LMFDB - Embedded newform 432.2.k.d.325.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (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			325.2
Character	$\chi$	$=$	432.325
Dual form			432.2.k.d.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36223 - 0.379905i) q^{2} +(1.71134 + 1.03504i) q^{4} +(2.51567 + 2.51567i) q^{5} -4.16864i q^{7} +(-1.93803 - 2.06011i) q^{8} +O(q^{10})$	\(q+(-1.36223 - 0.379905i) q^{2} +(1.71134 + 1.03504i) q^{4} +(2.51567 + 2.51567i) q^{5} -4.16864i q^{7} +(-1.93803 - 2.06011i) q^{8} +(-2.47121 - 4.38264i) q^{10} +(-2.68369 - 2.68369i) q^{11} +(3.57649 - 3.57649i) q^{13} +(-1.58369 + 5.67865i) q^{14} +(1.85740 + 3.54261i) q^{16} +1.83581 q^{17} +(0.593478 - 0.593478i) q^{19} +(1.70137 + 6.90899i) q^{20} +(2.63626 + 4.67536i) q^{22} +3.54846i q^{23} +7.65722i q^{25} +(-6.23073 + 3.51328i) q^{26} +(4.31470 - 7.13398i) q^{28} +(4.44782 - 4.44782i) q^{29} -3.33012 q^{31} +(-1.18435 - 5.53148i) q^{32} +(-2.50080 - 0.697434i) q^{34} +(10.4869 - 10.4869i) q^{35} +(4.47261 + 4.47261i) q^{37} +(-1.03392 + 0.582988i) q^{38} +(0.307105 - 10.0580i) q^{40} -2.15831i q^{41} +(3.59664 + 3.59664i) q^{43} +(-1.81500 - 7.37045i) q^{44} +(1.34808 - 4.83382i) q^{46} +4.26868 q^{47} -10.3776 q^{49} +(2.90902 - 10.4309i) q^{50} +(9.82241 - 2.41881i) q^{52} +(-7.72171 - 7.72171i) q^{53} -13.5026i q^{55} +(-8.58785 + 8.07896i) q^{56} +(-7.74870 + 4.36920i) q^{58} +(2.00827 + 2.00827i) q^{59} +(-7.90359 + 7.90359i) q^{61} +(4.53639 + 1.26513i) q^{62} +(-0.488079 + 7.98510i) q^{64} +17.9946 q^{65} +(8.67604 - 8.67604i) q^{67} +(3.14171 + 1.90013i) q^{68} +(-18.2697 + 10.3016i) q^{70} +12.0783i q^{71} +4.88954i q^{73} +(-4.39356 - 7.79189i) q^{74} +(1.62992 - 0.401374i) q^{76} +(-11.1874 + 11.1874i) q^{77} +0.386079 q^{79} +(-4.23943 + 13.5846i) q^{80} +(-0.819952 + 2.94011i) q^{82} +(-0.648182 + 0.648182i) q^{83} +(4.61830 + 4.61830i) q^{85} +(-3.53307 - 6.26584i) q^{86} +(-0.327616 + 10.7298i) q^{88} +2.87284i q^{89} +(-14.9091 - 14.9091i) q^{91} +(-3.67278 + 6.07263i) q^{92} +(-5.81492 - 1.62169i) q^{94} +2.98599 q^{95} +9.38060 q^{97} +(14.1367 + 3.94250i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

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 $

$2$	−1.36223	−	0.379905i	−0.963242	−	0.268633i
$2$	−1.36223	−	0.379905i	−0.963242	−	0.268633i
$3$		0			0
$3$		0			0
$4$	1.71134	+	1.03504i	0.855672	+	0.517518i
$5$	2.51567	+	2.51567i	1.12504	+	1.12504i	0.990972	+	0.134071i	$0.0428051\pi$
$5$	2.51567	+	2.51567i	1.12504	+	1.12504i	0.134071	+	0.990972i	$0.457195\pi$
$6$		0			0
$7$		−	4.16864i		−	1.57560i	−0.615932	−	0.787800i	$-0.711220\pi$
$7$		−	4.16864i		−	1.57560i	0.615932	−	0.787800i	$-0.288780\pi$
$8$	−1.93803	−	2.06011i	−0.685197	−	0.728358i
$9$		0			0
$10$	−2.47121	−	4.38264i	−0.781465	−	1.38591i
$11$	−2.68369	−	2.68369i	−0.809164	−	0.809164i	0.175343	−	0.984507i	$-0.443897\pi$
$11$	−2.68369	−	2.68369i	−0.809164	−	0.809164i	−0.984507	+	0.175343i	$0.943897\pi$
$12$		0			0
$13$	3.57649	−	3.57649i	0.991940	−	0.991940i	−0.00802760	−	0.999968i	$-0.502555\pi$
$13$	3.57649	−	3.57649i	0.991940	−	0.991940i	0.999968	+	0.00802760i	$0.00255529\pi$
$14$	−1.58369	+	5.67865i	−0.423259	+	1.51768i
$15$		0			0
$16$	1.85740	+	3.54261i	0.464350	+	0.885652i
$17$	1.83581			0.445250			0.222625	−	0.974904i	$-0.428537\pi$
$17$	1.83581			0.445250			0.222625	+	0.974904i	$0.428537\pi$
$18$		0			0
$19$	0.593478	−	0.593478i	0.136153	−	0.136153i	−0.635746	−	0.771899i	$-0.719307\pi$
$19$	0.593478	−	0.593478i	0.136153	−	0.136153i	0.771899	+	0.635746i	$0.219307\pi$
$20$	1.70137	+	6.90899i	0.380438	+	1.54490i
$21$		0			0
$22$	2.63626	+	4.67536i	0.562053	+	0.996790i
$23$			3.54846i			0.739905i	0.929051	+	0.369952i	$0.120626\pi$
$23$			3.54846i			0.739905i	−0.929051	+	0.369952i	$0.879374\pi$
$24$		0			0
$25$			7.65722i			1.53144i
$26$	−6.23073	+	3.51328i	−1.22195	+	0.689011i
$27$		0			0
$28$	4.31470	−	7.13398i	0.815401	−	1.34820i
$29$	4.44782	−	4.44782i	0.825939	−	0.825939i	−0.161014	−	0.986952i	$-0.551476\pi$
$29$	4.44782	−	4.44782i	0.825939	−	0.825939i	0.986952	+	0.161014i	$0.0514763\pi$
$30$		0			0
$31$	−3.33012			−0.598106			−0.299053	−	0.954236i	$-0.596671\pi$
$31$	−3.33012			−0.598106			−0.299053	+	0.954236i	$0.596671\pi$
$32$	−1.18435	−	5.53148i	−0.209366	−	0.977837i
$33$		0			0
$34$	−2.50080	−	0.697434i	−0.428883	−	0.119609i
$35$	10.4869	−	10.4869i	1.77262	−	1.77262i
$36$		0			0
$37$	4.47261	+	4.47261i	0.735293	+	0.735293i	0.971663	−	0.236370i	$-0.0759579\pi$
$37$	4.47261	+	4.47261i	0.735293	+	0.735293i	−0.236370	+	0.971663i	$0.575958\pi$
$38$	−1.03392	+	0.582988i	−0.167724	+	0.0945732i
$39$		0			0
$40$	0.307105	−	10.0580i	0.0485575	−	1.59031i
$41$		−	2.15831i		−	0.337071i	−0.985696	−	0.168536i	$-0.946096\pi$
$41$		−	2.15831i		−	0.337071i	0.985696	−	0.168536i	$-0.0539038\pi$
$42$		0			0
$43$	3.59664	+	3.59664i	0.548483	+	0.548483i	0.926002	−	0.377519i	$-0.123223\pi$
$43$	3.59664	+	3.59664i	0.548483	+	0.548483i	−0.377519	+	0.926002i	$0.623223\pi$
$44$	−1.81500	−	7.37045i	−0.273622	−	1.11114i
$45$		0			0
$46$	1.34808	−	4.83382i	0.198763	−	0.712708i
$47$	4.26868			0.622651			0.311325	−	0.950303i	$-0.399227\pi$
$47$	4.26868			0.622651			0.311325	+	0.950303i	$0.399227\pi$
$48$		0			0
$49$	−10.3776			−1.48251
$50$	2.90902	−	10.4309i	0.411397	−	1.47515i
$51$		0			0
$52$	9.82241	−	2.41881i	1.36212	−	0.335428i
$53$	−7.72171	−	7.72171i	−1.06066	−	1.06066i	−0.998037	−	0.0626217i	$-0.980054\pi$
$53$	−7.72171	−	7.72171i	−1.06066	−	1.06066i	−0.0626217	−	0.998037i	$-0.519946\pi$
$54$		0			0
$55$		−	13.5026i		−	1.82069i
$56$	−8.58785	+	8.07896i	−1.14760	+	1.07960i
$57$		0			0
$58$	−7.74870	+	4.36920i	−1.01745	+	0.573704i
$59$	2.00827	+	2.00827i	0.261455	+	0.261455i	0.825645	−	0.564190i	$-0.190811\pi$
$59$	2.00827	+	2.00827i	0.261455	+	0.261455i	−0.564190	+	0.825645i	$0.690811\pi$
$60$		0			0
$61$	−7.90359	+	7.90359i	−1.01195	+	1.01195i	−0.0120236	+	0.999928i	$0.503827\pi$
$61$	−7.90359	+	7.90359i	−1.01195	+	1.01195i	−0.999928	+	0.0120236i	$0.996173\pi$
$62$	4.53639	+	1.26513i	0.576122	+	0.160671i
$63$		0			0
$64$	−0.488079	+	7.98510i	−0.0610099	+	0.998137i
$65$	17.9946			2.23195
$66$		0			0
$67$	8.67604	−	8.67604i	1.05995	−	1.05995i	0.0618626	−	0.998085i	$-0.480296\pi$
$67$	8.67604	−	8.67604i	1.05995	−	1.05995i	0.998085	−	0.0618626i	$-0.0197041\pi$
$68$	3.14171	+	1.90013i	0.380988	+	0.230425i
$69$		0			0
$70$	−18.2697	+	10.3016i	−2.18364	+	1.23128i
$71$			12.0783i			1.43342i	0.697369	+	0.716712i	$0.254354\pi$
$71$			12.0783i			1.43342i	−0.697369	+	0.716712i	$0.745646\pi$
$72$		0			0
$73$			4.88954i			0.572277i	0.958188	+	0.286138i	$0.0923717\pi$
$73$			4.88954i			0.572277i	−0.958188	+	0.286138i	$0.907628\pi$
$74$	−4.39356	−	7.79189i	−0.510741	−	0.905789i
$75$		0			0
$76$	1.62992	−	0.401374i	0.186964	−	0.0460407i
$77$	−11.1874	+	11.1874i	−1.27492	+	1.27492i
$78$		0			0
$79$	0.386079			0.0434372			0.0217186	−	0.999764i	$-0.493086\pi$
$79$	0.386079			0.0434372			0.0217186	+	0.999764i	$0.493086\pi$
$80$	−4.23943	+	13.5846i	−0.473983	+	1.51881i
$81$		0			0
$82$	−0.819952	+	2.94011i	−0.0905485	+	0.324681i
$83$	−0.648182	+	0.648182i	−0.0711473	+	0.0711473i	−0.741785	−	0.670638i	$-0.766021\pi$
$83$	−0.648182	+	0.648182i	−0.0711473	+	0.0711473i	0.670638	+	0.741785i	$0.266021\pi$
$84$		0			0
$85$	4.61830	+	4.61830i	0.500925	+	0.500925i
$86$	−3.53307	−	6.26584i	−0.380981	−	0.675663i
$87$		0			0
$88$	−0.327616	+	10.7298i	−0.0349240	+	1.14380i
$89$			2.87284i			0.304520i	0.988340	+	0.152260i	$0.0486552\pi$
$89$			2.87284i			0.304520i	−0.988340	+	0.152260i	$0.951345\pi$
$90$		0			0
$91$	−14.9091	−	14.9091i	−1.56290	−	1.56290i
$92$	−3.67278	+	6.07263i	−0.382914	+	0.633116i
$93$		0			0
$94$	−5.81492	−	1.62169i	−0.599764	−	0.167265i
$95$	2.98599			0.306356
$96$		0			0
$97$	9.38060			0.952456			0.476228	−	0.879322i	$-0.342004\pi$
$97$	9.38060			0.952456			0.476228	+	0.879322i	$0.342004\pi$
$98$	14.1367	+	3.94250i	1.42802	+	0.398252i
$99$		0			0
$100$	−7.92550	+	13.1041i	−0.792550	+	1.31041i
$101$	−12.0134	−	12.0134i	−1.19538	−	1.19538i	−0.975534	−	0.219847i	$-0.929444\pi$
$101$	−12.0134	−	12.0134i	−1.19538	−	1.19538i	−0.219847	−	0.975534i	$-0.570556\pi$
$102$		0			0
$103$			14.8802i			1.46619i	0.680126	+	0.733095i	$0.261925\pi$
$103$			14.8802i			1.46619i	−0.680126	+	0.733095i	$0.738075\pi$
$104$	−14.2993	−	0.436606i	−1.40216	−	0.0428127i
$105$		0			0
$106$	7.58524	+	13.4523i	0.736743	+	1.30660i
$107$	−1.59131	−	1.59131i	−0.153838	−	0.153838i	0.625992	−	0.779830i	$-0.284694\pi$
$107$	−1.59131	−	1.59131i	−0.153838	−	0.153838i	−0.779830	+	0.625992i	$0.784694\pi$
$108$		0			0
$109$	−2.99342	+	2.99342i	−0.286717	+	0.286717i	−0.835781	−	0.549063i	$-0.814985\pi$
$109$	−2.99342	+	2.99342i	−0.286717	+	0.286717i	0.549063	+	0.835781i	$0.314985\pi$
$110$	−5.12970	+	18.3936i	−0.489098	+	1.75377i
$111$		0			0
$112$	14.7679	−	7.74283i	1.39543	−	0.731629i
$113$	1.51665			0.142675			0.0713373	−	0.997452i	$-0.477273\pi$
$113$	1.51665			0.142675			0.0713373	+	0.997452i	$0.477273\pi$
$114$		0			0
$115$	−8.92676	+	8.92676i	−0.832424	+	0.832424i
$116$	12.2154	−	3.00809i	1.13417	−	0.279294i
$117$		0			0
$118$	−1.97278	−	3.49869i	−0.181609	−	0.322080i
$119$		−	7.65284i		−	0.701535i
$120$		0			0
$121$			3.40443i			0.309494i
$122$	13.7691	−	7.76390i	1.24660	−	0.702911i
$123$		0			0
$124$	−5.69897	−	3.44679i	−0.511783	−	0.309531i
$125$	−6.68469	+	6.68469i	−0.597897	+	0.597897i
$126$		0			0
$127$	−11.7986			−1.04695			−0.523477	−	0.852040i	$-0.675365\pi$
$127$	−11.7986			−1.04695			−0.523477	+	0.852040i	$0.675365\pi$
$128$	3.69845	−	10.6921i	0.326900	−	0.945059i
$129$		0			0
$130$	−24.5127	−	6.83622i	−2.14991	−	0.599577i
$131$	−6.46311	+	6.46311i	−0.564684	+	0.564684i	−0.930634	−	0.365950i	$-0.880744\pi$
$131$	−6.46311	+	6.46311i	−0.564684	+	0.564684i	0.365950	+	0.930634i	$0.380744\pi$
$132$		0			0
$133$	−2.47400	−	2.47400i	−0.214523	−	0.214523i
$134$	−15.1148	+	8.52270i	−1.30572	+	0.736249i
$135$		0			0
$136$	−3.55786	−	3.78197i	−0.305084	−	0.324301i
$137$		−	1.55291i		−	0.132674i	−0.997797	−	0.0663371i	$-0.978869\pi$
$137$		−	1.55291i		−	0.132674i	0.997797	−	0.0663371i	$-0.0211313\pi$
$138$		0			0
$139$	−5.06973	−	5.06973i	−0.430009	−	0.430009i	0.458623	−	0.888631i	$-0.348343\pi$
$139$	−5.06973	−	5.06973i	−0.430009	−	0.430009i	−0.888631	+	0.458623i	$0.848343\pi$
$140$	28.8011	−	7.09240i	2.43414	−	0.599417i
$141$		0			0
$142$	4.58859	−	16.4534i	0.385066	−	1.38074i
$143$	−19.1964			−1.60529
$144$		0			0
$145$	22.3785			1.85843
$146$	1.85756	−	6.66068i	0.153733	−	0.551241i
$147$		0			0
$148$	3.02486	+	12.2835i	0.248642	+	1.00970i
$149$	−5.65863	−	5.65863i	−0.463573	−	0.463573i	0.436252	−	0.899825i	$-0.356306\pi$
$149$	−5.65863	−	5.65863i	−0.463573	−	0.463573i	−0.899825	+	0.436252i	$0.856306\pi$
$150$		0			0
$151$		−	4.38608i		−	0.356934i	−0.983946	−	0.178467i	$-0.942886\pi$
$151$		−	4.38608i		−	0.356934i	0.983946	−	0.178467i	$-0.0571138\pi$
$152$	−2.37280	−	0.0724497i	−0.192460	−	0.00587645i
$153$		0			0
$154$	19.4899	−	10.9896i	1.57054	−	0.885570i
$155$	−8.37748	−	8.37748i	−0.672895	−	0.672895i
$156$		0			0
$157$	−12.0011	+	12.0011i	−0.957791	+	0.957791i	−0.999145	−	0.0413535i	$-0.986833\pi$
$157$	−12.0011	+	12.0011i	−0.957791	+	0.957791i	0.0413535	+	0.999145i	$0.486833\pi$
$158$	−0.525928	−	0.146673i	−0.0418406	−	0.0116687i
$159$		0			0
$160$	10.9360	−	16.8948i	0.864564	−	1.33565i
$161$	14.7923			1.16579
$162$		0			0
$163$	0.111754	−	0.111754i	0.00875324	−	0.00875324i	−0.702717	−	0.711470i	$-0.748030\pi$
$163$	0.111754	−	0.111754i	0.00875324	−	0.00875324i	0.711470	+	0.702717i	$0.248030\pi$
$164$	2.23393	−	3.69361i	0.174440	−	0.288422i
$165$		0			0
$166$	1.12922	−	0.636726i	0.0876446	−	0.0494195i
$167$			19.8270i			1.53426i	0.641490	+	0.767131i	$0.278317\pi$
$167$			19.8270i			1.53426i	−0.641490	+	0.767131i	$0.721683\pi$
$168$		0			0
$169$		−	12.5826i		−	0.967891i
$170$	−4.53667	−	8.04571i	−0.347947	−	0.617078i
$171$		0			0
$172$	2.43244	+	9.87775i	0.185472	+	0.753171i
$173$	−12.9193	+	12.9193i	−0.982233	+	0.982233i	−0.999845	−	0.0176116i	$-0.994394\pi$
$173$	−12.9193	+	12.9193i	−0.982233	+	0.982233i	0.0176116	+	0.999845i	$0.494394\pi$
$174$		0			0
$175$	31.9202			2.41294
$176$	4.52259	−	14.4920i	0.340903	−	1.09237i
$177$		0			0
$178$	1.09141	−	3.91347i	0.0818043	−	0.293327i
$179$	5.48566	−	5.48566i	0.410017	−	0.410017i	−0.471727	−	0.881744i	$-0.656369\pi$
$179$	5.48566	−	5.48566i	0.410017	−	0.410017i	0.881744	+	0.471727i	$0.156369\pi$
$180$		0			0
$181$	3.16904	+	3.16904i	0.235553	+	0.235553i	0.815006	−	0.579453i	$-0.196734\pi$
$181$	3.16904	+	3.16904i	0.235553	+	0.235553i	−0.579453	+	0.815006i	$0.696734\pi$
$182$	14.6456	+	25.9737i	1.08560	+	1.92530i
$183$		0			0
$184$	7.31020	−	6.87702i	0.538915	−	0.506980i
$185$			22.5032i			1.65447i
$186$		0			0
$187$	−4.92676	−	4.92676i	−0.360280	−	0.360280i
$188$	7.30518	+	4.41824i	0.532785	+	0.322233i
$189$		0			0
$190$	−4.06761	−	1.13439i	−0.295095	−	0.0822975i
$191$	6.79960			0.492002			0.246001	−	0.969270i	$-0.420883\pi$
$191$	6.79960			0.492002			0.246001	+	0.969270i	$0.420883\pi$
$192$		0			0
$193$	−13.3611			−0.961756			−0.480878	−	0.876788i	$-0.659682\pi$
$193$	−13.3611			−0.961756			−0.480878	+	0.876788i	$0.659682\pi$
$194$	−12.7785	−	3.56374i	−0.917446	−	0.255862i
$195$		0			0
$196$	−17.7596	−	10.7412i	−1.26854	−	0.767227i
$197$	19.6219	+	19.6219i	1.39800	+	1.39800i	0.805756	+	0.592248i	$0.201759\pi$
$197$	19.6219	+	19.6219i	1.39800	+	1.39800i	0.592248	+	0.805756i	$0.298241\pi$
$198$		0			0
$199$			3.25360i			0.230642i	0.993328	+	0.115321i	$0.0367896\pi$
$199$			3.25360i			0.230642i	−0.993328	+	0.115321i	$0.963210\pi$
$200$	15.7747	−	14.8399i	1.11544	−	1.04934i
$201$		0			0
$202$	11.8011	+	20.9290i	0.830323	+	1.47256i
$203$	−18.5414	−	18.5414i	−1.30135	−	1.30135i
$204$		0			0
$205$	5.42960	−	5.42960i	0.379219	−	0.379219i
$206$	5.65306	−	20.2703i	0.393868	−	1.41230i
$207$		0			0
$208$	19.3131	+	6.02713i	1.33912	+	0.417907i
$209$	−3.18543			−0.220340
$210$		0			0
$211$	2.55266	−	2.55266i	0.175732	−	0.175732i	−0.613760	−	0.789492i	$-0.710344\pi$
$211$	2.55266	−	2.55266i	0.175732	−	0.175732i	0.789492	+	0.613760i	$0.210344\pi$
$212$	−5.22226	−	21.2068i	−0.358666	−	1.45649i
$213$		0			0
$214$	1.56319	+	2.77228i	0.106857	+	0.189509i
$215$			18.0959i			1.23413i
$216$		0			0
$217$			13.8821i			0.942376i
$218$	5.21494	−	2.94051i	0.353200	−	0.199156i
$219$		0			0
$220$	13.9757	−	23.1076i	0.942240	−	1.55791i
$221$	6.56576	−	6.56576i	0.441661	−	0.441661i
$222$		0			0
$223$	7.78256			0.521159			0.260580	−	0.965452i	$-0.416086\pi$
$223$	7.78256			0.521159			0.260580	+	0.965452i	$0.416086\pi$
$224$	−23.0588	+	4.93714i	−1.54068	+	0.329876i
$225$		0			0
$226$	−2.06603	−	0.576183i	−0.137430	−	0.0383271i
$227$	8.01568	−	8.01568i	0.532019	−	0.532019i	−0.389154	−	0.921173i	$-0.627232\pi$
$227$	8.01568	−	8.01568i	0.532019	−	0.532019i	0.921173	+	0.389154i	$0.127232\pi$
$228$		0			0
$229$	−11.9400	−	11.9400i	−0.789019	−	0.789019i	0.192314	−	0.981333i	$-0.438401\pi$
$229$	−11.9400	−	11.9400i	−0.789019	−	0.789019i	−0.981333	+	0.192314i	$0.938401\pi$
$230$	15.5516	−	8.76898i	1.02544	−	0.578210i
$231$		0			0
$232$	−17.7830	−	0.542974i	−1.16751	−	0.0356480i
$233$		−	25.5036i		−	1.67079i	−0.549647	−	0.835397i	$-0.685238\pi$
$233$		−	25.5036i		−	1.67079i	0.549647	−	0.835397i	$-0.314762\pi$
$234$		0			0
$235$	10.7386	+	10.7386i	0.700509	+	0.700509i
$236$	1.35821	+	5.51549i	0.0884120	+	0.359028i
$237$		0			0
$238$	−2.90735	+	10.4249i	−0.188456	+	0.675748i
$239$	−25.6692			−1.66040			−0.830201	−	0.557465i	$-0.811774\pi$
$239$	−25.6692			−1.66040			−0.830201	+	0.557465i	$0.811774\pi$
$240$		0			0
$241$	3.20197			0.206257			0.103129	−	0.994668i	$-0.467115\pi$
$241$	3.20197			0.206257			0.103129	+	0.994668i	$0.467115\pi$
$242$	1.29336	−	4.63762i	0.0831404	−	0.298118i
$243$		0			0
$244$	−21.7063	+	5.34526i	−1.38960	+	0.342195i
$245$	−26.1066	−	26.1066i	−1.66789	−	1.66789i
$246$		0			0
$247$		−	4.24513i		−	0.270111i
$248$	6.45386	+	6.86039i	0.409821	+	0.435635i
$249$		0			0
$250$	11.6456	−	6.56654i	0.736534	−	0.415304i
$251$	−9.45755	−	9.45755i	−0.596955	−	0.596955i	0.342546	−	0.939501i	$-0.388711\pi$
$251$	−9.45755	−	9.45755i	−0.596955	−	0.596955i	−0.939501	+	0.342546i	$0.888711\pi$
$252$		0			0
$253$	9.52298	−	9.52298i	0.598704	−	0.598704i
$254$	16.0724	+	4.48234i	1.00847	+	0.281247i
$255$		0			0
$256$	−9.10014	+	13.1601i	−0.568759	+	0.822504i
$257$	6.86696			0.428349			0.214175	−	0.976795i	$-0.431294\pi$
$257$	6.86696			0.428349			0.214175	+	0.976795i	$0.431294\pi$
$258$		0			0
$259$	18.6447	−	18.6447i	1.15853	−	1.15853i
$260$	30.7949	+	18.6250i	1.90982	+	1.15508i
$261$		0			0
$262$	11.2596	−	6.34887i	0.695621	−	0.392235i
$263$			6.86038i			0.423029i	0.977375	+	0.211515i	$0.0678396\pi$
$263$			6.86038i			0.423029i	−0.977375	+	0.211515i	$0.932160\pi$
$264$		0			0
$265$		−	38.8506i		−	2.38657i
$266$	2.43027	+	4.31004i	0.149009	+	0.264265i
$267$		0			0
$268$	23.8277	−	5.86768i	1.45551	−	0.358425i
$269$	0.428345	−	0.428345i	0.0261166	−	0.0261166i	−0.693928	−	0.720045i	$-0.744121\pi$
$269$	0.428345	−	0.428345i	0.0261166	−	0.0261166i	0.720045	+	0.693928i	$0.244121\pi$
$270$		0			0
$271$	−13.8785			−0.843061			−0.421530	−	0.906814i	$-0.638507\pi$
$271$	−13.8785			−0.843061			−0.421530	+	0.906814i	$0.638507\pi$
$272$	3.40983	+	6.50356i	0.206752	+	0.394336i
$273$		0			0
$274$	−0.589959	+	2.11542i	−0.0356407	+	0.127797i
$275$	20.5496	−	20.5496i	1.23919	−	1.23919i
$276$		0			0
$277$	−11.7986	−	11.7986i	−0.708911	−	0.708911i	0.257395	−	0.966306i	$-0.417136\pi$
$277$	−11.7986	−	11.7986i	−0.708911	−	0.708911i	−0.966306	+	0.257395i	$0.917136\pi$
$278$	4.98012	+	8.83215i	0.298688	+	0.529717i
$279$		0			0
$280$	−41.9282	−	1.28021i	−2.50569	−	0.0765072i
$281$			32.9130i			1.96342i	0.190372	+	0.981712i	$0.439031\pi$
$281$			32.9130i			1.96342i	−0.190372	+	0.981712i	$0.560969\pi$
$282$		0			0
$283$	20.8818	+	20.8818i	1.24129	+	1.24129i	0.959464	+	0.281830i	$0.0909414\pi$
$283$	20.8818	+	20.8818i	1.24129	+	1.24129i	0.281830	+	0.959464i	$0.409059\pi$
$284$	−12.5014	+	20.6700i	−0.741824	+	1.22654i
$285$		0			0
$286$	26.1500	+	7.29282i	1.54628	+	0.431233i
$287$	−8.99722			−0.531089
$288$		0			0
$289$	−13.6298			−0.801753
$290$	−30.4847	−	8.50170i	−1.79012	−	0.499237i
$291$		0			0
$292$	−5.06085	+	8.36768i	−0.296164	+	0.489681i
$293$	−3.21904	−	3.21904i	−0.188058	−	0.188058i	0.606798	−	0.794856i	$-0.292454\pi$
$293$	−3.21904	−	3.21904i	−0.188058	−	0.188058i	−0.794856	+	0.606798i	$0.792454\pi$
$294$		0			0
$295$			10.1043i			0.588296i
$296$	0.546001	−	17.8821i	0.0317357	−	1.03938i
$297$		0			0
$298$	5.55862	+	9.85810i	0.322002	+	0.571064i
$299$	12.6910	+	12.6910i	0.733941	+	0.733941i
$300$		0			0
$301$	14.9931	−	14.9931i	0.864189	−	0.864189i
$302$	−1.66629	+	5.97485i	−0.0958844	+	0.343814i
$303$		0			0
$304$	3.20478	+	1.00013i	0.183807	+	0.0573616i
$305$	−39.7657			−2.27698
$306$		0			0
$307$	−9.06389	+	9.06389i	−0.517303	+	0.517303i	−0.916755	−	0.399451i	$-0.869201\pi$
$307$	−9.06389	+	9.06389i	−0.517303	+	0.517303i	0.399451	+	0.916755i	$0.369201\pi$
$308$	−30.7248	+	7.56610i	−1.75071	+	0.431119i
$309$		0			0
$310$	8.22941	+	14.5947i	0.467399	+	0.828924i
$311$			28.6552i			1.62489i	0.583041	+	0.812443i	$0.301863\pi$
$311$			28.6552i			1.62489i	−0.583041	+	0.812443i	$0.698137\pi$
$312$		0			0
$313$		−	9.70501i		−	0.548560i	−0.961650	−	0.274280i	$-0.911561\pi$
$313$		−	9.70501i		−	0.548560i	0.961650	−	0.274280i	$-0.0884394\pi$
$314$	20.9075	−	11.7890i	1.17988	−	0.665290i
$315$		0			0
$316$	0.660713	+	0.399605i	0.0371680	+	0.0224796i
$317$	3.56688	−	3.56688i	0.200336	−	0.200336i	−0.599808	−	0.800144i	$-0.704756\pi$
$317$	3.56688	−	3.56688i	0.200336	−	0.200336i	0.800144	+	0.599808i	$0.204756\pi$
$318$		0			0
$319$	−23.8732			−1.33664
$320$	−21.3157	+	18.8600i	−1.19159	+	1.05431i
$321$		0			0
$322$	−20.1505	−	5.61965i	−1.12294	−	0.313171i
$323$	1.08951	−	1.08951i	0.0606221	−	0.0606221i
$324$		0			0
$325$	27.3860	+	27.3860i	1.51910	+	1.51910i
$326$	−0.194690	+	0.109779i	−0.0107829	+	0.00608008i
$327$		0			0
$328$	−4.44634	+	4.18287i	−0.245508	+	0.230960i
$329$		−	17.7946i		−	0.981048i
$330$		0			0
$331$	7.71036	+	7.71036i	0.423800	+	0.423800i	0.886510	−	0.462710i	$-0.153123\pi$
$331$	7.71036	+	7.71036i	0.423800	+	0.423800i	−0.462710	+	0.886510i	$0.653123\pi$
$332$	−1.78016	+	0.438371i	−0.0976987	+	0.0240587i
$333$		0			0
$334$	7.53239	−	27.0090i	0.412154	−	1.47787i
$335$	43.6522			2.38497
$336$		0			0
$337$	6.05327			0.329743			0.164871	−	0.986315i	$-0.447279\pi$
$337$	6.05327			0.329743			0.164871	+	0.986315i	$0.447279\pi$
$338$	−4.78018	+	17.1404i	−0.260008	+	0.932313i
$339$		0			0
$340$	3.12339	+	12.6836i	0.169390	+	0.687865i
$341$	8.93701	+	8.93701i	0.483966	+	0.483966i
$342$		0			0
$343$			14.0800i			0.760247i
$344$	0.439066	−	14.3799i	0.0236728	−	0.775310i
$345$		0			0
$346$	22.5071	−	12.6909i	1.20999	−	0.682268i
$347$	25.0045	+	25.0045i	1.34231	+	1.34231i	0.893756	+	0.448554i	$0.148061\pi$
$347$	25.0045	+	25.0045i	1.34231	+	1.34231i	0.448554	+	0.893756i	$0.351939\pi$
$348$		0			0
$349$	16.1649	−	16.1649i	0.865289	−	0.865289i	−0.126658	−	0.991947i	$-0.540425\pi$
$349$	16.1649	−	16.1649i	0.865289	−	0.865289i	0.991947	+	0.126658i	$0.0404249\pi$
$350$	−43.4827	−	12.1266i	−2.32425	−	0.648197i
$351$		0			0
$352$	−11.6664	+	18.0233i	−0.621820	+	0.960642i
$353$	16.1412			0.859108			0.429554	−	0.903041i	$-0.358671\pi$
$353$	16.1412			0.859108			0.429554	+	0.903041i	$0.358671\pi$
$354$		0			0
$355$	−30.3849	+	30.3849i	−1.61266	+	1.61266i
$356$	−2.97349	+	4.91642i	−0.157595	+	0.260570i
$357$		0			0
$358$	−9.55676	+	5.38870i	−0.505090	+	0.284802i
$359$		−	8.85573i		−	0.467388i	−0.972310	−	0.233694i	$-0.924919\pi$
$359$		−	8.85573i		−	0.467388i	0.972310	−	0.233694i	$-0.0750813\pi$
$360$		0			0
$361$			18.2956i			0.962925i
$362$	−3.11303	−	5.52090i	−0.163617	−	0.290172i
$363$		0			0
$364$	−10.0832	−	40.9461i	−0.528501	−	2.14616i
$365$	−12.3005	+	12.3005i	−0.643836	+	0.643836i
$366$		0			0
$367$	−10.6885			−0.557934			−0.278967	−	0.960301i	$-0.589992\pi$
$367$	−10.6885			−0.557934			−0.278967	+	0.960301i	$0.589992\pi$
$368$	−12.5708	+	6.59090i	−0.655298	+	0.343575i
$369$		0			0
$370$	8.54910	−	30.6546i	0.444446	−	1.59366i
$371$	−32.1891	+	32.1891i	−1.67117	+	1.67117i
$372$		0			0
$373$	−25.1627	−	25.1627i	−1.30287	−	1.30287i	−0.926446	−	0.376427i	$-0.877153\pi$
$373$	−25.1627	−	25.1627i	−1.30287	−	1.30287i	−0.376427	−	0.926446i	$-0.622847\pi$
$374$	4.83968	+	8.58308i	0.250254	+	0.443821i
$375$		0			0
$376$	−8.27283	−	8.79393i	−0.426638	−	0.453512i
$377$		−	31.8151i		−	1.63856i
$378$		0			0
$379$	−5.67305	−	5.67305i	−0.291405	−	0.291405i	0.546230	−	0.837635i	$-0.316062\pi$
$379$	−5.67305	−	5.67305i	−0.291405	−	0.291405i	−0.837635	+	0.546230i	$0.816062\pi$
$380$	5.11006	+	3.09061i	0.262140	+	0.158545i
$381$		0			0
$382$	−9.26262	−	2.58320i	−0.473917	−	0.132168i
$383$	9.95307			0.508578			0.254289	−	0.967128i	$-0.418159\pi$
$383$	9.95307			0.508578			0.254289	+	0.967128i	$0.418159\pi$
$384$		0			0
$385$	−56.2875			−2.86868
$386$	18.2010	+	5.07596i	0.926404	+	0.258360i
$387$		0			0
$388$	16.0534	+	9.70927i	0.814990	+	0.492913i
$389$	1.62905	+	1.62905i	0.0825961	+	0.0825961i	0.747198	−	0.664602i	$-0.231399\pi$
$389$	1.62905	+	1.62905i	0.0825961	+	0.0825961i	−0.664602	+	0.747198i	$0.731399\pi$
$390$		0			0
$391$			6.51430i			0.329442i
$392$	20.1121	+	21.3789i	1.01581	+	1.07980i
$393$		0			0
$394$	−19.2751	−	34.1840i	−0.971066	−	1.72217i
$395$	0.971247	+	0.971247i	0.0488688	+	0.0488688i
$396$		0			0
$397$	−0.915584	+	0.915584i	−0.0459519	+	0.0459519i	−0.729709	−	0.683757i	$-0.760345\pi$
$397$	−0.915584	+	0.915584i	−0.0459519	+	0.0459519i	0.683757	+	0.729709i	$0.260345\pi$
$398$	1.23606	−	4.43216i	0.0619581	−	0.222164i
$399$		0			0
$400$	−27.1265	+	14.2225i	−1.35633	+	0.711125i
$401$	16.7542			0.836667			0.418333	−	0.908294i	$-0.362614\pi$
$401$	16.7542			0.836667			0.418333	+	0.908294i	$0.362614\pi$
$402$		0			0
$403$	−11.9101	+	11.9101i	−0.593286	+	0.593286i
$404$	−8.12478	−	32.9935i	−0.404223	−	1.64149i
$405$		0			0
$406$	18.2137	+	32.3016i	0.903928	+	1.60310i
$407$		−	24.0062i		−	1.18995i
$408$		0			0
$409$			28.8064i			1.42439i	0.701984	+	0.712193i	$0.252298\pi$
$409$			28.8064i			1.42439i	−0.701984	+	0.712193i	$0.747702\pi$
$410$	−9.45909	+	5.33363i	−0.467151	+	0.263409i
$411$		0			0
$412$	−15.4016	+	25.4652i	−0.758780	+	1.25458i
$413$	8.37178	−	8.37178i	0.411948	−	0.411948i
$414$		0			0
$415$	−3.26123			−0.160087
$416$	−24.0191	−	15.5475i	−1.17763	−	0.762278i
$417$		0			0
$418$	4.33928	+	1.21016i	0.212241	+	0.0591908i
$419$	11.7664	−	11.7664i	0.574828	−	0.574828i	−0.358646	−	0.933474i	$-0.616761\pi$
$419$	11.7664	−	11.7664i	0.574828	−	0.574828i	0.933474	+	0.358646i	$0.116761\pi$
$420$		0			0
$421$	14.3903	+	14.3903i	0.701338	+	0.701338i	0.964698	−	0.263359i	$-0.0848305\pi$
$421$	14.3903	+	14.3903i	0.701338	+	0.701338i	−0.263359	+	0.964698i	$0.584831\pi$
$422$	−4.44707	+	2.50754i	−0.216480	+	0.122065i
$423$		0			0
$424$	−0.942641	+	30.8725i	−0.0457787	+	1.49930i
$425$			14.0572i			0.681875i
$426$		0			0
$427$	32.9473	+	32.9473i	1.59443	+	1.59443i
$428$	−1.07622	−	4.37035i	−0.0520209	−	0.211249i
$429$		0			0
$430$	6.87474	−	24.6509i	0.331529	−	1.18877i
$431$	27.8049			1.33932			0.669658	−	0.742670i	$-0.266441\pi$
$431$	27.8049			1.33932			0.669658	+	0.742670i	$0.266441\pi$
$432$		0			0
$433$	13.4661			0.647139			0.323569	−	0.946204i	$-0.395117\pi$
$433$	13.4661			0.647139			0.323569	+	0.946204i	$0.395117\pi$
$434$	5.27387	−	18.9106i	0.253154	−	0.907737i
$435$		0			0
$436$	−8.22106	+	2.02447i	−0.393717	+	0.0969546i
$437$	2.10593	+	2.10593i	0.100740	+	0.100740i
$438$		0			0
$439$			7.80500i			0.372512i	0.982501	+	0.186256i	$0.0596354\pi$
$439$			7.80500i			0.372512i	−0.982501	+	0.186256i	$0.940365\pi$
$440$	−27.8168	+	26.1684i	−1.32611	+	1.24753i
$441$		0			0
$442$	−11.4385	+	6.44972i	−0.544072	+	0.306782i
$443$	−20.2218	−	20.2218i	−0.960767	−	0.960767i	0.0384918	−	0.999259i	$-0.487745\pi$
$443$	−20.2218	−	20.2218i	−0.960767	−	0.960767i	−0.999259	+	0.0384918i	$0.987745\pi$
$444$		0			0
$445$	−7.22712	+	7.22712i	−0.342598	+	0.342598i
$446$	−10.6016	−	2.95664i	−0.502003	−	0.140001i
$447$		0			0
$448$	33.2870	+	2.03463i	1.57266	+	0.0961271i
$449$	4.30671			0.203246			0.101623	−	0.994823i	$-0.467596\pi$
$449$	4.30671			0.203246			0.101623	+	0.994823i	$0.467596\pi$
$450$		0			0
$451$	−5.79224	+	5.79224i	−0.272746	+	0.272746i
$452$	2.59551	+	1.56979i	0.122083	+	0.0738367i
$453$		0			0
$454$	−13.9644	+	7.87400i	−0.655382	+	0.369545i
$455$		−	75.0129i		−	3.51666i
$456$		0			0
$457$		−	2.62877i		−	0.122969i	−0.998108	−	0.0614844i	$-0.980417\pi$
$457$		−	2.62877i		−	0.122969i	0.998108	−	0.0614844i	$-0.0195834\pi$
$458$	11.7290	+	20.8011i	0.548060	+	0.971973i
$459$		0			0
$460$	−24.5163	+	6.03724i	−1.14308	+	0.281488i
$461$	20.7230	−	20.7230i	0.965167	−	0.965167i	−0.0342469	−	0.999413i	$-0.510903\pi$
$461$	20.7230	−	20.7230i	0.965167	−	0.965167i	0.999413	+	0.0342469i	$0.0109033\pi$
$462$		0			0
$463$	3.01348			0.140048			0.0700241	−	0.997545i	$-0.477692\pi$
$463$	3.01348			0.140048			0.0700241	+	0.997545i	$0.477692\pi$
$464$	24.0182	+	7.49550i	1.11502	+	0.347970i
$465$		0			0
$466$	−9.68894	+	34.7417i	−0.448831	+	1.60938i
$467$	10.6162	−	10.6162i	0.491261	−	0.491261i	−0.417442	−	0.908704i	$-0.637073\pi$
$467$	10.6162	−	10.6162i	0.491261	−	0.491261i	0.908704	+	0.417442i	$0.137073\pi$
$468$		0			0
$469$	−36.1673	−	36.1673i	−1.67005	−	1.67005i
$470$	−10.5488	−	18.7081i	−0.486580	−	0.862940i
$471$		0			0
$472$	0.245163	−	8.02935i	0.0112846	−	0.369581i
$473$		−	19.3046i		−	0.887625i
$474$		0			0
$475$	4.54439	+	4.54439i	0.208511	+	0.208511i
$476$	7.92097	−	13.0967i	0.363057	−	0.600284i
$477$		0			0
$478$	34.9673	+	9.75185i	1.59937	+	0.446039i
$479$	−27.1604			−1.24099			−0.620496	−	0.784210i	$-0.713069\pi$
$479$	−27.1604			−1.24099			−0.620496	+	0.784210i	$0.713069\pi$
$480$		0			0
$481$	31.9925			1.45873
$482$	−4.36183	−	1.21645i	−0.198676	−	0.0554076i
$483$		0			0
$484$	−3.52371	+	5.82616i	−0.160169	+	0.264825i
$485$	23.5985	+	23.5985i	1.07155	+	1.07155i
$486$		0			0
$487$		−	23.4453i		−	1.06241i	−0.847244	−	0.531204i	$-0.821740\pi$
$487$		−	23.4453i		−	1.06241i	0.847244	−	0.531204i	$-0.178260\pi$
$488$	31.5996	+	0.964844i	1.43045	+	0.0436764i
$489$		0			0
$490$	25.6452	+	45.4813i	1.15853	+	2.05463i
$491$	5.30333	+	5.30333i	0.239336	+	0.239336i	0.816575	−	0.577239i	$-0.195870\pi$
$491$	5.30333	+	5.30333i	0.239336	+	0.239336i	−0.577239	+	0.816575i	$0.695870\pi$
$492$		0			0
$493$	8.16535	−	8.16535i	0.367749	−	0.367749i
$494$	−1.61275	+	5.78285i	−0.0725610	+	0.260183i
$495$		0			0
$496$	−6.18535	−	11.7973i	−0.277731	−	0.529714i
$497$	50.3499			2.25850
$498$		0			0
$499$	−0.576370	+	0.576370i	−0.0258019	+	0.0258019i	−0.719890	−	0.694088i	$-0.755808\pi$
$499$	−0.576370	+	0.576370i	−0.0258019	+	0.0258019i	0.694088	+	0.719890i	$0.255808\pi$
$500$	−18.3587	+	4.52091i	−0.821026	+	0.202181i
$501$		0			0
$502$	9.29039	+	16.4763i	0.414650	+	0.735374i
$503$		−	17.9556i		−	0.800599i	−0.916384	−	0.400299i	$-0.868906\pi$
$503$		−	17.9556i		−	0.800599i	0.916384	−	0.400299i	$-0.131094\pi$
$504$		0			0
$505$		−	60.4437i		−	2.68971i
$506$	−16.5903	+	9.35466i	−0.737530	+	0.415866i
$507$		0			0
$508$	−20.1914	−	12.2119i	−0.895849	−	0.541818i
$509$	22.5807	−	22.5807i	1.00087	−	1.00087i	0.000872491	−	1.00000i	$-0.499722\pi$
$509$	22.5807	−	22.5807i	1.00087	−	1.00087i	1.00000		0.000872491i	$-0.000277722\pi$
$510$		0			0
$511$	20.3827			0.901679
$512$	17.3961	−	14.4699i	0.768805	−	0.639484i
$513$		0			0
$514$	−9.35438	−	2.60879i	−0.412604	−	0.115069i
$515$	−37.4337	+	37.4337i	−1.64953	+	1.64953i
$516$		0			0
$517$	−11.4558	−	11.4558i	−0.503827	−	0.503827i
$518$	−32.4816	+	18.3152i	−1.42716	+	0.804723i
$519$		0			0
$520$	−34.8740	−	37.0707i	−1.52933	−	1.62566i
$521$			24.8374i			1.08814i	0.839038	+	0.544072i	$0.183118\pi$
$521$			24.8374i			1.08814i	−0.839038	+	0.544072i	$0.816882\pi$
$522$		0			0
$523$	−21.2444	−	21.2444i	−0.928951	−	0.928951i	0.0686874	−	0.997638i	$-0.478119\pi$
$523$	−21.2444	−	21.2444i	−0.928951	−	0.928951i	−0.997638	+	0.0686874i	$0.978119\pi$
$524$	−17.7501	+	4.37105i	−0.775419	+	0.190950i
$525$		0			0
$526$	2.60629	−	9.34543i	0.113640	−	0.407480i
$527$	−6.11347			−0.266307
$528$		0			0
$529$	10.4084			0.452541
$530$	−14.7595	+	52.9235i	−0.641114	+	2.29885i
$531$		0			0
$532$	−1.67318	−	6.79454i	−0.0725417	−	0.294581i
$533$	−7.71917	−	7.71917i	−0.334354	−	0.334354i
$534$		0			0
$535$		−	8.00643i		−	0.346148i
$536$	−34.6880	−	1.05914i	−1.49829	−	0.0457480i
$537$		0			0
$538$	−0.746234	+	0.420774i	−0.0321725	+	0.0181409i
$539$	27.8503	+	27.8503i	1.19960	+	1.19960i
$540$		0			0
$541$	−2.33381	+	2.33381i	−0.100338	+	0.100338i	−0.755494	−	0.655156i	$-0.772603\pi$
$541$	−2.33381	+	2.33381i	−0.100338	+	0.100338i	0.655156	+	0.755494i	$0.272603\pi$
$542$	18.9058	+	5.27252i	0.812072	+	0.226474i
$543$		0			0
$544$	−2.17425	−	10.1548i	−0.0932200	−	0.435382i
$545$	−15.0609			−0.645139
$546$		0			0
$547$	18.6726	−	18.6726i	0.798383	−	0.798383i	−0.184457	−	0.982841i	$-0.559053\pi$
$547$	18.6726	−	18.6726i	0.798383	−	0.798383i	0.982841	+	0.184457i	$0.0590527\pi$
$548$	1.60732	−	2.65757i	0.0686613	−	0.113526i
$549$		0			0
$550$	−35.8002	+	20.1864i	−1.52653	+	0.860752i
$551$		−	5.27936i		−	0.224908i
$552$		0			0
$553$		−	1.60942i		−	0.0684397i
$554$	11.5901	+	20.5548i	0.492416	+	0.873290i
$555$		0			0
$556$	−3.42870	−	13.9234i	−0.145409	−	0.590484i
$557$	−19.2009	+	19.2009i	−0.813567	+	0.813567i	−0.985167	−	0.171600i	$-0.945106\pi$
$557$	−19.2009	+	19.2009i	−0.813567	+	0.813567i	0.171600	+	0.985167i	$0.445106\pi$
$558$		0			0
$559$	25.7267			1.08812
$560$	56.6296	+	17.6727i	2.39304	+	0.746807i
$561$		0			0
$562$	12.5038	−	44.8351i	0.527441	−	1.89125i
$563$	17.1324	−	17.1324i	0.722043	−	0.722043i	−0.246978	−	0.969021i	$-0.579438\pi$
$563$	17.1324	−	17.1324i	0.722043	−	0.722043i	0.969021	+	0.246978i	$0.0794375\pi$
$564$		0			0
$565$	3.81540	+	3.81540i	0.160515	+	0.160515i
$566$	−20.5127	−	36.3789i	−0.862214	−	1.52912i
$567$		0			0
$568$	24.8825	−	23.4080i	1.04405	−	0.982179i
$569$			35.5333i			1.48964i	0.667268	+	0.744818i	$0.267463\pi$
$569$			35.5333i			1.48964i	−0.667268	+	0.744818i	$0.732537\pi$
$570$		0			0
$571$	−6.26636	−	6.26636i	−0.262239	−	0.262239i	0.563724	−	0.825963i	$-0.309368\pi$
$571$	−6.26636	−	6.26636i	−0.262239	−	0.262239i	−0.825963	+	0.563724i	$0.809368\pi$
$572$	−32.8517	−	19.8690i	−1.37360	−	0.830764i
$573$		0			0
$574$	12.2563	+	3.41809i	0.511567	+	0.142668i
$575$	−27.1713			−1.13312
$576$		0			0
$577$	−31.8119			−1.32435			−0.662173	−	0.749351i	$-0.730365\pi$
$577$	−31.8119			−1.32435			−0.662173	+	0.749351i	$0.730365\pi$
$578$	18.5669	+	5.17803i	0.772282	+	0.215378i
$579$		0			0
$580$	38.2973	+	23.1626i	1.59021	+	0.961773i
$581$	2.70204	+	2.70204i	0.112100	+	0.112100i
$582$		0			0
$583$			41.4454i			1.71650i
$584$	10.0730	−	9.47607i	0.416822	−	0.392122i
$585$		0			0
$586$	3.16214	+	5.60800i	0.130627	+	0.231664i
$587$	15.9018	+	15.9018i	0.656336	+	0.656336i	0.954511	−	0.298175i	$-0.0963779\pi$
$587$	15.9018	+	15.9018i	0.656336	+	0.656336i	−0.298175	+	0.954511i	$0.596378\pi$
$588$		0			0
$589$	−1.97635	+	1.97635i	−0.0814340	+	0.0814340i
$590$	3.83868	−	13.7644i	0.158036	−	0.566672i
$591$		0			0
$592$	−7.53728	+	24.1521i	−0.309780	+	0.992646i
$593$	−24.3769			−1.00104			−0.500519	−	0.865726i	$-0.666857\pi$
$593$	−24.3769			−1.00104			−0.500519	+	0.865726i	$0.666857\pi$
$594$		0			0
$595$	19.2520	−	19.2520i	0.789257	−	0.789257i
$596$	−3.82698	−	15.5408i	−0.156759	−	0.636574i
$597$		0			0
$598$	−12.4667	−	22.1095i	−0.509802	−	0.904124i
$599$			6.40544i			0.261719i	0.991401	+	0.130860i	$0.0417737\pi$
$599$			6.40544i			0.261719i	−0.991401	+	0.130860i	$0.958226\pi$
$600$		0			0
$601$			22.7193i			0.926738i	0.886165	+	0.463369i	$0.153360\pi$
$601$			22.7193i			0.926738i	−0.886165	+	0.463369i	$0.846640\pi$
$602$	−26.1200	+	14.7281i	−1.06457	+	0.600273i
$603$		0			0
$604$	4.53975	−	7.50609i	0.184720	−	0.305419i
$605$	−8.56444	+	8.56444i	−0.348194	+	0.348194i
$606$		0			0
$607$	35.5457			1.44276			0.721378	−	0.692542i	$-0.243509\pi$
$607$	35.5457			1.44276			0.721378	+	0.692542i	$0.243509\pi$
$608$	−3.98570	−	2.57993i	−0.161641	−	0.104630i
$609$		0			0
$610$	54.1701	+	15.1072i	2.19328	+	0.611672i
$611$	15.2669	−	15.2669i	0.617632	−	0.617632i
$612$		0			0
$613$	25.7897	+	25.7897i	1.04164	+	1.04164i	0.999095	+	0.0425431i	$0.0135460\pi$
$613$	25.7897	+	25.7897i	1.04164	+	1.04164i	0.0425431	+	0.999095i	$0.486454\pi$
$614$	15.7905	−	8.90369i	0.637254	−	0.359324i
$615$		0			0
$616$	44.7286	+	1.36572i	1.80217	+	0.0550263i
$617$		−	23.4215i		−	0.942913i	−0.881889	−	0.471457i	$-0.843728\pi$
$617$		−	23.4215i		−	0.942913i	0.881889	−	0.471457i	$-0.156272\pi$
$618$		0			0
$619$	−27.4016	−	27.4016i	−1.10137	−	1.10137i	−0.994246	−	0.107119i	$-0.965837\pi$
$619$	−27.4016	−	27.4016i	−1.10137	−	1.10137i	−0.107119	−	0.994246i	$-0.534163\pi$
$620$	−5.66576	−	23.0078i	−0.227542	−	0.924014i
$621$		0			0
$622$	10.8862	−	39.0350i	0.436499	−	1.56516i
$623$	11.9758			0.479802
$624$		0			0
$625$	4.65311			0.186125
$626$	−3.68698	+	13.2205i	−0.147361	+	0.528396i
$627$		0			0
$628$	−32.9596	+	8.11643i	−1.31523	+	0.323881i
$629$	8.21087	+	8.21087i	0.327389	+	0.327389i
$630$		0			0
$631$			33.2708i			1.32449i	0.749287	+	0.662246i	$0.230397\pi$
$631$			33.2708i			1.32449i	−0.749287	+	0.662246i	$0.769603\pi$
$632$	−0.748232	−	0.795363i	−0.0297631	−	0.0316378i
$633$		0			0
$634$	−6.21399	+	3.50384i	−0.246789	+	0.139155i
$635$	−29.6813	−	29.6813i	−1.17787	−	1.17787i
$636$		0			0
$637$	−37.1154	+	37.1154i	−1.47056	+	1.47056i
$638$	32.5207	+	9.06953i	1.28751	+	0.359066i
$639$		0			0
$640$	36.2020	−	17.5938i	1.43101	−	0.695455i
$641$	−44.8754			−1.77247			−0.886235	−	0.463235i	$-0.846688\pi$
$641$	−44.8754			−1.77247			−0.886235	+	0.463235i	$0.846688\pi$
$642$		0			0
$643$	7.73814	−	7.73814i	0.305163	−	0.305163i	−0.537867	−	0.843030i	$-0.680770\pi$
$643$	7.73814	−	7.73814i	0.305163	−	0.305163i	0.843030	+	0.537867i	$0.180770\pi$
$644$	25.3146	+	15.3105i	0.997537	+	0.603319i
$645$		0			0
$646$	−1.89808	+	1.07026i	−0.0746789	+	0.0421087i
$647$			48.9157i			1.92307i	0.274676	+	0.961537i	$0.411429\pi$
$647$			48.9157i			1.92307i	−0.274676	+	0.961537i	$0.588571\pi$
$648$		0			0
$649$		−	10.7792i		−	0.423120i
$650$	−26.9019	−	47.7101i	−1.05518	−	1.87134i
$651$		0			0
$652$	0.306919	−	0.0755800i	0.0120199	−	0.00295994i
$653$	34.0217	−	34.0217i	1.33137	−	1.33137i	0.427230	−	0.904143i	$-0.359490\pi$
$653$	34.0217	−	34.0217i	1.33137	−	1.33137i	0.904143	−	0.427230i	$-0.140510\pi$
$654$		0			0
$655$	−32.5181			−1.27059
$656$	7.64604	−	4.00884i	0.298528	−	0.156519i
$657$		0			0
$658$	−6.76026	+	24.2403i	−0.263542	+	0.944987i
$659$	−25.9010	+	25.9010i	−1.00896	+	1.00896i	−0.00899853	+	0.999960i	$0.502864\pi$
$659$	−25.9010	+	25.9010i	−1.00896	+	1.00896i	−0.999960	+	0.00899853i	$0.997136\pi$
$660$		0			0
$661$	14.1560	+	14.1560i	0.550603	+	0.550603i	0.926615	−	0.376012i	$-0.122705\pi$
$661$	14.1560	+	14.1560i	0.550603	+	0.550603i	−0.376012	+	0.926615i	$0.622705\pi$
$662$	−7.57408	−	13.4325i	−0.294375	−	0.522068i
$663$		0			0
$664$	2.59152	+	0.0791279i	0.100571	+	0.00307076i
$665$		−	12.4475i		−	0.482695i
$666$		0			0
$667$	15.7829	+	15.7829i	0.611116	+	0.611116i
$668$	−20.5217	+	33.9309i	−0.794009	+	1.31283i
$669$		0			0
$670$	−59.4643	−	16.5837i	−2.29731	−	0.640683i
$671$	42.4217			1.63767
$672$		0			0
$673$	38.7906			1.49527			0.747633	−	0.664112i	$-0.231190\pi$
$673$	38.7906			1.49527			0.747633	+	0.664112i	$0.231190\pi$
$674$	−8.24595	−	2.29967i	−0.317622	−	0.0885799i
$675$		0			0
$676$	13.0234	−	21.5331i	0.500901	−	0.828197i
$677$	12.5376	+	12.5376i	0.481860	+	0.481860i	0.905725	−	0.423865i	$-0.139327\pi$
$677$	12.5376	+	12.5376i	0.481860	+	0.481860i	−0.423865	+	0.905725i	$0.639327\pi$
$678$		0			0
$679$		−	39.1044i		−	1.50069i
$680$	0.563787	−	18.4646i	0.0216202	−	0.708085i
$681$		0			0
$682$	−8.77906	−	15.5695i	−0.336167	−	0.596187i
$683$	23.3735	+	23.3735i	0.894363	+	0.894363i	0.994930	−	0.100567i	$-0.0320658\pi$
$683$	23.3735	+	23.3735i	0.894363	+	0.894363i	−0.100567	+	0.994930i	$0.532066\pi$
$684$		0			0
$685$	3.90662	−	3.90662i	0.149264	−	0.149264i
$686$	5.34905	−	19.1802i	0.204228	−	0.732302i
$687$		0			0
$688$	−6.06109	+	19.4219i	−0.231077	+	0.740453i
$689$	−55.2333			−2.10422
$690$		0			0
$691$	3.34670	−	3.34670i	0.127314	−	0.127314i	−0.640578	−	0.767893i	$-0.721305\pi$
$691$	3.34670	−	3.34670i	0.127314	−	0.127314i	0.767893	+	0.640578i	$0.221305\pi$
$692$	−35.4812	+	8.73740i	−1.34879	+	0.332146i
$693$		0			0
$694$	−24.5625	−	43.5612i	−0.932381	−	1.65356i
$695$		−	25.5075i		−	0.967556i
$696$		0			0
$697$		−	3.96225i		−	0.150081i
$698$	−28.1615	+	15.8792i	−1.06593	+	0.601038i
$699$		0			0
$700$	54.6265	+	33.0386i	2.06469	+	1.24874i
$701$	2.51411	−	2.51411i	0.0949566	−	0.0949566i	−0.658033	−	0.752989i	$-0.728611\pi$
$701$	2.51411	−	2.51411i	0.0949566	−	0.0949566i	0.752989	+	0.658033i	$0.228611\pi$
$702$		0			0
$703$	5.30879			0.200225
$704$	22.7394	−	20.1197i	0.857024	−	0.758290i
$705$		0			0
$706$	−21.9880	−	6.13211i	−0.827529	−	0.230785i
$707$	−50.0797	+	50.0797i	−1.88344	+	1.88344i
$708$		0			0
$709$	14.3349	+	14.3349i	0.538358	+	0.538358i	0.923047	−	0.384688i	$-0.125691\pi$
$709$	14.3349	+	14.3349i	0.538358	+	0.538358i	−0.384688	+	0.923047i	$0.625691\pi$
$710$	52.9347	−	29.8479i	1.98660	−	1.12017i
$711$		0			0
$712$	5.91835	−	5.56765i	0.221800	−	0.208656i
$713$		−	11.8168i		−	0.442542i
$714$		0			0
$715$	−48.2919	−	48.2919i	−1.80602	−	1.80602i
$716$	15.0657	−	3.70999i	0.563032	−	0.138649i
$717$		0			0
$718$	−3.36434	+	12.0635i	−0.125556	+	0.450208i
$719$	−33.1678			−1.23695			−0.618474	−	0.785805i	$-0.712249\pi$
$719$	−33.1678			−1.23695			−0.618474	+	0.785805i	$0.712249\pi$
$720$		0			0
$721$	62.0303			2.31013
$722$	6.95058	−	24.9228i	0.258674	−	0.927530i
$723$		0			0
$724$	2.14325	+	8.70340i	0.0796532	+	0.323459i
$725$	34.0579	+	34.0579i	1.26488	+	1.26488i
$726$		0			0
$727$			14.8365i			0.550256i	0.961408	+	0.275128i	$0.0887203\pi$
$727$			14.8365i			0.550256i	−0.961408	+	0.275128i	$0.911280\pi$
$728$	−1.82005	+	59.6087i	−0.0674557	+	2.20924i
$729$		0			0
$730$	21.4291	−	12.0831i	0.793126	−	0.447214i
$731$	6.60276	+	6.60276i	0.244212	+	0.244212i
$732$		0			0
$733$	−31.9028	+	31.9028i	−1.17836	+	1.17836i	−0.198194	+	0.980163i	$0.563508\pi$
$733$	−31.9028	+	31.9028i	−1.17836	+	1.17836i	−0.980163	+	0.198194i	$0.936492\pi$
$734$	14.5602	+	4.06061i	0.537426	+	0.149880i
$735$		0			0
$736$	19.6282	−	4.20262i	0.723506	−	0.154911i
$737$	−46.5677			−1.71534
$738$		0			0
$739$	−11.5108	+	11.5108i	−0.423433	+	0.423433i	−0.886384	−	0.462951i	$-0.846791\pi$
$739$	−11.5108	+	11.5108i	−0.423433	+	0.423433i	0.462951	+	0.886384i	$0.346791\pi$
$740$	−23.2917	+	38.5108i	−0.856219	+	1.41569i
$741$		0			0
$742$	56.0777	−	31.6202i	2.05868	−	1.16081i
$743$		−	23.0489i		−	0.845581i	−0.906228	−	0.422790i	$-0.861051\pi$
$743$		−	23.0489i		−	0.845581i	0.906228	−	0.422790i	$-0.138949\pi$
$744$		0			0
$745$		−	28.4705i		−	1.04308i
$746$	24.7179	+	43.8368i	0.904988	+	1.60498i
$747$		0			0
$748$	−3.33201	−	13.5308i	−0.121830	−	0.494733i
$749$	−6.63361	+	6.63361i	−0.242387	+	0.242387i
$750$		0			0
$751$	−50.5096			−1.84312			−0.921560	−	0.388236i	$-0.873084\pi$
$751$	−50.5096			−1.84312			−0.921560	+	0.388236i	$0.873084\pi$
$752$	7.92864	+	15.1223i	0.289128	+	0.551452i
$753$		0			0
$754$	−12.0867	+	43.3396i	−0.440173	+	1.57833i
$755$	11.0339	−	11.0339i	0.401566	−	0.401566i
$756$		0			0
$757$	−22.0796	−	22.0796i	−0.802498	−	0.802498i	0.180988	−	0.983485i	$-0.442071\pi$
$757$	−22.0796	−	22.0796i	−0.802498	−	0.802498i	−0.983485	+	0.180988i	$0.942071\pi$
$758$	5.57278	+	9.88322i	0.202413	+	0.358975i
$759$		0			0
$760$	−5.78694	−	6.15146i	−0.209914	−	0.223137i
$761$		−	10.2647i		−	0.372094i	−0.982541	−	0.186047i	$-0.940432\pi$
$761$		−	10.2647i		−	0.372094i	0.982541	−	0.186047i	$-0.0595677\pi$
$762$		0			0
$763$	12.4785	+	12.4785i	0.451752	+	0.451752i
$764$	11.6365	+	7.03783i	0.420992	+	0.254620i
$765$		0			0
$766$	−13.5584	−	3.78122i	−0.489884	−	0.136621i
$767$	14.3652			0.518696
$768$		0			0
$769$	−15.8159			−0.570336			−0.285168	−	0.958478i	$-0.592049\pi$
$769$	−15.8159			−0.570336			−0.285168	+	0.958478i	$0.592049\pi$
$770$	76.6766	+	21.3839i	2.76323	+	0.770622i
$771$		0			0
$772$	−22.8655	−	13.8293i	−0.822948	−	0.497726i
$773$	−19.6859	−	19.6859i	−0.708054	−	0.708054i	0.258072	−	0.966126i	$-0.416913\pi$
$773$	−19.6859	−	19.6859i	−0.708054	−	0.708054i	−0.966126	+	0.258072i	$0.916913\pi$
$774$		0			0
$775$		−	25.4994i		−	0.915966i
$776$	−18.1799	−	19.3250i	−0.652620	−	0.693729i
$777$		0			0
$778$	−1.60026	−	2.83803i	−0.0573720	−	0.101748i
$779$	−1.28091	−	1.28091i	−0.0458933	−	0.0458933i
$780$		0			0
$781$	32.4143	−	32.4143i	1.15988	−	1.15988i
$782$	2.47482	−	8.87398i	0.0884992	−	0.317333i
$783$		0			0
$784$	−19.2753	−	36.7637i	−0.688404	−	1.31299i
$785$	−60.3816			−2.15511
$786$		0			0
$787$	33.5052	−	33.5052i	1.19433	−	1.19433i	0.218491	−	0.975839i	$-0.429887\pi$
$787$	33.5052	−	33.5052i	1.19433	−	1.19433i	0.975839	−	0.218491i	$-0.0701133\pi$
$788$	13.2705	+	53.8893i	0.472740	+	1.91973i
$789$		0			0
$790$	−0.954081	−	1.69204i	−0.0339447	−	0.0602002i
$791$		−	6.32238i		−	0.224798i
$792$		0			0
$793$			56.5343i			2.00759i
$794$	1.59507	−	0.899402i	0.0566070	−	0.0319186i
$795$		0			0
$796$	−3.36760	+	5.56804i	−0.119361	+	0.197354i
$797$	−12.8477	+	12.8477i	−0.455089	+	0.455089i	−0.897039	−	0.441951i	$-0.854287\pi$
$797$	−12.8477	+	12.8477i	−0.455089	+	0.455089i	0.441951	+	0.897039i	$0.354287\pi$
$798$		0			0
$799$	7.83649			0.277235
$800$	42.3558	−	9.06883i	1.49750	−	0.320632i
$801$		0			0
$802$	−22.8231	−	6.36502i	−0.805913	−	0.224757i
$803$	13.1220	−	13.1220i	0.463066	−	0.463066i
$804$		0			0
$805$	37.2125	+	37.2125i	1.31157	+	1.31157i
$806$	20.7491	−	11.6996i	0.730855	−	0.412102i
$807$		0			0
$808$	−1.46656	+	48.0314i	−0.0515934	+	1.68974i
$809$			9.11690i			0.320533i	0.987074	+	0.160267i	$0.0512354\pi$
$809$			9.11690i			0.320533i	−0.987074	+	0.160267i	$0.948765\pi$
$810$		0			0
$811$	2.98744	+	2.98744i	0.104903	+	0.104903i	0.757610	−	0.652707i	$-0.226367\pi$
$811$	2.98744	+	2.98744i	0.104903	+	0.104903i	−0.652707	+	0.757610i	$0.726367\pi$
$812$	−12.5397	−	50.9216i	−0.440056	−	1.78700i
$813$		0			0
$814$	−9.12009	+	32.7020i	−0.319659	+	1.14621i
$815$	0.562272			0.0196955
$816$		0			0
$817$	4.26905			0.149355
$818$	10.9437	−	39.2410i	0.382637	−	1.37203i
$819$		0			0
$820$	14.9117	−	3.67208i	0.520740	−	0.128235i
$821$	19.7603	+	19.7603i	0.689639	+	0.689639i	0.962152	−	0.272513i	$-0.0878547\pi$
$821$	19.7603	+	19.7603i	0.689639	+	0.689639i	−0.272513	+	0.962152i	$0.587855\pi$
$822$		0			0
$823$		−	14.0736i		−	0.490575i	−0.969450	−	0.245287i	$-0.921118\pi$
$823$		−	14.0736i		−	0.490575i	0.969450	−	0.245287i	$-0.0788823\pi$
$824$	30.6548	−	28.8383i	1.06791	−	1.00463i
$825$		0			0
$826$	−14.5848	+	8.22381i	−0.507469	+	0.286143i
$827$	−30.3530	−	30.3530i	−1.05548	−	1.05548i	−0.998368	−	0.0571087i	$-0.981812\pi$
$827$	−30.3530	−	30.3530i	−1.05548	−	1.05548i	−0.0571087	−	0.998368i	$-0.518188\pi$
$828$		0			0
$829$	−0.768357	+	0.768357i	−0.0266861	+	0.0266861i	−0.720324	−	0.693638i	$-0.756007\pi$
$829$	−0.768357	+	0.768357i	−0.0266861	+	0.0266861i	0.693638	+	0.720324i	$0.256007\pi$
$830$	4.44255	+	1.23896i	0.154203	+	0.0430048i
$831$		0			0
$832$	26.8130	+	30.3042i	0.929574	+	1.05061i
$833$	−19.0513			−0.660088
$834$		0			0
$835$	−49.8783	+	49.8783i	−1.72611	+	1.72611i
$836$	−5.45136	−	3.29703i	−0.188539	−	0.114030i
$837$		0			0
$838$	−20.4987	+	11.5585i	−0.708117	+	0.399281i
$839$			8.89072i			0.306942i	0.988153	+	0.153471i	$0.0490451\pi$
$839$			8.89072i			0.306942i	−0.988153	+	0.153471i	$0.950955\pi$
$840$		0			0
$841$		−	10.5661i		−	0.364349i
$842$	−14.1359	−	25.0698i	−0.487156	−	0.863962i
$843$		0			0
$844$	7.01056	−	1.72638i	0.241314	−	0.0594245i
$845$	31.6536	−	31.6536i	1.08892	−	1.08892i
$846$		0			0
$847$	14.1919			0.487639
$848$	13.0127	−	41.6973i	0.446858	−	1.43189i
$849$		0			0
$850$	5.34040	−	19.1492i	0.183174	−	0.656811i
$851$	−15.8709	+	15.8709i	−0.544046	+	0.544046i
$852$		0			0
$853$	−2.53367	−	2.53367i	−0.0867514	−	0.0867514i	0.662399	−	0.749151i	$-0.269538\pi$
$853$	−2.53367	−	2.53367i	−0.0867514	−	0.0867514i	−0.749151	+	0.662399i	$0.769538\pi$
$854$	−32.3649	−	57.3986i	−1.10751	−	1.96414i
$855$		0			0
$856$	−0.194262	+	6.36228i	−0.00663973	+	0.217458i
$857$		−	33.5479i		−	1.14597i	−0.819564	−	0.572987i	$-0.805784\pi$
$857$		−	33.5479i		−	1.14597i	0.819564	−	0.572987i	$-0.194216\pi$
$858$		0			0
$859$	−27.8684	−	27.8684i	−0.950859	−	0.950859i	0.0479893	−	0.998848i	$-0.484719\pi$
$859$	−27.8684	−	27.8684i	−0.950859	−	0.950859i	−0.998848	+	0.0479893i	$0.984719\pi$
$860$	−18.7300	+	30.9684i	−0.638687	+	1.05601i
$861$		0			0
$862$	−37.8767	−	10.5632i	−1.29009	−	0.359785i
$863$	−31.0522			−1.05703			−0.528514	−	0.848925i	$-0.677251\pi$
$863$	−31.0522			−1.05703			−0.528514	+	0.848925i	$0.677251\pi$
$864$		0			0
$865$	−65.0013			−2.21011
$866$	−18.3439	−	5.11583i	−0.623352	−	0.173843i
$867$		0			0
$868$	−14.3684	+	23.7570i	−0.487697	+	0.806365i
$869$	−1.03612	−	1.03612i	−0.0351479	−	0.0351479i
$870$		0			0
$871$		−	62.0596i		−	2.10281i
$872$	11.9681	+	0.365426i	0.405291	+	0.0123749i
$873$		0			0
$874$	−2.06871	−	3.66882i	−0.0699751	−	0.124100i
$875$	27.8661	+	27.8661i	0.942045	+	0.942045i
$876$		0			0
$877$	21.6548	−	21.6548i	0.731230	−	0.731230i	−0.239633	−	0.970864i	$-0.577027\pi$
$877$	21.6548	−	21.6548i	0.731230	−	0.731230i	0.970864	+	0.239633i	$0.0770272\pi$
$878$	2.96516	−	10.6322i	0.100069	−	0.358820i
$879$		0			0
$880$	47.8344	−	25.0797i	1.61250	−	0.845437i
$881$	15.5268			0.523110			0.261555	−	0.965189i	$-0.415765\pi$
$881$	15.5268			0.523110			0.261555	+	0.965189i	$0.415765\pi$
$882$		0			0
$883$	32.5979	−	32.5979i	1.09701	−	1.09701i	0.102247	−	0.994759i	$-0.467397\pi$
$883$	32.5979	−	32.5979i	1.09701	−	1.09701i	0.994759	−	0.102247i	$-0.0326033\pi$
$884$	18.0321	−	4.44048i	0.606485	−	0.149349i
$885$		0			0
$886$	19.8644	+	35.2291i	0.667358	+	1.18355i
$887$		−	9.94232i		−	0.333830i	−0.985971	−	0.166915i	$-0.946619\pi$
$887$		−	9.94232i		−	0.333830i	0.985971	−	0.166915i	$-0.0533806\pi$
$888$		0			0
$889$			49.1840i			1.64958i
$890$	12.5906	−	7.09939i	0.422039	−	0.237972i
$891$		0			0
$892$	13.3186	+	8.05524i	0.445941	+	0.269709i
$893$	2.53336	−	2.53336i	0.0847758	−	0.0847758i
$894$		0			0
$895$	27.6002			0.922574
$896$	−44.5716	−	15.4175i	−1.48903	−	0.515064i
$897$		0			0
$898$	−5.86673	−	1.63614i	−0.195775	−	0.0545987i
$899$	−14.8117	+	14.8117i	−0.493999	+	0.493999i
$900$		0			0
$901$	−14.1756	−	14.1756i	−0.472258	−	0.472258i
$902$	10.0909	−	5.68986i	0.335989	−	0.189452i
$903$		0			0
$904$	−2.93932	−	3.12446i	−0.0977602	−	0.103918i
$905$			15.9445i			0.530015i
$906$		0			0
$907$	2.24034	+	2.24034i	0.0743894	+	0.0743894i	0.743323	−	0.668933i	$-0.233249\pi$
$907$	2.24034	+	2.24034i	0.0743894	+	0.0743894i	−0.668933	+	0.743323i	$0.733249\pi$
$908$	22.0141	−	5.42107i	0.730564	−	0.179904i
$909$		0			0
$910$	−28.4978	+	102.185i	−0.944692	+	3.38740i
$911$	10.5162			0.348416			0.174208	−	0.984709i	$-0.444263\pi$
$911$	10.5162			0.348416			0.174208	+	0.984709i	$0.444263\pi$
$912$		0			0
$913$	3.47905			0.115140
$914$	−0.998684	+	3.58099i	−0.0330335	+	0.118449i
$915$		0			0
$916$	−8.07513	−	32.7919i	−0.266810	−	1.08347i
$917$	26.9424	+	26.9424i	0.889716	+	0.889716i
$918$		0			0
$919$			10.9252i			0.360389i	0.983631	+	0.180194i	$0.0576727\pi$
$919$			10.9252i			0.360389i	−0.983631	+	0.180194i	$0.942327\pi$
$920$	35.6904	+	1.08975i	1.17668	+	0.0359279i
$921$		0			0
$922$	−36.1023	+	20.3567i	−1.18897	+	0.670413i
$923$	43.1978	+	43.1978i	1.42187	+	1.42187i
$924$		0			0
$925$	−34.2478	+	34.2478i	−1.12606	+	1.12606i
$926$	−4.10505	−	1.14484i	−0.134900	−	0.0376216i
$927$		0			0
$928$	−29.8708	−	19.3352i	−0.980557	−	0.634710i
$929$	12.5406			0.411442			0.205721	−	0.978611i	$-0.434046\pi$
$929$	12.5406			0.411442			0.205721	+	0.978611i	$0.434046\pi$
$930$		0			0
$931$	−6.15887	+	6.15887i	−0.201849	+	0.201849i
$932$	26.3971	−	43.6454i	0.864667	−	1.42965i
$933$		0			0
$934$	−18.4949	+	10.4286i	−0.605173	+	0.341235i
$935$		−	24.7882i		−	0.810661i
$936$		0			0
$937$			0.161784i			0.00528526i	0.999997	+	0.00264263i	$0.000841176\pi$
$937$			0.161784i			0.00528526i	−0.999997	+	0.00264263i	$0.999159\pi$
$938$	35.5281	+	63.0084i	1.16003	+	2.05730i
$939$		0			0
$940$	7.26260	+	29.4923i	0.236880	+	0.961932i
$941$	−3.51389	+	3.51389i	−0.114550	+	0.114550i	−0.762058	−	0.647509i	$-0.775811\pi$
$941$	−3.51389	+	3.51389i	−0.114550	+	0.114550i	0.647509	+	0.762058i	$0.275811\pi$
$942$		0			0
$943$	7.65866			0.249400
$944$	−3.38436	+	10.8447i	−0.110152	+	0.352965i
$945$		0			0
$946$	−7.33391	+	26.2973i	−0.238446	+	0.854999i
$947$	−20.6515	+	20.6515i	−0.671085	+	0.671085i	−0.957966	−	0.286881i	$-0.907382\pi$
$947$	−20.6515	+	20.6515i	−0.671085	+	0.671085i	0.286881	+	0.957966i	$0.407382\pi$
$948$		0			0
$949$	17.4874	+	17.4874i	0.567664	+	0.567664i
$950$	−4.46407	−	7.91694i	−0.144833	−	0.256859i
$951$		0			0
$952$	−15.7657	+	14.8314i	−0.510968	+	0.480690i
$953$			2.38373i			0.0772166i	0.999254	+	0.0386083i	$0.0122925\pi$
$953$			2.38373i			0.0772166i	−0.999254	+	0.0386083i	$0.987708\pi$
$954$		0			0
$955$	17.1056	+	17.1056i	0.553523	+	0.553523i
$956$	−43.9288	−	26.5685i	−1.42076	−	0.859288i
$957$		0			0
$958$	36.9988	+	10.3184i	1.19538	+	0.333372i
$959$	−6.47354			−0.209041
$960$		0			0
$961$	−19.9103			−0.642269
$962$	−43.5812	−	12.1541i	−1.40511	−	0.391864i
$963$		0			0
$964$	5.47968	+	3.31416i	0.176489	+	0.106742i
$965$	−33.6123	−	33.6123i	−1.08202	−	1.08202i
$966$		0			0
$967$			24.6637i			0.793131i	0.918007	+	0.396565i	$0.129798\pi$
$967$			24.6637i			0.793131i	−0.918007	+	0.396565i	$0.870202\pi$
$968$	7.01350	−	6.59790i	0.225422	−	0.212064i
$969$		0			0
$970$	−23.1814	−	41.1118i	−0.744311	−	1.32002i
$971$	−18.1877	−	18.1877i	−0.583672	−	0.583672i	0.352238	−	0.935910i	$-0.385421\pi$
$971$	−18.1877	−	18.1877i	−0.583672	−	0.583672i	−0.935910	+	0.352238i	$0.885421\pi$
$972$		0			0
$973$	−21.1339	+	21.1339i	−0.677521	+	0.677521i
$974$	−8.90700	+	31.9379i	−0.285399	+	1.02336i
$975$		0			0
$976$	−42.6795	−	13.3192i	−1.36614	−	0.426337i
$977$	11.9368			0.381891			0.190946	−	0.981601i	$-0.438845\pi$
$977$	11.9368			0.381891			0.190946	+	0.981601i	$0.438845\pi$
$978$		0			0
$979$	7.70982	−	7.70982i	0.246407	−	0.246407i
$980$	−17.6561	−	71.6987i	−0.564004	−	2.29033i
$981$		0			0
$982$	−5.20960	−	9.23913i	−0.166245	−	0.294832i
$983$		−	34.4565i		−	1.09899i	−0.835497	−	0.549495i	$-0.814820\pi$
$983$		−	34.4565i		−	1.09899i	0.835497	−	0.549495i	$-0.185180\pi$
$984$		0			0
$985$			98.7246i			3.14563i
$986$	−14.2251	+	8.02103i	−0.453021	+	0.255442i
$987$		0			0
$988$	4.39387	−	7.26489i	0.139788	−	0.231127i
$989$	−12.7625	+	12.7625i	−0.405825	+	0.405825i
$990$		0			0
$991$	−47.2718			−1.50164			−0.750819	−	0.660508i	$-0.770341\pi$
$991$	−47.2718			−1.50164			−0.750819	+	0.660508i	$0.770341\pi$
$992$	3.94403	+	18.4205i	0.125223	+	0.584851i
$993$		0			0
$994$	−68.5882	−	19.1282i	−2.17549	−	0.606709i
$995$	−8.18500	+	8.18500i	−0.259482	+	0.259482i
$996$		0			0
$997$	−19.7430	−	19.7430i	−0.625267	−	0.625267i	0.321607	−	0.946873i	$-0.395777\pi$
$997$	−19.7430	−	19.7430i	−0.625267	−	0.625267i	−0.946873	+	0.321607i	$0.895777\pi$
$998$	1.00411	−	0.566183i	0.0317847	−	0.0179222i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.325.2	yes	32
3.2	odd	2	inner	432.2.k.d.325.15	yes	32
4.3	odd	2		1728.2.k.d.433.15		32
12.11	even	2		1728.2.k.d.433.2		32
16.3	odd	4		1728.2.k.d.1297.15		32
16.13	even	4	inner	432.2.k.d.109.2	✓	32
48.29	odd	4	inner	432.2.k.d.109.15	yes	32
48.35	even	4		1728.2.k.d.1297.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.2	✓	32	16.13	even	4	inner
432.2.k.d.109.15	yes	32	48.29	odd	4	inner
432.2.k.d.325.2	yes	32	1.1	even	1	trivial
432.2.k.d.325.15	yes	32	3.2	odd	2	inner
1728.2.k.d.433.2		32	12.11	even	2
1728.2.k.d.433.15		32	4.3	odd	2
1728.2.k.d.1297.2		32	48.35	even	4
1728.2.k.d.1297.15		32	16.3	odd	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36223 - 0.379905i) q^{2} +(1.71134 + 1.03504i) q^{4} +(2.51567 + 2.51567i) q^{5} -4.16864i q^{7} +(-1.93803 - 2.06011i) q^{8} +O(q^{10})\)	\(q+(-1.36223 - 0.379905i) q^{2} +(1.71134 + 1.03504i) q^{4} +(2.51567 + 2.51567i) q^{5} -4.16864i q^{7} +(-1.93803 - 2.06011i) q^{8} +(-2.47121 - 4.38264i) q^{10} +(-2.68369 - 2.68369i) q^{11} +(3.57649 - 3.57649i) q^{13} +(-1.58369 + 5.67865i) q^{14} +(1.85740 + 3.54261i) q^{16} +1.83581 q^{17} +(0.593478 - 0.593478i) q^{19} +(1.70137 + 6.90899i) q^{20} +(2.63626 + 4.67536i) q^{22} +3.54846i q^{23} +7.65722i q^{25} +(-6.23073 + 3.51328i) q^{26} +(4.31470 - 7.13398i) q^{28} +(4.44782 - 4.44782i) q^{29} -3.33012 q^{31} +(-1.18435 - 5.53148i) q^{32} +(-2.50080 - 0.697434i) q^{34} +(10.4869 - 10.4869i) q^{35} +(4.47261 + 4.47261i) q^{37} +(-1.03392 + 0.582988i) q^{38} +(0.307105 - 10.0580i) q^{40} -2.15831i q^{41} +(3.59664 + 3.59664i) q^{43} +(-1.81500 - 7.37045i) q^{44} +(1.34808 - 4.83382i) q^{46} +4.26868 q^{47} -10.3776 q^{49} +(2.90902 - 10.4309i) q^{50} +(9.82241 - 2.41881i) q^{52} +(-7.72171 - 7.72171i) q^{53} -13.5026i q^{55} +(-8.58785 + 8.07896i) q^{56} +(-7.74870 + 4.36920i) q^{58} +(2.00827 + 2.00827i) q^{59} +(-7.90359 + 7.90359i) q^{61} +(4.53639 + 1.26513i) q^{62} +(-0.488079 + 7.98510i) q^{64} +17.9946 q^{65} +(8.67604 - 8.67604i) q^{67} +(3.14171 + 1.90013i) q^{68} +(-18.2697 + 10.3016i) q^{70} +12.0783i q^{71} +4.88954i q^{73} +(-4.39356 - 7.79189i) q^{74} +(1.62992 - 0.401374i) q^{76} +(-11.1874 + 11.1874i) q^{77} +0.386079 q^{79} +(-4.23943 + 13.5846i) q^{80} +(-0.819952 + 2.94011i) q^{82} +(-0.648182 + 0.648182i) q^{83} +(4.61830 + 4.61830i) q^{85} +(-3.53307 - 6.26584i) q^{86} +(-0.327616 + 10.7298i) q^{88} +2.87284i q^{89} +(-14.9091 - 14.9091i) q^{91} +(-3.67278 + 6.07263i) q^{92} +(-5.81492 - 1.62169i) q^{94} +2.98599 q^{95} +9.38060 q^{97} +(14.1367 + 3.94250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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