LMFDB - Embedded newform 1134.2.k.a.647.7

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			647.7
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.a.971.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.714925 + 1.23829i) q^{5} +(2.10995 - 1.59628i) q^{7} -1.00000i q^{8} +(1.23829 + 0.714925i) q^{10} +(-2.96133 - 1.70972i) q^{11} -6.33715i q^{13} +(1.02913 - 2.43739i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.14201 + 1.97802i) q^{17} +(-1.87673 + 1.08353i) q^{19} +1.42985 q^{20} -3.41945 q^{22} +(6.97507 - 4.02706i) q^{23} +(1.47776 - 2.55956i) q^{25} +(-3.16857 - 5.48813i) q^{26} +(-0.327442 - 2.62541i) q^{28} +0.345115i q^{29} +(3.76052 + 2.17114i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.28402i q^{34} +(3.48511 + 1.47150i) q^{35} +(1.07786 + 1.86690i) q^{37} +(-1.08353 + 1.87673i) q^{38} +(1.23829 - 0.714925i) q^{40} -0.404360 q^{41} -5.81766 q^{43} +(-2.96133 + 1.70972i) q^{44} +(4.02706 - 6.97507i) q^{46} +(2.75915 + 4.77898i) q^{47} +(1.90379 - 6.73614i) q^{49} -2.95553i q^{50} +(-5.48813 - 3.16857i) q^{52} +(8.56310 + 4.94391i) q^{53} -4.88930i q^{55} +(-1.59628 - 2.10995i) q^{56} +(0.172558 + 0.298879i) q^{58} +(-5.51480 + 9.55191i) q^{59} +(9.94175 - 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(7.84721 - 4.53059i) q^{65} +(-2.12683 + 3.68377i) q^{67} +(1.14201 + 1.97802i) q^{68} +(3.75394 - 0.468194i) q^{70} -3.55393i q^{71} +(-0.201057 - 0.116080i) q^{73} +(1.86690 + 1.07786i) q^{74} +2.16707i q^{76} +(-8.97745 + 1.11967i) q^{77} +(-7.28100 - 12.6111i) q^{79} +(0.714925 - 1.23829i) q^{80} +(-0.350186 + 0.202180i) q^{82} -1.62325 q^{83} -3.26580 q^{85} +(-5.03824 + 2.90883i) q^{86} +(-1.70972 + 2.96133i) q^{88} +(-2.02974 - 3.51562i) q^{89} +(-10.1159 - 13.3711i) q^{91} -8.05411i q^{92} +(4.77898 + 2.75915i) q^{94} +(-2.68345 - 1.54929i) q^{95} +10.6085i q^{97} +(-1.71934 - 6.78556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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
$5$	0.714925	+	1.23829i	0.319724	+	0.553779i	0.980430	−	0.196866i	$-0.0630764\pi$
$5$	0.714925	+	1.23829i	0.319724	+	0.553779i	−0.660706	+	0.750645i	$0.729743\pi$
$6$		0			0
$7$	2.10995	−	1.59628i	0.797487	−	0.603337i
$7$	2.10995	−	1.59628i	0.797487	−	0.603337i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.23829	+	0.714925i	0.391581	+	0.226079i
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.0179923	−	0.999838i	$-0.505727\pi$
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.874881	+	0.484337i	$0.839061\pi$
$12$		0			0
$13$		−	6.33715i		−	1.75761i	−0.477182	−	0.878804i	$-0.658342\pi$
$13$		−	6.33715i		−	1.75761i	0.477182	−	0.878804i	$-0.341658\pi$
$14$	1.02913	−	2.43739i	0.275047	−	0.651421i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.14201	+	1.97802i	−0.276978	+	0.479739i	−0.970632	−	0.240569i	$-0.922666\pi$
$17$	−1.14201	+	1.97802i	−0.276978	+	0.479739i	0.693655	+	0.720308i	$0.255999\pi$
$18$		0			0
$19$	−1.87673	+	1.08353i	−0.430553	+	0.248580i	−0.699582	−	0.714552i	$-0.746630\pi$
$19$	−1.87673	+	1.08353i	−0.430553	+	0.248580i	0.269029	+	0.963132i	$0.413297\pi$
$20$	1.42985			0.319724
$21$		0			0
$22$	−3.41945			−0.729028
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.455675	−	0.890146i	$-0.349398\pi$
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.998727	+	0.0504469i	$0.0160646\pi$
$24$		0			0
$25$	1.47776	−	2.55956i	0.295553	−	0.511912i
$26$	−3.16857	−	5.48813i	−0.621408	−	1.07631i
$27$		0			0
$28$	−0.327442	−	2.62541i	−0.0618808	−	0.496156i
$29$			0.345115i			0.0640863i	0.999486	+	0.0320431i	$0.0102014\pi$
$29$			0.345115i			0.0640863i	−0.999486	+	0.0320431i	$0.989799\pi$
$30$		0			0
$31$	3.76052	+	2.17114i	0.675410	+	0.389948i	0.798123	−	0.602494i	$-0.205826\pi$
$31$	3.76052	+	2.17114i	0.675410	+	0.389948i	−0.122713	+	0.992442i	$0.539160\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			2.28402i			0.391706i
$35$	3.48511	+	1.47150i	0.589091	+	0.248730i
$36$		0			0
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	0.940920	−	0.338629i	$-0.109963\pi$
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	−0.763721	+	0.645546i	$0.776630\pi$
$38$	−1.08353	+	1.87673i	−0.175772	+	0.304447i
$39$		0			0
$40$	1.23829	−	0.714925i	0.195790	−	0.113040i
$41$	−0.404360			−0.0631504			−0.0315752	−	0.999501i	$-0.510052\pi$
$41$	−0.404360			−0.0631504			−0.0315752	+	0.999501i	$0.510052\pi$
$42$		0			0
$43$	−5.81766			−0.887185			−0.443592	−	0.896229i	$-0.646296\pi$
$43$	−5.81766			−0.887185			−0.443592	+	0.896229i	$0.646296\pi$
$44$	−2.96133	+	1.70972i	−0.446437	+	0.257750i
$45$		0			0
$46$	4.02706	−	6.97507i	0.593757	−	1.02842i
$47$	2.75915	+	4.77898i	0.402463	+	0.697086i	0.994023	−	0.109175i	$-0.0348209\pi$
$47$	2.75915	+	4.77898i	0.402463	+	0.697086i	−0.591560	+	0.806261i	$0.701488\pi$
$48$		0			0
$49$	1.90379	−	6.73614i	0.271970	−	0.962306i
$50$		−	2.95553i		−	0.417975i
$51$		0			0
$52$	−5.48813	−	3.16857i	−0.761067	−	0.439402i
$53$	8.56310	+	4.94391i	1.17623	+	0.679098i	0.955140	−	0.296155i	$-0.0957044\pi$
$53$	8.56310	+	4.94391i	1.17623	+	0.679098i	0.221093	+	0.975253i	$0.429038\pi$
$54$		0			0
$55$		−	4.88930i		−	0.659273i
$56$	−1.59628	−	2.10995i	−0.213312	−	0.281954i
$57$		0			0
$58$	0.172558	+	0.298879i	0.0226579	+	0.0392447i
$59$	−5.51480	+	9.55191i	−0.717966	+	1.24355i	0.243839	+	0.969816i	$0.421593\pi$
$59$	−5.51480	+	9.55191i	−0.717966	+	1.24355i	−0.961805	+	0.273737i	$0.911740\pi$
$60$		0			0
$61$	9.94175	−	5.73987i	1.27291	−	0.734915i	0.297376	−	0.954760i	$-0.403888\pi$
$61$	9.94175	−	5.73987i	1.27291	−	0.734915i	0.975535	+	0.219845i	$0.0705551\pi$
$62$	4.34228			0.551470
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.84721	−	4.53059i	0.973326	−	0.561950i
$66$		0			0
$67$	−2.12683	+	3.68377i	−0.259833	+	0.450045i	−0.966197	−	0.257804i	$-0.917001\pi$
$67$	−2.12683	+	3.68377i	−0.259833	+	0.450045i	0.706364	+	0.707849i	$0.250334\pi$
$68$	1.14201	+	1.97802i	0.138489	+	0.239870i
$69$		0			0
$70$	3.75394	−	0.468194i	0.448682	−	0.0559599i
$71$		−	3.55393i		−	0.421773i	−0.977511	−	0.210887i	$-0.932365\pi$
$71$		−	3.55393i		−	0.421773i	0.977511	−	0.210887i	$-0.0676351\pi$
$72$		0			0
$73$	−0.201057	−	0.116080i	−0.0235320	−	0.0135862i	0.488188	−	0.872739i	$-0.337658\pi$
$73$	−0.201057	−	0.116080i	−0.0235320	−	0.0135862i	−0.511720	+	0.859152i	$0.670991\pi$
$74$	1.86690	+	1.07786i	0.217023	+	0.125298i
$75$		0			0
$76$			2.16707i			0.248580i
$77$	−8.97745	+	1.11967i	−1.02308	+	0.127598i
$78$		0			0
$79$	−7.28100	−	12.6111i	−0.819177	−	1.41886i	−0.906290	−	0.422657i	$-0.861097\pi$
$79$	−7.28100	−	12.6111i	−0.819177	−	1.41886i	0.0871130	−	0.996198i	$-0.472236\pi$
$80$	0.714925	−	1.23829i	0.0799311	−	0.138445i
$81$		0			0
$82$	−0.350186	+	0.202180i	−0.0386716	+	0.0223270i
$83$	−1.62325			−0.178175			−0.0890873	−	0.996024i	$-0.528395\pi$
$83$	−1.62325			−0.178175			−0.0890873	+	0.996024i	$0.528395\pi$
$84$		0			0
$85$	−3.26580			−0.354226
$86$	−5.03824	+	2.90883i	−0.543287	+	0.313667i
$87$		0			0
$88$	−1.70972	+	2.96133i	−0.182257	+	0.315679i
$89$	−2.02974	−	3.51562i	−0.215152	−	0.372655i	0.738167	−	0.674618i	$-0.235691\pi$
$89$	−2.02974	−	3.51562i	−0.215152	−	0.372655i	−0.953320	+	0.301963i	$0.902358\pi$
$90$		0			0
$91$	−10.1159	−	13.3711i	−1.06043	−	1.40167i
$92$		−	8.05411i		−	0.839699i
$93$		0			0
$94$	4.77898	+	2.75915i	0.492914	+	0.284584i
$95$	−2.68345	−	1.54929i	−0.275316	−	0.158954i
$96$		0			0
$97$			10.6085i			1.07713i	0.842585	+	0.538563i	$0.181033\pi$
$97$			10.6085i			1.07713i	−0.842585	+	0.538563i	$0.818967\pi$
$98$	−1.71934	−	6.78556i	−0.173680	−	0.685445i
$99$		0			0
$100$	−1.47776	−	2.55956i	−0.147776	−	0.255956i
$101$	−4.02443	+	6.97052i	−0.400446	+	0.693593i	−0.993780	−	0.111364i	$-0.964478\pi$
$101$	−4.02443	+	6.97052i	−0.400446	+	0.693593i	0.593334	+	0.804957i	$0.297811\pi$
$102$		0			0
$103$	2.43692	−	1.40695i	0.240117	−	0.138631i	−0.375114	−	0.926979i	$-0.622396\pi$
$103$	2.43692	−	1.40695i	0.240117	−	0.138631i	0.615230	+	0.788347i	$0.289063\pi$
$104$	−6.33715			−0.621408
$105$		0			0
$106$	9.88782			0.960390
$107$	−13.7019	+	7.91078i	−1.32461	+	0.764764i	−0.984460	−	0.175607i	$-0.943811\pi$
$107$	−13.7019	+	7.91078i	−1.32461	+	0.764764i	−0.340150	+	0.940371i	$0.610478\pi$
$108$		0			0
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	−0.510784	−	0.859709i	$-0.670645\pi$
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	0.999922	+	0.0124977i	$0.00397826\pi$
$110$	−2.44465	−	4.23425i	−0.233088	−	0.403720i
$111$		0			0
$112$	−2.43739	−	1.02913i	−0.230312	−	0.0972438i
$113$			8.41555i			0.791668i	0.918322	+	0.395834i	$0.129545\pi$
$113$			8.41555i			0.791668i	−0.918322	+	0.395834i	$0.870455\pi$
$114$		0			0
$115$	9.97330	+	5.75809i	0.930015	+	0.536945i
$116$	0.298879	+	0.172558i	0.0277502	+	0.0160216i
$117$		0			0
$118$			11.0296i			1.01536i
$119$	0.747884	+	5.99648i	0.0685584	+	0.549696i
$120$		0			0
$121$	0.346305	+	0.599818i	0.0314823	+	0.0545289i
$122$	5.73987	−	9.94175i	0.519664	−	0.900084i
$123$		0			0
$124$	3.76052	−	2.17114i	0.337705	−	0.194974i
$125$	11.3752			1.01743
$126$		0			0
$127$	5.77773			0.512691			0.256345	−	0.966585i	$-0.417482\pi$
$127$	5.77773			0.512691			0.256345	+	0.966585i	$0.417482\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	4.53059	−	7.84721i	0.397359	−	0.688246i
$131$	2.22833	+	3.85959i	0.194690	+	0.337214i	0.946799	−	0.321825i	$-0.104296\pi$
$131$	2.22833	+	3.85959i	0.194690	+	0.337214i	−0.752109	+	0.659039i	$0.770963\pi$
$132$		0			0
$133$	−2.23020	+	5.28199i	−0.193383	+	0.458007i
$134$			4.25366i			0.367460i
$135$		0			0
$136$	1.97802	+	1.14201i	0.169613	+	0.0979264i
$137$	−8.36293	−	4.82834i	−0.714493	−	0.412513i	0.0982292	−	0.995164i	$-0.468682\pi$
$137$	−8.36293	−	4.82834i	−0.714493	−	0.412513i	−0.812723	+	0.582651i	$0.802016\pi$
$138$		0			0
$139$			18.5537i			1.57371i	0.617141	+	0.786853i	$0.288291\pi$
$139$			18.5537i			1.57371i	−0.617141	+	0.786853i	$0.711709\pi$
$140$	3.01691	−	2.28244i	0.254976	−	0.192901i
$141$		0			0
$142$	−1.77696	−	3.07779i	−0.149119	−	0.258282i
$143$	−10.8348	+	18.7664i	−0.906049	+	1.56932i
$144$		0			0
$145$	−0.427352	+	0.246732i	−0.0354896	+	0.0204899i
$146$	−0.232161			−0.0192138
$147$		0			0
$148$	2.15571			0.177199
$149$	5.63517	−	3.25347i	0.461651	−	0.266535i	−0.251087	−	0.967965i	$-0.580788\pi$
$149$	5.63517	−	3.25347i	0.461651	−	0.266535i	0.712738	+	0.701430i	$0.247455\pi$
$150$		0			0
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	−0.959078	−	0.283142i	$-0.908623\pi$
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	0.724747	+	0.689015i	$0.241956\pi$
$152$	1.08353	+	1.87673i	0.0878862	+	0.152223i
$153$		0			0
$154$	−7.21486	+	5.45839i	−0.581390	+	0.439850i
$155$			6.20881i			0.498704i
$156$		0			0
$157$	−6.89669	−	3.98180i	−0.550415	−	0.317783i	0.198874	−	0.980025i	$-0.436272\pi$
$157$	−6.89669	−	3.98180i	−0.550415	−	0.317783i	−0.749290	+	0.662243i	$0.769605\pi$
$158$	−12.6111	−	7.28100i	−1.00328	−	0.579245i
$159$		0			0
$160$		−	1.42985i		−	0.113040i
$161$	8.28874	−	19.6310i	0.653245	−	1.54714i
$162$		0			0
$163$	5.69256	+	9.85980i	0.445876	+	0.772279i	0.998113	−	0.0614080i	$-0.0195591\pi$
$163$	5.69256	+	9.85980i	0.445876	+	0.772279i	−0.552237	+	0.833687i	$0.686226\pi$
$164$	−0.202180	+	0.350186i	−0.0157876	+	0.0273449i
$165$		0			0
$166$	−1.40577	+	0.811624i	−0.109109	+	0.0629942i
$167$	11.3284			0.876615			0.438308	−	0.898825i	$-0.355578\pi$
$167$	11.3284			0.876615			0.438308	+	0.898825i	$0.355578\pi$
$168$		0			0
$169$	−27.1594			−2.08919
$170$	−2.82827	+	1.63290i	−0.216918	+	0.125238i
$171$		0			0
$172$	−2.90883	+	5.03824i	−0.221796	+	0.384162i
$173$	10.8457	+	18.7853i	0.824584	+	1.42822i	0.902237	+	0.431241i	$0.141924\pi$
$173$	10.8457	+	18.7853i	0.824584	+	1.42822i	−0.0776528	+	0.996980i	$0.524743\pi$
$174$		0			0
$175$	−0.967765	−	7.75947i	−0.0731562	−	0.586561i
$176$			3.41945i			0.257750i
$177$		0			0
$178$	−3.51562	−	2.02974i	−0.263507	−	0.152136i
$179$	−18.0057	−	10.3956i	−1.34581	−	0.777002i	−0.358155	−	0.933662i	$-0.616594\pi$
$179$	−18.0057	−	10.3956i	−1.34581	−	0.777002i	−0.987653	+	0.156660i	$0.949927\pi$
$180$		0			0
$181$			21.5301i			1.60032i	0.599788	+	0.800159i	$0.295252\pi$
$181$			21.5301i			1.60032i	−0.599788	+	0.800159i	$0.704748\pi$
$182$	−15.4461	−	6.52176i	−1.14494	−	0.483425i
$183$		0			0
$184$	−4.02706	−	6.97507i	−0.296879	−	0.514209i
$185$	−1.54117	+	2.66939i	−0.113309	+	0.196258i
$186$		0			0
$187$	6.76372	−	3.90503i	0.494612	−	0.285564i
$188$	5.51829			0.402463
$189$		0			0
$190$	−3.09858			−0.224795
$191$	−6.38207	+	3.68469i	−0.461791	+	0.266615i	−0.712797	−	0.701371i	$-0.752572\pi$
$191$	−6.38207	+	3.68469i	−0.461791	+	0.266615i	0.251006	+	0.967985i	$0.419239\pi$
$192$		0			0
$193$	1.41279	−	2.44703i	0.101695	−	0.176141i	−0.810688	−	0.585478i	$-0.800907\pi$
$193$	1.41279	−	2.44703i	0.101695	−	0.176141i	0.912383	+	0.409337i	$0.134240\pi$
$194$	5.30423	+	9.18719i	0.380821	+	0.659602i
$195$		0			0
$196$	−4.88178	−	5.01680i	−0.348698	−	0.358343i
$197$			26.0883i			1.85871i	0.369183	+	0.929357i	$0.379637\pi$
$197$			26.0883i			1.85871i	−0.369183	+	0.929357i	$0.620363\pi$
$198$		0			0
$199$	13.3511	+	7.70826i	0.946434	+	0.546424i	0.891971	−	0.452092i	$-0.149322\pi$
$199$	13.3511	+	7.70826i	0.946434	+	0.546424i	0.0544625	+	0.998516i	$0.482655\pi$
$200$	−2.55956	−	1.47776i	−0.180988	−	0.104494i
$201$		0			0
$202$			8.04886i			0.566316i
$203$	0.550900	+	0.728176i	0.0386656	+	0.0511079i
$204$		0			0
$205$	−0.289087	−	0.500713i	−0.0201907	−	0.0349713i
$206$	1.40695	−	2.43692i	0.0980272	−	0.169788i
$207$		0			0
$208$	−5.48813	+	3.16857i	−0.380533	+	0.219701i
$209$	7.41017			0.512572
$210$		0			0
$211$	−8.84930			−0.609211			−0.304605	−	0.952479i	$-0.598525\pi$
$211$	−8.84930			−0.609211			−0.304605	+	0.952479i	$0.598525\pi$
$212$	8.56310	−	4.94391i	0.588116	−	0.339549i
$213$		0			0
$214$	−7.91078	+	13.7019i	−0.540770	+	0.936641i
$215$	−4.15919	−	7.20393i	−0.283655	−	0.491304i
$216$		0			0
$217$	11.4003	−	1.42185i	0.773901	−	0.0965212i
$218$		−	10.2135i		−	0.691745i
$219$		0			0
$220$	−4.23425	−	2.44465i	−0.285473	−	0.164818i
$221$	12.5350	+	7.23707i	0.843194	+	0.486818i
$222$		0			0
$223$			7.95544i			0.532736i	0.963871	+	0.266368i	$0.0858236\pi$
$223$			7.95544i			0.532736i	−0.963871	+	0.266368i	$0.914176\pi$
$224$	−2.62541	+	0.327442i	−0.175418	+	0.0218782i
$225$		0			0
$226$	4.20778	+	7.28808i	0.279897	+	0.484796i
$227$	4.61984	−	8.00180i	0.306630	−	0.531098i	−0.670993	−	0.741464i	$-0.734132\pi$
$227$	4.61984	−	8.00180i	0.306630	−	0.531098i	0.977623	+	0.210365i	$0.0674654\pi$
$228$		0			0
$229$	7.31319	−	4.22227i	0.483269	−	0.279016i	−0.238509	−	0.971140i	$-0.576659\pi$
$229$	7.31319	−	4.22227i	0.483269	−	0.279016i	0.721778	+	0.692125i	$0.243325\pi$
$230$	11.5162			0.759354
$231$		0			0
$232$	0.345115			0.0226579
$233$	14.4176	−	8.32399i	0.944526	−	0.545323i	0.0531500	−	0.998587i	$-0.483074\pi$
$233$	14.4176	−	8.32399i	0.944526	−	0.545323i	0.891376	+	0.453264i	$0.149741\pi$
$234$		0			0
$235$	−3.94517	+	6.83323i	−0.257354	+	0.445751i
$236$	5.51480	+	9.55191i	0.358983	+	0.621776i
$237$		0			0
$238$	3.64593	+	4.81916i	0.236330	+	0.312380i
$239$		−	27.2885i		−	1.76514i	−0.470177	−	0.882572i	$-0.655810\pi$
$239$		−	27.2885i		−	1.76514i	0.470177	−	0.882572i	$-0.344190\pi$
$240$		0			0
$241$	21.9018	+	12.6450i	1.41082	+	0.814537i	0.995466	−	0.0951223i	$-0.0303242\pi$
$241$	21.9018	+	12.6450i	1.41082	+	0.814537i	0.415354	+	0.909660i	$0.363658\pi$
$242$	0.599818	+	0.346305i	0.0385578	+	0.0222613i
$243$		0			0
$244$		−	11.4797i		−	0.734915i
$245$	9.70234	−	2.45840i	0.619860	−	0.157062i
$246$		0			0
$247$	6.86651	+	11.8931i	0.436906	+	0.756743i
$248$	2.17114	−	3.76052i	0.137868	−	0.238794i
$249$		0			0
$250$	9.85123	−	5.68761i	0.623046	−	0.359716i
$251$	−8.19337			−0.517161			−0.258581	−	0.965990i	$-0.583255\pi$
$251$	−8.19337			−0.517161			−0.258581	+	0.965990i	$0.583255\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$	5.00366	−	2.88886i	0.313958	−	0.181264i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.31723	−	5.74560i	−0.206923	−	0.358401i	0.743821	−	0.668379i	$-0.233012\pi$
$257$	−3.31723	−	5.74560i	−0.206923	−	0.358401i	−0.950744	+	0.309978i	$0.899678\pi$
$258$		0			0
$259$	5.25432	+	2.21851i	0.326488	+	0.137852i
$260$		−	9.06117i		−	0.561950i
$261$		0			0
$262$	3.85959	+	2.22833i	0.238446	+	0.137667i
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	0.329807	−	0.944048i	$-0.393016\pi$
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	−0.652666	+	0.757645i	$0.726350\pi$
$264$		0			0
$265$			14.1381i			0.868497i
$266$	0.709590	+	5.68944i	0.0435077	+	0.348842i
$267$		0			0
$268$	2.12683	+	3.68377i	0.129917	+	0.225022i
$269$	3.41069	−	5.90750i	0.207954	−	0.360186i	−0.743116	−	0.669163i	$-0.766653\pi$
$269$	3.41069	−	5.90750i	0.207954	−	0.360186i	0.951070	+	0.308976i	$0.0999863\pi$
$270$		0			0
$271$	−4.39780	+	2.53907i	−0.267148	+	0.154238i	−0.627591	−	0.778543i	$-0.715959\pi$
$271$	−4.39780	+	2.53907i	−0.267148	+	0.154238i	0.360443	+	0.932781i	$0.382625\pi$
$272$	2.28402			0.138489
$273$		0			0
$274$	−9.65668			−0.583381
$275$	−8.75228	+	5.05313i	−0.527783	+	0.304715i
$276$		0			0
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	−0.834765	−	0.550607i	$-0.814396\pi$
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	0.894222	+	0.447624i	$0.147730\pi$
$278$	9.27686	+	16.0680i	0.556389	+	0.963694i
$279$		0			0
$280$	1.47150	−	3.48511i	0.0879392	−	0.208275i
$281$			17.6326i			1.05187i	0.850523	+	0.525937i	$0.176285\pi$
$281$			17.6326i			1.05187i	−0.850523	+	0.525937i	$0.823715\pi$
$282$		0			0
$283$	−4.46337	−	2.57693i	−0.265320	−	0.153182i	0.361439	−	0.932396i	$-0.382286\pi$
$283$	−4.46337	−	2.57693i	−0.265320	−	0.153182i	−0.626759	+	0.779213i	$0.715619\pi$
$284$	−3.07779	−	1.77696i	−0.182633	−	0.105443i
$285$		0			0
$286$			21.6695i			1.28135i
$287$	−0.853179	+	0.645471i	−0.0503616	+	0.0381009i
$288$		0			0
$289$	5.89164	+	10.2046i	0.346567	+	0.600271i
$290$	−0.246732	+	0.427352i	−0.0144886	+	0.0250949i
$291$		0			0
$292$	−0.201057	+	0.116080i	−0.0117660	+	0.00679310i
$293$	−2.06497			−0.120637			−0.0603183	−	0.998179i	$-0.519212\pi$
$293$	−2.06497			−0.120637			−0.0603183	+	0.998179i	$0.519212\pi$
$294$		0			0
$295$	−15.7707			−0.918204
$296$	1.86690	−	1.07786i	0.108511	−	0.0626491i
$297$		0			0
$298$	3.25347	−	5.63517i	0.188468	−	0.326437i
$299$	−25.5201	−	44.2020i	−1.47586	−	2.55627i
$300$		0			0
$301$	−12.2750	+	9.28661i	−0.707518	+	0.535271i
$302$			5.75901i			0.331394i
$303$		0			0
$304$	1.87673	+	1.08353i	0.107638	+	0.0621449i
$305$	14.2152	+	8.20716i	0.813961	+	0.469941i
$306$		0			0
$307$		−	1.09119i		−	0.0622772i	−0.999515	−	0.0311386i	$-0.990087\pi$
$307$		−	1.09119i		−	0.0622772i	0.999515	−	0.0311386i	$-0.00991333\pi$
$308$	−3.51906	+	8.33454i	−0.200517	+	0.474904i
$309$		0			0
$310$	3.10441	+	5.37699i	0.176318	+	0.305392i
$311$	−7.61100	+	13.1826i	−0.431580	+	0.747519i	−0.997010	−	0.0772777i	$-0.975377\pi$
$311$	−7.61100	+	13.1826i	−0.431580	+	0.747519i	0.565429	+	0.824797i	$0.308711\pi$
$312$		0			0
$313$	−10.0202	+	5.78518i	−0.566377	+	0.326998i	−0.755701	−	0.654917i	$-0.772704\pi$
$313$	−10.0202	+	5.78518i	−0.566377	+	0.326998i	0.189324	+	0.981915i	$0.439370\pi$
$314$	−7.96361			−0.449412
$315$		0			0
$316$	−14.5620			−0.819177
$317$	14.8613	−	8.58020i	0.834696	−	0.481912i	−0.0207618	−	0.999784i	$-0.506609\pi$
$317$	14.8613	−	8.58020i	0.834696	−	0.481912i	0.855458	+	0.517872i	$0.173276\pi$
$318$		0			0
$319$	0.590051	−	1.02200i	0.0330365	−	0.0572210i
$320$	−0.714925	−	1.23829i	−0.0399655	−	0.0692223i
$321$		0			0
$322$	−2.63726	−	21.1454i	−0.146969	−	1.17838i
$323$		−	4.94962i		−	0.275404i
$324$		0			0
$325$	−16.2203	−	9.36481i	−0.899742	−	0.519466i
$326$	9.85980	+	5.69256i	0.546084	+	0.315282i
$327$		0			0
$328$			0.404360i			0.0223270i
$329$	13.4503	+	5.67905i	0.741537	+	0.313096i
$330$		0			0
$331$	13.2466	+	22.9437i	0.728096	+	1.26110i	0.957687	+	0.287812i	$0.0929280\pi$
$331$	13.2466	+	22.9437i	0.728096	+	1.26110i	−0.229591	+	0.973287i	$0.573739\pi$
$332$	−0.811624	+	1.40577i	−0.0445436	+	0.0771519i
$333$		0			0
$334$	9.81065	−	5.66418i	0.536815	−	0.309930i
$335$	−6.08209			−0.332300
$336$		0			0
$337$	−8.12902			−0.442816			−0.221408	−	0.975181i	$-0.571065\pi$
$337$	−8.12902			−0.442816			−0.221408	+	0.975181i	$0.571065\pi$
$338$	−23.5208	+	13.5797i	−1.27936	+	0.738640i
$339$		0			0
$340$	−1.63290	+	2.82827i	−0.0885565	+	0.153384i
$341$	−7.42410	−	12.8589i	−0.402037	−	0.696349i
$342$		0			0
$343$	−6.73586	−	17.2519i	−0.363702	−	0.931515i
$344$			5.81766i			0.313667i
$345$		0			0
$346$	18.7853	+	10.8457i	1.00991	+	0.583069i
$347$	−22.1851	−	12.8086i	−1.19096	−	0.687599i	−0.232433	−	0.972612i	$-0.574669\pi$
$347$	−22.1851	−	12.8086i	−1.19096	−	0.687599i	−0.958524	+	0.285013i	$0.908002\pi$
$348$		0			0
$349$		−	10.5301i		−	0.563663i	−0.959464	−	0.281831i	$-0.909058\pi$
$349$		−	10.5301i		−	0.563663i	0.959464	−	0.281831i	$-0.0909418\pi$
$350$	−4.71785	−	6.23602i	−0.252179	−	0.333329i
$351$		0			0
$352$	1.70972	+	2.96133i	0.0911285	+	0.157839i
$353$	6.42186	−	11.1230i	0.341801	−	0.592017i	−0.642966	−	0.765895i	$-0.722296\pi$
$353$	6.42186	−	11.1230i	0.341801	−	0.592017i	0.984767	+	0.173878i	$0.0556297\pi$
$354$		0			0
$355$	4.40078	−	2.54079i	0.233569	−	0.134851i
$356$	−4.05949			−0.215152
$357$		0			0
$358$	−20.7912			−1.09885
$359$	25.6881	−	14.8311i	1.35577	−	0.782753i	0.366718	−	0.930332i	$-0.380482\pi$
$359$	25.6881	−	14.8311i	1.35577	−	0.782753i	0.989050	+	0.147579i	$0.0471482\pi$
$360$		0			0
$361$	−7.15191	+	12.3875i	−0.376416	+	0.651972i
$362$	10.7650	+	18.6456i	0.565798	+	0.979991i
$363$		0			0
$364$	−16.6376	+	2.07505i	−0.872048	+	0.108762i
$365$		−	0.331955i		−	0.0173753i
$366$		0			0
$367$	−20.7828	−	11.9989i	−1.08485	−	0.626340i	−0.152651	−	0.988280i	$-0.548781\pi$
$367$	−20.7828	−	11.9989i	−1.08485	−	0.626340i	−0.932201	+	0.361940i	$0.882115\pi$
$368$	−6.97507	−	4.02706i	−0.363600	−	0.209925i
$369$		0			0
$370$			3.08235i			0.160244i
$371$	25.9596	−	3.23769i	1.34775	−	0.168093i
$372$		0			0
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	0.977594	−	0.210500i	$-0.0675091\pi$
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	−0.671095	+	0.741371i	$0.734176\pi$
$374$	3.90503	−	6.76372i	0.201925	−	0.349744i
$375$		0			0
$376$	4.77898	−	2.75915i	0.246457	−	0.142292i
$377$	2.18705			0.112639
$378$		0			0
$379$	−13.1379			−0.674850			−0.337425	−	0.941352i	$-0.609556\pi$
$379$	−13.1379			−0.674850			−0.337425	+	0.941352i	$0.609556\pi$
$380$	−2.68345	+	1.54929i	−0.137658	+	0.0794769i
$381$		0			0
$382$	−3.68469	+	6.38207i	−0.188525	+	0.326535i
$383$	−8.77603	−	15.2005i	−0.448434	−	0.776711i	0.549850	−	0.835263i	$-0.314685\pi$
$383$	−8.77603	−	15.2005i	−0.448434	−	0.776711i	−0.998284	+	0.0585527i	$0.981351\pi$
$384$		0			0
$385$	−7.80468	−	10.3162i	−0.397763	−	0.525761i
$386$		−	2.82559i		−	0.143819i
$387$		0			0
$388$	9.18719	+	5.30423i	0.466409	+	0.269281i
$389$	−18.9148	−	10.9205i	−0.959020	−	0.553691i	−0.0631489	−	0.998004i	$-0.520114\pi$
$389$	−18.9148	−	10.9205i	−0.959020	−	0.553691i	−0.895871	+	0.444313i	$0.853448\pi$
$390$		0			0
$391$			18.3957i			0.930312i
$392$	−6.73614	−	1.90379i	−0.340226	−	0.0961558i
$393$		0			0
$394$	13.0441	+	22.5931i	0.657154	+	1.13822i
$395$	10.4107	−	18.0319i	0.523821	−	0.907285i
$396$		0			0
$397$	33.7636	−	19.4935i	1.69455	−	0.978348i	0.743792	−	0.668411i	$-0.233025\pi$
$397$	33.7636	−	19.4935i	1.69455	−	0.978348i	0.950757	−	0.309937i	$-0.100308\pi$
$398$	15.4165			0.772760
$399$		0			0
$400$	−2.95553			−0.147776
$401$	20.0899	−	11.5989i	1.00324	−	0.579223i	0.0940373	−	0.995569i	$-0.470023\pi$
$401$	20.0899	−	11.5989i	1.00324	−	0.579223i	0.909206	+	0.416346i	$0.136689\pi$
$402$		0			0
$403$	13.7588	−	23.8310i	0.685376	−	1.18711i
$404$	4.02443	+	6.97052i	0.200223	+	0.346796i
$405$		0			0
$406$	0.841182	+	0.355169i	0.0417471	+	0.0176267i
$407$		−	7.37134i		−	0.365384i
$408$		0			0
$409$	21.3205	+	12.3094i	1.05423	+	0.608659i	0.923830	−	0.382803i	$-0.125041\pi$
$409$	21.3205	+	12.3094i	1.05423	+	0.608659i	0.130398	+	0.991462i	$0.458374\pi$
$410$	−0.500713	−	0.289087i	−0.0247285	−	0.0142770i
$411$		0			0
$412$		−	2.81391i		−	0.138631i
$413$	3.61156	+	28.9572i	0.177713	+	1.42489i
$414$		0			0
$415$	−1.16050	−	2.01005i	−0.0569667	−	0.0986693i
$416$	−3.16857	+	5.48813i	−0.155352	+	0.269078i
$417$		0			0
$418$	6.41739	−	3.70508i	0.313885	−	0.181222i
$419$	−17.0799			−0.834409			−0.417204	−	0.908813i	$-0.636990\pi$
$419$	−17.0799			−0.834409			−0.417204	+	0.908813i	$0.636990\pi$
$420$		0			0
$421$	14.7130			0.717069			0.358535	−	0.933516i	$-0.383276\pi$
$421$	14.7130			0.717069			0.358535	+	0.933516i	$0.383276\pi$
$422$	−7.66371	+	4.42465i	−0.373064	+	0.215388i
$423$		0			0
$424$	4.94391	−	8.56310i	0.240097	−	0.415861i
$425$	3.37524	+	5.84608i	0.163723	+	0.283577i
$426$		0			0
$427$	11.8142	−	27.9807i	0.571728	−	1.35408i
$428$			15.8216i			0.764764i
$429$		0			0
$430$	−7.20393	−	4.15919i	−0.347404	−	0.200574i
$431$	−8.32286	−	4.80521i	−0.400898	−	0.231459i	0.285973	−	0.958238i	$-0.407683\pi$
$431$	−8.32286	−	4.80521i	−0.400898	−	0.231459i	−0.686871	+	0.726779i	$0.741016\pi$
$432$		0			0
$433$			9.04314i			0.434585i	0.976106	+	0.217293i	$0.0697226\pi$
$433$			9.04314i			0.434585i	−0.976106	+	0.217293i	$0.930277\pi$
$434$	9.16200	−	6.93149i	0.439790	−	0.332722i
$435$		0			0
$436$	−5.10675	−	8.84514i	−0.244569	−	0.423606i
$437$	−8.72690	+	15.1154i	−0.417464	+	0.723069i
$438$		0			0
$439$	−0.791370	+	0.456897i	−0.0377700	+	0.0218065i	−0.518766	−	0.854916i	$-0.673608\pi$
$439$	−0.791370	+	0.456897i	−0.0377700	+	0.0218065i	0.480996	+	0.876723i	$0.340275\pi$
$440$	−4.88930			−0.233088
$441$		0			0
$442$	14.4741			0.688465
$443$	−25.4279	+	14.6808i	−1.20812	+	0.697507i	−0.962348	−	0.271821i	$-0.912374\pi$
$443$	−25.4279	+	14.6808i	−1.20812	+	0.697507i	−0.245770	+	0.969328i	$0.579041\pi$
$444$		0			0
$445$	2.90223	−	5.02681i	0.137579	−	0.238294i
$446$	3.97772	+	6.88961i	0.188351	+	0.326233i
$447$		0			0
$448$	−2.10995	+	1.59628i	−0.0996858	+	0.0754171i
$449$			3.36736i			0.158915i	0.996838	+	0.0794577i	$0.0253189\pi$
$449$			3.36736i			0.158915i	−0.996838	+	0.0794577i	$0.974681\pi$
$450$		0			0
$451$	1.19744	+	0.691343i	0.0563853	+	0.0325541i
$452$	7.28808	+	4.20778i	0.342802	+	0.197917i
$453$		0			0
$454$		−	9.23968i		−	0.433640i
$455$	9.32514	−	22.0856i	0.437169	−	1.03539i
$456$		0			0
$457$	7.55693	+	13.0890i	0.353498	+	0.612277i	0.986860	−	0.161579i	$-0.0516588\pi$
$457$	7.55693	+	13.0890i	0.353498	+	0.612277i	−0.633362	+	0.773856i	$0.718325\pi$
$458$	4.22227	−	7.31319i	0.197294	−	0.341723i
$459$		0			0
$460$	9.97330	−	5.75809i	0.465008	−	0.268472i
$461$	−10.3889			−0.483860			−0.241930	−	0.970294i	$-0.577780\pi$
$461$	−10.3889			−0.483860			−0.241930	+	0.970294i	$0.577780\pi$
$462$		0			0
$463$	5.31444			0.246983			0.123492	−	0.992346i	$-0.460591\pi$
$463$	5.31444			0.246983			0.123492	+	0.992346i	$0.460591\pi$
$464$	0.298879	−	0.172558i	0.0138751	−	0.00801078i
$465$		0			0
$466$	8.32399	−	14.4176i	0.385601	−	0.667881i
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	0.998459	−	0.0554907i	$-0.0176723\pi$
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	−0.547286	+	0.836946i	$0.684339\pi$
$468$		0			0
$469$	1.39283	+	11.1676i	0.0643148	+	0.515672i
$470$			7.89034i			0.363954i
$471$		0			0
$472$	9.55191	+	5.51480i	0.439662	+	0.253839i
$473$	17.2280	+	9.94659i	0.792144	+	0.457345i
$474$		0			0
$475$			6.40483i			0.293874i
$476$	5.56705	+	2.35055i	0.255165	+	0.107737i
$477$		0			0
$478$	−13.6442	−	23.6325i	−0.624073	−	1.08093i
$479$	−13.9012	+	24.0776i	−0.635163	+	1.10013i	0.351318	+	0.936256i	$0.385734\pi$
$479$	−13.9012	+	24.0776i	−0.635163	+	1.10013i	−0.986481	+	0.163878i	$0.947600\pi$
$480$		0			0
$481$	11.8308	−	6.83054i	0.539440	−	0.311446i
$482$	25.2900			1.15193
$483$		0			0
$484$	0.692610			0.0314823
$485$	−13.1363	+	7.58425i	−0.596489	+	0.344383i
$486$		0			0
$487$	3.73838	−	6.47506i	0.169402	−	0.293413i	−0.768808	−	0.639480i	$-0.779150\pi$
$487$	3.73838	−	6.47506i	0.169402	−	0.293413i	0.938210	+	0.346067i	$0.112483\pi$
$488$	−5.73987	−	9.94175i	−0.259832	−	0.450042i
$489$		0			0
$490$	7.17327	−	6.98021i	0.324055	−	0.315334i
$491$			22.1086i			0.997746i	0.866675	+	0.498873i	$0.166253\pi$
$491$			22.1086i			0.997746i	−0.866675	+	0.498873i	$0.833747\pi$
$492$		0			0
$493$	−0.682643	−	0.394124i	−0.0307447	−	0.0177505i
$494$	11.8931	+	6.86651i	0.535098	+	0.308939i
$495$		0			0
$496$		−	4.34228i		−	0.194974i
$497$	−5.67306	−	7.49861i	−0.254471	−	0.336359i
$498$		0			0
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	−0.954063	−	0.299606i	$-0.903145\pi$
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	0.217565	−	0.976046i	$-0.430189\pi$
$500$	5.68761	−	9.85123i	0.254358	−	0.440560i
$501$		0			0
$502$	−7.09567	+	4.09669i	−0.316695	+	0.182844i
$503$	−25.6142			−1.14208			−0.571039	−	0.820923i	$-0.693460\pi$
$503$	−25.6142			−1.14208			−0.571039	+	0.820923i	$0.693460\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$	−23.8509	+	13.7703i	−1.06030	+	0.612165i
$507$		0			0
$508$	2.88886	−	5.00366i	0.128173	−	0.222002i
$509$	−10.7358	−	18.5950i	−0.475857	−	0.824209i	0.523760	−	0.851866i	$-0.324529\pi$
$509$	−10.7358	−	18.5950i	−0.475857	−	0.824209i	−0.999617	+	0.0276567i	$0.991195\pi$
$510$		0			0
$511$	−0.609518	+	0.0760193i	−0.0269635	+	0.00336290i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−5.74560	−	3.31723i	−0.253428	−	0.146317i
$515$	3.48443	+	2.01173i	0.153542	+	0.0886476i
$516$		0			0
$517$		−	18.8695i		−	0.829880i
$518$	5.65963	−	0.705872i	0.248670	−	0.0310142i
$519$		0			0
$520$	−4.53059	−	7.84721i	−0.198679	−	0.344123i
$521$	−3.23087	+	5.59604i	−0.141547	+	0.245167i	−0.928079	−	0.372382i	$-0.878541\pi$
$521$	−3.23087	+	5.59604i	−0.141547	+	0.245167i	0.786532	+	0.617549i	$0.211874\pi$
$522$		0			0
$523$	11.7830	−	6.80291i	0.515234	−	0.297470i	−0.219749	−	0.975557i	$-0.570524\pi$
$523$	11.7830	−	6.80291i	0.515234	−	0.297470i	0.734982	+	0.678086i	$0.237190\pi$
$524$	4.45667			0.194690
$525$		0			0
$526$	−6.04590			−0.263614
$527$	−8.58910	+	4.95892i	−0.374147	+	0.216014i
$528$		0			0
$529$	20.9344	−	36.2594i	0.910190	−	1.57649i
$530$	7.06905	+	12.2440i	0.307060	+	0.531843i
$531$		0			0
$532$	3.45924	+	4.57241i	0.149977	+	0.198239i
$533$			2.56249i			0.110994i
$534$		0			0
$535$	−19.5916	−	11.3112i	−0.847020	−	0.489027i
$536$	3.68377	+	2.12683i	0.159115	+	0.0918650i
$537$		0			0
$538$		−	6.82139i		−	0.294091i
$539$	−17.1547	+	16.6930i	−0.738904	+	0.719017i
$540$		0			0
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	−0.985022	−	0.172428i	$-0.944839\pi$
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	0.343184	−	0.939268i	$-0.388494\pi$
$542$	−2.53907	+	4.39780i	−0.109063	+	0.188902i
$543$		0			0
$544$	1.97802	−	1.14201i	0.0848067	−	0.0489632i
$545$	14.6038			0.625557
$546$		0			0
$547$	18.1441			0.775787			0.387894	−	0.921704i	$-0.373203\pi$
$547$	18.1441			0.775787			0.387894	+	0.921704i	$0.373203\pi$
$548$	−8.36293	+	4.82834i	−0.357247	+	0.206256i
$549$		0			0
$550$	−5.05313	+	8.75228i	−0.215466	+	0.373199i
$551$	−0.373944	−	0.647690i	−0.0159305	−	0.0275925i
$552$		0			0
$553$	−35.4933	−	14.9862i	−1.50933	−	0.637279i
$554$		−	1.97913i		−	0.0840854i
$555$		0			0
$556$	16.0680	+	9.27686i	0.681435	+	0.393426i
$557$	−32.5079	−	18.7684i	−1.37740	−	0.795245i	−0.385558	−	0.922684i	$-0.625991\pi$
$557$	−32.5079	−	18.7684i	−1.37740	−	0.795245i	−0.991846	+	0.127439i	$0.959324\pi$
$558$		0			0
$559$			36.8674i			1.55932i
$560$	−0.468194	−	3.75394i	−0.0197848	−	0.158633i
$561$		0			0
$562$	8.81631	+	15.2703i	0.371894	+	0.644139i
$563$	−3.55341	+	6.15468i	−0.149758	+	0.259389i	−0.931138	−	0.364667i	$-0.881183\pi$
$563$	−3.55341	+	6.15468i	−0.149758	+	0.259389i	0.781380	+	0.624056i	$0.214516\pi$
$564$		0			0
$565$	−10.4209	+	6.01649i	−0.438409	+	0.253116i
$566$	−5.15385			−0.216633
$567$		0			0
$568$	−3.55393			−0.149119
$569$	35.6499	−	20.5825i	1.49452	−	0.862862i	0.494541	−	0.869154i	$-0.335336\pi$
$569$	35.6499	−	20.5825i	1.49452	−	0.862862i	0.999980	+	0.00629202i	$0.00200283\pi$
$570$		0			0
$571$	−2.21293	+	3.83290i	−0.0926080	+	0.160402i	−0.908608	−	0.417650i	$-0.862854\pi$
$571$	−2.21293	+	3.83290i	−0.0926080	+	0.160402i	0.816000	+	0.578052i	$0.196187\pi$
$572$	10.8348	+	18.7664i	0.453024	+	0.784661i
$573$		0			0
$574$	−0.416140	+	0.985584i	−0.0173693	+	0.0411375i
$575$		−	23.8042i		−	0.992702i
$576$		0			0
$577$	2.37542	+	1.37145i	0.0988900	+	0.0570941i	0.548629	−	0.836066i	$-0.315150\pi$
$577$	2.37542	+	1.37145i	0.0988900	+	0.0570941i	−0.449739	+	0.893160i	$0.648483\pi$
$578$	10.2046	+	5.89164i	0.424456	+	0.245060i
$579$		0			0
$580$			0.493463i			0.0204899i
$581$	−3.42497	+	2.59116i	−0.142092	+	0.107499i
$582$		0			0
$583$	−16.9054	−	29.2811i	−0.700151	−	1.21270i
$584$	−0.116080	+	0.201057i	−0.00480344	+	0.00831981i
$585$		0			0
$586$	−1.78831	+	1.03248i	−0.0738745	+	0.0426515i
$587$	−19.8050			−0.817438			−0.408719	−	0.912660i	$-0.634024\pi$
$587$	−19.8050			−0.817438			−0.408719	+	0.912660i	$0.634024\pi$
$588$		0			0
$589$	−9.41001			−0.387733
$590$	−13.6578	+	7.88534i	−0.562283	+	0.324634i
$591$		0			0
$592$	1.07786	−	1.86690i	0.0442996	−	0.0767292i
$593$	0.434850	+	0.753183i	0.0178572	+	0.0309295i	0.874816	−	0.484456i	$-0.160982\pi$
$593$	0.434850	+	0.753183i	0.0178572	+	0.0309295i	−0.856959	+	0.515385i	$0.827649\pi$
$594$		0			0
$595$	−6.89068	+	5.21313i	−0.282490	+	0.213717i
$596$		−	6.50694i		−	0.266535i
$597$		0			0
$598$	−44.2020	−	25.5201i	−1.80756	−	1.04359i
$599$	2.33277	+	1.34682i	0.0953143	+	0.0550297i	0.546899	−	0.837198i	$-0.315808\pi$
$599$	2.33277	+	1.34682i	0.0953143	+	0.0550297i	−0.451585	+	0.892228i	$0.649141\pi$
$600$		0			0
$601$		−	0.133165i		−	0.00543193i	−0.999996	−	0.00271596i	$-0.999135\pi$
$601$		−	0.133165i		−	0.00543193i	0.999996	−	0.00271596i	$-0.000864519\pi$
$602$	−5.98714	+	14.1799i	−0.244018	+	0.577931i
$603$		0			0
$604$	2.87950	+	4.98745i	0.117165	+	0.202936i
$605$	−0.495165	+	0.857650i	−0.0201313	+	0.0348684i
$606$		0			0
$607$	38.3860	−	22.1622i	1.55804	−	0.899534i	0.560594	−	0.828091i	$-0.310573\pi$
$607$	38.3860	−	22.1622i	1.55804	−	0.899534i	0.997445	−	0.0714432i	$-0.0227605\pi$
$608$	2.16707			0.0878862
$609$		0			0
$610$	16.4143			0.664596
$611$	30.2851	−	17.4851i	1.22520	−	0.707372i
$612$		0			0
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	−0.791680	−	0.610936i	$-0.790793\pi$
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	0.924926	+	0.380147i	$0.124127\pi$
$614$	−0.545593	−	0.944994i	−0.0220183	−	0.0381369i
$615$		0			0
$616$	1.11967	+	8.97745i	0.0451129	+	0.361712i
$617$		−	9.23125i		−	0.371636i	−0.982584	−	0.185818i	$-0.940506\pi$
$617$		−	9.23125i		−	0.371636i	0.982584	−	0.185818i	$-0.0594935\pi$
$618$		0			0
$619$	5.66289	+	3.26947i	0.227611	+	0.131411i	0.609469	−	0.792810i	$-0.291383\pi$
$619$	5.66289	+	3.26947i	0.227611	+	0.131411i	−0.381859	+	0.924221i	$0.624716\pi$
$620$	5.37699	+	3.10441i	0.215945	+	0.124676i
$621$		0			0
$622$			15.2220i			0.610347i
$623$	−9.89457	−	4.17775i	−0.396417	−	0.167378i
$624$		0			0
$625$	0.743610	+	1.28797i	0.0297444	+	0.0515188i
$626$	−5.78518	+	10.0202i	−0.231222	+	0.400489i
$627$		0			0
$628$	−6.89669	+	3.98180i	−0.275208	+	0.158891i
$629$	−4.92368			−0.196320
$630$		0			0
$631$	13.8837			0.552699			0.276350	−	0.961057i	$-0.410875\pi$
$631$	13.8837			0.552699			0.276350	+	0.961057i	$0.410875\pi$
$632$	−12.6111	+	7.28100i	−0.501641	+	0.289623i
$633$		0			0
$634$	8.58020	−	14.8613i	0.340763	−	0.590219i
$635$	4.13064	+	7.15449i	0.163920	+	0.283917i
$636$		0			0
$637$	−42.6879	−	12.0646i	−1.69136	−	0.478016i
$638$		−	1.18010i		−	0.0467207i
$639$		0			0
$640$	−1.23829	−	0.714925i	−0.0489476	−	0.0282599i
$641$	13.1940	+	7.61757i	0.521133	+	0.300876i	0.737398	−	0.675459i	$-0.236054\pi$
$641$	13.1940	+	7.61757i	0.521133	+	0.300876i	−0.216265	+	0.976335i	$0.569388\pi$
$642$		0			0
$643$		−	19.1465i		−	0.755064i	−0.925997	−	0.377532i	$-0.876773\pi$
$643$		−	19.1465i		−	0.755064i	0.925997	−	0.377532i	$-0.123227\pi$
$644$	−12.8566	−	16.9938i	−0.506621	−	0.669649i
$645$		0			0
$646$	−2.47481	−	4.28649i	−0.0973700	−	0.168650i
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	−0.849996	−	0.526789i	$-0.823396\pi$
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	0.881211	+	0.472723i	$0.156729\pi$
$648$		0			0
$649$	32.6622	−	18.8576i	1.28211	−	0.740224i
$650$	−18.7296			−0.734636
$651$		0			0
$652$	11.3851			0.445876
$653$	15.5572	−	8.98197i	0.608802	−	0.351492i	−0.163695	−	0.986511i	$-0.552341\pi$
$653$	15.5572	−	8.98197i	0.608802	−	0.351492i	0.772496	+	0.635019i	$0.219008\pi$
$654$		0			0
$655$	−3.18619	+	5.51863i	−0.124495	+	0.215631i
$656$	0.202180	+	0.350186i	0.00789380	+	0.0136725i
$657$		0			0
$658$	14.4878	−	1.80692i	0.564793	−	0.0704412i
$659$		−	11.6573i		−	0.454105i	−0.973883	−	0.227052i	$-0.927091\pi$
$659$		−	11.6573i		−	0.454105i	0.973883	−	0.227052i	$-0.0729089\pi$
$660$		0			0
$661$	15.7786	+	9.10975i	0.613715	+	0.354328i	0.774418	−	0.632674i	$-0.218043\pi$
$661$	15.7786	+	9.10975i	0.613715	+	0.354328i	−0.160703	+	0.987003i	$0.551376\pi$
$662$	22.9437	+	13.2466i	0.891732	+	0.514842i
$663$		0			0
$664$			1.62325i			0.0629942i
$665$	−8.13505	+	1.01461i	−0.315464	+	0.0393448i
$666$		0			0
$667$	1.38980	+	2.40720i	0.0538132	+	0.0932072i
$668$	5.66418	−	9.81065i	0.219154	−	0.379585i
$669$		0			0
$670$	−5.26725	+	3.04105i	−0.203491	+	0.117486i
$671$	−39.2544			−1.51540
$672$		0			0
$673$	−4.82212			−0.185879			−0.0929395	−	0.995672i	$-0.529626\pi$
$673$	−4.82212			−0.185879			−0.0929395	+	0.995672i	$0.529626\pi$
$674$	−7.03993	+	4.06451i	−0.271168	+	0.156559i
$675$		0			0
$676$	−13.5797	+	23.5208i	−0.522297	+	0.904645i
$677$	−11.5645	−	20.0303i	−0.444460	−	0.769827i	0.553554	−	0.832813i	$-0.313271\pi$
$677$	−11.5645	−	20.0303i	−0.444460	−	0.769827i	−0.998014	+	0.0629856i	$0.979938\pi$
$678$		0			0
$679$	16.9341	+	22.3833i	0.649869	+	0.858993i
$680$			3.26580i			0.125238i
$681$		0			0
$682$	−12.8589	−	7.42410i	−0.492393	−	0.284283i
$683$	−6.80041	−	3.92622i	−0.260210	−	0.150233i	0.364220	−	0.931313i	$-0.381336\pi$
$683$	−6.80041	−	3.92622i	−0.260210	−	0.150233i	−0.624431	+	0.781080i	$0.714669\pi$
$684$		0			0
$685$		−	13.8076i		−	0.527562i
$686$	−14.4594	−	11.5727i	−0.552062	−	0.441846i
$687$		0			0
$688$	2.90883	+	5.03824i	0.110898	+	0.192081i
$689$	31.3303	−	54.2656i	1.19359	−	2.06736i
$690$		0			0
$691$	14.8676	−	8.58379i	0.565589	−	0.326543i	−0.189797	−	0.981823i	$-0.560783\pi$
$691$	14.8676	−	8.58379i	0.565589	−	0.326543i	0.755386	+	0.655281i	$0.227450\pi$
$692$	21.6914			0.824584
$693$		0			0
$694$	−25.6171			−0.972412
$695$	−22.9748	+	13.2645i	−0.871485	+	0.503152i
$696$		0			0
$697$	0.461782	−	0.799830i	0.0174912	−	0.0302957i
$698$	−5.26504	−	9.11932i	−0.199285	−	0.345171i
$699$		0			0
$700$	−7.20378	−	3.04163i	−0.272277	−	0.114963i
$701$		−	34.9404i		−	1.31968i	−0.751406	−	0.659840i	$-0.770624\pi$
$701$		−	34.9404i		−	1.31968i	0.751406	−	0.659840i	$-0.229376\pi$
$702$		0			0
$703$	−4.04570	−	2.33579i	−0.152587	−	0.0880959i
$704$	2.96133	+	1.70972i	0.111609	+	0.0644376i
$705$		0			0
$706$		−	12.8437i		−	0.483380i
$707$	2.63554	+	21.1316i	0.0991197	+	0.794735i
$708$		0			0
$709$	12.1668	+	21.0735i	0.456933	+	0.791432i	0.998797	−	0.0490345i	$-0.0156144\pi$
$709$	12.1668	+	21.0735i	0.456933	+	0.791432i	−0.541864	+	0.840466i	$0.682281\pi$
$710$	2.54079	−	4.40078i	0.0953542	−	0.165158i
$711$		0			0
$712$	−3.51562	+	2.02974i	−0.131753	+	0.0760678i
$713$	34.9732			1.30976
$714$		0			0
$715$	−30.9842			−1.15874
$716$	−18.0057	+	10.3956i	−0.672904	+	0.388501i
$717$		0			0
$718$	14.8311	−	25.6881i	0.553490	−	0.958673i
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	0.981920	−	0.189297i	$-0.0606210\pi$
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	−0.654896	+	0.755719i	$0.727288\pi$
$720$		0			0
$721$	2.89588	−	6.85860i	0.107848	−	0.255428i
$722$			14.3038i			0.532333i
$723$		0			0
$724$	18.6456	+	10.7650i	0.692958	+	0.400079i
$725$	0.883344	+	0.509999i	0.0328066	+	0.0189409i
$726$		0			0
$727$			39.1013i			1.45019i	0.688650	+	0.725094i	$0.258204\pi$
$727$			39.1013i			1.45019i	−0.688650	+	0.725094i	$0.741796\pi$
$728$	−13.3711	+	10.1159i	−0.495565	+	0.374919i
$729$		0			0
$730$	−0.165978	−	0.287482i	−0.00614311	−	0.0106402i
$731$	6.64381	−	11.5074i	0.245730	−	0.425617i
$732$		0			0
$733$	−20.3073	+	11.7245i	−0.750069	+	0.433053i	−0.825719	−	0.564082i	$-0.809230\pi$
$733$	−20.3073	+	11.7245i	−0.750069	+	0.433053i	0.0756499	+	0.997134i	$0.475897\pi$
$734$	−23.9979			−0.885779
$735$		0			0
$736$	−8.05411			−0.296879
$737$	12.5965	−	7.27257i	0.463997	−	0.267889i
$738$		0			0
$739$	13.3662	−	23.1509i	0.491682	−	0.851618i	−0.508272	−	0.861197i	$-0.669716\pi$
$739$	13.3662	−	23.1509i	0.491682	−	0.851618i	0.999954	+	0.00957820i	$0.00304888\pi$
$740$	1.54117	+	2.66939i	0.0566547	+	0.0981288i
$741$		0			0
$742$	20.8628	−	15.7837i	0.765898	−	0.579438i
$743$		−	12.8072i		−	0.469851i	−0.972013	−	0.234925i	$-0.924515\pi$
$743$		−	12.8072i		−	0.469851i	0.972013	−	0.234925i	$-0.0754846\pi$
$744$		0			0
$745$	8.05745	+	4.65197i	0.295202	+	0.170435i
$746$	10.2528	+	5.91948i	0.375383	+	0.216727i
$747$		0			0
$748$		−	7.81007i		−	0.285564i
$749$	−16.2825	+	38.5634i	−0.594949	+	1.40908i
$750$		0			0
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	0.944243	−	0.329249i	$-0.106796\pi$
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	−0.757260	+	0.653114i	$0.773462\pi$
$752$	2.75915	−	4.77898i	0.100616	−	0.174272i
$753$		0			0
$754$	1.89404	−	1.09352i	0.0689768	−	0.0398238i
$755$	−8.23452			−0.299685
$756$		0			0
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$	−11.3778	+	6.56897i	−0.413260	+	0.238596i
$759$		0			0
$760$	−1.54929	+	2.68345i	−0.0561987	+	0.0973390i
$761$	−8.14993	−	14.1161i	−0.295435	−	0.511708i	0.679651	−	0.733536i	$-0.262131\pi$
$761$	−8.14993	−	14.1161i	−0.295435	−	0.511708i	−0.975086	+	0.221827i	$0.928798\pi$
$762$		0			0
$763$	−3.34433	−	26.8146i	−0.121073	−	0.970754i
$764$			7.36938i			0.266615i
$765$		0			0
$766$	−15.2005	−	8.77603i	−0.549217	−	0.317091i
$767$	60.5319	+	34.9481i	2.18568	+	1.26190i
$768$		0			0
$769$			47.8096i			1.72406i	0.506859	+	0.862029i	$0.330807\pi$
$769$			47.8096i			1.72406i	−0.506859	+	0.862029i	$0.669193\pi$
$770$	−11.9171	−	5.03173i	−0.429464	−	0.181331i
$771$		0			0
$772$	−1.41279	−	2.44703i	−0.0508476	−	0.0880706i
$773$	−6.25441	+	10.8330i	−0.224956	+	0.389635i	−0.956306	−	0.292367i	$-0.905557\pi$
$773$	−6.25441	+	10.8330i	−0.224956	+	0.389635i	0.731350	+	0.682002i	$0.238890\pi$
$774$		0			0
$775$	11.1143	−	6.41686i	0.399239	−	0.230501i
$776$	10.6085			0.380821
$777$		0			0
$778$	−21.8410			−0.783037
$779$	0.758876	−	0.438137i	0.0271896	−	0.0156979i
$780$		0			0
$781$	−6.07623	+	10.5243i	−0.217425	+	0.376590i
$782$	9.19786	+	15.9312i	0.328915	+	0.569697i
$783$		0			0
$784$	−6.78556	+	1.71934i	−0.242342	+	0.0614051i
$785$		−	11.3868i		−	0.406411i
$786$		0			0
$787$	−0.226048	−	0.130509i	−0.00805773	−	0.00465213i	0.495966	−	0.868342i	$-0.334814\pi$
$787$	−0.226048	−	0.130509i	−0.00805773	−	0.00465213i	−0.504023	+	0.863690i	$0.668147\pi$
$788$	22.5931	+	13.0441i	0.804846	+	0.464678i
$789$		0			0
$790$		−	20.8215i		−	0.740795i
$791$	13.4336	+	17.7564i	0.477643	+	0.631345i
$792$		0			0
$793$	−36.3744	−	63.0024i	−1.29169	−	2.23728i
$794$	19.4935	−	33.7636i	0.691797	−	1.19823i
$795$		0			0
$796$	13.3511	−	7.70826i	0.473217	−	0.273212i
$797$	−3.70440			−0.131217			−0.0656083	−	0.997845i	$-0.520899\pi$
$797$	−3.70440			−0.131217			−0.0656083	+	0.997845i	$0.520899\pi$
$798$		0			0
$799$	−12.6039			−0.445893
$800$	−2.55956	+	1.47776i	−0.0904942	+	0.0522468i
$801$		0			0
$802$	11.5989	−	20.0899i	0.409573	−	0.709400i
$803$	0.396931	+	0.687504i	0.0140074	+	0.0242615i
$804$		0			0
$805$	30.2347	−	3.77088i	1.06563	−	0.132906i
$806$		−	27.5177i		−	0.969269i
$807$		0			0
$808$	6.97052	+	4.02443i	0.245222	+	0.141579i
$809$	5.94276	+	3.43105i	0.208936	+	0.120629i	0.600817	−	0.799387i	$-0.294842\pi$
$809$	5.94276	+	3.43105i	0.208936	+	0.120629i	−0.391881	+	0.920016i	$0.628175\pi$
$810$		0			0
$811$		−	23.1945i		−	0.814470i	−0.913323	−	0.407235i	$-0.866493\pi$
$811$		−	23.1945i		−	0.814470i	0.913323	−	0.407235i	$-0.133507\pi$
$812$	0.906069	−	0.113005i	0.0317968	−	0.00396571i
$813$		0			0
$814$	−3.68567	−	6.38377i	−0.129183	−	0.223751i
$815$	−8.13951	+	14.0980i	−0.285114	+	0.493833i
$816$		0			0
$817$	10.9182	−	6.30363i	0.381980	−	0.220536i
$818$	24.6187			0.860774
$819$		0			0
$820$	−0.578174			−0.0201907
$821$	−3.28550	+	1.89688i	−0.114665	+	0.0662017i	−0.556236	−	0.831025i	$-0.687755\pi$
$821$	−3.28550	+	1.89688i	−0.114665	+	0.0662017i	0.441571	+	0.897226i	$0.354421\pi$
$822$		0			0
$823$	7.45395	−	12.9106i	0.259828	−	0.450036i	−0.706368	−	0.707845i	$-0.749667\pi$
$823$	7.45395	−	12.9106i	0.259828	−	0.450036i	0.966196	+	0.257810i	$0.0830007\pi$
$824$	−1.40695	−	2.43692i	−0.0490136	−	0.0848940i
$825$		0			0
$826$	17.6063	+	23.2719i	0.612602	+	0.809733i
$827$		−	21.9819i		−	0.764384i	−0.924083	−	0.382192i	$-0.875169\pi$
$827$		−	21.9819i		−	0.764384i	0.924083	−	0.382192i	$-0.124831\pi$
$828$		0			0
$829$	12.2406	+	7.06713i	0.425135	+	0.245452i	0.697272	−	0.716807i	$-0.254397\pi$
$829$	12.2406	+	7.06713i	0.425135	+	0.245452i	−0.272137	+	0.962259i	$0.587730\pi$
$830$	−2.01005	−	1.16050i	−0.0697697	−	0.0402816i
$831$		0			0
$832$			6.33715i			0.219701i
$833$	11.1501	+	11.4584i	0.386326	+	0.397012i
$834$		0			0
$835$	8.09893	+	14.0278i	0.280275	+	0.485451i
$836$	3.70508	−	6.41739i	0.128143	−	0.221950i
$837$		0			0
$838$	−14.7916	+	8.53996i	−0.510969	+	0.295008i
$839$	−17.8498			−0.616242			−0.308121	−	0.951347i	$-0.599700\pi$
$839$	−17.8498			−0.616242			−0.308121	+	0.951347i	$0.599700\pi$
$840$		0			0
$841$	28.8809			0.995893
$842$	12.7419	−	7.35652i	0.439114	−	0.253522i
$843$		0			0
$844$	−4.42465	+	7.66371i	−0.152303	+	0.263796i
$845$	−19.4170	−	33.6312i	−0.667964	−	1.15695i
$846$		0			0
$847$	1.68816	+	0.712787i	0.0580060	+	0.0244917i
$848$		−	9.88782i		−	0.339549i
$849$		0			0
$850$	5.84608	+	3.37524i	0.200519	+	0.115770i
$851$	15.0362	+	8.68118i	0.515436	+	0.297587i
$852$		0			0
$853$		−	40.6907i		−	1.39322i	−0.717448	−	0.696612i	$-0.754690\pi$
$853$		−	40.6907i		−	1.39322i	0.717448	−	0.696612i	$-0.245310\pi$
$854$	−3.75896	−	30.1391i	−0.128629	−	1.03134i
$855$		0			0
$856$	7.91078	+	13.7019i	0.270385	+	0.468320i
$857$	2.72896	−	4.72669i	0.0932194	−	0.161461i	−0.815645	−	0.578553i	$-0.803618\pi$
$857$	2.72896	−	4.72669i	0.0932194	−	0.161461i	0.908864	+	0.417092i	$0.136951\pi$
$858$		0			0
$859$	−38.8822	+	22.4487i	−1.32664	+	0.765938i	−0.984779	−	0.173810i	$-0.944392\pi$
$859$	−38.8822	+	22.4487i	−1.32664	+	0.765938i	−0.341865	+	0.939749i	$0.611059\pi$
$860$	−8.31838			−0.283655
$861$		0			0
$862$	−9.61042			−0.327332
$863$	19.6689	−	11.3559i	0.669539	−	0.386558i	−0.126363	−	0.991984i	$-0.540330\pi$
$863$	19.6689	−	11.3559i	0.669539	−	0.386558i	0.795902	+	0.605426i	$0.206997\pi$
$864$		0			0
$865$	−15.5077	+	26.8602i	−0.527279	+	0.913274i
$866$	4.52157	+	7.83159i	0.153649	+	0.266128i
$867$		0			0
$868$	4.46878	−	10.5838i	0.151680	−	0.359239i
$869$			49.7940i			1.68915i
$870$		0			0
$871$	23.3446	+	13.4780i	0.791002	+	0.456685i
$872$	−8.84514	−	5.10675i	−0.299534	−	0.172936i
$873$		0			0
$874$			17.4538i			0.590384i
$875$	24.0011	−	18.1580i	0.811387	−	0.613853i
$876$		0			0
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	0.999853	+	0.0171413i	$0.00545653\pi$
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	−0.485082	+	0.874469i	$0.661210\pi$
$878$	−0.456897	+	0.791370i	−0.0154195	+	0.0267074i
$879$		0			0
$880$	−4.23425	+	2.44465i	−0.142737	+	0.0824091i
$881$	29.3810			0.989871			0.494935	−	0.868930i	$-0.335192\pi$
$881$	29.3810			0.989871			0.494935	+	0.868930i	$0.335192\pi$
$882$		0			0
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$	12.5350	−	7.23707i	0.421597	−	0.243409i
$885$		0			0
$886$	−14.6808	+	25.4279i	−0.493212	+	0.854268i
$887$	−16.3537	−	28.3254i	−0.549103	−	0.951074i	−0.998336	−	0.0576593i	$-0.981636\pi$
$887$	−16.3537	−	28.3254i	−0.549103	−	0.951074i	0.449234	−	0.893414i	$-0.351697\pi$
$888$		0			0
$889$	12.1907	−	9.22287i	0.408864	−	0.309325i
$890$		−	5.80446i		−	0.194566i
$891$		0			0
$892$	6.88961	+	3.97772i	0.230681	+	0.133184i
$893$	−10.3564	−	5.97926i	−0.346563	−	0.200088i
$894$		0			0
$895$		−	29.7283i		−	0.993706i
$896$	−1.02913	+	2.43739i	−0.0343809	+	0.0814276i
$897$		0			0
$898$	1.68368	+	2.91622i	0.0561851	+	0.0973154i
$899$	−0.749293	+	1.29781i	−0.0249903	+	0.0432845i
$900$		0			0
$901$	−19.5583	+	11.2920i	−0.651580	+	0.376190i
$902$	1.38269			0.0460384
$903$		0			0
$904$	8.41555			0.279897
$905$	−26.6604	+	15.3924i	−0.886222	+	0.511661i
$906$		0			0
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.178123	+	0.984008i	$0.557002\pi$
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.763115	+	0.646263i	$0.776331\pi$
$908$	−4.61984	−	8.00180i	−0.153315	−	0.265549i
$909$		0			0
$910$	−2.96701	−	23.7893i	−0.0983555	−	0.788608i
$911$		−	0.717987i		−	0.0237880i	−0.999929	−	0.0118940i	$-0.996214\pi$
$911$		−	0.717987i		−	0.0237880i	0.999929	−	0.0118940i	$-0.00378606\pi$
$912$		0			0
$913$	4.80697	+	2.77530i	0.159087	+	0.0918492i
$914$	13.0890	+	7.55693i	0.432945	+	0.249961i
$915$		0			0
$916$		−	8.44454i		−	0.279016i
$917$	10.8627	+	4.58650i	0.358717	+	0.151460i
$918$		0			0
$919$	18.9720	+	32.8605i	0.625829	+	1.08397i	0.988380	+	0.152004i	$0.0485727\pi$
$919$	18.9720	+	32.8605i	0.625829	+	1.08397i	−0.362550	+	0.931964i	$0.618094\pi$
$920$	5.75809	−	9.97330i	0.189839	−	0.328810i
$921$		0			0
$922$	−8.99706	+	5.19445i	−0.296302	+	0.171070i
$923$	−22.5218			−0.741313
$924$		0			0
$925$	6.37127			0.209486
$926$	4.60244	−	2.65722i	0.151246	−	0.0873217i
$927$		0			0
$928$	0.172558	−	0.298879i	0.00566448	−	0.00981117i
$929$	−21.4350	−	37.1265i	−0.703259	−	1.21808i	−0.967316	−	0.253574i	$-0.918394\pi$
$929$	−21.4350	−	37.1265i	−0.703259	−	1.21808i	0.264057	−	0.964507i	$-0.414939\pi$
$930$		0			0
$931$	3.72593	+	14.7048i	0.122112	+	0.481929i
$932$		−	16.6480i		−	0.545323i
$933$		0			0
$934$	16.8874	+	9.74994i	0.552572	+	0.319028i
$935$	9.67111	+	5.58362i	0.316279	+	0.182604i
$936$		0			0
$937$			8.64637i			0.282464i	0.989976	+	0.141232i	$0.0451064\pi$
$937$			8.64637i			0.282464i	−0.989976	+	0.141232i	$0.954894\pi$
$938$	6.79002	+	8.97501i	0.221702	+	0.293044i
$939$		0			0
$940$	3.94517	+	6.83323i	0.128677	+	0.222875i
$941$	−5.04603	+	8.73997i	−0.164496	+	0.284915i	−0.936476	−	0.350731i	$-0.885933\pi$
$941$	−5.04603	+	8.73997i	−0.164496	+	0.284915i	0.771980	+	0.635646i	$0.219266\pi$
$942$		0			0
$943$	−2.82044	+	1.62838i	−0.0918460	+	0.0530273i
$944$	11.0296			0.358983
$945$		0			0
$946$	19.8932			0.646783
$947$	50.4627	−	29.1346i	1.63982	−	0.946749i	0.658922	−	0.752212i	$-0.271013\pi$
$947$	50.4627	−	29.1346i	1.63982	−	0.946749i	0.980895	−	0.194537i	$-0.0623205\pi$
$948$		0			0
$949$	−0.735619	+	1.27413i	−0.0238792	+	0.0413600i
$950$	3.20241	+	5.54674i	0.103900	+	0.179960i
$951$		0			0
$952$	5.99648	−	0.747884i	0.194347	−	0.0242391i
$953$			46.9356i			1.52039i	0.649694	+	0.760196i	$0.274897\pi$
$953$			46.9356i			1.52039i	−0.649694	+	0.760196i	$0.725103\pi$
$954$		0			0
$955$	−9.12541	−	5.26856i	−0.295291	−	0.170487i
$956$	−23.6325	−	13.6442i	−0.764330	−	0.441286i
$957$		0			0
$958$			27.8024i			0.898256i
$959$	−25.3528	+	3.16201i	−0.818683	+	0.102107i
$960$		0			0
$961$	−6.07230	−	10.5175i	−0.195881	−	0.339275i
$962$	6.83054	−	11.8308i	0.220225	−	0.381441i
$963$		0			0
$964$	21.9018	−	12.6450i	0.705410	−	0.407269i
$965$	4.04017			0.130058
$966$		0			0
$967$	−12.8629			−0.413643			−0.206822	−	0.978379i	$-0.566312\pi$
$967$	−12.8629			−0.413643			−0.206822	+	0.978379i	$0.566312\pi$
$968$	0.599818	−	0.346305i	0.0192789	−	0.0111307i
$969$		0			0
$970$	−7.58425	+	13.1363i	−0.243516	+	0.421782i
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	0.997699	+	0.0677990i	$0.0215977\pi$
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	−0.440134	+	0.897932i	$0.645069\pi$
$972$		0			0
$973$	29.6169	+	39.1474i	0.949474	+	1.25501i
$974$		−	7.47675i		−	0.239571i
$975$		0			0
$976$	−9.94175	−	5.73987i	−0.318228	−	0.183729i
$977$	−17.6381	−	10.1834i	−0.564293	−	0.325795i	0.190574	−	0.981673i	$-0.438965\pi$
$977$	−17.6381	−	10.1834i	−0.564293	−	0.325795i	−0.754867	+	0.655878i	$0.772299\pi$
$978$		0			0
$979$			13.8812i			0.443645i
$980$	2.72213	−	9.63167i	0.0869553	−	0.307673i
$981$		0			0
$982$	11.0543	+	19.1466i	0.352756	+	0.610992i
$983$	−14.6682	+	25.4061i	−0.467843	+	0.810328i	−0.999325	−	0.0367416i	$-0.988302\pi$
$983$	−14.6682	+	25.4061i	−0.467843	+	0.810328i	0.531482	+	0.847070i	$0.321635\pi$
$984$		0			0
$985$	−32.3048	+	18.6512i	−1.02932	+	0.594276i
$986$	−0.788249			−0.0251030
$987$		0			0
$988$	13.7330			0.436906
$989$	−40.5786	+	23.4280i	−1.29032	+	0.744968i
$990$		0			0
$991$	−14.8114	+	25.6540i	−0.470498	+	0.814927i	−0.999431	−	0.0337371i	$-0.989259\pi$
$991$	−14.8114	+	25.6540i	−0.470498	+	0.814927i	0.528933	+	0.848664i	$0.322592\pi$
$992$	−2.17114	−	3.76052i	−0.0689338	−	0.119397i
$993$		0			0
$994$	−8.66232	−	3.65746i	−0.274752	−	0.116008i
$995$			22.0433i			0.698820i
$996$		0			0
$997$	−23.4011	−	13.5106i	−0.741120	−	0.427886i	0.0813562	−	0.996685i	$-0.474075\pi$
$997$	−23.4011	−	13.5106i	−0.741120	−	0.427886i	−0.822477	+	0.568799i	$0.807408\pi$
$998$	−28.4959	−	16.4521i	−0.902022	−	0.520783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.a.647.7		16
3.2	odd	2		1134.2.k.b.647.2		16
7.5	odd	6		1134.2.k.b.971.2		16
9.2	odd	6		126.2.t.a.59.6	yes	16
9.4	even	3		126.2.l.a.101.7	yes	16
9.5	odd	6		378.2.l.a.143.2		16
9.7	even	3		378.2.t.a.17.2		16
21.5	even	6	inner	1134.2.k.a.971.7		16
36.7	odd	6		3024.2.df.c.17.3		16
36.11	even	6		1008.2.df.c.689.6		16
36.23	even	6		3024.2.ca.c.2033.3		16
36.31	odd	6		1008.2.ca.c.353.3		16
63.2	odd	6		882.2.l.b.509.2		16
63.4	even	3		882.2.m.b.587.1		16
63.5	even	6		378.2.t.a.89.2		16
63.11	odd	6		882.2.m.a.293.4		16
63.13	odd	6		882.2.l.b.227.6		16
63.16	even	3		2646.2.l.a.1097.7		16
63.20	even	6		882.2.t.a.815.7		16
63.23	odd	6		2646.2.t.b.1979.3		16
63.25	even	3		2646.2.m.a.881.7		16
63.31	odd	6		882.2.m.a.587.4		16
63.32	odd	6		2646.2.m.b.1763.6		16
63.34	odd	6		2646.2.t.b.2285.3		16
63.38	even	6		882.2.m.b.293.1		16
63.40	odd	6		126.2.t.a.47.6	yes	16
63.41	even	6		2646.2.l.a.521.3		16
63.47	even	6		126.2.l.a.5.3	✓	16
63.52	odd	6		2646.2.m.b.881.6		16
63.58	even	3		882.2.t.a.803.7		16
63.59	even	6		2646.2.m.a.1763.7		16
63.61	odd	6		378.2.l.a.341.6		16
252.47	odd	6		1008.2.ca.c.257.3		16
252.103	even	6		1008.2.df.c.929.6		16
252.131	odd	6		3024.2.df.c.1601.3		16
252.187	even	6		3024.2.ca.c.2609.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	63.47	even	6
126.2.l.a.101.7	yes	16	9.4	even	3
126.2.t.a.47.6	yes	16	63.40	odd	6
126.2.t.a.59.6	yes	16	9.2	odd	6
378.2.l.a.143.2		16	9.5	odd	6
378.2.l.a.341.6		16	63.61	odd	6
378.2.t.a.17.2		16	9.7	even	3
378.2.t.a.89.2		16	63.5	even	6
882.2.l.b.227.6		16	63.13	odd	6
882.2.l.b.509.2		16	63.2	odd	6
882.2.m.a.293.4		16	63.11	odd	6
882.2.m.a.587.4		16	63.31	odd	6
882.2.m.b.293.1		16	63.38	even	6
882.2.m.b.587.1		16	63.4	even	3
882.2.t.a.803.7		16	63.58	even	3
882.2.t.a.815.7		16	63.20	even	6
1008.2.ca.c.257.3		16	252.47	odd	6
1008.2.ca.c.353.3		16	36.31	odd	6
1008.2.df.c.689.6		16	36.11	even	6
1008.2.df.c.929.6		16	252.103	even	6
1134.2.k.a.647.7		16	1.1	even	1	trivial
1134.2.k.a.971.7		16	21.5	even	6	inner
1134.2.k.b.647.2		16	3.2	odd	2
1134.2.k.b.971.2		16	7.5	odd	6
2646.2.l.a.521.3		16	63.41	even	6
2646.2.l.a.1097.7		16	63.16	even	3
2646.2.m.a.881.7		16	63.25	even	3
2646.2.m.a.1763.7		16	63.59	even	6
2646.2.m.b.881.6		16	63.52	odd	6
2646.2.m.b.1763.6		16	63.32	odd	6
2646.2.t.b.1979.3		16	63.23	odd	6
2646.2.t.b.2285.3		16	63.34	odd	6
3024.2.ca.c.2033.3		16	36.23	even	6
3024.2.ca.c.2609.3		16	252.187	even	6
3024.2.df.c.17.3		16	36.7	odd	6
3024.2.df.c.1601.3		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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.714925 + 1.23829i) q^{5} +(2.10995 - 1.59628i) q^{7} -1.00000i q^{8} +(1.23829 + 0.714925i) q^{10} +(-2.96133 - 1.70972i) q^{11} -6.33715i q^{13} +(1.02913 - 2.43739i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.14201 + 1.97802i) q^{17} +(-1.87673 + 1.08353i) q^{19} +1.42985 q^{20} -3.41945 q^{22} +(6.97507 - 4.02706i) q^{23} +(1.47776 - 2.55956i) q^{25} +(-3.16857 - 5.48813i) q^{26} +(-0.327442 - 2.62541i) q^{28} +0.345115i q^{29} +(3.76052 + 2.17114i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.28402i q^{34} +(3.48511 + 1.47150i) q^{35} +(1.07786 + 1.86690i) q^{37} +(-1.08353 + 1.87673i) q^{38} +(1.23829 - 0.714925i) q^{40} -0.404360 q^{41} -5.81766 q^{43} +(-2.96133 + 1.70972i) q^{44} +(4.02706 - 6.97507i) q^{46} +(2.75915 + 4.77898i) q^{47} +(1.90379 - 6.73614i) q^{49} -2.95553i q^{50} +(-5.48813 - 3.16857i) q^{52} +(8.56310 + 4.94391i) q^{53} -4.88930i q^{55} +(-1.59628 - 2.10995i) q^{56} +(0.172558 + 0.298879i) q^{58} +(-5.51480 + 9.55191i) q^{59} +(9.94175 - 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(7.84721 - 4.53059i) q^{65} +(-2.12683 + 3.68377i) q^{67} +(1.14201 + 1.97802i) q^{68} +(3.75394 - 0.468194i) q^{70} -3.55393i q^{71} +(-0.201057 - 0.116080i) q^{73} +(1.86690 + 1.07786i) q^{74} +2.16707i q^{76} +(-8.97745 + 1.11967i) q^{77} +(-7.28100 - 12.6111i) q^{79} +(0.714925 - 1.23829i) q^{80} +(-0.350186 + 0.202180i) q^{82} -1.62325 q^{83} -3.26580 q^{85} +(-5.03824 + 2.90883i) q^{86} +(-1.70972 + 2.96133i) q^{88} +(-2.02974 - 3.51562i) q^{89} +(-10.1159 - 13.3711i) q^{91} -8.05411i q^{92} +(4.77898 + 2.75915i) q^{94} +(-2.68345 - 1.54929i) q^{95} +10.6085i q^{97} +(-1.71934 - 6.78556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 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

Introduction

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