LMFDB - Embedded newform 432.2.l.b.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	432.107
Dual form			432.2.l.b.323.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.762934 - 1.19077i) q^{2} +(-0.835863 - 1.81696i) q^{4} +(3.06203 - 3.06203i) q^{5} +1.75946 q^{7} +(-2.80128 - 0.390900i) q^{8} +O(q^{10})$	\(q+(0.762934 - 1.19077i) q^{2} +(-0.835863 - 1.81696i) q^{4} +(3.06203 - 3.06203i) q^{5} +1.75946 q^{7} +(-2.80128 - 0.390900i) q^{8} +(-1.31004 - 5.98230i) q^{10} +(2.61910 + 2.61910i) q^{11} +(-3.12275 + 3.12275i) q^{13} +(1.34235 - 2.09511i) q^{14} +(-2.60267 + 3.03745i) q^{16} +0.448503i q^{17} +(-2.39534 - 2.39534i) q^{19} +(-8.12301 - 3.00414i) q^{20} +(5.11694 - 1.12054i) q^{22} +6.52896i q^{23} -13.7521i q^{25} +(1.33602 + 6.10093i) q^{26} +(-1.47066 - 3.19686i) q^{28} +(-1.11604 - 1.11604i) q^{29} +5.03474i q^{31} +(1.63124 + 5.41655i) q^{32} +(0.534063 + 0.342178i) q^{34} +(5.38751 - 5.38751i) q^{35} +(-6.18962 - 6.18962i) q^{37} +(-4.67979 + 1.02481i) q^{38} +(-9.77456 + 7.38067i) q^{40} +6.21456 q^{41} +(-0.0280014 + 0.0280014i) q^{43} +(2.56958 - 6.94799i) q^{44} +(7.77449 + 4.98117i) q^{46} +0.0301338 q^{47} -3.90431 q^{49} +(-16.3755 - 10.4919i) q^{50} +(8.28410 + 3.06372i) q^{52} +(-1.25969 + 1.25969i) q^{53} +16.0395 q^{55} +(-4.92874 - 0.687771i) q^{56} +(-2.18042 + 0.477482i) q^{58} +(2.95409 + 2.95409i) q^{59} +(-1.22879 + 1.22879i) q^{61} +(5.99521 + 3.84117i) q^{62} +(7.69440 + 2.19004i) q^{64} +19.1239i q^{65} +(4.25948 + 4.25948i) q^{67} +(0.814910 - 0.374887i) q^{68} +(-2.30497 - 10.5256i) q^{70} -11.1146i q^{71} +10.5499i q^{73} +(-12.0927 + 2.64814i) q^{74} +(-2.35006 + 6.35441i) q^{76} +(4.60819 + 4.60819i) q^{77} +15.4697i q^{79} +(1.33133 + 17.2702i) q^{80} +(4.74130 - 7.40011i) q^{82} +(4.30188 - 4.30188i) q^{83} +(1.37333 + 1.37333i) q^{85} +(0.0119800 + 0.0547064i) q^{86} +(-6.31303 - 8.36064i) q^{88} -0.159313 q^{89} +(-5.49435 + 5.49435i) q^{91} +(11.8628 - 5.45732i) q^{92} +(0.0229901 - 0.0358825i) q^{94} -14.6692 q^{95} -6.07049 q^{97} +(-2.97873 + 4.64913i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.762934	−	1.19077i	0.539476	−	0.842001i
$2$	0.762934	−	1.19077i	0.539476	−	0.842001i
$3$		0			0
$3$		0			0
$4$	−0.835863	−	1.81696i	−0.417931	−	0.908479i
$5$	3.06203	−	3.06203i	1.36938	−	1.36938i	0.508060	−	0.861322i	$-0.330363\pi$
$5$	3.06203	−	3.06203i	1.36938	−	1.36938i	0.861322	−	0.508060i	$-0.169637\pi$
$6$		0			0
$7$	1.75946			0.665012			0.332506	−	0.943101i	$-0.392106\pi$
$7$	1.75946			0.665012			0.332506	+	0.943101i	$0.392106\pi$
$8$	−2.80128	−	0.390900i	−0.990404	−	0.138204i
$9$		0			0
$10$	−1.31004	−	5.98230i	−0.414272	−	1.89177i
$11$	2.61910	+	2.61910i	0.789687	+	0.789687i	0.981443	−	0.191755i	$-0.0614180\pi$
$11$	2.61910	+	2.61910i	0.789687	+	0.789687i	−0.191755	+	0.981443i	$0.561418\pi$
$12$		0			0
$13$	−3.12275	+	3.12275i	−0.866096	+	0.866096i	−0.992038	−	0.125942i	$-0.959805\pi$
$13$	−3.12275	+	3.12275i	−0.866096	+	0.866096i	0.125942	+	0.992038i	$0.459805\pi$
$14$	1.34235	−	2.09511i	0.358758	−	0.559941i
$15$		0			0
$16$	−2.60267	+	3.03745i	−0.650667	+	0.759363i
$17$			0.448503i			0.108778i	0.998520	+	0.0543890i	$0.0173211\pi$
$17$			0.448503i			0.108778i	−0.998520	+	0.0543890i	$0.982679\pi$
$18$		0			0
$19$	−2.39534	−	2.39534i	−0.549529	−	0.549529i	0.376775	−	0.926305i	$-0.377033\pi$
$19$	−2.39534	−	2.39534i	−0.549529	−	0.549529i	−0.926305	+	0.376775i	$0.877033\pi$
$20$	−8.12301	−	3.00414i	−1.81636	−	0.671746i
$21$		0			0
$22$	5.11694	−	1.12054i	1.09093	−	0.238900i
$23$			6.52896i			1.36138i	0.732570	+	0.680692i	$0.238321\pi$
$23$			6.52896i			1.36138i	−0.732570	+	0.680692i	$0.761679\pi$
$24$		0			0
$25$		−	13.7521i		−	2.75041i
$26$	1.33602	+	6.10093i	0.262016	+	1.19649i
$27$		0			0
$28$	−1.47066	−	3.19686i	−0.277930	−	0.604150i
$29$	−1.11604	−	1.11604i	−0.207244	−	0.207244i	0.595851	−	0.803095i	$-0.296815\pi$
$29$	−1.11604	−	1.11604i	−0.207244	−	0.207244i	−0.803095	+	0.595851i	$0.796815\pi$
$30$		0			0
$31$			5.03474i			0.904266i	0.891951	+	0.452133i	$0.149337\pi$
$31$			5.03474i			0.904266i	−0.891951	+	0.452133i	$0.850663\pi$
$32$	1.63124	+	5.41655i	0.288366	+	0.957520i
$33$		0			0
$34$	0.534063	+	0.342178i	0.0915911	+	0.0586831i
$35$	5.38751	−	5.38751i	0.910656	−	0.910656i
$36$		0			0
$37$	−6.18962	−	6.18962i	−1.01757	−	1.01757i	−0.999843	−	0.0177251i	$-0.994358\pi$
$37$	−6.18962	−	6.18962i	−1.01757	−	1.01757i	−0.0177251	−	0.999843i	$-0.505642\pi$
$38$	−4.67979	+	1.02481i	−0.759162	+	0.166246i
$39$		0			0
$40$	−9.77456	+	7.38067i	−1.54549	+	1.16699i
$41$	6.21456			0.970551			0.485276	−	0.874361i	$-0.338719\pi$
$41$	6.21456			0.970551			0.485276	+	0.874361i	$0.338719\pi$
$42$		0			0
$43$	−0.0280014	+	0.0280014i	−0.00427017	+	0.00427017i	−0.709239	−	0.704968i	$-0.750961\pi$
$43$	−0.0280014	+	0.0280014i	−0.00427017	+	0.00427017i	0.704968	+	0.709239i	$0.250961\pi$
$44$	2.56958	−	6.94799i	0.387379	−	1.04745i
$45$		0			0
$46$	7.77449	+	4.98117i	1.14629	+	0.734434i
$47$	0.0301338			0.00439547			0.00219774	−	0.999998i	$-0.499300\pi$
$47$	0.0301338			0.00439547			0.00219774	+	0.999998i	$0.499300\pi$
$48$		0			0
$49$	−3.90431			−0.557758
$50$	−16.3755	−	10.4919i	−2.31585	−	1.48378i
$51$		0			0
$52$	8.28410	+	3.06372i	1.14880	+	0.424861i
$53$	−1.25969	+	1.25969i	−0.173032	+	0.173032i	−0.788310	−	0.615278i	$-0.789044\pi$
$53$	−1.25969	+	1.25969i	−0.173032	+	0.173032i	0.615278	+	0.788310i	$0.289044\pi$
$54$		0			0
$55$	16.0395			2.16277
$56$	−4.92874	−	0.687771i	−0.658631	−	0.0919073i
$57$		0			0
$58$	−2.18042	+	0.477482i	−0.286303	+	0.0626964i
$59$	2.95409	+	2.95409i	0.384589	+	0.384589i	0.872752	−	0.488163i	$-0.162333\pi$
$59$	2.95409	+	2.95409i	0.384589	+	0.384589i	−0.488163	+	0.872752i	$0.662333\pi$
$60$		0			0
$61$	−1.22879	+	1.22879i	−0.157331	+	0.157331i	−0.781383	−	0.624052i	$-0.785485\pi$
$61$	−1.22879	+	1.22879i	−0.157331	+	0.157331i	0.624052	+	0.781383i	$0.285485\pi$
$62$	5.99521	+	3.84117i	0.761393	+	0.487830i
$63$		0			0
$64$	7.69440	+	2.19004i	0.961799	+	0.273755i
$65$			19.1239i			2.37203i
$66$		0			0
$67$	4.25948	+	4.25948i	0.520379	+	0.520379i	0.917686	−	0.397307i	$-0.130055\pi$
$67$	4.25948	+	4.25948i	0.520379	+	0.520379i	−0.397307	+	0.917686i	$0.630055\pi$
$68$	0.814910	−	0.374887i	0.0988224	−	0.0454617i
$69$		0			0
$70$	−2.30497	−	10.5256i	−0.275496	−	1.25805i
$71$		−	11.1146i		−	1.31906i	−0.751676	−	0.659532i	$-0.770754\pi$
$71$		−	11.1146i		−	1.31906i	0.751676	−	0.659532i	$-0.229246\pi$
$72$		0			0
$73$			10.5499i			1.23478i	0.786658	+	0.617389i	$0.211810\pi$
$73$			10.5499i			1.23478i	−0.786658	+	0.617389i	$0.788190\pi$
$74$	−12.0927	+	2.64814i	−1.40575	+	0.307840i
$75$		0			0
$76$	−2.35006	+	6.35441i	−0.269570	+	0.728901i
$77$	4.60819	+	4.60819i	0.525152	+	0.525152i
$78$		0			0
$79$			15.4697i			1.74048i	0.492626	+	0.870241i	$0.336037\pi$
$79$			15.4697i			1.74048i	−0.492626	+	0.870241i	$0.663963\pi$
$80$	1.33133	+	17.2702i	0.148847	+	1.93087i
$81$		0			0
$82$	4.74130	−	7.40011i	0.523589	−	0.817205i
$83$	4.30188	−	4.30188i	0.472193	−	0.472193i	−0.430431	−	0.902624i	$-0.641638\pi$
$83$	4.30188	−	4.30188i	0.472193	−	0.472193i	0.902624	+	0.430431i	$0.141638\pi$
$84$		0			0
$85$	1.37333	+	1.37333i	0.148958	+	0.148958i
$86$	0.0119800	+	0.0547064i	0.00129183	+	0.00589914i
$87$		0			0
$88$	−6.31303	−	8.36064i	−0.672971	−	0.891247i
$89$	−0.159313			−0.0168871			−0.00844356	−	0.999964i	$-0.502688\pi$
$89$	−0.159313			−0.0168871			−0.00844356	+	0.999964i	$0.502688\pi$
$90$		0			0
$91$	−5.49435	+	5.49435i	−0.575964	+	0.575964i
$92$	11.8628	−	5.45732i	1.23679	−	0.568965i
$93$		0			0
$94$	0.0229901	−	0.0358825i	0.00237125	−	0.00370099i
$95$	−14.6692			−1.50503
$96$		0			0
$97$	−6.07049			−0.616364			−0.308182	−	0.951327i	$-0.599721\pi$
$97$	−6.07049			−0.616364			−0.308182	+	0.951327i	$0.599721\pi$
$98$	−2.97873	+	4.64913i	−0.300897	+	0.469633i
$99$		0			0
$100$	−24.9869	+	11.4948i	−2.49869	+	1.14948i
$101$	6.65814	−	6.65814i	0.662510	−	0.662510i	−0.293461	−	0.955971i	$-0.594807\pi$
$101$	6.65814	−	6.65814i	0.662510	−	0.662510i	0.955971	+	0.293461i	$0.0948071\pi$
$102$		0			0
$103$	−6.61441			−0.651737			−0.325869	−	0.945415i	$-0.605657\pi$
$103$	−6.61441			−0.651737			−0.325869	+	0.945415i	$0.605657\pi$
$104$	9.96840	−	7.52704i	0.977482	−	0.738087i
$105$		0			0
$106$	0.538940	+	2.46106i	0.0523464	+	0.239039i
$107$	−0.669937	−	0.669937i	−0.0647652	−	0.0647652i	0.673982	−	0.738748i	$-0.264582\pi$
$107$	−0.669937	−	0.669937i	−0.0647652	−	0.0647652i	−0.738748	+	0.673982i	$0.764582\pi$
$108$		0			0
$109$	10.3070	−	10.3070i	0.987236	−	0.987236i	−0.0126836	−	0.999920i	$-0.504037\pi$
$109$	10.3070	−	10.3070i	0.987236	−	0.987236i	0.999920	+	0.0126836i	$0.00403742\pi$
$110$	12.2371	−	19.0993i	1.16676	−	1.82105i
$111$		0			0
$112$	−4.57928	+	5.34427i	−0.432702	+	0.504986i
$113$			0.721004i			0.0678264i	0.999425	+	0.0339132i	$0.0107970\pi$
$113$			0.721004i			0.0678264i	−0.999425	+	0.0339132i	$0.989203\pi$
$114$		0			0
$115$	19.9919	+	19.9919i	1.86425	+	1.86425i
$116$	−1.09494	+	2.96066i	−0.101663	+	0.274890i
$117$		0			0
$118$	5.77141	−	1.26386i	0.531301	−	0.116348i
$119$			0.789122i			0.0723387i
$120$		0			0
$121$			2.71933i			0.247212i
$122$	0.525720	+	2.40069i	0.0475964	+	0.217349i
$123$		0			0
$124$	9.14790	−	4.20835i	0.821506	−	0.377921i
$125$	−26.7991	−	26.7991i	−2.39698	−	2.39698i
$126$		0			0
$127$		−	10.1058i		−	0.896744i	−0.893847	−	0.448372i	$-0.852004\pi$
$127$		−	10.1058i		−	0.896744i	0.893847	−	0.448372i	$-0.147996\pi$
$128$	8.47815	−	7.49139i	0.749370	−	0.662152i
$129$		0			0
$130$	22.7722	+	14.5903i	1.99725	+	1.27965i
$131$	12.8566	−	12.8566i	1.12329	−	1.12329i	0.132041	−	0.991244i	$-0.457847\pi$
$131$	12.8566	−	12.8566i	1.12329	−	1.12329i	0.991244	−	0.132041i	$-0.0421530\pi$
$132$		0			0
$133$	−4.21450	−	4.21450i	−0.365444	−	0.365444i
$134$	8.32177	−	1.82236i	0.718891	−	0.157428i
$135$		0			0
$136$	0.175320	−	1.25638i	0.0150335	−	0.107734i
$137$	11.1669			0.954054			0.477027	−	0.878889i	$-0.341714\pi$
$137$	11.1669			0.954054			0.477027	+	0.878889i	$0.341714\pi$
$138$		0			0
$139$	9.80802	−	9.80802i	0.831906	−	0.831906i	−0.155872	−	0.987777i	$-0.549819\pi$
$139$	9.80802	−	9.80802i	0.831906	−	0.831906i	0.987777	+	0.155872i	$0.0498186\pi$
$140$	−14.2921	−	5.28566i	−1.20790	−	0.446720i
$141$		0			0
$142$	−13.2350	−	8.47974i	−1.11065	−	0.711604i
$143$	−16.3576			−1.36789
$144$		0			0
$145$	−6.83471			−0.567592
$146$	12.5626	+	8.04892i	1.03968	+	0.666133i
$147$		0			0
$148$	−6.07261	+	16.4200i	−0.499165	+	1.34971i
$149$	−2.23921	+	2.23921i	−0.183443	+	0.183443i	−0.792854	−	0.609411i	$-0.791406\pi$
$149$	−2.23921	+	2.23921i	−0.183443	+	0.183443i	0.609411	+	0.792854i	$0.291406\pi$
$150$		0			0
$151$	−20.7213			−1.68627			−0.843137	−	0.537700i	$-0.819293\pi$
$151$	−20.7213			−1.68627			−0.843137	+	0.537700i	$0.819293\pi$
$152$	5.77370	+	7.64637i	0.468309	+	0.620203i
$153$		0			0
$154$	9.00303	−	1.97154i	0.725485	−	0.158872i
$155$	15.4165	+	15.4165i	1.23828	+	1.23828i
$156$		0			0
$157$	−3.82507	+	3.82507i	−0.305274	+	0.305274i	−0.843073	−	0.537799i	$-0.819256\pi$
$157$	−3.82507	+	3.82507i	−0.305274	+	0.305274i	0.537799	+	0.843073i	$0.319256\pi$
$158$	18.4209	+	11.8024i	1.46549	+	0.938948i
$159$		0			0
$160$	21.5806	+	11.5907i	1.70609	+	0.916328i
$161$			11.4874i			0.905337i
$162$		0			0
$163$	1.54039	+	1.54039i	0.120653	+	0.120653i	0.764855	−	0.644202i	$-0.222811\pi$
$163$	1.54039	+	1.54039i	0.120653	+	0.120653i	−0.644202	+	0.764855i	$0.722811\pi$
$164$	−5.19452	−	11.2916i	−0.405624	−	0.881725i
$165$		0			0
$166$	−1.84049	−	8.40460i	−0.142850	−	0.652323i
$167$			13.9675i			1.08084i	0.841396	+	0.540419i	$0.181734\pi$
$167$			13.9675i			1.08084i	−0.841396	+	0.540419i	$0.818266\pi$
$168$		0			0
$169$		−	6.50316i		−	0.500243i
$170$	2.68308	−	0.587558i	0.205783	−	0.0450637i
$171$		0			0
$172$	0.0742826	+	0.0274720i	0.00566400	+	0.00209472i
$173$	−5.83129	−	5.83129i	−0.443345	−	0.443345i	0.449790	−	0.893135i	$-0.351499\pi$
$173$	−5.83129	−	5.83129i	−0.443345	−	0.443345i	−0.893135	+	0.449790i	$0.851499\pi$
$174$		0			0
$175$		−	24.1962i		−	1.82906i
$176$	−14.7720	+	1.13875i	−1.11348	+	0.0858362i
$177$		0			0
$178$	−0.121545	+	0.189705i	−0.00911020	+	0.0142190i
$179$	−14.9405	+	14.9405i	−1.11670	+	1.11670i	−0.124480	+	0.992222i	$0.539726\pi$
$179$	−14.9405	+	14.9405i	−1.11670	+	1.11670i	−0.992222	+	0.124480i	$0.960274\pi$
$180$		0			0
$181$	−8.02173	−	8.02173i	−0.596251	−	0.596251i	0.343062	−	0.939313i	$-0.388536\pi$
$181$	−8.02173	−	8.02173i	−0.596251	−	0.596251i	−0.939313	+	0.343062i	$0.888536\pi$
$182$	2.35067	+	10.7343i	0.174244	+	0.795681i
$183$		0			0
$184$	2.55217	−	18.2895i	0.188148	−	1.34832i
$185$	−37.9056			−2.78688
$186$		0			0
$187$	−1.17467	+	1.17467i	−0.0859005	+	0.0859005i
$188$	−0.0251878	−	0.0547519i	−0.00183701	−	0.00399319i
$189$		0			0
$190$	−11.1916	+	17.4677i	−0.811928	+	1.26724i
$191$	−20.7609			−1.50221			−0.751104	−	0.660184i	$-0.770478\pi$
$191$	−20.7609			−1.50221			−0.751104	+	0.660184i	$0.770478\pi$
$192$		0			0
$193$	−3.75098			−0.270001			−0.135001	−	0.990846i	$-0.543104\pi$
$193$	−3.75098			−0.270001			−0.135001	+	0.990846i	$0.543104\pi$
$194$	−4.63138	+	7.22855i	−0.332514	+	0.518979i
$195$		0			0
$196$	3.26347	+	7.09396i	0.233105	+	0.506712i
$197$	17.5431	−	17.5431i	1.24989	−	1.24989i	0.294123	−	0.955767i	$-0.404972\pi$
$197$	17.5431	−	17.5431i	1.24989	−	1.24989i	0.955767	−	0.294123i	$-0.0950277\pi$
$198$		0			0
$199$	−7.86524			−0.557552			−0.278776	−	0.960356i	$-0.589929\pi$
$199$	−7.86524			−0.557552			−0.278776	+	0.960356i	$0.589929\pi$
$200$	−5.37567	+	38.5234i	−0.380117	+	2.72402i
$201$		0			0
$202$	−2.84859	−	13.0080i	−0.200426	−	0.915242i
$203$	−1.96363	−	1.96363i	−0.137820	−	0.137820i
$204$		0			0
$205$	19.0292	−	19.0292i	1.32906	−	1.32906i
$206$	−5.04636	+	7.87624i	−0.351597	+	0.548763i
$207$		0			0
$208$	−1.35773	−	17.6127i	−0.0941415	−	1.22122i
$209$		−	12.5473i		−	0.867912i
$210$		0			0
$211$	−6.21186	−	6.21186i	−0.427642	−	0.427642i	0.460182	−	0.887824i	$-0.347784\pi$
$211$	−6.21186	−	6.21186i	−0.427642	−	0.427642i	−0.887824	+	0.460182i	$0.847784\pi$
$212$	3.34173	+	1.23588i	0.229511	+	0.0848803i
$213$		0			0
$214$	−1.30886	+	0.286622i	−0.0894716	+	0.0195931i
$215$			0.171482i			0.0116950i
$216$		0			0
$217$			8.85841i			0.601348i
$218$	−4.40971	−	20.1369i	−0.298664	−	1.36384i
$219$		0			0
$220$	−13.4068	−	29.1431i	−0.903888	−	1.96483i
$221$	−1.40056	−	1.40056i	−0.0942121	−	0.0942121i
$222$		0			0
$223$			2.61329i			0.174999i	0.996165	+	0.0874995i	$0.0278876\pi$
$223$			2.61329i			0.174999i	−0.996165	+	0.0874995i	$0.972112\pi$
$224$	2.87010	+	9.53020i	0.191767	+	0.636763i
$225$		0			0
$226$	0.858549	+	0.550079i	0.0571099	+	0.0365907i
$227$	−7.40991	+	7.40991i	−0.491813	+	0.491813i	−0.908877	−	0.417064i	$-0.863059\pi$
$227$	−7.40991	+	7.40991i	−0.491813	+	0.491813i	0.417064	+	0.908877i	$0.363059\pi$
$228$		0			0
$229$	11.8950	+	11.8950i	0.786046	+	0.786046i	0.980844	−	0.194797i	$-0.0624049\pi$
$229$	11.8950	+	11.8950i	0.786046	+	0.786046i	−0.194797	+	0.980844i	$0.562405\pi$
$230$	39.0582	−	8.55323i	2.57542	−	0.563983i
$231$		0			0
$232$	2.69009	+	3.56261i	0.176613	+	0.233897i
$233$	17.2123			1.12762			0.563808	−	0.825906i	$-0.309336\pi$
$233$	17.2123			1.12762			0.563808	+	0.825906i	$0.309336\pi$
$234$		0			0
$235$	0.0922708	−	0.0922708i	0.00601908	−	0.00601908i
$236$	2.89824	−	7.83666i	0.188659	−	0.510123i
$237$		0			0
$238$	0.939662	+	0.602048i	0.0609092	+	0.0390250i
$239$	−9.75948			−0.631288			−0.315644	−	0.948878i	$-0.602221\pi$
$239$	−9.75948			−0.631288			−0.315644	+	0.948878i	$0.602221\pi$
$240$		0			0
$241$	3.14317			0.202469			0.101235	−	0.994863i	$-0.467721\pi$
$241$	3.14317			0.202469			0.101235	+	0.994863i	$0.467721\pi$
$242$	3.23810	+	2.07467i	0.208153	+	0.133365i
$243$		0			0
$244$	3.25976	+	1.20556i	0.208685	+	0.0771781i
$245$	−11.9551	+	11.9551i	−0.763784	+	0.763784i
$246$		0			0
$247$	14.9601			0.951889
$248$	1.96808	−	14.1037i	0.124973	−	0.895588i
$249$		0			0
$250$	−52.3574	+	11.4656i	−3.31137	+	0.725147i
$251$	−12.1674	−	12.1674i	−0.768000	−	0.768000i	0.209754	−	0.977754i	$-0.432734\pi$
$251$	−12.1674	−	12.1674i	−0.768000	−	0.768000i	−0.977754	+	0.209754i	$0.932734\pi$
$252$		0			0
$253$	−17.1000	+	17.1000i	−1.07507	+	1.07507i
$254$	−12.0337	−	7.71005i	−0.755059	−	0.483772i
$255$		0			0
$256$	−2.45224	−	15.8110i	−0.153265	−	0.988185i
$257$			17.2721i			1.07740i	0.842497	+	0.538702i	$0.181085\pi$
$257$			17.2721i			1.07740i	−0.842497	+	0.538702i	$0.818915\pi$
$258$		0			0
$259$	−10.8904	−	10.8904i	−0.676695	−	0.676695i
$260$	34.7473	−	15.9850i	2.15494	−	0.991346i
$261$		0			0
$262$	−5.50050	−	25.1180i	−0.339822	−	1.55179i
$263$			9.67642i			0.596674i	0.954461	+	0.298337i	$0.0964319\pi$
$263$			9.67642i			0.596674i	−0.954461	+	0.298337i	$0.903568\pi$
$264$		0			0
$265$			7.71442i			0.473893i
$266$	−8.23389	+	1.80311i	−0.504852	+	0.110556i
$267$		0			0
$268$	4.17896	−	11.2996i	0.255270	−	0.690235i
$269$	1.29660	+	1.29660i	0.0790549	+	0.0790549i	0.745529	−	0.666474i	$-0.232197\pi$
$269$	1.29660	+	1.29660i	0.0790549	+	0.0790549i	−0.666474	+	0.745529i	$0.732197\pi$
$270$		0			0
$271$			14.6755i			0.891476i	0.895163	+	0.445738i	$0.147059\pi$
$271$			14.6755i			0.891476i	−0.895163	+	0.445738i	$0.852941\pi$
$272$	−1.36231	−	1.16730i	−0.0826019	−	0.0707782i
$273$		0			0
$274$	8.51962	−	13.2972i	0.514689	−	0.803314i
$275$	36.0180	−	36.0180i	2.17196	−	2.17196i
$276$		0			0
$277$	−13.4707	−	13.4707i	−0.809377	−	0.809377i	0.175163	−	0.984539i	$-0.443955\pi$
$277$	−13.4707	−	13.4707i	−0.809377	−	0.809377i	−0.984539	+	0.175163i	$0.943955\pi$
$278$	−4.19621	−	19.1620i	−0.251672	−	1.14926i
$279$		0			0
$280$	−17.1979	+	12.9860i	−1.02777	+	0.776061i
$281$	1.66954			0.0995963			0.0497982	−	0.998759i	$-0.484142\pi$
$281$	1.66954			0.0995963			0.0497982	+	0.998759i	$0.484142\pi$
$282$		0			0
$283$	−0.345867	+	0.345867i	−0.0205597	+	0.0205597i	−0.717312	−	0.696752i	$-0.754628\pi$
$283$	−0.345867	+	0.345867i	−0.0205597	+	0.0205597i	0.696752	+	0.717312i	$0.254628\pi$
$284$	−20.1948	+	9.29031i	−1.19834	+	0.551279i
$285$		0			0
$286$	−12.4798	+	19.4781i	−0.737943	+	1.15176i
$287$	10.9343			0.645429
$288$		0			0
$289$	16.7988			0.988167
$290$	−5.21443	+	8.13856i	−0.306202	+	0.477913i
$291$		0			0
$292$	19.1688	−	8.81831i	1.12177	−	0.516052i
$293$	3.41759	−	3.41759i	0.199658	−	0.199658i	−0.600195	−	0.799853i	$-0.704911\pi$
$293$	3.41759	−	3.41759i	0.199658	−	0.199658i	0.799853	+	0.600195i	$0.204911\pi$
$294$		0			0
$295$	18.0910			1.05330
$296$	14.9194	+	19.7584i	0.867171	+	1.14843i
$297$		0			0
$298$	0.958010	+	4.37474i	0.0554960	+	0.253422i
$299$	−20.3883	−	20.3883i	−1.17909	−	1.17909i
$300$		0			0
$301$	−0.0492672	+	0.0492672i	−0.00283972	+	0.00283972i
$302$	−15.8090	+	24.6742i	−0.909704	+	1.41984i
$303$		0			0
$304$	13.5100	−	1.04146i	0.774853	−	0.0597319i
$305$			7.52519i			0.430891i
$306$		0			0
$307$	−15.2472	−	15.2472i	−0.870206	−	0.870206i	0.122289	−	0.992495i	$-0.460977\pi$
$307$	−15.2472	−	15.2472i	−0.870206	−	0.870206i	−0.992495	+	0.122289i	$0.960977\pi$
$308$	4.52107	−	12.2247i	0.257612	−	0.696567i
$309$		0			0
$310$	30.1193	−	6.59573i	1.71066	−	0.374612i
$311$		−	1.38517i		−	0.0785458i	−0.999229	−	0.0392729i	$-0.987496\pi$
$311$		−	1.38517i		−	0.0785458i	0.999229	−	0.0392729i	$-0.0125042\pi$
$312$		0			0
$313$		−	11.4856i		−	0.649207i	−0.945850	−	0.324604i	$-0.894769\pi$
$313$		−	11.4856i		−	0.649207i	0.945850	−	0.324604i	$-0.105231\pi$
$314$	1.63650	+	7.47306i	0.0923531	+	0.421729i
$315$		0			0
$316$	28.1079	−	12.9306i	1.58119	−	0.727402i
$317$	−10.2723	−	10.2723i	−0.576952	−	0.576952i	0.357110	−	0.934062i	$-0.383762\pi$
$317$	−10.2723	−	10.2723i	−0.576952	−	0.576952i	−0.934062	+	0.357110i	$0.883762\pi$
$318$		0			0
$319$		−	5.84604i		−	0.327316i
$320$	30.2664	−	16.8545i	1.69195	−	0.942195i
$321$		0			0
$322$	13.6789	+	8.76416i	0.762294	+	0.488407i
$323$	1.07432	−	1.07432i	0.0597766	−	0.0597766i
$324$		0			0
$325$	42.9443	+	42.9443i	2.38212	+	2.38212i
$326$	3.00946	−	0.659032i	0.166679	−	0.0365004i
$327$		0			0
$328$	−17.4088	−	2.42927i	−0.961238	−	0.134134i
$329$	0.0530192			0.00292304
$330$		0			0
$331$	−15.2923	+	15.2923i	−0.840538	+	0.840538i	−0.988929	−	0.148391i	$-0.952591\pi$
$331$	−15.2923	+	15.2923i	−0.840538	+	0.840538i	0.148391	+	0.988929i	$0.452591\pi$
$332$	−11.4121	−	4.22055i	−0.626321	−	0.231633i
$333$		0			0
$334$	16.6321	+	10.6563i	0.910067	+	0.583087i
$335$	26.0853			1.42519
$336$		0			0
$337$	17.1800			0.935852			0.467926	−	0.883768i	$-0.345001\pi$
$337$	17.1800			0.935852			0.467926	+	0.883768i	$0.345001\pi$
$338$	−7.74376	−	4.96148i	−0.421205	−	0.269869i
$339$		0			0
$340$	1.34737	−	3.64319i	0.0730712	−	0.197580i
$341$	−13.1865	+	13.1865i	−0.714087	+	0.714087i
$342$		0			0
$343$	−19.1857			−1.03593
$344$	0.0893855	−	0.0674941i	0.00481935	−	0.00363904i
$345$		0			0
$346$	−11.3926	+	2.49483i	−0.612471	+	0.134123i
$347$	9.79435	+	9.79435i	0.525788	+	0.525788i	0.919314	−	0.393525i	$-0.128745\pi$
$347$	9.79435	+	9.79435i	0.525788	+	0.525788i	−0.393525	+	0.919314i	$0.628745\pi$
$348$		0			0
$349$	−7.53642	+	7.53642i	−0.403415	+	0.403415i	−0.879435	−	0.476019i	$-0.842079\pi$
$349$	−7.53642	+	7.53642i	−0.403415	+	0.403415i	0.476019	+	0.879435i	$0.342079\pi$
$350$	−28.8120	−	18.4601i	−1.54007	−	0.986733i
$351$		0			0
$352$	−9.91410	+	18.4589i	−0.528423	+	0.983860i
$353$			26.4345i			1.40697i	0.710712	+	0.703483i	$0.248373\pi$
$353$			26.4345i			1.40697i	−0.710712	+	0.703483i	$0.751627\pi$
$354$		0			0
$355$	−34.0334	−	34.0334i	−1.80630	−	1.80630i
$356$	0.133164	+	0.289465i	0.00705766	+	0.0153416i
$357$		0			0
$358$	6.39205	+	29.1892i	0.337830	+	1.54270i
$359$		−	26.5901i		−	1.40337i	−0.712486	−	0.701687i	$-0.752431\pi$
$359$		−	26.5901i		−	1.40337i	0.712486	−	0.701687i	$-0.247569\pi$
$360$		0			0
$361$		−	7.52467i		−	0.396035i
$362$	−15.6721	+	3.43198i	−0.823706	+	0.180381i
$363$		0			0
$364$	14.5755	+	5.39048i	0.763965	+	0.282538i
$365$	32.3043	+	32.3043i	1.69088	+	1.69088i
$366$		0			0
$367$			11.1610i			0.582602i	0.956632	+	0.291301i	$0.0940881\pi$
$367$			11.1610i			0.582602i	−0.956632	+	0.291301i	$0.905912\pi$
$368$	−19.8314	−	16.9927i	−1.03378	−	0.885807i
$369$		0			0
$370$	−28.9195	+	45.1369i	−1.50345	+	2.34655i
$371$	−2.21637	+	2.21637i	−0.115068	+	0.115068i
$372$		0			0
$373$	−2.85013	−	2.85013i	−0.147574	−	0.147574i	0.629459	−	0.777033i	$-0.283276\pi$
$373$	−2.85013	−	2.85013i	−0.147574	−	0.147574i	−0.777033	+	0.629459i	$0.783276\pi$
$374$	0.502566	+	2.29496i	0.0259871	+	0.118670i
$375$		0			0
$376$	−0.0844135	−	0.0117793i	−0.00435329	−	0.000607471i
$377$	6.97025			0.358986
$378$		0			0
$379$	21.4189	−	21.4189i	1.10021	−	1.10021i	0.105829	−	0.994384i	$-0.466250\pi$
$379$	21.4189	−	21.4189i	1.10021	−	1.10021i	0.994384	−	0.105829i	$-0.0337497\pi$
$380$	12.2615	+	26.6533i	0.628999	+	1.36729i
$381$		0			0
$382$	−15.8392	+	24.7215i	−0.810405	+	1.26486i
$383$	−14.6490			−0.748527			−0.374263	−	0.927322i	$-0.622104\pi$
$383$	−14.6490			−0.748527			−0.374263	+	0.927322i	$0.622104\pi$
$384$		0			0
$385$	28.2208			1.43827
$386$	−2.86175	+	4.46655i	−0.145659	+	0.227341i
$387$		0			0
$388$	5.07409	+	11.0298i	0.257598	+	0.559954i
$389$	15.5300	−	15.5300i	0.787403	−	0.787403i	−0.193665	−	0.981068i	$-0.562038\pi$
$389$	15.5300	−	15.5300i	0.787403	−	0.787403i	0.981068	+	0.193665i	$0.0620375\pi$
$390$		0			0
$391$	−2.92826			−0.148088
$392$	10.9371	+	1.52619i	0.552406	+	0.0770844i
$393$		0			0
$394$	−7.50553	−	34.2739i	−0.378123	−	1.72670i
$395$	47.3688	+	47.3688i	2.38338	+	2.38338i
$396$		0			0
$397$	−28.0132	+	28.0132i	−1.40594	+	1.40594i	−0.626606	+	0.779336i	$0.715556\pi$
$397$	−28.0132	+	28.0132i	−1.40594	+	1.40594i	−0.779336	+	0.626606i	$0.784444\pi$
$398$	−6.00066	+	9.36569i	−0.300786	+	0.469460i
$399$		0			0
$400$	41.7712	+	35.7920i	2.08856	+	1.78960i
$401$		−	30.7338i		−	1.53477i	−0.641185	−	0.767386i	$-0.721557\pi$
$401$		−	30.7338i		−	1.53477i	0.641185	−	0.767386i	$-0.278443\pi$
$402$		0			0
$403$	−15.7222	−	15.7222i	−0.783180	−	0.783180i
$404$	−17.6629	−	6.53227i	−0.878760	−	0.324993i
$405$		0			0
$406$	−3.83635	+	0.840109i	−0.190395	+	0.0416939i
$407$		−	32.4224i		−	1.60712i
$408$		0			0
$409$			11.2856i			0.558039i	0.960285	+	0.279019i	$0.0900093\pi$
$409$			11.2856i			0.558039i	−0.960285	+	0.279019i	$0.909991\pi$
$410$	−8.14135	−	37.1774i	−0.402072	−	1.83606i
$411$		0			0
$412$	5.52874	+	12.0181i	0.272381	+	0.592089i
$413$	5.19759	+	5.19759i	0.255757	+	0.255757i
$414$		0			0
$415$		−	26.3450i		−	1.29322i
$416$	−22.0085	−	11.8206i	−1.07906	−	0.579552i
$417$		0			0
$418$	−14.9409	−	9.57274i	−0.730783	−	0.468218i
$419$	−6.72234	+	6.72234i	−0.328408	+	0.328408i	−0.851981	−	0.523573i	$-0.824599\pi$
$419$	−6.72234	+	6.72234i	−0.328408	+	0.328408i	0.523573	+	0.851981i	$0.324599\pi$
$420$		0			0
$421$	8.52467	+	8.52467i	0.415467	+	0.415467i	0.883638	−	0.468171i	$-0.155087\pi$
$421$	8.52467	+	8.52467i	0.415467	+	0.415467i	−0.468171	+	0.883638i	$0.655087\pi$
$422$	−12.1361	+	2.65765i	−0.590778	+	0.129372i
$423$		0			0
$424$	4.02116	−	3.03634i	0.195285	−	0.147458i
$425$	6.16784			0.299184
$426$		0			0
$427$	−2.16201	+	2.16201i	−0.104627	+	0.104627i
$428$	−0.657271	+	1.77722i	−0.0317704	+	0.0859052i
$429$		0			0
$430$	0.204196	+	0.130830i	0.00984719	+	0.00630916i
$431$	1.04283			0.0502311			0.0251156	−	0.999685i	$-0.492005\pi$
$431$	1.04283			0.0502311			0.0251156	+	0.999685i	$0.492005\pi$
$432$		0			0
$433$	−20.6786			−0.993748			−0.496874	−	0.867823i	$-0.665519\pi$
$433$	−20.6786			−0.993748			−0.496874	+	0.867823i	$0.665519\pi$
$434$	10.5483	+	6.75838i	0.506335	+	0.324413i
$435$		0			0
$436$	−27.3427	−	10.1122i	−1.30948	−	0.484286i
$437$	15.6391	−	15.6391i	0.748120	−	0.748120i
$438$		0			0
$439$	22.4587			1.07190			0.535948	−	0.844251i	$-0.319954\pi$
$439$	22.4587			1.07190			0.535948	+	0.844251i	$0.319954\pi$
$440$	−44.9312	−	6.26983i	−2.14201	−	0.298903i
$441$		0			0
$442$	−2.73628	+	0.599210i	−0.130152	+	0.0285015i
$443$	−6.25609	−	6.25609i	−0.297236	−	0.297236i	0.542694	−	0.839930i	$-0.317404\pi$
$443$	−6.25609	−	6.25609i	−0.297236	−	0.297236i	−0.839930	+	0.542694i	$0.817404\pi$
$444$		0			0
$445$	−0.487821	+	0.487821i	−0.0231249	+	0.0231249i
$446$	3.11183	+	1.99377i	0.147349	+	0.0944078i
$447$		0			0
$448$	13.5380	+	3.85329i	0.639609	+	0.182051i
$449$			8.10608i			0.382549i	0.981537	+	0.191275i	$0.0612621\pi$
$449$			8.10608i			0.382549i	−0.981537	+	0.191275i	$0.938738\pi$
$450$		0			0
$451$	16.2765	+	16.2765i	0.766432	+	0.766432i
$452$	1.31003	−	0.602660i	0.0616188	−	0.0283468i
$453$		0			0
$454$	3.17022	+	14.4768i	0.148786	+	0.679428i
$455$			33.6477i			1.57743i
$456$		0			0
$457$			36.2270i			1.69463i	0.531092	+	0.847314i	$0.321782\pi$
$457$			36.2270i			1.69463i	−0.531092	+	0.847314i	$0.678218\pi$
$458$	23.2394	−	5.08911i	1.08590	−	0.237799i
$459$		0			0
$460$	19.6139	−	53.0349i	0.914504	−	2.47276i
$461$	−6.26974	−	6.26974i	−0.292011	−	0.292011i	0.545863	−	0.837874i	$-0.316202\pi$
$461$	−6.26974	−	6.26974i	−0.292011	−	0.292011i	−0.837874	+	0.545863i	$0.816202\pi$
$462$		0			0
$463$			0.856648i			0.0398118i	0.999802	+	0.0199059i	$0.00633667\pi$
$463$			0.856648i			0.0398118i	−0.999802	+	0.0199059i	$0.993663\pi$
$464$	6.29461	−	0.485239i	0.292220	−	0.0225267i
$465$		0			0
$466$	13.1319	−	20.4959i	0.608322	−	0.949454i
$467$	−10.7339	+	10.7339i	−0.496705	+	0.496705i	−0.910411	−	0.413705i	$-0.864234\pi$
$467$	−10.7339	+	10.7339i	−0.496705	+	0.496705i	0.413705	+	0.910411i	$0.364234\pi$
$468$		0			0
$469$	7.49438	+	7.49438i	0.346058	+	0.346058i
$470$	−0.0394767	−	0.180270i	−0.00182092	−	0.00831522i
$471$		0			0
$472$	−7.12048	−	9.42998i	−0.327747	−	0.434050i
$473$	−0.146677			−0.00674420
$474$		0			0
$475$	−32.9409	+	32.9409i	−1.51143	+	1.51143i
$476$	1.43380	−	0.659597i	0.0657181	−	0.0302326i
$477$		0			0
$478$	−7.44584	+	11.6213i	−0.340565	+	0.531545i
$479$	22.2295			1.01569			0.507847	−	0.861447i	$-0.330442\pi$
$479$	22.2295			1.01569			0.507847	+	0.861447i	$0.330442\pi$
$480$		0			0
$481$	38.6573			1.76262
$482$	2.39803	−	3.74279i	0.109227	−	0.170479i
$483$		0			0
$484$	4.94091	−	2.27299i	0.224587	−	0.103318i
$485$	−18.5880	+	18.5880i	−0.844038	+	0.844038i
$486$		0			0
$487$	−24.2793			−1.10020			−0.550100	−	0.835099i	$-0.685411\pi$
$487$	−24.2793			−1.10020			−0.550100	+	0.835099i	$0.685411\pi$
$488$	3.92253	−	2.96186i	0.177565	−	0.134077i
$489$		0			0
$490$	5.11481	+	23.3567i	0.231064	+	1.05515i
$491$	−12.8511	−	12.8511i	−0.579962	−	0.579962i	0.354931	−	0.934893i	$-0.384504\pi$
$491$	−12.8511	−	12.8511i	−0.579962	−	0.579962i	−0.934893	+	0.354931i	$0.884504\pi$
$492$		0			0
$493$	0.500548	−	0.500548i	0.0225436	−	0.0225436i
$494$	11.4136	−	17.8140i	0.513522	−	0.801492i
$495$		0			0
$496$	−15.2928	−	13.1037i	−0.686666	−	0.588376i
$497$		−	19.5557i		−	0.877195i
$498$		0			0
$499$	22.4433	+	22.4433i	1.00470	+	1.00470i	0.999989	+	0.00471316i	$0.00150025\pi$
$499$	22.4433	+	22.4433i	1.00470	+	1.00470i	0.00471316	+	0.999989i	$0.498500\pi$
$500$	−26.2924	+	71.0931i	−1.17583	+	3.17938i
$501$		0			0
$502$	−23.7715	+	5.20564i	−1.06097	+	0.232339i
$503$			37.1578i			1.65678i	0.560150	+	0.828391i	$0.310744\pi$
$503$			37.1578i			1.65678i	−0.560150	+	0.828391i	$0.689256\pi$
$504$		0			0
$505$		−	40.7749i		−	1.81446i
$506$	7.31597	+	33.4083i	0.325235	+	1.48518i
$507$		0			0
$508$	−18.3618	+	8.44705i	−0.814672	+	0.374777i
$509$	2.87291	+	2.87291i	0.127339	+	0.127339i	0.767904	−	0.640565i	$-0.221300\pi$
$509$	2.87291	+	2.87291i	0.127339	+	0.127339i	−0.640565	+	0.767904i	$0.721300\pi$
$510$		0			0
$511$			18.5622i			0.821143i
$512$	−20.6981	−	9.14267i	−0.914736	−	0.404053i
$513$		0			0
$514$	20.5671	+	13.1775i	0.907175	+	0.581233i
$515$	−20.2535	+	20.2535i	−0.892477	+	0.892477i
$516$		0			0
$517$	0.0789235	+	0.0789235i	0.00347105	+	0.00347105i
$518$	−21.2766	+	4.65929i	−0.934839	+	0.204717i
$519$		0			0
$520$	7.47553	−	53.5716i	0.327824	−	2.34927i
$521$	33.4415			1.46510			0.732549	−	0.680715i	$-0.238331\pi$
$521$	33.4415			1.46510			0.732549	+	0.680715i	$0.238331\pi$
$522$		0			0
$523$	11.0889	−	11.0889i	0.484883	−	0.484883i	−0.421804	−	0.906687i	$-0.638603\pi$
$523$	11.0889	−	11.0889i	0.484883	−	0.484883i	0.906687	+	0.421804i	$0.138603\pi$
$524$	−34.1062	−	12.6135i	−1.48994	−	0.551025i
$525$		0			0
$526$	11.5224	+	7.38247i	0.502400	+	0.321891i
$527$	−2.25809			−0.0983641
$528$		0			0
$529$	−19.6274			−0.853364
$530$	9.18609	+	5.88559i	0.399018	+	0.255654i
$531$		0			0
$532$	−4.13483	+	11.1803i	−0.179267	+	0.484728i
$533$	−19.4065	+	19.4065i	−0.840590	+	0.840590i
$534$		0			0
$535$	−4.10273			−0.177377
$536$	−10.2670	−	13.5971i	−0.443467	−	0.587303i
$537$		0			0
$538$	2.53317	−	0.554729i	0.109213	−	0.0239161i
$539$	−10.2258	−	10.2258i	−0.440455	−	0.440455i
$540$		0			0
$541$	20.6974	−	20.6974i	0.889850	−	0.889850i	−0.104659	−	0.994508i	$-0.533375\pi$
$541$	20.6974	−	20.6974i	0.889850	−	0.889850i	0.994508	+	0.104659i	$0.0333750\pi$
$542$	17.4752	+	11.1965i	0.750624	+	0.480930i
$543$		0			0
$544$	−2.42934	+	0.731616i	−0.104157	+	0.0313678i
$545$		−	63.1210i		−	2.70381i
$546$		0			0
$547$	13.7038	+	13.7038i	0.585930	+	0.585930i	0.936527	−	0.350596i	$-0.114021\pi$
$547$	13.7038	+	13.7038i	0.585930	+	0.585930i	−0.350596	+	0.936527i	$0.614021\pi$
$548$	−9.33401	−	20.2898i	−0.398729	−	0.866738i
$549$		0			0
$550$	−15.4097	−	70.3684i	−0.657074	−	3.00052i
$551$			5.34661i			0.227773i
$552$		0			0
$553$			27.2184i			1.15744i
$554$	−26.3178	+	5.76324i	−1.11814	+	0.244857i
$555$		0			0
$556$	−26.0189	−	9.62260i	−1.10345	−	0.408089i
$557$	0.933912	+	0.933912i	0.0395711	+	0.0395711i	0.726615	−	0.687044i	$-0.241092\pi$
$557$	0.933912	+	0.933912i	0.0395711	+	0.0395711i	−0.687044	+	0.726615i	$0.741092\pi$
$558$		0			0
$559$		−	0.174883i		−	0.00739675i
$560$	2.34241	+	30.3862i	0.0989851	+	1.28405i
$561$		0			0
$562$	1.27375	−	1.98804i	0.0537298	−	0.0838602i
$563$	−21.6342	+	21.6342i	−0.911773	+	0.911773i	−0.996412	−	0.0846386i	$-0.973026\pi$
$563$	−21.6342	+	21.6342i	−0.911773	+	0.911773i	0.0846386	+	0.996412i	$0.473026\pi$
$564$		0			0
$565$	2.20774	+	2.20774i	0.0928802	+	0.0928802i
$566$	0.147974	+	0.675722i	0.00621981	+	0.0284027i
$567$		0			0
$568$	−4.34471	+	31.1353i	−0.182300	+	1.30641i
$569$	12.9760			0.543981			0.271990	−	0.962300i	$-0.412318\pi$
$569$	12.9760			0.543981			0.271990	+	0.962300i	$0.412318\pi$
$570$		0			0
$571$	14.9657	−	14.9657i	0.626297	−	0.626297i	−0.320837	−	0.947134i	$-0.603964\pi$
$571$	14.9657	−	14.9657i	0.626297	−	0.626297i	0.947134	+	0.320837i	$0.103964\pi$
$572$	13.6727	+	29.7210i	0.571684	+	1.24270i
$573$		0			0
$574$	8.34212	−	13.0202i	0.348193	−	0.543452i
$575$	89.7867			3.74436
$576$		0			0
$577$	22.0674			0.918679			0.459340	−	0.888261i	$-0.348086\pi$
$577$	22.0674			0.918679			0.459340	+	0.888261i	$0.348086\pi$
$578$	12.8164	−	20.0035i	0.533093	−	0.832038i
$579$		0			0
$580$	5.71288	+	12.4184i	0.237214	+	0.515645i
$581$	7.56897	−	7.56897i	0.314014	−	0.314014i
$582$		0			0
$583$	−6.59850			−0.273282
$584$	4.12397	−	29.5534i	0.170651	−	1.22293i
$585$		0			0
$586$	−1.46217	−	6.67697i	−0.0604015	−	0.275823i
$587$	13.0188	+	13.0188i	0.537345	+	0.537345i	0.922748	−	0.385403i	$-0.125938\pi$
$587$	13.0188	+	13.0188i	0.537345	+	0.537345i	−0.385403	+	0.922748i	$0.625938\pi$
$588$		0			0
$589$	12.0599	−	12.0599i	0.496920	−	0.496920i
$590$	13.8022	−	21.5422i	0.568229	−	0.886878i
$591$		0			0
$592$	34.9102	−	2.69116i	1.43480	−	0.110606i
$593$			18.5087i			0.760059i	0.924974	+	0.380030i	$0.124086\pi$
$593$			18.5087i			0.760059i	−0.924974	+	0.380030i	$0.875914\pi$
$594$		0			0
$595$	2.41631	+	2.41631i	0.0990592	+	0.0990592i
$596$	5.94021	+	2.19687i	0.243320	+	0.0899874i
$597$		0			0
$598$	−39.8328	+	8.72284i	−1.62888	+	0.356704i
$599$			16.1242i			0.658818i	0.944187	+	0.329409i	$0.106850\pi$
$599$			16.1242i			0.658818i	−0.944187	+	0.329409i	$0.893150\pi$
$600$		0			0
$601$		−	7.47082i		−	0.304741i	−0.988323	−	0.152371i	$-0.951309\pi$
$601$		−	7.47082i		−	0.304741i	0.988323	−	0.152371i	$-0.0486907\pi$
$602$	0.0210782	+	0.0962535i	0.000859085	+	0.00392300i
$603$		0			0
$604$	17.3201	+	37.6497i	0.704746	+	1.53194i
$605$	8.32668	+	8.32668i	0.338528	+	0.338528i
$606$		0			0
$607$		−	15.3808i		−	0.624288i	−0.950035	−	0.312144i	$-0.898953\pi$
$607$		−	15.3808i		−	0.624288i	0.950035	−	0.312144i	$-0.101047\pi$
$608$	9.06712	−	16.8819i	0.367720	−	0.684651i
$609$		0			0
$610$	8.96077	+	5.74123i	0.362811	+	0.232455i
$611$	−0.0941005	+	0.0941005i	−0.00380690	+	0.00380690i
$612$		0			0
$613$	−16.6507	−	16.6507i	−0.672514	−	0.672514i	0.285781	−	0.958295i	$-0.407747\pi$
$613$	−16.6507	−	16.6507i	−0.672514	−	0.672514i	−0.958295	+	0.285781i	$0.907747\pi$
$614$	−29.7886	+	6.52330i	−1.20217	+	0.263259i
$615$		0			0
$616$	−11.1075	−	14.7102i	−0.447534	−	0.592690i
$617$	−29.8839			−1.20308			−0.601540	−	0.798842i	$-0.705446\pi$
$617$	−29.8839			−1.20308			−0.601540	+	0.798842i	$0.705446\pi$
$618$		0			0
$619$	27.6299	−	27.6299i	1.11054	−	1.11054i	0.117460	−	0.993078i	$-0.462525\pi$
$619$	27.6299	−	27.6299i	1.11054	−	1.11054i	0.993078	−	0.117460i	$-0.0374751\pi$
$620$	15.1251	−	40.8972i	0.607437	−	1.64247i
$621$		0			0
$622$	−1.64942	−	1.05679i	−0.0661356	−	0.0423736i
$623$	−0.280304			−0.0112301
$624$		0			0
$625$	−95.3588			−3.81435
$626$	−13.6768	−	8.76279i	−0.546633	−	0.350232i
$627$		0			0
$628$	10.1472	+	3.75276i	0.404919	+	0.149751i
$629$	2.77606	−	2.77606i	0.110689	−	0.110689i
$630$		0			0
$631$	−37.9982			−1.51268			−0.756342	−	0.654177i	$-0.773015\pi$
$631$	−37.9982			−1.51268			−0.756342	+	0.654177i	$0.773015\pi$
$632$	6.04712	−	43.3352i	0.240541	−	1.72378i
$633$		0			0
$634$	−20.0691	+	4.39487i	−0.797047	+	0.174543i
$635$	−30.9442	−	30.9442i	−1.22798	−	1.22798i
$636$		0			0
$637$	12.1922	−	12.1922i	0.483072	−	0.483072i
$638$	−6.96129	−	4.46015i	−0.275600	−	0.176579i
$639$		0			0
$640$	3.02149	−	48.8992i	0.119435	−	1.93291i
$641$		−	45.2112i		−	1.78574i	−0.450318	−	0.892868i	$-0.648689\pi$
$641$		−	45.2112i		−	1.78574i	0.450318	−	0.892868i	$-0.351311\pi$
$642$		0			0
$643$	3.96585	+	3.96585i	0.156398	+	0.156398i	0.780968	−	0.624570i	$-0.214726\pi$
$643$	3.96585	+	3.96585i	0.156398	+	0.156398i	−0.624570	+	0.780968i	$0.714726\pi$
$644$	20.8722	−	9.60192i	0.822479	−	0.378369i
$645$		0			0
$646$	−0.459631	−	2.09890i	−0.0180839	−	0.0825800i
$647$		−	44.1138i		−	1.73429i	−0.498053	−	0.867147i	$-0.665952\pi$
$647$		−	44.1138i		−	1.73429i	0.498053	−	0.867147i	$-0.334048\pi$
$648$		0			0
$649$			15.4741i			0.607410i
$650$	83.9003	−	18.3731i	3.29084	−	0.720650i
$651$		0			0
$652$	1.51127	−	4.08637i	0.0591858	−	0.160035i
$653$	19.0931	+	19.0931i	0.747172	+	0.747172i	0.973947	−	0.226775i	$-0.0728181\pi$
$653$	19.0931	+	19.0931i	0.747172	+	0.747172i	−0.226775	+	0.973947i	$0.572818\pi$
$654$		0			0
$655$		−	78.7345i		−	3.07641i
$656$	−16.1744	+	18.8764i	−0.631506	+	0.737001i
$657$		0			0
$658$	0.0404502	−	0.0631337i	0.00157691	−	0.00246121i
$659$	28.5947	−	28.5947i	1.11389	−	1.11389i	0.121271	−	0.992619i	$-0.461303\pi$
$659$	28.5947	−	28.5947i	1.11389	−	1.11389i	0.992619	−	0.121271i	$-0.0386972\pi$
$660$		0			0
$661$	−26.5406	−	26.5406i	−1.03231	−	1.03231i	−0.999460	−	0.0328503i	$-0.989542\pi$
$661$	−26.5406	−	26.5406i	−1.03231	−	1.03231i	−0.0328503	−	0.999460i	$-0.510458\pi$
$662$	6.54256	+	29.8765i	0.254284	+	1.16118i
$663$		0			0
$664$	−13.7324	+	10.3692i	−0.532920	+	0.402403i
$665$	−25.8099			−1.00086
$666$		0			0
$667$	7.28660	−	7.28660i	0.282138	−	0.282138i
$668$	25.3784	−	11.6749i	0.981919	−	0.451716i
$669$		0			0
$670$	19.9014	−	31.0616i	0.768858	−	1.20001i
$671$	−6.43665			−0.248484
$672$		0			0
$673$	−11.5147			−0.443859			−0.221930	−	0.975063i	$-0.571236\pi$
$673$	−11.5147			−0.443859			−0.221930	+	0.975063i	$0.571236\pi$
$674$	13.1072	−	20.4574i	0.504870	−	0.787988i
$675$		0			0
$676$	−11.8160	+	5.43575i	−0.454460	+	0.209067i
$677$	−9.76533	+	9.76533i	−0.375312	+	0.375312i	−0.869408	−	0.494096i	$-0.835499\pi$
$677$	−9.76533	+	9.76533i	−0.375312	+	0.375312i	0.494096	+	0.869408i	$0.335499\pi$
$678$		0			0
$679$	−10.6808			−0.409890
$680$	−3.31025	−	4.38392i	−0.126942	−	0.168116i
$681$		0			0
$682$	5.64163	+	25.7624i	0.216029	+	0.986495i
$683$	−14.7093	−	14.7093i	−0.562837	−	0.562837i	0.367275	−	0.930112i	$-0.380291\pi$
$683$	−14.7093	−	14.7093i	−0.562837	−	0.562837i	−0.930112	+	0.367275i	$0.880291\pi$
$684$		0			0
$685$	34.1934	−	34.1934i	1.30646	−	1.30646i
$686$	−14.6374	+	22.8457i	−0.558859	+	0.872253i
$687$		0			0
$688$	−0.0121746	−	0.157931i	−0.000464152	−	0.00602107i
$689$		−	7.86740i		−	0.299724i
$690$		0			0
$691$	−29.5653	−	29.5653i	−1.12472	−	1.12472i	−0.991022	−	0.133696i	$-0.957315\pi$
$691$	−29.5653	−	29.5653i	−1.12472	−	1.12472i	−0.133696	−	0.991022i	$-0.542685\pi$
$692$	−5.72105	+	15.4694i	−0.217482	+	0.588057i
$693$		0			0
$694$	19.1353	−	4.19037i	0.726365	−	0.159064i
$695$		−	60.0649i		−	2.27839i
$696$		0			0
$697$			2.78725i			0.105575i
$698$	3.22434	+	14.7239i	0.122043	+	0.557309i
$699$		0			0
$700$	−43.9634	+	20.2247i	−1.66166	+	0.764420i
$701$	21.6780	+	21.6780i	0.818767	+	0.818767i	0.985929	−	0.167162i	$-0.0534604\pi$
$701$	21.6780	+	21.6780i	0.818767	+	0.818767i	−0.167162	+	0.985929i	$0.553460\pi$
$702$		0			0
$703$			29.6525i			1.11837i
$704$	14.4164	+	25.8883i	0.543340	+	0.975702i
$705$		0			0
$706$	31.4774	+	20.1678i	1.18467	+	0.759024i
$707$	11.7147	−	11.7147i	0.440577	−	0.440577i
$708$		0			0
$709$	−18.4582	−	18.4582i	−0.693211	−	0.693211i	0.269726	−	0.962937i	$-0.413067\pi$
$709$	−18.4582	−	18.4582i	−0.693211	−	0.693211i	−0.962937	+	0.269726i	$0.913067\pi$
$710$	−66.4911	+	14.5607i	−2.49537	+	0.546452i
$711$		0			0
$712$	0.446281	+	0.0622753i	0.0167251	+	0.00233387i
$713$	−32.8716			−1.23105
$714$		0			0
$715$	−50.0874	+	50.0874i	−1.87316	+	1.87316i
$716$	39.6343	+	14.6580i	1.48120	+	0.547795i
$717$		0			0
$718$	−31.6627	−	20.2865i	−1.18164	−	0.757086i
$719$	−20.2125			−0.753797			−0.376899	−	0.926254i	$-0.623010\pi$
$719$	−20.2125			−0.753797			−0.376899	+	0.926254i	$0.623010\pi$
$720$		0			0
$721$	−11.6378			−0.433413
$722$	−8.96015	−	5.74083i	−0.333462	−	0.213652i
$723$		0			0
$724$	−7.87008	+	21.2802i	−0.292489	+	0.790873i
$725$	−15.3479	+	15.3479i	−0.570006	+	0.570006i
$726$		0			0
$727$	6.90279			0.256010			0.128005	−	0.991773i	$-0.459143\pi$
$727$	6.90279			0.256010			0.128005	+	0.991773i	$0.459143\pi$
$728$	17.5390	−	13.2435i	0.650038	−	0.490837i
$729$		0			0
$730$	63.1129	−	13.8209i	2.33591	−	0.511534i
$731$	−0.0125587	−	0.0125587i	−0.000464500	−	0.000464500i
$732$		0			0
$733$	−7.21306	+	7.21306i	−0.266420	+	0.266420i	−0.827656	−	0.561236i	$-0.810326\pi$
$733$	−7.21306	+	7.21306i	−0.266420	+	0.266420i	0.561236	+	0.827656i	$0.310326\pi$
$734$	13.2902	+	8.51514i	0.490551	+	0.314300i
$735$		0			0
$736$	−35.3645	+	10.6503i	−1.30355	+	0.392576i
$737$			22.3120i			0.821873i
$738$		0			0
$739$	18.1088	+	18.1088i	0.666144	+	0.666144i	0.956821	−	0.290677i	$-0.0938805\pi$
$739$	18.1088	+	18.1088i	0.666144	+	0.666144i	−0.290677	+	0.956821i	$0.593880\pi$
$740$	31.6839	+	68.8729i	1.16472	+	2.53182i
$741$		0			0
$742$	0.948241	+	4.33013i	0.0348110	+	0.158964i
$743$			10.0240i			0.367747i	0.982950	+	0.183873i	$0.0588636\pi$
$743$			10.0240i			0.367747i	−0.982950	+	0.183873i	$0.941136\pi$
$744$		0			0
$745$			13.7130i			0.502407i
$746$	−5.56831	+	1.21939i	−0.203870	+	0.0446449i
$747$		0			0
$748$	3.11619	+	1.15246i	0.113939	+	0.0421383i
$749$	−1.17872	−	1.17872i	−0.0430697	−	0.0430697i
$750$		0			0
$751$			30.3314i			1.10681i	0.832913	+	0.553404i	$0.186671\pi$
$751$			30.3314i			1.10681i	−0.832913	+	0.553404i	$0.813329\pi$
$752$	−0.0784284	+	0.0915302i	−0.00285999	+	0.00333776i
$753$		0			0
$754$	5.31784	−	8.29995i	0.193664	−	0.302267i
$755$	−63.4492	+	63.4492i	−2.30915	+	2.30915i
$756$		0			0
$757$	−23.7407	−	23.7407i	−0.862872	−	0.862872i	0.128799	−	0.991671i	$-0.458888\pi$
$757$	−23.7407	−	23.7407i	−0.862872	−	0.862872i	−0.991671	+	0.128799i	$0.958888\pi$
$758$	−9.16374	−	41.8461i	−0.332842	−	1.51992i
$759$		0			0
$760$	41.0927	+	5.73419i	1.49059	+	0.208001i
$761$	−10.8329			−0.392694			−0.196347	−	0.980534i	$-0.562908\pi$
$761$	−10.8329			−0.392694			−0.196347	+	0.980534i	$0.562908\pi$
$762$		0			0
$763$	18.1348	−	18.1348i	0.656524	−	0.656524i
$764$	17.3533	+	37.7217i	0.627820	+	1.36472i
$765$		0			0
$766$	−11.1762	+	17.4435i	−0.403812	+	0.630260i
$767$	−18.4497			−0.666182
$768$		0			0
$769$	35.6751			1.28648			0.643239	−	0.765666i	$-0.277590\pi$
$769$	35.6751			1.28648			0.643239	+	0.765666i	$0.277590\pi$
$770$	21.5306	−	33.6045i	0.775910	−	1.21102i
$771$		0			0
$772$	3.13530	+	6.81537i	0.112842	+	0.245290i
$773$	−30.1773	+	30.1773i	−1.08540	+	1.08540i	−0.0894086	+	0.995995i	$0.528498\pi$
$773$	−30.1773	+	30.1773i	−1.08540	+	1.08540i	−0.995995	+	0.0894086i	$0.971502\pi$
$774$		0			0
$775$	69.2380			2.48710
$776$	17.0052	+	2.37295i	0.610450	+	0.0851839i
$777$		0			0
$778$	−6.64428	−	30.3410i	−0.238209	−	1.08778i
$779$	−14.8860	−	14.8860i	−0.533346	−	0.533346i
$780$		0			0
$781$	29.1103	−	29.1103i	1.04165	−	1.04165i
$782$	−2.23407	+	3.48688i	−0.0798901	+	0.124691i
$783$		0			0
$784$	10.1616	−	11.8592i	0.362915	−	0.423541i
$785$			23.4250i			0.836074i
$786$		0			0
$787$	23.6479	+	23.6479i	0.842956	+	0.842956i	0.989242	−	0.146287i	$-0.0467322\pi$
$787$	23.6479	+	23.6479i	0.842956	+	0.842956i	−0.146287	+	0.989242i	$0.546732\pi$
$788$	−46.5386	−	17.2114i	−1.65787	−	0.613131i
$789$		0			0
$790$	92.5446	−	20.2660i	3.29259	−	0.721033i
$791$			1.26858i			0.0451054i
$792$		0			0
$793$		−	7.67442i		−	0.272527i
$794$	11.9850	+	54.7295i	0.425333	+	1.94228i
$795$		0			0
$796$	6.57426	+	14.2908i	0.233019	+	0.506524i
$797$	23.9532	+	23.9532i	0.848466	+	0.848466i	0.989942	−	0.141475i	$-0.0451846\pi$
$797$	23.9532	+	23.9532i	0.848466	+	0.848466i	−0.141475	+	0.989942i	$0.545185\pi$
$798$		0			0
$799$			0.0135151i			0.000478130i
$800$	74.4887	−	22.4329i	2.63357	−	0.793124i
$801$		0			0
$802$	−36.5968	−	23.4479i	−1.29228	−	0.827973i
$803$	−27.6313	+	27.6313i	−0.975088	+	0.975088i
$804$		0			0
$805$	35.1749	+	35.1749i	1.23975	+	1.23975i
$806$	−30.7166	+	6.72652i	−1.08195	+	0.236932i
$807$		0			0
$808$	−21.2540	+	16.0487i	−0.747714	+	0.564591i
$809$	1.54640			0.0543684			0.0271842	−	0.999630i	$-0.491346\pi$
$809$	1.54640			0.0543684			0.0271842	+	0.999630i	$0.491346\pi$
$810$		0			0
$811$	−12.0150	+	12.0150i	−0.421904	+	0.421904i	−0.885859	−	0.463955i	$-0.846430\pi$
$811$	−12.0150	+	12.0150i	−0.421904	+	0.421904i	0.463955	+	0.885859i	$0.346430\pi$
$812$	−1.92651	+	5.20915i	−0.0676071	+	0.182805i
$813$		0			0
$814$	−38.6076	−	24.7362i	−1.35320	−	0.867003i
$815$	9.43343			0.330439
$816$		0			0
$817$	0.134146			0.00469317
$818$	13.4386	+	8.61020i	0.469869	+	0.301048i
$819$		0			0
$820$	−50.4810	−	18.6694i	−1.76287	−	0.651964i
$821$	21.3158	−	21.3158i	0.743927	−	0.743927i	−0.229404	−	0.973331i	$-0.573678\pi$
$821$	21.3158	−	21.3158i	0.743927	−	0.743927i	0.973331	+	0.229404i	$0.0736777\pi$
$822$		0			0
$823$	−4.25201			−0.148216			−0.0741080	−	0.997250i	$-0.523611\pi$
$823$	−4.25201			−0.148216			−0.0741080	+	0.997250i	$0.523611\pi$
$824$	18.5288	+	2.58557i	0.645483	+	0.0900726i
$825$		0			0
$826$	10.1545	−	2.22371i	0.353322	−	0.0773727i
$827$	−35.9314	−	35.9314i	−1.24946	−	1.24946i	−0.955961	−	0.293495i	$-0.905182\pi$
$827$	−35.9314	−	35.9314i	−1.24946	−	1.24946i	−0.293495	−	0.955961i	$-0.594818\pi$
$828$		0			0
$829$	−27.3995	+	27.3995i	−0.951622	+	0.951622i	−0.998883	−	0.0472602i	$-0.984951\pi$
$829$	−27.3995	+	27.3995i	−0.951622	+	0.951622i	0.0472602	+	0.998883i	$0.484951\pi$
$830$	−31.3708	−	20.0995i	−1.08890	−	0.697663i
$831$		0			0
$832$	−30.8666	+	17.1887i	−1.07011	+	0.595912i
$833$		−	1.75109i		−	0.0606718i
$834$		0			0
$835$	42.7690	+	42.7690i	1.48008	+	1.48008i
$836$	−22.7978	+	10.4878i	−0.788480	+	0.362728i
$837$		0			0
$838$	2.87605	+	13.1335i	0.0993515	+	0.453688i
$839$			30.9947i			1.07006i	0.844835	+	0.535028i	$0.179699\pi$
$839$			30.9947i			1.07006i	−0.844835	+	0.535028i	$0.820301\pi$
$840$		0			0
$841$		−	26.5089i		−	0.914100i
$842$	16.6547	−	3.64715i	0.573958	−	0.125689i
$843$		0			0
$844$	−6.09443	+	16.4790i	−0.209779	+	0.567229i
$845$	−19.9129	−	19.9129i	−0.685023	−	0.685023i
$846$		0			0
$847$			4.78455i			0.164399i
$848$	−0.547695	−	7.10481i	−0.0188079	−	0.243980i
$849$		0			0
$850$	4.70565	−	7.34447i	0.161403	−	0.251913i
$851$	40.4118	−	40.4118i	1.38530	−	1.38530i
$852$		0			0
$853$	5.47135	+	5.47135i	0.187335	+	0.187335i	0.794543	−	0.607208i	$-0.207710\pi$
$853$	5.47135	+	5.47135i	0.187335	+	0.187335i	−0.607208	+	0.794543i	$0.707710\pi$
$854$	0.924982	+	4.22392i	0.0316522	+	0.144540i
$855$		0			0
$856$	1.61481	+	2.13856i	0.0551929	+	0.0730945i
$857$	−6.44109			−0.220023			−0.110012	−	0.993930i	$-0.535089\pi$
$857$	−6.44109			−0.220023			−0.110012	+	0.993930i	$0.535089\pi$
$858$		0			0
$859$	9.03648	−	9.03648i	0.308321	−	0.308321i	−0.535937	−	0.844258i	$-0.680042\pi$
$859$	9.03648	−	9.03648i	0.308321	−	0.308321i	0.844258	+	0.535937i	$0.180042\pi$
$860$	0.311576	−	0.143335i	0.0106246	−	0.00488770i
$861$		0			0
$862$	0.795607	−	1.24176i	0.0270985	−	0.0422947i
$863$	9.22133			0.313898			0.156949	−	0.987607i	$-0.449834\pi$
$863$	9.22133			0.313898			0.156949	+	0.987607i	$0.449834\pi$
$864$		0			0
$865$	−35.7112			−1.21422
$866$	−15.7764	+	24.6234i	−0.536103	+	0.836737i
$867$		0			0
$868$	16.0953	−	7.40441i	0.546312	−	0.251322i
$869$	−40.5168	+	40.5168i	−1.37444	+	1.37444i
$870$		0			0
$871$	−26.6026			−0.901395
$872$	−32.9020	+	24.8440i	−1.11420	+	0.841322i
$873$		0			0
$874$	−6.69095	−	30.5542i	−0.226325	−	1.03351i
$875$	−47.1518	−	47.1518i	−1.59402	−	1.59402i
$876$		0			0
$877$	−5.14256	+	5.14256i	−0.173652	+	0.173652i	−0.788582	−	0.614930i	$-0.789184\pi$
$877$	−5.14256	+	5.14256i	−0.173652	+	0.173652i	0.614930	+	0.788582i	$0.289184\pi$
$878$	17.1345	−	26.7431i	0.578262	−	0.902537i
$879$		0			0
$880$	−41.7455	+	48.7192i	−1.40724	+	1.64233i
$881$		−	46.2283i		−	1.55747i	−0.627353	−	0.778735i	$-0.715862\pi$
$881$		−	46.2283i		−	1.55747i	0.627353	−	0.778735i	$-0.284138\pi$
$882$		0			0
$883$	9.04018	+	9.04018i	0.304226	+	0.304226i	0.842665	−	0.538439i	$-0.180986\pi$
$883$	9.04018	+	9.04018i	0.304226	+	0.304226i	−0.538439	+	0.842665i	$0.680986\pi$
$884$	−1.37408	+	3.71544i	−0.0462155	+	0.124964i
$885$		0			0
$886$	−12.2225	+	2.67657i	−0.410624	+	0.0899212i
$887$		−	21.5534i		−	0.723691i	−0.932238	−	0.361845i	$-0.882147\pi$
$887$		−	21.5534i		−	0.723691i	0.932238	−	0.361845i	$-0.117853\pi$
$888$		0			0
$889$		−	17.7807i		−	0.596346i
$890$	0.208707	+	0.953057i	0.00699586	+	0.0319465i
$891$		0			0
$892$	4.74824	−	2.18435i	0.158983	−	0.0731376i
$893$	−0.0721809	−	0.0721809i	−0.00241544	−	0.00241544i
$894$		0			0
$895$			91.4962i			3.05838i
$896$	14.9169	−	13.1808i	0.498340	−	0.440339i
$897$		0			0
$898$	9.65247	+	6.18440i	0.322107	+	0.206376i
$899$	5.61898	−	5.61898i	0.187403	−	0.187403i
$900$		0			0
$901$	−0.564975	−	0.564975i	−0.0188220	−	0.0188220i
$902$	31.7995	−	6.96367i	1.05881	−	0.231865i
$903$		0			0
$904$	0.281840	−	2.01974i	0.00937386	−	0.0671755i
$905$	−49.1256			−1.63299
$906$		0			0
$907$	42.0902	−	42.0902i	1.39758	−	1.39758i	0.590666	−	0.806916i	$-0.298865\pi$
$907$	42.0902	−	42.0902i	1.39758	−	1.39758i	0.806916	−	0.590666i	$-0.201135\pi$
$908$	19.6572	+	7.26982i	0.652346	+	0.241258i
$909$		0			0
$910$	40.0667	+	25.6710i	1.32820	+	0.850985i
$911$	30.3277			1.00480			0.502401	−	0.864635i	$-0.332450\pi$
$911$	30.3277			1.00480			0.502401	+	0.864635i	$0.332450\pi$
$912$		0			0
$913$	22.5341			0.745769
$914$	43.1380	+	27.6388i	1.42688	+	0.914211i
$915$		0			0
$916$	11.6702	−	31.5554i	0.385593	−	1.04262i
$917$	22.6206	−	22.6206i	0.746999	−	0.746999i
$918$		0			0
$919$	39.3035			1.29650			0.648251	−	0.761426i	$-0.275501\pi$
$919$	39.3035			1.29650			0.648251	+	0.761426i	$0.275501\pi$
$920$	−48.1881	−	63.8178i	−1.58872	−	2.10401i
$921$		0			0
$922$	−12.2492	+	2.68241i	−0.403406	+	0.0883405i
$923$	34.7083	+	34.7083i	1.14244	+	1.14244i
$924$		0			0
$925$	−85.1201	+	85.1201i	−2.79873	+	2.79873i
$926$	1.02007	+	0.653566i	0.0335216	+	0.0214775i
$927$		0			0
$928$	4.22457	−	7.86564i	0.138678	−	0.258202i
$929$		−	19.2682i		−	0.632169i	−0.948731	−	0.316084i	$-0.897632\pi$
$929$		−	19.2682i		−	0.632169i	0.948731	−	0.316084i	$-0.102368\pi$
$930$		0			0
$931$	9.35216	+	9.35216i	0.306505	+	0.306505i
$932$	−14.3871	−	31.2741i	−0.471266	−	1.02442i
$933$		0			0
$934$	4.59233	+	20.9708i	0.150266	+	0.686187i
$935$			7.19376i			0.235261i
$936$		0			0
$937$			1.98205i			0.0647508i	0.999476	+	0.0323754i	$0.0103072\pi$
$937$			1.98205i			0.0647508i	−0.999476	+	0.0323754i	$0.989693\pi$
$938$	14.6418	−	3.20636i	0.478071	−	0.104691i
$939$		0			0
$940$	−0.244778	−	0.0905263i	−0.00798377	−	0.00295264i
$941$	−17.8685	−	17.8685i	−0.582495	−	0.582495i	0.353093	−	0.935588i	$-0.385130\pi$
$941$	−17.8685	−	17.8685i	−0.582495	−	0.582495i	−0.935588	+	0.353093i	$0.885130\pi$
$942$		0			0
$943$			40.5746i			1.32129i
$944$	−16.6614	+	1.28439i	−0.542282	+	0.0418035i
$945$		0			0
$946$	−0.111905	+	0.174658i	−0.00363833	+	0.00567862i
$947$	−39.4289	+	39.4289i	−1.28127	+	1.28127i	−0.341319	+	0.939948i	$0.610873\pi$
$947$	−39.4289	+	39.4289i	−1.28127	+	1.28127i	−0.939948	+	0.341319i	$0.889127\pi$
$948$		0			0
$949$	−32.9449	−	32.9449i	−1.06944	−	1.06944i
$950$	14.0933	+	64.3567i	0.457246	+	2.08801i
$951$		0			0
$952$	0.308467	−	2.21055i	0.00999748	−	0.0716445i
$953$	54.3468			1.76046			0.880232	−	0.474543i	$-0.157387\pi$
$953$	54.3468			1.76046			0.880232	+	0.474543i	$0.157387\pi$
$954$		0			0
$955$	−63.5706	+	63.5706i	−2.05710	+	2.05710i
$956$	8.15758	+	17.7325i	0.263835	+	0.573512i
$957$		0			0
$958$	16.9597	−	26.4703i	0.547942	−	0.855215i
$959$	19.6477			0.634458
$960$		0			0
$961$	5.65142			0.182304
$962$	29.4930	−	46.0319i	0.950892	−	1.48413i
$963$		0			0
$964$	−2.62726	−	5.71101i	−0.0846183	−	0.183939i
$965$	−11.4856	+	11.4856i	−0.369735	+	0.369735i
$966$		0			0
$967$	33.9330			1.09121			0.545607	−	0.838041i	$-0.316299\pi$
$967$	33.9330			1.09121			0.545607	+	0.838041i	$0.316299\pi$
$968$	1.06299	−	7.61762i	0.0341657	−	0.244840i
$969$		0			0
$970$	7.95260	+	36.3155i	0.255343	+	1.16602i
$971$	34.4850	+	34.4850i	1.10667	+	1.10667i	0.993585	+	0.113090i	$0.0360748\pi$
$971$	34.4850	+	34.4850i	1.10667	+	1.10667i	0.113090	+	0.993585i	$0.463925\pi$
$972$		0			0
$973$	17.2568	−	17.2568i	0.553228	−	0.553228i
$974$	−18.5235	+	28.9111i	−0.593532	+	0.926370i
$975$		0			0
$976$	−0.534261	−	6.93053i	−0.0171013	−	0.221841i
$977$		−	6.37762i		−	0.204038i	−0.994782	−	0.102019i	$-0.967470\pi$
$977$		−	6.37762i		−	0.204038i	0.994782	−	0.102019i	$-0.0325303\pi$
$978$		0			0
$979$	−0.417256	−	0.417256i	−0.0133355	−	0.0133355i
$980$	31.7148	+	11.7291i	1.01309	+	0.374672i
$981$		0			0
$982$	−25.1072	+	5.49815i	−0.801204	+	0.175453i
$983$			30.7424i			0.980530i	0.871574	+	0.490265i	$0.163100\pi$
$983$			30.7424i			0.980530i	−0.871574	+	0.490265i	$0.836900\pi$
$984$		0			0
$985$		−	107.435i		−	3.42315i
$986$	−0.214152	−	0.977922i	−0.00681999	−	0.0311434i
$987$		0			0
$988$	−12.5046	−	27.1819i	−0.397824	−	0.864771i
$989$	−0.182820	−	0.182820i	−0.00581334	−	0.00581334i
$990$		0			0
$991$		−	20.5482i		−	0.652736i	−0.945243	−	0.326368i	$-0.894175\pi$
$991$		−	20.5482i		−	0.652736i	0.945243	−	0.326368i	$-0.105825\pi$
$992$	−27.2709	+	8.21287i	−0.865853	+	0.260759i
$993$		0			0
$994$	−23.2864	−	14.9197i	−0.738599	−	0.473225i
$995$	−24.0836	+	24.0836i	−0.763502	+	0.763502i
$996$		0			0
$997$	33.6210	+	33.6210i	1.06479	+	1.06479i	0.997750	+	0.0670380i	$0.0213549\pi$
$997$	33.6210	+	33.6210i	1.06479	+	1.06479i	0.0670380	+	0.997750i	$0.478645\pi$
$998$	43.8476	−	9.60205i	1.38797	−	0.303947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.107.11	yes	32
3.2	odd	2	inner	432.2.l.b.107.6	✓	32
4.3	odd	2		1728.2.l.b.1295.16		32
12.11	even	2		1728.2.l.b.1295.1		32
16.3	odd	4	inner	432.2.l.b.323.6	yes	32
16.13	even	4		1728.2.l.b.431.1		32
48.29	odd	4		1728.2.l.b.431.16		32
48.35	even	4	inner	432.2.l.b.323.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.6	✓	32	3.2	odd	2	inner
432.2.l.b.107.11	yes	32	1.1	even	1	trivial
432.2.l.b.323.6	yes	32	16.3	odd	4	inner
432.2.l.b.323.11	yes	32	48.35	even	4	inner
1728.2.l.b.431.1		32	16.13	even	4
1728.2.l.b.431.16		32	48.29	odd	4
1728.2.l.b.1295.1		32	12.11	even	2
1728.2.l.b.1295.16		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.762934 - 1.19077i) q^{2} +(-0.835863 - 1.81696i) q^{4} +(3.06203 - 3.06203i) q^{5} +1.75946 q^{7} +(-2.80128 - 0.390900i) q^{8} +O(q^{10})\)	\(q+(0.762934 - 1.19077i) q^{2} +(-0.835863 - 1.81696i) q^{4} +(3.06203 - 3.06203i) q^{5} +1.75946 q^{7} +(-2.80128 - 0.390900i) q^{8} +(-1.31004 - 5.98230i) q^{10} +(2.61910 + 2.61910i) q^{11} +(-3.12275 + 3.12275i) q^{13} +(1.34235 - 2.09511i) q^{14} +(-2.60267 + 3.03745i) q^{16} +0.448503i q^{17} +(-2.39534 - 2.39534i) q^{19} +(-8.12301 - 3.00414i) q^{20} +(5.11694 - 1.12054i) q^{22} +6.52896i q^{23} -13.7521i q^{25} +(1.33602 + 6.10093i) q^{26} +(-1.47066 - 3.19686i) q^{28} +(-1.11604 - 1.11604i) q^{29} +5.03474i q^{31} +(1.63124 + 5.41655i) q^{32} +(0.534063 + 0.342178i) q^{34} +(5.38751 - 5.38751i) q^{35} +(-6.18962 - 6.18962i) q^{37} +(-4.67979 + 1.02481i) q^{38} +(-9.77456 + 7.38067i) q^{40} +6.21456 q^{41} +(-0.0280014 + 0.0280014i) q^{43} +(2.56958 - 6.94799i) q^{44} +(7.77449 + 4.98117i) q^{46} +0.0301338 q^{47} -3.90431 q^{49} +(-16.3755 - 10.4919i) q^{50} +(8.28410 + 3.06372i) q^{52} +(-1.25969 + 1.25969i) q^{53} +16.0395 q^{55} +(-4.92874 - 0.687771i) q^{56} +(-2.18042 + 0.477482i) q^{58} +(2.95409 + 2.95409i) q^{59} +(-1.22879 + 1.22879i) q^{61} +(5.99521 + 3.84117i) q^{62} +(7.69440 + 2.19004i) q^{64} +19.1239i q^{65} +(4.25948 + 4.25948i) q^{67} +(0.814910 - 0.374887i) q^{68} +(-2.30497 - 10.5256i) q^{70} -11.1146i q^{71} +10.5499i q^{73} +(-12.0927 + 2.64814i) q^{74} +(-2.35006 + 6.35441i) q^{76} +(4.60819 + 4.60819i) q^{77} +15.4697i q^{79} +(1.33133 + 17.2702i) q^{80} +(4.74130 - 7.40011i) q^{82} +(4.30188 - 4.30188i) q^{83} +(1.37333 + 1.37333i) q^{85} +(0.0119800 + 0.0547064i) q^{86} +(-6.31303 - 8.36064i) q^{88} -0.159313 q^{89} +(-5.49435 + 5.49435i) q^{91} +(11.8628 - 5.45732i) q^{92} +(0.0229901 - 0.0358825i) q^{94} -14.6692 q^{95} -6.07049 q^{97} +(-2.97873 + 4.64913i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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