LMFDB - Embedded newform 468.2.bl.b.337.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(25,468)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("468.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.8
Character	$\chi$	$=$	468.337
Dual form			468.2.bl.b.25.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.444415 + 1.67407i) q^{3} +(2.13836 + 1.23458i) q^{5} +(0.836915 - 0.483193i) q^{7} +(-2.60499 + 1.48796i) q^{9} +(3.21548 - 1.85646i) q^{11} +(3.60327 + 0.128201i) q^{13} +(-1.11645 + 4.12841i) q^{15} -2.85159 q^{17} +0.604961i q^{19} +(1.18083 + 1.18631i) q^{21} +(-3.15810 + 5.47000i) q^{23} +(0.548379 + 0.949821i) q^{25} +(-3.64864 - 3.69966i) q^{27} +(0.550851 + 0.954102i) q^{29} +(-8.22775 - 4.75029i) q^{31} +(4.53684 + 4.55789i) q^{33} +2.38617 q^{35} -1.98412i q^{37} +(1.38673 + 6.08909i) q^{39} +(10.2623 + 5.92492i) q^{41} +(-4.32783 - 7.49603i) q^{43} +(-7.40741 - 0.0342863i) q^{45} +(-2.83777 + 1.63839i) q^{47} +(-3.03305 + 5.25339i) q^{49} +(-1.26729 - 4.77375i) q^{51} +5.79913 q^{53} +9.16780 q^{55} +(-1.01274 + 0.268853i) q^{57} +(5.40887 + 3.12281i) q^{59} +(4.03552 + 6.98973i) q^{61} +(-1.46119 + 2.50401i) q^{63} +(7.54681 + 4.72267i) q^{65} +(-7.70819 - 4.45033i) q^{67} +(-10.5606 - 2.85593i) q^{69} -14.5420i q^{71} -13.9731i q^{73} +(-1.34635 + 1.34014i) q^{75} +(1.79406 - 3.10740i) q^{77} +(-4.13435 - 7.16090i) q^{79} +(4.57196 - 7.75224i) q^{81} +(-1.62677 + 0.939215i) q^{83} +(-6.09771 - 3.52052i) q^{85} +(-1.35242 + 1.34618i) q^{87} -0.377612i q^{89} +(3.07758 - 1.63378i) q^{91} +(4.29577 - 15.8849i) q^{93} +(-0.746873 + 1.29362i) q^{95} +(5.89116 - 3.40126i) q^{97} +(-5.61397 + 9.62057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 2 q^{9} + 5 q^{13} - 4 q^{17} - 22 q^{23} + 16 q^{25} - 18 q^{27} + 22 q^{29} + 8 q^{35} + 37 q^{39} - 2 q^{43} + 22 q^{49} - 38 q^{51} - 12 q^{53} + 48 q^{55} + 8 q^{61} - q^{65} - 26 q^{69}+ \cdots - 48 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 + 2 * q^9 + 5 * q^13 - 4 * q^17 - 22 * q^23 + 16 * q^25 - 18 * q^27 + 22 * q^29 + 8 * q^35 + 37 * q^39 - 2 * q^43 + 22 * q^49 - 38 * q^51 - 12 * q^53 + 48 * q^55 + 8 * q^61 - q^65 - 26 * q^69 - 64 * q^75 - 24 * q^77 - 8 * q^79 + 2 * q^81 - 40 * q^87 + 22 * q^91 - 48 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.444415	+	1.67407i	0.256583	+	0.966522i
$3$	0.444415	+	1.67407i	0.256583	+	0.966522i
$4$		0			0
$5$	2.13836	+	1.23458i	0.956302	+	0.552121i	0.895033	−	0.446000i	$-0.147152\pi$
$5$	2.13836	+	1.23458i	0.956302	+	0.552121i	0.0612692	+	0.998121i	$0.480485\pi$
$6$		0			0
$7$	0.836915	−	0.483193i	0.316324	−	0.182630i	−0.333429	−	0.942775i	$-0.608206\pi$
$7$	0.836915	−	0.483193i	0.316324	−	0.182630i	0.649753	+	0.760145i	$0.274872\pi$
$8$		0			0
$9$	−2.60499	+	1.48796i	−0.868330	+	0.495986i
$10$		0			0
$11$	3.21548	−	1.85646i	0.969505	−	0.559744i	0.0704194	−	0.997517i	$-0.477566\pi$
$11$	3.21548	−	1.85646i	0.969505	−	0.559744i	0.899085	+	0.437774i	$0.144233\pi$
$12$		0			0
$13$	3.60327	+	0.128201i	0.999368	+	0.0355565i
$13$	3.60327	+	0.128201i	0.999368	+	0.0355565i
$14$		0			0
$15$	−1.11645	+	4.12841i	−0.288267	+	1.06595i
$16$		0			0
$17$	−2.85159			−0.691612			−0.345806	−	0.938306i	$-0.612394\pi$
$17$	−2.85159			−0.691612			−0.345806	+	0.938306i	$0.612394\pi$
$18$		0			0
$19$			0.604961i			0.138787i	0.997589	+	0.0693937i	$0.0221065\pi$
$19$			0.604961i			0.138787i	−0.997589	+	0.0693937i	$0.977894\pi$
$20$		0			0
$21$	1.18083	+	1.18631i	0.257679	+	0.258875i
$22$		0			0
$23$	−3.15810	+	5.47000i	−0.658510	+	1.14057i	0.322491	+	0.946573i	$0.395480\pi$
$23$	−3.15810	+	5.47000i	−0.658510	+	1.14057i	−0.981001	+	0.194001i	$0.937854\pi$
$24$		0			0
$25$	0.548379	+	0.949821i	0.109676	+	0.189964i
$26$		0			0
$27$	−3.64864	−	3.69966i	−0.702180	−	0.711999i
$28$		0			0
$29$	0.550851	+	0.954102i	0.102290	+	0.177172i	0.912628	−	0.408791i	$-0.134050\pi$
$29$	0.550851	+	0.954102i	0.102290	+	0.177172i	−0.810337	+	0.585963i	$0.800716\pi$
$30$		0			0
$31$	−8.22775	−	4.75029i	−1.47775	−	0.853178i	−0.478064	−	0.878325i	$-0.658661\pi$
$31$	−8.22775	−	4.75029i	−1.47775	−	0.853178i	−0.999684	+	0.0251470i	$0.991995\pi$
$32$		0			0
$33$	4.53684	+	4.55789i	0.789763	+	0.793427i
$34$		0			0
$35$	2.38617			0.403336
$36$		0			0
$37$		−	1.98412i		−	0.326187i	−0.986611	−	0.163093i	$-0.947853\pi$
$37$		−	1.98412i		−	0.326187i	0.986611	−	0.163093i	$-0.0521472\pi$
$38$		0			0
$39$	1.38673	+	6.08909i	0.222055	+	0.975034i
$40$		0			0
$41$	10.2623	+	5.92492i	1.60270	+	0.925317i	0.990945	+	0.134266i	$0.0428675\pi$
$41$	10.2623	+	5.92492i	1.60270	+	0.925317i	0.611750	+	0.791051i	$0.290466\pi$
$42$		0			0
$43$	−4.32783	−	7.49603i	−0.659988	−	1.14313i	−0.980618	−	0.195929i	$-0.937228\pi$
$43$	−4.32783	−	7.49603i	−0.659988	−	1.14313i	0.320630	−	0.947205i	$-0.396105\pi$
$44$		0			0
$45$	−7.40741	−	0.0342863i	−1.10423	−	0.00511110i
$46$		0			0
$47$	−2.83777	+	1.63839i	−0.413931	+	0.238983i	−0.692477	−	0.721440i	$-0.743481\pi$
$47$	−2.83777	+	1.63839i	−0.413931	+	0.238983i	0.278546	+	0.960423i	$0.410147\pi$
$48$		0			0
$49$	−3.03305	+	5.25339i	−0.433293	+	0.750485i
$50$		0			0
$51$	−1.26729	−	4.77375i	−0.177456	−	0.668458i
$52$		0			0
$53$	5.79913			0.796572			0.398286	−	0.917261i	$-0.369605\pi$
$53$	5.79913			0.796572			0.398286	+	0.917261i	$0.369605\pi$
$54$		0			0
$55$	9.16780			1.23619
$56$		0			0
$57$	−1.01274	+	0.268853i	−0.134141	+	0.0356105i
$58$		0			0
$59$	5.40887	+	3.12281i	0.704175	+	0.406556i	0.808901	−	0.587945i	$-0.200063\pi$
$59$	5.40887	+	3.12281i	0.704175	+	0.406556i	−0.104725	+	0.994501i	$0.533396\pi$
$60$		0			0
$61$	4.03552	+	6.98973i	0.516695	+	0.894943i	0.999812	+	0.0193867i	$0.00617136\pi$
$61$	4.03552	+	6.98973i	0.516695	+	0.894943i	−0.483117	+	0.875556i	$0.660495\pi$
$62$		0			0
$63$	−1.46119	+	2.50401i	−0.184092	+	0.315476i
$64$		0			0
$65$	7.54681	+	4.72267i	0.936066	+	0.585775i
$66$		0			0
$67$	−7.70819	−	4.45033i	−0.941705	−	0.543694i	−0.0512109	−	0.998688i	$-0.516308\pi$
$67$	−7.70819	−	4.45033i	−0.941705	−	0.543694i	−0.890494	+	0.454994i	$0.849641\pi$
$68$		0			0
$69$	−10.5606	−	2.85593i	−1.27135	−	0.343813i
$70$		0			0
$71$		−	14.5420i		−	1.72582i	−0.505357	−	0.862910i	$-0.668639\pi$
$71$		−	14.5420i		−	1.72582i	0.505357	−	0.862910i	$-0.331361\pi$
$72$		0			0
$73$		−	13.9731i		−	1.63542i	−0.575629	−	0.817711i	$-0.695243\pi$
$73$		−	13.9731i		−	1.63542i	0.575629	−	0.817711i	$-0.304757\pi$
$74$		0			0
$75$	−1.34635	+	1.34014i	−0.155464	+	0.154746i
$76$		0			0
$77$	1.79406	−	3.10740i	0.204452	−	0.354121i
$78$		0			0
$79$	−4.13435	−	7.16090i	−0.465151	−	0.805664i	0.534058	−	0.845448i	$-0.320666\pi$
$79$	−4.13435	−	7.16090i	−0.465151	−	0.805664i	−0.999208	+	0.0397836i	$0.987333\pi$
$80$		0			0
$81$	4.57196	−	7.75224i	0.507995	−	0.861360i
$82$		0			0
$83$	−1.62677	+	0.939215i	−0.178561	+	0.103092i	−0.586616	−	0.809865i	$-0.699540\pi$
$83$	−1.62677	+	0.939215i	−0.178561	+	0.103092i	0.408055	+	0.912957i	$0.366207\pi$
$84$		0			0
$85$	−6.09771	−	3.52052i	−0.661390	−	0.381854i
$86$		0			0
$87$	−1.35242	+	1.34618i	−0.144995	+	0.144325i
$88$		0			0
$89$		−	0.377612i		−	0.0400268i	−0.999800	−	0.0200134i	$-0.993629\pi$
$89$		−	0.377612i		−	0.0400268i	0.999800	−	0.0200134i	$-0.00637089\pi$
$90$		0			0
$91$	3.07758	−	1.63378i	0.322618	−	0.171267i
$92$		0			0
$93$	4.29577	−	15.8849i	0.445451	−	1.64719i
$94$		0			0
$95$	−0.746873	+	1.29362i	−0.0766275	+	0.132723i
$96$		0			0
$97$	5.89116	−	3.40126i	0.598157	−	0.345346i	−0.170159	−	0.985417i	$-0.554428\pi$
$97$	5.89116	−	3.40126i	0.598157	−	0.345346i	0.768316	+	0.640071i	$0.221095\pi$
$98$		0			0
$99$	−5.61397	+	9.62057i	−0.564225	+	0.966903i
$100$		0			0
$101$	−2.74567	−	4.75564i	−0.273204	−	0.473204i	0.696476	−	0.717580i	$-0.254750\pi$
$101$	−2.74567	−	4.75564i	−0.273204	−	0.473204i	−0.969681	+	0.244376i	$0.921417\pi$
$102$		0			0
$103$	5.54471	−	9.60373i	0.546337	−	0.946283i	−0.452185	−	0.891924i	$-0.649355\pi$
$103$	5.54471	−	9.60373i	0.546337	−	0.946283i	0.998521	−	0.0543589i	$-0.0173115\pi$
$104$		0			0
$105$	1.06045	+	3.99460i	0.103489	+	0.389833i
$106$		0			0
$107$	4.13605			0.399847			0.199924	−	0.979811i	$-0.435931\pi$
$107$	4.13605			0.399847			0.199924	+	0.979811i	$0.435931\pi$
$108$		0			0
$109$		−	0.950905i		−	0.0910801i	−0.998963	−	0.0455401i	$-0.985499\pi$
$109$		−	0.950905i		−	0.0910801i	0.998963	−	0.0455401i	$-0.0145009\pi$
$110$		0			0
$111$	3.32154	−	0.881770i	0.315267	−	0.0836939i
$112$		0			0
$113$	−6.14525	+	10.6439i	−0.578096	+	1.00129i	0.417602	+	0.908630i	$0.362871\pi$
$113$	−6.14525	+	10.6439i	−0.578096	+	1.00129i	−0.995698	+	0.0926615i	$0.970463\pi$
$114$		0			0
$115$	−13.5063	+	7.79787i	−1.25947	+	0.727155i
$116$		0			0
$117$	−9.57725	+	5.02756i	−0.885417	+	0.464798i
$118$		0			0
$119$	−2.38654	+	1.37787i	−0.218774	+	0.126309i
$120$		0			0
$121$	1.39289	−	2.41255i	0.126626	−	0.219323i
$122$		0			0
$123$	−5.35800	+	19.8128i	−0.483115	+	1.78646i
$124$		0			0
$125$		−	9.63773i		−	0.862025i
$126$		0			0
$127$	−0.285266			−0.0253133			−0.0126566	−	0.999920i	$-0.504029\pi$
$127$	−0.285266			−0.0253133			−0.0126566	+	0.999920i	$0.504029\pi$
$128$		0			0
$129$	10.6255	−	10.5764i	0.935522	−	0.931202i
$130$		0			0
$131$	−1.91413	+	3.31537i	−0.167238	+	0.289665i	−0.937448	−	0.348126i	$-0.886818\pi$
$131$	−1.91413	+	3.31537i	−0.167238	+	0.289665i	0.770210	+	0.637791i	$0.220152\pi$
$132$		0			0
$133$	0.292313	+	0.506301i	0.0253467	+	0.0439019i
$134$		0			0
$135$	−3.23456	−	12.4157i	−0.278387	−	1.06858i
$136$		0			0
$137$	−9.55752	+	5.51804i	−0.816554	+	0.471438i	−0.849227	−	0.528028i	$-0.822931\pi$
$137$	−9.55752	+	5.51804i	−0.816554	+	0.471438i	0.0326726	+	0.999466i	$0.489598\pi$
$138$		0			0
$139$	0.590037	−	1.02197i	0.0500463	−	0.0866827i	−0.839917	−	0.542715i	$-0.817396\pi$
$139$	0.590037	−	1.02197i	0.0500463	−	0.0866827i	0.889963	+	0.456032i	$0.150730\pi$
$140$		0			0
$141$	−4.00391	−	4.02249i	−0.337190	−	0.338755i
$142$		0			0
$143$	11.8243	−	6.27710i	0.988794	−	0.524918i
$144$		0			0
$145$			2.72028i			0.225907i
$146$		0			0
$147$	−10.1425	−	2.74284i	−0.836536	−	0.226225i
$148$		0			0
$149$	2.33150	+	1.34609i	0.191004	+	0.110276i	0.592453	−	0.805605i	$-0.298160\pi$
$149$	2.33150	+	1.34609i	0.191004	+	0.110276i	−0.401448	+	0.915882i	$0.631493\pi$
$150$		0			0
$151$	2.45457	−	1.41715i	0.199750	−	0.115326i	−0.396789	−	0.917910i	$-0.629875\pi$
$151$	2.45457	−	1.41715i	0.199750	−	0.115326i	0.596539	+	0.802584i	$0.296542\pi$
$152$		0			0
$153$	7.42836	−	4.24305i	0.600548	−	0.343030i
$154$		0			0
$155$	−11.7292	−	20.3156i	−0.942116	−	1.63179i
$156$		0			0
$157$	7.69413	−	13.3266i	0.614058	−	1.06358i	−0.376491	−	0.926420i	$-0.622869\pi$
$157$	7.69413	−	13.3266i	0.614058	−	1.06358i	0.990549	−	0.137159i	$-0.0437973\pi$
$158$		0			0
$159$	2.57722	+	9.70813i	0.204387	+	0.769905i
$160$		0			0
$161$			6.10390i			0.481055i
$162$		0			0
$163$			7.58832i			0.594363i	0.954821	+	0.297182i	$0.0960467\pi$
$163$			7.58832i			0.594363i	−0.954821	+	0.297182i	$0.903953\pi$
$164$		0			0
$165$	4.07430	+	15.3475i	0.317184	+	1.19480i
$166$		0			0
$167$	4.65877	+	2.68974i	0.360506	+	0.208138i	0.669303	−	0.742990i	$-0.266593\pi$
$167$	4.65877	+	2.68974i	0.360506	+	0.208138i	−0.308796	+	0.951128i	$0.599926\pi$
$168$		0			0
$169$	12.9671	+	0.923883i	0.997471	+	0.0710679i
$170$		0			0
$171$	−0.900156	−	1.57592i	−0.0688367	−	0.120513i
$172$		0			0
$173$	−8.69857	−	15.0664i	−0.661340	−	1.14547i	−0.980264	−	0.197694i	$-0.936655\pi$
$173$	−8.69857	−	15.0664i	−0.661340	−	1.14547i	0.318924	−	0.947780i	$-0.396679\pi$
$174$		0			0
$175$	0.917894	+	0.529947i	0.0693863	+	0.0400602i
$176$		0			0
$177$	−2.82401	+	10.4426i	−0.212266	+	0.784916i
$178$		0			0
$179$	−9.46824			−0.707690			−0.353845	−	0.935304i	$-0.615126\pi$
$179$	−9.46824			−0.707690			−0.353845	+	0.935304i	$0.615126\pi$
$180$		0			0
$181$	−8.43962			−0.627312			−0.313656	−	0.949537i	$-0.601554\pi$
$181$	−8.43962			−0.627312			−0.313656	+	0.949537i	$0.601554\pi$
$182$		0			0
$183$	−9.90782	+	9.86206i	−0.732407	+	0.729025i
$184$		0			0
$185$	2.44955	−	4.24275i	0.180095	−	0.311933i
$186$		0			0
$187$	−9.16924	+	5.29386i	−0.670521	+	0.387125i
$188$		0			0
$189$	−4.84125	−	1.33330i	−0.352149	−	0.0969835i
$190$		0			0
$191$	8.24996	+	14.2894i	0.596946	+	1.03394i	0.993269	+	0.115830i	$0.0369528\pi$
$191$	8.24996	+	14.2894i	0.596946	+	1.03394i	−0.396323	+	0.918111i	$0.629714\pi$
$192$		0			0
$193$	16.0793	+	9.28338i	1.15741	+	0.668232i	0.950682	−	0.310166i	$-0.100385\pi$
$193$	16.0793	+	9.28338i	1.15741	+	0.668232i	0.206729	+	0.978398i	$0.433718\pi$
$194$		0			0
$195$	−4.55215	+	14.7327i	−0.325986	+	1.05503i
$196$		0			0
$197$			10.3879i			0.740110i	0.929010	+	0.370055i	$0.120661\pi$
$197$			10.3879i			0.740110i	−0.929010	+	0.370055i	$0.879339\pi$
$198$		0			0
$199$	−11.7516			−0.833050			−0.416525	−	0.909124i	$-0.636752\pi$
$199$	−11.7516			−0.833050			−0.416525	+	0.909124i	$0.636752\pi$
$200$		0			0
$201$	4.02450	−	14.8818i	0.283867	−	1.04968i
$202$		0			0
$203$	0.922032	+	0.532335i	0.0647139	+	0.0373626i
$204$		0			0
$205$	14.6296	+	25.3392i	1.02177	+	1.76976i
$206$		0			0
$207$	0.0877056	−	18.9484i	0.00609596	−	1.31701i
$208$		0			0
$209$	1.12309	+	1.94524i	0.0776854	+	0.134555i
$210$		0			0
$211$	−7.90926	+	13.6992i	−0.544496	+	0.943095i	0.454142	+	0.890929i	$0.349946\pi$
$211$	−7.90926	+	13.6992i	−0.544496	+	0.943095i	−0.998638	+	0.0521656i	$0.983388\pi$
$212$		0			0
$213$	24.3443	−	6.46269i	1.66804	−	0.442816i
$214$		0			0
$215$		−	21.3722i		−	1.45757i
$216$		0			0
$217$	−9.18124			−0.623263
$218$		0			0
$219$	23.3918	−	6.20983i	1.58067	−	0.419621i
$220$		0			0
$221$	−10.2750	−	0.365575i	−0.691175	−	0.0245913i
$222$		0			0
$223$	−9.84728	+	5.68533i	−0.659423	+	0.380718i	−0.792057	−	0.610447i	$-0.790990\pi$
$223$	−9.84728	+	5.68533i	−0.659423	+	0.380718i	0.132634	+	0.991165i	$0.457656\pi$
$224$		0			0
$225$	−2.84182	−	1.65831i	−0.189454	−	0.110554i
$226$		0			0
$227$	−9.13976	+	5.27685i	−0.606627	+	0.350237i	−0.771644	−	0.636054i	$-0.780565\pi$
$227$	−9.13976	+	5.27685i	−0.606627	+	0.350237i	0.165017	+	0.986291i	$0.447232\pi$
$228$		0			0
$229$	25.9319	+	14.9718i	1.71363	+	0.989365i	0.929542	+	0.368715i	$0.120202\pi$
$229$	25.9319	+	14.9718i	1.71363	+	0.989365i	0.784088	+	0.620650i	$0.213131\pi$
$230$		0			0
$231$	5.99930	+	1.62240i	0.394725	+	0.106746i
$232$		0			0
$233$	−21.4256			−1.40364			−0.701819	−	0.712356i	$-0.747628\pi$
$233$	−21.4256			−1.40364			−0.701819	+	0.712356i	$0.747628\pi$
$234$		0			0
$235$	−8.09088			−0.527791
$236$		0			0
$237$	10.1505	−	10.1036i	0.659343	−	0.656298i
$238$		0			0
$239$	22.8507	+	13.1929i	1.47809	+	0.853375i	0.999693	−	0.0247696i	$-0.00788521\pi$
$239$	22.8507	+	13.1929i	1.47809	+	0.853375i	0.478396	+	0.878144i	$0.341219\pi$
$240$		0			0
$241$	9.17135	−	5.29508i	0.590779	−	0.341086i	−0.174627	−	0.984635i	$-0.555872\pi$
$241$	9.17135	−	5.29508i	0.590779	−	0.341086i	0.765405	+	0.643548i	$0.222539\pi$
$242$		0			0
$243$	15.0096	+	4.20855i	0.962866	+	0.269979i
$244$		0			0
$245$	−12.9715	+	7.48909i	−0.828717	+	0.478460i
$246$		0			0
$247$	−0.0775563	+	2.17984i	−0.00493479	+	0.138700i
$248$		0			0
$249$	−2.29527	−	2.30592i	−0.145457	−	0.146131i
$250$		0			0
$251$	29.2257			1.84471			0.922356	−	0.386340i	$-0.126261\pi$
$251$	29.2257			1.84471			0.922356	+	0.386340i	$0.126261\pi$
$252$		0			0
$253$			23.4516i			1.47439i
$254$		0			0
$255$	3.18366	−	11.7725i	0.199369	−	0.737225i
$256$		0			0
$257$	−4.12597	+	7.14638i	−0.257371	+	0.445779i	−0.965537	−	0.260267i	$-0.916189\pi$
$257$	−4.12597	+	7.14638i	−0.257371	+	0.445779i	0.708166	+	0.706046i	$0.249523\pi$
$258$		0			0
$259$	−0.958711	−	1.66054i	−0.0595714	−	0.103181i
$260$		0			0
$261$	−2.85463	−	1.66578i	−0.176697	−	0.103109i
$262$		0			0
$263$	0.243109	+	0.421077i	0.0149907	+	0.0259647i	0.873423	−	0.486961i	$-0.161895\pi$
$263$	0.243109	+	0.421077i	0.0149907	+	0.0259647i	−0.858433	+	0.512926i	$0.828561\pi$
$264$		0			0
$265$	12.4006	+	7.15950i	0.761764	+	0.439804i
$266$		0			0
$267$	0.632148	−	0.167816i	0.0386868	−	0.0102702i
$268$		0			0
$269$	10.1445			0.618519			0.309260	−	0.950978i	$-0.399919\pi$
$269$	10.1445			0.618519			0.309260	+	0.950978i	$0.399919\pi$
$270$		0			0
$271$		−	24.5027i		−	1.48843i	−0.667938	−	0.744217i	$-0.732823\pi$
$271$		−	24.5027i		−	1.48843i	0.667938	−	0.744217i	$-0.267177\pi$
$272$		0			0
$273$	4.10278	+	4.42599i	0.248312	+	0.267873i
$274$		0			0
$275$	3.52661	+	2.03609i	0.212663	+	0.122781i
$276$		0			0
$277$	−12.5962	−	21.8173i	−0.756833	−	1.31087i	−0.944458	−	0.328632i	$-0.893412\pi$
$277$	−12.5962	−	21.8173i	−0.756833	−	1.31087i	0.187625	−	0.982241i	$-0.439921\pi$
$278$		0			0
$279$	28.5015	+	0.131923i	1.70634	+	0.00789804i
$280$		0			0
$281$	−15.9234	+	9.19338i	−0.949911	+	0.548431i	−0.893053	−	0.449951i	$-0.851441\pi$
$281$	−15.9234	+	9.19338i	−0.949911	+	0.548431i	−0.0568575	+	0.998382i	$0.518108\pi$
$282$		0			0
$283$	−15.2630	+	26.4363i	−0.907292	+	1.57148i	−0.0894819	+	0.995988i	$0.528521\pi$
$283$	−15.2630	+	26.4363i	−0.907292	+	1.57148i	−0.817810	+	0.575488i	$0.804812\pi$
$284$		0			0
$285$	−2.49753	−	0.675410i	−0.147941	−	0.0400078i
$286$		0			0
$287$	11.4515			0.675962
$288$		0			0
$289$	−8.86844			−0.521673
$290$		0			0
$291$	8.31205	+	8.35062i	0.487261	+	0.489522i
$292$		0			0
$293$	−13.5381	−	7.81623i	−0.790904	−	0.456629i	0.0493765	−	0.998780i	$-0.484277\pi$
$293$	−13.5381	−	7.81623i	−0.790904	−	0.456629i	−0.840281	+	0.542151i	$0.817610\pi$
$294$		0			0
$295$	7.71073	+	13.3554i	0.448936	+	0.777580i
$296$		0			0
$297$	−18.6004	−	5.12263i	−1.07930	−	0.297245i
$298$		0			0
$299$	−12.0808	+	19.3050i	−0.698649	+	1.11644i
$300$		0			0
$301$	−7.24406	−	4.18236i	−0.417541	−	0.241067i
$302$		0			0
$303$	6.74104	−	6.70991i	0.387262	−	0.385474i
$304$		0			0
$305$			19.9287i			1.14111i
$306$		0			0
$307$			28.8097i			1.64426i	0.569303	+	0.822128i	$0.307213\pi$
$307$			28.8097i			1.64426i	−0.569303	+	0.822128i	$0.692787\pi$
$308$		0			0
$309$	18.5414	+	5.01418i	1.05478	+	0.285247i
$310$		0			0
$311$	8.33245	−	14.4322i	0.472490	−	0.818377i	−0.527014	−	0.849856i	$-0.676689\pi$
$311$	8.33245	−	14.4322i	0.472490	−	0.818377i	0.999504	+	0.0314797i	$0.0100219\pi$
$312$		0			0
$313$	−11.7801	−	20.4038i	−0.665852	−	1.15329i	−0.979054	−	0.203603i	$-0.934735\pi$
$313$	−11.7801	−	20.4038i	−0.665852	−	1.15329i	0.313201	−	0.949687i	$-0.398599\pi$
$314$		0			0
$315$	−6.21594	+	3.55051i	−0.350228	+	0.200049i
$316$		0			0
$317$	−9.56285	+	5.52111i	−0.537103	+	0.310097i	−0.743904	−	0.668286i	$-0.767028\pi$
$317$	−9.56285	+	5.52111i	−0.537103	+	0.310097i	0.206801	+	0.978383i	$0.433695\pi$
$318$		0			0
$319$	3.54250	+	2.04527i	0.198342	+	0.114513i
$320$		0			0
$321$	1.83812	+	6.92402i	0.102594	+	0.386461i
$322$		0			0
$323$		−	1.72510i		−	0.0959871i
$324$		0			0
$325$	1.85419	+	3.49276i	0.102852	+	0.193744i
$326$		0			0
$327$	1.59188	−	0.422596i	0.0880310	−	0.0233696i
$328$		0			0
$329$	−1.58331	+	2.74238i	−0.0872910	+	0.151192i
$330$		0			0
$331$	29.4521	−	17.0042i	1.61883	−	0.934634i	0.631610	−	0.775286i	$-0.282394\pi$
$331$	29.4521	−	17.0042i	1.61883	−	0.934634i	0.987223	−	0.159348i	$-0.0509391\pi$
$332$		0			0
$333$	2.95228	+	5.16860i	0.161784	+	0.283238i
$334$		0			0
$335$	−10.9886	−	19.0328i	−0.600370	−	1.03987i
$336$		0			0
$337$	−13.4264	+	23.2553i	−0.731384	+	1.26679i	0.224908	+	0.974380i	$0.427792\pi$
$337$	−13.4264	+	23.2553i	−0.731384	+	1.26679i	−0.956292	+	0.292414i	$0.905541\pi$
$338$		0			0
$339$	−20.5496	−	5.55725i	−1.11610	−	0.301828i
$340$		0			0
$341$	−35.2749			−1.91024
$342$		0			0
$343$			12.6269i			0.681789i
$344$		0			0
$345$	−19.0565	−	19.1450i	−1.02597	−	1.03073i
$346$		0			0
$347$	−2.38126	+	4.12447i	−0.127833	+	0.221413i	−0.922837	−	0.385191i	$-0.874135\pi$
$347$	−2.38126	+	4.12447i	−0.127833	+	0.221413i	0.795004	+	0.606604i	$0.207469\pi$
$348$		0			0
$349$	−21.2143	+	12.2481i	−1.13557	+	0.655624i	−0.945331	−	0.326113i	$-0.894261\pi$
$349$	−21.2143	+	12.2481i	−1.13557	+	0.655624i	−0.190244	+	0.981737i	$0.560928\pi$
$350$		0			0
$351$	−12.6727	−	13.7986i	−0.676420	−	0.736516i
$352$		0			0
$353$	−6.66472	+	3.84788i	−0.354727	+	0.204802i	−0.666765	−	0.745268i	$-0.732322\pi$
$353$	−6.66472	+	3.84788i	−0.354727	+	0.204802i	0.312038	+	0.950070i	$0.398988\pi$
$354$		0			0
$355$	17.9533	−	31.0960i	0.952862	−	1.65041i
$356$		0			0
$357$	−3.36726	−	3.38288i	−0.178214	−	0.179041i
$358$		0			0
$359$		−	27.6325i		−	1.45839i	−0.684307	−	0.729194i	$-0.739895\pi$
$359$		−	27.6325i		−	1.45839i	0.684307	−	0.729194i	$-0.260105\pi$
$360$		0			0
$361$	18.6340			0.980738
$362$		0			0
$363$	4.65779	+	1.25961i	0.244470	+	0.0661124i
$364$		0			0
$365$	17.2509	−	29.8794i	0.902951	−	1.56396i
$366$		0			0
$367$	5.13322	+	8.89100i	0.267952	+	0.464106i	0.968333	−	0.249663i	$-0.0803198\pi$
$367$	5.13322	+	8.89100i	0.267952	+	0.464106i	−0.700381	+	0.713769i	$0.746986\pi$
$368$		0			0
$369$	−35.5491	−	0.164544i	−1.85061	−	0.00856584i
$370$		0			0
$371$	4.85338	−	2.80210i	0.251975	−	0.145478i
$372$		0			0
$373$	−11.8096	+	20.4548i	−0.611476	+	1.05911i	0.379516	+	0.925185i	$0.376091\pi$
$373$	−11.8096	+	20.4548i	−0.611476	+	1.05911i	−0.990992	+	0.133922i	$0.957243\pi$
$374$		0			0
$375$	16.1342	−	4.28315i	0.833166	−	0.221181i
$376$		0			0
$377$	1.86255	+	3.50851i	0.0959262	+	0.180697i
$378$		0			0
$379$			2.97603i			0.152869i	0.997075	+	0.0764343i	$0.0243535\pi$
$379$			2.97603i			0.152869i	−0.997075	+	0.0764343i	$0.975646\pi$
$380$		0			0
$381$	−0.126777	−	0.477555i	−0.00649496	−	0.0244659i
$382$		0			0
$383$	−23.6642	−	13.6625i	−1.20918	−	0.698122i	−0.246602	−	0.969117i	$-0.579314\pi$
$383$	−23.6642	−	13.6625i	−1.20918	−	0.698122i	−0.962581	+	0.270995i	$0.912647\pi$
$384$		0			0
$385$	7.67267	−	4.42982i	0.391036	−	0.225765i
$386$		0			0
$387$	22.4277	+	13.0874i	1.14007	+	0.665272i
$388$		0			0
$389$	−13.0974	−	22.6854i	−0.664066	−	1.15020i	−0.979538	−	0.201261i	$-0.935496\pi$
$389$	−13.0974	−	22.6854i	−0.664066	−	1.15020i	0.315471	−	0.948935i	$-0.397837\pi$
$390$		0			0
$391$	9.00562	−	15.5982i	0.455434	−	0.788834i
$392$		0			0
$393$	−6.40081	−	1.73098i	−0.322878	−	0.0873164i
$394$		0			0
$395$		−	20.4167i		−	1.02728i
$396$		0			0
$397$			15.4798i			0.776908i	0.921468	+	0.388454i	$0.126991\pi$
$397$			15.4798i			0.776908i	−0.921468	+	0.388454i	$0.873009\pi$
$398$		0			0
$399$	−0.717673	+	0.714359i	−0.0359286	+	0.0357627i
$400$		0			0
$401$	2.58648	+	1.49330i	0.129163	+	0.0745721i	0.563189	−	0.826328i	$-0.309574\pi$
$401$	2.58648	+	1.49330i	0.129163	+	0.0745721i	−0.434027	+	0.900900i	$0.642908\pi$
$402$		0			0
$403$	−29.0378	−	18.1714i	−1.44648	−	0.905182i
$404$		0			0
$405$	19.3472	−	10.9326i	0.961372	−	0.543245i
$406$		0			0
$407$	−3.68343	−	6.37989i	−0.182581	−	0.316239i
$408$		0			0
$409$	−24.1716	−	13.9555i	−1.19521	−	0.690055i	−0.235727	−	0.971819i	$-0.575747\pi$
$409$	−24.1716	−	13.9555i	−1.19521	−	0.690055i	−0.959484	+	0.281764i	$0.909081\pi$
$410$		0			0
$411$	−13.4851	−	13.5476i	−0.665169	−	0.668255i
$412$		0			0
$413$	6.03569			0.296997
$414$		0			0
$415$	−4.63815			−0.227678
$416$		0			0
$417$	1.97307	+	0.533580i	0.0966217	+	0.0261295i
$418$		0			0
$419$	−5.20703	+	9.01883i	−0.254380	+	0.440599i	−0.964727	−	0.263253i	$-0.915205\pi$
$419$	−5.20703	+	9.01883i	−0.254380	+	0.440599i	0.710347	+	0.703852i	$0.248538\pi$
$420$		0			0
$421$	7.33296	−	4.23369i	0.357387	−	0.206337i	−0.310547	−	0.950558i	$-0.600512\pi$
$421$	7.33296	−	4.23369i	0.357387	−	0.206337i	0.667934	+	0.744221i	$0.267179\pi$
$422$		0			0
$423$	4.95451	−	8.49046i	0.240897	−	0.412820i
$424$		0			0
$425$	−1.56375	−	2.70850i	−0.0758531	−	0.131381i
$426$		0			0
$427$	6.75478	+	3.89987i	0.326887	+	0.188728i
$428$		0			0
$429$	15.7632	+	17.0049i	0.761052	+	0.821007i
$430$		0			0
$431$		−	14.4601i		−	0.696520i	−0.937398	−	0.348260i	$-0.886773\pi$
$431$		−	14.4601i		−	0.696520i	0.937398	−	0.348260i	$-0.113227\pi$
$432$		0			0
$433$	18.2767			0.878320			0.439160	−	0.898409i	$-0.355276\pi$
$433$	18.2767			0.878320			0.439160	+	0.898409i	$0.355276\pi$
$434$		0			0
$435$	−4.55393	+	1.20893i	−0.218344	+	0.0579639i
$436$		0			0
$437$	−3.30913	−	1.91053i	−0.158297	−	0.0913930i
$438$		0			0
$439$	13.3139	+	23.0604i	0.635438	+	1.10061i	0.986422	+	0.164229i	$0.0525137\pi$
$439$	13.3139	+	23.0604i	0.635438	+	1.10061i	−0.350984	+	0.936381i	$0.614153\pi$
$440$		0			0
$441$	0.0842326	−	18.1981i	0.00401107	−	0.866576i
$442$		0			0
$443$	10.2947	+	17.8309i	0.489115	+	0.847173i	0.999922	−	0.0125231i	$-0.00398632\pi$
$443$	10.2947	+	17.8309i	0.489115	+	0.847173i	−0.510806	+	0.859696i	$0.670653\pi$
$444$		0			0
$445$	0.466193	−	0.807470i	0.0220997	−	0.0382777i
$446$		0			0
$447$	−1.21730	+	4.50132i	−0.0575761	+	0.212905i
$448$		0			0
$449$			21.1213i			0.996777i	0.866954	+	0.498389i	$0.166075\pi$
$449$			21.1213i			0.996777i	−0.866954	+	0.498389i	$0.833925\pi$
$450$		0			0
$451$	43.9975			2.07176
$452$		0			0
$453$	3.46324	+	3.47931i	0.162717	+	0.163472i
$454$		0			0
$455$	8.59800	+	0.305908i	0.403080	+	0.0143412i
$456$		0			0
$457$	14.1429	−	8.16541i	0.661577	−	0.381962i	−0.131301	−	0.991343i	$-0.541915\pi$
$457$	14.1429	−	8.16541i	0.661577	−	0.381962i	0.792878	+	0.609381i	$0.208582\pi$
$458$		0			0
$459$	10.4044	+	10.5499i	0.485636	+	0.492427i
$460$		0			0
$461$	15.1548	−	8.74962i	0.705829	−	0.407510i	−0.103686	−	0.994610i	$-0.533064\pi$
$461$	15.1548	−	8.74962i	0.705829	−	0.407510i	0.809515	+	0.587100i	$0.199730\pi$
$462$		0			0
$463$	−12.2690	−	7.08352i	−0.570190	−	0.329199i	0.187036	−	0.982353i	$-0.440112\pi$
$463$	−12.2690	−	7.08352i	−0.570190	−	0.329199i	−0.757225	+	0.653154i	$0.773445\pi$
$464$		0			0
$465$	28.7971	−	28.6641i	1.33543	−	1.32927i
$466$		0			0
$467$	−41.3643			−1.91411			−0.957057	−	0.289901i	$-0.906377\pi$
$467$	−41.3643			−1.91411			−0.957057	+	0.289901i	$0.906377\pi$
$468$		0			0
$469$	−8.60147			−0.397179
$470$		0			0
$471$	25.7290	+	6.95793i	1.18553	+	0.320604i
$472$		0			0
$473$	−27.8321	−	16.0689i	−1.27972	−	0.738849i
$474$		0			0
$475$	−0.574604	+	0.331748i	−0.0263646	+	0.0152216i
$476$		0			0
$477$	−15.1067	+	8.62887i	−0.691688	+	0.395089i
$478$		0			0
$479$	−10.7120	+	6.18459i	−0.489445	+	0.282581i	−0.724344	−	0.689439i	$-0.757857\pi$
$479$	−10.7120	+	6.18459i	−0.489445	+	0.282581i	0.234899	+	0.972020i	$0.424524\pi$
$480$		0			0
$481$	0.254365	−	7.14931i	0.0115980	−	0.325980i
$482$		0			0
$483$	−10.2183	+	2.71266i	−0.464950	+	0.123430i
$484$		0			0
$485$	16.7965			0.762691
$486$		0			0
$487$		−	4.59653i		−	0.208289i	−0.994562	−	0.104144i	$-0.966790\pi$
$487$		−	4.59653i		−	0.208289i	0.994562	−	0.104144i	$-0.0332104\pi$
$488$		0			0
$489$	−12.7033	+	3.37236i	−0.574465	+	0.152503i
$490$		0			0
$491$	−10.1989	+	17.6651i	−0.460272	+	0.797214i	−0.998974	−	0.0452823i	$-0.985581\pi$
$491$	−10.1989	+	17.6651i	−0.460272	+	0.797214i	0.538703	+	0.842496i	$0.318915\pi$
$492$		0			0
$493$	−1.57080	−	2.72071i	−0.0707453	−	0.122534i
$494$		0			0
$495$	−23.8820	+	13.6413i	−1.07342	+	0.613131i
$496$		0			0
$497$	−7.02661	−	12.1704i	−0.315187	−	0.545919i
$498$		0			0
$499$	2.19017	+	1.26449i	0.0980453	+	0.0566065i	0.548221	−	0.836334i	$-0.315305\pi$
$499$	2.19017	+	1.26449i	0.0980453	+	0.0566065i	−0.450176	+	0.892940i	$0.648639\pi$
$500$		0			0
$501$	−2.43238	+	8.99445i	−0.108671	+	0.401842i
$502$		0			0
$503$	32.7292			1.45932			0.729662	−	0.683808i	$-0.239677\pi$
$503$	32.7292			1.45932			0.729662	+	0.683808i	$0.239677\pi$
$504$		0			0
$505$		−	13.5590i		−	0.603368i
$506$		0			0
$507$	4.21614	+	22.1184i	0.187245	+	0.982313i
$508$		0			0
$509$	−23.9961	−	13.8541i	−1.06361	−	0.614074i	−0.137180	−	0.990546i	$-0.543804\pi$
$509$	−23.9961	−	13.8541i	−1.06361	−	0.614074i	−0.926428	+	0.376472i	$0.877137\pi$
$510$		0			0
$511$	−6.75169	−	11.6943i	−0.298677	−	0.517324i
$512$		0			0
$513$	2.23815	−	2.20728i	0.0988166	−	0.0974538i
$514$		0			0
$515$	23.7132	−	13.6908i	1.04493	−	0.603288i
$516$		0			0
$517$	−6.08320	+	10.5364i	−0.267539	+	0.463391i
$518$		0			0
$519$	21.3563	−	21.2577i	0.937438	−	0.933109i
$520$		0			0
$521$	27.7798			1.21705			0.608527	−	0.793533i	$-0.291761\pi$
$521$	27.7798			1.21705			0.608527	+	0.793533i	$0.291761\pi$
$522$		0			0
$523$	−22.3749			−0.978385			−0.489192	−	0.872176i	$-0.662708\pi$
$523$	−22.3749			−0.978385			−0.489192	+	0.872176i	$0.662708\pi$
$524$		0			0
$525$	−0.479240	+	1.77213i	−0.0209157	+	0.0773421i
$526$		0			0
$527$	23.4622	+	13.5459i	1.02203	+	0.590068i
$528$		0			0
$529$	−8.44725	−	14.6311i	−0.367272	−	0.636134i
$530$		0			0
$531$	−18.7367	−	0.0867255i	−0.813103	−	0.00376357i
$532$		0			0
$533$	36.2181	+	22.6647i	1.56878	+	0.981718i
$534$		0			0
$535$	8.84435	+	5.10629i	0.382375	+	0.220764i
$536$		0			0
$537$	−4.20783	−	15.8505i	−0.181581	−	0.683998i
$538$		0			0
$539$			22.5229i			0.970131i
$540$		0			0
$541$		−	29.6979i		−	1.27681i	−0.769699	−	0.638407i	$-0.779594\pi$
$541$		−	29.6979i		−	1.27681i	0.769699	−	0.638407i	$-0.220406\pi$
$542$		0			0
$543$	−3.75069	−	14.1285i	−0.160958	−	0.606311i
$544$		0			0
$545$	1.17397	−	2.03337i	0.0502873	−	0.0871001i
$546$		0			0
$547$	−6.40592	−	11.0954i	−0.273897	−	0.474404i	0.695959	−	0.718082i	$-0.254980\pi$
$547$	−6.40592	−	11.0954i	−0.273897	−	0.474404i	−0.969856	+	0.243677i	$0.921646\pi$
$548$		0			0
$549$	−20.9129	−	12.2035i	−0.892542	−	0.520832i
$550$		0			0
$551$	−0.577194	+	0.333243i	−0.0245893	+	0.0141966i
$552$		0			0
$553$	−6.92020	−	3.99538i	−0.294277	−	0.169901i
$554$		0			0
$555$	8.19125	+	2.21517i	0.347699	+	0.0940287i
$556$		0			0
$557$			0.852804i			0.0361345i	0.999837	+	0.0180672i	$0.00575129\pi$
$557$			0.852804i			0.0361345i	−0.999837	+	0.0180672i	$0.994249\pi$
$558$		0			0
$559$	−14.6334	−	27.5650i	−0.618925	−	1.16588i
$560$		0			0
$561$	−12.9372	−	12.9972i	−0.546210	−	0.548744i
$562$		0			0
$563$	9.36436	−	16.2195i	0.394661	−	0.683572i	−0.598397	−	0.801200i	$-0.704195\pi$
$563$	9.36436	−	16.2195i	0.394661	−	0.683572i	0.993058	+	0.117627i	$0.0375288\pi$
$564$		0			0
$565$	−26.2815	+	15.1736i	−1.10567	+	0.638358i
$566$		0			0
$567$	0.0805134	−	8.69711i	0.00338125	−	0.365244i
$568$		0			0
$569$	−9.83795	−	17.0398i	−0.412428	−	0.714347i	0.582726	−	0.812668i	$-0.301986\pi$
$569$	−9.83795	−	17.0398i	−0.412428	−	0.714347i	−0.995155	+	0.0983215i	$0.968653\pi$
$570$		0			0
$571$	−9.02737	+	15.6359i	−0.377784	+	0.654340i	−0.990739	−	0.135777i	$-0.956647\pi$
$571$	−9.02737	+	15.6359i	−0.377784	+	0.654340i	0.612956	+	0.790117i	$0.289980\pi$
$572$		0			0
$573$	−20.2549	+	20.1614i	−0.846161	+	0.842254i
$574$		0			0
$575$	−6.92736			−0.288891
$576$		0			0
$577$		−	18.9118i		−	0.787308i	−0.919259	−	0.393654i	$-0.871211\pi$
$577$		−	18.9118i		−	0.787308i	0.919259	−	0.393654i	$-0.128789\pi$
$578$		0			0
$579$	−8.39511	+	31.0434i	−0.348889	+	1.29012i
$580$		0			0
$581$	−0.907645	+	1.57209i	−0.0376555	+	0.0652212i
$582$		0			0
$583$	18.6470	−	10.7659i	0.772280	−	0.445876i
$584$		0			0
$585$	−26.6865	−	1.07318i	−1.10335	−	0.0443704i
$586$		0			0
$587$	9.12219	−	5.26670i	0.376513	−	0.217380i	−0.299787	−	0.954006i	$-0.596916\pi$
$587$	9.12219	−	5.26670i	0.376513	−	0.217380i	0.676300	+	0.736626i	$0.263582\pi$
$588$		0			0
$589$	2.87374	−	4.97746i	0.118410	−	0.205093i
$590$		0			0
$591$	−17.3901	+	4.61655i	−0.715333	+	0.189900i
$592$		0			0
$593$			31.4536i			1.29164i	0.763489	+	0.645821i	$0.223485\pi$
$593$			31.4536i			1.29164i	−0.763489	+	0.645821i	$0.776515\pi$
$594$		0			0
$595$	−6.80436			−0.278952
$596$		0			0
$597$	−5.22259	−	19.6730i	−0.213746	−	0.805162i
$598$		0			0
$599$	−20.9691	+	36.3196i	−0.856776	+	1.48398i	0.0182122	+	0.999834i	$0.494203\pi$
$599$	−20.9691	+	36.3196i	−0.856776	+	1.48398i	−0.874988	+	0.484145i	$0.839131\pi$
$600$		0			0
$601$	14.1771	+	24.5554i	0.578295	+	1.00164i	0.995675	+	0.0929046i	$0.0296152\pi$
$601$	14.1771	+	24.5554i	0.578295	+	1.00164i	−0.417380	+	0.908732i	$0.637052\pi$
$602$		0			0
$603$	26.7017	+	0.123593i	1.08738	+	0.00503308i
$604$		0			0
$605$	5.95698	−	3.43926i	0.242186	−	0.139826i
$606$		0			0
$607$	4.57424	−	7.92281i	0.185663	−	0.321577i	−0.758137	−	0.652095i	$-0.773890\pi$
$607$	4.57424	−	7.92281i	0.185663	−	0.321577i	0.943800	+	0.330518i	$0.107224\pi$
$608$		0			0
$609$	−0.481400	+	1.78012i	−0.0195073	+	0.0721341i
$610$		0			0
$611$	−10.4353	+	5.53975i	−0.422167	+	0.224114i
$612$		0			0
$613$			33.4190i			1.34978i	0.737918	+	0.674890i	$0.235809\pi$
$613$			33.4190i			1.34978i	−0.737918	+	0.674890i	$0.764191\pi$
$614$		0			0
$615$	−35.9178	+	35.7520i	−1.44835	+	1.44166i
$616$		0			0
$617$	26.0079	+	15.0157i	1.04704	+	0.604508i	0.921819	−	0.387621i	$-0.126703\pi$
$617$	26.0079	+	15.0157i	1.04704	+	0.604508i	0.125219	+	0.992129i	$0.460037\pi$
$618$		0			0
$619$	−38.6197	+	22.2971i	−1.55226	+	0.896195i	−0.554297	+	0.832319i	$0.687013\pi$
$619$	−38.6197	+	22.2971i	−1.55226	+	0.896195i	−0.997958	+	0.0638764i	$0.979654\pi$
$620$		0			0
$621$	31.7599	−	8.27413i	1.27448	−	0.332030i
$622$		0			0
$623$	−0.182460	−	0.316030i	−0.00731009	−	0.0126615i
$624$		0			0
$625$	14.6405	−	25.3580i	0.585618	−	1.01432i
$626$		0			0
$627$	−2.75734	+	2.74461i	−0.110118	+	0.109609i
$628$		0			0
$629$			5.65788i			0.225595i
$630$		0			0
$631$		−	3.10797i		−	0.123726i	−0.998085	−	0.0618632i	$-0.980296\pi$
$631$		−	3.10797i		−	0.123726i	0.998085	−	0.0618632i	$-0.0197042\pi$
$632$		0			0
$633$	−26.4484	−	7.15248i	−1.05123	−	0.284285i
$634$		0			0
$635$	−0.610001	−	0.352184i	−0.0242072	−	0.0139760i
$636$		0			0
$637$	−11.6024	+	18.5406i	−0.459703	+	0.734604i
$638$		0			0
$639$	21.6379	+	37.8818i	0.855983	+	1.49858i
$640$		0			0
$641$	18.6677	+	32.3333i	0.737328	+	1.27709i	0.953694	+	0.300778i	$0.0972462\pi$
$641$	18.6677	+	32.3333i	0.737328	+	1.27709i	−0.216366	+	0.976312i	$0.569420\pi$
$642$		0			0
$643$	−23.3479	−	13.4799i	−0.920751	−	0.531596i	−0.0368765	−	0.999320i	$-0.511741\pi$
$643$	−23.3479	−	13.4799i	−0.920751	−	0.531596i	−0.883875	+	0.467724i	$0.845074\pi$
$644$		0			0
$645$	35.7785	−	9.49814i	1.40878	−	0.373989i
$646$		0			0
$647$	−26.3718			−1.03678			−0.518391	−	0.855143i	$-0.673469\pi$
$647$	−26.3718			−1.03678			−0.518391	+	0.855143i	$0.673469\pi$
$648$		0			0
$649$	23.1895			0.910268
$650$		0			0
$651$	−4.08028	−	15.3700i	−0.159919	−	0.602398i
$652$		0			0
$653$	13.9271	−	24.1224i	0.545009	−	0.943984i	−0.453597	−	0.891207i	$-0.649859\pi$
$653$	13.9271	−	24.1224i	0.545009	−	0.943984i	0.998606	−	0.0527770i	$-0.0168072\pi$
$654$		0			0
$655$	−8.18618	+	4.72629i	−0.319861	+	0.184672i
$656$		0			0
$657$	20.7913	+	36.3997i	0.811147	+	1.42009i
$658$		0			0
$659$	0.417010	+	0.722282i	0.0162444	+	0.0281361i	0.874033	−	0.485866i	$-0.161496\pi$
$659$	0.417010	+	0.722282i	0.0162444	+	0.0281361i	−0.857789	+	0.514002i	$0.828162\pi$
$660$		0			0
$661$	9.53031	+	5.50233i	0.370686	+	0.214016i	0.673758	−	0.738952i	$-0.264679\pi$
$661$	9.53031	+	5.50233i	0.370686	+	0.214016i	−0.303072	+	0.952968i	$0.598012\pi$
$662$		0			0
$663$	−3.95439	−	17.3636i	−0.153576	−	0.674345i
$664$		0			0
$665$			1.44354i			0.0559779i
$666$		0			0
$667$	−6.95858			−0.269437
$668$		0			0
$669$	−13.8939	−	13.9584i	−0.537169	−	0.539661i
$670$		0			0
$671$	25.9523	+	14.9836i	1.00188	+	0.578434i
$672$		0			0
$673$	13.6492	+	23.6410i	0.526136	+	0.911295i	0.999536	+	0.0304475i	$0.00969322\pi$
$673$	13.6492	+	23.6410i	0.526136	+	0.911295i	−0.473400	+	0.880848i	$0.656973\pi$
$674$		0			0
$675$	1.51317	−	5.49437i	0.0582421	−	0.211478i
$676$		0			0
$677$	22.7311	+	39.3714i	0.873626	+	1.51317i	0.858219	+	0.513284i	$0.171571\pi$
$677$	22.7311	+	39.3714i	0.873626	+	1.51317i	0.0154074	+	0.999881i	$0.495095\pi$
$678$		0			0
$679$	3.28693	−	5.69314i	0.126141	−	0.218483i
$680$		0			0
$681$	−12.8956	−	12.9555i	−0.494162	−	0.496454i
$682$		0			0
$683$			4.27442i			0.163556i	0.996651	+	0.0817782i	$0.0260599\pi$
$683$			4.27442i			0.163556i	−0.996651	+	0.0817782i	$0.973940\pi$
$684$		0			0
$685$	−27.2499			−1.04116
$686$		0			0
$687$	−13.5393	+	50.0654i	−0.516555	+	1.91012i
$688$		0			0
$689$	20.8959	+	0.743452i	0.796069	+	0.0283233i
$690$		0			0
$691$	44.0686	−	25.4430i	1.67645	−	0.967897i	0.712550	−	0.701621i	$-0.247540\pi$
$691$	44.0686	−	25.4430i	1.67645	−	0.967897i	0.963897	−	0.266276i	$-0.0857932\pi$
$692$		0			0
$693$	−0.0498239	+	10.7642i	−0.00189265	+	0.408899i
$694$		0			0
$695$	2.52342	−	1.45690i	0.0957187	−	0.0552632i
$696$		0			0
$697$	−29.2637	−	16.8954i	−1.10844	−	0.639960i
$698$		0			0
$699$	−9.52185	−	35.8678i	−0.360149	−	1.35665i
$700$		0			0
$701$	−22.3325			−0.843488			−0.421744	−	0.906715i	$-0.638582\pi$
$701$	−22.3325			−0.843488			−0.421744	+	0.906715i	$0.638582\pi$
$702$		0			0
$703$	1.20031			0.0452706
$704$		0			0
$705$	−3.59571	−	13.5447i	−0.135422	−	0.510122i
$706$		0			0
$707$	−4.59579	−	2.65338i	−0.172842	−	0.0997906i
$708$		0			0
$709$	30.6075	−	17.6712i	1.14949	−	0.663657i	0.200726	−	0.979647i	$-0.435670\pi$
$709$	30.6075	−	17.6712i	1.14949	−	0.663657i	0.948763	+	0.315990i	$0.102337\pi$
$710$		0			0
$711$	21.4251	+	12.5023i	0.803503	+	0.468875i
$712$		0			0
$713$	51.9682	−	30.0039i	1.94622	−	1.12365i
$714$		0			0
$715$	33.0341	+	1.17532i	1.23540	+	0.0439544i
$716$		0			0
$717$	−11.9305	+	44.1167i	−0.445554	+	1.64757i
$718$		0			0
$719$	38.7053			1.44346			0.721732	−	0.692172i	$-0.243346\pi$
$719$	38.7053			1.44346			0.721732	+	0.692172i	$0.243346\pi$
$720$		0			0
$721$		−	10.7167i		−	0.399110i
$722$		0			0
$723$	12.9402	+	13.0002i	0.481251	+	0.483484i
$724$		0			0
$725$	−0.604151	+	1.04642i	−0.0224376	+	0.0388631i
$726$		0			0
$727$	13.8426	+	23.9762i	0.513395	+	0.889227i	0.999879	+	0.0155372i	$0.00494584\pi$
$727$	13.8426	+	23.9762i	0.513395	+	0.889227i	−0.486484	+	0.873689i	$0.661721\pi$
$728$		0			0
$729$	−0.374906	+	26.9974i	−0.0138854	+	0.999904i
$730$		0			0
$731$	12.3412	+	21.3756i	0.456456	+	0.790605i
$732$		0			0
$733$	−3.00643	−	1.73576i	−0.111045	−	0.0641119i	0.443449	−	0.896300i	$-0.353755\pi$
$733$	−3.00643	−	1.73576i	−0.111045	−	0.0641119i	−0.554494	+	0.832188i	$0.687088\pi$
$734$		0			0
$735$	−18.3019	−	18.3868i	−0.675077	−	0.678209i
$736$		0			0
$737$	−33.0474			−1.21732
$738$		0			0
$739$			11.4153i			0.419920i	0.977710	+	0.209960i	$0.0673334\pi$
$739$			11.4153i			0.419920i	−0.977710	+	0.209960i	$0.932667\pi$
$740$		0			0
$741$	−3.68366	+	0.838917i	−0.135323	+	0.0308184i
$742$		0			0
$743$	−7.91486	−	4.56965i	−0.290368	−	0.167644i	0.347740	−	0.937591i	$-0.386949\pi$
$743$	−7.91486	−	4.56965i	−0.290368	−	0.167644i	−0.638108	+	0.769947i	$0.720283\pi$
$744$		0			0
$745$	3.32373	+	5.75686i	0.121772	+	0.210915i
$746$		0			0
$747$	2.84020	−	4.86721i	0.103918	−	0.178082i
$748$		0			0
$749$	3.46153	−	1.99851i	0.126481	−	0.0730241i
$750$		0			0
$751$	−4.52322	+	7.83444i	−0.165055	+	0.285883i	−0.936675	−	0.350201i	$-0.886113\pi$
$751$	−4.52322	+	7.83444i	−0.165055	+	0.285883i	0.771620	+	0.636084i	$0.219447\pi$
$752$		0			0
$753$	12.9883	+	48.9258i	0.473322	+	1.78296i
$754$		0			0
$755$	6.99833			0.254695
$756$		0			0
$757$	12.0569			0.438216			0.219108	−	0.975701i	$-0.429685\pi$
$757$	12.0569			0.438216			0.219108	+	0.975701i	$0.429685\pi$
$758$		0			0
$759$	−39.2595	+	10.4222i	−1.42503	+	0.378303i
$760$		0			0
$761$	15.1457	+	8.74438i	0.549032	+	0.316984i	0.748731	−	0.662874i	$-0.230663\pi$
$761$	15.1457	+	8.74438i	0.549032	+	0.316984i	−0.199700	+	0.979857i	$0.563997\pi$
$762$		0			0
$763$	−0.459471	−	0.795827i	−0.0166340	−	0.0288109i
$764$		0			0
$765$	21.1229	+	0.0977704i	0.763699	+	0.00353489i
$766$		0			0
$767$	19.0893	+	11.9458i	0.689274	+	0.431337i
$768$		0			0
$769$	−10.8002	−	6.23549i	−0.389464	−	0.224857i	0.292464	−	0.956277i	$-0.405525\pi$
$769$	−10.8002	−	6.23549i	−0.389464	−	0.224857i	−0.681928	+	0.731419i	$0.738858\pi$
$770$		0			0
$771$	−13.7972	−	3.73118i	−0.496892	−	0.134375i
$772$		0			0
$773$		−	31.1669i		−	1.12100i	−0.828155	−	0.560499i	$-0.810610\pi$
$773$		−	31.1669i		−	1.12100i	0.828155	−	0.560499i	$-0.189390\pi$
$774$		0			0
$775$		−	10.4199i		−	0.374292i
$776$		0			0
$777$	2.35378	−	2.34291i	0.0844415	−	0.0840515i
$778$		0			0
$779$	−3.58434	+	6.20826i	−0.128422	+	0.222434i
$780$		0			0
$781$	−26.9967	−	46.7596i	−0.966017	−	1.67319i
$782$		0			0
$783$	1.51999	−	5.51913i	0.0543202	−	0.197238i
$784$		0			0
$785$	32.9056	−	18.9980i	1.17445	−	0.678069i
$786$		0			0
$787$	−7.34438	−	4.24028i	−0.261799	−	0.151150i	0.363356	−	0.931650i	$-0.381631\pi$
$787$	−7.34438	−	4.24028i	−0.261799	−	0.151150i	−0.625155	+	0.780501i	$0.714964\pi$
$788$		0			0
$789$	−0.596869	+	0.594113i	−0.0212491	+	0.0211510i
$790$		0			0
$791$			11.8774i			0.422311i
$792$		0			0
$793$	13.6450	+	25.7032i	0.484548	+	0.912749i
$794$		0			0
$795$	−6.47446	+	23.9412i	−0.229625	+	0.849108i
$796$		0			0
$797$	−25.2381	+	43.7137i	−0.893980	+	1.54842i	−0.0589177	+	0.998263i	$0.518765\pi$
$797$	−25.2381	+	43.7137i	−0.893980	+	1.54842i	−0.835062	+	0.550156i	$0.814568\pi$
$798$		0			0
$799$	8.09215	−	4.67200i	0.286280	−	0.165284i
$800$		0			0
$801$	0.561871	+	0.983677i	0.0198527	+	0.0347565i
$802$		0			0
$803$	−25.9404	−	44.9301i	−0.915417	−	1.58555i
$804$		0			0
$805$	−7.53576	+	13.0523i	−0.265601	+	0.460034i
$806$		0			0
$807$	4.50835	+	16.9825i	0.158701	+	0.597812i
$808$		0			0
$809$	−49.7947			−1.75069			−0.875344	−	0.483501i	$-0.839365\pi$
$809$	−49.7947			−1.75069			−0.875344	+	0.483501i	$0.839365\pi$
$810$		0			0
$811$		−	48.5676i		−	1.70544i	−0.522370	−	0.852719i	$-0.674952\pi$
$811$		−	48.5676i		−	1.70544i	0.522370	−	0.852719i	$-0.325048\pi$
$812$		0			0
$813$	41.0192	−	10.8894i	1.43861	−	0.381907i
$814$		0			0
$815$	−9.36840	+	16.2265i	−0.328161	+	0.568391i
$816$		0			0
$817$	4.53480	−	2.61817i	0.158653	−	0.0915981i
$818$		0			0
$819$	−5.58606	+	8.83530i	−0.195193	+	0.308730i
$820$		0			0
$821$	33.0145	−	19.0609i	1.15221	−	0.665231i	0.202789	−	0.979223i	$-0.435000\pi$
$821$	33.0145	−	19.0609i	1.15221	−	0.665231i	0.949426	+	0.313991i	$0.101666\pi$
$822$		0			0
$823$	6.58476	−	11.4051i	0.229530	−	0.397558i	−0.728139	−	0.685430i	$-0.759614\pi$
$823$	6.58476	−	11.4051i	0.229530	−	0.397558i	0.957669	+	0.287872i	$0.0929477\pi$
$824$		0			0
$825$	−1.84127	+	6.80864i	−0.0641048	+	0.237046i
$826$		0			0
$827$			51.3046i			1.78403i	0.452001	+	0.892017i	$0.350710\pi$
$827$			51.3046i			1.78403i	−0.452001	+	0.892017i	$0.649290\pi$
$828$		0			0
$829$	2.43558			0.0845912			0.0422956	−	0.999105i	$-0.486533\pi$
$829$	2.43558			0.0845912			0.0422956	+	0.999105i	$0.486533\pi$
$830$		0			0
$831$	30.9256	−	30.7828i	1.07280	−	1.06784i
$832$		0			0
$833$	8.64901	−	14.9805i	0.299670	−	0.519044i
$834$		0			0
$835$	6.64141	+	11.5033i	0.229835	+	0.398087i
$836$		0			0
$837$	12.4456	+	47.7719i	0.430183	+	1.65124i
$838$		0			0
$839$	1.70711	−	0.985602i	0.0589361	−	0.0340268i	−0.470242	−	0.882537i	$-0.655834\pi$
$839$	1.70711	−	0.985602i	0.0589361	−	0.0340268i	0.529179	+	0.848511i	$0.322500\pi$
$840$		0			0
$841$	13.8931	−	24.0636i	0.479073	−	0.829779i
$842$		0			0
$843$	−22.4669	−	22.5712i	−0.773802	−	0.777392i
$844$		0			0
$845$	26.5877	+	17.9846i	0.914646	+	0.618688i
$846$		0			0
$847$		−	2.69213i		−	0.0925029i
$848$		0			0
$849$	−51.0392	−	13.8026i	−1.75166	−	0.473704i
$850$		0			0
$851$	10.8531	+	6.26604i	0.372040	+	0.214797i
$852$		0			0
$853$	−20.8994	+	12.0663i	−0.715581	+	0.413141i	−0.813124	−	0.582091i	$-0.802235\pi$
$853$	−20.8994	+	12.0663i	−0.715581	+	0.413141i	0.0975432	+	0.995231i	$0.468902\pi$
$854$		0			0
$855$	0.0207418	−	4.48119i	0.000709356	−	0.153253i
$856$		0			0
$857$	8.35232	+	14.4667i	0.285310	+	0.494171i	0.972684	−	0.232132i	$-0.0745701\pi$
$857$	8.35232	+	14.4667i	0.285310	+	0.494171i	−0.687374	+	0.726303i	$0.741237\pi$
$858$		0			0
$859$	10.8152	−	18.7326i	0.369011	−	0.639147i	−0.620400	−	0.784286i	$-0.713030\pi$
$859$	10.8152	−	18.7326i	0.369011	−	0.639147i	0.989411	+	0.145139i	$0.0463630\pi$
$860$		0			0
$861$	5.08922	+	19.1706i	0.173440	+	0.653332i
$862$		0			0
$863$		−	5.05668i		−	0.172131i	−0.996289	−	0.0860657i	$-0.972570\pi$
$863$		−	5.05668i		−	0.172131i	0.996289	−	0.0860657i	$-0.0274295\pi$
$864$		0			0
$865$		−	42.9563i		−	1.46056i
$866$		0			0
$867$	−3.94126	−	14.8463i	−0.133852	−	0.504208i
$868$		0			0
$869$	−26.5879	−	15.3505i	−0.901931	−	0.520730i
$870$		0			0
$871$	−27.2042	−	17.0239i	−0.921778	−	0.576834i
$872$		0			0
$873$	−10.2855	+	17.6261i	−0.348111	+	0.596552i
$874$		0			0
$875$	−4.65689	−	8.06597i	−0.157432	−	0.272679i
$876$		0			0
$877$	23.2344	+	13.4144i	0.784572	+	0.452973i	0.838048	−	0.545597i	$-0.183697\pi$
$877$	23.2344	+	13.4144i	0.784572	+	0.452973i	−0.0534764	+	0.998569i	$0.517030\pi$
$878$		0			0
$879$	7.06835	−	26.1373i	0.238409	−	0.881590i
$880$		0			0
$881$	−37.4816			−1.26279			−0.631394	−	0.775462i	$-0.717517\pi$
$881$	−37.4816			−1.26279			−0.631394	+	0.775462i	$0.717517\pi$
$882$		0			0
$883$	14.6841			0.494160			0.247080	−	0.968995i	$-0.420529\pi$
$883$	14.6841			0.494160			0.247080	+	0.968995i	$0.420529\pi$
$884$		0			0
$885$	−18.9310	+	18.8436i	−0.636359	+	0.633421i
$886$		0			0
$887$	21.6755	−	37.5431i	0.727793	−	1.26057i	−0.230021	−	0.973186i	$-0.573880\pi$
$887$	21.6755	−	37.5431i	0.727793	−	1.26057i	0.957814	−	0.287388i	$-0.0927871\pi$
$888$		0			0
$889$	−0.238744	+	0.137839i	−0.00800721	+	0.00462297i
$890$		0			0
$891$	0.309338	−	33.4148i	0.0103632	−	1.11944i
$892$		0			0
$893$	−0.991159	−	1.71674i	−0.0331679	−	0.0574484i
$894$		0			0
$895$	−20.2465	−	11.6893i	−0.676765	−	0.390731i
$896$		0			0
$897$	−37.6867	−	11.6446i	−1.25832	−	0.388801i
$898$		0			0
$899$		−	10.4668i		−	0.349088i
$900$		0			0
$901$	−16.5367			−0.550919
$902$		0			0
$903$	3.78218	−	13.9857i	0.125863	−	0.465416i
$904$		0			0
$905$	−18.0469	−	10.4194i	−0.599900	−	0.346352i
$906$		0			0
$907$	9.37590	+	16.2395i	0.311322	+	0.539225i	0.978649	−	0.205540i	$-0.0658950\pi$
$907$	9.37590	+	16.2395i	0.311322	+	0.539225i	−0.667327	+	0.744765i	$0.732562\pi$
$908$		0			0
$909$	14.2286	+	8.30296i	0.471934	+	0.275392i
$910$		0			0
$911$	−1.80609	−	3.12824i	−0.0598385	−	0.103643i	0.834554	−	0.550926i	$-0.185725\pi$
$911$	−1.80609	−	3.12824i	−0.0598385	−	0.103643i	−0.894393	+	0.447282i	$0.852392\pi$
$912$		0			0
$913$	−3.48723	+	6.04006i	−0.115410	+	0.199897i
$914$		0			0
$915$	−33.3620	+	8.85661i	−1.10291	+	0.292790i
$916$		0			0
$917$			3.69958i			0.122171i
$918$		0			0
$919$	11.3389			0.374037			0.187018	−	0.982356i	$-0.440118\pi$
$919$	11.3389			0.374037			0.187018	+	0.982356i	$0.440118\pi$
$920$		0			0
$921$	−48.2293	+	12.8034i	−1.58921	+	0.421888i
$922$		0			0
$923$	1.86430	−	52.3989i	0.0613641	−	1.72473i
$924$		0			0
$925$	1.88455	−	1.08805i	0.0619638	−	0.0357748i
$926$		0			0
$927$	−0.153986	+	33.2679i	−0.00505755	+	1.09266i
$928$		0			0
$929$	26.2595	−	15.1609i	0.861547	−	0.497414i	−0.00298336	−	0.999996i	$-0.500950\pi$
$929$	26.2595	−	15.1609i	0.861547	−	0.497414i	0.864530	+	0.502581i	$0.167616\pi$
$930$		0			0
$931$	−3.17810	−	1.83487i	−0.104158	−	0.0601356i
$932$		0			0
$933$	27.8636	+	7.53518i	0.912212	+	0.246691i
$934$		0			0
$935$	−26.1428			−0.854961
$936$		0			0
$937$	21.5357			0.703539			0.351770	−	0.936087i	$-0.385580\pi$
$937$	21.5357			0.703539			0.351770	+	0.936087i	$0.385580\pi$
$938$		0			0
$939$	28.9220	−	28.7884i	0.943834	−	0.939475i
$940$		0			0
$941$	−31.6998	−	18.3019i	−1.03338	−	0.596624i	−0.115431	−	0.993315i	$-0.536825\pi$
$941$	−31.6998	−	18.3019i	−1.03338	−	0.596624i	−0.917952	+	0.396691i	$0.870158\pi$
$942$		0			0
$943$	−64.8186	+	37.4230i	−2.11078	+	1.21866i
$944$		0			0
$945$	−8.70625	−	8.82799i	−0.283214	−	0.287175i
$946$		0			0
$947$	−1.88636	+	1.08909i	−0.0612983	+	0.0353906i	−0.530336	−	0.847788i	$-0.677934\pi$
$947$	−1.88636	+	1.08909i	−0.0612983	+	0.0353906i	0.469038	+	0.883178i	$0.344601\pi$
$948$		0			0
$949$	1.79135	−	50.3487i	0.0581498	−	1.63439i
$950$		0			0
$951$	−13.4926	−	13.5552i	−0.437527	−	0.439557i
$952$		0			0
$953$	14.2017			0.460038			0.230019	−	0.973186i	$-0.426121\pi$
$953$	14.2017			0.460038			0.230019	+	0.973186i	$0.426121\pi$
$954$		0			0
$955$			40.7410i			1.31835i
$956$		0			0
$957$	−1.84957	+	6.83933i	−0.0597881	+	0.221084i
$958$		0			0
$959$	−5.33256	+	9.23626i	−0.172197	+	0.298254i
$960$		0			0
$961$	29.6306	+	51.3217i	0.955825	+	1.65554i
$962$		0			0
$963$	−10.7744	+	6.15427i	−0.347200	+	0.198319i
$964$		0			0
$965$	22.9222	+	39.7023i	0.737890	+	1.27806i
$966$		0			0
$967$	38.4346	+	22.1903i	1.23597	+	0.713590i	0.968269	−	0.249910i	$-0.0804011\pi$
$967$	38.4346	+	22.1903i	1.23597	+	0.713590i	0.267706	+	0.963501i	$0.413734\pi$
$968$		0			0
$969$	2.88793	−	0.766659i	0.0927736	−	0.0246286i
$970$		0			0
$971$	2.43486			0.0781385			0.0390693	−	0.999237i	$-0.487561\pi$
$971$	2.43486			0.0781385			0.0390693	+	0.999237i	$0.487561\pi$
$972$		0			0
$973$		−	1.14041i		−	0.0365598i
$974$		0			0
$975$	−5.02309	+	4.65627i	−0.160868	+	0.149120i
$976$		0			0
$977$	−2.66609	−	1.53927i	−0.0852959	−	0.0492456i	0.456745	−	0.889597i	$-0.349015\pi$
$977$	−2.66609	−	1.53927i	−0.0852959	−	0.0492456i	−0.542041	+	0.840352i	$0.682348\pi$
$978$		0			0
$979$	−0.701022	−	1.21421i	−0.0224048	−	0.0388062i
$980$		0			0
$981$	1.41491	+	2.47710i	0.0451745	+	0.0790877i
$982$		0			0
$983$	−31.3772	+	18.1156i	−1.00078	+	0.577799i	−0.908478	−	0.417933i	$-0.862755\pi$
$983$	−31.3772	+	18.1156i	−1.00078	+	0.577799i	−0.0922985	+	0.995731i	$0.529421\pi$
$984$		0			0
$985$	−12.8248	+	22.2131i	−0.408631	+	0.707769i
$986$		0			0
$987$	−5.29457	−	1.43182i	−0.168528	−	0.0455753i
$988$		0			0
$989$	54.6710			1.73844
$990$		0			0
$991$	32.5893			1.03523			0.517616	−	0.855613i	$-0.326820\pi$
$991$	32.5893			1.03523			0.517616	+	0.855613i	$0.326820\pi$
$992$		0			0
$993$	41.5550	+	41.7478i	1.31871	+	1.32483i
$994$		0			0
$995$	−25.1292	−	14.5083i	−0.796648	−	0.459945i
$996$		0			0
$997$	−28.5185	−	49.3955i	−0.903191	−	1.56437i	−0.823327	−	0.567567i	$-0.807885\pi$
$997$	−28.5185	−	49.3955i	−0.903191	−	1.56437i	−0.0798637	−	0.996806i	$-0.525448\pi$
$998$		0			0
$999$	−7.34054	+	7.23932i	−0.232245	+	0.229042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.bl.b.337.8	yes	24
3.2	odd	2		1404.2.bl.b.1117.3		24
9.2	odd	6		1404.2.bl.b.181.10		24
9.4	even	3		4212.2.b.g.649.3		12
9.5	odd	6		4212.2.b.h.649.10		12
9.7	even	3	inner	468.2.bl.b.25.7	✓	24
13.12	even	2	inner	468.2.bl.b.337.7	yes	24
39.38	odd	2		1404.2.bl.b.1117.10		24
117.25	even	6	inner	468.2.bl.b.25.8	yes	24
117.38	odd	6		1404.2.bl.b.181.3		24
117.77	odd	6		4212.2.b.h.649.3		12
117.103	even	6		4212.2.b.g.649.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bl.b.25.7	✓	24	9.7	even	3	inner
468.2.bl.b.25.8	yes	24	117.25	even	6	inner
468.2.bl.b.337.7	yes	24	13.12	even	2	inner
468.2.bl.b.337.8	yes	24	1.1	even	1	trivial
1404.2.bl.b.181.3		24	117.38	odd	6
1404.2.bl.b.181.10		24	9.2	odd	6
1404.2.bl.b.1117.3		24	3.2	odd	2
1404.2.bl.b.1117.10		24	39.38	odd	2
4212.2.b.g.649.3		12	9.4	even	3
4212.2.b.g.649.10		12	117.103	even	6
4212.2.b.h.649.3		12	117.77	odd	6
4212.2.b.h.649.10		12	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.444415 + 1.67407i) q^{3} +(2.13836 + 1.23458i) q^{5} +(0.836915 - 0.483193i) q^{7} +(-2.60499 + 1.48796i) q^{9} +(3.21548 - 1.85646i) q^{11} +(3.60327 + 0.128201i) q^{13} +(-1.11645 + 4.12841i) q^{15} -2.85159 q^{17} +0.604961i q^{19} +(1.18083 + 1.18631i) q^{21} +(-3.15810 + 5.47000i) q^{23} +(0.548379 + 0.949821i) q^{25} +(-3.64864 - 3.69966i) q^{27} +(0.550851 + 0.954102i) q^{29} +(-8.22775 - 4.75029i) q^{31} +(4.53684 + 4.55789i) q^{33} +2.38617 q^{35} -1.98412i q^{37} +(1.38673 + 6.08909i) q^{39} +(10.2623 + 5.92492i) q^{41} +(-4.32783 - 7.49603i) q^{43} +(-7.40741 - 0.0342863i) q^{45} +(-2.83777 + 1.63839i) q^{47} +(-3.03305 + 5.25339i) q^{49} +(-1.26729 - 4.77375i) q^{51} +5.79913 q^{53} +9.16780 q^{55} +(-1.01274 + 0.268853i) q^{57} +(5.40887 + 3.12281i) q^{59} +(4.03552 + 6.98973i) q^{61} +(-1.46119 + 2.50401i) q^{63} +(7.54681 + 4.72267i) q^{65} +(-7.70819 - 4.45033i) q^{67} +(-10.5606 - 2.85593i) q^{69} -14.5420i q^{71} -13.9731i q^{73} +(-1.34635 + 1.34014i) q^{75} +(1.79406 - 3.10740i) q^{77} +(-4.13435 - 7.16090i) q^{79} +(4.57196 - 7.75224i) q^{81} +(-1.62677 + 0.939215i) q^{83} +(-6.09771 - 3.52052i) q^{85} +(-1.35242 + 1.34618i) q^{87} -0.377612i q^{89} +(3.07758 - 1.63378i) q^{91} +(4.29577 - 15.8849i) q^{93} +(-0.746873 + 1.29362i) q^{95} +(5.89116 - 3.40126i) q^{97} +(-5.61397 + 9.62057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 2 q^{9} + 5 q^{13} - 4 q^{17} - 22 q^{23} + 16 q^{25} - 18 q^{27} + 22 q^{29} + 8 q^{35} + 37 q^{39} - 2 q^{43} + 22 q^{49} - 38 q^{51} - 12 q^{53} + 48 q^{55} + 8 q^{61} - q^{65} - 26 q^{69}+ \cdots - 48 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 + 2 * q^9 + 5 * q^13 - 4 * q^17 - 22 * q^23 + 16 * q^25 - 18 * q^27 + 22 * q^29 + 8 * q^35 + 37 * q^39 - 2 * q^43 + 22 * q^49 - 38 * q^51 - 12 * q^53 + 48 * q^55 + 8 * q^61 - q^65 - 26 * q^69 - 64 * q^75 - 24 * q^77 - 8 * q^79 + 2 * q^81 - 40 * q^87 + 22 * q^91 - 48 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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