LMFDB - Embedded newform 525.2.i.f.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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, 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("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (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:	$4.19214610612$
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			151.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.151
Dual form			525.2.i.f.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.366025	+	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	$0.750000\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.732051	−	1.26795i	0.366025	−	0.633975i
$5$		0			0
$5$		0			0
$6$	−0.732051			−0.298858
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$	2.53590			0.896575
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.36603	−	2.36603i	0.411872	−	0.713384i	−0.583222	−	0.812313i	$-0.698208\pi$
$11$	1.36603	−	2.36603i	0.411872	−	0.713384i	0.995094	+	0.0989291i	$0.0315417\pi$
$12$	0.732051	+	1.26795i	0.211325	+	0.366025i
$13$	−5.73205			−1.58978			−0.794892	−	0.606750i	$-0.792473\pi$
$13$	−5.73205			−1.58978			−0.794892	+	0.606750i	$0.792473\pi$
$14$	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	$-0.137356\pi$
$18$	0.366025	−	0.633975i	0.0862730	−	0.149429i
$19$	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	$0.742119\pi$
$20$		0			0
$21$	1.73205	+	2.00000i	0.377964	+	0.436436i
$22$	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	$0.875535\pi$
$24$	−1.26795	+	2.19615i	−0.258819	+	0.448288i
$25$		0			0
$26$	−2.09808	−	3.63397i	−0.411467	−	0.712681i
$27$	1.00000			0.192450
$28$	−2.53590	−	2.92820i	−0.479240	−	0.553378i
$29$	6.19615			1.15060			0.575298	−	0.817944i	$-0.304886\pi$
$29$	6.19615			1.15060			0.575298	+	0.817944i	$0.304886\pi$
$30$		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
$33$	1.36603	+	2.36603i	0.237795	+	0.411872i
$34$	4.92820			0.845180
$35$		0			0
$36$	−1.46410			−0.244017
$37$	3.59808	+	6.23205i	0.591520	+	1.02454i	0.994028	+	0.109126i	$0.0348053\pi$
$37$	3.59808	+	6.23205i	0.591520	+	1.02454i	−0.402508	+	0.915417i	$0.631861\pi$
$38$	−0.901924	+	1.56218i	−0.146311	+	0.253419i
$39$	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	$0.431567\pi$
$42$	−0.633975	+	1.83013i	−0.0978244	+	0.282395i
$43$	7.19615			1.09740			0.548701	−	0.836018i	$-0.315122\pi$
$43$	7.19615			1.09740			0.548701	+	0.836018i	$0.315122\pi$
$44$	−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	$0.786737\pi$
$48$	1.07180			0.154701
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	3.36603	+	5.83013i	0.471338	+	0.816381i
$52$	−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	$0.971129\pi$
$54$	0.366025	+	0.633975i	0.0498097	+	0.0862730i
$55$		0			0
$56$	2.19615	−	6.33975i	0.293473	−	0.847184i
$57$	−2.46410			−0.326378
$58$	2.26795	+	3.92820i	0.297796	+	0.515798i
$59$	−5.09808	+	8.83013i	−0.663713	+	1.14958i	0.315920	+	0.948786i	$0.397687\pi$
$59$	−5.09808	+	8.83013i	−0.663713	+	1.14958i	−0.979633	+	0.200799i	$0.935646\pi$
$60$		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
$63$	−2.59808	+	0.500000i	−0.327327	+	0.0629941i
$64$	2.14359			0.267949
$65$		0			0
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	1.33013	−	2.30385i	0.162501	−	0.281460i	−0.773264	−	0.634084i	$-0.781377\pi$
$67$	1.33013	−	2.30385i	0.162501	−	0.281460i	0.935765	+	0.352624i	$0.114711\pi$
$68$	−4.92820	−	8.53590i	−0.597632	−	1.03513i
$69$	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	$0.580101\pi$
$72$	−1.26795	−	2.19615i	−0.149429	−	0.258819i
$73$	−2.33013	+	4.03590i	−0.272721	+	0.472366i	−0.969558	−	0.244864i	$-0.921257\pi$
$73$	−2.33013	+	4.03590i	−0.272721	+	0.472366i	0.696837	+	0.717230i	$0.254590\pi$
$74$	−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
$78$	4.19615			0.475121
$79$	−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			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	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	$0.333052\pi$
$84$	3.80385	−	0.732051i	0.415034	−	0.0798733i
$85$		0			0
$86$	2.63397	+	4.56218i	0.284029	+	0.491952i
$87$	−3.09808	+	5.36603i	−0.332149	+	0.575298i
$88$	3.46410	−	6.00000i	0.369274	−	0.639602i
$89$	4.56218	+	7.90192i	0.483590	+	0.837602i	0.999822	−	0.0188462i	$-0.00599930\pi$
$89$	4.56218	+	7.90192i	0.483590	+	0.837602i	−0.516233	+	0.856448i	$0.672666\pi$
$90$		0			0
$91$	−4.96410	+	14.3301i	−0.520379	+	1.50221i
$92$	−1.85641			−0.193544
$93$	−3.23205	−	5.59808i	−0.335148	−	0.580493i
$94$	−0.732051	+	1.26795i	−0.0755053	+	0.130779i
$95$		0			0
$96$	2.92820	+	5.07180i	0.298858	+	0.517638i
$97$	−1.07180			−0.108824			−0.0544122	−	0.998519i	$-0.517329\pi$
$97$	−1.07180			−0.108824			−0.0544122	+	0.998519i	$0.517329\pi$
$98$	0.732051	−	5.07180i	0.0739483	−	0.512329i
$99$	−2.73205			−0.274581
$100$		0			0
$101$	5.36603	−	9.29423i	0.533939	−	0.924810i	−0.465274	−	0.885167i	$-0.654044\pi$
$101$	5.36603	−	9.29423i	0.533939	−	0.924810i	0.999214	−	0.0396438i	$-0.0126223\pi$
$102$	−2.46410	+	4.26795i	−0.243982	+	0.422590i
$103$	0.598076	+	1.03590i	0.0589302	+	0.102070i	0.893985	−	0.448096i	$-0.147898\pi$
$103$	0.598076	+	1.03590i	0.0589302	+	0.102070i	−0.835055	+	0.550166i	$0.814564\pi$
$104$	−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	$0.962996\pi$
$108$	0.732051	−	1.26795i	0.0704416	−	0.122008i
$109$	−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	$0.990057\pi$
$110$		0			0
$111$	−7.19615			−0.683029
$112$	−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	$0.425537\pi$
$114$	−0.901924	−	1.56218i	−0.0844729	−	0.146311i
$115$		0			0
$116$	4.53590	−	7.85641i	0.421148	−	0.729449i
$117$	2.86603	+	4.96410i	0.264964	+	0.458931i
$118$	−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
$123$	−1.36603	+	2.36603i	−0.123170	+	0.213337i
$124$	4.73205	+	8.19615i	0.424951	+	0.736036i
$125$		0			0
$126$	−1.26795	−	1.46410i	−0.112958	−	0.130433i
$127$	−15.1962			−1.34844			−0.674220	−	0.738530i	$-0.735520\pi$
$127$	−15.1962			−1.34844			−0.674220	+	0.738530i	$0.735520\pi$
$128$	−5.07180	−	8.78461i	−0.448288	−	0.776457i
$129$	−3.59808	+	6.23205i	−0.316793	+	0.548701i
$130$		0			0
$131$	−4.26795	−	7.39230i	−0.372892	−	0.645869i	0.617117	−	0.786872i	$-0.288301\pi$
$131$	−4.26795	−	7.39230i	−0.372892	−	0.645869i	−0.990009	+	0.141003i	$0.954967\pi$
$132$	4.00000			0.348155
$133$	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	$0.280527\pi$
$138$	0.464102	+	0.803848i	0.0395070	+	0.0684280i
$139$	−7.92820			−0.672461			−0.336231	−	0.941780i	$-0.609152\pi$
$139$	−7.92820			−0.672461			−0.336231	+	0.941780i	$0.609152\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$	−1.53590	−	2.66025i	−0.128890	−	0.223244i
$143$	−7.83013	+	13.5622i	−0.654788	+	1.13413i
$144$	−0.535898	+	0.928203i	−0.0446582	+	0.0773503i
$145$		0			0
$146$	−3.41154			−0.282341
$147$	6.50000	−	2.59808i	0.536111	−	0.214286i
$148$	10.5359			0.866046
$149$	10.9282	+	18.9282i	0.895273	+	1.55066i	0.833466	+	0.552571i	$0.186353\pi$
$149$	10.9282	+	18.9282i	0.895273	+	1.55066i	0.0618073	+	0.998088i	$0.480314\pi$
$150$		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
$153$	−6.73205			−0.544254
$154$	1.73205	−	5.00000i	0.139573	−	0.402911i
$155$		0			0
$156$	−4.19615	−	7.26795i	−0.335961	−	0.581902i
$157$	−7.19615	+	12.4641i	−0.574315	+	0.994744i	0.421800	+	0.906689i	$0.361398\pi$
$157$	−7.19615	+	12.4641i	−0.574315	+	0.994744i	−0.996116	+	0.0880548i	$0.971935\pi$
$158$	4.90192	−	8.49038i	0.389976	−	0.675458i
$159$	−4.19615	−	7.26795i	−0.332777	−	0.576386i
$160$		0			0
$161$	−3.29423	+	0.633975i	−0.259622	+	0.0499642i
$162$	−0.732051			−0.0575153
$163$	−2.92820	−	5.07180i	−0.229355	−	0.397254i	0.728262	−	0.685298i	$-0.240328\pi$
$163$	−2.92820	−	5.07180i	−0.229355	−	0.397254i	−0.957617	+	0.288045i	$0.906995\pi$
$164$	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	$0.495816\pi$
$168$	4.39230	+	5.07180i	0.338874	+	0.391298i
$169$	19.8564			1.52742
$170$		0			0
$171$	1.23205	−	2.13397i	0.0942173	−	0.163189i
$172$	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	$0.529552\pi$
$174$	−4.53590			−0.343866
$175$		0			0
$176$	−2.92820			−0.220722
$177$	−5.09808	−	8.83013i	−0.383195	−	0.663713i
$178$	−3.33975	+	5.78461i	−0.250325	+	0.433575i
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$		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
$183$	4.00000			0.295689
$184$	−1.60770	−	2.78461i	−0.118521	−	0.205284i
$185$		0			0
$186$	2.36603	−	4.09808i	0.173485	−	0.300486i
$187$	−9.19615	−	15.9282i	−0.672489	−	1.16479i
$188$	2.92820			0.213561
$189$	0.866025	−	2.50000i	0.0629941	−	0.181848i
$190$		0			0
$191$	−2.46410	−	4.26795i	−0.178296	−	0.308818i	0.763001	−	0.646397i	$-0.223725\pi$
$191$	−2.46410	−	4.26795i	−0.178296	−	0.308818i	−0.941297	+	0.337579i	$0.890392\pi$
$192$	−1.07180	+	1.85641i	−0.0773503	+	0.133975i
$193$	−4.59808	+	7.96410i	−0.330977	+	0.573269i	−0.982704	−	0.185185i	$-0.940712\pi$
$193$	−4.59808	+	7.96410i	−0.330977	+	0.573269i	0.651727	+	0.758454i	$0.274045\pi$
$194$	−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	$0.283415\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$	−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	$0.882003\pi$
$200$		0			0
$201$	1.33013	+	2.30385i	0.0938199	+	0.162501i
$202$	7.85641			0.552775
$203$	5.36603	−	15.4904i	0.376621	−	1.08721i
$204$	9.85641			0.690086
$205$		0			0
$206$	−0.437822	+	0.758330i	−0.0305045	+	0.0528354i
$207$	−0.633975	+	1.09808i	−0.0440643	+	0.0763216i
$208$	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
$213$	2.09808	−	3.63397i	0.143758	−	0.248996i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$	2.53590			0.172546
$217$	11.1962	+	12.9282i	0.760044	+	0.877624i
$218$	−8.05256			−0.545388
$219$	−2.33013	−	4.03590i	−0.157455	−	0.272721i
$220$		0			0
$221$	−19.2942	+	33.4186i	−1.29787	+	2.24798i
$222$	−2.63397	−	4.56218i	−0.176781	−	0.306193i
$223$	−0.392305			−0.0262707			−0.0131353	−	0.999914i	$-0.504181\pi$
$223$	−0.392305			−0.0262707			−0.0131353	+	0.999914i	$0.504181\pi$
$224$	−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	$-0.00729102\pi$
$228$	−1.80385	+	3.12436i	−0.119463	+	0.206916i
$229$	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			0
$231$	7.09808	−	1.36603i	0.467019	−	0.0898779i
$232$	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	$-0.358699\pi$
$234$	−2.09808	+	3.63397i	−0.137156	+	0.237560i
$235$		0			0
$236$	7.46410	+	12.9282i	0.485872	+	0.841554i
$237$	13.3923			0.869924
$238$	4.26795	−	12.3205i	0.276650	−	0.798620i
$239$	20.9282			1.35373			0.676866	−	0.736106i	$-0.263337\pi$
$239$	20.9282			1.35373			0.676866	+	0.736106i	$0.263337\pi$
$240$		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
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−5.85641			−0.374918
$245$		0			0
$246$	−2.00000			−0.127515
$247$	−7.06218	−	12.2321i	−0.449356	−	0.778307i
$248$	−8.19615	+	14.1962i	−0.520456	+	0.901457i
$249$	−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	$0.433327\pi$
$252$	−1.26795	+	3.66025i	−0.0798733	+	0.230574i
$253$	−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	$0.714856\pi$
$258$	−5.26795			−0.327968
$259$	18.6962	−	3.59808i	1.16172	−	0.223574i
$260$		0			0
$261$	−3.09808	−	5.36603i	−0.191766	−	0.332149i
$262$	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	$0.291456\pi$
$264$	3.46410	+	6.00000i	0.213201	+	0.369274i
$265$		0			0
$266$	3.12436	+	3.60770i	0.191567	+	0.221202i
$267$	−9.12436			−0.558401
$268$	−1.94744	−	3.37307i	−0.118959	−	0.206043i
$269$	9.73205	−	16.8564i	0.593374	−	1.02775i	−0.400401	−	0.916340i	$-0.631129\pi$
$269$	9.73205	−	16.8564i	0.593374	−	1.02775i	0.993774	−	0.111413i	$-0.0355377\pi$
$270$		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
$273$	−9.92820	−	11.4641i	−0.600882	−	0.693839i
$274$	−6.00000			−0.362473
$275$		0			0
$276$	0.928203	−	1.60770i	0.0558713	−	0.0967719i
$277$	1.33013	−	2.30385i	0.0799196	−	0.138425i	−0.823295	−	0.567613i	$-0.807867\pi$
$277$	1.33013	−	2.30385i	0.0799196	−	0.138425i	0.903215	+	0.429188i	$0.141200\pi$
$278$	−2.90192	−	5.02628i	−0.174046	−	0.301456i
$279$	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	$0.635625\pi$
$282$	−0.732051	−	1.26795i	−0.0435930	−	0.0755053i
$283$	0.0621778	−	0.107695i	0.00369609	−	0.00640181i	−0.864171	−	0.503197i	$-0.832157\pi$
$283$	0.0621778	−	0.107695i	0.00369609	−	0.00640181i	0.867868	+	0.496796i	$0.165490\pi$
$284$	−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
$288$	−5.85641			−0.345092
$289$	−14.1603	−	24.5263i	−0.832956	−	1.44272i
$290$		0			0
$291$	0.535898	−	0.928203i	0.0314149	−	0.0544122i
$292$	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	$0.547331\pi$
$294$	4.02628	+	3.16987i	0.234817	+	0.184871i
$295$		0			0
$296$	9.12436	+	15.8038i	0.530342	+	0.918580i
$297$	1.36603	−	2.36603i	0.0792648	−	0.137291i
$298$	−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
$303$	5.36603	+	9.29423i	0.308270	+	0.533939i
$304$	1.32051	−	2.28719i	0.0757363	−	0.131179i
$305$		0			0
$306$	−2.46410	−	4.26795i	−0.140863	−	0.243982i
$307$	7.87564			0.449487			0.224743	−	0.974418i	$-0.427846\pi$
$307$	7.87564			0.449487			0.224743	+	0.974418i	$0.427846\pi$
$308$	−10.3923	+	2.00000i	−0.592157	+	0.113961i
$309$	−1.19615			−0.0680467
$310$		0			0
$311$	7.56218	−	13.0981i	0.428812	−	0.742724i	−0.567956	−	0.823059i	$-0.692266\pi$
$311$	7.56218	−	13.0981i	0.428812	−	0.742724i	0.996768	+	0.0803351i	$0.0255990\pi$
$312$	7.26795	−	12.5885i	0.411467	−	0.712681i
$313$	2.33013	+	4.03590i	0.131707	+	0.228122i	0.924335	−	0.381583i	$-0.124621\pi$
$313$	2.33013	+	4.03590i	0.131707	+	0.228122i	−0.792628	+	0.609706i	$0.791288\pi$
$314$	−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	$0.506905\pi$
$318$	3.07180	−	5.32051i	0.172258	−	0.298359i
$319$	8.46410	−	14.6603i	0.473899	−	0.820817i
$320$		0			0
$321$	8.19615			0.457465
$322$	−1.60770	−	1.85641i	−0.0895933	−	0.103453i
$323$	16.5885			0.923006
$324$	0.732051	+	1.26795i	0.0406695	+	0.0704416i
$325$		0			0
$326$	2.14359	−	3.71281i	0.118723	−	0.205634i
$327$	−5.50000	−	9.52628i	−0.304151	−	0.526804i
$328$	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
$333$	3.59808	−	6.23205i	0.197173	−	0.341514i
$334$	0.124356	+	0.215390i	0.00680444	+	0.0117856i
$335$		0			0
$336$	0.928203	−	2.67949i	0.0506376	−	0.146178i
$337$	33.9808			1.85105			0.925525	−	0.378686i	$-0.123624\pi$
$337$	33.9808			1.85105			0.925525	+	0.378686i	$0.123624\pi$
$338$	7.26795	+	12.5885i	0.395324	+	0.684722i
$339$	−2.46410	+	4.26795i	−0.133832	+	0.231803i
$340$		0			0
$341$	8.83013	+	15.2942i	0.478178	+	0.828229i
$342$	1.80385			0.0975409
$343$	−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	$0.779781\pi$
$348$	4.53590	+	7.85641i	0.243150	+	0.421148i
$349$	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			0
$351$	−5.73205			−0.305954
$352$	−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	$-0.0233659\pi$
$354$	3.73205	−	6.46410i	0.198356	−	0.343563i
$355$		0			0
$356$	13.3590			0.708025
$357$	17.4904	−	3.36603i	0.925689	−	0.178149i
$358$	7.32051			0.386901
$359$	2.36603	+	4.09808i	0.124874	+	0.216288i	0.921684	−	0.387942i	$-0.126814\pi$
$359$	2.36603	+	4.09808i	0.124874	+	0.216288i	−0.796810	+	0.604230i	$0.793481\pi$
$360$		0			0
$361$	6.46410	−	11.1962i	0.340216	−	0.589271i
$362$	3.77757	+	6.54294i	0.198545	+	0.343889i
$363$	−3.53590			−0.185587
$364$	14.5359	+	16.7846i	0.761888	+	0.879753i
$365$		0			0
$366$	1.46410	+	2.53590i	0.0765298	+	0.132554i
$367$	0.401924	−	0.696152i	0.0209803	−	0.0363389i	−0.855345	−	0.518059i	$-0.826655\pi$
$367$	0.401924	−	0.696152i	0.0209803	−	0.0363389i	0.876325	+	0.481721i	$0.159988\pi$
$368$	−0.679492	+	1.17691i	−0.0354210	+	0.0613509i
$369$	−1.36603	−	2.36603i	−0.0711124	−	0.123170i
$370$		0			0
$371$	14.5359	+	16.7846i	0.754666	+	0.871414i
$372$	−9.46410			−0.490691
$373$	−9.25833	−	16.0359i	−0.479378	−	0.830307i	0.520342	−	0.853958i	$-0.325804\pi$
$373$	−9.25833	−	16.0359i	−0.479378	−	0.830307i	−0.999720	+	0.0236505i	$0.992471\pi$
$374$	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
$378$	1.90192	−	0.366025i	0.0978244	−	0.0188263i
$379$	−28.3205			−1.45473			−0.727363	−	0.686253i	$-0.759255\pi$
$379$	−28.3205			−1.45473			−0.727363	+	0.686253i	$0.759255\pi$
$380$		0			0
$381$	7.59808	−	13.1603i	0.389261	−	0.674220i
$382$	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	$0.739936\pi$
$384$	10.1436			0.517638
$385$		0			0
$386$	−6.73205			−0.342652
$387$	−3.59808	−	6.23205i	−0.182900	−	0.316793i
$388$	−0.784610	+	1.35898i	−0.0398325	+	0.0689920i
$389$	−18.2942	+	31.6865i	−0.927554	+	1.60657i	−0.140153	+	0.990130i	$0.544760\pi$
$389$	−18.2942	+	31.6865i	−0.927554	+	1.60657i	−0.787401	+	0.616441i	$0.788574\pi$
$390$		0			0
$391$	−8.53590			−0.431679
$392$	−13.9474	−	10.9808i	−0.704452	−	0.554612i
$393$	8.53590			0.430579
$394$	6.46410	+	11.1962i	0.325657	+	0.564054i
$395$		0			0
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	−10.4019	−	18.0167i	−0.522058	−	0.904230i	−0.999671	−	0.0256600i	$-0.991831\pi$
$397$	−10.4019	−	18.0167i	−0.522058	−	0.904230i	0.477613	−	0.878570i	$-0.341502\pi$
$398$	−16.1051			−0.807277
$399$	−2.13397	+	6.16025i	−0.106832	+	0.308398i
$400$		0			0
$401$	−2.19615	−	3.80385i	−0.109671	−	0.189955i	0.805966	−	0.591962i	$-0.201646\pi$
$401$	−2.19615	−	3.80385i	−0.109671	−	0.189955i	−0.915637	+	0.402006i	$0.868313\pi$
$402$	−0.973721	+	1.68653i	−0.0485648	+	0.0841166i
$403$	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
$408$	8.53590	+	14.7846i	0.422590	+	0.731947i
$409$	−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	$0.890454\pi$
$410$		0			0
$411$	−4.09808	−	7.09808i	−0.202143	−	0.350122i
$412$	1.75129			0.0862798
$413$	17.6603	+	20.3923i	0.869004	+	1.00344i
$414$	−0.928203			−0.0456187
$415$		0			0
$416$	−16.7846	+	29.0718i	−0.822933	+	1.42536i
$417$	3.96410	−	6.86603i	0.194123	−	0.336231i
$418$	2.46410	+	4.26795i	0.120523	+	0.208752i
$419$	−28.5359			−1.39407			−0.697035	−	0.717037i	$-0.745498\pi$
$419$	−28.5359			−1.39407			−0.697035	+	0.717037i	$0.745498\pi$
$420$		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
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$	−10.6410	+	18.4308i	−0.516773	+	0.895078i
$425$		0			0
$426$	3.07180			0.148829
$427$	−10.3923	+	2.00000i	−0.502919	+	0.0967868i
$428$	−12.0000			−0.580042
$429$	−7.83013	−	13.5622i	−0.378042	−	0.654788i
$430$		0			0
$431$	8.66025	−	15.0000i	0.417150	−	0.722525i	−0.578502	−	0.815681i	$-0.696362\pi$
$431$	8.66025	−	15.0000i	0.417150	−	0.722525i	0.995651	+	0.0931566i	$0.0296957\pi$
$432$	−0.535898	−	0.928203i	−0.0257834	−	0.0446582i
$433$	−4.80385			−0.230858			−0.115429	−	0.993316i	$-0.536824\pi$
$433$	−4.80385			−0.230858			−0.115429	+	0.993316i	$0.536824\pi$
$434$	−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
$438$	1.70577	−	2.95448i	0.0815049	−	0.141171i
$439$	−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	$0.890335\pi$
$440$		0			0
$441$	−1.00000	+	6.92820i	−0.0476190	+	0.329914i
$442$	−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	$0.814146\pi$
$444$	−5.26795	+	9.12436i	−0.250006	+	0.433023i
$445$		0			0
$446$	−0.143594	−	0.248711i	−0.00679935	−	0.0117768i
$447$	−21.8564			−1.03377
$448$	1.85641	−	5.35898i	0.0877070	−	0.253188i
$449$	−8.14359			−0.384320			−0.192160	−	0.981364i	$-0.561549\pi$
$449$	−8.14359			−0.384320			−0.192160	+	0.981364i	$0.561549\pi$
$450$		0			0
$451$	3.73205	−	6.46410i	0.175735	−	0.304383i
$452$	3.60770	−	6.24871i	0.169692	−	0.293915i
$453$	−2.46410	−	4.26795i	−0.115774	−	0.200526i
$454$	11.4641			0.538037
$455$		0			0
$456$	−6.24871			−0.292623
$457$	0.330127	+	0.571797i	0.0154427	+	0.0267475i	0.873643	−	0.486567i	$-0.161751\pi$
$457$	0.330127	+	0.571797i	0.0154427	+	0.0267475i	−0.858201	+	0.513314i	$0.828418\pi$
$458$	−1.09808	+	1.90192i	−0.0513097	+	0.0888711i
$459$	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	$0.803048\pi$
$462$	3.46410	+	4.00000i	0.161165	+	0.186097i
$463$	−22.2679			−1.03488			−0.517440	−	0.855720i	$-0.673115\pi$
$463$	−22.2679			−1.03488			−0.517440	+	0.855720i	$0.673115\pi$
$464$	−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	$-0.389610\pi$
$468$	8.39230			0.387934
$469$	−4.60770	−	5.32051i	−0.212764	−	0.245678i
$470$		0			0
$471$	−7.19615	−	12.4641i	−0.331581	−	0.574315i
$472$	−12.9282	+	22.3923i	−0.595069	+	1.03069i
$473$	9.83013	−	17.0263i	0.451990	−	0.782869i
$474$	4.90192	+	8.49038i	0.225153	+	0.389976i
$475$		0			0
$476$	−25.6077	+	4.92820i	−1.17373	+	0.225884i
$477$	8.39230			0.384257
$478$	7.66025	+	13.2679i	0.350372	+	0.606862i
$479$	16.3923	−	28.3923i	0.748984	−	1.29728i	−0.199327	−	0.979933i	$-0.563876\pi$
$479$	16.3923	−	28.3923i	0.748984	−	1.29728i	0.948310	−	0.317344i	$-0.102791\pi$
$480$		0			0
$481$	−20.6244	−	35.7224i	−0.940390	−	1.62880i
$482$	−4.78461			−0.217933
$483$	1.09808	−	3.16987i	0.0499642	−	0.144234i
$484$	5.17691			0.235314
$485$		0			0
$486$	0.366025	−	0.633975i	0.0166032	−	0.0287577i
$487$	−15.7942	+	27.3564i	−0.715705	+	1.23964i	0.246982	+	0.969020i	$0.420561\pi$
$487$	−15.7942	+	27.3564i	−0.715705	+	1.23964i	−0.962687	+	0.270617i	$0.912772\pi$
$488$	−5.07180	−	8.78461i	−0.229589	−	0.397661i
$489$	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	$0.425716\pi$
$492$	2.00000	+	3.46410i	0.0901670	+	0.156174i
$493$	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
$498$	−6.67949			−0.299315
$499$	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			0
$501$	−0.169873	+	0.294229i	−0.00758937	+	0.0131452i
$502$	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	$0.454483\pi$
$504$	−6.58846	+	1.26795i	−0.293473	+	0.0564789i
$505$		0			0
$506$	−1.26795	−	2.19615i	−0.0563672	−	0.0976309i
$507$	−9.92820	+	17.1962i	−0.440927	+	0.763708i
$508$	−11.1244	+	19.2679i	−0.493563	+	0.854877i
$509$	−5.73205	−	9.92820i	−0.254069	−	0.440060i	0.710573	−	0.703623i	$-0.248436\pi$
$509$	−5.73205	−	9.92820i	−0.254069	−	0.440060i	−0.964642	+	0.263563i	$0.915102\pi$
$510$		0			0
$511$	8.07180	+	9.32051i	0.357075	+	0.412315i
$512$	−11.7128			−0.517638
$513$	1.23205	+	2.13397i	0.0543964	+	0.0942173i
$514$	−4.26795	+	7.39230i	−0.188251	+	0.326061i
$515$		0			0
$516$	5.26795	+	9.12436i	0.231909	+	0.401677i
$517$	5.46410			0.240311
$518$	9.12436	+	10.5359i	0.400901	+	0.462921i
$519$	−21.4641			−0.942169
$520$		0			0
$521$	−0.732051	+	1.26795i	−0.0320717	+	0.0555499i	−0.881616	−	0.471968i	$-0.843544\pi$
$521$	−0.732051	+	1.26795i	−0.0320717	+	0.0555499i	0.849544	+	0.527518i	$0.176877\pi$
$522$	2.26795	−	3.92820i	0.0992654	−	0.171933i
$523$	−12.1340	−	21.0167i	−0.530582	−	0.918994i	−0.999363	−	0.0356803i	$-0.988640\pi$
$523$	−12.1340	−	21.0167i	−0.530582	−	0.918994i	0.468782	−	0.883314i	$-0.344693\pi$
$524$	−12.4974			−0.545952
$525$		0			0
$526$	−9.07180			−0.395549
$527$	21.7583	+	37.6865i	0.947808	+	1.64165i
$528$	1.46410	−	2.53590i	0.0637168	−	0.110361i
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$		0			0
$531$	10.1962			0.442475
$532$	3.12436	−	9.01924i	0.135458	−	0.391034i
$533$	−15.6603			−0.678321
$534$	−3.33975	−	5.78461i	−0.144525	−	0.250325i
$535$		0			0
$536$	3.37307	−	5.84232i	0.145694	−	0.252350i
$537$	5.00000	+	8.66025i	0.215766	+	0.373718i
$538$	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
$543$	−5.16025	+	8.93782i	−0.221448	+	0.383559i
$544$	−19.7128	−	34.1436i	−0.845180	−	1.46389i
$545$		0			0
$546$	3.63397	−	10.4904i	0.155520	−	0.448947i
$547$	−22.2487			−0.951286			−0.475643	−	0.879638i	$-0.657785\pi$
$547$	−22.2487			−0.951286			−0.475643	+	0.879638i	$0.657785\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	−2.00000	+	3.46410i	−0.0853579	+	0.147844i
$550$		0			0
$551$	7.63397	+	13.2224i	0.325218	+	0.563295i
$552$	3.21539			0.136856
$553$	−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	$0.974597\pi$
$558$	2.36603	+	4.09808i	0.100162	+	0.173485i
$559$	−41.2487			−1.74463
$560$		0			0
$561$	18.3923			0.776524
$562$	−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	$0.290503\pi$
$564$	−1.46410	+	2.53590i	−0.0616498	+	0.106781i
$565$		0			0
$566$	0.0910347			0.00382647
$567$	1.73205	+	2.00000i	0.0727393	+	0.0839921i
$568$	−10.6410			−0.446487
$569$	13.2224	+	22.9019i	0.554313	+	0.960099i	0.997957	+	0.0638952i	$0.0203523\pi$
$569$	13.2224	+	22.9019i	0.554313	+	0.960099i	−0.443643	+	0.896203i	$0.646314\pi$
$570$		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
$573$	4.92820			0.205879
$574$	5.19615	−	1.00000i	0.216883	−	0.0417392i
$575$		0			0
$576$	−1.07180	−	1.85641i	−0.0446582	−	0.0773503i
$577$	5.66987	−	9.82051i	0.236040	−	0.408833i	−0.723534	−	0.690288i	$-0.757484\pi$
$577$	5.66987	−	9.82051i	0.236040	−	0.408833i	0.959574	+	0.281455i	$0.0908171\pi$
$578$	10.3660	−	17.9545i	0.431170	−	0.746808i
$579$	−4.59808	−	7.96410i	−0.191090	−	0.330977i
$580$		0			0
$581$	7.90192	−	22.8109i	0.327827	−	0.946355i
$582$	0.784610			0.0325231
$583$	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	$0.779298\pi$
$588$	1.46410	−	10.1436i	0.0603785	−	0.418315i
$589$	−15.9282			−0.656310
$590$		0			0
$591$	−8.83013	+	15.2942i	−0.363223	+	0.629121i
$592$	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	$-0.450619\pi$
$594$	2.00000			0.0820610
$595$		0			0
$596$	32.0000			1.31077
$597$	−11.0000	−	19.0526i	−0.450200	−	0.779769i
$598$	−2.66025	+	4.60770i	−0.108786	+	0.188423i
$599$	−5.12436	+	8.87564i	−0.209375	+	0.362649i	−0.951518	−	0.307593i	$-0.900476\pi$
$599$	−5.12436	+	8.87564i	−0.209375	+	0.362649i	0.742142	+	0.670242i	$0.233810\pi$
$600$		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
$603$	−2.66025			−0.108334
$604$	3.60770	+	6.24871i	0.146795	+	0.254256i
$605$		0			0
$606$	−3.92820	+	6.80385i	−0.159572	+	0.276387i
$607$	−3.59808	−	6.23205i	−0.146041	−	0.252951i	0.783720	−	0.621115i	$-0.213320\pi$
$607$	−3.59808	−	6.23205i	−0.146041	−	0.252951i	−0.929761	+	0.368164i	$0.879987\pi$
$608$	14.4308			0.585245
$609$	10.7321	+	12.3923i	0.434885	+	0.502162i
$610$		0			0
$611$	−5.73205	−	9.92820i	−0.231894	−	0.401652i
$612$	−4.92820	+	8.53590i	−0.199211	+	0.345043i
$613$	−6.53590	+	11.3205i	−0.263982	+	0.457231i	−0.967297	−	0.253648i	$-0.918369\pi$
$613$	−6.53590	+	11.3205i	−0.263982	+	0.457231i	0.703314	+	0.710879i	$0.251703\pi$
$614$	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	$0.579299\pi$
$618$	−0.437822	−	0.758330i	−0.0176118	−	0.0305045i
$619$	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	$-0.177686\pi$
$620$		0			0
$621$	−0.633975	−	1.09808i	−0.0254405	−	0.0440643i
$622$	11.0718			0.443939
$623$	23.7058	−	4.56218i	0.949752	−	0.182780i
$624$	−6.14359			−0.245941
$625$		0			0
$626$	−1.70577	+	2.95448i	−0.0681763	+	0.118085i
$627$	−3.36603	+	5.83013i	−0.134426	+	0.232833i
$628$	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
$633$	−10.4641	+	18.1244i	−0.415911	+	0.720378i
$634$	−11.1436	+	19.3013i	−0.442569	+	0.766551i
$635$		0			0
$636$	−12.2872			−0.487219
$637$	31.5263	+	24.8205i	1.24912	+	0.983424i
$638$	12.3923			0.490616
$639$	2.09808	+	3.63397i	0.0829986	+	0.143758i
$640$		0			0
$641$	−7.09808	+	12.2942i	−0.280357	+	0.485593i	−0.971473	−	0.237151i	$-0.923786\pi$
$641$	−7.09808	+	12.2942i	−0.280357	+	0.485593i	0.691116	+	0.722744i	$0.257120\pi$
$642$	3.00000	+	5.19615i	0.118401	+	0.205076i
$643$	40.5167			1.59782			0.798911	−	0.601450i	$-0.205410\pi$
$643$	40.5167			1.59782			0.798911	+	0.601450i	$0.205410\pi$
$644$	−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	$-0.100969\pi$
$648$	−1.26795	+	2.19615i	−0.0498097	+	0.0862730i
$649$	13.9282	+	24.1244i	0.546730	+	0.946964i
$650$		0			0
$651$	−16.7942	+	3.23205i	−0.658218	+	0.126674i
$652$	−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	$0.917853\pi$
$654$	4.02628	−	6.97372i	0.157440	−	0.272694i
$655$		0			0
$656$	−1.46410	−	2.53590i	−0.0571636	−	0.0990102i
$657$	4.66025			0.181814
$658$	2.53590	+	2.92820i	0.0988596	+	0.114153i
$659$	−10.9282			−0.425702			−0.212851	−	0.977085i	$-0.568275\pi$
$659$	−10.9282			−0.425702			−0.212851	+	0.977085i	$0.568275\pi$
$660$		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
$663$	−19.2942	−	33.4186i	−0.749326	−	1.29787i
$664$	23.1384			0.897946
$665$		0			0
$666$	5.26795			0.204129
$667$	−3.92820	−	6.80385i	−0.152101	−	0.263446i
$668$	0.248711	−	0.430781i	0.00962293	−	0.0166674i
$669$	0.196152	−	0.339746i	0.00758369	−	0.0131353i
$670$		0			0
$671$	−10.9282			−0.421879
$672$	15.2154	−	2.92820i	0.586946	−	0.112958i
$673$	44.6603			1.72153			0.860763	−	0.509006i	$-0.169987\pi$
$673$	44.6603			1.72153			0.860763	+	0.509006i	$0.169987\pi$
$674$	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	$0.887891\pi$
$678$	−3.60770			−0.138553
$679$	−0.928203	+	2.67949i	−0.0356212	+	0.102829i
$680$		0			0
$681$	7.83013	+	13.5622i	0.300051	+	0.519704i
$682$	−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	$0.105064\pi$
$684$	−1.80385	−	3.12436i	−0.0689718	−	0.119463i
$685$		0			0
$686$	−12.0455	−	6.22243i	−0.459900	−	0.237574i
$687$	−3.00000			−0.114457
$688$	−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
$693$	−2.36603	+	6.83013i	−0.0898779	+	0.259455i
$694$	−25.5692			−0.970594
$695$		0			0
$696$	−7.85641	+	13.6077i	−0.297796	+	0.515798i
$697$	9.19615	−	15.9282i	0.348329	−	0.603324i
$698$	8.05256	+	13.9474i	0.304794	+	0.527918i
$699$	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	$0.359719\pi$
$702$	−2.09808	−	3.63397i	−0.0791868	−	0.137156i
$703$	−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
$708$	−14.9282			−0.561036
$709$	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	$0.742893\pi$
$710$		0			0
$711$	−6.69615	+	11.5981i	−0.251125	+	0.434962i
$712$	11.5692	+	20.0385i	0.433575	+	0.750974i
$713$	8.19615			0.306948
$714$	8.53590	+	9.85641i	0.319448	+	0.368867i
$715$		0			0
$716$	−7.32051	−	12.6795i	−0.273580	−	0.473855i
$717$	−10.4641	+	18.1244i	−0.390789	+	0.676866i
$718$	−1.73205	+	3.00000i	−0.0646396	+	0.111959i
$719$	13.7321	+	23.7846i	0.512119	+	0.887016i	0.999901	+	0.0140509i	$0.00447269\pi$
$719$	13.7321	+	23.7846i	0.512119	+	0.887016i	−0.487782	+	0.872965i	$0.662194\pi$
$720$		0			0
$721$	3.10770	−	0.598076i	0.115737	−	0.0222735i
$722$	9.46410			0.352217
$723$	−3.26795	−	5.66025i	−0.121536	−	0.210507i
$724$	7.55514	−	13.0859i	0.280784	−	0.486333i
$725$		0			0
$726$	−1.29423	−	2.24167i	−0.0480333	−	0.0831962i
$727$	30.6603			1.13713			0.568563	−	0.822640i	$-0.307500\pi$
$727$	30.6603			1.13713			0.568563	+	0.822640i	$0.307500\pi$
$728$	−12.5885	+	36.3397i	−0.466559	+	1.34684i
$729$	1.00000			0.0370370
$730$		0			0
$731$	24.2224	−	41.9545i	0.895899	−	1.55174i
$732$	2.92820	−	5.07180i	0.108230	−	0.187459i
$733$	−9.33013	−	16.1603i	−0.344616	−	0.596893i	0.640668	−	0.767818i	$-0.278658\pi$
$733$	−9.33013	−	16.1603i	−0.344616	−	0.596893i	−0.985284	+	0.170926i	$0.945324\pi$
$734$	0.588457			0.0217204
$735$		0			0
$736$	−7.42563			−0.273712
$737$	−3.63397	−	6.29423i	−0.133859	−	0.231851i
$738$	1.00000	−	1.73205i	0.0368105	−	0.0637577i
$739$	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	$0.0850725\pi$
$740$		0			0
$741$	14.1244			0.518871
$742$	−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	$0.868198\pi$
$744$	−8.19615	−	14.1962i	−0.300486	−	0.520456i
$745$		0			0
$746$	6.77757	−	11.7391i	0.248144	−	0.429799i
$747$	−4.56218	−	7.90192i	−0.166921	−	0.289116i
$748$	−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
$753$	−3.29423	+	5.70577i	−0.120048	+	0.207930i
$754$	−13.0000	−	22.5167i	−0.473432	−	0.820008i
$755$		0			0
$756$	−2.53590	−	2.92820i	−0.0922297	−	0.106498i
$757$	0.143594			0.00521900			0.00260950	−	0.999997i	$-0.499169\pi$
$757$	0.143594			0.00521900			0.00260950	+	0.999997i	$0.499169\pi$
$758$	−10.3660	−	17.9545i	−0.376511	−	0.652136i
$759$	1.73205	−	3.00000i	0.0628695	−	0.108893i
$760$		0			0
$761$	−21.6340	−	37.4711i	−0.784231	−	1.35833i	−0.929457	−	0.368929i	$-0.879724\pi$
$761$	−21.6340	−	37.4711i	−0.784231	−	1.35833i	0.145226	−	0.989398i	$-0.453609\pi$
$762$	11.1244			0.402993
$763$	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
$768$	5.85641	+	10.1436i	0.211325	+	0.366025i
$769$	17.6795			0.637539			0.318769	−	0.947832i	$-0.396730\pi$
$769$	17.6795			0.637539			0.318769	+	0.947832i	$0.396730\pi$
$770$		0			0
$771$	−11.6603			−0.419934
$772$	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	$0.175350\pi$
$774$	2.63397	−	4.56218i	0.0946763	−	0.163984i
$775$		0			0
$776$	−2.71797			−0.0975694
$777$	−6.23205	+	17.9904i	−0.223574	+	0.645401i
$778$	−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
$783$	6.19615			0.221432
$784$	−1.07180	+	7.42563i	−0.0382785	+	0.265201i
$785$		0			0
$786$	3.12436	+	5.41154i	0.111442	+	0.193023i
$787$	3.26795	−	5.66025i	0.116490	−	0.201766i	−0.801885	−	0.597479i	$-0.796169\pi$
$787$	3.26795	−	5.66025i	0.116490	−	0.201766i	0.918374	+	0.395713i	$0.129502\pi$
$788$	12.9282	−	22.3923i	0.460548	−	0.797693i
$789$	−6.19615	−	10.7321i	−0.220589	−	0.382071i
$790$		0			0
$791$	4.26795	−	12.3205i	0.151751	−	0.438067i
$792$	−6.92820			−0.246183
$793$	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	$0.232550\pi$
$798$	−4.68653	+	0.901924i	−0.165901	+	0.0319278i
$799$	13.4641			0.476326
$800$		0			0
$801$	4.56218	−	7.90192i	0.161197	−	0.279201i
$802$	1.60770	−	2.78461i	0.0567697	−	0.0983280i
$803$	6.36603	+	11.0263i	0.224652	+	0.389109i
$804$	3.89488			0.137362
$805$		0			0
$806$	27.1244			0.955415
$807$	9.73205	+	16.8564i	0.342584	+	0.593374i
$808$	13.6077	−	23.5692i	0.478717	−	0.829162i
$809$	14.8564	−	25.7321i	0.522323	−	0.904691i	−0.477339	−	0.878719i	$-0.658399\pi$
$809$	14.8564	−	25.7321i	0.522323	−	0.904691i	0.999663	−	0.0259716i	$-0.00826796\pi$
$810$		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
$813$	16.9282			0.593698
$814$	7.19615	+	12.4641i	0.252225	+	0.436867i
$815$		0			0
$816$	3.60770	−	6.24871i	0.126295	−	0.218749i
$817$	8.86603	+	15.3564i	0.310183	+	0.537253i
$818$	−22.5885			−0.789787
$819$	14.8923	−	2.86603i	0.520379	−	0.100147i
$820$		0			0
$821$	−9.75833	−	16.9019i	−0.340568	−	0.589881i	0.643970	−	0.765051i	$-0.277286\pi$
$821$	−9.75833	−	16.9019i	−0.340568	−	0.589881i	−0.984538	+	0.175169i	$0.943953\pi$
$822$	3.00000	−	5.19615i	0.104637	−	0.181237i
$823$	−11.5885	+	20.0718i	−0.403948	+	0.699659i	−0.994198	−	0.107561i	$-0.965696\pi$
$823$	−11.5885	+	20.0718i	−0.403948	+	0.699659i	0.590250	+	0.807220i	$0.299029\pi$
$824$	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	$0.137280\pi$
$828$	0.928203	+	1.60770i	0.0322573	+	0.0558713i
$829$	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	$0.0213063\pi$
$830$		0			0
$831$	1.33013	+	2.30385i	0.0461416	+	0.0799196i
$832$	−12.2872			−0.425982
$833$	−43.7583	+	17.4904i	−1.51614	+	0.606006i
$834$	5.80385			0.200971
$835$		0			0
$836$	4.92820	−	8.53590i	0.170445	−	0.295220i
$837$	−3.23205	+	5.59808i	−0.111716	+	0.193498i
$838$	−10.4449	−	18.0910i	−0.360812	−	0.624944i
$839$	−40.4449			−1.39631			−0.698156	−	0.715946i	$-0.745996\pi$
$839$	−40.4449			−1.39631			−0.698156	+	0.715946i	$0.745996\pi$
$840$		0			0
$841$	9.39230			0.323873
$842$	5.09808	+	8.83013i	0.175691	+	0.304306i
$843$	6.92820	−	12.0000i	0.238620	−	0.413302i
$844$	15.3205	−	26.5359i	0.527354	−	0.913403i
$845$		0			0
$846$	1.46410			0.0503369
$847$	9.18653	−	1.76795i	0.315653	−	0.0607475i
$848$	8.99485			0.308884
$849$	0.0621778	+	0.107695i	0.00213394	+	0.00369609i
$850$		0			0
$851$	4.56218	−	7.90192i	0.156389	−	0.270874i
$852$	−3.07180	−	5.32051i	−0.105238	−	0.182278i
$853$	−19.9808			−0.684128			−0.342064	−	0.939677i	$-0.611126\pi$
$853$	−19.9808			−0.684128			−0.342064	+	0.939677i	$0.611126\pi$
$854$	−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	$0.140129\pi$
$858$	5.73205	−	9.92820i	0.195689	−	0.338943i
$859$	−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	$0.836243\pi$
$860$		0			0
$861$	4.73205	+	5.46410i	0.161268	+	0.186216i
$862$	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	$0.868034\pi$
$864$	2.92820	−	5.07180i	0.0996195	−	0.172546i
$865$		0			0
$866$	−1.75833	−	3.04552i	−0.0597505	−	0.103491i
$867$	28.3205			0.961815
$868$	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
$873$	0.535898	+	0.928203i	0.0181374	+	0.0314149i
$874$	2.28719			0.0773653
$875$		0			0
$876$	−6.82309			−0.230531
$877$	−15.9282	−	27.5885i	−0.537857	−	0.931596i	−0.999019	−	0.0442800i	$-0.985901\pi$
$877$	−15.9282	−	27.5885i	−0.537857	−	0.931596i	0.461162	−	0.887316i	$-0.347433\pi$
$878$	2.73205	−	4.73205i	0.0922022	−	0.159699i
$879$	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	$0.597253\pi$
$882$	−4.75833	+	1.90192i	−0.160221	+	0.0640411i
$883$	−22.4115			−0.754208			−0.377104	−	0.926171i	$-0.623080\pi$
$883$	−22.4115			−0.754208			−0.377104	+	0.926171i	$0.623080\pi$
$884$	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	$0.993555\pi$
$888$	−18.2487			−0.612387
$889$	−13.1603	+	37.9904i	−0.441381	+	1.27416i
$890$		0			0
$891$	1.36603	+	2.36603i	0.0457636	+	0.0792648i
$892$	−0.287187	+	0.497423i	−0.00961573	+	0.0166549i
$893$	−2.46410	+	4.26795i	−0.0824580	+	0.142821i
$894$	−8.00000	−	13.8564i	−0.267560	−	0.463428i
$895$		0			0
$896$	−26.3538	+	5.07180i	−0.880420	+	0.169437i
$897$	−7.26795			−0.242670
$898$	−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
$903$	12.4641	+	14.3923i	0.414779	+	0.478946i
$904$	12.4974			0.415658
$905$		0			0
$906$	1.80385	−	3.12436i	0.0599288	−	0.103800i
$907$	1.20577	−	2.08846i	0.0400370	−	0.0693461i	−0.845313	−	0.534272i	$-0.820586\pi$
$907$	1.20577	−	2.08846i	0.0400370	−	0.0693461i	0.885350	+	0.464926i	$0.153919\pi$
$908$	−11.4641	−	19.8564i	−0.380450	−	0.658958i
$909$	−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	$0.559767\pi$
$912$	1.32051	+	2.28719i	0.0437264	+	0.0757363i
$913$	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
$918$	4.92820			0.162655
$919$	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	$0.816822\pi$
$920$		0			0
$921$	−3.93782	+	6.82051i	−0.129756	+	0.224743i
$922$	−12.8038	−	22.1769i	−0.421672	−	0.730358i
$923$	24.0526			0.791700
$924$	3.46410	−	10.0000i	0.113961	−	0.328976i
$925$		0			0
$926$	−8.15064	−	14.1173i	−0.267846	−	0.463924i
$927$	0.598076	−	1.03590i	0.0196434	−	0.0340234i
$928$	18.1436	−	31.4256i	0.595593	−	1.03160i
$929$	−3.22243	−	5.58142i	−0.105725	−	0.183120i	0.808309	−	0.588758i	$-0.200383\pi$
$929$	−3.22243	−	5.58142i	−0.105725	−	0.183120i	−0.914034	+	0.405638i	$0.867050\pi$
$930$		0			0
$931$	2.46410	−	17.0718i	0.0807577	−	0.559506i
$932$	−25.3590			−0.830661
$933$	7.56218	+	13.0981i	0.247575	+	0.428812i
$934$	10.1962	−	17.6603i	0.333628	−	0.577861i
$935$		0			0
$936$	7.26795	+	12.5885i	0.237560	+	0.411467i
$937$	−28.2679			−0.923474			−0.461737	−	0.887017i	$-0.652774\pi$
$937$	−28.2679			−0.923474			−0.461737	+	0.887017i	$0.652774\pi$
$938$	1.68653	−	4.86860i	0.0550673	−	0.158966i
$939$	−4.66025			−0.152082
$940$		0			0
$941$	−4.02628	+	6.97372i	−0.131253	+	0.227337i	−0.924160	−	0.382006i	$-0.875233\pi$
$941$	−4.02628	+	6.97372i	−0.131253	+	0.227337i	0.792907	+	0.609343i	$0.208567\pi$
$942$	5.26795	−	9.12436i	0.171639	−	0.297288i
$943$	−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	$0.772662\pi$
$948$	9.80385	−	16.9808i	0.318414	−	0.551510i
$949$	13.3564	−	23.1340i	0.433567	−	0.750961i
$950$		0			0
$951$	−30.4449			−0.987242
$952$	−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	$0.725049\pi$
$954$	3.07180	+	5.32051i	0.0994531	+	0.172258i
$955$		0			0
$956$	15.3205	−	26.5359i	0.495501	−	0.858232i
$957$	8.46410	+	14.6603i	0.273606	+	0.473899i
$958$	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
$963$	−4.09808	+	7.09808i	−0.132059	+	0.228732i
$964$	4.78461	+	8.28719i	0.154102	+	0.266912i
$965$		0			0
$966$	2.41154	−	0.464102i	0.0775901	−	0.0149322i
$967$	−14.1244			−0.454209			−0.227104	−	0.973870i	$-0.572926\pi$
$967$	−14.1244			−0.454209			−0.227104	+	0.973870i	$0.572926\pi$
$968$	4.48334	+	7.76537i	0.144100	+	0.249589i
$969$	−8.29423	+	14.3660i	−0.266449	+	0.461503i
$970$		0			0
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	0.991783	−	0.127933i	$-0.0408342\pi$
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	−0.606685	+	0.794943i	$0.707501\pi$
$972$	−1.46410			−0.0469611
$973$	−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	$0.0916936\pi$
$978$	2.14359	+	3.71281i	0.0685446	+	0.118723i
$979$	24.9282			0.796709
$980$		0			0
$981$	11.0000			0.351203
$982$	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	$0.0622851\pi$
$984$	−3.46410	+	6.00000i	−0.110432	+	0.191273i
$985$		0			0
$986$	30.5359			0.972461
$987$	−1.73205	+	5.00000i	−0.0551318	+	0.159152i
$988$	−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
$993$	21.9282			0.695870
$994$	−7.98076	+	1.53590i	−0.253134	+	0.0487157i
$995$		0			0
$996$	6.67949	+	11.5692i	0.211648	+	0.366585i
$997$	−2.00962	+	3.48076i	−0.0636453	+	0.110237i	−0.896092	−	0.443868i	$-0.853606\pi$
$997$	−2.00962	+	3.48076i	−0.0636453	+	0.110237i	0.832447	+	0.554105i	$0.186939\pi$
$998$	−7.49038	+	12.9737i	−0.237104	+	0.410676i
$999$	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.i.f.151.2		4
5.2	odd	4		525.2.r.a.424.2		4
5.3	odd	4		525.2.r.f.424.1		4
5.4	even	2		105.2.i.d.46.1	yes	4
7.2	even	3	inner	525.2.i.f.226.2		4
7.3	odd	6		3675.2.a.be.1.1		2
7.4	even	3		3675.2.a.bg.1.1		2
15.14	odd	2		315.2.j.c.46.2		4
20.19	odd	2		1680.2.bg.o.1201.2		4
35.2	odd	12		525.2.r.f.499.1		4
35.4	even	6		735.2.a.g.1.2		2
35.9	even	6		105.2.i.d.16.1	✓	4
35.19	odd	6		735.2.i.l.226.1		4
35.23	odd	12		525.2.r.a.499.2		4
35.24	odd	6		735.2.a.h.1.2		2
35.34	odd	2		735.2.i.l.361.1		4
105.44	odd	6		315.2.j.c.226.2		4
105.59	even	6		2205.2.a.ba.1.1		2
105.74	odd	6		2205.2.a.z.1.1		2
140.79	odd	6		1680.2.bg.o.961.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.1	✓	4	35.9	even	6
105.2.i.d.46.1	yes	4	5.4	even	2
315.2.j.c.46.2		4	15.14	odd	2
315.2.j.c.226.2		4	105.44	odd	6
525.2.i.f.151.2		4	1.1	even	1	trivial
525.2.i.f.226.2		4	7.2	even	3	inner
525.2.r.a.424.2		4	5.2	odd	4
525.2.r.a.499.2		4	35.23	odd	12
525.2.r.f.424.1		4	5.3	odd	4
525.2.r.f.499.1		4	35.2	odd	12
735.2.a.g.1.2		2	35.4	even	6
735.2.a.h.1.2		2	35.24	odd	6
735.2.i.l.226.1		4	35.19	odd	6
735.2.i.l.361.1		4	35.34	odd	2
1680.2.bg.o.961.2		4	140.79	odd	6
1680.2.bg.o.1201.2		4	20.19	odd	2
2205.2.a.z.1.1		2	105.74	odd	6
2205.2.a.ba.1.1		2	105.59	even	6
3675.2.a.be.1.1		2	7.3	odd	6
3675.2.a.bg.1.1		2	7.4	even	3

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.i (of order \(3\), degree \(2\), minimal)

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

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