LMFDB - Embedded newform 1323.2.s.b.962.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			962.3
Root			$-0.539982 + 0.935277i$ of defining polynomial
Character	$\chi$	$=$	1323.962
Dual form			1323.2.s.b.656.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.254498 + 0.146935i) q^{2} +(-0.956820 - 1.65726i) q^{4} +3.06027 q^{5} -1.15010i q^{8} +O(q^{10})$	\(q+(0.254498 + 0.146935i) q^{2} +(-0.956820 - 1.65726i) q^{4} +3.06027 q^{5} -1.15010i q^{8} +(0.778834 + 0.449660i) q^{10} -3.89647i q^{11} +(-2.02935 - 1.17164i) q^{13} +(-1.74465 + 3.02182i) q^{16} +(1.68263 - 2.91440i) q^{17} +(-2.20696 + 1.27419i) q^{19} +(-2.92813 - 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} -2.98075i q^{23} +4.36525 q^{25} +(-0.344311 - 0.596363i) q^{26} +(3.67241 - 2.12027i) q^{29} +(0.409400 - 0.236367i) q^{31} +(-2.88005 + 1.66280i) q^{32} +(0.856452 - 0.494473i) q^{34} +(-3.89395 - 6.74451i) q^{37} -0.748891 q^{38} -3.51962i q^{40} +(-3.12737 + 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} +(-6.45748 + 3.72823i) q^{44} +(0.437976 - 0.758597i) q^{46} +(-2.02694 + 3.51076i) q^{47} +(1.11095 + 0.641408i) q^{50} +4.48421i q^{52} +(4.99439 + 2.88351i) q^{53} -11.9243i q^{55} +1.24616 q^{58} +(-2.34352 - 4.05910i) q^{59} +(1.38580 + 0.800092i) q^{61} +0.138922 q^{62} +6.00131 q^{64} +(-6.21035 - 3.58555i) q^{65} +(-0.787831 - 1.36456i) q^{67} -6.43989 q^{68} -13.6132i q^{71} +(0.856452 + 0.494473i) q^{73} -2.28862i q^{74} +(4.22333 + 2.43834i) q^{76} +(4.63908 - 8.03512i) q^{79} +(-5.33910 + 9.24760i) q^{80} +(-1.59182 + 0.919038i) q^{82} +(-5.49361 - 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +1.21186i q^{86} -4.48133 q^{88} +(2.15849 + 3.73861i) q^{89} +(-4.93989 + 2.85205i) q^{92} +(-1.03171 + 0.595655i) q^{94} +(-6.75390 + 3.89937i) q^{95} +(4.98797 - 2.87980i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 + 15 * q^10 - 6 * q^13 - 6 * q^16 - 12 * q^17 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 14 * q^25 + 3 * q^26 + 15 * q^29 + 9 * q^31 - 48 * q^32 - 3 * q^34 + 6 * q^37 + 36 * q^38 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 + 15 * q^47 - 3 * q^50 + 9 * q^53 - 16 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 - 54 * q^68 - 3 * q^73 - 9 * q^76 + 20 * q^79 - 30 * q^80 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 16 * q^88 + 24 * q^89 - 39 * q^92 + 3 * q^94 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.254498	+	0.146935i	0.179958	+	0.103899i	0.587273	−	0.809389i	$-0.300202\pi$
$2$	0.254498	+	0.146935i	0.179958	+	0.103899i	−0.407315	+	0.913288i	$0.633535\pi$
$3$		0			0
$3$		0			0
$4$	−0.956820	−	1.65726i	−0.478410	−	0.828631i
$5$	3.06027			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$5$	3.06027			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.15010i		−	0.406622i
$9$		0			0
$10$	0.778834	+	0.449660i	0.246289	+	0.142195i
$11$		−	3.89647i		−	1.17483i	−0.809285	−	0.587416i	$-0.800145\pi$
$11$		−	3.89647i		−	1.17483i	0.809285	−	0.587416i	$-0.199855\pi$
$12$		0			0
$13$	−2.02935	−	1.17164i	−0.562840	−	0.324956i	0.191445	−	0.981503i	$-0.438683\pi$
$13$	−2.02935	−	1.17164i	−0.562840	−	0.324956i	−0.754285	+	0.656548i	$0.772016\pi$
$14$		0			0
$15$		0			0
$16$	−1.74465	+	3.02182i	−0.436163	+	0.755456i
$17$	1.68263	−	2.91440i	0.408097	−	0.706845i	−0.586579	−	0.809892i	$-0.699526\pi$
$17$	1.68263	−	2.91440i	0.408097	−	0.706845i	0.994677	+	0.103047i	$0.0328591\pi$
$18$		0			0
$19$	−2.20696	+	1.27419i	−0.506312	+	0.292319i	−0.731316	−	0.682038i	$-0.761094\pi$
$19$	−2.20696	+	1.27419i	−0.506312	+	0.292319i	0.225004	+	0.974358i	$0.427760\pi$
$20$	−2.92813	−	5.07167i	−0.654750	−	1.13406i
$21$		0			0
$22$	0.572527	−	0.991647i	0.122063	−	0.211420i
$23$		−	2.98075i		−	0.621530i	−0.950487	−	0.310765i	$-0.899415\pi$
$23$		−	2.98075i		−	0.621530i	0.950487	−	0.310765i	$-0.100585\pi$
$24$		0			0
$25$	4.36525			0.873051
$26$	−0.344311	−	0.596363i	−0.0675249	−	0.116956i
$27$		0			0
$28$		0			0
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	−0.118640	−	0.992937i	$-0.537853\pi$
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	0.800589	+	0.599214i	$0.204520\pi$
$30$		0			0
$31$	0.409400	−	0.236367i	0.0735305	−	0.0424528i	−0.462784	−	0.886471i	$-0.653149\pi$
$31$	0.409400	−	0.236367i	0.0735305	−	0.0424528i	0.536314	+	0.844018i	$0.319816\pi$
$32$	−2.88005	+	1.66280i	−0.509126	+	0.293944i
$33$		0			0
$34$	0.856452	−	0.494473i	0.146880	−	0.0848014i
$35$		0			0
$36$		0			0
$37$	−3.89395	−	6.74451i	−0.640161	−	1.10879i	−0.985397	−	0.170275i	$-0.945534\pi$
$37$	−3.89395	−	6.74451i	−0.640161	−	1.10879i	0.345236	−	0.938516i	$-0.387799\pi$
$38$	−0.748891			−0.121486
$39$		0			0
$40$		−	3.51962i		−	0.556500i
$41$	−3.12737	+	5.41676i	−0.488413	+	0.845956i	−0.999911	−	0.0133282i	$-0.995757\pi$
$41$	−3.12737	+	5.41676i	−0.488413	+	0.845956i	0.511498	+	0.859284i	$0.329091\pi$
$42$		0			0
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	0.979318	−	0.202328i	$-0.0648506\pi$
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	−0.664880	+	0.746950i	$0.731517\pi$
$44$	−6.45748	+	3.72823i	−0.973501	+	0.562051i
$45$		0			0
$46$	0.437976	−	0.758597i	0.0645761	−	0.111849i
$47$	−2.02694	+	3.51076i	−0.295659	+	0.512097i	−0.975138	−	0.221598i	$-0.928873\pi$
$47$	−2.02694	+	3.51076i	−0.295659	+	0.512097i	0.679479	+	0.733695i	$0.262206\pi$
$48$		0			0
$49$		0			0
$50$	1.11095	+	0.641408i	0.157112	+	0.0907087i
$51$		0			0
$52$			4.48421i			0.621848i
$53$	4.99439	+	2.88351i	0.686033	+	0.396081i	0.802124	−	0.597157i	$-0.203703\pi$
$53$	4.99439	+	2.88351i	0.686033	+	0.396081i	−0.116091	+	0.993239i	$0.537037\pi$
$54$		0			0
$55$		−	11.9243i		−	1.60787i
$56$		0			0
$57$		0			0
$58$	1.24616			0.163629
$59$	−2.34352	−	4.05910i	−0.305101	−	0.528450i	0.672183	−	0.740385i	$-0.265357\pi$
$59$	−2.34352	−	4.05910i	−0.305101	−	0.528450i	−0.977284	+	0.211935i	$0.932023\pi$
$60$		0			0
$61$	1.38580	+	0.800092i	0.177433	+	0.102441i	0.586086	−	0.810249i	$-0.300668\pi$
$61$	1.38580	+	0.800092i	0.177433	+	0.102441i	−0.408653	+	0.912690i	$0.634001\pi$
$62$	0.138922			0.0176432
$63$		0			0
$64$	6.00131			0.750164
$65$	−6.21035	−	3.58555i	−0.770299	−	0.444733i
$66$		0			0
$67$	−0.787831	−	1.36456i	−0.0962489	−	0.166708i	0.813880	−	0.581033i	$-0.197351\pi$
$67$	−0.787831	−	1.36456i	−0.0962489	−	0.166708i	−0.910129	+	0.414325i	$0.864018\pi$
$68$	−6.43989			−0.780951
$69$		0			0
$70$		0			0
$71$		−	13.6132i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$71$		−	13.6132i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$72$		0			0
$73$	0.856452	+	0.494473i	0.100240	+	0.0578737i	0.549282	−	0.835637i	$-0.314901\pi$
$73$	0.856452	+	0.494473i	0.100240	+	0.0578737i	−0.449042	+	0.893511i	$0.648235\pi$
$74$		−	2.28862i		−	0.266047i
$75$		0			0
$76$	4.22333	+	2.43834i	0.484450	+	0.279697i
$77$		0			0
$78$		0			0
$79$	4.63908	−	8.03512i	0.521937	−	0.904021i	−0.477737	−	0.878503i	$-0.658543\pi$
$79$	4.63908	−	8.03512i	0.521937	−	0.904021i	0.999674	−	0.0255186i	$-0.00812370\pi$
$80$	−5.33910	+	9.24760i	−0.596930	+	1.03391i
$81$		0			0
$82$	−1.59182	+	0.919038i	−0.175787	+	0.101491i
$83$	−5.49361	−	9.51520i	−0.603002	−	1.04443i	−0.992364	−	0.123345i	$-0.960638\pi$
$83$	−5.49361	−	9.51520i	−0.603002	−	1.04443i	0.389362	−	0.921085i	$-0.372695\pi$
$84$		0			0
$85$	5.14930	−	8.91884i	0.558519	−	0.967384i
$86$			1.21186i			0.130679i
$87$		0			0
$88$	−4.48133			−0.477712
$89$	2.15849	+	3.73861i	0.228799	+	0.396292i	0.957452	−	0.288591i	$-0.0931868\pi$
$89$	2.15849	+	3.73861i	0.228799	+	0.396292i	−0.728653	+	0.684883i	$0.759853\pi$
$90$		0			0
$91$		0			0
$92$	−4.93989	+	2.85205i	−0.515019	+	0.297346i
$93$		0			0
$94$	−1.03171	+	0.595655i	−0.106412	+	0.0614371i
$95$	−6.75390	+	3.89937i	−0.692936	+	0.400067i
$96$		0			0
$97$	4.98797	−	2.87980i	0.506451	−	0.292400i	−0.224923	−	0.974377i	$-0.572213\pi$
$97$	4.98797	−	2.87980i	0.506451	−	0.292400i	0.731374	+	0.681977i	$0.238880\pi$
$98$		0			0
$99$		0			0
$100$	−4.17676	−	7.23437i	−0.417676	−	0.723437i
$101$	17.1580			1.70728			0.853642	−	0.520860i	$-0.174389\pi$
$101$	17.1580			1.70728			0.853642	+	0.520860i	$0.174389\pi$
$102$		0			0
$103$			9.81983i			0.967577i	0.875185	+	0.483788i	$0.160740\pi$
$103$			9.81983i			0.967577i	−0.875185	+	0.483788i	$0.839260\pi$
$104$	−1.34751	+	2.33395i	−0.132134	+	0.228863i
$105$		0			0
$106$	0.847377	+	1.46770i	0.0823045	+	0.142556i
$107$	−3.00501	+	1.73494i	−0.290505	+	0.167723i	−0.638170	−	0.769896i	$-0.720308\pi$
$107$	−3.00501	+	1.73494i	−0.290505	+	0.167723i	0.347664	+	0.937619i	$0.386975\pi$
$108$		0			0
$109$	0.611066	−	1.05840i	0.0585295	−	0.101376i	−0.835276	−	0.549831i	$-0.814692\pi$
$109$	0.611066	−	1.05840i	0.0585295	−	0.101376i	0.893806	+	0.448455i	$0.148025\pi$
$110$	1.75209	−	3.03471i	0.167055	−	0.289348i
$111$		0			0
$112$		0			0
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	0.585673	−	0.810547i	$-0.300830\pi$
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	−0.409118	+	0.912482i	$0.634164\pi$
$114$		0			0
$115$		−	9.12191i		−	0.850623i
$116$	−7.02767	−	4.05743i	−0.652503	−	0.376723i
$117$		0			0
$118$		−	1.37738i		−	0.126798i
$119$		0			0
$120$		0			0
$121$	−4.18251			−0.380228
$122$	0.235123	+	0.407244i	0.0212870	+	0.0368702i
$123$		0			0
$124$	−0.783445	−	0.452322i	−0.0703555	−	0.0406198i
$125$	−1.94249			−0.173742
$126$		0			0
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$	7.28743	+	4.20740i	0.644124	+	0.371885i
$129$		0			0
$130$	−1.05368	−	1.82503i	−0.0924141	−	0.160066i
$131$	−7.47821			−0.653375			−0.326687	−	0.945132i	$-0.605932\pi$
$131$	−7.47821			−0.653375			−0.326687	+	0.945132i	$0.605932\pi$
$132$		0			0
$133$		0			0
$134$		−	0.463039i		−	0.0400005i
$135$		0			0
$136$	−3.35185	−	1.93519i	−0.287418	−	0.165941i
$137$		−	12.2088i		−	1.04307i	−0.853231	−	0.521533i	$-0.825360\pi$
$137$		−	12.2088i		−	1.04307i	0.853231	−	0.521533i	$-0.174640\pi$
$138$		0			0
$139$	−11.5501	−	6.66842i	−0.979663	−	0.565608i	−0.0774943	−	0.996993i	$-0.524692\pi$
$139$	−11.5501	−	6.66842i	−0.979663	−	0.565608i	−0.902168	+	0.431384i	$0.858025\pi$
$140$		0			0
$141$		0			0
$142$	2.00026	−	3.46454i	0.167858	−	0.290738i
$143$	−4.56528	+	7.90730i	−0.381768	+	0.661242i
$144$		0			0
$145$	11.2386	−	6.48859i	0.933312	−	0.538848i
$146$	0.145310	+	0.251685i	0.0120260	+	0.0208296i
$147$		0			0
$148$	−7.45161	+	12.9066i	−0.612519	+	1.06091i
$149$			8.47350i			0.694176i	0.937832	+	0.347088i	$0.112830\pi$
$149$			8.47350i			0.694176i	−0.937832	+	0.347088i	$0.887170\pi$
$150$		0			0
$151$	−3.35654			−0.273152			−0.136576	−	0.990630i	$-0.543610\pi$
$151$	−3.35654			−0.273152			−0.136576	+	0.990630i	$0.543610\pi$
$152$	1.46545	+	2.53823i	0.118863	+	0.205877i
$153$		0			0
$154$		0			0
$155$	1.25288	−	0.723348i	0.100633	−	0.0581007i
$156$		0			0
$157$	14.4700	−	8.35426i	1.15483	−	0.666743i	0.204772	−	0.978810i	$-0.434355\pi$
$157$	14.4700	−	8.35426i	1.15483	−	0.666743i	0.950060	+	0.312067i	$0.101021\pi$
$158$	2.36128	−	1.36328i	0.187853	−	0.108457i
$159$		0			0
$160$	−8.81374	+	5.08862i	−0.696787	+	0.402290i
$161$		0			0
$162$		0			0
$163$	12.6662	+	21.9385i	0.992094	+	1.71836i	0.604731	+	0.796430i	$0.293281\pi$
$163$	12.6662	+	21.9385i	0.992094	+	1.71836i	0.387363	+	0.921927i	$0.373386\pi$
$164$	11.9693			0.934647
$165$		0			0
$166$		−	3.22881i		−	0.250604i
$167$	−0.875828	+	1.51698i	−0.0677736	+	0.117387i	−0.897921	−	0.440157i	$-0.854923\pi$
$167$	−0.875828	+	1.51698i	−0.0677736	+	0.117387i	0.830147	+	0.557544i	$0.188256\pi$
$168$		0			0
$169$	−3.75450	−	6.50298i	−0.288808	−	0.500229i
$170$	2.62097	−	1.51322i	0.201020	−	0.116059i
$171$		0			0
$172$	3.94575	−	6.83424i	0.300861	−	0.521106i
$173$	11.9633	−	20.7210i	0.909551	−	1.57539i	0.0948622	−	0.995490i	$-0.469759\pi$
$173$	11.9633	−	20.7210i	0.909551	−	1.57539i	0.814689	−	0.579898i	$-0.196908\pi$
$174$		0			0
$175$		0			0
$176$	11.7745	+	6.79799i	0.887533	+	0.512418i
$177$		0			0
$178$			1.26863i			0.0950875i
$179$	21.9857	+	12.6935i	1.64329	+	0.948755i	0.979652	+	0.200702i	$0.0643223\pi$
$179$	21.9857	+	12.6935i	1.64329	+	0.948755i	0.663639	+	0.748053i	$0.269011\pi$
$180$		0			0
$181$			22.4032i			1.66522i	0.553859	+	0.832610i	$0.313155\pi$
$181$			22.4032i			1.66522i	−0.553859	+	0.832610i	$0.686845\pi$
$182$		0			0
$183$		0			0
$184$	−3.42816			−0.252728
$185$	−11.9165	−	20.6400i	−0.876121	−	1.51749i
$186$		0			0
$187$	−11.3559	−	6.55631i	−0.830423	−	0.479445i
$188$	7.75766			0.565786
$189$		0			0
$190$	−2.29181			−0.166265
$191$	3.71434	+	2.14447i	0.268760	+	0.155169i	0.628324	−	0.777952i	$-0.283741\pi$
$191$	3.71434	+	2.14447i	0.268760	+	0.155169i	−0.359564	+	0.933120i	$0.617075\pi$
$192$		0			0
$193$	11.6725	+	20.2173i	0.840203	+	1.45527i	0.889723	+	0.456501i	$0.150897\pi$
$193$	11.6725	+	20.2173i	0.840203	+	1.45527i	−0.0495201	+	0.998773i	$0.515769\pi$
$194$	1.69257			0.121520
$195$		0			0
$196$		0			0
$197$			18.7811i			1.33809i	0.743220	+	0.669047i	$0.233298\pi$
$197$			18.7811i			1.33809i	−0.743220	+	0.669047i	$0.766702\pi$
$198$		0			0
$199$	3.92927	+	2.26856i	0.278539	+	0.160814i	0.632762	−	0.774347i	$-0.281921\pi$
$199$	3.92927	+	2.26856i	0.278539	+	0.160814i	−0.354223	+	0.935161i	$0.615255\pi$
$200$		−	5.02048i		−	0.355001i
$201$		0			0
$202$	4.36668	+	2.52111i	0.307239	+	0.177384i
$203$		0			0
$204$		0			0
$205$	−9.57060	+	16.5768i	−0.668439	+	1.15777i
$206$	−1.44287	+	2.49913i	−0.100530	+	0.174123i
$207$		0			0
$208$	7.08101	−	4.08822i	0.490980	−	0.283467i
$209$	4.96485	+	8.59937i	0.343426	+	0.594831i
$210$		0			0
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	−0.959829	−	0.280584i	$-0.909472\pi$
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	0.722908	+	0.690944i	$0.242805\pi$
$212$		−	11.0360i		−	0.757957i
$213$		0			0
$214$	−1.01969			−0.0697049
$215$	6.31000	+	10.9292i	0.430338	+	0.745368i
$216$		0			0
$217$		0			0
$218$	0.311031	−	0.179574i	0.0210657	−	0.0121623i
$219$		0			0
$220$	−19.7616	+	11.4094i	−1.33233	+	0.769220i
$221$	−6.82927	+	3.94288i	−0.459387	+	0.265227i
$222$		0			0
$223$	5.57176	−	3.21686i	0.373113	−	0.215417i	−0.301705	−	0.953401i	$-0.597556\pi$
$223$	5.57176	−	3.21686i	0.373113	−	0.215417i	0.674818	+	0.737985i	$0.264222\pi$
$224$		0			0
$225$		0			0
$226$	0.318430	+	0.551537i	0.0211816	+	0.0366877i
$227$	−19.7397			−1.31017			−0.655084	−	0.755556i	$-0.727367\pi$
$227$	−19.7397			−1.31017			−0.655084	+	0.755556i	$0.727367\pi$
$228$		0			0
$229$			10.9069i			0.720747i	0.932808	+	0.360373i	$0.117351\pi$
$229$			10.9069i			0.720747i	−0.932808	+	0.360373i	$0.882649\pi$
$230$	1.34033	−	2.32151i	0.0883785	−	0.153076i
$231$		0			0
$232$	−2.43852	−	4.22364i	−0.160097	−	0.277295i
$233$	17.9944	−	10.3891i	1.17885	−	0.680611i	0.223104	−	0.974795i	$-0.428381\pi$
$233$	17.9944	−	10.3891i	1.17885	−	0.680611i	0.955749	+	0.294184i	$0.0950478\pi$
$234$		0			0
$235$	−6.20298	+	10.7439i	−0.404638	+	0.700853i
$236$	−4.48466	+	7.76766i	−0.291927	+	0.505632i
$237$		0			0
$238$		0			0
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.999300	−	0.0373991i	$-0.988093\pi$
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.532039	−	0.846720i	$-0.678574\pi$
$240$		0			0
$241$			21.3259i			1.37372i	0.726788	+	0.686861i	$0.241012\pi$
$241$			21.3259i			1.37372i	−0.726788	+	0.686861i	$0.758988\pi$
$242$	−1.06444	−	0.614556i	−0.0684250	−	0.0395052i
$243$		0			0
$244$		−	3.06218i		−	0.196036i
$245$		0			0
$246$		0			0
$247$	5.97159			0.379963
$248$	−0.271846	−	0.470851i	−0.0172622	−	0.0298991i
$249$		0			0
$250$	−0.494361	−	0.285419i	−0.0312661	−	0.0180515i
$251$	26.7381			1.68769			0.843847	−	0.536584i	$-0.180286\pi$
$251$	26.7381			1.68769			0.843847	+	0.536584i	$0.180286\pi$
$252$		0			0
$253$	−11.6144			−0.730193
$254$	0.699589	+	0.403908i	0.0438961	+	0.0253434i
$255$		0			0
$256$	−4.76489	−	8.25303i	−0.297805	−	0.515814i
$257$	−3.05279			−0.190428			−0.0952140	−	0.995457i	$-0.530354\pi$
$257$	−3.05279			−0.190428			−0.0952140	+	0.995457i	$0.530354\pi$
$258$		0			0
$259$		0			0
$260$			13.7229i			0.851058i
$261$		0			0
$262$	−1.90319	−	1.09881i	−0.117580	−	0.0678847i
$263$			16.2174i			1.00001i	0.866024	+	0.500003i	$0.166668\pi$
$263$			16.2174i			1.00001i	−0.866024	+	0.500003i	$0.833332\pi$
$264$		0			0
$265$	15.2842	+	8.82433i	0.938901	+	0.542074i
$266$		0			0
$267$		0			0
$268$	−1.50763	+	2.61128i	−0.0920929	+	0.159510i
$269$	−0.303255	+	0.525254i	−0.0184898	+	0.0320253i	−0.875122	−	0.483902i	$-0.839219\pi$
$269$	−0.303255	+	0.525254i	−0.0184898	+	0.0320253i	0.856632	+	0.515927i	$0.172552\pi$
$270$		0			0
$271$	−19.8948	+	11.4863i	−1.20852	+	0.697742i	−0.962437	−	0.271505i	$-0.912479\pi$
$271$	−19.8948	+	11.4863i	−1.20852	+	0.697742i	−0.246088	+	0.969248i	$0.579145\pi$
$272$	5.87120	+	10.1692i	0.355994	+	0.616599i
$273$		0			0
$274$	1.79389	−	3.10711i	0.108373	−	0.187708i
$275$		−	17.0091i		−	1.02569i
$276$		0			0
$277$	13.2835			0.798125			0.399063	−	0.916924i	$-0.369336\pi$
$277$	13.2835			0.798125			0.399063	+	0.916924i	$0.369336\pi$
$278$	−1.95965	−	3.39421i	−0.117532	−	0.203571i
$279$		0			0
$280$		0			0
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	−0.659859	−	0.751390i	$-0.729384\pi$
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	0.320793	+	0.947149i	$0.396050\pi$
$282$		0			0
$283$	−2.57413	+	1.48617i	−0.153016	+	0.0883437i	−0.574553	−	0.818467i	$-0.694824\pi$
$283$	−2.57413	+	1.48617i	−0.153016	+	0.0883437i	0.421537	+	0.906811i	$0.361491\pi$
$284$	−22.5607	+	13.0254i	−1.33873	+	0.772916i
$285$		0			0
$286$	−2.32371	+	1.34160i	−0.137404	+	0.0793303i
$287$		0			0
$288$		0			0
$289$	2.83753	+	4.91475i	0.166914	+	0.289103i
$290$	3.81360			0.223942
$291$		0			0
$292$		−	1.89249i		−	0.110749i
$293$	−3.03087	+	5.24962i	−0.177065	+	0.306686i	−0.940874	−	0.338756i	$-0.889994\pi$
$293$	−3.03087	+	5.24962i	−0.177065	+	0.306686i	0.763809	+	0.645443i	$0.223327\pi$
$294$		0			0
$295$	−7.17181	−	12.4219i	−0.417559	−	0.723234i
$296$	−7.75686	+	4.47843i	−0.450858	+	0.260303i
$297$		0			0
$298$	−1.24505	+	2.15649i	−0.0721239	+	0.124922i
$299$	−3.49238	+	6.04899i	−0.201970	+	0.349822i
$300$		0			0
$301$		0			0
$302$	−0.854235	−	0.493193i	−0.0491557	−	0.0283801i
$303$		0			0
$304$		−	8.89207i		−	0.509995i
$305$	4.24092	+	2.44850i	0.242834	+	0.140201i
$306$		0			0
$307$			21.6030i			1.23295i	0.787375	+	0.616474i	$0.211439\pi$
$307$			21.6030i			1.23295i	−0.787375	+	0.616474i	$0.788561\pi$
$308$		0			0
$309$		0			0
$310$	0.425140			0.0241463
$311$	5.51171	+	9.54656i	0.312540	+	0.541336i	0.978912	−	0.204284i	$-0.0654868\pi$
$311$	5.51171	+	9.54656i	0.312540	+	0.541336i	−0.666371	+	0.745620i	$0.732153\pi$
$312$		0			0
$313$	11.7383	+	6.77710i	0.663487	+	0.383064i	0.793604	−	0.608434i	$-0.208202\pi$
$313$	11.7383	+	6.77710i	0.663487	+	0.383064i	−0.130117	+	0.991499i	$0.541535\pi$
$314$	4.91012			0.277094
$315$		0			0
$316$	−17.7551			−0.998800
$317$	9.65977	+	5.57707i	0.542547	+	0.313240i	0.746111	−	0.665822i	$-0.231919\pi$
$317$	9.65977	+	5.57707i	0.542547	+	0.313240i	−0.203564	+	0.979062i	$0.565252\pi$
$318$		0			0
$319$	−8.26156	−	14.3094i	−0.462559	−	0.801175i
$320$	18.3656			1.02667
$321$		0			0
$322$		0			0
$323$			8.57595i			0.477179i
$324$		0			0
$325$	−8.85862	−	5.11453i	−0.491388	−	0.283703i
$326$			7.44442i			0.412308i
$327$		0			0
$328$	6.22982	+	3.59679i	0.343984	+	0.198599i
$329$		0			0
$330$		0			0
$331$	9.51009	−	16.4720i	0.522722	−	0.905380i	−0.476929	−	0.878942i	$-0.658250\pi$
$331$	9.51009	−	16.4720i	0.522722	−	0.905380i	0.999650	−	0.0264385i	$-0.00841661\pi$
$332$	−10.5128	+	18.2087i	−0.576964	+	0.999331i
$333$		0			0
$334$	−0.445794	+	0.257379i	−0.0243927	+	0.0140832i
$335$	−2.41098	−	4.17593i	−0.131726	−	0.228156i
$336$		0			0
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	−0.761091	−	0.648645i	$-0.775336\pi$
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	0.942289	+	0.334802i	$0.108669\pi$
$338$		−	2.20666i		−	0.120027i
$339$		0			0
$340$	−19.7078			−1.06881
$341$	−0.921000	−	1.59522i	−0.0498749	−	0.0863859i
$342$		0			0
$343$		0			0
$344$	4.10738	−	2.37140i	0.221455	−	0.127857i
$345$		0			0
$346$	6.08927	−	3.51564i	0.327361	−	0.189002i
$347$	23.0796	−	13.3250i	1.23898	−	0.715325i	0.270094	−	0.962834i	$-0.412945\pi$
$347$	23.0796	−	13.3250i	1.23898	−	0.715325i	0.968886	+	0.247509i	$0.0796118\pi$
$348$		0			0
$349$	−20.5135	+	11.8435i	−1.09806	+	0.633966i	−0.935711	−	0.352768i	$-0.885241\pi$
$349$	−20.5135	+	11.8435i	−1.09806	+	0.633966i	−0.162350	+	0.986733i	$0.551907\pi$
$350$		0			0
$351$		0			0
$352$	6.47905	+	11.2221i	0.345335	+	0.598137i
$353$	4.58845			0.244218			0.122109	−	0.992517i	$-0.461034\pi$
$353$	4.58845			0.244218			0.122109	+	0.992517i	$0.461034\pi$
$354$		0			0
$355$		−	41.6602i		−	2.21109i
$356$	4.13057	−	7.15435i	0.218920	−	0.379180i
$357$		0			0
$358$	3.73022	+	6.46094i	0.197148	+	0.341471i
$359$	−5.30942	+	3.06540i	−0.280221	+	0.161785i	−0.633523	−	0.773724i	$-0.718392\pi$
$359$	−5.30942	+	3.06540i	−0.280221	+	0.161785i	0.353303	+	0.935509i	$0.385059\pi$
$360$		0			0
$361$	−6.25288	+	10.8303i	−0.329099	+	0.570016i
$362$	−3.29182	+	5.70159i	−0.173014	+	0.299669i
$363$		0			0
$364$		0			0
$365$	2.62097	+	1.51322i	0.137188	+	0.0792056i
$366$		0			0
$367$		−	26.4264i		−	1.37945i	−0.724072	−	0.689725i	$-0.757732\pi$
$367$		−	26.4264i		−	1.37945i	0.724072	−	0.689725i	$-0.242268\pi$
$368$	9.00732	+	5.20038i	0.469539	+	0.271088i
$369$		0			0
$370$		−	7.00381i		−	0.364111i
$371$		0			0
$372$		0			0
$373$	20.1162			1.04158			0.520789	−	0.853686i	$-0.325638\pi$
$373$	20.1162			1.04158			0.520789	+	0.853686i	$0.325638\pi$
$374$	−1.92670	−	3.33714i	−0.0996273	−	0.172560i
$375$		0			0
$376$	4.03772	+	2.33118i	0.208230	+	0.120221i
$377$	−9.93679			−0.511771
$378$		0			0
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$	12.9245	+	7.46199i	0.663015	+	0.382792i
$381$		0			0
$382$	0.630195	+	1.09153i	0.0322436	+	0.0558476i
$383$	−28.0633			−1.43397			−0.716985	−	0.697089i	$-0.754478\pi$
$383$	−28.0633			−1.43397			−0.716985	+	0.697089i	$0.754478\pi$
$384$		0			0
$385$		0			0
$386$			6.86037i			0.349183i
$387$		0			0
$388$	−9.54517	−	5.51091i	−0.484583	−	0.279774i
$389$		−	34.2392i		−	1.73600i	−0.496566	−	0.867999i	$-0.665406\pi$
$389$		−	34.2392i		−	1.73600i	0.496566	−	0.867999i	$-0.334594\pi$
$390$		0			0
$391$	−8.68710	−	5.01550i	−0.439325	−	0.253645i
$392$		0			0
$393$		0			0
$394$	−2.75959	+	4.77975i	−0.139026	+	0.240800i
$395$	14.1968	−	24.5896i	0.714320	−	1.23724i
$396$		0			0
$397$	11.2926	−	6.51981i	0.566762	−	0.327220i	−0.189093	−	0.981959i	$-0.560555\pi$
$397$	11.2926	−	6.51981i	0.566762	−	0.327220i	0.755855	+	0.654739i	$0.227222\pi$
$398$	0.666662	+	1.15469i	0.0334167	+	0.0578795i
$399$		0			0
$400$	−7.61585	+	13.1910i	−0.380792	+	0.659552i
$401$			18.3532i			0.916514i	0.888820	+	0.458257i	$0.151526\pi$
$401$			18.3532i			0.916514i	−0.888820	+	0.458257i	$0.848474\pi$
$402$		0			0
$403$	−1.10775			−0.0551812
$404$	−16.4171	−	28.4353i	−0.816782	−	1.41471i
$405$		0			0
$406$		0			0
$407$	−26.2798	+	15.1727i	−1.30264	+	0.752081i
$408$		0			0
$409$	5.60133	−	3.23393i	0.276968	−	0.159907i	−0.355082	−	0.934835i	$-0.615547\pi$
$409$	5.60133	−	3.23393i	0.276968	−	0.159907i	0.632050	+	0.774928i	$0.282214\pi$
$410$	−4.87140	+	2.81251i	−0.240581	+	0.138900i
$411$		0			0
$412$	16.2740	−	9.39581i	0.801764	−	0.462899i
$413$		0			0
$414$		0			0
$415$	−16.8119	−	29.1191i	−0.825265	−	1.42940i
$416$	7.79284			0.382075
$417$		0			0
$418$			2.91804i			0.142726i
$419$	−7.11542	+	12.3243i	−0.347611	+	0.602080i	−0.985825	−	0.167779i	$-0.946340\pi$
$419$	−7.11542	+	12.3243i	−0.347611	+	0.602080i	0.638214	+	0.769859i	$0.279674\pi$
$420$		0			0
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	0.952753	+	0.303747i	$0.0982378\pi$
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	−0.213324	+	0.976982i	$0.568429\pi$
$422$	−1.75170	+	1.01135i	−0.0852716	+	0.0492316i
$423$		0			0
$424$	3.31633	−	5.74405i	0.161055	−	0.278956i
$425$	7.34510	−	12.7221i	0.356290	−	0.617112i
$426$		0			0
$427$		0			0
$428$	5.75051	+	3.32006i	0.277962	+	0.160481i
$429$		0			0
$430$			3.70863i			0.178846i
$431$	−2.12663	−	1.22781i	−0.102436	−	0.0591415i	0.447907	−	0.894080i	$-0.352170\pi$
$431$	−2.12663	−	1.22781i	−0.102436	−	0.0591415i	−0.550343	+	0.834939i	$0.685503\pi$
$432$		0			0
$433$		−	12.4545i		−	0.598525i	−0.954171	−	0.299262i	$-0.903259\pi$
$433$		−	12.4545i		−	0.598525i	0.954171	−	0.299262i	$-0.0967406\pi$
$434$		0			0
$435$		0			0
$436$	−2.33872			−0.112004
$437$	3.79805	+	6.57841i	0.181685	+	0.314688i
$438$		0			0
$439$	15.1815	+	8.76502i	0.724571	+	0.418331i	0.816433	−	0.577440i	$-0.195948\pi$
$439$	15.1815	+	8.76502i	0.724571	+	0.418331i	−0.0918615	+	0.995772i	$0.529282\pi$
$440$	−13.7141			−0.653794
$441$		0			0
$442$	−2.31739			−0.110227
$443$	−7.79825	−	4.50232i	−0.370506	−	0.213912i	0.303173	−	0.952935i	$-0.401954\pi$
$443$	−7.79825	−	4.50232i	−0.370506	−	0.213912i	−0.673680	+	0.739024i	$0.735287\pi$
$444$		0			0
$445$	6.60555	+	11.4411i	0.313133	+	0.542362i
$446$	1.89067			0.0895260
$447$		0			0
$448$		0			0
$449$		−	30.8120i		−	1.45411i	−0.686581	−	0.727054i	$-0.740889\pi$
$449$		−	30.8120i		−	1.45411i	0.686581	−	0.727054i	$-0.259111\pi$
$450$		0			0
$451$	21.1063	+	12.1857i	0.993856	+	0.573803i
$452$		−	4.14715i		−	0.195065i
$453$		0			0
$454$	−5.02371	−	2.90044i	−0.235775	−	0.136125i
$455$		0			0
$456$		0			0
$457$	−6.91430	+	11.9759i	−0.323437	+	0.560210i	−0.981195	−	0.193020i	$-0.938172\pi$
$457$	−6.91430	+	11.9759i	−0.323437	+	0.560210i	0.657758	+	0.753230i	$0.271505\pi$
$458$	−1.60260	+	2.77578i	−0.0748846	+	0.129704i
$459$		0			0
$460$	−15.1174	+	8.72803i	−0.704852	+	0.406947i
$461$	−6.16989	−	10.6866i	−0.287360	−	0.497723i	0.685818	−	0.727773i	$-0.259444\pi$
$461$	−6.16989	−	10.6866i	−0.287360	−	0.497723i	−0.973179	+	0.230050i	$0.926111\pi$
$462$		0			0
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	−0.678900	−	0.734230i	$-0.737543\pi$
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	0.975312	+	0.220830i	$0.0708765\pi$
$464$			14.7965i			0.686910i
$465$		0			0
$466$	6.10606			0.282858
$467$	5.48999	+	9.50894i	0.254046	+	0.440021i	0.964636	−	0.263585i	$-0.0849051\pi$
$467$	5.48999	+	9.50894i	0.254046	+	0.440021i	−0.710590	+	0.703607i	$0.751572\pi$
$468$		0			0
$469$		0			0
$470$	−3.15730	+	1.82287i	−0.145635	+	0.0840825i
$471$		0			0
$472$	−4.66837	+	2.69528i	−0.214879	+	0.124061i
$473$	13.9156	−	8.03417i	0.639840	−	0.369412i
$474$		0			0
$475$	−9.63396	+	5.56217i	−0.442036	+	0.255210i
$476$		0			0
$477$		0			0
$478$	−4.01665	−	6.95704i	−0.183717	−	0.318208i
$479$	−11.1946			−0.511493			−0.255747	−	0.966744i	$-0.582321\pi$
$479$	−11.1946			−0.511493			−0.255747	+	0.966744i	$0.582321\pi$
$480$		0			0
$481$			18.2493i			0.832096i
$482$	−3.13352	+	5.42741i	−0.142728	+	0.247212i
$483$		0			0
$484$	4.00191	+	6.93152i	0.181905	+	0.315069i
$485$	15.2645	−	8.81298i	0.693126	−	0.400177i
$486$		0			0
$487$	−1.48332	+	2.56919i	−0.0672158	+	0.116421i	−0.897675	−	0.440659i	$-0.854745\pi$
$487$	−1.48332	+	2.56919i	−0.0672158	+	0.116421i	0.830459	+	0.557080i	$0.188078\pi$
$488$	0.920185	−	1.59381i	0.0416548	−	0.0721483i
$489$		0			0
$490$		0			0
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.880653	−	0.473762i	$-0.157104\pi$
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.0300367	+	0.999549i	$0.490438\pi$
$492$		0			0
$493$		−	14.2705i		−	0.642710i
$494$	1.51976	+	0.877435i	0.0683773	+	0.0394776i
$495$		0			0
$496$			1.64952i			0.0740654i
$497$		0			0
$498$		0			0
$499$	−4.58592			−0.205294			−0.102647	−	0.994718i	$-0.532731\pi$
$499$	−4.58592			−0.205294			−0.102647	+	0.994718i	$0.532731\pi$
$500$	1.85862	+	3.21922i	0.0831198	+	0.143968i
$501$		0			0
$502$	6.80480	+	3.92875i	0.303713	+	0.175349i
$503$	23.1383			1.03169			0.515844	−	0.856683i	$-0.327479\pi$
$503$	23.1383			1.03169			0.515844	+	0.856683i	$0.327479\pi$
$504$		0			0
$505$	52.5081			2.33658
$506$	−2.95585	−	1.70656i	−0.131404	−	0.0758660i
$507$		0			0
$508$	−2.63020	−	4.55563i	−0.116696	−	0.202123i
$509$	9.65706			0.428042			0.214021	−	0.976829i	$-0.431344\pi$
$509$	9.65706			0.428042			0.214021	+	0.976829i	$0.431344\pi$
$510$		0			0
$511$		0			0
$512$		−	19.6301i		−	0.867536i
$513$		0			0
$514$	−0.776931	−	0.448561i	−0.0342690	−	0.0197852i
$515$			30.0513i			1.32422i
$516$		0			0
$517$	13.6796	+	7.89791i	0.601627	+	0.347350i
$518$		0			0
$519$		0			0
$520$	−4.12374	+	7.14252i	−0.180838	+	0.313220i
$521$	−5.00035	+	8.66086i	−0.219069	+	0.379439i	−0.954524	−	0.298135i	$-0.903635\pi$
$521$	−5.00035	+	8.66086i	−0.219069	+	0.379439i	0.735454	+	0.677574i	$0.236969\pi$
$522$		0			0
$523$	10.7796	−	6.22361i	0.471359	−	0.272139i	−0.245449	−	0.969409i	$-0.578935\pi$
$523$	10.7796	−	6.22361i	0.471359	−	0.272139i	0.716809	+	0.697270i	$0.245602\pi$
$524$	7.15531	+	12.3934i	0.312581	+	0.541406i
$525$		0			0
$526$	−2.38289	+	4.12729i	−0.103899	+	0.179959i
$527$		−	1.59087i		−	0.0692995i
$528$		0			0
$529$	14.1151			0.613700
$530$	2.59320	+	4.49156i	0.112641	+	0.195101i
$531$		0			0
$532$		0			0
$533$	12.6930	−	7.32833i	0.549797	−	0.317425i
$534$		0			0
$535$	−9.19615	+	5.30940i	−0.397584	+	0.229545i
$536$	−1.56938	+	0.906084i	−0.0677870	+	0.0391369i
$537$		0			0
$538$	−0.154356	+	0.0891175i	−0.00665476	+	0.00384213i
$539$		0			0
$540$		0			0
$541$	6.96514	+	12.0640i	0.299455	+	0.518671i	0.976011	−	0.217720i	$-0.0698619\pi$
$541$	6.96514	+	12.0640i	0.299455	+	0.518671i	−0.676557	+	0.736391i	$0.736529\pi$
$542$	−6.75094			−0.289978
$543$		0			0
$544$			11.1915i			0.479831i
$545$	1.87003	−	3.23898i	0.0801032	−	0.138743i
$546$		0			0
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.788584	−	0.614926i	$-0.789186\pi$
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.138250	−	0.990397i	$-0.544148\pi$
$548$	−20.2331	+	11.6816i	−0.864316	+	0.499013i
$549$		0			0
$550$	2.49923	−	4.32879i	0.106567	−	0.184580i
$551$	−5.40325	+	9.35870i	−0.230186	+	0.398694i
$552$		0			0
$553$		0			0
$554$	3.38062	+	1.95180i	0.143629	+	0.0829241i
$555$		0			0
$556$			25.5219i			1.08237i
$557$	−31.1339	−	17.9752i	−1.31919	−	0.761632i	−0.335588	−	0.942009i	$-0.608935\pi$
$557$	−31.1339	−	17.9752i	−1.31919	−	0.761632i	−0.983598	+	0.180377i	$0.942268\pi$
$558$		0			0
$559$		−	9.66329i		−	0.408714i
$560$		0			0
$561$		0			0
$562$	−1.92868			−0.0813565
$563$	3.05554	+	5.29235i	0.128776	+	0.223046i	0.923202	−	0.384314i	$-0.125562\pi$
$563$	3.05554	+	5.29235i	0.128776	+	0.223046i	−0.794427	+	0.607360i	$0.792229\pi$
$564$		0			0
$565$	5.74354	+	3.31603i	0.241633	+	0.139507i
$566$	−0.873481			−0.0367151
$567$		0			0
$568$	−15.6566			−0.656935
$569$	−16.7182	−	9.65223i	−0.700861	−	0.404642i	0.106807	−	0.994280i	$-0.465937\pi$
$569$	−16.7182	−	9.65223i	−0.700861	−	0.404642i	−0.807668	+	0.589637i	$0.799271\pi$
$570$		0			0
$571$	−6.36118	−	11.0179i	−0.266207	−	0.461085i	0.701672	−	0.712500i	$-0.252437\pi$
$571$	−6.36118	−	11.0179i	−0.266207	−	0.461085i	−0.967879	+	0.251416i	$0.919104\pi$
$572$	17.4726			0.730567
$573$		0			0
$574$		0			0
$575$		−	13.0118i		−	0.542628i
$576$		0			0
$577$	−7.05520	−	4.07332i	−0.293712	−	0.169575i	0.345903	−	0.938270i	$-0.387573\pi$
$577$	−7.05520	−	4.07332i	−0.293712	−	0.169575i	−0.639615	+	0.768696i	$0.720906\pi$
$578$			1.66773i			0.0693683i
$579$		0			0
$580$	−21.5066	−	12.4168i	−0.893012	−	0.515581i
$581$		0			0
$582$		0			0
$583$	11.2355	−	19.4605i	0.465328	−	0.805973i
$584$	0.568693	−	0.985005i	0.0235327	−	0.0407598i
$585$		0			0
$586$	−1.54270	+	0.890680i	−0.0637285	+	0.0367937i
$587$	−12.3041	−	21.3113i	−0.507843	−	0.879610i	−0.999959	−	0.00908019i	$-0.997110\pi$
$587$	−12.3041	−	21.3113i	−0.507843	−	0.879610i	0.492116	−	0.870530i	$-0.336224\pi$
$588$		0			0
$589$	−0.602354	+	1.04331i	−0.0248196	+	0.0429888i
$590$		−	4.21515i		−	0.173535i
$591$		0			0
$592$	27.1743			1.11686
$593$	18.9321	+	32.7913i	0.777447	+	1.34658i	0.933409	+	0.358814i	$0.116819\pi$
$593$	18.9321	+	32.7913i	0.777447	+	1.34658i	−0.155962	+	0.987763i	$0.549848\pi$
$594$		0			0
$595$		0			0
$596$	14.0428	−	8.10762i	0.575216	−	0.332101i
$597$		0			0
$598$	−1.77761	+	1.02631i	−0.0726920	+	0.0419687i
$599$	−9.22572	+	5.32647i	−0.376953	+	0.217634i	−0.676492	−	0.736450i	$-0.736501\pi$
$599$	−9.22572	+	5.32647i	−0.376953	+	0.217634i	0.299539	+	0.954084i	$0.403167\pi$
$600$		0			0
$601$	39.8636	−	23.0153i	1.62607	−	0.938812i	0.640821	−	0.767691i	$-0.278594\pi$
$601$	39.8636	−	23.0153i	1.62607	−	0.938812i	0.985250	−	0.171122i	$-0.0547391\pi$
$602$		0			0
$603$		0			0
$604$	3.21161	+	5.56267i	0.130679	+	0.226342i
$605$	−12.7996			−0.520378
$606$		0			0
$607$			4.31931i			0.175315i	0.996151	+	0.0876576i	$0.0279381\pi$
$607$			4.31931i			0.175315i	−0.996151	+	0.0876576i	$0.972062\pi$
$608$	4.23745	−	7.33947i	0.171851	−	0.297655i
$609$		0			0
$610$	0.719539	+	1.24628i	0.0291333	+	0.0504603i
$611$	8.22672	−	4.74970i	0.332818	−	0.192152i
$612$		0			0
$613$	14.3838	−	24.9135i	0.580956	−	1.00624i	−0.414411	−	0.910090i	$-0.636012\pi$
$613$	14.3838	−	24.9135i	0.580956	−	1.00624i	0.995366	−	0.0961549i	$-0.0306544\pi$
$614$	−3.17423	+	5.49793i	−0.128102	+	0.221878i
$615$		0			0
$616$		0			0
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	0.481051	−	0.876693i	$-0.340255\pi$
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	−0.518713	+	0.854949i	$0.673589\pi$
$618$		0			0
$619$			7.58787i			0.304982i	0.988305	+	0.152491i	$0.0487295\pi$
$619$			7.58787i			0.304982i	−0.988305	+	0.152491i	$0.951270\pi$
$620$	−2.39755	−	1.38423i	−0.0962881	−	0.0555920i
$621$		0			0
$622$			3.23944i			0.129890i
$623$		0			0
$624$		0			0
$625$	−27.7708			−1.11083
$626$	1.99158	+	3.44952i	0.0795996	+	0.137871i
$627$		0			0
$628$	−27.6904	−	15.9871i	−1.10497	−	0.637953i
$629$	−26.2082			−1.04499
$630$		0			0
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$	−9.24118	−	5.33540i	−0.367595	−	0.212231i
$633$		0			0
$634$	1.63893	+	2.83871i	0.0650903	+	0.112740i
$635$	8.41235			0.333834
$636$		0			0
$637$		0			0
$638$		−	4.85564i		−	0.192237i
$639$		0			0
$640$	22.3015	+	12.8758i	0.881544	+	0.508960i
$641$			31.0879i			1.22790i	0.789346	+	0.613949i	$0.210420\pi$
$641$			31.0879i			1.22790i	−0.789346	+	0.613949i	$0.789580\pi$
$642$		0			0
$643$	0.977928	+	0.564607i	0.0385657	+	0.0222659i	0.519159	−	0.854678i	$-0.326245\pi$
$643$	0.977928	+	0.564607i	0.0385657	+	0.0222659i	−0.480593	+	0.876944i	$0.659579\pi$
$644$		0			0
$645$		0			0
$646$	−1.26011	+	2.18257i	−0.0495782	+	0.0858719i
$647$	13.5992	−	23.5545i	0.534640	−	0.926023i	−0.464541	−	0.885552i	$-0.653781\pi$
$647$	13.5992	−	23.5545i	0.534640	−	0.926023i	0.999181	−	0.0404713i	$-0.0128859\pi$
$648$		0			0
$649$	−15.8162	+	9.13148i	−0.620839	+	0.358442i
$650$	−1.50300	−	2.60328i	−0.0589526	−	0.102109i
$651$		0			0
$652$	24.2386	−	41.9824i	0.949256	−	1.64416i
$653$			22.2892i			0.872243i	0.899888	+	0.436121i	$0.143648\pi$
$653$			22.2892i			0.872243i	−0.899888	+	0.436121i	$0.856352\pi$
$654$		0			0
$655$	−22.8854			−0.894205
$656$	−10.9123	−	18.9007i	−0.426055	−	0.737949i
$657$		0			0
$658$		0			0
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	−0.342641	−	0.939467i	$-0.611321\pi$
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	0.642282	+	0.766469i	$0.277988\pi$
$660$		0			0
$661$	−16.7724	+	9.68352i	−0.652369	+	0.376645i	−0.789363	−	0.613926i	$-0.789589\pi$
$661$	−16.7724	+	9.68352i	−0.652369	+	0.376645i	0.136994	+	0.990572i	$0.456256\pi$
$662$	4.84060	−	2.79472i	0.188135	−	0.108620i
$663$		0			0
$664$	−10.9434	+	6.31819i	−0.424687	+	0.245193i
$665$		0			0
$666$		0			0
$667$	−6.31999	−	10.9465i	−0.244711	−	0.423852i
$668$	3.35204			0.129694
$669$		0			0
$670$		−	1.41702i		−	0.0547444i
$671$	3.11754	−	5.39973i	0.120351	−	0.208454i
$672$		0			0
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	0.998154	−	0.0607292i	$-0.0193426\pi$
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	−0.551670	+	0.834062i	$0.686009\pi$
$674$	1.69310	−	0.977511i	0.0652157	−	0.0376523i
$675$		0			0
$676$	−7.18476	+	12.4444i	−0.276337	+	0.478630i
$677$	1.56346	−	2.70800i	0.0600887	−	0.104077i	−0.834416	−	0.551135i	$-0.814195\pi$
$677$	1.56346	−	2.70800i	0.0600887	−	0.104077i	0.894505	+	0.447058i	$0.147528\pi$
$678$		0			0
$679$		0			0
$680$	−10.2576	−	5.92220i	−0.393359	−	0.227106i
$681$		0			0
$682$		−	0.541307i		−	0.0207277i
$683$	−27.1966	−	15.7020i	−1.04065	−	0.600819i	−0.120632	−	0.992697i	$-0.538492\pi$
$683$	−27.1966	−	15.7020i	−1.04065	−	0.600819i	−0.920017	+	0.391878i	$0.871825\pi$
$684$		0			0
$685$		−	37.3621i		−	1.42753i
$686$		0			0
$687$		0			0
$688$	−14.3892			−0.548585
$689$	−6.75691	−	11.7033i	−0.257418	−	0.445860i
$690$		0			0
$691$	−38.2557	−	22.0869i	−1.45532	−	0.840227i	−0.456540	−	0.889703i	$-0.650912\pi$
$691$	−38.2557	−	22.0869i	−1.45532	−	0.840227i	−0.998775	+	0.0494760i	$0.984245\pi$
$692$	−45.7868			−1.74055
$693$		0			0
$694$	7.83164			0.297285
$695$	−35.3463	−	20.4072i	−1.34076	−	0.774089i
$696$		0			0
$697$	10.5244	+	18.2288i	0.398640	+	0.690465i
$698$	−6.96086			−0.263472
$699$		0			0
$700$		0			0
$701$			9.69906i			0.366328i	0.983082	+	0.183164i	$0.0586340\pi$
$701$			9.69906i			0.366328i	−0.983082	+	0.183164i	$0.941366\pi$
$702$		0			0
$703$	17.1876	+	9.92326i	0.648242	+	0.374263i
$704$		−	23.3840i		−	0.881316i
$705$		0			0
$706$	1.16775	+	0.674202i	0.0439490	+	0.0253739i
$707$		0			0
$708$		0			0
$709$	0.548932	−	0.950778i	0.0206156	−	0.0357072i	−0.855534	−	0.517747i	$-0.826771\pi$
$709$	0.548932	−	0.950778i	0.0206156	−	0.0357072i	0.876149	+	0.482040i	$0.160104\pi$
$710$	6.12132	−	10.6024i	0.229729	−	0.397903i
$711$		0			0
$712$	4.29977	−	2.48247i	0.161141	−	0.0930346i
$713$	−0.704553	−	1.22032i	−0.0263857	−	0.0457014i
$714$		0			0
$715$	−13.9710	+	24.1985i	−0.522486	+	0.904972i
$716$		−	48.5815i		−	1.81558i
$717$		0			0
$718$	−1.80165			−0.0672371
$719$	−11.3648	−	19.6844i	−0.423835	−	0.734103i	0.572476	−	0.819921i	$-0.305983\pi$
$719$	−11.3648	−	19.6844i	−0.423835	−	0.734103i	−0.996311	+	0.0858183i	$0.972650\pi$
$720$		0			0
$721$		0			0
$722$	−3.18269	+	1.83753i	−0.118448	+	0.0683858i
$723$		0			0
$724$	37.1280	−	21.4359i	1.37985	−	0.796658i
$725$	16.0310	−	9.25550i	0.595376	−	0.343741i
$726$		0			0
$727$	−3.47919	+	2.00871i	−0.129036	+	0.0744990i	−0.563129	−	0.826369i	$-0.690402\pi$
$727$	−3.47919	+	2.00871i	−0.129036	+	0.0744990i	0.434093	+	0.900868i	$0.357069\pi$
$728$		0			0
$729$		0			0
$730$	0.444689	+	0.770224i	0.0164587	+	0.0285073i
$731$	13.8777			0.513285
$732$		0			0
$733$		−	8.31602i		−	0.307159i	−0.988136	−	0.153580i	$-0.950920\pi$
$733$		−	8.31602i		−	0.307159i	0.988136	−	0.153580i	$-0.0490801\pi$
$734$	3.88296	−	6.72549i	0.143323	−	0.248242i
$735$		0			0
$736$	4.95640	+	8.58473i	0.182695	+	0.316437i
$737$	−5.31698	+	3.06976i	−0.195854	+	0.113076i
$738$		0			0
$739$	−2.28507	+	3.95785i	−0.0840576	+	0.145592i	−0.904989	−	0.425434i	$-0.860121\pi$
$739$	−2.28507	+	3.95785i	−0.0840576	+	0.145592i	0.820932	+	0.571026i	$0.193455\pi$
$740$	−22.8040	+	39.4976i	−0.838290	+	1.45196i
$741$		0			0
$742$		0			0
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	0.471998	−	0.881600i	$-0.343533\pi$
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	−0.527489	+	0.849562i	$0.676866\pi$
$744$		0			0
$745$			25.9312i			0.950046i
$746$	5.11954	+	2.95577i	0.187440	+	0.108218i
$747$		0			0
$748$			25.0929i			0.917486i
$749$		0			0
$750$		0			0
$751$	5.83293			0.212847			0.106423	−	0.994321i	$-0.466060\pi$
$751$	5.83293			0.212847			0.106423	+	0.994321i	$0.466060\pi$
$752$	−7.07260	−	12.2501i	−0.257911	−	0.446715i
$753$		0			0
$754$	−2.52890	−	1.46006i	−0.0920970	−	0.0531723i
$755$	−10.2719			−0.373834
$756$		0			0
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$	−4.44255	−	2.56491i	−0.161361	−	0.0931617i
$759$		0			0
$760$	4.48466	+	7.76766i	0.162676	+	0.281763i
$761$	0.586863			0.0212738			0.0106369	−	0.999943i	$-0.496614\pi$
$761$	0.586863			0.0212738			0.0106369	+	0.999943i	$0.496614\pi$
$762$		0			0
$763$		0			0
$764$		−	8.20750i		−	0.296937i
$765$		0			0
$766$	−7.14208	−	4.12348i	−0.258054	−	0.148987i
$767$			10.9831i			0.396577i
$768$		0			0
$769$	−45.1905	−	26.0907i	−1.62961	−	0.940856i	−0.984208	−	0.177014i	$-0.943356\pi$
$769$	−45.1905	−	26.0907i	−1.62961	−	0.940856i	−0.645403	−	0.763843i	$-0.723310\pi$
$770$		0			0
$771$		0			0
$772$	22.3369	−	38.6887i	0.803923	−	1.39244i
$773$	16.3906	−	28.3894i	0.589530	−	1.02110i	−0.404764	−	0.914421i	$-0.632646\pi$
$773$	16.3906	−	28.3894i	0.589530	−	1.02110i	0.994294	−	0.106674i	$-0.0340202\pi$
$774$		0			0
$775$	1.78714	−	1.03180i	0.0641959	−	0.0370635i
$776$	−3.31206	−	5.73666i	−0.118896	−	0.205934i
$777$		0			0
$778$	5.03093	−	8.71383i	0.180368	−	0.312406i
$779$		−	15.9395i		−	0.571090i
$780$		0			0
$781$	−53.0436			−1.89805
$782$	−1.47390	−	2.55287i	−0.0527066	−	0.0912906i
$783$		0			0
$784$		0			0
$785$	44.2821	−	25.5663i	1.58050	−	0.912500i
$786$		0			0
$787$	35.5013	−	20.4967i	1.26549	−	0.730628i	0.291355	−	0.956615i	$-0.405894\pi$
$787$	35.5013	−	20.4967i	1.26549	−	0.730628i	0.974130	+	0.225987i	$0.0725605\pi$
$788$	31.1251	−	17.9701i	1.10879	−	0.640158i
$789$		0			0
$790$	7.22614	−	4.17201i	0.257095	−	0.148434i
$791$		0			0
$792$		0			0
$793$	−1.87485	−	3.24733i	−0.0665778	−	0.115316i
$794$	3.83195			0.135991
$795$		0			0
$796$		−	8.68244i		−	0.307741i
$797$	17.0441	−	29.5213i	0.603734	−	1.04570i	−0.388516	−	0.921442i	$-0.627012\pi$
$797$	17.0441	−	29.5213i	0.603734	−	1.04570i	0.992250	−	0.124256i	$-0.0396544\pi$
$798$		0			0
$799$	6.82116	+	11.8146i	0.241315	+	0.417971i
$800$	−12.5722	+	7.25854i	−0.444493	+	0.256628i
$801$		0			0
$802$	−2.69672	+	4.67086i	−0.0952245	+	0.164934i
$803$	1.92670	−	3.33714i	0.0679918	−	0.117765i
$804$		0			0
$805$		0			0
$806$	−0.281922	−	0.162768i	−0.00993027	−	0.00573324i
$807$		0			0
$808$		−	19.7334i		−	0.694219i
$809$	−6.01547	−	3.47304i	−0.211493	−	0.122105i	0.390512	−	0.920598i	$-0.372298\pi$
$809$	−6.01547	−	3.47304i	−0.211493	−	0.122105i	−0.602005	+	0.798492i	$0.705631\pi$
$810$		0			0
$811$		−	39.8573i		−	1.39958i	−0.714350	−	0.699789i	$-0.753277\pi$
$811$		−	39.8573i		−	1.39958i	0.714350	−	0.699789i	$-0.246723\pi$
$812$		0			0
$813$		0			0
$814$	−8.91756			−0.312560
$815$	38.7620	+	67.1378i	1.35777	+	2.35173i
$816$		0			0
$817$	−9.10111	−	5.25453i	−0.318408	−	0.183833i
$818$	1.90071			0.0664566
$819$		0			0
$820$	36.6294			1.27915
$821$	36.4612	+	21.0509i	1.27250	+	0.734680i	0.975459	−	0.220183i	$-0.0706655\pi$
$821$	36.4612	+	21.0509i	1.27250	+	0.734680i	0.297045	+	0.954863i	$0.403999\pi$
$822$		0			0
$823$	−16.3411	−	28.3035i	−0.569614	−	0.986600i	−0.996604	−	0.0823435i	$-0.973760\pi$
$823$	−16.3411	−	28.3035i	−0.569614	−	0.986600i	0.426990	−	0.904256i	$-0.359574\pi$
$824$	11.2938			0.393438
$825$		0			0
$826$		0			0
$827$			31.4399i			1.09327i	0.837370	+	0.546637i	$0.184092\pi$
$827$			31.4399i			1.09327i	−0.837370	+	0.546637i	$0.815908\pi$
$828$		0			0
$829$	−35.7122	−	20.6185i	−1.24034	−	0.716109i	−0.271174	−	0.962530i	$-0.587412\pi$
$829$	−35.7122	−	20.6185i	−1.24034	−	0.716109i	−0.969163	+	0.246421i	$0.920745\pi$
$830$		−	9.88102i		−	0.342975i
$831$		0			0
$832$	−12.1788	−	7.03141i	−0.422222	−	0.243770i
$833$		0			0
$834$		0			0
$835$	−2.68027	+	4.64236i	−0.0927546	+	0.160656i
$836$	9.50094	−	16.4561i	0.328597	−	0.569147i
$837$		0			0
$838$	−3.62173	+	2.09100i	−0.125110	+	0.0722326i
$839$	4.04385	+	7.00416i	0.139609	+	0.241810i	0.927349	−	0.374198i	$-0.122082\pi$
$839$	4.04385	+	7.00416i	0.139609	+	0.241810i	−0.787740	+	0.616009i	$0.788749\pi$
$840$		0			0
$841$	−5.50894	+	9.54177i	−0.189963	+	0.329026i
$842$			8.91707i			0.307302i
$843$		0			0
$844$	13.1715			0.453382
$845$	−11.4898	−	19.9009i	−0.395260	−	0.684611i
$846$		0			0
$847$		0			0
$848$	−17.4269	+	10.0615i	−0.598444	+	0.345512i
$849$		0			0
$850$	3.73863	−	2.15850i	0.128234	−	0.0740359i
$851$	−20.1037	+	11.6069i	−0.689147	+	0.397879i
$852$		0			0
$853$	−24.5887	+	14.1963i	−0.841900	+	0.486071i	−0.857910	−	0.513801i	$-0.828237\pi$
$853$	−24.5887	+	14.1963i	−0.841900	+	0.486071i	0.0160098	+	0.999872i	$0.494904\pi$
$854$		0			0
$855$		0			0
$856$	1.99536	+	3.45606i	0.0682000	+	0.118126i
$857$	−51.3174			−1.75297			−0.876485	−	0.481429i	$-0.840118\pi$
$857$	−51.3174			−1.75297			−0.876485	+	0.481429i	$0.840118\pi$
$858$		0			0
$859$			16.7702i			0.572191i	0.958201	+	0.286096i	$0.0923575\pi$
$859$			16.7702i			0.572191i	−0.958201	+	0.286096i	$0.907642\pi$
$860$	12.0751	−	20.9146i	0.411756	−	0.713183i
$861$		0			0
$862$	−0.360816	−	0.624951i	−0.0122894	−	0.0212859i
$863$	−14.2380	+	8.22033i	−0.484668	+	0.279823i	−0.722360	−	0.691517i	$-0.756943\pi$
$863$	−14.2380	+	8.22033i	−0.484668	+	0.279823i	0.237692	+	0.971341i	$0.423609\pi$
$864$		0			0
$865$	36.6109	−	63.4119i	1.24481	−	2.15607i
$866$	1.83000	−	3.16965i	0.0621859	−	0.107709i
$867$		0			0
$868$		0			0
$869$	−31.3086	−	18.0760i	−1.06207	−	0.613188i
$870$		0			0
$871$			3.69223i			0.125106i
$872$	−1.21726	−	0.702787i	−0.0412217	−	0.0237994i
$873$		0			0
$874$			2.23226i			0.0755074i
$875$		0			0
$876$		0			0
$877$	6.12350			0.206776			0.103388	−	0.994641i	$-0.467032\pi$
$877$	6.12350			0.206776			0.103388	+	0.994641i	$0.467032\pi$
$878$	2.57577	+	4.46137i	0.0869281	+	0.150564i
$879$		0			0
$880$	36.0330	+	20.8037i	1.21467	+	0.701292i
$881$	−41.3283			−1.39238			−0.696192	−	0.717855i	$-0.745124\pi$
$881$	−41.3283			−1.39238			−0.696192	+	0.717855i	$0.745124\pi$
$882$		0			0
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$	13.0688	+	7.54526i	0.439550	+	0.253775i
$885$		0			0
$886$	−1.32310	−	2.29167i	−0.0444502	−	0.0769901i
$887$	6.70071			0.224988			0.112494	−	0.993652i	$-0.464116\pi$
$887$	6.70071			0.224988			0.112494	+	0.993652i	$0.464116\pi$
$888$		0			0
$889$		0			0
$890$			3.88234i			0.130136i
$891$		0			0
$892$	−10.6624	−	6.15591i	−0.357002	−	0.206115i
$893$		−	10.3308i		−	0.345708i
$894$		0			0
$895$	67.2823	+	38.8455i	2.24900	+	1.29846i
$896$		0			0
$897$		0			0
$898$	4.52735	−	7.84160i	0.151080	−	0.261678i
$899$	1.00232	−	1.73608i	0.0334294	−	0.0579014i
$900$		0			0
$901$	16.8074	−	9.70376i	0.559936	−	0.323279i
$902$	3.58101	+	6.20249i	0.119235	+	0.206520i
$903$		0			0
$904$	1.24622	−	2.15852i	0.0414487	−	0.0717912i
$905$			68.5600i			2.27901i
$906$		0			0
$907$	20.2988			0.674010			0.337005	−	0.941503i	$-0.390586\pi$
$907$	20.2988			0.674010			0.337005	+	0.941503i	$0.390586\pi$
$908$	18.8873	+	32.7138i	0.626798	+	1.08565i
$909$		0			0
$910$		0			0
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.0967861	−	0.995305i	$-0.469144\pi$
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.910353	+	0.413833i	$0.135810\pi$
$912$		0			0
$913$	−37.0757	+	21.4057i	−1.22703	+	0.708425i
$914$	−3.51936	+	2.03190i	−0.116410	+	0.0672093i
$915$		0			0
$916$	18.0756	−	10.4359i	0.597233	−	0.344813i
$917$		0			0
$918$		0			0
$919$	−16.9132	−	29.2946i	−0.557916	−	0.966339i	−0.997670	−	0.0682206i	$-0.978268\pi$
$919$	−16.9132	−	29.2946i	−0.557916	−	0.966339i	0.439754	−	0.898118i	$-0.355066\pi$
$920$	−10.4911			−0.345882
$921$		0			0
$922$		−	3.62629i		−	0.119425i
$923$	−15.9499	+	27.6260i	−0.524996	+	0.909320i
$924$		0			0
$925$	−16.9981	−	29.4415i	−0.558893	−	0.968031i
$926$	3.24639	−	1.87431i	0.106683	−	0.0615935i
$927$		0			0
$928$	−7.05115	+	12.2130i	−0.231465	+	0.400910i
$929$	16.0586	−	27.8142i	0.526864	−	0.912555i	−0.472646	−	0.881252i	$-0.656701\pi$
$929$	16.0586	−	27.8142i	0.526864	−	0.912555i	0.999510	−	0.0313029i	$-0.00996565\pi$
$930$		0			0
$931$		0			0
$932$	−34.4348	−	19.8810i	−1.12795	−	0.651222i
$933$		0			0
$934$			3.22668i			0.105580i
$935$	−34.7520	−	20.0641i	−1.13651	−	0.656166i
$936$		0			0
$937$			13.9224i			0.454824i	0.973799	+	0.227412i	$0.0730263\pi$
$937$			13.9224i			0.454824i	−0.973799	+	0.227412i	$0.926974\pi$
$938$		0			0
$939$		0			0
$940$	23.7405			0.774331
$941$	28.6047	+	49.5448i	0.932487	+	1.61512i	0.779054	+	0.626956i	$0.215700\pi$
$941$	28.6047	+	49.5448i	0.932487	+	1.61512i	0.153433	+	0.988159i	$0.450967\pi$
$942$		0			0
$943$	16.1460	+	9.32192i	0.525787	+	0.303563i
$944$	16.3545			0.532294
$945$		0			0
$946$	4.72200			0.153525
$947$	−29.8658	−	17.2430i	−0.970509	−	0.560324i	−0.0711175	−	0.997468i	$-0.522657\pi$
$947$	−29.8658	−	17.2430i	−0.970509	−	0.560324i	−0.899391	+	0.437144i	$0.855990\pi$
$948$		0			0
$949$	−1.15869	−	2.00691i	−0.0376128	−	0.0651472i
$950$	−3.26910			−0.106064
$951$		0			0
$952$		0			0
$953$		−	2.58761i		−	0.0838209i	−0.999121	−	0.0419104i	$-0.986656\pi$
$953$		−	2.58761i		−	0.0838209i	0.999121	−	0.0419104i	$-0.0133444\pi$
$954$		0			0
$955$	11.3669	+	6.56267i	0.367824	+	0.212363i
$956$			52.3119i			1.69189i
$957$		0			0
$958$	−2.84900	−	1.64487i	−0.0920470	−	0.0531434i
$959$		0			0
$960$		0			0
$961$	−15.3883	+	26.6532i	−0.496396	+	0.859782i
$962$	−2.68145	+	4.64441i	−0.0864535	+	0.149742i
$963$		0			0
$964$	35.3426	−	20.4051i	1.13831	−	0.657203i
$965$	35.7209	+	61.8704i	1.14990	+	1.99168i
$966$		0			0
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	−0.817585	−	0.575808i	$-0.804688\pi$
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	0.907457	+	0.420145i	$0.138021\pi$
$968$			4.81030i			0.154609i
$969$		0			0
$970$	5.17973			0.166311
$971$	−8.01661	−	13.8852i	−0.257265	−	0.445597i	0.708243	−	0.705969i	$-0.249488\pi$
$971$	−8.01661	−	13.8852i	−0.257265	−	0.445597i	−0.965508	+	0.260372i	$0.916155\pi$
$972$		0			0
$973$		0			0
$974$	−0.755007	+	0.435904i	−0.0241920	+	0.0139673i
$975$		0			0
$976$	−4.83547	+	2.79176i	−0.154780	+	0.0893621i
$977$	38.0208	−	21.9513i	1.21639	−	0.702285i	0.252248	−	0.967663i	$-0.418830\pi$
$977$	38.0208	−	21.9513i	1.21639	−	0.702285i	0.964144	+	0.265378i	$0.0854967\pi$
$978$		0			0
$979$	14.5674	−	8.41048i	0.465576	−	0.268800i
$980$		0			0
$981$		0			0
$982$	3.42377	+	5.93015i	0.109257	+	0.189239i
$983$	−18.1762			−0.579730			−0.289865	−	0.957068i	$-0.593610\pi$
$983$	−18.1762			−0.579730			−0.289865	+	0.957068i	$0.593610\pi$
$984$		0			0
$985$			57.4751i			1.83131i
$986$	2.09683	−	3.63181i	0.0667766	−	0.115660i
$987$		0			0
$988$	−5.71374	−	9.89649i	−0.181778	−	0.314849i
$989$	10.6453	−	6.14604i	0.338499	−	0.195433i
$990$		0			0
$991$	−23.8146	+	41.2481i	−0.756496	+	1.31029i	0.188131	+	0.982144i	$0.439757\pi$
$991$	−23.8146	+	41.2481i	−0.756496	+	1.31029i	−0.944627	+	0.328145i	$0.893576\pi$
$992$	−0.786063	+	1.36150i	−0.0249575	+	0.0432277i
$993$		0			0
$994$		0			0
$995$	12.0246	+	6.94242i	0.381206	+	0.220090i
$996$		0			0
$997$		−	32.8902i		−	1.04164i	−0.853666	−	0.520822i	$-0.825626\pi$
$997$		−	32.8902i		−	1.04164i	0.853666	−	0.520822i	$-0.174374\pi$
$998$	−1.16711	−	0.673830i	−0.0369442	−	0.0213297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.b.962.3		10
3.2	odd	2		441.2.s.b.374.3		10
7.2	even	3		189.2.i.b.152.3		10
7.3	odd	6		1323.2.o.d.881.3		10
7.4	even	3		1323.2.o.c.881.3		10
7.5	odd	6		1323.2.i.b.1097.3		10
7.6	odd	2		189.2.s.b.17.3		10
9.2	odd	6		1323.2.i.b.521.3		10
9.7	even	3		441.2.i.b.227.3		10
21.2	odd	6		63.2.i.b.5.3	✓	10
21.5	even	6		441.2.i.b.68.3		10
21.11	odd	6		441.2.o.d.293.3		10
21.17	even	6		441.2.o.c.293.3		10
21.20	even	2		63.2.s.b.59.3	yes	10
28.23	odd	6		3024.2.ca.b.2609.1		10
28.27	even	2		3024.2.df.b.17.1		10
63.2	odd	6		189.2.s.b.89.3		10
63.11	odd	6		1323.2.o.d.440.3		10
63.13	odd	6		567.2.p.d.80.3		10
63.16	even	3		63.2.s.b.47.3	yes	10
63.20	even	6		189.2.i.b.143.3		10
63.23	odd	6		567.2.p.d.404.3		10
63.25	even	3		441.2.o.c.146.3		10
63.34	odd	6		63.2.i.b.38.3	yes	10
63.38	even	6		1323.2.o.c.440.3		10
63.41	even	6		567.2.p.c.80.3		10
63.47	even	6	inner	1323.2.s.b.656.3		10
63.52	odd	6		441.2.o.d.146.3		10
63.58	even	3		567.2.p.c.404.3		10
63.61	odd	6		441.2.s.b.362.3		10
84.23	even	6		1008.2.ca.b.257.4		10
84.83	odd	2		1008.2.df.b.689.5		10
252.79	odd	6		1008.2.df.b.929.5		10
252.83	odd	6		3024.2.ca.b.2033.1		10
252.191	even	6		3024.2.df.b.1601.1		10
252.223	even	6		1008.2.ca.b.353.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	21.2	odd	6
63.2.i.b.38.3	yes	10	63.34	odd	6
63.2.s.b.47.3	yes	10	63.16	even	3
63.2.s.b.59.3	yes	10	21.20	even	2
189.2.i.b.143.3		10	63.20	even	6
189.2.i.b.152.3		10	7.2	even	3
189.2.s.b.17.3		10	7.6	odd	2
189.2.s.b.89.3		10	63.2	odd	6
441.2.i.b.68.3		10	21.5	even	6
441.2.i.b.227.3		10	9.7	even	3
441.2.o.c.146.3		10	63.25	even	3
441.2.o.c.293.3		10	21.17	even	6
441.2.o.d.146.3		10	63.52	odd	6
441.2.o.d.293.3		10	21.11	odd	6
441.2.s.b.362.3		10	63.61	odd	6
441.2.s.b.374.3		10	3.2	odd	2
567.2.p.c.80.3		10	63.41	even	6
567.2.p.c.404.3		10	63.58	even	3
567.2.p.d.80.3		10	63.13	odd	6
567.2.p.d.404.3		10	63.23	odd	6
1008.2.ca.b.257.4		10	84.23	even	6
1008.2.ca.b.353.4		10	252.223	even	6
1008.2.df.b.689.5		10	84.83	odd	2
1008.2.df.b.929.5		10	252.79	odd	6
1323.2.i.b.521.3		10	9.2	odd	6
1323.2.i.b.1097.3		10	7.5	odd	6
1323.2.o.c.440.3		10	63.38	even	6
1323.2.o.c.881.3		10	7.4	even	3
1323.2.o.d.440.3		10	63.11	odd	6
1323.2.o.d.881.3		10	7.3	odd	6
1323.2.s.b.656.3		10	63.47	even	6	inner
1323.2.s.b.962.3		10	1.1	even	1	trivial
3024.2.ca.b.2033.1		10	252.83	odd	6
3024.2.ca.b.2609.1		10	28.23	odd	6
3024.2.df.b.17.1		10	28.27	even	2
3024.2.df.b.1601.1		10	252.191	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.254498 + 0.146935i) q^{2} +(-0.956820 - 1.65726i) q^{4} +3.06027 q^{5} -1.15010i q^{8} +O(q^{10})\)	\(q+(0.254498 + 0.146935i) q^{2} +(-0.956820 - 1.65726i) q^{4} +3.06027 q^{5} -1.15010i q^{8} +(0.778834 + 0.449660i) q^{10} -3.89647i q^{11} +(-2.02935 - 1.17164i) q^{13} +(-1.74465 + 3.02182i) q^{16} +(1.68263 - 2.91440i) q^{17} +(-2.20696 + 1.27419i) q^{19} +(-2.92813 - 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} -2.98075i q^{23} +4.36525 q^{25} +(-0.344311 - 0.596363i) q^{26} +(3.67241 - 2.12027i) q^{29} +(0.409400 - 0.236367i) q^{31} +(-2.88005 + 1.66280i) q^{32} +(0.856452 - 0.494473i) q^{34} +(-3.89395 - 6.74451i) q^{37} -0.748891 q^{38} -3.51962i q^{40} +(-3.12737 + 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} +(-6.45748 + 3.72823i) q^{44} +(0.437976 - 0.758597i) q^{46} +(-2.02694 + 3.51076i) q^{47} +(1.11095 + 0.641408i) q^{50} +4.48421i q^{52} +(4.99439 + 2.88351i) q^{53} -11.9243i q^{55} +1.24616 q^{58} +(-2.34352 - 4.05910i) q^{59} +(1.38580 + 0.800092i) q^{61} +0.138922 q^{62} +6.00131 q^{64} +(-6.21035 - 3.58555i) q^{65} +(-0.787831 - 1.36456i) q^{67} -6.43989 q^{68} -13.6132i q^{71} +(0.856452 + 0.494473i) q^{73} -2.28862i q^{74} +(4.22333 + 2.43834i) q^{76} +(4.63908 - 8.03512i) q^{79} +(-5.33910 + 9.24760i) q^{80} +(-1.59182 + 0.919038i) q^{82} +(-5.49361 - 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +1.21186i q^{86} -4.48133 q^{88} +(2.15849 + 3.73861i) q^{89} +(-4.93989 + 2.85205i) q^{92} +(-1.03171 + 0.595655i) q^{94} +(-6.75390 + 3.89937i) q^{95} +(4.98797 - 2.87980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 + 15 * q^10 - 6 * q^13 - 6 * q^16 - 12 * q^17 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 14 * q^25 + 3 * q^26 + 15 * q^29 + 9 * q^31 - 48 * q^32 - 3 * q^34 + 6 * q^37 + 36 * q^38 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 + 15 * q^47 - 3 * q^50 + 9 * q^53 - 16 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 - 54 * q^68 - 3 * q^73 - 9 * q^76 + 20 * q^79 - 30 * q^80 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 16 * q^88 + 24 * q^89 - 39 * q^92 + 3 * q^94 - 6 * q^97

Introduction

L-functions

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Database

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