\pi$
$239$	−2.64821	+	8.15034i	−0.171298	+	0.527202i	0.828147	+	0.560511i	$0.189395\pi$
$240$		0			0
$241$	7.97000			0.513393			0.256696	−	0.966492i	$-0.417366\pi$
$241$	7.97000			0.513393			0.256696	+	0.966492i	$0.417366\pi$
$242$	0.403010	+	10.9926i	0.0259065	+	0.706632i
$243$		0			0
$244$	3.03046	+	2.20175i	0.194005	+	0.140953i
$245$	5.90278	−	18.1669i	0.377115	−	1.16064i
$246$		0			0
$247$	0.0847231	−	0.0615549i	0.00539080	−	0.00391665i
$248$	−6.86933	+	4.99086i	−0.436203	+	0.316920i
$249$		0			0
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	16.3904	+	11.9083i	1.03455	+	0.751645i	0.969215	−	0.246218i	$-0.0791879\pi$
$251$	16.3904	+	11.9083i	1.03455	+	0.751645i	0.0653367	+	0.997863i	$0.479188\pi$
$252$		0			0
$253$	9.64909	−	19.8273i	0.606633	−	1.24653i
$254$	−6.96281			−0.436886
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.16916	+	18.9867i	0.384822	+	1.18436i	0.936609	+	0.350375i	$0.113946\pi$
$257$	6.16916	+	18.9867i	0.384822	+	1.18436i	−0.551788	+	0.833985i	$0.686054\pi$
$258$		0			0
$259$	16.2565	−	11.8110i	1.01013	−	0.733903i
$260$	0.412052	+	1.26816i	0.0255544	+	0.0786482i
$261$		0			0
$262$	−1.77916	−	1.29264i	−0.109917	−	0.0798593i
$263$	0.696114			0.0429242			0.0214621	−	0.999770i	$-0.493168\pi$
$263$	0.696114			0.0429242			0.0214621	+	0.999770i	$0.493168\pi$
$264$		0			0
$265$	−10.3451			−0.635492
$266$	0.324614	+	0.235846i	0.0199034	+	0.0144606i
$267$		0			0
$268$	0.181713	+	0.559255i	0.0110999	+	0.0341619i
$269$	4.79079	−	3.48071i	0.292100	−	0.212223i	−0.432078	−	0.901836i	$-0.642219\pi$
$269$	4.79079	−	3.48071i	0.292100	−	0.212223i	0.724178	+	0.689613i	$0.242219\pi$
$270$		0			0
$271$	−4.29983	−	13.2335i	−0.261196	−	0.803880i	−0.992545	−	0.121876i	$-0.961109\pi$
$271$	−4.29983	−	13.2335i	−0.261196	−	0.803880i	0.731349	−	0.682003i	$-0.238891\pi$
$272$	−0.239663	+	0.737606i	−0.0145317	+	0.0447239i
$273$		0			0
$274$	2.17590			0.131451
$275$	2.38778	+	2.30185i	0.143989	+	0.138807i
$276$		0			0
$277$	8.17313	+	5.93813i	0.491076	+	0.356787i	0.805598	−	0.592463i	$-0.201844\pi$
$277$	8.17313	+	5.93813i	0.491076	+	0.356787i	−0.314522	+	0.949250i	$0.601844\pi$
$278$	3.18517	−	9.80293i	0.191034	−	0.587941i
$279$		0			0
$280$	−4.13326	+	3.00299i	−0.247010	+	0.179463i
$281$	23.3871	−	16.9918i	1.39516	−	1.01364i	0.399883	−	0.916566i	$-0.369051\pi$
$281$	23.3871	−	16.9918i	1.39516	−	1.01364i	0.995277	−	0.0970773i	$-0.0309494\pi$
$282$		0			0
$283$	−4.05464	+	12.4789i	−0.241023	+	0.741793i	0.755242	+	0.655446i	$0.227519\pi$
$283$	−4.05464	+	12.4789i	−0.241023	+	0.741793i	−0.996265	+	0.0863469i	$0.972481\pi$
$284$	−1.87292	−	1.36076i	−0.111138	−	0.0807462i
$285$		0			0
$286$	−4.37997	−	0.611682i	−0.258993	−	0.0361695i
$287$	60.7775			3.58759
$288$		0			0
$289$	−5.06741	+	15.5959i	−0.298083	+	0.917406i
$290$	0.623850	+	1.92001i	0.0366338	+	0.112747i
$291$		0			0
$292$	−8.85410	+	6.43288i	−0.518147	+	0.376456i
$293$	−7.00236	−	21.5511i	−0.409082	−	1.25903i	−0.917438	−	0.397879i	$-0.869746\pi$
$293$	−7.00236	−	21.5511i	−0.409082	−	1.25903i	0.508356	−	0.861147i	$-0.330254\pi$
$294$		0			0
$295$	−4.30902	−	3.13068i	−0.250881	−	0.182275i
$296$	−3.93310			−0.228607
$297$		0			0
$298$	15.2477			0.883276
$299$	7.17216	+	5.21088i	0.414777	+	0.301353i
$300$		0			0
$301$	−9.49096	−	29.2102i	−0.547050	−	1.68365i
$302$	−5.31461	+	3.86129i	−0.305821	+	0.222192i
$303$		0			0
$304$	−0.0242693	−	0.0746932i	−0.00139194	−	0.00428395i
$305$	−1.15753	+	3.56251i	−0.0662800	+	0.203989i
$306$		0			0
$307$	−29.3158			−1.67314			−0.836571	−	0.547859i	$-0.815443\pi$
$307$	−29.3158			−1.67314			−0.836571	+	0.547859i	$0.815443\pi$
$308$	−2.95691	−	16.6846i	−0.168485	−	0.950694i
$309$		0			0
$310$	−6.86933	−	4.99086i	−0.390152	−	0.283462i
$311$	−3.50950	+	10.8011i	−0.199005	+	0.612476i	0.800901	+	0.598797i	$0.204354\pi$
$311$	−3.50950	+	10.8011i	−0.199005	+	0.612476i	−0.999906	+	0.0136789i	$0.995646\pi$
$312$		0			0
$313$	2.56995	−	1.86718i	0.145262	−	0.105539i	−0.512781	−	0.858520i	$-0.671385\pi$
$313$	2.56995	−	1.86718i	0.145262	−	0.105539i	0.658043	+	0.752980i	$0.271385\pi$
$314$	7.53046	−	5.47120i	0.424968	−	0.308757i
$315$		0			0
$316$	3.80916	−	11.7234i	0.214282	−	0.659492i
$317$	3.82747	+	2.78082i	0.214972	+	0.156186i	0.690060	−	0.723752i	$-0.257584\pi$
$317$	3.82747	+	2.78082i	0.214972	+	0.156186i	−0.475088	+	0.879938i	$0.657584\pi$
$318$		0			0
$319$	−6.63132	−	0.926093i	−0.371283	−	0.0518512i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−10.4964	+	32.3046i	−0.584942	+	1.80027i
$323$	0.0188224	+	0.0579294i	0.00104731	+	0.00322328i
$324$		0			0
$325$	−1.07877	+	0.783769i	−0.0598391	+	0.0434757i
$326$	−5.77916	−	17.7864i	−0.320078	−	0.985099i
$327$		0			0
$328$	−9.62422	−	6.99241i	−0.531409	−	0.386091i
$329$	−33.5635			−1.85042
$330$		0			0
$331$	30.0424			1.65128			0.825639	−	0.564199i	$-0.190815\pi$
$331$	30.0424			1.65128			0.825639	+	0.564199i	$0.190815\pi$
$332$	−6.47214	−	4.70228i	−0.355205	−	0.258071i
$333$		0			0
$334$	0.733846	+	2.25855i	0.0401543	+	0.123582i
$335$	−0.475731	+	0.345639i	−0.0259919	+	0.0188843i
$336$		0			0
$337$	−7.83574	−	24.1159i	−0.426840	−	1.31368i	−0.901222	−	0.433359i	$-0.857328\pi$
$337$	−7.83574	−	24.1159i	−0.426840	−	1.31368i	0.474382	−	0.880319i	$-0.342672\pi$
$338$	−3.46778	+	10.6727i	−0.188622	+	0.580520i
$339$		0			0
$340$	−0.775565			−0.0420609
$341$	24.8535	−	13.2426i	1.34589	−	0.717125i
$342$		0			0
$343$	−50.0199	−	36.3416i	−2.70082	−	1.96226i
$344$	−1.85770	+	5.71740i	−0.100160	+	0.308262i
$345$		0			0
$346$	2.35770	−	1.71297i	0.126751	−	0.0920897i
$347$	−2.56995	+	1.86718i	−0.137962	+	0.100235i	−0.654626	−	0.755953i	$-0.727174\pi$
$347$	−2.56995	+	1.86718i	−0.137962	+	0.100235i	0.516664	+	0.856189i	$0.327174\pi$
$348$		0			0
$349$	−2.15034	+	6.61807i	−0.115105	+	0.354257i	−0.991969	−	0.126482i	$-0.959632\pi$
$349$	−2.15034	+	6.61807i	−0.115105	+	0.354257i	0.876864	+	0.480739i	$0.159632\pi$
$350$	−4.13326	−	3.00299i	−0.220932	−	0.160517i
$351$		0			0
$352$	−1.45132	+	2.98223i	−0.0773556	+	0.158953i
$353$	−8.01163			−0.426416			−0.213208	−	0.977007i	$-0.568391\pi$
$353$	−8.01163			−0.426416			−0.213208	+	0.977007i	$0.568391\pi$
$354$		0			0
$355$	0.715393	−	2.20175i	0.0379691	−	0.116857i
$356$	2.99073	+	9.20452i	0.158508	+	0.487839i
$357$		0			0
$358$	1.26393	−	0.918300i	0.0668009	−	0.0485337i
$359$	0.0557281	+	0.171513i	0.00294122	+	0.00905213i	0.952516	−	0.304487i	$-0.0984852\pi$
$359$	0.0557281	+	0.171513i	0.00294122	+	0.00905213i	−0.949575	+	0.313540i	$0.898485\pi$
$360$		0			0
$361$	15.3663	+	11.1643i	0.808754	+	0.587594i
$362$	18.4721			0.970874
$363$		0			0
$364$	6.81247			0.357070
$365$	−8.85410	−	6.43288i	−0.463445	−	0.336712i
$366$		0			0
$367$	9.53950	+	29.3596i	0.497958	+	1.53256i	0.812296	+	0.583245i	$0.198217\pi$
$367$	9.53950	+	29.3596i	0.497958	+	1.53256i	−0.314338	+	0.949311i	$0.601783\pi$
$368$	5.37874	−	3.90788i	0.280386	−	0.203713i
$369$		0			0
$370$	−1.21539	−	3.74060i	−0.0631853	−	0.194464i
$371$	−16.3324	+	50.2660i	−0.847937	+	2.60968i
$372$		0			0
$373$	16.1018			0.833720			0.416860	−	0.908971i	$-0.363131\pi$
$373$	16.1018			0.833720			0.416860	+	0.908971i	$0.363131\pi$
$374$	1.12559	−	2.31291i	0.0582030	−	0.119598i
$375$		0			0
$376$	5.31483	+	3.86145i	0.274092	+	0.199139i
$377$	0.831859	−	2.56020i	0.0428429	−	0.131857i
$378$		0			0
$379$	−26.3324	+	19.1316i	−1.35261	+	0.982726i	−0.353729	+	0.935348i	$0.615086\pi$
$379$	−26.3324	+	19.1316i	−1.35261	+	0.982726i	−0.998877	+	0.0473775i	$0.984914\pi$
$380$	0.0635378	−	0.0461629i	0.00325942	−	0.00236811i
$381$		0			0
$382$	−6.40523	+	19.7133i	−0.327720	+	1.00862i
$383$	1.70561	+	1.23920i	0.0871527	+	0.0633202i	0.630508	−	0.776182i	$-0.282846\pi$
$383$	1.70561	+	1.23920i	0.0871527	+	0.0633202i	−0.543356	+	0.839503i	$0.682846\pi$
$384$		0			0
$385$	14.9543	−	7.96802i	0.762141	−	0.406088i
$386$	1.37079			0.0697714
$387$		0			0
$388$	−4.15753	+	12.7956i	−0.211067	+	0.649596i
$389$	3.89460	+	11.9864i	0.197464	+	0.607732i	0.999939	+	0.0110463i	$0.00351620\pi$
$389$	3.89460	+	11.9864i	0.197464	+	0.607732i	−0.802475	+	0.596686i	$0.796484\pi$
$390$		0			0
$391$	−4.17156	+	3.03082i	−0.210965	+	0.153275i
$392$	5.90278	+	18.1669i	0.298135	+	0.917567i
$393$		0			0
$394$	−4.05427	−	2.94560i	−0.204251	−	0.148397i
$395$	12.3267			0.620223
$396$		0			0
$397$	−30.6341			−1.53748			−0.768741	−	0.639560i	$-0.779116\pi$
$397$	−30.6341			−1.53748			−0.768741	+	0.639560i	$0.779116\pi$
$398$	−18.8571	−	13.7005i	−0.945219	−	0.686742i
$399$		0			0
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−16.1537	+	11.7364i	−0.806678	+	0.586086i	−0.912865	−	0.408260i	$-0.866136\pi$
$401$	−16.1537	+	11.7364i	−0.806678	+	0.586086i	0.106188	+	0.994346i	$0.466136\pi$
$402$		0			0
$403$	3.49871	+	10.7679i	0.174283	+	0.536389i
$404$	3.28820	−	10.1200i	0.163594	−	0.503491i
$405$		0			0
$406$	10.3141			0.511883
$407$	12.9192	+	1.80423i	0.640382	+	0.0894322i
$408$		0			0
$409$	5.77608	+	4.19656i	0.285609	+	0.207507i	0.721360	−	0.692560i	$-0.243517\pi$
$409$	5.77608	+	4.19656i	0.285609	+	0.207507i	−0.435751	+	0.900067i	$0.643517\pi$
$410$	3.67612	−	11.3139i	0.181551	−	0.558756i
$411$		0			0
$412$	−13.5176	+	9.82110i	−0.665964	+	0.483851i
$413$	−22.0147	+	15.9946i	−1.08327	+	0.787045i
$414$		0			0
$415$	2.47214	−	7.60845i	0.121352	−	0.373484i
$416$	−1.07877	−	0.783769i	−0.0528908	−	0.0384274i
$417$		0			0
$418$	0.0454545	+	0.256481i	0.00222325	+	0.0125449i
$419$	22.3691			1.09280			0.546400	−	0.837524i	$-0.315998\pi$
$419$	22.3691			1.09280			0.546400	+	0.837524i	$0.315998\pi$
$420$		0			0
$421$	−1.87292	+	5.76427i	−0.0912807	+	0.280933i	−0.986267	−	0.165161i	$-0.947186\pi$
$421$	−1.87292	+	5.76427i	−0.0912807	+	0.280933i	0.894986	+	0.446095i	$0.147186\pi$
$422$	−6.20635	−	19.1012i	−0.302120	−	0.929831i
$423$		0			0
$424$	8.36933	−	6.08067i	0.406451	−	0.295304i
$425$	−0.239663	−	0.737606i	−0.0116254	−	0.0357791i
$426$		0			0
$427$	15.4826	+	11.2487i	0.749254	+	0.544365i
$428$	−17.5511			−0.848366
$429$		0			0
$430$	−6.01163			−0.289907
$431$	30.0649	+	21.8434i	1.44818	+	1.05216i	0.986253	+	0.165240i	$0.0528399\pi$
$431$	30.0649	+	21.8434i	1.44818	+	1.05216i	0.461922	+	0.886921i	$0.347160\pi$
$432$		0			0
$433$	9.47259	+	29.1536i	0.455224	+	1.40103i	0.870872	+	0.491509i	$0.163555\pi$
$433$	9.47259	+	29.1536i	0.455224	+	1.40103i	−0.415649	+	0.909525i	$0.636445\pi$
$434$	−35.0954	+	25.4983i	−1.68463	+	1.22396i
$435$		0			0
$436$	−2.76393	−	8.50651i	−0.132368	−	0.407388i
$437$	0.161354	−	0.496597i	0.00771861	−	0.0237554i
$438$		0			0
$439$	7.06017			0.336964			0.168482	−	0.985705i	$-0.446114\pi$
$439$	7.06017			0.336964			0.168482	+	0.985705i	$0.446114\pi$
$440$	−3.28475	−	0.458729i	−0.156594	−	0.0218691i
$441$		0			0
$442$	0.836653	+	0.607864i	0.0397955	+	0.0289131i
$443$	−4.50932	+	13.8783i	−0.214244	+	0.659377i	0.784962	+	0.619544i	$0.212682\pi$
$443$	−4.50932	+	13.8783i	−0.214244	+	0.659377i	−0.999206	+	0.0398326i	$0.987318\pi$
$444$		0			0
$445$	−7.82983	+	5.68871i	−0.371170	+	0.269671i
$446$	−7.36933	+	5.35413i	−0.348948	+	0.253525i
$447$		0			0
$448$	1.57877	−	4.85894i	0.0745897	−	0.229563i
$449$	10.3301	+	7.50523i	0.487506	+	0.354194i	0.804224	−	0.594326i	$-0.202581\pi$
$449$	10.3301	+	7.50523i	0.487506	+	0.354194i	−0.316719	+	0.948520i	$0.602581\pi$
$450$		0			0
$451$	28.4055	+	27.3832i	1.33756	+	1.28942i
$452$	5.72703			0.269377
$453$		0			0
$454$	−6.39360	+	19.6775i	−0.300066	+	0.923510i
$455$	2.10517	+	6.47904i	0.0986919	+	0.303742i
$456$		0			0
$457$	14.0305	−	10.1937i	0.656317	−	0.476842i	−0.209100	−	0.977894i	$-0.567053\pi$
$457$	14.0305	−	10.1937i	0.656317	−	0.476842i	0.865417	+	0.501052i	$0.167053\pi$
$458$	3.39360	+	10.4444i	0.158572	+	0.488036i
$459$		0			0
$460$	5.37874	+	3.90788i	0.250785	+	0.182206i
$461$	2.99355			0.139424			0.0697118	−	0.997567i	$-0.477792\pi$
$461$	2.99355			0.139424			0.0697118	+	0.997567i	$0.477792\pi$
$462$		0			0
$463$	−16.2589			−0.755614			−0.377807	−	0.925884i	$-0.623322\pi$
$463$	−16.2589			−0.755614			−0.377807	+	0.925884i	$0.623322\pi$
$464$	−1.63326	−	1.18663i	−0.0758223	−	0.0550881i
$465$		0			0
$466$	0.915646	+	2.81807i	0.0424165	+	0.130545i
$467$	−15.0240	+	10.9156i	−0.695228	+	0.505113i	−0.878375	−	0.477973i	$-0.841372\pi$
$467$	−15.0240	+	10.9156i	−0.695228	+	0.505113i	0.183147	+	0.983086i	$0.441372\pi$
$468$		0			0
$469$	0.928370	+	2.85723i	0.0428682	+	0.131935i
$470$	−2.03009	+	6.24796i	−0.0936409	+	0.288197i
$471$		0			0
$472$	5.32624			0.245160
$473$	8.72480	−	17.9280i	0.401167	−	0.824332i
$474$		0			0
$475$	0.0635378	+	0.0461629i	0.00291531	+	0.00211810i
$476$	−1.22444	+	3.76842i	−0.0561219	+	0.172725i
$477$		0			0
$478$	6.93310	−	5.03719i	0.317112	−	0.230396i
$479$	−24.7198	+	17.9600i	−1.12948	+	0.820614i	−0.985619	−	0.168984i	$-0.945951\pi$
$479$	−24.7198	+	17.9600i	−1.12948	+	0.820614i	−0.143859	+	0.989598i	$0.545951\pi$
$480$		0			0
$481$	−1.62064	+	4.98781i	−0.0738948	+	0.227425i
$482$	−6.44787	−	4.68465i	−0.293692	−	0.213380i
$483$		0			0
$484$	6.13525	−	9.13010i	0.278875	−	0.415004i
$485$	−13.4541			−0.610917
$486$		0			0
$487$	−0.157074	+	0.483424i	−0.00711771	+	0.0219061i	−0.954552	−	0.298043i	$-0.903666\pi$
$487$	−0.157074	+	0.483424i	−0.00711771	+	0.0219061i	0.947435	+	0.319950i	$0.103666\pi$
$488$	−1.15753	−	3.56251i	−0.0523990	−	0.161267i
$489$		0			0
$490$	−15.4537	+	11.2278i	−0.698126	+	0.507218i
$491$	−12.1735	−	37.4662i	−0.549383	−	1.69083i	−0.710333	−	0.703865i	$-0.751456\pi$
$491$	−12.1735	−	37.4662i	−0.549383	−	1.69083i	0.160950	−	0.986963i	$-0.448544\pi$
$492$		0			0
$493$	1.26670	+	0.920312i	0.0570493	+	0.0414488i
$494$	−0.104723			−0.00471173
$495$		0			0
$496$	8.49096			0.381255
$497$	−9.56876	−	6.95211i	−0.429217	−	0.311845i
$498$		0			0
$499$	6.63175	+	20.4104i	0.296878	+	0.913696i	0.982584	+	0.185818i	$0.0594934\pi$
$499$	6.63175	+	20.4104i	0.296878	+	0.913696i	−0.685706	+	0.727878i	$0.740507\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$		0			0
$502$	−6.26057	−	19.2680i	−0.279423	−	0.859975i
$503$	7.27779	−	22.3987i	0.324500	−	0.998710i	−0.647165	−	0.762350i	$-0.724046\pi$
$503$	7.27779	−	22.3987i	0.324500	−	0.998710i	0.971666	−	0.236360i	$-0.0759544\pi$
$504$		0			0
$505$	10.6408			0.473511
$506$	−19.4605	+	10.3690i	−0.865123	+	0.460959i
$507$		0			0
$508$	5.63303	+	4.09264i	0.249925	+	0.181581i
$509$	−11.9645	+	36.8228i	−0.530316	+	1.63214i	0.223243	+	0.974763i	$0.428336\pi$
$509$	−11.9645	+	36.8228i	−0.530316	+	1.63214i	−0.753558	+	0.657381i	$0.771664\pi$
$510$		0			0
$511$	−45.2355	+	32.8655i	−2.00110	+	1.45389i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	6.16916	−	18.9867i	0.272110	−	0.837469i
$515$	−13.5176	−	9.82110i	−0.595656	−	0.432770i
$516$		0			0
$517$	−15.6865	−	15.1220i	−0.689893	−	0.665063i
$518$	−20.0942			−0.882887
$519$		0			0
$520$	0.412052	−	1.26816i	0.0180697	−	0.0556127i
$521$	−0.784660	−	2.41494i	−0.0343766	−	0.105800i	0.932396	−	0.361439i	$-0.117714\pi$
$521$	−0.784660	−	2.41494i	−0.0343766	−	0.105800i	−0.966772	+	0.255638i	$0.917714\pi$
$522$		0			0
$523$	−30.1927	+	21.9363i	−1.32024	+	0.959207i	−0.320306	+	0.947314i	$0.603786\pi$
$523$	−30.1927	+	21.9363i	−1.32024	+	0.959207i	−0.999929	+	0.0118928i	$0.996214\pi$
$524$	0.679579	+	2.09153i	0.0296875	+	0.0913688i
$525$		0			0
$526$	−0.563168	−	0.409166i	−0.0245553	−	0.0178405i
$527$	−6.58529			−0.286860
$528$		0			0
$529$	21.2024			0.921844
$530$	8.36933	+	6.08067i	0.363540	+	0.264128i
$531$		0			0
$532$	−0.123992	−	0.381607i	−0.00537572	−	0.0165448i
$533$	−12.8332	+	9.32386i	−0.555868	+	0.403861i
$534$		0			0
$535$	−5.42360	−	16.6921i	−0.234483	−	0.721663i
$536$	0.181713	−	0.559255i	0.00784880	−	0.0241561i
$537$		0			0
$538$	−5.92175			−0.255305
$539$	−11.0555	−	62.3814i	−0.476193	−	2.68696i
$540$		0			0
$541$	7.47140	+	5.42829i	0.321220	+	0.233380i	0.736696	−	0.676224i	$-0.236385\pi$
$541$	7.47140	+	5.42829i	0.321220	+	0.233380i	−0.415476	+	0.909604i	$0.636385\pi$
$542$	−4.29983	+	13.2335i	−0.184694	+	0.568429i
$543$		0			0
$544$	0.627445	−	0.455866i	0.0269015	−	0.0195451i
$545$	7.23607	−	5.25731i	0.309959	−	0.225198i
$546$		0			0
$547$	−7.84155	+	24.1338i	−0.335281	+	1.03189i	0.631303	+	0.775536i	$0.282520\pi$
$547$	−7.84155	+	24.1338i	−0.335281	+	1.03189i	−0.966584	+	0.256351i	$0.917480\pi$
$548$	−1.76034	−	1.27896i	−0.0751979	−	0.0546345i
$549$		0			0
$550$	−0.578765	−	3.26574i	−0.0246786	−	0.139251i
$551$	−0.158552			−0.00675456
$552$		0			0
$553$	19.4610	−	59.8947i	0.827564	−	2.54698i
$554$	−3.12186	−	9.60809i	−0.132635	−	0.408209i
$555$		0			0
$556$	−8.33887	+	6.05855i	−0.353647	+	0.256940i
$557$	3.27888	+	10.0913i	0.138930	+	0.427584i	0.996181	−	0.0873160i	$-0.0278290\pi$
$557$	3.27888	+	10.0913i	0.138930	+	0.427584i	−0.857250	+	0.514900i	$0.827829\pi$
$558$		0			0
$559$	6.48514	+	4.71173i	0.274292	+	0.199285i
$560$	5.10899			0.215894
$561$		0			0
$562$	−28.9081			−1.21941
$563$	−3.75748	−	2.72997i	−0.158359	−	0.115055i	0.505784	−	0.862660i	$-0.331203\pi$
$563$	−3.75748	−	2.72997i	−0.158359	−	0.115055i	−0.664143	+	0.747606i	$0.731203\pi$
$564$		0			0
$565$	1.76975	+	5.44673i	0.0744539	+	0.229145i
$566$	10.6152	−	7.71238i	0.446189	−	0.324175i
$567$		0			0
$568$	0.715393	+	2.20175i	0.0300172	+	0.0923836i
$569$	10.8497	−	33.3920i	0.454844	−	1.39987i	−0.416473	−	0.909148i	$-0.636734\pi$
$569$	10.8497	−	33.3920i	0.454844	−	1.39987i	0.871318	−	0.490719i	$-0.163266\pi$
$570$		0			0
$571$	17.7758			0.743896			0.371948	−	0.928254i	$-0.378690\pi$
$571$	17.7758			0.743896			0.371948	+	0.928254i	$0.378690\pi$
$572$	3.18393	+	3.06934i	0.133127	+	0.128336i
$573$		0			0
$574$	−49.1701	−	35.7241i	−2.05232	−	1.49110i
$575$	−2.05450	+	6.32309i	−0.0856784	+	0.263691i
$576$		0			0
$577$	−2.94029	+	2.13624i	−0.122406	+	0.0889329i	−0.647304	−	0.762232i	$-0.724103\pi$
$577$	−2.94029	+	2.13624i	−0.122406	+	0.0889329i	0.524898	+	0.851165i	$0.324103\pi$
$578$	13.2667	−	9.63880i	0.551820	−	0.400921i
$579$		0			0
$580$	0.623850	−	1.92001i	0.0259040	−	0.0797243i
$581$	−33.0661	−	24.0239i	−1.37181	−	0.996680i
$582$		0			0
$583$	−30.2805	+	16.1342i	−1.25409	+	0.668211i
$584$	10.9443			0.452877
$585$		0			0
$586$	−7.00236	+	21.5511i	−0.289265	+	0.890266i
$587$	−2.28461	−	7.03130i	−0.0942958	−	0.290213i	0.892774	−	0.450505i	$-0.148756\pi$
$587$	−2.28461	−	7.03130i	−0.0942958	−	0.290213i	−0.987070	+	0.160293i	$0.948756\pi$
$588$		0			0
$589$	0.539497	−	0.391967i	0.0222296	−	0.0161507i
$590$	1.64590	+	5.06555i	0.0677605	+	0.208546i
$591$		0			0
$592$	3.18194	+	2.31182i	0.130777	+	0.0950150i
$593$	35.9315			1.47553			0.737766	−	0.675057i	$-0.235881\pi$
$593$	35.9315			1.47553			0.737766	+	0.675057i	$0.235881\pi$
$594$		0			0
$595$	−3.96236			−0.162441
$596$	−12.3356	−	8.96237i	−0.505288	−	0.367113i
$597$		0			0
$598$	−2.73952	−	8.43138i	−0.112027	−	0.344785i
$599$	−16.6297	+	12.0822i	−0.679470	+	0.493664i	−0.873182	−	0.487395i	$-0.837947\pi$
$599$	−16.6297	+	12.0822i	−0.679470	+	0.493664i	0.193712	+	0.981058i	$0.437947\pi$
$600$		0			0
$601$	−1.58259	−	4.87071i	−0.0645551	−	0.198680i	0.913577	−	0.406667i	$-0.133309\pi$
$601$	−1.58259	−	4.87071i	−0.0645551	−	0.198680i	−0.978132	+	0.207986i	$0.933309\pi$
$602$	−9.49096	+	29.2102i	−0.386823	+	1.19052i
$603$		0			0
$604$	6.56921			0.267297
$605$	10.5791	+	3.01362i	0.430103	+	0.122521i
$606$		0			0
$607$	30.2529	+	21.9800i	1.22793	+	0.892141i	0.996733	−	0.0807668i	$-0.0257369\pi$
$607$	30.2529	+	21.9800i	1.22793	+	0.892141i	0.231194	+	0.972908i	$0.425737\pi$
$608$	−0.0242693	+	0.0746932i	−0.000984249	+	0.00302921i
$609$		0			0
$610$	3.03046	−	2.20175i	0.122700	−	0.0891464i
$611$	7.08694	−	5.14897i	0.286707	−	0.208305i
$612$		0			0
$613$	−2.59477	+	7.98588i	−0.104802	+	0.322546i	−0.989684	−	0.143268i	$-0.954239\pi$
$613$	−2.59477	+	7.98588i	−0.104802	+	0.322546i	0.884882	+	0.465815i	$0.154239\pi$
$614$	23.7170	+	17.2314i	0.957139	+	0.695403i
$615$		0			0
$616$	−7.41478	+	15.2362i	−0.298750	+	0.613883i
$617$	25.9029			1.04281			0.521406	−	0.853309i	$-0.325408\pi$
$617$	25.9029			1.04281			0.521406	+	0.853309i	$0.325408\pi$
$618$		0			0
$619$	7.76994	−	23.9134i	0.312300	−	0.961162i	−0.664551	−	0.747243i	$-0.731377\pi$
$619$	7.76994	−	23.9134i	0.312300	−	0.961162i	0.976851	−	0.213919i	$-0.0686228\pi$
$620$	2.62385	+	8.07538i	0.105376	+	0.324315i
$621$		0			0
$622$	9.18799	−	6.67546i	0.368405	−	0.267662i
$623$	15.2796	+	47.0258i	0.612165	+	1.88405i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−3.17664			−0.126964
$627$		0			0
$628$	−9.30815			−0.371436
$629$	−2.46780	−	1.79296i	−0.0983977	−	0.0714901i
$630$		0			0
$631$	−12.9922	−	39.9858i	−0.517210	−	1.59181i	−0.779224	−	0.626746i	$-0.784387\pi$
$631$	−12.9922	−	39.9858i	−0.517210	−	1.59181i	0.262014	−	0.965064i	$-0.415613\pi$
$632$	−9.97251	+	7.24545i	−0.396685	+	0.288209i
$633$		0			0
$634$	−1.46196	−	4.49946i	−0.0580620	−	0.178696i
$635$	−2.15163	+	6.62203i	−0.0853847	+	0.262787i
$636$		0			0
$637$	25.4709			1.00919
$638$	4.82051	+	4.64702i	0.190846	+	0.183977i
$639$		0			0
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	0.653762	−	2.01207i	0.0258220	−	0.0794720i	−0.937315	−	0.348483i	$-0.886697\pi$
$641$	0.653762	−	2.01207i	0.0258220	−	0.0794720i	0.963137	+	0.269011i	$0.0866968\pi$
$642$		0			0
$643$	31.9422	−	23.2073i	1.25968	−	0.915208i	0.260934	−	0.965357i	$-0.415970\pi$
$643$	31.9422	−	23.2073i	1.25968	−	0.915208i	0.998742	+	0.0501487i	$0.0159695\pi$
$644$	27.4799	−	19.9653i	1.08286	−	0.786745i
$645$		0			0
$646$	0.0188224	−	0.0579294i	0.000740558	−	0.00227920i
$647$	−13.0619	−	9.49005i	−0.513518	−	0.373092i	0.300639	−	0.953738i	$-0.402800\pi$
$647$	−13.0619	−	9.49005i	−0.513518	−	0.373092i	−0.814156	+	0.580646i	$0.802800\pi$
$648$		0			0
$649$	−17.4953	−	2.44330i	−0.686752	−	0.0959080i
$650$	1.33343			0.0523013
$651$		0			0
$652$	−5.77916	+	17.7864i	−0.226329	+	0.696570i
$653$	0.399046	+	1.22814i	0.0156159	+	0.0480607i	0.958561	−	0.284888i	$-0.0919564\pi$
$653$	0.399046	+	1.22814i	0.0156159	+	0.0480607i	−0.942945	+	0.332949i	$0.891956\pi$
$654$		0			0
$655$	−1.77916	+	1.29264i	−0.0695175	+	0.0505074i
$656$	3.67612	+	11.3139i	0.143529	+	0.441736i
$657$		0			0
$658$	27.1534	+	19.7281i	1.05855	+	0.769083i
$659$	23.7015			0.923278			0.461639	−	0.887068i	$-0.347262\pi$
$659$	23.7015			0.923278			0.461639	+	0.887068i	$0.347262\pi$
$660$		0			0
$661$	−17.0796			−0.664318			−0.332159	−	0.943223i	$-0.607777\pi$
$661$	−17.0796			−0.664318			−0.332159	+	0.943223i	$0.607777\pi$
$662$	−24.3048	−	17.6585i	−0.944632	−	0.686316i
$663$		0			0
$664$	2.47214	+	7.60845i	0.0959375	+	0.295265i
$665$	0.324614	−	0.235846i	0.0125880	−	0.00914572i
$666$		0			0
$667$	−4.14766	−	12.7652i	−0.160598	−	0.494270i
$668$	0.733846	−	2.25855i	0.0283934	−	0.0873858i
$669$		0			0
$670$	0.588036			0.0227178
$671$	2.16797	+	12.2330i	0.0836935	+	0.472248i
$672$		0			0
$673$	6.88530	+	5.00246i	0.265409	+	0.192831i	0.712528	−	0.701644i	$-0.247550\pi$
$673$	6.88530	+	5.00246i	0.265409	+	0.192831i	−0.447119	+	0.894474i	$0.647550\pi$
$674$	−7.83574	+	24.1159i	−0.301821	+	0.928910i
$675$		0			0
$676$	9.07877	−	6.59611i	0.349183	−	0.253697i
$677$	18.3748	−	13.3501i	0.706200	−	0.513084i	−0.175746	−	0.984436i	$-0.556234\pi$
$677$	18.3748	−	13.3501i	0.706200	−	0.513084i	0.881946	+	0.471351i	$0.156234\pi$
$678$		0			0
$679$	−21.2408	+	65.3724i	−0.815147	+	2.50876i
$680$	0.627445	+	0.455866i	0.0240614	+	0.0174816i
$681$		0			0
$682$	−27.8907	−	3.89505i	−1.06799	−	0.149149i
$683$	11.0419			0.422507			0.211254	−	0.977431i	$-0.432245\pi$
$683$	11.0419			0.422507			0.211254	+	0.977431i	$0.432245\pi$
$684$		0			0
$685$	0.672389	−	2.06940i	0.0256907	−	0.0790677i
$686$	19.1059	+	58.8019i	0.729467	+	2.24507i
$687$		0			0
$688$	4.86351	−	3.53355i	0.185420	−	0.134715i
$689$	−4.26270	−	13.1192i	−0.162396	−	0.499803i
$690$		0			0
$691$	−7.68513	−	5.58357i	−0.292356	−	0.212409i	0.431933	−	0.901906i	$-0.357832\pi$
$691$	−7.68513	−	5.58357i	−0.292356	−	0.212409i	−0.724289	+	0.689497i	$0.757832\pi$
$692$	−2.91427			−0.110784
$693$		0			0
$694$	3.17664			0.120583
$695$	−8.33887	−	6.05855i	−0.316312	−	0.229814i
$696$		0			0
$697$	−2.85107	−	8.77470i	−0.107992	−	0.332366i
$698$	5.62967	−	4.09019i	0.213086	−	0.154816i
$699$		0			0
$700$	1.57877	+	4.85894i	0.0596717	+	0.183651i
$701$	−7.97028	+	24.5300i	−0.301033	+	0.926486i	0.680094	+	0.733125i	$0.261939\pi$
$701$	−7.97028	+	24.5300i	−0.301033	+	0.926486i	−0.981128	+	0.193361i	$0.938061\pi$
$702$		0			0
$703$	0.308894			0.0116501
$704$	2.92705	−	1.55961i	0.110317	−	0.0587799i
$705$		0			0
$706$	6.48155	+	4.70912i	0.243936	+	0.177230i
$707$	16.7994	−	51.7032i	0.631806	−	1.94450i
$708$		0			0
$709$	11.1583	−	8.10696i	0.419058	−	0.304463i	−0.358201	−	0.933645i	$-0.616610\pi$
$709$	11.1583	−	8.10696i	0.419058	−	0.304463i	0.777259	+	0.629181i	$0.216610\pi$
$710$	−1.87292	+	1.36076i	−0.0702896	+	0.0510684i
$711$		0			0
$712$	2.99073	−	9.20452i	0.112082	−	0.344954i
$713$	45.6707	+	33.1817i	1.71038	+	1.24266i
$714$		0			0
$715$	−1.93523	+	3.97658i	−0.0723735	+	0.148716i
$716$	−1.56231			−0.0583861
$717$		0			0
$718$	0.0557281	−	0.171513i	0.00207975	−	0.00640082i
$719$	5.99601	+	18.4538i	0.223614	+	0.688212i	0.998429	+	0.0560248i	$0.0178426\pi$
$719$	5.99601	+	18.4538i	0.223614	+	0.688212i	−0.774816	+	0.632187i	$0.782157\pi$
$720$		0			0
$721$	−69.0613	+	50.1759i	−2.57198	+	1.86865i
$722$	−5.86942	−	18.0642i	−0.218437	−	0.672280i
$723$		0			0
$724$	−14.9443	−	10.8576i	−0.555399	−	0.403521i
$725$	2.01882			0.0749772
$726$		0			0
$727$	−1.37752			−0.0510895			−0.0255447	−	0.999674i	$-0.508132\pi$
$727$	−1.37752			−0.0510895			−0.0255447	+	0.999674i	$0.508132\pi$
$728$	−5.51140	−	4.00427i	−0.204266	−	0.148408i
$729$		0			0
$730$	3.38197	+	10.4086i	0.125172	+	0.385240i
$731$	−3.77197	+	2.74050i	−0.139511	+	0.101361i
$732$		0			0
$733$	6.76062	+	20.8070i	0.249709	+	0.768526i	0.994826	+	0.101592i	$0.0323936\pi$
$733$	6.76062	+	20.8070i	0.249709	+	0.768526i	−0.745117	+	0.666934i	$0.767606\pi$
$734$	9.53950	−	29.3596i	0.352109	−	1.08368i
$735$		0			0
$736$	−6.64849			−0.245067
$737$	−0.853428	+	1.75365i	−0.0314364	+	0.0645967i
$738$		0			0
$739$	−0.425058	−	0.308822i	−0.0156360	−	0.0113602i	0.579940	−	0.814659i	$-0.303076\pi$
$739$	−0.425058	−	0.308822i	−0.0156360	−	0.0113602i	−0.595576	+	0.803299i	$0.703076\pi$
$740$	−1.21539	+	3.74060i	−0.0446788	+	0.137507i
$741$		0			0
$742$	42.7588	−	31.0661i	1.56973	−	1.14047i
$743$	38.7413	−	28.1472i	1.42128	−	1.03262i	0.429720	−	0.902962i	$-0.358612\pi$
$743$	38.7413	−	28.1472i	1.42128	−	1.03262i	0.991559	−	0.129657i	$-0.0413876\pi$
$744$		0			0
$745$	4.71180	−	14.5014i	0.172627	−	0.531291i
$746$	−13.0266	−	9.46440i	−0.476939	−	0.346516i
$747$		0			0
$748$	−2.27012	+	1.20958i	−0.0830037	+	0.0442265i
$749$	−89.6686			−3.27642
$750$		0			0
$751$	11.1723	−	34.3848i	0.407683	−	1.25472i	−0.510951	−	0.859610i	$-0.670707\pi$
$751$	11.1723	−	34.3848i	0.407683	−	1.25472i	0.918634	−	0.395110i	$-0.129293\pi$
$752$	−2.03009	−	6.24796i	−0.0740296	−	0.227840i
$753$		0			0
$754$	−2.17784	+	1.58229i	−0.0793121	+	0.0576236i
$755$	2.03000	+	6.24769i	0.0738792	+	0.227377i
$756$		0			0
$757$	35.2824	+	25.6341i	1.28236	+	0.931689i	0.999622	−	0.0275084i	$-0.00875730\pi$
$757$	35.2824	+	25.6341i	1.28236	+	0.931689i	0.282738	+	0.959197i	$0.408757\pi$
$758$	32.5487			1.18222
$759$		0			0
$760$	−0.0785371			−0.00284884
$761$	−0.891747	−	0.647892i	−0.0323258	−	0.0234861i	0.571505	−	0.820599i	$-0.306360\pi$
$761$	−0.891747	−	0.647892i	−0.0323258	−	0.0234861i	−0.603831	+	0.797112i	$0.706360\pi$
$762$		0			0
$763$	−14.1209	−	43.4597i	−0.511211	−	1.57335i
$764$	16.7691	−	12.1835i	0.606685	−	0.440783i
$765$		0			0
$766$	−0.651486	−	2.00507i	−0.0235391	−	0.0724461i
$767$	2.19469	−	6.75455i	0.0792455	−	0.243893i
$768$		0			0
$769$	−26.9983			−0.973583			−0.486791	−	0.873518i	$-0.661833\pi$
$769$	−26.9983			−0.973583			−0.486791	+	0.873518i	$0.661833\pi$
$770$	−16.7818	−	2.34364i	−0.604772	−	0.0844591i
$771$		0			0
$772$	−1.10899	−	0.805730i	−0.0399135	−	0.0289989i
$773$	7.26427	−	22.3571i	0.261278	−	0.804130i	−0.731250	−	0.682109i	$-0.761063\pi$
$773$	7.26427	−	22.3571i	0.261278	−	0.804130i	0.992528	−	0.122020i	$-0.0389373\pi$
$774$		0			0
$775$	−6.86933	+	4.99086i	−0.246754	+	0.179277i
$776$	10.8846	−	7.90809i	0.390733	−	0.283884i
$777$		0			0
$778$	3.89460	−	11.9864i	0.139628	−	0.429732i
$779$	0.755858	+	0.549163i	0.0270814	+	0.0196758i
$780$		0			0
$781$	−1.33988	−	7.56038i	−0.0479446	−	0.270532i
$782$	5.15633			0.184390
$783$		0			0
$784$	5.90278	−	18.1669i	0.210814	−	0.648818i
$785$	−2.87638	−	8.85258i	−0.102662	−	0.315962i
$786$		0			0
$787$	26.1826	−	19.0227i	0.933308	−	0.678088i	−0.0134929	−	0.999909i	$-0.504295\pi$
$787$	26.1826	−	19.0227i	0.933308	−	0.678088i	0.946800	+	0.321821i	$0.104295\pi$
$788$	1.54859	+	4.76608i	0.0551663	+	0.169784i
$789$		0			0
$790$	−9.97251	−	7.24545i	−0.354806	−	0.257782i
$791$	29.2593			1.04034
$792$		0			0
$793$	−4.99482			−0.177371
$794$	24.7835	+	18.0063i	0.879534	+	0.639019i
$795$		0			0
$796$	7.20276	+	22.1678i	0.255295	+	0.785717i
$797$	−32.6868	+	23.7483i	−1.15782	+	0.841209i	−0.989501	−	0.144523i	$-0.953835\pi$
$797$	−32.6868	+	23.7483i	−1.15782	+	0.841209i	−0.168323	+	0.985732i	$0.553835\pi$
$798$		0			0
$799$	1.57446	+	4.84570i	0.0557005	+	0.171429i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$		0			0
$802$	19.9671			0.705062
$803$	−35.9492	−	5.02046i	−1.26862	−	0.177168i
$804$		0			0
$805$	27.4799	+	19.9653i	0.968541	+	0.703686i
$806$	3.49871	−	10.7679i	0.123237	−	0.379284i
$807$		0			0
$808$	−8.60862	+	6.25453i	−0.302850	+	0.220034i
$809$	9.89956	−	7.19245i	0.348050	−	0.252873i	−0.400001	−	0.916515i	$-0.630990\pi$
$809$	9.89956	−	7.19245i	0.348050	−	0.252873i	0.748050	+	0.663642i	$0.230990\pi$
$810$		0			0
$811$	−4.68730	+	14.4260i	−0.164593	+	0.506566i	−0.999006	−	0.0445737i	$-0.985807\pi$
$811$	−4.68730	+	14.4260i	−0.164593	+	0.506566i	0.834413	+	0.551140i	$0.185807\pi$
$812$	−8.34432	−	6.06250i	−0.292828	−	0.212752i
$813$		0			0
$814$	−9.39138	−	9.05338i	−0.329168	−	0.317321i
$815$	−18.7018			−0.655094
$816$		0			0
$817$	0.145898	−	0.449028i	0.00510433	−	0.0157095i
$818$	−2.20626	−	6.79018i	−0.0771402	−	0.237413i
$819$		0			0
$820$	−9.62422	+	6.99241i	−0.336092	+	0.244185i
$821$	4.47242	+	13.7647i	0.156088	+	0.480391i	0.998270	−	0.0588039i	$-0.0187287\pi$
$821$	4.47242	+	13.7647i	0.156088	+	0.480391i	−0.842181	+	0.539195i	$0.818729\pi$
$822$		0			0
$823$	−2.86910	−	2.08452i	−0.100011	−	0.0726619i	0.536656	−	0.843801i	$-0.319687\pi$
$823$	−2.86910	−	2.08452i	−0.100011	−	0.0726619i	−0.636667	+	0.771139i	$0.719687\pi$
$824$	16.7087			0.582074
$825$		0			0
$826$	27.2117			0.946816
$827$	−30.1130	−	21.8784i	−1.04713	−	0.760785i	−0.0754661	−	0.997148i	$-0.524044\pi$
$827$	−30.1130	−	21.8784i	−1.04713	−	0.760785i	−0.971665	+	0.236363i	$0.924044\pi$
$828$		0			0
$829$	−12.6297	−	38.8701i	−0.438646	−	1.35001i	−0.889303	−	0.457318i	$-0.848810\pi$
$829$	−12.6297	−	38.8701i	−0.438646	−	1.35001i	0.450657	−	0.892697i	$-0.351190\pi$
$830$	−6.47214	+	4.70228i	−0.224651	+	0.163219i
$831$		0			0
$832$	0.412052	+	1.26816i	0.0142853	+	0.0439657i
$833$	−4.57799	+	14.0896i	−0.158618	+	0.488176i
$834$		0			0
$835$	2.37478			0.0821825
$836$	0.113982	−	0.234215i	0.00394216	−	0.00810050i
$837$		0			0
$838$	−18.0970	−	13.1482i	−0.625149	−	0.454197i
$839$	5.07209	−	15.6103i	0.175108	−	0.538927i	−0.824530	−	0.565818i	$-0.808561\pi$
$839$	5.07209	−	15.6103i	0.175108	−	0.538927i	0.999638	+	0.0268909i	$0.00856067\pi$
$840$		0			0
$841$	20.1642	−	14.6502i	0.695318	−	0.505178i
$842$	4.90338	−	3.56251i	0.168982	−	0.122772i
$843$		0			0
$844$	−6.20635	+	19.1012i	−0.213631	+	0.657490i
$845$	9.07877	+	6.59611i	0.312319	+	0.226913i
$846$		0			0
$847$	31.3450	−	46.6456i	1.07703	−	1.60276i
$848$	−10.3451			−0.355251
$849$		0			0
$850$	−0.239663	+	0.737606i	−0.00822036	+	0.0252997i
$851$	8.08053	+	24.8693i	0.276997	+	0.852509i
$852$		0			0
$853$	−14.7144	+	10.6906i	−0.503811	+	0.366040i	−0.810471	−	0.585779i	$-0.800789\pi$
$853$	−14.7144	+	10.6906i	−0.503811	+	0.366040i	0.306660	+	0.951819i	$0.400789\pi$
$854$	−5.91382	−	18.2009i	−0.202367	−	0.622820i
$855$		0			0
$856$	14.1992	+	10.3163i	0.485317	+	0.352604i
$857$	−48.5679			−1.65905			−0.829525	−	0.558470i	$-0.811389\pi$
$857$	−48.5679			−1.65905			−0.829525	+	0.558470i	$0.811389\pi$
$858$		0			0
$859$	−29.1564			−0.994805			−0.497402	−	0.867520i	$-0.665713\pi$
$859$	−29.1564			−0.994805			−0.497402	+	0.867520i	$0.665713\pi$
$860$	4.86351	+	3.53355i	0.165844	+	0.120493i
$861$		0			0
$862$	−11.4838	−	35.3434i	−0.391139	−	1.20380i
$863$	−24.0405	+	17.4664i	−0.818348	+	0.594564i	−0.916239	−	0.400633i	$-0.868790\pi$
$863$	−24.0405	+	17.4664i	−0.818348	+	0.594564i	0.0978910	+	0.995197i	$0.468790\pi$
$864$		0			0
$865$	−0.900560	−	2.77164i	−0.0306200	−	0.0942385i
$866$	9.47259	−	29.1536i	0.321892	−	0.990681i
$867$		0			0
$868$	43.3802			1.47242
$869$	36.0809	−	19.2248i	1.22396	−	0.652156i
$870$		0			0
$871$	−0.634352	−	0.460884i	−0.0214942	−	0.0156165i
$872$	−2.76393	+	8.50651i	−0.0935985	+	0.288067i
$873$		0			0
$874$	−0.422430	+	0.306914i	−0.0142889	+	0.0103815i
$875$	−4.13326	+	3.00299i	−0.139730	+	0.101520i
$876$		0			0
$877$	8.25674	−	25.4116i	0.278810	−	0.858090i	−0.709376	−	0.704831i	$-0.751023\pi$
$877$	8.25674	−	25.4116i	0.278810	−	0.858090i	0.988186	−	0.153259i	$-0.0489770\pi$
$878$	−5.71180	−	4.14986i	−0.192764	−	0.140051i
$879$		0			0
$880$	2.38778	+	2.30185i	0.0804921	+	0.0775952i
$881$	−2.72012			−0.0916431			−0.0458216	−	0.998950i	$-0.514591\pi$
$881$	−2.72012			−0.0916431			−0.0458216	+	0.998950i	$0.514591\pi$
$882$		0			0
$883$	10.7306	−	33.0255i	0.361114	−	1.11140i	−0.591265	−	0.806478i	$-0.701371\pi$
$883$	10.7306	−	33.0255i	0.361114	−	1.11140i	0.952379	−	0.304917i	$-0.0986289\pi$
$884$	−0.319573	−	0.983544i	−0.0107484	−	0.0330802i
$885$		0			0
$886$	11.8056	−	8.57724i	0.396616	−	0.288158i
$887$	11.5157	+	35.4418i	0.386661	+	1.19002i	0.935268	+	0.353939i	$0.115158\pi$
$887$	11.5157	+	35.4418i	0.386661	+	1.19002i	−0.548608	+	0.836080i	$0.684842\pi$
$888$		0			0
$889$	28.7791	+	20.9093i	0.965221	+	0.701274i
$890$	9.67821			0.324414
$891$		0			0
$892$	9.10899			0.304992
$893$	−0.417411	−	0.303267i	−0.0139681	−	0.0101484i
$894$		0			0
$895$	−0.482779	−	1.48584i	−0.0161375	−	0.0496662i
$896$	−4.13326	+	3.00299i	−0.138083	+	0.100323i
$897$		0			0
$898$	−3.94573	−	12.1437i	−0.131671	−	0.405241i
$899$	5.29709	−	16.3028i	0.176668	−	0.543728i
$900$		0			0
$901$	8.02327			0.267294
$902$	−6.88510	−	38.8498i	−0.229249	−	1.29356i
$903$		0			0
$904$	−4.63326	−	3.36626i	−0.154100	−	0.111960i
$905$	5.70820	−	17.5680i	0.189747	−	0.583982i
$906$		0			0
$907$	32.1937	−	23.3901i	1.06898	−	0.776656i	0.0932477	−	0.995643i	$-0.470275\pi$
$907$	32.1937	−	23.3901i	1.06898	−	0.776656i	0.975728	+	0.218987i	$0.0702752\pi$
$908$	16.7387	−	12.1613i	0.555492	−	0.403589i
$909$		0			0
$910$	2.10517	−	6.47904i	0.0697857	−	0.214778i
$911$	−10.3743	−	7.53738i	−0.343717	−	0.249725i	0.402512	−	0.915415i	$-0.368137\pi$
$911$	−10.3743	−	7.53738i	−0.343717	−	0.249725i	−0.746228	+	0.665690i	$0.768137\pi$
$912$		0			0
$913$	−4.63012	−	26.1259i	−0.153235	−	0.864641i
$914$	−17.3426			−0.573642
$915$		0			0
$916$	3.39360	−	10.4444i	0.112128	−	0.345093i
$917$	3.47196	+	10.6856i	0.114654	+	0.352870i
$918$		0			0
$919$	30.0258	−	21.8150i	0.990459	−	0.719610i	0.0304373	−	0.999537i	$-0.490310\pi$
$919$	30.0258	−	21.8150i	0.990459	−	0.719610i	0.960022	+	0.279926i	$0.0903100\pi$
$920$	−2.05450	−	6.32309i	−0.0677347	−	0.208466i
$921$		0			0
$922$	−2.42183	−	1.75956i	−0.0797588	−	0.0579482i
$923$	3.08697			0.101609
$924$		0			0
$925$	−3.93310			−0.129319
$926$	13.1537	+	9.55673i	0.432258	+	0.314054i
$927$		0			0
$928$	0.623850	+	1.92001i	0.0204789	+	0.0630276i
$929$	8.06590	−	5.86022i	0.264634	−	0.192268i	−0.447554	−	0.894257i	$-0.647705\pi$
$929$	8.06590	−	5.86022i	0.264634	−	0.192268i	0.712187	+	0.701989i	$0.247705\pi$
$930$		0			0
$931$	−0.463587	−	1.42677i	−0.0151935	−	0.0467606i
$932$	0.915646	−	2.81807i	0.0299930	−	0.0923090i
$933$		0			0
$934$	18.5707			0.607652
$935$	−1.85188	−	1.78523i	−0.0605630	−	0.0583833i
$936$		0			0
$937$	−9.68938	−	7.03975i	−0.316538	−	0.229979i	0.418159	−	0.908374i	$-0.362676\pi$
$937$	−9.68938	−	7.03975i	−0.316538	−	0.229979i	−0.734697	+	0.678395i	$0.762676\pi$
$938$	0.928370	−	2.85723i	0.0303124	−	0.0932919i
$939$		0			0
$940$	5.31483	−	3.86145i	0.173351	−	0.125947i
$941$	4.45765	−	3.23867i	0.145315	−	0.105578i	−0.512752	−	0.858537i	$-0.671374\pi$
$941$	4.45765	−	3.23867i	0.145315	−	0.105578i	0.658068	+	0.752959i	$0.271374\pi$
$942$		0			0
$943$	−24.4407	+	75.2207i	−0.795898	+	2.44952i
$944$	−4.30902	−	3.13068i	−0.140247	−	0.101895i
$945$		0			0
$946$	−17.5964	+	9.37578i	−0.572107	+	0.304833i
$947$	27.3946			0.890206			0.445103	−	0.895479i	$-0.353167\pi$
$947$	27.3946			0.890206			0.445103	+	0.895479i	$0.353167\pi$
$948$		0			0
$949$	4.50961	−	13.8791i	0.146388	−	0.450536i
$950$	−0.0242693	−	0.0746932i	−0.000787400	−	0.00242337i
$951$		0			0
$952$	3.20561	−	2.32901i	0.103895	−	0.0754838i
$953$	−2.46900	−	7.59879i	−0.0799787	−	0.246149i	0.903070	−	0.429493i	$-0.141308\pi$
$953$	−2.46900	−	7.59879i	−0.0799787	−	0.246149i	−0.983049	+	0.183344i	$0.941308\pi$
$954$		0			0
$955$	16.7691	+	12.1835i	0.542636	+	0.394248i
$956$	−8.56978			−0.277166
$957$		0			0
$958$	30.5554			0.987200
$959$	−8.99355	−	6.53420i	−0.290417	−	0.211000i
$960$		0			0
$961$	12.6995	+	39.0850i	0.409661	+	1.26081i
$962$	4.24289	−	3.08264i	0.136796	−	0.0993883i
$963$		0			0
$964$	2.46287	+	7.57992i	0.0793236	+	0.244133i
$965$	0.423597	−	1.30370i	0.0136361	−	0.0419675i
$966$		0			0
$967$	−19.0966			−0.614106			−0.307053	−	0.951692i	$-0.599343\pi$
$967$	−19.0966			−0.614106			−0.307053	+	0.951692i	$0.599343\pi$
$968$	−10.3301	+	3.78019i	−0.332021	+	0.121500i
$969$		0			0
$970$	10.8846	+	7.90809i	0.349482	+	0.253914i
$971$	−0.0462836	+	0.142446i	−0.00148531	+	0.00457131i	−0.951796	−	0.306730i	$-0.900765\pi$
$971$	−0.0462836	+	0.142446i	−0.00148531	+	0.00457131i	0.950311	+	0.311302i	$0.100765\pi$
$972$		0			0
$973$	−42.6032	+	30.9531i	−1.36580	+	0.992310i
$974$	0.411225	−	0.298773i	0.0131765	−	0.00957330i
$975$		0			0
$976$	−1.15753	+	3.56251i	−0.0370517	+	0.114033i
$977$	−15.4833	−	11.2493i	−0.495355	−	0.359897i	0.311885	−	0.950120i	$-0.399040\pi$
$977$	−15.4833	−	11.2493i	−0.495355	−	0.359897i	−0.807240	+	0.590223i	$0.799040\pi$
$978$		0			0
$979$	−14.0462	+	28.8626i	−0.448918	+	0.922452i
$980$	19.1018			0.610185
$981$		0			0
$982$	−12.1735	+	37.4662i	−0.388473	+	1.19560i
$983$	−2.65314	−	8.16553i	−0.0846221	−	0.260440i	0.899788	−	0.436327i	$-0.143721\pi$
$983$	−2.65314	−	8.16553i	−0.0846221	−	0.260440i	−0.984410	+	0.175887i	$0.943721\pi$
$984$		0			0
$985$	−4.05427	+	2.94560i	−0.129180	+	0.0938546i
$986$	−0.483837	−	1.48910i	−0.0154085	−	0.0474225i
$987$		0			0
$988$	0.0847231	+	0.0615549i	0.00269540	+	0.00195832i
$989$	39.9683			1.27092
$990$		0			0
$991$	−11.3086			−0.359230			−0.179615	−	0.983737i	$-0.557485\pi$
$991$	−11.3086			−0.359230			−0.179615	+	0.983737i	$0.557485\pi$
$992$	−6.86933	−	4.99086i	−0.218101	−	0.158460i
$993$		0			0
$994$	3.65494	+	11.2487i	0.115928	+	0.356789i
$995$	−18.8571	+	13.7005i	−0.597809	+	0.434334i
$996$		0			0
$997$	−11.4436	−	35.2196i	−0.362421	−	1.11542i	−0.951580	−	0.307400i	$-0.900541\pi$
$997$	−11.4436	−	35.2196i	−0.362421	−	1.11542i	0.589159	−	0.808017i	$-0.299459\pi$
$998$	6.63175	−	20.4104i	0.209924	−	0.646081i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.i.631.2		8
3.2	odd	2		330.2.m.f.301.2	yes	8
11.3	even	5	inner	990.2.n.i.91.2		8
33.5	odd	10		3630.2.a.bq.1.4		4
33.14	odd	10		330.2.m.f.91.2	✓	8
33.17	even	10		3630.2.a.bs.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.91.2	✓	8	33.14	odd	10
330.2.m.f.301.2	yes	8	3.2	odd	2
990.2.n.i.91.2		8	11.3	even	5	inner
990.2.n.i.631.2		8	1.1	even	1	trivial
3630.2.a.bq.1.4		4	33.5	odd	10
3630.2.a.bs.1.1		4	33.17	even	10

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.57877 + 4.85894i) q^{7} +(0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(-1.45132 + 2.98223i) q^{11} +(-1.07877 - 0.783769i) q^{13} +(1.57877 - 4.85894i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.627445 - 0.455866i) q^{17} +(-0.0242693 + 0.0746932i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(2.92705 - 1.55961i) q^{22} -6.64849 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.412052 + 1.26816i) q^{26} +(-4.13326 + 3.00299i) q^{28} +(0.623850 + 1.92001i) q^{29} +(-6.86933 - 4.99086i) q^{31} +1.00000 q^{32} -0.775565 q^{34} +(-4.13326 - 3.00299i) q^{35} +(-1.21539 - 3.74060i) q^{37} +(0.0635378 - 0.0461629i) q^{38} +(0.309017 + 0.951057i) q^{40} +(3.67612 - 11.3139i) q^{41} -6.01163 q^{43} +(-3.28475 - 0.458729i) q^{44} +(5.37874 + 3.90788i) q^{46} +(-2.03009 + 6.24796i) q^{47} +(-15.4537 + 11.2278i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(0.412052 - 1.26816i) q^{52} +(8.36933 + 6.08067i) q^{53} +(-0.578765 - 3.26574i) q^{55} +5.10899 q^{56} +(0.623850 - 1.92001i) q^{58} +(1.64590 + 5.06555i) q^{59} +(3.03046 - 2.20175i) q^{61} +(2.62385 + 8.07538i) q^{62} +(-0.809017 - 0.587785i) q^{64} +1.33343 q^{65} +0.588036 q^{67} +(0.627445 + 0.455866i) q^{68} +(1.57877 + 4.85894i) q^{70} +(-1.87292 + 1.36076i) q^{71} +(3.38197 + 10.4086i) q^{73} +(-1.21539 + 3.74060i) q^{74} -0.0785371 q^{76} +(-16.7818 - 2.34364i) q^{77} +(-9.97251 - 7.24545i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-9.62422 + 6.99241i) q^{82} +(-6.47214 + 4.70228i) q^{83} +(-0.239663 + 0.737606i) q^{85} +(4.86351 + 3.53355i) q^{86} +(2.38778 + 2.30185i) q^{88} +9.67821 q^{89} +(2.10517 - 6.47904i) q^{91} +(-2.05450 - 6.32309i) q^{92} +(5.31483 - 3.86145i) q^{94} +(-0.0242693 - 0.0746932i) q^{95} +(10.8846 + 7.90809i) q^{97} +19.1018 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8} + 8 q^{10} - 10 q^{11} + q^{13} + 3 q^{14} - 2 q^{16} - 3 q^{17} - 12 q^{19} - 2 q^{20} + 10 q^{22} - 2 q^{25} + q^{26} - 2 q^{28} - 27 q^{29} - 6 q^{31}+ \cdots + 62 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8 + 8 * q^10 - 10 * q^11 + q^13 + 3 * q^14 - 2 * q^16 - 3 * q^17 - 12 * q^19 - 2 * q^20 + 10 * q^22 - 2 * q^25 + q^26 - 2 * q^28 - 27 * q^29 - 6 * q^31 + 8 * q^32 + 22 * q^34 - 2 * q^35 - 4 * q^37 + 13 * q^38 - 2 * q^40 + 23 * q^41 - 2 * q^43 - 10 * q^44 - 5 * q^46 - 5 * q^47 - 53 * q^49 - 2 * q^50 + q^52 + 18 * q^53 + 5 * q^55 - 2 * q^56 - 27 * q^58 + 40 * q^59 - 20 * q^61 - 11 * q^62 - 2 * q^64 - 4 * q^65 + 18 * q^67 - 3 * q^68 + 3 * q^70 + 10 * q^71 + 36 * q^73 - 4 * q^74 - 2 * q^76 - 50 * q^77 - 11 * q^79 - 2 * q^80 - 12 * q^82 - 16 * q^83 - 8 * q^85 + 13 * q^86 + 5 * q^88 + 46 * q^89 - 39 * q^91 + 5 * q^92 + 15 * q^94 - 12 * q^95 + 16 * q^97 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more