LMFDB - Embedded newform 1008.2.r.n.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.6095158642368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 $ x^10 - 4x^9 + 6x^8 - 7x^7 + 25x^6 - 66x^5 + 75x^4 - 63x^3 + 162x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.2
Root			$1.34147 + 1.09565i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.n.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.742385 - 1.56488i) q^{3} +(-1.76217 - 3.05216i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.89773 + 2.32349i) q^{9} +O(q^{10})$	\(q+(-0.742385 - 1.56488i) q^{3} +(-1.76217 - 3.05216i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.89773 + 2.32349i) q^{9} +(-2.08386 + 3.60934i) q^{11} +(-1.52051 - 2.63361i) q^{13} +(-3.46807 + 5.02347i) q^{15} +3.79546 q^{17} -5.40544 q^{19} +(1.72642 + 0.139518i) q^{21} +(4.48540 + 7.76894i) q^{23} +(-3.71046 + 6.42670i) q^{25} +(5.04485 + 1.24480i) q^{27} +(1.46107 - 2.53065i) q^{29} +(-3.08767 - 5.34801i) q^{31} +(7.19523 + 0.581470i) q^{33} +3.52433 q^{35} -4.66649 q^{37} +(-2.99249 + 4.33458i) q^{39} +(1.83828 + 3.18400i) q^{41} +(-1.31777 + 2.28244i) q^{43} +(10.4358 + 1.69779i) q^{45} +(0.860518 - 1.49046i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.81769 - 5.93945i) q^{51} +11.4209 q^{53} +14.6884 q^{55} +(4.01292 + 8.45890i) q^{57} +(-0.564482 - 0.977712i) q^{59} +(-6.03597 + 10.4546i) q^{61} +(-1.06334 - 2.80523i) q^{63} +(-5.35880 + 9.28171i) q^{65} +(1.12782 + 1.95345i) q^{67} +(8.82761 - 12.7867i) q^{69} +9.92978 q^{71} +2.50106 q^{73} +(12.8116 + 1.03535i) q^{75} +(-2.08386 - 3.60934i) q^{77} +(-3.16763 + 5.48650i) q^{79} +(-1.79726 - 8.81872i) q^{81} +(-5.52319 + 9.56645i) q^{83} +(-6.68823 - 11.5843i) q^{85} +(-5.04485 - 0.407691i) q^{87} -13.4697 q^{89} +3.04103 q^{91} +(-6.07677 + 8.80214i) q^{93} +(9.52529 + 16.4983i) q^{95} +(-9.46871 + 16.4003i) q^{97} +(-4.43170 - 11.6914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 3 * q^5 - 5 * q^7	$ 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) $ 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.742385	−	1.56488i	−0.428616	−	0.903487i
$3$	−0.742385	−	1.56488i	−0.428616	−	0.903487i
$4$		0			0
$5$	−1.76217	−	3.05216i	−0.788065	−	1.36497i	−0.927151	−	0.374688i	$-0.877750\pi$
$5$	−1.76217	−	3.05216i	−0.788065	−	1.36497i	0.139086	−	0.990280i	$-0.455583\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	−1.89773	+	2.32349i	−0.632576	+	0.774498i
$10$		0			0
$11$	−2.08386	+	3.60934i	−0.628306	+	1.08826i	0.359585	+	0.933112i	$0.382918\pi$
$11$	−2.08386	+	3.60934i	−0.628306	+	1.08826i	−0.987892	+	0.155146i	$0.950415\pi$
$12$		0			0
$13$	−1.52051	−	2.63361i	−0.421715	−	0.730431i	0.574393	−	0.818580i	$-0.305238\pi$
$13$	−1.52051	−	2.63361i	−0.421715	−	0.730431i	−0.996107	+	0.0881486i	$0.971905\pi$
$14$		0			0
$15$	−3.46807	+	5.02347i	−0.895453	+	1.29705i
$16$		0			0
$17$	3.79546			0.920533			0.460267	−	0.887781i	$-0.347754\pi$
$17$	3.79546			0.920533			0.460267	+	0.887781i	$0.347754\pi$
$18$		0			0
$19$	−5.40544			−1.24009			−0.620047	−	0.784565i	$-0.712886\pi$
$19$	−5.40544			−1.24009			−0.620047	+	0.784565i	$0.712886\pi$
$20$		0			0
$21$	1.72642	+	0.139518i	0.376736	+	0.0304453i
$22$		0			0
$23$	4.48540	+	7.76894i	0.935271	+	1.61994i	0.774150	+	0.633002i	$0.218178\pi$
$23$	4.48540	+	7.76894i	0.935271	+	1.61994i	0.161121	+	0.986935i	$0.448489\pi$
$24$		0			0
$25$	−3.71046	+	6.42670i	−0.742092	+	1.28534i
$26$		0			0
$27$	5.04485	+	1.24480i	0.970881	+	0.239561i
$28$		0			0
$29$	1.46107	−	2.53065i	0.271314	−	0.469929i	−0.697885	−	0.716210i	$-0.745875\pi$
$29$	1.46107	−	2.53065i	0.271314	−	0.469929i	0.969199	+	0.246281i	$0.0792086\pi$
$30$		0			0
$31$	−3.08767	−	5.34801i	−0.554563	−	0.960531i	−0.997937	−	0.0641943i	$-0.979552\pi$
$31$	−3.08767	−	5.34801i	−0.554563	−	0.960531i	0.443375	−	0.896336i	$-0.353781\pi$
$32$		0			0
$33$	7.19523	+	0.581470i	1.25253	+	0.101221i
$34$		0			0
$35$	3.52433			0.595721
$36$		0			0
$37$	−4.66649			−0.767166			−0.383583	−	0.923506i	$-0.625310\pi$
$37$	−4.66649			−0.767166			−0.383583	+	0.923506i	$0.625310\pi$
$38$		0			0
$39$	−2.99249	+	4.33458i	−0.479181	+	0.694088i
$40$		0			0
$41$	1.83828	+	3.18400i	0.287092	+	0.497257i	0.973114	−	0.230323i	$-0.0739782\pi$
$41$	1.83828	+	3.18400i	0.287092	+	0.497257i	−0.686023	+	0.727580i	$0.740645\pi$
$42$		0			0
$43$	−1.31777	+	2.28244i	−0.200958	+	0.348069i	−0.948837	−	0.315765i	$-0.897739\pi$
$43$	−1.31777	+	2.28244i	−0.200958	+	0.348069i	0.747879	+	0.663835i	$0.231072\pi$
$44$		0			0
$45$	10.4358	+	1.69779i	1.55568	+	0.253091i
$46$		0			0
$47$	0.860518	−	1.49046i	0.125519	−	0.217406i	−0.796416	−	0.604749i	$-0.793274\pi$
$47$	0.860518	−	1.49046i	0.125519	−	0.217406i	0.921936	+	0.387343i	$0.126607\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−2.81769	−	5.93945i	−0.394556	−	0.831690i
$52$		0			0
$53$	11.4209			1.56878			0.784392	−	0.620265i	$-0.212975\pi$
$53$	11.4209			1.56878			0.784392	+	0.620265i	$0.212975\pi$
$54$		0			0
$55$	14.6884			1.98058
$56$		0			0
$57$	4.01292	+	8.45890i	0.531524	+	1.12041i
$58$		0			0
$59$	−0.564482	−	0.977712i	−0.0734894	−	0.127287i	0.826939	−	0.562292i	$-0.190080\pi$
$59$	−0.564482	−	0.977712i	−0.0734894	−	0.127287i	−0.900428	+	0.435004i	$0.856747\pi$
$60$		0			0
$61$	−6.03597	+	10.4546i	−0.772826	+	1.33857i	0.163182	+	0.986596i	$0.447824\pi$
$61$	−6.03597	+	10.4546i	−0.772826	+	1.33857i	−0.936008	+	0.351979i	$0.885509\pi$
$62$		0			0
$63$	−1.06334	−	2.80523i	−0.133968	−	0.353426i
$64$		0			0
$65$	−5.35880	+	9.28171i	−0.664677	+	1.15125i
$66$		0			0
$67$	1.12782	+	1.95345i	0.137786	+	0.238652i	0.926658	−	0.375905i	$-0.122668\pi$
$67$	1.12782	+	1.95345i	0.137786	+	0.238652i	−0.788873	+	0.614557i	$0.789335\pi$
$68$		0			0
$69$	8.82761	−	12.7867i	1.06272	−	1.53934i
$70$		0			0
$71$	9.92978			1.17845			0.589224	−	0.807970i	$-0.299434\pi$
$71$	9.92978			1.17845			0.589224	+	0.807970i	$0.299434\pi$
$72$		0			0
$73$	2.50106			0.292727			0.146364	−	0.989231i	$-0.453243\pi$
$73$	2.50106			0.292727			0.146364	+	0.989231i	$0.453243\pi$
$74$		0			0
$75$	12.8116	+	1.03535i	1.47936	+	0.119552i
$76$		0			0
$77$	−2.08386	−	3.60934i	−0.237477	−	0.411323i
$78$		0			0
$79$	−3.16763	+	5.48650i	−0.356387	+	0.617280i	−0.987354	−	0.158530i	$-0.949325\pi$
$79$	−3.16763	+	5.48650i	−0.356387	+	0.617280i	0.630968	+	0.775809i	$0.282658\pi$
$80$		0			0
$81$	−1.79726	−	8.81872i	−0.199695	−	0.979858i
$82$		0			0
$83$	−5.52319	+	9.56645i	−0.606249	+	1.05005i	0.385604	+	0.922664i	$0.373993\pi$
$83$	−5.52319	+	9.56645i	−0.606249	+	1.05005i	−0.991853	+	0.127390i	$0.959340\pi$
$84$		0			0
$85$	−6.68823	−	11.5843i	−0.725440	−	1.25650i
$86$		0			0
$87$	−5.04485	−	0.407691i	−0.540864	−	0.0437090i
$88$		0			0
$89$	−13.4697			−1.42779			−0.713895	−	0.700253i	$-0.753071\pi$
$89$	−13.4697			−1.42779			−0.713895	+	0.700253i	$0.753071\pi$
$90$		0			0
$91$	3.04103			0.318786
$92$		0			0
$93$	−6.07677	+	8.80214i	−0.630132	+	0.912739i
$94$		0			0
$95$	9.52529	+	16.4983i	0.977274	+	1.69269i
$96$		0			0
$97$	−9.46871	+	16.4003i	−0.961401	+	1.66520i	−0.242414	+	0.970173i	$0.577939\pi$
$97$	−9.46871	+	16.4003i	−0.961401	+	1.66520i	−0.718987	+	0.695023i	$0.755394\pi$
$98$		0			0
$99$	−4.43170	−	11.6914i	−0.445403	−	1.17503i
$100$		0			0
$101$	−4.82940	+	8.36477i	−0.480544	+	0.832326i	−0.999751	−	0.0223224i	$-0.992894\pi$
$101$	−4.82940	+	8.36477i	−0.480544	+	0.832326i	0.519207	+	0.854648i	$0.326227\pi$
$102$		0			0
$103$	−0.981584	−	1.70015i	−0.0967183	−	0.167521i	0.813606	−	0.581416i	$-0.197501\pi$
$103$	−0.981584	−	1.70015i	−0.0967183	−	0.167521i	−0.910324	+	0.413895i	$0.864168\pi$
$104$		0			0
$105$	−2.61641	−	5.51517i	−0.255336	−	0.538226i
$106$		0			0
$107$	−18.5072			−1.78916			−0.894578	−	0.446912i	$-0.852524\pi$
$107$	−18.5072			−1.78916			−0.894578	+	0.446912i	$0.852524\pi$
$108$		0			0
$109$	2.67237			0.255967			0.127983	−	0.991776i	$-0.459150\pi$
$109$	2.67237			0.255967			0.127983	+	0.991776i	$0.459150\pi$
$110$		0			0
$111$	3.46433	+	7.30252i	0.328820	+	0.693125i
$112$		0			0
$113$	−4.65605	−	8.06452i	−0.438005	−	0.758646i	0.559531	−	0.828809i	$-0.310981\pi$
$113$	−4.65605	−	8.06452i	−0.438005	−	0.758646i	−0.997536	+	0.0701632i	$0.977648\pi$
$114$		0			0
$115$	15.8080	−	27.3803i	1.47411	−	2.55323i
$116$		0			0
$117$	9.00470	+	1.46497i	0.832485	+	0.135436i
$118$		0			0
$119$	−1.89773	+	3.28696i	−0.173964	+	0.301315i
$120$		0			0
$121$	−3.18491	−	5.51642i	−0.289537	−	0.501493i
$122$		0			0
$123$	3.61788	−	5.24046i	0.326213	−	0.472516i
$124$		0			0
$125$	8.53213			0.763137
$126$		0			0
$127$	−16.7663			−1.48777			−0.743883	−	0.668310i	$-0.767018\pi$
$127$	−16.7663			−1.48777			−0.743883	+	0.668310i	$0.767018\pi$
$128$		0			0
$129$	4.55005	+	0.367705i	0.400610	+	0.0323746i
$130$		0			0
$131$	−1.36566	−	2.36539i	−0.119318	−	0.206665i	0.800180	−	0.599761i	$-0.204737\pi$
$131$	−1.36566	−	2.36539i	−0.119318	−	0.206665i	−0.919498	+	0.393096i	$0.871404\pi$
$132$		0			0
$133$	2.70272	−	4.68125i	0.234356	−	0.405916i
$134$		0			0
$135$	−5.09054	−	17.5912i	−0.438124	−	1.51401i
$136$		0			0
$137$	−8.12870	+	14.0793i	−0.694482	+	1.20288i	0.275873	+	0.961194i	$0.411033\pi$
$137$	−8.12870	+	14.0793i	−0.694482	+	1.20288i	−0.970355	+	0.241684i	$0.922300\pi$
$138$		0			0
$139$	0.654057	+	1.13286i	0.0554764	+	0.0960879i	0.892430	−	0.451186i	$-0.148999\pi$
$139$	0.654057	+	1.13286i	0.0554764	+	0.0960879i	−0.836954	+	0.547274i	$0.815666\pi$
$140$		0			0
$141$	−2.97124	−	0.240115i	−0.250223	−	0.0202214i
$142$		0			0
$143$	12.6741			1.05986
$144$		0			0
$145$	−10.2986			−0.855251
$146$		0			0
$147$	−0.984037	+	1.42537i	−0.0811620	+	0.117562i
$148$		0			0
$149$	6.54580	+	11.3377i	0.536253	+	0.928818i	0.999102	+	0.0423802i	$0.0134941\pi$
$149$	6.54580	+	11.3377i	0.536253	+	0.928818i	−0.462848	+	0.886437i	$0.653173\pi$
$150$		0			0
$151$	7.10933	−	12.3137i	0.578549	−	1.00208i	−0.417097	−	0.908862i	$-0.636952\pi$
$151$	7.10933	−	12.3137i	0.578549	−	1.00208i	0.995646	−	0.0932143i	$-0.0297142\pi$
$152$		0			0
$153$	−7.20274	+	8.81872i	−0.582307	+	0.712951i
$154$		0			0
$155$	−10.8820	+	18.8482i	−0.874062	+	1.51392i
$156$		0			0
$157$	4.87043	+	8.43584i	0.388703	+	0.673253i	0.992275	−	0.124055i	$-0.0395899\pi$
$157$	4.87043	+	8.43584i	0.388703	+	0.673253i	−0.603572	+	0.797308i	$0.706257\pi$
$158$		0			0
$159$	−8.47872	−	17.8724i	−0.672406	−	1.41738i
$160$		0			0
$161$	−8.97080			−0.706998
$162$		0			0
$163$	−18.2129			−1.42655			−0.713274	−	0.700886i	$-0.752788\pi$
$163$	−18.2129			−1.42655			−0.713274	+	0.700886i	$0.752788\pi$
$164$		0			0
$165$	−10.9045	−	22.9857i	−0.848910	−	1.78943i
$166$		0			0
$167$	−7.81475	−	13.5355i	−0.604724	−	1.04741i	−0.992095	−	0.125488i	$-0.959950\pi$
$167$	−7.81475	−	13.5355i	−0.604724	−	1.04741i	0.387371	−	0.921924i	$-0.373383\pi$
$168$		0			0
$169$	1.87607	−	3.24945i	0.144313	−	0.249958i
$170$		0			0
$171$	10.2581	−	12.5595i	0.784454	−	0.960450i
$172$		0			0
$173$	5.23991	−	9.07579i	0.398383	−	0.690019i	−0.595144	−	0.803619i	$-0.702905\pi$
$173$	5.23991	−	9.07579i	0.398383	−	0.690019i	0.993527	+	0.113600i	$0.0362382\pi$
$174$		0			0
$175$	−3.71046	−	6.42670i	−0.280484	−	0.485813i
$176$		0			0
$177$	−1.11094	+	1.60919i	−0.0835036	+	0.120954i
$178$		0			0
$179$	18.0874			1.35192			0.675958	−	0.736940i	$-0.263730\pi$
$179$	18.0874			1.35192			0.675958	+	0.736940i	$0.263730\pi$
$180$		0			0
$181$	22.4020			1.66513			0.832564	−	0.553929i	$-0.186872\pi$
$181$	22.4020			1.66513			0.832564	+	0.553929i	$0.186872\pi$
$182$		0			0
$183$	20.8413	+	1.68425i	1.54063	+	0.124503i
$184$		0			0
$185$	8.22313	+	14.2429i	0.604577	+	1.04716i
$186$		0			0
$187$	−7.90918	+	13.6991i	−0.578377	+	1.00178i
$188$		0			0
$189$	−3.60045	+	3.74657i	−0.261894	+	0.272523i
$190$		0			0
$191$	−1.69490	+	2.93566i	−0.122639	+	0.212417i	−0.920808	−	0.390017i	$-0.872469\pi$
$191$	−1.69490	+	2.93566i	−0.122639	+	0.212417i	0.798169	+	0.602434i	$0.205802\pi$
$192$		0			0
$193$	−7.99828	−	13.8534i	−0.575729	−	0.997191i	−0.995962	−	0.0897754i	$-0.971385\pi$
$193$	−7.99828	−	13.8534i	−0.575729	−	0.997191i	0.420233	−	0.907416i	$-0.361948\pi$
$194$		0			0
$195$	18.5031	+	1.49530i	1.32503	+	0.107080i
$196$		0			0
$197$	−6.75083			−0.480977			−0.240488	−	0.970652i	$-0.577308\pi$
$197$	−6.75083			−0.480977			−0.240488	+	0.970652i	$0.577308\pi$
$198$		0			0
$199$	−11.4209			−0.809608			−0.404804	−	0.914404i	$-0.632660\pi$
$199$	−11.4209			−0.809608			−0.404804	+	0.914404i	$0.632660\pi$
$200$		0			0
$201$	2.21964	−	3.21513i	0.156561	−	0.226777i
$202$		0			0
$203$	1.46107	+	2.53065i	0.102547	+	0.177617i
$204$		0			0
$205$	6.47872	−	11.2215i	0.452494	−	0.783742i
$206$		0			0
$207$	−26.5632	−	4.32154i	−1.84627	−	0.300368i
$208$		0			0
$209$	11.2642	−	19.5101i	0.779158	−	1.34954i
$210$		0			0
$211$	6.40147	+	11.0877i	0.440695	+	0.763307i	0.997741	−	0.0671751i	$-0.0213986\pi$
$211$	6.40147	+	11.0877i	0.440695	+	0.763307i	−0.557046	+	0.830482i	$0.688065\pi$
$212$		0			0
$213$	−7.37172	−	15.5390i	−0.505102	−	1.06471i
$214$		0			0
$215$	9.28851			0.633471
$216$		0			0
$217$	6.17535			0.419210
$218$		0			0
$219$	−1.85675	−	3.91387i	−0.125468	−	0.264475i
$220$		0			0
$221$	−5.77105	−	9.99574i	−0.388203	−	0.672387i
$222$		0			0
$223$	−5.86357	+	10.1560i	−0.392654	+	0.680096i	−0.992799	−	0.119795i	$-0.961776\pi$
$223$	−5.86357	+	10.1560i	−0.392654	+	0.680096i	0.600145	+	0.799891i	$0.295110\pi$
$224$		0			0
$225$	−7.89097	−	20.8174i	−0.526065	−	1.38782i
$226$		0			0
$227$	−6.30312	+	10.9173i	−0.418353	+	0.724608i	−0.995774	−	0.0918384i	$-0.970726\pi$
$227$	−6.30312	+	10.9173i	−0.418353	+	0.724608i	0.577421	+	0.816446i	$0.304059\pi$
$228$		0			0
$229$	4.34480	+	7.52542i	0.287113	+	0.497294i	0.973119	−	0.230302i	$-0.0739713\pi$
$229$	4.34480	+	7.52542i	0.287113	+	0.497294i	−0.686007	+	0.727595i	$0.740638\pi$
$230$		0			0
$231$	−4.10118	+	5.94052i	−0.269838	+	0.390857i
$232$		0			0
$233$	12.9251			0.846748			0.423374	−	0.905955i	$-0.360846\pi$
$233$	12.9251			0.846748			0.423374	+	0.905955i	$0.360846\pi$
$234$		0			0
$235$	−6.06550			−0.395670
$236$		0			0
$237$	10.9373	+	0.883883i	0.710457	+	0.0574143i
$238$		0			0
$239$	−10.8020	−	18.7097i	−0.698725	−	1.21023i	−0.968909	−	0.247419i	$-0.920418\pi$
$239$	−10.8020	−	18.7097i	−0.698725	−	1.21023i	0.270183	−	0.962809i	$-0.412916\pi$
$240$		0			0
$241$	−1.66179	+	2.87831i	−0.107046	+	0.185408i	−0.914572	−	0.404423i	$-0.867472\pi$
$241$	−1.66179	+	2.87831i	−0.107046	+	0.185408i	0.807527	+	0.589831i	$0.200806\pi$
$242$		0			0
$243$	−12.4660	+	9.35939i	−0.799696	+	0.600405i
$244$		0			0
$245$	−1.76217	+	3.05216i	−0.112581	+	0.194995i
$246$		0			0
$247$	8.21905	+	14.2358i	0.522966	+	0.905803i
$248$		0			0
$249$	19.0707	+	1.54117i	1.20856	+	0.0976675i
$250$		0			0
$251$	−2.67969			−0.169140			−0.0845701	−	0.996418i	$-0.526952\pi$
$251$	−2.67969			−0.169140			−0.0845701	+	0.996418i	$0.526952\pi$
$252$		0			0
$253$	−37.3877			−2.35055
$254$		0			0
$255$	−13.1629	+	19.0663i	−0.824294	+	1.19398i
$256$		0			0
$257$	−3.75443	−	6.50286i	−0.234195	−	0.405637i	0.724844	−	0.688913i	$-0.241912\pi$
$257$	−3.75443	−	6.50286i	−0.234195	−	0.405637i	−0.959038	+	0.283276i	$0.908579\pi$
$258$		0			0
$259$	2.33325	−	4.04130i	0.144981	−	0.251114i
$260$		0			0
$261$	3.10723	+	8.19727i	0.192333	+	0.507398i
$262$		0			0
$263$	9.35062	−	16.1957i	0.576584	−	0.998672i	−0.419284	−	0.907855i	$-0.637719\pi$
$263$	9.35062	−	16.1957i	0.576584	−	0.998672i	0.995868	−	0.0908171i	$-0.0289479\pi$
$264$		0			0
$265$	−20.1256	−	34.8585i	−1.23630	−	2.14134i
$266$		0			0
$267$	9.99974	+	21.0786i	0.611974	+	1.28999i
$268$		0			0
$269$	−17.0035			−1.03672			−0.518360	−	0.855163i	$-0.673457\pi$
$269$	−17.0035			−1.03672			−0.518360	+	0.855163i	$0.673457\pi$
$270$		0			0
$271$	−23.1427			−1.40582			−0.702910	−	0.711279i	$-0.748116\pi$
$271$	−23.1427			−1.40582			−0.702910	+	0.711279i	$0.748116\pi$
$272$		0			0
$273$	−2.25761	−	4.75886i	−0.136637	−	0.288019i
$274$		0			0
$275$	−15.4641	−	26.7846i	−0.932522	−	1.61518i
$276$		0			0
$277$	6.93092	−	12.0047i	0.416438	−	0.721293i	−0.579140	−	0.815228i	$-0.696611\pi$
$277$	6.93092	−	12.0047i	0.416438	−	0.721293i	0.995578	+	0.0939357i	$0.0299448\pi$
$278$		0			0
$279$	18.2856	+	2.97487i	1.09473	+	0.178101i
$280$		0			0
$281$	−4.56926	+	7.91419i	−0.272579	+	0.472121i	−0.969521	−	0.245006i	$-0.921210\pi$
$281$	−4.56926	+	7.91419i	−0.272579	+	0.472121i	0.696942	+	0.717127i	$0.254543\pi$
$282$		0			0
$283$	−3.45421	−	5.98287i	−0.205331	−	0.355645i	0.744907	−	0.667169i	$-0.232494\pi$
$283$	−3.45421	−	5.98287i	−0.205331	−	0.355645i	−0.950238	+	0.311524i	$0.899161\pi$
$284$		0			0
$285$	18.7465	−	27.1541i	1.11045	−	1.60847i
$286$		0			0
$287$	−3.67657			−0.217021
$288$		0			0
$289$	−2.59451			−0.152618
$290$		0			0
$291$	32.6940	+	2.64211i	1.91655	+	0.154883i
$292$		0			0
$293$	9.30083	+	16.1095i	0.543361	+	0.941128i	0.998708	+	0.0508143i	$0.0161817\pi$
$293$	9.30083	+	16.1095i	0.543361	+	0.941128i	−0.455348	+	0.890314i	$0.650485\pi$
$294$		0			0
$295$	−1.98942	+	3.44578i	−0.115829	+	0.200621i
$296$		0			0
$297$	−15.0056	+	15.6146i	−0.870715	+	0.906051i
$298$		0			0
$299$	13.6402	−	23.6256i	0.788835	−	1.36630i
$300$		0			0
$301$	−1.31777	−	2.28244i	−0.0759550	−	0.131558i
$302$		0			0
$303$	16.6752	+	1.34758i	0.957964	+	0.0774162i
$304$		0			0
$305$	42.5455			2.43615
$306$		0			0
$307$	−13.9553			−0.796473			−0.398236	−	0.917283i	$-0.630378\pi$
$307$	−13.9553			−0.796473			−0.398236	+	0.917283i	$0.630378\pi$
$308$		0			0
$309$	−1.93183	+	2.79823i	−0.109898	+	0.159186i
$310$		0			0
$311$	−8.86140	−	15.3484i	−0.502484	−	0.870327i	−0.999996	−	0.00287031i	$-0.999086\pi$
$311$	−8.86140	−	15.3484i	−0.502484	−	0.870327i	0.497512	−	0.867457i	$-0.334247\pi$
$312$		0			0
$313$	−7.38305	+	12.7878i	−0.417315	+	0.722810i	−0.995668	−	0.0929758i	$-0.970362\pi$
$313$	−7.38305	+	12.7878i	−0.417315	+	0.722810i	0.578354	+	0.815786i	$0.303695\pi$
$314$		0			0
$315$	−6.68823	+	8.18877i	−0.376839	+	0.461385i
$316$		0			0
$317$	1.28820	−	2.23122i	0.0723523	−	0.125318i	−0.827580	−	0.561348i	$-0.810283\pi$
$317$	1.28820	−	2.23122i	0.0723523	−	0.125318i	0.899932	+	0.436031i	$0.143616\pi$
$318$		0			0
$319$	6.08932	+	10.5470i	0.340936	+	0.590519i
$320$		0			0
$321$	13.7395	+	28.9616i	0.766861	+	1.61648i
$322$		0			0
$323$	−20.5161			−1.14155
$324$		0			0
$325$	22.5672			1.25180
$326$		0			0
$327$	−1.98393	−	4.18195i	−0.109712	−	0.231263i
$328$		0			0
$329$	0.860518	+	1.49046i	0.0474419	+	0.0821718i
$330$		0			0
$331$	−0.158777	+	0.275009i	−0.00872716	+	0.0151159i	−0.870356	−	0.492423i	$-0.836111\pi$
$331$	−0.158777	+	0.275009i	−0.00872716	+	0.0151159i	0.861629	+	0.507539i	$0.169445\pi$
$332$		0			0
$333$	8.85573	−	10.8426i	0.485291	−	0.594169i
$334$		0			0
$335$	3.97483	−	6.88460i	0.217168	−	0.376146i
$336$		0			0
$337$	6.97761	+	12.0856i	0.380095	+	0.658343i	0.991075	−	0.133302i	$-0.0425581\pi$
$337$	6.97761	+	12.0856i	0.380095	+	0.658343i	−0.610981	+	0.791645i	$0.709225\pi$
$338$		0			0
$339$	−9.16346	+	13.2732i	−0.497691	+	0.720899i
$340$		0			0
$341$	25.7371			1.39374
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−54.5827	−	4.41101i	−2.93864	−	0.237481i
$346$		0			0
$347$	12.0401	+	20.8540i	0.646344	+	1.11950i	0.983989	+	0.178228i	$0.0570364\pi$
$347$	12.0401	+	20.8540i	0.646344	+	1.11950i	−0.337645	+	0.941274i	$0.609630\pi$
$348$		0			0
$349$	13.1616	−	22.7966i	0.704526	−	1.22027i	−0.262337	−	0.964976i	$-0.584493\pi$
$349$	13.1616	−	22.7966i	0.704526	−	1.22027i	0.966862	−	0.255298i	$-0.0821736\pi$
$350$		0			0
$351$	−4.39245	−	15.1789i	−0.234452	−	0.810189i
$352$		0			0
$353$	−1.30502	+	2.26036i	−0.0694590	+	0.120307i	−0.898663	−	0.438639i	$-0.855461\pi$
$353$	−1.30502	+	2.26036i	−0.0694590	+	0.120307i	0.829204	+	0.558946i	$0.188794\pi$
$354$		0			0
$355$	−17.4979	−	30.3073i	−0.928693	−	1.60854i
$356$		0			0
$357$	6.55256	+	0.529534i	0.346798	+	0.0280259i
$358$		0			0
$359$	−3.48082			−0.183711			−0.0918553	−	0.995772i	$-0.529280\pi$
$359$	−3.48082			−0.183711			−0.0918553	+	0.995772i	$0.529280\pi$
$360$		0			0
$361$	10.2188			0.537832
$362$		0			0
$363$	−6.26814	+	9.07932i	−0.328992	+	0.476541i
$364$		0			0
$365$	−4.40729	−	7.63365i	−0.230688	−	0.399563i
$366$		0			0
$367$	0.960991	−	1.66449i	0.0501633	−	0.0868854i	−0.839853	−	0.542813i	$-0.817359\pi$
$367$	0.960991	−	1.66449i	0.0501633	−	0.0868854i	0.890017	+	0.455928i	$0.150692\pi$
$368$		0			0
$369$	−10.8866	−	1.77113i	−0.566732	−	0.0922011i
$370$		0			0
$371$	−5.71046	+	9.89081i	−0.296472	+	0.513505i
$372$		0			0
$373$	−16.1228	−	27.9255i	−0.834806	−	1.44593i	−0.894189	−	0.447691i	$-0.852247\pi$
$373$	−16.1228	−	27.9255i	−0.834806	−	1.44593i	0.0593828	−	0.998235i	$-0.481087\pi$
$374$		0			0
$375$	−6.33412	−	13.3518i	−0.327093	−	0.689484i
$376$		0			0
$377$	−8.88631			−0.457668
$378$		0			0
$379$	4.98892			0.256264			0.128132	−	0.991757i	$-0.459102\pi$
$379$	4.98892			0.256264			0.128132	+	0.991757i	$0.459102\pi$
$380$		0			0
$381$	12.4470	+	26.2373i	0.637680	+	1.34418i
$382$		0			0
$383$	−0.284377	−	0.492556i	−0.0145310	−	0.0251684i	0.858668	−	0.512531i	$-0.171292\pi$
$383$	−0.284377	−	0.492556i	−0.0145310	−	0.0251684i	−0.873199	+	0.487363i	$0.837959\pi$
$384$		0			0
$385$	−7.34420	+	12.7205i	−0.374295	+	0.648298i
$386$		0			0
$387$	−2.80248	−	7.39329i	−0.142458	−	0.375822i
$388$		0			0
$389$	−12.4259	+	21.5223i	−0.630017	+	1.09122i	0.357531	+	0.933901i	$0.383619\pi$
$389$	−12.4259	+	21.5223i	−0.630017	+	1.09122i	−0.987548	+	0.157320i	$0.949715\pi$
$390$		0			0
$391$	17.0241	+	29.4867i	0.860948	+	1.49121i
$392$		0			0
$393$	−2.68772	+	3.89313i	−0.135577	+	0.196382i
$394$		0			0
$395$	22.3276			1.12342
$396$		0			0
$397$	−3.87576			−0.194519			−0.0972593	−	0.995259i	$-0.531008\pi$
$397$	−3.87576			−0.194519			−0.0972593	+	0.995259i	$0.531008\pi$
$398$		0			0
$399$	−9.33208	−	0.754156i	−0.467188	−	0.0377550i
$400$		0			0
$401$	7.43200	+	12.8726i	0.371136	+	0.642827i	0.989741	−	0.142876i	$-0.0456349\pi$
$401$	7.43200	+	12.8726i	0.371136	+	0.642827i	−0.618604	+	0.785703i	$0.712302\pi$
$402$		0			0
$403$	−9.38970	+	16.2634i	−0.467734	+	0.810140i
$404$		0			0
$405$	−23.7491	+	21.0256i	−1.18010	+	1.04477i
$406$		0			0
$407$	9.72429	−	16.8430i	0.482015	−	0.834875i
$408$		0			0
$409$	11.6707	+	20.2142i	0.577078	+	0.999529i	0.995812	+	0.0914201i	$0.0291406\pi$
$409$	11.6707	+	20.2142i	0.577078	+	0.999529i	−0.418734	+	0.908109i	$0.637526\pi$
$410$		0			0
$411$	28.0671	+	2.26820i	1.38445	+	0.111882i
$412$		0			0
$413$	1.12896			0.0555527
$414$		0			0
$415$	38.9311			1.91105
$416$		0			0
$417$	1.28723	−	1.86454i	0.0630360	−	0.0913070i
$418$		0			0
$419$	10.7749	+	18.6627i	0.526389	+	0.911733i	0.999527	+	0.0307446i	$0.00978785\pi$
$419$	10.7749	+	18.6627i	0.526389	+	0.911733i	−0.473138	+	0.880988i	$0.656879\pi$
$420$		0			0
$421$	9.83901	−	17.0417i	0.479524	−	0.830560i	−0.520200	−	0.854044i	$-0.674143\pi$
$421$	9.83901	−	17.0417i	0.479524	−	0.830560i	0.999724	+	0.0234847i	$0.00747609\pi$
$422$		0			0
$423$	1.83005	+	4.82790i	0.0889800	+	0.234740i
$424$		0			0
$425$	−14.0829	+	24.3923i	−0.683120	+	1.18320i
$426$		0			0
$427$	−6.03597	−	10.4546i	−0.292101	−	0.505934i
$428$		0			0
$429$	−9.40909	−	19.8335i	−0.454275	−	0.957573i
$430$		0			0
$431$	19.3862			0.933798			0.466899	−	0.884311i	$-0.345371\pi$
$431$	19.3862			0.933798			0.466899	+	0.884311i	$0.345371\pi$
$432$		0			0
$433$	34.9983			1.68191			0.840956	−	0.541104i	$-0.181993\pi$
$433$	34.9983			1.68191			0.840956	+	0.541104i	$0.181993\pi$
$434$		0			0
$435$	7.64552	+	16.1161i	0.366575	+	0.772708i
$436$		0			0
$437$	−24.2456	−	41.9946i	−1.15982	−	2.00887i
$438$		0			0
$439$	−1.94437	+	3.36775i	−0.0927999	+	0.160734i	−0.908688	−	0.417475i	$-0.862915\pi$
$439$	−1.94437	+	3.36775i	−0.0927999	+	0.160734i	0.815888	+	0.578209i	$0.196248\pi$
$440$		0			0
$441$	2.96107	+	0.481734i	0.141003	+	0.0229397i
$442$		0			0
$443$	−10.8632	+	18.8156i	−0.516126	+	0.893956i	0.483699	+	0.875235i	$0.339293\pi$
$443$	−10.8632	+	18.8156i	−0.516126	+	0.893956i	−0.999825	+	0.0187219i	$0.994040\pi$
$444$		0			0
$445$	23.7359	+	41.1118i	1.12519	+	1.94889i
$446$		0			0
$447$	12.8826	−	18.6603i	0.609327	−	0.882604i
$448$		0			0
$449$	−19.3098			−0.911287			−0.455643	−	0.890162i	$-0.650591\pi$
$449$	−19.3098			−0.911287			−0.455643	+	0.890162i	$0.650591\pi$
$450$		0			0
$451$	−15.3229			−0.721526
$452$		0			0
$453$	−24.5474	−	1.98376i	−1.15334	−	0.0932050i
$454$		0			0
$455$	−5.35880	−	9.28171i	−0.251224	−	0.435133i
$456$		0			0
$457$	8.03867	−	13.9234i	0.376033	−	0.651308i	−0.614448	−	0.788957i	$-0.710621\pi$
$457$	8.03867	−	13.9234i	0.376033	−	0.651308i	0.990481	+	0.137649i	$0.0439546\pi$
$458$		0			0
$459$	19.1475	+	4.72458i	0.893729	+	0.220524i
$460$		0			0
$461$	−16.6888	+	28.9058i	−0.777274	+	1.34628i	0.156233	+	0.987720i	$0.450065\pi$
$461$	−16.6888	+	28.9058i	−0.777274	+	1.34628i	−0.933507	+	0.358558i	$0.883269\pi$
$462$		0			0
$463$	6.67623	+	11.5636i	0.310271	+	0.537404i	0.978421	−	0.206622i	$-0.0662470\pi$
$463$	6.67623	+	11.5636i	0.310271	+	0.537404i	−0.668150	+	0.744026i	$0.732914\pi$
$464$		0			0
$465$	37.5738	+	3.03646i	1.74244	+	0.140813i
$466$		0			0
$467$	−11.4976			−0.532047			−0.266023	−	0.963967i	$-0.585710\pi$
$467$	−11.4976			−0.532047			−0.266023	+	0.963967i	$0.585710\pi$
$468$		0			0
$469$	−2.25565			−0.104156
$470$		0			0
$471$	9.58537	−	13.8843i	0.441671	−	0.639755i
$472$		0			0
$473$	−5.49208	−	9.51256i	−0.252526	−	0.437388i
$474$		0			0
$475$	20.0567	−	34.7392i	0.920264	−	1.59394i
$476$		0			0
$477$	−21.6738	+	26.5364i	−0.992375	+	1.21502i
$478$		0			0
$479$	−2.48078	+	4.29684i	−0.113350	+	0.196328i	−0.917119	−	0.398614i	$-0.869491\pi$
$479$	−2.48078	+	4.29684i	−0.113350	+	0.196328i	0.803769	+	0.594941i	$0.202825\pi$
$480$		0			0
$481$	7.09547	+	12.2897i	0.323525	+	0.560363i
$482$		0			0
$483$	6.65979	+	14.0383i	0.303031	+	0.638764i
$484$		0			0
$485$	66.7417			3.03059
$486$		0			0
$487$	−26.4801			−1.19993			−0.599964	−	0.800027i	$-0.704818\pi$
$487$	−26.4801			−1.19993			−0.599964	+	0.800027i	$0.704818\pi$
$488$		0			0
$489$	13.5210	+	28.5011i	0.611441	+	1.28887i
$490$		0			0
$491$	−10.7019	−	18.5362i	−0.482970	−	0.836529i	0.516839	−	0.856083i	$-0.327109\pi$
$491$	−10.7019	−	18.5362i	−0.482970	−	0.836529i	−0.999809	+	0.0195540i	$0.993775\pi$
$492$		0			0
$493$	5.54543	−	9.60496i	0.249753	−	0.432586i
$494$		0			0
$495$	−27.8746	+	34.1284i	−1.25287	+	1.53396i
$496$		0			0
$497$	−4.96489	+	8.59944i	−0.222706	+	0.385738i
$498$		0			0
$499$	−6.63554	−	11.4931i	−0.297048	−	0.514501i	0.678412	−	0.734682i	$-0.262669\pi$
$499$	−6.63554	−	11.4931i	−0.297048	−	0.514501i	−0.975459	+	0.220181i	$0.929335\pi$
$500$		0			0
$501$	−15.3800	+	22.2778i	−0.687128	+	0.995298i
$502$		0			0
$503$	32.3009			1.44022			0.720112	−	0.693857i	$-0.244090\pi$
$503$	32.3009			1.44022			0.720112	+	0.693857i	$0.244090\pi$
$504$		0			0
$505$	34.0409			1.51480
$506$		0			0
$507$	−6.47779	−	0.523491i	−0.287689	−	0.0232491i
$508$		0			0
$509$	−11.3401	−	19.6417i	−0.502642	−	0.870601i	−0.999995	−	0.00305334i	$-0.999028\pi$
$509$	−11.3401	−	19.6417i	−0.502642	−	0.870601i	0.497353	−	0.867548i	$-0.334305\pi$
$510$		0			0
$511$	−1.25053	+	2.16598i	−0.0553203	+	0.0958175i
$512$		0			0
$513$	−27.2696	−	6.72868i	−1.20398	−	0.297079i
$514$		0			0
$515$	−3.45943	+	5.99190i	−0.152441	+	0.264035i
$516$		0			0
$517$	3.58639	+	6.21181i	0.157729	+	0.273195i
$518$		0			0
$519$	−18.0926	−	1.46212i	−0.794177	−	0.0641800i
$520$		0			0
$521$	−23.2159			−1.01710			−0.508552	−	0.861031i	$-0.669819\pi$
$521$	−23.2159			−1.01710			−0.508552	+	0.861031i	$0.669819\pi$
$522$		0			0
$523$	20.4196			0.892885			0.446442	−	0.894812i	$-0.352691\pi$
$523$	20.4196			0.892885			0.446442	+	0.894812i	$0.352691\pi$
$524$		0			0
$525$	−7.30246	+	10.5775i	−0.318706	+	0.461641i
$526$		0			0
$527$	−11.7191	−	20.2981i	−0.510493	−	0.884200i
$528$		0			0
$529$	−28.7377	+	49.7751i	−1.24946	+	2.16413i
$530$		0			0
$531$	3.34294	+	0.543860i	0.145071	+	0.0236015i
$532$		0			0
$533$	5.59027	−	9.68264i	0.242142	−	0.419402i
$534$		0			0
$535$	32.6127	+	56.4869i	1.40997	+	2.44214i
$536$		0			0
$537$	−13.4278	−	28.3047i	−0.579454	−	1.22144i
$538$		0			0
$539$	4.16771			0.179516
$540$		0			0
$541$	−39.4226			−1.69491			−0.847455	−	0.530868i	$-0.821866\pi$
$541$	−39.4226			−1.69491			−0.847455	+	0.530868i	$0.821866\pi$
$542$		0			0
$543$	−16.6309	−	35.0566i	−0.713701	−	1.50442i
$544$		0			0
$545$	−4.70916	−	8.15651i	−0.201718	−	0.349386i
$546$		0			0
$547$	12.2911	−	21.2888i	0.525529	−	0.910243i	−0.474029	−	0.880509i	$-0.657201\pi$
$547$	12.2911	−	21.2888i	0.525529	−	0.910243i	0.999558	−	0.0297339i	$-0.00946598\pi$
$548$		0			0
$549$	−12.8366	−	33.8645i	−0.547852	−	1.44530i
$550$		0			0
$551$	−7.89773	+	13.6793i	−0.336455	+	0.582756i
$552$		0			0
$553$	−3.16763	−	5.48650i	−0.134701	−	0.233310i
$554$		0			0
$555$	16.1837	−	23.4420i	0.686962	−	0.995056i
$556$		0			0
$557$	−12.4619			−0.528026			−0.264013	−	0.964519i	$-0.585046\pi$
$557$	−12.4619			−0.528026			−0.264013	+	0.964519i	$0.585046\pi$
$558$		0			0
$559$	8.01475			0.338988
$560$		0			0
$561$	27.3092	+	2.20694i	1.15299	+	0.0931773i
$562$		0			0
$563$	−5.24949	−	9.09239i	−0.221240	−	0.383198i	0.733945	−	0.679209i	$-0.237677\pi$
$563$	−5.24949	−	9.09239i	−0.221240	−	0.383198i	−0.955185	+	0.296011i	$0.904344\pi$
$564$		0			0
$565$	−16.4095	+	28.4221i	−0.690352	+	1.19572i
$566$		0			0
$567$	8.53587	+	2.85289i	0.358473	+	0.119810i
$568$		0			0
$569$	5.11698	−	8.86288i	0.214515	−	0.371551i	−0.738607	−	0.674136i	$-0.764516\pi$
$569$	5.11698	−	8.86288i	0.214515	−	0.371551i	0.953122	+	0.302585i	$0.0978495\pi$
$570$		0			0
$571$	−2.34986	−	4.07008i	−0.0983387	−	0.170328i	0.812658	−	0.582740i	$-0.198020\pi$
$571$	−2.34986	−	4.07008i	−0.0983387	−	0.170328i	−0.910997	+	0.412413i	$0.864686\pi$
$572$		0			0
$573$	5.85224	+	0.472939i	0.244481	+	0.0197573i
$574$		0			0
$575$	−66.5716			−2.77623
$576$		0			0
$577$	−27.3980			−1.14060			−0.570298	−	0.821438i	$-0.693172\pi$
$577$	−27.3980			−1.14060			−0.570298	+	0.821438i	$0.693172\pi$
$578$		0			0
$579$	−15.7412	+	22.8010i	−0.654182	+	0.947576i
$580$		0			0
$581$	−5.52319	−	9.56645i	−0.229141	−	0.396883i
$582$		0			0
$583$	−23.7995	+	41.2220i	−0.985677	+	1.70724i
$584$		0			0
$585$	−11.3965	−	30.0653i	−0.471186	−	1.24305i
$586$		0			0
$587$	−0.334943	+	0.580138i	−0.0138246	+	0.0239448i	−0.872855	−	0.487980i	$-0.837734\pi$
$587$	−0.334943	+	0.580138i	−0.0138246	+	0.0239448i	0.859030	+	0.511925i	$0.171067\pi$
$588$		0			0
$589$	16.6902	+	28.9084i	0.687710	+	1.19115i
$590$		0			0
$591$	5.01172	+	10.5643i	0.206155	+	0.434556i
$592$		0			0
$593$	−9.83861			−0.404023			−0.202012	−	0.979383i	$-0.564748\pi$
$593$	−9.83861			−0.404023			−0.202012	+	0.979383i	$0.564748\pi$
$594$		0			0
$595$	13.3765			0.548381
$596$		0			0
$597$	8.47872	+	17.8724i	0.347011	+	0.731470i
$598$		0			0
$599$	−0.0135159	−	0.0234103i	−0.000552245	−	0.000956517i	0.865749	−	0.500478i	$-0.166842\pi$
$599$	−0.0135159	−	0.0234103i	−0.000552245	−	0.000956517i	−0.866301	+	0.499522i	$0.833509\pi$
$600$		0			0
$601$	18.1676	−	31.4672i	0.741073	−	1.28358i	−0.210934	−	0.977500i	$-0.567651\pi$
$601$	18.1676	−	31.4672i	0.741073	−	1.28358i	0.952007	−	0.306076i	$-0.0990160\pi$
$602$		0			0
$603$	−6.67913	−	1.08662i	−0.271995	−	0.0442506i
$604$		0			0
$605$	−11.2247	+	19.4417i	−0.456348	+	0.790418i
$606$		0			0
$607$	10.6590	+	18.4620i	0.432637	+	0.749349i	0.997099	−	0.0761098i	$-0.0242500\pi$
$607$	10.6590	+	18.4620i	0.432637	+	0.749349i	−0.564463	+	0.825459i	$0.690917\pi$
$608$		0			0
$609$	2.87549	−	4.16512i	0.116521	−	0.168779i
$610$		0			0
$611$	−5.23372			−0.211734
$612$		0			0
$613$	−12.5229			−0.505793			−0.252897	−	0.967493i	$-0.581383\pi$
$613$	−12.5229			−0.505793			−0.252897	+	0.967493i	$0.581383\pi$
$614$		0			0
$615$	−22.3700	−	1.80779i	−0.902046	−	0.0728973i
$616$		0			0
$617$	22.2691	+	38.5713i	0.896521	+	1.55282i	0.831911	+	0.554910i	$0.187247\pi$
$617$	22.2691	+	38.5713i	0.896521	+	1.55282i	0.0646104	+	0.997911i	$0.479420\pi$
$618$		0			0
$619$	14.4100	−	24.9588i	0.579186	−	1.00318i	−0.416387	−	0.909187i	$-0.636704\pi$
$619$	14.4100	−	24.9588i	0.579186	−	1.00318i	0.995573	−	0.0939920i	$-0.0299628\pi$
$620$		0			0
$621$	12.9574	+	44.7766i	0.519963	+	1.79682i
$622$		0			0
$623$	6.73487	−	11.6651i	0.269827	−	0.467354i
$624$		0			0
$625$	3.51728	+	6.09210i	0.140691	+	0.243684i
$626$		0			0
$627$	−38.8934	−	3.14310i	−1.55325	−	0.125523i
$628$		0			0
$629$	−17.7115			−0.706202
$630$		0			0
$631$	35.3192			1.40604			0.703018	−	0.711172i	$-0.251835\pi$
$631$	35.3192			1.40604			0.703018	+	0.711172i	$0.251835\pi$
$632$		0			0
$633$	12.5986	−	18.2489i	0.500748	−	0.725328i
$634$		0			0
$635$	29.5449	+	51.1733i	1.17246	+	2.03075i
$636$		0			0
$637$	−1.52051	+	2.63361i	−0.0602450	+	0.104347i
$638$		0			0
$639$	−18.8440	+	23.0718i	−0.745458	+	0.912706i
$640$		0			0
$641$	18.2261	−	31.5685i	0.719888	−	1.24688i	−0.241156	−	0.970486i	$-0.577526\pi$
$641$	18.2261	−	31.5685i	0.719888	−	1.24688i	0.961044	−	0.276396i	$-0.0891402\pi$
$642$		0			0
$643$	19.8629	+	34.4036i	0.783317	+	1.35674i	0.929999	+	0.367561i	$0.119807\pi$
$643$	19.8629	+	34.4036i	0.783317	+	1.35674i	−0.146682	+	0.989184i	$0.546860\pi$
$644$		0			0
$645$	−6.89566	−	14.5355i	−0.271516	−	0.572333i
$646$		0			0
$647$	0.649904			0.0255504			0.0127752	−	0.999918i	$-0.495933\pi$
$647$	0.649904			0.0255504			0.0127752	+	0.999918i	$0.495933\pi$
$648$		0			0
$649$	4.70520			0.184695
$650$		0			0
$651$	−4.58449	−	9.66371i	−0.179680	−	0.378751i
$652$		0			0
$653$	−7.40239	−	12.8213i	−0.289678	−	0.501737i	0.684055	−	0.729430i	$-0.260215\pi$
$653$	−7.40239	−	12.8213i	−0.289678	−	0.501737i	−0.973733	+	0.227694i	$0.926881\pi$
$654$		0			0
$655$	−4.81303	+	8.33641i	−0.188061	+	0.325731i
$656$		0			0
$657$	−4.74634	+	5.81121i	−0.185172	+	0.226717i
$658$		0			0
$659$	−3.53713	+	6.12649i	−0.137787	+	0.238654i	−0.926659	−	0.375904i	$-0.877332\pi$
$659$	−3.53713	+	6.12649i	−0.137787	+	0.238654i	0.788872	+	0.614558i	$0.210666\pi$
$660$		0			0
$661$	12.3419	+	21.3767i	0.480043	+	0.831459i	0.999738	−	0.0228933i	$-0.00728778\pi$
$661$	12.3419	+	21.3767i	0.480043	+	0.831459i	−0.519695	+	0.854352i	$0.673954\pi$
$662$		0			0
$663$	−11.3578	+	16.4517i	−0.441102	+	0.638932i
$664$		0			0
$665$	−19.0506			−0.738750
$666$		0			0
$667$	26.2139			1.01501
$668$		0			0
$669$	20.2460	+	1.63615i	0.782756	+	0.0632571i
$670$		0			0
$671$	−25.1562	−	43.5718i	−0.971143	−	1.68207i
$672$		0			0
$673$	16.5508	−	28.6669i	0.637988	−	1.10503i	−0.347886	−	0.937537i	$-0.613100\pi$
$673$	16.5508	−	28.6669i	0.637988	−	1.10503i	0.985874	−	0.167491i	$-0.0535664\pi$
$674$		0			0
$675$	−26.7186	+	27.8030i	−1.02840	+	1.07014i
$676$		0			0
$677$	−5.59003	+	9.68222i	−0.214842	+	0.372118i	−0.953224	−	0.302265i	$-0.902257\pi$
$677$	−5.59003	+	9.68222i	−0.214842	+	0.372118i	0.738381	+	0.674383i	$0.235590\pi$
$678$		0			0
$679$	−9.46871	−	16.4003i	−0.363376	−	0.629385i
$680$		0			0
$681$	21.7637	+	1.75879i	0.833986	+	0.0673972i
$682$		0			0
$683$	33.1925			1.27008			0.635039	−	0.772480i	$-0.280984\pi$
$683$	33.1925			1.27008			0.635039	+	0.772480i	$0.280984\pi$
$684$		0			0
$685$	57.2965			2.18919
$686$		0			0
$687$	8.55089	−	12.3859i	0.326237	−	0.472551i
$688$		0			0
$689$	−17.3657	−	30.0782i	−0.661579	−	1.14589i
$690$		0			0
$691$	8.96460	−	15.5271i	0.341030	−	0.590680i	−0.643595	−	0.765367i	$-0.722558\pi$
$691$	8.96460	−	15.5271i	0.341030	−	0.590680i	0.984624	+	0.174686i	$0.0558911\pi$
$692$		0			0
$693$	12.3409	+	2.00773i	0.468791	+	0.0762672i
$694$		0			0
$695$	2.30511	−	3.99257i	0.0874379	−	0.151447i
$696$		0			0
$697$	6.97713	+	12.0847i	0.264277	+	0.457742i
$698$		0			0
$699$	−9.59537	−	20.2262i	−0.362930	−	0.765026i
$700$		0			0
$701$	22.6754			0.856438			0.428219	−	0.903675i	$-0.359141\pi$
$701$	22.6754			0.856438			0.428219	+	0.903675i	$0.359141\pi$
$702$		0			0
$703$	25.2245			0.951358
$704$		0			0
$705$	4.50294	+	9.49181i	0.169591	+	0.357482i
$706$		0			0
$707$	−4.82940	−	8.36477i	−0.181628	−	0.314590i
$708$		0			0
$709$	−4.47722	+	7.75477i	−0.168146	+	0.291237i	−0.937768	−	0.347263i	$-0.887111\pi$
$709$	−4.47722	+	7.75477i	−0.168146	+	0.291237i	0.769622	+	0.638499i	$0.220445\pi$
$710$		0			0
$711$	−6.73655	−	17.7719i	−0.252640	−	0.666497i
$712$		0			0
$713$	27.6989	−	47.9759i	1.03733	−	1.79671i
$714$		0			0
$715$	−22.3339	−	38.6835i	−0.835241	−	1.44668i
$716$		0			0
$717$	−21.2592	+	30.7937i	−0.793939	+	1.15001i
$718$		0			0
$719$	33.9896			1.26760			0.633799	−	0.773498i	$-0.281495\pi$
$719$	33.9896			1.26760			0.633799	+	0.773498i	$0.281495\pi$
$720$		0			0
$721$	1.96317			0.0731122
$722$		0			0
$723$	5.73792	+	0.463700i	0.213396	+	0.0172452i
$724$		0			0
$725$	10.8425	+	18.7797i	0.402680	+	0.697461i
$726$		0			0
$727$	6.95103	−	12.0395i	0.257799	−	0.446521i	−0.707853	−	0.706360i	$-0.750336\pi$
$727$	6.95103	−	12.0395i	0.257799	−	0.446521i	0.965652	+	0.259839i	$0.0836693\pi$
$728$		0			0
$729$	23.9010	+	12.5596i	0.885221	+	0.465171i
$730$		0			0
$731$	−5.00154	+	8.66291i	−0.184988	+	0.320409i
$732$		0			0
$733$	−14.3180	−	24.7996i	−0.528849	−	0.915993i	−0.999434	−	0.0336388i	$-0.989290\pi$
$733$	−14.3180	−	24.7996i	−0.528849	−	0.915993i	0.470585	−	0.882355i	$-0.344043\pi$
$734$		0			0
$735$	6.08449	+	0.491707i	0.224430	+	0.0181369i
$736$		0			0
$737$	−9.40089			−0.346286
$738$		0			0
$739$	−16.2398			−0.597389			−0.298695	−	0.954349i	$-0.596551\pi$
$739$	−16.2398			−0.597389			−0.298695	+	0.954349i	$0.596551\pi$
$740$		0			0
$741$	16.1757	−	23.4303i	0.594230	−	0.860735i
$742$		0			0
$743$	5.10227	+	8.83739i	0.187184	+	0.324213i	0.944310	−	0.329056i	$-0.106731\pi$
$743$	5.10227	+	8.83739i	0.187184	+	0.324213i	−0.757126	+	0.653269i	$0.773397\pi$
$744$		0			0
$745$	23.0696	−	39.9577i	0.845204	−	1.46394i
$746$		0			0
$747$	−11.7461	−	30.9876i	−0.429766	−	1.13378i
$748$		0			0
$749$	9.25359	−	16.0277i	0.338119	−	0.585639i
$750$		0			0
$751$	5.09533	+	8.82537i	0.185931	+	0.322042i	0.943890	−	0.330260i	$-0.107137\pi$
$751$	5.09533	+	8.82537i	0.185931	+	0.322042i	−0.757959	+	0.652303i	$0.773803\pi$
$752$		0			0
$753$	1.98936	+	4.19340i	0.0724963	+	0.152816i
$754$		0			0
$755$	−50.1113			−1.82374
$756$		0			0
$757$	−50.9880			−1.85319			−0.926595	−	0.376061i	$-0.877278\pi$
$757$	−50.9880			−1.85319			−0.926595	+	0.376061i	$0.877278\pi$
$758$		0			0
$759$	27.7561	+	58.5075i	1.00748	+	2.12369i
$760$		0			0
$761$	4.54569	+	7.87336i	0.164781	+	0.285409i	0.936578	−	0.350460i	$-0.113975\pi$
$761$	4.54569	+	7.87336i	0.164781	+	0.285409i	−0.771796	+	0.635870i	$0.780642\pi$
$762$		0			0
$763$	−1.33619	+	2.31434i	−0.0483732	+	0.0837848i
$764$		0			0
$765$	39.6086	+	6.44388i	1.43205	+	0.232979i
$766$		0			0
$767$	−1.71661	+	2.97325i	−0.0619831	+	0.107358i
$768$		0			0
$769$	−10.4748	−	18.1429i	−0.377731	−	0.654250i	0.613001	−	0.790082i	$-0.289962\pi$
$769$	−10.4748	−	18.1429i	−0.377731	−	0.654250i	−0.990732	+	0.135833i	$0.956629\pi$
$770$		0			0
$771$	−7.38899	+	10.7029i	−0.266108	+	0.385455i
$772$		0			0
$773$	−0.323229			−0.0116258			−0.00581288	−	0.999983i	$-0.501850\pi$
$773$	−0.323229			−0.0116258			−0.00581288	+	0.999983i	$0.501850\pi$
$774$		0			0
$775$	45.8268			1.64615
$776$		0			0
$777$	−8.05634	−	0.651059i	−0.289019	−	0.0233566i
$778$		0			0
$779$	−9.93674	−	17.2109i	−0.356021	−	0.616646i
$780$		0			0
$781$	−20.6922	+	35.8400i	−0.740426	+	1.28246i
$782$		0			0
$783$	10.5210	−	10.9480i	0.375990	−	0.391249i
$784$		0			0
$785$	17.1650	−	29.7307i	0.612646	−	1.06113i
$786$		0			0
$787$	−27.3607	−	47.3901i	−0.975302	−	1.68927i	−0.678934	−	0.734200i	$-0.737558\pi$
$787$	−27.3607	−	47.3901i	−0.975302	−	1.68927i	−0.296369	−	0.955074i	$-0.595776\pi$
$788$		0			0
$789$	−32.2862	−	2.60916i	−1.14942	−	0.0928884i
$790$		0			0
$791$	9.31211			0.331100
$792$		0			0
$793$	36.7111			1.30365
$794$		0			0
$795$	−39.6086	+	57.3726i	−1.40477	+	2.03480i
$796$		0			0
$797$	−15.0498	−	26.0670i	−0.533091	−	0.923341i	−0.999253	−	0.0386418i	$-0.987697\pi$
$797$	−15.0498	−	26.0670i	−0.533091	−	0.923341i	0.466162	−	0.884699i	$-0.345636\pi$
$798$		0			0
$799$	3.26606	−	5.65698i	0.115545	−	0.200130i
$800$		0			0
$801$	25.5619	−	31.2969i	0.903186	−	1.10582i
$802$		0			0
$803$	−5.21185	+	9.02720i	−0.183922	+	0.318563i
$804$		0			0
$805$	15.8080	+	27.3803i	0.557160	+	0.965030i
$806$		0			0
$807$	12.6231	+	26.6085i	0.444355	+	0.936662i
$808$		0			0
$809$	8.81348			0.309866			0.154933	−	0.987925i	$-0.450484\pi$
$809$	8.81348			0.309866			0.154933	+	0.987925i	$0.450484\pi$
$810$		0			0
$811$	42.3997			1.48886			0.744428	−	0.667702i	$-0.232722\pi$
$811$	42.3997			1.48886			0.744428	+	0.667702i	$0.232722\pi$
$812$		0			0
$813$	17.1808	+	36.2157i	0.602557	+	1.27014i
$814$		0			0
$815$	32.0942	+	55.5888i	1.12421	+	1.94719i
$816$		0			0
$817$	7.12313	−	12.3376i	0.249207	−	0.431639i
$818$		0			0
$819$	−5.77105	+	7.06581i	−0.201657	+	0.246900i
$820$		0			0
$821$	9.67904	−	16.7646i	0.337801	−	0.585088i	−0.646218	−	0.763153i	$-0.723650\pi$
$821$	9.67904	−	16.7646i	0.337801	−	0.585088i	0.984019	+	0.178065i	$0.0569836\pi$
$822$		0			0
$823$	12.2996	+	21.3035i	0.428737	+	0.742594i	0.996761	−	0.0804178i	$-0.0256254\pi$
$823$	12.2996	+	21.3035i	0.428737	+	0.742594i	−0.568024	+	0.823012i	$0.692292\pi$
$824$		0			0
$825$	−30.4345	+	44.0841i	−1.05960	+	1.53481i
$826$		0			0
$827$	39.3747			1.36919			0.684597	−	0.728922i	$-0.259978\pi$
$827$	39.3747			1.36919			0.684597	+	0.728922i	$0.259978\pi$
$828$		0			0
$829$	7.25597			0.252010			0.126005	−	0.992030i	$-0.459784\pi$
$829$	7.25597			0.252010			0.126005	+	0.992030i	$0.459784\pi$
$830$		0			0
$831$	−23.9314	−	1.93397i	−0.830170	−	0.0670888i
$832$		0			0
$833$	−1.89773	−	3.28696i	−0.0657524	−	0.113886i
$834$		0			0
$835$	−27.5418	+	47.7038i	−0.953123	+	1.65086i
$836$		0			0
$837$	−8.91965	−	30.8234i	−0.308308	−	1.06541i
$838$		0			0
$839$	−5.72910	+	9.92309i	−0.197790	+	0.342583i	−0.947812	−	0.318831i	$-0.896710\pi$
$839$	−5.72910	+	9.92309i	−0.197790	+	0.342583i	0.750021	+	0.661414i	$0.230043\pi$
$840$		0			0
$841$	10.2306	+	17.7198i	0.352778	+	0.611029i
$842$		0			0
$843$	15.7769	+	1.27499i	0.543387	+	0.0439129i
$844$		0			0
$845$	−13.2238			−0.454913
$846$		0			0
$847$	6.36982			0.218869
$848$		0			0
$849$	−6.79814	+	9.84703i	−0.233312	+	0.337949i
$850$		0			0
$851$	−20.9311	−	36.2537i	−0.717509	−	1.24276i
$852$		0			0
$853$	−25.1979	+	43.6440i	−0.862758	+	1.49434i	0.00649778	+	0.999979i	$0.497932\pi$
$853$	−25.1979	+	43.6440i	−0.862758	+	1.49434i	−0.869256	+	0.494362i	$0.835402\pi$
$854$		0			0
$855$	−56.4101	−	9.17730i	−1.92918	−	0.313857i
$856$		0			0
$857$	24.0113	−	41.5888i	0.820211	−	1.42065i	−0.0853131	−	0.996354i	$-0.527189\pi$
$857$	24.0113	−	41.5888i	0.820211	−	1.42065i	0.905525	−	0.424294i	$-0.139478\pi$
$858$		0			0
$859$	−19.1422	−	33.1552i	−0.653123	−	1.13124i	−0.982361	−	0.186995i	$-0.940125\pi$
$859$	−19.1422	−	33.1552i	−0.653123	−	1.13124i	0.329238	−	0.944247i	$-0.393208\pi$
$860$		0			0
$861$	2.72943	+	5.75340i	0.0930187	+	0.196075i
$862$		0			0
$863$	13.2049			0.449500			0.224750	−	0.974416i	$-0.427843\pi$
$863$	13.2049			0.449500			0.224750	+	0.974416i	$0.427843\pi$
$864$		0			0
$865$	−36.9344			−1.25581
$866$		0			0
$867$	1.92613	+	4.06011i	0.0654147	+	0.137889i
$868$		0			0
$869$	−13.2018	−	22.8662i	−0.447840	−	0.775681i
$870$		0			0
$871$	3.42974	−	5.94049i	0.116212	−	0.201286i
$872$		0			0
$873$	−20.1369	−	53.1238i	−0.681532	−	1.79797i
$874$		0			0
$875$	−4.26606	+	7.38904i	−0.144219	+	0.249795i
$876$		0			0
$877$	−11.9815	−	20.7526i	−0.404586	−	0.700764i	0.589687	−	0.807632i	$-0.299251\pi$
$877$	−11.9815	−	20.7526i	−0.404586	−	0.700764i	−0.994273	+	0.106868i	$0.965918\pi$
$878$		0			0
$879$	18.3047	−	26.5142i	0.617403	−	0.894302i
$880$		0			0
$881$	39.3964			1.32730			0.663650	−	0.748044i	$-0.269007\pi$
$881$	39.3964			1.32730			0.663650	+	0.748044i	$0.269007\pi$
$882$		0			0
$883$	−18.3593			−0.617840			−0.308920	−	0.951088i	$-0.599967\pi$
$883$	−18.3593			−0.617840			−0.308920	+	0.951088i	$0.599967\pi$
$884$		0			0
$885$	6.86917	+	0.555120i	0.230905	+	0.0186602i
$886$		0			0
$887$	15.3324	+	26.5566i	0.514813	+	0.891682i	0.999852	+	0.0171897i	$0.00547191\pi$
$887$	15.3324	+	26.5566i	0.514813	+	0.891682i	−0.485039	+	0.874492i	$0.661195\pi$
$888$		0			0
$889$	8.38313	−	14.5200i	0.281161	−	0.486985i
$890$		0			0
$891$	35.5750	+	11.8900i	1.19181	+	0.398331i
$892$		0			0
$893$	−4.65148	+	8.05660i	−0.155656	+	0.269604i
$894$		0			0
$895$	−31.8730	−	55.2057i	−1.06540	−	1.84532i
$896$		0			0
$897$	−47.0976	−	3.80611i	−1.57254	−	0.127082i
$898$		0			0
$899$	−18.0452			−0.601842
$900$		0			0
$901$	43.3476			1.44412
$902$		0			0
$903$	−2.59347	+	3.75661i	−0.0863052	+	0.125012i
$904$		0			0
$905$	−39.4761	−	68.3745i	−1.31223	−	2.27285i
$906$		0			0
$907$	−20.9899	+	36.3556i	−0.696960	+	1.20717i	0.272556	+	0.962140i	$0.412131\pi$
$907$	−20.9899	+	36.3556i	−0.696960	+	1.20717i	−0.969516	+	0.245030i	$0.921202\pi$
$908$		0			0
$909$	−10.2706	−	27.0952i	−0.340655	−	0.898690i
$910$		0			0
$911$	18.5714	−	32.1667i	0.615299	−	1.06573i	−0.375033	−	0.927012i	$-0.622369\pi$
$911$	18.5714	−	32.1667i	0.615299	−	1.06573i	0.990332	−	0.138718i	$-0.0442981\pi$
$912$		0			0
$913$	−23.0191	−	39.8702i	−0.761820	−	1.31951i
$914$		0			0
$915$	−31.5852	−	66.5788i	−1.04417	−	2.20103i
$916$		0			0
$917$	2.73131			0.0901960
$918$		0			0
$919$	−16.5903			−0.547263			−0.273632	−	0.961835i	$-0.588225\pi$
$919$	−16.5903			−0.547263			−0.273632	+	0.961835i	$0.588225\pi$
$920$		0			0
$921$	10.3602	+	21.8385i	0.341381	+	0.719602i
$922$		0			0
$923$	−15.0984	−	26.1511i	−0.496969	−	0.860775i
$924$		0			0
$925$	17.3148	−	29.9902i	0.569308	−	0.986071i
$926$		0			0
$927$	5.81308	+	0.945724i	0.190926	+	0.0310616i
$928$		0			0
$929$	18.5800	−	32.1814i	0.609589	−	1.05584i	−0.381719	−	0.924278i	$-0.624668\pi$
$929$	18.5800	−	32.1814i	0.609589	−	1.05584i	0.991308	−	0.131560i	$-0.0419987\pi$
$930$		0			0
$931$	2.70272	+	4.68125i	0.0885781	+	0.153422i
$932$		0			0
$933$	−17.4399	+	25.2615i	−0.570956	+	0.827024i
$934$		0			0
$935$	55.7492			1.82319
$936$		0			0
$937$	−54.5323			−1.78149			−0.890746	−	0.454502i	$-0.849817\pi$
$937$	−54.5323			−1.78149			−0.890746	+	0.454502i	$0.849817\pi$
$938$		0			0
$939$	25.4925	+	2.06014i	0.831917	+	0.0672300i
$940$		0			0
$941$	−20.9394	−	36.2682i	−0.682606	−	1.18231i	−0.974183	−	0.225761i	$-0.927513\pi$
$941$	−20.9394	−	36.2682i	−0.682606	−	1.18231i	0.291577	−	0.956547i	$-0.405820\pi$
$942$		0			0
$943$	−16.4909	+	28.5630i	−0.537017	+	0.930141i
$944$		0			0
$945$	17.7797	+	4.38708i	0.578374	+	0.142712i
$946$		0			0
$947$	−6.71450	+	11.6299i	−0.218192	+	0.377919i	−0.954255	−	0.298993i	$-0.903349\pi$
$947$	−6.71450	+	11.6299i	−0.218192	+	0.377919i	0.736063	+	0.676913i	$0.236683\pi$
$948$		0			0
$949$	−3.80290	−	6.58682i	−0.123447	−	0.213817i
$950$		0			0
$951$	−4.44794	−	0.359453i	−0.144234	−	0.0116560i
$952$		0			0
$953$	−22.1328			−0.716950			−0.358475	−	0.933539i	$-0.616703\pi$
$953$	−22.1328			−0.716950			−0.358475	+	0.933539i	$0.616703\pi$
$954$		0			0
$955$	11.9468			0.386590
$956$		0			0
$957$	11.9842	−	17.3590i	0.387395	−	0.561137i
$958$		0			0
$959$	−8.12870	−	14.0793i	−0.262489	−	0.454645i
$960$		0			0
$961$	−3.56746	+	6.17902i	−0.115079	+	0.199323i
$962$		0			0
$963$	35.1216	−	43.0013i	1.13178	−	1.38570i
$964$		0			0
$965$	−28.1886	+	48.8241i	−0.907423	+	1.57170i
$966$		0			0
$967$	−14.9516	−	25.8969i	−0.480811	−	0.832788i	0.518947	−	0.854806i	$-0.326324\pi$
$967$	−14.9516	−	25.8969i	−0.480811	−	0.832788i	−0.999758	+	0.0220180i	$0.992991\pi$
$968$		0			0
$969$	15.2309	+	32.1054i	0.489286	+	1.03137i
$970$		0			0
$971$	−17.0708			−0.547827			−0.273914	−	0.961754i	$-0.588318\pi$
$971$	−17.0708			−0.547827			−0.273914	+	0.961754i	$0.588318\pi$
$972$		0			0
$973$	−1.30811			−0.0419362
$974$		0			0
$975$	−16.7536	−	35.3151i	−0.536544	−	1.13099i
$976$		0			0
$977$	16.6299	+	28.8038i	0.532037	+	0.921515i	0.999300	+	0.0373970i	$0.0119066\pi$
$977$	16.6299	+	28.8038i	0.532037	+	0.921515i	−0.467263	+	0.884118i	$0.654760\pi$
$978$		0			0
$979$	28.0690	−	48.6169i	0.897089	−	1.55380i
$980$		0			0
$981$	−5.07143	+	6.20924i	−0.161918	+	0.198246i
$982$		0			0
$983$	−13.2794	+	23.0006i	−0.423548	+	0.733606i	−0.996284	−	0.0861339i	$-0.972549\pi$
$983$	−13.2794	+	23.0006i	−0.423548	+	0.733606i	0.572736	+	0.819740i	$0.305882\pi$
$984$		0			0
$985$	11.8961	+	20.6046i	0.379041	+	0.656518i
$986$		0			0
$987$	1.69356	−	2.45311i	0.0539067	−	0.0780833i
$988$		0			0
$989$	−23.6429			−0.751800
$990$		0			0
$991$	−48.1268			−1.52880			−0.764398	−	0.644744i	$-0.776964\pi$
$991$	−48.1268			−1.52880			−0.764398	+	0.644744i	$0.776964\pi$
$992$		0			0
$993$	0.548232	+	0.0443044i	0.0173976	+	0.00140596i
$994$		0			0
$995$	20.1256	+	34.8585i	0.638023	+	1.10509i
$996$		0			0
$997$	−9.67869	+	16.7640i	−0.306527	+	0.530921i	−0.977600	−	0.210471i	$-0.932500\pi$
$997$	−9.67869	+	16.7640i	−0.306527	+	0.530921i	0.671073	+	0.741391i	$0.265834\pi$
$998$		0			0
$999$	−23.5417	−	5.80884i	−0.744828	−	0.183783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.n.673.2		10
3.2	odd	2		3024.2.r.n.2017.5		10
4.3	odd	2		504.2.r.f.169.4	✓	10
9.2	odd	6		9072.2.a.cm.1.1		5
9.4	even	3	inner	1008.2.r.n.337.2		10
9.5	odd	6		3024.2.r.n.1009.5		10
9.7	even	3		9072.2.a.cn.1.5		5
12.11	even	2		1512.2.r.f.505.5		10
36.7	odd	6		4536.2.a.bd.1.5		5
36.11	even	6		4536.2.a.bc.1.1		5
36.23	even	6		1512.2.r.f.1009.5		10
36.31	odd	6		504.2.r.f.337.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.f.169.4	✓	10	4.3	odd	2
504.2.r.f.337.4	yes	10	36.31	odd	6
1008.2.r.n.337.2		10	9.4	even	3	inner
1008.2.r.n.673.2		10	1.1	even	1	trivial
1512.2.r.f.505.5		10	12.11	even	2
1512.2.r.f.1009.5		10	36.23	even	6
3024.2.r.n.1009.5		10	9.5	odd	6
3024.2.r.n.2017.5		10	3.2	odd	2
4536.2.a.bc.1.1		5	36.11	even	6
4536.2.a.bd.1.5		5	36.7	odd	6
9072.2.a.cm.1.1		5	9.2	odd	6
9072.2.a.cn.1.5		5	9.7	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.742385 - 1.56488i) q^{3} +(-1.76217 - 3.05216i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.89773 + 2.32349i) q^{9} +O(q^{10})\)	\(q+(-0.742385 - 1.56488i) q^{3} +(-1.76217 - 3.05216i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.89773 + 2.32349i) q^{9} +(-2.08386 + 3.60934i) q^{11} +(-1.52051 - 2.63361i) q^{13} +(-3.46807 + 5.02347i) q^{15} +3.79546 q^{17} -5.40544 q^{19} +(1.72642 + 0.139518i) q^{21} +(4.48540 + 7.76894i) q^{23} +(-3.71046 + 6.42670i) q^{25} +(5.04485 + 1.24480i) q^{27} +(1.46107 - 2.53065i) q^{29} +(-3.08767 - 5.34801i) q^{31} +(7.19523 + 0.581470i) q^{33} +3.52433 q^{35} -4.66649 q^{37} +(-2.99249 + 4.33458i) q^{39} +(1.83828 + 3.18400i) q^{41} +(-1.31777 + 2.28244i) q^{43} +(10.4358 + 1.69779i) q^{45} +(0.860518 - 1.49046i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.81769 - 5.93945i) q^{51} +11.4209 q^{53} +14.6884 q^{55} +(4.01292 + 8.45890i) q^{57} +(-0.564482 - 0.977712i) q^{59} +(-6.03597 + 10.4546i) q^{61} +(-1.06334 - 2.80523i) q^{63} +(-5.35880 + 9.28171i) q^{65} +(1.12782 + 1.95345i) q^{67} +(8.82761 - 12.7867i) q^{69} +9.92978 q^{71} +2.50106 q^{73} +(12.8116 + 1.03535i) q^{75} +(-2.08386 - 3.60934i) q^{77} +(-3.16763 + 5.48650i) q^{79} +(-1.79726 - 8.81872i) q^{81} +(-5.52319 + 9.56645i) q^{83} +(-6.68823 - 11.5843i) q^{85} +(-5.04485 - 0.407691i) q^{87} -13.4697 q^{89} +3.04103 q^{91} +(-6.07677 + 8.80214i) q^{93} +(9.52529 + 16.4983i) q^{95} +(-9.46871 + 16.4003i) q^{97} +(-4.43170 - 11.6914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 3 * q^5 - 5 * q^7	\( 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) \) 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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