LMFDB - Embedded newform 525.2.r.a.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.a.424.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.633975 - 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 - 1.26795i) q^{4} -0.732051 q^{6} +(2.50000 - 0.866025i) q^{7} +2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.633975 - 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 - 1.26795i) q^{4} -0.732051 q^{6} +(2.50000 - 0.866025i) q^{7} +2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{11} +(-1.26795 - 0.732051i) q^{12} -5.73205i q^{13} +(-1.90192 - 0.366025i) q^{14} +(-0.535898 + 0.928203i) q^{16} +(5.83013 - 3.36603i) q^{17} +(-0.633975 + 0.366025i) q^{18} +(-1.23205 + 2.13397i) q^{19} +(1.73205 - 2.00000i) q^{21} -2.00000i q^{22} +(-1.09808 - 0.633975i) q^{23} +(1.26795 + 2.19615i) q^{24} +(-2.09808 + 3.63397i) q^{26} -1.00000i q^{27} +(-2.92820 - 2.53590i) q^{28} -6.19615 q^{29} +(-3.23205 - 5.59808i) q^{31} +(5.07180 - 2.92820i) q^{32} +(2.36603 + 1.36603i) q^{33} -4.92820 q^{34} -1.46410 q^{36} +(-6.23205 - 3.59808i) q^{37} +(1.56218 - 0.901924i) q^{38} +(-2.86603 - 4.96410i) q^{39} +2.73205 q^{41} +(-1.83013 + 0.633975i) q^{42} +7.19615i q^{43} +(2.00000 - 3.46410i) q^{44} +(0.464102 + 0.803848i) q^{46} +(-1.73205 - 1.00000i) q^{47} +1.07180i q^{48} +(5.50000 - 4.33013i) q^{49} +(3.36603 - 5.83013i) q^{51} +(-7.26795 + 4.19615i) q^{52} +(7.26795 - 4.19615i) q^{53} +(-0.366025 + 0.633975i) q^{54} +(2.19615 + 6.33975i) q^{56} +2.46410i q^{57} +(3.92820 + 2.26795i) q^{58} +(5.09808 + 8.83013i) q^{59} +(-2.00000 + 3.46410i) q^{61} +4.73205i q^{62} +(0.500000 - 2.59808i) q^{63} -2.14359 q^{64} +(-1.00000 - 1.73205i) q^{66} +(2.30385 - 1.33013i) q^{67} +(-8.53590 - 4.92820i) q^{68} -1.26795 q^{69} -4.19615 q^{71} +(2.19615 + 1.26795i) q^{72} +(4.03590 - 2.33013i) q^{73} +(2.63397 + 4.56218i) q^{74} +3.60770 q^{76} +(5.46410 + 4.73205i) q^{77} +4.19615i q^{78} +(6.69615 - 11.5981i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} +9.12436i q^{83} +(-3.80385 - 0.732051i) q^{84} +(2.63397 - 4.56218i) q^{86} +(-5.36603 + 3.09808i) q^{87} +(-6.00000 + 3.46410i) q^{88} +(-4.56218 + 7.90192i) q^{89} +(-4.96410 - 14.3301i) q^{91} +1.85641i q^{92} +(-5.59808 - 3.23205i) q^{93} +(0.732051 + 1.26795i) q^{94} +(2.92820 - 5.07180i) q^{96} +1.07180i q^{97} +(-5.07180 + 0.732051i) q^{98} +2.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 + 4 * q^4 + 4 * q^6 + 10 * q^7 + 2 * q^9	$ 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9} + 2 q^{11} - 12 q^{12} - 18 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{18} + 2 q^{19} + 6 q^{23} + 12 q^{24} + 2 q^{26} + 16 q^{28} - 4 q^{29} - 6 q^{31} + 48 q^{32} + 6 q^{33} + 8 q^{34} + 8 q^{36} - 18 q^{37} - 18 q^{38} - 8 q^{39} + 4 q^{41} + 10 q^{42} + 8 q^{44} - 12 q^{46} + 22 q^{49} + 10 q^{51} - 36 q^{52} + 36 q^{53} + 2 q^{54} - 12 q^{56} - 12 q^{58} + 10 q^{59} - 8 q^{61} + 2 q^{63} - 64 q^{64} - 4 q^{66} + 30 q^{67} - 48 q^{68} - 12 q^{69} + 4 q^{71} - 12 q^{72} + 30 q^{73} + 14 q^{74} + 56 q^{76} + 8 q^{77} + 6 q^{79} - 2 q^{81} - 36 q^{84} + 14 q^{86} - 18 q^{87} - 24 q^{88} + 6 q^{89} - 6 q^{91} - 12 q^{93} - 4 q^{94} - 16 q^{96} - 48 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 + 4 * q^4 + 4 * q^6 + 10 * q^7 + 2 * q^9 + 2 * q^11 - 12 * q^12 - 18 * q^14 - 16 * q^16 + 6 * q^17 - 6 * q^18 + 2 * q^19 + 6 * q^23 + 12 * q^24 + 2 * q^26 + 16 * q^28 - 4 * q^29 - 6 * q^31 + 48 * q^32 + 6 * q^33 + 8 * q^34 + 8 * q^36 - 18 * q^37 - 18 * q^38 - 8 * q^39 + 4 * q^41 + 10 * q^42 + 8 * q^44 - 12 * q^46 + 22 * q^49 + 10 * q^51 - 36 * q^52 + 36 * q^53 + 2 * q^54 - 12 * q^56 - 12 * q^58 + 10 * q^59 - 8 * q^61 + 2 * q^63 - 64 * q^64 - 4 * q^66 + 30 * q^67 - 48 * q^68 - 12 * q^69 + 4 * q^71 - 12 * q^72 + 30 * q^73 + 14 * q^74 + 56 * q^76 + 8 * q^77 + 6 * q^79 - 2 * q^81 - 36 * q^84 + 14 * q^86 - 18 * q^87 - 24 * q^88 + 6 * q^89 - 6 * q^91 - 12 * q^93 - 4 * q^94 - 16 * q^96 - 48 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.633975	−	0.366025i	−0.448288	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$2$	−0.633975	−	0.366025i	−0.448288	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.732051	−	1.26795i	−0.366025	−	0.633975i
$5$		0			0
$5$		0			0
$6$	−0.732051			−0.298858
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$			2.53590i			0.896575i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.36603	+	2.36603i	0.411872	+	0.713384i	0.995094	−	0.0989291i	$-0.0315417\pi$
$11$	1.36603	+	2.36603i	0.411872	+	0.713384i	−0.583222	+	0.812313i	$0.698208\pi$
$12$	−1.26795	−	0.732051i	−0.366025	−	0.211325i
$13$		−	5.73205i		−	1.58978i	−0.606750	−	0.794892i	$-0.707527\pi$
$13$		−	5.73205i		−	1.58978i	0.606750	−	0.794892i	$-0.292473\pi$
$14$	−1.90192	−	0.366025i	−0.508311	−	0.0978244i
$15$		0			0
$16$	−0.535898	+	0.928203i	−0.133975	+	0.232051i
$17$	5.83013	−	3.36603i	1.41401	−	0.816381i	0.418250	−	0.908332i	$-0.362644\pi$
$17$	5.83013	−	3.36603i	1.41401	−	0.816381i	0.995764	+	0.0919509i	$0.0293103\pi$
$18$	−0.633975	+	0.366025i	−0.149429	+	0.0862730i
$19$	−1.23205	+	2.13397i	−0.282652	+	0.489567i	−0.972037	−	0.234828i	$-0.924547\pi$
$19$	−1.23205	+	2.13397i	−0.282652	+	0.489567i	0.689385	+	0.724395i	$0.257881\pi$
$20$		0			0
$21$	1.73205	−	2.00000i	0.377964	−	0.436436i
$22$		−	2.00000i		−	0.426401i
$23$	−1.09808	−	0.633975i	−0.228965	−	0.132193i	0.381130	−	0.924522i	$-0.375535\pi$
$23$	−1.09808	−	0.633975i	−0.228965	−	0.132193i	−0.610094	+	0.792329i	$0.708868\pi$
$24$	1.26795	+	2.19615i	0.258819	+	0.448288i
$25$		0			0
$26$	−2.09808	+	3.63397i	−0.411467	+	0.712681i
$27$		−	1.00000i		−	0.192450i
$28$	−2.92820	−	2.53590i	−0.553378	−	0.479240i
$29$	−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	−0.995421	−	0.0955896i	$-0.969526\pi$
$31$	−3.23205	−	5.59808i	−0.580493	−	1.00544i	0.414927	−	0.909855i	$-0.363807\pi$
$32$	5.07180	−	2.92820i	0.896575	−	0.517638i
$33$	2.36603	+	1.36603i	0.411872	+	0.237795i
$34$	−4.92820			−0.845180
$35$		0			0
$36$	−1.46410			−0.244017
$37$	−6.23205	−	3.59808i	−1.02454	−	0.591520i	−0.109126	−	0.994028i	$-0.534805\pi$
$37$	−6.23205	−	3.59808i	−1.02454	−	0.591520i	−0.915417	+	0.402508i	$0.868139\pi$
$38$	1.56218	−	0.901924i	0.253419	−	0.146311i
$39$	−2.86603	−	4.96410i	−0.458931	−	0.794892i
$40$		0			0
$41$	2.73205			0.426675			0.213337	−	0.976979i	$-0.431567\pi$
$41$	2.73205			0.426675			0.213337	+	0.976979i	$0.431567\pi$
$42$	−1.83013	+	0.633975i	−0.282395	+	0.0978244i
$43$			7.19615i			1.09740i	0.836018	+	0.548701i	$0.184878\pi$
$43$			7.19615i			1.09740i	−0.836018	+	0.548701i	$0.815122\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	0.464102	+	0.803848i	0.0684280	+	0.118521i
$47$	−1.73205	−	1.00000i	−0.252646	−	0.145865i	0.368329	−	0.929695i	$-0.379930\pi$
$47$	−1.73205	−	1.00000i	−0.252646	−	0.145865i	−0.620975	+	0.783830i	$0.713263\pi$
$48$			1.07180i			0.154701i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	3.36603	−	5.83013i	0.471338	−	0.816381i
$52$	−7.26795	+	4.19615i	−1.00788	+	0.581902i
$53$	7.26795	−	4.19615i	0.998330	−	0.576386i	0.0905760	−	0.995890i	$-0.471129\pi$
$53$	7.26795	−	4.19615i	0.998330	−	0.576386i	0.907754	+	0.419504i	$0.137796\pi$
$54$	−0.366025	+	0.633975i	−0.0498097	+	0.0862730i
$55$		0			0
$56$	2.19615	+	6.33975i	0.293473	+	0.847184i
$57$			2.46410i			0.326378i
$58$	3.92820	+	2.26795i	0.515798	+	0.297796i
$59$	5.09808	+	8.83013i	0.663713	+	1.14958i	0.979633	+	0.200799i	$0.0643537\pi$
$59$	5.09808	+	8.83013i	0.663713	+	1.14958i	−0.315920	+	0.948786i	$0.602313\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$			4.73205i			0.600971i
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	−2.14359			−0.267949
$65$		0			0
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	2.30385	−	1.33013i	0.281460	−	0.162501i	−0.352624	−	0.935765i	$-0.614711\pi$
$67$	2.30385	−	1.33013i	0.281460	−	0.162501i	0.634084	+	0.773264i	$0.281377\pi$
$68$	−8.53590	−	4.92820i	−1.03513	−	0.597632i
$69$	−1.26795			−0.152643
$70$		0			0
$71$	−4.19615			−0.497992			−0.248996	−	0.968505i	$-0.580101\pi$
$71$	−4.19615			−0.497992			−0.248996	+	0.968505i	$0.580101\pi$
$72$	2.19615	+	1.26795i	0.258819	+	0.149429i
$73$	4.03590	−	2.33013i	0.472366	−	0.272721i	−0.244864	−	0.969558i	$-0.578743\pi$
$73$	4.03590	−	2.33013i	0.472366	−	0.272721i	0.717230	+	0.696837i	$0.245410\pi$
$74$	2.63397	+	4.56218i	0.306193	+	0.530342i
$75$		0			0
$76$	3.60770			0.413831
$77$	5.46410	+	4.73205i	0.622692	+	0.539267i
$78$			4.19615i			0.475121i
$79$	6.69615	−	11.5981i	0.753376	−	1.30489i	−0.192802	−	0.981238i	$-0.561757\pi$
$79$	6.69615	−	11.5981i	0.753376	−	1.30489i	0.946178	−	0.323648i	$-0.104909\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.73205	−	1.00000i	−0.191273	−	0.110432i
$83$			9.12436i			1.00153i	0.865584	+	0.500764i	$0.166948\pi$
$83$			9.12436i			1.00153i	−0.865584	+	0.500764i	$0.833052\pi$
$84$	−3.80385	−	0.732051i	−0.415034	−	0.0798733i
$85$		0			0
$86$	2.63397	−	4.56218i	0.284029	−	0.491952i
$87$	−5.36603	+	3.09808i	−0.575298	+	0.332149i
$88$	−6.00000	+	3.46410i	−0.639602	+	0.369274i
$89$	−4.56218	+	7.90192i	−0.483590	+	0.837602i	−0.999822	−	0.0188462i	$-0.994001\pi$
$89$	−4.56218	+	7.90192i	−0.483590	+	0.837602i	0.516233	+	0.856448i	$0.327334\pi$
$90$		0			0
$91$	−4.96410	−	14.3301i	−0.520379	−	1.50221i
$92$			1.85641i			0.193544i
$93$	−5.59808	−	3.23205i	−0.580493	−	0.335148i
$94$	0.732051	+	1.26795i	0.0755053	+	0.130779i
$95$		0			0
$96$	2.92820	−	5.07180i	0.298858	−	0.517638i
$97$			1.07180i			0.108824i	0.998519	+	0.0544122i	$0.0173285\pi$
$97$			1.07180i			0.108824i	−0.998519	+	0.0544122i	$0.982671\pi$
$98$	−5.07180	+	0.732051i	−0.512329	+	0.0739483i
$99$	2.73205			0.274581
$100$		0			0
$101$	5.36603	+	9.29423i	0.533939	+	0.924810i	0.999214	+	0.0396438i	$0.0126223\pi$
$101$	5.36603	+	9.29423i	0.533939	+	0.924810i	−0.465274	+	0.885167i	$0.654044\pi$
$102$	−4.26795	+	2.46410i	−0.422590	+	0.243982i
$103$	1.03590	+	0.598076i	0.102070	+	0.0589302i	0.550166	−	0.835055i	$-0.314564\pi$
$103$	1.03590	+	0.598076i	0.102070	+	0.0589302i	−0.448096	+	0.893985i	$0.647898\pi$
$104$	14.5359			1.42536
$105$		0			0
$106$	−6.14359			−0.596719
$107$	7.09808	+	4.09808i	0.686197	+	0.396176i	0.802186	−	0.597075i	$-0.203670\pi$
$107$	7.09808	+	4.09808i	0.686197	+	0.396176i	−0.115989	+	0.993251i	$0.537004\pi$
$108$	−1.26795	+	0.732051i	−0.122008	+	0.0704416i
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	0.999512	+	0.0312328i	$0.00994332\pi$
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	−0.472708	+	0.881219i	$0.656723\pi$
$110$		0			0
$111$	−7.19615			−0.683029
$112$	−0.535898	+	2.78461i	−0.0506376	+	0.263121i
$113$			4.92820i			0.463606i	0.972763	+	0.231803i	$0.0744625\pi$
$113$			4.92820i			0.463606i	−0.972763	+	0.231803i	$0.925537\pi$
$114$	0.901924	−	1.56218i	0.0844729	−	0.146311i
$115$		0			0
$116$	4.53590	+	7.85641i	0.421148	+	0.729449i
$117$	−4.96410	−	2.86603i	−0.458931	−	0.264964i
$118$		−	7.46410i		−	0.687126i
$119$	11.6603	−	13.4641i	1.06889	−	1.23425i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$	2.53590	−	1.46410i	0.229589	−	0.132554i
$123$	2.36603	−	1.36603i	0.213337	−	0.123170i
$124$	−4.73205	+	8.19615i	−0.424951	+	0.736036i
$125$		0			0
$126$	−1.26795	+	1.46410i	−0.112958	+	0.130433i
$127$			15.1962i			1.34844i	0.738530	+	0.674220i	$0.235520\pi$
$127$			15.1962i			1.34844i	−0.738530	+	0.674220i	$0.764480\pi$
$128$	−8.78461	−	5.07180i	−0.776457	−	0.448288i
$129$	3.59808	+	6.23205i	0.316793	+	0.548701i
$130$		0			0
$131$	−4.26795	+	7.39230i	−0.372892	+	0.645869i	−0.990009	−	0.141003i	$-0.954967\pi$
$131$	−4.26795	+	7.39230i	−0.372892	+	0.645869i	0.617117	+	0.786872i	$0.288301\pi$
$132$		−	4.00000i		−	0.348155i
$133$	−1.23205	+	6.40192i	−0.106832	+	0.555117i
$134$	−1.94744			−0.168233
$135$		0			0
$136$	8.53590	+	14.7846i	0.731947	+	1.26777i
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	−0.771567	−	0.636148i	$-0.780527\pi$
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	0.165137	+	0.986271i	$0.447193\pi$
$138$	0.803848	+	0.464102i	0.0684280	+	0.0395070i
$139$	7.92820			0.672461			0.336231	−	0.941780i	$-0.390848\pi$
$139$	7.92820			0.672461			0.336231	+	0.941780i	$0.390848\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$	2.66025	+	1.53590i	0.223244	+	0.128890i
$143$	13.5622	−	7.83013i	1.13413	−	0.654788i
$144$	0.535898	+	0.928203i	0.0446582	+	0.0773503i
$145$		0			0
$146$	−3.41154			−0.282341
$147$	2.59808	−	6.50000i	0.214286	−	0.536111i
$148$			10.5359i			0.866046i
$149$	−10.9282	+	18.9282i	−0.895273	+	1.55066i	−0.0618073	+	0.998088i	$0.519686\pi$
$149$	−10.9282	+	18.9282i	−0.895273	+	1.55066i	−0.833466	+	0.552571i	$0.813647\pi$
$150$		0			0
$151$	−2.46410	−	4.26795i	−0.200526	−	0.347321i	0.748172	−	0.663505i	$-0.230932\pi$
$151$	−2.46410	−	4.26795i	−0.200526	−	0.347321i	−0.948698	+	0.316184i	$0.897598\pi$
$152$	−5.41154	−	3.12436i	−0.438934	−	0.253419i
$153$		−	6.73205i		−	0.544254i
$154$	−1.73205	−	5.00000i	−0.139573	−	0.402911i
$155$		0			0
$156$	−4.19615	+	7.26795i	−0.335961	+	0.581902i
$157$	−12.4641	+	7.19615i	−0.994744	+	0.574315i	−0.906689	−	0.421800i	$-0.861398\pi$
$157$	−12.4641	+	7.19615i	−0.994744	+	0.574315i	−0.0880548	+	0.996116i	$0.528065\pi$
$158$	−8.49038	+	4.90192i	−0.675458	+	0.389976i
$159$	4.19615	−	7.26795i	0.332777	−	0.576386i
$160$		0			0
$161$	−3.29423	−	0.633975i	−0.259622	−	0.0499642i
$162$			0.732051i			0.0575153i
$163$	−5.07180	−	2.92820i	−0.397254	−	0.229355i	0.288045	−	0.957617i	$-0.406995\pi$
$163$	−5.07180	−	2.92820i	−0.397254	−	0.229355i	−0.685298	+	0.728262i	$0.740328\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$		0			0
$166$	3.33975	−	5.78461i	0.259215	−	0.448973i
$167$		−	0.339746i		−	0.0262903i	−0.999914	−	0.0131452i	$-0.995816\pi$
$167$		−	0.339746i		−	0.0262903i	0.999914	−	0.0131452i	$-0.00418436\pi$
$168$	5.07180	+	4.39230i	0.391298	+	0.338874i
$169$	−19.8564			−1.52742
$170$		0			0
$171$	1.23205	+	2.13397i	0.0942173	+	0.163189i
$172$	9.12436	−	5.26795i	0.695726	−	0.401677i
$173$	18.5885	+	10.7321i	1.41325	+	0.815943i	0.995693	−	0.0927063i	$-0.0295518\pi$
$173$	18.5885	+	10.7321i	1.41325	+	0.815943i	0.417561	+	0.908649i	$0.362885\pi$
$174$	4.53590			0.343866
$175$		0			0
$176$	−2.92820			−0.220722
$177$	8.83013	+	5.09808i	0.663713	+	0.383195i
$178$	5.78461	−	3.33975i	0.433575	−	0.250325i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	10.3205			0.767117			0.383559	−	0.923517i	$-0.374698\pi$
$181$	10.3205			0.767117			0.383559	+	0.923517i	$0.374698\pi$
$182$	−2.09808	+	10.9019i	−0.155520	+	0.808104i
$183$			4.00000i			0.295689i
$184$	1.60770	−	2.78461i	0.118521	−	0.205284i
$185$		0			0
$186$	2.36603	+	4.09808i	0.173485	+	0.300486i
$187$	15.9282	+	9.19615i	1.16479	+	0.672489i
$188$			2.92820i			0.213561i
$189$	−0.866025	−	2.50000i	−0.0629941	−	0.181848i
$190$		0			0
$191$	−2.46410	+	4.26795i	−0.178296	+	0.308818i	−0.941297	−	0.337579i	$-0.890392\pi$
$191$	−2.46410	+	4.26795i	−0.178296	+	0.308818i	0.763001	+	0.646397i	$0.223725\pi$
$192$	−1.85641	+	1.07180i	−0.133975	+	0.0773503i
$193$	7.96410	−	4.59808i	0.573269	−	0.330977i	−0.185185	−	0.982704i	$-0.559288\pi$
$193$	7.96410	−	4.59808i	0.573269	−	0.330977i	0.758454	+	0.651727i	$0.225955\pi$
$194$	0.392305	−	0.679492i	0.0281658	−	0.0487847i
$195$		0			0
$196$	−9.51666	−	3.80385i	−0.679761	−	0.271703i
$197$		−	17.6603i		−	1.25824i	−0.777308	−	0.629121i	$-0.783415\pi$
$197$		−	17.6603i		−	1.25824i	0.777308	−	0.629121i	$-0.216585\pi$
$198$	−1.73205	−	1.00000i	−0.123091	−	0.0710669i
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$		0			0
$201$	1.33013	−	2.30385i	0.0938199	−	0.162501i
$202$		−	7.85641i		−	0.552775i
$203$	−15.4904	+	5.36603i	−1.08721	+	0.376621i
$204$	−9.85641			−0.690086
$205$		0			0
$206$	−0.437822	−	0.758330i	−0.0305045	−	0.0528354i
$207$	−1.09808	+	0.633975i	−0.0763216	+	0.0440643i
$208$	5.32051	+	3.07180i	0.368911	+	0.212991i
$209$	−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	$0.243968\pi$
$212$	−10.6410	−	6.14359i	−0.730828	−	0.421944i
$213$	−3.63397	+	2.09808i	−0.248996	+	0.143758i
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$		0			0
$216$	2.53590			0.172546
$217$	−12.9282	−	11.1962i	−0.877624	−	0.760044i
$218$		−	8.05256i		−	0.545388i
$219$	2.33013	−	4.03590i	0.157455	−	0.272721i
$220$		0			0
$221$	−19.2942	−	33.4186i	−1.29787	−	2.24798i
$222$	4.56218	+	2.63397i	0.306193	+	0.176781i
$223$		−	0.392305i		−	0.0262707i	−0.999914	−	0.0131353i	$-0.995819\pi$
$223$		−	0.392305i		−	0.0262707i	0.999914	−	0.0131353i	$-0.00418123\pi$
$224$	10.1436	−	11.7128i	0.677747	−	0.782595i
$225$		0			0
$226$	1.80385	−	3.12436i	0.119990	−	0.207829i
$227$	13.5622	−	7.83013i	0.900153	−	0.519704i	0.0229034	−	0.999738i	$-0.492709\pi$
$227$	13.5622	−	7.83013i	0.900153	−	0.519704i	0.877250	+	0.480034i	$0.159376\pi$
$228$	3.12436	−	1.80385i	0.206916	−	0.119463i
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	−0.911322	−	0.411695i	$-0.864937\pi$
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	0.812199	+	0.583380i	$0.198270\pi$
$230$		0			0
$231$	7.09808	+	1.36603i	0.467019	+	0.0898779i
$232$		−	15.7128i		−	1.03160i
$233$	−15.0000	−	8.66025i	−0.982683	−	0.567352i	−0.0796037	−	0.996827i	$-0.525365\pi$
$233$	−15.0000	−	8.66025i	−0.982683	−	0.567352i	−0.903079	+	0.429474i	$0.858699\pi$
$234$	2.09808	+	3.63397i	0.137156	+	0.237560i
$235$		0			0
$236$	7.46410	−	12.9282i	0.485872	−	0.841554i
$237$		−	13.3923i		−	0.869924i
$238$	−12.3205	+	4.26795i	−0.798620	+	0.276650i
$239$	−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	0.741366	−	0.671101i	$-0.234178\pi$
$241$	−3.26795	−	5.66025i	−0.210507	−	0.364609i	−0.951873	+	0.306492i	$0.900845\pi$
$242$	−2.24167	+	1.29423i	−0.144100	+	0.0831962i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.85641			0.374918
$245$		0			0
$246$	−2.00000			−0.127515
$247$	12.2321	+	7.06218i	0.778307	+	0.449356i
$248$	14.1962	−	8.19615i	0.901457	−	0.520456i
$249$	4.56218	+	7.90192i	0.289116	+	0.500764i
$250$		0			0
$251$	6.58846			0.415860			0.207930	−	0.978144i	$-0.433327\pi$
$251$	6.58846			0.415860			0.207930	+	0.978144i	$0.433327\pi$
$252$	−3.66025	+	1.26795i	−0.230574	+	0.0798733i
$253$		−	3.46410i		−	0.217786i
$254$	5.56218	−	9.63397i	0.349002	−	0.604489i
$255$		0			0
$256$	5.85641	+	10.1436i	0.366025	+	0.633975i
$257$	−10.0981	−	5.83013i	−0.629901	−	0.363673i	0.150813	−	0.988562i	$-0.451811\pi$
$257$	−10.0981	−	5.83013i	−0.629901	−	0.363673i	−0.780714	+	0.624889i	$0.785144\pi$
$258$		−	5.26795i		−	0.327968i
$259$	−18.6962	−	3.59808i	−1.16172	−	0.223574i
$260$		0			0
$261$	−3.09808	+	5.36603i	−0.191766	+	0.332149i
$262$	5.41154	−	3.12436i	0.334326	−	0.193023i
$263$	10.7321	−	6.19615i	0.661767	−	0.382071i	−0.131183	−	0.991358i	$-0.541878\pi$
$263$	10.7321	−	6.19615i	0.661767	−	0.382071i	0.792950	+	0.609287i	$0.208544\pi$
$264$	−3.46410	+	6.00000i	−0.213201	+	0.369274i
$265$		0			0
$266$	3.12436	−	3.60770i	0.191567	−	0.221202i
$267$			9.12436i			0.558401i
$268$	−3.37307	−	1.94744i	−0.206043	−	0.118959i
$269$	−9.73205	−	16.8564i	−0.593374	−	1.02775i	−0.993774	−	0.111413i	$-0.964462\pi$
$269$	−9.73205	−	16.8564i	−0.593374	−	1.02775i	0.400401	−	0.916340i	$-0.368871\pi$
$270$		0			0
$271$	−8.46410	+	14.6603i	−0.514158	+	0.890547i	0.485708	+	0.874121i	$0.338562\pi$
$271$	−8.46410	+	14.6603i	−0.514158	+	0.890547i	−0.999865	+	0.0164256i	$0.994771\pi$
$272$			7.21539i			0.437497i
$273$	−11.4641	−	9.92820i	−0.693839	−	0.600882i
$274$	6.00000			0.362473
$275$		0			0
$276$	0.928203	+	1.60770i	0.0558713	+	0.0967719i
$277$	2.30385	−	1.33013i	0.138425	−	0.0799196i	−0.429188	−	0.903215i	$-0.641200\pi$
$277$	2.30385	−	1.33013i	0.138425	−	0.0799196i	0.567613	+	0.823295i	$0.307867\pi$
$278$	−5.02628	−	2.90192i	−0.301456	−	0.174046i
$279$	−6.46410			−0.386996
$280$		0			0
$281$	−13.8564			−0.826604			−0.413302	−	0.910594i	$-0.635625\pi$
$281$	−13.8564			−0.826604			−0.413302	+	0.910594i	$0.635625\pi$
$282$	1.26795	+	0.732051i	0.0755053	+	0.0435930i
$283$	−0.107695	+	0.0621778i	−0.00640181	+	0.00369609i	−0.503197	−	0.864171i	$-0.667843\pi$
$283$	−0.107695	+	0.0621778i	−0.00640181	+	0.00369609i	0.496796	+	0.867868i	$0.334510\pi$
$284$	3.07180	+	5.32051i	0.182278	+	0.315714i
$285$		0			0
$286$	−11.4641			−0.677887
$287$	6.83013	−	2.36603i	0.403170	−	0.139662i
$288$		−	5.85641i		−	0.345092i
$289$	14.1603	−	24.5263i	0.832956	−	1.44272i
$290$		0			0
$291$	0.535898	+	0.928203i	0.0314149	+	0.0544122i
$292$	−5.90897	−	3.41154i	−0.345796	−	0.199645i
$293$		−	5.07180i		−	0.296298i	−0.988965	−	0.148149i	$-0.952669\pi$
$293$		−	5.07180i		−	0.296298i	0.988965	−	0.148149i	$-0.0473314\pi$
$294$	−4.02628	+	3.16987i	−0.234817	+	0.184871i
$295$		0			0
$296$	9.12436	−	15.8038i	0.530342	−	0.918580i
$297$	2.36603	−	1.36603i	0.137291	−	0.0792648i
$298$	13.8564	−	8.00000i	0.802680	−	0.463428i
$299$	−3.63397	+	6.29423i	−0.210158	+	0.364005i
$300$		0			0
$301$	6.23205	+	17.9904i	0.359209	+	1.03695i
$302$			3.60770i			0.207600i
$303$	9.29423	+	5.36603i	0.533939	+	0.308270i
$304$	−1.32051	−	2.28719i	−0.0757363	−	0.131179i
$305$		0			0
$306$	−2.46410	+	4.26795i	−0.140863	+	0.243982i
$307$		−	7.87564i		−	0.449487i	−0.974418	−	0.224743i	$-0.927846\pi$
$307$		−	7.87564i		−	0.449487i	0.974418	−	0.224743i	$-0.0721544\pi$
$308$	2.00000	−	10.3923i	0.113961	−	0.592157i
$309$	1.19615			0.0680467
$310$		0			0
$311$	7.56218	+	13.0981i	0.428812	+	0.742724i	0.996768	−	0.0803351i	$-0.0255990\pi$
$311$	7.56218	+	13.0981i	0.428812	+	0.742724i	−0.567956	+	0.823059i	$0.692266\pi$
$312$	12.5885	−	7.26795i	0.712681	−	0.411467i
$313$	4.03590	+	2.33013i	0.228122	+	0.131707i	0.609706	−	0.792628i	$-0.291288\pi$
$313$	4.03590	+	2.33013i	0.228122	+	0.131707i	−0.381583	+	0.924335i	$0.624621\pi$
$314$	10.5359			0.594575
$315$		0			0
$316$	−19.6077			−1.10302
$317$	−26.3660	−	15.2224i	−1.48086	−	0.854977i	−0.481099	−	0.876666i	$-0.659762\pi$
$317$	−26.3660	−	15.2224i	−1.48086	−	0.854977i	−0.999765	+	0.0216894i	$0.993095\pi$
$318$	−5.32051	+	3.07180i	−0.298359	+	0.172258i
$319$	−8.46410	−	14.6603i	−0.473899	−	0.820817i
$320$		0			0
$321$	8.19615			0.457465
$322$	1.85641	+	1.60770i	0.103453	+	0.0895933i
$323$			16.5885i			0.923006i
$324$	−0.732051	+	1.26795i	−0.0406695	+	0.0704416i
$325$		0			0
$326$	2.14359	+	3.71281i	0.118723	+	0.205634i
$327$	9.52628	+	5.50000i	0.526804	+	0.304151i
$328$			6.92820i			0.382546i
$329$	−5.19615	−	1.00000i	−0.286473	−	0.0551318i
$330$		0			0
$331$	−10.9641	+	18.9904i	−0.602642	+	1.04381i	0.389778	+	0.920909i	$0.372552\pi$
$331$	−10.9641	+	18.9904i	−0.602642	+	1.04381i	−0.992419	+	0.122897i	$0.960782\pi$
$332$	11.5692	−	6.67949i	0.634943	−	0.366585i
$333$	−6.23205	+	3.59808i	−0.341514	+	0.197173i
$334$	−0.124356	+	0.215390i	−0.00680444	+	0.0117856i
$335$		0			0
$336$	0.928203	+	2.67949i	0.0506376	+	0.146178i
$337$		−	33.9808i		−	1.85105i	−0.378686	−	0.925525i	$-0.623624\pi$
$337$		−	33.9808i		−	1.85105i	0.378686	−	0.925525i	$-0.376376\pi$
$338$	12.5885	+	7.26795i	0.684722	+	0.395324i
$339$	2.46410	+	4.26795i	0.133832	+	0.231803i
$340$		0			0
$341$	8.83013	−	15.2942i	0.478178	−	0.828229i
$342$		−	1.80385i		−	0.0975409i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−18.2487			−0.983905
$345$		0			0
$346$	−7.85641	−	13.6077i	−0.422363	−	0.731554i
$347$	−30.2487	+	17.4641i	−1.62384	+	0.937522i	−0.637955	+	0.770074i	$0.720219\pi$
$347$	−30.2487	+	17.4641i	−1.62384	+	0.937522i	−0.985881	+	0.167449i	$0.946447\pi$
$348$	7.85641	+	4.53590i	0.421148	+	0.243150i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	−5.73205			−0.305954
$352$	13.8564	+	8.00000i	0.738549	+	0.426401i
$353$	−18.2942	+	10.5622i	−0.973704	+	0.562168i	−0.900363	−	0.435139i	$-0.856699\pi$
$353$	−18.2942	+	10.5622i	−0.973704	+	0.562168i	−0.0733402	+	0.997307i	$0.523366\pi$
$354$	−3.73205	−	6.46410i	−0.198356	−	0.343563i
$355$		0			0
$356$	13.3590			0.708025
$357$	3.36603	−	17.4904i	0.178149	−	0.925689i
$358$			7.32051i			0.386901i
$359$	−2.36603	+	4.09808i	−0.124874	+	0.216288i	−0.921684	−	0.387942i	$-0.873186\pi$
$359$	−2.36603	+	4.09808i	−0.124874	+	0.216288i	0.796810	+	0.604230i	$0.206519\pi$
$360$		0			0
$361$	6.46410	+	11.1962i	0.340216	+	0.589271i
$362$	−6.54294	−	3.77757i	−0.343889	−	0.198545i
$363$		−	3.53590i		−	0.185587i
$364$	−14.5359	+	16.7846i	−0.761888	+	0.879753i
$365$		0			0
$366$	1.46410	−	2.53590i	0.0765298	−	0.132554i
$367$	0.696152	−	0.401924i	0.0363389	−	0.0209803i	−0.481721	−	0.876325i	$-0.659988\pi$
$367$	0.696152	−	0.401924i	0.0363389	−	0.0209803i	0.518059	+	0.855345i	$0.326655\pi$
$368$	1.17691	−	0.679492i	0.0613509	−	0.0354210i
$369$	1.36603	−	2.36603i	0.0711124	−	0.123170i
$370$		0			0
$371$	14.5359	−	16.7846i	0.754666	−	0.871414i
$372$			9.46410i			0.490691i
$373$	−16.0359	−	9.25833i	−0.830307	−	0.479378i	0.0236505	−	0.999720i	$-0.492471\pi$
$373$	−16.0359	−	9.25833i	−0.830307	−	0.479378i	−0.853958	+	0.520342i	$0.825804\pi$
$374$	−6.73205	−	11.6603i	−0.348106	−	0.602937i
$375$		0			0
$376$	2.53590	−	4.39230i	0.130779	−	0.226516i
$377$			35.5167i			1.82920i
$378$	−0.366025	+	1.90192i	−0.0188263	+	0.0978244i
$379$	28.3205			1.45473			0.727363	−	0.686253i	$-0.240745\pi$
$379$	28.3205			1.45473			0.727363	+	0.686253i	$0.240745\pi$
$380$		0			0
$381$	7.59808	+	13.1603i	0.389261	+	0.674220i
$382$	3.12436	−	1.80385i	0.159856	−	0.0922929i
$383$	9.80385	+	5.66025i	0.500953	+	0.289225i	0.729107	−	0.684400i	$-0.239936\pi$
$383$	9.80385	+	5.66025i	0.500953	+	0.289225i	−0.228154	+	0.973625i	$0.573269\pi$
$384$	−10.1436			−0.517638
$385$		0			0
$386$	−6.73205			−0.342652
$387$	6.23205	+	3.59808i	0.316793	+	0.182900i
$388$	1.35898	−	0.784610i	0.0689920	−	0.0398325i
$389$	18.2942	+	31.6865i	0.927554	+	1.60657i	0.787401	+	0.616441i	$0.211426\pi$
$389$	18.2942	+	31.6865i	0.927554	+	1.60657i	0.140153	+	0.990130i	$0.455240\pi$
$390$		0			0
$391$	−8.53590			−0.431679
$392$	10.9808	+	13.9474i	0.554612	+	0.704452i
$393$			8.53590i			0.430579i
$394$	−6.46410	+	11.1962i	−0.325657	+	0.564054i
$395$		0			0
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	18.0167	+	10.4019i	0.904230	+	0.522058i	0.878570	−	0.477613i	$-0.158498\pi$
$397$	18.0167	+	10.4019i	0.904230	+	0.522058i	0.0256600	+	0.999671i	$0.491831\pi$
$398$		−	16.1051i		−	0.807277i
$399$	2.13397	+	6.16025i	0.106832	+	0.308398i
$400$		0			0
$401$	−2.19615	+	3.80385i	−0.109671	+	0.189955i	−0.915637	−	0.402006i	$-0.868313\pi$
$401$	−2.19615	+	3.80385i	−0.109671	+	0.189955i	0.805966	+	0.591962i	$0.201646\pi$
$402$	−1.68653	+	0.973721i	−0.0841166	+	0.0485648i
$403$	−32.0885	+	18.5263i	−1.59844	+	0.922860i
$404$	7.85641	−	13.6077i	0.390871	−	0.677008i
$405$		0			0
$406$	11.7846	+	2.26795i	0.584860	+	0.112556i
$407$		−	19.6603i		−	0.974523i
$408$	14.7846	+	8.53590i	0.731947	+	0.422590i
$409$	15.4282	+	26.7224i	0.762876	+	1.32134i	0.941362	+	0.337397i	$0.109546\pi$
$409$	15.4282	+	26.7224i	0.762876	+	1.32134i	−0.178487	+	0.983942i	$0.557120\pi$
$410$		0			0
$411$	−4.09808	+	7.09808i	−0.202143	+	0.350122i
$412$		−	1.75129i		−	0.0862798i
$413$	20.3923	+	17.6603i	1.00344	+	0.869004i
$414$	0.928203			0.0456187
$415$		0			0
$416$	−16.7846	−	29.0718i	−0.822933	−	1.42536i
$417$	6.86603	−	3.96410i	0.336231	−	0.194123i
$418$	4.26795	+	2.46410i	0.208752	+	0.120523i
$419$	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	$0.389773\pi$
$422$	−13.2679	−	7.66025i	−0.645874	−	0.372895i
$423$	−1.73205	+	1.00000i	−0.0842152	+	0.0486217i
$424$	10.6410	+	18.4308i	0.516773	+	0.895078i
$425$		0			0
$426$	3.07180			0.148829
$427$	−2.00000	+	10.3923i	−0.0967868	+	0.502919i
$428$		−	12.0000i		−	0.580042i
$429$	7.83013	−	13.5622i	0.378042	−	0.654788i
$430$		0			0
$431$	8.66025	+	15.0000i	0.417150	+	0.722525i	0.995651	−	0.0931566i	$-0.0296957\pi$
$431$	8.66025	+	15.0000i	0.417150	+	0.722525i	−0.578502	+	0.815681i	$0.696362\pi$
$432$	0.928203	+	0.535898i	0.0446582	+	0.0257834i
$433$		−	4.80385i		−	0.230858i	−0.993316	−	0.115429i	$-0.963176\pi$
$433$		−	4.80385i		−	0.230858i	0.993316	−	0.115429i	$-0.0368243\pi$
$434$	4.09808	+	11.8301i	0.196714	+	0.567864i
$435$		0			0
$436$	8.05256	−	13.9474i	0.385648	−	0.667961i
$437$	2.70577	−	1.56218i	0.129435	−	0.0747291i
$438$	−2.95448	+	1.70577i	−0.141171	+	0.0815049i
$439$	3.73205	−	6.46410i	0.178121	−	0.308515i	−0.763116	−	0.646262i	$-0.776331\pi$
$439$	3.73205	−	6.46410i	0.178121	−	0.308515i	0.941237	+	0.337747i	$0.109665\pi$
$440$		0			0
$441$	−1.00000	−	6.92820i	−0.0476190	−	0.329914i
$442$			28.2487i			1.34365i
$443$	2.19615	+	1.26795i	0.104342	+	0.0602421i	0.551263	−	0.834331i	$-0.314146\pi$
$443$	2.19615	+	1.26795i	0.104342	+	0.0602421i	−0.446921	+	0.894574i	$0.647479\pi$
$444$	5.26795	+	9.12436i	0.250006	+	0.433023i
$445$		0			0
$446$	−0.143594	+	0.248711i	−0.00679935	+	0.0117768i
$447$			21.8564i			1.03377i
$448$	−5.35898	+	1.85641i	−0.253188	+	0.0877070i
$449$	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
$452$	6.24871	−	3.60770i	0.293915	−	0.169692i
$453$	−4.26795	−	2.46410i	−0.200526	−	0.115774i
$454$	−11.4641			−0.538037
$455$		0			0
$456$	−6.24871			−0.292623
$457$	−0.571797	−	0.330127i	−0.0267475	−	0.0154427i	0.486567	−	0.873643i	$-0.338249\pi$
$457$	−0.571797	−	0.330127i	−0.0267475	−	0.0154427i	−0.513314	+	0.858201i	$0.671582\pi$
$458$	1.90192	−	1.09808i	0.0888711	−	0.0513097i
$459$	−3.36603	−	5.83013i	−0.157113	−	0.272127i
$460$		0			0
$461$	−34.9808			−1.62922			−0.814608	−	0.580012i	$-0.803048\pi$
$461$	−34.9808			−1.62922			−0.814608	+	0.580012i	$0.803048\pi$
$462$	−4.00000	−	3.46410i	−0.186097	−	0.161165i
$463$		−	22.2679i		−	1.03488i	−0.855720	−	0.517440i	$-0.826885\pi$
$463$		−	22.2679i		−	1.03488i	0.855720	−	0.517440i	$-0.173115\pi$
$464$	3.32051	−	5.75129i	0.154151	−	0.266997i
$465$		0			0
$466$	6.33975	+	10.9808i	0.293683	+	0.508674i
$467$	24.1244	+	13.9282i	1.11634	+	0.644520i	0.940465	−	0.339892i	$-0.110390\pi$
$467$	24.1244	+	13.9282i	1.11634	+	0.644520i	0.175877	+	0.984412i	$0.443724\pi$
$468$			8.39230i			0.387934i
$469$	4.60770	−	5.32051i	0.212764	−	0.245678i
$470$		0			0
$471$	−7.19615	+	12.4641i	−0.331581	+	0.574315i
$472$	−22.3923	+	12.9282i	−1.03069	+	0.595069i
$473$	−17.0263	+	9.83013i	−0.782869	+	0.451990i
$474$	−4.90192	+	8.49038i	−0.225153	+	0.389976i
$475$		0			0
$476$	−25.6077	−	4.92820i	−1.17373	−	0.225884i
$477$		−	8.39230i		−	0.384257i
$478$	13.2679	+	7.66025i	0.606862	+	0.350372i
$479$	−16.3923	−	28.3923i	−0.748984	−	1.29728i	−0.948310	−	0.317344i	$-0.897209\pi$
$479$	−16.3923	−	28.3923i	−0.748984	−	1.29728i	0.199327	−	0.979933i	$-0.436124\pi$
$480$		0			0
$481$	−20.6244	+	35.7224i	−0.940390	+	1.62880i
$482$			4.78461i			0.217933i
$483$	−3.16987	+	1.09808i	−0.144234	+	0.0499642i
$484$	−5.17691			−0.235314
$485$		0			0
$486$	0.366025	+	0.633975i	0.0166032	+	0.0287577i
$487$	−27.3564	+	15.7942i	−1.23964	+	0.715705i	−0.969020	−	0.246982i	$-0.920561\pi$
$487$	−27.3564	+	15.7942i	−1.23964	+	0.715705i	−0.270617	+	0.962687i	$0.587228\pi$
$488$	−8.78461	−	5.07180i	−0.397661	−	0.229589i
$489$	−5.85641			−0.264836
$490$		0			0
$491$	10.2487			0.462518			0.231259	−	0.972892i	$-0.425716\pi$
$491$	10.2487			0.462518			0.231259	+	0.972892i	$0.425716\pi$
$492$	−3.46410	−	2.00000i	−0.156174	−	0.0901670i
$493$	−36.1244	+	20.8564i	−1.62696	+	0.939325i
$494$	−5.16987	−	8.95448i	−0.232604	−	0.402881i
$495$		0			0
$496$	6.92820			0.311086
$497$	−10.4904	+	3.63397i	−0.470558	+	0.163006i
$498$		−	6.67949i		−	0.299315i
$499$	−10.2321	+	17.7224i	−0.458050	+	0.793365i	−0.998858	−	0.0477808i	$-0.984785\pi$
$499$	−10.2321	+	17.7224i	−0.458050	+	0.793365i	0.540808	+	0.841146i	$0.318118\pi$
$500$		0			0
$501$	−0.169873	−	0.294229i	−0.00758937	−	0.0131452i
$502$	−4.17691	−	2.41154i	−0.186425	−	0.107632i
$503$			6.39230i			0.285019i	0.989793	+	0.142509i	$0.0455171\pi$
$503$			6.39230i			0.285019i	−0.989793	+	0.142509i	$0.954483\pi$
$504$	6.58846	+	1.26795i	0.293473	+	0.0564789i
$505$		0			0
$506$	−1.26795	+	2.19615i	−0.0563672	+	0.0976309i
$507$	−17.1962	+	9.92820i	−0.763708	+	0.440927i
$508$	19.2679	−	11.1244i	0.854877	−	0.493563i
$509$	5.73205	−	9.92820i	0.254069	−	0.440060i	−0.710573	−	0.703623i	$-0.751564\pi$
$509$	5.73205	−	9.92820i	0.254069	−	0.440060i	0.964642	+	0.263563i	$0.0848977\pi$
$510$		0			0
$511$	8.07180	−	9.32051i	0.357075	−	0.412315i
$512$			11.7128i			0.517638i
$513$	2.13397	+	1.23205i	0.0942173	+	0.0543964i
$514$	4.26795	+	7.39230i	0.188251	+	0.326061i
$515$		0			0
$516$	5.26795	−	9.12436i	0.231909	−	0.401677i
$517$		−	5.46410i		−	0.240311i
$518$	10.5359	+	9.12436i	0.462921	+	0.400901i
$519$	21.4641			0.942169
$520$		0			0
$521$	−0.732051	−	1.26795i	−0.0320717	−	0.0555499i	0.849544	−	0.527518i	$-0.176877\pi$
$521$	−0.732051	−	1.26795i	−0.0320717	−	0.0555499i	−0.881616	+	0.471968i	$0.843544\pi$
$522$	3.92820	−	2.26795i	0.171933	−	0.0992654i
$523$	−21.0167	−	12.1340i	−0.918994	−	0.530582i	−0.0356803	−	0.999363i	$-0.511360\pi$
$523$	−21.0167	−	12.1340i	−0.918994	−	0.530582i	−0.883314	+	0.468782i	$0.844693\pi$
$524$	12.4974			0.545952
$525$		0			0
$526$	−9.07180			−0.395549
$527$	−37.6865	−	21.7583i	−1.64165	−	0.947808i
$528$	−2.53590	+	1.46410i	−0.110361	+	0.0637168i
$529$	−10.6962	−	18.5263i	−0.465050	−	0.805490i
$530$		0			0
$531$	10.1962			0.442475
$532$	9.01924	−	3.12436i	0.391034	−	0.135458i
$533$		−	15.6603i		−	0.678321i
$534$	3.33975	−	5.78461i	0.144525	−	0.250325i
$535$		0			0
$536$	3.37307	+	5.84232i	0.145694	+	0.252350i
$537$	−8.66025	−	5.00000i	−0.373718	−	0.215766i
$538$			14.2487i			0.614306i
$539$	17.7583	+	7.09808i	0.764905	+	0.305736i
$540$		0			0
$541$	17.8923	−	30.9904i	0.769250	−	1.33238i	−0.168720	−	0.985664i	$-0.553963\pi$
$541$	17.8923	−	30.9904i	0.769250	−	1.33238i	0.937970	−	0.346716i	$-0.112703\pi$
$542$	10.7321	−	6.19615i	0.460981	−	0.266148i
$543$	8.93782	−	5.16025i	0.383559	−	0.221448i
$544$	19.7128	−	34.1436i	0.845180	−	1.46389i
$545$		0			0
$546$	3.63397	+	10.4904i	0.155520	+	0.448947i
$547$			22.2487i			0.951286i	0.879638	+	0.475643i	$0.157785\pi$
$547$			22.2487i			0.951286i	−0.879638	+	0.475643i	$0.842215\pi$
$548$	10.3923	+	6.00000i	0.443937	+	0.256307i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$		0			0
$551$	7.63397	−	13.2224i	0.325218	−	0.563295i
$552$		−	3.21539i		−	0.136856i
$553$	6.69615	−	34.7942i	0.284749	−	1.47960i
$554$	−1.94744			−0.0827388
$555$		0			0
$556$	−5.80385	−	10.0526i	−0.246138	−	0.426323i
$557$	−23.1962	+	13.3923i	−0.982853	+	0.567450i	−0.903130	−	0.429367i	$-0.858737\pi$
$557$	−23.1962	+	13.3923i	−0.982853	+	0.567450i	−0.0797224	+	0.996817i	$0.525403\pi$
$558$	4.09808	+	2.36603i	0.173485	+	0.100162i
$559$	41.2487			1.74463
$560$		0			0
$561$	18.3923			0.776524
$562$	8.78461	+	5.07180i	0.370556	+	0.213941i
$563$	15.5885	−	9.00000i	0.656975	−	0.379305i	−0.134148	−	0.990961i	$-0.542830\pi$
$563$	15.5885	−	9.00000i	0.656975	−	0.379305i	0.791123	+	0.611656i	$0.209497\pi$
$564$	1.46410	+	2.53590i	0.0616498	+	0.106781i
$565$		0			0
$566$	0.0910347			0.00382647
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$		−	10.6410i		−	0.446487i
$569$	−13.2224	+	22.9019i	−0.554313	+	0.960099i	0.443643	+	0.896203i	$0.353686\pi$
$569$	−13.2224	+	22.9019i	−0.554313	+	0.960099i	−0.997957	+	0.0638952i	$0.979648\pi$
$570$		0			0
$571$	−19.6962	−	34.1147i	−0.824258	−	1.42766i	−0.902485	−	0.430722i	$-0.858259\pi$
$571$	−19.6962	−	34.1147i	−0.824258	−	1.42766i	0.0782265	−	0.996936i	$-0.475074\pi$
$572$	−19.8564	−	11.4641i	−0.830238	−	0.479338i
$573$			4.92820i			0.205879i
$574$	−5.19615	−	1.00000i	−0.216883	−	0.0417392i
$575$		0			0
$576$	−1.07180	+	1.85641i	−0.0446582	+	0.0773503i
$577$	9.82051	−	5.66987i	0.408833	−	0.236040i	−0.281455	−	0.959574i	$-0.590817\pi$
$577$	9.82051	−	5.66987i	0.408833	−	0.236040i	0.690288	+	0.723534i	$0.257484\pi$
$578$	−17.9545	+	10.3660i	−0.746808	+	0.431170i
$579$	4.59808	−	7.96410i	0.191090	−	0.330977i
$580$		0			0
$581$	7.90192	+	22.8109i	0.327827	+	0.946355i
$582$		−	0.784610i		−	0.0325231i
$583$	19.8564	+	11.4641i	0.822368	+	0.474795i
$584$	5.90897	+	10.2346i	0.244515	+	0.423512i
$585$		0			0
$586$	−1.85641	+	3.21539i	−0.0766874	+	0.132827i
$587$			37.2679i			1.53821i	0.639121	+	0.769106i	$0.279298\pi$
$587$			37.2679i			1.53821i	−0.639121	+	0.769106i	$0.720702\pi$
$588$	−10.1436	+	1.46410i	−0.418315	+	0.0603785i
$589$	15.9282			0.656310
$590$		0			0
$591$	−8.83013	−	15.2942i	−0.363223	−	0.629121i
$592$	6.67949	−	3.85641i	0.274525	−	0.158497i
$593$	−32.8301	−	18.9545i	−1.34817	−	0.778367i	−0.360181	−	0.932882i	$-0.617285\pi$
$593$	−32.8301	−	18.9545i	−1.34817	−	0.778367i	−0.987990	+	0.154515i	$0.950619\pi$
$594$	−2.00000			−0.0820610
$595$		0			0
$596$	32.0000			1.31077
$597$	19.0526	+	11.0000i	0.779769	+	0.450200i
$598$	4.60770	−	2.66025i	0.188423	−	0.108786i
$599$	5.12436	+	8.87564i	0.209375	+	0.362649i	0.951518	−	0.307593i	$-0.0995236\pi$
$599$	5.12436	+	8.87564i	0.209375	+	0.362649i	−0.742142	+	0.670242i	$0.766190\pi$
$600$		0			0
$601$	−13.9282			−0.568143			−0.284072	−	0.958803i	$-0.591685\pi$
$601$	−13.9282			−0.568143			−0.284072	+	0.958803i	$0.591685\pi$
$602$	2.63397	−	13.6865i	0.107353	−	0.557821i
$603$		−	2.66025i		−	0.108334i
$604$	−3.60770	+	6.24871i	−0.146795	+	0.254256i
$605$		0			0
$606$	−3.92820	−	6.80385i	−0.159572	−	0.276387i
$607$	6.23205	+	3.59808i	0.252951	+	0.146041i	0.621115	−	0.783720i	$-0.286680\pi$
$607$	6.23205	+	3.59808i	0.252951	+	0.146041i	−0.368164	+	0.929761i	$0.620013\pi$
$608$			14.4308i			0.585245i
$609$	−10.7321	+	12.3923i	−0.434885	+	0.502162i
$610$		0			0
$611$	−5.73205	+	9.92820i	−0.231894	+	0.401652i
$612$	−8.53590	+	4.92820i	−0.345043	+	0.199211i
$613$	11.3205	−	6.53590i	0.457231	−	0.263982i	−0.253648	−	0.967297i	$-0.581631\pi$
$613$	11.3205	−	6.53590i	0.457231	−	0.263982i	0.710879	+	0.703314i	$0.248297\pi$
$614$	−2.88269	+	4.99296i	−0.116336	+	0.201499i
$615$		0			0
$616$	−12.0000	+	13.8564i	−0.483494	+	0.558291i
$617$			12.2487i			0.493115i	0.969128	+	0.246557i	$0.0792993\pi$
$617$			12.2487i			0.493115i	−0.969128	+	0.246557i	$0.920701\pi$
$618$	−0.758330	−	0.437822i	−0.0305045	−	0.0176118i
$619$	−21.9641	−	38.0429i	−0.882812	−	1.52907i	−0.848201	−	0.529674i	$-0.822314\pi$
$619$	−21.9641	−	38.0429i	−0.882812	−	1.52907i	−0.0346105	−	0.999401i	$-0.511019\pi$
$620$		0			0
$621$	−0.633975	+	1.09808i	−0.0254405	+	0.0440643i
$622$		−	11.0718i		−	0.443939i
$623$	−4.56218	+	23.7058i	−0.182780	+	0.949752i
$624$	6.14359			0.245941
$625$		0			0
$626$	−1.70577	−	2.95448i	−0.0681763	−	0.118085i
$627$	−5.83013	+	3.36603i	−0.232833	+	0.134426i
$628$	18.2487	+	10.5359i	0.728203	+	0.420428i
$629$	−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	$0.454126\pi$
$632$	29.4115	+	16.9808i	1.16993	+	0.675458i
$633$	18.1244	−	10.4641i	0.720378	−	0.415911i
$634$	11.1436	+	19.3013i	0.442569	+	0.766551i
$635$		0			0
$636$	−12.2872			−0.487219
$637$	−24.8205	−	31.5263i	−0.983424	−	1.24912i
$638$			12.3923i			0.490616i
$639$	−2.09808	+	3.63397i	−0.0829986	+	0.143758i
$640$		0			0
$641$	−7.09808	−	12.2942i	−0.280357	−	0.485593i	0.691116	−	0.722744i	$-0.257120\pi$
$641$	−7.09808	−	12.2942i	−0.280357	−	0.485593i	−0.971473	+	0.237151i	$0.923786\pi$
$642$	−5.19615	−	3.00000i	−0.205076	−	0.118401i
$643$			40.5167i			1.59782i	0.601450	+	0.798911i	$0.294590\pi$
$643$			40.5167i			1.59782i	−0.601450	+	0.798911i	$0.705410\pi$
$644$	1.60770	+	4.64102i	0.0633521	+	0.182882i
$645$		0			0
$646$	6.07180	−	10.5167i	0.238892	−	0.413772i
$647$	32.8301	−	18.9545i	1.29069	−	0.745178i	0.311910	−	0.950112i	$-0.399031\pi$
$647$	32.8301	−	18.9545i	1.29069	−	0.745178i	0.978776	+	0.204934i	$0.0656980\pi$
$648$	2.19615	−	1.26795i	0.0862730	−	0.0498097i
$649$	−13.9282	+	24.1244i	−0.546730	+	0.946964i
$650$		0			0
$651$	−16.7942	−	3.23205i	−0.658218	−	0.126674i
$652$			8.57437i			0.335798i
$653$	−11.6147	−	6.70577i	−0.454520	−	0.262417i	0.255217	−	0.966884i	$-0.417853\pi$
$653$	−11.6147	−	6.70577i	−0.454520	−	0.262417i	−0.709737	+	0.704467i	$0.751186\pi$
$654$	−4.02628	−	6.97372i	−0.157440	−	0.272694i
$655$		0			0
$656$	−1.46410	+	2.53590i	−0.0571636	+	0.0990102i
$657$		−	4.66025i		−	0.181814i
$658$	2.92820	+	2.53590i	0.114153	+	0.0988596i
$659$	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	0.829593	−	0.558369i	$-0.188573\pi$
$661$	−1.76795	−	3.06218i	−0.0687653	−	0.119105i	−0.898358	+	0.439264i	$0.855239\pi$
$662$	13.9019	−	8.02628i	0.540314	−	0.311950i
$663$	−33.4186	−	19.2942i	−1.29787	−	0.749326i
$664$	−23.1384			−0.897946
$665$		0			0
$666$	5.26795			0.204129
$667$	6.80385	+	3.92820i	0.263446	+	0.152101i
$668$	−0.430781	+	0.248711i	−0.0166674	+	0.00962293i
$669$	−0.196152	−	0.339746i	−0.00758369	−	0.0131353i
$670$		0			0
$671$	−10.9282			−0.421879
$672$	2.92820	−	15.2154i	0.112958	−	0.586946i
$673$			44.6603i			1.72153i	0.509006	+	0.860763i	$0.330013\pi$
$673$			44.6603i			1.72153i	−0.509006	+	0.860763i	$0.669987\pi$
$674$	−12.4378	+	21.5429i	−0.479087	+	0.829803i
$675$		0			0
$676$	14.5359	+	25.1769i	0.559073	+	0.968343i
$677$	7.68653	+	4.43782i	0.295417	+	0.170559i	0.640382	−	0.768056i	$-0.278776\pi$
$677$	7.68653	+	4.43782i	0.295417	+	0.170559i	−0.344965	+	0.938616i	$0.612109\pi$
$678$		−	3.60770i		−	0.138553i
$679$	0.928203	+	2.67949i	0.0356212	+	0.102829i
$680$		0			0
$681$	7.83013	−	13.5622i	0.300051	−	0.519704i
$682$	−11.1962	+	6.46410i	−0.428723	+	0.247523i
$683$	−8.70577	+	5.02628i	−0.333117	+	0.192325i	−0.657224	−	0.753695i	$-0.728270\pi$
$683$	−8.70577	+	5.02628i	−0.333117	+	0.192325i	0.324107	+	0.946020i	$0.394936\pi$
$684$	1.80385	−	3.12436i	0.0689718	−	0.119463i
$685$		0			0
$686$	−12.0455	+	6.22243i	−0.459900	+	0.237574i
$687$			3.00000i			0.114457i
$688$	−6.67949	−	3.85641i	−0.254653	−	0.147024i
$689$	−24.0526	−	41.6603i	−0.916330	−	1.58713i
$690$		0			0
$691$	9.42820	−	16.3301i	0.358666	−	0.621227i	−0.629072	−	0.777347i	$-0.716565\pi$
$691$	9.42820	−	16.3301i	0.358666	−	0.621227i	0.987738	+	0.156119i	$0.0498985\pi$
$692$		−	31.4256i		−	1.19462i
$693$	6.83013	−	2.36603i	0.259455	−	0.0898779i
$694$	25.5692			0.970594
$695$		0			0
$696$	−7.85641	−	13.6077i	−0.297796	−	0.515798i
$697$	15.9282	−	9.19615i	0.603324	−	0.348329i
$698$	13.9474	+	8.05256i	0.527918	+	0.304794i
$699$	−17.3205			−0.655122
$700$		0			0
$701$	22.5885			0.853154			0.426577	−	0.904451i	$-0.359719\pi$
$701$	22.5885			0.853154			0.426577	+	0.904451i	$0.359719\pi$
$702$	3.63397	+	2.09808i	0.137156	+	0.0791868i
$703$	15.3564	−	8.86603i	0.579178	−	0.334388i
$704$	−2.92820	−	5.07180i	−0.110361	−	0.191151i
$705$		0			0
$706$	15.4641			0.581999
$707$	21.4641	+	18.5885i	0.807241	+	0.699091i
$708$		−	14.9282i		−	0.561036i
$709$	−7.46410	+	12.9282i	−0.280320	+	0.485529i	−0.971464	−	0.237189i	$-0.923774\pi$
$709$	−7.46410	+	12.9282i	−0.280320	+	0.485529i	0.691143	+	0.722718i	$0.257107\pi$
$710$		0			0
$711$	−6.69615	−	11.5981i	−0.251125	−	0.434962i
$712$	−20.0385	−	11.5692i	−0.750974	−	0.433575i
$713$			8.19615i			0.306948i
$714$	−8.53590	+	9.85641i	−0.319448	+	0.368867i
$715$		0			0
$716$	−7.32051	+	12.6795i	−0.273580	+	0.473855i
$717$	−18.1244	+	10.4641i	−0.676866	+	0.390789i
$718$	3.00000	−	1.73205i	0.111959	−	0.0646396i
$719$	−13.7321	+	23.7846i	−0.512119	+	0.887016i	0.487782	+	0.872965i	$0.337806\pi$
$719$	−13.7321	+	23.7846i	−0.512119	+	0.887016i	−0.999901	+	0.0140509i	$0.995527\pi$
$720$		0			0
$721$	3.10770	+	0.598076i	0.115737	+	0.0222735i
$722$		−	9.46410i		−	0.352217i
$723$	−5.66025	−	3.26795i	−0.210507	−	0.121536i
$724$	−7.55514	−	13.0859i	−0.280784	−	0.486333i
$725$		0			0
$726$	−1.29423	+	2.24167i	−0.0480333	+	0.0831962i
$727$		−	30.6603i		−	1.13713i	−0.822640	−	0.568563i	$-0.807500\pi$
$727$		−	30.6603i		−	1.13713i	0.822640	−	0.568563i	$-0.192500\pi$
$728$	36.3397	−	12.5885i	1.34684	−	0.466559i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	24.2224	+	41.9545i	0.895899	+	1.55174i
$732$	5.07180	−	2.92820i	0.187459	−	0.108230i
$733$	−16.1603	−	9.33013i	−0.596893	−	0.344616i	0.170926	−	0.985284i	$-0.445324\pi$
$733$	−16.1603	−	9.33013i	−0.596893	−	0.344616i	−0.767818	+	0.640668i	$0.778658\pi$
$734$	−0.588457			−0.0217204
$735$		0			0
$736$	−7.42563			−0.273712
$737$	6.29423	+	3.63397i	0.231851	+	0.133859i
$738$	−1.73205	+	1.00000i	−0.0637577	+	0.0368105i
$739$	−6.89230	−	11.9378i	−0.253538	−	0.439140i	0.710960	−	0.703233i	$-0.248261\pi$
$739$	−6.89230	−	11.9378i	−0.253538	−	0.439140i	−0.964497	+	0.264093i	$0.914927\pi$
$740$		0			0
$741$	14.1244			0.518871
$742$	−15.3590	+	5.32051i	−0.563846	+	0.195322i
$743$		−	49.9090i		−	1.83098i	−0.402338	−	0.915491i	$-0.631802\pi$
$743$		−	49.9090i		−	1.83098i	0.402338	−	0.915491i	$-0.368198\pi$
$744$	8.19615	−	14.1962i	0.300486	−	0.520456i
$745$		0			0
$746$	6.77757	+	11.7391i	0.248144	+	0.429799i
$747$	7.90192	+	4.56218i	0.289116	+	0.166921i
$748$		−	26.9282i		−	0.984593i
$749$	21.2942	+	4.09808i	0.778074	+	0.149740i
$750$		0			0
$751$	−15.9641	+	27.6506i	−0.582538	+	1.00899i	0.412639	+	0.910895i	$0.364607\pi$
$751$	−15.9641	+	27.6506i	−0.582538	+	1.00899i	−0.995177	+	0.0980914i	$0.968726\pi$
$752$	1.85641	−	1.07180i	0.0676962	−	0.0390844i
$753$	5.70577	−	3.29423i	0.207930	−	0.120048i
$754$	13.0000	−	22.5167i	0.473432	−	0.820008i
$755$		0			0
$756$	−2.53590	+	2.92820i	−0.0922297	+	0.106498i
$757$		−	0.143594i		−	0.00521900i	−0.999997	−	0.00260950i	$-0.999169\pi$
$757$		−	0.143594i		−	0.00521900i	0.999997	−	0.00260950i	$-0.000830630\pi$
$758$	−17.9545	−	10.3660i	−0.652136	−	0.376511i
$759$	−1.73205	−	3.00000i	−0.0628695	−	0.108893i
$760$		0			0
$761$	−21.6340	+	37.4711i	−0.784231	+	1.35833i	0.145226	+	0.989398i	$0.453609\pi$
$761$	−21.6340	+	37.4711i	−0.784231	+	1.35833i	−0.929457	+	0.368929i	$0.879724\pi$
$762$		−	11.1244i		−	0.402993i
$763$	22.0000	+	19.0526i	0.796453	+	0.689749i
$764$	7.21539			0.261044
$765$		0			0
$766$	−4.14359	−	7.17691i	−0.149714	−	0.259312i
$767$	50.6147	−	29.2224i	1.82759	−	1.05516i
$768$	10.1436	+	5.85641i	0.366025	+	0.211325i
$769$	−17.6795			−0.637539			−0.318769	−	0.947832i	$-0.603270\pi$
$769$	−17.6795			−0.637539			−0.318769	+	0.947832i	$0.603270\pi$
$770$		0			0
$771$	−11.6603			−0.419934
$772$	−11.6603	−	6.73205i	−0.419662	−	0.242292i
$773$	1.31347	−	0.758330i	0.0472421	−	0.0272752i	−0.476193	−	0.879341i	$-0.657984\pi$
$773$	1.31347	−	0.758330i	0.0472421	−	0.0272752i	0.523435	+	0.852066i	$0.324650\pi$
$774$	−2.63397	−	4.56218i	−0.0946763	−	0.163984i
$775$		0			0
$776$	−2.71797			−0.0975694
$777$	−17.9904	+	6.23205i	−0.645401	+	0.223574i
$778$		−	26.7846i		−	0.960275i
$779$	−3.36603	+	5.83013i	−0.120600	+	0.208886i
$780$		0			0
$781$	−5.73205	−	9.92820i	−0.205109	−	0.355259i
$782$	5.41154	+	3.12436i	0.193516	+	0.111727i
$783$			6.19615i			0.221432i
$784$	1.07180	+	7.42563i	0.0382785	+	0.265201i
$785$		0			0
$786$	3.12436	−	5.41154i	0.111442	−	0.193023i
$787$	5.66025	−	3.26795i	0.201766	−	0.116490i	−0.395713	−	0.918374i	$-0.629502\pi$
$787$	5.66025	−	3.26795i	0.201766	−	0.116490i	0.597479	+	0.801885i	$0.296169\pi$
$788$	−22.3923	+	12.9282i	−0.797693	+	0.460548i
$789$	6.19615	−	10.7321i	0.220589	−	0.382071i
$790$		0			0
$791$	4.26795	+	12.3205i	0.151751	+	0.438067i
$792$			6.92820i			0.246183i
$793$	19.8564	+	11.4641i	0.705122	+	0.407102i
$794$	−7.61474	−	13.1891i	−0.270237	−	0.468064i
$795$		0			0
$796$	16.1051	−	27.8949i	0.570831	−	0.988708i
$797$		−	42.0526i		−	1.48958i	−0.667300	−	0.744789i	$-0.732550\pi$
$797$		−	42.0526i		−	1.48958i	0.667300	−	0.744789i	$-0.267450\pi$
$798$	0.901924	−	4.68653i	0.0319278	−	0.165901i
$799$	−13.4641			−0.476326
$800$		0			0
$801$	4.56218	+	7.90192i	0.161197	+	0.279201i
$802$	2.78461	−	1.60770i	0.0983280	−	0.0567697i
$803$	11.0263	+	6.36603i	0.389109	+	0.224652i
$804$	−3.89488			−0.137362
$805$		0			0
$806$	27.1244			0.955415
$807$	−16.8564	−	9.73205i	−0.593374	−	0.342584i
$808$	−23.5692	+	13.6077i	−0.829162	+	0.478717i
$809$	−14.8564	−	25.7321i	−0.522323	−	0.904691i	−0.999663	−	0.0259716i	$-0.991732\pi$
$809$	−14.8564	−	25.7321i	−0.522323	−	0.904691i	0.477339	−	0.878719i	$-0.341601\pi$
$810$		0			0
$811$	3.46410			0.121641			0.0608205	−	0.998149i	$-0.480628\pi$
$811$	3.46410			0.121641			0.0608205	+	0.998149i	$0.480628\pi$
$812$	18.1436	+	15.7128i	0.636715	+	0.551412i
$813$			16.9282i			0.593698i
$814$	−7.19615	+	12.4641i	−0.252225	+	0.436867i
$815$		0			0
$816$	3.60770	+	6.24871i	0.126295	+	0.218749i
$817$	−15.3564	−	8.86603i	−0.537253	−	0.310183i
$818$		−	22.5885i		−	0.789787i
$819$	−14.8923	−	2.86603i	−0.520379	−	0.100147i
$820$		0			0
$821$	−9.75833	+	16.9019i	−0.340568	+	0.589881i	−0.984538	−	0.175169i	$-0.943953\pi$
$821$	−9.75833	+	16.9019i	−0.340568	+	0.589881i	0.643970	+	0.765051i	$0.277286\pi$
$822$	5.19615	−	3.00000i	0.181237	−	0.104637i
$823$	20.0718	−	11.5885i	0.699659	−	0.403948i	−0.107561	−	0.994198i	$-0.534304\pi$
$823$	20.0718	−	11.5885i	0.699659	−	0.403948i	0.807220	+	0.590250i	$0.200971\pi$
$824$	−1.51666	+	2.62693i	−0.0528354	+	0.0915135i
$825$		0			0
$826$	−6.46410	−	18.6603i	−0.224915	−	0.649273i
$827$		−	52.2487i		−	1.81687i	−0.418031	−	0.908433i	$-0.637280\pi$
$827$		−	52.2487i		−	1.81687i	0.418031	−	0.908433i	$-0.362720\pi$
$828$	1.60770	+	0.928203i	0.0558713	+	0.0322573i
$829$	−12.6962	−	21.9904i	−0.440956	−	0.763758i	0.556805	−	0.830643i	$-0.312027\pi$
$829$	−12.6962	−	21.9904i	−0.440956	−	0.763758i	−0.997761	+	0.0668857i	$0.978694\pi$
$830$		0			0
$831$	1.33013	−	2.30385i	0.0461416	−	0.0799196i
$832$			12.2872i			0.425982i
$833$	17.4904	−	43.7583i	0.606006	−	1.51614i
$834$	−5.80385			−0.200971
$835$		0			0
$836$	4.92820	+	8.53590i	0.170445	+	0.295220i
$837$	−5.59808	+	3.23205i	−0.193498	+	0.111716i
$838$	−18.0910	−	10.4449i	−0.624944	−	0.360812i
$839$	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
$842$	−8.83013	−	5.09808i	−0.304306	−	0.175691i
$843$	−12.0000	+	6.92820i	−0.413302	+	0.238620i
$844$	−15.3205	−	26.5359i	−0.527354	−	0.913403i
$845$		0			0
$846$	1.46410			0.0503369
$847$	1.76795	−	9.18653i	0.0607475	−	0.315653i
$848$			8.99485i			0.308884i
$849$	−0.0621778	+	0.107695i	−0.00213394	+	0.00369609i
$850$		0			0
$851$	4.56218	+	7.90192i	0.156389	+	0.270874i
$852$	5.32051	+	3.07180i	0.182278	+	0.105238i
$853$		−	19.9808i		−	0.684128i	−0.939677	−	0.342064i	$-0.888874\pi$
$853$		−	19.9808i		−	0.684128i	0.939677	−	0.342064i	$-0.111126\pi$
$854$	5.07180	−	5.85641i	0.173553	−	0.200402i
$855$		0			0
$856$	−10.3923	+	18.0000i	−0.355202	+	0.615227i
$857$	4.22243	−	2.43782i	0.144236	−	0.0832744i	−0.426146	−	0.904655i	$-0.640129\pi$
$857$	4.22243	−	2.43782i	0.144236	−	0.0832744i	0.570381	+	0.821380i	$0.306796\pi$
$858$	−9.92820	+	5.73205i	−0.338943	+	0.195689i
$859$	0.267949	−	0.464102i	0.00914231	−	0.0158349i	−0.861418	−	0.507897i	$-0.830423\pi$
$859$	0.267949	−	0.464102i	0.00914231	−	0.0158349i	0.870560	+	0.492062i	$0.163757\pi$
$860$		0			0
$861$	4.73205	−	5.46410i	0.161268	−	0.186216i
$862$		−	12.6795i		−	0.431865i
$863$	−5.53590	−	3.19615i	−0.188444	−	0.108798i	0.402810	−	0.915284i	$-0.368034\pi$
$863$	−5.53590	−	3.19615i	−0.188444	−	0.108798i	−0.591254	+	0.806485i	$0.701367\pi$
$864$	−2.92820	−	5.07180i	−0.0996195	−	0.172546i
$865$		0			0
$866$	−1.75833	+	3.04552i	−0.0597505	+	0.103491i
$867$		−	28.3205i		−	0.961815i
$868$	−4.73205	+	24.5885i	−0.160616	+	0.834587i
$869$	36.5885			1.24118
$870$		0			0
$871$	−7.62436	−	13.2058i	−0.258341	−	0.447460i
$872$	−24.1577	+	13.9474i	−0.818082	+	0.472320i
$873$	0.928203	+	0.535898i	0.0314149	+	0.0181374i
$874$	−2.28719			−0.0773653
$875$		0			0
$876$	−6.82309			−0.230531
$877$	27.5885	+	15.9282i	0.931596	+	0.537857i	0.887316	−	0.461162i	$-0.152567\pi$
$877$	27.5885	+	15.9282i	0.931596	+	0.537857i	0.0442800	+	0.999019i	$0.485901\pi$
$878$	−4.73205	+	2.73205i	−0.159699	+	0.0922022i
$879$	−2.53590	−	4.39230i	−0.0855337	−	0.148149i
$880$		0			0
$881$	−17.8564			−0.601598			−0.300799	−	0.953688i	$-0.597253\pi$
$881$	−17.8564			−0.601598			−0.300799	+	0.953688i	$0.597253\pi$
$882$	−1.90192	+	4.75833i	−0.0640411	+	0.160221i
$883$		−	22.4115i		−	0.754208i	−0.926171	−	0.377104i	$-0.876920\pi$
$883$		−	22.4115i		−	0.754208i	0.926171	−	0.377104i	$-0.123080\pi$
$884$	−28.2487	+	48.9282i	−0.950107	+	1.64563i
$885$		0			0
$886$	−0.928203	−	1.60770i	−0.0311836	−	0.0540116i
$887$	24.8827	+	14.3660i	0.835479	+	0.482364i	0.855725	−	0.517431i	$-0.173112\pi$
$887$	24.8827	+	14.3660i	0.835479	+	0.482364i	−0.0202460	+	0.999795i	$0.506445\pi$
$888$		−	18.2487i		−	0.612387i
$889$	13.1603	+	37.9904i	0.441381	+	1.27416i
$890$		0			0
$891$	1.36603	−	2.36603i	0.0457636	−	0.0792648i
$892$	−0.497423	+	0.287187i	−0.0166549	+	0.00961573i
$893$	4.26795	−	2.46410i	0.142821	−	0.0824580i
$894$	8.00000	−	13.8564i	0.267560	−	0.463428i
$895$		0			0
$896$	−26.3538	−	5.07180i	−0.880420	−	0.169437i
$897$			7.26795i			0.242670i
$898$	−5.16283	−	2.98076i	−0.172286	−	0.0994693i
$899$	20.0263	+	34.6865i	0.667914	+	1.15686i
$900$		0			0
$901$	28.2487	−	48.9282i	0.941101	−	1.63003i
$902$		−	5.46410i		−	0.181935i
$903$	14.3923	+	12.4641i	0.478946	+	0.414779i
$904$	−12.4974			−0.415658
$905$		0			0
$906$	1.80385	+	3.12436i	0.0599288	+	0.103800i
$907$	2.08846	−	1.20577i	0.0693461	−	0.0400370i	−0.464926	−	0.885350i	$-0.653919\pi$
$907$	2.08846	−	1.20577i	0.0693461	−	0.0400370i	0.534272	+	0.845313i	$0.320586\pi$
$908$	−19.8564	−	11.4641i	−0.658958	−	0.380450i
$909$	10.7321			0.355960
$910$		0			0
$911$	−11.2679			−0.373324			−0.186662	−	0.982424i	$-0.559767\pi$
$911$	−11.2679			−0.373324			−0.186662	+	0.982424i	$0.559767\pi$
$912$	−2.28719	−	1.32051i	−0.0757363	−	0.0437264i
$913$	−21.5885	+	12.4641i	−0.714474	+	0.412502i
$914$	0.241670	+	0.418584i	0.00799372	+	0.0138455i
$915$		0			0
$916$	4.39230			0.145126
$917$	−4.26795	+	22.1769i	−0.140940	+	0.732346i
$918$			4.92820i			0.162655i
$919$	−1.57180	+	2.72243i	−0.0518488	+	0.0898047i	−0.890785	−	0.454425i	$-0.849845\pi$
$919$	−1.57180	+	2.72243i	−0.0518488	+	0.0898047i	0.838936	+	0.544230i	$0.183178\pi$
$920$		0			0
$921$	−3.93782	−	6.82051i	−0.129756	−	0.224743i
$922$	22.1769	+	12.8038i	0.730358	+	0.421672i
$923$			24.0526i			0.791700i
$924$	−3.46410	−	10.0000i	−0.113961	−	0.328976i
$925$		0			0
$926$	−8.15064	+	14.1173i	−0.267846	+	0.463924i
$927$	1.03590	−	0.598076i	0.0340234	−	0.0196434i
$928$	−31.4256	+	18.1436i	−1.03160	+	0.595593i
$929$	3.22243	−	5.58142i	0.105725	−	0.183120i	−0.808309	−	0.588758i	$-0.799617\pi$
$929$	3.22243	−	5.58142i	0.105725	−	0.183120i	0.914034	+	0.405638i	$0.132950\pi$
$930$		0			0
$931$	2.46410	+	17.0718i	0.0807577	+	0.559506i
$932$			25.3590i			0.830661i
$933$	13.0981	+	7.56218i	0.428812	+	0.247575i
$934$	−10.1962	−	17.6603i	−0.333628	−	0.577861i
$935$		0			0
$936$	7.26795	−	12.5885i	0.237560	−	0.411467i
$937$			28.2679i			0.923474i	0.887017	+	0.461737i	$0.152774\pi$
$937$			28.2679i			0.923474i	−0.887017	+	0.461737i	$0.847226\pi$
$938$	−4.86860	+	1.68653i	−0.158966	+	0.0550673i
$939$	4.66025			0.152082
$940$		0			0
$941$	−4.02628	−	6.97372i	−0.131253	−	0.227337i	0.792907	−	0.609343i	$-0.208567\pi$
$941$	−4.02628	−	6.97372i	−0.131253	−	0.227337i	−0.924160	+	0.382006i	$0.875233\pi$
$942$	9.12436	−	5.26795i	0.297288	−	0.171639i
$943$	−3.00000	−	1.73205i	−0.0976934	−	0.0564033i
$944$	−10.9282			−0.355683
$945$		0			0
$946$	14.3923			0.467934
$947$	−10.0981	−	5.83013i	−0.328143	−	0.189454i	0.326873	−	0.945068i	$-0.394005\pi$
$947$	−10.0981	−	5.83013i	−0.328143	−	0.189454i	−0.655017	+	0.755615i	$0.727338\pi$
$948$	−16.9808	+	9.80385i	−0.551510	+	0.318414i
$949$	−13.3564	−	23.1340i	−0.433567	−	0.750961i
$950$		0			0
$951$	−30.4449			−0.987242
$952$	34.1436	+	29.5692i	1.10660	+	0.958344i
$953$		−	40.1051i		−	1.29913i	−0.760305	−	0.649566i	$-0.774951\pi$
$953$		−	40.1051i		−	1.29913i	0.760305	−	0.649566i	$-0.225049\pi$
$954$	−3.07180	+	5.32051i	−0.0994531	+	0.172258i
$955$		0			0
$956$	15.3205	+	26.5359i	0.495501	+	0.858232i
$957$	−14.6603	−	8.46410i	−0.473899	−	0.273606i
$958$			24.0000i			0.775405i
$959$	−14.1962	+	16.3923i	−0.458418	+	0.529335i
$960$		0			0
$961$	−5.39230	+	9.33975i	−0.173945	+	0.301282i
$962$	26.1506	−	15.0981i	0.843130	−	0.486782i
$963$	7.09808	−	4.09808i	0.228732	−	0.132059i
$964$	−4.78461	+	8.28719i	−0.154102	+	0.266912i
$965$		0			0
$966$	2.41154	+	0.464102i	0.0775901	+	0.0149322i
$967$			14.1244i			0.454209i	0.973870	+	0.227104i	$0.0729258\pi$
$967$			14.1244i			0.454209i	−0.973870	+	0.227104i	$0.927074\pi$
$968$	7.76537	+	4.48334i	0.249589	+	0.144100i
$969$	8.29423	+	14.3660i	0.266449	+	0.461503i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$			1.46410i			0.0469611i
$973$	19.8205	−	6.86603i	0.635416	−	0.220115i
$974$	23.1244			0.740952
$975$		0			0
$976$	−2.14359	−	3.71281i	−0.0686148	−	0.118844i
$977$	12.6340	−	7.29423i	0.404197	−	0.233363i	−0.284097	−	0.958796i	$-0.591694\pi$
$977$	12.6340	−	7.29423i	0.404197	−	0.233363i	0.688293	+	0.725433i	$0.258360\pi$
$978$	3.71281	+	2.14359i	0.118723	+	0.0685446i
$979$	−24.9282			−0.796709
$980$		0			0
$981$	11.0000			0.351203
$982$	−6.49742	−	3.75129i	−0.207341	−	0.119708i
$983$	−17.4904	+	10.0981i	−0.557857	+	0.322079i	−0.752285	−	0.658838i	$-0.771048\pi$
$983$	−17.4904	+	10.0981i	−0.557857	+	0.322079i	0.194428	+	0.980917i	$0.437715\pi$
$984$	3.46410	+	6.00000i	0.110432	+	0.191273i
$985$		0			0
$986$	30.5359			0.972461
$987$	−5.00000	+	1.73205i	−0.159152	+	0.0551318i
$988$		−	20.6795i		−	0.657902i
$989$	4.56218	−	7.90192i	0.145069	−	0.251267i
$990$		0			0
$991$	−27.5526	−	47.7224i	−0.875236	−	1.51595i	−0.856511	−	0.516128i	$-0.827373\pi$
$991$	−27.5526	−	47.7224i	−0.875236	−	1.51595i	−0.0187246	−	0.999825i	$-0.505961\pi$
$992$	−32.7846	−	18.9282i	−1.04091	−	0.600971i
$993$			21.9282i			0.695870i
$994$	7.98076	+	1.53590i	0.253134	+	0.0487157i
$995$		0			0
$996$	6.67949	−	11.5692i	0.211648	−	0.366585i
$997$	−3.48076	+	2.00962i	−0.110237	+	0.0636453i	−0.554105	−	0.832447i	$-0.686939\pi$
$997$	−3.48076	+	2.00962i	−0.110237	+	0.0636453i	0.443868	+	0.896092i	$0.353606\pi$
$998$	12.9737	−	7.49038i	0.410676	−	0.237104i
$999$	−3.59808	+	6.23205i	−0.113838	+	0.197173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.a.499.2		4
5.2	odd	4		525.2.i.f.226.2		4
5.3	odd	4		105.2.i.d.16.1	✓	4
5.4	even	2		525.2.r.f.499.1		4
7.4	even	3		525.2.r.f.424.1		4
15.8	even	4		315.2.j.c.226.2		4
20.3	even	4		1680.2.bg.o.961.2		4
35.2	odd	12		3675.2.a.bg.1.1		2
35.3	even	12		735.2.i.l.361.1		4
35.4	even	6	inner	525.2.r.a.424.2		4
35.12	even	12		3675.2.a.be.1.1		2
35.13	even	4		735.2.i.l.226.1		4
35.18	odd	12		105.2.i.d.46.1	yes	4
35.23	odd	12		735.2.a.g.1.2		2
35.32	odd	12		525.2.i.f.151.2		4
35.33	even	12		735.2.a.h.1.2		2
105.23	even	12		2205.2.a.z.1.1		2
105.53	even	12		315.2.j.c.46.2		4
105.68	odd	12		2205.2.a.ba.1.1		2
140.123	even	12		1680.2.bg.o.1201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.1	✓	4	5.3	odd	4
105.2.i.d.46.1	yes	4	35.18	odd	12
315.2.j.c.46.2		4	105.53	even	12
315.2.j.c.226.2		4	15.8	even	4
525.2.i.f.151.2		4	35.32	odd	12
525.2.i.f.226.2		4	5.2	odd	4
525.2.r.a.424.2		4	35.4	even	6	inner
525.2.r.a.499.2		4	1.1	even	1	trivial
525.2.r.f.424.1		4	7.4	even	3
525.2.r.f.499.1		4	5.4	even	2
735.2.a.g.1.2		2	35.23	odd	12
735.2.a.h.1.2		2	35.33	even	12
735.2.i.l.226.1		4	35.13	even	4
735.2.i.l.361.1		4	35.3	even	12
1680.2.bg.o.961.2		4	20.3	even	4
1680.2.bg.o.1201.2		4	140.123	even	12
2205.2.a.z.1.1		2	105.23	even	12
2205.2.a.ba.1.1		2	105.68	odd	12
3675.2.a.be.1.1		2	35.12	even	12
3675.2.a.bg.1.1		2	35.2	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.633975 - 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 - 1.26795i) q^{4} -0.732051 q^{6} +(2.50000 - 0.866025i) q^{7} +2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.633975 - 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 - 1.26795i) q^{4} -0.732051 q^{6} +(2.50000 - 0.866025i) q^{7} +2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{11} +(-1.26795 - 0.732051i) q^{12} -5.73205i q^{13} +(-1.90192 - 0.366025i) q^{14} +(-0.535898 + 0.928203i) q^{16} +(5.83013 - 3.36603i) q^{17} +(-0.633975 + 0.366025i) q^{18} +(-1.23205 + 2.13397i) q^{19} +(1.73205 - 2.00000i) q^{21} -2.00000i q^{22} +(-1.09808 - 0.633975i) q^{23} +(1.26795 + 2.19615i) q^{24} +(-2.09808 + 3.63397i) q^{26} -1.00000i q^{27} +(-2.92820 - 2.53590i) q^{28} -6.19615 q^{29} +(-3.23205 - 5.59808i) q^{31} +(5.07180 - 2.92820i) q^{32} +(2.36603 + 1.36603i) q^{33} -4.92820 q^{34} -1.46410 q^{36} +(-6.23205 - 3.59808i) q^{37} +(1.56218 - 0.901924i) q^{38} +(-2.86603 - 4.96410i) q^{39} +2.73205 q^{41} +(-1.83013 + 0.633975i) q^{42} +7.19615i q^{43} +(2.00000 - 3.46410i) q^{44} +(0.464102 + 0.803848i) q^{46} +(-1.73205 - 1.00000i) q^{47} +1.07180i q^{48} +(5.50000 - 4.33013i) q^{49} +(3.36603 - 5.83013i) q^{51} +(-7.26795 + 4.19615i) q^{52} +(7.26795 - 4.19615i) q^{53} +(-0.366025 + 0.633975i) q^{54} +(2.19615 + 6.33975i) q^{56} +2.46410i q^{57} +(3.92820 + 2.26795i) q^{58} +(5.09808 + 8.83013i) q^{59} +(-2.00000 + 3.46410i) q^{61} +4.73205i q^{62} +(0.500000 - 2.59808i) q^{63} -2.14359 q^{64} +(-1.00000 - 1.73205i) q^{66} +(2.30385 - 1.33013i) q^{67} +(-8.53590 - 4.92820i) q^{68} -1.26795 q^{69} -4.19615 q^{71} +(2.19615 + 1.26795i) q^{72} +(4.03590 - 2.33013i) q^{73} +(2.63397 + 4.56218i) q^{74} +3.60770 q^{76} +(5.46410 + 4.73205i) q^{77} +4.19615i q^{78} +(6.69615 - 11.5981i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} +9.12436i q^{83} +(-3.80385 - 0.732051i) q^{84} +(2.63397 - 4.56218i) q^{86} +(-5.36603 + 3.09808i) q^{87} +(-6.00000 + 3.46410i) q^{88} +(-4.56218 + 7.90192i) q^{89} +(-4.96410 - 14.3301i) q^{91} +1.85641i q^{92} +(-5.59808 - 3.23205i) q^{93} +(0.732051 + 1.26795i) q^{94} +(2.92820 - 5.07180i) q^{96} +1.07180i q^{97} +(-5.07180 + 0.732051i) q^{98} +2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 + 4 * q^4 + 4 * q^6 + 10 * q^7 + 2 * q^9	\( 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9} + 2 q^{11} - 12 q^{12} - 18 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{18} + 2 q^{19} + 6 q^{23} + 12 q^{24} + 2 q^{26} + 16 q^{28} - 4 q^{29} - 6 q^{31} + 48 q^{32} + 6 q^{33} + 8 q^{34} + 8 q^{36} - 18 q^{37} - 18 q^{38} - 8 q^{39} + 4 q^{41} + 10 q^{42} + 8 q^{44} - 12 q^{46} + 22 q^{49} + 10 q^{51} - 36 q^{52} + 36 q^{53} + 2 q^{54} - 12 q^{56} - 12 q^{58} + 10 q^{59} - 8 q^{61} + 2 q^{63} - 64 q^{64} - 4 q^{66} + 30 q^{67} - 48 q^{68} - 12 q^{69} + 4 q^{71} - 12 q^{72} + 30 q^{73} + 14 q^{74} + 56 q^{76} + 8 q^{77} + 6 q^{79} - 2 q^{81} - 36 q^{84} + 14 q^{86} - 18 q^{87} - 24 q^{88} + 6 q^{89} - 6 q^{91} - 12 q^{93} - 4 q^{94} - 16 q^{96} - 48 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 4 * q^4 + 4 * q^6 + 10 * q^7 + 2 * q^9 + 2 * q^11 - 12 * q^12 - 18 * q^14 - 16 * q^16 + 6 * q^17 - 6 * q^18 + 2 * q^19 + 6 * q^23 + 12 * q^24 + 2 * q^26 + 16 * q^28 - 4 * q^29 - 6 * q^31 + 48 * q^32 + 6 * q^33 + 8 * q^34 + 8 * q^36 - 18 * q^37 - 18 * q^38 - 8 * q^39 + 4 * q^41 + 10 * q^42 + 8 * q^44 - 12 * q^46 + 22 * q^49 + 10 * q^51 - 36 * q^52 + 36 * q^53 + 2 * q^54 - 12 * q^56 - 12 * q^58 + 10 * q^59 - 8 * q^61 + 2 * q^63 - 64 * q^64 - 4 * q^66 + 30 * q^67 - 48 * q^68 - 12 * q^69 + 4 * q^71 - 12 * q^72 + 30 * q^73 + 14 * q^74 + 56 * q^76 + 8 * q^77 + 6 * q^79 - 2 * q^81 - 36 * q^84 + 14 * q^86 - 18 * q^87 - 24 * q^88 + 6 * q^89 - 6 * q^91 - 12 * q^93 - 4 * q^94 - 16 * q^96 - 48 * q^98 + 4 * q^99

Introduction

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