LMFDB - Embedded newform 1008.2.df.e.929.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			929.9
Character	$\chi$	$=$	1008.929
Dual form			1008.2.df.e.689.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.930597 + 1.46082i) q^{3} +1.36828 q^{5} +(-2.64451 + 0.0810554i) q^{7} +(-1.26798 - 2.71887i) q^{9} -1.20384i q^{11} +(0.639364 - 0.369137i) q^{13} +(-1.27332 + 1.99881i) q^{15} +(-0.693066 - 1.20043i) q^{17} +(-2.81671 - 1.62623i) q^{19} +(2.34257 - 3.93858i) q^{21} -3.81129i q^{23} -3.12781 q^{25} +(5.15174 + 0.677887i) q^{27} +(-3.50030 - 2.02090i) q^{29} +(-1.02924 - 0.594230i) q^{31} +(1.75859 + 1.12029i) q^{33} +(-3.61843 + 0.110906i) q^{35} +(5.10537 - 8.84276i) q^{37} +(-0.0557487 + 1.27751i) q^{39} +(-0.670586 - 1.16149i) q^{41} +(0.490044 - 0.848782i) q^{43} +(-1.73495 - 3.72017i) q^{45} +(1.63634 + 2.83422i) q^{47} +(6.98686 - 0.428704i) q^{49} +(2.39857 + 0.104670i) q^{51} +(-5.77421 + 3.33374i) q^{53} -1.64718i q^{55} +(4.99684 - 2.60133i) q^{57} +(6.73912 - 11.6725i) q^{59} +(-4.36067 + 2.51764i) q^{61} +(3.57356 + 7.08729i) q^{63} +(0.874829 - 0.505083i) q^{65} +(2.19665 - 3.80471i) q^{67} +(5.56760 + 3.54678i) q^{69} +8.84538i q^{71} +(10.2939 - 5.94320i) q^{73} +(2.91073 - 4.56917i) q^{75} +(0.0975775 + 3.18356i) q^{77} +(-6.34799 - 10.9950i) q^{79} +(-5.78447 + 6.89492i) q^{81} +(3.14219 - 5.44243i) q^{83} +(-0.948308 - 1.64252i) q^{85} +(6.20953 - 3.23266i) q^{87} +(-6.05868 + 10.4939i) q^{89} +(-1.66088 + 1.02801i) q^{91} +(1.82587 - 0.950538i) q^{93} +(-3.85404 - 2.22513i) q^{95} +(10.9781 + 6.33821i) q^{97} +(-3.27307 + 1.52644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.930597	+	1.46082i	−0.537281	+	0.843404i
$3$	−0.930597	+	1.46082i	−0.537281	+	0.843404i
$4$		0			0
$5$	1.36828			0.611913			0.305956	−	0.952046i	$-0.401024\pi$
$5$	1.36828			0.611913			0.305956	+	0.952046i	$0.401024\pi$
$6$		0			0
$7$	−2.64451	+	0.0810554i	−0.999531	+	0.0306361i
$7$	−2.64451	+	0.0810554i	−0.999531	+	0.0306361i
$8$		0			0
$9$	−1.26798	−	2.71887i	−0.422659	−	0.906289i
$10$		0			0
$11$		−	1.20384i		−	0.362971i	−0.983394	−	0.181485i	$-0.941910\pi$
$11$		−	1.20384i		−	0.362971i	0.983394	−	0.181485i	$-0.0580905\pi$
$12$		0			0
$13$	0.639364	−	0.369137i	0.177328	−	0.102380i	−0.408709	−	0.912665i	$-0.634021\pi$
$13$	0.639364	−	0.369137i	0.177328	−	0.102380i	0.586037	+	0.810285i	$0.300687\pi$
$14$		0			0
$15$	−1.27332	+	1.99881i	−0.328769	+	0.516089i
$16$		0			0
$17$	−0.693066	−	1.20043i	−0.168093	−	0.291146i	0.769656	−	0.638459i	$-0.220428\pi$
$17$	−0.693066	−	1.20043i	−0.168093	−	0.291146i	−0.937749	+	0.347313i	$0.887094\pi$
$18$		0			0
$19$	−2.81671	−	1.62623i	−0.646197	−	0.373082i	0.140801	−	0.990038i	$-0.455032\pi$
$19$	−2.81671	−	1.62623i	−0.646197	−	0.373082i	−0.786998	+	0.616956i	$0.788366\pi$
$20$		0			0
$21$	2.34257	−	3.93858i	0.511190	−	0.859468i
$22$		0			0
$23$		−	3.81129i		−	0.794709i	−0.917665	−	0.397355i	$-0.869928\pi$
$23$		−	3.81129i		−	0.794709i	0.917665	−	0.397355i	$-0.130072\pi$
$24$		0			0
$25$	−3.12781			−0.625563
$26$		0			0
$27$	5.15174	+	0.677887i	0.991454	+	0.130459i
$28$		0			0
$29$	−3.50030	−	2.02090i	−0.649989	−	0.375271i	0.138463	−	0.990368i	$-0.455784\pi$
$29$	−3.50030	−	2.02090i	−0.649989	−	0.375271i	−0.788452	+	0.615096i	$0.789117\pi$
$30$		0			0
$31$	−1.02924	−	0.594230i	−0.184856	−	0.106727i	0.404716	−	0.914442i	$-0.367370\pi$
$31$	−1.02924	−	0.594230i	−0.184856	−	0.106727i	−0.589572	+	0.807716i	$0.700704\pi$
$32$		0			0
$33$	1.75859	+	1.12029i	0.306131	+	0.195017i
$34$		0			0
$35$	−3.61843	+	0.110906i	−0.611626	+	0.0187466i
$36$		0			0
$37$	5.10537	−	8.84276i	0.839317	−	1.45374i	−0.0511491	−	0.998691i	$-0.516288\pi$
$37$	5.10537	−	8.84276i	0.839317	−	1.45374i	0.890466	−	0.455049i	$-0.150378\pi$
$38$		0			0
$39$	−0.0557487	+	1.27751i	−0.00892693	+	0.204566i
$40$		0			0
$41$	−0.670586	−	1.16149i	−0.104728	−	0.181394i	0.808899	−	0.587948i	$-0.200064\pi$
$41$	−0.670586	−	1.16149i	−0.104728	−	0.181394i	−0.913627	+	0.406553i	$0.866731\pi$
$42$		0			0
$43$	0.490044	−	0.848782i	0.0747311	−	0.129438i	−0.826238	−	0.563321i	$-0.809524\pi$
$43$	0.490044	−	0.848782i	0.0747311	−	0.129438i	0.900969	+	0.433883i	$0.142857\pi$
$44$		0			0
$45$	−1.73495	−	3.72017i	−0.258630	−	0.554570i
$46$		0			0
$47$	1.63634	+	2.83422i	0.238684	+	0.413413i	0.960337	−	0.278842i	$-0.0899506\pi$
$47$	1.63634	+	2.83422i	0.238684	+	0.413413i	−0.721653	+	0.692255i	$0.756617\pi$
$48$		0			0
$49$	6.98686	−	0.428704i	0.998123	−	0.0612434i
$50$		0			0
$51$	2.39857	+	0.104670i	0.335867	+	0.0146567i
$52$		0			0
$53$	−5.77421	+	3.33374i	−0.793148	+	0.457924i	−0.841070	−	0.540927i	$-0.818074\pi$
$53$	−5.77421	+	3.33374i	−0.793148	+	0.457924i	0.0479213	+	0.998851i	$0.484740\pi$
$54$		0			0
$55$		−	1.64718i		−	0.222106i
$56$		0			0
$57$	4.99684	−	2.60133i	0.661848	−	0.344555i
$58$		0			0
$59$	6.73912	−	11.6725i	0.877359	−	1.51963i	0.0231309	−	0.999732i	$-0.492637\pi$
$59$	6.73912	−	11.6725i	0.877359	−	1.51963i	0.854228	−	0.519898i	$-0.174030\pi$
$60$		0			0
$61$	−4.36067	+	2.51764i	−0.558327	+	0.322350i	−0.752474	−	0.658622i	$-0.771140\pi$
$61$	−4.36067	+	2.51764i	−0.558327	+	0.322350i	0.194147	+	0.980972i	$0.437806\pi$
$62$		0			0
$63$	3.57356	+	7.08729i	0.450226	+	0.892915i
$64$		0			0
$65$	0.874829	−	0.505083i	0.108509	−	0.0626478i
$66$		0			0
$67$	2.19665	−	3.80471i	0.268364	−	0.464819i	−0.700076	−	0.714069i	$-0.746850\pi$
$67$	2.19665	−	3.80471i	0.268364	−	0.464819i	0.968439	+	0.249249i	$0.0801838\pi$
$68$		0			0
$69$	5.56760	+	3.54678i	0.670261	+	0.426982i
$70$		0			0
$71$			8.84538i			1.04975i	0.851178	+	0.524877i	$0.175889\pi$
$71$			8.84538i			1.04975i	−0.851178	+	0.524877i	$0.824111\pi$
$72$		0			0
$73$	10.2939	−	5.94320i	1.20481	−	0.695599i	0.243191	−	0.969978i	$-0.421806\pi$
$73$	10.2939	−	5.94320i	1.20481	−	0.695599i	0.961621	+	0.274380i	$0.0884726\pi$
$74$		0			0
$75$	2.91073	−	4.56917i	0.336103	−	0.527602i
$76$		0			0
$77$	0.0975775	+	3.18356i	0.0111200	+	0.362800i
$78$		0			0
$79$	−6.34799	−	10.9950i	−0.714205	−	1.23704i	−0.963265	−	0.268551i	$-0.913455\pi$
$79$	−6.34799	−	10.9950i	−0.714205	−	1.23704i	0.249060	−	0.968488i	$-0.419878\pi$
$80$		0			0
$81$	−5.78447	+	6.89492i	−0.642719	+	0.766102i
$82$		0			0
$83$	3.14219	−	5.44243i	0.344900	−	0.597384i	−0.640436	−	0.768012i	$-0.721246\pi$
$83$	3.14219	−	5.44243i	0.344900	−	0.597384i	0.985336	+	0.170628i	$0.0545795\pi$
$84$		0			0
$85$	−0.948308	−	1.64252i	−0.102858	−	0.178156i
$86$		0			0
$87$	6.20953	−	3.23266i	0.665732	−	0.346577i
$88$		0			0
$89$	−6.05868	+	10.4939i	−0.642219	+	1.11236i	0.342718	+	0.939438i	$0.388653\pi$
$89$	−6.05868	+	10.4939i	−0.642219	+	1.11236i	−0.984936	+	0.172917i	$0.944681\pi$
$90$		0			0
$91$	−1.66088	+	1.02801i	−0.174108	+	0.107765i
$92$		0			0
$93$	1.82587	−	0.950538i	0.189334	−	0.0985662i
$94$		0			0
$95$	−3.85404	−	2.22513i	−0.395416	−	0.228294i
$96$		0			0
$97$	10.9781	+	6.33821i	1.11466	+	0.643548i	0.940032	−	0.341087i	$-0.110795\pi$
$97$	10.9781	+	6.33821i	1.11466	+	0.643548i	0.174626	+	0.984635i	$0.444128\pi$
$98$		0			0
$99$	−3.27307	+	1.52644i	−0.328956	+	0.153413i
$100$		0			0
$101$	−13.2437			−1.31779			−0.658897	−	0.752233i	$-0.728977\pi$
$101$	−13.2437			−1.31779			−0.658897	+	0.752233i	$0.728977\pi$
$102$		0			0
$103$		−	13.1827i		−	1.29893i	−0.760391	−	0.649465i	$-0.774993\pi$
$103$		−	13.1827i		−	1.29893i	0.760391	−	0.649465i	$-0.225007\pi$
$104$		0			0
$105$	3.20528	−	5.38907i	0.312804	−	0.525919i
$106$		0			0
$107$	−15.8800	−	9.16833i	−1.53518	−	0.886336i	−0.999111	−	0.0421621i	$-0.986575\pi$
$107$	−15.8800	−	9.16833i	−1.53518	−	0.886336i	−0.536069	−	0.844174i	$-0.680091\pi$
$108$		0			0
$109$	−8.74665	−	15.1496i	−0.837777	−	1.45107i	−0.891749	−	0.452531i	$-0.850521\pi$
$109$	−8.74665	−	15.1496i	−0.837777	−	1.45107i	0.0539715	−	0.998542i	$-0.482812\pi$
$110$		0			0
$111$	8.16661	+	15.6871i	0.775141	+	1.48895i
$112$		0			0
$113$	−4.13627	+	2.38808i	−0.389108	+	0.224652i	−0.681774	−	0.731563i	$-0.738791\pi$
$113$	−4.13627	+	2.38808i	−0.389108	+	0.224652i	0.292666	+	0.956215i	$0.405458\pi$
$114$		0			0
$115$		−	5.21491i		−	0.486293i
$116$		0			0
$117$	−1.81433	−	1.27029i	−0.167735	−	0.117438i
$118$		0			0
$119$	1.93012	+	3.11836i	0.176934	+	0.285860i
$120$		0			0
$121$	9.55078			0.868252
$122$		0			0
$123$	2.32077	+	0.101275i	0.209257	+	0.00913164i
$124$		0			0
$125$	−11.1211			−0.994703
$126$		0			0
$127$	4.81674			0.427416			0.213708	−	0.976898i	$-0.431446\pi$
$127$	4.81674			0.427416			0.213708	+	0.976898i	$0.431446\pi$
$128$		0			0
$129$	0.783881	+	1.50574i	0.0690169	+	0.132573i
$130$		0			0
$131$	6.14127			0.536566			0.268283	−	0.963340i	$-0.413544\pi$
$131$	6.14127			0.536566			0.268283	+	0.963340i	$0.413544\pi$
$132$		0			0
$133$	7.58063	+	4.07226i	0.657324	+	0.353110i
$134$		0			0
$135$	7.04902	+	0.927538i	0.606683	+	0.0798298i
$136$		0			0
$137$			3.51935i			0.300678i	0.988634	+	0.150339i	$0.0480366\pi$
$137$			3.51935i			0.300678i	−0.988634	+	0.150339i	$0.951963\pi$
$138$		0			0
$139$	12.6807	−	7.32119i	1.07556	−	0.620975i	0.145865	−	0.989304i	$-0.453403\pi$
$139$	12.6807	−	7.32119i	1.07556	−	0.620975i	0.929695	+	0.368329i	$0.120070\pi$
$140$		0			0
$141$	−5.66304	−	0.247126i	−0.476914	−	0.0208118i
$142$		0			0
$143$	−0.444381	−	0.769691i	−0.0371610	−	0.0643648i
$144$		0			0
$145$	−4.78939	−	2.76515i	−0.397737	−	0.229633i
$146$		0			0
$147$	−5.87570	+	10.6055i	−0.484619	+	0.874725i
$148$		0			0
$149$			14.8374i			1.21553i	0.794118	+	0.607763i	$0.207933\pi$
$149$			14.8374i			1.21553i	−0.794118	+	0.607763i	$0.792067\pi$
$150$		0			0
$151$	−2.92894			−0.238354			−0.119177	−	0.992873i	$-0.538026\pi$
$151$	−2.92894			−0.238354			−0.119177	+	0.992873i	$0.538026\pi$
$152$		0			0
$153$	−2.38501	+	3.40647i	−0.192816	+	0.275396i
$154$		0			0
$155$	−1.40828	−	0.813072i	−0.113116	−	0.0653075i
$156$		0			0
$157$	−16.8177	−	9.70973i	−1.34220	−	0.774920i	−0.355071	−	0.934839i	$-0.615543\pi$
$157$	−16.8177	−	9.70973i	−1.34220	−	0.774920i	−0.987130	+	0.159919i	$0.948877\pi$
$158$		0			0
$159$	0.503476	−	11.5374i	0.0399282	−	0.914978i
$160$		0			0
$161$	0.308926	+	10.0790i	0.0243468	+	0.794336i
$162$		0			0
$163$	−4.94115	+	8.55832i	−0.387021	+	0.670340i	−0.992047	−	0.125866i	$-0.959829\pi$
$163$	−4.94115	+	8.55832i	−0.387021	+	0.670340i	0.605027	+	0.796205i	$0.293162\pi$
$164$		0			0
$165$	2.40624	+	1.53287i	0.187325	+	0.119333i
$166$		0			0
$167$	9.58375	+	16.5995i	0.741613	+	1.28451i	0.951761	+	0.306841i	$0.0992721\pi$
$167$	9.58375	+	16.5995i	0.741613	+	1.28451i	−0.210148	+	0.977670i	$0.567395\pi$
$168$		0			0
$169$	−6.22748	+	10.7863i	−0.479037	+	0.829716i
$170$		0			0
$171$	−0.849974	+	9.72027i	−0.0649991	+	0.743328i
$172$		0			0
$173$	1.88299	+	3.26143i	0.143161	+	0.247962i	0.928685	−	0.370869i	$-0.120940\pi$
$173$	1.88299	+	3.26143i	0.143161	+	0.247962i	−0.785524	+	0.618831i	$0.787607\pi$
$174$		0			0
$175$	8.27153	−	0.253526i	0.625269	−	0.0191648i
$176$		0			0
$177$	10.7800	+	20.7070i	0.810274	+	1.55644i
$178$		0			0
$179$	−22.7425	+	13.1304i	−1.69986	+	0.981412i	−0.753971	+	0.656908i	$0.771864\pi$
$179$	−22.7425	+	13.1304i	−1.69986	+	0.981412i	−0.945884	+	0.324504i	$0.894802\pi$
$180$		0			0
$181$			7.60186i			0.565042i	0.959261	+	0.282521i	$0.0911706\pi$
$181$			7.60186i			0.565042i	−0.959261	+	0.282521i	$0.908829\pi$
$182$		0			0
$183$	0.380224	−	8.71305i	0.0281070	−	0.644087i
$184$		0			0
$185$	6.98557	−	12.0994i	0.513589	−	0.889562i
$186$		0			0
$187$	−1.44512	+	0.834339i	−0.105677	+	0.0610129i
$188$		0			0
$189$	−13.6788	−	1.37510i	−0.994985	−	0.100024i
$190$		0			0
$191$	−16.2060	+	9.35655i	−1.17263	+	0.677016i	−0.954297	−	0.298859i	$-0.903394\pi$
$191$	−16.2060	+	9.35655i	−1.17263	+	0.677016i	−0.218329	+	0.975875i	$0.570061\pi$
$192$		0			0
$193$	−6.82526	+	11.8217i	−0.491293	+	0.850945i	−0.999950	−	0.0100249i	$-0.996809\pi$
$193$	−6.82526	+	11.8217i	−0.491293	+	0.850945i	0.508657	+	0.860969i	$0.330142\pi$
$194$		0			0
$195$	−0.0762797	+	1.74799i	−0.00546250	+	0.125176i
$196$		0			0
$197$		−	16.3308i		−	1.16352i	−0.813361	−	0.581760i	$-0.802364\pi$
$197$		−	16.3308i		−	1.16352i	0.813361	−	0.581760i	$-0.197636\pi$
$198$		0			0
$199$	−10.3429	+	5.97146i	−0.733186	+	0.423305i	−0.819587	−	0.572955i	$-0.805797\pi$
$199$	−10.3429	+	5.97146i	−0.733186	+	0.423305i	0.0864004	+	0.996260i	$0.472464\pi$
$200$		0			0
$201$	3.51379	+	6.74956i	0.247844	+	0.476077i
$202$		0			0
$203$	9.42038	+	5.06057i	0.661181	+	0.355182i
$204$		0			0
$205$	−0.917549	−	1.58924i	−0.0640844	−	0.110997i
$206$		0			0
$207$	−10.3624	+	4.83263i	−0.720236	+	0.335891i
$208$		0			0
$209$	−1.95771	+	3.39086i	−0.135418	+	0.234551i
$210$		0			0
$211$	8.33236	+	14.4321i	0.573623	+	0.993544i	0.996190	+	0.0872125i	$0.0277959\pi$
$211$	8.33236	+	14.4321i	0.573623	+	0.993544i	−0.422567	+	0.906332i	$0.638871\pi$
$212$		0			0
$213$	−12.9215	−	8.23149i	−0.885366	−	0.564012i
$214$		0			0
$215$	0.670517	−	1.16137i	0.0457289	−	0.0792048i
$216$		0			0
$217$	2.76999	+	1.48802i	0.188039	+	0.101014i
$218$		0			0
$219$	−0.897567	+	20.5683i	−0.0606519	+	1.38987i
$220$		0			0
$221$	−0.886244	−	0.511673i	−0.0596152	−	0.0344188i
$222$		0			0
$223$	−2.30524	−	1.33093i	−0.154370	−	0.0891258i	0.420825	−	0.907142i	$-0.361741\pi$
$223$	−2.30524	−	1.33093i	−0.154370	−	0.0891258i	−0.575195	+	0.818016i	$0.695074\pi$
$224$		0			0
$225$	3.96600	+	8.50411i	0.264400	+	0.566940i
$226$		0			0
$227$	−4.68069			−0.310669			−0.155334	−	0.987862i	$-0.549645\pi$
$227$	−4.68069			−0.310669			−0.155334	+	0.987862i	$0.549645\pi$
$228$		0			0
$229$		−	4.29143i		−	0.283586i	−0.989896	−	0.141793i	$-0.954713\pi$
$229$		−	4.29143i		−	0.283586i	0.989896	−	0.141793i	$-0.0452867\pi$
$230$		0			0
$231$	−4.74140	−	2.82007i	−0.311961	−	0.185547i
$232$		0			0
$233$	3.00156	+	1.73295i	0.196639	+	0.113530i	0.595087	−	0.803661i	$-0.297118\pi$
$233$	3.00156	+	1.73295i	0.196639	+	0.113530i	−0.398448	+	0.917191i	$0.630451\pi$
$234$		0			0
$235$	2.23896	+	3.87800i	0.146054	+	0.252973i
$236$		0			0
$237$	21.9692	+	0.958701i	1.42705	+	0.0622743i
$238$		0			0
$239$	−22.5074	+	12.9946i	−1.45588	+	0.840554i	−0.998805	−	0.0488730i	$-0.984437\pi$
$239$	−22.5074	+	12.9946i	−1.45588	+	0.840554i	−0.457077	+	0.889427i	$0.651104\pi$
$240$		0			0
$241$		−	14.7470i		−	0.949939i	−0.880002	−	0.474970i	$-0.842459\pi$
$241$		−	14.7470i		−	0.949939i	0.880002	−	0.474970i	$-0.157541\pi$
$242$		0			0
$243$	−4.68921	−	14.8664i	−0.300813	−	0.953683i
$244$		0			0
$245$	9.55997	−	0.586586i	0.610764	−	0.0374756i
$246$		0			0
$247$	−2.40120			−0.152785
$248$		0			0
$249$	5.02628	+	9.65487i	0.318528	+	0.611853i
$250$		0			0
$251$	13.2564			0.836734			0.418367	−	0.908278i	$-0.362603\pi$
$251$	13.2564			0.836734			0.418367	+	0.908278i	$0.362603\pi$
$252$		0			0
$253$	−4.58818			−0.288456
$254$		0			0
$255$	3.28191	+	0.143217i	0.205521	+	0.00896862i
$256$		0			0
$257$	24.9917			1.55894			0.779471	−	0.626438i	$-0.215488\pi$
$257$	24.9917			1.55894			0.779471	+	0.626438i	$0.215488\pi$
$258$		0			0
$259$	−12.7844	+	23.7986i	−0.794386	+	1.47877i
$260$		0			0
$261$	−1.05625	+	12.0793i	−0.0653805	+	0.747690i
$262$		0			0
$263$		−	14.5621i		−	0.897940i	−0.893547	−	0.448970i	$-0.851791\pi$
$263$		−	14.5621i		−	0.897940i	0.893547	−	0.448970i	$-0.148209\pi$
$264$		0			0
$265$	−7.90073	+	4.56149i	−0.485338	+	0.280210i
$266$		0			0
$267$	−9.69154	−	18.6163i	−0.593113	−	1.13930i
$268$		0			0
$269$	−8.64288	−	14.9699i	−0.526966	−	0.912731i	−0.999506	−	0.0314225i	$-0.989996\pi$
$269$	−8.64288	−	14.9699i	−0.526966	−	0.912731i	0.472540	−	0.881309i	$-0.343337\pi$
$270$		0			0
$271$	−3.37299	−	1.94740i	−0.204895	−	0.118296i	0.394042	−	0.919092i	$-0.371076\pi$
$271$	−3.37299	−	1.94740i	−0.204895	−	0.118296i	−0.598936	+	0.800797i	$0.704410\pi$
$272$		0			0
$273$	0.0438785	−	3.38291i	0.00265565	−	0.204743i
$274$		0			0
$275$			3.76538i			0.227061i
$276$		0			0
$277$	19.7457			1.18641			0.593203	−	0.805053i	$-0.297863\pi$
$277$	19.7457			1.18641			0.593203	+	0.805053i	$0.297863\pi$
$278$		0			0
$279$	−0.310584	+	3.55183i	−0.0185942	+	0.212642i
$280$		0			0
$281$	−1.41396	−	0.816352i	−0.0843499	−	0.0486994i	0.457232	−	0.889348i	$-0.348841\pi$
$281$	−1.41396	−	0.816352i	−0.0843499	−	0.0486994i	−0.541582	+	0.840648i	$0.682174\pi$
$282$		0			0
$283$	23.1548	+	13.3684i	1.37641	+	0.794671i	0.991726	−	0.128376i	$-0.0409765\pi$
$283$	23.1548	+	13.3684i	1.37641	+	0.794671i	0.384686	+	0.923048i	$0.374310\pi$
$284$		0			0
$285$	6.83707	−	3.55935i	0.404993	−	0.210838i
$286$		0			0
$287$	1.86752	+	3.01722i	0.110236	+	0.178101i
$288$		0			0
$289$	7.53932	−	13.0585i	0.443489	−	0.768146i
$290$		0			0
$291$	−19.4752	+	10.1387i	−1.14166	+	0.594341i
$292$		0			0
$293$	−5.68847	−	9.85271i	−0.332324	−	0.575602i	0.650643	−	0.759383i	$-0.274499\pi$
$293$	−5.68847	−	9.85271i	−0.332324	−	0.575602i	−0.982967	+	0.183782i	$0.941166\pi$
$294$		0			0
$295$	9.22100	−	15.9712i	0.536867	−	0.929882i
$296$		0			0
$297$	0.816065	−	6.20186i	0.0473529	−	0.359868i
$298$		0			0
$299$	−1.40689	−	2.43681i	−0.0813626	−	0.140924i
$300$		0			0
$301$	−1.22713	+	2.28433i	−0.0707305	+	0.131667i
$302$		0			0
$303$	12.3245	−	19.3466i	0.708026	−	1.11143i
$304$		0			0
$305$	−5.96662	+	3.44483i	−0.341647	+	0.197250i
$306$		0			0
$307$		−	19.4683i		−	1.11111i	−0.831479	−	0.555556i	$-0.812505\pi$
$307$		−	19.4683i		−	1.11111i	0.831479	−	0.555556i	$-0.187495\pi$
$308$		0			0
$309$	19.2575	+	12.2678i	1.09552	+	0.697890i
$310$		0			0
$311$	−11.0992	+	19.2243i	−0.629375	+	1.09011i	0.358302	+	0.933606i	$0.383356\pi$
$311$	−11.0992	+	19.2243i	−0.629375	+	1.09011i	−0.987677	+	0.156504i	$0.949978\pi$
$312$		0			0
$313$	−12.1557	+	7.01812i	−0.687083	+	0.396688i	−0.802518	−	0.596627i	$-0.796507\pi$
$313$	−12.1557	+	7.01812i	−0.687083	+	0.396688i	0.115435	+	0.993315i	$0.463174\pi$
$314$		0			0
$315$	4.88962	+	9.69739i	0.275499	+	0.546386i
$316$		0			0
$317$	11.2557	−	6.49848i	0.632183	−	0.364991i	−0.149414	−	0.988775i	$-0.547739\pi$
$317$	11.2557	−	6.49848i	0.632183	−	0.364991i	0.781597	+	0.623784i	$0.214405\pi$
$318$		0			0
$319$	−2.43283	+	4.21379i	−0.136212	+	0.235927i
$320$		0			0
$321$	28.1712	−	14.6658i	1.57236	−	0.818564i
$322$		0			0
$323$			4.50833i			0.250850i
$324$		0			0
$325$	−1.99981	+	1.15459i	−0.110930	+	0.0640453i
$326$		0			0
$327$	30.2705	+	1.32096i	1.67396	+	0.0730491i
$328$		0			0
$329$	−4.55703	−	7.36248i	−0.251237	−	0.405906i
$330$		0			0
$331$	6.26139	+	10.8451i	0.344157	+	0.596098i	0.985200	−	0.171407i	$-0.0548313\pi$
$331$	6.26139	+	10.8451i	0.344157	+	0.596098i	−0.641043	+	0.767505i	$0.721498\pi$
$332$		0			0
$333$	−30.5158	−	2.66840i	−1.67225	−	0.146227i
$334$		0			0
$335$	3.00563	−	5.20590i	0.164215	−	0.284429i
$336$		0			0
$337$	−10.9647	−	18.9915i	−0.597287	−	1.03453i	−0.993220	−	0.116251i	$-0.962912\pi$
$337$	−10.9647	−	18.9915i	−0.597287	−	1.03453i	0.395933	−	0.918279i	$-0.370421\pi$
$338$		0			0
$339$	0.360658	−	8.26468i	0.0195882	−	0.448876i
$340$		0			0
$341$	−0.715356	+	1.23903i	−0.0387387	+	0.0670974i
$342$		0			0
$343$	−18.4421	+	1.70003i	−0.995778	+	0.0917932i
$344$		0			0
$345$	7.61803	+	4.85298i	0.410141	+	0.261276i
$346$		0			0
$347$	1.33668	+	0.771734i	0.0717569	+	0.0414288i	0.535449	−	0.844567i	$-0.320142\pi$
$347$	1.33668	+	0.771734i	0.0717569	+	0.0414288i	−0.463692	+	0.885996i	$0.653476\pi$
$348$		0			0
$349$	5.10876	+	2.94954i	0.273465	+	0.157885i	0.630461	−	0.776221i	$-0.282866\pi$
$349$	5.10876	+	2.94954i	0.273465	+	0.157885i	−0.356996	+	0.934106i	$0.616199\pi$
$350$		0			0
$351$	3.54408	−	1.46828i	0.189169	−	0.0783712i
$352$		0			0
$353$	12.3268			0.656091			0.328046	−	0.944662i	$-0.393610\pi$
$353$	12.3268			0.656091			0.328046	+	0.944662i	$0.393610\pi$
$354$		0			0
$355$			12.1030i			0.642358i
$356$		0			0
$357$	−6.35152	−	0.0823832i	−0.336158	−	0.00436018i
$358$		0			0
$359$	4.03896	+	2.33189i	0.213168	+	0.123073i	0.602783	−	0.797905i	$-0.294059\pi$
$359$	4.03896	+	2.33189i	0.213168	+	0.123073i	−0.389615	+	0.920978i	$0.627392\pi$
$360$		0			0
$361$	−4.21077	−	7.29327i	−0.221619	−	0.383856i
$362$		0			0
$363$	−8.88793	+	13.9519i	−0.466495	+	0.732287i
$364$		0			0
$365$	14.0850	−	8.13195i	0.737240	−	0.425646i
$366$		0			0
$367$		−	23.4243i		−	1.22274i	−0.791345	−	0.611370i	$-0.790619\pi$
$367$		−	23.4243i		−	1.22274i	0.791345	−	0.611370i	$-0.209381\pi$
$368$		0			0
$369$	−2.30765	+	3.29598i	−0.120131	+	0.171582i
$370$		0			0
$371$	14.9997	−	9.28414i	0.778747	−	0.482008i
$372$		0			0
$373$	−12.0306			−0.622923			−0.311461	−	0.950259i	$-0.600818\pi$
$373$	−12.0306			−0.622923			−0.311461	+	0.950259i	$0.600818\pi$
$374$		0			0
$375$	10.3493	−	16.2459i	0.534435	−	0.838936i
$376$		0			0
$377$	−2.98396			−0.153682
$378$		0			0
$379$	31.6065			1.62352			0.811758	−	0.583994i	$-0.198511\pi$
$379$	31.6065			1.62352			0.811758	+	0.583994i	$0.198511\pi$
$380$		0			0
$381$	−4.48244	+	7.03637i	−0.229642	+	0.360484i
$382$		0			0
$383$	22.2570			1.13728			0.568641	−	0.822586i	$-0.307470\pi$
$383$	22.2570			1.13728			0.568641	+	0.822586i	$0.307470\pi$
$384$		0			0
$385$	0.133513	+	4.35600i	0.00680447	+	0.222002i
$386$		0			0
$387$	−2.92909	−	0.256129i	−0.148894	−	0.0130198i
$388$		0			0
$389$		−	35.5575i		−	1.80283i	−0.432951	−	0.901417i	$-0.642528\pi$
$389$		−	35.5575i		−	1.80283i	0.432951	−	0.901417i	$-0.357472\pi$
$390$		0			0
$391$	−4.57517	+	2.64148i	−0.231376	+	0.133585i
$392$		0			0
$393$	−5.71505	+	8.97128i	−0.288286	+	0.452541i
$394$		0			0
$395$	−8.68582	−	15.0443i	−0.437031	−	0.756960i
$396$		0			0
$397$	−5.16204	−	2.98030i	−0.259075	−	0.149577i	0.364837	−	0.931071i	$-0.381125\pi$
$397$	−5.16204	−	2.98030i	−0.259075	−	0.149577i	−0.623913	+	0.781494i	$0.714458\pi$
$398$		0			0
$399$	−13.0033	+	7.28428i	−0.650982	+	0.364670i
$400$		0			0
$401$			19.1472i			0.956165i	0.878315	+	0.478083i	$0.158668\pi$
$401$			19.1472i			0.956165i	−0.878315	+	0.478083i	$0.841332\pi$
$402$		0			0
$403$	−0.877410			−0.0437069
$404$		0			0
$405$	−7.91477	+	9.43417i	−0.393288	+	0.468788i
$406$		0			0
$407$	−10.6452	−	6.14603i	−0.527665	−	0.304647i
$408$		0			0
$409$	−8.83357	−	5.10006i	−0.436792	−	0.252182i	0.265444	−	0.964126i	$-0.414481\pi$
$409$	−8.83357	−	5.10006i	−0.436792	−	0.252182i	−0.702236	+	0.711944i	$0.747815\pi$
$410$		0			0
$411$	−5.14113	−	3.27510i	−0.253593	−	0.161549i
$412$		0			0
$413$	−16.8756	+	31.4143i	−0.830392	+	1.54580i
$414$		0			0
$415$	4.29939	−	7.44676i	0.211049	−	0.365547i
$416$		0			0
$417$	−1.10568	+	25.3372i	−0.0541453	+	1.24077i
$418$		0			0
$419$	−3.14385	−	5.44530i	−0.153587	−	0.266021i	0.778957	−	0.627078i	$-0.215749\pi$
$419$	−3.14385	−	5.44530i	−0.153587	−	0.266021i	−0.932544	+	0.361057i	$0.882416\pi$
$420$		0			0
$421$	−1.14723	+	1.98705i	−0.0559123	+	0.0968430i	−0.892627	−	0.450796i	$-0.851140\pi$
$421$	−1.14723	+	1.98705i	−0.0559123	+	0.0968430i	0.836714	+	0.547639i	$0.184473\pi$
$422$		0			0
$423$	5.63102	−	8.04270i	0.273790	−	0.391049i
$424$		0			0
$425$	2.16778	+	3.75471i	0.105153	+	0.182130i
$426$		0			0
$427$	11.3278	−	7.01137i	0.548189	−	0.339304i
$428$		0			0
$429$	1.53792	+	0.0671123i	0.0742514	+	0.00324021i
$430$		0			0
$431$	−19.3251	+	11.1574i	−0.930859	+	0.537432i	−0.887083	−	0.461610i	$-0.847272\pi$
$431$	−19.3251	+	11.1574i	−0.930859	+	0.537432i	−0.0437761	+	0.999041i	$0.513939\pi$
$432$		0			0
$433$			36.2306i			1.74113i	0.492053	+	0.870565i	$0.336247\pi$
$433$			36.2306i			1.74113i	−0.492053	+	0.870565i	$0.663753\pi$
$434$		0			0
$435$	8.49637	−	4.42317i	0.407370	−	0.212075i
$436$		0			0
$437$	−6.19803	+	10.7353i	−0.296492	+	0.513539i
$438$		0			0
$439$	15.6320	−	9.02511i	0.746072	−	0.430745i	−0.0782007	−	0.996938i	$-0.524917\pi$
$439$	15.6320	−	9.02511i	0.746072	−	0.430745i	0.824273	+	0.566193i	$0.191584\pi$
$440$		0			0
$441$	−10.0248	−	18.4528i	−0.477370	−	0.878702i
$442$		0			0
$443$	−10.7590	+	6.21170i	−0.511174	+	0.295127i	−0.733316	−	0.679888i	$-0.762029\pi$
$443$	−10.7590	+	6.21170i	−0.511174	+	0.295127i	0.222142	+	0.975014i	$0.428695\pi$
$444$		0			0
$445$	−8.28996	+	14.3586i	−0.392982	+	0.680665i
$446$		0			0
$447$	−21.6747	−	13.8076i	−1.02518	−	0.653079i
$448$		0			0
$449$		−	19.5762i		−	0.923858i	−0.886917	−	0.461929i	$-0.847158\pi$
$449$		−	19.5762i		−	0.923858i	0.886917	−	0.461929i	$-0.152842\pi$
$450$		0			0
$451$	−1.39824	+	0.807277i	−0.0658407	+	0.0380132i
$452$		0			0
$453$	2.72567	−	4.27865i	0.128063	−	0.201029i
$454$		0			0
$455$	−2.27255	+	1.40661i	−0.106539	+	0.0659427i
$456$		0			0
$457$	−11.8799	−	20.5765i	−0.555717	−	0.962530i	−0.997847	−	0.0655789i	$-0.979111\pi$
$457$	−11.8799	−	20.5765i	−0.555717	−	0.962530i	0.442131	−	0.896951i	$-0.354223\pi$
$458$		0			0
$459$	−2.75675	−	6.65411i	−0.128674	−	0.310587i
$460$		0			0
$461$	10.6541	−	18.4535i	0.496213	−	0.859466i	−0.503778	−	0.863833i	$-0.668057\pi$
$461$	10.6541	−	18.4535i	0.496213	−	0.859466i	0.999990	+	0.00436764i	$0.00139027\pi$
$462$		0			0
$463$	−8.72943	−	15.1198i	−0.405691	−	0.702677i	0.588711	−	0.808344i	$-0.299636\pi$
$463$	−8.72943	−	15.1198i	−0.405691	−	0.702677i	−0.994402	+	0.105667i	$0.966302\pi$
$464$		0			0
$465$	2.49829	−	1.30060i	0.115856	−	0.0603139i
$466$		0			0
$467$	−5.11806	+	8.86473i	−0.236835	+	0.410211i	−0.959804	−	0.280669i	$-0.909444\pi$
$467$	−5.11806	+	8.86473i	−0.236835	+	0.410211i	0.722969	+	0.690880i	$0.242777\pi$
$468$		0			0
$469$	−5.50067	+	10.2396i	−0.253997	+	0.472823i
$470$		0			0
$471$	29.8347	−	15.5318i	1.37471	−	0.715668i
$472$		0			0
$473$	−1.02179	−	0.589933i	−0.0469822	−	0.0271252i
$474$		0			0
$475$	8.81014	+	5.08654i	0.404237	+	0.233386i
$476$		0			0
$477$	16.3856	+	11.4722i	0.750243	+	0.525276i
$478$		0			0
$479$	−15.1247			−0.691063			−0.345531	−	0.938407i	$-0.612301\pi$
$479$	−15.1247			−0.691063			−0.345531	+	0.938407i	$0.612301\pi$
$480$		0			0
$481$		−	7.53832i		−	0.343718i
$482$		0			0
$483$	−15.0111	−	8.92821i	−0.683027	−	0.406247i
$484$		0			0
$485$	15.0211	+	8.67244i	0.682074	+	0.393795i
$486$		0			0
$487$	17.3450	+	30.0425i	0.785979	+	1.36136i	0.928412	+	0.371551i	$0.121174\pi$
$487$	17.3450	+	30.0425i	0.785979	+	1.36136i	−0.142433	+	0.989804i	$0.545493\pi$
$488$		0			0
$489$	−7.90393	−	15.1825i	−0.357428	−	0.686575i
$490$		0			0
$491$	11.2050	−	6.46922i	0.505676	−	0.291952i	−0.225379	−	0.974271i	$-0.572362\pi$
$491$	11.2050	−	6.46922i	0.505676	−	0.291952i	0.731054	+	0.682319i	$0.239029\pi$
$492$		0			0
$493$			5.60247i			0.252322i
$494$		0			0
$495$	−4.47847	+	2.08859i	−0.201292	+	0.0938752i
$496$		0			0
$497$	−0.716966	−	23.3917i	−0.0321603	−	1.04926i
$498$		0			0
$499$	7.04669			0.315453			0.157727	−	0.987483i	$-0.449584\pi$
$499$	7.04669			0.315453			0.157727	+	0.987483i	$0.449584\pi$
$500$		0			0
$501$	−33.1675	−	1.44738i	−1.48182	−	0.0646641i
$502$		0			0
$503$	36.3853			1.62234			0.811170	−	0.584810i	$-0.198831\pi$
$503$	36.3853			1.62234			0.811170	+	0.584810i	$0.198831\pi$
$504$		0			0
$505$	−18.1210			−0.806376
$506$		0			0
$507$	−9.96155	−	19.1349i	−0.442408	−	0.849811i
$508$		0			0
$509$	36.7611			1.62941			0.814704	−	0.579877i	$-0.196899\pi$
$509$	36.7611			1.62941			0.814704	+	0.579877i	$0.196899\pi$
$510$		0			0
$511$	−26.7406	+	16.5512i	−1.18294	+	0.732183i
$512$		0			0
$513$	−13.4086	−	10.2873i	−0.592003	−	0.454196i
$514$		0			0
$515$		−	18.0376i		−	0.794832i
$516$		0			0
$517$	3.41193	−	1.96988i	0.150057	−	0.0866353i
$518$		0			0
$519$	−6.51666	−	0.284377i	−0.286050	−	0.0124828i
$520$		0			0
$521$	13.9686	+	24.1943i	0.611976	+	1.05997i	0.990907	+	0.134548i	$0.0429583\pi$
$521$	13.9686	+	24.1943i	0.611976	+	1.05997i	−0.378931	+	0.925425i	$0.623708\pi$
$522$		0			0
$523$	−15.0082	−	8.66497i	−0.656261	−	0.378893i	0.134590	−	0.990901i	$-0.457028\pi$
$523$	−15.0082	−	8.66497i	−0.656261	−	0.378893i	−0.790851	+	0.612009i	$0.790362\pi$
$524$		0			0
$525$	−7.32711	+	12.3191i	−0.319781	+	0.537651i
$526$		0			0
$527$			1.64736i			0.0717603i
$528$		0			0
$529$	8.47405			0.368437
$530$		0			0
$531$	−40.2810	−	3.52231i	−1.74805	−	0.152855i
$532$		0			0
$533$	−0.857498	−	0.495077i	−0.0371424	−	0.0214442i
$534$		0			0
$535$	−21.7283	−	12.5448i	−0.939396	−	0.542361i
$536$		0			0
$537$	1.98301	−	45.4418i	0.0855731	−	1.96096i
$538$		0			0
$539$	−0.516089	−	8.41104i	−0.0222295	−	0.362289i
$540$		0			0
$541$	5.30043	−	9.18061i	0.227883	−	0.394705i	−0.729297	−	0.684197i	$-0.760153\pi$
$541$	5.30043	−	9.18061i	0.227883	−	0.394705i	0.957181	+	0.289491i	$0.0934862\pi$
$542$		0			0
$543$	−11.1049	−	7.07427i	−0.476558	−	0.303586i
$544$		0			0
$545$	−11.9679	−	20.7289i	−0.512647	−	0.887930i
$546$		0			0
$547$	8.55403	−	14.8160i	0.365744	−	0.633487i	−0.623151	−	0.782101i	$-0.714148\pi$
$547$	8.55403	−	14.8160i	0.365744	−	0.633487i	0.988895	+	0.148614i	$0.0474813\pi$
$548$		0			0
$549$	12.3743	+	8.66378i	0.528124	+	0.369761i
$550$		0			0
$551$	6.57288	+	11.3846i	0.280014	+	0.484999i
$552$		0			0
$553$	17.6785	+	28.5620i	0.751768	+	1.21458i
$554$		0			0
$555$	11.1742	+	21.4643i	0.474318	+	0.911107i
$556$		0			0
$557$	2.02890	−	1.17139i	0.0859673	−	0.0496333i	−0.456400	−	0.889775i	$-0.650861\pi$
$557$	2.02890	−	1.17139i	0.0859673	−	0.0496333i	0.542367	+	0.840141i	$0.317528\pi$
$558$		0			0
$559$		−	0.723574i		−	0.0306039i
$560$		0			0
$561$	0.126005	−	2.88749i	0.00531995	−	0.121910i
$562$		0			0
$563$	21.0507	−	36.4608i	0.887180	−	1.53664i	0.0439857	−	0.999032i	$-0.485994\pi$
$563$	21.0507	−	36.4608i	0.887180	−	1.53664i	0.843194	−	0.537609i	$-0.180672\pi$
$564$		0			0
$565$	−5.65958	+	3.26756i	−0.238100	+	0.137467i
$566$		0			0
$567$	14.7382	−	18.7025i	0.618947	−	0.785433i
$568$		0			0
$569$	−35.0375	+	20.2289i	−1.46885	+	0.848040i	−0.999390	−	0.0349152i	$-0.988884\pi$
$569$	−35.0375	+	20.2289i	−1.46885	+	0.848040i	−0.469458	+	0.882955i	$0.655551\pi$
$570$		0			0
$571$	0.160538	−	0.278060i	0.00671832	−	0.0116365i	−0.862647	−	0.505807i	$-0.831195\pi$
$571$	0.160538	−	0.278060i	0.00671832	−	0.0116365i	0.869365	+	0.494170i	$0.164528\pi$
$572$		0			0
$573$	1.41307	−	32.3812i	0.0590317	−	1.35275i
$574$		0			0
$575$			11.9210i			0.497141i
$576$		0			0
$577$	20.9395	−	12.0894i	0.871721	−	0.503288i	0.00380123	−	0.999993i	$-0.498790\pi$
$577$	20.9395	−	12.0894i	0.871721	−	0.503288i	0.867920	+	0.496704i	$0.165457\pi$
$578$		0			0
$579$	−10.9178	−	20.9717i	−0.453727	−	0.871554i
$580$		0			0
$581$	−7.86841	+	14.6472i	−0.326436	+	0.607670i
$582$		0			0
$583$	4.01328	+	6.95120i	0.166213	+	0.287889i
$584$		0			0
$585$	−2.48251	−	1.73811i	−0.102639	−	0.0718620i
$586$		0			0
$587$	14.4257	−	24.9860i	0.595411	−	1.03128i	−0.398077	−	0.917352i	$-0.630322\pi$
$587$	14.4257	−	24.9860i	0.595411	−	1.03128i	0.993489	−	0.113931i	$-0.0363442\pi$
$588$		0			0
$589$	1.93271	+	3.34755i	0.0796358	+	0.137933i
$590$		0			0
$591$	23.8563	+	15.1974i	0.981317	+	0.625137i
$592$		0			0
$593$	1.07472	−	1.86147i	0.0441335	−	0.0764414i	−0.843115	−	0.537734i	$-0.819281\pi$
$593$	1.07472	−	1.86147i	0.0441335	−	0.0764414i	0.887248	+	0.461292i	$0.152614\pi$
$594$		0			0
$595$	2.64094	+	4.26679i	0.108268	+	0.174921i
$596$		0			0
$597$	0.901835	−	20.6661i	0.0369096	−	0.845806i
$598$		0			0
$599$	5.58798	+	3.22622i	0.228319	+	0.131820i	0.609796	−	0.792558i	$-0.291251\pi$
$599$	5.58798	+	3.22622i	0.228319	+	0.131820i	−0.381477	+	0.924378i	$0.624585\pi$
$600$		0			0
$601$	10.6341	+	6.13960i	0.433774	+	0.250439i	0.700953	−	0.713207i	$-0.252758\pi$
$601$	10.6341	+	6.13960i	0.433774	+	0.250439i	−0.267179	+	0.963647i	$0.586092\pi$
$602$		0			0
$603$	−13.1298	−	1.14811i	−0.534687	−	0.0467548i
$604$		0			0
$605$	13.0681			0.531295
$606$		0			0
$607$			38.3682i			1.55732i	0.627448	+	0.778658i	$0.284099\pi$
$607$			38.3682i			1.55732i	−0.627448	+	0.778658i	$0.715901\pi$
$608$		0			0
$609$	−16.1591	+	9.05211i	−0.654802	+	0.366810i
$610$		0			0
$611$	2.09243	+	1.20806i	0.0846506	+	0.0488731i
$612$		0			0
$613$	6.96098	+	12.0568i	0.281151	+	0.486969i	0.971669	−	0.236347i	$-0.0759503\pi$
$613$	6.96098	+	12.0568i	0.281151	+	0.486969i	−0.690517	+	0.723316i	$0.742617\pi$
$614$		0			0
$615$	3.17546	+	0.138572i	0.128047	+	0.00558777i
$616$		0			0
$617$	15.0193	−	8.67142i	0.604656	−	0.349098i	−0.166215	−	0.986090i	$-0.553155\pi$
$617$	15.0193	−	8.67142i	0.604656	−	0.349098i	0.770871	+	0.636991i	$0.219821\pi$
$618$		0			0
$619$		−	29.6508i		−	1.19177i	−0.803071	−	0.595884i	$-0.796802\pi$
$619$		−	29.6508i		−	1.19177i	0.803071	−	0.595884i	$-0.203198\pi$
$620$		0			0
$621$	2.58362	−	19.6348i	0.103677	−	0.787918i
$622$		0			0
$623$	15.1716	−	28.2424i	0.607839	−	1.13151i
$624$		0			0
$625$	0.422282			0.0168913
$626$		0			0
$627$	−3.13158	−	6.01538i	−0.125063	−	0.240231i
$628$		0			0
$629$	−14.1534			−0.564334
$630$		0			0
$631$	16.6402			0.662437			0.331218	−	0.943554i	$-0.392540\pi$
$631$	16.6402			0.662437			0.331218	+	0.943554i	$0.392540\pi$
$632$		0			0
$633$	−28.8367	−	1.25839i	−1.14616	−	0.0500164i
$634$		0			0
$635$	6.59064			0.261541
$636$		0			0
$637$	4.30890	−	2.85321i	0.170725	−	0.113048i
$638$		0			0
$639$	24.0494	−	11.2157i	0.951380	−	0.443688i
$640$		0			0
$641$		−	15.5930i		−	0.615888i	−0.951404	−	0.307944i	$-0.900359\pi$
$641$		−	15.5930i		−	0.615888i	0.951404	−	0.307944i	$-0.0996410\pi$
$642$		0			0
$643$	−13.7474	+	7.93708i	−0.542146	+	0.313008i	−0.745948	−	0.666004i	$-0.768003\pi$
$643$	−13.7474	+	7.93708i	−0.542146	+	0.313008i	0.203802	+	0.979012i	$0.434670\pi$
$644$		0			0
$645$	1.07257	+	2.06027i	0.0422323	+	0.0811231i
$646$		0			0
$647$	−1.18164	−	2.04666i	−0.0464549	−	0.0804623i	0.841863	−	0.539691i	$-0.181459\pi$
$647$	−1.18164	−	2.04666i	−0.0464549	−	0.0804623i	−0.888318	+	0.459229i	$0.848126\pi$
$648$		0			0
$649$	−14.0518	−	8.11281i	−0.551581	−	0.318455i
$650$		0			0
$651$	−4.75148	+	2.66170i	−0.186225	+	0.104320i
$652$		0			0
$653$			18.6821i			0.731088i	0.930794	+	0.365544i	$0.119117\pi$
$653$			18.6821i			0.731088i	−0.930794	+	0.365544i	$0.880883\pi$
$654$		0			0
$655$	8.40297			0.328331
$656$		0			0
$657$	−29.2112	−	20.4520i	−1.13964	−	0.797907i
$658$		0			0
$659$	17.5543	+	10.1350i	0.683819	+	0.394803i	0.801293	−	0.598273i	$-0.204146\pi$
$659$	17.5543	+	10.1350i	0.683819	+	0.394803i	−0.117473	+	0.993076i	$0.537479\pi$
$660$		0			0
$661$	27.1506	+	15.6754i	1.05604	+	0.609703i	0.924333	−	0.381586i	$-0.124622\pi$
$661$	27.1506	+	15.6754i	1.05604	+	0.609703i	0.131704	+	0.991289i	$0.457955\pi$
$662$		0			0
$663$	1.57220	−	0.818479i	0.0610591	−	0.0317871i
$664$		0			0
$665$	10.3724	+	5.57199i	0.402225	+	0.216073i
$666$		0			0
$667$	−7.70224	+	13.3407i	−0.298232	+	0.516553i
$668$		0			0
$669$	4.08950	−	2.12898i	0.158109	−	0.0823110i
$670$		0			0
$671$	3.03082	+	5.24954i	0.117004	+	0.202656i
$672$		0			0
$673$	9.49210	−	16.4408i	0.365893	−	0.633746i	−0.623026	−	0.782201i	$-0.714097\pi$
$673$	9.49210	−	16.4408i	0.365893	−	0.633746i	0.988919	+	0.148455i	$0.0474301\pi$
$674$		0			0
$675$	−16.1137	−	2.12030i	−0.620216	−	0.0816105i
$676$		0			0
$677$	−12.8417	−	22.2424i	−0.493545	−	0.854845i	0.506427	−	0.862283i	$-0.330966\pi$
$677$	−12.8417	−	22.2424i	−0.493545	−	0.854845i	−0.999972	+	0.00743750i	$0.997633\pi$
$678$		0			0
$679$	−29.5455	−	15.8716i	−1.13385	−	0.609097i
$680$		0			0
$681$	4.35584	−	6.83764i	0.166916	−	0.262019i
$682$		0			0
$683$	32.2147	−	18.5992i	1.23266	−	0.711677i	0.265078	−	0.964227i	$-0.414602\pi$
$683$	32.2147	−	18.5992i	1.23266	−	0.711677i	0.967584	+	0.252550i	$0.0812691\pi$
$684$		0			0
$685$			4.81545i			0.183989i
$686$		0			0
$687$	6.26900	+	3.99360i	0.239177	+	0.152365i
$688$		0			0
$689$	−2.46122	+	4.26295i	−0.0937648	+	0.162405i
$690$		0			0
$691$	−38.8499	+	22.4300i	−1.47792	+	0.853277i	−0.999689	−	0.0249572i	$-0.992055\pi$
$691$	−38.8499	+	22.4300i	−1.47792	+	0.853277i	−0.478231	+	0.878234i	$0.658722\pi$
$692$		0			0
$693$	8.53194	−	4.30198i	0.324102	−	0.163419i
$694$		0			0
$695$	17.3507	−	10.0174i	0.658150	−	0.379983i
$696$		0			0
$697$	−0.929521	+	1.60998i	−0.0352081	+	0.0609823i
$698$		0			0
$699$	−5.32478	+	2.77206i	−0.201402	+	0.104849i
$700$		0			0
$701$		−	26.0630i		−	0.984387i	−0.870486	−	0.492194i	$-0.836195\pi$
$701$		−	26.0630i		−	0.984387i	0.870486	−	0.492194i	$-0.163805\pi$
$702$		0			0
$703$	−28.7607	+	16.6050i	−1.08473	+	0.626269i
$704$		0			0
$705$	−7.74862	−	0.338138i	−0.291830	−	0.0127350i
$706$		0			0
$707$	35.0230	−	1.07347i	1.31718	−	0.0403721i
$708$		0			0
$709$	−16.6461	−	28.8319i	−0.625158	−	1.08281i	−0.988510	−	0.151154i	$-0.951701\pi$
$709$	−16.6461	−	28.8319i	−0.625158	−	1.08281i	0.363352	−	0.931652i	$-0.381632\pi$
$710$		0			0
$711$	−21.8450	+	31.2008i	−0.819250	+	1.17012i
$712$		0			0
$713$	−2.26478	+	3.92272i	−0.0848169	+	0.146907i
$714$		0			0
$715$	−0.608037	−	1.05315i	−0.0227393	−	0.0393856i
$716$		0			0
$717$	1.96251	−	44.9720i	0.0732912	−	1.67951i
$718$		0			0
$719$	−24.3474	+	42.1709i	−0.908003	+	1.57271i	−0.0911690	+	0.995835i	$0.529060\pi$
$719$	−24.3474	+	42.1709i	−0.908003	+	1.57271i	−0.816834	+	0.576872i	$0.804273\pi$
$720$		0			0
$721$	1.06853	+	34.8618i	0.0397941	+	1.29832i
$722$		0			0
$723$	21.5427	+	13.7235i	0.801182	+	0.510384i
$724$		0			0
$725$	10.9483	+	6.32099i	0.406609	+	0.234756i
$726$		0			0
$727$	8.76540	+	5.06071i	0.325091	+	0.187691i	0.653659	−	0.756789i	$-0.273233\pi$
$727$	8.76540	+	5.06071i	0.325091	+	0.187691i	−0.328569	+	0.944480i	$0.606566\pi$
$728$		0			0
$729$	26.0809	+	6.98460i	0.965961	+	0.258689i
$730$		0			0
$731$	−1.35853			−0.0502471
$732$		0			0
$733$			18.6611i			0.689262i	0.938738	+	0.344631i	$0.111996\pi$
$733$			18.6611i			0.689262i	−0.938738	+	0.344631i	$0.888004\pi$
$734$		0			0
$735$	−8.03959	+	14.5113i	−0.296545	+	0.535256i
$736$		0			0
$737$	−4.58025	−	2.64441i	−0.168716	−	0.0974081i
$738$		0			0
$739$	13.5646	+	23.4946i	0.498983	+	0.864264i	0.999999	−	0.00117395i	$-0.000373681\pi$
$739$	13.5646	+	23.4946i	0.498983	+	0.864264i	−0.501016	+	0.865438i	$0.667040\pi$
$740$		0			0
$741$	2.23455	−	3.50772i	0.0820884	−	0.128859i
$742$		0			0
$743$	−13.9378	+	8.04698i	−0.511328	+	0.295215i	−0.733379	−	0.679820i	$-0.762058\pi$
$743$	−13.9378	+	8.04698i	−0.511328	+	0.295215i	0.222052	+	0.975035i	$0.428725\pi$
$744$		0			0
$745$			20.3017i			0.743796i
$746$		0			0
$747$	−18.7815	−	1.64231i	−0.687178	−	0.0600891i
$748$		0			0
$749$	42.7380	+	22.9586i	1.56161	+	0.838888i
$750$		0			0
$751$	−47.6328			−1.73815			−0.869073	−	0.494683i	$-0.835284\pi$
$751$	−47.6328			−1.73815			−0.869073	+	0.494683i	$0.835284\pi$
$752$		0			0
$753$	−12.3363	+	19.3651i	−0.449561	+	0.705704i
$754$		0			0
$755$	−4.00761			−0.145852
$756$		0			0
$757$	50.4788			1.83468			0.917341	−	0.398102i	$-0.130331\pi$
$757$	50.4788			1.83468			0.917341	+	0.398102i	$0.130331\pi$
$758$		0			0
$759$	4.26974	−	6.70249i	0.154982	−	0.243285i
$760$		0			0
$761$	6.39506			0.231821			0.115910	−	0.993260i	$-0.463021\pi$
$761$	6.39506			0.231821			0.115910	+	0.993260i	$0.463021\pi$
$762$		0			0
$763$	24.3586	+	39.3544i	0.881839	+	1.42473i
$764$		0			0
$765$	−3.26335	+	4.66100i	−0.117987	+	0.168519i
$766$		0			0
$767$		−	9.95065i		−	0.359297i
$768$		0			0
$769$	21.1676	−	12.2211i	0.763322	−	0.440704i	−0.0671654	−	0.997742i	$-0.521396\pi$
$769$	21.1676	−	12.2211i	0.763322	−	0.440704i	0.830487	+	0.557038i	$0.188062\pi$
$770$		0			0
$771$	−23.2573	+	36.5084i	−0.837590	+	1.31482i
$772$		0			0
$773$	8.32573	+	14.4206i	0.299456	+	0.518672i	0.976011	−	0.217719i	$-0.0698616\pi$
$773$	8.32573	+	14.4206i	0.299456	+	0.518672i	−0.676556	+	0.736391i	$0.736528\pi$
$774$		0			0
$775$	3.21926	+	1.85864i	0.115639	+	0.0667643i
$776$		0			0
$777$	−22.8682	−	40.8226i	−0.820392	−	1.46450i
$778$		0			0
$779$			4.36210i			0.156289i
$780$		0			0
$781$	10.6484			0.381030
$782$		0			0
$783$	−16.6627	−	12.7840i	−0.595477	−	0.456861i
$784$		0			0
$785$	−23.0114	−	13.2856i	−0.821310	−	0.474184i
$786$		0			0
$787$	−1.21582	−	0.701955i	−0.0433394	−	0.0250220i	0.478174	−	0.878265i	$-0.341299\pi$
$787$	−1.21582	−	0.701955i	−0.0433394	−	0.0250220i	−0.521513	+	0.853243i	$0.674632\pi$
$788$		0			0
$789$	21.2726	+	13.5515i	0.757326	+	0.482446i
$790$		0			0
$791$	10.7448	−	6.65056i	0.382043	−	0.236467i
$792$		0			0
$793$	−1.85871	+	3.21937i	−0.0660046	+	0.114323i
$794$		0			0
$795$	0.688895	−	15.7864i	0.0244326	−	0.559887i
$796$		0			0
$797$	14.7211	+	25.4977i	0.521448	+	0.903174i	0.999689	+	0.0249452i	$0.00794114\pi$
$797$	14.7211	+	25.4977i	0.521448	+	0.903174i	−0.478241	+	0.878229i	$0.658726\pi$
$798$		0			0
$799$	2.26818	−	3.92860i	0.0802423	−	0.138984i
$800$		0			0
$801$	36.2139	+	3.16667i	1.27955	+	0.111889i
$802$		0			0
$803$	−7.15464	−	12.3922i	−0.252482	−	0.437311i
$804$		0			0
$805$	0.422697	+	13.7909i	0.0148981	+	0.486065i
$806$		0			0
$807$	29.9114	+	1.30528i	1.05293	+	0.0459482i
$808$		0			0
$809$	41.2228	−	23.8000i	1.44932	−	0.836764i	0.450877	−	0.892586i	$-0.351111\pi$
$809$	41.2228	−	23.8000i	1.44932	−	0.836764i	0.998441	+	0.0558222i	$0.0177780\pi$
$810$		0			0
$811$		−	24.9460i		−	0.875973i	−0.898981	−	0.437987i	$-0.855692\pi$
$811$		−	24.9460i		−	0.875973i	0.898981	−	0.437987i	$-0.144308\pi$
$812$		0			0
$813$	5.98369	−	3.11508i	0.209857	−	0.109251i
$814$		0			0
$815$	−6.76087	+	11.7102i	−0.236823	+	0.410189i
$816$		0			0
$817$	−2.76062	+	1.59385i	−0.0965820	+	0.0557616i
$818$		0			0
$819$	4.90099	+	3.21223i	0.171254	+	0.112244i
$820$		0			0
$821$	−5.91506	+	3.41506i	−0.206437	+	0.119186i	−0.599654	−	0.800259i	$-0.704695\pi$
$821$	−5.91506	+	3.41506i	−0.206437	+	0.119186i	0.393218	+	0.919445i	$0.371362\pi$
$822$		0			0
$823$	3.68905	−	6.38962i	0.128592	−	0.222728i	−0.794539	−	0.607213i	$-0.792288\pi$
$823$	3.68905	−	6.38962i	0.128592	−	0.222728i	0.923131	+	0.384485i	$0.125621\pi$
$824$		0			0
$825$	−5.50053	−	3.50405i	−0.191504	−	0.121995i
$826$		0			0
$827$		−	21.1804i		−	0.736516i	−0.929724	−	0.368258i	$-0.879954\pi$
$827$		−	21.1804i		−	0.736516i	0.929724	−	0.368258i	$-0.120046\pi$
$828$		0			0
$829$	−1.60383	+	0.925970i	−0.0557032	+	0.0321603i	−0.527593	−	0.849497i	$-0.676905\pi$
$829$	−1.60383	+	0.925970i	−0.0557032	+	0.0321603i	0.471890	+	0.881658i	$0.343572\pi$
$830$		0			0
$831$	−18.3753	+	28.8449i	−0.637432	+	1.00062i
$832$		0			0
$833$	−5.35698	−	8.09009i	−0.185608	−	0.280305i
$834$		0			0
$835$	13.1132	+	22.7128i	0.453802	+	0.786009i
$836$		0			0
$837$	−4.89954	−	3.75903i	−0.169353	−	0.129931i
$838$		0			0
$839$	−7.90568	+	13.6930i	−0.272934	+	0.472736i	−0.969612	−	0.244648i	$-0.921328\pi$
$839$	−7.90568	+	13.6930i	−0.272934	+	0.472736i	0.696678	+	0.717384i	$0.254661\pi$
$840$		0			0
$841$	−6.33194	−	10.9672i	−0.218343	−	0.378181i
$842$		0			0
$843$	2.50837	−	1.30585i	0.0863929	−	0.0449757i
$844$		0			0
$845$	−8.52092	+	14.7587i	−0.293129	+	0.507714i
$846$		0			0
$847$	−25.2571	+	0.774142i	−0.867845	+	0.0265998i
$848$		0			0
$849$	−41.0767	+	21.3843i	−1.40975	+	0.733909i
$850$		0			0
$851$	−33.7023	−	19.4581i	−1.15530	−	0.667013i
$852$		0			0
$853$	−8.16324	−	4.71305i	−0.279504	−	0.161372i	0.353695	−	0.935361i	$-0.384925\pi$
$853$	−8.16324	−	4.71305i	−0.279504	−	0.161372i	−0.633199	+	0.773989i	$0.718258\pi$
$854$		0			0
$855$	−1.16300	+	13.3000i	−0.0397738	+	0.454852i
$856$		0			0
$857$	−30.8222			−1.05287			−0.526433	−	0.850217i	$-0.676471\pi$
$857$	−30.8222			−1.05287			−0.526433	+	0.850217i	$0.676471\pi$
$858$		0			0
$859$		−	1.53925i		−	0.0525185i	−0.999655	−	0.0262592i	$-0.991640\pi$
$859$		−	1.53925i		−	0.0525185i	0.999655	−	0.0262592i	$-0.00835953\pi$
$860$		0			0
$861$	−6.14551	−	0.0797110i	−0.209438	−	0.00271655i
$862$		0			0
$863$	0.645937	+	0.372932i	0.0219879	+	0.0126947i	0.510954	−	0.859608i	$-0.329292\pi$
$863$	0.645937	+	0.372932i	0.0219879	+	0.0126947i	−0.488966	+	0.872303i	$0.662626\pi$
$864$		0			0
$865$	2.57645	+	4.46255i	0.0876020	+	0.151731i
$866$		0			0
$867$	12.0600	+	23.1658i	0.409579	+	0.786751i
$868$		0			0
$869$	−13.2362	+	7.64195i	−0.449009	+	0.259235i
$870$		0			0
$871$		−	3.24346i		−	0.109901i
$872$		0			0
$873$	3.31277	−	37.8847i	0.112120	−	1.28220i
$874$		0			0
$875$	29.4099	−	0.901427i	0.994236	−	0.0304738i
$876$		0			0
$877$	3.47691			0.117407			0.0587034	−	0.998275i	$-0.481303\pi$
$877$	3.47691			0.117407			0.0587034	+	0.998275i	$0.481303\pi$
$878$		0			0
$879$	19.6867	+	0.859096i	0.664015	+	0.0289766i
$880$		0			0
$881$	49.4437			1.66580			0.832900	−	0.553424i	$-0.186679\pi$
$881$	49.4437			1.66580			0.832900	+	0.553424i	$0.186679\pi$
$882$		0			0
$883$	−3.02160			−0.101685			−0.0508424	−	0.998707i	$-0.516191\pi$
$883$	−3.02160			−0.101685			−0.0508424	+	0.998707i	$0.516191\pi$
$884$		0			0
$885$	14.7500	+	28.3330i	0.495817	+	0.952403i
$886$		0			0
$887$	35.5134			1.19242			0.596212	−	0.802827i	$-0.296672\pi$
$887$	35.5134			1.19242			0.596212	+	0.802827i	$0.296672\pi$
$888$		0			0
$889$	−12.7379	+	0.390423i	−0.427216	+	0.0130944i
$890$		0			0
$891$	8.30036	+	6.96356i	0.278073	+	0.233288i
$892$		0			0
$893$		−	10.6442i		−	0.356195i
$894$		0			0
$895$	−31.1181	+	17.9660i	−1.04016	+	0.600539i
$896$		0			0
$897$	4.86898	+	0.212474i	0.162570	+	0.00709432i
$898$		0			0
$899$	2.40176	+	4.15997i	0.0801031	+	0.138743i
$900$		0			0
$901$	8.00381	+	4.62100i	0.266646	+	0.153948i
$902$		0			0
$903$	−2.19503	−	3.91840i	−0.0730460	−	0.130396i
$904$		0			0
$905$			10.4015i			0.345756i
$906$		0			0
$907$	16.1292			0.535561			0.267781	−	0.963480i	$-0.413710\pi$
$907$	16.1292			0.535561			0.267781	+	0.963480i	$0.413710\pi$
$908$		0			0
$909$	16.7927	+	36.0078i	0.556978	+	1.19430i
$910$		0			0
$911$	−16.7485	−	9.66977i	−0.554903	−	0.320374i	0.196194	−	0.980565i	$-0.437142\pi$
$911$	−16.7485	−	9.66977i	−0.554903	−	0.320374i	−0.751097	+	0.660191i	$0.770475\pi$
$912$		0			0
$913$	−6.55180	−	3.78268i	−0.216833	−	0.125188i
$914$		0			0
$915$	0.520252	−	11.9219i	0.0171990	−	0.394125i
$916$		0			0
$917$	−16.2407	+	0.497784i	−0.536314	+	0.0164383i
$918$		0			0
$919$	18.3378	−	31.7620i	0.604908	−	1.04773i	−0.387158	−	0.922014i	$-0.626543\pi$
$919$	18.3378	−	31.7620i	0.604908	−	1.04773i	0.992066	−	0.125718i	$-0.0401236\pi$
$920$		0			0
$921$	28.4396	+	18.1171i	0.937117	+	0.596980i
$922$		0			0
$923$	3.26516	+	5.65542i	0.107474	+	0.186151i
$924$		0			0
$925$	−15.9686	+	27.6585i	−0.525046	+	0.909405i
$926$		0			0
$927$	−35.8420	+	16.7154i	−1.17721	+	0.549005i
$928$		0			0
$929$	−12.4172	−	21.5073i	−0.407397	−	0.705632i	0.587200	−	0.809442i	$-0.300230\pi$
$929$	−12.4172	−	21.5073i	−0.407397	−	0.705632i	−0.994597	+	0.103810i	$0.966897\pi$
$930$		0			0
$931$	−20.3771	−	10.1547i	−0.667833	−	0.332807i
$932$		0			0
$933$	−17.7543	−	34.1039i	−0.581251	−	1.11651i
$934$		0			0
$935$	−1.97732	+	1.14161i	−0.0646654	+	0.0373346i
$936$		0			0
$937$			53.1227i			1.73544i	0.497050	+	0.867722i	$0.334416\pi$
$937$			53.1227i			1.73544i	−0.497050	+	0.867722i	$0.665584\pi$
$938$		0			0
$939$	1.05991	−	24.2884i	0.0345887	−	0.792621i
$940$		0			0
$941$	−17.2471	+	29.8729i	−0.562240	+	0.973829i	0.435060	+	0.900401i	$0.356727\pi$
$941$	−17.2471	+	29.8729i	−0.562240	+	0.973829i	−0.997301	+	0.0734277i	$0.976606\pi$
$942$		0			0
$943$	−4.42678	+	2.55580i	−0.144156	+	0.0832283i
$944$		0			0
$945$	−18.7164	−	1.88152i	−0.608844	−	0.0612059i
$946$		0			0
$947$	−17.2611	+	9.96572i	−0.560912	+	0.323842i	−0.753511	−	0.657435i	$-0.771641\pi$
$947$	−17.2611	+	9.96572i	−0.560912	+	0.323842i	0.192600	+	0.981277i	$0.438308\pi$
$948$		0			0
$949$	4.38771	−	7.59974i	0.142431	−	0.246698i
$950$		0			0
$951$	−0.981428	+	22.4900i	−0.0318250	+	0.729288i
$952$		0			0
$953$			37.0472i			1.20008i	0.799971	+	0.600039i	$0.204848\pi$
$953$			37.0472i			1.20008i	−0.799971	+	0.600039i	$0.795152\pi$
$954$		0			0
$955$	−22.1744	+	12.8024i	−0.717545	+	0.414275i
$956$		0			0
$957$	−3.89159	−	7.47527i	−0.125797	−	0.241641i
$958$		0			0
$959$	−0.285263	−	9.30696i	−0.00921161	−	0.300537i
$960$		0			0
$961$	−14.7938	−	25.6236i	−0.477219	−	0.826567i
$962$		0			0
$963$	−4.79198	+	54.8009i	−0.154419	+	1.76593i
$964$		0			0
$965$	−9.33886	+	16.1754i	−0.300629	+	0.520704i
$966$		0			0
$967$	−16.5292	−	28.6294i	−0.531543	−	0.920659i	−0.999322	−	0.0368136i	$-0.988279\pi$
$967$	−16.5292	−	28.6294i	−0.531543	−	0.920659i	0.467780	−	0.883845i	$-0.345054\pi$
$968$		0			0
$969$	−6.58585	−	4.19544i	−0.211568	−	0.134777i
$970$		0			0
$971$	−13.1441	+	22.7662i	−0.421813	+	0.730602i	−0.996117	−	0.0880404i	$-0.971940\pi$
$971$	−13.1441	+	22.7662i	−0.421813	+	0.730602i	0.574304	+	0.818642i	$0.305273\pi$
$972$		0			0
$973$	−32.9407	+	20.3888i	−1.05603	+	0.653635i
$974$		0			0
$975$	0.174371	−	3.99582i	0.00558435	−	0.127969i
$976$		0			0
$977$	−24.7246	−	14.2748i	−0.791011	−	0.456690i	0.0493073	−	0.998784i	$-0.484299\pi$
$977$	−24.7246	−	14.2748i	−0.791011	−	0.456690i	−0.840318	+	0.542093i	$0.817632\pi$
$978$		0			0
$979$	12.6330	+	7.29366i	0.403752	+	0.233106i
$980$		0			0
$981$	−30.0993	+	42.9904i	−0.960997	+	1.37258i
$982$		0			0
$983$	−3.12317			−0.0996138			−0.0498069	−	0.998759i	$-0.515861\pi$
$983$	−3.12317			−0.0996138			−0.0498069	+	0.998759i	$0.515861\pi$
$984$		0			0
$985$		−	22.3451i		−	0.711973i
$986$		0			0
$987$	14.9960	+	0.194507i	0.477328	+	0.00619124i
$988$		0			0
$989$	−3.23496	−	1.86770i	−0.102866	−	0.0593895i
$990$		0			0
$991$	9.31103	+	16.1272i	0.295775	+	0.512297i	0.975165	−	0.221481i	$-0.0710889\pi$
$991$	9.31103	+	16.1272i	0.295775	+	0.512297i	−0.679390	+	0.733777i	$0.737756\pi$
$992$		0			0
$993$	−21.6695	−	0.945622i	−0.687660	−	0.0300084i
$994$		0			0
$995$	−14.1519	+	8.17062i	−0.448646	+	0.259026i
$996$		0			0
$997$			0.0372304i			0.00117910i	1.00000		0.000589549i	$0.000187659\pi$
$997$			0.0372304i			0.00117910i	−1.00000		0.000589549i	$0.999812\pi$
$998$		0			0
$999$	32.2959	−	42.0948i	1.02180	−	1.33182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.e.929.9		48
3.2	odd	2		3024.2.df.e.1601.9		48
4.3	odd	2		504.2.cx.a.425.16	yes	48
7.3	odd	6		1008.2.ca.e.353.1		48
9.4	even	3		3024.2.ca.e.2609.9		48
9.5	odd	6		1008.2.ca.e.257.1		48
12.11	even	2		1512.2.cx.a.89.9		48
21.17	even	6		3024.2.ca.e.2033.9		48
28.3	even	6		504.2.bs.a.353.24	yes	48
36.23	even	6		504.2.bs.a.257.24	✓	48
36.31	odd	6		1512.2.bs.a.1097.9		48
63.31	odd	6		3024.2.df.e.17.9		48
63.59	even	6	inner	1008.2.df.e.689.9		48
84.59	odd	6		1512.2.bs.a.521.9		48
252.31	even	6		1512.2.cx.a.17.9		48
252.59	odd	6		504.2.cx.a.185.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.24	✓	48	36.23	even	6
504.2.bs.a.353.24	yes	48	28.3	even	6
504.2.cx.a.185.16	yes	48	252.59	odd	6
504.2.cx.a.425.16	yes	48	4.3	odd	2
1008.2.ca.e.257.1		48	9.5	odd	6
1008.2.ca.e.353.1		48	7.3	odd	6
1008.2.df.e.689.9		48	63.59	even	6	inner
1008.2.df.e.929.9		48	1.1	even	1	trivial
1512.2.bs.a.521.9		48	84.59	odd	6
1512.2.bs.a.1097.9		48	36.31	odd	6
1512.2.cx.a.17.9		48	252.31	even	6
1512.2.cx.a.89.9		48	12.11	even	2
3024.2.ca.e.2033.9		48	21.17	even	6
3024.2.ca.e.2609.9		48	9.4	even	3
3024.2.df.e.17.9		48	63.31	odd	6
3024.2.df.e.1601.9		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.930597 + 1.46082i) q^{3} +1.36828 q^{5} +(-2.64451 + 0.0810554i) q^{7} +(-1.26798 - 2.71887i) q^{9} -1.20384i q^{11} +(0.639364 - 0.369137i) q^{13} +(-1.27332 + 1.99881i) q^{15} +(-0.693066 - 1.20043i) q^{17} +(-2.81671 - 1.62623i) q^{19} +(2.34257 - 3.93858i) q^{21} -3.81129i q^{23} -3.12781 q^{25} +(5.15174 + 0.677887i) q^{27} +(-3.50030 - 2.02090i) q^{29} +(-1.02924 - 0.594230i) q^{31} +(1.75859 + 1.12029i) q^{33} +(-3.61843 + 0.110906i) q^{35} +(5.10537 - 8.84276i) q^{37} +(-0.0557487 + 1.27751i) q^{39} +(-0.670586 - 1.16149i) q^{41} +(0.490044 - 0.848782i) q^{43} +(-1.73495 - 3.72017i) q^{45} +(1.63634 + 2.83422i) q^{47} +(6.98686 - 0.428704i) q^{49} +(2.39857 + 0.104670i) q^{51} +(-5.77421 + 3.33374i) q^{53} -1.64718i q^{55} +(4.99684 - 2.60133i) q^{57} +(6.73912 - 11.6725i) q^{59} +(-4.36067 + 2.51764i) q^{61} +(3.57356 + 7.08729i) q^{63} +(0.874829 - 0.505083i) q^{65} +(2.19665 - 3.80471i) q^{67} +(5.56760 + 3.54678i) q^{69} +8.84538i q^{71} +(10.2939 - 5.94320i) q^{73} +(2.91073 - 4.56917i) q^{75} +(0.0975775 + 3.18356i) q^{77} +(-6.34799 - 10.9950i) q^{79} +(-5.78447 + 6.89492i) q^{81} +(3.14219 - 5.44243i) q^{83} +(-0.948308 - 1.64252i) q^{85} +(6.20953 - 3.23266i) q^{87} +(-6.05868 + 10.4939i) q^{89} +(-1.66088 + 1.02801i) q^{91} +(1.82587 - 0.950538i) q^{93} +(-3.85404 - 2.22513i) q^{95} +(10.9781 + 6.33821i) q^{97} +(-3.27307 + 1.52644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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