LMFDB - Embedded newform 572.2.i.c.133.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 $ x^10 - x^9 + 9x^8 + 6x^7 + 59x^6 + 2x^5 + 47x^4 - 26x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.4
Root			$0.334488 + 0.579350i$ of defining polynomial
Character	$\chi$	$=$	572.133
Dual form			572.2.i.c.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.334488 + 0.579350i) q^{3} -4.07313 q^{5} +(-0.950388 + 1.64612i) q^{7} +(1.27624 - 2.21051i) q^{9} +O(q^{10})$	\(q+(0.334488 + 0.579350i) q^{3} -4.07313 q^{5} +(-0.950388 + 1.64612i) q^{7} +(1.27624 - 2.21051i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(3.16717 - 1.72308i) q^{13} +(-1.36241 - 2.35976i) q^{15} +(1.91549 - 3.31772i) q^{17} +(2.09481 - 3.62833i) q^{19} -1.27157 q^{21} +(-2.68099 - 4.64361i) q^{23} +11.5904 q^{25} +3.71447 q^{27} +(-3.05991 - 5.29992i) q^{29} -7.32221 q^{31} +(0.334488 - 0.579350i) q^{33} +(3.87105 - 6.70486i) q^{35} +(-0.945211 - 1.63715i) q^{37} +(2.05765 + 1.25855i) q^{39} +(-1.24651 - 2.15902i) q^{41} +(-3.53656 + 6.12551i) q^{43} +(-5.19827 + 9.00367i) q^{45} +7.24205 q^{47} +(1.69352 + 2.93327i) q^{49} +2.56283 q^{51} -8.63012 q^{53} +(2.03656 + 3.52743i) q^{55} +2.80276 q^{57} +(-4.87271 + 8.43978i) q^{59} +(3.70208 - 6.41218i) q^{61} +(2.42584 + 4.20168i) q^{63} +(-12.9003 + 7.01834i) q^{65} +(-2.78218 - 4.81888i) q^{67} +(1.79352 - 3.10646i) q^{69} +(2.31678 - 4.01277i) q^{71} -1.84836 q^{73} +(3.87683 + 6.71487i) q^{75} +1.90078 q^{77} +9.03770 q^{79} +(-2.58626 - 4.47954i) q^{81} +5.28182 q^{83} +(-7.80201 + 13.5135i) q^{85} +(2.04701 - 3.54552i) q^{87} +(-0.677012 - 1.17262i) q^{89} +(-0.173639 + 6.85115i) q^{91} +(-2.44919 - 4.24212i) q^{93} +(-8.53244 + 14.7786i) q^{95} +(6.18176 - 10.7071i) q^{97} -2.55247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$	0.334488	+	0.579350i	0.193117	+	0.334488i	0.946281	−	0.323344i	$-0.104807\pi$
$3$	0.334488	+	0.579350i	0.193117	+	0.334488i	−0.753165	+	0.657832i	$0.771474\pi$
$4$		0			0
$5$	−4.07313			−1.82156			−0.910779	−	0.412895i	$-0.864518\pi$
$5$	−4.07313			−1.82156			−0.910779	+	0.412895i	$0.864518\pi$
$6$		0			0
$7$	−0.950388	+	1.64612i	−0.359213	+	0.622175i	−0.987830	−	0.155540i	$-0.950288\pi$
$7$	−0.950388	+	1.64612i	−0.359213	+	0.622175i	0.628617	+	0.777715i	$0.283622\pi$
$8$		0			0
$9$	1.27624	−	2.21051i	0.425412	−	0.736835i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	3.16717	−	1.72308i	0.878416	−	0.477898i
$13$	3.16717	−	1.72308i	0.878416	−	0.477898i
$14$		0			0
$15$	−1.36241	−	2.35976i	−0.351773	−	0.609289i
$16$		0			0
$17$	1.91549	−	3.31772i	0.464573	−	0.804665i	−0.534609	−	0.845100i	$-0.679541\pi$
$17$	1.91549	−	3.31772i	0.464573	−	0.804665i	0.999182	+	0.0404349i	$0.0128743\pi$
$18$		0			0
$19$	2.09481	−	3.62833i	0.480583	−	0.832395i	−0.519168	−	0.854672i	$-0.673758\pi$
$19$	2.09481	−	3.62833i	0.480583	−	0.832395i	0.999752	+	0.0222770i	$0.00709159\pi$
$20$		0			0
$21$	−1.27157			−0.277480
$22$		0			0
$23$	−2.68099	−	4.64361i	−0.559025	−	0.968260i	−0.997578	−	0.0695543i	$-0.977842\pi$
$23$	−2.68099	−	4.64361i	−0.559025	−	0.968260i	0.438553	−	0.898705i	$-0.355491\pi$
$24$		0			0
$25$	11.5904			2.31807
$26$		0			0
$27$	3.71447			0.714850
$28$		0			0
$29$	−3.05991	−	5.29992i	−0.568211	−	0.984171i	−0.996743	−	0.0806442i	$-0.974302\pi$
$29$	−3.05991	−	5.29992i	−0.568211	−	0.984171i	0.428532	−	0.903527i	$-0.359031\pi$
$30$		0			0
$31$	−7.32221			−1.31511			−0.657554	−	0.753408i	$-0.728409\pi$
$31$	−7.32221			−1.31511			−0.657554	+	0.753408i	$0.728409\pi$
$32$		0			0
$33$	0.334488	−	0.579350i	0.0582268	−	0.100852i
$34$		0			0
$35$	3.87105	−	6.70486i	0.654327	−	1.13333i
$36$		0			0
$37$	−0.945211	−	1.63715i	−0.155392	−	0.269146i	0.777810	−	0.628500i	$-0.216331\pi$
$37$	−0.945211	−	1.63715i	−0.155392	−	0.269146i	−0.933202	+	0.359353i	$0.882997\pi$
$38$		0			0
$39$	2.05765	+	1.25855i	0.329487	+	0.201529i
$40$		0			0
$41$	−1.24651	−	2.15902i	−0.194672	−	0.337182i	0.752121	−	0.659025i	$-0.229031\pi$
$41$	−1.24651	−	2.15902i	−0.194672	−	0.337182i	−0.946793	+	0.321843i	$0.895698\pi$
$42$		0			0
$43$	−3.53656	+	6.12551i	−0.539321	+	0.934131i	0.459620	+	0.888116i	$0.347986\pi$
$43$	−3.53656	+	6.12551i	−0.539321	+	0.934131i	−0.998941	+	0.0460153i	$0.985348\pi$
$44$		0			0
$45$	−5.19827	+	9.00367i	−0.774912	+	1.34219i
$46$		0			0
$47$	7.24205			1.05636			0.528181	−	0.849132i	$-0.322874\pi$
$47$	7.24205			1.05636			0.528181	+	0.849132i	$0.322874\pi$
$48$		0			0
$49$	1.69352	+	2.93327i	0.241932	+	0.419039i
$50$		0			0
$51$	2.56283			0.358867
$52$		0			0
$53$	−8.63012			−1.18544			−0.592719	−	0.805409i	$-0.701946\pi$
$53$	−8.63012			−1.18544			−0.592719	+	0.805409i	$0.701946\pi$
$54$		0			0
$55$	2.03656	+	3.52743i	0.274610	+	0.475639i
$56$		0			0
$57$	2.80276			0.371235
$58$		0			0
$59$	−4.87271	+	8.43978i	−0.634373	+	1.09877i	0.352275	+	0.935897i	$0.385408\pi$
$59$	−4.87271	+	8.43978i	−0.634373	+	1.09877i	−0.986648	+	0.162869i	$0.947925\pi$
$60$		0			0
$61$	3.70208	−	6.41218i	0.474002	−	0.820996i	−0.525555	−	0.850760i	$-0.676142\pi$
$61$	3.70208	−	6.41218i	0.474002	−	0.820996i	0.999557	+	0.0297640i	$0.00947556\pi$
$62$		0			0
$63$	2.42584	+	4.20168i	0.305627	+	0.529361i
$64$		0			0
$65$	−12.9003	+	7.01834i	−1.60008	+	0.870518i
$66$		0			0
$67$	−2.78218	−	4.81888i	−0.339897	−	0.588720i	0.644516	−	0.764591i	$-0.277059\pi$
$67$	−2.78218	−	4.81888i	−0.339897	−	0.588720i	−0.984413	+	0.175871i	$0.943726\pi$
$68$		0			0
$69$	1.79352	−	3.10646i	0.215914	−	0.373974i
$70$		0			0
$71$	2.31678	−	4.01277i	0.274951	−	0.476229i	−0.695172	−	0.718843i	$-0.744672\pi$
$71$	2.31678	−	4.01277i	0.274951	−	0.476229i	0.970123	+	0.242615i	$0.0780051\pi$
$72$		0			0
$73$	−1.84836			−0.216334			−0.108167	−	0.994133i	$-0.534498\pi$
$73$	−1.84836			−0.216334			−0.108167	+	0.994133i	$0.534498\pi$
$74$		0			0
$75$	3.87683	+	6.71487i	0.447658	+	0.775366i
$76$		0			0
$77$	1.90078			0.216614
$78$		0			0
$79$	9.03770			1.01682			0.508410	−	0.861115i	$-0.330233\pi$
$79$	9.03770			1.01682			0.508410	+	0.861115i	$0.330233\pi$
$80$		0			0
$81$	−2.58626	−	4.47954i	−0.287363	−	0.497727i
$82$		0			0
$83$	5.28182			0.579755			0.289877	−	0.957064i	$-0.406385\pi$
$83$	5.28182			0.579755			0.289877	+	0.957064i	$0.406385\pi$
$84$		0			0
$85$	−7.80201	+	13.5135i	−0.846247	+	1.46574i
$86$		0			0
$87$	2.04701	−	3.54552i	0.219462	−	0.380119i
$88$		0			0
$89$	−0.677012	−	1.17262i	−0.0717632	−	0.124297i	0.827911	−	0.560860i	$-0.189529\pi$
$89$	−0.677012	−	1.17262i	−0.0717632	−	0.124297i	−0.899674	+	0.436562i	$0.856196\pi$
$90$		0			0
$91$	−0.173639	+	6.85115i	−0.0182023	+	0.718195i
$92$		0			0
$93$	−2.44919	−	4.24212i	−0.253969	−	0.439887i
$94$		0			0
$95$	−8.53244	+	14.7786i	−0.875410	+	1.51625i
$96$		0			0
$97$	6.18176	−	10.7071i	0.627662	−	1.08714i	−0.360357	−	0.932814i	$-0.617345\pi$
$97$	6.18176	−	10.7071i	0.627662	−	1.08714i	0.988020	−	0.154329i	$-0.0493215\pi$
$98$		0			0
$99$	−2.55247			−0.256533
$100$		0			0
$101$	−4.68385	−	8.11266i	−0.466060	−	0.807240i	0.533188	−	0.845997i	$-0.320994\pi$
$101$	−4.68385	−	8.11266i	−0.466060	−	0.807240i	−0.999249	+	0.0387563i	$0.987660\pi$
$102$		0			0
$103$	12.7367			1.25499			0.627493	−	0.778622i	$-0.284081\pi$
$103$	12.7367			1.25499			0.627493	+	0.778622i	$0.284081\pi$
$104$		0			0
$105$	5.17928			0.505446
$106$		0			0
$107$	−4.84081	−	8.38453i	−0.467979	−	0.810563i	0.531352	−	0.847151i	$-0.321684\pi$
$107$	−4.84081	−	8.38453i	−0.467979	−	0.810563i	−0.999330	+	0.0365883i	$0.988351\pi$
$108$		0			0
$109$	−19.9462			−1.91050			−0.955248	−	0.295807i	$-0.904412\pi$
$109$	−19.9462			−1.91050			−0.955248	+	0.295807i	$0.904412\pi$
$110$		0			0
$111$	0.632323	−	1.09522i	0.0600175	−	0.103953i
$112$		0			0
$113$	9.34298	−	16.1825i	0.878914	−	1.52232i	0.0263801	−	0.999652i	$-0.491602\pi$
$113$	9.34298	−	16.1825i	0.878914	−	1.52232i	0.852534	−	0.522672i	$-0.175065\pi$
$114$		0			0
$115$	10.9200	+	18.9140i	1.01830	+	1.76374i
$116$		0			0
$117$	0.233172	−	9.20011i	0.0215568	−	0.850551i
$118$		0			0
$119$	3.64091	+	6.30624i	0.333762	+	0.578092i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	0.833885	−	1.44433i	0.0751888	−	0.130231i
$124$		0			0
$125$	−26.8433			−2.40094
$126$		0			0
$127$	5.78743	+	10.0241i	0.513551	+	0.889497i	0.999876	+	0.0157189i	$0.00500369\pi$
$127$	5.78743	+	10.0241i	0.513551	+	0.889497i	−0.486325	+	0.873778i	$0.661663\pi$
$128$		0			0
$129$	−4.73175			−0.416607
$130$		0			0
$131$	0.138747			0.0121223			0.00606117	−	0.999982i	$-0.498071\pi$
$131$	0.138747			0.0121223			0.00606117	+	0.999982i	$0.498071\pi$
$132$		0			0
$133$	3.98177	+	6.89664i	0.345264	+	0.598014i
$134$		0			0
$135$	−15.1295			−1.30214
$136$		0			0
$137$	−0.604655	+	1.04729i	−0.0516591	+	0.0894762i	−0.890699	−	0.454594i	$-0.849784\pi$
$137$	−0.604655	+	1.04729i	−0.0516591	+	0.0894762i	0.839040	+	0.544071i	$0.183118\pi$
$138$		0			0
$139$	−9.91102	+	17.1664i	−0.840642	+	1.45603i	0.0487108	+	0.998813i	$0.484489\pi$
$139$	−9.91102	+	17.1664i	−0.840642	+	1.45603i	−0.889353	+	0.457222i	$0.848845\pi$
$140$		0			0
$141$	2.42238	+	4.19568i	0.204001	+	0.353340i
$142$		0			0
$143$	−3.07582	−	1.88131i	−0.257213	−	0.157323i
$144$		0			0
$145$	12.4634	+	21.5873i	1.03503	+	1.79272i
$146$		0			0
$147$	−1.13293	+	1.96229i	−0.0934422	+	0.161847i
$148$		0			0
$149$	−7.29171	+	12.6296i	−0.597360	+	1.03466i	0.395849	+	0.918316i	$0.370450\pi$
$149$	−7.29171	+	12.6296i	−0.597360	+	1.03466i	−0.993209	+	0.116343i	$0.962883\pi$
$150$		0			0
$151$	−3.44599			−0.280431			−0.140215	−	0.990121i	$-0.544780\pi$
$151$	−3.44599			−0.280431			−0.140215	+	0.990121i	$0.544780\pi$
$152$		0			0
$153$	−4.88922	−	8.46838i	−0.395270	−	0.684628i
$154$		0			0
$155$	29.8243			2.39554
$156$		0			0
$157$	−10.6935			−0.853435			−0.426718	−	0.904385i	$-0.640330\pi$
$157$	−10.6935			−0.853435			−0.426718	+	0.904385i	$0.640330\pi$
$158$		0			0
$159$	−2.88667	−	4.99986i	−0.228928	−	0.396515i
$160$		0			0
$161$	10.1919			0.803236
$162$		0			0
$163$	6.35454	−	11.0064i	0.497726	−	0.862086i	−0.502271	−	0.864710i	$-0.667502\pi$
$163$	6.35454	−	11.0064i	0.497726	−	0.862086i	0.999997	+	0.00262397i	$0.000835236\pi$
$164$		0			0
$165$	−1.36241	+	2.35976i	−0.106064	+	0.183707i
$166$		0			0
$167$	5.54987	+	9.61265i	0.429462	+	0.743849i	0.996825	−	0.0796180i	$-0.0253700\pi$
$167$	5.54987	+	9.61265i	0.429462	+	0.743849i	−0.567364	+	0.823467i	$0.692037\pi$
$168$		0			0
$169$	7.06196	−	10.9146i	0.543228	−	0.839585i
$170$		0			0
$171$	−5.34696	−	9.26120i	−0.408892	−	0.708222i
$172$		0			0
$173$	−3.82015	+	6.61669i	−0.290441	+	0.503058i	−0.973914	−	0.226918i	$-0.927135\pi$
$173$	−3.82015	+	6.61669i	−0.290441	+	0.503058i	0.683473	+	0.729975i	$0.260469\pi$
$174$		0			0
$175$	−11.0153	+	19.0791i	−0.832681	+	1.44225i
$176$		0			0
$177$	−6.51945			−0.490032
$178$		0			0
$179$	6.04174	+	10.4646i	0.451581	+	0.782161i	0.998484	−	0.0550346i	$-0.0175269\pi$
$179$	6.04174	+	10.4646i	0.451581	+	0.782161i	−0.546904	+	0.837196i	$0.684194\pi$
$180$		0			0
$181$	13.6983			1.01819			0.509093	−	0.860712i	$-0.329981\pi$
$181$	13.6983			1.01819			0.509093	+	0.860712i	$0.329981\pi$
$182$		0			0
$183$	4.95319			0.366151
$184$		0			0
$185$	3.84996	+	6.66833i	0.283055	+	0.490266i
$186$		0			0
$187$	−3.83097			−0.280148
$188$		0			0
$189$	−3.53019	+	6.11446i	−0.256783	+	0.444762i
$190$		0			0
$191$	−10.7617	+	18.6398i	−0.778691	+	1.34873i	0.154006	+	0.988070i	$0.450783\pi$
$191$	−10.7617	+	18.6398i	−0.778691	+	1.34873i	−0.932697	+	0.360662i	$0.882551\pi$
$192$		0			0
$193$	5.98687	+	10.3696i	0.430944	+	0.746417i	0.996955	−	0.0779806i	$-0.0248472\pi$
$193$	5.98687	+	10.3696i	0.430944	+	0.746417i	−0.566011	+	0.824398i	$0.691514\pi$
$194$		0			0
$195$	−8.38106	−	5.12623i	−0.600180	−	0.367097i
$196$		0			0
$197$	7.25831	+	12.5718i	0.517133	+	0.895701i	0.999802	+	0.0198980i	$0.00633414\pi$
$197$	7.25831	+	12.5718i	0.517133	+	0.895701i	−0.482669	+	0.875803i	$0.660333\pi$
$198$		0			0
$199$	4.55768	−	7.89413i	0.323085	−	0.559600i	−0.658038	−	0.752985i	$-0.728613\pi$
$199$	4.55768	−	7.89413i	0.323085	−	0.559600i	0.981123	+	0.193385i	$0.0619466\pi$
$200$		0			0
$201$	1.86121	−	3.22371i	0.131280	−	0.227383i
$202$		0			0
$203$	11.6324			0.816436
$204$		0			0
$205$	5.07719	+	8.79395i	0.354606	+	0.614196i
$206$		0			0
$207$	−13.6863			−0.951264
$208$		0			0
$209$	−4.18963			−0.289803
$210$		0			0
$211$	−13.5790	−	23.5195i	−0.934818	−	1.61915i	−0.774958	−	0.632013i	$-0.782229\pi$
$211$	−13.5790	−	23.5195i	−0.934818	−	1.61915i	−0.159860	−	0.987140i	$-0.551104\pi$
$212$		0			0
$213$	3.09973			0.212390
$214$		0			0
$215$	14.4049	−	24.9500i	0.982404	−	1.70157i
$216$		0			0
$217$	6.95894	−	12.0532i	0.472404	−	0.818227i
$218$		0			0
$219$	−0.618253	−	1.07085i	−0.0417777	−	0.0723611i
$220$		0			0
$221$	0.349965	−	13.8083i	0.0235412	−	0.928849i
$222$		0			0
$223$	−0.510814	−	0.884755i	−0.0342066	−	0.0592476i	0.848415	−	0.529331i	$-0.177557\pi$
$223$	−0.510814	−	0.884755i	−0.0342066	−	0.0592476i	−0.882622	+	0.470084i	$0.844224\pi$
$224$		0			0
$225$	14.7920	−	25.6205i	0.986135	−	1.70804i
$226$		0			0
$227$	7.81357	−	13.5335i	0.518605	−	0.898250i	−0.481162	−	0.876632i	$-0.659785\pi$
$227$	7.81357	−	13.5335i	0.518605	−	0.898250i	0.999766	−	0.0216177i	$-0.00688166\pi$
$228$		0			0
$229$	−6.29332			−0.415875			−0.207937	−	0.978142i	$-0.566675\pi$
$229$	−6.29332			−0.415875			−0.207937	+	0.978142i	$0.566675\pi$
$230$		0			0
$231$	0.635786	+	1.10121i	0.0418317	+	0.0724546i
$232$		0			0
$233$	−22.3544			−1.46449			−0.732243	−	0.681043i	$-0.761526\pi$
$233$	−22.3544			−1.46449			−0.732243	+	0.681043i	$0.761526\pi$
$234$		0			0
$235$	−29.4978			−1.92422
$236$		0			0
$237$	3.02300	+	5.23599i	0.196365	+	0.340114i
$238$		0			0
$239$	18.2348			1.17951			0.589754	−	0.807583i	$-0.299225\pi$
$239$	18.2348			1.17951			0.589754	+	0.807583i	$0.299225\pi$
$240$		0			0
$241$	5.33786	−	9.24545i	0.343842	−	0.595552i	−0.641301	−	0.767290i	$-0.721605\pi$
$241$	5.33786	−	9.24545i	0.343842	−	0.595552i	0.985143	+	0.171738i	$0.0549382\pi$
$242$		0			0
$243$	7.30185	−	12.6472i	0.468414	−	0.811316i
$244$		0			0
$245$	−6.89794	−	11.9476i	−0.440693	−	0.763303i
$246$		0			0
$247$	0.382729	−	15.1011i	0.0243524	−	0.960858i
$248$		0			0
$249$	1.76670	+	3.06002i	0.111960	+	0.193921i
$250$		0			0
$251$	−3.29886	+	5.71379i	−0.208222	+	0.360651i	−0.951155	−	0.308715i	$-0.900101\pi$
$251$	−3.29886	+	5.71379i	−0.208222	+	0.360651i	0.742932	+	0.669366i	$0.233434\pi$
$252$		0			0
$253$	−2.68099	+	4.64361i	−0.168552	+	0.291941i
$254$		0			0
$255$	−10.4387			−0.653697
$256$		0			0
$257$	3.98486	+	6.90198i	0.248569	+	0.430534i	0.963129	−	0.269040i	$-0.0867065\pi$
$257$	3.98486	+	6.90198i	0.248569	+	0.430534i	−0.714560	+	0.699574i	$0.753373\pi$
$258$		0			0
$259$	3.59327			0.223275
$260$		0			0
$261$	−15.6207			−0.966896
$262$		0			0
$263$	−12.4446	−	21.5546i	−0.767364	−	1.32911i	−0.938988	−	0.343951i	$-0.888235\pi$
$263$	−12.4446	−	21.5546i	−0.767364	−	1.32911i	0.171623	−	0.985163i	$-0.445099\pi$
$264$		0			0
$265$	35.1516			2.15934
$266$		0			0
$267$	0.452905	−	0.784454i	0.0277173	−	0.0480078i
$268$		0			0
$269$	7.23412	−	12.5299i	0.441072	−	0.763959i	−0.556697	−	0.830715i	$-0.687932\pi$
$269$	7.23412	−	12.5299i	0.441072	−	0.763959i	0.997769	+	0.0667564i	$0.0212650\pi$
$270$		0			0
$271$	10.1754	+	17.6243i	0.618110	+	1.07060i	0.989830	+	0.142254i	$0.0454348\pi$
$271$	10.1754	+	17.6243i	0.618110	+	1.07060i	−0.371720	+	0.928345i	$0.621232\pi$
$272$		0			0
$273$	−4.02729	+	2.19103i	−0.243743	+	0.132607i
$274$		0			0
$275$	−5.79518	−	10.0375i	−0.349462	−	0.605286i
$276$		0			0
$277$	−6.38928	+	11.0666i	−0.383894	+	0.664925i	−0.991615	−	0.129226i	$-0.958751\pi$
$277$	−6.38928	+	11.0666i	−0.383894	+	0.664925i	0.607721	+	0.794151i	$0.292084\pi$
$278$		0			0
$279$	−9.34486	+	16.1858i	−0.559462	+	0.969017i
$280$		0			0
$281$	−14.1564			−0.844497			−0.422249	−	0.906480i	$-0.638759\pi$
$281$	−14.1564			−0.844497			−0.422249	+	0.906480i	$0.638759\pi$
$282$		0			0
$283$	3.01882	+	5.22875i	0.179450	+	0.310817i	0.941692	−	0.336475i	$-0.109235\pi$
$283$	3.01882	+	5.22875i	0.179450	+	0.310817i	−0.762242	+	0.647292i	$0.775901\pi$
$284$		0			0
$285$	−11.4160			−0.676225
$286$		0			0
$287$	4.73867			0.279715
$288$		0			0
$289$	1.16183	+	2.01235i	0.0683430	+	0.118374i
$290$		0			0
$291$	8.27089			0.484848
$292$		0			0
$293$	16.7884	−	29.0784i	0.980789	−	1.69878i	0.321456	−	0.946925i	$-0.395828\pi$
$293$	16.7884	−	29.0784i	0.980789	−	1.69878i	0.659333	−	0.751851i	$-0.270839\pi$
$294$		0			0
$295$	19.8472	−	34.3763i	1.15555	−	2.00147i
$296$		0			0
$297$	−1.85723	−	3.21682i	−0.107768	−	0.186659i
$298$		0			0
$299$	−16.4925	−	10.0875i	−0.953785	−	0.583378i
$300$		0			0
$301$	−6.72222	−	11.6432i	−0.387462	−	0.671104i
$302$		0			0
$303$	3.13338	−	5.42717i	0.180008	−	0.311783i
$304$		0			0
$305$	−15.0790	+	26.1176i	−0.863422	+	1.49549i
$306$		0			0
$307$	−1.45292			−0.0829225			−0.0414612	−	0.999140i	$-0.513201\pi$
$307$	−1.45292			−0.0829225			−0.0414612	+	0.999140i	$0.513201\pi$
$308$		0			0
$309$	4.26027	+	7.37901i	0.242358	+	0.419777i
$310$		0			0
$311$	15.4542			0.876326			0.438163	−	0.898895i	$-0.355629\pi$
$311$	15.4542			0.876326			0.438163	+	0.898895i	$0.355629\pi$
$312$		0			0
$313$	24.5747			1.38905			0.694523	−	0.719470i	$-0.255615\pi$
$313$	24.5747			1.38905			0.694523	+	0.719470i	$0.255615\pi$
$314$		0			0
$315$	−9.88075	−	17.1140i	−0.556717	−	0.964262i
$316$		0			0
$317$	9.29382			0.521993			0.260996	−	0.965340i	$-0.415949\pi$
$317$	9.29382			0.521993			0.260996	+	0.965340i	$0.415949\pi$
$318$		0			0
$319$	−3.05991	+	5.29992i	−0.171322	+	0.296739i
$320$		0			0
$321$	3.23838	−	5.60905i	0.180749	−	0.313066i
$322$		0			0
$323$	−8.02517	−	13.9000i	−0.446533	−	0.773417i
$324$		0			0
$325$	36.7086	−	19.9712i	2.03623	−	1.10780i
$326$		0			0
$327$	−6.67175	−	11.5558i	−0.368948	−	0.639037i
$328$		0			0
$329$	−6.88276	+	11.9213i	−0.379459	+	0.657242i
$330$		0			0
$331$	8.48959	−	14.7044i	0.466630	−	0.808227i	−0.532643	−	0.846340i	$-0.678801\pi$
$331$	8.48959	−	14.7044i	0.466630	−	0.808227i	0.999273	+	0.0381126i	$0.0121346\pi$
$332$		0			0
$333$	−4.82525			−0.264422
$334$		0			0
$335$	11.3322	+	19.6279i	0.619143	+	1.07239i
$336$		0			0
$337$	−26.3070			−1.43304			−0.716518	−	0.697569i	$-0.754265\pi$
$337$	−26.3070			−1.43304			−0.716518	+	0.697569i	$0.754265\pi$
$338$		0			0
$339$	12.5005			0.678932
$340$		0			0
$341$	3.66110	+	6.34122i	0.198260	+	0.343396i
$342$		0			0
$343$	−19.7435			−1.06605
$344$		0			0
$345$	−7.30522	+	12.6530i	−0.393300	+	0.681215i
$346$		0			0
$347$	−9.02903	+	15.6387i	−0.484704	+	0.839531i	−0.999846	−	0.0175737i	$-0.994406\pi$
$347$	−9.02903	+	15.6387i	−0.484704	+	0.839531i	0.515142	+	0.857105i	$0.327739\pi$
$348$		0			0
$349$	13.3597	+	23.1396i	0.715126	+	1.23864i	0.962911	+	0.269820i	$0.0869642\pi$
$349$	13.3597	+	23.1396i	0.715126	+	1.23864i	−0.247785	+	0.968815i	$0.579703\pi$
$350$		0			0
$351$	11.7644	−	6.40034i	0.627935	−	0.341625i
$352$		0			0
$353$	11.7627	+	20.3735i	0.626064	+	1.08437i	0.988334	+	0.152301i	$0.0486684\pi$
$353$	11.7627	+	20.3735i	0.626064	+	1.08437i	−0.362270	+	0.932073i	$0.617998\pi$
$354$		0			0
$355$	−9.43652	+	16.3445i	−0.500838	+	0.867477i
$356$		0			0
$357$	−2.43568	+	4.21872i	−0.128910	+	0.223278i
$358$		0			0
$359$	−21.2203			−1.11997			−0.559983	−	0.828504i	$-0.689192\pi$
$359$	−21.2203			−1.11997			−0.559983	+	0.828504i	$0.689192\pi$
$360$		0			0
$361$	0.723504	+	1.25315i	0.0380791	+	0.0659550i
$362$		0			0
$363$	−0.668975			−0.0351121
$364$		0			0
$365$	7.52859			0.394065
$366$		0			0
$367$	10.9956	+	19.0450i	0.573966	+	0.994139i	0.996153	+	0.0876299i	$0.0279293\pi$
$367$	10.9956	+	19.0450i	0.573966	+	0.994139i	−0.422187	+	0.906509i	$0.638737\pi$
$368$		0			0
$369$	−6.36336			−0.331263
$370$		0			0
$371$	8.20197	−	14.2062i	0.425825	−	0.737550i
$372$		0			0
$373$	5.56958	−	9.64680i	0.288382	−	0.499492i	−0.685042	−	0.728504i	$-0.740216\pi$
$373$	5.56958	−	9.64680i	0.288382	−	0.499492i	0.973424	+	0.229012i	$0.0735494\pi$
$374$		0			0
$375$	−8.97876	−	15.5517i	−0.463661	−	0.803085i
$376$		0			0
$377$	−18.8235	−	11.5133i	−0.969459	−	0.592964i
$378$		0			0
$379$	6.17290	+	10.6918i	0.317081	+	0.549200i	0.979878	−	0.199600i	$-0.0639641\pi$
$379$	6.17290	+	10.6918i	0.317081	+	0.549200i	−0.662797	+	0.748799i	$0.730631\pi$
$380$		0			0
$381$	−3.87165	+	6.70589i	−0.198351	+	0.343553i
$382$		0			0
$383$	7.96615	−	13.7978i	0.407051	−	0.705034i	−0.587506	−	0.809220i	$-0.699890\pi$
$383$	7.96615	−	13.7978i	0.407051	−	0.705034i	0.994558	+	0.104186i	$0.0332236\pi$
$384$		0			0
$385$	−7.74210			−0.394574
$386$		0			0
$387$	9.02698	+	15.6352i	0.458867	+	0.794781i
$388$		0			0
$389$	15.9404			0.808213			0.404106	−	0.914712i	$-0.367583\pi$
$389$	15.9404			0.808213			0.404106	+	0.914712i	$0.367583\pi$
$390$		0			0
$391$	−20.5416			−1.03883
$392$		0			0
$393$	0.0464090	+	0.0803828i	0.00234103	+	0.00405478i
$394$		0			0
$395$	−36.8117			−1.85220
$396$		0			0
$397$	7.52231	−	13.0290i	0.377534	−	0.653908i	−0.613169	−	0.789952i	$-0.710105\pi$
$397$	7.52231	−	13.0290i	0.377534	−	0.653908i	0.990703	+	0.136044i	$0.0434388\pi$
$398$		0			0
$399$	−2.66371	+	4.61368i	−0.133352	+	0.230973i
$400$		0			0
$401$	−6.09394	−	10.5550i	−0.304317	−	0.527093i	0.672792	−	0.739832i	$-0.265095\pi$
$401$	−6.09394	−	10.5550i	−0.304317	−	0.527093i	−0.977109	+	0.212739i	$0.931762\pi$
$402$		0			0
$403$	−23.1907	+	12.6168i	−1.15521	+	0.628487i
$404$		0			0
$405$	10.5342	+	18.2457i	0.523448	+	0.906638i
$406$		0			0
$407$	−0.945211	+	1.63715i	−0.0468524	+	0.0811507i
$408$		0			0
$409$	1.55789	−	2.69835i	0.0770329	−	0.133425i	−0.824936	−	0.565227i	$-0.808789\pi$
$409$	1.55789	−	2.69835i	0.0770329	−	0.133425i	0.901969	+	0.431802i	$0.142122\pi$
$410$		0			0
$411$	−0.808998			−0.0399049
$412$		0			0
$413$	−9.26193	−	16.0421i	−0.455750	−	0.789382i
$414$		0			0
$415$	−21.5135			−1.05606
$416$		0			0
$417$	−13.2605			−0.649368
$418$		0			0
$419$	7.59702	+	13.1584i	0.371139	+	0.642831i	0.989741	−	0.142873i	$-0.0456341\pi$
$419$	7.59702	+	13.1584i	0.371139	+	0.642831i	−0.618602	+	0.785704i	$0.712301\pi$
$420$		0			0
$421$	26.6735			1.29999			0.649995	−	0.759939i	$-0.274771\pi$
$421$	26.6735			1.29999			0.649995	+	0.759939i	$0.274771\pi$
$422$		0			0
$423$	9.24256	−	16.0086i	0.449389	−	0.778364i
$424$		0			0
$425$	22.2012	−	38.4535i	1.07691	−	1.86527i
$426$		0			0
$427$	7.03682	+	12.1881i	0.340535	+	0.589825i
$428$		0			0
$429$	0.0611119	−	2.41125i	0.00295051	−	0.116416i
$430$		0			0
$431$	16.6386	+	28.8190i	0.801455	+	1.38816i	0.918659	+	0.395052i	$0.129274\pi$
$431$	16.6386	+	28.8190i	0.801455	+	1.38816i	−0.117204	+	0.993108i	$0.537393\pi$
$432$		0			0
$433$	15.2509	−	26.4154i	0.732913	−	1.26944i	−0.222720	−	0.974882i	$-0.571494\pi$
$433$	15.2509	−	26.4154i	0.732913	−	1.26944i	0.955633	−	0.294560i	$-0.0951732\pi$
$434$		0			0
$435$	−8.33771	+	14.4413i	−0.399763	+	0.692409i
$436$		0			0
$437$	−22.4647			−1.07463
$438$		0			0
$439$	13.3564	+	23.1340i	0.637468	+	1.10413i	0.985986	+	0.166825i	$0.0533516\pi$
$439$	13.3564	+	23.1340i	0.637468	+	1.10413i	−0.348518	+	0.937302i	$0.613315\pi$
$440$		0			0
$441$	8.64535			0.411683
$442$		0			0
$443$	39.8622			1.89391			0.946956	−	0.321364i	$-0.104141\pi$
$443$	39.8622			1.89391			0.946956	+	0.321364i	$0.104141\pi$
$444$		0			0
$445$	2.75756	+	4.77623i	0.130721	+	0.226415i
$446$		0			0
$447$	−9.75595			−0.461441
$448$		0			0
$449$	−13.9003	+	24.0761i	−0.655997	+	1.13622i	0.325646	+	0.945492i	$0.394418\pi$
$449$	−13.9003	+	24.0761i	−0.655997	+	1.13622i	−0.981643	+	0.190728i	$0.938915\pi$
$450$		0			0
$451$	−1.24651	+	2.15902i	−0.0586959	+	0.101664i
$452$		0			0
$453$	−1.15264	−	1.99643i	−0.0541559	−	0.0938007i
$454$		0			0
$455$	0.707252	−	27.9056i	0.0331565	−	1.30823i
$456$		0			0
$457$	−17.7997	−	30.8300i	−0.832637	−	1.44217i	−0.895940	−	0.444175i	$-0.853497\pi$
$457$	−17.7997	−	30.8300i	−0.832637	−	1.44217i	0.0633037	−	0.997994i	$-0.479836\pi$
$458$		0			0
$459$	7.11501	−	12.3236i	0.332100	−	0.575214i
$460$		0			0
$461$	6.02094	−	10.4286i	0.280423	−	0.485707i	−0.691066	−	0.722792i	$-0.742859\pi$
$461$	6.02094	−	10.4286i	0.280423	−	0.485707i	0.971489	+	0.237085i	$0.0761920\pi$
$462$		0			0
$463$	−12.4785			−0.579924			−0.289962	−	0.957038i	$-0.593643\pi$
$463$	−12.4785			−0.579924			−0.289962	+	0.957038i	$0.593643\pi$
$464$		0			0
$465$	9.97585	+	17.2787i	0.462619	+	0.801280i
$466$		0			0
$467$	13.0416			0.603492			0.301746	−	0.953388i	$-0.402431\pi$
$467$	13.0416			0.603492			0.301746	+	0.953388i	$0.402431\pi$
$468$		0			0
$469$	10.5766			0.488382
$470$		0			0
$471$	−3.57685	−	6.19528i	−0.164812	−	0.285464i
$472$		0			0
$473$	7.07313			0.325223
$474$		0			0
$475$	24.2796	−	42.0536i	1.11403	−	1.92955i
$476$		0			0
$477$	−11.0141	+	19.0769i	−0.504300	+	0.873473i
$478$		0			0
$479$	−4.64190	−	8.04000i	−0.212094	−	0.367357i	0.740276	−	0.672303i	$-0.234695\pi$
$479$	−4.64190	−	8.04000i	−0.212094	−	0.367357i	−0.952370	+	0.304946i	$0.901362\pi$
$480$		0			0
$481$	−5.81460	−	3.55647i	−0.265123	−	0.162161i
$482$		0			0
$483$	3.40907	+	5.90469i	0.155118	+	0.268673i
$484$		0			0
$485$	−25.1791	+	43.6114i	−1.14332	+	1.98029i
$486$		0			0
$487$	5.46198	−	9.46042i	0.247506	−	0.428693i	−0.715327	−	0.698790i	$-0.753722\pi$
$487$	5.46198	−	9.46042i	0.247506	−	0.428693i	0.962833	+	0.270097i	$0.0870557\pi$
$488$		0			0
$489$	8.50206			0.384476
$490$		0			0
$491$	0.221796	+	0.384162i	0.0100095	+	0.0173370i	0.870987	−	0.491306i	$-0.163480\pi$
$491$	0.221796	+	0.384162i	0.0100095	+	0.0173370i	−0.860977	+	0.508643i	$0.830147\pi$
$492$		0			0
$493$	−23.4449			−1.05590
$494$		0			0
$495$	10.3965			0.467290
$496$		0			0
$497$	4.40367	+	7.62738i	0.197532	+	0.342135i
$498$		0			0
$499$	−25.6822			−1.14969			−0.574847	−	0.818261i	$-0.694938\pi$
$499$	−25.6822			−1.14969			−0.574847	+	0.818261i	$0.694938\pi$
$500$		0			0
$501$	−3.71272	+	6.43063i	−0.165872	+	0.287299i
$502$		0			0
$503$	0.424647	−	0.735510i	0.0189341	−	0.0327948i	−0.856403	−	0.516308i	$-0.827306\pi$
$503$	0.424647	−	0.735510i	0.0189341	−	0.0327948i	0.875337	+	0.483513i	$0.160639\pi$
$504$		0			0
$505$	19.0779	+	33.0439i	0.848956	+	1.47043i
$506$		0			0
$507$	8.68552	+	0.440542i	0.385737	+	0.0195652i
$508$		0			0
$509$	6.01149	+	10.4122i	0.266455	+	0.461513i	0.967944	−	0.251167i	$-0.0808144\pi$
$509$	6.01149	+	10.4122i	0.266455	+	0.461513i	−0.701489	+	0.712680i	$0.747481\pi$
$510$		0			0
$511$	1.75666	−	3.04262i	0.0777100	−	0.134598i
$512$		0			0
$513$	7.78112	−	13.4773i	0.343545	−	0.595037i
$514$		0			0
$515$	−51.8782			−2.28603
$516$		0			0
$517$	−3.62102	−	6.27180i	−0.159252	−	0.275833i
$518$		0			0
$519$	−5.11117			−0.224356
$520$		0			0
$521$	−33.1378			−1.45179			−0.725897	−	0.687803i	$-0.758575\pi$
$521$	−33.1378			−1.45179			−0.725897	+	0.687803i	$0.758575\pi$
$522$		0			0
$523$	21.5955	+	37.4045i	0.944306	+	1.63559i	0.757135	+	0.653259i	$0.226599\pi$
$523$	21.5955	+	37.4045i	0.944306	+	1.63559i	0.187171	+	0.982327i	$0.440068\pi$
$524$		0			0
$525$	−14.7380			−0.643218
$526$		0			0
$527$	−14.0256	+	24.2930i	−0.610964	+	1.05822i
$528$		0			0
$529$	−2.87541	+	4.98035i	−0.125018	+	0.216537i
$530$		0			0
$531$	12.4375	+	21.5423i	0.539740	+	0.934856i
$532$		0			0
$533$	−7.66808	−	4.69014i	−0.332142	−	0.203153i
$534$		0			0
$535$	19.7172	+	34.1512i	0.852450	+	1.47649i
$536$		0			0
$537$	−4.04178	+	7.00056i	−0.174415	+	0.302096i
$538$		0			0
$539$	1.69352	−	2.93327i	0.0729453	−	0.126345i
$540$		0			0
$541$	30.3664			1.30555			0.652777	−	0.757550i	$-0.273604\pi$
$541$	30.3664			1.30555			0.652777	+	0.757550i	$0.273604\pi$
$542$		0			0
$543$	4.58191	+	7.93610i	0.196629	+	0.340571i
$544$		0			0
$545$	81.2432			3.48008
$546$		0			0
$547$	−0.275358			−0.0117735			−0.00588673	−	0.999983i	$-0.501874\pi$
$547$	−0.275358			−0.0117735			−0.00588673	+	0.999983i	$0.501874\pi$
$548$		0			0
$549$	−9.44944	−	16.3669i	−0.403292	−	0.698523i
$550$		0			0
$551$	−25.6398			−1.09229
$552$		0			0
$553$	−8.58932	+	14.8771i	−0.365255	+	0.632641i
$554$		0			0
$555$	−2.57553	+	4.46095i	−0.109325	+	0.189357i
$556$		0			0
$557$	−15.5178	−	26.8776i	−0.657509	−	1.13884i	−0.981258	−	0.192696i	$-0.938277\pi$
$557$	−15.5178	−	26.8776i	−0.657509	−	1.13884i	0.323749	−	0.946143i	$-0.395057\pi$
$558$		0			0
$559$	−0.646140	+	25.4943i	−0.0273288	+	1.07830i
$560$		0			0
$561$	−1.28141	−	2.21947i	−0.0541013	−	0.0937062i
$562$		0			0
$563$	−10.8100	+	18.7234i	−0.455586	+	0.789099i	−0.998722	−	0.0505465i	$-0.983904\pi$
$563$	−10.8100	+	18.7234i	−0.455586	+	0.789099i	0.543135	+	0.839645i	$0.317237\pi$
$564$		0			0
$565$	−38.0551	+	65.9135i	−1.60099	+	2.77300i
$566$		0			0
$567$	9.83182			0.412898
$568$		0			0
$569$	18.7168	+	32.4185i	0.784651	+	1.35906i	0.929207	+	0.369559i	$0.120491\pi$
$569$	18.7168	+	32.4185i	0.784651	+	1.35906i	−0.144557	+	0.989497i	$0.546176\pi$
$570$		0			0
$571$	−43.1759			−1.80686			−0.903429	−	0.428739i	$-0.858958\pi$
$571$	−43.1759			−1.80686			−0.903429	+	0.428739i	$0.858958\pi$
$572$		0			0
$573$	−14.3987			−0.601512
$574$		0			0
$575$	−31.0736	−	53.8211i	−1.29586	−	2.24449i
$576$		0			0
$577$	11.4984			0.478685			0.239343	−	0.970935i	$-0.423068\pi$
$577$	11.4984			0.478685			0.239343	+	0.970935i	$0.423068\pi$
$578$		0			0
$579$	−4.00507	+	6.93698i	−0.166445	+	0.288291i
$580$		0			0
$581$	−5.01978	+	8.69451i	−0.208256	+	0.360709i
$582$		0			0
$583$	4.31506	+	7.47391i	0.178712	+	0.309538i
$584$		0			0
$585$	−0.949739	+	37.4732i	−0.0392669	+	1.54933i
$586$		0			0
$587$	−13.2702	−	22.9846i	−0.547719	−	0.948677i	−0.998430	−	0.0560074i	$-0.982163\pi$
$587$	−13.2702	−	22.9846i	−0.547719	−	0.948677i	0.450711	−	0.892670i	$-0.351170\pi$
$588$		0			0
$589$	−15.3387	+	26.5673i	−0.632019	+	1.09469i
$590$		0			0
$591$	−4.85563	+	8.41020i	−0.199734	+	0.345949i
$592$		0			0
$593$	9.23551			0.379257			0.189629	−	0.981856i	$-0.439272\pi$
$593$	9.23551			0.379257			0.189629	+	0.981856i	$0.439272\pi$
$594$		0			0
$595$	−14.8299	−	25.6861i	−0.607966	−	1.05303i
$596$		0			0
$597$	6.09795			0.249572
$598$		0			0
$599$	−42.6899			−1.74426			−0.872130	−	0.489274i	$-0.837262\pi$
$599$	−42.6899			−1.74426			−0.872130	+	0.489274i	$0.837262\pi$
$600$		0			0
$601$	8.45778	+	14.6493i	0.345000	+	0.597558i	0.985354	−	0.170522i	$-0.0545455\pi$
$601$	8.45778	+	14.6493i	0.345000	+	0.597558i	−0.640354	+	0.768080i	$0.721212\pi$
$602$		0			0
$603$	−14.2029			−0.578386
$604$		0			0
$605$	2.03656	−	3.52743i	0.0827981	−	0.143410i
$606$		0			0
$607$	15.6838	−	27.1652i	0.636587	−	1.10260i	−0.349589	−	0.936903i	$-0.613679\pi$
$607$	15.6838	−	27.1652i	0.636587	−	1.10260i	0.986176	−	0.165698i	$-0.0529878\pi$
$608$		0			0
$609$	3.89090	+	6.73924i	0.157667	+	0.273088i
$610$		0			0
$611$	22.9368	−	12.4787i	0.927924	−	0.504832i
$612$		0			0
$613$	−8.69959	−	15.0681i	−0.351373	−	0.608596i	0.635117	−	0.772416i	$-0.280952\pi$
$613$	−8.69959	−	15.0681i	−0.351373	−	0.608596i	−0.986490	+	0.163820i	$0.947619\pi$
$614$		0			0
$615$	−3.39652	+	5.88294i	−0.136961	+	0.237223i
$616$		0			0
$617$	−10.2358	+	17.7290i	−0.412080	+	0.713743i	−0.995117	−	0.0987024i	$-0.968531\pi$
$617$	−10.2358	+	17.7290i	−0.412080	+	0.713743i	0.583037	+	0.812445i	$0.301864\pi$
$618$		0			0
$619$	18.2154			0.732139			0.366070	−	0.930587i	$-0.380703\pi$
$619$	18.2154			0.732139			0.366070	+	0.930587i	$0.380703\pi$
$620$		0			0
$621$	−9.95845	−	17.2485i	−0.399619	−	0.692160i
$622$		0			0
$623$	2.57370			0.103113
$624$		0			0
$625$	51.3845			2.05538
$626$		0			0
$627$	−1.40138	−	2.42726i	−0.0559657	−	0.0969354i
$628$		0			0
$629$	−7.24215			−0.288764
$630$		0			0
$631$	13.4540	−	23.3029i	0.535594	−	0.927675i	−0.463541	−	0.886076i	$-0.653421\pi$
$631$	13.4540	−	23.3029i	0.535594	−	0.927675i	0.999134	−	0.0415997i	$-0.0132454\pi$
$632$		0			0
$633$	9.08403	−	15.7340i	0.361058	−	0.625370i
$634$		0			0
$635$	−23.5729	−	40.8295i	−0.935463	−	1.62027i
$636$		0			0
$637$	10.4180	+	6.37209i	0.412774	+	0.252471i
$638$		0			0
$639$	−5.91350	−	10.2425i	−0.233935	−	0.405187i
$640$		0			0
$641$	4.66460	−	8.07933i	0.184241	−	0.319114i	−0.759080	−	0.650998i	$-0.774351\pi$
$641$	4.66460	−	8.07933i	0.184241	−	0.319114i	0.943320	+	0.331883i	$0.107684\pi$
$642$		0			0
$643$	−9.22173	+	15.9725i	−0.363670	+	0.629894i	−0.988562	−	0.150817i	$-0.951810\pi$
$643$	−9.22173	+	15.9725i	−0.363670	+	0.629894i	0.624892	+	0.780711i	$0.285143\pi$
$644$		0			0
$645$	19.2730			0.758874
$646$		0			0
$647$	3.27475	+	5.67204i	0.128744	+	0.222991i	0.923190	−	0.384343i	$-0.125572\pi$
$647$	3.27475	+	5.67204i	0.128744	+	0.222991i	−0.794446	+	0.607334i	$0.792239\pi$
$648$		0			0
$649$	9.74542			0.382541
$650$		0			0
$651$	9.31072			0.364916
$652$		0			0
$653$	15.7976	+	27.3623i	0.618209	+	1.07077i	0.989812	+	0.142378i	$0.0454748\pi$
$653$	15.7976	+	27.3623i	0.618209	+	1.07077i	−0.371603	+	0.928392i	$0.621192\pi$
$654$		0			0
$655$	−0.565132			−0.0220815
$656$		0			0
$657$	−2.35894	+	4.08581i	−0.0920311	+	0.159402i
$658$		0			0
$659$	−5.25507	+	9.10205i	−0.204708	+	0.354565i	−0.950040	−	0.312129i	$-0.898958\pi$
$659$	−5.25507	+	9.10205i	−0.204708	+	0.354565i	0.745331	+	0.666694i	$0.232291\pi$
$660$		0			0
$661$	0.173035	+	0.299706i	0.00673030	+	0.0116572i	0.869371	−	0.494160i	$-0.164524\pi$
$661$	0.173035	+	0.299706i	0.00673030	+	0.0116572i	−0.862641	+	0.505817i	$0.831191\pi$
$662$		0			0
$663$	8.11691	−	4.41596i	0.315235	−	0.171502i
$664$		0			0
$665$	−16.2183	−	28.0909i	−0.628917	−	1.08932i
$666$		0			0
$667$	−16.4072	+	28.4181i	−0.635289	+	1.10035i
$668$		0			0
$669$	0.341722	−	0.591880i	0.0132117	−	0.0228834i
$670$		0			0
$671$	−7.40415			−0.285834
$672$		0			0
$673$	−5.12900	−	8.88369i	−0.197709	−	0.342441i	0.750077	−	0.661351i	$-0.230017\pi$
$673$	−5.12900	−	8.88369i	−0.197709	−	0.342441i	−0.947785	+	0.318910i	$0.896683\pi$
$674$		0			0
$675$	43.0520			1.65707
$676$		0			0
$677$	−0.105792			−0.00406592			−0.00203296	−	0.999998i	$-0.500647\pi$
$677$	−0.105792			−0.00406592			−0.00203296	+	0.999998i	$0.500647\pi$
$678$		0			0
$679$	11.7501	+	20.3518i	0.450929	+	0.781032i
$680$		0			0
$681$	10.4542			0.400605
$682$		0			0
$683$	−12.9069	+	22.3555i	−0.493871	+	0.855409i	−0.999975	−	0.00706315i	$-0.997752\pi$
$683$	−12.9069	+	22.3555i	−0.493871	+	0.855409i	0.506104	+	0.862472i	$0.331085\pi$
$684$		0			0
$685$	2.46283	−	4.26575i	0.0941001	−	0.162986i
$686$		0			0
$687$	−2.10504	−	3.64604i	−0.0803123	−	0.139105i
$688$		0			0
$689$	−27.3331	+	14.8704i	−1.04131	+	0.566518i
$690$		0			0
$691$	−23.9504	−	41.4834i	−0.911117	−	1.57810i	−0.812489	−	0.582977i	$-0.801888\pi$
$691$	−23.9504	−	41.4834i	−0.911117	−	1.57810i	−0.0986285	−	0.995124i	$-0.531446\pi$
$692$		0			0
$693$	2.42584	−	4.20168i	0.0921500	−	0.159608i
$694$		0			0
$695$	40.3688	−	69.9209i	1.53128	−	2.65225i
$696$		0			0
$697$	−9.55069			−0.361758
$698$		0			0
$699$	−7.47728	−	12.9510i	−0.282817	−	0.489853i
$700$		0			0
$701$	41.1026			1.55242			0.776211	−	0.630473i	$-0.217139\pi$
$701$	41.1026			1.55242			0.776211	+	0.630473i	$0.217139\pi$
$702$		0			0
$703$	−7.92017			−0.298715
$704$		0			0
$705$	−9.86664	−	17.0895i	−0.371599	−	0.643629i
$706$		0			0
$707$	17.8059			0.669660
$708$		0			0
$709$	−10.2035	+	17.6730i	−0.383201	+	0.663724i	−0.991518	−	0.129970i	$-0.958512\pi$
$709$	−10.2035	+	17.6730i	−0.383201	+	0.663724i	0.608317	+	0.793694i	$0.291845\pi$
$710$		0			0
$711$	11.5342	−	19.9779i	0.432568	−	0.749229i
$712$		0			0
$713$	19.6308	+	34.0015i	0.735178	+	1.27336i
$714$		0			0
$715$	12.5282	+	7.66281i	0.468528	+	0.286573i
$716$		0			0
$717$	6.09931	+	10.5643i	0.227783	+	0.394531i
$718$		0			0
$719$	−2.18752	+	3.78889i	−0.0815807	+	0.141302i	−0.903929	−	0.427682i	$-0.859330\pi$
$719$	−2.18752	+	3.78889i	−0.0815807	+	0.141302i	0.822348	+	0.568984i	$0.192663\pi$
$720$		0			0
$721$	−12.1048	+	20.9662i	−0.450807	+	0.780821i
$722$		0			0
$723$	7.14180			0.265606
$724$		0			0
$725$	−35.4655	−	61.4280i	−1.31715	−	2.28138i
$726$		0			0
$727$	37.8601			1.40415			0.702077	−	0.712101i	$-0.252256\pi$
$727$	37.8601			1.40415			0.702077	+	0.712101i	$0.252256\pi$
$728$		0			0
$729$	−5.74807			−0.212891
$730$		0			0
$731$	13.5485	+	23.4666i	0.501108	+	0.867945i
$732$		0			0
$733$	−39.0486			−1.44229			−0.721146	−	0.692783i	$-0.756384\pi$
$733$	−39.0486			−1.44229			−0.721146	+	0.692783i	$0.756384\pi$
$734$		0			0
$735$	4.61455	−	7.99264i	0.170210	−	0.294813i
$736$		0			0
$737$	−2.78218	+	4.81888i	−0.102483	+	0.177506i
$738$		0			0
$739$	20.7062	+	35.8642i	0.761689	+	1.31928i	0.941979	+	0.335671i	$0.108963\pi$
$739$	20.7062	+	35.8642i	0.761689	+	1.31928i	−0.180290	+	0.983614i	$0.557704\pi$
$740$		0			0
$741$	8.87682	−	4.82939i	0.326098	−	0.177412i
$742$		0			0
$743$	−20.4578	−	35.4339i	−0.750522	−	1.29994i	−0.947570	−	0.319549i	$-0.896469\pi$
$743$	−20.4578	−	35.4339i	−0.750522	−	1.29994i	0.197048	−	0.980394i	$-0.436865\pi$
$744$		0			0
$745$	29.7001	−	51.4420i	1.08813	−	1.88469i
$746$		0			0
$747$	6.74085	−	11.6755i	0.246635	−	0.427184i
$748$		0			0
$749$	18.4026			0.672416
$750$		0			0
$751$	−24.6530	−	42.7003i	−0.899601	−	1.55816i	−0.828004	−	0.560722i	$-0.810524\pi$
$751$	−24.6530	−	42.7003i	−0.899601	−	1.55816i	−0.0715970	−	0.997434i	$-0.522810\pi$
$752$		0			0
$753$	−4.41371			−0.160845
$754$		0			0
$755$	14.0360			0.510821
$756$		0			0
$757$	−10.4694	−	18.1335i	−0.380516	−	0.659073i	0.610620	−	0.791924i	$-0.290920\pi$
$757$	−10.4694	−	18.1335i	−0.380516	−	0.659073i	−0.991136	+	0.132851i	$0.957587\pi$
$758$		0			0
$759$	−3.58703			−0.130201
$760$		0			0
$761$	−0.0815301	+	0.141214i	−0.00295546	+	0.00511901i	−0.867499	−	0.497438i	$-0.834274\pi$
$761$	−0.0815301	+	0.141214i	−0.00295546	+	0.00511901i	0.864544	+	0.502557i	$0.167607\pi$
$762$		0			0
$763$	18.9566	−	32.8338i	0.686275	−	1.18866i
$764$		0			0
$765$	19.9144	+	34.4928i	0.720007	+	1.24709i
$766$		0			0
$767$	−0.890258	+	35.1263i	−0.0321454	+	1.26834i
$768$		0			0
$769$	−12.9208	−	22.3795i	−0.465936	−	0.807025i	0.533307	−	0.845922i	$-0.320949\pi$
$769$	−12.9208	−	22.3795i	−0.465936	−	0.807025i	−0.999243	+	0.0388968i	$0.987616\pi$
$770$		0			0
$771$	−2.66577	+	4.61725i	−0.0960055	+	0.166286i
$772$		0			0
$773$	15.3074	−	26.5132i	0.550570	−	0.953615i	−0.447664	−	0.894202i	$-0.647744\pi$
$773$	15.3074	−	26.5132i	0.550570	−	0.953615i	0.998233	−	0.0594129i	$-0.0189229\pi$
$774$		0			0
$775$	−84.8670			−3.04851
$776$		0			0
$777$	1.20191	+	2.08176i	0.0431181	+	0.0746827i
$778$		0			0
$779$	−10.4448			−0.374225
$780$		0			0
$781$	−4.63355			−0.165801
$782$		0			0
$783$	−11.3659	−	19.6864i	−0.406186	−	0.703534i
$784$		0			0
$785$	43.5560			1.55458
$786$		0			0
$787$	−3.43090	+	5.94249i	−0.122298	+	0.211827i	−0.920674	−	0.390333i	$-0.872360\pi$
$787$	−3.43090	+	5.94249i	−0.122298	+	0.211827i	0.798375	+	0.602160i	$0.205693\pi$
$788$		0			0
$789$	8.32510	−	14.4195i	0.296381	−	0.513348i
$790$		0			0
$791$	17.7589	+	30.7594i	0.631435	+	1.09368i
$792$		0			0
$793$	0.676380	−	26.6875i	0.0240189	−	0.947700i
$794$		0			0
$795$	11.7578	+	20.3651i	0.417005	+	0.722274i
$796$		0			0
$797$	0.691646	−	1.19797i	0.0244994	−	0.0424341i	−0.853516	−	0.521067i	$-0.825534\pi$
$797$	0.691646	−	1.19797i	0.0244994	−	0.0424341i	0.878015	+	0.478633i	$0.158867\pi$
$798$		0			0
$799$	13.8720	−	24.0271i	0.490757	−	0.850017i
$800$		0			0
$801$	−3.45611			−0.122116
$802$		0			0
$803$	0.924179	+	1.60073i	0.0326136	+	0.0564884i
$804$		0			0
$805$	−41.5130			−1.46314
$806$		0			0
$807$	9.67889			0.340713
$808$		0			0
$809$	11.5698	+	20.0395i	0.406772	+	0.704550i	0.994526	−	0.104490i	$-0.0333210\pi$
$809$	11.5698	+	20.0395i	0.406772	+	0.704550i	−0.587754	+	0.809040i	$0.699988\pi$
$810$		0			0
$811$	−21.0313			−0.738508			−0.369254	−	0.929329i	$-0.620387\pi$
$811$	−21.0313			−0.738508			−0.369254	+	0.929329i	$0.620387\pi$
$812$		0			0
$813$	−6.80708	+	11.7902i	−0.238735	+	0.413501i
$814$		0			0
$815$	−25.8828	+	44.8304i	−0.906636	+	1.57034i
$816$		0			0
$817$	14.8169	+	25.6636i	0.518377	+	0.897856i
$818$		0			0
$819$	14.9229	+	9.12751i	0.521448	+	0.318941i
$820$		0			0
$821$	19.2988	+	33.4265i	0.673532	+	1.16659i	0.976896	+	0.213717i	$0.0685571\pi$
$821$	19.2988	+	33.4265i	0.673532	+	1.16659i	−0.303363	+	0.952875i	$0.598110\pi$
$822$		0			0
$823$	13.0427	−	22.5907i	0.454641	−	0.787461i	−0.544027	−	0.839068i	$-0.683101\pi$
$823$	13.0427	−	22.5907i	0.454641	−	0.787461i	0.998667	+	0.0516071i	$0.0164343\pi$
$824$		0			0
$825$	3.87683	−	6.71487i	0.134974	−	0.233782i
$826$		0			0
$827$	37.7682			1.31333			0.656664	−	0.754183i	$-0.271967\pi$
$827$	37.7682			1.31333			0.656664	+	0.754183i	$0.271967\pi$
$828$		0			0
$829$	−14.2229	−	24.6347i	−0.493980	−	0.855599i	0.505996	−	0.862536i	$-0.331125\pi$
$829$	−14.2229	−	24.6347i	−0.493980	−	0.855599i	−0.999976	+	0.00693710i	$0.997792\pi$
$830$		0			0
$831$	−8.54854			−0.296545
$832$		0			0
$833$	12.9757			0.449581
$834$		0			0
$835$	−22.6053	−	39.1535i	−0.782289	−	1.35496i
$836$		0			0
$837$	−27.1981			−0.940104
$838$		0			0
$839$	−11.1137	+	19.2495i	−0.383688	+	0.664567i	−0.991586	−	0.129448i	$-0.958680\pi$
$839$	−11.1137	+	19.2495i	−0.383688	+	0.664567i	0.607898	+	0.794015i	$0.292013\pi$
$840$		0			0
$841$	−4.22612	+	7.31986i	−0.145728	+	0.252409i
$842$		0			0
$843$	−4.73513	−	8.20148i	−0.163086	−	0.282474i
$844$		0			0
$845$	−28.7643	+	44.4566i	−0.989520	+	1.52935i
$846$		0			0
$847$	−0.950388	−	1.64612i	−0.0326557	−	0.0565614i
$848$		0			0
$849$	−2.01952	+	3.49791i	−0.0693097	+	0.120048i
$850$		0			0
$851$	−5.06820	+	8.77838i	−0.173736	+	0.300919i
$852$		0			0
$853$	−11.0553			−0.378527			−0.189263	−	0.981926i	$-0.560610\pi$
$853$	−11.0553			−0.378527			−0.189263	+	0.981926i	$0.560610\pi$
$854$		0			0
$855$	21.7788	+	37.7220i	0.744820	+	1.29007i
$856$		0			0
$857$	32.0384			1.09441			0.547206	−	0.836998i	$-0.315691\pi$
$857$	32.0384			1.09441			0.547206	+	0.836998i	$0.315691\pi$
$858$		0			0
$859$	−29.3803			−1.00244			−0.501221	−	0.865319i	$-0.667116\pi$
$859$	−29.3803			−1.00244			−0.501221	+	0.865319i	$0.667116\pi$
$860$		0			0
$861$	1.58503	+	2.74535i	0.0540176	+	0.0935613i
$862$		0			0
$863$	−4.45831			−0.151763			−0.0758813	−	0.997117i	$-0.524177\pi$
$863$	−4.45831			−0.151763			−0.0758813	+	0.997117i	$0.524177\pi$
$864$		0			0
$865$	15.5599	−	26.9506i	0.529054	−	0.916349i
$866$		0			0
$867$	−0.777236	+	1.34621i	−0.0263963	+	0.0457198i
$868$		0			0
$869$	−4.51885	−	7.82688i	−0.153292	−	0.265509i
$870$		0			0
$871$	−17.1150	−	10.4683i	−0.579919	−	0.354704i
$872$		0			0
$873$	−15.7788	−	27.3296i	−0.534030	−	0.924967i
$874$		0			0
$875$	25.5116	−	44.1874i	0.862449	−	1.49381i
$876$		0			0
$877$	15.8980	−	27.5361i	0.536836	−	0.929828i	−0.462236	−	0.886757i	$-0.652953\pi$
$877$	15.8980	−	27.5361i	0.536836	−	0.929828i	0.999072	−	0.0430708i	$-0.0137141\pi$
$878$		0			0
$879$	22.4621			0.757626
$880$		0			0
$881$	−5.99423	−	10.3823i	−0.201951	−	0.349789i	0.747206	−	0.664592i	$-0.231395\pi$
$881$	−5.99423	−	10.3823i	−0.201951	−	0.349789i	−0.949157	+	0.314803i	$0.898061\pi$
$882$		0			0
$883$	−5.90882			−0.198848			−0.0994239	−	0.995045i	$-0.531700\pi$
$883$	−5.90882			−0.198848			−0.0994239	+	0.995045i	$0.531700\pi$
$884$		0			0
$885$	26.5545			0.892621
$886$		0			0
$887$	11.6993	+	20.2637i	0.392823	+	0.680390i	0.992821	−	0.119612i	$-0.0381651\pi$
$887$	11.6993	+	20.2637i	0.392823	+	0.680390i	−0.599998	+	0.800002i	$0.704832\pi$
$888$		0			0
$889$	−22.0012			−0.737897
$890$		0			0
$891$	−2.58626	+	4.47954i	−0.0866431	+	0.150070i
$892$		0			0
$893$	15.1707	−	26.2765i	0.507670	−	0.879310i
$894$		0			0
$895$	−24.6088	−	42.6236i	−0.822580	−	1.42475i
$896$		0			0
$897$	0.327680	−	12.9291i	0.0109409	−	0.431689i
$898$		0			0
$899$	22.4053	+	38.8071i	0.747259	+	1.29429i
$900$		0			0
$901$	−16.5309	+	28.6323i	−0.550723	+	0.953881i
$902$		0			0
$903$	4.49700	−	7.78903i	0.149651	−	0.259203i
$904$		0			0
$905$	−55.7948			−1.85468
$906$		0			0
$907$	20.1765	+	34.9467i	0.669950	+	1.16039i	0.977918	+	0.208991i	$0.0670179\pi$
$907$	20.1765	+	34.9467i	0.669950	+	1.16039i	−0.307968	+	0.951397i	$0.599649\pi$
$908$		0			0
$909$	−23.9108			−0.793071
$910$		0			0
$911$	29.5640			0.979500			0.489750	−	0.871863i	$-0.337088\pi$
$911$	29.5640			0.979500			0.489750	+	0.871863i	$0.337088\pi$
$912$		0			0
$913$	−2.64091	−	4.57419i	−0.0874014	−	0.151384i
$914$		0			0
$915$	−20.1750			−0.666964
$916$		0			0
$917$	−0.131863	+	0.228394i	−0.00435450	+	0.00754222i
$918$		0			0
$919$	−20.7658	+	35.9674i	−0.684999	+	1.18645i	0.288438	+	0.957499i	$0.406864\pi$
$919$	−20.7658	+	35.9674i	−0.684999	+	1.18645i	−0.973437	+	0.228955i	$0.926469\pi$
$920$		0			0
$921$	−0.485984	−	0.841748i	−0.0160137	−	0.0277365i
$922$		0			0
$923$	0.423281	−	16.7011i	0.0139325	−	0.549725i
$924$		0			0
$925$	−10.9553	−	18.9752i	−0.360209	−	0.623900i
$926$		0			0
$927$	16.2550	−	28.1546i	0.533886	−	0.924717i
$928$		0			0
$929$	10.3378	−	17.9055i	0.339171	−	0.587462i	−0.645106	−	0.764093i	$-0.723187\pi$
$929$	10.3378	−	17.9055i	0.339171	−	0.587462i	0.984277	+	0.176631i	$0.0565200\pi$
$930$		0			0
$931$	14.1905			0.465074
$932$		0			0
$933$	5.16923	+	8.95338i	0.169233	+	0.293120i
$934$		0			0
$935$	15.6040			0.510306
$936$		0			0
$937$	7.22194			0.235930			0.117965	−	0.993018i	$-0.462363\pi$
$937$	7.22194			0.235930			0.117965	+	0.993018i	$0.462363\pi$
$938$		0			0
$939$	8.21995	+	14.2374i	0.268248	+	0.464619i
$940$		0			0
$941$	−15.6232			−0.509303			−0.254652	−	0.967033i	$-0.581961\pi$
$941$	−15.6232			−0.509303			−0.254652	+	0.967033i	$0.581961\pi$
$942$		0			0
$943$	−6.68376	+	11.5766i	−0.217653	+	0.376986i
$944$		0			0
$945$	14.3789	−	24.9050i	0.467745	−	0.810159i
$946$		0			0
$947$	1.53156	+	2.65273i	0.0497689	+	0.0862023i	0.889837	−	0.456279i	$-0.150818\pi$
$947$	1.53156	+	2.65273i	0.0497689	+	0.0862023i	−0.840068	+	0.542482i	$0.817485\pi$
$948$		0			0
$949$	−5.85407	+	3.18488i	−0.190031	+	0.103385i
$950$		0			0
$951$	3.10867	+	5.38437i	0.100805	+	0.174600i
$952$		0			0
$953$	10.2498	−	17.7531i	0.332022	−	0.575079i	−0.650886	−	0.759175i	$-0.725602\pi$
$953$	10.2498	−	17.7531i	0.332022	−	0.575079i	0.982908	+	0.184096i	$0.0589358\pi$
$954$		0			0
$955$	43.8338	−	75.9224i	1.41843	−	2.45679i
$956$		0			0
$957$	−4.09401			−0.132341
$958$		0			0
$959$	−1.14931	−	1.99067i	−0.0371133	−	0.0642820i
$960$		0			0
$961$	22.6147			0.729507
$962$		0			0
$963$	−24.7121			−0.796335
$964$		0			0
$965$	−24.3853	−	42.2365i	−0.784990	−	1.35964i
$966$		0			0
$967$	38.3471			1.23316			0.616580	−	0.787292i	$-0.288518\pi$
$967$	38.3471			1.23316			0.616580	+	0.787292i	$0.288518\pi$
$968$		0			0
$969$	5.36864	−	9.29876i	0.172466	−	0.298719i
$970$		0			0
$971$	−11.9062	+	20.6221i	−0.382088	+	0.661795i	−0.991361	−	0.131165i	$-0.958128\pi$
$971$	−11.9062	+	20.6221i	−0.382088	+	0.661795i	0.609273	+	0.792961i	$0.291461\pi$
$972$		0			0
$973$	−18.8386	−	32.6295i	−0.603939	−	1.04605i
$974$		0			0
$975$	23.8489	+	14.5870i	0.763775	+	0.467159i
$976$		0			0
$977$	−7.49317	−	12.9786i	−0.239728	−	0.415221i	0.720908	−	0.693030i	$-0.243725\pi$
$977$	−7.49317	−	12.9786i	−0.239728	−	0.415221i	−0.960636	+	0.277810i	$0.910392\pi$
$978$		0			0
$979$	−0.677012	+	1.17262i	−0.0216374	+	0.0374771i
$980$		0			0
$981$	−25.4560	+	44.0911i	−0.812748	+	1.40772i
$982$		0			0
$983$	55.4955			1.77003			0.885016	−	0.465561i	$-0.154147\pi$
$983$	55.4955			1.77003			0.885016	+	0.465561i	$0.154147\pi$
$984$		0			0
$985$	−29.5640	−	51.2064i	−0.941988	−	1.63157i
$986$		0			0
$987$	−9.20879			−0.293119
$988$		0			0
$989$	37.9259			1.20597
$990$		0			0
$991$	−0.987490	−	1.71038i	−0.0313686	−	0.0543321i	0.849915	−	0.526920i	$-0.176653\pi$
$991$	−0.987490	−	1.71038i	−0.0313686	−	0.0543321i	−0.881284	+	0.472588i	$0.843320\pi$
$992$		0			0
$993$	11.3587			0.360456
$994$		0			0
$995$	−18.5640	+	32.1538i	−0.588518	+	1.01934i
$996$		0			0
$997$	18.3795	−	31.8342i	0.582084	−	1.00820i	−0.413148	−	0.910664i	$-0.635571\pi$
$997$	18.3795	−	31.8342i	0.582084	−	1.00820i	0.995232	−	0.0975350i	$-0.0310958\pi$
$998$		0			0
$999$	−3.51096	−	6.08116i	−0.111082	−	0.192399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.c.133.4	✓	10
13.3	even	3		7436.2.a.r.1.2		5
13.9	even	3	inner	572.2.i.c.529.4	yes	10
13.10	even	6		7436.2.a.q.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.c.133.4	✓	10	1.1	even	1	trivial
572.2.i.c.529.4	yes	10	13.9	even	3	inner
7436.2.a.q.1.2		5	13.10	even	6
7436.2.a.r.1.2		5	13.3	even	3

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.334488 + 0.579350i) q^{3} -4.07313 q^{5} +(-0.950388 + 1.64612i) q^{7} +(1.27624 - 2.21051i) q^{9} +O(q^{10})\)	\(q+(0.334488 + 0.579350i) q^{3} -4.07313 q^{5} +(-0.950388 + 1.64612i) q^{7} +(1.27624 - 2.21051i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(3.16717 - 1.72308i) q^{13} +(-1.36241 - 2.35976i) q^{15} +(1.91549 - 3.31772i) q^{17} +(2.09481 - 3.62833i) q^{19} -1.27157 q^{21} +(-2.68099 - 4.64361i) q^{23} +11.5904 q^{25} +3.71447 q^{27} +(-3.05991 - 5.29992i) q^{29} -7.32221 q^{31} +(0.334488 - 0.579350i) q^{33} +(3.87105 - 6.70486i) q^{35} +(-0.945211 - 1.63715i) q^{37} +(2.05765 + 1.25855i) q^{39} +(-1.24651 - 2.15902i) q^{41} +(-3.53656 + 6.12551i) q^{43} +(-5.19827 + 9.00367i) q^{45} +7.24205 q^{47} +(1.69352 + 2.93327i) q^{49} +2.56283 q^{51} -8.63012 q^{53} +(2.03656 + 3.52743i) q^{55} +2.80276 q^{57} +(-4.87271 + 8.43978i) q^{59} +(3.70208 - 6.41218i) q^{61} +(2.42584 + 4.20168i) q^{63} +(-12.9003 + 7.01834i) q^{65} +(-2.78218 - 4.81888i) q^{67} +(1.79352 - 3.10646i) q^{69} +(2.31678 - 4.01277i) q^{71} -1.84836 q^{73} +(3.87683 + 6.71487i) q^{75} +1.90078 q^{77} +9.03770 q^{79} +(-2.58626 - 4.47954i) q^{81} +5.28182 q^{83} +(-7.80201 + 13.5135i) q^{85} +(2.04701 - 3.54552i) q^{87} +(-0.677012 - 1.17262i) q^{89} +(-0.173639 + 6.85115i) q^{91} +(-2.44919 - 4.24212i) q^{93} +(-8.53244 + 14.7786i) q^{95} +(6.18176 - 10.7071i) q^{97} -2.55247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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