LMFDB - Embedded newform 468.2.cg.a.437.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(5,468)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("468.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			437.10
Character	$\chi$	$=$	468.437
Dual form			468.2.cg.a.317.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930898 + 1.46063i) q^{3} +(0.734125 + 2.73979i) q^{5} +(1.89332 + 0.507313i) q^{7} +(-1.26686 + 2.71939i) q^{9} +(-0.158535 + 0.591661i) q^{11} +(-0.394879 - 3.58386i) q^{13} +(-3.31842 + 3.62275i) q^{15} -0.329188 q^{17} +(-2.29971 - 2.29971i) q^{19} +(1.02149 + 3.23769i) q^{21} +(-0.458575 + 0.794276i) q^{23} +(-2.63740 + 1.52270i) q^{25} +(-5.15132 + 0.681067i) q^{27} +(3.53714 - 2.04217i) q^{29} +(3.62256 - 0.970663i) q^{31} +(-1.01178 + 0.319216i) q^{33} +5.55973i q^{35} +(-5.24778 + 5.24778i) q^{37} +(4.86709 - 3.91298i) q^{39} +(1.35806 + 5.06836i) q^{41} +(6.65352 - 3.84141i) q^{43} +(-8.38059 - 1.47456i) q^{45} +(1.27379 - 4.75386i) q^{47} +(-2.73489 - 1.57899i) q^{49} +(-0.306441 - 0.480821i) q^{51} +10.3025i q^{53} -1.73741 q^{55} +(1.21822 - 5.49982i) q^{57} +(7.68473 - 2.05912i) q^{59} +(-3.51473 - 6.08768i) q^{61} +(-3.77815 + 4.50598i) q^{63} +(9.52915 - 3.71289i) q^{65} +(11.9181 - 3.19344i) q^{67} +(-1.58703 + 0.0695826i) q^{69} +(-0.769386 + 0.769386i) q^{71} +(-5.02343 + 5.02343i) q^{73} +(-4.67925 - 2.43477i) q^{75} +(-0.600315 + 1.03978i) q^{77} +(-4.63505 - 8.02814i) q^{79} +(-5.79014 - 6.89016i) q^{81} +(16.7195 + 4.47998i) q^{83} +(-0.241666 - 0.901908i) q^{85} +(6.27556 + 3.26539i) q^{87} +(-8.13868 - 8.13868i) q^{89} +(1.07051 - 6.98572i) q^{91} +(4.79001 + 4.38762i) q^{93} +(4.61246 - 7.98901i) q^{95} +(2.01196 - 7.50874i) q^{97} +(-1.40811 - 1.18067i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{7} - 12 q^{11} - 12 q^{15} + 4 q^{19} - 12 q^{21} + 36 q^{27} - 4 q^{31} + 12 q^{33} - 4 q^{37} + 24 q^{41} + 6 q^{45} + 66 q^{47} - 48 q^{57} - 30 q^{63} - 78 q^{65} - 14 q^{67} + 28 q^{73}+ \cdots + 54 q^{99}+O(q^{100}) $ 56 * q - 2 * q^7 - 12 * q^11 - 12 * q^15 + 4 * q^19 - 12 * q^21 + 36 * q^27 - 4 * q^31 + 12 * q^33 - 4 * q^37 + 24 * q^41 + 6 * q^45 + 66 * q^47 - 48 * q^57 - 30 * q^63 - 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 - 78 * q^83 + 36 * q^85 - 8 * q^91 + 6 * q^93 + 26 * q^97 + 54 * q^99

Character values

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

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.930898	+	1.46063i	0.537454	+	0.843293i
$3$	0.930898	+	1.46063i	0.537454	+	0.843293i
$4$		0			0
$5$	0.734125	+	2.73979i	0.328311	+	1.22527i	0.910941	+	0.412536i	$0.135357\pi$
$5$	0.734125	+	2.73979i	0.328311	+	1.22527i	−0.582631	+	0.812737i	$0.697977\pi$
$6$		0			0
$7$	1.89332	+	0.507313i	0.715607	+	0.191746i	0.598211	−	0.801339i	$-0.295879\pi$
$7$	1.89332	+	0.507313i	0.715607	+	0.191746i	0.117396	+	0.993085i	$0.462545\pi$
$8$		0			0
$9$	−1.26686	+	2.71939i	−0.422286	+	0.906463i
$10$		0			0
$11$	−0.158535	+	0.591661i	−0.0478001	+	0.178393i	−0.985699	−	0.168517i	$-0.946102\pi$
$11$	−0.158535	+	0.591661i	−0.0478001	+	0.178393i	0.937899	+	0.346909i	$0.112769\pi$
$12$		0			0
$13$	−0.394879	−	3.58386i	−0.109520	−	0.993985i
$13$	−0.394879	−	3.58386i	−0.109520	−	0.993985i
$14$		0			0
$15$	−3.31842	+	3.62275i	−0.856812	+	0.935390i
$16$		0			0
$17$	−0.329188			−0.0798399			−0.0399200	−	0.999203i	$-0.512710\pi$
$17$	−0.329188			−0.0798399			−0.0399200	+	0.999203i	$0.512710\pi$
$18$		0			0
$19$	−2.29971	−	2.29971i	−0.527590	−	0.527590i	0.392263	−	0.919853i	$-0.371692\pi$
$19$	−2.29971	−	2.29971i	−0.527590	−	0.527590i	−0.919853	+	0.392263i	$0.871692\pi$
$20$		0			0
$21$	1.02149	+	3.23769i	0.222908	+	0.706522i
$22$		0			0
$23$	−0.458575	+	0.794276i	−0.0956196	+	0.165618i	−0.909867	−	0.414900i	$-0.863817\pi$
$23$	−0.458575	+	0.794276i	−0.0956196	+	0.165618i	0.814247	+	0.580518i	$0.197150\pi$
$24$		0			0
$25$	−2.63740	+	1.52270i	−0.527480	+	0.304541i
$26$		0			0
$27$	−5.15132	+	0.681067i	−0.991373	+	0.131071i
$28$		0			0
$29$	3.53714	−	2.04217i	0.656830	−	0.379221i	−0.134238	−	0.990949i	$-0.542859\pi$
$29$	3.53714	−	2.04217i	0.656830	−	0.379221i	0.791068	+	0.611728i	$0.209525\pi$
$30$		0			0
$31$	3.62256	−	0.970663i	0.650632	−	0.174336i	0.0816173	−	0.996664i	$-0.473991\pi$
$31$	3.62256	−	0.970663i	0.650632	−	0.174336i	0.569015	+	0.822327i	$0.307325\pi$
$32$		0			0
$33$	−1.01178	+	0.319216i	−0.176128	+	0.0555683i
$34$		0			0
$35$			5.55973i			0.939767i
$36$		0			0
$37$	−5.24778	+	5.24778i	−0.862730	+	0.862730i	−0.991654	−	0.128925i	$-0.958847\pi$
$37$	−5.24778	+	5.24778i	−0.862730	+	0.862730i	0.128925	+	0.991654i	$0.458847\pi$
$38$		0			0
$39$	4.86709	−	3.91298i	0.779358	−	0.626579i
$40$		0			0
$41$	1.35806	+	5.06836i	0.212094	+	0.791545i	0.987169	+	0.159677i	$0.0510452\pi$
$41$	1.35806	+	5.06836i	0.212094	+	0.791545i	−0.775075	+	0.631869i	$0.782288\pi$
$42$		0			0
$43$	6.65352	−	3.84141i	1.01465	−	0.585810i	0.102102	−	0.994774i	$-0.467443\pi$
$43$	6.65352	−	3.84141i	1.01465	−	0.585810i	0.912550	+	0.408964i	$0.134110\pi$
$44$		0			0
$45$	−8.38059	−	1.47456i	−1.24931	−	0.219814i
$46$		0			0
$47$	1.27379	−	4.75386i	0.185802	−	0.693421i	−0.808656	−	0.588282i	$-0.799804\pi$
$47$	1.27379	−	4.75386i	0.185802	−	0.693421i	0.994457	−	0.105139i	$-0.0335289\pi$
$48$		0			0
$49$	−2.73489	−	1.57899i	−0.390698	−	0.225570i
$50$		0			0
$51$	−0.306441	−	0.480821i	−0.0429103	−	0.0673285i
$52$		0			0
$53$			10.3025i			1.41516i	0.706633	+	0.707581i	$0.250213\pi$
$53$			10.3025i			1.41516i	−0.706633	+	0.707581i	$0.749787\pi$
$54$		0			0
$55$	−1.73741			−0.234273
$56$		0			0
$57$	1.21822	−	5.49982i	0.161357	−	0.728469i
$58$		0			0
$59$	7.68473	−	2.05912i	1.00047	−	0.268074i	0.278826	−	0.960342i	$-0.410055\pi$
$59$	7.68473	−	2.05912i	1.00047	−	0.268074i	0.721641	+	0.692268i	$0.243388\pi$
$60$		0			0
$61$	−3.51473	−	6.08768i	−0.450015	−	0.779448i	0.548372	−	0.836235i	$-0.315248\pi$
$61$	−3.51473	−	6.08768i	−0.450015	−	0.779448i	−0.998386	+	0.0567865i	$0.981915\pi$
$62$		0			0
$63$	−3.77815	+	4.50598i	−0.476002	+	0.567700i
$64$		0			0
$65$	9.52915	−	3.71289i	1.18195	−	0.460528i
$66$		0			0
$67$	11.9181	−	3.19344i	1.45602	−	0.390140i	0.557909	−	0.829902i	$-0.311604\pi$
$67$	11.9181	−	3.19344i	1.45602	−	0.390140i	0.898115	+	0.439762i	$0.144937\pi$
$68$		0			0
$69$	−1.58703	+	0.0695826i	−0.191056	+	0.00837676i
$70$		0			0
$71$	−0.769386	+	0.769386i	−0.0913093	+	0.0913093i	−0.751286	−	0.659977i	$-0.770566\pi$
$71$	−0.769386	+	0.769386i	−0.0913093	+	0.0913093i	0.659977	+	0.751286i	$0.270566\pi$
$72$		0			0
$73$	−5.02343	+	5.02343i	−0.587949	+	0.587949i	−0.937075	−	0.349127i	$-0.886478\pi$
$73$	−5.02343	+	5.02343i	−0.587949	+	0.587949i	0.349127	+	0.937075i	$0.386478\pi$
$74$		0			0
$75$	−4.67925	−	2.43477i	−0.540314	−	0.281144i
$76$		0			0
$77$	−0.600315	+	1.03978i	−0.0684122	+	0.118493i
$78$		0			0
$79$	−4.63505	−	8.02814i	−0.521484	−	0.903236i	−0.999688	−	0.0249875i	$-0.992045\pi$
$79$	−4.63505	−	8.02814i	−0.521484	−	0.903236i	0.478204	−	0.878249i	$-0.341288\pi$
$80$		0			0
$81$	−5.79014	−	6.89016i	−0.643349	−	0.765573i
$82$		0			0
$83$	16.7195	+	4.47998i	1.83521	+	0.491742i	0.998441	−	0.0558197i	$-0.0177772\pi$
$83$	16.7195	+	4.47998i	1.83521	+	0.491742i	0.836765	+	0.547562i	$0.184444\pi$
$84$		0			0
$85$	−0.241666	−	0.901908i	−0.0262123	−	0.0978257i
$86$		0			0
$87$	6.27556	+	3.26539i	0.672810	+	0.350086i
$88$		0			0
$89$	−8.13868	−	8.13868i	−0.862699	−	0.862699i	0.128952	−	0.991651i	$-0.458839\pi$
$89$	−8.13868	−	8.13868i	−0.862699	−	0.862699i	−0.991651	+	0.128952i	$0.958839\pi$
$90$		0			0
$91$	1.07051	−	6.98572i	0.112220	−	0.732303i
$92$		0			0
$93$	4.79001	+	4.38762i	0.496701	+	0.454975i
$94$		0			0
$95$	4.61246	−	7.98901i	0.473228	−	0.819655i
$96$		0			0
$97$	2.01196	−	7.50874i	0.204284	−	0.762397i	−0.785383	−	0.619010i	$-0.787534\pi$
$97$	2.01196	−	7.50874i	0.204284	−	0.762397i	0.989667	−	0.143387i	$-0.0457994\pi$
$98$		0			0
$99$	−1.40811	−	1.18067i	−0.141521	−	0.118662i
$100$		0			0
$101$	6.13315	+	10.6229i	0.610271	+	1.05702i	0.991194	+	0.132414i	$0.0422729\pi$
$101$	6.13315	+	10.6229i	0.610271	+	1.05702i	−0.380923	+	0.924607i	$0.624394\pi$
$102$		0			0
$103$	−8.32770	−	4.80800i	−0.820553	−	0.473746i	0.0300543	−	0.999548i	$-0.490432\pi$
$103$	−8.32770	−	4.80800i	−0.820553	−	0.473746i	−0.850607	+	0.525802i	$0.823765\pi$
$104$		0			0
$105$	−8.12069	+	5.17555i	−0.792499	+	0.505082i
$106$		0			0
$107$			1.85058i			0.178902i	0.995991	+	0.0894511i	$0.0285113\pi$
$107$			1.85058i			0.178902i	−0.995991	+	0.0894511i	$0.971489\pi$
$108$		0			0
$109$	0.523808	+	0.523808i	0.0501717	+	0.0501717i	0.731748	−	0.681576i	$-0.238705\pi$
$109$	0.523808	+	0.523808i	0.0501717	+	0.0501717i	−0.681576	+	0.731748i	$0.738705\pi$
$110$		0			0
$111$	−12.5502	−	2.77990i	−1.19121	−	0.263856i
$112$		0			0
$113$	−15.5927	−	9.00243i	−1.46683	−	0.846877i	−0.467523	−	0.883981i	$-0.654854\pi$
$113$	−15.5927	−	9.00243i	−1.46683	−	0.846877i	−0.999311	+	0.0371036i	$0.988187\pi$
$114$		0			0
$115$	−2.51280	−	0.673304i	−0.234320	−	0.0627859i
$116$		0			0
$117$	10.2462	+	3.46641i	0.947259	+	0.320470i
$118$		0			0
$119$	−0.623259	−	0.167002i	−0.0571340	−	0.0153090i
$120$		0			0
$121$	9.20135	+	5.31240i	0.836486	+	0.482946i
$122$		0			0
$123$	−6.13877	+	6.70175i	−0.553514	+	0.604277i
$124$		0			0
$125$	3.92026	+	3.92026i	0.350639	+	0.350639i
$126$		0			0
$127$		−	15.2754i		−	1.35547i	−0.735305	−	0.677737i	$-0.762961\pi$
$127$		−	15.2754i		−	1.35547i	0.735305	−	0.677737i	$-0.237039\pi$
$128$		0			0
$129$	11.8046	+	6.14234i	1.03934	+	0.540803i
$130$		0			0
$131$	−9.56197	−	5.52061i	−0.835434	−	0.482338i	0.0202759	−	0.999794i	$-0.493546\pi$
$131$	−9.56197	−	5.52061i	−0.835434	−	0.482338i	−0.855709	+	0.517457i	$0.826879\pi$
$132$		0			0
$133$	−3.18741	−	5.52076i	−0.276384	−	0.478711i
$134$		0			0
$135$	−5.64770	−	13.6136i	−0.486077	−	1.17167i
$136$		0			0
$137$	3.82658	−	14.2810i	0.326927	−	1.22011i	−0.585434	−	0.810720i	$-0.699076\pi$
$137$	3.82658	−	14.2810i	0.326927	−	1.22011i	0.912361	−	0.409387i	$-0.134258\pi$
$138$		0			0
$139$	6.38084	−	11.0519i	0.541216	−	0.937414i	−0.457619	−	0.889149i	$-0.651297\pi$
$139$	6.38084	−	11.0519i	0.541216	−	0.937414i	0.998835	−	0.0482650i	$-0.0153692\pi$
$140$		0			0
$141$	8.12938	−	2.56482i	0.684617	−	0.215997i
$142$		0			0
$143$	2.18303	+	0.334533i	0.182554	+	0.0279751i
$144$		0			0
$145$	8.19182	+	8.19182i	0.680293	+	0.680293i
$146$		0			0
$147$	−0.239590	−	5.46452i	−0.0197610	−	0.450706i
$148$		0			0
$149$	1.24307	+	4.63919i	0.101836	+	0.380057i	0.997967	−	0.0637324i	$-0.0203004\pi$
$149$	1.24307	+	4.63919i	0.101836	+	0.380057i	−0.896131	+	0.443790i	$0.853634\pi$
$150$		0			0
$151$	10.4275	+	2.79405i	0.848581	+	0.227377i	0.656803	−	0.754062i	$-0.271908\pi$
$151$	10.4275	+	2.79405i	0.848581	+	0.227377i	0.191778	+	0.981438i	$0.438575\pi$
$152$		0			0
$153$	0.417035	−	0.895191i	0.0337153	−	0.0723719i
$154$		0			0
$155$	5.31883	+	9.21249i	0.427219	+	0.739965i
$156$		0			0
$157$	−3.88990	+	6.73750i	−0.310448	+	0.537711i	−0.978459	−	0.206440i	$-0.933812\pi$
$157$	−3.88990	+	6.73750i	−0.310448	+	0.537711i	0.668012	+	0.744151i	$0.267146\pi$
$158$		0			0
$159$	−15.0481	+	9.59060i	−1.19340	+	0.760584i
$160$		0			0
$161$	−1.27118	+	1.27118i	−0.100183	+	0.100183i
$162$		0			0
$163$	11.6439	−	11.6439i	0.912020	−	0.912020i	−0.0844107	−	0.996431i	$-0.526901\pi$
$163$	11.6439	−	11.6439i	0.912020	−	0.912020i	0.996431	+	0.0844107i	$0.0269008\pi$
$164$		0			0
$165$	−1.61735	−	2.53771i	−0.125911	−	0.197561i
$166$		0			0
$167$	−4.62520	+	1.23932i	−0.357909	+	0.0959014i	−0.433293	−	0.901253i	$-0.642648\pi$
$167$	−4.62520	+	1.23932i	−0.357909	+	0.0959014i	0.0753839	+	0.997155i	$0.475982\pi$
$168$		0			0
$169$	−12.6881	+	2.83039i	−0.976011	+	0.217722i
$170$		0			0
$171$	9.16722	−	3.34040i	0.701035	−	0.255447i
$172$		0			0
$173$	−9.66477	−	16.7399i	−0.734799	−	1.27271i	−0.954812	−	0.297212i	$-0.903943\pi$
$173$	−9.66477	−	16.7399i	−0.734799	−	1.27271i	0.220013	−	0.975497i	$-0.429390\pi$
$174$		0			0
$175$	−5.76593	+	1.54498i	−0.435863	+	0.116789i
$176$		0			0
$177$	10.1613	+	9.30769i	0.763770	+	0.699609i
$178$		0			0
$179$	−12.5587			−0.938684			−0.469342	−	0.883017i	$-0.655509\pi$
$179$	−12.5587			−0.938684			−0.469342	+	0.883017i	$0.655509\pi$
$180$		0			0
$181$			21.1579i			1.57265i	0.617811	+	0.786327i	$0.288020\pi$
$181$			21.1579i			1.57265i	−0.617811	+	0.786327i	$0.711980\pi$
$182$		0			0
$183$	5.61998	−	10.8007i	0.415441	−	0.798412i
$184$		0			0
$185$	−18.2304	−	10.5253i	−1.34032	−	0.773836i
$186$		0			0
$187$	0.0521879	−	0.194768i	0.00381636	−	0.0142428i
$188$		0			0
$189$	−10.0986	−	1.32386i	−0.734566	−	0.0962965i
$190$		0			0
$191$	−18.1736	+	10.4925i	−1.31500	+	0.759213i	−0.982919	−	0.184039i	$-0.941083\pi$
$191$	−18.1736	+	10.4925i	−1.31500	+	0.759213i	−0.332077	+	0.943252i	$0.607749\pi$
$192$		0			0
$193$	2.34772	+	8.76182i	0.168993	+	0.630690i	0.997497	+	0.0707070i	$0.0225255\pi$
$193$	2.34772	+	8.76182i	0.168993	+	0.630690i	−0.828504	+	0.559983i	$0.810808\pi$
$194$		0			0
$195$	14.2938	+	10.4622i	1.02360	+	0.749214i
$196$		0			0
$197$	−11.0033	+	11.0033i	−0.783953	+	0.783953i	−0.980495	−	0.196542i	$-0.937029\pi$
$197$	−11.0033	+	11.0033i	−0.783953	+	0.783953i	0.196542	+	0.980495i	$0.437029\pi$
$198$		0			0
$199$		−	9.40693i		−	0.666839i	−0.942778	−	0.333420i	$-0.891797\pi$
$199$		−	9.40693i		−	0.666839i	0.942778	−	0.333420i	$-0.108203\pi$
$200$		0			0
$201$	15.7589	+	14.4351i	1.11155	+	1.01817i
$202$		0			0
$203$	7.73295	−	2.07204i	0.542746	−	0.145428i
$204$		0			0
$205$	−12.8893	+	7.44163i	−0.900226	+	0.519746i
$206$		0			0
$207$	−1.57899	−	2.25328i	−0.109748	−	0.156614i
$208$		0			0
$209$	1.72524	−	0.996065i	0.119337	−	0.0688993i
$210$		0			0
$211$	−11.9952	+	20.7763i	−0.825784	+	1.43030i	0.0755338	+	0.997143i	$0.475934\pi$
$211$	−11.9952	+	20.7763i	−0.825784	+	1.43030i	−0.901318	+	0.433157i	$0.857399\pi$
$212$		0			0
$213$	−1.84000	−	0.407565i	−0.126075	−	0.0279259i
$214$		0			0
$215$	15.4092	+	15.4092i	1.05090	+	1.05090i
$216$		0			0
$217$	7.35110			0.499025
$218$		0			0
$219$	−12.0137	−	2.66106i	−0.811808	−	0.179817i
$220$		0			0
$221$	0.129990	+	1.17977i	0.00874406	+	0.0793597i
$222$		0			0
$223$	−6.16331	+	23.0018i	−0.412726	+	1.54031i	0.376621	+	0.926367i	$0.377086\pi$
$223$	−6.16331	+	23.0018i	−0.412726	+	1.54031i	−0.789347	+	0.613947i	$0.789581\pi$
$224$		0			0
$225$	−0.799611	−	9.10117i	−0.0533074	−	0.606744i
$226$		0			0
$227$	26.9440	+	7.21963i	1.78834	+	0.479183i	0.992062	−	0.125751i	$-0.0401341\pi$
$227$	26.9440	+	7.21963i	1.78834	+	0.479183i	0.796275	+	0.604935i	$0.206801\pi$
$228$		0			0
$229$	0.731872	+	2.73139i	0.0483635	+	0.180495i	0.985882	−	0.167439i	$-0.0535499\pi$
$229$	0.731872	+	2.73139i	0.0483635	+	0.180495i	−0.937519	+	0.347934i	$0.886883\pi$
$230$		0			0
$231$	−2.07756	+	0.0910897i	−0.136693	+	0.00599326i
$232$		0			0
$233$	−5.37193			−0.351927			−0.175963	−	0.984397i	$-0.556304\pi$
$233$	−5.37193			−0.351927			−0.175963	+	0.984397i	$0.556304\pi$
$234$		0			0
$235$	13.9597			0.910631
$236$		0			0
$237$	7.41135	−	14.2435i	0.481419	−	0.925212i
$238$		0			0
$239$	−0.885927	−	3.30632i	−0.0573058	−	0.213868i	0.931336	−	0.364162i	$-0.118645\pi$
$239$	−0.885927	−	3.30632i	−0.0573058	−	0.213868i	−0.988641	+	0.150294i	$0.951978\pi$
$240$		0			0
$241$	27.8499	+	7.46235i	1.79397	+	0.480692i	0.993010	−	0.118030i	$-0.0376580\pi$
$241$	27.8499	+	7.46235i	1.79397	+	0.480692i	0.800957	+	0.598722i	$0.204325\pi$
$242$		0			0
$243$	4.67391	−	14.8713i	0.299831	−	0.953992i
$244$		0			0
$245$	2.31835	−	8.65220i	0.148114	−	0.552769i
$246$		0			0
$247$	−7.33374	+	9.14996i	−0.466635	+	0.582198i
$248$		0			0
$249$	9.02059	+	28.5914i	0.571657	+	1.81191i
$250$		0			0
$251$	0.889720			0.0561587			0.0280793	−	0.999606i	$-0.491061\pi$
$251$	0.889720			0.0561587			0.0280793	+	0.999606i	$0.491061\pi$
$252$		0			0
$253$	−0.397242	−	0.397242i	−0.0249744	−	0.0249744i
$254$		0			0
$255$	1.09239	−	1.19257i	0.0684078	−	0.0746815i
$256$		0			0
$257$	12.1369	−	21.0217i	0.757079	−	1.31130i	−0.187256	−	0.982311i	$-0.559959\pi$
$257$	12.1369	−	21.0217i	0.757079	−	1.31130i	0.944334	−	0.328987i	$-0.106707\pi$
$258$		0			0
$259$	−12.5980	+	7.27345i	−0.782801	+	0.451950i
$260$		0			0
$261$	1.07239	+	12.2060i	0.0663796	+	0.755531i
$262$		0			0
$263$	−16.3337	+	9.43028i	−1.00718	+	0.581496i	−0.910365	−	0.413806i	$-0.864199\pi$
$263$	−16.3337	+	9.43028i	−1.00718	+	0.581496i	−0.0968159	+	0.995302i	$0.530866\pi$
$264$		0			0
$265$	−28.2268	+	7.56335i	−1.73396	+	0.464613i
$266$		0			0
$267$	4.31129	−	19.4639i	0.263847	−	1.19117i
$268$		0			0
$269$			24.2986i			1.48151i	0.671774	+	0.740757i	$0.265533\pi$
$269$			24.2986i			1.48151i	−0.671774	+	0.740757i	$0.734467\pi$
$270$		0			0
$271$	−10.8607	+	10.8607i	−0.659741	+	0.659741i	−0.955319	−	0.295578i	$-0.904488\pi$
$271$	−10.8607	+	10.8607i	−0.659741	+	0.659741i	0.295578	+	0.955319i	$0.404488\pi$
$272$		0			0
$273$	11.2001	−	4.93938i	0.677859	−	0.298945i
$274$		0			0
$275$	−0.482804	−	1.80185i	−0.0291142	−	0.108656i
$276$		0			0
$277$	3.90814	−	2.25637i	0.234818	−	0.135572i	−0.377975	−	0.925816i	$-0.623379\pi$
$277$	3.90814	−	2.25637i	0.234818	−	0.135572i	0.612793	+	0.790244i	$0.290046\pi$
$278$		0			0
$279$	−1.94966	+	11.0809i	−0.116723	+	0.663393i
$280$		0			0
$281$	4.77388	−	17.8164i	0.284786	−	1.06284i	−0.664210	−	0.747546i	$-0.731232\pi$
$281$	4.77388	−	17.8164i	0.284786	−	1.06284i	0.948996	−	0.315289i	$-0.102102\pi$
$282$		0			0
$283$	2.60463	+	1.50378i	0.154829	+	0.0893906i	0.575413	−	0.817863i	$-0.304841\pi$
$283$	2.60463	+	1.50378i	0.154829	+	0.0893906i	−0.420584	+	0.907254i	$0.638175\pi$
$284$		0			0
$285$	15.9627	−	0.699878i	0.945548	−	0.0414572i
$286$		0			0
$287$			10.2850i			0.607104i
$288$		0			0
$289$	−16.8916			−0.993626
$290$		0			0
$291$	12.8404	−	4.05115i	0.752717	−	0.237483i
$292$		0			0
$293$	−6.13275	+	1.64326i	−0.358279	+	0.0960005i	−0.433469	−	0.901169i	$-0.642710\pi$
$293$	−6.13275	+	1.64326i	−0.358279	+	0.0960005i	0.0751896	+	0.997169i	$0.476044\pi$
$294$		0			0
$295$	11.2831	+	19.5429i	0.656928	+	1.13783i
$296$		0			0
$297$	0.413705	−	3.15581i	0.0240056	−	0.183119i
$298$		0			0
$299$	3.02766	+	1.32983i	0.175094	+	0.0769059i
$300$		0			0
$301$	14.5460	−	3.89760i	0.838420	−	0.224654i
$302$		0			0
$303$	−9.80679	+	18.8471i	−0.563385	+	1.08274i
$304$		0			0
$305$	14.0987	−	14.0987i	0.807292	−	0.807292i
$306$		0			0
$307$	1.50595	−	1.50595i	0.0859492	−	0.0859492i	−0.662825	−	0.748774i	$-0.730643\pi$
$307$	1.50595	−	1.50595i	0.0859492	−	0.0859492i	0.748774	+	0.662825i	$0.230643\pi$
$308$		0			0
$309$	−0.729549	−	16.6394i	−0.0415026	−	0.946583i
$310$		0			0
$311$	−6.93805	+	12.0170i	−0.393420	+	0.681424i	−0.992898	−	0.118967i	$-0.962042\pi$
$311$	−6.93805	+	12.0170i	−0.393420	+	0.681424i	0.599478	+	0.800391i	$0.295375\pi$
$312$		0			0
$313$	3.70337	+	6.41442i	0.209327	+	0.362565i	0.951503	−	0.307641i	$-0.0995394\pi$
$313$	3.70337	+	6.41442i	0.209327	+	0.362565i	−0.742176	+	0.670205i	$0.766206\pi$
$314$		0			0
$315$	−15.1191	−	7.04339i	−0.851863	−	0.396850i
$316$		0			0
$317$	−31.1462	−	8.34561i	−1.74935	−	0.468736i	−0.764860	−	0.644197i	$-0.777192\pi$
$317$	−31.1462	−	8.34561i	−1.74935	−	0.468736i	−0.984486	+	0.175461i	$0.943859\pi$
$318$		0			0
$319$	0.647510	+	2.41654i	0.0362536	+	0.135300i
$320$		0			0
$321$	−2.70300	+	1.72270i	−0.150867	+	0.0961517i
$322$		0			0
$323$	0.757039	+	0.757039i	0.0421228	+	0.0421228i
$324$		0			0
$325$	6.49862	+	8.85080i	0.360478	+	0.490954i
$326$		0			0
$327$	−0.277476	+	1.25270i	−0.0153445	+	0.0692745i
$328$		0			0
$329$	4.82339	−	8.35436i	0.265922	−	0.460591i
$330$		0			0
$331$	2.15355	−	8.03717i	0.118370	−	0.441763i	−0.881147	−	0.472843i	$-0.843228\pi$
$331$	2.15355	−	8.03717i	0.118370	−	0.441763i	0.999517	+	0.0310796i	$0.00989455\pi$
$332$		0			0
$333$	−7.62256	−	20.9189i	−0.417714	−	1.14635i
$334$		0			0
$335$	17.4987	+	30.3087i	0.956057	+	1.65594i
$336$		0			0
$337$	−6.73189	−	3.88666i	−0.366709	−	0.211720i	0.305310	−	0.952253i	$-0.401240\pi$
$337$	−6.73189	−	3.88666i	−0.366709	−	0.211720i	−0.672020	+	0.740533i	$0.734573\pi$
$338$		0			0
$339$	−1.36600	−	31.1554i	−0.0741907	−	1.69213i
$340$		0			0
$341$			2.29721i			0.124401i
$342$		0			0
$343$	−14.0790	−	14.0790i	−0.760195	−	0.760195i
$344$		0			0
$345$	−1.35572	−	4.29704i	−0.0729895	−	0.231345i
$346$		0			0
$347$	−27.0008	−	15.5889i	−1.44948	−	0.836856i	−0.451027	−	0.892510i	$-0.648942\pi$
$347$	−27.0008	−	15.5889i	−1.44948	−	0.836856i	−0.998450	+	0.0556541i	$0.982276\pi$
$348$		0			0
$349$	−4.81905	−	1.29126i	−0.257958	−	0.0691195i	0.127522	−	0.991836i	$-0.459297\pi$
$349$	−4.81905	−	1.29126i	−0.257958	−	0.0691195i	−0.385480	+	0.922716i	$0.625964\pi$
$350$		0			0
$351$	4.47500	+	18.1927i	0.238858	+	0.971055i
$352$		0			0
$353$	−2.79861	−	0.749885i	−0.148955	−	0.0399124i	0.183571	−	0.983006i	$-0.441234\pi$
$353$	−2.79861	−	0.749885i	−0.148955	−	0.0399124i	−0.332526	+	0.943094i	$0.607901\pi$
$354$		0			0
$355$	−2.67278	−	1.54313i	−0.141857	−	0.0819009i
$356$		0			0
$357$	−0.336263	−	1.06581i	−0.0177969	−	0.0564086i
$358$		0			0
$359$	−20.8996	−	20.8996i	−1.10304	−	1.10304i	−0.994042	−	0.108997i	$-0.965236\pi$
$359$	−20.8996	−	20.8996i	−1.10304	−	1.10304i	−0.108997	−	0.994042i	$-0.534764\pi$
$360$		0			0
$361$		−	8.42265i		−	0.443297i
$362$		0			0
$363$	0.806085	+	18.3850i	0.0423085	+	0.964964i
$364$		0			0
$365$	−17.4510	−	10.0753i	−0.913427	−	0.527368i
$366$		0			0
$367$	5.85980	+	10.1495i	0.305879	+	0.529798i	0.977457	−	0.211136i	$-0.0677163\pi$
$367$	5.85980	+	10.1495i	0.305879	+	0.529798i	−0.671577	+	0.740934i	$0.734383\pi$
$368$		0			0
$369$	−15.5033	−	2.72779i	−0.807071	−	0.142003i
$370$		0			0
$371$	−5.22661	+	19.5060i	−0.271352	+	1.01270i
$372$		0			0
$373$	6.42101	−	11.1215i	0.332467	−	0.575850i	−0.650528	−	0.759482i	$-0.725452\pi$
$373$	6.42101	−	11.1215i	0.332467	−	0.575850i	0.982995	+	0.183632i	$0.0587856\pi$
$374$		0			0
$375$	−2.07667	+	9.37540i	−0.107239	+	0.484144i
$376$		0			0
$377$	−8.71559	−	11.8702i	−0.448876	−	0.611346i
$378$		0			0
$379$	9.13990	+	9.13990i	0.469485	+	0.469485i	0.901748	−	0.432263i	$-0.142285\pi$
$379$	9.13990	+	9.13990i	0.469485	+	0.469485i	−0.432263	+	0.901748i	$0.642285\pi$
$380$		0			0
$381$	22.3117	−	14.2198i	1.14306	−	0.728505i
$382$		0			0
$383$	−3.97277	−	14.8266i	−0.202999	−	0.757603i	−0.990050	−	0.140715i	$-0.955060\pi$
$383$	−3.97277	−	14.8266i	−0.202999	−	0.757603i	0.787051	−	0.616888i	$-0.211607\pi$
$384$		0			0
$385$	−3.28948	−	0.881413i	−0.167647	−	0.0449210i
$386$		0			0
$387$	2.01722	+	22.9600i	0.102541	+	1.16712i
$388$		0			0
$389$	−19.1965	−	33.2493i	−0.973302	−	1.68581i	−0.685428	−	0.728141i	$-0.740385\pi$
$389$	−19.1965	−	33.2493i	−0.973302	−	1.68581i	−0.287875	−	0.957668i	$-0.592949\pi$
$390$		0			0
$391$	0.150958	−	0.261466i	0.00763426	−	0.0132229i
$392$		0			0
$393$	−0.837677	−	19.1056i	−0.0422552	−	0.963750i
$394$		0			0
$395$	18.5927	−	18.5927i	0.935502	−	0.935502i
$396$		0			0
$397$	10.6225	−	10.6225i	0.533130	−	0.533130i	−0.388372	−	0.921503i	$-0.626962\pi$
$397$	10.6225	−	10.6225i	0.533130	−	0.533130i	0.921503	+	0.388372i	$0.126962\pi$
$398$		0			0
$399$	5.09661	−	9.79489i	0.255150	−	0.490358i
$400$		0			0
$401$	−16.1747	+	4.33401i	−0.807727	+	0.216430i	−0.638974	−	0.769228i	$-0.720641\pi$
$401$	−16.1747	+	4.33401i	−0.807727	+	0.216430i	−0.168753	+	0.985658i	$0.553974\pi$
$402$		0			0
$403$	−4.90920	−	12.5995i	−0.244545	−	0.627625i
$404$		0			0
$405$	14.6269	−	20.9220i	0.726817	−	1.03962i
$406$		0			0
$407$	−2.27295	−	3.93686i	−0.112666	−	0.195143i
$408$		0			0
$409$	−13.8034	+	3.69860i	−0.682532	+	0.182884i	−0.583394	−	0.812190i	$-0.698275\pi$
$409$	−13.8034	+	3.69860i	−0.682532	+	0.182884i	−0.0991389	+	0.995074i	$0.531609\pi$
$410$		0			0
$411$	24.4213	−	7.70494i	1.20462	−	0.380057i
$412$		0			0
$413$	15.5943			0.767344
$414$		0			0
$415$			49.0969i			2.41007i
$416$		0			0
$417$	22.0827	−	0.968206i	1.08139	−	0.0474133i
$418$		0			0
$419$	−4.26586	−	2.46289i	−0.208401	−	0.120320i	0.392167	−	0.919894i	$-0.371725\pi$
$419$	−4.26586	−	2.46289i	−0.208401	−	0.120320i	−0.600568	+	0.799574i	$0.705059\pi$
$420$		0			0
$421$	−2.49475	+	9.31053i	−0.121587	+	0.453768i	−0.999695	−	0.0246942i	$-0.992139\pi$
$421$	−2.49475	+	9.31053i	−0.121587	+	0.453768i	0.878108	+	0.478462i	$0.158805\pi$
$422$		0			0
$423$	11.3139	+	9.48640i	0.550099	+	0.461244i
$424$		0			0
$425$	0.868202	−	0.501257i	0.0421140	−	0.0243145i
$426$		0			0
$427$	−3.56614	−	13.3090i	−0.172577	−	0.644068i
$428$		0			0
$429$	1.54355	+	3.50001i	0.0745235	+	0.168982i
$430$		0			0
$431$	0.315102	−	0.315102i	0.0151779	−	0.0151779i	−0.699477	−	0.714655i	$-0.746584\pi$
$431$	0.315102	−	0.315102i	0.0151779	−	0.0151779i	0.714655	+	0.699477i	$0.246584\pi$
$432$		0			0
$433$		−	30.2736i		−	1.45485i	−0.686185	−	0.727427i	$-0.740716\pi$
$433$		−	30.2736i		−	1.45485i	0.686185	−	0.727427i	$-0.259284\pi$
$434$		0			0
$435$	−4.33944	+	19.5909i	−0.208060	+	0.939313i
$436$		0			0
$437$	2.88120	−	0.772015i	0.137826	−	0.0369305i
$438$		0			0
$439$	31.2977	−	18.0697i	1.49376	−	0.862421i	0.493783	−	0.869585i	$-0.335614\pi$
$439$	31.2977	−	18.0697i	1.49376	−	0.862421i	0.999974	+	0.00716374i	$0.00228031\pi$
$440$		0			0
$441$	7.75859	−	5.43687i	0.369457	−	0.258898i
$442$		0			0
$443$	1.98825	−	1.14792i	0.0944646	−	0.0545391i	−0.452024	−	0.892006i	$-0.649298\pi$
$443$	1.98825	−	1.14792i	0.0944646	−	0.0545391i	0.546488	+	0.837467i	$0.315964\pi$
$444$		0			0
$445$	16.3235	−	28.2731i	0.773808	−	1.34027i
$446$		0			0
$447$	−5.61895	+	6.13427i	−0.265767	+	0.290141i
$448$		0			0
$449$	−6.47243	−	6.47243i	−0.305453	−	0.305453i	0.537690	−	0.843143i	$-0.319297\pi$
$449$	−6.47243	−	6.47243i	−0.305453	−	0.305453i	−0.843143	+	0.537690i	$0.819297\pi$
$450$		0			0
$451$	−3.21405			−0.151344
$452$		0			0
$453$	5.62591	+	17.8317i	0.264328	+	0.837807i
$454$		0			0
$455$	19.9253	−	2.19543i	0.934114	−	0.102923i
$456$		0			0
$457$	−6.28764	+	23.4658i	−0.294123	+	1.09768i	0.647788	+	0.761821i	$0.275694\pi$
$457$	−6.28764	+	23.4658i	−0.294123	+	1.09768i	−0.941911	+	0.335862i	$0.890972\pi$
$458$		0			0
$459$	1.69576	−	0.224199i	0.0791511	−	0.0104647i
$460$		0			0
$461$	16.3089	+	4.36996i	0.759583	+	0.203530i	0.617764	−	0.786363i	$-0.288039\pi$
$461$	16.3089	+	4.36996i	0.759583	+	0.203530i	0.141818	+	0.989893i	$0.454705\pi$
$462$		0			0
$463$	−6.61478	−	24.6867i	−0.307415	−	1.14729i	−0.930847	−	0.365410i	$-0.880929\pi$
$463$	−6.61478	−	24.6867i	−0.307415	−	1.14729i	0.623432	−	0.781878i	$-0.285738\pi$
$464$		0			0
$465$	−8.50471	+	16.3447i	−0.394397	+	0.757968i
$466$		0			0
$467$	−23.4460			−1.08495			−0.542477	−	0.840071i	$-0.682513\pi$
$467$	−23.4460			−1.08495			−0.542477	+	0.840071i	$0.682513\pi$
$468$		0			0
$469$	24.1848			1.11675
$470$		0			0
$471$	−13.4621	+	0.590240i	−0.620300	+	0.0271968i
$472$		0			0
$473$	1.21800	+	4.54563i	0.0560036	+	0.209008i
$474$		0			0
$475$	9.56704	+	2.56348i	0.438966	+	0.117621i
$476$		0			0
$477$	−28.0166	−	13.0518i	−1.28279	−	0.597603i
$478$		0			0
$479$	−4.96669	+	18.5359i	−0.226934	+	0.846928i	0.754687	+	0.656085i	$0.227789\pi$
$479$	−4.96669	+	18.5359i	−0.226934	+	0.846928i	−0.981621	+	0.190843i	$0.938878\pi$
$480$		0			0
$481$	20.8796	+	16.7351i	0.952026	+	0.763054i
$482$		0			0
$483$	−3.04005	−	0.673378i	−0.138327	−	0.0306398i
$484$		0			0
$485$	22.0494			1.00121
$486$		0			0
$487$	−15.8625	−	15.8625i	−0.718800	−	0.718800i	0.249560	−	0.968359i	$-0.419714\pi$
$487$	−15.8625	−	15.8625i	−0.718800	−	0.718800i	−0.968359	+	0.249560i	$0.919714\pi$
$488$		0			0
$489$	27.8467	+	6.16810i	1.25927	+	0.278931i
$490$		0			0
$491$	−3.74118	+	6.47991i	−0.168837	+	0.292434i	−0.938011	−	0.346605i	$-0.887334\pi$
$491$	−3.74118	+	6.47991i	−0.168837	+	0.292434i	0.769174	+	0.639039i	$0.220668\pi$
$492$		0			0
$493$	−1.16438	+	0.672258i	−0.0524412	+	0.0302770i
$494$		0			0
$495$	2.20106	−	4.72470i	0.0989301	−	0.212360i
$496$		0			0
$497$	−1.84701	+	1.06637i	−0.0828498	+	0.0478334i
$498$		0			0
$499$	11.2248	−	3.00769i	0.502493	−	0.134643i	0.00133618	−	0.999999i	$-0.499575\pi$
$499$	11.2248	−	3.00769i	0.502493	−	0.134643i	0.501157	+	0.865357i	$0.332908\pi$
$500$		0			0
$501$	−6.11578	−	5.60201i	−0.273233	−	0.250280i
$502$		0			0
$503$			9.78116i			0.436120i	0.975935	+	0.218060i	$0.0699729\pi$
$503$			9.78116i			0.436120i	−0.975935	+	0.218060i	$0.930027\pi$
$504$		0			0
$505$	−24.6021	+	24.6021i	−1.09478	+	1.09478i
$506$		0			0
$507$	−15.9455	−	15.8978i	−0.708165	−	0.706047i
$508$		0			0
$509$	4.47063	+	16.6846i	0.198157	+	0.739533i	0.991427	+	0.130662i	$0.0417104\pi$
$509$	4.47063	+	16.6846i	0.198157	+	0.739533i	−0.793270	+	0.608870i	$0.791623\pi$
$510$		0			0
$511$	−12.0594	+	6.96251i	−0.533477	+	0.308003i
$512$		0			0
$513$	13.4128	+	10.2803i	0.592191	+	0.453887i
$514$		0			0
$515$	7.05935	−	26.3459i	0.311072	−	1.16094i
$516$		0			0
$517$	2.61073	+	1.50731i	0.114820	+	0.0662913i
$518$		0			0
$519$	15.4538	−	29.6997i	0.678346	−	1.30367i
$520$		0			0
$521$		−	7.17847i		−	0.314495i	−0.987559	−	0.157247i	$-0.949738\pi$
$521$		−	7.17847i		−	0.314495i	0.987559	−	0.157247i	$-0.0502620\pi$
$522$		0			0
$523$	24.9245			1.08987			0.544936	−	0.838478i	$-0.316554\pi$
$523$	24.9245			1.08987			0.544936	+	0.838478i	$0.316554\pi$
$524$		0			0
$525$	−7.62412	−	6.98365i	−0.332744	−	0.304792i
$526$		0			0
$527$	−1.19251	+	0.319531i	−0.0519464	+	0.0139190i
$528$		0			0
$529$	11.0794	+	19.1901i	0.481714	+	0.834353i
$530$		0			0
$531$	−4.13592	+	23.5064i	−0.179484	+	1.02009i
$532$		0			0
$533$	17.6280	−	6.86851i	0.763555	−	0.297508i
$534$		0			0
$535$	−5.07020	+	1.35856i	−0.219204	+	0.0587355i
$536$		0			0
$537$	−11.6909	−	18.3436i	−0.504500	−	0.791585i
$538$		0			0
$539$	1.36780	−	1.36780i	0.0589154	−	0.0589154i
$540$		0			0
$541$	−27.7003	+	27.7003i	−1.19093	+	1.19093i	−0.214120	+	0.976807i	$0.568688\pi$
$541$	−27.7003	+	27.7003i	−1.19093	+	1.19093i	−0.976807	+	0.214120i	$0.931312\pi$
$542$		0			0
$543$	−30.9038	+	19.6958i	−1.32621	+	0.845229i
$544$		0			0
$545$	−1.05059	+	1.81967i	−0.0450021	+	0.0779460i
$546$		0			0
$547$	−15.7394	−	27.2614i	−0.672966	−	1.16561i	−0.977059	−	0.212969i	$-0.931687\pi$
$547$	−15.7394	−	27.2614i	−0.672966	−	1.16561i	0.304093	−	0.952642i	$-0.401647\pi$
$548$		0			0
$549$	21.0074	−	1.84567i	0.896576	−	0.0787714i
$550$		0			0
$551$	−12.8308	−	3.43800i	−0.546610	−	0.146464i
$552$		0			0
$553$	−4.70284	−	17.5513i	−0.199985	−	0.746355i
$554$		0			0
$555$	−1.59707	−	36.4257i	−0.0677919	−	1.54619i
$556$		0			0
$557$	−0.834344	−	0.834344i	−0.0353523	−	0.0353523i	0.689210	−	0.724562i	$-0.257958\pi$
$557$	−0.834344	−	0.834344i	−0.0353523	−	0.0353523i	−0.724562	+	0.689210i	$0.757958\pi$
$558$		0			0
$559$	−16.3944	−	22.3284i	−0.693410	−	0.944391i
$560$		0			0
$561$	0.333065	−	0.105082i	0.0140620	−	0.00443657i
$562$		0			0
$563$	1.64883	−	2.85585i	0.0694898	−	0.120360i	−0.829187	−	0.558971i	$-0.811196\pi$
$563$	1.64883	−	2.85585i	0.0694898	−	0.120360i	0.898677	+	0.438611i	$0.144530\pi$
$564$		0			0
$565$	13.2178	−	49.3296i	0.556078	−	2.07531i
$566$		0			0
$567$	−7.46712	−	15.9827i	−0.313590	−	0.671209i
$568$		0			0
$569$	10.9777	+	19.0140i	0.460210	+	0.797107i	0.998971	−	0.0453513i	$-0.0144407\pi$
$569$	10.9777	+	19.0140i	0.460210	+	0.797107i	−0.538761	+	0.842459i	$0.681107\pi$
$570$		0			0
$571$	36.3726	+	20.9997i	1.52215	+	0.878811i	0.999658	+	0.0261646i	$0.00832939\pi$
$571$	36.3726	+	20.9997i	1.52215	+	0.878811i	0.522488	+	0.852647i	$0.325004\pi$
$572$		0			0
$573$	−32.2434	−	16.7774i	−1.34699	−	0.700884i
$574$		0			0
$575$		−	2.79310i		−	0.116480i
$576$		0			0
$577$	−8.86716	−	8.86716i	−0.369145	−	0.369145i	0.498021	−	0.867165i	$-0.334060\pi$
$577$	−8.86716	−	8.86716i	−0.369145	−	0.369145i	−0.867165	+	0.498021i	$0.834060\pi$
$578$		0			0
$579$	−10.6123	+	11.5855i	−0.441030	+	0.481477i
$580$		0			0
$581$	29.3826	+	16.9641i	1.21900	+	0.703788i
$582$		0			0
$583$	−6.09560	−	1.63331i	−0.252454	−	0.0676449i
$584$		0			0
$585$	−1.97528	+	30.6172i	−0.0816680	+	1.26586i
$586$		0			0
$587$	−2.00254	−	0.536579i	−0.0826537	−	0.0221470i	0.217255	−	0.976115i	$-0.430290\pi$
$587$	−2.00254	−	0.536579i	−0.0826537	−	0.0221470i	−0.299909	+	0.953968i	$0.596956\pi$
$588$		0			0
$589$	−10.5631	−	6.09861i	−0.435245	−	0.251289i
$590$		0			0
$591$	−26.3147	−	5.82876i	−1.08244	−	0.239763i
$592$		0			0
$593$	17.1296	+	17.1296i	0.703427	+	0.703427i	0.965145	−	0.261717i	$-0.0842888\pi$
$593$	17.1296	+	17.1296i	0.703427	+	0.703427i	−0.261717	+	0.965145i	$0.584289\pi$
$594$		0			0
$595$		−	1.83020i		−	0.0750309i
$596$		0			0
$597$	13.7400	−	8.75689i	0.562341	−	0.358396i
$598$		0			0
$599$	−1.29688	−	0.748751i	−0.0529889	−	0.0305931i	0.473272	−	0.880917i	$-0.343073\pi$
$599$	−1.29688	−	0.748751i	−0.0529889	−	0.0305931i	−0.526260	+	0.850323i	$0.676406\pi$
$600$		0			0
$601$	−9.10896	−	15.7772i	−0.371562	−	0.643565i	0.618244	−	0.785986i	$-0.287844\pi$
$601$	−9.10896	−	15.7772i	−0.371562	−	0.643565i	−0.989806	+	0.142422i	$0.954511\pi$
$602$		0			0
$603$	−6.41430	+	36.4555i	−0.261211	+	1.48458i
$604$		0			0
$605$	−7.79994	+	29.1098i	−0.317113	+	1.18348i
$606$		0			0
$607$	−0.761886	+	1.31963i	−0.0309240	+	0.0535619i	−0.881073	−	0.472980i	$-0.843178\pi$
$607$	−0.761886	+	1.31963i	−0.0309240	+	0.0535619i	0.850149	+	0.526542i	$0.176512\pi$
$608$		0			0
$609$	10.2251	+	9.36609i	0.414340	+	0.379533i
$610$		0			0
$611$	−17.5402	−	2.68790i	−0.709599	−	0.108741i
$612$		0			0
$613$	−25.9101	−	25.9101i	−1.04650	−	1.04650i	−0.998865	−	0.0476336i	$-0.984832\pi$
$613$	−25.9101	−	25.9101i	−1.04650	−	1.04650i	−0.0476336	−	0.998865i	$-0.515168\pi$
$614$		0			0
$615$	−22.8680	−	11.8990i	−0.922128	−	0.479815i
$616$		0			0
$617$	7.30263	+	27.2538i	0.293993	+	1.09720i	0.942014	+	0.335574i	$0.108930\pi$
$617$	7.30263	+	27.2538i	0.293993	+	1.09720i	−0.648021	+	0.761623i	$0.724403\pi$
$618$		0			0
$619$	−7.55294	−	2.02380i	−0.303578	−	0.0813435i	0.103814	−	0.994597i	$-0.466895\pi$
$619$	−7.55294	−	2.02380i	−0.303578	−	0.0813435i	−0.407392	+	0.913253i	$0.633562\pi$
$620$		0			0
$621$	1.82132	−	4.40389i	0.0730869	−	0.176722i
$622$		0			0
$623$	−11.2803	−	19.5380i	−0.451934	−	0.782773i
$624$		0			0
$625$	−15.4763	+	26.8057i	−0.619051	+	1.07223i
$626$		0			0
$627$	3.06090	+	1.59269i	0.122240	+	0.0636059i
$628$		0			0
$629$	1.72751	−	1.72751i	0.0688803	−	0.0688803i
$630$		0			0
$631$	−10.5595	+	10.5595i	−0.420368	+	0.420368i	−0.885330	−	0.464963i	$-0.846068\pi$
$631$	−10.5595	+	10.5595i	−0.420368	+	0.420368i	0.464963	+	0.885330i	$0.346068\pi$
$632$		0			0
$633$	−41.5128	+	1.82011i	−1.64998	+	0.0723429i
$634$		0			0
$635$	41.8515	−	11.2141i	1.66082	−	0.445017i
$636$		0			0
$637$	−4.57892	+	10.4250i	−0.181424	+	0.413052i
$638$		0			0
$639$	−1.11756	−	3.06696i	−0.0442098	−	0.121327i
$640$		0			0
$641$	3.66091	+	6.34089i	0.144597	+	0.250450i	0.929223	−	0.369520i	$-0.120478\pi$
$641$	3.66091	+	6.34089i	0.144597	+	0.250450i	−0.784625	+	0.619970i	$0.787145\pi$
$642$		0			0
$643$	−37.2708	+	9.98668i	−1.46982	+	0.393836i	−0.902869	−	0.429917i	$-0.858543\pi$
$643$	−37.2708	+	9.98668i	−1.46982	+	0.393836i	−0.566949	+	0.823753i	$0.691876\pi$
$644$		0			0
$645$	−8.16268	+	36.8515i	−0.321405	+	1.45102i
$646$		0			0
$647$	−16.7465			−0.658373			−0.329186	−	0.944265i	$-0.606774\pi$
$647$	−16.7465			−0.658373			−0.329186	+	0.944265i	$0.606774\pi$
$648$		0			0
$649$			4.87320i			0.191290i
$650$		0			0
$651$	6.84313	+	10.7372i	0.268203	+	0.420825i
$652$		0			0
$653$	30.1333	+	17.3975i	1.17921	+	0.680816i	0.955831	−	0.293917i	$-0.0949588\pi$
$653$	30.1333	+	17.3975i	1.17921	+	0.680816i	0.223376	+	0.974732i	$0.428292\pi$
$654$		0			0
$655$	8.10564	−	30.2507i	0.316713	−	1.18199i
$656$		0			0
$657$	−7.29669	−	20.0246i	−0.284671	−	0.781236i
$658$		0			0
$659$	−0.801546	+	0.462773i	−0.0312238	+	0.0180271i	−0.515531	−	0.856871i	$-0.672405\pi$
$659$	−0.801546	+	0.462773i	−0.0312238	+	0.0180271i	0.484307	+	0.874898i	$0.339072\pi$
$660$		0			0
$661$	3.13696	+	11.7073i	0.122013	+	0.455361i	0.999716	−	0.0238460i	$-0.00759115\pi$
$661$	3.13696	+	11.7073i	0.122013	+	0.455361i	−0.877702	+	0.479207i	$0.840924\pi$
$662$		0			0
$663$	−1.60219	+	1.28811i	−0.0622239	+	0.0500260i
$664$		0			0
$665$	12.7858	−	12.7858i	0.495812	−	0.495812i
$666$		0			0
$667$			3.74595i			0.145044i
$668$		0			0
$669$	−39.3344	+	12.4100i	−1.52076	+	0.479800i
$670$		0			0
$671$	4.15905	−	1.11442i	0.160558	−	0.0430215i
$672$		0			0
$673$	−14.4389	+	8.33628i	−0.556577	+	0.321340i	−0.751771	−	0.659425i	$-0.770800\pi$
$673$	−14.4389	+	8.33628i	−0.556577	+	0.321340i	0.195193	+	0.980765i	$0.437467\pi$
$674$		0			0
$675$	12.5490	−	9.64019i	0.483013	−	0.371051i
$676$		0			0
$677$	9.98589	−	5.76536i	0.383789	−	0.221581i	−0.295677	−	0.955288i	$-0.595545\pi$
$677$	9.98589	−	5.76536i	0.383789	−	0.221581i	0.679466	+	0.733707i	$0.262212\pi$
$678$		0			0
$679$	7.61857	−	13.1957i	0.292374	−	0.506406i
$680$		0			0
$681$	14.5370	+	46.0759i	0.557057	+	1.76563i
$682$		0			0
$683$	30.5505	+	30.5505i	1.16898	+	1.16898i	0.982449	+	0.186534i	$0.0597254\pi$
$683$	30.5505	+	30.5505i	1.16898	+	1.16898i	0.186534	+	0.982449i	$0.440275\pi$
$684$		0			0
$685$	41.9362			1.60230
$686$		0			0
$687$	−3.30823	+	3.61163i	−0.126217	+	0.137792i
$688$		0			0
$689$	36.9228	−	4.06826i	1.40665	−	0.154988i
$690$		0			0
$691$	−3.82152	+	14.2621i	−0.145377	+	0.542556i	0.854361	+	0.519680i	$0.173949\pi$
$691$	−3.82152	+	14.2621i	−0.145377	+	0.542556i	−0.999738	+	0.0228759i	$0.992718\pi$
$692$		0			0
$693$	−2.06704	−	2.94974i	−0.0785204	−	0.112051i
$694$		0			0
$695$	34.9644	+	9.36868i	1.32627	+	0.355374i
$696$		0			0
$697$	−0.447059	−	1.66845i	−0.0169336	−	0.0631969i
$698$		0			0
$699$	−5.00072	−	7.84638i	−0.189145	−	0.296777i
$700$		0			0
$701$	−29.4233			−1.11130			−0.555652	−	0.831415i	$-0.687531\pi$
$701$	−29.4233			−1.11130			−0.555652	+	0.831415i	$0.687531\pi$
$702$		0			0
$703$	24.1368			0.910335
$704$		0			0
$705$	12.9951	+	20.3899i	0.489423	+	0.767929i
$706$		0			0
$707$	6.22286	+	23.2240i	0.234035	+	0.873429i
$708$		0			0
$709$	−4.51061	−	1.20861i	−0.169399	−	0.0453904i	0.173122	−	0.984900i	$-0.444614\pi$
$709$	−4.51061	−	1.20861i	−0.169399	−	0.0453904i	−0.342522	+	0.939510i	$0.611281\pi$
$710$		0			0
$711$	27.7036	−	2.43398i	1.03897	−	0.0912815i
$712$		0			0
$713$	−0.890245	+	3.32244i	−0.0333399	+	0.124426i
$714$		0			0
$715$	0.686069	+	6.22665i	0.0256575	+	0.232864i
$716$		0			0
$717$	4.00460	−	4.37186i	0.149554	−	0.163270i
$718$		0			0
$719$	−19.8659			−0.740872			−0.370436	−	0.928858i	$-0.620792\pi$
$719$	−19.8659			−0.740872			−0.370436	+	0.928858i	$0.620792\pi$
$720$		0			0
$721$	−13.3278	−	13.3278i	−0.496354	−	0.496354i
$722$		0			0
$723$	15.0257	+	47.6249i	0.558811	+	1.77119i
$724$		0			0
$725$	−6.21923	+	10.7720i	−0.230976	+	0.400063i
$726$		0			0
$727$	13.8730	−	8.00959i	0.514521	−	0.297059i	−0.220169	−	0.975462i	$-0.570661\pi$
$727$	13.8730	−	8.00959i	0.514521	−	0.297059i	0.734690	+	0.678403i	$0.237327\pi$
$728$		0			0
$729$	26.0723	−	7.01680i	0.965641	−	0.259881i
$730$		0			0
$731$	−2.19026	+	1.26455i	−0.0810098	+	0.0467710i
$732$		0			0
$733$	23.8314	−	6.38561i	0.880234	−	0.235858i	0.209726	−	0.977760i	$-0.432743\pi$
$733$	23.8314	−	6.38561i	0.880234	−	0.235858i	0.670508	+	0.741902i	$0.266076\pi$
$734$		0			0
$735$	14.7958	−	4.66807i	0.545751	−	0.172184i
$736$		0			0
$737$			7.55773i			0.278393i
$738$		0			0
$739$	8.61409	−	8.61409i	0.316874	−	0.316874i	−0.530691	−	0.847565i	$-0.678068\pi$
$739$	8.61409	−	8.61409i	0.316874	−	0.316874i	0.847565	+	0.530691i	$0.178068\pi$
$740$		0			0
$741$	−20.1916	−	2.19418i	−0.741758	−	0.0806051i
$742$		0			0
$743$	9.05462	+	33.7923i	0.332182	+	1.23972i	0.906892	+	0.421363i	$0.138448\pi$
$743$	9.05462	+	33.7923i	0.332182	+	1.23972i	−0.574710	+	0.818357i	$0.694885\pi$
$744$		0			0
$745$	−11.7979	+	6.81150i	−0.432240	+	0.249554i
$746$		0			0
$747$	−33.3641	+	39.7914i	−1.22073	+	1.45589i
$748$		0			0
$749$	−0.938823	+	3.50374i	−0.0343039	+	0.128024i
$750$		0			0
$751$	38.9810	+	22.5057i	1.42244	+	0.821243i	0.996507	−	0.0835132i	$-0.0266141\pi$
$751$	38.9810	+	22.5057i	1.42244	+	0.821243i	0.425929	+	0.904757i	$0.359947\pi$
$752$		0			0
$753$	0.828239	+	1.29955i	0.0301827	+	0.0473582i
$754$		0			0
$755$			30.6205i			1.11439i
$756$		0			0
$757$	29.8931			1.08648			0.543241	−	0.839577i	$-0.317197\pi$
$757$	29.8931			1.08648			0.543241	+	0.839577i	$0.317197\pi$
$758$		0			0
$759$	0.210430	−	0.950013i	0.00763813	−	0.0344833i
$760$		0			0
$761$	−27.7687	+	7.44060i	−1.00661	+	0.269721i	−0.724214	−	0.689575i	$-0.757797\pi$
$761$	−27.7687	+	7.44060i	−1.00661	+	0.269721i	−0.282400	+	0.959297i	$0.591131\pi$
$762$		0			0
$763$	0.726001	+	1.25747i	0.0262830	+	0.0455235i
$764$		0			0
$765$	2.75879	+	0.485407i	0.0997444	+	0.0175499i
$766$		0			0
$767$	−10.4141	−	26.7279i	−0.376033	−	0.965089i
$768$		0			0
$769$	11.7305	−	3.14317i	0.423011	−	0.113346i	−0.0410325	−	0.999158i	$-0.513065\pi$
$769$	11.7305	−	3.14317i	0.423011	−	0.113346i	0.464044	+	0.885812i	$0.346398\pi$
$770$		0			0
$771$	42.0031	−	1.84161i	1.51270	−	0.0663239i
$772$		0			0
$773$	20.2102	−	20.2102i	0.726909	−	0.726909i	−0.243093	−	0.970003i	$-0.578162\pi$
$773$	20.2102	−	20.2102i	0.726909	−	0.726909i	0.970003	+	0.243093i	$0.0781622\pi$
$774$		0			0
$775$	−8.07612	+	8.07612i	−0.290103	+	0.290103i
$776$		0			0
$777$	−22.3512	−	11.6301i	−0.801846	−	0.417228i
$778$		0			0
$779$	8.53262	−	14.7789i	0.305713	−	0.529510i
$780$		0			0
$781$	−0.333241	−	0.577190i	−0.0119243	−	0.0206535i
$782$		0			0
$783$	−16.8301	+	12.9289i	−0.601458	+	0.462041i
$784$		0			0
$785$	−21.3150	−	5.71135i	−0.760767	−	0.203847i
$786$		0			0
$787$	−9.99498	−	37.3018i	−0.356283	−	1.32967i	−0.878863	−	0.477075i	$-0.841697\pi$
$787$	−9.99498	−	37.3018i	−0.356283	−	1.32967i	0.522580	−	0.852590i	$-0.324970\pi$
$788$		0			0
$789$	−28.9792	−	15.0788i	−1.03169	−	0.536821i
$790$		0			0
$791$	−24.9548	−	24.9548i	−0.887292	−	0.887292i
$792$		0			0
$793$	−20.4295	+	15.0002i	−0.725474	+	0.532673i
$794$		0			0
$795$	−37.3235	−	34.1881i	−1.32373	−	1.21253i
$796$		0			0
$797$	−26.6753	+	46.2030i	−0.944887	+	1.63659i	−0.188911	+	0.981994i	$0.560496\pi$
$797$	−26.6753	+	46.2030i	−0.944887	+	1.63659i	−0.755976	+	0.654599i	$0.772838\pi$
$798$		0			0
$799$	−0.419318	+	1.56492i	−0.0148344	+	0.0553627i
$800$		0			0
$801$	32.4428	−	11.8217i	1.14631	−	0.417699i
$802$		0			0
$803$	−2.17578	−	3.76856i	−0.0767816	−	0.132990i
$804$		0			0
$805$	−4.41596	−	2.54956i	−0.155642	−	0.0898601i
$806$		0			0
$807$	−35.4912	+	22.6195i	−1.24935	+	0.796245i
$808$		0			0
$809$			11.7326i			0.412496i	0.978500	+	0.206248i	$0.0661253\pi$
$809$			11.7326i			0.412496i	−0.978500	+	0.206248i	$0.933875\pi$
$810$		0			0
$811$	22.6077	+	22.6077i	0.793864	+	0.793864i	0.982120	−	0.188256i	$-0.0602834\pi$
$811$	22.6077	+	22.6077i	0.793864	+	0.793864i	−0.188256	+	0.982120i	$0.560283\pi$
$812$		0			0
$813$	−25.9736	−	5.75322i	−0.910936	−	0.201774i
$814$		0			0
$815$	40.4499	+	23.3538i	1.41690	+	0.818048i
$816$		0			0
$817$	−24.1353	−	6.46704i	−0.844388	−	0.226253i
$818$		0			0
$819$	17.6407	+	11.7610i	0.616416	+	0.410964i
$820$		0			0
$821$	−8.85980	−	2.37398i	−0.309209	−	0.0828524i	0.100878	−	0.994899i	$-0.467835\pi$
$821$	−8.85980	−	2.37398i	−0.309209	−	0.0828524i	−0.410087	+	0.912046i	$0.634502\pi$
$822$		0			0
$823$	−15.7820	−	9.11177i	−0.550128	−	0.317616i	0.199046	−	0.979990i	$-0.436216\pi$
$823$	−15.7820	−	9.11177i	−0.550128	−	0.317616i	−0.749173	+	0.662374i	$0.769549\pi$
$824$		0			0
$825$	2.18239	−	2.38253i	0.0759810	−	0.0829492i
$826$		0			0
$827$	−15.8768	−	15.8768i	−0.552091	−	0.552091i	0.374953	−	0.927044i	$-0.377659\pi$
$827$	−15.8768	−	15.8768i	−0.552091	−	0.552091i	−0.927044	+	0.374953i	$0.877659\pi$
$828$		0			0
$829$		−	38.3708i		−	1.33267i	−0.745652	−	0.666336i	$-0.767862\pi$
$829$		−	38.3708i		−	1.33267i	0.745652	−	0.666336i	$-0.232138\pi$
$830$		0			0
$831$	6.93379	+	3.60789i	0.240531	+	0.125156i
$832$		0			0
$833$	0.900293	+	0.519785i	0.0311933	+	0.0180095i
$834$		0			0
$835$	−6.79096	−	11.7623i	−0.235011	−	0.407051i
$836$		0			0
$837$	−17.9999	+	7.46741i	−0.622168	+	0.258112i
$838$		0			0
$839$	−12.8700	+	48.0316i	−0.444323	+	1.65823i	0.273397	+	0.961901i	$0.411853\pi$
$839$	−12.8700	+	48.0316i	−0.444323	+	1.65823i	−0.717719	+	0.696333i	$0.754814\pi$
$840$		0			0
$841$	−6.15911	+	10.6679i	−0.212383	+	0.367858i
$842$		0			0
$843$	30.4671	−	9.61237i	1.04934	−	0.331068i
$844$		0			0
$845$	−17.0694	−	32.6850i	−0.587204	−	1.12440i
$846$		0			0
$847$	14.7260	+	14.7260i	0.505993	+	0.505993i
$848$		0			0
$849$	0.228179	+	5.20426i	0.00783107	+	0.178610i
$850$		0			0
$851$	−1.76168	−	6.57469i	−0.0603897	−	0.225377i
$852$		0			0
$853$	0.0631577	+	0.0169231i	0.00216248	+	0.000579435i	0.259900	−	0.965636i	$-0.416310\pi$
$853$	0.0631577	+	0.0169231i	0.00216248	+	0.000579435i	−0.257738	+	0.966215i	$0.582977\pi$
$854$		0			0
$855$	15.8819	+	22.6640i	0.543149	+	0.775093i
$856$		0			0
$857$	−25.2762	−	43.7796i	−0.863418	−	1.49548i	−0.868609	−	0.495498i	$-0.834986\pi$
$857$	−25.2762	−	43.7796i	−0.863418	−	1.49548i	0.00519107	−	0.999987i	$-0.498348\pi$
$858$		0			0
$859$	−10.9462	+	18.9593i	−0.373478	+	0.646883i	−0.990098	−	0.140378i	$-0.955168\pi$
$859$	−10.9462	+	18.9593i	−0.373478	+	0.646883i	0.616620	+	0.787261i	$0.288502\pi$
$860$		0			0
$861$	−15.0225	+	9.57428i	−0.511966	+	0.326291i
$862$		0			0
$863$	35.0101	−	35.0101i	1.19176	−	1.19176i	0.215183	−	0.976574i	$-0.430965\pi$
$863$	35.0101	−	35.0101i	1.19176	−	1.19176i	0.976574	−	0.215183i	$-0.0690348\pi$
$864$		0			0
$865$	38.7686	−	38.7686i	1.31817	−	1.31817i
$866$		0			0
$867$	−15.7244	−	24.6724i	−0.534028	−	0.837917i
$868$		0			0
$869$	5.48476	−	1.46964i	0.186058	−	0.0498540i
$870$		0			0
$871$	−16.1510	−	41.4517i	−0.547257	−	1.40454i
$872$		0			0
$873$	17.8703	+	14.9838i	0.604818	+	0.507125i
$874$		0			0
$875$	5.43351	+	9.41111i	0.183686	+	0.318154i
$876$		0			0
$877$	35.2700	−	9.45057i	1.19098	−	0.319123i	0.391709	−	0.920089i	$-0.371884\pi$
$877$	35.2700	−	9.45057i	1.19098	−	0.319123i	0.799275	+	0.600966i	$0.205217\pi$
$878$		0			0
$879$	−8.10916	−	7.42794i	−0.273515	−	0.250538i
$880$		0			0
$881$	39.1376			1.31858			0.659289	−	0.751889i	$-0.270857\pi$
$881$	39.1376			1.31858			0.659289	+	0.751889i	$0.270857\pi$
$882$		0			0
$883$			26.4173i			0.889013i	0.895776	+	0.444506i	$0.146621\pi$
$883$			26.4173i			0.889013i	−0.895776	+	0.444506i	$0.853379\pi$
$884$		0			0
$885$	−18.0415	+	34.6729i	−0.606458	+	1.16552i
$886$		0			0
$887$	7.90171	+	4.56206i	0.265314	+	0.153179i	0.626756	−	0.779216i	$-0.284382\pi$
$887$	7.90171	+	4.56206i	0.265314	+	0.153179i	−0.361442	+	0.932394i	$0.617716\pi$
$888$		0			0
$889$	7.74942	−	28.9212i	0.259907	−	0.969987i
$890$		0			0
$891$	4.99458	−	2.33347i	0.167325	−	0.0781742i
$892$		0			0
$893$	−13.8619	+	8.00315i	−0.463869	+	0.267815i
$894$		0			0
$895$	−9.21968	−	34.4083i	−0.308180	−	1.15014i
$896$		0			0
$897$	0.876059	+	5.66021i	0.0292508	+	0.188989i
$898$		0			0
$899$	10.8313	−	10.8313i	0.361242	−	0.361242i
$900$		0			0
$901$		−	3.39147i		−	0.112986i
$902$		0			0
$903$	19.2338	+	17.6181i	0.640061	+	0.586292i
$904$		0			0
$905$	−57.9683	+	15.5325i	−1.92693	+	0.516319i
$906$		0			0
$907$	6.32175	−	3.64986i	0.209910	−	0.121192i	−0.391359	−	0.920238i	$-0.627995\pi$
$907$	6.32175	−	3.64986i	0.209910	−	0.121192i	0.601270	+	0.799046i	$0.294662\pi$
$908$		0			0
$909$	−36.6577	+	3.22068i	−1.21586	+	0.106823i
$910$		0			0
$911$	1.74335	−	1.00652i	0.0577596	−	0.0333475i	−0.470842	−	0.882218i	$-0.656050\pi$
$911$	1.74335	−	1.00652i	0.0577596	−	0.0333475i	0.528602	+	0.848870i	$0.322717\pi$
$912$		0			0
$913$	−5.30126	+	9.18206i	−0.175446	+	0.303882i
$914$		0			0
$915$	33.7175	+	7.46851i	1.11467	+	0.246901i
$916$		0			0
$917$	−15.3032	−	15.3032i	−0.505356	−	0.505356i
$918$		0			0
$919$	11.0173			0.363427			0.181713	−	0.983352i	$-0.441836\pi$
$919$	11.0173			0.363427			0.181713	+	0.983352i	$0.441836\pi$
$920$		0			0
$921$	3.60152	+	0.797745i	0.118674	+	0.0262866i
$922$		0			0
$923$	3.06119	+	2.45356i	0.100760	+	0.0807598i
$924$		0			0
$925$	5.84968	−	21.8313i	0.192336	−	0.717809i
$926$		0			0
$927$	23.6248	−	16.5552i	0.775941	−	0.543744i
$928$		0			0
$929$	18.6161	+	4.98816i	0.610773	+	0.163656i	0.550930	−	0.834552i	$-0.314273\pi$
$929$	18.6161	+	4.98816i	0.610773	+	0.163656i	0.0598435	+	0.998208i	$0.480940\pi$
$930$		0			0
$931$	2.65824	+	9.92067i	0.0871202	+	0.325137i
$932$		0			0
$933$	−24.0110	+	1.05275i	−0.786086	+	0.0344656i
$934$		0			0
$935$	0.571937			0.0187043
$936$		0			0
$937$	−34.3465			−1.12205			−0.561026	−	0.827798i	$-0.689593\pi$
$937$	−34.3465			−1.12205			−0.561026	+	0.827798i	$0.689593\pi$
$938$		0			0
$939$	−5.92162	+	11.3804i	−0.193245	+	0.371386i
$940$		0			0
$941$	10.0928	+	37.6670i	0.329017	+	1.22791i	0.910212	+	0.414143i	$0.135919\pi$
$941$	10.0928	+	37.6670i	0.329017	+	1.22791i	−0.581195	+	0.813765i	$0.697415\pi$
$942$		0			0
$943$	−4.64845	−	1.24555i	−0.151374	−	0.0405607i
$944$		0			0
$945$	−3.78655	−	28.6400i	−0.123177	−	0.931659i
$946$		0			0
$947$	3.30407	−	12.3309i	0.107368	−	0.400702i	−0.891235	−	0.453541i	$-0.850160\pi$
$947$	3.30407	−	12.3309i	0.107368	−	0.400702i	0.998603	+	0.0528395i	$0.0168272\pi$
$948$		0			0
$949$	19.9870	+	16.0196i	0.648804	+	0.520020i
$950$		0			0
$951$	−16.8041	−	53.2619i	−0.544912	−	1.72714i
$952$		0			0
$953$	50.6036			1.63921			0.819605	−	0.572929i	$-0.194193\pi$
$953$	50.6036			1.63921			0.819605	+	0.572929i	$0.194193\pi$
$954$		0			0
$955$	−42.0891	−	42.0891i	−1.36197	−	1.36197i
$956$		0			0
$957$	−2.92690	+	3.19532i	−0.0946131	+	0.103290i
$958$		0			0
$959$	14.4899	−	25.0972i	0.467902	−	0.810431i
$960$		0			0
$961$	−14.6660	+	8.46742i	−0.473097	+	0.273143i
$962$		0			0
$963$	−5.03244	−	2.34442i	−0.162168	−	0.0755479i
$964$		0			0
$965$	−22.2821	+	12.8646i	−0.717285	+	0.414125i
$966$		0			0
$967$	8.28527	−	2.22003i	0.266436	−	0.0713914i	−0.123128	−	0.992391i	$-0.539292\pi$
$967$	8.28527	−	2.22003i	0.266436	−	0.0713914i	0.389564	+	0.920999i	$0.372626\pi$
$968$		0			0
$969$	−0.401025	+	1.81048i	−0.0128828	+	0.0581609i
$970$		0			0
$971$		−	30.6193i		−	0.982619i	−0.870985	−	0.491309i	$-0.836518\pi$
$971$		−	30.6193i		−	0.982619i	0.870985	−	0.491309i	$-0.163482\pi$
$972$		0			0
$973$	17.6878	−	17.6878i	0.567044	−	0.567044i
$974$		0			0
$975$	−6.87816	+	17.7312i	−0.220277	+	0.567854i
$976$		0			0
$977$	−5.62750	−	21.0021i	−0.180040	−	0.671917i	−0.995638	−	0.0932987i	$-0.970259\pi$
$977$	−5.62750	−	21.0021i	−0.180040	−	0.671917i	0.815599	−	0.578618i	$-0.196408\pi$
$978$		0			0
$979$	6.10561	−	3.52508i	0.195136	−	0.112662i
$980$		0			0
$981$	−2.08803	+	0.760847i	−0.0666656	+	0.0242920i
$982$		0			0
$983$	5.66506	−	21.1423i	0.180687	−	0.674335i	−0.814825	−	0.579707i	$-0.803167\pi$
$983$	5.66506	−	21.1423i	0.180687	−	0.674335i	0.995513	−	0.0946281i	$-0.0301662\pi$
$984$		0			0
$985$	−38.2246	−	22.0690i	−1.21794	−	0.703176i
$986$		0			0
$987$	16.6927	−	0.731884i	0.531334	−	0.0232961i
$988$		0			0
$989$			7.04631i			0.224060i
$990$		0			0
$991$	−8.94034			−0.283999			−0.142000	−	0.989867i	$-0.545353\pi$
$991$	−8.94034			−0.283999			−0.142000	+	0.989867i	$0.545353\pi$
$992$		0			0
$993$	13.7440	−	4.33625i	0.436154	−	0.137607i
$994$		0			0
$995$	25.7730	−	6.90586i	0.817060	−	0.218931i
$996$		0			0
$997$	16.9719	+	29.3961i	0.537504	+	0.930985i	0.999038	+	0.0438619i	$0.0139662\pi$
$997$	16.9719	+	29.3961i	0.537504	+	0.930985i	−0.461533	+	0.887123i	$0.652701\pi$
$998$		0			0
$999$	23.4589	−	30.6071i	0.742208	−	0.968366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.cg.a.437.10	yes	56
3.2	odd	2		1404.2.cj.a.125.3		56
9.2	odd	6	inner	468.2.cg.a.281.10	yes	56
9.7	even	3		1404.2.cj.a.1061.3		56
13.5	odd	4	inner	468.2.cg.a.5.10	✓	56
39.5	even	4		1404.2.cj.a.1097.3		56
117.70	odd	12		1404.2.cj.a.629.3		56
117.83	even	12	inner	468.2.cg.a.317.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.cg.a.5.10	✓	56	13.5	odd	4	inner
468.2.cg.a.281.10	yes	56	9.2	odd	6	inner
468.2.cg.a.317.10	yes	56	117.83	even	12	inner
468.2.cg.a.437.10	yes	56	1.1	even	1	trivial
1404.2.cj.a.125.3		56	3.2	odd	2
1404.2.cj.a.629.3		56	117.70	odd	12
1404.2.cj.a.1061.3		56	9.7	even	3
1404.2.cj.a.1097.3		56	39.5	even	4

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.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930898 + 1.46063i) q^{3} +(0.734125 + 2.73979i) q^{5} +(1.89332 + 0.507313i) q^{7} +(-1.26686 + 2.71939i) q^{9} +(-0.158535 + 0.591661i) q^{11} +(-0.394879 - 3.58386i) q^{13} +(-3.31842 + 3.62275i) q^{15} -0.329188 q^{17} +(-2.29971 - 2.29971i) q^{19} +(1.02149 + 3.23769i) q^{21} +(-0.458575 + 0.794276i) q^{23} +(-2.63740 + 1.52270i) q^{25} +(-5.15132 + 0.681067i) q^{27} +(3.53714 - 2.04217i) q^{29} +(3.62256 - 0.970663i) q^{31} +(-1.01178 + 0.319216i) q^{33} +5.55973i q^{35} +(-5.24778 + 5.24778i) q^{37} +(4.86709 - 3.91298i) q^{39} +(1.35806 + 5.06836i) q^{41} +(6.65352 - 3.84141i) q^{43} +(-8.38059 - 1.47456i) q^{45} +(1.27379 - 4.75386i) q^{47} +(-2.73489 - 1.57899i) q^{49} +(-0.306441 - 0.480821i) q^{51} +10.3025i q^{53} -1.73741 q^{55} +(1.21822 - 5.49982i) q^{57} +(7.68473 - 2.05912i) q^{59} +(-3.51473 - 6.08768i) q^{61} +(-3.77815 + 4.50598i) q^{63} +(9.52915 - 3.71289i) q^{65} +(11.9181 - 3.19344i) q^{67} +(-1.58703 + 0.0695826i) q^{69} +(-0.769386 + 0.769386i) q^{71} +(-5.02343 + 5.02343i) q^{73} +(-4.67925 - 2.43477i) q^{75} +(-0.600315 + 1.03978i) q^{77} +(-4.63505 - 8.02814i) q^{79} +(-5.79014 - 6.89016i) q^{81} +(16.7195 + 4.47998i) q^{83} +(-0.241666 - 0.901908i) q^{85} +(6.27556 + 3.26539i) q^{87} +(-8.13868 - 8.13868i) q^{89} +(1.07051 - 6.98572i) q^{91} +(4.79001 + 4.38762i) q^{93} +(4.61246 - 7.98901i) q^{95} +(2.01196 - 7.50874i) q^{97} +(-1.40811 - 1.18067i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{7} - 12 q^{11} - 12 q^{15} + 4 q^{19} - 12 q^{21} + 36 q^{27} - 4 q^{31} + 12 q^{33} - 4 q^{37} + 24 q^{41} + 6 q^{45} + 66 q^{47} - 48 q^{57} - 30 q^{63} - 78 q^{65} - 14 q^{67} + 28 q^{73}+ \cdots + 54 q^{99}+O(q^{100}) \) 56 * q - 2 * q^7 - 12 * q^11 - 12 * q^15 + 4 * q^19 - 12 * q^21 + 36 * q^27 - 4 * q^31 + 12 * q^33 - 4 * q^37 + 24 * q^41 + 6 * q^45 + 66 * q^47 - 48 * q^57 - 30 * q^63 - 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 - 78 * q^83 + 36 * q^85 - 8 * q^91 + 6 * q^93 + 26 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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