LMFDB - Embedded newform 1134.2.k.a.647.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.4
Root			$1.27866 + 1.16834i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.a.971.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} +(-1.14420 - 2.38554i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} +(-1.14420 - 2.38554i) q^{7} +1.00000i q^{8} +(-3.07634 - 1.77612i) q^{10} +(-2.61745 - 1.51119i) q^{11} -1.02646i q^{13} +(2.18368 + 1.49384i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.809204 + 1.40158i) q^{17} +(-7.12643 + 4.11444i) q^{19} +3.55225 q^{20} +3.02237 q^{22} +(-2.90837 + 1.67915i) q^{23} +(-3.80924 + 6.59779i) q^{25} +(0.513232 + 0.888944i) q^{26} +(-2.63804 - 0.201867i) q^{28} +4.27608i q^{29} +(-5.18382 - 2.99288i) q^{31} +(0.866025 + 0.500000i) q^{32} -1.61841i q^{34} +(5.30650 - 7.75696i) q^{35} +(2.92323 + 5.06319i) q^{37} +(4.11444 - 7.12643i) q^{38} +(-3.07634 + 1.77612i) q^{40} -0.0944452 q^{41} -6.11799 q^{43} +(-2.61745 + 1.51119i) q^{44} +(1.67915 - 2.90837i) q^{46} +(2.57023 + 4.45176i) q^{47} +(-4.38163 + 5.45906i) q^{49} -7.61848i q^{50} +(-0.888944 - 0.513232i) q^{52} +(-2.76235 - 1.59484i) q^{53} -10.7362i q^{55} +(2.38554 - 1.14420i) q^{56} +(-2.13804 - 3.70319i) q^{58} +(4.42036 - 7.65628i) q^{59} +(4.06195 - 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(3.15775 - 1.82313i) q^{65} +(0.187838 - 0.325345i) q^{67} +(0.809204 + 1.40158i) q^{68} +(-0.717083 + 9.37097i) q^{70} +13.9868i q^{71} +(1.13546 + 0.655556i) q^{73} +(-5.06319 - 2.92323i) q^{74} +8.22889i q^{76} +(-0.610118 + 7.97313i) q^{77} +(-0.462067 - 0.800324i) q^{79} +(1.77612 - 3.07634i) q^{80} +(0.0817920 - 0.0472226i) q^{82} -10.8642 q^{83} -5.74899 q^{85} +(5.29833 - 3.05899i) q^{86} +(1.51119 - 2.61745i) q^{88} +(-2.35495 - 4.07888i) q^{89} +(-2.44867 + 1.17448i) q^{91} +3.35830i q^{92} +(-4.45176 - 2.57023i) q^{94} +(-25.3148 - 14.6155i) q^{95} -15.3956i q^{97} +(1.06507 - 6.91850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 4 * q^7	$ 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49} + 6 q^{52} - 36 q^{53} - 6 q^{56} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{70} - 18 q^{74} + 24 q^{77} - 16 q^{79} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 66 q^{95} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 - 12 * q^11 - 8 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^31 + 30 * q^35 - 2 * q^37 + 12 * q^41 + 4 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 - 2 * q^49 + 6 * q^52 - 36 * q^53 - 6 * q^56 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^70 - 18 * q^74 + 24 * q^77 - 16 * q^79 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 66 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.77612	+	3.07634i	0.794307	+	1.37578i	0.923278	+	0.384132i	$0.125499\pi$
$5$	1.77612	+	3.07634i	0.794307	+	1.37578i	−0.128971	+	0.991648i	$0.541167\pi$
$6$		0			0
$7$	−1.14420	−	2.38554i	−0.432466	−	0.901650i
$7$	−1.14420	−	2.38554i	−0.432466	−	0.901650i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.07634	−	1.77612i	−0.972824	−	0.561660i
$11$	−2.61745	−	1.51119i	−0.789191	−	0.455639i	0.0504869	−	0.998725i	$-0.483923\pi$
$11$	−2.61745	−	1.51119i	−0.789191	−	0.455639i	−0.839678	+	0.543085i	$0.817256\pi$
$12$		0			0
$13$		−	1.02646i		−	0.284690i	−0.989817	−	0.142345i	$-0.954536\pi$
$13$		−	1.02646i		−	0.284690i	0.989817	−	0.142345i	$-0.0454642\pi$
$14$	2.18368	+	1.49384i	0.583612	+	0.399246i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.809204	+	1.40158i	−0.196261	+	0.339934i	−0.947313	−	0.320309i	$-0.896213\pi$
$17$	−0.809204	+	1.40158i	−0.196261	+	0.339934i	0.751052	+	0.660243i	$0.229547\pi$
$18$		0			0
$19$	−7.12643	+	4.11444i	−1.63491	+	0.943918i	−0.652368	+	0.757903i	$0.726224\pi$
$19$	−7.12643	+	4.11444i	−1.63491	+	0.943918i	−0.982547	+	0.186016i	$0.940442\pi$
$20$	3.55225			0.794307
$21$		0			0
$22$	3.02237			0.644371
$23$	−2.90837	+	1.67915i	−0.606438	+	0.350127i	−0.771570	−	0.636144i	$-0.780528\pi$
$23$	−2.90837	+	1.67915i	−0.606438	+	0.350127i	0.165132	+	0.986271i	$0.447195\pi$
$24$		0			0
$25$	−3.80924	+	6.59779i	−0.761848	+	1.31956i
$26$	0.513232	+	0.888944i	0.100653	+	0.174336i
$27$		0			0
$28$	−2.63804	−	0.201867i	−0.498543	−	0.0381493i
$29$			4.27608i			0.794048i	0.917808	+	0.397024i	$0.129957\pi$
$29$			4.27608i			0.794048i	−0.917808	+	0.397024i	$0.870043\pi$
$30$		0			0
$31$	−5.18382	−	2.99288i	−0.931041	−	0.537537i	−0.0439006	−	0.999036i	$-0.513978\pi$
$31$	−5.18382	−	2.99288i	−0.931041	−	0.537537i	−0.887141	+	0.461499i	$0.847312\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	1.61841i		−	0.277555i
$35$	5.30650	−	7.75696i	0.896962	−	1.31117i
$36$		0			0
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	0.999752	−	0.0222846i	$-0.00709398\pi$
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	−0.519175	+	0.854668i	$0.673761\pi$
$38$	4.11444	−	7.12643i	0.667451	−	1.15606i
$39$		0			0
$40$	−3.07634	+	1.77612i	−0.486412	+	0.280830i
$41$	−0.0944452			−0.0147499			−0.00737493	−	0.999973i	$-0.502348\pi$
$41$	−0.0944452			−0.0147499			−0.00737493	+	0.999973i	$0.502348\pi$
$42$		0			0
$43$	−6.11799			−0.932985			−0.466492	−	0.884525i	$-0.654482\pi$
$43$	−6.11799			−0.932985			−0.466492	+	0.884525i	$0.654482\pi$
$44$	−2.61745	+	1.51119i	−0.394595	+	0.227820i
$45$		0			0
$46$	1.67915	−	2.90837i	0.247577	−	0.428816i
$47$	2.57023	+	4.45176i	0.374906	+	0.649356i	0.990313	−	0.138853i	$-0.0443416\pi$
$47$	2.57023	+	4.45176i	0.374906	+	0.649356i	−0.615407	+	0.788210i	$0.711008\pi$
$48$		0			0
$49$	−4.38163	+	5.45906i	−0.625946	+	0.779866i
$50$		−	7.61848i		−	1.07742i
$51$		0			0
$52$	−0.888944	−	0.513232i	−0.123274	−	0.0711725i
$53$	−2.76235	−	1.59484i	−0.379438	−	0.219068i	0.298136	−	0.954523i	$-0.403635\pi$
$53$	−2.76235	−	1.59484i	−0.379438	−	0.219068i	−0.677574	+	0.735455i	$0.736968\pi$
$54$		0			0
$55$		−	10.7362i		−	1.44767i
$56$	2.38554	−	1.14420i	0.318782	−	0.152900i
$57$		0			0
$58$	−2.13804	−	3.70319i	−0.280738	−	0.486253i
$59$	4.42036	−	7.65628i	0.575481	−	0.996763i	−0.420508	−	0.907289i	$-0.638148\pi$
$59$	4.42036	−	7.65628i	0.575481	−	0.996763i	0.995989	−	0.0894739i	$-0.0285186\pi$
$60$		0			0
$61$	4.06195	−	2.34517i	0.520080	−	0.300268i	−0.216887	−	0.976197i	$-0.569590\pi$
$61$	4.06195	−	2.34517i	0.520080	−	0.300268i	0.736967	+	0.675928i	$0.236257\pi$
$62$	5.98576			0.760192
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.15775	−	1.82313i	0.391671	−	0.226131i
$66$		0			0
$67$	0.187838	−	0.325345i	0.0229480	−	0.0397472i	−0.854323	−	0.519742i	$-0.826028\pi$
$67$	0.187838	−	0.325345i	0.0229480	−	0.0397472i	0.877271	+	0.479995i	$0.159361\pi$
$68$	0.809204	+	1.40158i	0.0981304	+	0.169967i
$69$		0			0
$70$	−0.717083	+	9.37097i	−0.0857078	+	1.12005i
$71$			13.9868i			1.65993i	0.557815	+	0.829966i	$0.311640\pi$
$71$			13.9868i			1.65993i	−0.557815	+	0.829966i	$0.688360\pi$
$72$		0			0
$73$	1.13546	+	0.655556i	0.132895	+	0.0767270i	0.564974	−	0.825109i	$-0.308886\pi$
$73$	1.13546	+	0.655556i	0.132895	+	0.0767270i	−0.432079	+	0.901836i	$0.642220\pi$
$74$	−5.06319	−	2.92323i	−0.588584	−	0.339819i
$75$		0			0
$76$			8.22889i			0.943918i
$77$	−0.610118	+	7.97313i	−0.0695294	+	0.908623i
$78$		0			0
$79$	−0.462067	−	0.800324i	−0.0519866	−	0.0900434i	0.838861	−	0.544346i	$-0.183222\pi$
$79$	−0.462067	−	0.800324i	−0.0519866	−	0.0900434i	−0.890848	+	0.454302i	$0.849889\pi$
$80$	1.77612	−	3.07634i	0.198577	−	0.343945i
$81$		0			0
$82$	0.0817920	−	0.0472226i	0.00903241	−	0.00521487i
$83$	−10.8642			−1.19250			−0.596250	−	0.802799i	$-0.703343\pi$
$83$	−10.8642			−1.19250			−0.596250	+	0.802799i	$0.703343\pi$
$84$		0			0
$85$	−5.74899			−0.623566
$86$	5.29833	−	3.05899i	0.571334	−	0.329860i
$87$		0			0
$88$	1.51119	−	2.61745i	0.161093	−	0.279021i
$89$	−2.35495	−	4.07888i	−0.249624	−	0.432361i	0.713798	−	0.700352i	$-0.246974\pi$
$89$	−2.35495	−	4.07888i	−0.249624	−	0.432361i	−0.963421	+	0.267991i	$0.913640\pi$
$90$		0			0
$91$	−2.44867	+	1.17448i	−0.256691	+	0.123119i
$92$			3.35830i			0.350127i
$93$		0			0
$94$	−4.45176	−	2.57023i	−0.459164	−	0.265099i
$95$	−25.3148	−	14.6155i	−2.59725	−	1.49952i
$96$		0			0
$97$		−	15.3956i		−	1.56319i	−0.623786	−	0.781595i	$-0.714406\pi$
$97$		−	15.3956i		−	1.56319i	0.623786	−	0.781595i	$-0.285594\pi$
$98$	1.06507	−	6.91850i	0.107588	−	0.698874i
$99$		0			0
$100$	3.80924	+	6.59779i	0.380924	+	0.659779i
$101$	−6.85234	+	11.8686i	−0.681833	+	1.18097i	0.292588	+	0.956239i	$0.405484\pi$
$101$	−6.85234	+	11.8686i	−0.681833	+	1.18097i	−0.974421	+	0.224731i	$0.927850\pi$
$102$		0			0
$103$	−2.64014	+	1.52429i	−0.260141	+	0.150192i	−0.624399	−	0.781106i	$-0.714656\pi$
$103$	−2.64014	+	1.52429i	−0.260141	+	0.150192i	0.364258	+	0.931298i	$0.381323\pi$
$104$	1.02646			0.100653
$105$		0			0
$106$	3.18968			0.309810
$107$	−11.3681	+	6.56336i	−1.09899	+	0.634504i	−0.935956	−	0.352116i	$-0.885462\pi$
$107$	−11.3681	+	6.56336i	−1.09899	+	0.634504i	−0.163037	+	0.986620i	$0.552129\pi$
$108$		0			0
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	−0.493692	−	0.869637i	$-0.664353\pi$
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	0.999974	−	0.00726875i	$-0.00231373\pi$
$110$	5.36811	+	9.29783i	0.511829	+	0.886514i
$111$		0			0
$112$	−1.49384	+	2.18368i	−0.141155	+	0.206338i
$113$			12.2999i			1.15707i	0.815656	+	0.578537i	$0.196376\pi$
$113$			12.2999i			1.15707i	−0.815656	+	0.578537i	$0.803624\pi$
$114$		0			0
$115$	−10.3313	−	5.96476i	−0.963396	−	0.556217i
$116$	3.70319	+	2.13804i	0.343833	+	0.198512i
$117$		0			0
$118$			8.84071i			0.813853i
$119$	4.26942	+	0.326704i	0.391377	+	0.0299489i
$120$		0			0
$121$	−0.932639	−	1.61538i	−0.0847854	−	0.146853i
$122$	−2.34517	+	4.06195i	−0.212322	+	0.367752i
$123$		0			0
$124$	−5.18382	+	2.99288i	−0.465521	+	0.268768i
$125$	−9.30148			−0.831950
$126$		0			0
$127$	0.287164			0.0254817			0.0127408	−	0.999919i	$-0.495944\pi$
$127$	0.287164			0.0254817			0.0127408	+	0.999919i	$0.495944\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.82313	+	3.15775i	−0.159899	+	0.276953i
$131$	0.186474	+	0.322983i	0.0162923	+	0.0282192i	0.874057	−	0.485824i	$-0.161480\pi$
$131$	0.186474	+	0.322983i	0.0162923	+	0.0282192i	−0.857764	+	0.514043i	$0.828147\pi$
$132$		0			0
$133$	17.9692	+	12.2927i	1.55813	+	1.06591i
$134$			0.375675i			0.0324534i
$135$		0			0
$136$	−1.40158	−	0.809204i	−0.120185	−	0.0693887i
$137$	−6.11607	−	3.53111i	−0.522531	−	0.301683i	0.215439	−	0.976517i	$-0.430882\pi$
$137$	−6.11607	−	3.53111i	−0.522531	−	0.301683i	−0.737969	+	0.674834i	$0.764215\pi$
$138$		0			0
$139$		−	14.5862i		−	1.23718i	−0.785713	−	0.618591i	$-0.787704\pi$
$139$		−	14.5862i		−	1.23718i	0.785713	−	0.618591i	$-0.212296\pi$
$140$	−4.06447	−	8.47404i	−0.343511	−	0.716187i
$141$		0			0
$142$	−6.99341	−	12.1129i	−0.586874	−	1.01650i
$143$	−1.55118	+	2.68672i	−0.129716	+	0.224675i
$144$		0			0
$145$	−13.1547	+	7.59485i	−1.09244	+	0.630718i
$146$	−1.31111			−0.108508
$147$		0			0
$148$	5.84647			0.480577
$149$	9.26832	−	5.35107i	0.759290	−	0.438376i	−0.0697505	−	0.997564i	$-0.522220\pi$
$149$	9.26832	−	5.35107i	0.759290	−	0.438376i	0.829041	+	0.559188i	$0.188887\pi$
$150$		0			0
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	0.331777	+	0.943358i	$0.392352\pi$
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	−0.982860	+	0.184352i	$0.940981\pi$
$152$	−4.11444	−	7.12643i	−0.333726	−	0.578030i
$153$		0			0
$154$	−3.45819	−	7.20999i	−0.278669	−	0.580998i
$155$		−	21.2629i		−	1.70788i
$156$		0			0
$157$	9.98239	+	5.76334i	0.796681	+	0.459964i	0.842309	−	0.538994i	$-0.181196\pi$
$157$	9.98239	+	5.76334i	0.796681	+	0.459964i	−0.0456280	+	0.998958i	$0.514529\pi$
$158$	0.800324	+	0.462067i	0.0636703	+	0.0367601i
$159$		0			0
$160$			3.55225i			0.280830i
$161$	7.33344	+	5.01677i	0.577956	+	0.395377i
$162$		0			0
$163$	1.37386	+	2.37960i	0.107609	+	0.186385i	0.914801	−	0.403904i	$-0.132347\pi$
$163$	1.37386	+	2.37960i	0.107609	+	0.186385i	−0.807192	+	0.590289i	$0.799014\pi$
$164$	−0.0472226	+	0.0817920i	−0.00368747	+	0.00638688i
$165$		0			0
$166$	9.40866	−	5.43209i	0.730254	−	0.421612i
$167$	5.53892			0.428614			0.214307	−	0.976766i	$-0.431251\pi$
$167$	5.53892			0.428614			0.214307	+	0.976766i	$0.431251\pi$
$168$		0			0
$169$	11.9464			0.918952
$170$	4.97877	−	2.87450i	0.381854	−	0.220464i
$171$		0			0
$172$	−3.05899	+	5.29833i	−0.233246	+	0.403994i
$173$	−5.60253	−	9.70387i	−0.425953	−	0.737772i	0.570556	−	0.821259i	$-0.306728\pi$
$173$	−5.60253	−	9.70387i	−0.425953	−	0.737772i	−0.996509	+	0.0834869i	$0.973394\pi$
$174$		0			0
$175$	20.0978	+	1.53792i	1.51925	+	0.116256i
$176$			3.02237i			0.227820i
$177$		0			0
$178$	4.07888	+	2.35495i	0.305725	+	0.176511i
$179$	−2.37445	−	1.37089i	−0.177475	−	0.102465i	0.408631	−	0.912700i	$-0.366006\pi$
$179$	−2.37445	−	1.37089i	−0.177475	−	0.102465i	−0.586106	+	0.810235i	$0.699340\pi$
$180$		0			0
$181$		−	22.2899i		−	1.65679i	−0.560142	−	0.828397i	$-0.689253\pi$
$181$		−	22.2899i		−	1.65679i	0.560142	−	0.828397i	$-0.310747\pi$
$182$	1.53338	−	2.24146i	0.113661	−	0.166148i
$183$		0			0
$184$	−1.67915	−	2.90837i	−0.123789	−	0.214408i
$185$	−10.3841	+	17.9857i	−0.763451	+	1.32234i
$186$		0			0
$187$	4.23610	−	2.44571i	0.309774	−	0.178848i
$188$	5.14045			0.374906
$189$		0			0
$190$	29.2311			2.12064
$191$	4.44499	−	2.56632i	0.321628	−	0.185692i	−0.330490	−	0.943810i	$-0.607214\pi$
$191$	4.44499	−	2.56632i	0.321628	−	0.185692i	0.652118	+	0.758117i	$0.273881\pi$
$192$		0			0
$193$	−7.99235	+	13.8432i	−0.575302	+	0.996452i	0.420707	+	0.907197i	$0.361782\pi$
$193$	−7.99235	+	13.8432i	−0.575302	+	0.996452i	−0.996009	+	0.0892557i	$0.971551\pi$
$194$	7.69782	+	13.3330i	0.552671	+	0.957254i
$195$		0			0
$196$	2.53687	+	6.52413i	0.181205	+	0.466009i
$197$		−	4.72572i		−	0.336694i	−0.985728	−	0.168347i	$-0.946157\pi$
$197$		−	4.72572i		−	0.336694i	0.985728	−	0.168347i	$-0.0538428\pi$
$198$		0			0
$199$	1.83679	+	1.06047i	0.130207	+	0.0751749i	0.563689	−	0.825987i	$-0.309382\pi$
$199$	1.83679	+	1.06047i	0.130207	+	0.0751749i	−0.433482	+	0.901162i	$0.642715\pi$
$200$	−6.59779	−	3.80924i	−0.466534	−	0.269354i
$201$		0			0
$202$		−	13.7047i		−	0.964258i
$203$	10.2008	−	4.89268i	0.715953	−	0.343399i
$204$		0			0
$205$	−0.167747	−	0.290545i	−0.0117159	−	0.0202926i
$206$	1.52429	−	2.64014i	0.106202	−	0.183947i
$207$		0			0
$208$	−0.888944	+	0.513232i	−0.0616372	+	0.0355863i
$209$	24.8707			1.72035
$210$		0			0
$211$	27.6159			1.90116			0.950578	−	0.310487i	$-0.100492\pi$
$211$	27.6159			1.90116			0.950578	+	0.310487i	$0.100492\pi$
$212$	−2.76235	+	1.59484i	−0.189719	+	0.109534i
$213$		0			0
$214$	6.56336	−	11.3681i	0.448662	−	0.777105i
$215$	−10.8663	−	18.8210i	−0.741076	−	1.28358i
$216$		0			0
$217$	−1.20833	+	15.7907i	−0.0820267	+	1.07194i
$218$			10.5715i			0.715990i
$219$		0			0
$220$	−9.29783	−	5.36811i	−0.626860	−	0.361918i
$221$	1.43867	+	0.830619i	0.0967757	+	0.0558735i
$222$		0			0
$223$			20.3469i			1.36253i	0.732037	+	0.681264i	$0.238570\pi$
$223$			20.3469i			1.36253i	−0.732037	+	0.681264i	$0.761430\pi$
$224$	0.201867	−	2.63804i	0.0134878	−	0.176261i
$225$		0			0
$226$	−6.14993	−	10.6520i	−0.409087	−	0.708560i
$227$	−2.08000	+	3.60266i	−0.138054	+	0.239117i	−0.926760	−	0.375654i	$-0.877418\pi$
$227$	−2.08000	+	3.60266i	−0.138054	+	0.239117i	0.788706	+	0.614771i	$0.210752\pi$
$228$		0			0
$229$	5.16986	−	2.98482i	0.341634	−	0.197242i	−0.319361	−	0.947633i	$-0.603468\pi$
$229$	5.16986	−	2.98482i	0.341634	−	0.197242i	0.660994	+	0.750391i	$0.270135\pi$
$230$	11.9295			0.786609
$231$		0			0
$232$	−4.27608			−0.280738
$233$	−3.88603	+	2.24360i	−0.254582	+	0.146983i	−0.621861	−	0.783128i	$-0.713623\pi$
$233$	−3.88603	+	2.24360i	−0.254582	+	0.146983i	0.367278	+	0.930111i	$0.380290\pi$
$234$		0			0
$235$	−9.13009	+	15.8138i	−0.595581	+	1.03158i
$236$	−4.42036	−	7.65628i	−0.287741	−	0.498381i
$237$		0			0
$238$	−3.86078	+	1.85178i	−0.250257	+	0.120033i
$239$		−	3.49809i		−	0.226273i	−0.993579	−	0.113136i	$-0.963910\pi$
$239$		−	3.49809i		−	0.226273i	0.993579	−	0.113136i	$-0.0360897\pi$
$240$		0			0
$241$	−10.0170	−	5.78332i	−0.645252	−	0.372537i	0.141383	−	0.989955i	$-0.454845\pi$
$241$	−10.0170	−	5.78332i	−0.645252	−	0.372537i	−0.786635	+	0.617419i	$0.788179\pi$
$242$	1.61538	+	0.932639i	0.103840	+	0.0599523i
$243$		0			0
$244$		−	4.69034i		−	0.300268i
$245$	−24.5762	−	3.78339i	−1.57012	−	0.241712i
$246$		0			0
$247$	4.22333	+	7.31502i	0.268724	+	0.465444i
$248$	2.99288	−	5.18382i	0.190048	−	0.329173i
$249$		0			0
$250$	8.05532	−	4.65074i	0.509463	−	0.294139i
$251$	26.7426			1.68798			0.843988	−	0.536361i	$-0.180202\pi$
$251$	26.7426			1.68798			0.843988	+	0.536361i	$0.180202\pi$
$252$		0			0
$253$	10.1500			0.638127
$254$	−0.248691	+	0.143582i	−0.0156043	+	0.00900913i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.60614	+	4.51396i	0.162566	+	0.281573i	0.935788	−	0.352562i	$-0.114690\pi$
$257$	2.60614	+	4.51396i	0.162566	+	0.281573i	−0.773222	+	0.634135i	$0.781356\pi$
$258$		0			0
$259$	8.73370	−	12.7668i	0.542686	−	0.793290i
$260$		−	3.64626i		−	0.226131i
$261$		0			0
$262$	−0.322983	−	0.186474i	−0.0199540	−	0.0115204i
$263$	13.0228	+	7.51869i	0.803018	+	0.463622i	0.844525	−	0.535516i	$-0.179883\pi$
$263$	13.0228	+	7.51869i	0.803018	+	0.463622i	−0.0415076	+	0.999138i	$0.513216\pi$
$264$		0			0
$265$		−	11.3306i		−	0.696030i
$266$	−21.7081	−	1.66114i	−1.33101	−	0.101851i
$267$		0			0
$268$	−0.187838	−	0.325345i	−0.0114740	−	0.0198736i
$269$	−11.5657	+	20.0323i	−0.705170	+	1.22139i	0.261460	+	0.965214i	$0.415796\pi$
$269$	−11.5657	+	20.0323i	−0.705170	+	1.22139i	−0.966630	+	0.256177i	$0.917537\pi$
$270$		0			0
$271$	8.58661	−	4.95748i	0.521599	−	0.301146i	−0.215989	−	0.976396i	$-0.569298\pi$
$271$	8.58661	−	4.95748i	0.521599	−	0.301146i	0.737589	+	0.675250i	$0.235964\pi$
$272$	1.61841			0.0981304
$273$		0			0
$274$	7.06222			0.426645
$275$	19.9410	−	11.5129i	1.20249	−	0.694256i
$276$		0			0
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	−0.707564	−	0.706650i	$-0.750206\pi$
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	0.965758	+	0.259443i	$0.0835391\pi$
$278$	7.29308	+	12.6320i	0.437410	+	0.757616i
$279$		0			0
$280$	7.75696	+	5.30650i	0.463567	+	0.317124i
$281$			20.7278i			1.23652i	0.785975	+	0.618258i	$0.212161\pi$
$281$			20.7278i			1.23652i	−0.785975	+	0.618258i	$0.787839\pi$
$282$		0			0
$283$	2.04997	+	1.18355i	0.121858	+	0.0703547i	0.559690	−	0.828702i	$-0.310920\pi$
$283$	2.04997	+	1.18355i	0.121858	+	0.0703547i	−0.437832	+	0.899057i	$0.644254\pi$
$284$	12.1129	+	6.99341i	0.718771	+	0.414983i
$285$		0			0
$286$		−	3.10236i		−	0.183446i
$287$	0.108064	+	0.225303i	0.00637882	+	0.0132992i
$288$		0			0
$289$	7.19038	+	12.4541i	0.422963	+	0.732594i
$290$	7.59485	−	13.1547i	0.445985	−	0.772468i
$291$		0			0
$292$	1.13546	−	0.655556i	0.0664475	−	0.0383635i
$293$	−17.6755			−1.03261			−0.516306	−	0.856404i	$-0.672693\pi$
$293$	−17.6755			−1.03261			−0.516306	+	0.856404i	$0.672693\pi$
$294$		0			0
$295$	31.4044			1.82844
$296$	−5.06319	+	2.92323i	−0.294292	+	0.169910i
$297$		0			0
$298$	−5.35107	+	9.26832i	−0.309979	+	0.536899i
$299$	1.72359	+	2.98534i	0.0996777	+	0.172647i
$300$		0			0
$301$	7.00019	+	14.5947i	0.403484	+	0.841226i
$302$		−	16.0013i		−	0.920771i
$303$		0			0
$304$	7.12643	+	4.11444i	0.408729	+	0.235980i
$305$	14.4291	+	8.33063i	0.826206	+	0.477011i
$306$		0			0
$307$			1.28155i			0.0731422i	0.999331	+	0.0365711i	$0.0116435\pi$
$307$			1.28155i			0.0731422i	−0.999331	+	0.0365711i	$0.988356\pi$
$308$	6.59987	+	4.51494i	0.376063	+	0.257263i
$309$		0			0
$310$	10.6315	+	18.4142i	0.603826	+	1.04586i
$311$	−6.26643	+	10.8538i	−0.355336	+	0.615461i	−0.987175	−	0.159639i	$-0.948967\pi$
$311$	−6.26643	+	10.8538i	−0.355336	+	0.615461i	0.631839	+	0.775100i	$0.282300\pi$
$312$		0			0
$313$	−7.58105	+	4.37692i	−0.428507	+	0.247398i	−0.698710	−	0.715405i	$-0.746242\pi$
$313$	−7.58105	+	4.37692i	−0.428507	+	0.247398i	0.270204	+	0.962803i	$0.412909\pi$
$314$	−11.5267			−0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$	11.8458	−	6.83920i	0.665329	−	0.384128i	−0.128976	−	0.991648i	$-0.541169\pi$
$317$	11.8458	−	6.83920i	0.665329	−	0.384128i	0.794304	+	0.607520i	$0.207836\pi$
$318$		0			0
$319$	6.46195	−	11.1924i	0.361799	−	0.626655i
$320$	−1.77612	−	3.07634i	−0.0992884	−	0.171973i
$321$		0			0
$322$	−8.85933	−	0.677931i	−0.493711	−	0.0377796i
$323$		−	13.3177i		−	0.741017i
$324$		0			0
$325$	6.77240	+	3.91005i	0.375665	+	0.216890i
$326$	−2.37960	−	1.37386i	−0.131794	−	0.0760912i
$327$		0			0
$328$		−	0.0944452i		−	0.00521487i
$329$	7.67902	−	11.2251i	0.423358	−	0.618859i
$330$		0			0
$331$	5.44858	+	9.43721i	0.299481	+	0.518716i	0.976017	−	0.217693i	$-0.0698532\pi$
$331$	5.44858	+	9.43721i	0.299481	+	0.518716i	−0.676536	+	0.736409i	$0.736520\pi$
$332$	−5.43209	+	9.40866i	−0.298125	+	0.516367i
$333$		0			0
$334$	−4.79685	+	2.76946i	−0.262472	+	0.151538i
$335$	1.33449			0.0729111
$336$		0			0
$337$	−25.6180			−1.39550			−0.697749	−	0.716342i	$-0.745815\pi$
$337$	−25.6180			−1.39550			−0.697749	+	0.716342i	$0.745815\pi$
$338$	−10.3459	+	5.97319i	−0.562741	+	0.324898i
$339$		0			0
$340$	−2.87450	+	4.97877i	−0.155891	+	0.270012i
$341$	9.04559	+	15.6674i	0.489846	+	0.848438i
$342$		0			0
$343$	18.0363	+	4.20631i	0.973867	+	0.227119i
$344$		−	6.11799i		−	0.329860i
$345$		0			0
$346$	9.70387	+	5.60253i	0.521683	+	0.301194i
$347$	14.5166	+	8.38116i	0.779291	+	0.449924i	0.836179	−	0.548457i	$-0.184784\pi$
$347$	14.5166	+	8.38116i	0.779291	+	0.449924i	−0.0568878	+	0.998381i	$0.518118\pi$
$348$		0			0
$349$		−	16.6802i		−	0.892871i	−0.894816	−	0.446435i	$-0.852693\pi$
$349$		−	16.6802i		−	0.892871i	0.894816	−	0.446435i	$-0.147307\pi$
$350$	−18.1742	+	8.71704i	−0.971452	+	0.465945i
$351$		0			0
$352$	−1.51119	−	2.61745i	−0.0805464	−	0.139511i
$353$	−17.9568	+	31.1021i	−0.955746	+	1.65540i	−0.223093	+	0.974797i	$0.571615\pi$
$353$	−17.9568	+	31.1021i	−0.955746	+	1.65540i	−0.732653	+	0.680603i	$0.761718\pi$
$354$		0			0
$355$	−43.0282	+	24.8424i	−2.28370	+	1.31850i
$356$	−4.70989			−0.249624
$357$		0			0
$358$	2.74178			0.144908
$359$	24.7248	−	14.2749i	1.30493	−	0.753399i	0.323681	−	0.946166i	$-0.395079\pi$
$359$	24.7248	−	14.2749i	1.30493	−	0.753399i	0.981245	+	0.192767i	$0.0617461\pi$
$360$		0			0
$361$	24.3573	−	42.1881i	1.28196	−	2.22043i
$362$	11.1449	+	19.3036i	0.585765	+	1.01457i
$363$		0			0
$364$	−0.207210	+	2.70785i	−0.0108607	+	0.141930i
$365$			4.65739i			0.243779i
$366$		0			0
$367$	−0.310665	−	0.179362i	−0.0162166	−	0.00936264i	0.491870	−	0.870669i	$-0.336314\pi$
$367$	−0.310665	−	0.179362i	−0.0162166	−	0.00936264i	−0.508086	+	0.861306i	$0.669647\pi$
$368$	2.90837	+	1.67915i	0.151609	+	0.0875317i
$369$		0			0
$370$		−	20.7681i		−	1.07968i
$371$	−0.643893	+	8.41451i	−0.0334293	+	0.436860i
$372$		0			0
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	−0.981433	−	0.191807i	$-0.938565\pi$
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	0.324606	−	0.945849i	$-0.394768\pi$
$374$	−2.44571	+	4.23610i	−0.126465	+	0.219044i
$375$		0			0
$376$	−4.45176	+	2.57023i	−0.229582	+	0.132549i
$377$	4.38924			0.226057
$378$		0			0
$379$	26.9063			1.38209			0.691043	−	0.722814i	$-0.257152\pi$
$379$	26.9063			1.38209			0.691043	+	0.722814i	$0.257152\pi$
$380$	−25.3148	+	14.6155i	−1.29862	+	0.749761i
$381$		0			0
$382$	−2.56632	+	4.44499i	−0.131304	+	0.227426i
$383$	−6.28586	−	10.8874i	−0.321192	−	0.556322i	0.659542	−	0.751668i	$-0.270750\pi$
$383$	−6.28586	−	10.8874i	−0.321192	−	0.556322i	−0.980734	+	0.195346i	$0.937417\pi$
$384$		0			0
$385$	−25.6117	+	12.2843i	−1.30529	+	0.626068i
$386$		−	15.9847i		−	0.813600i
$387$		0			0
$388$	−13.3330	−	7.69782i	−0.676881	−	0.390798i
$389$	14.0805	+	8.12937i	0.713909	+	0.412175i	0.812507	−	0.582952i	$-0.198102\pi$
$389$	14.0805	+	8.12937i	0.713909	+	0.412175i	−0.0985980	+	0.995127i	$0.531436\pi$
$390$		0			0
$391$		−	5.43510i		−	0.274865i
$392$	−5.45906	−	4.38163i	−0.275724	−	0.221305i
$393$		0			0
$394$	2.36286	+	4.09259i	0.119039	+	0.206182i
$395$	1.64138	−	2.84295i	0.0825866	−	0.143044i
$396$		0			0
$397$	−12.7252	+	7.34692i	−0.638662	+	0.368732i	−0.784099	−	0.620636i	$-0.786875\pi$
$397$	−12.7252	+	7.34692i	−0.638662	+	0.368732i	0.145437	+	0.989368i	$0.453541\pi$
$398$	−2.12095			−0.106313
$399$		0			0
$400$	7.61848			0.380924
$401$	−14.4162	+	8.32318i	−0.719909	+	0.415640i	−0.814719	−	0.579855i	$-0.803109\pi$
$401$	−14.4162	+	8.32318i	−0.719909	+	0.415640i	0.0948099	+	0.995495i	$0.469776\pi$
$402$		0			0
$403$	−3.07208	+	5.32101i	−0.153031	+	0.265058i
$404$	6.85234	+	11.8686i	0.340917	+	0.590485i
$405$		0			0
$406$	−6.38778	+	9.33756i	−0.317020	+	0.463416i
$407$		−	17.6702i		−	0.875879i
$408$		0			0
$409$	2.43254	+	1.40443i	0.120282	+	0.0694446i	0.558934	−	0.829212i	$-0.311211\pi$
$409$	2.43254	+	1.40443i	0.120282	+	0.0694446i	−0.438652	+	0.898657i	$0.644544\pi$
$410$	0.290545	+	0.167747i	0.0143490	+	0.00828441i
$411$		0			0
$412$			3.04857i			0.150192i
$413$	−23.3221	−	1.78465i	−1.14761	−	0.0878169i
$414$		0			0
$415$	−19.2962	−	33.4219i	−0.947211	−	1.64062i
$416$	0.513232	−	0.888944i	0.0251633	−	0.0435841i
$417$		0			0
$418$	−21.5387	+	12.4354i	−1.05349	+	0.608234i
$419$	−14.9472			−0.730221			−0.365110	−	0.930964i	$-0.618969\pi$
$419$	−14.9472			−0.730221			−0.365110	+	0.930964i	$0.618969\pi$
$420$		0			0
$421$	15.6067			0.760625			0.380312	−	0.924858i	$-0.375816\pi$
$421$	15.6067			0.760625			0.380312	+	0.924858i	$0.375816\pi$
$422$	−23.9160	+	13.8079i	−1.16421	+	0.672160i
$423$		0			0
$424$	1.59484	−	2.76235i	0.0774524	−	0.134151i
$425$	−6.16490	−	10.6779i	−0.299042	−	0.517955i
$426$		0			0
$427$	−10.2422	−	7.00663i	−0.495654	−	0.339074i
$428$			13.1267i			0.634504i
$429$		0			0
$430$	18.8210	+	10.8663i	0.907629	+	0.524020i
$431$	−14.0087	−	8.08792i	−0.674775	−	0.389581i	0.123109	−	0.992393i	$-0.460714\pi$
$431$	−14.0087	−	8.08792i	−0.674775	−	0.389581i	−0.797883	+	0.602812i	$0.794047\pi$
$432$		0			0
$433$			27.2499i			1.30955i	0.755824	+	0.654774i	$0.227236\pi$
$433$			27.2499i			1.30955i	−0.755824	+	0.654774i	$0.772764\pi$
$434$	−6.84889	−	14.2793i	−0.328757	−	0.685427i
$435$		0			0
$436$	−5.28574	−	9.15516i	−0.253141	−	0.438453i
$437$	13.8175	−	23.9327i	0.660983	−	1.14486i
$438$		0			0
$439$	−28.6955	+	16.5674i	−1.36956	+	0.790717i	−0.990872	−	0.134806i	$-0.956959\pi$
$439$	−28.6955	+	16.5674i	−1.36956	+	0.790717i	−0.378690	+	0.925523i	$0.623625\pi$
$440$	10.7362			0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$	19.2808	−	11.1318i	0.916060	−	0.528887i	0.0336837	−	0.999433i	$-0.489276\pi$
$443$	19.2808	−	11.1318i	0.916060	−	0.528887i	0.882376	+	0.470545i	$0.155943\pi$
$444$		0			0
$445$	8.36535	−	14.4892i	0.396556	−	0.686855i
$446$	−10.1734	−	17.6209i	−0.481727	−	0.834375i
$447$		0			0
$448$	1.14420	+	2.38554i	0.0540582	+	0.112706i
$449$			6.80819i			0.321298i	0.987012	+	0.160649i	$0.0513588\pi$
$449$			6.80819i			0.321298i	−0.987012	+	0.160649i	$0.948641\pi$
$450$		0			0
$451$	0.247206	+	0.142724i	0.0116405	+	0.00672062i
$452$	10.6520	+	6.14993i	0.501027	+	0.289268i
$453$		0			0
$454$		−	4.16000i		−	0.195238i
$455$	−7.96224	−	5.44693i	−0.373276	−	0.255356i
$456$		0			0
$457$	−7.61298	−	13.1861i	−0.356120	−	0.616818i	0.631189	−	0.775629i	$-0.282567\pi$
$457$	−7.61298	−	13.1861i	−0.356120	−	0.616818i	−0.987309	+	0.158811i	$0.949234\pi$
$458$	−2.98482	+	5.16986i	−0.139471	+	0.241572i
$459$		0			0
$460$	−10.3313	+	5.96476i	−0.481698	+	0.278108i
$461$	−0.206761			−0.00962983			−0.00481492	−	0.999988i	$-0.501533\pi$
$461$	−0.206761			−0.00962983			−0.00481492	+	0.999988i	$0.501533\pi$
$462$		0			0
$463$	15.2043			0.706605			0.353303	−	0.935509i	$-0.385059\pi$
$463$	15.2043			0.706605			0.353303	+	0.935509i	$0.385059\pi$
$464$	3.70319	−	2.13804i	0.171916	−	0.0992560i
$465$		0			0
$466$	2.24360	−	3.88603i	0.103933	−	0.180017i
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	0.891495	−	0.453030i	$-0.149657\pi$
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	−0.838083	+	0.545542i	$0.816324\pi$
$468$		0			0
$469$	−0.991047	−	0.0758366i	−0.0457623	−	0.00350181i
$470$		−	18.2602i		−	0.842279i
$471$		0			0
$472$	7.65628	+	4.42036i	0.352409	+	0.203463i
$473$	16.0135	+	9.24541i	0.736303	+	0.425105i
$474$		0			0
$475$		−	62.6916i		−	2.87649i
$476$	2.41765	−	3.53408i	0.110813	−	0.161984i
$477$		0			0
$478$	1.74905	+	3.02944i	0.0799996	+	0.138563i
$479$	6.21659	−	10.7674i	0.284043	−	0.491977i	−0.688334	−	0.725394i	$-0.741657\pi$
$479$	6.21659	−	10.7674i	0.284043	−	0.491977i	0.972377	+	0.233417i	$0.0749908\pi$
$480$		0			0
$481$	5.19719	−	3.00060i	0.236971	−	0.136815i
$482$	11.5666			0.526846
$483$		0			0
$484$	−1.86528			−0.0847854
$485$	47.3622	−	27.3446i	2.15061	−	1.24165i
$486$		0			0
$487$	−18.6503	+	32.3033i	−0.845128	+	1.46380i	0.0403829	+	0.999184i	$0.487142\pi$
$487$	−18.6503	+	32.3033i	−0.845128	+	1.46380i	−0.885510	+	0.464620i	$0.846191\pi$
$488$	2.34517	+	4.06195i	0.106161	+	0.183876i
$489$		0			0
$490$	23.1753	−	9.01161i	1.04695	−	0.407103i
$491$		−	13.6475i		−	0.615905i	−0.951402	−	0.307952i	$-0.900356\pi$
$491$		−	13.6475i		−	0.615905i	0.951402	−	0.307952i	$-0.0996438\pi$
$492$		0			0
$493$	−5.99328	−	3.46022i	−0.269924	−	0.155840i
$494$	−7.31502	−	4.22333i	−0.329118	−	0.190017i
$495$		0			0
$496$			5.98576i			0.268768i
$497$	33.3662	−	16.0037i	1.49668	−	0.717864i
$498$		0			0
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	0.999415	−	0.0342021i	$-0.0108890\pi$
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	−0.529327	+	0.848418i	$0.677556\pi$
$500$	−4.65074	+	8.05532i	−0.207987	+	0.360245i
$501$		0			0
$502$	−23.1598	+	13.3713i	−1.03367	+	0.596790i
$503$	−22.3018			−0.994388			−0.497194	−	0.867639i	$-0.665636\pi$
$503$	−22.3018			−0.994388			−0.497194	+	0.867639i	$0.665636\pi$
$504$		0			0
$505$	−48.6824			−2.16634
$506$	−8.79018	+	5.07501i	−0.390771	+	0.225612i
$507$		0			0
$508$	0.143582	−	0.248691i	0.00637042	−	0.0110339i
$509$	−10.9589	−	18.9814i	−0.485746	−	0.841337i	0.514120	−	0.857719i	$-0.328119\pi$
$509$	−10.9589	−	18.9814i	−0.485746	−	0.841337i	−0.999866	+	0.0163813i	$0.994785\pi$
$510$		0			0
$511$	0.264671	−	3.45876i	0.0117083	−	0.153007i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−4.51396	−	2.60614i	−0.199102	−	0.114952i
$515$	−9.37844	−	5.41465i	−0.413264	−	0.238598i
$516$		0			0
$517$		−	15.5364i		−	0.683288i
$518$	−1.18021	+	15.4232i	−0.0518555	+	0.677657i
$519$		0			0
$520$	1.82313	+	3.15775i	0.0799495	+	0.138477i
$521$	13.3839	−	23.1816i	0.586358	−	1.01560i	−0.408346	−	0.912827i	$-0.633894\pi$
$521$	13.3839	−	23.1816i	0.586358	−	1.01560i	0.994705	−	0.102775i	$-0.0327723\pi$
$522$		0			0
$523$	14.8576	−	8.57805i	0.649678	−	0.375092i	−0.138655	−	0.990341i	$-0.544278\pi$
$523$	14.8576	−	8.57805i	0.649678	−	0.375092i	0.788333	+	0.615249i	$0.210945\pi$
$524$	0.372949			0.0162923
$525$		0			0
$526$	−15.0374			−0.655661
$527$	8.38954	−	4.84370i	0.365454	−	0.210995i
$528$		0			0
$529$	−5.86091	+	10.1514i	−0.254822	+	0.441365i
$530$	5.66528	+	9.81255i	0.246084	+	0.426230i
$531$		0			0
$532$	19.6304	−	9.41547i	0.851084	−	0.408212i
$533$			0.0969447i			0.00419914i
$534$		0			0
$535$	−40.3822	−	23.3147i	−1.74588	−	1.00798i
$536$	0.325345	+	0.187838i	0.0140527	+	0.00811336i
$537$		0			0
$538$		−	23.1313i		−	0.997262i
$539$	19.7183	−	7.66737i	0.849329	−	0.330257i
$540$		0			0
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	−0.989578	−	0.144000i	$-0.954004\pi$
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	0.370081	−	0.928999i	$-0.379330\pi$
$542$	−4.95748	+	8.58661i	−0.212942	+	0.368827i
$543$		0			0
$544$	−1.40158	+	0.809204i	−0.0600924	+	0.0346943i
$545$	37.5525			1.60857
$546$		0			0
$547$	32.8091			1.40281			0.701407	−	0.712761i	$-0.252555\pi$
$547$	32.8091			1.40281			0.701407	+	0.712761i	$0.252555\pi$
$548$	−6.11607	+	3.53111i	−0.261265	+	0.150842i
$549$		0			0
$550$	−11.5129	+	19.9410i	−0.490913	+	0.850286i
$551$	−17.5937	−	30.4732i	−0.749516	−	1.29820i
$552$		0			0
$553$	−1.38051	+	2.01801i	−0.0587053	+	0.0858144i
$554$			8.59443i			0.365142i
$555$		0			0
$556$	−12.6320	−	7.29308i	−0.535715	−	0.309295i
$557$	−40.0544	−	23.1254i	−1.69716	−	0.979855i	−0.948434	−	0.316975i	$-0.897333\pi$
$557$	−40.0544	−	23.1254i	−1.69716	−	0.979855i	−0.748725	−	0.662880i	$-0.769334\pi$
$558$		0			0
$559$			6.27990i			0.265611i
$560$	−9.37097	−	0.717083i	−0.395996	−	0.0303023i
$561$		0			0
$562$	−10.3639	−	17.9508i	−0.437174	−	0.757208i
$563$	−0.988637	+	1.71237i	−0.0416661	+	0.0721678i	−0.886106	−	0.463482i	$-0.846600\pi$
$563$	−0.988637	+	1.71237i	−0.0416661	+	0.0721678i	0.844440	+	0.535650i	$0.179933\pi$
$564$		0			0
$565$	−37.8385	+	21.8461i	−1.59188	+	0.919071i
$566$	−2.36710			−0.0994966
$567$		0			0
$568$	−13.9868			−0.586874
$569$	−28.5702	+	16.4950i	−1.19773	+	0.691508i	−0.960048	−	0.279836i	$-0.909720\pi$
$569$	−28.5702	+	16.4950i	−1.19773	+	0.691508i	−0.237679	+	0.971344i	$0.576387\pi$
$570$		0			0
$571$	−7.40326	+	12.8228i	−0.309817	+	0.536618i	−0.978322	−	0.207089i	$-0.933601\pi$
$571$	−7.40326	+	12.8228i	−0.309817	+	0.536618i	0.668505	+	0.743707i	$0.266934\pi$
$572$	1.55118	+	2.68672i	0.0648580	+	0.112337i
$573$		0			0
$574$	−0.206238	−	0.141086i	−0.00860820	−	0.00588883i
$575$		−	25.5851i		−	1.06697i
$576$		0			0
$577$	−15.9505	−	9.20901i	−0.664027	−	0.383376i	0.129783	−	0.991542i	$-0.458572\pi$
$577$	−15.9505	−	9.20901i	−0.664027	−	0.383376i	−0.793810	+	0.608166i	$0.791905\pi$
$578$	−12.4541	−	7.19038i	−0.518022	−	0.299080i
$579$		0			0
$580$			15.1897i			0.630718i
$581$	12.4308	+	25.9170i	0.515715	+	1.07522i
$582$		0			0
$583$	4.82020	+	8.34884i	0.199632	+	0.345774i
$584$	−0.655556	+	1.13546i	−0.0271271	+	0.0469855i
$585$		0			0
$586$	15.3074	−	8.83774i	0.632343	−	0.365084i
$587$	−46.2130			−1.90741			−0.953707	−	0.300739i	$-0.902767\pi$
$587$	−46.2130			−1.90741			−0.953707	+	0.300739i	$0.902767\pi$
$588$		0			0
$589$	49.2561			2.02956
$590$	−27.1970	+	15.7022i	−1.11968	+	0.646450i
$591$		0			0
$592$	2.92323	−	5.06319i	0.120144	−	0.208096i
$593$	6.80465	+	11.7860i	0.279434	+	0.483993i	0.971244	−	0.238086i	$-0.0765200\pi$
$593$	6.80465	+	11.7860i	0.279434	+	0.483993i	−0.691810	+	0.722079i	$0.743187\pi$
$594$		0			0
$595$	6.57798	+	13.7145i	0.269671	+	0.562238i
$596$		−	10.7021i		−	0.438376i
$597$		0			0
$598$	−2.98534	−	1.72359i	−0.122080	−	0.0704827i
$599$	20.4214	+	11.7903i	0.834396	+	0.481739i	0.855355	−	0.518042i	$-0.173339\pi$
$599$	20.4214	+	11.7903i	0.834396	+	0.481739i	−0.0209595	+	0.999780i	$0.506672\pi$
$600$		0			0
$601$			35.8841i			1.46374i	0.681443	+	0.731871i	$0.261353\pi$
$601$			35.8841i			1.46374i	−0.681443	+	0.731871i	$0.738647\pi$
$602$	−13.3597	−	9.13931i	−0.544501	−	0.372490i
$603$		0			0
$604$	8.00065	+	13.8575i	0.325542	+	0.563855i
$605$	3.31297	−	5.73823i	0.134691	−	0.233292i
$606$		0			0
$607$	16.8502	−	9.72845i	0.683928	−	0.394866i	−0.117406	−	0.993084i	$-0.537458\pi$
$607$	16.8502	−	9.72845i	0.683928	−	0.394866i	0.801333	+	0.598218i	$0.204124\pi$
$608$	−8.22889			−0.333726
$609$		0			0
$610$	−16.6613			−0.674595
$611$	4.56958	−	2.63825i	0.184865	−	0.106732i
$612$		0			0
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	0.0253526	+	0.999679i	$0.491929\pi$
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	−0.878423	+	0.477883i	$0.841404\pi$
$614$	−0.640777	−	1.10986i	−0.0258597	−	0.0447902i
$615$		0			0
$616$	−7.97313	−	0.610118i	−0.321247	−	0.0245823i
$617$			11.1274i			0.447972i	0.974592	+	0.223986i	$0.0719069\pi$
$617$			11.1274i			0.447972i	−0.974592	+	0.223986i	$0.928093\pi$
$618$		0			0
$619$	−8.71387	−	5.03096i	−0.350240	−	0.202211i	0.314551	−	0.949241i	$-0.398146\pi$
$619$	−8.71387	−	5.03096i	−0.350240	−	0.202211i	−0.664791	+	0.747029i	$0.731479\pi$
$620$	−18.4142	−	10.6315i	−0.739533	−	0.426969i
$621$		0			0
$622$		−	12.5329i		−	0.502522i
$623$	−7.03583	+	10.2849i	−0.281885	+	0.412055i
$624$		0			0
$625$	2.52560	+	4.37447i	0.101024	+	0.174979i
$626$	4.37692	−	7.58105i	0.174937	−	0.303000i
$627$		0			0
$628$	9.98239	−	5.76334i	0.398341	−	0.229982i
$629$	−9.46198			−0.377274
$630$		0			0
$631$	10.3528			0.412139			0.206070	−	0.978537i	$-0.433933\pi$
$631$	10.3528			0.412139			0.206070	+	0.978537i	$0.433933\pi$
$632$	0.800324	−	0.462067i	0.0318352	−	0.0183800i
$633$		0			0
$634$	−6.83920	+	11.8458i	−0.271619	+	0.470459i
$635$	0.510039	+	0.883413i	0.0202403	+	0.0350572i
$636$		0			0
$637$	5.60353	+	4.49758i	0.222020	+	0.178201i
$638$			12.9239i			0.511662i
$639$		0			0
$640$	3.07634	+	1.77612i	0.121603	+	0.0702075i
$641$	23.0678	+	13.3182i	0.911123	+	0.526037i	0.880792	−	0.473503i	$-0.157011\pi$
$641$	23.0678	+	13.3182i	0.911123	+	0.526037i	0.0303310	+	0.999540i	$0.490344\pi$
$642$		0			0
$643$			46.2449i			1.82372i	0.410498	+	0.911861i	$0.365355\pi$
$643$			46.2449i			1.82372i	−0.410498	+	0.911861i	$0.634645\pi$
$644$	8.01137	−	3.84256i	0.315692	−	0.151418i
$645$		0			0
$646$	6.65885	+	11.5335i	0.261989	+	0.453778i
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	0.372611	+	0.927988i	$0.378463\pi$
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	−0.989966	+	0.141303i	$0.954871\pi$
$648$		0			0
$649$	−23.1401	+	13.3600i	−0.908329	+	0.524424i
$650$	−7.82009			−0.306729
$651$		0			0
$652$	2.74773			0.107609
$653$	−39.9639	+	23.0732i	−1.56391	+	0.902924i	−0.567054	+	0.823681i	$0.691917\pi$
$653$	−39.9639	+	23.0732i	−1.56391	+	0.902924i	−0.996855	+	0.0792429i	$0.974750\pi$
$654$		0			0
$655$	−0.662404	+	1.14732i	−0.0258823	+	0.0448294i
$656$	0.0472226	+	0.0817920i	0.00184373	+	0.00319344i
$657$		0			0
$658$	−1.03769	+	13.5607i	−0.0404534	+	0.528652i
$659$		−	1.36315i		−	0.0531008i	−0.999647	−	0.0265504i	$-0.991548\pi$
$659$		−	1.36315i		−	0.0531008i	0.999647	−	0.0265504i	$-0.00845225\pi$
$660$		0			0
$661$	−6.23888	−	3.60202i	−0.242664	−	0.140102i	0.373736	−	0.927535i	$-0.378076\pi$
$661$	−6.23888	−	3.60202i	−0.242664	−	0.140102i	−0.616401	+	0.787433i	$0.711410\pi$
$662$	−9.43721	−	5.44858i	−0.366788	−	0.211765i
$663$		0			0
$664$		−	10.8642i		−	0.421612i
$665$	−5.90080	+	77.1127i	−0.228823	+	2.99030i
$666$		0			0
$667$	−7.18018	−	12.4364i	−0.278018	−	0.481541i
$668$	2.76946	−	4.79685i	0.107154	−	0.185596i
$669$		0			0
$670$	−1.15570	+	0.667247i	−0.0446488	+	0.0257780i
$671$	−14.1759			−0.547256
$672$		0			0
$673$	−38.9418			−1.50110			−0.750548	−	0.660816i	$-0.770210\pi$
$673$	−38.9418			−1.50110			−0.750548	+	0.660816i	$0.770210\pi$
$674$	22.1858	−	12.8090i	0.854565	−	0.493383i
$675$		0			0
$676$	5.97319	−	10.3459i	0.229738	−	0.397918i
$677$	−1.20505	−	2.08722i	−0.0463140	−	0.0802182i	0.841939	−	0.539573i	$-0.181414\pi$
$677$	−1.20505	−	2.08722i	−0.0463140	−	0.0802182i	−0.888253	+	0.459354i	$0.848081\pi$
$678$		0			0
$679$	−36.7269	+	17.6156i	−1.40945	+	0.676026i
$680$		−	5.74899i		−	0.220464i
$681$		0			0
$682$	−15.6674	−	9.04559i	−0.599937	−	0.346374i
$683$	24.5302	+	14.1625i	0.938624	+	0.541915i	0.889529	−	0.456879i	$-0.151033\pi$
$683$	24.5302	+	14.1625i	0.938624	+	0.541915i	0.0490952	+	0.998794i	$0.484366\pi$
$684$		0			0
$685$		−	25.0868i		−	0.958517i
$686$	−17.7230	+	5.37536i	−0.676668	+	0.205232i
$687$		0			0
$688$	3.05899	+	5.29833i	0.116623	+	0.201997i
$689$	−1.63705	+	2.83545i	−0.0623666	+	0.108022i
$690$		0			0
$691$	2.95334	−	1.70511i	0.112350	−	0.0648655i	−0.442772	−	0.896634i	$-0.646005\pi$
$691$	2.95334	−	1.70511i	0.112350	−	0.0648655i	0.555122	+	0.831769i	$0.312672\pi$
$692$	−11.2051			−0.425953
$693$		0			0
$694$	−16.7623			−0.636289
$695$	44.8719	−	25.9068i	1.70209	−	0.982702i
$696$		0			0
$697$	0.0764255	−	0.132373i	0.00289482	−	0.00501398i
$698$	8.34010	+	14.4455i	0.315678	+	0.546769i
$699$		0			0
$700$	11.3808	−	16.6363i	0.430154	−	0.628792i
$701$			51.4943i			1.94491i	0.233087	+	0.972456i	$0.425117\pi$
$701$			51.4943i			1.94491i	−0.233087	+	0.972456i	$0.574883\pi$
$702$		0			0
$703$	−41.6644	−	24.0550i	−1.57140	−	0.907251i
$704$	2.61745	+	1.51119i	0.0986488	+	0.0569549i
$705$		0			0
$706$		−	35.9137i		−	1.35163i
$707$	36.1535	+	2.76653i	1.35969	+	0.104046i
$708$		0			0
$709$	−5.04218	−	8.73331i	−0.189363	−	0.327986i	0.755675	−	0.654947i	$-0.227309\pi$
$709$	−5.04218	−	8.73331i	−0.189363	−	0.327986i	−0.945038	+	0.326960i	$0.893976\pi$
$710$	24.8424	−	43.0282i	0.932317	−	1.61482i
$711$		0			0
$712$	4.07888	−	2.35495i	0.152863	−	0.0882553i
$713$	20.1020			0.752825
$714$		0			0
$715$	−11.0203			−0.412137
$716$	−2.37445	+	1.37089i	−0.0887375	+	0.0512326i
$717$		0			0
$718$	−14.2749	+	24.7248i	−0.532734	+	0.922722i
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	−0.993526	−	0.113605i	$-0.963760\pi$
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	0.398378	−	0.917221i	$-0.369573\pi$
$720$		0			0
$721$	6.65709	+	4.55409i	0.247923	+	0.169603i
$722$			48.7146i			1.81297i
$723$		0			0
$724$	−19.3036	−	11.1449i	−0.717413	−	0.414198i
$725$	−28.2127	−	16.2886i	−1.04779	−	0.604943i
$726$		0			0
$727$			20.7079i			0.768014i	0.923330	+	0.384007i	$0.125456\pi$
$727$			20.7079i			0.768014i	−0.923330	+	0.384007i	$0.874544\pi$
$728$	−1.17448	−	2.44867i	−0.0435290	−	0.0907539i
$729$		0			0
$730$	−2.32870	−	4.03342i	−0.0861889	−	0.149284i
$731$	4.95070	−	8.57487i	0.183108	−	0.317153i
$732$		0			0
$733$	−7.69996	+	4.44558i	−0.284405	+	0.164201i	−0.635416	−	0.772170i	$-0.719171\pi$
$733$	−7.69996	+	4.44558i	−0.284405	+	0.164201i	0.351011	+	0.936371i	$0.385838\pi$
$734$	0.358725			0.0132408
$735$		0			0
$736$	−3.35830			−0.123789
$737$	−0.983312	+	0.567715i	−0.0362207	+	0.0209121i
$738$		0			0
$739$	−16.3882	+	28.3851i	−0.602848	+	1.04416i	0.389539	+	0.921010i	$0.372634\pi$
$739$	−16.3882	+	28.3851i	−0.602848	+	1.04416i	−0.992388	+	0.123154i	$0.960699\pi$
$740$	10.3841	+	17.9857i	0.381726	+	0.661168i
$741$		0			0
$742$	−3.64963	−	7.60913i	−0.133982	−	0.279340i
$743$		−	7.71403i		−	0.283000i	−0.989938	−	0.141500i	$-0.954807\pi$
$743$		−	7.71403i		−	0.283000i	0.989938	−	0.141500i	$-0.0451926\pi$
$744$		0			0
$745$	32.9234	+	19.0083i	1.20622	+	0.696411i
$746$	21.9718	+	12.6854i	0.804445	+	0.464446i
$747$		0			0
$748$		−	4.89143i		−	0.178848i
$749$	28.6645	+	19.6092i	1.04738	+	0.716506i
$750$		0			0
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	−0.997389	−	0.0722207i	$-0.976991\pi$
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	0.436149	−	0.899874i	$-0.356342\pi$
$752$	2.57023	−	4.45176i	0.0937265	−	0.162339i
$753$		0			0
$754$	−3.80120	+	2.19462i	−0.138431	+	0.0799234i
$755$	−56.8406			−2.06864
$756$		0			0
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$	−23.3016	+	13.4532i	−0.846351	+	0.488641i
$759$		0			0
$760$	14.6155	−	25.3148i	0.530161	−	0.918266i
$761$	−18.5959	−	32.2090i	−0.674099	−	1.16757i	−0.976731	−	0.214467i	$-0.931199\pi$
$761$	−18.5959	−	32.2090i	−0.674099	−	1.16757i	0.302632	−	0.953107i	$-0.402135\pi$
$762$		0			0
$763$	−27.8880	−	2.13403i	−1.00961	−	0.0772572i
$764$		−	5.13264i		−	0.185692i
$765$		0			0
$766$	10.8874	+	6.28586i	0.393379	+	0.227117i
$767$	−7.85890	−	4.53734i	−0.283768	−	0.163834i
$768$		0			0
$769$		−	14.1233i		−	0.509300i	−0.967033	−	0.254650i	$-0.918040\pi$
$769$		−	14.1233i		−	0.509300i	0.967033	−	0.254650i	$-0.0819603\pi$
$770$	16.0382	−	23.4444i	0.577977	−	0.844878i
$771$		0			0
$772$	7.99235	+	13.8432i	0.287651	+	0.498226i
$773$	15.4728	−	26.7996i	0.556517	−	0.963915i	−0.441267	−	0.897376i	$-0.645471\pi$
$773$	15.4728	−	26.7996i	0.556517	−	0.963915i	0.997784	−	0.0665393i	$-0.0211958\pi$
$774$		0			0
$775$	39.4928	−	22.8012i	1.41862	−	0.819043i
$776$	15.3956			0.552671
$777$		0			0
$778$	−16.2587			−0.582904
$779$	0.673057	−	0.388590i	0.0241148	−	0.0139227i
$780$		0			0
$781$	21.1367	−	36.6098i	0.756330	−	1.31000i
$782$	2.71755	+	4.70694i	0.0971794	+	0.168320i
$783$		0			0
$784$	6.91850	+	1.06507i	0.247089	+	0.0380381i
$785$			40.9456i			1.46141i
$786$		0			0
$787$	15.8704	+	9.16280i	0.565720	+	0.326619i	0.755438	−	0.655220i	$-0.227424\pi$
$787$	15.8704	+	9.16280i	0.565720	+	0.326619i	−0.189718	+	0.981839i	$0.560757\pi$
$788$	−4.09259	−	2.36286i	−0.145793	−	0.0841734i
$789$		0			0
$790$			3.28275i			0.116795i
$791$	29.3418	−	14.0735i	1.04328	−	0.500395i
$792$		0			0
$793$	−2.40723	−	4.16945i	−0.0854834	−	0.148062i
$794$	7.34692	−	12.7252i	0.260733	−	0.451602i
$795$		0			0
$796$	1.83679	−	1.06047i	0.0651034	−	0.0375875i
$797$	2.15361			0.0762849			0.0381424	−	0.999272i	$-0.487856\pi$
$797$	2.15361			0.0762849			0.0381424	+	0.999272i	$0.487856\pi$
$798$		0			0
$799$	−8.31935			−0.294318
$800$	−6.59779	+	3.80924i	−0.233267	+	0.134677i
$801$		0			0
$802$	8.32318	−	14.4162i	0.293902	−	0.509053i
$803$	−1.98133	−	3.43177i	−0.0699197	−	0.121104i
$804$		0			0
$805$	−2.40818	+	31.4705i	−0.0848772	+	1.10919i
$806$		−	6.14417i		−	0.216419i
$807$		0			0
$808$	−11.8686	−	6.85234i	−0.417536	−	0.241064i
$809$	17.0147	+	9.82342i	0.598204	+	0.345373i	0.768335	−	0.640048i	$-0.221086\pi$
$809$	17.0147	+	9.82342i	0.598204	+	0.345373i	−0.170131	+	0.985421i	$0.554419\pi$
$810$		0			0
$811$		−	12.3340i		−	0.433105i	−0.976271	−	0.216552i	$-0.930519\pi$
$811$		−	12.3340i		−	0.433105i	0.976271	−	0.216552i	$-0.0694812\pi$
$812$	0.863200	−	11.2805i	0.0302924	−	0.395867i
$813$		0			0
$814$	8.83510	+	15.3028i	0.309670	+	0.536364i
$815$	−4.88030	+	8.45293i	−0.170950	+	0.296093i
$816$		0			0
$817$	43.5994	−	25.1721i	1.52535	−	0.880661i
$818$	−2.80886			−0.0982095
$819$		0			0
$820$	−0.335493			−0.0117159
$821$	−19.3763	+	11.1869i	−0.676238	+	0.390426i	−0.798436	−	0.602079i	$-0.794339\pi$
$821$	−19.3763	+	11.1869i	−0.676238	+	0.390426i	0.122198	+	0.992506i	$0.461006\pi$
$822$		0			0
$823$	−13.5033	+	23.3883i	−0.470694	+	0.815266i	−0.999438	−	0.0335154i	$-0.989330\pi$
$823$	−13.5033	+	23.3883i	−0.470694	+	0.815266i	0.528744	+	0.848781i	$0.322663\pi$
$824$	−1.52429	−	2.64014i	−0.0531010	−	0.0919737i
$825$		0			0
$826$	21.0899	−	10.1155i	0.733811	−	0.351964i
$827$		−	26.3189i		−	0.915196i	−0.889159	−	0.457598i	$-0.848710\pi$
$827$		−	26.3189i		−	0.915196i	0.889159	−	0.457598i	$-0.151290\pi$
$828$		0			0
$829$	28.8691	+	16.6676i	1.00266	+	0.578888i	0.909035	−	0.416719i	$-0.136820\pi$
$829$	28.8691	+	16.6676i	1.00266	+	0.578888i	0.0936287	+	0.995607i	$0.470153\pi$
$830$	33.4219	+	19.2962i	1.16009	+	0.669779i
$831$		0			0
$832$			1.02646i			0.0355863i
$833$	−4.10570	−	10.5587i	−0.142254	−	0.365838i
$834$		0			0
$835$	9.83781	+	17.0396i	0.340452	+	0.589679i
$836$	12.4354	−	21.5387i	0.430086	−	0.744932i
$837$		0			0
$838$	12.9447	−	7.47362i	0.447167	−	0.258172i
$839$	37.3792			1.29047			0.645236	−	0.763983i	$-0.276759\pi$
$839$	37.3792			1.29047			0.645236	+	0.763983i	$0.276759\pi$
$840$		0			0
$841$	10.7152			0.369488
$842$	−13.5158	+	7.80336i	−0.465786	+	0.268922i
$843$		0			0
$844$	13.8079	−	23.9160i	0.475289	−	0.823224i
$845$	21.2182	+	36.7511i	0.729930	+	1.26428i
$846$		0			0
$847$	−2.78643	+	4.07316i	−0.0957429	+	0.139956i
$848$			3.18968i			0.109534i
$849$		0			0
$850$	10.6779	+	6.16490i	0.366250	+	0.211454i
$851$	−17.0037	−	9.81710i	−0.582880	−	0.336526i
$852$		0			0
$853$			5.37858i			0.184159i	0.995752	+	0.0920795i	$0.0293514\pi$
$853$			5.37858i			0.184159i	−0.995752	+	0.0920795i	$0.970649\pi$
$854$	12.3733	+	0.946827i	0.423406	+	0.0323997i
$855$		0			0
$856$	−6.56336	−	11.3681i	−0.224331	−	0.388553i
$857$	22.7000	−	39.3176i	0.775418	−	1.34306i	−0.159142	−	0.987256i	$-0.550873\pi$
$857$	22.7000	−	39.3176i	0.775418	−	1.34306i	0.934559	−	0.355807i	$-0.115794\pi$
$858$		0			0
$859$	−3.36261	+	1.94141i	−0.114731	+	0.0662399i	−0.556267	−	0.831003i	$-0.687767\pi$
$859$	−3.36261	+	1.94141i	−0.114731	+	0.0662399i	0.441536	+	0.897243i	$0.354434\pi$
$860$	−21.7326			−0.741076
$861$		0			0
$862$	16.1758			0.550951
$863$	−20.3332	+	11.7394i	−0.692152	+	0.399614i	−0.804418	−	0.594064i	$-0.797522\pi$
$863$	−20.3332	+	11.7394i	−0.692152	+	0.399614i	0.112266	+	0.993678i	$0.464189\pi$
$864$		0			0
$865$	19.9016	−	34.4706i	0.676674	−	1.17203i
$866$	−13.6250	−	23.5991i	−0.462995	−	0.801931i
$867$		0			0
$868$	13.0710	+	8.94178i	0.443657	+	0.303504i
$869$			2.79307i			0.0947486i
$870$		0			0
$871$	−0.333955	−	0.192809i	−0.0113156	−	0.00653308i
$872$	9.15516	+	5.28574i	0.310033	+	0.178998i
$873$		0			0
$874$			27.6351i			0.934770i
$875$	10.6427	+	22.1891i	0.359790	+	0.750128i
$876$		0			0
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	−0.997787	−	0.0664896i	$-0.978820\pi$
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	0.441312	−	0.897354i	$-0.354513\pi$
$878$	16.5674	−	28.6955i	0.559121	−	0.968427i
$879$		0			0
$880$	−9.29783	+	5.36811i	−0.313430	+	0.180959i
$881$	7.44403			0.250796			0.125398	−	0.992107i	$-0.459979\pi$
$881$	7.44403			0.250796			0.125398	+	0.992107i	$0.459979\pi$
$882$		0			0
$883$	−28.2839			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$883$	−28.2839			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$884$	1.43867	−	0.830619i	0.0483879	−	0.0279368i
$885$		0			0
$886$	−11.1318	+	19.2808i	−0.373980	+	0.647752i
$887$	6.06377	+	10.5028i	0.203602	+	0.352648i	0.949686	−	0.313203i	$-0.101402\pi$
$887$	6.06377	+	10.5028i	0.203602	+	0.352648i	−0.746085	+	0.665851i	$0.768069\pi$
$888$		0			0
$889$	−0.328572	−	0.685042i	−0.0110200	−	0.0229756i
$890$			16.7307i			0.560814i
$891$		0			0
$892$	17.6209	+	10.1734i	0.589992	+	0.340632i
$893$	−36.6331	−	21.1501i	−1.22588	−	0.707761i
$894$		0			0
$895$		−	9.73949i		−	0.325555i
$896$	−2.18368	−	1.49384i	−0.0729515	−	0.0499057i
$897$		0			0
$898$	−3.40409	−	5.89606i	−0.113596	−	0.196754i
$899$	12.7978	−	22.1664i	0.426830	−	0.739291i
$900$		0			0
$901$	4.47061	−	2.58111i	0.148938	−	0.0859891i
$902$	−0.285448			−0.00950439
$903$		0			0
$904$	−12.2999			−0.409087
$905$	68.5712	−	39.5896i	2.27938	−	1.31600i
$906$		0			0
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	−0.172709	−	0.984973i	$-0.555252\pi$
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	0.939366	−	0.342916i	$-0.111415\pi$
$908$	2.08000	+	3.60266i	0.0690272	+	0.119559i
$909$		0			0
$910$	9.61897	+	0.736060i	0.318866	+	0.0244002i
$911$			14.6975i			0.486949i	0.969907	+	0.243475i	$0.0782872\pi$
$911$			14.6975i			0.486949i	−0.969907	+	0.243475i	$0.921713\pi$
$912$		0			0
$913$	28.4365	+	16.4178i	0.941110	+	0.543350i
$914$	13.1861	+	7.61298i	0.436156	+	0.251815i
$915$		0			0
$916$		−	5.96964i		−	0.197242i
$917$	0.557126	−	0.814399i	0.0183979	−	0.0268938i
$918$		0			0
$919$	−12.9345	−	22.4033i	−0.426671	−	0.739015i	0.569904	−	0.821711i	$-0.306980\pi$
$919$	−12.9345	−	22.4033i	−0.426671	−	0.739015i	−0.996575	+	0.0826958i	$0.973647\pi$
$920$	5.96476	−	10.3313i	0.196652	−	0.340612i
$921$		0			0
$922$	0.179060	−	0.103381i	0.00589704	−	0.00340466i
$923$	14.3570			0.472566
$924$		0			0
$925$	−44.5412			−1.46451
$926$	−13.1673	+	7.60217i	−0.432706	+	0.249823i
$927$		0			0
$928$	−2.13804	+	3.70319i	−0.0701846	+	0.121563i
$929$	−6.59673	−	11.4259i	−0.216432	−	0.374870i	0.737283	−	0.675584i	$-0.236108\pi$
$929$	−6.59673	−	11.4259i	−0.216432	−	0.374870i	−0.953714	+	0.300714i	$0.902775\pi$
$930$		0			0
$931$	8.76432	−	56.9316i	0.287239	−	1.86586i
$932$			4.48720i			0.146983i
$933$		0			0
$934$	−1.99921	−	1.15424i	−0.0654161	−	0.0377680i
$935$	15.0477	+	8.68779i	0.492112	+	0.284121i
$936$		0			0
$937$		−	8.86021i		−	0.289451i	−0.989472	−	0.144725i	$-0.953770\pi$
$937$		−	8.86021i		−	0.289451i	0.989472	−	0.144725i	$-0.0462298\pi$
$938$	0.896190	−	0.429847i	0.0292616	−	0.0140350i
$939$		0			0
$940$	9.13009	+	15.8138i	0.297791	+	0.515788i
$941$	2.05919	−	3.56663i	0.0671278	−	0.116269i	−0.830508	−	0.557007i	$-0.811950\pi$
$941$	2.05919	−	3.56663i	0.0671278	−	0.116269i	0.897636	+	0.440738i	$0.145283\pi$
$942$		0			0
$943$	0.274682	−	0.158588i	0.00894488	−	0.00516433i
$944$	−8.84071			−0.287741
$945$		0			0
$946$	−18.4908			−0.601189
$947$	−21.4498	+	12.3840i	−0.697024	+	0.402427i	−0.806238	−	0.591591i	$-0.798500\pi$
$947$	−21.4498	+	12.3840i	−0.697024	+	0.402427i	0.109214	+	0.994018i	$0.465167\pi$
$948$		0			0
$949$	0.672905	−	1.16550i	0.0218434	−	0.0378339i
$950$	31.3458	+	54.2925i	1.01699	+	1.76148i
$951$		0			0
$952$	−0.326704	+	4.26942i	−0.0105885	+	0.138373i
$953$			9.62625i			0.311825i	0.987771	+	0.155912i	$0.0498317\pi$
$953$			9.62625i			0.311825i	−0.987771	+	0.155912i	$0.950168\pi$
$954$		0			0
$955$	15.7897	+	9.11620i	0.510944	+	0.294993i
$956$	−3.02944	−	1.74905i	−0.0979790	−	0.0565682i
$957$		0			0
$958$			12.4332i			0.401698i
$959$	−1.42563	+	18.6304i	−0.0460361	+	0.601608i
$960$		0			0
$961$	2.41465	+	4.18230i	0.0778920	+	0.134913i
$962$	−3.00060	+	5.19719i	−0.0967431	+	0.167564i
$963$		0			0
$964$	−10.0170	+	5.78332i	−0.322626	+	0.186268i
$965$	−56.7817			−1.82787
$966$		0			0
$967$	−10.1112			−0.325153			−0.162576	−	0.986696i	$-0.551980\pi$
$967$	−10.1112			−0.325153			−0.162576	+	0.986696i	$0.551980\pi$
$968$	1.61538	−	0.932639i	0.0519202	−	0.0299762i
$969$		0			0
$970$	−27.3446	+	47.3622i	−0.877981	+	1.52071i
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	0.588264	−	0.808669i	$-0.299812\pi$
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	−0.994460	+	0.105117i	$0.966478\pi$
$972$		0			0
$973$	−34.7959	+	16.6894i	−1.11550	+	0.535039i
$974$		−	37.3007i		−	1.19519i
$975$		0			0
$976$	−4.06195	−	2.34517i	−0.130020	−	0.0750671i
$977$	7.84008	+	4.52647i	0.250826	+	0.144815i	0.620143	−	0.784489i	$-0.287075\pi$
$977$	7.84008	+	4.52647i	0.250826	+	0.144815i	−0.369316	+	0.929304i	$0.620408\pi$
$978$		0			0
$979$			14.2350i			0.454954i
$980$	−15.5646	+	19.3920i	−0.497194	+	0.619453i
$981$		0			0
$982$	6.82377	+	11.8191i	0.217755	+	0.377163i
$983$	−3.19651	+	5.53653i	−0.101953	+	0.176588i	−0.912489	−	0.409101i	$-0.865842\pi$
$983$	−3.19651	+	5.53653i	−0.101953	+	0.176588i	0.810536	+	0.585688i	$0.199176\pi$
$984$		0			0
$985$	14.5379	−	8.39347i	0.463216	−	0.267438i
$986$	6.92044			0.220392
$987$		0			0
$988$	8.44666			0.268724
$989$	17.7934	−	10.2730i	0.565797	−	0.326663i
$990$		0			0
$991$	6.92230	−	11.9898i	0.219894	−	0.380868i	−0.734881	−	0.678196i	$-0.762762\pi$
$991$	6.92230	−	11.9898i	0.219894	−	0.380868i	0.954775	+	0.297328i	$0.0960954\pi$
$992$	−2.99288	−	5.18382i	−0.0950240	−	0.164586i
$993$		0			0
$994$	−20.8941	+	30.5427i	−0.662721	+	0.968755i
$995$			7.53413i			0.238848i
$996$		0			0
$997$	5.99391	+	3.46059i	0.189829	+	0.109598i	0.591903	−	0.806010i	$-0.298377\pi$
$997$	5.99391	+	3.46059i	0.189829	+	0.109598i	−0.402073	+	0.915607i	$0.631710\pi$
$998$	−18.1882	−	10.5010i	−0.575737	−	0.332402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.a.647.4		16
3.2	odd	2		1134.2.k.b.647.5		16
7.5	odd	6		1134.2.k.b.971.5		16
9.2	odd	6		126.2.t.a.59.4	yes	16
9.4	even	3		126.2.l.a.101.2	yes	16
9.5	odd	6		378.2.l.a.143.5		16
9.7	even	3		378.2.t.a.17.5		16
21.5	even	6	inner	1134.2.k.a.971.4		16
36.7	odd	6		3024.2.df.c.17.1		16
36.11	even	6		1008.2.df.c.689.3		16
36.23	even	6		3024.2.ca.c.2033.1		16
36.31	odd	6		1008.2.ca.c.353.7		16
63.2	odd	6		882.2.l.b.509.7		16
63.4	even	3		882.2.m.b.587.8		16
63.5	even	6		378.2.t.a.89.5		16
63.11	odd	6		882.2.m.a.293.5		16
63.13	odd	6		882.2.l.b.227.3		16
63.16	even	3		2646.2.l.a.1097.4		16
63.20	even	6		882.2.t.a.815.1		16
63.23	odd	6		2646.2.t.b.1979.8		16
63.25	even	3		2646.2.m.a.881.4		16
63.31	odd	6		882.2.m.a.587.5		16
63.32	odd	6		2646.2.m.b.1763.1		16
63.34	odd	6		2646.2.t.b.2285.8		16
63.38	even	6		882.2.m.b.293.8		16
63.40	odd	6		126.2.t.a.47.4	yes	16
63.41	even	6		2646.2.l.a.521.8		16
63.47	even	6		126.2.l.a.5.6	✓	16
63.52	odd	6		2646.2.m.b.881.1		16
63.58	even	3		882.2.t.a.803.1		16
63.59	even	6		2646.2.m.a.1763.4		16
63.61	odd	6		378.2.l.a.341.1		16
252.47	odd	6		1008.2.ca.c.257.7		16
252.103	even	6		1008.2.df.c.929.3		16
252.131	odd	6		3024.2.df.c.1601.1		16
252.187	even	6		3024.2.ca.c.2609.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	63.47	even	6
126.2.l.a.101.2	yes	16	9.4	even	3
126.2.t.a.47.4	yes	16	63.40	odd	6
126.2.t.a.59.4	yes	16	9.2	odd	6
378.2.l.a.143.5		16	9.5	odd	6
378.2.l.a.341.1		16	63.61	odd	6
378.2.t.a.17.5		16	9.7	even	3
378.2.t.a.89.5		16	63.5	even	6
882.2.l.b.227.3		16	63.13	odd	6
882.2.l.b.509.7		16	63.2	odd	6
882.2.m.a.293.5		16	63.11	odd	6
882.2.m.a.587.5		16	63.31	odd	6
882.2.m.b.293.8		16	63.38	even	6
882.2.m.b.587.8		16	63.4	even	3
882.2.t.a.803.1		16	63.58	even	3
882.2.t.a.815.1		16	63.20	even	6
1008.2.ca.c.257.7		16	252.47	odd	6
1008.2.ca.c.353.7		16	36.31	odd	6
1008.2.df.c.689.3		16	36.11	even	6
1008.2.df.c.929.3		16	252.103	even	6
1134.2.k.a.647.4		16	1.1	even	1	trivial
1134.2.k.a.971.4		16	21.5	even	6	inner
1134.2.k.b.647.5		16	3.2	odd	2
1134.2.k.b.971.5		16	7.5	odd	6
2646.2.l.a.521.8		16	63.41	even	6
2646.2.l.a.1097.4		16	63.16	even	3
2646.2.m.a.881.4		16	63.25	even	3
2646.2.m.a.1763.4		16	63.59	even	6
2646.2.m.b.881.1		16	63.52	odd	6
2646.2.m.b.1763.1		16	63.32	odd	6
2646.2.t.b.1979.8		16	63.23	odd	6
2646.2.t.b.2285.8		16	63.34	odd	6
3024.2.ca.c.2033.1		16	36.23	even	6
3024.2.ca.c.2609.1		16	252.187	even	6
3024.2.df.c.17.1		16	36.7	odd	6
3024.2.df.c.1601.1		16	252.131	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} +(-1.14420 - 2.38554i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} +(-1.14420 - 2.38554i) q^{7} +1.00000i q^{8} +(-3.07634 - 1.77612i) q^{10} +(-2.61745 - 1.51119i) q^{11} -1.02646i q^{13} +(2.18368 + 1.49384i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.809204 + 1.40158i) q^{17} +(-7.12643 + 4.11444i) q^{19} +3.55225 q^{20} +3.02237 q^{22} +(-2.90837 + 1.67915i) q^{23} +(-3.80924 + 6.59779i) q^{25} +(0.513232 + 0.888944i) q^{26} +(-2.63804 - 0.201867i) q^{28} +4.27608i q^{29} +(-5.18382 - 2.99288i) q^{31} +(0.866025 + 0.500000i) q^{32} -1.61841i q^{34} +(5.30650 - 7.75696i) q^{35} +(2.92323 + 5.06319i) q^{37} +(4.11444 - 7.12643i) q^{38} +(-3.07634 + 1.77612i) q^{40} -0.0944452 q^{41} -6.11799 q^{43} +(-2.61745 + 1.51119i) q^{44} +(1.67915 - 2.90837i) q^{46} +(2.57023 + 4.45176i) q^{47} +(-4.38163 + 5.45906i) q^{49} -7.61848i q^{50} +(-0.888944 - 0.513232i) q^{52} +(-2.76235 - 1.59484i) q^{53} -10.7362i q^{55} +(2.38554 - 1.14420i) q^{56} +(-2.13804 - 3.70319i) q^{58} +(4.42036 - 7.65628i) q^{59} +(4.06195 - 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(3.15775 - 1.82313i) q^{65} +(0.187838 - 0.325345i) q^{67} +(0.809204 + 1.40158i) q^{68} +(-0.717083 + 9.37097i) q^{70} +13.9868i q^{71} +(1.13546 + 0.655556i) q^{73} +(-5.06319 - 2.92323i) q^{74} +8.22889i q^{76} +(-0.610118 + 7.97313i) q^{77} +(-0.462067 - 0.800324i) q^{79} +(1.77612 - 3.07634i) q^{80} +(0.0817920 - 0.0472226i) q^{82} -10.8642 q^{83} -5.74899 q^{85} +(5.29833 - 3.05899i) q^{86} +(1.51119 - 2.61745i) q^{88} +(-2.35495 - 4.07888i) q^{89} +(-2.44867 + 1.17448i) q^{91} +3.35830i q^{92} +(-4.45176 - 2.57023i) q^{94} +(-25.3148 - 14.6155i) q^{95} -15.3956i q^{97} +(1.06507 - 6.91850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 4 * q^7	\( 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49} + 6 q^{52} - 36 q^{53} - 6 q^{56} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{70} - 18 q^{74} + 24 q^{77} - 16 q^{79} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 66 q^{95} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 - 12 * q^11 - 8 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^31 + 30 * q^35 - 2 * q^37 + 12 * q^41 + 4 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 - 2 * q^49 + 6 * q^52 - 36 * q^53 - 6 * q^56 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^70 - 18 * q^74 + 24 * q^77 - 16 * q^79 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 66 * q^95 - 24 * q^98

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