LMFDB - Embedded newform 432.2.l.a.107.12

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			107.12
Character	$\chi$	$=$	432.107
Dual form			432.2.l.a.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.932009 - 1.06365i) q^{2} +(-0.262720 - 1.98267i) q^{4} +(-2.82387 + 2.82387i) q^{5} -3.49224 q^{7} +(-2.35373 - 1.56842i) q^{8} +O(q^{10})$	\(q+(0.932009 - 1.06365i) q^{2} +(-0.262720 - 1.98267i) q^{4} +(-2.82387 + 2.82387i) q^{5} -3.49224 q^{7} +(-2.35373 - 1.56842i) q^{8} +(0.371751 + 5.63550i) q^{10} +(-1.04434 - 1.04434i) q^{11} +(0.232068 - 0.232068i) q^{13} +(-3.25480 + 3.71453i) q^{14} +(-3.86196 + 1.04177i) q^{16} +6.83177i q^{17} +(-3.59498 - 3.59498i) q^{19} +(6.34070 + 4.85692i) q^{20} +(-2.08416 + 0.137483i) q^{22} +3.02976i q^{23} -10.9485i q^{25} +(-0.0305507 - 0.463129i) q^{26} +(0.917482 + 6.92396i) q^{28} +(-4.56568 - 4.56568i) q^{29} +1.60037i q^{31} +(-2.49129 + 5.07873i) q^{32} +(7.26665 + 6.36727i) q^{34} +(9.86165 - 9.86165i) q^{35} +(0.0478917 + 0.0478917i) q^{37} +(-7.17437 + 0.473264i) q^{38} +(11.0757 - 2.21762i) q^{40} +5.73402 q^{41} +(8.10123 - 8.10123i) q^{43} +(-1.79622 + 2.34496i) q^{44} +(3.22262 + 2.82376i) q^{46} -4.46856 q^{47} +5.19573 q^{49} +(-11.6455 - 10.2041i) q^{50} +(-0.521083 - 0.399145i) q^{52} +(-3.08126 + 3.08126i) q^{53} +5.89819 q^{55} +(8.21980 + 5.47730i) q^{56} +(-9.11156 + 0.601052i) q^{58} +(-2.53529 - 2.53529i) q^{59} +(-5.63186 + 5.63186i) q^{61} +(1.70224 + 1.49156i) q^{62} +(3.08011 + 7.38329i) q^{64} +1.31066i q^{65} +(-4.61823 - 4.61823i) q^{67} +(13.5452 - 1.79485i) q^{68} +(-1.29824 - 19.6805i) q^{70} -5.63903i q^{71} +11.3342i q^{73} +(0.0955757 - 0.00630473i) q^{74} +(-6.18319 + 8.07214i) q^{76} +(3.64710 + 3.64710i) q^{77} +4.86489i q^{79} +(7.96384 - 13.8475i) q^{80} +(5.34416 - 6.09902i) q^{82} +(-0.847057 + 0.847057i) q^{83} +(-19.2921 - 19.2921i) q^{85} +(-1.06649 - 16.1673i) q^{86} +(0.820134 + 4.09608i) q^{88} -13.9912 q^{89} +(-0.810436 + 0.810436i) q^{91} +(6.00701 - 0.795979i) q^{92} +(-4.16474 + 4.75300i) q^{94} +20.3036 q^{95} +2.87328 q^{97} +(4.84247 - 5.52646i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) $ 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * 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 $

$2$	0.932009	−	1.06365i	0.659030	−	0.752117i
$2$	0.932009	−	1.06365i	0.659030	−	0.752117i
$3$		0			0
$3$		0			0
$4$	−0.262720	−	1.98267i	−0.131360	−	0.991335i
$5$	−2.82387	+	2.82387i	−1.26288	+	1.26288i	−0.313182	+	0.949693i	$0.601395\pi$
$5$	−2.82387	+	2.82387i	−1.26288	+	1.26288i	−0.949693	+	0.313182i	$0.898605\pi$
$6$		0			0
$7$	−3.49224			−1.31994			−0.659971	−	0.751291i	$-0.729432\pi$
$7$	−3.49224			−1.31994			−0.659971	+	0.751291i	$0.729432\pi$
$8$	−2.35373	−	1.56842i	−0.832170	−	0.554521i
$9$		0			0
$10$	0.371751	+	5.63550i	0.117558	+	1.78210i
$11$	−1.04434	−	1.04434i	−0.314881	−	0.314881i	0.531916	−	0.846797i	$-0.321472\pi$
$11$	−1.04434	−	1.04434i	−0.314881	−	0.314881i	−0.846797	+	0.531916i	$0.821472\pi$
$12$		0			0
$13$	0.232068	−	0.232068i	0.0643640	−	0.0643640i	−0.674192	−	0.738556i	$-0.735508\pi$
$13$	0.232068	−	0.232068i	0.0643640	−	0.0643640i	0.738556	+	0.674192i	$0.235508\pi$
$14$	−3.25480	+	3.71453i	−0.869881	+	0.992751i
$15$		0			0
$16$	−3.86196	+	1.04177i	−0.965489	+	0.260444i
$17$			6.83177i			1.65695i	0.560027	+	0.828474i	$0.310791\pi$
$17$			6.83177i			1.65695i	−0.560027	+	0.828474i	$0.689209\pi$
$18$		0			0
$19$	−3.59498	−	3.59498i	−0.824746	−	0.824746i	0.162039	−	0.986784i	$-0.448193\pi$
$19$	−3.59498	−	3.59498i	−0.824746	−	0.824746i	−0.986784	+	0.162039i	$0.948193\pi$
$20$	6.34070	+	4.85692i	1.41782	+	1.08604i
$21$		0			0
$22$	−2.08416	+	0.137483i	−0.444344	+	0.0293115i
$23$			3.02976i			0.631748i	0.948801	+	0.315874i	$0.102298\pi$
$23$			3.02976i			0.631748i	−0.948801	+	0.315874i	$0.897702\pi$
$24$		0			0
$25$		−	10.9485i		−	2.18971i
$26$	−0.0305507	−	0.463129i	−0.00599149	−	0.0908271i
$27$		0			0
$28$	0.917482	+	6.92396i	0.173388	+	1.30850i
$29$	−4.56568	−	4.56568i	−0.847826	−	0.847826i	0.142035	−	0.989862i	$-0.454635\pi$
$29$	−4.56568	−	4.56568i	−0.847826	−	0.847826i	−0.989862	+	0.142035i	$0.954635\pi$
$30$		0			0
$31$			1.60037i			0.287435i	0.989619	+	0.143717i	$0.0459057\pi$
$31$			1.60037i			0.287435i	−0.989619	+	0.143717i	$0.954094\pi$
$32$	−2.49129	+	5.07873i	−0.440402	+	0.897801i
$33$		0			0
$34$	7.26665	+	6.36727i	1.24622	+	1.09198i
$35$	9.86165	−	9.86165i	1.66692	−	1.66692i
$36$		0			0
$37$	0.0478917	+	0.0478917i	0.00787335	+	0.00787335i	0.711032	−	0.703159i	$-0.248228\pi$
$37$	0.0478917	+	0.0478917i	0.00787335	+	0.00787335i	−0.703159	+	0.711032i	$0.748228\pi$
$38$	−7.17437	+	0.473264i	−1.16384	+	0.0767735i
$39$		0			0
$40$	11.0757	−	2.21762i	1.75122	−	0.350636i
$41$	5.73402			0.895504			0.447752	−	0.894158i	$-0.352225\pi$
$41$	5.73402			0.895504			0.447752	+	0.894158i	$0.352225\pi$
$42$		0			0
$43$	8.10123	−	8.10123i	1.23543	−	1.23543i	0.273575	−	0.961851i	$-0.411794\pi$
$43$	8.10123	−	8.10123i	1.23543	−	1.23543i	0.961851	−	0.273575i	$-0.0882062\pi$
$44$	−1.79622	+	2.34496i	−0.270790	+	0.353516i
$45$		0			0
$46$	3.22262	+	2.82376i	0.475149	+	0.416341i
$47$	−4.46856			−0.651806			−0.325903	−	0.945403i	$-0.605668\pi$
$47$	−4.46856			−0.651806			−0.325903	+	0.945403i	$0.605668\pi$
$48$		0			0
$49$	5.19573			0.742248
$50$	−11.6455	−	10.2041i	−1.64692	−	1.44308i
$51$		0			0
$52$	−0.521083	−	0.399145i	−0.0722612	−	0.0553514i
$53$	−3.08126	+	3.08126i	−0.423243	+	0.423243i	−0.886319	−	0.463076i	$-0.846746\pi$
$53$	−3.08126	+	3.08126i	−0.423243	+	0.423243i	0.463076	+	0.886319i	$0.346746\pi$
$54$		0			0
$55$	5.89819			0.795312
$56$	8.21980	+	5.47730i	1.09842	+	0.731935i
$57$		0			0
$58$	−9.11156	+	0.601052i	−1.19641	+	0.0789220i
$59$	−2.53529	−	2.53529i	−0.330067	−	0.330067i	0.522545	−	0.852612i	$-0.324983\pi$
$59$	−2.53529	−	2.53529i	−0.330067	−	0.330067i	−0.852612	+	0.522545i	$0.824983\pi$
$60$		0			0
$61$	−5.63186	+	5.63186i	−0.721085	+	0.721085i	−0.968826	−	0.247741i	$-0.920312\pi$
$61$	−5.63186	+	5.63186i	−0.721085	+	0.721085i	0.247741	+	0.968826i	$0.420312\pi$
$62$	1.70224	+	1.49156i	0.216185	+	0.189428i
$63$		0			0
$64$	3.08011	+	7.38329i	0.385014	+	0.922911i
$65$			1.31066i			0.162567i
$66$		0			0
$67$	−4.61823	−	4.61823i	−0.564207	−	0.564207i	0.366293	−	0.930500i	$-0.380627\pi$
$67$	−4.61823	−	4.61823i	−0.564207	−	0.564207i	−0.930500	+	0.366293i	$0.880627\pi$
$68$	13.5452	−	1.79485i	1.64259	−	0.217657i
$69$		0			0
$70$	−1.29824	−	19.6805i	−0.155170	−	2.35227i
$71$		−	5.63903i		−	0.669230i	−0.942355	−	0.334615i	$-0.891394\pi$
$71$		−	5.63903i		−	0.669230i	0.942355	−	0.334615i	$-0.108606\pi$
$72$		0			0
$73$			11.3342i			1.32657i	0.748369	+	0.663283i	$0.230837\pi$
$73$			11.3342i			1.32657i	−0.748369	+	0.663283i	$0.769163\pi$
$74$	0.0955757	−	0.00630473i	0.0111105	−	0.000732910i
$75$		0			0
$76$	−6.18319	+	8.07214i	−0.709260	+	0.925938i
$77$	3.64710	+	3.64710i	0.415625	+	0.415625i
$78$		0			0
$79$			4.86489i			0.547343i	0.961823	+	0.273672i	$0.0882382\pi$
$79$			4.86489i			0.547343i	−0.961823	+	0.273672i	$0.911762\pi$
$80$	7.96384	−	13.8475i	0.890384	−	1.54820i
$81$		0			0
$82$	5.34416	−	6.09902i	0.590164	−	0.673524i
$83$	−0.847057	+	0.847057i	−0.0929766	+	0.0929766i	−0.752065	−	0.659089i	$-0.770942\pi$
$83$	−0.847057	+	0.847057i	−0.0929766	+	0.0929766i	0.659089	+	0.752065i	$0.270942\pi$
$84$		0			0
$85$	−19.2921	−	19.2921i	−2.09252	−	2.09252i
$86$	−1.06649	−	16.1673i	−0.115003	−	1.74337i
$87$		0			0
$88$	0.820134	+	4.09608i	0.0874266	+	0.436643i
$89$	−13.9912			−1.48306			−0.741532	−	0.670917i	$-0.765901\pi$
$89$	−13.9912			−1.48306			−0.741532	+	0.670917i	$0.765901\pi$
$90$		0			0
$91$	−0.810436	+	0.810436i	−0.0849568	+	0.0849568i
$92$	6.00701	−	0.795979i	0.626274	−	0.0829865i
$93$		0			0
$94$	−4.16474	+	4.75300i	−0.429560	+	0.490235i
$95$	20.3036			2.08310
$96$		0			0
$97$	2.87328			0.291738			0.145869	−	0.989304i	$-0.453402\pi$
$97$	2.87328			0.291738			0.145869	+	0.989304i	$0.453402\pi$
$98$	4.84247	−	5.52646i	0.489163	−	0.558257i
$99$		0			0
$100$	−21.7073	+	2.87640i	−2.17073	+	0.287640i
$101$	−2.52589	+	2.52589i	−0.251335	+	0.251335i	−0.821518	−	0.570183i	$-0.806872\pi$
$101$	−2.52589	+	2.52589i	−0.251335	+	0.251335i	0.570183	+	0.821518i	$0.306872\pi$
$102$		0			0
$103$	17.9034			1.76408			0.882040	−	0.471175i	$-0.156170\pi$
$103$	17.9034			1.76408			0.882040	+	0.471175i	$0.156170\pi$
$104$	−0.910206	+	0.182245i	−0.0892530	+	0.0178706i
$105$		0			0
$106$	0.405634	+	6.14915i	0.0393986	+	0.597258i
$107$	2.33160	+	2.33160i	0.225404	+	0.225404i	0.810769	−	0.585366i	$-0.199049\pi$
$107$	2.33160	+	2.33160i	0.225404	+	0.225404i	−0.585366	+	0.810769i	$0.699049\pi$
$108$		0			0
$109$	−12.4336	+	12.4336i	−1.19092	+	1.19092i	−0.214113	+	0.976809i	$0.568686\pi$
$109$	−12.4336	+	12.4336i	−1.19092	+	1.19092i	−0.976809	+	0.214113i	$0.931314\pi$
$110$	5.49716	−	6.27364i	0.524134	−	0.598168i
$111$		0			0
$112$	13.4869	−	3.63813i	1.27439	−	0.343771i
$113$			3.34233i			0.314420i	0.987565	+	0.157210i	$0.0502499\pi$
$113$			3.34233i			0.314420i	−0.987565	+	0.157210i	$0.949750\pi$
$114$		0			0
$115$	−8.55566	−	8.55566i	−0.797819	−	0.797819i
$116$	−7.85274	+	10.2517i	−0.729109	+	0.951850i
$117$		0			0
$118$	−5.05959	+	0.333760i	−0.465773	+	0.0307251i
$119$		−	23.8582i		−	2.18708i
$120$		0			0
$121$		−	8.81869i		−	0.801699i
$122$	0.741409	+	11.2393i	0.0671240	+	1.01756i
$123$		0			0
$124$	3.17301	−	0.420450i	0.284944	−	0.0377575i
$125$	16.7979	+	16.7979i	1.50245	+	1.50245i
$126$		0			0
$127$			7.33827i			0.651166i	0.945513	+	0.325583i	$0.105561\pi$
$127$			7.33827i			0.651166i	−0.945513	+	0.325583i	$0.894439\pi$
$128$	10.7240	+	3.60512i	0.947872	+	0.318650i
$129$		0			0
$130$	1.39409	+	1.22155i	0.122270	+	0.107137i
$131$	1.31055	−	1.31055i	0.114503	−	0.114503i	−0.647534	−	0.762037i	$-0.724199\pi$
$131$	1.31055	−	1.31055i	0.114503	−	0.114503i	0.762037	+	0.647534i	$0.224199\pi$
$132$		0			0
$133$	12.5545	+	12.5545i	1.08862	+	1.08862i
$134$	−9.21643	+	0.607970i	−0.796178	+	0.0525206i
$135$		0			0
$136$	10.7151	−	16.0802i	0.918812	−	1.37886i
$137$	−9.34212			−0.798151			−0.399076	−	0.916918i	$-0.630669\pi$
$137$	−9.34212			−0.798151			−0.399076	+	0.916918i	$0.630669\pi$
$138$		0			0
$139$	−11.2794	+	11.2794i	−0.956704	+	0.956704i	−0.999101	−	0.0423964i	$-0.986501\pi$
$139$	−11.2794	+	11.2794i	−0.956704	+	0.956704i	0.0423964	+	0.999101i	$0.486501\pi$
$140$	−22.1432	−	16.9615i	−1.87145	−	1.43351i
$141$		0			0
$142$	−5.99798	−	5.25563i	−0.503339	−	0.441042i
$143$	−0.484717			−0.0405341
$144$		0			0
$145$	25.7858			2.14140
$146$	12.0556	+	10.5636i	0.997732	+	0.874246i
$147$		0			0
$148$	0.0823713	−	0.107536i	0.00677088	−	0.00883937i
$149$	−2.91548	+	2.91548i	−0.238845	+	0.238845i	−0.816372	−	0.577527i	$-0.804018\pi$
$149$	−2.91548	+	2.91548i	−0.238845	+	0.238845i	0.577527	+	0.816372i	$0.304018\pi$
$150$		0			0
$151$	−9.43937			−0.768165			−0.384083	−	0.923299i	$-0.625482\pi$
$151$	−9.43937			−0.768165			−0.384083	+	0.923299i	$0.625482\pi$
$152$	2.82318	+	14.1001i	0.228990	+	1.14367i
$153$		0			0
$154$	7.27838	−	0.480124i	0.586508	−	0.0386895i
$155$	−4.51925	−	4.51925i	−0.362995	−	0.362995i
$156$		0			0
$157$	6.77607	−	6.77607i	0.540789	−	0.540789i	−0.382971	−	0.923760i	$-0.625099\pi$
$157$	6.77607	−	6.77607i	0.540789	−	0.540789i	0.923760	+	0.382971i	$0.125099\pi$
$158$	5.17456	+	4.53412i	0.411666	+	0.360715i
$159$		0			0
$160$	−7.30661	−	21.3768i	−0.577638	−	1.68998i
$161$		−	10.5806i		−	0.833872i
$162$		0			0
$163$	−8.01118	−	8.01118i	−0.627484	−	0.627484i	0.319950	−	0.947434i	$-0.396334\pi$
$163$	−8.01118	−	8.01118i	−0.627484	−	0.627484i	−0.947434	+	0.319950i	$0.896334\pi$
$164$	−1.50644	−	11.3687i	−0.117633	−	0.887744i
$165$		0			0
$166$	0.111511	+	1.69044i	0.00865496	+	0.131204i
$167$		−	19.7351i		−	1.52715i	−0.645720	−	0.763575i	$-0.723443\pi$
$167$		−	19.7351i		−	1.52715i	0.645720	−	0.763575i	$-0.276557\pi$
$168$		0			0
$169$			12.8923i			0.991715i
$170$	−38.5005	+	2.53972i	−2.95285	+	0.194787i
$171$		0			0
$172$	−18.1904	−	13.9337i	−1.38701	−	1.06243i
$173$	−9.69695	−	9.69695i	−0.737246	−	0.737246i	0.234798	−	0.972044i	$-0.424557\pi$
$173$	−9.69695	−	9.69695i	−0.737246	−	0.737246i	−0.972044	+	0.234798i	$0.924557\pi$
$174$		0			0
$175$			38.2349i			2.89029i
$176$	5.12118	+	2.94524i	0.386023	+	0.222006i
$177$		0			0
$178$	−13.0399	+	14.8818i	−0.977383	+	1.11544i
$179$	−7.48591	+	7.48591i	−0.559523	+	0.559523i	−0.929172	−	0.369648i	$-0.879478\pi$
$179$	−7.48591	+	7.48591i	−0.559523	+	0.559523i	0.369648	+	0.929172i	$0.379478\pi$
$180$		0			0
$181$	1.99423	+	1.99423i	0.148230	+	0.148230i	0.777327	−	0.629097i	$-0.216575\pi$
$181$	1.99423	+	1.99423i	0.148230	+	0.148230i	−0.629097	+	0.777327i	$0.716575\pi$
$182$	0.106690	+	1.61736i	0.00790842	+	0.119887i
$183$		0			0
$184$	4.75194	−	7.13124i	0.350318	−	0.525722i
$185$	−0.270480			−0.0198861
$186$		0			0
$187$	7.13472	−	7.13472i	0.521742	−	0.521742i
$188$	1.17398	+	8.85968i	0.0856213	+	0.646158i
$189$		0			0
$190$	18.9231	−	21.5960i	1.37283	−	1.56674i
$191$	3.21357			0.232526			0.116263	−	0.993218i	$-0.462908\pi$
$191$	3.21357			0.232526			0.116263	+	0.993218i	$0.462908\pi$
$192$		0			0
$193$	6.64075			0.478012			0.239006	−	0.971018i	$-0.423178\pi$
$193$	6.64075			0.478012			0.239006	+	0.971018i	$0.423178\pi$
$194$	2.67792	−	3.05618i	0.192264	−	0.219421i
$195$		0			0
$196$	−1.36502	−	10.3014i	−0.0975017	−	0.735816i
$197$	16.0021	−	16.0021i	1.14011	−	1.14011i	0.151675	−	0.988430i	$-0.451533\pi$
$197$	16.0021	−	16.0021i	1.14011	−	1.14011i	0.988430	−	0.151675i	$-0.0484668\pi$
$198$		0			0
$199$	−7.64621			−0.542025			−0.271013	−	0.962576i	$-0.587359\pi$
$199$	−7.64621			−0.542025			−0.271013	+	0.962576i	$0.587359\pi$
$200$	−17.1719	+	25.7699i	−1.21424	+	1.82221i
$201$		0			0
$202$	0.332522	+	5.04082i	0.0233962	+	0.354671i
$203$	15.9445	+	15.9445i	1.11908	+	1.11908i
$204$		0			0
$205$	−16.1922	+	16.1922i	−1.13091	+	1.13091i
$206$	16.6862	−	19.0431i	1.16258	−	1.32679i
$207$		0			0
$208$	−0.654473	+	1.13800i	−0.0453796	+	0.0789060i
$209$			7.50879i			0.519394i
$210$		0			0
$211$	11.6941	+	11.6941i	0.805055	+	0.805055i	0.983881	−	0.178825i	$-0.0572297\pi$
$211$	11.6941	+	11.6941i	0.805055	+	0.805055i	−0.178825	+	0.983881i	$0.557230\pi$
$212$	6.91862	+	5.29960i	0.475173	+	0.363978i
$213$		0			0
$214$	4.65308	−	0.306944i	0.318078	−	0.0209823i
$215$			45.7537i			3.12038i
$216$		0			0
$217$		−	5.58888i		−	0.379398i
$218$	1.63683	+	24.8133i	0.110860	+	1.68057i
$219$		0			0
$220$	−1.54957	−	11.6942i	−0.104472	−	0.788420i
$221$	1.58543	+	1.58543i	0.106648	+	0.106648i
$222$		0			0
$223$			11.1836i			0.748909i	0.927245	+	0.374454i	$0.122170\pi$
$223$			11.1836i			0.748909i	−0.927245	+	0.374454i	$0.877830\pi$
$224$	8.70017	−	17.7361i	0.581305	−	1.18505i
$225$		0			0
$226$	3.55508	+	3.11508i	0.236481	+	0.207212i
$227$	−16.2484	+	16.2484i	−1.07844	+	1.07844i	−0.0817944	+	0.996649i	$0.526065\pi$
$227$	−16.2484	+	16.2484i	−1.07844	+	1.07844i	−0.996649	+	0.0817944i	$0.973935\pi$
$228$		0			0
$229$	8.86904	+	8.86904i	0.586083	+	0.586083i	0.936568	−	0.350485i	$-0.113983\pi$
$229$	8.86904	+	8.86904i	0.586083	+	0.586083i	−0.350485	+	0.936568i	$0.613983\pi$
$230$	−17.0742	+	1.12631i	−1.12584	+	0.0742670i
$231$		0			0
$232$	3.58548	+	17.9073i	0.235398	+	1.17567i
$233$	−1.62473			−0.106440			−0.0532199	−	0.998583i	$-0.516948\pi$
$233$	−1.62473			−0.106440			−0.0532199	+	0.998583i	$0.516948\pi$
$234$		0			0
$235$	12.6187	−	12.6187i	0.823150	−	0.823150i
$236$	−4.36058	+	5.69272i	−0.283849	+	0.370565i
$237$		0			0
$238$	−25.3769	−	22.2360i	−1.64494	−	1.44135i
$239$	−23.4506			−1.51690			−0.758448	−	0.651734i	$-0.774042\pi$
$239$	−23.4506			−1.51690			−0.758448	+	0.651734i	$0.774042\pi$
$240$		0			0
$241$	22.3544			1.43998			0.719988	−	0.693986i	$-0.244147\pi$
$241$	22.3544			1.43998			0.719988	+	0.693986i	$0.244147\pi$
$242$	−9.38004	−	8.21910i	−0.602972	−	0.528344i
$243$		0			0
$244$	12.6457	+	9.68651i	0.809559	+	0.620115i
$245$	−14.6721	+	14.6721i	−0.937366	+	0.937366i
$246$		0			0
$247$	−1.66856			−0.106168
$248$	2.51006	−	3.76684i	0.159389	−	0.239195i
$249$		0			0
$250$	33.5230	−	2.21137i	2.12018	−	0.139860i
$251$	−7.46789	−	7.46789i	−0.471369	−	0.471369i	0.430988	−	0.902357i	$-0.358165\pi$
$251$	−7.46789	−	7.46789i	−0.471369	−	0.471369i	−0.902357	+	0.430988i	$0.858165\pi$
$252$		0			0
$253$	3.16411	−	3.16411i	0.198926	−	0.198926i
$254$	7.80538	+	6.83933i	0.489753	+	0.429138i
$255$		0			0
$256$	13.8294	−	8.04658i	0.864338	−	0.502911i
$257$			7.42519i			0.463171i	0.972815	+	0.231585i	$0.0743913\pi$
$257$			7.42519i			0.463171i	−0.972815	+	0.231585i	$0.925609\pi$
$258$		0			0
$259$	−0.167249	−	0.167249i	−0.0103924	−	0.0103924i
$260$	2.59861	−	0.344337i	0.161159	−	0.0213549i
$261$		0			0
$262$	−0.172528	−	2.61541i	−0.0106588	−	0.161581i
$263$			3.59594i			0.221735i	0.993835	+	0.110868i	$0.0353629\pi$
$263$			3.59594i			0.221735i	−0.993835	+	0.110868i	$0.964637\pi$
$264$		0			0
$265$		−	17.4022i		−	1.06901i
$266$	25.0546	−	1.65275i	1.53620	−	0.101337i
$267$		0			0
$268$	−7.94312	+	10.3697i	−0.485203	+	0.633432i
$269$	−0.0462496	−	0.0462496i	−0.00281989	−	0.00281989i	0.705695	−	0.708515i	$-0.250635\pi$
$269$	−0.0462496	−	0.0462496i	−0.00281989	−	0.00281989i	−0.708515	+	0.705695i	$0.750635\pi$
$270$		0			0
$271$		−	20.4615i		−	1.24294i	−0.783436	−	0.621472i	$-0.786535\pi$
$271$		−	20.4615i		−	1.24294i	0.783436	−	0.621472i	$-0.213465\pi$
$272$	−7.11717	−	26.3840i	−0.431542	−	1.59977i
$273$		0			0
$274$	−8.70693	+	9.93678i	−0.526005	+	0.600303i
$275$	−11.4340	+	11.4340i	−0.689498	+	0.689498i
$276$		0			0
$277$	−6.75384	−	6.75384i	−0.405799	−	0.405799i	0.474472	−	0.880271i	$-0.342639\pi$
$277$	−6.75384	−	6.75384i	−0.405799	−	0.405799i	−0.880271	+	0.474472i	$0.842639\pi$
$278$	1.48488	+	22.5098i	0.0890572	+	1.35005i
$279$		0			0
$280$	−38.6789	+	7.74445i	−2.31151	+	0.462820i
$281$	16.1522			0.963558			0.481779	−	0.876293i	$-0.339991\pi$
$281$	16.1522			0.963558			0.481779	+	0.876293i	$0.339991\pi$
$282$		0			0
$283$	2.06204	−	2.06204i	0.122575	−	0.122575i	−0.643158	−	0.765733i	$-0.722376\pi$
$283$	2.06204	−	2.06204i	0.122575	−	0.122575i	0.765733	+	0.643158i	$0.222376\pi$
$284$	−11.1803	+	1.48149i	−0.663431	+	0.0879101i
$285$		0			0
$286$	−0.451760	+	0.515571i	−0.0267132	+	0.0304864i
$287$	−20.0246			−1.18201
$288$		0			0
$289$	−29.6731			−1.74548
$290$	24.0326	−	27.4272i	1.41124	−	1.61058i
$291$		0			0
$292$	22.4719	−	2.97772i	1.31507	−	0.174258i
$293$	9.16203	−	9.16203i	0.535251	−	0.535251i	−0.386879	−	0.922130i	$-0.626447\pi$
$293$	9.16203	−	9.16203i	0.535251	−	0.535251i	0.922130	+	0.386879i	$0.126447\pi$
$294$		0			0
$295$	14.3187			0.833667
$296$	−0.0376099	−	0.187839i	−0.00218603	−	0.0109179i
$297$		0			0
$298$	0.383810	+	5.81831i	0.0222335	+	0.337045i
$299$	0.703110	+	0.703110i	0.0406619	+	0.0406619i
$300$		0			0
$301$	−28.2914	+	28.2914i	−1.63069	+	1.63069i
$302$	−8.79758	+	10.0402i	−0.506244	+	0.577750i
$303$		0			0
$304$	17.6288	+	10.1385i	1.01108	+	0.581483i
$305$		−	31.8073i		−	1.82128i
$306$		0			0
$307$	−18.2013	−	18.2013i	−1.03880	−	1.03880i	−0.999216	−	0.0395861i	$-0.987396\pi$
$307$	−18.2013	−	18.2013i	−1.03880	−	1.03880i	−0.0395861	−	0.999216i	$-0.512604\pi$
$308$	6.27282	−	8.18915i	0.357427	−	0.466620i
$309$		0			0
$310$	−9.01889	+	0.594939i	−0.512239	+	0.0337902i
$311$			17.7227i			1.00496i	0.864589	+	0.502480i	$0.167579\pi$
$311$			17.7227i			1.00496i	−0.864589	+	0.502480i	$0.832421\pi$
$312$		0			0
$313$			0.370162i			0.0209228i	0.999945	+	0.0104614i	$0.00333003\pi$
$313$			0.370162i			0.0209228i	−0.999945	+	0.0104614i	$0.996670\pi$
$314$	−0.892040	−	13.5228i	−0.0503407	−	0.763133i
$315$		0			0
$316$	9.64548	−	1.27811i	0.542600	−	0.0718991i
$317$	−3.06429	−	3.06429i	−0.172108	−	0.172108i	0.615797	−	0.787905i	$-0.288834\pi$
$317$	−3.06429	−	3.06429i	−0.172108	−	0.172108i	−0.787905	+	0.615797i	$0.788834\pi$
$318$		0			0
$319$			9.53628i			0.533929i
$320$	−29.5473	−	12.1516i	−1.65175	−	0.679297i
$321$		0			0
$322$	−11.2541	−	9.86125i	−0.627169	−	0.549546i
$323$	24.5601	−	24.5601i	1.36656	−	1.36656i
$324$		0			0
$325$	−2.54080	−	2.54080i	−0.140938	−	0.140938i
$326$	−15.9876	+	1.05464i	−0.885472	+	0.0584109i
$327$		0			0
$328$	−13.4964	−	8.99337i	−0.745212	−	0.496576i
$329$	15.6053			0.860347
$330$		0			0
$331$	−8.48964	+	8.48964i	−0.466633	+	0.466633i	−0.900822	−	0.434189i	$-0.857035\pi$
$331$	−8.48964	+	8.48964i	−0.466633	+	0.466633i	0.434189	+	0.900822i	$0.357035\pi$
$332$	1.90197	+	1.45690i	0.104384	+	0.0799575i
$333$		0			0
$334$	−20.9913	−	18.3933i	−1.14859	−	1.00644i
$335$	26.0826			1.42505
$336$		0			0
$337$	−11.7714			−0.641230			−0.320615	−	0.947210i	$-0.603890\pi$
$337$	−11.7714			−0.641230			−0.320615	+	0.947210i	$0.603890\pi$
$338$	13.7129	+	12.0157i	0.745885	+	0.653569i
$339$		0			0
$340$	−33.1814	+	43.3182i	−1.79951	+	2.34926i
$341$	1.67134	−	1.67134i	0.0905079	−	0.0905079i
$342$		0			0
$343$	6.30093			0.340218
$344$	−31.7743	+	6.36198i	−1.71315	+	0.343015i
$345$		0			0
$346$	−19.3518	+	1.27656i	−1.04036	+	0.0686283i
$347$	−8.81089	−	8.81089i	−0.472994	−	0.472994i	0.429888	−	0.902882i	$-0.358553\pi$
$347$	−8.81089	−	8.81089i	−0.472994	−	0.472994i	−0.902882	+	0.429888i	$0.858553\pi$
$348$		0			0
$349$	9.43832	−	9.43832i	0.505222	−	0.505222i	−0.407834	−	0.913056i	$-0.633716\pi$
$349$	9.43832	−	9.43832i	0.505222	−	0.505222i	0.913056	+	0.407834i	$0.133716\pi$
$350$	40.6687	+	35.6353i	2.17383	+	1.90479i
$351$		0			0
$352$	7.90570	−	2.70218i	0.421375	−	0.144026i
$353$		−	13.1519i		−	0.700007i	−0.936748	−	0.350004i	$-0.886180\pi$
$353$		−	13.1519i		−	0.700007i	0.936748	−	0.350004i	$-0.113820\pi$
$354$		0			0
$355$	15.9239	+	15.9239i	0.845154	+	0.845154i
$356$	3.67577	+	27.7399i	0.194815	+	1.47021i
$357$		0			0
$358$	0.985487	+	14.9394i	0.0520846	+	0.789570i
$359$			17.2661i			0.911269i	0.890167	+	0.455634i	$0.150588\pi$
$359$			17.2661i			0.911269i	−0.890167	+	0.455634i	$0.849412\pi$
$360$		0			0
$361$			6.84780i			0.360411i
$362$	3.97981	−	0.262532i	0.209174	−	0.0137984i
$363$		0			0
$364$	1.81975	+	1.39391i	0.0953806	+	0.0730607i
$365$	−32.0063	−	32.0063i	−1.67529	−	1.67529i
$366$		0			0
$367$		−	10.5034i		−	0.548272i	−0.961691	−	0.274136i	$-0.911608\pi$
$367$		−	10.5034i		−	0.548272i	0.961691	−	0.274136i	$-0.0883919\pi$
$368$	−3.15633	−	11.7008i	−0.164535	−	0.609946i
$369$		0			0
$370$	−0.252090	+	0.287698i	−0.0131055	+	0.0149567i
$371$	10.7605	−	10.7605i	0.558656	−	0.558656i
$372$		0			0
$373$	−8.07410	−	8.07410i	−0.418061	−	0.418061i	0.466474	−	0.884535i	$-0.345524\pi$
$373$	−8.07410	−	8.07410i	−0.418061	−	0.418061i	−0.884535	+	0.466474i	$0.845524\pi$
$374$	−0.939254	−	14.2385i	−0.0485677	−	0.736255i
$375$		0			0
$376$	10.5178	+	7.00858i	0.542414	+	0.361440i
$377$	−2.11910			−0.109139
$378$		0			0
$379$	15.2056	−	15.2056i	0.781061	−	0.781061i	−0.198949	−	0.980010i	$-0.563753\pi$
$379$	15.2056	−	15.2056i	0.781061	−	0.781061i	0.980010	+	0.198949i	$0.0637528\pi$
$380$	−5.33416	−	40.2553i	−0.273636	−	2.06505i
$381$		0			0
$382$	2.99507	−	3.41813i	0.153241	−	0.174887i
$383$	−4.56566			−0.233295			−0.116647	−	0.993173i	$-0.537215\pi$
$383$	−4.56566			−0.233295			−0.116647	+	0.993173i	$0.537215\pi$
$384$		0			0
$385$	−20.5979			−1.04977
$386$	6.18924	−	7.06347i	0.315024	−	0.359521i
$387$		0			0
$388$	−0.754869	−	5.69677i	−0.0383227	−	0.289210i
$389$	19.8480	−	19.8480i	1.00633	−	1.00633i	0.00635288	−	0.999980i	$-0.497978\pi$
$389$	19.8480	−	19.8480i	1.00633	−	1.00633i	0.999980	−	0.00635288i	$-0.00202220\pi$
$390$		0			0
$391$	−20.6986			−1.04677
$392$	−12.2294	−	8.14910i	−0.617676	−	0.411592i
$393$		0			0
$394$	−2.10661	−	31.9349i	−0.106130	−	1.60886i
$395$	−13.7379	−	13.7379i	−0.691226	−	0.691226i
$396$		0			0
$397$	3.43072	−	3.43072i	0.172183	−	0.172183i	−0.615755	−	0.787938i	$-0.711149\pi$
$397$	3.43072	−	3.43072i	0.172183	−	0.172183i	0.787938	+	0.615755i	$0.211149\pi$
$398$	−7.12633	+	8.13292i	−0.357211	+	0.407666i
$399$		0			0
$400$	11.4059	+	42.2828i	0.570295	+	2.11414i
$401$			27.7827i			1.38740i	0.720263	+	0.693701i	$0.244021\pi$
$401$			27.7827i			1.38740i	−0.720263	+	0.693701i	$0.755979\pi$
$402$		0			0
$403$	0.371394	+	0.371394i	0.0185005	+	0.0185005i
$404$	5.67160	+	4.34440i	0.282173	+	0.216142i
$405$		0			0
$406$	31.8198	−	2.09902i	1.57919	−	0.104173i
$407$		−	0.100031i		−	0.00495834i
$408$		0			0
$409$		−	15.4360i		−	0.763259i	−0.924315	−	0.381629i	$-0.875363\pi$
$409$		−	15.4360i		−	0.763259i	0.924315	−	0.381629i	$-0.124637\pi$
$410$	2.13163	+	32.3141i	0.105274	+	1.59588i
$411$		0			0
$412$	−4.70360	−	35.4966i	−0.231730	−	1.74879i
$413$	8.85385	+	8.85385i	0.435669	+	0.435669i
$414$		0			0
$415$		−	4.78397i		−	0.234836i
$416$	0.600462	+	1.75676i	0.0294400	+	0.0861321i
$417$		0			0
$418$	7.98676	+	6.99826i	0.390645	+	0.342296i
$419$	3.80731	−	3.80731i	0.186000	−	0.186000i	−0.607965	−	0.793964i	$-0.708014\pi$
$419$	3.80731	−	3.80731i	0.186000	−	0.186000i	0.793964	+	0.607965i	$0.208014\pi$
$420$		0			0
$421$	−21.9222	−	21.9222i	−1.06842	−	1.06842i	−0.997480	−	0.0709444i	$-0.977399\pi$
$421$	−21.9222	−	21.9222i	−1.06842	−	1.06842i	−0.0709444	−	0.997480i	$-0.522601\pi$
$422$	23.3375	−	1.53948i	1.13605	−	0.0749406i
$423$		0			0
$424$	12.0852	−	2.41974i	0.586907	−	0.117513i
$425$	74.7980			3.62823
$426$		0			0
$427$	19.6678	−	19.6678i	0.951791	−	0.951791i
$428$	4.01023	−	5.23534i	0.193842	−	0.253060i
$429$		0			0
$430$	48.6661	+	42.6429i	2.34689	+	2.05642i
$431$	−13.7104			−0.660409			−0.330204	−	0.943909i	$-0.607118\pi$
$431$	−13.7104			−0.660409			−0.330204	+	0.943909i	$0.607118\pi$
$432$		0			0
$433$	28.9638			1.39191			0.695956	−	0.718085i	$-0.254981\pi$
$433$	28.9638			1.39191			0.695956	+	0.718085i	$0.254981\pi$
$434$	−5.94463	−	5.20888i	−0.285351	−	0.250034i
$435$		0			0
$436$	27.9183	+	21.3851i	1.33704	+	1.02416i
$437$	10.8919	−	10.8919i	0.521032	−	0.521032i
$438$		0			0
$439$	29.5288			1.40933			0.704666	−	0.709539i	$-0.251097\pi$
$439$	29.5288			1.40933			0.704666	+	0.709539i	$0.251097\pi$
$440$	−13.8828	−	9.25085i	−0.661835	−	0.441017i
$441$		0			0
$442$	3.16399	−	0.208716i	0.150496	−	0.00992758i
$443$	24.5661	+	24.5661i	1.16717	+	1.16717i	0.982870	+	0.184303i	$0.0590026\pi$
$443$	24.5661	+	24.5661i	1.16717	+	1.16717i	0.184303	+	0.982870i	$0.440997\pi$
$444$		0			0
$445$	39.5094	−	39.5094i	1.87293	−	1.87293i
$446$	11.8955	+	10.4232i	0.563267	+	0.493553i
$447$		0			0
$448$	−10.7565	−	25.7842i	−0.508196	−	1.21819i
$449$		−	17.2682i		−	0.814938i	−0.913219	−	0.407469i	$-0.866411\pi$
$449$		−	17.2682i		−	0.814938i	0.913219	−	0.407469i	$-0.133589\pi$
$450$		0			0
$451$	−5.98829	−	5.98829i	−0.281978	−	0.281978i
$452$	6.62674	−	0.878098i	0.311695	−	0.0413022i
$453$		0			0
$454$	2.13903	+	32.4263i	0.100390	+	1.52184i
$455$		−	4.57714i		−	0.214580i
$456$		0			0
$457$			30.6182i			1.43226i	0.697968	+	0.716129i	$0.254088\pi$
$457$			30.6182i			1.43226i	−0.697968	+	0.716129i	$0.745912\pi$
$458$	17.6996	−	1.16757i	0.827049	−	0.0545570i
$459$		0			0
$460$	−14.7153	+	19.2108i	−0.686104	+	0.895708i
$461$	−17.6631	−	17.6631i	−0.822654	−	0.822654i	0.163834	−	0.986488i	$-0.447614\pi$
$461$	−17.6631	−	17.6631i	−0.822654	−	0.822654i	−0.986488	+	0.163834i	$0.947614\pi$
$462$		0			0
$463$		−	34.1440i		−	1.58680i	−0.608697	−	0.793402i	$-0.708308\pi$
$463$		−	34.1440i		−	1.58680i	0.608697	−	0.793402i	$-0.291692\pi$
$464$	22.3889	+	12.8761i	1.03938	+	0.597756i
$465$		0			0
$466$	−1.51426	+	1.72815i	−0.0701470	+	0.0800552i
$467$	12.8687	−	12.8687i	0.595492	−	0.595492i	−0.343618	−	0.939110i	$-0.611652\pi$
$467$	12.8687	−	12.8687i	0.595492	−	0.595492i	0.939110	+	0.343618i	$0.111652\pi$
$468$		0			0
$469$	16.1280	+	16.1280i	0.744720	+	0.744720i
$470$	−1.66119	−	25.1826i	−0.0766250	−	1.16159i
$471$		0			0
$472$	1.99099	+	9.94381i	0.0916429	+	0.457701i
$473$	−16.9209			−0.778025
$474$		0			0
$475$	−39.3598	+	39.3598i	−1.80595	+	1.80595i
$476$	−47.3029	+	6.26803i	−2.16813	+	0.287295i
$477$		0			0
$478$	−21.8562	+	24.9434i	−0.999679	+	1.14088i
$479$	−27.7604			−1.26841			−0.634204	−	0.773166i	$-0.718672\pi$
$479$	−27.7604			−1.26841			−0.634204	+	0.773166i	$0.718672\pi$
$480$		0			0
$481$	0.0222283			0.00101352
$482$	20.8345	−	23.7774i	0.948987	−	1.08303i
$483$		0			0
$484$	−17.4846	+	2.31685i	−0.794752	+	0.105311i
$485$	−8.11379	+	8.11379i	−0.368428	+	0.368428i
$486$		0			0
$487$	−18.7274			−0.848620			−0.424310	−	0.905517i	$-0.639483\pi$
$487$	−18.7274			−0.848620			−0.424310	+	0.905517i	$0.639483\pi$
$488$	22.0890	−	4.42276i	0.999922	−	0.200209i
$489$		0			0
$490$	1.93152	+	29.2806i	0.0872571	+	1.32276i
$491$	13.1322	+	13.1322i	0.592650	+	0.592650i	0.938346	−	0.345696i	$-0.112357\pi$
$491$	13.1322	+	13.1322i	0.592650	+	0.592650i	−0.345696	+	0.938346i	$0.612357\pi$
$492$		0			0
$493$	31.1917	−	31.1917i	1.40480	−	1.40480i
$494$	−1.55511	+	1.77477i	−0.0699678	+	0.0798507i
$495$		0			0
$496$	−1.66723	−	6.18056i	−0.0748606	−	0.277515i
$497$			19.6929i			0.883345i
$498$		0			0
$499$	−21.7298	−	21.7298i	−0.972762	−	0.972762i	0.0268772	−	0.999639i	$-0.491444\pi$
$499$	−21.7298	−	21.7298i	−0.972762	−	0.972762i	−0.999639	+	0.0268772i	$0.991444\pi$
$500$	28.8916	−	37.7179i	1.29207	−	1.68680i
$501$		0			0
$502$	−14.9034	+	0.983115i	−0.665171	+	0.0438786i
$503$			4.25454i			0.189701i	0.995492	+	0.0948504i	$0.0302373\pi$
$503$			4.25454i			0.189701i	−0.995492	+	0.0948504i	$0.969763\pi$
$504$		0			0
$505$		−	14.2656i		−	0.634810i
$506$	−0.416541	−	6.31449i	−0.0185175	−	0.280714i
$507$		0			0
$508$	14.5494	−	1.92791i	0.645524	−	0.0855373i
$509$	−6.41057	−	6.41057i	−0.284144	−	0.284144i	0.550615	−	0.834759i	$-0.314393\pi$
$509$	−6.41057	−	6.41057i	−0.284144	−	0.284144i	−0.834759	+	0.550615i	$0.814393\pi$
$510$		0			0
$511$		−	39.5817i		−	1.75099i
$512$	4.33036	−	22.2092i	0.191377	−	0.981517i
$513$		0			0
$514$	7.89784	+	6.92034i	0.348359	+	0.305243i
$515$	−50.5571	+	50.5571i	−2.22781	+	2.22781i
$516$		0			0
$517$	4.66671	+	4.66671i	0.205242	+	0.205242i
$518$	−0.333773	+	0.0220176i	−0.0146652	+	0.000967399i
$519$		0			0
$520$	2.05567	−	3.08494i	0.0901470	−	0.135284i
$521$	−39.1263			−1.71415			−0.857077	−	0.515188i	$-0.827722\pi$
$521$	−39.1263			−1.71415			−0.857077	+	0.515188i	$0.827722\pi$
$522$		0			0
$523$	−29.3283	+	29.3283i	−1.28244	+	1.28244i	−0.343159	+	0.939277i	$0.611497\pi$
$523$	−29.3283	+	29.3283i	−1.28244	+	1.28244i	−0.939277	+	0.343159i	$0.888503\pi$
$524$	−2.94269	−	2.25408i	−0.128552	−	0.0984698i
$525$		0			0
$526$	3.82484	+	3.35145i	0.166771	+	0.146130i
$527$	−10.9334			−0.476265
$528$		0			0
$529$	13.8206			0.600894
$530$	−18.5099	−	16.2190i	−0.804018	−	0.704507i
$531$		0			0
$532$	21.5932	−	28.1898i	0.936183	−	1.22218i
$533$	1.33068	−	1.33068i	0.0576382	−	0.0576382i
$534$		0			0
$535$	−13.1683			−0.569314
$536$	3.62675	+	18.1134i	0.156652	+	0.782380i
$537$		0			0
$538$	−0.0922986	+	0.00608856i	−0.00397928	+	0.000262496i
$539$	−5.42613	−	5.42613i	−0.233720	−	0.233720i
$540$		0			0
$541$	−15.5493	+	15.5493i	−0.668517	+	0.668517i	−0.957373	−	0.288856i	$-0.906725\pi$
$541$	−15.5493	+	15.5493i	−0.668517	+	0.668517i	0.288856	+	0.957373i	$0.406725\pi$
$542$	−21.7639	−	19.0702i	−0.934840	−	0.819137i
$543$		0			0
$544$	−34.6967	−	17.0199i	−1.48761	−	0.729723i
$545$		−	70.2218i		−	3.00797i
$546$		0			0
$547$	−17.0243	−	17.0243i	−0.727908	−	0.727908i	0.242294	−	0.970203i	$-0.422100\pi$
$547$	−17.0243	−	17.0243i	−0.727908	−	0.727908i	−0.970203	+	0.242294i	$0.922100\pi$
$548$	2.45436	+	18.5223i	0.104845	+	0.791235i
$549$		0			0
$550$	1.50524	+	22.8185i	0.0641837	+	0.972983i
$551$			32.8271i			1.39848i
$552$		0			0
$553$		−	16.9894i		−	0.722462i
$554$	−13.4784	+	0.889114i	−0.572642	+	0.0377748i
$555$		0			0
$556$	25.3266	+	19.4000i	1.07409	+	0.822742i
$557$	31.8390	+	31.8390i	1.34906	+	1.34906i	0.886683	+	0.462378i	$0.153004\pi$
$557$	31.8390	+	31.8390i	1.34906	+	1.34906i	0.462378	+	0.886683i	$0.346996\pi$
$558$		0			0
$559$		−	3.76007i		−	0.159034i
$560$	−27.8116	+	48.3589i	−1.17526	+	2.04353i
$561$		0			0
$562$	15.0540	−	17.1803i	0.635013	−	0.724709i
$563$	−31.4611	+	31.4611i	−1.32593	+	1.32593i	−0.417039	+	0.908889i	$0.636932\pi$
$563$	−31.4611	+	31.4611i	−1.32593	+	1.32593i	−0.908889	+	0.417039i	$0.863068\pi$
$564$		0			0
$565$	−9.43832	−	9.43832i	−0.397073	−	0.397073i
$566$	−0.271458	−	4.11513i	−0.0114102	−	0.172972i
$567$		0			0
$568$	−8.84438	+	13.2728i	−0.371102	+	0.556913i
$569$	−29.9445			−1.25534			−0.627668	−	0.778481i	$-0.715991\pi$
$569$	−29.9445			−1.25534			−0.627668	+	0.778481i	$0.715991\pi$
$570$		0			0
$571$	−5.15810	+	5.15810i	−0.215860	+	0.215860i	−0.806751	−	0.590891i	$-0.798776\pi$
$571$	−5.15810	+	5.15810i	−0.215860	+	0.215860i	0.590891	+	0.806751i	$0.298776\pi$
$572$	0.127345	+	0.961034i	0.00532456	+	0.0401828i
$573$		0			0
$574$	−18.6631	+	21.2992i	−0.778982	+	0.889013i
$575$	33.1714			1.38334
$576$		0			0
$577$	−22.1629			−0.922653			−0.461326	−	0.887230i	$-0.652626\pi$
$577$	−22.1629			−0.922653			−0.461326	+	0.887230i	$0.652626\pi$
$578$	−27.6556	+	31.5620i	−1.15032	+	1.31280i
$579$		0			0
$580$	−6.77446	−	51.1248i	−0.281294	−	2.12284i
$581$	2.95813	−	2.95813i	0.122724	−	0.122724i
$582$		0			0
$583$	6.43578			0.266543
$584$	17.7768	−	26.6776i	0.735608	−	1.10393i
$585$		0			0
$586$	−1.20614	−	18.2843i	−0.0498252	−	0.755318i
$587$	−5.63868	−	5.63868i	−0.232733	−	0.232733i	0.581099	−	0.813833i	$-0.302623\pi$
$587$	−5.63868	−	5.63868i	−0.232733	−	0.232733i	−0.813833	+	0.581099i	$0.802623\pi$
$588$		0			0
$589$	5.75330	−	5.75330i	0.237061	−	0.237061i
$590$	13.3452	−	15.2301i	0.549411	−	0.627015i
$591$		0			0
$592$	−0.234848	−	0.135063i	−0.00965220	−	0.00555107i
$593$			32.1028i			1.31830i	0.752011	+	0.659151i	$0.229084\pi$
$593$			32.1028i			1.31830i	−0.752011	+	0.659151i	$0.770916\pi$
$594$		0			0
$595$	67.3726	+	67.3726i	2.76201	+	2.76201i
$596$	6.54638	+	5.01447i	0.268150	+	0.205401i
$597$		0			0
$598$	1.40317	−	0.0925613i	0.0573799	−	0.00378511i
$599$		−	36.1364i		−	1.47649i	−0.674530	−	0.738247i	$-0.735654\pi$
$599$		−	36.1364i		−	1.47649i	0.674530	−	0.738247i	$-0.264346\pi$
$600$		0			0
$601$			14.7508i			0.601699i	0.953672	+	0.300850i	$0.0972703\pi$
$601$			14.7508i			0.601699i	−0.953672	+	0.300850i	$0.902730\pi$
$602$	3.72444	+	56.4601i	0.151797	+	2.30114i
$603$		0			0
$604$	2.47991	+	18.7152i	0.100906	+	0.761509i
$605$	24.9029	+	24.9029i	1.01245	+	1.01245i
$606$		0			0
$607$			6.70271i			0.272054i	0.990705	+	0.136027i	$0.0434335\pi$
$607$			6.70271i			0.272054i	−0.990705	+	0.136027i	$0.956567\pi$
$608$	27.2141	−	9.30180i	1.10368	−	0.377238i
$609$		0			0
$610$	−33.8320	−	29.6447i	−1.36982	−	1.20028i
$611$	−1.03701	+	1.03701i	−0.0419529	+	0.0419529i
$612$		0			0
$613$	13.5746	+	13.5746i	0.548273	+	0.548273i	0.925941	−	0.377668i	$-0.123274\pi$
$613$	13.5746	+	13.5746i	0.548273	+	0.548273i	−0.377668	+	0.925941i	$0.623274\pi$
$614$	−36.3236	+	2.39612i	−1.46590	+	0.0966995i
$615$		0			0
$616$	−2.86410	−	14.3045i	−0.115398	−	0.576344i
$617$	29.4666			1.18628			0.593141	−	0.805099i	$-0.297888\pi$
$617$	29.4666			1.18628			0.593141	+	0.805099i	$0.297888\pi$
$618$		0			0
$619$	8.12555	−	8.12555i	0.326593	−	0.326593i	−0.524696	−	0.851290i	$-0.675821\pi$
$619$	8.12555	−	8.12555i	0.326593	−	0.326593i	0.851290	+	0.524696i	$0.175821\pi$
$620$	−7.77287	+	10.1475i	−0.312166	+	0.407532i
$621$		0			0
$622$	18.8508	+	16.5177i	0.755848	+	0.662299i
$623$	48.8606			1.95756
$624$		0			0
$625$	−40.1278			−1.60511
$626$	0.393725	+	0.344995i	0.0157364	+	0.0137888i
$627$		0			0
$628$	−15.2149	−	11.6545i	−0.607141	−	0.465065i
$629$	−0.327185	+	0.327185i	−0.0130457	+	0.0130457i
$630$		0			0
$631$	−20.5182			−0.816816			−0.408408	−	0.912800i	$-0.633916\pi$
$631$	−20.5182			−0.816816			−0.408408	+	0.912800i	$0.633916\pi$
$632$	7.63020	−	11.4507i	0.303513	−	0.455483i
$633$		0			0
$634$	−6.11529	+	0.403400i	−0.242869	+	0.0160211i
$635$	−20.7224	−	20.7224i	−0.822342	−	0.822342i
$636$		0			0
$637$	1.20576	−	1.20576i	0.0477741	−	0.0477741i
$638$	10.1433	+	8.88790i	0.401577	+	0.351875i
$639$		0			0
$640$	−40.4635	+	20.1027i	−1.59946	+	0.794629i
$641$			0.543078i			0.0214503i	0.999942	+	0.0107251i	$0.00341398\pi$
$641$			0.543078i			0.0214503i	−0.999942	+	0.0107251i	$0.996586\pi$
$642$		0			0
$643$	18.7586	+	18.7586i	0.739768	+	0.739768i	0.972533	−	0.232765i	$-0.0747772\pi$
$643$	18.7586	+	18.7586i	0.739768	+	0.739768i	−0.232765	+	0.972533i	$0.574777\pi$
$644$	−20.9779	+	2.77975i	−0.826646	+	0.109537i
$645$		0			0
$646$	−3.23323	−	49.0137i	−0.127210	−	1.92842i
$647$		−	12.4062i		−	0.487739i	−0.969808	−	0.243870i	$-0.921583\pi$
$647$		−	12.4062i		−	0.487739i	0.969808	−	0.243870i	$-0.0784169\pi$
$648$		0			0
$649$			5.29543i			0.207864i
$650$	−5.07059	+	0.334486i	−0.198885	+	0.0131196i
$651$		0			0
$652$	−13.7788	+	17.9882i	−0.539620	+	0.704473i
$653$	15.5300	+	15.5300i	0.607734	+	0.607734i	0.942353	−	0.334619i	$-0.108608\pi$
$653$	15.5300	+	15.5300i	0.607734	+	0.607734i	−0.334619	+	0.942353i	$0.608608\pi$
$654$		0			0
$655$			7.40165i			0.289206i
$656$	−22.1445	+	5.97356i	−0.864599	+	0.233228i
$657$		0			0
$658$	14.5443	−	16.5986i	0.566994	−	0.647081i
$659$	8.80210	−	8.80210i	0.342881	−	0.342881i	−0.514568	−	0.857449i	$-0.672048\pi$
$659$	8.80210	−	8.80210i	0.342881	−	0.342881i	0.857449	+	0.514568i	$0.172048\pi$
$660$		0			0
$661$	11.6925	+	11.6925i	0.454786	+	0.454786i	0.896939	−	0.442153i	$-0.145785\pi$
$661$	11.6925	+	11.6925i	0.454786	+	0.454786i	−0.442153	+	0.896939i	$0.645785\pi$
$662$	1.11762	+	16.9425i	0.0434377	+	0.658487i
$663$		0			0
$664$	3.32229	−	0.665203i	0.128930	−	0.0258149i
$665$	−70.9049			−2.74957
$666$		0			0
$667$	13.8329	−	13.8329i	0.535613	−	0.535613i
$668$	−39.1282	+	5.18481i	−1.51392	+	0.200606i
$669$		0			0
$670$	24.3092	−	27.7429i	0.939147	−	1.07180i
$671$	11.7632			0.454113
$672$		0			0
$673$	−14.5944			−0.562571			−0.281286	−	0.959624i	$-0.590761\pi$
$673$	−14.5944			−0.562571			−0.281286	+	0.959624i	$0.590761\pi$
$674$	−10.9711	+	12.5207i	−0.422589	+	0.482280i
$675$		0			0
$676$	25.5611	−	3.38706i	0.983121	−	0.130272i
$677$	2.61762	−	2.61762i	0.100603	−	0.100603i	−0.655014	−	0.755617i	$-0.727337\pi$
$677$	2.61762	−	2.61762i	0.100603	−	0.100603i	0.755617	+	0.655014i	$0.227337\pi$
$678$		0			0
$679$	−10.0342			−0.385077
$680$	15.1503	+	75.6665i	0.580986	+	2.90168i
$681$		0			0
$682$	−0.220024	−	3.33542i	−0.00842516	−	0.127720i
$683$	1.82014	+	1.82014i	0.0696456	+	0.0696456i	0.741072	−	0.671426i	$-0.234318\pi$
$683$	1.82014	+	1.82014i	0.0696456	+	0.0696456i	−0.671426	+	0.741072i	$0.734318\pi$
$684$		0			0
$685$	26.3810	−	26.3810i	1.00797	−	1.00797i
$686$	5.87252	−	6.70201i	0.224214	−	0.255884i
$687$		0			0
$688$	−22.8469	+	39.7262i	−0.871031	+	1.51455i
$689$			1.43012i			0.0544832i
$690$		0			0
$691$	1.06909	+	1.06909i	0.0406700	+	0.0406700i	0.727149	−	0.686479i	$-0.240845\pi$
$691$	1.06909	+	1.06909i	0.0406700	+	0.0406700i	−0.686479	+	0.727149i	$0.740845\pi$
$692$	−16.6783	+	21.7734i	−0.634013	+	0.827702i
$693$		0			0
$694$	−17.5836	+	1.15992i	−0.667463	+	0.0440298i
$695$		−	63.7031i		−	2.41640i
$696$		0			0
$697$			39.1736i			1.48380i
$698$	−1.24251	−	18.8357i	−0.0470298	−	0.712942i
$699$		0			0
$700$	75.8072	−	10.0451i	2.86524	−	0.379668i
$701$	9.02410	+	9.02410i	0.340835	+	0.340835i	0.856681	−	0.515846i	$-0.172522\pi$
$701$	9.02410	+	9.02410i	0.340835	+	0.340835i	−0.515846	+	0.856681i	$0.672522\pi$
$702$		0			0
$703$		−	0.344340i		−	0.0129870i
$704$	4.49400	−	10.9274i	0.169374	−	0.411841i
$705$		0			0
$706$	−13.9891	−	12.2577i	−0.526487	−	0.461326i
$707$	8.82100	−	8.82100i	0.331748	−	0.331748i
$708$		0			0
$709$	18.0427	+	18.0427i	0.677609	+	0.677609i	0.959459	−	0.281850i	$-0.0909480\pi$
$709$	18.0427	+	18.0427i	0.677609	+	0.677609i	−0.281850	+	0.959459i	$0.590948\pi$
$710$	31.7788	−	2.09631i	1.19264	−	0.0786733i
$711$		0			0
$712$	32.9315	+	21.9441i	1.23416	+	0.822390i
$713$	−4.84874			−0.181587
$714$		0			0
$715$	1.36878	−	1.36878i	0.0511895	−	0.0511895i
$716$	16.8088	+	12.8754i	0.628174	+	0.481176i
$717$		0			0
$718$	18.3651	+	16.0921i	0.685381	+	0.600553i
$719$	−50.7768			−1.89365			−0.946827	−	0.321742i	$-0.895732\pi$
$719$	−50.7768			−1.89365			−0.946827	+	0.321742i	$0.895732\pi$
$720$		0			0
$721$	−62.5231			−2.32848
$722$	7.28369	+	6.38221i	0.271071	+	0.237521i
$723$		0			0
$724$	3.42998	−	4.47782i	0.127474	−	0.166417i
$725$	−49.9876	+	49.9876i	−1.85649	+	1.85649i
$726$		0			0
$727$	−33.9843			−1.26041			−0.630204	−	0.776430i	$-0.717029\pi$
$727$	−33.9843			−1.26041			−0.630204	+	0.776430i	$0.717029\pi$
$728$	3.17866	−	0.636444i	0.117809	−	0.0235882i
$729$		0			0
$730$	−63.8738	+	4.21349i	−2.36408	+	0.155948i
$731$	55.3458	+	55.3458i	2.04704	+	2.04704i
$732$		0			0
$733$	−29.7181	+	29.7181i	−1.09766	+	1.09766i	−0.102979	+	0.994684i	$0.532837\pi$
$733$	−29.7181	+	29.7181i	−1.09766	+	1.09766i	−0.994684	+	0.102979i	$0.967163\pi$
$734$	−11.1720	−	9.78924i	−0.412365	−	0.361328i
$735$		0			0
$736$	−15.3873	−	7.54800i	−0.567184	−	0.278223i
$737$			9.64604i			0.355316i
$738$		0			0
$739$	−5.21758	−	5.21758i	−0.191932	−	0.191932i	0.604599	−	0.796530i	$-0.293334\pi$
$739$	−5.21758	−	5.21758i	−0.191932	−	0.191932i	−0.796530	+	0.604599i	$0.793334\pi$
$740$	0.0710607	+	0.536273i	0.00261224	+	0.0197138i
$741$		0			0
$742$	−1.41657	−	21.4743i	−0.0520039	−	0.788346i
$743$		−	4.21791i		−	0.154740i	−0.997002	−	0.0773701i	$-0.975348\pi$
$743$		−	4.21791i		−	0.154740i	0.997002	−	0.0773701i	$-0.0246523\pi$
$744$		0			0
$745$		−	16.4659i		−	0.603263i
$746$	−16.1132	+	1.06292i	−0.589945	+	0.0389162i
$747$		0			0
$748$	−16.0202	−	12.2714i	−0.585757	−	0.448685i
$749$	−8.14249	−	8.14249i	−0.297520	−	0.297520i
$750$		0			0
$751$		−	18.8637i		−	0.688346i	−0.938906	−	0.344173i	$-0.888159\pi$
$751$		−	18.8637i		−	0.688346i	0.938906	−	0.344173i	$-0.111841\pi$
$752$	17.2574	−	4.65523i	0.629312	−	0.169759i
$753$		0			0
$754$	−1.97502	+	2.25399i	−0.0719258	+	0.0820853i
$755$	26.6556	−	26.6556i	0.970097	−	0.970097i
$756$		0			0
$757$	−1.56895	−	1.56895i	−0.0570243	−	0.0570243i	0.678020	−	0.735044i	$-0.262838\pi$
$757$	−1.56895	−	1.56895i	−0.0570243	−	0.0570243i	−0.735044	+	0.678020i	$0.762838\pi$
$758$	−2.00175	−	30.3453i	−0.0727070	−	1.10219i
$759$		0			0
$760$	−47.7891	−	31.8445i	−1.73349	−	1.15512i
$761$	−22.6380			−0.820626			−0.410313	−	0.911945i	$-0.634581\pi$
$761$	−22.6380			−0.820626			−0.410313	+	0.911945i	$0.634581\pi$
$762$		0			0
$763$	43.4211	−	43.4211i	1.57195	−	1.57195i
$764$	−0.844270	−	6.37145i	−0.0305446	−	0.230511i
$765$		0			0
$766$	−4.25524	+	4.85629i	−0.153748	+	0.175465i
$767$	−1.17672			−0.0424889
$768$		0			0
$769$	8.26910			0.298191			0.149096	−	0.988823i	$-0.452364\pi$
$769$	8.26910			0.298191			0.149096	+	0.988823i	$0.452364\pi$
$770$	−19.1974	+	21.9090i	−0.691827	+	0.789547i
$771$		0			0
$772$	−1.74466	−	13.1664i	−0.0627917	−	0.473870i
$773$	17.5970	−	17.5970i	0.632920	−	0.632920i	−0.315880	−	0.948799i	$-0.602300\pi$
$773$	17.5970	−	17.5970i	0.632920	−	0.632920i	0.948799	+	0.315880i	$0.102300\pi$
$774$		0			0
$775$	17.5217			0.629399
$776$	−6.76294	−	4.50652i	−0.242775	−	0.161775i
$777$		0			0
$778$	−2.61290	−	39.6099i	−0.0936770	−	1.42008i
$779$	−20.6137	−	20.6137i	−0.738563	−	0.738563i
$780$		0			0
$781$	−5.88909	+	5.88909i	−0.210728	+	0.210728i
$782$	−19.2913	+	22.0162i	−0.689856	+	0.787297i
$783$		0			0
$784$	−20.0657	+	5.41278i	−0.716632	+	0.193314i
$785$			38.2696i			1.36590i
$786$		0			0
$787$	34.0406	+	34.0406i	1.21342	+	1.21342i	0.969896	+	0.243519i	$0.0783018\pi$
$787$	34.0406	+	34.0406i	1.21342	+	1.21342i	0.243519	+	0.969896i	$0.421698\pi$
$788$	−35.9311	−	27.5229i	−1.27999	−	0.980462i
$789$		0			0
$790$	−27.4161	+	1.80853i	−0.975422	+	0.0643445i
$791$		−	11.6722i		−	0.415016i
$792$		0			0
$793$			2.61395i			0.0928239i
$794$	−0.451639	−	6.84656i	−0.0160281	−	0.242975i
$795$		0			0
$796$	2.00881	+	15.1599i	0.0712005	+	0.537328i
$797$	8.72498	+	8.72498i	0.309055	+	0.309055i	0.844543	−	0.535488i	$-0.179872\pi$
$797$	8.72498	+	8.72498i	0.309055	+	0.309055i	−0.535488	+	0.844543i	$0.679872\pi$
$798$		0			0
$799$		−	30.5282i		−	1.08001i
$800$	55.6047	+	27.2760i	1.96592	+	0.964351i
$801$		0			0
$802$	29.5512	+	25.8937i	1.04349	+	0.914339i
$803$	11.8368	−	11.8368i	0.417711	−	0.417711i
$804$		0			0
$805$	29.8784	+	29.8784i	1.05308	+	1.05308i
$806$	0.741178	−	0.0488924i	0.0261069	−	0.00172216i
$807$		0			0
$808$	9.90692	−	1.98361i	0.348524	−	0.0697830i
$809$	14.0389			0.493583			0.246792	−	0.969069i	$-0.420624\pi$
$809$	14.0389			0.493583			0.246792	+	0.969069i	$0.420624\pi$
$810$		0			0
$811$	−25.7221	+	25.7221i	−0.903226	+	0.903226i	−0.995714	−	0.0924881i	$-0.970518\pi$
$811$	−25.7221	+	25.7221i	−0.903226	+	0.903226i	0.0924881	+	0.995714i	$0.470518\pi$
$812$	27.4237	−	35.8015i	0.962382	−	1.25639i
$813$		0			0
$814$	−0.106398	−	0.0932296i	−0.00372925	−	0.00326769i
$815$	45.2451			1.58487
$816$		0			0
$817$	−58.2476			−2.03782
$818$	−16.4185	−	14.3864i	−0.574060	−	0.503010i
$819$		0			0
$820$	36.3577	+	27.8497i	1.26967	+	0.972554i
$821$	−17.2882	+	17.2882i	−0.603363	+	0.603363i	−0.941203	−	0.337841i	$-0.890304\pi$
$821$	−17.2882	+	17.2882i	−0.603363	+	0.603363i	0.337841	+	0.941203i	$0.390304\pi$
$822$		0			0
$823$	28.0410			0.977448			0.488724	−	0.872438i	$-0.337462\pi$
$823$	28.0410			0.977448			0.488724	+	0.872438i	$0.337462\pi$
$824$	−42.1399	−	28.0802i	−1.46801	−	0.978218i
$825$		0			0
$826$	17.6693	−	1.16557i	0.614794	−	0.0405554i
$827$	2.47300	+	2.47300i	0.0859945	+	0.0859945i	0.748796	−	0.662801i	$-0.230632\pi$
$827$	2.47300	+	2.47300i	0.0859945	+	0.0859945i	−0.662801	+	0.748796i	$0.730632\pi$
$828$		0			0
$829$	−1.56384	+	1.56384i	−0.0543144	+	0.0543144i	−0.733742	−	0.679428i	$-0.762228\pi$
$829$	−1.56384	+	1.56384i	−0.0543144	+	0.0543144i	0.679428	+	0.733742i	$0.262228\pi$
$830$	−5.08849	−	4.45870i	−0.176624	−	0.154764i
$831$		0			0
$832$	2.42822	+	0.998629i	0.0841833	+	0.0346212i
$833$			35.4961i			1.22987i
$834$		0			0
$835$	55.7295	+	55.7295i	1.92860	+	1.92860i
$836$	14.8875	−	1.97271i	0.514893	−	0.0682277i
$837$		0			0
$838$	−0.501216	−	7.59812i	−0.0173142	−	0.262473i
$839$		−	2.11605i		−	0.0730540i	−0.999333	−	0.0365270i	$-0.988371\pi$
$839$		−	2.11605i		−	0.0730540i	0.999333	−	0.0365270i	$-0.0116295\pi$
$840$		0			0
$841$			12.6909i			0.437619i
$842$	−43.7494	+	2.88597i	−1.50770	+	0.0994570i
$843$		0			0
$844$	20.1133	−	26.2578i	0.692327	−	0.903832i
$845$	−36.4062	−	36.4062i	−1.25241	−	1.25241i
$846$		0			0
$847$			30.7970i			1.05820i
$848$	8.68970	−	15.1096i	0.298406	−	0.518867i
$849$		0			0
$850$	69.7123	−	79.5592i	2.39111	−	2.72886i
$851$	−0.145100	+	0.145100i	−0.00497398	+	0.00497398i
$852$		0			0
$853$	39.0512	+	39.0512i	1.33709	+	1.33709i	0.898866	+	0.438223i	$0.144392\pi$
$853$	39.0512	+	39.0512i	1.33709	+	1.33709i	0.438223	+	0.898866i	$0.355608\pi$
$854$	−2.58918	−	39.2503i	−0.0885998	−	1.34312i
$855$		0			0
$856$	−1.83103	−	9.14488i	−0.0625832	−	0.312566i
$857$	21.9751			0.750654			0.375327	−	0.926893i	$-0.377530\pi$
$857$	21.9751			0.750654			0.375327	+	0.926893i	$0.377530\pi$
$858$		0			0
$859$	−34.5462	+	34.5462i	−1.17870	+	1.17870i	−0.198627	+	0.980075i	$0.563648\pi$
$859$	−34.5462	+	34.5462i	−1.17870	+	1.17870i	−0.980075	+	0.198627i	$0.936352\pi$
$860$	90.7145	−	12.0204i	3.09334	−	0.409893i
$861$		0			0
$862$	−12.7783	+	14.5832i	−0.435229	+	0.496705i
$863$	−35.3792			−1.20432			−0.602161	−	0.798375i	$-0.705693\pi$
$863$	−35.3792			−1.20432			−0.602161	+	0.798375i	$0.705693\pi$
$864$		0			0
$865$	54.7660			1.86210
$866$	26.9945	−	30.8075i	0.917311	−	1.04688i
$867$		0			0
$868$	−11.0809	+	1.46831i	−0.376110	+	0.0498377i
$869$	5.08062	−	5.08062i	0.172348	−	0.172348i
$870$		0			0
$871$	−2.14349			−0.0726292
$872$	48.7665	−	9.76423i	1.65144	−	0.330659i
$873$		0			0
$874$	−1.43387	−	21.7366i	−0.0485015	−	0.735252i
$875$	−58.6624	−	58.6624i	−1.98315	−	1.98315i
$876$		0			0
$877$	18.4117	−	18.4117i	0.621719	−	0.621719i	−0.324252	−	0.945971i	$-0.605113\pi$
$877$	18.4117	−	18.4117i	0.621719	−	0.621719i	0.945971	+	0.324252i	$0.105113\pi$
$878$	27.5211	−	31.4084i	0.928792	−	1.05998i
$879$		0			0
$880$	−22.7786	+	6.14459i	−0.767865	+	0.207134i
$881$		−	4.20444i		−	0.141651i	−0.997489	−	0.0708256i	$-0.977437\pi$
$881$		−	4.20444i		−	0.141651i	0.997489	−	0.0708256i	$-0.0225634\pi$
$882$		0			0
$883$	−0.790399	−	0.790399i	−0.0265990	−	0.0265990i	0.693682	−	0.720281i	$-0.255987\pi$
$883$	−0.790399	−	0.790399i	−0.0265990	−	0.0265990i	−0.720281	+	0.693682i	$0.755987\pi$
$884$	2.72687	−	3.55992i	0.0917145	−	0.119733i
$885$		0			0
$886$	49.0257	−	3.23402i	1.64705	−	0.108649i
$887$			23.5992i			0.792382i	0.918168	+	0.396191i	$0.129668\pi$
$887$			23.5992i			0.792382i	−0.918168	+	0.396191i	$0.870332\pi$
$888$		0			0
$889$		−	25.6270i		−	0.859502i
$890$	−5.20124	−	78.8474i	−0.174346	−	2.64297i
$891$		0			0
$892$	22.1734	−	2.93816i	0.742419	−	0.0983767i
$893$	16.0644	+	16.0644i	0.537574	+	0.537574i
$894$		0			0
$895$		−	42.2786i		−	1.41322i
$896$	−37.4506	−	12.5899i	−1.25114	−	0.420600i
$897$		0			0
$898$	−18.3674	−	16.0941i	−0.612929	−	0.537068i
$899$	7.30678	−	7.30678i	0.243695	−	0.243695i
$900$		0			0
$901$	−21.0504	−	21.0504i	−0.701292	−	0.701292i
$902$	−11.9506	+	0.788332i	−0.397912	+	0.0262486i
$903$		0			0
$904$	5.24218	−	7.86695i	0.174352	−	0.261651i
$905$	−11.2629			−0.374392
$906$		0			0
$907$	−22.6842	+	22.6842i	−0.753216	+	0.753216i	−0.975078	−	0.221862i	$-0.928787\pi$
$907$	−22.6842	+	22.6842i	−0.753216	+	0.753216i	0.221862	+	0.975078i	$0.428787\pi$
$908$	36.4840	+	27.9464i	1.21076	+	0.927434i
$909$		0			0
$910$	−4.86850	−	4.26593i	−0.161389	−	0.141414i
$911$	27.0633			0.896647			0.448324	−	0.893871i	$-0.352021\pi$
$911$	27.0633			0.896647			0.448324	+	0.893871i	$0.352021\pi$
$912$		0			0
$913$	1.76924			0.0585532
$914$	32.5671	+	28.5364i	1.07723	+	0.943900i
$915$		0			0
$916$	15.2543	−	19.9145i	0.504016	−	0.657992i
$917$	−4.57675	+	4.57675i	−0.151138	+	0.151138i
$918$		0			0
$919$	45.1750			1.49018			0.745092	−	0.666962i	$-0.232405\pi$
$919$	45.1750			1.49018			0.745092	+	0.666962i	$0.232405\pi$
$920$	6.71885	+	33.5566i	0.221514	+	1.10633i
$921$		0			0
$922$	−35.2497	+	2.32527i	−1.16089	+	0.0765788i
$923$	−1.30864	−	1.30864i	−0.0430744	−	0.0430744i
$924$		0			0
$925$	0.524344	−	0.524344i	0.0172403	−	0.0172403i
$926$	−36.3174	−	31.8225i	−1.19346	−	1.04575i
$927$		0			0
$928$	34.5623	−	11.8134i	1.13456	−	0.387795i
$929$			2.53089i			0.0830358i	0.999138	+	0.0415179i	$0.0132194\pi$
$929$			2.53089i			0.0830358i	−0.999138	+	0.0415179i	$0.986781\pi$
$930$		0			0
$931$	−18.6786	−	18.6786i	−0.612166	−	0.612166i
$932$	0.426850	+	3.22131i	0.0139819	+	0.105517i
$933$		0			0
$934$	−1.69411	−	25.6816i	−0.0554329	−	0.840327i
$935$			40.2951i			1.31779i
$936$		0			0
$937$			41.3441i			1.35065i	0.737519	+	0.675326i	$0.235997\pi$
$937$			41.3441i			1.35065i	−0.737519	+	0.675326i	$0.764003\pi$
$938$	32.1860	−	2.12318i	1.05091	−	0.0693242i
$939$		0			0
$940$	−28.3338	−	21.7034i	−0.924146	−	0.707888i
$941$	−28.2951	−	28.2951i	−0.922393	−	0.922393i	0.0748056	−	0.997198i	$-0.476166\pi$
$941$	−28.2951	−	28.2951i	−0.922393	−	0.922393i	−0.997198	+	0.0748056i	$0.976166\pi$
$942$		0			0
$943$			17.3727i			0.565733i
$944$	12.4324	+	7.14999i	0.404640	+	0.232712i
$945$		0			0
$946$	−15.7705	+	17.9980i	−0.512742	+	0.585166i
$947$	27.4370	−	27.4370i	0.891584	−	0.891584i	−0.103088	−	0.994672i	$-0.532872\pi$
$947$	27.4370	−	27.4370i	0.891584	−	0.891584i	0.994672	+	0.103088i	$0.0328724\pi$
$948$		0			0
$949$	2.63030	+	2.63030i	0.0853831	+	0.0853831i
$950$	5.18154	+	78.5489i	0.168112	+	2.54846i
$951$		0			0
$952$	−37.4197	+	56.1558i	−1.21278	+	1.82002i
$953$	49.7428			1.61133			0.805664	−	0.592373i	$-0.201809\pi$
$953$	49.7428			1.61133			0.805664	+	0.592373i	$0.201809\pi$
$954$		0			0
$955$	−9.07472	+	9.07472i	−0.293651	+	0.293651i
$956$	6.16095	+	46.4949i	0.199260	+	1.50375i
$957$		0			0
$958$	−25.8730	+	29.5275i	−0.835918	+	0.953991i
$959$	32.6249			1.05351
$960$		0			0
$961$	28.4388			0.917381
$962$	0.0207169	−	0.0236432i	0.000667940	−	0.000762286i
$963$		0			0
$964$	−5.87296	−	44.3215i	−0.189155	−	1.42750i
$965$	−18.7527	+	18.7527i	−0.603669	+	0.603669i
$966$		0			0
$967$	−8.28275			−0.266355			−0.133178	−	0.991092i	$-0.542518\pi$
$967$	−8.28275			−0.266355			−0.133178	+	0.991092i	$0.542518\pi$
$968$	−13.8314	+	20.7568i	−0.444559	+	0.667150i
$969$		0			0
$970$	1.06814	+	16.1924i	0.0342961	+	0.519906i
$971$	24.2318	+	24.2318i	0.777635	+	0.777635i	0.979428	−	0.201793i	$-0.0646768\pi$
$971$	24.2318	+	24.2318i	0.777635	+	0.777635i	−0.201793	+	0.979428i	$0.564677\pi$
$972$		0			0
$973$	39.3903	−	39.3903i	1.26279	−	1.26279i
$974$	−17.4541	+	19.9195i	−0.559265	+	0.638261i
$975$		0			0
$976$	15.8829	−	27.6171i	0.508398	−	0.884002i
$977$			16.9430i			0.542055i	0.962572	+	0.271027i	$0.0873634\pi$
$977$			16.9430i			0.542055i	−0.962572	+	0.271027i	$0.912637\pi$
$978$		0			0
$979$	14.6116	+	14.6116i	0.466989	+	0.466989i
$980$	32.9446	+	25.2353i	1.05238	+	0.806111i
$981$		0			0
$982$	26.2075	−	1.72880i	0.836316	−	0.0551683i
$983$		−	32.4955i		−	1.03645i	−0.855246	−	0.518223i	$-0.826594\pi$
$983$		−	32.4955i		−	1.03645i	0.855246	−	0.518223i	$-0.173406\pi$
$984$		0			0
$985$			90.3761i			2.87962i
$986$	−4.10625	−	62.2482i	−0.130770	−	1.98239i
$987$		0			0
$988$	0.438364	+	3.30820i	0.0139462	+	0.105248i
$989$	24.5448	+	24.5448i	0.780478	+	0.780478i
$990$		0			0
$991$			25.3636i			0.805700i	0.915266	+	0.402850i	$0.131980\pi$
$991$			25.3636i			0.805700i	−0.915266	+	0.402850i	$0.868020\pi$
$992$	−8.12785	−	3.98698i	−0.258059	−	0.126587i
$993$		0			0
$994$	20.9464	+	18.3539i	0.664379	+	0.582151i
$995$	21.5919	−	21.5919i	0.684510	−	0.684510i
$996$		0			0
$997$	−22.7251	−	22.7251i	−0.719712	−	0.719712i	0.248834	−	0.968546i	$-0.419953\pi$
$997$	−22.7251	−	22.7251i	−0.719712	−	0.719712i	−0.968546	+	0.248834i	$0.919953\pi$
$998$	−43.3654	+	2.86064i	−1.37271	+	0.0905519i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.a.107.12	yes	32
3.2	odd	2	inner	432.2.l.a.107.5	✓	32
4.3	odd	2		1728.2.l.a.1295.1		32
12.11	even	2		1728.2.l.a.1295.16		32
16.3	odd	4	inner	432.2.l.a.323.5	yes	32
16.13	even	4		1728.2.l.a.431.16		32
48.29	odd	4		1728.2.l.a.431.1		32
48.35	even	4	inner	432.2.l.a.323.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.a.107.5	✓	32	3.2	odd	2	inner
432.2.l.a.107.12	yes	32	1.1	even	1	trivial
432.2.l.a.323.5	yes	32	16.3	odd	4	inner
432.2.l.a.323.12	yes	32	48.35	even	4	inner
1728.2.l.a.431.1		32	48.29	odd	4
1728.2.l.a.431.16		32	16.13	even	4
1728.2.l.a.1295.1		32	4.3	odd	2
1728.2.l.a.1295.16		32	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(0.932009 - 1.06365i) q^{2} +(-0.262720 - 1.98267i) q^{4} +(-2.82387 + 2.82387i) q^{5} -3.49224 q^{7} +(-2.35373 - 1.56842i) q^{8} +O(q^{10})\)	\(q+(0.932009 - 1.06365i) q^{2} +(-0.262720 - 1.98267i) q^{4} +(-2.82387 + 2.82387i) q^{5} -3.49224 q^{7} +(-2.35373 - 1.56842i) q^{8} +(0.371751 + 5.63550i) q^{10} +(-1.04434 - 1.04434i) q^{11} +(0.232068 - 0.232068i) q^{13} +(-3.25480 + 3.71453i) q^{14} +(-3.86196 + 1.04177i) q^{16} +6.83177i q^{17} +(-3.59498 - 3.59498i) q^{19} +(6.34070 + 4.85692i) q^{20} +(-2.08416 + 0.137483i) q^{22} +3.02976i q^{23} -10.9485i q^{25} +(-0.0305507 - 0.463129i) q^{26} +(0.917482 + 6.92396i) q^{28} +(-4.56568 - 4.56568i) q^{29} +1.60037i q^{31} +(-2.49129 + 5.07873i) q^{32} +(7.26665 + 6.36727i) q^{34} +(9.86165 - 9.86165i) q^{35} +(0.0478917 + 0.0478917i) q^{37} +(-7.17437 + 0.473264i) q^{38} +(11.0757 - 2.21762i) q^{40} +5.73402 q^{41} +(8.10123 - 8.10123i) q^{43} +(-1.79622 + 2.34496i) q^{44} +(3.22262 + 2.82376i) q^{46} -4.46856 q^{47} +5.19573 q^{49} +(-11.6455 - 10.2041i) q^{50} +(-0.521083 - 0.399145i) q^{52} +(-3.08126 + 3.08126i) q^{53} +5.89819 q^{55} +(8.21980 + 5.47730i) q^{56} +(-9.11156 + 0.601052i) q^{58} +(-2.53529 - 2.53529i) q^{59} +(-5.63186 + 5.63186i) q^{61} +(1.70224 + 1.49156i) q^{62} +(3.08011 + 7.38329i) q^{64} +1.31066i q^{65} +(-4.61823 - 4.61823i) q^{67} +(13.5452 - 1.79485i) q^{68} +(-1.29824 - 19.6805i) q^{70} -5.63903i q^{71} +11.3342i q^{73} +(0.0955757 - 0.00630473i) q^{74} +(-6.18319 + 8.07214i) q^{76} +(3.64710 + 3.64710i) q^{77} +4.86489i q^{79} +(7.96384 - 13.8475i) q^{80} +(5.34416 - 6.09902i) q^{82} +(-0.847057 + 0.847057i) q^{83} +(-19.2921 - 19.2921i) q^{85} +(-1.06649 - 16.1673i) q^{86} +(0.820134 + 4.09608i) q^{88} -13.9912 q^{89} +(-0.810436 + 0.810436i) q^{91} +(6.00701 - 0.795979i) q^{92} +(-4.16474 + 4.75300i) q^{94} +20.3036 q^{95} +2.87328 q^{97} +(4.84247 - 5.52646i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Introduction

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