LMFDB - Embedded newform 567.2.e.d.163.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(163,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.163"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$2.11692 - 0.978886i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.d.487.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.186423 + 0.322894i) q^{2} +(0.930493 + 1.61166i) q^{4} +(0.710717 - 1.23100i) q^{5} +(2.62597 - 0.322894i) q^{7} -1.43955 q^{8} +(0.264988 + 0.458972i) q^{10} +(1.88190 + 3.25955i) q^{11} +1.86099 q^{13} +(-0.385281 + 0.908105i) q^{14} +(-1.59262 + 2.75850i) q^{16} +(-3.76718 - 6.52496i) q^{17} +(0.837872 - 1.45124i) q^{19} +2.64527 q^{20} -1.40332 q^{22} +(-0.255930 + 0.443283i) q^{23} +(1.48976 + 2.58034i) q^{25} +(-0.346930 + 0.600901i) q^{26} +(2.96385 + 3.93173i) q^{28} +8.72197 q^{29} +(1.46665 + 2.54031i) q^{31} +(-2.03335 - 3.52187i) q^{32} +2.80916 q^{34} +(1.46884 - 3.46206i) q^{35} +(-2.16551 + 3.75077i) q^{37} +(0.312397 + 0.541087i) q^{38} +(-1.02311 + 1.77209i) q^{40} -6.84051 q^{41} -4.53673 q^{43} +(-3.50220 + 6.06598i) q^{44} +(-0.0954222 - 0.165276i) q^{46} +(-3.71978 + 6.44284i) q^{47} +(6.79148 - 1.69582i) q^{49} -1.11090 q^{50} +(1.73163 + 2.99928i) q^{52} +(-0.416437 - 0.721290i) q^{53} +5.35001 q^{55} +(-3.78022 + 0.464822i) q^{56} +(-1.62597 + 2.81627i) q^{58} +(6.51126 + 11.2778i) q^{59} +(5.15189 - 8.92333i) q^{61} -1.09367 q^{62} -4.85423 q^{64} +(1.32264 - 2.29087i) q^{65} +(-3.25813 - 5.64324i) q^{67} +(7.01068 - 12.1429i) q^{68} +(0.844050 + 1.11969i) q^{70} +4.11854 q^{71} +(-2.84737 - 4.93179i) q^{73} +(-0.807399 - 1.39846i) q^{74} +3.11854 q^{76} +(5.99432 + 7.95185i) q^{77} +(-0.132152 + 0.228895i) q^{79} +(2.26381 + 3.92103i) q^{80} +(1.27523 - 2.20876i) q^{82} -7.90046 q^{83} -10.7096 q^{85} +(0.845750 - 1.46488i) q^{86} +(-2.70910 - 4.69229i) q^{88} +(-0.398321 + 0.689912i) q^{89} +(4.88690 - 0.600901i) q^{91} -0.952563 q^{92} +(-1.38690 - 2.40218i) q^{94} +(-1.19098 - 2.06284i) q^{95} -12.8800 q^{97} +(-0.718516 + 2.50907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} - 10 q^{13} + 23 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} + 16 q^{20} - 14 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} + 20 q^{29}+ \cdots - 11 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 - 10 * q^13 + 23 * q^14 + q^16 + 6 * q^17 + 8 * q^19 + 16 * q^20 - 14 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 + 20 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 + 10 * q^41 - 14 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 17 * q^49 - 76 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 - 39 * q^56 + 7 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 + 51 * q^68 + 17 * q^70 + 18 * q^71 + 6 * q^73 + 10 * q^76 + 37 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 - 18 * q^83 - 18 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 + 72 * q^92 + 15 * q^94 - 16 * q^95 - 18 * q^97 - 11 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.186423	+	0.322894i	−0.131821	+	0.228320i	−0.924378	−	0.381477i	$-0.875416\pi$
$2$	−0.186423	+	0.322894i	−0.131821	+	0.228320i	0.792558	+	0.609797i	$0.208749\pi$
$3$		0			0
$3$		0			0
$4$	0.930493	+	1.61166i	0.465247	+	0.805831i
$5$	0.710717	−	1.23100i	0.317843	−	0.550519i	−0.662195	−	0.749331i	$-0.730375\pi$
$5$	0.710717	−	1.23100i	0.317843	−	0.550519i	0.980038	+	0.198812i	$0.0637083\pi$
$6$		0			0
$7$	2.62597	−	0.322894i	0.992525	−	0.122042i
$7$	2.62597	−	0.322894i	0.992525	−	0.122042i
$8$	−1.43955			−0.508958
$9$		0			0
$10$	0.264988	+	0.458972i	0.0837965	+	0.145140i
$11$	1.88190	+	3.25955i	0.567415	+	0.982792i	0.996820	+	0.0796802i	$0.0253899\pi$
$11$	1.88190	+	3.25955i	0.567415	+	0.982792i	−0.429405	+	0.903112i	$0.641277\pi$
$12$		0			0
$13$	1.86099			0.516145			0.258072	−	0.966126i	$-0.416913\pi$
$13$	1.86099			0.516145			0.258072	+	0.966126i	$0.416913\pi$
$14$	−0.385281	+	0.908105i	−0.102971	+	0.242701i
$15$		0			0
$16$	−1.59262	+	2.75850i	−0.398155	+	0.689625i
$17$	−3.76718	−	6.52496i	−0.913676	−	1.58253i	−0.808828	−	0.588046i	$-0.799897\pi$
$17$	−3.76718	−	6.52496i	−0.913676	−	1.58253i	−0.104849	−	0.994488i	$-0.533436\pi$
$18$		0			0
$19$	0.837872	−	1.45124i	0.192221	−	0.332937i	−0.753765	−	0.657144i	$-0.771764\pi$
$19$	0.837872	−	1.45124i	0.192221	−	0.332937i	0.945986	+	0.324208i	$0.105098\pi$
$20$	2.64527			0.591501
$21$		0			0
$22$	−1.40332			−0.299189
$23$	−0.255930	+	0.443283i	−0.0533650	+	0.0924309i	−0.891474	−	0.453072i	$-0.850328\pi$
$23$	−0.255930	+	0.443283i	−0.0533650	+	0.0924309i	0.838109	+	0.545503i	$0.183661\pi$
$24$		0			0
$25$	1.48976	+	2.58034i	0.297952	+	0.516068i
$26$	−0.346930	+	0.600901i	−0.0680386	+	0.117846i
$27$		0			0
$28$	2.96385	+	3.93173i	0.560114	+	0.743027i
$29$	8.72197			1.61963			0.809815	−	0.586686i	$-0.199568\pi$
$29$	8.72197			1.61963			0.809815	+	0.586686i	$0.199568\pi$
$30$		0			0
$31$	1.46665	+	2.54031i	0.263418	+	0.456253i	0.967148	−	0.254215i	$-0.0818170\pi$
$31$	1.46665	+	2.54031i	0.263418	+	0.456253i	−0.703730	+	0.710467i	$0.748484\pi$
$32$	−2.03335	−	3.52187i	−0.359449	−	0.622585i
$33$		0			0
$34$	2.80916			0.481766
$35$	1.46884	−	3.46206i	0.248280	−	0.585194i
$36$		0			0
$37$	−2.16551	+	3.75077i	−0.356007	+	0.616622i	−0.987290	−	0.158931i	$-0.949195\pi$
$37$	−2.16551	+	3.75077i	−0.356007	+	0.616622i	0.631283	+	0.775553i	$0.282529\pi$
$38$	0.312397	+	0.541087i	0.0506775	+	0.0877759i
$39$		0			0
$40$	−1.02311	+	1.77209i	−0.161769	+	0.280191i
$41$	−6.84051			−1.06831			−0.534154	−	0.845387i	$-0.679370\pi$
$41$	−6.84051			−1.06831			−0.534154	+	0.845387i	$0.679370\pi$
$42$		0			0
$43$	−4.53673			−0.691845			−0.345922	−	0.938263i	$-0.612434\pi$
$43$	−4.53673			−0.691845			−0.345922	+	0.938263i	$0.612434\pi$
$44$	−3.50220	+	6.06598i	−0.527976	+	0.914481i
$45$		0			0
$46$	−0.0954222	−	0.165276i	−0.0140692	−	0.0243686i
$47$	−3.71978	+	6.44284i	−0.542585	+	0.939785i	0.456170	+	0.889893i	$0.349221\pi$
$47$	−3.71978	+	6.44284i	−0.542585	+	0.939785i	−0.998755	+	0.0498920i	$0.984112\pi$
$48$		0			0
$49$	6.79148	−	1.69582i	0.970211	−	0.242260i
$50$	−1.11090			−0.157105
$51$		0			0
$52$	1.73163	+	2.99928i	0.240135	+	0.415925i
$53$	−0.416437	−	0.721290i	−0.0572020	−	0.0990768i	0.836006	−	0.548720i	$-0.184885\pi$
$53$	−0.416437	−	0.721290i	−0.0572020	−	0.0990768i	−0.893208	+	0.449643i	$0.851551\pi$
$54$		0			0
$55$	5.35001			0.721395
$56$	−3.78022	+	0.464822i	−0.505154	+	0.0621145i
$57$		0			0
$58$	−1.62597	+	2.81627i	−0.213501	+	0.369794i
$59$	6.51126	+	11.2778i	0.847693	+	1.46825i	0.883262	+	0.468880i	$0.155342\pi$
$59$	6.51126	+	11.2778i	0.847693	+	1.46825i	−0.0355684	+	0.999367i	$0.511324\pi$
$60$		0			0
$61$	5.15189	−	8.92333i	0.659632	−	1.14252i	−0.321079	−	0.947052i	$-0.604046\pi$
$61$	5.15189	−	8.92333i	0.659632	−	1.14252i	0.980711	−	0.195463i	$-0.0626211\pi$
$62$	−1.09367			−0.138896
$63$		0			0
$64$	−4.85423			−0.606779
$65$	1.32264	−	2.29087i	0.164053	−	0.284148i
$66$		0			0
$67$	−3.25813	−	5.64324i	−0.398043	−	0.689432i	0.595441	−	0.803399i	$-0.296977\pi$
$67$	−3.25813	−	5.64324i	−0.398043	−	0.689432i	−0.993484	+	0.113967i	$0.963644\pi$
$68$	7.01068	−	12.1429i	0.850170	−	1.47254i
$69$		0			0
$70$	0.844050	+	1.11969i	0.100883	+	0.133828i
$71$	4.11854			0.488780			0.244390	−	0.969677i	$-0.421412\pi$
$71$	4.11854			0.488780			0.244390	+	0.969677i	$0.421412\pi$
$72$		0			0
$73$	−2.84737	−	4.93179i	−0.333259	−	0.577222i	0.649889	−	0.760029i	$-0.274815\pi$
$73$	−2.84737	−	4.93179i	−0.333259	−	0.577222i	−0.983149	+	0.182806i	$0.941482\pi$
$74$	−0.807399	−	1.39846i	−0.0938582	−	0.162567i
$75$		0			0
$76$	3.11854			0.357721
$77$	5.99432	+	7.95185i	0.683116	+	0.906197i
$78$		0			0
$79$	−0.132152	+	0.228895i	−0.0148683	+	0.0257527i	−0.873364	−	0.487068i	$-0.838066\pi$
$79$	−0.132152	+	0.228895i	−0.0148683	+	0.0257527i	0.858496	+	0.512821i	$0.171400\pi$
$80$	2.26381	+	3.92103i	0.253101	+	0.438384i
$81$		0			0
$82$	1.27523	−	2.20876i	0.140825	−	0.243916i
$83$	−7.90046			−0.867188			−0.433594	−	0.901108i	$-0.642755\pi$
$83$	−7.90046			−0.867188			−0.433594	+	0.901108i	$0.642755\pi$
$84$		0			0
$85$	−10.7096			−1.16162
$86$	0.845750	−	1.46488i	0.0911995	−	0.157962i
$87$		0			0
$88$	−2.70910	−	4.69229i	−0.288791	−	0.500200i
$89$	−0.398321	+	0.689912i	−0.0422219	+	0.0731305i	−0.886364	−	0.462989i	$-0.846777\pi$
$89$	−0.398321	+	0.689912i	−0.0422219	+	0.0731305i	0.844142	+	0.536119i	$0.180110\pi$
$90$		0			0
$91$	4.88690	−	0.600901i	0.512286	−	0.0629915i
$92$	−0.952563			−0.0993116
$93$		0			0
$94$	−1.38690	−	2.40218i	−0.143048	−	0.247766i
$95$	−1.19098	−	2.06284i	−0.122192	−	0.211643i
$96$		0			0
$97$	−12.8800			−1.30776			−0.653882	−	0.756596i	$-0.726861\pi$
$97$	−12.8800			−1.30776			−0.653882	+	0.756596i	$0.726861\pi$
$98$	−0.718516	+	2.50907i	−0.0725811	+	0.253454i
$99$		0			0
$100$	−2.77243	+	4.80198i	−0.277243	+	0.480198i
$101$	−6.42931	−	11.1359i	−0.639741	−	1.10806i	−0.985490	−	0.169736i	$-0.945708\pi$
$101$	−6.42931	−	11.1359i	−0.639741	−	1.10806i	0.345749	−	0.938327i	$-0.387625\pi$
$102$		0			0
$103$	9.87792	−	17.1091i	0.973301	−	1.68581i	0.287868	−	0.957670i	$-0.407054\pi$
$103$	9.87792	−	17.1091i	0.973301	−	1.68581i	0.685433	−	0.728136i	$-0.259613\pi$
$104$	−2.67899			−0.262696
$105$		0			0
$106$	0.310533			0.0301617
$107$	3.61530	−	6.26188i	0.349504	−	0.605358i	−0.636658	−	0.771147i	$-0.719684\pi$
$107$	3.61530	−	6.26188i	0.349504	−	0.605358i	0.986161	+	0.165788i	$0.0530168\pi$
$108$		0			0
$109$	−4.88410	−	8.45951i	−0.467812	−	0.810274i	0.531512	−	0.847051i	$-0.321624\pi$
$109$	−4.88410	−	8.45951i	−0.467812	−	0.810274i	−0.999323	+	0.0367769i	$0.988291\pi$
$110$	−0.997363	+	1.72748i	−0.0950948	+	0.164709i
$111$		0			0
$112$	−3.29148	+	7.75800i	−0.311016	+	0.733062i
$113$	−16.9072			−1.59050			−0.795248	−	0.606284i	$-0.792660\pi$
$113$	−16.9072			−1.59050			−0.795248	+	0.606284i	$0.792660\pi$
$114$		0			0
$115$	0.363787	+	0.630098i	0.0339233	+	0.0587570i
$116$	8.11574	+	14.0569i	0.753527	+	1.30515i
$117$		0			0
$118$	−4.85538			−0.446974
$119$	−11.9994	−	15.9180i	−1.09998	−	1.45920i
$120$		0			0
$121$	−1.58312	+	2.74205i	−0.143920	+	0.249277i
$122$	1.92086	+	3.32702i	0.173906	+	0.301215i
$123$		0			0
$124$	−2.72941	+	4.72748i	−0.245108	+	0.424540i
$125$	11.3424			1.01449
$126$		0			0
$127$	−16.1715			−1.43499			−0.717495	−	0.696563i	$-0.754711\pi$
$127$	−16.1715			−1.43499			−0.717495	+	0.696563i	$0.754711\pi$
$128$	4.97164	−	8.61114i	0.439435	−	0.761125i
$129$		0			0
$130$	0.493139	+	0.854141i	0.0432511	+	0.0749131i
$131$	6.81078	−	11.7966i	0.595060	−	1.03067i	−0.398478	−	0.917178i	$-0.630462\pi$
$131$	6.81078	−	11.7966i	0.595060	−	1.03067i	0.993538	−	0.113497i	$-0.0362052\pi$
$132$		0			0
$133$	1.73163	−	4.08145i	0.150152	−	0.353907i
$134$	2.42956			0.209882
$135$		0			0
$136$	5.42306	+	9.39301i	0.465023	+	0.805444i
$137$	3.25593	+	5.63944i	0.278173	+	0.481809i	0.970931	−	0.239361i	$-0.0769379\pi$
$137$	3.25593	+	5.63944i	0.278173	+	0.481809i	−0.692758	+	0.721170i	$0.743605\pi$
$138$		0			0
$139$	−17.9072			−1.51887			−0.759435	−	0.650583i	$-0.774525\pi$
$139$	−17.9072			−1.51887			−0.759435	+	0.650583i	$0.774525\pi$
$140$	6.94641	−	0.854141i	0.587079	−	0.0721881i
$141$		0			0
$142$	−0.767789	+	1.32985i	−0.0644314	+	0.111598i
$143$	3.50220	+	6.06598i	0.292868	+	0.507263i
$144$		0			0
$145$	6.19886	−	10.7367i	0.514787	−	0.891638i
$146$	2.12326			0.175722
$147$		0			0
$148$	−8.05995			−0.662524
$149$	−9.98460	+	17.2938i	−0.817970	+	1.41677i	0.0892051	+	0.996013i	$0.471567\pi$
$149$	−9.98460	+	17.2938i	−0.817970	+	1.41677i	−0.907175	+	0.420753i	$0.861766\pi$
$150$		0			0
$151$	−3.15933	−	5.47211i	−0.257102	−	0.445314i	0.708362	−	0.705849i	$-0.249434\pi$
$151$	−3.15933	−	5.47211i	−0.257102	−	0.445314i	−0.965464	+	0.260535i	$0.916101\pi$
$152$	−1.20616	+	2.08913i	−0.0978325	+	0.169451i
$153$		0			0
$154$	−3.68508	+	0.453123i	−0.296952	+	0.0365137i
$155$	4.16949			0.334901
$156$		0			0
$157$	3.24789	+	5.62551i	0.259210	+	0.448964i	0.966030	−	0.258428i	$-0.0832046\pi$
$157$	3.24789	+	5.62551i	0.259210	+	0.448964i	−0.706821	+	0.707393i	$0.749871\pi$
$158$	−0.0492724	−	0.0853424i	−0.00391990	−	0.00678947i
$159$		0			0
$160$	−5.78056			−0.456993
$161$	−0.528931	+	1.24669i	−0.0416856	+	0.0982528i
$162$		0			0
$163$	9.61631	−	16.6559i	0.753208	−	1.30459i	−0.193053	−	0.981188i	$-0.561839\pi$
$163$	9.61631	−	16.6559i	0.753208	−	1.30459i	0.946260	−	0.323406i	$-0.104828\pi$
$164$	−6.36505	−	11.0246i	−0.497027	−	0.860875i
$165$		0			0
$166$	1.47283	−	2.55101i	0.114313	−	0.197997i
$167$	10.3772			0.803015			0.401507	−	0.915856i	$-0.368486\pi$
$167$	10.3772			0.803015			0.401507	+	0.915856i	$0.368486\pi$
$168$		0			0
$169$	−9.53673			−0.733595
$170$	1.99652	−	3.45807i	0.153126	−	0.265222i
$171$		0			0
$172$	−4.22140	−	7.31167i	−0.321878	−	0.557510i
$173$	−6.61005	+	11.4490i	−0.502553	+	0.870448i	0.497443	+	0.867497i	$0.334273\pi$
$173$	−6.61005	+	11.4490i	−0.502553	+	0.870448i	−0.999996	+	0.00295062i	$0.999061\pi$
$174$		0			0
$175$	4.74525	+	6.29488i	0.358707	+	0.475848i
$176$	−11.9886			−0.903678
$177$		0			0
$178$	−0.148512	−	0.257230i	−0.0111315	−	0.0192802i
$179$	−5.74745	−	9.95487i	−0.429584	−	0.744062i	0.567252	−	0.823544i	$-0.308007\pi$
$179$	−5.74745	−	9.95487i	−0.429584	−	0.744062i	−0.996836	+	0.0794823i	$0.974673\pi$
$180$		0			0
$181$	−13.7040			−1.01861			−0.509306	−	0.860586i	$-0.670098\pi$
$181$	−13.7040			−1.01861			−0.509306	+	0.860586i	$0.670098\pi$
$182$	−0.717003	+	1.68997i	−0.0531478	+	0.125269i
$183$		0			0
$184$	0.368424	−	0.638129i	0.0271606	−	0.0470435i
$185$	3.07812	+	5.33147i	0.226308	+	0.391977i
$186$		0			0
$187$	14.1790	−	24.5587i	1.03687	−	1.79591i
$188$	−13.8449			−1.00974
$189$		0			0
$190$	0.888103			0.0644298
$191$	−3.87167	+	6.70592i	−0.280144	+	0.485223i	−0.971420	−	0.237367i	$-0.923716\pi$
$191$	−3.87167	+	6.70592i	−0.280144	+	0.485223i	0.691276	+	0.722591i	$0.257049\pi$
$192$		0			0
$193$	−7.91002	−	13.7005i	−0.569375	−	0.986187i	−0.996628	−	0.0820547i	$-0.973852\pi$
$193$	−7.91002	−	13.7005i	−0.569375	−	0.986187i	0.427252	−	0.904132i	$-0.359482\pi$
$194$	2.40112	−	4.15886i	0.172390	−	0.298589i
$195$		0			0
$196$	9.05251	+	9.36762i	0.646608	+	0.669115i
$197$	3.64966			0.260028			0.130014	−	0.991512i	$-0.458498\pi$
$197$	3.64966			0.260028			0.130014	+	0.991512i	$0.458498\pi$
$198$		0			0
$199$	10.3582	+	17.9409i	0.734272	+	1.27180i	0.955042	+	0.296471i	$0.0958098\pi$
$199$	10.3582	+	17.9409i	0.734272	+	1.27180i	−0.220770	+	0.975326i	$0.570857\pi$
$200$	−2.14459	−	3.71454i	−0.151645	−	0.262657i
$201$		0			0
$202$	4.79428			0.337324
$203$	22.9037	−	2.81627i	1.60752	−	0.197663i
$204$		0			0
$205$	−4.86167	+	8.42066i	−0.339554	+	0.588124i
$206$	3.68294	+	6.37904i	0.256602	+	0.444449i
$207$		0			0
$208$	−2.96385	+	5.13353i	−0.205506	+	0.355946i
$209$	6.30718			0.436277
$210$		0			0
$211$	19.8539			1.36680			0.683400	−	0.730045i	$-0.260501\pi$
$211$	19.8539			1.36680			0.683400	+	0.730045i	$0.260501\pi$
$212$	0.774984	−	1.34231i	0.0532261	−	0.0921903i
$213$		0			0
$214$	1.34795	+	2.33471i	0.0921437	+	0.159598i
$215$	−3.22433	+	5.58471i	−0.219898	+	0.380874i
$216$		0			0
$217$	4.67163	+	6.19721i	0.317131	+	0.420694i
$218$	3.64203			0.246669
$219$		0			0
$220$	4.97814	+	8.62240i	0.335626	+	0.581322i
$221$	−7.01068	−	12.1429i	−0.471589	−	0.816817i
$222$		0			0
$223$	16.0720			1.07626			0.538130	−	0.842862i	$-0.319131\pi$
$223$	16.0720			1.07626			0.538130	+	0.842862i	$0.319131\pi$
$224$	−6.47672	−	8.59178i	−0.432744	−	0.574063i
$225$		0			0
$226$	3.15189	−	5.45923i	0.209661	−	0.363143i
$227$	0.428873	+	0.742829i	0.0284653	+	0.0493033i	0.879907	−	0.475146i	$-0.157605\pi$
$227$	0.428873	+	0.742829i	0.0284653	+	0.0493033i	−0.851442	+	0.524449i	$0.824271\pi$
$228$		0			0
$229$	−2.87792	+	4.98471i	−0.190178	+	0.329399i	−0.945309	−	0.326175i	$-0.894240\pi$
$229$	−2.87792	+	4.98471i	−0.190178	+	0.329399i	0.755131	+	0.655574i	$0.227573\pi$
$230$	−0.271273			−0.0178872
$231$		0			0
$232$	−12.5557			−0.824324
$233$	3.69430	−	6.39872i	0.242022	−	0.419194i	−0.719268	−	0.694732i	$-0.755523\pi$
$233$	3.69430	−	6.39872i	0.242022	−	0.419194i	0.961290	+	0.275539i	$0.0888562\pi$
$234$		0			0
$235$	5.28742	+	9.15808i	0.344913	+	0.597407i
$236$	−12.1174	+	20.9879i	−0.788773	+	1.36619i
$237$		0			0
$238$	7.37677	−	0.907059i	0.478165	−	0.0587959i
$239$	−13.8010			−0.892715			−0.446357	−	0.894855i	$-0.647279\pi$
$239$	−13.8010			−0.892715			−0.446357	+	0.894855i	$0.647279\pi$
$240$		0			0
$241$	9.87792	+	17.1091i	0.636293	+	1.10209i	0.986240	+	0.165322i	$0.0528663\pi$
$241$	9.87792	+	17.1091i	0.636293	+	1.10209i	−0.349947	+	0.936770i	$0.613800\pi$
$242$	−0.590260	−	1.02236i	−0.0379434	−	0.0657198i
$243$		0			0
$244$	19.1752			1.22757
$245$	2.73927	−	9.56555i	0.175006	−	0.611121i
$246$		0			0
$247$	1.55927	−	2.70073i	0.0992139	−	0.171843i
$248$	−2.11131	−	3.65690i	−0.134069	−	0.232214i
$249$		0			0
$250$	−2.11448	+	3.66238i	−0.133731	+	0.231629i
$251$	−9.45207			−0.596609			−0.298305	−	0.954471i	$-0.596421\pi$
$251$	−9.45207			−0.596609			−0.298305	+	0.954471i	$0.596421\pi$
$252$		0			0
$253$	−1.92654			−0.121121
$254$	3.01474	−	5.22168i	0.189162	−	0.327637i
$255$		0			0
$256$	−3.00058	−	5.19715i	−0.187536	−	0.324822i
$257$	3.73663	−	6.47204i	0.233085	−	0.403715i	−0.725630	−	0.688086i	$-0.758451\pi$
$257$	3.73663	−	6.47204i	0.233085	−	0.403715i	0.958714	+	0.284371i	$0.0917847\pi$
$258$		0			0
$259$	−4.47546	+	10.5486i	−0.278092	+	0.655461i
$260$	4.92281			0.305300
$261$		0			0
$262$	2.53937	+	4.39831i	0.156883	+	0.271729i
$263$	12.9056	+	22.3531i	0.795793	+	1.37835i	0.922334	+	0.386393i	$0.126279\pi$
$263$	12.9056	+	22.3531i	0.795793	+	1.37835i	−0.126541	+	0.991961i	$0.540388\pi$
$264$		0			0
$265$	−1.18388			−0.0727249
$266$	0.995059	+	1.32001i	0.0610110	+	0.0809350i
$267$		0			0
$268$	6.06333	−	10.5020i	0.370377	−	0.641511i
$269$	−3.24349	−	5.61790i	−0.197759	−	0.342529i	0.750042	−	0.661390i	$-0.230033\pi$
$269$	−3.24349	−	5.61790i	−0.197759	−	0.342529i	−0.947802	+	0.318861i	$0.896700\pi$
$270$		0			0
$271$	9.11980	−	15.7959i	0.553988	−	0.959536i	−0.443993	−	0.896030i	$-0.646439\pi$
$271$	9.11980	−	15.7959i	0.553988	−	0.959536i	0.997981	−	0.0635055i	$-0.0202280\pi$
$272$	23.9988			1.45514
$273$		0			0
$274$	−2.42792			−0.146676
$275$	−5.60717	+	9.71191i	−0.338125	+	0.585650i
$276$		0			0
$277$	1.52328	+	2.63840i	0.0915249	+	0.158526i	0.908153	−	0.418638i	$-0.137493\pi$
$277$	1.52328	+	2.63840i	0.0915249	+	0.158526i	−0.816628	+	0.577164i	$0.804159\pi$
$278$	3.33831	−	5.78213i	0.200219	−	0.346789i
$279$		0			0
$280$	−2.11448	+	4.98381i	−0.126364	+	0.297840i
$281$	28.5445			1.70282			0.851412	−	0.524498i	$-0.175747\pi$
$281$	28.5445			1.70282			0.851412	+	0.524498i	$0.175747\pi$
$282$		0			0
$283$	4.77043	+	8.26262i	0.283572	+	0.491162i	0.972262	−	0.233895i	$-0.0751470\pi$
$283$	4.77043	+	8.26262i	0.283572	+	0.491162i	−0.688690	+	0.725056i	$0.741814\pi$
$284$	3.83227	+	6.63769i	0.227403	+	0.393874i
$285$		0			0
$286$	−2.61156			−0.154425
$287$	−17.9630	+	2.20876i	−1.06032	+	0.130379i
$288$		0			0
$289$	−19.8834	+	34.4390i	−1.16961	+	2.02582i
$290$	2.31122	+	4.00314i	0.135719	+	0.235073i
$291$		0			0
$292$	5.29892	−	9.17799i	0.310096	−	0.537101i
$293$	−12.6307			−0.737891			−0.368946	−	0.929451i	$-0.620281\pi$
$293$	−12.6307			−0.737891			−0.368946	+	0.929451i	$0.620281\pi$
$294$		0			0
$295$	18.5107			1.07773
$296$	3.11736	−	5.39942i	0.181193	−	0.313835i
$297$		0			0
$298$	−3.72271	−	6.44793i	−0.215651	−	0.373518i
$299$	−0.476282	+	0.824944i	−0.0275441	+	0.0477077i
$300$		0			0
$301$	−11.9133	+	1.46488i	−0.686673	+	0.0844344i
$302$	2.35588			0.135566
$303$		0			0
$304$	2.66883	+	4.62254i	0.153068	+	0.265121i
$305$	−7.32308	−	12.6839i	−0.419318	−	0.726280i
$306$		0			0
$307$	−10.9319			−0.623918			−0.311959	−	0.950096i	$-0.600985\pi$
$307$	−10.9319			−0.623918			−0.311959	+	0.950096i	$0.600985\pi$
$308$	−7.23801	+	17.0600i	−0.412424	+	0.972081i
$309$		0			0
$310$	−0.777287	+	1.34630i	−0.0441469	+	0.0764648i
$311$	−2.38028	−	4.12277i	−0.134973	−	0.233781i	0.790614	−	0.612315i	$-0.209762\pi$
$311$	−2.38028	−	4.12277i	−0.134973	−	0.233781i	−0.925587	+	0.378534i	$0.876428\pi$
$312$		0			0
$313$	−3.60550	+	6.24490i	−0.203795	+	0.352983i	−0.949748	−	0.313015i	$-0.898661\pi$
$313$	−3.60550	+	6.24490i	−0.203795	+	0.352983i	0.745953	+	0.665998i	$0.231994\pi$
$314$	−2.42192			−0.136677
$315$		0			0
$316$	−0.491868			−0.0276697
$317$	3.64459	−	6.31261i	0.204700	−	0.354552i	−0.745337	−	0.666688i	$-0.767711\pi$
$317$	3.64459	−	6.31261i	0.204700	−	0.354552i	0.950037	+	0.312137i	$0.101045\pi$
$318$		0			0
$319$	16.4139	+	28.4297i	0.919003	+	1.59176i
$320$	−3.44999	+	5.97555i	−0.192860	+	0.334044i
$321$		0			0
$322$	−0.303943	−	0.403200i	−0.0169381	−	0.0224694i
$323$	−12.6257			−0.702511
$324$		0			0
$325$	2.77243	+	4.80198i	0.153786	+	0.266366i
$326$	3.58540	+	6.21009i	0.198577	+	0.343945i
$327$		0			0
$328$	9.84726			0.543724
$329$	−7.68768	+	18.1198i	−0.423836	+	0.998978i
$330$		0			0
$331$	0.609557	−	1.05578i	0.0335043	−	0.0580311i	−0.848787	−	0.528735i	$-0.822667\pi$
$331$	0.609557	−	1.05578i	0.0335043	−	0.0580311i	0.882291	+	0.470704i	$0.156000\pi$
$332$	−7.35132	−	12.7329i	−0.403456	−	0.698807i
$333$		0			0
$334$	−1.93455	+	3.35074i	−0.105854	+	0.183345i
$335$	−9.26243			−0.506061
$336$		0			0
$337$	−14.9140			−0.812416			−0.406208	−	0.913781i	$-0.633149\pi$
$337$	−14.9140			−0.812416			−0.406208	+	0.913781i	$0.633149\pi$
$338$	1.77786	−	3.07935i	0.0967030	−	0.167495i
$339$		0			0
$340$	−9.96522	−	17.2603i	−0.540440	−	0.936070i
$341$	−5.52018	+	9.56123i	−0.298934	+	0.517769i
$342$		0			0
$343$	17.2867	−	6.64611i	0.933393	−	0.358856i
$344$	6.53086			0.352120
$345$		0			0
$346$	−2.46453	−	4.26869i	−0.132494	−	0.229486i
$347$	−2.57914	−	4.46720i	−0.138456	−	0.239812i	0.788457	−	0.615090i	$-0.210880\pi$
$347$	−2.57914	−	4.46720i	−0.138456	−	0.239812i	−0.926912	+	0.375278i	$0.877547\pi$
$348$		0			0
$349$	−24.4507			−1.30882			−0.654408	−	0.756142i	$-0.727082\pi$
$349$	−24.4507			−1.30882			−0.654408	+	0.756142i	$0.727082\pi$
$350$	−2.91720	+	0.358703i	−0.155931	+	0.0191735i
$351$		0			0
$352$	7.65315	−	13.2556i	0.407914	−	0.706528i
$353$	7.45473	+	12.9120i	0.396775	+	0.687235i	0.993326	−	0.115340i	$-0.0367959\pi$
$353$	7.45473	+	12.9120i	0.396775	+	0.687235i	−0.596551	+	0.802575i	$0.703463\pi$
$354$		0			0
$355$	2.92712	−	5.06991i	0.155355	−	0.269083i
$356$	−1.48254			−0.0785744
$357$		0			0
$358$	4.28582			0.226513
$359$	−1.07390	+	1.86005i	−0.0566783	+	0.0981697i	−0.892972	−	0.450111i	$-0.851384\pi$
$359$	−1.07390	+	1.86005i	−0.0566783	+	0.0981697i	0.836294	+	0.548281i	$0.184718\pi$
$360$		0			0
$361$	8.09594	+	14.0226i	0.426102	+	0.738031i
$362$	2.55474	−	4.42494i	0.134274	−	0.232570i
$363$		0			0
$364$	5.51568	+	7.31690i	0.289100	+	0.383510i
$365$	−8.09470			−0.423696
$366$		0			0
$367$	7.93049	+	13.7360i	0.413968	+	0.717014i	0.995320	−	0.0966385i	$-0.0308091\pi$
$367$	7.93049	+	13.7360i	0.413968	+	0.717014i	−0.581351	+	0.813653i	$0.697476\pi$
$368$	−0.815198	−	1.41196i	−0.0424951	−	0.0736037i
$369$		0			0
$370$	−2.29533			−0.119329
$371$	−1.32645	−	1.75962i	−0.0688660	−	0.0913551i
$372$		0			0
$373$	−5.86842	+	10.1644i	−0.303855	+	0.526293i	−0.977006	−	0.213213i	$-0.931607\pi$
$373$	−5.86842	+	10.1644i	−0.303855	+	0.526293i	0.673150	+	0.739506i	$0.264941\pi$
$374$	5.28656	+	9.15659i	0.273362	+	0.473476i
$375$		0			0
$376$	5.35481	−	9.27480i	0.276153	−	0.478311i
$377$	16.2315			0.835963
$378$		0			0
$379$	18.9400			0.972885			0.486442	−	0.873713i	$-0.338294\pi$
$379$	18.9400			0.972885			0.486442	+	0.873713i	$0.338294\pi$
$380$	2.21640	−	3.83891i	0.113699	−	0.196932i
$381$		0			0
$382$	−1.44353	−	2.50027i	−0.0738576	−	0.127925i
$383$	14.8406	−	25.7047i	0.758319	−	1.31345i	−0.185389	−	0.982665i	$-0.559354\pi$
$383$	14.8406	−	25.7047i	0.758319	−	1.31345i	0.943708	−	0.330781i	$-0.107312\pi$
$384$		0			0
$385$	14.0490	−	1.72748i	0.716002	−	0.0880407i
$386$	5.89843			0.300222
$387$		0			0
$388$	−11.9847	−	20.7582i	−0.608433	−	1.05384i
$389$	−0.639093	−	1.10694i	−0.0324033	−	0.0561241i	0.849369	−	0.527799i	$-0.176983\pi$
$389$	−0.639093	−	1.10694i	−0.0324033	−	0.0561241i	−0.881772	+	0.471675i	$0.843649\pi$
$390$		0			0
$391$	3.85654			0.195033
$392$	−9.77668	+	2.44122i	−0.493797	+	0.123300i
$393$		0			0
$394$	−0.680380	+	1.17845i	−0.0342771	+	0.0593696i
$395$	0.187846	+	0.325359i	0.00945156	+	0.0163706i
$396$		0			0
$397$	3.21734	−	5.57259i	0.161473	−	0.279680i	−0.773924	−	0.633279i	$-0.781709\pi$
$397$	3.21734	−	5.57259i	0.161473	−	0.279680i	0.935397	+	0.353598i	$0.115042\pi$
$398$	−7.72401			−0.387169
$399$		0			0
$400$	−9.49050			−0.474525
$401$	13.8455	−	23.9811i	0.691412	−	1.19756i	−0.279964	−	0.960011i	$-0.590322\pi$
$401$	13.8455	−	23.9811i	0.691412	−	1.19756i	0.971375	−	0.237549i	$-0.0763442\pi$
$402$		0			0
$403$	2.72941	+	4.72748i	0.135962	+	0.235492i
$404$	11.9649	−	20.7237i	0.595274	−	1.03105i
$405$		0			0
$406$	−3.36041	+	7.92047i	−0.166774	+	0.393086i
$407$	−16.3011			−0.808015
$408$		0			0
$409$	6.01362	+	10.4159i	0.297354	+	0.515033i	0.975530	−	0.219867i	$-0.0705625\pi$
$409$	6.01362	+	10.4159i	0.297354	+	0.515033i	−0.678176	+	0.734900i	$0.737229\pi$
$410$	−1.81265	−	3.13960i	−0.0895205	−	0.155054i
$411$		0			0
$412$	36.7654			1.81130
$413$	20.7399	+	27.5128i	1.02054	+	1.35382i
$414$		0			0
$415$	−5.61500	+	9.72546i	−0.275629	+	0.477404i
$416$	−3.78404	−	6.55415i	−0.185528	−	0.321344i
$417$		0			0
$418$	−1.17580	+	2.03655i	−0.0575103	+	0.0996108i
$419$	18.0190			0.880286			0.440143	−	0.897928i	$-0.354928\pi$
$419$	18.0190			0.880286			0.440143	+	0.897928i	$0.354928\pi$
$420$		0			0
$421$	−17.2572			−0.841066			−0.420533	−	0.907277i	$-0.638157\pi$
$421$	−17.2572			−0.841066			−0.420533	+	0.907277i	$0.638157\pi$
$422$	−3.70122	+	6.41070i	−0.180173	+	0.312068i
$423$		0			0
$424$	0.599482	+	1.03833i	0.0291134	+	0.0504260i
$425$	11.2244	−	19.4413i	0.544464	−	0.943039i
$426$		0			0
$427$	10.6474	−	25.0960i	0.515266	−	1.21448i
$428$	13.4560			0.650422
$429$		0			0
$430$	−1.20218	−	2.08223i	−0.0579742	−	0.100414i
$431$	4.28368	+	7.41955i	0.206338	+	0.357387i	0.950558	−	0.310547i	$-0.100512\pi$
$431$	4.28368	+	7.41955i	0.206338	+	0.357387i	−0.744220	+	0.667934i	$0.767179\pi$
$432$		0			0
$433$	1.58971			0.0763967			0.0381984	−	0.999270i	$-0.487838\pi$
$433$	1.58971			0.0763967			0.0381984	+	0.999270i	$0.487838\pi$
$434$	−2.87194	+	0.353138i	−0.137857	+	0.0169512i
$435$		0			0
$436$	9.08924	−	15.7430i	0.435296	−	0.753954i
$437$	0.428873	+	0.742829i	0.0205158	+	0.0355343i
$438$		0			0
$439$	−11.2218	+	19.4367i	−0.535588	+	0.927665i	0.463547	+	0.886072i	$0.346577\pi$
$439$	−11.2218	+	19.4367i	−0.535588	+	0.927665i	−0.999135	+	0.0415927i	$0.986757\pi$
$440$	−7.70161			−0.367160
$441$		0			0
$442$	5.22780			0.248661
$443$	−12.1605	+	21.0626i	−0.577763	+	1.00072i	0.417972	+	0.908460i	$0.362741\pi$
$443$	−12.1605	+	21.0626i	−0.577763	+	1.00072i	−0.995735	+	0.0922553i	$0.970592\pi$
$444$		0			0
$445$	0.566187	+	0.980665i	0.0268398	+	0.0464880i
$446$	−2.99618	+	5.18954i	−0.141873	+	0.245732i
$447$		0			0
$448$	−12.7471	+	1.56740i	−0.602243	+	0.0740527i
$449$	−12.9016			−0.608865			−0.304432	−	0.952534i	$-0.598467\pi$
$449$	−12.9016			−0.608865			−0.304432	+	0.952534i	$0.598467\pi$
$450$		0			0
$451$	−12.8732	−	22.2970i	−0.606174	−	1.04992i
$452$	−15.7320	−	27.2487i	−0.739973	−	1.28167i
$453$		0			0
$454$	−0.319806			−0.0150093
$455$	2.73350	−	6.44284i	0.128148	−	0.302045i
$456$		0			0
$457$	−0.593880	+	1.02863i	−0.0277806	+	0.0481173i	−0.879581	−	0.475748i	$-0.842177\pi$
$457$	−0.593880	+	1.02863i	−0.0277806	+	0.0481173i	0.851801	+	0.523866i	$0.175511\pi$
$458$	−1.07302	−	1.85853i	−0.0501389	−	0.0868432i
$459$		0			0
$460$	−0.677003	+	1.17260i	−0.0315654	+	0.0546729i
$461$	−16.1674			−0.752991			−0.376495	−	0.926418i	$-0.622871\pi$
$461$	−16.1674			−0.752991			−0.376495	+	0.926418i	$0.622871\pi$
$462$		0			0
$463$	−0.531128			−0.0246836			−0.0123418	−	0.999924i	$-0.503929\pi$
$463$	−0.531128			−0.0246836			−0.0123418	+	0.999924i	$0.503929\pi$
$464$	−13.8908	+	24.0596i	−0.644864	+	1.11694i
$465$		0			0
$466$	1.37740	+	2.38573i	0.0638070	+	0.110517i
$467$	−10.7393	+	18.6011i	−0.496958	+	0.860756i	−0.999994	−	0.00350930i	$-0.998883\pi$
$467$	−10.7393	+	18.6011i	−0.496958	+	0.860756i	0.503036	+	0.864265i	$0.332216\pi$
$468$		0			0
$469$	−10.3779	−	13.7670i	−0.479208	−	0.635700i
$470$	−3.94278			−0.181867
$471$		0			0
$472$	−9.37329	−	16.2350i	−0.431440	−	0.747277i
$473$	−8.53769	−	14.7877i	−0.392563	−	0.679940i
$474$		0			0
$475$	4.99292			0.229091
$476$	14.4890	−	34.1505i	0.664103	−	1.56529i
$477$		0			0
$478$	2.57283	−	4.45627i	0.117678	−	0.203825i
$479$	−14.1765	−	24.5543i	−0.647739	−	1.12192i	−0.983662	−	0.180027i	$-0.942381\pi$
$479$	−14.1765	−	24.5543i	−0.647739	−	1.12192i	0.335923	−	0.941890i	$-0.390952\pi$
$480$		0			0
$481$	−4.02998	+	6.98012i	−0.183751	+	0.318266i
$482$	−7.36588			−0.335507
$483$		0			0
$484$	−5.89234			−0.267834
$485$	−9.15403	+	15.8552i	−0.415663	+	0.719950i
$486$		0			0
$487$	−3.93513	−	6.81584i	−0.178318	−	0.308855i	0.762987	−	0.646414i	$-0.223732\pi$
$487$	−3.93513	−	6.81584i	−0.178318	−	0.308855i	−0.941304	+	0.337559i	$0.890399\pi$
$488$	−7.41641	+	12.8456i	−0.335725	+	0.581493i
$489$		0			0
$490$	2.57799	+	2.66773i	0.116462	+	0.120516i
$491$	28.3183			1.27799			0.638994	−	0.769212i	$-0.279351\pi$
$491$	28.3183			1.27799			0.638994	+	0.769212i	$0.279351\pi$
$492$		0			0
$493$	−32.8573	−	56.9105i	−1.47982	−	2.56312i
$494$	0.581366	+	1.00696i	0.0261569	+	0.0453051i
$495$		0			0
$496$	−9.34325			−0.419524
$497$	10.8152	−	1.32985i	0.485127	−	0.0596519i
$498$		0			0
$499$	−3.42094	+	5.92524i	−0.153142	+	0.265250i	−0.932381	−	0.361477i	$-0.882273\pi$
$499$	−3.42094	+	5.92524i	−0.153142	+	0.265250i	0.779239	+	0.626727i	$0.215606\pi$
$500$	10.5540	+	18.2801i	0.471989	+	0.817509i
$501$		0			0
$502$	1.76208	−	3.05201i	0.0786455	−	0.136218i
$503$	30.5760			1.36332			0.681658	−	0.731671i	$-0.261259\pi$
$503$	30.5760			1.36332			0.681658	+	0.731671i	$0.261259\pi$
$504$		0			0
$505$	−18.2777			−0.813347
$506$	0.359151	−	0.622067i	0.0159662	−	0.0276543i
$507$		0			0
$508$	−15.0475	−	26.0630i	−0.667624	−	1.15636i
$509$	−17.0562	+	29.5421i	−0.756001	+	1.30943i	0.188874	+	0.982001i	$0.439516\pi$
$509$	−17.0562	+	29.5421i	−0.756001	+	1.30943i	−0.944875	+	0.327431i	$0.893817\pi$
$510$		0			0
$511$	−9.06956	−	12.0314i	−0.401214	−	0.532236i
$512$	22.1241			0.977756
$513$		0			0
$514$	1.39319	+	2.41307i	0.0614508	+	0.106436i
$515$	−14.0408	−	24.3194i	−0.618713	−	1.07164i
$516$		0			0
$517$	−28.0010			−1.23148
$518$	−2.57176	−	3.41160i	−0.112997	−	0.149897i
$519$		0			0
$520$	−1.90400	+	3.29783i	−0.0834960	+	0.144619i
$521$	−7.37216	−	12.7690i	−0.322980	−	0.559418i	0.658121	−	0.752912i	$-0.271351\pi$
$521$	−7.37216	−	12.7690i	−0.322980	−	0.559418i	−0.981102	+	0.193494i	$0.938018\pi$
$522$		0			0
$523$	−2.03953	+	3.53257i	−0.0891825	+	0.154469i	−0.907166	−	0.420773i	$-0.861759\pi$
$523$	−2.03953	+	3.53257i	−0.0891825	+	0.154469i	0.817983	+	0.575242i	$0.195092\pi$
$524$	25.3495			1.10740
$525$		0			0
$526$	−9.62359			−0.419608
$527$	11.0503	−	19.1396i	0.481357	−	0.833735i
$528$		0			0
$529$	11.3690	+	19.6917i	0.494304	+	0.856160i
$530$	0.220701	−	0.382266i	0.00958666	−	0.0166046i
$531$		0			0
$532$	8.18920	−	1.00696i	0.355047	−	0.0436571i
$533$	−12.7301			−0.551402
$534$		0			0
$535$	−5.13891	−	8.90085i	−0.222174	−	0.384817i
$536$	4.69024	+	8.12373i	0.202588	+	0.350892i
$537$		0			0
$538$	2.41864			0.104275
$539$	18.3085	+	18.9458i	0.788604	+	0.816054i
$540$		0			0
$541$	−1.90052	+	3.29179i	−0.0817096	+	0.141525i	−0.903984	−	0.427565i	$-0.859371\pi$
$541$	−1.90052	+	3.29179i	−0.0817096	+	0.141525i	0.822275	+	0.569091i	$0.192705\pi$
$542$	3.40027	+	5.88945i	0.146054	+	0.252973i
$543$		0			0
$544$	−15.3200	+	26.5351i	−0.656841	+	1.13768i
$545$	−13.8849			−0.594762
$546$		0			0
$547$	−10.4778			−0.447999			−0.224000	−	0.974589i	$-0.571911\pi$
$547$	−10.4778			−0.447999			−0.224000	+	0.974589i	$0.571911\pi$
$548$	−6.05924	+	10.4949i	−0.258838	+	0.448320i
$549$		0			0
$550$	−2.09061	−	3.62104i	−0.0891439	−	0.154402i
$551$	7.30790	−	12.6576i	0.311327	−	0.539234i
$552$		0			0
$553$	−0.273120	+	0.643743i	−0.0116143	+	0.0273747i
$554$	−1.13589			−0.0482596
$555$		0			0
$556$	−16.6625	−	28.8604i	−0.706649	−	1.22395i
$557$	17.4975	+	30.3065i	0.741392	+	1.28413i	0.951862	+	0.306528i	$0.0991673\pi$
$557$	17.4975	+	30.3065i	0.741392	+	1.28413i	−0.210470	+	0.977600i	$0.567499\pi$
$558$		0			0
$559$	−8.44279			−0.357092
$560$	7.21077	+	9.56555i	0.304711	+	0.404218i
$561$		0			0
$562$	−5.32135	+	9.21685i	−0.224468	+	0.388789i
$563$	−14.5322	−	25.1705i	−0.612458	−	1.06081i	−0.990825	−	0.135153i	$-0.956848\pi$
$563$	−14.5322	−	25.1705i	−0.612458	−	1.06081i	0.378367	−	0.925656i	$-0.376486\pi$
$564$		0			0
$565$	−12.0163	+	20.8128i	−0.505528	+	0.875599i
$566$	−3.55726			−0.149523
$567$		0			0
$568$	−5.92884			−0.248769
$569$	11.0163	−	19.0808i	0.461829	−	0.799911i	−0.537224	−	0.843440i	$-0.680527\pi$
$569$	11.0163	−	19.0808i	0.461829	−	0.799911i	0.999052	+	0.0435292i	$0.0138602\pi$
$570$		0			0
$571$	−1.01413	−	1.75653i	−0.0424402	−	0.0735086i	0.844025	−	0.536304i	$-0.180180\pi$
$571$	−1.01413	−	1.75653i	−0.0424402	−	0.0735086i	−0.886465	+	0.462795i	$0.846847\pi$
$572$	−6.51754	+	11.2887i	−0.272512	+	0.472005i
$573$		0			0
$574$	2.63552	−	6.21190i	0.110004	−	0.259280i
$575$	−1.52510			−0.0636009
$576$		0			0
$577$	2.47060	+	4.27921i	0.102852	+	0.178146i	0.912859	−	0.408275i	$-0.133870\pi$
$577$	2.47060	+	4.27921i	0.102852	+	0.178146i	−0.810006	+	0.586421i	$0.800536\pi$
$578$	−7.41342	−	12.8404i	−0.308358	−	0.534091i
$579$		0			0
$580$	23.0720			0.958012
$581$	−20.7464	+	2.55101i	−0.860706	+	0.105834i
$582$		0			0
$583$	1.56739	−	2.71480i	0.0649146	−	0.112435i
$584$	4.09894	+	7.09956i	0.169615	+	0.293782i
$585$		0			0
$586$	2.35464	−	4.07836i	0.0972694	−	0.168476i
$587$	−32.4983			−1.34135			−0.670674	−	0.741752i	$-0.733995\pi$
$587$	−32.4983			−1.34135			−0.670674	+	0.741752i	$0.733995\pi$
$588$		0			0
$589$	4.91545			0.202538
$590$	−3.45081	+	5.97697i	−0.142067	+	0.246068i
$591$		0			0
$592$	−6.89766	−	11.9471i	−0.283492	−	0.491023i
$593$	−7.77361	+	13.4643i	−0.319224	+	0.552912i	−0.980326	−	0.197384i	$-0.936755\pi$
$593$	−7.77361	+	13.4643i	−0.319224	+	0.552912i	0.661103	+	0.750296i	$0.270089\pi$
$594$		0			0
$595$	−28.1232	+	3.45807i	−1.15294	+	0.141767i
$596$	−37.1624			−1.52223
$597$		0			0
$598$	−0.177579	−	0.307577i	−0.00726176	−	0.0125777i
$599$	11.9942	+	20.7745i	0.490068	+	0.848822i	0.999935	−	0.0114309i	$-0.00363865\pi$
$599$	11.9942	+	20.7745i	0.490068	+	0.848822i	−0.509867	+	0.860253i	$0.670305\pi$
$600$		0			0
$601$	−0.887066			−0.0361842			−0.0180921	−	0.999836i	$-0.505759\pi$
$601$	−0.887066			−0.0361842			−0.0180921	+	0.999836i	$0.505759\pi$
$602$	1.74792	−	4.11983i	0.0712397	−	0.167912i
$603$		0			0
$604$	5.87946	−	10.1835i	0.239232	−	0.414362i
$605$	2.25031	+	3.89764i	0.0914880	+	0.158462i
$606$		0			0
$607$	5.86030	−	10.1503i	0.237862	−	0.411990i	−0.722238	−	0.691644i	$-0.756887\pi$
$607$	5.86030	−	10.1503i	0.237862	−	0.411990i	0.960101	+	0.279655i	$0.0902199\pi$
$608$	−6.81476			−0.276375
$609$		0			0
$610$	5.46075			0.221099
$611$	−6.92245	+	11.9900i	−0.280052	+	0.485065i
$612$		0			0
$613$	4.83845	+	8.38044i	0.195423	+	0.338483i	0.947039	−	0.321118i	$-0.104059\pi$
$613$	4.83845	+	8.38044i	0.195423	+	0.338483i	−0.751616	+	0.659601i	$0.770725\pi$
$614$	2.03796	−	3.52985i	0.0822454	−	0.142453i
$615$		0			0
$616$	−8.62913	−	11.4471i	−0.347678	−	0.461216i
$617$	9.29027			0.374012			0.187006	−	0.982359i	$-0.440122\pi$
$617$	9.29027			0.374012			0.187006	+	0.982359i	$0.440122\pi$
$618$		0			0
$619$	15.1348	+	26.2142i	0.608319	+	1.05364i	0.991518	+	0.129973i	$0.0414890\pi$
$619$	15.1348	+	26.2142i	0.608319	+	1.05364i	−0.383199	+	0.923666i	$0.625178\pi$
$620$	3.87968	+	6.71980i	0.155812	+	0.269874i
$621$		0			0
$622$	1.77496			0.0711692
$623$	−0.823212	+	1.94031i	−0.0329813	+	0.0777367i
$624$		0			0
$625$	0.612415	−	1.06073i	0.0244966	−	0.0424294i
$626$	−1.34429	−	2.32838i	−0.0537288	−	0.0930609i
$627$		0			0
$628$	−6.04427	+	10.4690i	−0.241193	+	0.417758i
$629$	32.6314			1.30110
$630$		0			0
$631$	30.5921			1.21785			0.608926	−	0.793227i	$-0.291600\pi$
$631$	30.5921			1.21785			0.608926	+	0.793227i	$0.291600\pi$
$632$	0.190240	−	0.329506i	0.00756735	−	0.0131070i
$633$		0			0
$634$	1.35887	+	2.35363i	0.0539675	+	0.0934745i
$635$	−11.4934	+	19.9071i	−0.456101	+	0.789990i
$636$		0			0
$637$	12.6388	−	3.15590i	0.500769	−	0.125041i
$638$	−12.2397			−0.484575
$639$		0			0
$640$	−7.06687	−	12.2402i	−0.279343	−	0.483836i
$641$	16.4438	+	28.4815i	0.649491	+	1.12495i	0.983245	+	0.182292i	$0.0583515\pi$
$641$	16.4438	+	28.4815i	0.649491	+	1.12495i	−0.333753	+	0.942661i	$0.608315\pi$
$642$		0			0
$643$	5.37197			0.211850			0.105925	−	0.994374i	$-0.466220\pi$
$643$	5.37197			0.211850			0.105925	+	0.994374i	$0.466220\pi$
$644$	−2.50141	+	0.307577i	−0.0985692	+	0.0121202i
$645$		0			0
$646$	2.35371	−	4.07675i	0.0926056	−	0.160398i
$647$	6.93041	+	12.0038i	0.272463	+	0.471919i	0.969492	−	0.245124i	$-0.0788285\pi$
$647$	6.93041	+	12.0038i	0.272463	+	0.471919i	−0.697029	+	0.717043i	$0.745495\pi$
$648$		0			0
$649$	−24.5071	+	42.4476i	−0.961988	+	1.66621i
$650$	−2.06737			−0.0810890
$651$		0			0
$652$	35.7916			1.40171
$653$	16.6370	−	28.8161i	0.651056	−	1.12766i	−0.331812	−	0.943346i	$-0.607660\pi$
$653$	16.6370	−	28.8161i	0.651056	−	1.12766i	0.982867	−	0.184316i	$-0.0590069\pi$
$654$		0			0
$655$	−9.68108	−	16.7681i	−0.378271	−	0.655184i
$656$	10.8943	−	18.8695i	0.425352	−	0.736732i
$657$		0			0
$658$	−4.41762	−	5.86025i	−0.172217	−	0.228456i
$659$	−12.7890			−0.498189			−0.249094	−	0.968479i	$-0.580133\pi$
$659$	−12.7890			−0.498189			−0.249094	+	0.968479i	$0.580133\pi$
$660$		0			0
$661$	−20.5502	−	35.5940i	−0.799309	−	1.38444i	−0.920066	−	0.391762i	$-0.871866\pi$
$661$	−20.5502	−	35.5940i	−0.799309	−	1.38444i	0.120757	−	0.992682i	$-0.461468\pi$
$662$	0.227271	+	0.393644i	0.00883312	+	0.0152994i
$663$		0			0
$664$	11.3731			0.441363
$665$	−3.79356	−	5.03240i	−0.147108	−	0.195148i
$666$		0			0
$667$	−2.23221	+	3.86630i	−0.0864316	+	0.149704i
$668$	9.65595	+	16.7246i	0.373600	+	0.647094i
$669$		0			0
$670$	1.72673	−	2.99078i	0.0667093	−	0.115544i
$671$	38.7814			1.49714
$672$		0			0
$673$	28.6891			1.10589			0.552943	−	0.833219i	$-0.313505\pi$
$673$	28.6891			1.10589			0.552943	+	0.833219i	$0.313505\pi$
$674$	2.78030	−	4.81563i	0.107093	−	0.185491i
$675$		0			0
$676$	−8.87386	−	15.3700i	−0.341302	−	0.591153i
$677$	24.7561	−	42.8788i	0.951454	−	1.64797i	0.209173	−	0.977879i	$-0.432923\pi$
$677$	24.7561	−	42.8788i	0.951454	−	1.64797i	0.742281	−	0.670088i	$-0.233744\pi$
$678$		0			0
$679$	−33.8225	+	4.15886i	−1.29799	+	0.159603i
$680$	15.4170			0.591217
$681$		0			0
$682$	−2.05817	−	3.56486i	−0.0788115	−	0.136506i
$683$	−16.2536	−	28.1520i	−0.621926	−	1.07721i	−0.989127	−	0.147065i	$-0.953017\pi$
$683$	−16.2536	−	28.1520i	−0.621926	−	1.07721i	0.367201	−	0.930142i	$-0.380316\pi$
$684$		0			0
$685$	9.25618			0.353661
$686$	−1.07664	+	6.82074i	−0.0411065	+	0.260417i
$687$		0			0
$688$	7.22529	−	12.5146i	0.275462	−	0.477114i
$689$	−0.774984	−	1.34231i	−0.0295245	−	0.0511380i
$690$		0			0
$691$	7.08644	−	12.2741i	0.269581	−	0.466928i	−0.699173	−	0.714953i	$-0.746448\pi$
$691$	7.08644	−	12.2741i	0.269581	−	0.466928i	0.968754	+	0.248025i	$0.0797815\pi$
$692$	−24.6024			−0.935244
$693$		0			0
$694$	1.92324			0.0730053
$695$	−12.7270	+	22.0438i	−0.482762	+	0.836167i
$696$		0			0
$697$	25.7695	+	44.6340i	0.976088	+	1.69063i
$698$	4.55817	−	7.89498i	0.172529	−	0.298829i
$699$		0			0
$700$	−5.72979	+	13.5051i	−0.216566	+	0.510444i
$701$	−28.1485			−1.06316			−0.531578	−	0.847010i	$-0.678401\pi$
$701$	−28.1485			−1.06316			−0.531578	+	0.847010i	$0.678401\pi$
$702$		0			0
$703$	3.62883	+	6.28532i	0.136864	+	0.237055i
$704$	−9.13520	−	15.8226i	−0.344296	−	0.596338i
$705$		0			0
$706$	−5.55893			−0.209213
$707$	−20.4789	−	27.1666i	−0.770189	−	1.02170i
$708$		0			0
$709$	−12.2335	+	21.1890i	−0.459438	+	0.795769i	−0.998931	−	0.0462204i	$-0.985282\pi$
$709$	−12.2335	+	21.1890i	−0.459438	+	0.795769i	0.539494	+	0.841990i	$0.318616\pi$
$710$	1.09136	+	1.89029i	0.0409581	+	0.0709415i
$711$		0			0
$712$	0.573403	−	0.993163i	0.0214892	−	0.0372204i
$713$	−1.50143			−0.0562291
$714$		0			0
$715$	9.95629			0.372344
$716$	10.6959	−	18.5259i	0.399725	−	0.692345i
$717$		0			0
$718$	−0.400399	−	0.693511i	−0.0149428	−	0.0258816i
$719$	8.27732	−	14.3367i	0.308692	−	0.534670i	−0.669385	−	0.742916i	$-0.733442\pi$
$719$	8.27732	−	14.3367i	0.308692	−	0.534670i	0.978076	+	0.208246i	$0.0667755\pi$
$720$		0			0
$721$	20.4148	−	48.1175i	0.760285	−	1.79199i
$722$	−6.03707			−0.224676
$723$		0			0
$724$	−12.7515	−	22.0862i	−0.473905	−	0.820828i
$725$	12.9937	+	22.5057i	0.482572	+	0.835840i
$726$		0			0
$727$	−34.2381			−1.26982			−0.634911	−	0.772586i	$-0.718963\pi$
$727$	−34.2381			−1.26982			−0.634911	+	0.772586i	$0.718963\pi$
$728$	−7.03495	+	0.865027i	−0.260732	+	0.0320600i
$729$		0			0
$730$	1.50904	−	2.61373i	0.0558520	−	0.0967384i
$731$	17.0907	+	29.6020i	0.632122	+	1.09487i
$732$		0			0
$733$	6.14445	−	10.6425i	0.226951	−	0.393090i	−0.729952	−	0.683498i	$-0.760458\pi$
$733$	6.14445	−	10.6425i	0.226951	−	0.393090i	0.956903	+	0.290408i	$0.0937911\pi$
$734$	−5.91370			−0.218279
$735$		0			0
$736$	2.08158			0.0767281
$737$	12.2630	−	21.2401i	0.451712	−	0.782388i
$738$		0			0
$739$	21.6496	+	37.4982i	0.796394	+	1.37939i	0.921950	+	0.387308i	$0.126595\pi$
$739$	21.6496	+	37.4982i	0.796394	+	1.37939i	−0.125557	+	0.992086i	$0.540072\pi$
$740$	−5.72835	+	9.92179i	−0.210578	+	0.364732i
$741$		0			0
$742$	0.815453	−	0.100269i	0.0299362	−	0.00368100i
$743$	23.9478			0.878561			0.439281	−	0.898350i	$-0.355233\pi$
$743$	23.9478			0.878561			0.439281	+	0.898350i	$0.355233\pi$
$744$		0			0
$745$	14.1925	+	24.5821i	0.519971	+	0.900617i
$746$	−2.18802	−	3.78975i	−0.0801089	−	0.138753i
$747$		0			0
$748$	52.7737			1.92960
$749$	7.47175	−	17.6109i	0.273012	−	0.643487i
$750$		0			0
$751$	1.45149	−	2.51405i	0.0529656	−	0.0917391i	−0.838327	−	0.545168i	$-0.816466\pi$
$751$	1.45149	−	2.51405i	0.0529656	−	0.0917391i	0.891293	+	0.453429i	$0.149799\pi$
$752$	−11.8484	−	20.5220i	−0.432066	−	0.748361i
$753$		0			0
$754$	−3.02592	+	5.24104i	−0.110197	+	0.190867i
$755$	−8.98156			−0.326872
$756$		0			0
$757$	−8.99407			−0.326895			−0.163448	−	0.986552i	$-0.552261\pi$
$757$	−8.99407			−0.326895			−0.163448	+	0.986552i	$0.552261\pi$
$758$	−3.53086	+	6.11562i	−0.128246	+	0.222129i
$759$		0			0
$760$	1.71448	+	2.96956i	0.0621906	+	0.107717i
$761$	−19.0254	+	32.9530i	−0.689672	+	1.19455i	0.282272	+	0.959334i	$0.408912\pi$
$761$	−19.0254	+	32.9530i	−0.689672	+	1.19455i	−0.971944	+	0.235212i	$0.924421\pi$
$762$		0			0
$763$	−15.5570	−	20.6374i	−0.563203	−	0.747124i
$764$	−14.4102			−0.521344
$765$		0			0
$766$	5.53325	+	9.58386i	0.199924	+	0.346279i
$767$	12.1174	+	20.9879i	0.437532	+	0.757828i
$768$		0			0
$769$	22.8131			0.822660			0.411330	−	0.911486i	$-0.365064\pi$
$769$	22.8131			0.822660			0.411330	+	0.911486i	$0.365064\pi$
$770$	−2.06126	+	4.85837i	−0.0742825	+	0.175083i
$771$		0			0
$772$	14.7204	−	25.4965i	0.529800	−	0.917640i
$773$	−3.06443	−	5.30775i	−0.110220	−	0.190906i	0.805639	−	0.592407i	$-0.201822\pi$
$773$	−3.06443	−	5.30775i	−0.110220	−	0.190906i	−0.915859	+	0.401500i	$0.868489\pi$
$774$		0			0
$775$	−4.36991	+	7.56890i	−0.156972	+	0.271883i
$776$	18.5414			0.665597
$777$		0			0
$778$	0.476566			0.0170857
$779$	−5.73147	+	9.92720i	−0.205351	+	0.355679i
$780$		0			0
$781$	7.75069	+	13.4246i	0.277341	+	0.480369i
$782$	−0.718946	+	1.24525i	−0.0257095	+	0.0445301i
$783$		0			0
$784$	−6.13833	+	21.4351i	−0.219226	+	0.765539i
$785$	9.23332			0.329551
$786$		0			0
$787$	23.2314	+	40.2379i	0.828109	+	1.43433i	0.899520	+	0.436879i	$0.143916\pi$
$787$	23.2314	+	40.2379i	0.828109	+	1.43433i	−0.0714114	+	0.997447i	$0.522750\pi$
$788$	3.39599	+	5.88202i	0.120977	+	0.209538i
$789$		0			0
$790$	−0.140075			−0.00498365
$791$	−44.3979	+	5.45923i	−1.57861	+	0.194108i
$792$		0			0
$793$	9.58760	−	16.6062i	0.340465	−	0.589704i
$794$	1.19957	+	2.07771i	0.0425711	+	0.0737353i
$795$		0			0
$796$	−19.2764	+	33.3878i	−0.683235	+	1.18340i
$797$	7.63879			0.270580			0.135290	−	0.990806i	$-0.456803\pi$
$797$	7.63879			0.270580			0.135290	+	0.990806i	$0.456803\pi$
$798$		0			0
$799$	56.0523			1.98299
$800$	6.05842	−	10.4935i	0.214198	−	0.371001i
$801$		0			0
$802$	5.16223	+	8.94125i	0.182285	+	0.315727i
$803$	10.7170	−	18.5623i	0.378193	−	0.655050i
$804$		0			0
$805$	1.15875	+	1.53716i	0.0408406	+	0.0541777i
$806$	−2.03530			−0.0716903
$807$		0			0
$808$	9.25533	+	16.0307i	0.325601	+	0.563958i
$809$	−13.8316	−	23.9570i	−0.486293	−	0.842285i	0.513582	−	0.858040i	$-0.328318\pi$
$809$	−13.8316	−	23.9570i	−0.486293	−	0.842285i	−0.999876	+	0.0157553i	$0.994985\pi$
$810$		0			0
$811$	−34.0746			−1.19652			−0.598261	−	0.801301i	$-0.704141\pi$
$811$	−34.0746			−1.19652			−0.598261	+	0.801301i	$0.704141\pi$
$812$	25.8506	+	34.2924i	0.907178	+	1.20343i
$813$		0			0
$814$	3.03889	−	5.26352i	0.106513	−	0.184486i
$815$	−13.6690	−	23.6753i	−0.478803	−	0.829311i
$816$		0			0
$817$	−3.80120	+	6.58387i	−0.132987	+	0.230340i
$818$	−4.48430			−0.156790
$819$		0			0
$820$	−18.0950			−0.631905
$821$	−3.63723	+	6.29987i	−0.126940	+	0.219867i	−0.922490	−	0.386022i	$-0.873849\pi$
$821$	−3.63723	+	6.29987i	−0.126940	+	0.219867i	0.795549	+	0.605889i	$0.207182\pi$
$822$		0			0
$823$	2.83101	+	4.90345i	0.0986828	+	0.170924i	0.911140	−	0.412098i	$-0.135204\pi$
$823$	2.83101	+	4.90345i	0.0986828	+	0.170924i	−0.812457	+	0.583021i	$0.801870\pi$
$824$	−14.2198	+	24.6294i	−0.495369	+	0.858005i
$825$		0			0
$826$	−12.7501	+	1.56777i	−0.443633	+	0.0545498i
$827$	35.3143			1.22800			0.614000	−	0.789306i	$-0.289560\pi$
$827$	35.3143			1.22800			0.614000	+	0.789306i	$0.289560\pi$
$828$		0			0
$829$	−14.8684	−	25.7529i	−0.516402	−	0.894434i	−0.999819	−	0.0190438i	$-0.993938\pi$
$829$	−14.8684	−	25.7529i	−0.516402	−	0.894434i	0.483417	−	0.875390i	$-0.339396\pi$
$830$	−2.09353	−	3.62609i	−0.0726673	−	0.125864i
$831$		0			0
$832$	−9.03366			−0.313186
$833$	−36.6499	−	37.9256i	−1.26984	−	1.31405i
$834$		0			0
$835$	7.37529	−	12.7744i	0.255232	−	0.442075i
$836$	5.86879	+	10.1650i	0.202976	+	0.351565i
$837$		0			0
$838$	−3.35915	+	5.81822i	−0.116040	+	0.200987i
$839$	5.25058			0.181270			0.0906351	−	0.995884i	$-0.471110\pi$
$839$	5.25058			0.181270			0.0906351	+	0.995884i	$0.471110\pi$
$840$		0			0
$841$	47.0728			1.62320
$842$	3.21714	−	5.57225i	0.110870	−	0.192032i
$843$		0			0
$844$	18.4739	+	31.9978i	0.635899	+	1.10141i
$845$	−6.77792	+	11.7397i	−0.233168	+	0.403858i
$846$		0			0
$847$	−3.27185	+	7.71173i	−0.112422	+	0.264978i
$848$	2.65291			0.0911012
$849$		0			0
$850$	4.18497	+	7.24858i	0.143543	+	0.248624i
$851$	−1.10843	−	1.91986i	−0.0379966	−	0.0658121i
$852$		0			0
$853$	22.4915			0.770096			0.385048	−	0.922897i	$-0.374185\pi$
$853$	22.4915			0.770096			0.385048	+	0.922897i	$0.374185\pi$
$854$	6.11840	+	8.11645i	0.209367	+	0.277739i
$855$		0			0
$856$	−5.20440	+	9.01429i	−0.177883	+	0.308102i
$857$	27.6478	+	47.8874i	0.944432	+	1.63580i	0.756885	+	0.653548i	$0.226720\pi$
$857$	27.6478	+	47.8874i	0.944432	+	1.63580i	0.187546	+	0.982256i	$0.439947\pi$
$858$		0			0
$859$	−25.6352	+	44.4015i	−0.874662	+	1.51496i	−0.0175392	+	0.999846i	$0.505583\pi$
$859$	−25.6352	+	44.4015i	−0.874662	+	1.51496i	−0.857123	+	0.515112i	$0.827750\pi$
$860$	−12.0009			−0.409227
$861$		0			0
$862$	−3.19430			−0.108798
$863$	14.5908	−	25.2719i	0.496675	−	0.860267i	−0.503317	−	0.864102i	$-0.667887\pi$
$863$	14.5908	−	25.2719i	0.496675	−	0.860267i	0.999993	+	0.00383494i	$0.00122070\pi$
$864$		0			0
$865$	9.39576	+	16.2739i	0.319466	+	0.553330i
$866$	−0.296359	+	0.513308i	−0.0100707	+	0.0174429i
$867$		0			0
$868$	−5.64089	+	13.2955i	−0.191464	+	0.451280i
$869$	−0.994792			−0.0337460
$870$		0			0
$871$	−6.06333	−	10.5020i	−0.205448	−	0.355846i
$872$	7.03091	+	12.1779i	0.238097	+	0.412396i
$873$		0			0
$874$	−0.319806			−0.0108176
$875$	29.7848	−	3.66238i	1.00691	−	0.123811i
$876$		0			0
$877$	−8.98026	+	15.5543i	−0.303242	+	0.525230i	−0.976868	−	0.213842i	$-0.931402\pi$
$877$	−8.98026	+	15.5543i	−0.303242	+	0.525230i	0.673626	+	0.739072i	$0.264736\pi$
$878$	−4.18400	−	7.24690i	−0.141203	−	0.244571i
$879$		0			0
$880$	−8.52053	+	14.7580i	−0.287227	+	0.497492i
$881$	−45.7619			−1.54176			−0.770880	−	0.636981i	$-0.780183\pi$
$881$	−45.7619			−1.54176			−0.770880	+	0.636981i	$0.780183\pi$
$882$		0			0
$883$	40.8060			1.37323			0.686615	−	0.727021i	$-0.259096\pi$
$883$	40.8060			1.37323			0.686615	+	0.727021i	$0.259096\pi$
$884$	13.0468	−	22.5977i	0.438811	−	0.760042i
$885$		0			0
$886$	−4.53399	−	7.85310i	−0.152322	−	0.263830i
$887$	−19.4341	+	33.6609i	−0.652535	+	1.13022i	0.329971	+	0.943991i	$0.392961\pi$
$887$	−19.4341	+	33.6609i	−0.652535	+	1.13022i	−0.982506	+	0.186232i	$0.940372\pi$
$888$		0			0
$889$	−42.4660	+	5.22168i	−1.42426	+	0.175130i
$890$	−0.422200			−0.0141522
$891$		0			0
$892$	14.9549	+	25.9026i	0.500726	+	0.867283i
$893$	6.23339	+	10.7966i	0.208592	+	0.361293i
$894$		0			0
$895$	−16.3392			−0.546161
$896$	10.2749	−	24.2179i	0.343261	−	0.809065i
$897$		0			0
$898$	2.40515	−	4.16585i	0.0802610	−	0.139016i
$899$	12.7921	+	22.1565i	0.426639	+	0.738960i
$900$		0			0
$901$	−3.13759	+	5.43447i	−0.104528	+	0.181048i
$902$	9.59941			0.319626
$903$		0			0
$904$	24.3388			0.809497
$905$	−9.73968	+	16.8696i	−0.323758	+	0.560765i
$906$		0			0
$907$	14.0285	+	24.2981i	0.465809	+	0.806804i	0.999238	−	0.0390407i	$-0.0124302\pi$
$907$	14.0285	+	24.2981i	0.465809	+	0.806804i	−0.533429	+	0.845845i	$0.679097\pi$
$908$	−0.798126	+	1.38239i	−0.0264867	+	0.0458764i
$909$		0			0
$910$	1.57077	+	2.08372i	0.0520704	+	0.0690747i
$911$	12.3839			0.410296			0.205148	−	0.978731i	$-0.434232\pi$
$911$	12.3839			0.410296			0.205148	+	0.978731i	$0.434232\pi$
$912$		0			0
$913$	−14.8679	−	25.7520i	−0.492056	−	0.852266i
$914$	−0.221426	−	0.383520i	−0.00732411	−	0.0126857i
$915$		0			0
$916$	−10.7115			−0.353919
$917$	14.0759	−	33.1767i	0.464826	−	1.09559i
$918$		0			0
$919$	27.3029	−	47.2901i	0.900641	−	1.55996i	0.0739762	−	0.997260i	$-0.476431\pi$
$919$	27.3029	−	47.2901i	0.900641	−	1.55996i	0.826664	−	0.562695i	$-0.190236\pi$
$920$	−0.523690	−	0.907059i	−0.0172656	−	0.0299048i
$921$		0			0
$922$	3.01397	−	5.22035i	0.0992598	−	0.171923i
$923$	7.66454			0.252281
$924$		0			0
$925$	−12.9043			−0.424292
$926$	0.0990144	−	0.171498i	0.00325381	−	0.00563577i
$927$		0			0
$928$	−17.7348	−	30.7177i	−0.582175	−	1.00836i
$929$	6.40356	−	11.0913i	0.210094	−	0.363894i	−0.741650	−	0.670787i	$-0.765956\pi$
$929$	6.40356	−	11.0913i	0.210094	−	0.363894i	0.951744	+	0.306894i	$0.0992896\pi$
$930$		0			0
$931$	3.22935	−	11.2769i	0.105838	−	0.369586i
$932$	13.7501			0.450399
$933$		0			0
$934$	−4.00412	−	6.93534i	−0.131019	−	0.226931i
$935$	−20.1545	−	34.9086i	−0.659121	−	1.14163i
$936$		0			0
$937$	37.9601			1.24010			0.620051	−	0.784562i	$-0.287112\pi$
$937$	37.9601			1.24010			0.620051	+	0.784562i	$0.287112\pi$
$938$	6.37995	−	0.784488i	0.208313	−	0.0256144i
$939$		0			0
$940$	−9.83981	+	17.0431i	−0.320939	+	0.555883i
$941$	−9.13487	−	15.8221i	−0.297788	−	0.515784i	0.677841	−	0.735208i	$-0.262916\pi$
$941$	−9.13487	−	15.8221i	−0.297788	−	0.515784i	−0.975630	+	0.219424i	$0.929582\pi$
$942$		0			0
$943$	1.75069	−	3.03228i	0.0570103	−	0.0987447i
$944$	−41.4798			−1.35005
$945$		0			0
$946$	6.36648			0.206992
$947$	−20.7760	+	35.9850i	−0.675128	+	1.16936i	0.301303	+	0.953528i	$0.402578\pi$
$947$	−20.7760	+	35.9850i	−0.675128	+	1.16936i	−0.976431	+	0.215828i	$0.930755\pi$
$948$		0			0
$949$	−5.29892	−	9.17799i	−0.172010	−	0.297930i
$950$	−0.930793	+	1.61218i	−0.0301989	+	0.0523061i
$951$		0			0
$952$	17.2737	+	22.9147i	0.559845	+	0.742670i
$953$	−26.0298			−0.843186			−0.421593	−	0.906785i	$-0.638529\pi$
$953$	−26.0298			−0.843186			−0.421593	+	0.906785i	$0.638529\pi$
$954$		0			0
$955$	5.50332	+	9.53203i	0.178083	+	0.308449i
$956$	−12.8418	−	22.2426i	−0.415332	−	0.719377i
$957$		0			0
$958$	10.5713			0.341542
$959$	10.3709	+	13.7577i	0.334895	+	0.444259i
$960$		0			0
$961$	11.1979	−	19.3953i	0.361222	−	0.625655i
$962$	−1.50256	−	2.60251i	−0.0484444	−	0.0839082i
$963$		0			0
$964$	−18.3827	+	31.8397i	−0.592066	+	1.02549i
$965$	−22.4871			−0.723887
$966$		0			0
$967$	−14.6507			−0.471135			−0.235567	−	0.971858i	$-0.575695\pi$
$967$	−14.6507			−0.471135			−0.235567	+	0.971858i	$0.575695\pi$
$968$	2.27899	−	3.94732i	0.0732494	−	0.126872i
$969$		0			0
$970$	−3.41304	−	5.91156i	−0.109586	−	0.189809i
$971$	19.5007	−	33.7762i	0.625808	−	1.08393i	−0.362576	−	0.931954i	$-0.618103\pi$
$971$	19.5007	−	33.7762i	0.625808	−	1.08393i	0.988384	−	0.151977i	$-0.0485639\pi$
$972$		0			0
$973$	−47.0239	+	5.78213i	−1.50752	+	0.185366i
$974$	2.93439			0.0940239
$975$		0			0
$976$	16.4100	+	28.4230i	0.525272	+	0.909797i
$977$	9.55342	+	16.5470i	0.305641	+	0.529386i	0.977404	−	0.211380i	$-0.0677959\pi$
$977$	9.55342	+	16.5470i	0.305641	+	0.529386i	−0.671763	+	0.740766i	$0.734463\pi$
$978$		0			0
$979$	−2.99840			−0.0958294
$980$	17.9653	−	4.48591i	0.573881	−	0.143297i
$981$		0			0
$982$	−5.27918	+	9.14381i	−0.168465	+	0.291791i
$983$	6.44387	+	11.1611i	0.205527	+	0.355984i	0.950301	−	0.311334i	$-0.100776\pi$
$983$	6.44387	+	11.1611i	0.205527	+	0.355984i	−0.744773	+	0.667318i	$0.767442\pi$
$984$		0			0
$985$	2.59388	−	4.49273i	0.0826479	−	0.143150i
$986$	24.5014			0.780283
$987$		0			0
$988$	5.80355			0.184636
$989$	1.16108	−	2.01106i	0.0369203	−	0.0639479i
$990$		0			0
$991$	1.48644	+	2.57459i	0.0472184	+	0.0817846i	0.888669	−	0.458550i	$-0.151631\pi$
$991$	1.48644	+	2.57459i	0.0472184	+	0.0817846i	−0.841450	+	0.540335i	$0.818298\pi$
$992$	5.96442	−	10.3307i	0.189371	−	0.327999i
$993$		0			0
$994$	−1.58679	+	3.74006i	−0.0503300	+	0.118628i
$995$	29.4470			0.933532
$996$		0			0
$997$	−6.83444	−	11.8376i	−0.216449	−	0.374900i	0.737271	−	0.675597i	$-0.236114\pi$
$997$	−6.83444	−	11.8376i	−0.216449	−	0.374900i	−0.953720	+	0.300697i	$0.902781\pi$
$998$	−1.27548	−	2.20920i	−0.0403746	−	0.0699309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.d.163.2	yes	8
3.2	odd	2		567.2.e.c.163.3	✓	8
7.2	even	3		3969.2.a.s.1.3		4
7.4	even	3	inner	567.2.e.d.487.2	yes	8
7.5	odd	6		3969.2.a.t.1.3		4
9.2	odd	6		567.2.h.k.352.2		8
9.4	even	3		567.2.g.k.541.2		8
9.5	odd	6		567.2.g.j.541.3		8
9.7	even	3		567.2.h.j.352.3		8
21.2	odd	6		3969.2.a.x.1.2		4
21.5	even	6		3969.2.a.w.1.2		4
21.11	odd	6		567.2.e.c.487.3	yes	8
63.4	even	3		567.2.h.j.298.3		8
63.11	odd	6		567.2.g.j.109.3		8
63.25	even	3		567.2.g.k.109.2		8
63.32	odd	6		567.2.h.k.298.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.3	✓	8	3.2	odd	2
567.2.e.c.487.3	yes	8	21.11	odd	6
567.2.e.d.163.2	yes	8	1.1	even	1	trivial
567.2.e.d.487.2	yes	8	7.4	even	3	inner
567.2.g.j.109.3		8	63.11	odd	6
567.2.g.j.541.3		8	9.5	odd	6
567.2.g.k.109.2		8	63.25	even	3
567.2.g.k.541.2		8	9.4	even	3
567.2.h.j.298.3		8	63.4	even	3
567.2.h.j.352.3		8	9.7	even	3
567.2.h.k.298.2		8	63.32	odd	6
567.2.h.k.352.2		8	9.2	odd	6
3969.2.a.s.1.3		4	7.2	even	3
3969.2.a.t.1.3		4	7.5	odd	6
3969.2.a.w.1.2		4	21.5	even	6
3969.2.a.x.1.2		4	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.186423 + 0.322894i) q^{2} +(0.930493 + 1.61166i) q^{4} +(0.710717 - 1.23100i) q^{5} +(2.62597 - 0.322894i) q^{7} -1.43955 q^{8} +(0.264988 + 0.458972i) q^{10} +(1.88190 + 3.25955i) q^{11} +1.86099 q^{13} +(-0.385281 + 0.908105i) q^{14} +(-1.59262 + 2.75850i) q^{16} +(-3.76718 - 6.52496i) q^{17} +(0.837872 - 1.45124i) q^{19} +2.64527 q^{20} -1.40332 q^{22} +(-0.255930 + 0.443283i) q^{23} +(1.48976 + 2.58034i) q^{25} +(-0.346930 + 0.600901i) q^{26} +(2.96385 + 3.93173i) q^{28} +8.72197 q^{29} +(1.46665 + 2.54031i) q^{31} +(-2.03335 - 3.52187i) q^{32} +2.80916 q^{34} +(1.46884 - 3.46206i) q^{35} +(-2.16551 + 3.75077i) q^{37} +(0.312397 + 0.541087i) q^{38} +(-1.02311 + 1.77209i) q^{40} -6.84051 q^{41} -4.53673 q^{43} +(-3.50220 + 6.06598i) q^{44} +(-0.0954222 - 0.165276i) q^{46} +(-3.71978 + 6.44284i) q^{47} +(6.79148 - 1.69582i) q^{49} -1.11090 q^{50} +(1.73163 + 2.99928i) q^{52} +(-0.416437 - 0.721290i) q^{53} +5.35001 q^{55} +(-3.78022 + 0.464822i) q^{56} +(-1.62597 + 2.81627i) q^{58} +(6.51126 + 11.2778i) q^{59} +(5.15189 - 8.92333i) q^{61} -1.09367 q^{62} -4.85423 q^{64} +(1.32264 - 2.29087i) q^{65} +(-3.25813 - 5.64324i) q^{67} +(7.01068 - 12.1429i) q^{68} +(0.844050 + 1.11969i) q^{70} +4.11854 q^{71} +(-2.84737 - 4.93179i) q^{73} +(-0.807399 - 1.39846i) q^{74} +3.11854 q^{76} +(5.99432 + 7.95185i) q^{77} +(-0.132152 + 0.228895i) q^{79} +(2.26381 + 3.92103i) q^{80} +(1.27523 - 2.20876i) q^{82} -7.90046 q^{83} -10.7096 q^{85} +(0.845750 - 1.46488i) q^{86} +(-2.70910 - 4.69229i) q^{88} +(-0.398321 + 0.689912i) q^{89} +(4.88690 - 0.600901i) q^{91} -0.952563 q^{92} +(-1.38690 - 2.40218i) q^{94} +(-1.19098 - 2.06284i) q^{95} -12.8800 q^{97} +(-0.718516 + 2.50907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} - 10 q^{13} + 23 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} + 16 q^{20} - 14 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} + 20 q^{29}+ \cdots - 11 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 - 10 * q^13 + 23 * q^14 + q^16 + 6 * q^17 + 8 * q^19 + 16 * q^20 - 14 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 + 20 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 + 10 * q^41 - 14 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 17 * q^49 - 76 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 - 39 * q^56 + 7 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 + 51 * q^68 + 17 * q^70 + 18 * q^71 + 6 * q^73 + 10 * q^76 + 37 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 - 18 * q^83 - 18 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 + 72 * q^92 + 15 * q^94 - 16 * q^95 - 18 * q^97 - 11 * q^98

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