LMFDB - Embedded newform 315.2.j.c.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.46
Dual form			315.2.j.c.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.633975i) q^{2} +(0.732051 - 1.26795i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.866025 + 2.50000i) q^{7} +2.53590 q^{8} +O(q^{10})$	\(q+(0.366025 + 0.633975i) q^{2} +(0.732051 - 1.26795i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.866025 + 2.50000i) q^{7} +2.53590 q^{8} +(-0.366025 + 0.633975i) q^{10} +(-1.36603 + 2.36603i) q^{11} +5.73205 q^{13} +(-1.90192 + 0.366025i) q^{14} +(-0.535898 - 0.928203i) q^{16} +(3.36603 - 5.83013i) q^{17} +(1.23205 + 2.13397i) q^{19} +1.46410 q^{20} -2.00000 q^{22} +(-0.633975 - 1.09808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.09808 + 3.63397i) q^{26} +(2.53590 + 2.92820i) q^{28} -6.19615 q^{29} +(-3.23205 + 5.59808i) q^{31} +(2.92820 - 5.07180i) q^{32} +4.92820 q^{34} +(-2.59808 + 0.500000i) q^{35} +(-3.59808 - 6.23205i) q^{37} +(-0.901924 + 1.56218i) q^{38} +(1.26795 + 2.19615i) q^{40} -2.73205 q^{41} -7.19615 q^{43} +(2.00000 + 3.46410i) q^{44} +(0.464102 - 0.803848i) q^{46} +(1.00000 + 1.73205i) q^{47} +(-5.50000 - 4.33013i) q^{49} -0.732051 q^{50} +(4.19615 - 7.26795i) q^{52} +(-4.19615 + 7.26795i) q^{53} -2.73205 q^{55} +(-2.19615 + 6.33975i) q^{56} +(-2.26795 - 3.92820i) q^{58} +(5.09808 - 8.83013i) q^{59} +(-2.00000 - 3.46410i) q^{61} -4.73205 q^{62} +2.14359 q^{64} +(2.86603 + 4.96410i) q^{65} +(-1.33013 + 2.30385i) q^{67} +(-4.92820 - 8.53590i) q^{68} +(-1.26795 - 1.46410i) q^{70} +4.19615 q^{71} +(2.33013 - 4.03590i) q^{73} +(2.63397 - 4.56218i) q^{74} +3.60770 q^{76} +(-4.73205 - 5.46410i) q^{77} +(-6.69615 - 11.5981i) q^{79} +(0.535898 - 0.928203i) q^{80} +(-1.00000 - 1.73205i) q^{82} +9.12436 q^{83} +6.73205 q^{85} +(-2.63397 - 4.56218i) q^{86} +(-3.46410 + 6.00000i) q^{88} +(-4.56218 - 7.90192i) q^{89} +(-4.96410 + 14.3301i) q^{91} -1.85641 q^{92} +(-0.732051 + 1.26795i) q^{94} +(-1.23205 + 2.13397i) q^{95} +1.07180 q^{97} +(0.732051 - 5.07180i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8	$ 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8} + 2 q^{10} - 2 q^{11} + 16 q^{13} - 18 q^{14} - 16 q^{16} + 10 q^{17} - 2 q^{19} - 8 q^{20} - 8 q^{22} - 6 q^{23} - 2 q^{25} - 2 q^{26} + 24 q^{28} - 4 q^{29} - 6 q^{31} - 16 q^{32} - 8 q^{34} - 4 q^{37} - 14 q^{38} + 12 q^{40} - 4 q^{41} - 8 q^{43} + 8 q^{44} - 12 q^{46} + 4 q^{47} - 22 q^{49} + 4 q^{50} - 4 q^{52} + 4 q^{53} - 4 q^{55} + 12 q^{56} - 16 q^{58} + 10 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} + 8 q^{65} + 12 q^{67} + 8 q^{68} - 12 q^{70} - 4 q^{71} - 8 q^{73} + 14 q^{74} + 56 q^{76} - 12 q^{77} - 6 q^{79} + 16 q^{80} - 4 q^{82} - 12 q^{83} + 20 q^{85} - 14 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{92} + 4 q^{94} + 2 q^{95} + 32 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8 + 2 * q^10 - 2 * q^11 + 16 * q^13 - 18 * q^14 - 16 * q^16 + 10 * q^17 - 2 * q^19 - 8 * q^20 - 8 * q^22 - 6 * q^23 - 2 * q^25 - 2 * q^26 + 24 * q^28 - 4 * q^29 - 6 * q^31 - 16 * q^32 - 8 * q^34 - 4 * q^37 - 14 * q^38 + 12 * q^40 - 4 * q^41 - 8 * q^43 + 8 * q^44 - 12 * q^46 + 4 * q^47 - 22 * q^49 + 4 * q^50 - 4 * q^52 + 4 * q^53 - 4 * q^55 + 12 * q^56 - 16 * q^58 + 10 * q^59 - 8 * q^61 - 12 * q^62 + 64 * q^64 + 8 * q^65 + 12 * q^67 + 8 * q^68 - 12 * q^70 - 4 * q^71 - 8 * q^73 + 14 * q^74 + 56 * q^76 - 12 * q^77 - 6 * q^79 + 16 * q^80 - 4 * q^82 - 12 * q^83 + 20 * q^85 - 14 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^92 + 4 * q^94 + 2 * q^95 + 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.366025	+	0.633975i	0.258819	+	0.448288i	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	0.366025	+	0.633975i	0.258819	+	0.448288i	−0.707107	+	0.707107i	$0.750000\pi$
$3$		0			0
$3$		0			0
$4$	0.732051	−	1.26795i	0.366025	−	0.633975i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$8$	2.53590			0.896575
$9$		0			0
$10$	−0.366025	+	0.633975i	−0.115747	+	0.200480i
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	−0.995094	−	0.0989291i	$-0.968458\pi$
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	0.583222	+	0.812313i	$0.301792\pi$
$12$		0			0
$13$	5.73205			1.58978			0.794892	−	0.606750i	$-0.207527\pi$
$13$	5.73205			1.58978			0.794892	+	0.606750i	$0.207527\pi$
$14$	−1.90192	+	0.366025i	−0.508311	+	0.0978244i
$15$		0			0
$16$	−0.535898	−	0.928203i	−0.133975	−	0.232051i
$17$	3.36603	−	5.83013i	0.816381	−	1.41401i	−0.0919509	−	0.995764i	$-0.529310\pi$
$17$	3.36603	−	5.83013i	0.816381	−	1.41401i	0.908332	−	0.418250i	$-0.137356\pi$
$18$		0			0
$19$	1.23205	+	2.13397i	0.282652	+	0.489567i	0.972037	−	0.234828i	$-0.0754526\pi$
$19$	1.23205	+	2.13397i	0.282652	+	0.489567i	−0.689385	+	0.724395i	$0.742119\pi$
$20$	1.46410			0.327383
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.09808	+	3.63397i	0.411467	+	0.712681i
$27$		0			0
$28$	2.53590	+	2.92820i	0.479240	+	0.553378i
$29$	−6.19615			−1.15060			−0.575298	−	0.817944i	$-0.695114\pi$
$29$	−6.19615			−1.15060			−0.575298	+	0.817944i	$0.695114\pi$
$30$		0			0
$31$	−3.23205	+	5.59808i	−0.580493	+	1.00544i	0.414927	+	0.909855i	$0.363807\pi$
$31$	−3.23205	+	5.59808i	−0.580493	+	1.00544i	−0.995421	+	0.0955896i	$0.969526\pi$
$32$	2.92820	−	5.07180i	0.517638	−	0.896575i
$33$		0			0
$34$	4.92820			0.845180
$35$	−2.59808	+	0.500000i	−0.439155	+	0.0845154i
$36$		0			0
$37$	−3.59808	−	6.23205i	−0.591520	−	1.02454i	−0.994028	−	0.109126i	$-0.965195\pi$
$37$	−3.59808	−	6.23205i	−0.591520	−	1.02454i	0.402508	−	0.915417i	$-0.368139\pi$
$38$	−0.901924	+	1.56218i	−0.146311	+	0.253419i
$39$		0			0
$40$	1.26795	+	2.19615i	0.200480	+	0.347242i
$41$	−2.73205			−0.426675			−0.213337	−	0.976979i	$-0.568433\pi$
$41$	−2.73205			−0.426675			−0.213337	+	0.976979i	$0.568433\pi$
$42$		0			0
$43$	−7.19615			−1.09740			−0.548701	−	0.836018i	$-0.684878\pi$
$43$	−7.19615			−1.09740			−0.548701	+	0.836018i	$0.684878\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$		0			0
$46$	0.464102	−	0.803848i	0.0684280	−	0.118521i
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	−0.732051			−0.103528
$51$		0			0
$52$	4.19615	−	7.26795i	0.581902	−	1.00788i
$53$	−4.19615	+	7.26795i	−0.576386	+	0.998330i	0.419504	+	0.907754i	$0.362204\pi$
$53$	−4.19615	+	7.26795i	−0.576386	+	0.998330i	−0.995890	+	0.0905760i	$0.971129\pi$
$54$		0			0
$55$	−2.73205			−0.368390
$56$	−2.19615	+	6.33975i	−0.293473	+	0.847184i
$57$		0			0
$58$	−2.26795	−	3.92820i	−0.297796	−	0.515798i
$59$	5.09808	−	8.83013i	0.663713	−	1.14958i	−0.315920	−	0.948786i	$-0.602313\pi$
$59$	5.09808	−	8.83013i	0.663713	−	1.14958i	0.979633	−	0.200799i	$-0.0643537\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	−4.73205			−0.600971
$63$		0			0
$64$	2.14359			0.267949
$65$	2.86603	+	4.96410i	0.355487	+	0.615721i
$66$		0			0
$67$	−1.33013	+	2.30385i	−0.162501	+	0.281460i	−0.935765	−	0.352624i	$-0.885289\pi$
$67$	−1.33013	+	2.30385i	−0.162501	+	0.281460i	0.773264	+	0.634084i	$0.218623\pi$
$68$	−4.92820	−	8.53590i	−0.597632	−	1.03513i
$69$		0			0
$70$	−1.26795	−	1.46410i	−0.151549	−	0.174994i
$71$	4.19615			0.497992			0.248996	−	0.968505i	$-0.419899\pi$
$71$	4.19615			0.497992			0.248996	+	0.968505i	$0.419899\pi$
$72$		0			0
$73$	2.33013	−	4.03590i	0.272721	−	0.472366i	−0.696837	−	0.717230i	$-0.745410\pi$
$73$	2.33013	−	4.03590i	0.272721	−	0.472366i	0.969558	+	0.244864i	$0.0787432\pi$
$74$	2.63397	−	4.56218i	0.306193	−	0.530342i
$75$		0			0
$76$	3.60770			0.413831
$77$	−4.73205	−	5.46410i	−0.539267	−	0.622692i
$78$		0			0
$79$	−6.69615	−	11.5981i	−0.753376	−	1.30489i	−0.946178	−	0.323648i	$-0.895091\pi$
$79$	−6.69615	−	11.5981i	−0.753376	−	1.30489i	0.192802	−	0.981238i	$-0.438243\pi$
$80$	0.535898	−	0.928203i	0.0599153	−	0.103776i
$81$		0			0
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	9.12436			1.00153			0.500764	−	0.865584i	$-0.333052\pi$
$83$	9.12436			1.00153			0.500764	+	0.865584i	$0.333052\pi$
$84$		0			0
$85$	6.73205			0.730193
$86$	−2.63397	−	4.56218i	−0.284029	−	0.491952i
$87$		0			0
$88$	−3.46410	+	6.00000i	−0.369274	+	0.639602i
$89$	−4.56218	−	7.90192i	−0.483590	−	0.837602i	0.516233	−	0.856448i	$-0.327334\pi$
$89$	−4.56218	−	7.90192i	−0.483590	−	0.837602i	−0.999822	+	0.0188462i	$0.994001\pi$
$90$		0			0
$91$	−4.96410	+	14.3301i	−0.520379	+	1.50221i
$92$	−1.85641			−0.193544
$93$		0			0
$94$	−0.732051	+	1.26795i	−0.0755053	+	0.130779i
$95$	−1.23205	+	2.13397i	−0.126406	+	0.218941i
$96$		0			0
$97$	1.07180			0.108824			0.0544122	−	0.998519i	$-0.482671\pi$
$97$	1.07180			0.108824			0.0544122	+	0.998519i	$0.482671\pi$
$98$	0.732051	−	5.07180i	0.0739483	−	0.512329i
$99$		0			0
$100$	0.732051	+	1.26795i	0.0732051	+	0.126795i
$101$	−5.36603	+	9.29423i	−0.533939	+	0.924810i	0.465274	+	0.885167i	$0.345956\pi$
$101$	−5.36603	+	9.29423i	−0.533939	+	0.924810i	−0.999214	+	0.0396438i	$0.987378\pi$
$102$		0			0
$103$	−0.598076	−	1.03590i	−0.0589302	−	0.102070i	0.835055	−	0.550166i	$-0.185436\pi$
$103$	−0.598076	−	1.03590i	−0.0589302	−	0.102070i	−0.893985	+	0.448096i	$0.852102\pi$
$104$	14.5359			1.42536
$105$		0			0
$106$	−6.14359			−0.596719
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	0.597075	−	0.802186i	$-0.296330\pi$
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	−0.993251	+	0.115989i	$0.962996\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$		0			0
$112$	2.78461	−	0.535898i	0.263121	−	0.0506376i
$113$	4.92820			0.463606			0.231803	−	0.972763i	$-0.425537\pi$
$113$	4.92820			0.463606			0.231803	+	0.972763i	$0.425537\pi$
$114$		0			0
$115$	0.633975	−	1.09808i	0.0591184	−	0.102396i
$116$	−4.53590	+	7.85641i	−0.421148	+	0.729449i
$117$		0			0
$118$	7.46410			0.687126
$119$	11.6603	+	13.4641i	1.06889	+	1.23425i
$120$		0			0
$121$	1.76795	+	3.06218i	0.160723	+	0.278380i
$122$	1.46410	−	2.53590i	0.132554	−	0.229589i
$123$		0			0
$124$	4.73205	+	8.19615i	0.424951	+	0.736036i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	15.1962			1.34844			0.674220	−	0.738530i	$-0.264480\pi$
$127$	15.1962			1.34844			0.674220	+	0.738530i	$0.264480\pi$
$128$	−5.07180	−	8.78461i	−0.448288	−	0.776457i
$129$		0			0
$130$	−2.09808	+	3.63397i	−0.184013	+	0.318721i
$131$	4.26795	+	7.39230i	0.372892	+	0.645869i	0.990009	−	0.141003i	$-0.0450327\pi$
$131$	4.26795	+	7.39230i	0.372892	+	0.645869i	−0.617117	+	0.786872i	$0.711699\pi$
$132$		0			0
$133$	−6.40192	+	1.23205i	−0.555117	+	0.106832i
$134$	−1.94744			−0.168233
$135$		0			0
$136$	8.53590	−	14.7846i	0.731947	−	1.26777i
$137$	−4.09808	+	7.09808i	−0.350122	+	0.606430i	−0.986271	−	0.165137i	$-0.947193\pi$
$137$	−4.09808	+	7.09808i	−0.350122	+	0.606430i	0.636148	+	0.771567i	$0.280527\pi$
$138$		0			0
$139$	−7.92820			−0.672461			−0.336231	−	0.941780i	$-0.609152\pi$
$139$	−7.92820			−0.672461			−0.336231	+	0.941780i	$0.609152\pi$
$140$	−1.26795	+	3.66025i	−0.107161	+	0.309348i
$141$		0			0
$142$	1.53590	+	2.66025i	0.128890	+	0.223244i
$143$	−7.83013	+	13.5622i	−0.654788	+	1.13413i
$144$		0			0
$145$	−3.09808	−	5.36603i	−0.257281	−	0.445624i
$146$	3.41154			0.282341
$147$		0			0
$148$	−10.5359			−0.866046
$149$	−10.9282	−	18.9282i	−0.895273	−	1.55066i	−0.833466	−	0.552571i	$-0.813647\pi$
$149$	−10.9282	−	18.9282i	−0.895273	−	1.55066i	−0.0618073	−	0.998088i	$-0.519686\pi$
$150$		0			0
$151$	−2.46410	+	4.26795i	−0.200526	+	0.347321i	−0.948698	−	0.316184i	$-0.897598\pi$
$151$	−2.46410	+	4.26795i	−0.200526	+	0.347321i	0.748172	+	0.663505i	$0.230932\pi$
$152$	3.12436	+	5.41154i	0.253419	+	0.438934i
$153$		0			0
$154$	1.73205	−	5.00000i	0.139573	−	0.402911i
$155$	−6.46410			−0.519209
$156$		0			0
$157$	7.19615	−	12.4641i	0.574315	−	0.994744i	−0.421800	−	0.906689i	$-0.638602\pi$
$157$	7.19615	−	12.4641i	0.574315	−	0.994744i	0.996116	−	0.0880548i	$-0.0280651\pi$
$158$	4.90192	−	8.49038i	0.389976	−	0.675458i
$159$		0			0
$160$	5.85641			0.462990
$161$	3.29423	−	0.633975i	0.259622	−	0.0499642i
$162$		0			0
$163$	2.92820	+	5.07180i	0.229355	+	0.397254i	0.957617	−	0.288045i	$-0.0930051\pi$
$163$	2.92820	+	5.07180i	0.229355	+	0.397254i	−0.728262	+	0.685298i	$0.759672\pi$
$164$	−2.00000	+	3.46410i	−0.156174	+	0.270501i
$165$		0			0
$166$	3.33975	+	5.78461i	0.259215	+	0.448973i
$167$	0.339746			0.0262903			0.0131452	−	0.999914i	$-0.495816\pi$
$167$	0.339746			0.0262903			0.0131452	+	0.999914i	$0.495816\pi$
$168$		0			0
$169$	19.8564			1.52742
$170$	2.46410	+	4.26795i	0.188988	+	0.327337i
$171$		0			0
$172$	−5.26795	+	9.12436i	−0.401677	+	0.695726i
$173$	10.7321	+	18.5885i	0.815943	+	1.41325i	0.908649	+	0.417561i	$0.137115\pi$
$173$	10.7321	+	18.5885i	0.815943	+	1.41325i	−0.0927063	+	0.995693i	$0.529552\pi$
$174$		0			0
$175$	−1.73205	−	2.00000i	−0.130931	−	0.151186i
$176$	2.92820			0.220722
$177$		0			0
$178$	3.33975	−	5.78461i	0.250325	−	0.433575i
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	−0.990134	−	0.140122i	$-0.955250\pi$
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	0.616417	+	0.787420i	$0.288584\pi$
$180$		0			0
$181$	10.3205			0.767117			0.383559	−	0.923517i	$-0.374698\pi$
$181$	10.3205			0.767117			0.383559	+	0.923517i	$0.374698\pi$
$182$	−10.9019	+	2.09808i	−0.808104	+	0.155520i
$183$		0			0
$184$	−1.60770	−	2.78461i	−0.118521	−	0.205284i
$185$	3.59808	−	6.23205i	0.264536	−	0.458189i
$186$		0			0
$187$	9.19615	+	15.9282i	0.672489	+	1.16479i
$188$	2.92820			0.213561
$189$		0			0
$190$	−1.80385			−0.130865
$191$	2.46410	+	4.26795i	0.178296	+	0.308818i	0.941297	−	0.337579i	$-0.109608\pi$
$191$	2.46410	+	4.26795i	0.178296	+	0.308818i	−0.763001	+	0.646397i	$0.776275\pi$
$192$		0			0
$193$	4.59808	−	7.96410i	0.330977	−	0.573269i	−0.651727	−	0.758454i	$-0.725955\pi$
$193$	4.59808	−	7.96410i	0.330977	−	0.573269i	0.982704	+	0.185185i	$0.0592885\pi$
$194$	0.392305	+	0.679492i	0.0281658	+	0.0487847i
$195$		0			0
$196$	−9.51666	+	3.80385i	−0.679761	+	0.271703i
$197$	17.6603			1.25824			0.629121	−	0.777308i	$-0.283415\pi$
$197$	17.6603			1.25824			0.629121	+	0.777308i	$0.283415\pi$
$198$		0			0
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	0.152305	+	0.988334i	$0.451330\pi$
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	−0.932075	+	0.362267i	$0.882003\pi$
$200$	−1.26795	+	2.19615i	−0.0896575	+	0.155291i
$201$		0			0
$202$	−7.85641			−0.552775
$203$	5.36603	−	15.4904i	0.376621	−	1.08721i
$204$		0			0
$205$	−1.36603	−	2.36603i	−0.0954074	−	0.165250i
$206$	0.437822	−	0.758330i	0.0305045	−	0.0528354i
$207$		0			0
$208$	−3.07180	−	5.32051i	−0.212991	−	0.368911i
$209$	−6.73205			−0.465666
$210$		0			0
$211$	20.9282			1.44076			0.720378	−	0.693581i	$-0.243968\pi$
$211$	20.9282			1.44076			0.720378	+	0.693581i	$0.243968\pi$
$212$	6.14359	+	10.6410i	0.421944	+	0.730828i
$213$		0			0
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	−3.59808	−	6.23205i	−0.245387	−	0.425022i
$216$		0			0
$217$	−11.1962	−	12.9282i	−0.760044	−	0.877624i
$218$	−8.05256			−0.545388
$219$		0			0
$220$	−2.00000	+	3.46410i	−0.134840	+	0.233550i
$221$	19.2942	−	33.4186i	1.29787	−	2.24798i
$222$		0			0
$223$	0.392305			0.0262707			0.0131353	−	0.999914i	$-0.495819\pi$
$223$	0.392305			0.0262707			0.0131353	+	0.999914i	$0.495819\pi$
$224$	10.1436	+	11.7128i	0.677747	+	0.782595i
$225$		0			0
$226$	1.80385	+	3.12436i	0.119990	+	0.207829i
$227$	7.83013	−	13.5622i	0.519704	−	0.900153i	−0.480034	−	0.877250i	$-0.659376\pi$
$227$	7.83013	−	13.5622i	0.519704	−	0.900153i	0.999738	−	0.0229034i	$-0.00729102\pi$
$228$		0			0
$229$	1.50000	+	2.59808i	0.0991228	+	0.171686i	0.911322	−	0.411695i	$-0.135063\pi$
$229$	1.50000	+	2.59808i	0.0991228	+	0.171686i	−0.812199	+	0.583380i	$0.801730\pi$
$230$	0.928203			0.0612039
$231$		0			0
$232$	−15.7128			−1.03160
$233$	−8.66025	−	15.0000i	−0.567352	−	0.982683i	−0.996827	−	0.0796037i	$-0.974635\pi$
$233$	−8.66025	−	15.0000i	−0.567352	−	0.982683i	0.429474	−	0.903079i	$-0.358699\pi$
$234$		0			0
$235$	−1.00000	+	1.73205i	−0.0652328	+	0.112987i
$236$	−7.46410	−	12.9282i	−0.485872	−	0.841554i
$237$		0			0
$238$	−4.26795	+	12.3205i	−0.276650	+	0.798620i
$239$	−20.9282			−1.35373			−0.676866	−	0.736106i	$-0.736663\pi$
$239$	−20.9282			−1.35373			−0.676866	+	0.736106i	$0.736663\pi$
$240$		0			0
$241$	−3.26795	+	5.66025i	−0.210507	+	0.364609i	−0.951873	−	0.306492i	$-0.900845\pi$
$241$	−3.26795	+	5.66025i	−0.210507	+	0.364609i	0.741366	+	0.671101i	$0.234178\pi$
$242$	−1.29423	+	2.24167i	−0.0831962	+	0.144100i
$243$		0			0
$244$	−5.85641			−0.374918
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$		0			0
$247$	7.06218	+	12.2321i	0.449356	+	0.778307i
$248$	−8.19615	+	14.1962i	−0.520456	+	0.901457i
$249$		0			0
$250$	−0.366025	−	0.633975i	−0.0231495	−	0.0400961i
$251$	−6.58846			−0.415860			−0.207930	−	0.978144i	$-0.566673\pi$
$251$	−6.58846			−0.415860			−0.207930	+	0.978144i	$0.566673\pi$
$252$		0			0
$253$	3.46410			0.217786
$254$	5.56218	+	9.63397i	0.349002	+	0.604489i
$255$		0			0
$256$	5.85641	−	10.1436i	0.366025	−	0.633975i
$257$	5.83013	+	10.0981i	0.363673	+	0.629901i	0.988562	−	0.150813i	$-0.0481891\pi$
$257$	5.83013	+	10.0981i	0.363673	+	0.629901i	−0.624889	+	0.780714i	$0.714856\pi$
$258$		0			0
$259$	18.6962	−	3.59808i	1.16172	−	0.223574i
$260$	8.39230			0.520469
$261$		0			0
$262$	−3.12436	+	5.41154i	−0.193023	+	0.334326i
$263$	−6.19615	+	10.7321i	−0.382071	+	0.661767i	−0.991358	−	0.131183i	$-0.958122\pi$
$263$	−6.19615	+	10.7321i	−0.382071	+	0.661767i	0.609287	+	0.792950i	$0.291456\pi$
$264$		0			0
$265$	−8.39230			−0.515535
$266$	−3.12436	−	3.60770i	−0.191567	−	0.221202i
$267$		0			0
$268$	1.94744	+	3.37307i	0.118959	+	0.206043i
$269$	−9.73205	+	16.8564i	−0.593374	+	1.02775i	0.400401	+	0.916340i	$0.368871\pi$
$269$	−9.73205	+	16.8564i	−0.593374	+	1.02775i	−0.993774	+	0.111413i	$0.964462\pi$
$270$		0			0
$271$	−8.46410	−	14.6603i	−0.514158	−	0.890547i	−0.999865	−	0.0164256i	$-0.994771\pi$
$271$	−8.46410	−	14.6603i	−0.514158	−	0.890547i	0.485708	−	0.874121i	$-0.338562\pi$
$272$	−7.21539			−0.437497
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−1.36603	−	2.36603i	−0.0823744	−	0.142677i
$276$		0			0
$277$	−1.33013	+	2.30385i	−0.0799196	+	0.138425i	−0.903215	−	0.429188i	$-0.858800\pi$
$277$	−1.33013	+	2.30385i	−0.0799196	+	0.138425i	0.823295	+	0.567613i	$0.192133\pi$
$278$	−2.90192	−	5.02628i	−0.174046	−	0.301456i
$279$		0			0
$280$	−6.58846	+	1.26795i	−0.393736	+	0.0757745i
$281$	13.8564			0.826604			0.413302	−	0.910594i	$-0.364375\pi$
$281$	13.8564			0.826604			0.413302	+	0.910594i	$0.364375\pi$
$282$		0			0
$283$	−0.0621778	+	0.107695i	−0.00369609	+	0.00640181i	−0.867868	−	0.496796i	$-0.834510\pi$
$283$	−0.0621778	+	0.107695i	−0.00369609	+	0.00640181i	0.864171	+	0.503197i	$0.167843\pi$
$284$	3.07180	−	5.32051i	0.182278	−	0.315714i
$285$		0			0
$286$	−11.4641			−0.677887
$287$	2.36603	−	6.83013i	0.139662	−	0.403170i
$288$		0			0
$289$	−14.1603	−	24.5263i	−0.832956	−	1.44272i
$290$	2.26795	−	3.92820i	0.133179	−	0.230672i
$291$		0			0
$292$	−3.41154	−	5.90897i	−0.199645	−	0.345796i
$293$	−5.07180			−0.296298			−0.148149	−	0.988965i	$-0.547331\pi$
$293$	−5.07180			−0.296298			−0.148149	+	0.988965i	$0.547331\pi$
$294$		0			0
$295$	10.1962			0.593643
$296$	−9.12436	−	15.8038i	−0.530342	−	0.918580i
$297$		0			0
$298$	8.00000	−	13.8564i	0.463428	−	0.802680i
$299$	−3.63397	−	6.29423i	−0.210158	−	0.364005i
$300$		0			0
$301$	6.23205	−	17.9904i	0.359209	−	1.03695i
$302$	−3.60770			−0.207600
$303$		0			0
$304$	1.32051	−	2.28719i	0.0757363	−	0.131179i
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$		0			0
$307$	−7.87564			−0.449487			−0.224743	−	0.974418i	$-0.572154\pi$
$307$	−7.87564			−0.449487			−0.224743	+	0.974418i	$0.572154\pi$
$308$	−10.3923	+	2.00000i	−0.592157	+	0.113961i
$309$		0			0
$310$	−2.36603	−	4.09808i	−0.134381	−	0.232755i
$311$	−7.56218	+	13.0981i	−0.428812	+	0.742724i	−0.996768	−	0.0803351i	$-0.974401\pi$
$311$	−7.56218	+	13.0981i	−0.428812	+	0.742724i	0.567956	+	0.823059i	$0.307734\pi$
$312$		0			0
$313$	−2.33013	−	4.03590i	−0.131707	−	0.228122i	0.792628	−	0.609706i	$-0.208712\pi$
$313$	−2.33013	−	4.03590i	−0.131707	−	0.228122i	−0.924335	+	0.381583i	$0.875379\pi$
$314$	10.5359			0.594575
$315$		0			0
$316$	−19.6077			−1.10302
$317$	15.2224	+	26.3660i	0.854977	+	1.48086i	0.876666	+	0.481099i	$0.159762\pi$
$317$	15.2224	+	26.3660i	0.854977	+	1.48086i	−0.0216894	+	0.999765i	$0.506905\pi$
$318$		0			0
$319$	8.46410	−	14.6603i	0.473899	−	0.820817i
$320$	1.07180	+	1.85641i	0.0599153	+	0.103776i
$321$		0			0
$322$	1.60770	+	1.85641i	0.0895933	+	0.103453i
$323$	16.5885			0.923006
$324$		0			0
$325$	−2.86603	+	4.96410i	−0.158978	+	0.275359i
$326$	−2.14359	+	3.71281i	−0.118723	+	0.205634i
$327$		0			0
$328$	−6.92820			−0.382546
$329$	−5.19615	+	1.00000i	−0.286473	+	0.0551318i
$330$		0			0
$331$	−10.9641	−	18.9904i	−0.602642	−	1.04381i	−0.992419	−	0.122897i	$-0.960782\pi$
$331$	−10.9641	−	18.9904i	−0.602642	−	1.04381i	0.389778	−	0.920909i	$-0.372552\pi$
$332$	6.67949	−	11.5692i	0.366585	−	0.634943i
$333$		0			0
$334$	0.124356	+	0.215390i	0.00680444	+	0.0117856i
$335$	−2.66025			−0.145345
$336$		0			0
$337$	−33.9808			−1.85105			−0.925525	−	0.378686i	$-0.876376\pi$
$337$	−33.9808			−1.85105			−0.925525	+	0.378686i	$0.876376\pi$
$338$	7.26795	+	12.5885i	0.395324	+	0.684722i
$339$		0			0
$340$	4.92820	−	8.53590i	0.267269	−	0.462924i
$341$	−8.83013	−	15.2942i	−0.478178	−	0.828229i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−18.2487			−0.983905
$345$		0			0
$346$	−7.85641	+	13.6077i	−0.422363	+	0.731554i
$347$	−17.4641	+	30.2487i	−0.937522	+	1.62384i	−0.167449	+	0.985881i	$0.553553\pi$
$347$	−17.4641	+	30.2487i	−0.937522	+	1.62384i	−0.770074	+	0.637955i	$0.779781\pi$
$348$		0			0
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$	0.633975	−	1.83013i	0.0338874	−	0.0978244i
$351$		0			0
$352$	8.00000	+	13.8564i	0.426401	+	0.738549i
$353$	10.5622	−	18.2942i	0.562168	−	0.973704i	−0.435139	−	0.900363i	$-0.643301\pi$
$353$	10.5622	−	18.2942i	0.562168	−	0.973704i	0.997307	−	0.0733402i	$-0.0233659\pi$
$354$		0			0
$355$	2.09808	+	3.63397i	0.111354	+	0.192871i
$356$	−13.3590			−0.708025
$357$		0			0
$358$	−7.32051			−0.386901
$359$	−2.36603	−	4.09808i	−0.124874	−	0.216288i	0.796810	−	0.604230i	$-0.206519\pi$
$359$	−2.36603	−	4.09808i	−0.124874	−	0.216288i	−0.921684	+	0.387942i	$0.873186\pi$
$360$		0			0
$361$	6.46410	−	11.1962i	0.340216	−	0.589271i
$362$	3.77757	+	6.54294i	0.198545	+	0.343889i
$363$		0			0
$364$	14.5359	+	16.7846i	0.761888	+	0.879753i
$365$	4.66025			0.243929
$366$		0			0
$367$	−0.401924	+	0.696152i	−0.0209803	+	0.0363389i	−0.876325	−	0.481721i	$-0.840012\pi$
$367$	−0.401924	+	0.696152i	−0.0209803	+	0.0363389i	0.855345	+	0.518059i	$0.173345\pi$
$368$	−0.679492	+	1.17691i	−0.0354210	+	0.0613509i
$369$		0			0
$370$	5.26795			0.273868
$371$	−14.5359	−	16.7846i	−0.754666	−	0.871414i
$372$		0			0
$373$	9.25833	+	16.0359i	0.479378	+	0.830307i	0.999720	−	0.0236505i	$-0.00752890\pi$
$373$	9.25833	+	16.0359i	0.479378	+	0.830307i	−0.520342	+	0.853958i	$0.674196\pi$
$374$	−6.73205	+	11.6603i	−0.348106	+	0.602937i
$375$		0			0
$376$	2.53590	+	4.39230i	0.130779	+	0.226516i
$377$	−35.5167			−1.82920
$378$		0			0
$379$	−28.3205			−1.45473			−0.727363	−	0.686253i	$-0.759255\pi$
$379$	−28.3205			−1.45473			−0.727363	+	0.686253i	$0.759255\pi$
$380$	1.80385	+	3.12436i	0.0925354	+	0.160276i
$381$		0			0
$382$	−1.80385	+	3.12436i	−0.0922929	+	0.159856i
$383$	5.66025	+	9.80385i	0.289225	+	0.500953i	0.973625	−	0.228154i	$-0.0732689\pi$
$383$	5.66025	+	9.80385i	0.289225	+	0.500953i	−0.684400	+	0.729107i	$0.739936\pi$
$384$		0			0
$385$	2.36603	−	6.83013i	0.120584	−	0.348096i
$386$	6.73205			0.342652
$387$		0			0
$388$	0.784610	−	1.35898i	0.0398325	−	0.0689920i
$389$	18.2942	−	31.6865i	0.927554	−	1.60657i	0.140153	−	0.990130i	$-0.455240\pi$
$389$	18.2942	−	31.6865i	0.927554	−	1.60657i	0.787401	−	0.616441i	$-0.211426\pi$
$390$		0			0
$391$	−8.53590			−0.431679
$392$	−13.9474	−	10.9808i	−0.704452	−	0.554612i
$393$		0			0
$394$	6.46410	+	11.1962i	0.325657	+	0.564054i
$395$	6.69615	−	11.5981i	0.336920	−	0.583563i
$396$		0			0
$397$	10.4019	+	18.0167i	0.522058	+	0.904230i	0.999671	+	0.0256600i	$0.00816873\pi$
$397$	10.4019	+	18.0167i	0.522058	+	0.904230i	−0.477613	+	0.878570i	$0.658498\pi$
$398$	−16.1051			−0.807277
$399$		0			0
$400$	1.07180			0.0535898
$401$	2.19615	+	3.80385i	0.109671	+	0.189955i	0.915637	−	0.402006i	$-0.131687\pi$
$401$	2.19615	+	3.80385i	0.109671	+	0.189955i	−0.805966	+	0.591962i	$0.798354\pi$
$402$		0			0
$403$	−18.5263	+	32.0885i	−0.922860	+	1.59844i
$404$	7.85641	+	13.6077i	0.390871	+	0.677008i
$405$		0			0
$406$	11.7846	−	2.26795i	0.584860	−	0.112556i
$407$	19.6603			0.974523
$408$		0			0
$409$	−15.4282	+	26.7224i	−0.762876	+	1.32134i	0.178487	+	0.983942i	$0.442880\pi$
$409$	−15.4282	+	26.7224i	−0.762876	+	1.32134i	−0.941362	+	0.337397i	$0.890454\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$		0			0
$412$	−1.75129			−0.0862798
$413$	17.6603	+	20.3923i	0.869004	+	1.00344i
$414$		0			0
$415$	4.56218	+	7.90192i	0.223949	+	0.387890i
$416$	16.7846	−	29.0718i	0.822933	−	1.42536i
$417$		0			0
$418$	−2.46410	−	4.26795i	−0.120523	−	0.208752i
$419$	28.5359			1.39407			0.697035	−	0.717037i	$-0.254502\pi$
$419$	28.5359			1.39407			0.697035	+	0.717037i	$0.254502\pi$
$420$		0			0
$421$	13.9282			0.678819			0.339410	−	0.940639i	$-0.389773\pi$
$421$	13.9282			0.678819			0.339410	+	0.940639i	$0.389773\pi$
$422$	7.66025	+	13.2679i	0.372895	+	0.645874i
$423$		0			0
$424$	−10.6410	+	18.4308i	−0.516773	+	0.895078i
$425$	3.36603	+	5.83013i	0.163276	+	0.282803i
$426$		0			0
$427$	10.3923	−	2.00000i	0.502919	−	0.0967868i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	2.63397	−	4.56218i	0.127022	−	0.220008i
$431$	−8.66025	+	15.0000i	−0.417150	+	0.722525i	−0.995651	−	0.0931566i	$-0.970304\pi$
$431$	−8.66025	+	15.0000i	−0.417150	+	0.722525i	0.578502	+	0.815681i	$0.303638\pi$
$432$		0			0
$433$	4.80385			0.230858			0.115429	−	0.993316i	$-0.463176\pi$
$433$	4.80385			0.230858			0.115429	+	0.993316i	$0.463176\pi$
$434$	4.09808	−	11.8301i	0.196714	−	0.567864i
$435$		0			0
$436$	8.05256	+	13.9474i	0.385648	+	0.667961i
$437$	1.56218	−	2.70577i	0.0747291	−	0.129435i
$438$		0			0
$439$	−3.73205	−	6.46410i	−0.178121	−	0.308515i	0.763116	−	0.646262i	$-0.223669\pi$
$439$	−3.73205	−	6.46410i	−0.178121	−	0.308515i	−0.941237	+	0.337747i	$0.890335\pi$
$440$	−6.92820			−0.330289
$441$		0			0
$442$	28.2487			1.34365
$443$	1.26795	+	2.19615i	0.0602421	+	0.104342i	0.894574	−	0.446921i	$-0.147479\pi$
$443$	1.26795	+	2.19615i	0.0602421	+	0.104342i	−0.834331	+	0.551263i	$0.814146\pi$
$444$		0			0
$445$	4.56218	−	7.90192i	0.216268	−	0.374587i
$446$	0.143594	+	0.248711i	0.00679935	+	0.0117768i
$447$		0			0
$448$	−1.85641	+	5.35898i	−0.0877070	+	0.253188i
$449$	8.14359			0.384320			0.192160	−	0.981364i	$-0.438451\pi$
$449$	8.14359			0.384320			0.192160	+	0.981364i	$0.438451\pi$
$450$		0			0
$451$	3.73205	−	6.46410i	0.175735	−	0.304383i
$452$	3.60770	−	6.24871i	0.169692	−	0.293915i
$453$		0			0
$454$	11.4641			0.538037
$455$	−14.8923	+	2.86603i	−0.698162	+	0.134361i
$456$		0			0
$457$	−0.330127	−	0.571797i	−0.0154427	−	0.0267475i	0.858201	−	0.513314i	$-0.171582\pi$
$457$	−0.330127	−	0.571797i	−0.0154427	−	0.0267475i	−0.873643	+	0.486567i	$0.838249\pi$
$458$	−1.09808	+	1.90192i	−0.0513097	+	0.0888711i
$459$		0			0
$460$	−0.928203	−	1.60770i	−0.0432777	−	0.0749592i
$461$	34.9808			1.62922			0.814608	−	0.580012i	$-0.196952\pi$
$461$	34.9808			1.62922			0.814608	+	0.580012i	$0.196952\pi$
$462$		0			0
$463$	22.2679			1.03488			0.517440	−	0.855720i	$-0.326885\pi$
$463$	22.2679			1.03488			0.517440	+	0.855720i	$0.326885\pi$
$464$	3.32051	+	5.75129i	0.154151	+	0.266997i
$465$		0			0
$466$	6.33975	−	10.9808i	0.293683	−	0.508674i
$467$	−13.9282	−	24.1244i	−0.644520	−	1.11634i	−0.984412	−	0.175877i	$-0.943724\pi$
$467$	−13.9282	−	24.1244i	−0.644520	−	1.11634i	0.339892	−	0.940465i	$-0.389610\pi$
$468$		0			0
$469$	−4.60770	−	5.32051i	−0.212764	−	0.245678i
$470$	−1.46410			−0.0675340
$471$		0			0
$472$	12.9282	−	22.3923i	0.595069	−	1.03069i
$473$	9.83013	−	17.0263i	0.451990	−	0.782869i
$474$		0			0
$475$	−2.46410			−0.113061
$476$	25.6077	−	4.92820i	1.17373	−	0.225884i
$477$		0			0
$478$	−7.66025	−	13.2679i	−0.350372	−	0.606862i
$479$	−16.3923	+	28.3923i	−0.748984	+	1.29728i	0.199327	+	0.979933i	$0.436124\pi$
$479$	−16.3923	+	28.3923i	−0.748984	+	1.29728i	−0.948310	+	0.317344i	$0.897209\pi$
$480$		0			0
$481$	−20.6244	−	35.7224i	−0.940390	−	1.62880i
$482$	−4.78461			−0.217933
$483$		0			0
$484$	5.17691			0.235314
$485$	0.535898	+	0.928203i	0.0243339	+	0.0421475i
$486$		0			0
$487$	15.7942	−	27.3564i	0.715705	−	1.23964i	−0.246982	−	0.969020i	$-0.579439\pi$
$487$	15.7942	−	27.3564i	0.715705	−	1.23964i	0.962687	−	0.270617i	$-0.0872277\pi$
$488$	−5.07180	−	8.78461i	−0.229589	−	0.397661i
$489$		0			0
$490$	4.75833	−	1.90192i	0.214959	−	0.0859202i
$491$	−10.2487			−0.462518			−0.231259	−	0.972892i	$-0.574284\pi$
$491$	−10.2487			−0.462518			−0.231259	+	0.972892i	$0.574284\pi$
$492$		0			0
$493$	−20.8564	+	36.1244i	−0.939325	+	1.62696i
$494$	−5.16987	+	8.95448i	−0.232604	+	0.402881i
$495$		0			0
$496$	6.92820			0.311086
$497$	−3.63397	+	10.4904i	−0.163006	+	0.470558i
$498$		0			0
$499$	10.2321	+	17.7224i	0.458050	+	0.793365i	0.998858	−	0.0477808i	$-0.0152149\pi$
$499$	10.2321	+	17.7224i	0.458050	+	0.793365i	−0.540808	+	0.841146i	$0.681882\pi$
$500$	−0.732051	+	1.26795i	−0.0327383	+	0.0567044i
$501$		0			0
$502$	−2.41154	−	4.17691i	−0.107632	−	0.186425i
$503$	6.39230			0.285019			0.142509	−	0.989793i	$-0.454483\pi$
$503$	6.39230			0.285019			0.142509	+	0.989793i	$0.454483\pi$
$504$		0			0
$505$	−10.7321			−0.477570
$506$	1.26795	+	2.19615i	0.0563672	+	0.0976309i
$507$		0			0
$508$	11.1244	−	19.2679i	0.493563	−	0.854877i
$509$	5.73205	+	9.92820i	0.254069	+	0.440060i	0.964642	−	0.263563i	$-0.0848977\pi$
$509$	5.73205	+	9.92820i	0.254069	+	0.440060i	−0.710573	+	0.703623i	$0.751564\pi$
$510$		0			0
$511$	8.07180	+	9.32051i	0.357075	+	0.412315i
$512$	−11.7128			−0.517638
$513$		0			0
$514$	−4.26795	+	7.39230i	−0.188251	+	0.326061i
$515$	0.598076	−	1.03590i	0.0263544	−	0.0456471i
$516$		0			0
$517$	−5.46410			−0.240311
$518$	9.12436	+	10.5359i	0.400901	+	0.462921i
$519$		0			0
$520$	7.26795	+	12.5885i	0.318721	+	0.552040i
$521$	0.732051	−	1.26795i	0.0320717	−	0.0555499i	−0.849544	−	0.527518i	$-0.823123\pi$
$521$	0.732051	−	1.26795i	0.0320717	−	0.0555499i	0.881616	+	0.471968i	$0.156456\pi$
$522$		0			0
$523$	12.1340	+	21.0167i	0.530582	+	0.918994i	0.999363	+	0.0356803i	$0.0113598\pi$
$523$	12.1340	+	21.0167i	0.530582	+	0.918994i	−0.468782	+	0.883314i	$0.655307\pi$
$524$	12.4974			0.545952
$525$		0			0
$526$	−9.07180			−0.395549
$527$	21.7583	+	37.6865i	0.947808	+	1.64165i
$528$		0			0
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	−3.07180	−	5.32051i	−0.133430	−	0.231108i
$531$		0			0
$532$	−3.12436	+	9.01924i	−0.135458	+	0.391034i
$533$	−15.6603			−0.678321
$534$		0			0
$535$	4.09808	−	7.09808i	0.177175	−	0.306877i
$536$	−3.37307	+	5.84232i	−0.145694	+	0.252350i
$537$		0			0
$538$	−14.2487			−0.614306
$539$	17.7583	−	7.09808i	0.764905	−	0.305736i
$540$		0			0
$541$	17.8923	+	30.9904i	0.769250	+	1.33238i	0.937970	+	0.346716i	$0.112703\pi$
$541$	17.8923	+	30.9904i	0.769250	+	1.33238i	−0.168720	+	0.985664i	$0.553963\pi$
$542$	6.19615	−	10.7321i	0.266148	−	0.460981i
$543$		0			0
$544$	−19.7128	−	34.1436i	−0.845180	−	1.46389i
$545$	−11.0000			−0.471188
$546$		0			0
$547$	22.2487			0.951286			0.475643	−	0.879638i	$-0.342215\pi$
$547$	22.2487			0.951286			0.475643	+	0.879638i	$0.342215\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−7.63397	−	13.2224i	−0.325218	−	0.563295i
$552$		0			0
$553$	34.7942	−	6.69615i	1.47960	−	0.284749i
$554$	−1.94744			−0.0827388
$555$		0			0
$556$	−5.80385	+	10.0526i	−0.246138	+	0.426323i
$557$	−13.3923	+	23.1962i	−0.567450	+	0.982853i	0.429367	+	0.903130i	$0.358737\pi$
$557$	−13.3923	+	23.1962i	−0.567450	+	0.982853i	−0.996817	+	0.0797224i	$0.974597\pi$
$558$		0			0
$559$	−41.2487			−1.74463
$560$	1.85641	+	2.14359i	0.0784475	+	0.0905834i
$561$		0			0
$562$	5.07180	+	8.78461i	0.213941	+	0.370556i
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$	2.46410	+	4.26795i	0.103666	+	0.179554i
$566$	−0.0910347			−0.00382647
$567$		0			0
$568$	10.6410			0.446487
$569$	−13.2224	−	22.9019i	−0.554313	−	0.960099i	−0.997957	−	0.0638952i	$-0.979648\pi$
$569$	−13.2224	−	22.9019i	−0.554313	−	0.960099i	0.443643	−	0.896203i	$-0.353686\pi$
$570$		0			0
$571$	−19.6962	+	34.1147i	−0.824258	+	1.42766i	0.0782265	+	0.996936i	$0.475074\pi$
$571$	−19.6962	+	34.1147i	−0.824258	+	1.42766i	−0.902485	+	0.430722i	$0.858259\pi$
$572$	11.4641	+	19.8564i	0.479338	+	0.830238i
$573$		0			0
$574$	5.19615	−	1.00000i	0.216883	−	0.0417392i
$575$	1.26795			0.0528771
$576$		0			0
$577$	−5.66987	+	9.82051i	−0.236040	+	0.408833i	−0.959574	−	0.281455i	$-0.909183\pi$
$577$	−5.66987	+	9.82051i	−0.236040	+	0.408833i	0.723534	+	0.690288i	$0.242516\pi$
$578$	10.3660	−	17.9545i	0.431170	−	0.746808i
$579$		0			0
$580$	−9.07180			−0.376686
$581$	−7.90192	+	22.8109i	−0.327827	+	0.946355i
$582$		0			0
$583$	−11.4641	−	19.8564i	−0.474795	−	0.822368i
$584$	5.90897	−	10.2346i	0.244515	−	0.423512i
$585$		0			0
$586$	−1.85641	−	3.21539i	−0.0766874	−	0.132827i
$587$	−37.2679			−1.53821			−0.769106	−	0.639121i	$-0.779298\pi$
$587$	−37.2679			−1.53821			−0.769106	+	0.639121i	$0.779298\pi$
$588$		0			0
$589$	−15.9282			−0.656310
$590$	3.73205	+	6.46410i	0.153646	+	0.266123i
$591$		0			0
$592$	−3.85641	+	6.67949i	−0.158497	+	0.274525i
$593$	−18.9545	−	32.8301i	−0.778367	−	1.34817i	−0.932882	−	0.360181i	$-0.882715\pi$
$593$	−18.9545	−	32.8301i	−0.778367	−	1.34817i	0.154515	−	0.987990i	$-0.450619\pi$
$594$		0			0
$595$	−5.83013	+	16.8301i	−0.239012	+	0.689968i
$596$	−32.0000			−1.31077
$597$		0			0
$598$	2.66025	−	4.60770i	0.108786	−	0.188423i
$599$	5.12436	−	8.87564i	0.209375	−	0.362649i	−0.742142	−	0.670242i	$-0.766190\pi$
$599$	5.12436	−	8.87564i	0.209375	−	0.362649i	0.951518	+	0.307593i	$0.0995236\pi$
$600$		0			0
$601$	−13.9282			−0.568143			−0.284072	−	0.958803i	$-0.591685\pi$
$601$	−13.9282			−0.568143			−0.284072	+	0.958803i	$0.591685\pi$
$602$	13.6865	−	2.63397i	0.557821	−	0.107353i
$603$		0			0
$604$	3.60770	+	6.24871i	0.146795	+	0.254256i
$605$	−1.76795	+	3.06218i	−0.0718774	+	0.124495i
$606$		0			0
$607$	3.59808	+	6.23205i	0.146041	+	0.252951i	0.929761	−	0.368164i	$-0.120013\pi$
$607$	3.59808	+	6.23205i	0.146041	+	0.252951i	−0.783720	+	0.621115i	$0.786680\pi$
$608$	14.4308			0.585245
$609$		0			0
$610$	2.92820			0.118559
$611$	5.73205	+	9.92820i	0.231894	+	0.401652i
$612$		0			0
$613$	6.53590	−	11.3205i	0.263982	−	0.457231i	−0.703314	−	0.710879i	$-0.748297\pi$
$613$	6.53590	−	11.3205i	0.263982	−	0.457231i	0.967297	+	0.253648i	$0.0816306\pi$
$614$	−2.88269	−	4.99296i	−0.116336	−	0.201499i
$615$		0			0
$616$	−12.0000	−	13.8564i	−0.483494	−	0.558291i
$617$	−12.2487			−0.493115			−0.246557	−	0.969128i	$-0.579299\pi$
$617$	−12.2487			−0.493115			−0.246557	+	0.969128i	$0.579299\pi$
$618$		0			0
$619$	21.9641	−	38.0429i	0.882812	−	1.52907i	0.0346105	−	0.999401i	$-0.488981\pi$
$619$	21.9641	−	38.0429i	0.882812	−	1.52907i	0.848201	−	0.529674i	$-0.177686\pi$
$620$	−4.73205	+	8.19615i	−0.190044	+	0.329165i
$621$		0			0
$622$	−11.0718			−0.443939
$623$	23.7058	−	4.56218i	0.949752	−	0.182780i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.70577	−	2.95448i	0.0681763	−	0.118085i
$627$		0			0
$628$	−10.5359	−	18.2487i	−0.420428	−	0.728203i
$629$	−48.4449			−1.93162
$630$		0			0
$631$	7.21539			0.287240			0.143620	−	0.989633i	$-0.454126\pi$
$631$	7.21539			0.287240			0.143620	+	0.989633i	$0.454126\pi$
$632$	−16.9808	−	29.4115i	−0.675458	−	1.16993i
$633$		0			0
$634$	−11.1436	+	19.3013i	−0.442569	+	0.766551i
$635$	7.59808	+	13.1603i	0.301520	+	0.522249i
$636$		0			0
$637$	−31.5263	−	24.8205i	−1.24912	−	0.983424i
$638$	12.3923			0.490616
$639$		0			0
$640$	5.07180	−	8.78461i	0.200480	−	0.347242i
$641$	7.09808	−	12.2942i	0.280357	−	0.485593i	−0.691116	−	0.722744i	$-0.742880\pi$
$641$	7.09808	−	12.2942i	0.280357	−	0.485593i	0.971473	+	0.237151i	$0.0762138\pi$
$642$		0			0
$643$	−40.5167			−1.59782			−0.798911	−	0.601450i	$-0.794590\pi$
$643$	−40.5167			−1.59782			−0.798911	+	0.601450i	$0.794590\pi$
$644$	1.60770	−	4.64102i	0.0633521	−	0.182882i
$645$		0			0
$646$	6.07180	+	10.5167i	0.238892	+	0.413772i
$647$	18.9545	−	32.8301i	0.745178	−	1.29069i	−0.204934	−	0.978776i	$-0.565698\pi$
$647$	18.9545	−	32.8301i	0.745178	−	1.29069i	0.950112	−	0.311910i	$-0.100969\pi$
$648$		0			0
$649$	13.9282	+	24.1244i	0.546730	+	0.946964i
$650$	−4.19615			−0.164587
$651$		0			0
$652$	8.57437			0.335798
$653$	−6.70577	−	11.6147i	−0.262417	−	0.454520i	0.704467	−	0.709737i	$-0.251186\pi$
$653$	−6.70577	−	11.6147i	−0.262417	−	0.454520i	−0.966884	+	0.255217i	$0.917853\pi$
$654$		0			0
$655$	−4.26795	+	7.39230i	−0.166763	+	0.288841i
$656$	1.46410	+	2.53590i	0.0571636	+	0.0990102i
$657$		0			0
$658$	−2.53590	−	2.92820i	−0.0988596	−	0.114153i
$659$	10.9282			0.425702			0.212851	−	0.977085i	$-0.431725\pi$
$659$	10.9282			0.425702			0.212851	+	0.977085i	$0.431725\pi$
$660$		0			0
$661$	−1.76795	+	3.06218i	−0.0687653	+	0.119105i	−0.898358	−	0.439264i	$-0.855239\pi$
$661$	−1.76795	+	3.06218i	−0.0687653	+	0.119105i	0.829593	+	0.558369i	$0.188573\pi$
$662$	8.02628	−	13.9019i	0.311950	−	0.540314i
$663$		0			0
$664$	23.1384			0.897946
$665$	−4.26795	−	4.92820i	−0.165504	−	0.191108i
$666$		0			0
$667$	3.92820	+	6.80385i	0.152101	+	0.263446i
$668$	0.248711	−	0.430781i	0.00962293	−	0.0166674i
$669$		0			0
$670$	−0.973721	−	1.68653i	−0.0376181	−	0.0651565i
$671$	10.9282			0.421879
$672$		0			0
$673$	−44.6603			−1.72153			−0.860763	−	0.509006i	$-0.830013\pi$
$673$	−44.6603			−1.72153			−0.860763	+	0.509006i	$0.830013\pi$
$674$	−12.4378	−	21.5429i	−0.479087	−	0.829803i
$675$		0			0
$676$	14.5359	−	25.1769i	0.559073	−	0.968343i
$677$	−4.43782	−	7.68653i	−0.170559	−	0.295417i	0.768056	−	0.640382i	$-0.221224\pi$
$677$	−4.43782	−	7.68653i	−0.170559	−	0.295417i	−0.938616	+	0.344965i	$0.887891\pi$
$678$		0			0
$679$	−0.928203	+	2.67949i	−0.0356212	+	0.102829i
$680$	17.0718			0.654674
$681$		0			0
$682$	6.46410	−	11.1962i	0.247523	−	0.428723i
$683$	5.02628	−	8.70577i	0.192325	−	0.333117i	−0.753695	−	0.657224i	$-0.771730\pi$
$683$	5.02628	−	8.70577i	0.192325	−	0.333117i	0.946020	+	0.324107i	$0.105064\pi$
$684$		0			0
$685$	−8.19615			−0.313159
$686$	12.0455	+	6.22243i	0.459900	+	0.237574i
$687$		0			0
$688$	3.85641	+	6.67949i	0.147024	+	0.254653i
$689$	−24.0526	+	41.6603i	−0.916330	+	1.58713i
$690$		0			0
$691$	9.42820	+	16.3301i	0.358666	+	0.621227i	0.987738	−	0.156119i	$-0.0498985\pi$
$691$	9.42820	+	16.3301i	0.358666	+	0.621227i	−0.629072	+	0.777347i	$0.716565\pi$
$692$	31.4256			1.19462
$693$		0			0
$694$	−25.5692			−0.970594
$695$	−3.96410	−	6.86603i	−0.150367	−	0.260443i
$696$		0			0
$697$	−9.19615	+	15.9282i	−0.348329	+	0.603324i
$698$	8.05256	+	13.9474i	0.304794	+	0.527918i
$699$		0			0
$700$	−3.80385	+	0.732051i	−0.143772	+	0.0276689i
$701$	−22.5885			−0.853154			−0.426577	−	0.904451i	$-0.640281\pi$
$701$	−22.5885			−0.853154			−0.426577	+	0.904451i	$0.640281\pi$
$702$		0			0
$703$	8.86603	−	15.3564i	0.334388	−	0.579178i
$704$	−2.92820	+	5.07180i	−0.110361	+	0.191151i
$705$		0			0
$706$	15.4641			0.581999
$707$	−18.5885	−	21.4641i	−0.699091	−	0.807241i
$708$		0			0
$709$	7.46410	+	12.9282i	0.280320	+	0.485529i	0.971464	−	0.237189i	$-0.0762260\pi$
$709$	7.46410	+	12.9282i	0.280320	+	0.485529i	−0.691143	+	0.722718i	$0.742893\pi$
$710$	−1.53590	+	2.66025i	−0.0576412	+	0.0998376i
$711$		0			0
$712$	−11.5692	−	20.0385i	−0.433575	−	0.750974i
$713$	8.19615			0.306948
$714$		0			0
$715$	−15.6603			−0.585660
$716$	7.32051	+	12.6795i	0.273580	+	0.473855i
$717$		0			0
$718$	1.73205	−	3.00000i	0.0646396	−	0.111959i
$719$	−13.7321	−	23.7846i	−0.512119	−	0.887016i	−0.999901	−	0.0140509i	$-0.995527\pi$
$719$	−13.7321	−	23.7846i	−0.512119	−	0.887016i	0.487782	−	0.872965i	$-0.337806\pi$
$720$		0			0
$721$	3.10770	−	0.598076i	0.115737	−	0.0222735i
$722$	9.46410			0.352217
$723$		0			0
$724$	7.55514	−	13.0859i	0.280784	−	0.486333i
$725$	3.09808	−	5.36603i	0.115060	−	0.199289i
$726$		0			0
$727$	−30.6603			−1.13713			−0.568563	−	0.822640i	$-0.692500\pi$
$727$	−30.6603			−1.13713			−0.568563	+	0.822640i	$0.692500\pi$
$728$	−12.5885	+	36.3397i	−0.466559	+	1.34684i
$729$		0			0
$730$	1.70577	+	2.95448i	0.0631334	+	0.109350i
$731$	−24.2224	+	41.9545i	−0.895899	+	1.55174i
$732$		0			0
$733$	9.33013	+	16.1603i	0.344616	+	0.596893i	0.985284	−	0.170926i	$-0.0546758\pi$
$733$	9.33013	+	16.1603i	0.344616	+	0.596893i	−0.640668	+	0.767818i	$0.721342\pi$
$734$	−0.588457			−0.0217204
$735$		0			0
$736$	−7.42563			−0.273712
$737$	−3.63397	−	6.29423i	−0.133859	−	0.231851i
$738$		0			0
$739$	6.89230	−	11.9378i	0.253538	−	0.439140i	−0.710960	−	0.703233i	$-0.751739\pi$
$739$	6.89230	−	11.9378i	0.253538	−	0.439140i	0.964497	+	0.264093i	$0.0850725\pi$
$740$	−5.26795	−	9.12436i	−0.193654	−	0.335418i
$741$		0			0
$742$	5.32051	−	15.3590i	0.195322	−	0.563846i
$743$	−49.9090			−1.83098			−0.915491	−	0.402338i	$-0.868198\pi$
$743$	−49.9090			−1.83098			−0.915491	+	0.402338i	$0.868198\pi$
$744$		0			0
$745$	10.9282	−	18.9282i	0.400378	−	0.693476i
$746$	−6.77757	+	11.7391i	−0.248144	+	0.429799i
$747$		0			0
$748$	26.9282			0.984593
$749$	21.2942	−	4.09808i	0.778074	−	0.149740i
$750$		0			0
$751$	−15.9641	−	27.6506i	−0.582538	−	1.00899i	−0.995177	−	0.0980914i	$-0.968726\pi$
$751$	−15.9641	−	27.6506i	−0.582538	−	1.00899i	0.412639	−	0.910895i	$-0.364607\pi$
$752$	1.07180	−	1.85641i	0.0390844	−	0.0676962i
$753$		0			0
$754$	−13.0000	−	22.5167i	−0.473432	−	0.820008i
$755$	−4.92820			−0.179356
$756$		0			0
$757$	−0.143594			−0.00521900			−0.00260950	−	0.999997i	$-0.500831\pi$
$757$	−0.143594			−0.00521900			−0.00260950	+	0.999997i	$0.500831\pi$
$758$	−10.3660	−	17.9545i	−0.376511	−	0.652136i
$759$		0			0
$760$	−3.12436	+	5.41154i	−0.113332	+	0.196297i
$761$	21.6340	+	37.4711i	0.784231	+	1.35833i	0.929457	+	0.368929i	$0.120276\pi$
$761$	21.6340	+	37.4711i	0.784231	+	1.35833i	−0.145226	+	0.989398i	$0.546391\pi$
$762$		0			0
$763$	−19.0526	−	22.0000i	−0.689749	−	0.796453i
$764$	7.21539			0.261044
$765$		0			0
$766$	−4.14359	+	7.17691i	−0.149714	+	0.259312i
$767$	29.2224	−	50.6147i	1.05516	−	1.82759i
$768$		0			0
$769$	17.6795			0.637539			0.318769	−	0.947832i	$-0.396730\pi$
$769$	17.6795			0.637539			0.318769	+	0.947832i	$0.396730\pi$
$770$	5.19615	−	1.00000i	0.187256	−	0.0360375i
$771$		0			0
$772$	−6.73205	−	11.6603i	−0.242292	−	0.419662i
$773$	−0.758330	+	1.31347i	−0.0272752	+	0.0472421i	−0.879341	−	0.476193i	$-0.842016\pi$
$773$	−0.758330	+	1.31347i	−0.0272752	+	0.0472421i	0.852066	+	0.523435i	$0.175350\pi$
$774$		0			0
$775$	−3.23205	−	5.59808i	−0.116099	−	0.201089i
$776$	2.71797			0.0975694
$777$		0			0
$778$	26.7846			0.960275
$779$	−3.36603	−	5.83013i	−0.120600	−	0.208886i
$780$		0			0
$781$	−5.73205	+	9.92820i	−0.205109	+	0.355259i
$782$	−3.12436	−	5.41154i	−0.111727	−	0.193516i
$783$		0			0
$784$	−1.07180	+	7.42563i	−0.0382785	+	0.265201i
$785$	14.3923			0.513683
$786$		0			0
$787$	−3.26795	+	5.66025i	−0.116490	+	0.201766i	−0.918374	−	0.395713i	$-0.870498\pi$
$787$	−3.26795	+	5.66025i	−0.116490	+	0.201766i	0.801885	+	0.597479i	$0.203831\pi$
$788$	12.9282	−	22.3923i	0.460548	−	0.797693i
$789$		0			0
$790$	9.80385			0.348805
$791$	−4.26795	+	12.3205i	−0.151751	+	0.438067i
$792$		0			0
$793$	−11.4641	−	19.8564i	−0.407102	−	0.705122i
$794$	−7.61474	+	13.1891i	−0.270237	+	0.468064i
$795$		0			0
$796$	16.1051	+	27.8949i	0.570831	+	0.988708i
$797$	42.0526			1.48958			0.744789	−	0.667300i	$-0.232550\pi$
$797$	42.0526			1.48958			0.744789	+	0.667300i	$0.232550\pi$
$798$		0			0
$799$	13.4641			0.476326
$800$	2.92820	+	5.07180i	0.103528	+	0.179315i
$801$		0			0
$802$	−1.60770	+	2.78461i	−0.0567697	+	0.0983280i
$803$	6.36603	+	11.0263i	0.224652	+	0.389109i
$804$		0			0
$805$	2.19615	+	2.53590i	0.0774042	+	0.0893787i
$806$	−27.1244			−0.955415
$807$		0			0
$808$	−13.6077	+	23.5692i	−0.478717	+	0.829162i
$809$	−14.8564	+	25.7321i	−0.522323	+	0.904691i	0.477339	+	0.878719i	$0.341601\pi$
$809$	−14.8564	+	25.7321i	−0.522323	+	0.904691i	−0.999663	+	0.0259716i	$0.991732\pi$
$810$		0			0
$811$	3.46410			0.121641			0.0608205	−	0.998149i	$-0.480628\pi$
$811$	3.46410			0.121641			0.0608205	+	0.998149i	$0.480628\pi$
$812$	−15.7128	−	18.1436i	−0.551412	−	0.636715i
$813$		0			0
$814$	7.19615	+	12.4641i	0.252225	+	0.436867i
$815$	−2.92820	+	5.07180i	−0.102570	+	0.177657i
$816$		0			0
$817$	−8.86603	−	15.3564i	−0.310183	−	0.537253i
$818$	−22.5885			−0.789787
$819$		0			0
$820$	−4.00000			−0.139686
$821$	9.75833	+	16.9019i	0.340568	+	0.589881i	0.984538	−	0.175169i	$-0.0560473\pi$
$821$	9.75833	+	16.9019i	0.340568	+	0.589881i	−0.643970	+	0.765051i	$0.722714\pi$
$822$		0			0
$823$	11.5885	−	20.0718i	0.403948	−	0.699659i	−0.590250	−	0.807220i	$-0.700971\pi$
$823$	11.5885	−	20.0718i	0.403948	−	0.699659i	0.994198	+	0.107561i	$0.0343043\pi$
$824$	−1.51666	−	2.62693i	−0.0528354	−	0.0915135i
$825$		0			0
$826$	−6.46410	+	18.6603i	−0.224915	+	0.649273i
$827$	52.2487			1.81687			0.908433	−	0.418031i	$-0.137280\pi$
$827$	52.2487			1.81687			0.908433	+	0.418031i	$0.137280\pi$
$828$		0			0
$829$	12.6962	−	21.9904i	0.440956	−	0.763758i	−0.556805	−	0.830643i	$-0.687973\pi$
$829$	12.6962	−	21.9904i	0.440956	−	0.763758i	0.997761	+	0.0668857i	$0.0213063\pi$
$830$	−3.33975	+	5.78461i	−0.115924	+	0.200787i
$831$		0			0
$832$	12.2872			0.425982
$833$	−43.7583	+	17.4904i	−1.51614	+	0.606006i
$834$		0			0
$835$	0.169873	+	0.294229i	0.00587870	+	0.0101822i
$836$	−4.92820	+	8.53590i	−0.170445	+	0.295220i
$837$		0			0
$838$	10.4449	+	18.0910i	0.360812	+	0.624944i
$839$	40.4449			1.39631			0.698156	−	0.715946i	$-0.254004\pi$
$839$	40.4449			1.39631			0.698156	+	0.715946i	$0.254004\pi$
$840$		0			0
$841$	9.39230			0.323873
$842$	5.09808	+	8.83013i	0.175691	+	0.304306i
$843$		0			0
$844$	15.3205	−	26.5359i	0.527354	−	0.913403i
$845$	9.92820	+	17.1962i	0.341541	+	0.591566i
$846$		0			0
$847$	−9.18653	+	1.76795i	−0.315653	+	0.0607475i
$848$	8.99485			0.308884
$849$		0			0
$850$	−2.46410	+	4.26795i	−0.0845180	+	0.146389i
$851$	−4.56218	+	7.90192i	−0.156389	+	0.270874i
$852$		0			0
$853$	19.9808			0.684128			0.342064	−	0.939677i	$-0.388874\pi$
$853$	19.9808			0.684128			0.342064	+	0.939677i	$0.388874\pi$
$854$	5.07180	+	5.85641i	0.173553	+	0.200402i
$855$		0			0
$856$	−10.3923	−	18.0000i	−0.355202	−	0.615227i
$857$	2.43782	−	4.22243i	0.0832744	−	0.144236i	−0.821380	−	0.570381i	$-0.806796\pi$
$857$	2.43782	−	4.22243i	0.0832744	−	0.144236i	0.904655	+	0.426146i	$0.140129\pi$
$858$		0			0
$859$	−0.267949	−	0.464102i	−0.00914231	−	0.0158349i	0.861418	−	0.507897i	$-0.169577\pi$
$859$	−0.267949	−	0.464102i	−0.00914231	−	0.0158349i	−0.870560	+	0.492062i	$0.836243\pi$
$860$	−10.5359			−0.359271
$861$		0			0
$862$	−12.6795			−0.431865
$863$	−3.19615	−	5.53590i	−0.108798	−	0.188444i	0.806485	−	0.591254i	$-0.201367\pi$
$863$	−3.19615	−	5.53590i	−0.108798	−	0.188444i	−0.915284	+	0.402810i	$0.868034\pi$
$864$		0			0
$865$	−10.7321	+	18.5885i	−0.364901	+	0.632027i
$866$	1.75833	+	3.04552i	0.0597505	+	0.103491i
$867$		0			0
$868$	−24.5885	+	4.73205i	−0.834587	+	0.160616i
$869$	36.5885			1.24118
$870$		0			0
$871$	−7.62436	+	13.2058i	−0.258341	+	0.447460i
$872$	−13.9474	+	24.1577i	−0.472320	+	0.818082i
$873$		0			0
$874$	2.28719			0.0773653
$875$	0.866025	−	2.50000i	0.0292770	−	0.0845154i
$876$		0			0
$877$	15.9282	+	27.5885i	0.537857	+	0.931596i	0.999019	+	0.0442800i	$0.0140994\pi$
$877$	15.9282	+	27.5885i	0.537857	+	0.931596i	−0.461162	+	0.887316i	$0.652567\pi$
$878$	2.73205	−	4.73205i	0.0922022	−	0.159699i
$879$		0			0
$880$	1.46410	+	2.53590i	0.0493549	+	0.0854851i
$881$	17.8564			0.601598			0.300799	−	0.953688i	$-0.402747\pi$
$881$	17.8564			0.601598			0.300799	+	0.953688i	$0.402747\pi$
$882$		0			0
$883$	22.4115			0.754208			0.377104	−	0.926171i	$-0.376920\pi$
$883$	22.4115			0.754208			0.377104	+	0.926171i	$0.376920\pi$
$884$	−28.2487	−	48.9282i	−0.950107	−	1.64563i
$885$		0			0
$886$	−0.928203	+	1.60770i	−0.0311836	+	0.0540116i
$887$	−14.3660	−	24.8827i	−0.482364	−	0.835479i	0.517431	−	0.855725i	$-0.326888\pi$
$887$	−14.3660	−	24.8827i	−0.482364	−	0.835479i	−0.999795	+	0.0202460i	$0.993555\pi$
$888$		0			0
$889$	−13.1603	+	37.9904i	−0.441381	+	1.27416i
$890$	6.67949			0.223897
$891$		0			0
$892$	0.287187	−	0.497423i	0.00961573	−	0.0166549i
$893$	−2.46410	+	4.26795i	−0.0824580	+	0.142821i
$894$		0			0
$895$	−10.0000			−0.334263
$896$	26.3538	−	5.07180i	0.880420	−	0.169437i
$897$		0			0
$898$	2.98076	+	5.16283i	0.0994693	+	0.172286i
$899$	20.0263	−	34.6865i	0.667914	−	1.15686i
$900$		0			0
$901$	28.2487	+	48.9282i	0.941101	+	1.63003i
$902$	5.46410			0.181935
$903$		0			0
$904$	12.4974			0.415658
$905$	5.16025	+	8.93782i	0.171533	+	0.297103i
$906$		0			0
$907$	−1.20577	+	2.08846i	−0.0400370	+	0.0693461i	−0.885350	−	0.464926i	$-0.846081\pi$
$907$	−1.20577	+	2.08846i	−0.0400370	+	0.0693461i	0.845313	+	0.534272i	$0.179414\pi$
$908$	−11.4641	−	19.8564i	−0.380450	−	0.658958i
$909$		0			0
$910$	−7.26795	−	8.39230i	−0.240930	−	0.278202i
$911$	11.2679			0.373324			0.186662	−	0.982424i	$-0.440233\pi$
$911$	11.2679			0.373324			0.186662	+	0.982424i	$0.440233\pi$
$912$		0			0
$913$	−12.4641	+	21.5885i	−0.412502	+	0.714474i
$914$	0.241670	−	0.418584i	0.00799372	−	0.0138455i
$915$		0			0
$916$	4.39230			0.145126
$917$	−22.1769	+	4.26795i	−0.732346	+	0.140940i
$918$		0			0
$919$	1.57180	+	2.72243i	0.0518488	+	0.0898047i	0.890785	−	0.454425i	$-0.150155\pi$
$919$	1.57180	+	2.72243i	0.0518488	+	0.0898047i	−0.838936	+	0.544230i	$0.816822\pi$
$920$	1.60770	−	2.78461i	0.0530041	−	0.0918059i
$921$		0			0
$922$	12.8038	+	22.1769i	0.421672	+	0.730358i
$923$	24.0526			0.791700
$924$		0			0
$925$	7.19615			0.236608
$926$	8.15064	+	14.1173i	0.267846	+	0.463924i
$927$		0			0
$928$	−18.1436	+	31.4256i	−0.595593	+	1.03160i
$929$	3.22243	+	5.58142i	0.105725	+	0.183120i	0.914034	−	0.405638i	$-0.132950\pi$
$929$	3.22243	+	5.58142i	0.105725	+	0.183120i	−0.808309	+	0.588758i	$0.799617\pi$
$930$		0			0
$931$	2.46410	−	17.0718i	0.0807577	−	0.559506i
$932$	−25.3590			−0.830661
$933$		0			0
$934$	10.1962	−	17.6603i	0.333628	−	0.577861i
$935$	−9.19615	+	15.9282i	−0.300746	+	0.520908i
$936$		0			0
$937$	28.2679			0.923474			0.461737	−	0.887017i	$-0.347226\pi$
$937$	28.2679			0.923474			0.461737	+	0.887017i	$0.347226\pi$
$938$	1.68653	−	4.86860i	0.0550673	−	0.158966i
$939$		0			0
$940$	1.46410	+	2.53590i	0.0477537	+	0.0827119i
$941$	4.02628	−	6.97372i	0.131253	−	0.227337i	−0.792907	−	0.609343i	$-0.791433\pi$
$941$	4.02628	−	6.97372i	0.131253	−	0.227337i	0.924160	+	0.382006i	$0.124767\pi$
$942$		0			0
$943$	1.73205	+	3.00000i	0.0564033	+	0.0976934i
$944$	−10.9282			−0.355683
$945$		0			0
$946$	14.3923			0.467934
$947$	5.83013	+	10.0981i	0.189454	+	0.328143i	0.945068	−	0.326873i	$-0.105995\pi$
$947$	5.83013	+	10.0981i	0.189454	+	0.328143i	−0.755615	+	0.655017i	$0.772662\pi$
$948$		0			0
$949$	13.3564	−	23.1340i	0.433567	−	0.750961i
$950$	−0.901924	−	1.56218i	−0.0292623	−	0.0506837i
$951$		0			0
$952$	29.5692	+	34.1436i	0.958344	+	1.10660i
$953$	−40.1051			−1.29913			−0.649566	−	0.760305i	$-0.725049\pi$
$953$	−40.1051			−1.29913			−0.649566	+	0.760305i	$0.725049\pi$
$954$		0			0
$955$	−2.46410	+	4.26795i	−0.0797365	+	0.138108i
$956$	−15.3205	+	26.5359i	−0.495501	+	0.858232i
$957$		0			0
$958$	−24.0000			−0.775405
$959$	−14.1962	−	16.3923i	−0.458418	−	0.529335i
$960$		0			0
$961$	−5.39230	−	9.33975i	−0.173945	−	0.301282i
$962$	15.0981	−	26.1506i	0.486782	−	0.843130i
$963$		0			0
$964$	4.78461	+	8.28719i	0.154102	+	0.266912i
$965$	9.19615			0.296035
$966$		0			0
$967$	14.1244			0.454209			0.227104	−	0.973870i	$-0.427074\pi$
$967$	14.1244			0.454209			0.227104	+	0.973870i	$0.427074\pi$
$968$	4.48334	+	7.76537i	0.144100	+	0.249589i
$969$		0			0
$970$	−0.392305	+	0.679492i	−0.0125961	+	0.0218172i
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	6.86603	−	19.8205i	0.220115	−	0.635416i
$974$	23.1244			0.740952
$975$		0			0
$976$	−2.14359	+	3.71281i	−0.0686148	+	0.118844i
$977$	7.29423	−	12.6340i	0.233363	−	0.404197i	−0.725433	−	0.688293i	$-0.758360\pi$
$977$	7.29423	−	12.6340i	0.233363	−	0.404197i	0.958796	+	0.284097i	$0.0916936\pi$
$978$		0			0
$979$	24.9282			0.796709
$980$	−8.05256	−	6.33975i	−0.257230	−	0.202516i
$981$		0			0
$982$	−3.75129	−	6.49742i	−0.119708	−	0.207341i
$983$	10.0981	−	17.4904i	0.322079	−	0.557857i	−0.658838	−	0.752285i	$-0.728952\pi$
$983$	10.0981	−	17.4904i	0.322079	−	0.557857i	0.980917	+	0.194428i	$0.0622851\pi$
$984$		0			0
$985$	8.83013	+	15.2942i	0.281351	+	0.487315i
$986$	−30.5359			−0.972461
$987$		0			0
$988$	20.6795			0.657902
$989$	4.56218	+	7.90192i	0.145069	+	0.251267i
$990$		0			0
$991$	−27.5526	+	47.7224i	−0.875236	+	1.51595i	−0.0187246	+	0.999825i	$0.505961\pi$
$991$	−27.5526	+	47.7224i	−0.875236	+	1.51595i	−0.856511	+	0.516128i	$0.827373\pi$
$992$	18.9282	+	32.7846i	0.600971	+	1.04091i
$993$		0			0
$994$	−7.98076	+	1.53590i	−0.253134	+	0.0487157i
$995$	−22.0000			−0.697447
$996$		0			0
$997$	2.00962	−	3.48076i	0.0636453	−	0.110237i	−0.832447	−	0.554105i	$-0.813061\pi$
$997$	2.00962	−	3.48076i	0.0636453	−	0.110237i	0.896092	+	0.443868i	$0.146394\pi$
$998$	−7.49038	+	12.9737i	−0.237104	+	0.410676i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.c.46.2		4
3.2	odd	2		105.2.i.d.46.1	yes	4
7.2	even	3	inner	315.2.j.c.226.2		4
7.3	odd	6		2205.2.a.ba.1.1		2
7.4	even	3		2205.2.a.z.1.1		2
12.11	even	2		1680.2.bg.o.1201.2		4
15.2	even	4		525.2.r.f.424.1		4
15.8	even	4		525.2.r.a.424.2		4
15.14	odd	2		525.2.i.f.151.2		4
21.2	odd	6		105.2.i.d.16.1	✓	4
21.5	even	6		735.2.i.l.226.1		4
21.11	odd	6		735.2.a.g.1.2		2
21.17	even	6		735.2.a.h.1.2		2
21.20	even	2		735.2.i.l.361.1		4
84.23	even	6		1680.2.bg.o.961.2		4
105.2	even	12		525.2.r.a.499.2		4
105.23	even	12		525.2.r.f.499.1		4
105.44	odd	6		525.2.i.f.226.2		4
105.59	even	6		3675.2.a.be.1.1		2
105.74	odd	6		3675.2.a.bg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.1	✓	4	21.2	odd	6
105.2.i.d.46.1	yes	4	3.2	odd	2
315.2.j.c.46.2		4	1.1	even	1	trivial
315.2.j.c.226.2		4	7.2	even	3	inner
525.2.i.f.151.2		4	15.14	odd	2
525.2.i.f.226.2		4	105.44	odd	6
525.2.r.a.424.2		4	15.8	even	4
525.2.r.a.499.2		4	105.2	even	12
525.2.r.f.424.1		4	15.2	even	4
525.2.r.f.499.1		4	105.23	even	12
735.2.a.g.1.2		2	21.11	odd	6
735.2.a.h.1.2		2	21.17	even	6
735.2.i.l.226.1		4	21.5	even	6
735.2.i.l.361.1		4	21.20	even	2
1680.2.bg.o.961.2		4	84.23	even	6
1680.2.bg.o.1201.2		4	12.11	even	2
2205.2.a.z.1.1		2	7.4	even	3
2205.2.a.ba.1.1		2	7.3	odd	6
3675.2.a.be.1.1		2	105.59	even	6
3675.2.a.bg.1.1		2	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.633975i) q^{2} +(0.732051 - 1.26795i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.866025 + 2.50000i) q^{7} +2.53590 q^{8} +O(q^{10})\)	\(q+(0.366025 + 0.633975i) q^{2} +(0.732051 - 1.26795i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.866025 + 2.50000i) q^{7} +2.53590 q^{8} +(-0.366025 + 0.633975i) q^{10} +(-1.36603 + 2.36603i) q^{11} +5.73205 q^{13} +(-1.90192 + 0.366025i) q^{14} +(-0.535898 - 0.928203i) q^{16} +(3.36603 - 5.83013i) q^{17} +(1.23205 + 2.13397i) q^{19} +1.46410 q^{20} -2.00000 q^{22} +(-0.633975 - 1.09808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.09808 + 3.63397i) q^{26} +(2.53590 + 2.92820i) q^{28} -6.19615 q^{29} +(-3.23205 + 5.59808i) q^{31} +(2.92820 - 5.07180i) q^{32} +4.92820 q^{34} +(-2.59808 + 0.500000i) q^{35} +(-3.59808 - 6.23205i) q^{37} +(-0.901924 + 1.56218i) q^{38} +(1.26795 + 2.19615i) q^{40} -2.73205 q^{41} -7.19615 q^{43} +(2.00000 + 3.46410i) q^{44} +(0.464102 - 0.803848i) q^{46} +(1.00000 + 1.73205i) q^{47} +(-5.50000 - 4.33013i) q^{49} -0.732051 q^{50} +(4.19615 - 7.26795i) q^{52} +(-4.19615 + 7.26795i) q^{53} -2.73205 q^{55} +(-2.19615 + 6.33975i) q^{56} +(-2.26795 - 3.92820i) q^{58} +(5.09808 - 8.83013i) q^{59} +(-2.00000 - 3.46410i) q^{61} -4.73205 q^{62} +2.14359 q^{64} +(2.86603 + 4.96410i) q^{65} +(-1.33013 + 2.30385i) q^{67} +(-4.92820 - 8.53590i) q^{68} +(-1.26795 - 1.46410i) q^{70} +4.19615 q^{71} +(2.33013 - 4.03590i) q^{73} +(2.63397 - 4.56218i) q^{74} +3.60770 q^{76} +(-4.73205 - 5.46410i) q^{77} +(-6.69615 - 11.5981i) q^{79} +(0.535898 - 0.928203i) q^{80} +(-1.00000 - 1.73205i) q^{82} +9.12436 q^{83} +6.73205 q^{85} +(-2.63397 - 4.56218i) q^{86} +(-3.46410 + 6.00000i) q^{88} +(-4.56218 - 7.90192i) q^{89} +(-4.96410 + 14.3301i) q^{91} -1.85641 q^{92} +(-0.732051 + 1.26795i) q^{94} +(-1.23205 + 2.13397i) q^{95} +1.07180 q^{97} +(0.732051 - 5.07180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8	\( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 24 q^{8} + 2 q^{10} - 2 q^{11} + 16 q^{13} - 18 q^{14} - 16 q^{16} + 10 q^{17} - 2 q^{19} - 8 q^{20} - 8 q^{22} - 6 q^{23} - 2 q^{25} - 2 q^{26} + 24 q^{28} - 4 q^{29} - 6 q^{31} - 16 q^{32} - 8 q^{34} - 4 q^{37} - 14 q^{38} + 12 q^{40} - 4 q^{41} - 8 q^{43} + 8 q^{44} - 12 q^{46} + 4 q^{47} - 22 q^{49} + 4 q^{50} - 4 q^{52} + 4 q^{53} - 4 q^{55} + 12 q^{56} - 16 q^{58} + 10 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} + 8 q^{65} + 12 q^{67} + 8 q^{68} - 12 q^{70} - 4 q^{71} - 8 q^{73} + 14 q^{74} + 56 q^{76} - 12 q^{77} - 6 q^{79} + 16 q^{80} - 4 q^{82} - 12 q^{83} + 20 q^{85} - 14 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{92} + 4 q^{94} + 2 q^{95} + 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 24 * q^8 + 2 * q^10 - 2 * q^11 + 16 * q^13 - 18 * q^14 - 16 * q^16 + 10 * q^17 - 2 * q^19 - 8 * q^20 - 8 * q^22 - 6 * q^23 - 2 * q^25 - 2 * q^26 + 24 * q^28 - 4 * q^29 - 6 * q^31 - 16 * q^32 - 8 * q^34 - 4 * q^37 - 14 * q^38 + 12 * q^40 - 4 * q^41 - 8 * q^43 + 8 * q^44 - 12 * q^46 + 4 * q^47 - 22 * q^49 + 4 * q^50 - 4 * q^52 + 4 * q^53 - 4 * q^55 + 12 * q^56 - 16 * q^58 + 10 * q^59 - 8 * q^61 - 12 * q^62 + 64 * q^64 + 8 * q^65 + 12 * q^67 + 8 * q^68 - 12 * q^70 - 4 * q^71 - 8 * q^73 + 14 * q^74 + 56 * q^76 - 12 * q^77 - 6 * q^79 + 16 * q^80 - 4 * q^82 - 12 * q^83 + 20 * q^85 - 14 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^92 + 4 * q^94 + 2 * q^95 + 32 * q^97 - 4 * q^98

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