LMFDB - Embedded newform 845.2.n.b.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(484,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("845.484");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (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:	$6.74735897080$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.529
Dual form			845.2.n.b.484.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.73205 - 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 + 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.73205 - 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 + 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 - 1.86603i) q^{10} +(1.00000 - 1.73205i) q^{11} +2.00000i q^{12} +(-2.46410 - 3.73205i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{18} +(3.00000 + 5.19615i) q^{19} +(-0.133975 - 2.23205i) q^{20} +(-1.73205 + 1.00000i) q^{22} +(5.19615 + 3.00000i) q^{23} +(3.00000 - 5.19615i) q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000i q^{27} +(-3.00000 + 5.19615i) q^{29} +(0.267949 + 4.46410i) q^{30} +6.00000 q^{31} +(4.33013 - 2.50000i) q^{32} +(-3.46410 + 2.00000i) q^{33} +(0.500000 - 0.866025i) q^{36} +(-5.19615 - 3.00000i) q^{37} -6.00000i q^{38} +(-3.00000 + 6.00000i) q^{40} +(4.00000 - 6.92820i) q^{41} +(5.19615 - 3.00000i) q^{43} -2.00000 q^{44} +(0.133975 + 2.23205i) q^{45} +(-3.00000 - 5.19615i) q^{46} -8.00000i q^{47} +(-1.73205 + 1.00000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-0.598076 - 4.96410i) q^{50} -12.0000i q^{53} +(2.00000 - 3.46410i) q^{54} +(3.73205 - 2.46410i) q^{55} -12.0000i q^{57} +(5.19615 - 3.00000i) q^{58} +(1.00000 + 1.73205i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(-3.00000 - 5.19615i) q^{61} +(-5.19615 - 3.00000i) q^{62} -7.00000 q^{64} +4.00000 q^{66} +(10.3923 + 6.00000i) q^{67} +(-6.00000 - 10.3923i) q^{69} +(1.00000 + 1.73205i) q^{71} +(-2.59808 + 1.50000i) q^{72} -6.00000i q^{73} +(3.00000 + 5.19615i) q^{74} +(-1.19615 - 9.92820i) q^{75} +(3.00000 - 5.19615i) q^{76} +(1.86603 - 1.23205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-6.92820 + 4.00000i) q^{82} +4.00000i q^{83} -6.00000 q^{86} +(10.3923 - 6.00000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(-4.00000 + 6.92820i) q^{89} +(1.00000 - 2.00000i) q^{90} -6.00000i q^{92} +(-10.3923 - 6.00000i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(0.803848 + 13.3923i) q^{95} -10.0000 q^{96} +(5.19615 - 3.00000i) q^{97} +(6.06218 - 3.50000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^4 + 8 * q^5 + 4 * q^6 + 2 * q^9	$ 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{15} + 2 q^{16} + 12 q^{19} - 4 q^{20} + 12 q^{24} + 12 q^{25} - 12 q^{29} + 8 q^{30} + 24 q^{31} + 2 q^{36} - 12 q^{40} + 16 q^{41} - 8 q^{44} + 4 q^{45} - 12 q^{46} - 14 q^{49} + 8 q^{50} + 8 q^{54} + 8 q^{55} + 4 q^{59} - 8 q^{60} - 12 q^{61} - 28 q^{64} + 16 q^{66} - 24 q^{69} + 4 q^{71} + 12 q^{74} + 16 q^{75} + 12 q^{76} + 4 q^{80} + 22 q^{81} - 24 q^{86} - 16 q^{89} + 4 q^{90} - 16 q^{94} + 24 q^{95} - 40 q^{96} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^4 + 8 * q^5 + 4 * q^6 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^15 + 2 * q^16 + 12 * q^19 - 4 * q^20 + 12 * q^24 + 12 * q^25 - 12 * q^29 + 8 * q^30 + 24 * q^31 + 2 * q^36 - 12 * q^40 + 16 * q^41 - 8 * q^44 + 4 * q^45 - 12 * q^46 - 14 * q^49 + 8 * q^50 + 8 * q^54 + 8 * q^55 + 4 * q^59 - 8 * q^60 - 12 * q^61 - 28 * q^64 + 16 * q^66 - 24 * q^69 + 4 * q^71 + 12 * q^74 + 16 * q^75 + 12 * q^76 + 4 * q^80 + 22 * q^81 - 24 * q^86 - 16 * q^89 + 4 * q^90 - 16 * q^94 + 24 * q^95 - 40 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	0.161521	−	0.986869i	$-0.448360\pi$
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	−0.773893	+	0.633316i	$0.781693\pi$
$3$	−1.73205	−	1.00000i	−1.00000	−	0.577350i	−0.0917517	−	0.995782i	$-0.529247\pi$
$3$	−1.73205	−	1.00000i	−1.00000	−	0.577350i	−0.908248	+	0.418432i	$0.862580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	1.00000	+	1.73205i	0.408248	+	0.707107i
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$			3.00000i			1.06066i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.23205	−	1.86603i	−0.389609	−	0.590089i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$			2.00000i			0.577350i
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−2.46410	−	3.73205i	−0.636228	−	0.963611i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$		−	1.00000i		−	0.235702i
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−0.133975	−	2.23205i	−0.0299576	−	0.499102i
$21$		0			0
$22$	−1.73205	+	1.00000i	−0.369274	+	0.213201i
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.931831	−	0.362892i	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$	3.00000	−	5.19615i	0.612372	−	1.06066i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$			4.00000i			0.769800i
$28$		0			0
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	0.267949	+	4.46410i	0.0489206	+	0.815030i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	4.33013	−	2.50000i	0.765466	−	0.441942i
$33$	−3.46410	+	2.00000i	−0.603023	+	0.348155i
$34$		0			0
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−5.19615	−	3.00000i	−0.854242	−	0.493197i	0.00783774	−	0.999969i	$-0.497505\pi$
$37$	−5.19615	−	3.00000i	−0.854242	−	0.493197i	−0.862080	+	0.506772i	$0.830838\pi$
$38$		−	6.00000i		−	0.973329i
$39$		0			0
$40$	−3.00000	+	6.00000i	−0.474342	+	0.948683i
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	−0.363905	−	0.931436i	$-0.618557\pi$
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	0.988600	−	0.150567i	$-0.0481100\pi$
$42$		0			0
$43$	5.19615	−	3.00000i	0.792406	−	0.457496i	−0.0484030	−	0.998828i	$-0.515413\pi$
$43$	5.19615	−	3.00000i	0.792406	−	0.457496i	0.840809	+	0.541332i	$0.182080\pi$
$44$	−2.00000			−0.301511
$45$	0.133975	+	2.23205i	0.0199718	+	0.332734i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	−1.73205	+	1.00000i	−0.250000	+	0.144338i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	−0.598076	−	4.96410i	−0.0845807	−	0.702030i
$51$		0			0
$52$		0			0
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	3.73205	−	2.46410i	0.503230	−	0.332259i
$56$		0			0
$57$		−	12.0000i		−	1.58944i
$58$	5.19615	−	3.00000i	0.682288	−	0.393919i
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$	−2.00000	+	4.00000i	−0.258199	+	0.516398i
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$	−5.19615	−	3.00000i	−0.659912	−	0.381000i
$63$		0			0
$64$	−7.00000			−0.875000
$65$		0			0
$66$	4.00000			0.492366
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$		0			0
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$		0			0
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	0.919244	−	0.393688i	$-0.128801\pi$
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	−0.800566	+	0.599245i	$0.795468\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$	−1.19615	−	9.92820i	−0.138120	−	1.14641i
$76$	3.00000	−	5.19615i	0.344124	−	0.596040i
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.86603	−	1.23205i	0.208628	−	0.137747i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−6.92820	+	4.00000i	−0.765092	+	0.441726i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$		0			0
$86$	−6.00000			−0.646997
$87$	10.3923	−	6.00000i	1.11417	−	0.643268i
$88$	5.19615	+	3.00000i	0.553912	+	0.319801i
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	−0.996326	−	0.0856373i	$-0.972707\pi$
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	0.572327	+	0.820025i	$0.306041\pi$
$90$	1.00000	−	2.00000i	0.105409	−	0.210819i
$91$		0			0
$92$		−	6.00000i		−	0.625543i
$93$	−10.3923	−	6.00000i	−1.07763	−	0.622171i
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$	0.803848	+	13.3923i	0.0824730	+	1.37402i
$96$	−10.0000			−1.02062
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$	6.06218	−	3.50000i	0.612372	−	0.353553i
$99$	2.00000			0.201008
$100$	1.96410	−	4.59808i	0.196410	−	0.459808i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$		0			0
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$	3.46410	−	2.00000i	0.333333	−	0.192450i
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$	−4.46410	+	0.267949i	−0.425635	+	0.0255480i
$111$	6.00000	+	10.3923i	0.569495	+	0.986394i
$112$		0			0
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	−6.00000	+	10.3923i	−0.561951	+	0.973329i
$115$	7.39230	+	11.1962i	0.689336	+	1.04405i
$116$	6.00000			0.557086
$117$		0			0
$118$		−	2.00000i		−	0.184115i
$119$		0			0
$120$	11.1962	−	7.39230i	1.02206	−	0.674822i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$			6.00000i			0.543214i
$123$	−13.8564	+	8.00000i	−1.24939	+	0.721336i
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	−1.73205	−	1.00000i	−0.153695	−	0.0887357i	0.421180	−	0.906977i	$-0.361616\pi$
$127$	−1.73205	−	1.00000i	−0.153695	−	0.0887357i	−0.574875	+	0.818241i	$0.694949\pi$
$128$	−2.59808	−	1.50000i	−0.229640	−	0.132583i
$129$	−12.0000			−1.05654
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	3.46410	+	2.00000i	0.301511	+	0.174078i
$133$		0			0
$134$	−6.00000	−	10.3923i	−0.518321	−	0.897758i
$135$	−4.00000	+	8.00000i	−0.344265	+	0.688530i
$136$		0			0
$137$	1.73205	−	1.00000i	0.147979	−	0.0854358i	−0.424182	−	0.905577i	$-0.639438\pi$
$137$	1.73205	−	1.00000i	0.147979	−	0.0854358i	0.572161	+	0.820141i	$0.306105\pi$
$138$			12.0000i			1.02151i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$	−8.00000	+	13.8564i	−0.673722	+	1.16692i
$142$		−	2.00000i		−	0.167836i
$143$		0			0
$144$	1.00000			0.0833333
$145$	−11.1962	+	7.39230i	−0.929790	+	0.613898i
$146$	−3.00000	+	5.19615i	−0.248282	+	0.430037i
$147$	12.1244	−	7.00000i	1.00000	−	0.577350i
$148$			6.00000i			0.493197i
$149$	−10.0000	−	17.3205i	−0.819232	−	1.41895i	−0.906249	−	0.422744i	$-0.861067\pi$
$149$	−10.0000	−	17.3205i	−0.819232	−	1.41895i	0.0870170	−	0.996207i	$-0.472267\pi$
$150$	−3.92820	+	9.19615i	−0.320736	+	0.750863i
$151$	18.0000			1.46482			0.732410	−	0.680864i	$-0.238396\pi$
$151$	18.0000			1.46482			0.732410	+	0.680864i	$0.238396\pi$
$152$	−15.5885	+	9.00000i	−1.26439	+	0.729996i
$153$		0			0
$154$		0			0
$155$	12.0000	+	6.00000i	0.963863	+	0.481932i
$156$		0			0
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$	−12.0000	+	20.7846i	−0.951662	+	1.64833i
$160$	11.1603	−	0.669873i	0.882296	−	0.0529581i
$161$		0			0
$162$	−9.52628	+	5.50000i	−0.748455	+	0.432121i
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	−0.0343508	−	0.999410i	$-0.510936\pi$
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	0.848339	+	0.529454i	$0.177603\pi$
$164$	−8.00000			−0.624695
$165$	−8.92820	+	0.535898i	−0.695060	+	0.0417196i
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$	13.8564	+	8.00000i	1.07224	+	0.619059i	0.928793	−	0.370599i	$-0.120848\pi$
$167$	13.8564	+	8.00000i	1.07224	+	0.619059i	0.143448	+	0.989658i	$0.454181\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	−5.19615	−	3.00000i	−0.396203	−	0.228748i
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	−0.840002	−	0.542583i	$-0.817446\pi$
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	0.0498898	+	0.998755i	$0.484113\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		−	4.00000i		−	0.300658i
$178$	6.92820	−	4.00000i	0.519291	−	0.299813i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	1.86603	−	1.23205i	0.139085	−	0.0918316i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$			12.0000i			0.887066i
$184$	−9.00000	+	15.5885i	−0.663489	+	1.14920i
$185$	−7.39230	−	11.1962i	−0.543493	−	0.823157i
$186$	6.00000	+	10.3923i	0.439941	+	0.762001i
$187$		0			0
$188$	−6.92820	+	4.00000i	−0.505291	+	0.291730i
$189$		0			0
$190$	6.00000	−	12.0000i	0.435286	−	0.870572i
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	12.1244	+	7.00000i	0.875000	+	0.505181i
$193$	5.19615	+	3.00000i	0.374027	+	0.215945i	0.675216	−	0.737620i	$-0.264050\pi$
$193$	5.19615	+	3.00000i	0.374027	+	0.215945i	−0.301189	+	0.953564i	$0.597384\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	7.00000			0.500000
$197$	−1.73205	−	1.00000i	−0.123404	−	0.0712470i	0.437028	−	0.899448i	$-0.356031\pi$
$197$	−1.73205	−	1.00000i	−0.123404	−	0.0712470i	−0.560431	+	0.828201i	$0.689365\pi$
$198$	−1.73205	−	1.00000i	−0.123091	−	0.0710669i
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	−0.880616	−	0.473831i	$-0.842871\pi$
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	0.0299585	−	0.999551i	$-0.490462\pi$
$200$	−12.0000	+	9.00000i	−0.848528	+	0.636396i
$201$	−12.0000	−	20.7846i	−0.846415	−	1.46603i
$202$	−5.19615	+	3.00000i	−0.365600	+	0.211079i
$203$		0			0
$204$		0			0
$205$	14.9282	−	9.85641i	1.04263	−	0.688401i
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$			6.00000i			0.417029i
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	−10.3923	+	6.00000i	−0.713746	+	0.412082i
$213$		−	4.00000i		−	0.274075i
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$	13.3923	−	0.803848i	0.913348	−	0.0548219i
$216$	−12.0000			−0.816497
$217$		0			0
$218$	−10.3923	−	6.00000i	−0.703856	−	0.406371i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	−4.00000	−	2.00000i	−0.269680	−	0.134840i
$221$		0			0
$222$		−	12.0000i		−	0.805387i
$223$	20.7846	+	12.0000i	1.39184	+	0.803579i	0.993519	−	0.113666i	$-0.0362595\pi$
$223$	20.7846	+	12.0000i	1.39184	+	0.803579i	0.398321	+	0.917246i	$0.369593\pi$
$224$		0			0
$225$	−1.96410	+	4.59808i	−0.130940	+	0.306538i
$226$		0			0
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	−0.380615	−	0.924734i	$-0.624288\pi$
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	0.610535	+	0.791989i	$0.290954\pi$
$228$	−10.3923	+	6.00000i	−0.688247	+	0.397360i
$229$	12.0000			0.792982			0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000			0.792982			0.396491	+	0.918039i	$0.370228\pi$
$230$	−0.803848	−	13.3923i	−0.0530041	−	0.883062i
$231$		0			0
$232$	−15.5885	−	9.00000i	−1.02343	−	0.590879i
$233$			24.0000i			1.57229i	0.618041	+	0.786146i	$0.287927\pi$
$233$			24.0000i			1.57229i	−0.618041	+	0.786146i	$0.712073\pi$
$234$		0			0
$235$	8.00000	−	16.0000i	0.521862	−	1.04372i
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$		0			0
$238$		0			0
$239$	−10.0000			−0.646846			−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000			−0.646846			−0.323423	+	0.946254i	$0.604834\pi$
$240$	−4.46410	+	0.267949i	−0.288157	+	0.0172960i
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$		−	7.00000i		−	0.449977i
$243$	−8.66025	+	5.00000i	−0.555556	+	0.320750i
$244$	−3.00000	+	5.19615i	−0.192055	+	0.332650i
$245$	−13.0622	+	8.62436i	−0.834512	+	0.550990i
$246$	16.0000			1.02012
$247$		0			0
$248$			18.0000i			1.14300i
$249$	4.00000	−	6.92820i	0.253490	−	0.439057i
$250$	3.76795	−	10.5263i	0.238306	−	0.665740i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$		0			0
$253$	10.3923	−	6.00000i	0.653359	−	0.377217i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$	10.3923	+	6.00000i	0.646997	+	0.373544i
$259$		0			0
$260$		0			0
$261$	−6.00000			−0.371391
$262$	10.3923	+	6.00000i	0.642039	+	0.370681i
$263$	−5.19615	−	3.00000i	−0.320408	−	0.184988i	0.331166	−	0.943572i	$-0.392558\pi$
$263$	−5.19615	−	3.00000i	−0.320408	−	0.184988i	−0.651575	+	0.758585i	$0.725891\pi$
$264$	−6.00000	−	10.3923i	−0.369274	−	0.639602i
$265$	12.0000	−	24.0000i	0.737154	−	1.47431i
$266$		0			0
$267$	13.8564	−	8.00000i	0.847998	−	0.489592i
$268$		−	12.0000i		−	0.733017i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$	7.46410	−	4.92820i	0.454251	−	0.299921i
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	−0.760405	−	0.649449i	$-0.775000\pi$
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	0.942642	+	0.333805i	$0.108333\pi$
$272$		0			0
$273$		0			0
$274$	−2.00000			−0.120824
$275$	9.92820	−	1.19615i	0.598693	−	0.0721307i
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	10.3923	−	6.00000i	0.624413	−	0.360505i	−0.154172	−	0.988044i	$-0.549271\pi$
$277$	10.3923	−	6.00000i	0.624413	−	0.360505i	0.778585	+	0.627539i	$0.215938\pi$
$278$		−	4.00000i		−	0.239904i
$279$	3.00000	+	5.19615i	0.179605	+	0.311086i
$280$		0			0
$281$	−8.00000			−0.477240			−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000			−0.477240			−0.238620	+	0.971113i	$0.576695\pi$
$282$	13.8564	−	8.00000i	0.825137	−	0.476393i
$283$	−19.0526	−	11.0000i	−1.13256	−	0.653882i	−0.187980	−	0.982173i	$-0.560194\pi$
$283$	−19.0526	−	11.0000i	−1.13256	−	0.653882i	−0.944577	+	0.328291i	$0.893527\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	12.0000	−	24.0000i	0.710819	−	1.42164i
$286$		0			0
$287$		0			0
$288$	4.33013	+	2.50000i	0.255155	+	0.147314i
$289$	−8.50000	+	14.7224i	−0.500000	+	0.866025i
$290$	13.3923	−	0.803848i	0.786423	−	0.0472036i
$291$	−12.0000			−0.703452
$292$	−5.19615	+	3.00000i	−0.304082	+	0.175562i
$293$	−22.5167	+	13.0000i	−1.31544	+	0.759468i	−0.982991	−	0.183654i	$-0.941207\pi$
$293$	−22.5167	+	13.0000i	−1.31544	+	0.759468i	−0.332446	+	0.943122i	$0.607874\pi$
$294$	−14.0000			−0.816497
$295$	0.267949	+	4.46410i	0.0156006	+	0.259910i
$296$	9.00000	−	15.5885i	0.523114	−	0.906061i
$297$	6.92820	+	4.00000i	0.402015	+	0.232104i
$298$			20.0000i			1.15857i
$299$		0			0
$300$	−8.00000	+	6.00000i	−0.461880	+	0.346410i
$301$		0			0
$302$	−15.5885	−	9.00000i	−0.897015	−	0.517892i
$303$	−10.3923	+	6.00000i	−0.597022	+	0.344691i
$304$	6.00000			0.344124
$305$	−0.803848	−	13.3923i	−0.0460282	−	0.766841i
$306$		0			0
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		0			0
$309$	−6.00000	+	10.3923i	−0.341328	+	0.591198i
$310$	−7.39230	−	11.1962i	−0.419855	−	0.635899i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$			8.00000i			0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$			8.00000i			0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	6.00000	−	10.3923i	0.338600	−	0.586472i
$315$		0			0
$316$		0			0
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$	20.7846	−	12.0000i	1.16554	−	0.672927i
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$	−14.0000	−	7.00000i	−0.782624	−	0.391312i
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$		0			0
$323$		0			0
$324$	−11.0000			−0.611111
$325$		0			0
$326$	−12.0000			−0.664619
$327$	−20.7846	−	12.0000i	−1.14939	−	0.663602i
$328$	20.7846	+	12.0000i	1.14764	+	0.662589i
$329$		0			0
$330$	8.00000	+	4.00000i	0.440386	+	0.220193i
$331$	15.0000	+	25.9808i	0.824475	+	1.42803i	0.902320	+	0.431066i	$0.141863\pi$
$331$	15.0000	+	25.9808i	0.824475	+	1.42803i	−0.0778456	+	0.996965i	$0.524804\pi$
$332$	3.46410	−	2.00000i	0.190117	−	0.109764i
$333$		−	6.00000i		−	0.328798i
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$	14.7846	+	22.3923i	0.807770	+	1.22342i
$336$		0			0
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	5.19615	−	3.00000i	0.280976	−	0.162221i
$343$		0			0
$344$	9.00000	+	15.5885i	0.485247	+	0.840473i
$345$	−1.60770	−	26.7846i	−0.0865554	−	1.44203i
$346$	12.0000			0.645124
$347$	−5.19615	+	3.00000i	−0.278944	+	0.161048i	−0.632945	−	0.774197i	$-0.718154\pi$
$347$	−5.19615	+	3.00000i	−0.278944	+	0.161048i	0.354001	+	0.935245i	$0.384821\pi$
$348$	−10.3923	−	6.00000i	−0.557086	−	0.321634i
$349$	6.00000	−	10.3923i	0.321173	−	0.556287i	−0.659558	−	0.751654i	$-0.729256\pi$
$349$	6.00000	−	10.3923i	0.321173	−	0.556287i	0.980730	+	0.195367i	$0.0625897\pi$
$350$		0			0
$351$		0			0
$352$		−	10.0000i		−	0.533002i
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	0.141344	−	0.989960i	$-0.454858\pi$
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	−0.786659	+	0.617388i	$0.788191\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$	0.267949	+	4.46410i	0.0142213	+	0.236930i
$356$	8.00000			0.423999
$357$		0			0
$358$	10.3923	−	6.00000i	0.549250	−	0.317110i
$359$	2.00000			0.105556			0.0527780	−	0.998606i	$-0.483192\pi$
$359$	2.00000			0.105556			0.0527780	+	0.998606i	$0.483192\pi$
$360$	−6.69615	+	0.401924i	−0.352918	+	0.0211832i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−1.73205	−	1.00000i	−0.0910346	−	0.0525588i
$363$		−	14.0000i		−	0.734809i
$364$		0			0
$365$	6.00000	−	12.0000i	0.314054	−	0.628109i
$366$	6.00000	−	10.3923i	0.313625	−	0.543214i
$367$	15.5885	+	9.00000i	0.813711	+	0.469796i	0.848243	−	0.529607i	$-0.177661\pi$
$367$	15.5885	+	9.00000i	0.813711	+	0.469796i	−0.0345320	+	0.999404i	$0.510994\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$	8.00000			0.416463
$370$	0.803848	+	13.3923i	0.0417900	+	0.696233i
$371$		0			0
$372$			12.0000i			0.622171i
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	−0.407630	−	0.913147i	$-0.633645\pi$
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	0.586994	+	0.809591i	$0.300311\pi$
$374$		0			0
$375$	7.53590	−	21.0526i	0.389152	−	1.08715i
$376$	24.0000			1.23771
$377$		0			0
$378$		0			0
$379$	−9.00000	+	15.5885i	−0.462299	+	0.800725i	−0.999075	−	0.0429994i	$-0.986309\pi$
$379$	−9.00000	+	15.5885i	−0.462299	+	0.800725i	0.536776	+	0.843725i	$0.319642\pi$
$380$	11.1962	−	7.39230i	0.574351	−	0.379217i
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$		0			0
$383$	−6.92820	+	4.00000i	−0.354015	+	0.204390i	−0.666452	−	0.745548i	$-0.732188\pi$
$383$	−6.92820	+	4.00000i	−0.354015	+	0.204390i	0.312437	+	0.949938i	$0.398855\pi$
$384$	3.00000	+	5.19615i	0.153093	+	0.265165i
$385$		0			0
$386$	−3.00000	−	5.19615i	−0.152696	−	0.264477i
$387$	5.19615	+	3.00000i	0.264135	+	0.152499i
$388$	−5.19615	−	3.00000i	−0.263795	−	0.152302i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$	−18.1865	−	10.5000i	−0.918559	−	0.530330i
$393$	20.7846	+	12.0000i	1.04844	+	0.605320i
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−15.5885	+	9.00000i	−0.782362	+	0.451697i	−0.837267	−	0.546795i	$-0.815848\pi$
$397$	−15.5885	+	9.00000i	−0.782362	+	0.451697i	0.0549046	+	0.998492i	$0.482515\pi$
$398$			24.0000i			1.20301i
$399$		0			0
$400$	4.96410	−	0.598076i	0.248205	−	0.0299038i
$401$	8.00000	−	13.8564i	0.399501	−	0.691956i	−0.594163	−	0.804344i	$-0.702517\pi$
$401$	8.00000	−	13.8564i	0.399501	−	0.691956i	0.993664	+	0.112388i	$0.0358501\pi$
$402$			24.0000i			1.19701i
$403$		0			0
$404$	−6.00000			−0.298511
$405$	20.5263	−	13.5526i	1.01996	−	0.673432i
$406$		0			0
$407$	−10.3923	+	6.00000i	−0.515127	+	0.297409i
$408$		0			0
$409$	12.0000	+	20.7846i	0.593362	+	1.02773i	0.993776	+	0.111398i	$0.0355330\pi$
$409$	12.0000	+	20.7846i	0.593362	+	1.02773i	−0.400414	+	0.916334i	$0.631134\pi$
$410$	−17.8564	+	1.07180i	−0.881865	+	0.0529323i
$411$	−4.00000			−0.197305
$412$	−5.19615	+	3.00000i	−0.255996	+	0.147799i
$413$		0			0
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	−4.00000	+	8.00000i	−0.196352	+	0.392705i
$416$		0			0
$417$		−	8.00000i		−	0.391762i
$418$	−10.3923	−	6.00000i	−0.508304	−	0.293470i
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	36.0000			1.75453			0.877266	−	0.480004i	$-0.159365\pi$
$421$	36.0000			1.75453			0.877266	+	0.480004i	$0.159365\pi$
$422$	−10.3923	+	6.00000i	−0.505889	+	0.292075i
$423$	6.92820	−	4.00000i	0.336861	−	0.194487i
$424$	36.0000			1.74831
$425$		0			0
$426$	−2.00000	+	3.46410i	−0.0969003	+	0.167836i
$427$		0			0
$428$		−	6.00000i		−	0.290021i
$429$		0			0
$430$	−12.0000	−	6.00000i	−0.578691	−	0.289346i
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	−0.720113	−	0.693857i	$-0.755910\pi$
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	0.960954	+	0.276707i	$0.0892433\pi$
$432$	3.46410	+	2.00000i	0.166667	+	0.0962250i
$433$	−13.8564	+	8.00000i	−0.665896	+	0.384455i	−0.794520	−	0.607238i	$-0.792277\pi$
$433$	−13.8564	+	8.00000i	−0.665896	+	0.384455i	0.128624	+	0.991693i	$0.458944\pi$
$434$		0			0
$435$	26.7846	−	1.60770i	1.28422	−	0.0770831i
$436$	−6.00000	−	10.3923i	−0.287348	−	0.497701i
$437$			36.0000i			1.72211i
$438$	10.3923	−	6.00000i	0.496564	−	0.286691i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	7.39230	+	11.1962i	0.352414	+	0.533756i
$441$	−7.00000			−0.333333
$442$		0			0
$443$		−	6.00000i		−	0.285069i	−0.989790	−	0.142534i	$-0.954475\pi$
$443$		−	6.00000i		−	0.285069i	0.989790	−	0.142534i	$-0.0455251\pi$
$444$	6.00000	−	10.3923i	0.284747	−	0.493197i
$445$	−14.9282	+	9.85641i	−0.707665	+	0.467238i
$446$	−12.0000	−	20.7846i	−0.568216	−	0.984180i
$447$			40.0000i			1.89194i
$448$		0			0
$449$	−8.00000	−	13.8564i	−0.377543	−	0.653924i	0.613161	−	0.789958i	$-0.289898\pi$
$449$	−8.00000	−	13.8564i	−0.377543	−	0.653924i	−0.990704	+	0.136034i	$0.956564\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	−8.00000	−	13.8564i	−0.376705	−	0.652473i
$452$		0			0
$453$	−31.1769	−	18.0000i	−1.46482	−	0.845714i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	36.0000			1.68585
$457$	−25.9808	−	15.0000i	−1.21533	−	0.701670i	−0.251414	−	0.967880i	$-0.580895\pi$
$457$	−25.9808	−	15.0000i	−1.21533	−	0.701670i	−0.963915	+	0.266209i	$0.914229\pi$
$458$	−10.3923	−	6.00000i	−0.485601	−	0.280362i
$459$		0			0
$460$	6.00000	−	12.0000i	0.279751	−	0.559503i
$461$	2.00000	+	3.46410i	0.0931493	+	0.161339i	0.908835	−	0.417156i	$-0.136973\pi$
$461$	2.00000	+	3.46410i	0.0931493	+	0.161339i	−0.815685	+	0.578496i	$0.803640\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$	−14.7846	−	22.3923i	−0.685620	−	1.03842i
$466$	12.0000	−	20.7846i	0.555889	−	0.962828i
$467$		−	18.0000i		−	0.832941i	−0.909149	−	0.416470i	$-0.863267\pi$
$467$		−	18.0000i		−	0.832941i	0.909149	−	0.416470i	$-0.136733\pi$
$468$		0			0
$469$		0			0
$470$	−14.9282	+	9.85641i	−0.688587	+	0.454642i
$471$	12.0000	−	20.7846i	0.552931	−	0.957704i
$472$	−5.19615	+	3.00000i	−0.239172	+	0.138086i
$473$		−	12.0000i		−	0.551761i
$474$		0			0
$475$	−11.7846	+	27.5885i	−0.540715	+	1.26585i
$476$		0			0
$477$	10.3923	−	6.00000i	0.475831	−	0.274721i
$478$	8.66025	+	5.00000i	0.396111	+	0.228695i
$479$	11.0000	−	19.0526i	0.502603	−	0.870534i	−0.497393	−	0.867526i	$-0.665709\pi$
$479$	11.0000	−	19.0526i	0.502603	−	0.870534i	0.999995	−	0.00300810i	$-0.000957509\pi$
$480$	−20.0000	−	10.0000i	−0.912871	−	0.456435i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	13.3923	−	0.803848i	0.608113	−	0.0365008i
$486$	10.0000			0.453609
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$	15.5885	−	9.00000i	0.705656	−	0.407411i
$489$	−24.0000			−1.08532
$490$	15.6244	−	0.937822i	0.705836	−	0.0423665i
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$	13.8564	+	8.00000i	0.624695	+	0.360668i
$493$		0			0
$494$		0			0
$495$	4.00000	+	2.00000i	0.179787	+	0.0898933i
$496$	3.00000	−	5.19615i	0.134704	−	0.233314i
$497$		0			0
$498$	−6.92820	+	4.00000i	−0.310460	+	0.179244i
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$	8.52628	−	7.23205i	0.381307	−	0.323427i
$501$	−16.0000	−	27.7128i	−0.714827	−	1.23812i
$502$		−	12.0000i		−	0.535586i
$503$	5.19615	−	3.00000i	0.231685	−	0.133763i	−0.379664	−	0.925124i	$-0.623960\pi$
$503$	5.19615	−	3.00000i	0.231685	−	0.133763i	0.611349	+	0.791361i	$0.290627\pi$
$504$		0			0
$505$	11.1962	−	7.39230i	0.498222	−	0.328953i
$506$	−12.0000			−0.533465
$507$		0			0
$508$			2.00000i			0.0887357i
$509$	10.0000	−	17.3205i	0.443242	−	0.767718i	−0.554686	−	0.832060i	$-0.687161\pi$
$509$	10.0000	−	17.3205i	0.443242	−	0.767718i	0.997928	+	0.0643419i	$0.0204948\pi$
$510$		0			0
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$	−20.7846	+	12.0000i	−0.917663	+	0.529813i
$514$		0			0
$515$	6.00000	−	12.0000i	0.264392	−	0.528783i
$516$	6.00000	+	10.3923i	0.264135	+	0.457496i
$517$	−13.8564	−	8.00000i	−0.609404	−	0.351840i
$518$		0			0
$519$	24.0000			1.05348
$520$		0			0
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	5.19615	+	3.00000i	0.227429	+	0.131306i
$523$	−36.3731	−	21.0000i	−1.59048	−	0.918266i	−0.993224	−	0.116218i	$-0.962923\pi$
$523$	−36.3731	−	21.0000i	−1.59048	−	0.918266i	−0.597259	−	0.802048i	$-0.703744\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	3.00000	+	5.19615i	0.130806	+	0.226563i
$527$		0			0
$528$			4.00000i			0.174078i
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$	−22.3923	+	14.7846i	−0.972660	+	0.642202i
$531$	−1.00000	+	1.73205i	−0.0433963	+	0.0751646i
$532$		0			0
$533$		0			0
$534$	−16.0000			−0.692388
$535$	7.39230	+	11.1962i	0.319597	+	0.484052i
$536$	−18.0000	+	31.1769i	−0.777482	+	1.34664i
$537$	20.7846	−	12.0000i	0.896922	−	0.517838i
$538$		−	18.0000i		−	0.776035i
$539$	7.00000	+	12.1244i	0.301511	+	0.522233i
$540$	8.92820	−	0.535898i	0.384209	−	0.0230614i
$541$	−12.0000			−0.515920			−0.257960	−	0.966156i	$-0.583050\pi$
$541$	−12.0000			−0.515920			−0.257960	+	0.966156i	$0.583050\pi$
$542$	−5.19615	+	3.00000i	−0.223194	+	0.128861i
$543$	−3.46410	−	2.00000i	−0.148659	−	0.0858282i
$544$		0			0
$545$	24.0000	+	12.0000i	1.02805	+	0.514024i
$546$		0			0
$547$			18.0000i			0.769624i	0.922995	+	0.384812i	$0.125734\pi$
$547$			18.0000i			0.769624i	−0.922995	+	0.384812i	$0.874266\pi$
$548$	−1.73205	−	1.00000i	−0.0739895	−	0.0427179i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$	−9.19615	−	3.92820i	−0.392125	−	0.167499i
$551$	−36.0000			−1.53365
$552$	31.1769	−	18.0000i	1.32698	−	0.766131i
$553$		0			0
$554$	−12.0000			−0.509831
$555$	1.60770	+	26.7846i	0.0682429	+	1.13694i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−12.1244	−	7.00000i	−0.513725	−	0.296600i	0.220638	−	0.975356i	$-0.429186\pi$
$557$	−12.1244	−	7.00000i	−0.513725	−	0.296600i	−0.734364	+	0.678756i	$0.762519\pi$
$558$		−	6.00000i		−	0.254000i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	6.92820	+	4.00000i	0.292249	+	0.168730i
$563$	25.9808	−	15.0000i	1.09496	−	0.632175i	0.160066	−	0.987106i	$-0.448829\pi$
$563$	25.9808	−	15.0000i	1.09496	−	0.632175i	0.934892	+	0.354932i	$0.115496\pi$
$564$	16.0000			0.673722
$565$		0			0
$566$	11.0000	+	19.0526i	0.462364	+	0.800839i
$567$		0			0
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	−22.3923	+	14.7846i	−0.937910	+	0.619259i
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.58846	+	29.7846i	0.149649	+	1.24210i
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	14.7224	−	8.50000i	0.612372	−	0.353553i
$579$	−6.00000	−	10.3923i	−0.249351	−	0.431889i
$580$	12.0000	+	6.00000i	0.498273	+	0.249136i
$581$		0			0
$582$	10.3923	+	6.00000i	0.430775	+	0.248708i
$583$	−20.7846	−	12.0000i	−0.860811	−	0.496989i
$584$	18.0000			0.744845
$585$		0			0
$586$	26.0000			1.07405
$587$	17.3205	+	10.0000i	0.714894	+	0.412744i	0.812870	−	0.582445i	$-0.197904\pi$
$587$	17.3205	+	10.0000i	0.714894	+	0.412744i	−0.0979766	+	0.995189i	$0.531237\pi$
$588$	−12.1244	−	7.00000i	−0.500000	−	0.288675i
$589$	18.0000	+	31.1769i	0.741677	+	1.28462i
$590$	2.00000	−	4.00000i	0.0823387	−	0.164677i
$591$	2.00000	+	3.46410i	0.0822690	+	0.142494i
$592$	−5.19615	+	3.00000i	−0.213561	+	0.123299i
$593$		−	22.0000i		−	0.903432i	−0.892162	−	0.451716i	$-0.850812\pi$
$593$		−	22.0000i		−	0.903432i	0.892162	−	0.451716i	$-0.149188\pi$
$594$	−4.00000	−	6.92820i	−0.164122	−	0.284268i
$595$		0			0
$596$	−10.0000	+	17.3205i	−0.409616	+	0.709476i
$597$			48.0000i			1.96451i
$598$		0			0
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	29.7846	−	3.58846i	1.21595	−	0.146498i
$601$	3.00000	−	5.19615i	0.122373	−	0.211955i	−0.798330	−	0.602220i	$-0.794283\pi$
$601$	3.00000	−	5.19615i	0.122373	−	0.211955i	0.920703	+	0.390264i	$0.127616\pi$
$602$		0			0
$603$			12.0000i			0.488678i
$604$	−9.00000	−	15.5885i	−0.366205	−	0.634285i
$605$	0.937822	+	15.6244i	0.0381279	+	0.635220i
$606$	12.0000			0.487467
$607$	−15.5885	+	9.00000i	−0.632716	+	0.365299i	−0.781803	−	0.623525i	$-0.785700\pi$
$607$	−15.5885	+	9.00000i	−0.632716	+	0.365299i	0.149087	+	0.988824i	$0.452366\pi$
$608$	25.9808	+	15.0000i	1.05366	+	0.608330i
$609$		0			0
$610$	−6.00000	+	12.0000i	−0.242933	+	0.485866i
$611$		0			0
$612$		0			0
$613$	25.9808	+	15.0000i	1.04935	+	0.605844i	0.922468	−	0.386073i	$-0.126169\pi$
$613$	25.9808	+	15.0000i	1.04935	+	0.605844i	0.126885	+	0.991917i	$0.459502\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	−35.7128	+	2.14359i	−1.44008	+	0.0864380i
$616$		0			0
$617$	−29.4449	+	17.0000i	−1.18541	+	0.684394i	−0.957259	−	0.289233i	$-0.906600\pi$
$617$	−29.4449	+	17.0000i	−1.18541	+	0.684394i	−0.228147	+	0.973627i	$0.573267\pi$
$618$	10.3923	−	6.00000i	0.418040	−	0.241355i
$619$	−18.0000			−0.723481			−0.361741	−	0.932279i	$-0.617817\pi$
$619$	−18.0000			−0.723481			−0.361741	+	0.932279i	$0.617817\pi$
$620$	−0.803848	−	13.3923i	−0.0322833	−	0.537848i
$621$	−12.0000	+	20.7846i	−0.481543	+	0.834058i
$622$	20.7846	+	12.0000i	0.833387	+	0.481156i
$623$		0			0
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	−20.7846	−	12.0000i	−0.830057	−	0.479234i
$628$	10.3923	−	6.00000i	0.414698	−	0.239426i
$629$		0			0
$630$		0			0
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	0.993241	+	0.116071i	$0.0370299\pi$
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	−0.396100	+	0.918207i	$0.629637\pi$
$632$		0			0
$633$	−20.7846	+	12.0000i	−0.826114	+	0.476957i
$634$	1.00000	−	1.73205i	0.0397151	−	0.0687885i
$635$	−2.46410	−	3.73205i	−0.0977849	−	0.148102i
$636$	24.0000			0.951662
$637$		0			0
$638$		−	12.0000i		−	0.475085i
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$	−3.69615	−	5.59808i	−0.146103	−	0.221283i
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$			12.0000i			0.473602i
$643$	31.1769	−	18.0000i	1.22950	−	0.709851i	0.262573	−	0.964912i	$-0.415429\pi$
$643$	31.1769	−	18.0000i	1.22950	−	0.709851i	0.966925	+	0.255062i	$0.0820957\pi$
$644$		0			0
$645$	−24.0000	−	12.0000i	−0.944999	−	0.472500i
$646$		0			0
$647$	5.19615	+	3.00000i	0.204282	+	0.117942i	0.598651	−	0.801010i	$-0.295704\pi$
$647$	5.19615	+	3.00000i	0.204282	+	0.117942i	−0.394369	+	0.918952i	$0.629037\pi$
$648$	28.5788	+	16.5000i	1.12268	+	0.648181i
$649$	4.00000			0.157014
$650$		0			0
$651$		0			0
$652$	−10.3923	−	6.00000i	−0.406994	−	0.234978i
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.964928	−	0.262515i	$-0.0845520\pi$
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.255119	+	0.966910i	$0.417885\pi$
$654$	12.0000	+	20.7846i	0.469237	+	0.812743i
$655$	−24.0000	−	12.0000i	−0.937758	−	0.468879i
$656$	−4.00000	−	6.92820i	−0.156174	−	0.270501i
$657$	5.19615	−	3.00000i	0.202721	−	0.117041i
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$	4.92820	+	7.46410i	0.191830	+	0.290540i
$661$	−6.00000	+	10.3923i	−0.233373	+	0.404214i	−0.958799	−	0.284087i	$-0.908310\pi$
$661$	−6.00000	+	10.3923i	−0.233373	+	0.404214i	0.725426	+	0.688301i	$0.241643\pi$
$662$		−	30.0000i		−	1.16598i
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−3.00000	+	5.19615i	−0.116248	+	0.201347i
$667$	−31.1769	+	18.0000i	−1.20717	+	0.696963i
$668$		−	16.0000i		−	0.619059i
$669$	−24.0000	−	41.5692i	−0.927894	−	1.60716i
$670$	−1.60770	−	26.7846i	−0.0621107	−	1.03478i
$671$	−12.0000			−0.463255
$672$		0			0
$673$	41.5692	+	24.0000i	1.60238	+	0.925132i	0.991011	+	0.133783i	$0.0427126\pi$
$673$	41.5692	+	24.0000i	1.60238	+	0.925132i	0.611365	+	0.791349i	$0.290621\pi$
$674$	−16.0000	+	27.7128i	−0.616297	+	1.06746i
$675$	−16.0000	+	12.0000i	−0.615840	+	0.461880i
$676$		0			0
$677$			36.0000i			1.38359i	0.722093	+	0.691796i	$0.243180\pi$
$677$			36.0000i			1.38359i	−0.722093	+	0.691796i	$0.756820\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−8.00000			−0.306561
$682$	−10.3923	+	6.00000i	−0.397942	+	0.229752i
$683$	−38.1051	+	22.0000i	−1.45805	+	0.841807i	−0.998916	−	0.0465592i	$-0.985174\pi$
$683$	−38.1051	+	22.0000i	−1.45805	+	0.841807i	−0.459136	+	0.888366i	$0.651841\pi$
$684$	6.00000			0.229416
$685$	4.46410	−	0.267949i	0.170565	−	0.0102378i
$686$		0			0
$687$	−20.7846	−	12.0000i	−0.792982	−	0.457829i
$688$		−	6.00000i		−	0.228748i
$689$		0			0
$690$	−12.0000	+	24.0000i	−0.456832	+	0.913664i
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	10.3923	+	6.00000i	0.395056	+	0.228086i
$693$		0			0
$694$	6.00000			0.227757
$695$	0.535898	+	8.92820i	0.0203278	+	0.338666i
$696$	18.0000	+	31.1769i	0.682288	+	1.18176i
$697$		0			0
$698$	−10.3923	+	6.00000i	−0.393355	+	0.227103i
$699$	24.0000	−	41.5692i	0.907763	−	1.57229i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$		−	36.0000i		−	1.35777i
$704$	−7.00000	+	12.1244i	−0.263822	+	0.456954i
$705$	−29.8564	+	19.7128i	−1.12446	+	0.742427i
$706$	7.00000	+	12.1244i	0.263448	+	0.456306i
$707$		0			0
$708$	−3.46410	+	2.00000i	−0.130189	+	0.0751646i
$709$	−6.00000	−	10.3923i	−0.225335	−	0.390291i	0.731085	−	0.682286i	$-0.239014\pi$
$709$	−6.00000	−	10.3923i	−0.225335	−	0.390291i	−0.956420	+	0.291995i	$0.905681\pi$
$710$	2.00000	−	4.00000i	0.0750587	−	0.150117i
$711$		0			0
$712$	−20.7846	−	12.0000i	−0.778936	−	0.449719i
$713$	31.1769	+	18.0000i	1.16758	+	0.674105i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$	17.3205	+	10.0000i	0.646846	+	0.373457i
$718$	−1.73205	−	1.00000i	−0.0646396	−	0.0373197i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$		0			0
$722$	14.7224	−	8.50000i	0.547912	−	0.316337i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−29.7846	+	3.58846i	−1.10617	+	0.133272i
$726$	−7.00000	+	12.1244i	−0.259794	+	0.449977i
$727$			26.0000i			0.964287i	0.876092	+	0.482143i	$0.160142\pi$
$727$			26.0000i			0.964287i	−0.876092	+	0.482143i	$0.839858\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	−11.1962	+	7.39230i	−0.414388	+	0.273601i
$731$		0			0
$732$	10.3923	−	6.00000i	0.384111	−	0.221766i
$733$			42.0000i			1.55131i	0.631160	+	0.775653i	$0.282579\pi$
$733$			42.0000i			1.55131i	−0.631160	+	0.775653i	$0.717421\pi$
$734$	−9.00000	−	15.5885i	−0.332196	−	0.575380i
$735$	31.2487	−	1.87564i	1.15263	−	0.0691842i
$736$	30.0000			1.10581
$737$	20.7846	−	12.0000i	0.765611	−	0.442026i
$738$	−6.92820	−	4.00000i	−0.255031	−	0.147242i
$739$	−3.00000	+	5.19615i	−0.110357	+	0.191144i	−0.915914	−	0.401374i	$-0.868533\pi$
$739$	−3.00000	+	5.19615i	−0.110357	+	0.191144i	0.805557	+	0.592518i	$0.201866\pi$
$740$	−6.00000	+	12.0000i	−0.220564	+	0.441129i
$741$		0			0
$742$		0			0
$743$	−13.8564	−	8.00000i	−0.508342	−	0.293492i	0.223810	−	0.974633i	$-0.428151\pi$
$743$	−13.8564	−	8.00000i	−0.508342	−	0.293492i	−0.732152	+	0.681141i	$0.761484\pi$
$744$	18.0000	−	31.1769i	0.659912	−	1.14300i
$745$	−2.67949	−	44.6410i	−0.0981690	−	1.63552i
$746$	−4.00000			−0.146450
$747$	−3.46410	+	2.00000i	−0.126745	+	0.0731762i
$748$		0			0
$749$		0			0
$750$	−17.0526	+	14.4641i	−0.622671	+	0.528154i
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−6.92820	−	4.00000i	−0.252646	−	0.145865i
$753$		−	24.0000i		−	0.874609i
$754$		0			0
$755$	36.0000	+	18.0000i	1.31017	+	0.655087i
$756$		0			0
$757$	−17.3205	−	10.0000i	−0.629525	−	0.363456i	0.151043	−	0.988527i	$-0.451737\pi$
$757$	−17.3205	−	10.0000i	−0.629525	−	0.363456i	−0.780568	+	0.625071i	$0.785070\pi$
$758$	15.5885	−	9.00000i	0.566198	−	0.326895i
$759$	−24.0000			−0.871145
$760$	−40.1769	+	2.41154i	−1.45737	+	0.0874758i
$761$	−20.0000	−	34.6410i	−0.724999	−	1.25574i	−0.958974	−	0.283493i	$-0.908507\pi$
$761$	−20.0000	−	34.6410i	−0.724999	−	1.25574i	0.233975	−	0.972243i	$-0.424827\pi$
$762$		−	4.00000i		−	0.144905i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	8.00000			0.289052
$767$		0			0
$768$		−	34.0000i		−	1.22687i
$769$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$769$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$		0			0
$772$		−	6.00000i		−	0.215945i
$773$	−32.9090	+	19.0000i	−1.18365	+	0.683383i	−0.956857	−	0.290560i	$-0.906159\pi$
$773$	−32.9090	+	19.0000i	−1.18365	+	0.683383i	−0.226796	+	0.973942i	$0.572825\pi$
$774$	−3.00000	−	5.19615i	−0.107833	−	0.186772i
$775$	18.0000	+	24.0000i	0.646579	+	0.862105i
$776$	9.00000	+	15.5885i	0.323081	+	0.559593i
$777$		0			0
$778$	5.19615	+	3.00000i	0.186291	+	0.107555i
$779$	48.0000			1.71978
$780$		0			0
$781$	4.00000			0.143131
$782$		0			0
$783$	−20.7846	−	12.0000i	−0.742781	−	0.428845i
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	−12.0000	+	24.0000i	−0.428298	+	0.856597i
$786$	−12.0000	−	20.7846i	−0.428026	−	0.741362i
$787$	10.3923	−	6.00000i	0.370446	−	0.213877i	−0.303207	−	0.952925i	$-0.598058\pi$
$787$	10.3923	−	6.00000i	0.370446	−	0.213877i	0.673653	+	0.739048i	$0.264724\pi$
$788$			2.00000i			0.0712470i
$789$	6.00000	+	10.3923i	0.213606	+	0.369976i
$790$		0			0
$791$		0			0
$792$			6.00000i			0.213201i
$793$		0			0
$794$	18.0000			0.638796
$795$	−44.7846	+	29.5692i	−1.58835	+	1.04871i
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	−10.3923	+	6.00000i	−0.368114	+	0.212531i	−0.672634	−	0.739975i	$-0.734837\pi$
$797$	−10.3923	+	6.00000i	−0.368114	+	0.212531i	0.304520	+	0.952506i	$0.401504\pi$
$798$		0			0
$799$		0			0
$800$	22.9904	+	9.82051i	0.812833	+	0.347207i
$801$	−8.00000			−0.282666
$802$	−13.8564	+	8.00000i	−0.489287	+	0.282490i
$803$	−10.3923	−	6.00000i	−0.366736	−	0.211735i
$804$	−12.0000	+	20.7846i	−0.423207	+	0.733017i
$805$		0			0
$806$		0			0
$807$		−	36.0000i		−	1.26726i
$808$	15.5885	+	9.00000i	0.548400	+	0.316619i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$	−24.5526	+	1.47372i	−0.862689	+	0.0517813i
$811$	−30.0000			−1.05344			−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000			−1.05344			−0.526721	+	0.850038i	$0.676579\pi$
$812$		0			0
$813$	−10.3923	+	6.00000i	−0.364474	+	0.210429i
$814$	12.0000			0.420600
$815$	26.7846	−	1.60770i	0.938224	−	0.0563151i
$816$		0			0
$817$	31.1769	+	18.0000i	1.09074	+	0.629740i
$818$		−	24.0000i		−	0.839140i
$819$		0			0
$820$	−16.0000	−	8.00000i	−0.558744	−	0.279372i
$821$	−10.0000	+	17.3205i	−0.349002	+	0.604490i	−0.986073	−	0.166316i	$-0.946813\pi$
$821$	−10.0000	+	17.3205i	−0.349002	+	0.604490i	0.637070	+	0.770806i	$0.280146\pi$
$822$	3.46410	+	2.00000i	0.120824	+	0.0697580i
$823$	36.3731	−	21.0000i	1.26789	−	0.732014i	0.293298	−	0.956021i	$-0.405247\pi$
$823$	36.3731	−	21.0000i	1.26789	−	0.732014i	0.974588	+	0.224007i	$0.0719139\pi$
$824$	18.0000			0.627060
$825$	−18.3923	−	7.85641i	−0.640338	−	0.273525i
$826$		0			0
$827$			4.00000i			0.139094i	0.997579	+	0.0695468i	$0.0221553\pi$
$827$			4.00000i			0.139094i	−0.997579	+	0.0695468i	$0.977845\pi$
$828$	5.19615	−	3.00000i	0.180579	−	0.104257i
$829$	3.00000	−	5.19615i	0.104194	−	0.180470i	−0.809214	−	0.587513i	$-0.800107\pi$
$829$	3.00000	−	5.19615i	0.104194	−	0.180470i	0.913409	+	0.407044i	$0.133440\pi$
$830$	7.46410	−	4.92820i	0.259083	−	0.171060i
$831$	−24.0000			−0.832551
$832$		0			0
$833$		0			0
$834$	−4.00000	+	6.92820i	−0.138509	+	0.239904i
$835$	19.7128	+	29.8564i	0.682190	+	1.03322i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$			24.0000i			0.829561i
$838$	−10.3923	+	6.00000i	−0.358996	+	0.207267i
$839$	23.0000	+	39.8372i	0.794048	+	1.37533i	0.923442	+	0.383738i	$0.125364\pi$
$839$	23.0000	+	39.8372i	0.794048	+	1.37533i	−0.129394	+	0.991593i	$0.541303\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−31.1769	−	18.0000i	−1.07443	−	0.620321i
$843$	13.8564	+	8.00000i	0.477240	+	0.275535i
$844$	−12.0000			−0.413057
$845$		0			0
$846$	−8.00000			−0.275046
$847$		0			0
$848$	−10.3923	−	6.00000i	−0.356873	−	0.206041i
$849$	22.0000	+	38.1051i	0.755038	+	1.30776i
$850$		0			0
$851$	−18.0000	−	31.1769i	−0.617032	−	1.06873i
$852$	−3.46410	+	2.00000i	−0.118678	+	0.0685189i
$853$			54.0000i			1.84892i	0.381273	+	0.924462i	$0.375486\pi$
$853$			54.0000i			1.84892i	−0.381273	+	0.924462i	$0.624514\pi$
$854$		0			0
$855$	−11.1962	+	7.39230i	−0.382900	+	0.252811i
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$		−	24.0000i		−	0.819824i	−0.912125	−	0.409912i	$-0.865559\pi$
$857$		−	24.0000i		−	0.819824i	0.912125	−	0.409912i	$-0.134441\pi$
$858$		0			0
$859$	−36.0000			−1.22830			−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000			−1.22830			−0.614152	+	0.789188i	$0.710502\pi$
$860$	−7.39230	−	11.1962i	−0.252076	−	0.381786i
$861$		0			0
$862$	−8.66025	+	5.00000i	−0.294969	+	0.170301i
$863$			8.00000i			0.272323i	0.990687	+	0.136162i	$0.0434766\pi$
$863$			8.00000i			0.272323i	−0.990687	+	0.136162i	$0.956523\pi$
$864$	10.0000	+	17.3205i	0.340207	+	0.589256i
$865$	−26.7846	+	1.60770i	−0.910704	+	0.0546633i
$866$	16.0000			0.543702
$867$	29.4449	−	17.0000i	1.00000	−	0.577350i
$868$		0			0
$869$		0			0
$870$	−24.0000	−	12.0000i	−0.813676	−	0.406838i
$871$		0			0
$872$			36.0000i			1.21911i
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	18.0000	−	31.1769i	0.608859	−	1.05457i
$875$		0			0
$876$	12.0000			0.405442
$877$	−5.19615	+	3.00000i	−0.175462	+	0.101303i	−0.585159	−	0.810919i	$-0.698968\pi$
$877$	−5.19615	+	3.00000i	−0.175462	+	0.101303i	0.409697	+	0.912222i	$0.365634\pi$
$878$	−6.92820	+	4.00000i	−0.233816	+	0.134993i
$879$	52.0000			1.75392
$880$	−0.267949	−	4.46410i	−0.00903257	−	0.150485i
$881$	21.0000	−	36.3731i	0.707508	−	1.22544i	−0.258271	−	0.966073i	$-0.583153\pi$
$881$	21.0000	−	36.3731i	0.707508	−	1.22544i	0.965779	−	0.259367i	$-0.0835140\pi$
$882$	6.06218	+	3.50000i	0.204124	+	0.117851i
$883$		−	2.00000i		−	0.0673054i	−0.999434	−	0.0336527i	$-0.989286\pi$
$883$		−	2.00000i		−	0.0673054i	0.999434	−	0.0336527i	$-0.0107140\pi$
$884$		0			0
$885$	4.00000	−	8.00000i	0.134459	−	0.268917i
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	36.3731	+	21.0000i	1.22129	+	0.705111i	0.965193	−	0.261540i	$-0.0842305\pi$
$887$	36.3731	+	21.0000i	1.22129	+	0.705111i	0.256096	+	0.966651i	$0.417564\pi$
$888$	−31.1769	+	18.0000i	−1.04623	+	0.604040i
$889$		0			0
$890$	17.8564	−	1.07180i	0.598548	−	0.0359267i
$891$	−11.0000	−	19.0526i	−0.368514	−	0.638285i
$892$		−	24.0000i		−	0.803579i
$893$	41.5692	−	24.0000i	1.39106	−	0.803129i
$894$	20.0000	−	34.6410i	0.668900	−	1.15857i
$895$	−22.3923	+	14.7846i	−0.748492	+	0.494195i
$896$		0			0
$897$		0			0
$898$			16.0000i			0.533927i
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$	4.96410	−	0.598076i	0.165470	−	0.0199359i
$901$		0			0
$902$			16.0000i			0.532742i
$903$		0			0
$904$		0			0
$905$	4.00000	+	2.00000i	0.132964	+	0.0664822i
$906$	18.0000	+	31.1769i	0.598010	+	1.03578i
$907$	8.66025	+	5.00000i	0.287559	+	0.166022i	0.636841	−	0.770996i	$-0.280241\pi$
$907$	8.66025	+	5.00000i	0.287559	+	0.166022i	−0.349281	+	0.937018i	$0.613574\pi$
$908$	−3.46410	−	2.00000i	−0.114960	−	0.0663723i
$909$	6.00000			0.199007
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	−10.3923	−	6.00000i	−0.344124	−	0.198680i
$913$	6.92820	+	4.00000i	0.229290	+	0.132381i
$914$	15.0000	+	25.9808i	0.496156	+	0.859367i
$915$	−12.0000	+	24.0000i	−0.396708	+	0.793416i
$916$	−6.00000	−	10.3923i	−0.198246	−	0.343371i
$917$		0			0
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	−33.5885	+	22.1769i	−1.10738	+	0.731151i
$921$	12.0000	−	20.7846i	0.395413	−	0.684876i
$922$		−	4.00000i		−	0.131733i
$923$		0			0
$924$		0			0
$925$	−3.58846	−	29.7846i	−0.117988	−	0.979312i
$926$	−12.0000	+	20.7846i	−0.394344	+	0.683025i
$927$	5.19615	−	3.00000i	0.170664	−	0.0985329i
$928$			30.0000i			0.984798i
$929$	−8.00000	−	13.8564i	−0.262471	−	0.454614i	0.704427	−	0.709777i	$-0.251204\pi$
$929$	−8.00000	−	13.8564i	−0.262471	−	0.454614i	−0.966898	+	0.255163i	$0.917871\pi$
$930$	1.60770	+	26.7846i	0.0527184	+	0.878302i
$931$	−42.0000			−1.37649
$932$	20.7846	−	12.0000i	0.680823	−	0.393073i
$933$	41.5692	+	24.0000i	1.36092	+	0.785725i
$934$	−9.00000	+	15.5885i	−0.294489	+	0.510070i
$935$		0			0
$936$		0			0
$937$		−	56.0000i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$937$		−	56.0000i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$938$		0			0
$939$	8.00000	−	13.8564i	0.261070	−	0.452187i
$940$	−17.8564	+	1.07180i	−0.582412	+	0.0349582i
$941$	28.0000			0.912774			0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000			0.912774			0.456387	+	0.889781i	$0.349143\pi$
$942$	−20.7846	+	12.0000i	−0.677199	+	0.390981i
$943$	41.5692	−	24.0000i	1.35368	−	0.781548i
$944$	2.00000			0.0650945
$945$		0			0
$946$	−6.00000	+	10.3923i	−0.195077	+	0.337883i
$947$	−24.2487	−	14.0000i	−0.787977	−	0.454939i	0.0512727	−	0.998685i	$-0.483672\pi$
$947$	−24.2487	−	14.0000i	−0.787977	−	0.454939i	−0.839250	+	0.543746i	$0.817006\pi$
$948$		0			0
$949$		0			0
$950$	24.0000	−	18.0000i	0.778663	−	0.583997i
$951$	2.00000	−	3.46410i	0.0648544	−	0.112331i
$952$		0			0
$953$	−20.7846	+	12.0000i	−0.673280	+	0.388718i	−0.797318	−	0.603559i	$-0.793749\pi$
$953$	−20.7846	+	12.0000i	−0.673280	+	0.388718i	0.124039	+	0.992277i	$0.460415\pi$
$954$	−12.0000			−0.388514
$955$		0			0
$956$	5.00000	+	8.66025i	0.161712	+	0.280093i
$957$		−	24.0000i		−	0.775810i
$958$	−19.0526	+	11.0000i	−0.615560	+	0.355394i
$959$		0			0
$960$	17.2487	+	26.1244i	0.556700	+	0.843160i
$961$	5.00000			0.161290
$962$		0			0
$963$			6.00000i			0.193347i
$964$		0			0
$965$	7.39230	+	11.1962i	0.237967	+	0.360417i
$966$		0			0
$967$		−	48.0000i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$967$		−	48.0000i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$968$	−18.1865	+	10.5000i	−0.584537	+	0.337483i
$969$		0			0
$970$	−12.0000	−	6.00000i	−0.385297	−	0.192648i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	8.66025	+	5.00000i	0.277778	+	0.160375i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−6.00000			−0.192055
$977$	29.4449	+	17.0000i	0.942025	+	0.543878i	0.890594	−	0.454798i	$-0.150289\pi$
$977$	29.4449	+	17.0000i	0.942025	+	0.543878i	0.0514302	+	0.998677i	$0.483622\pi$
$978$	20.7846	+	12.0000i	0.664619	+	0.383718i
$979$	8.00000	+	13.8564i	0.255681	+	0.442853i
$980$	14.0000	+	7.00000i	0.447214	+	0.223607i
$981$	6.00000	+	10.3923i	0.191565	+	0.331801i
$982$	−10.3923	+	6.00000i	−0.331632	+	0.191468i
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$	−24.0000	−	41.5692i	−0.765092	−	1.32518i
$985$	−2.46410	−	3.73205i	−0.0785128	−	0.118913i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	36.0000			1.14473
$990$	−2.46410	−	3.73205i	−0.0783143	−	0.118612i
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	25.9808	−	15.0000i	0.824890	−	0.476250i
$993$		−	60.0000i		−	1.90404i
$994$		0			0
$995$	−3.21539	−	53.5692i	−0.101935	−	1.69826i
$996$	−8.00000			−0.253490
$997$	−51.9615	+	30.0000i	−1.64564	+	0.950110i	−0.666861	+	0.745182i	$0.732362\pi$
$997$	−51.9615	+	30.0000i	−1.64564	+	0.950110i	−0.978777	+	0.204927i	$0.934304\pi$
$998$	5.19615	+	3.00000i	0.164481	+	0.0949633i
$999$	12.0000	−	20.7846i	0.379663	−	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.b.529.1		4
5.4	even	2	inner	845.2.n.b.529.2		4
13.2	odd	12		845.2.l.a.699.2		4
13.3	even	3	inner	845.2.n.b.484.2		4
13.4	even	6		845.2.b.a.339.1		2
13.5	odd	4		845.2.l.a.654.1		4
13.6	odd	12		65.2.d.b.64.2	yes	2
13.7	odd	12		65.2.d.a.64.2	yes	2
13.8	odd	4		845.2.l.b.654.1		4
13.9	even	3		845.2.b.b.339.2		2
13.10	even	6		845.2.n.a.484.1		4
13.11	odd	12		845.2.l.b.699.2		4
13.12	even	2		845.2.n.a.529.2		4
39.20	even	12		585.2.h.c.64.1		2
39.32	even	12		585.2.h.b.64.2		2
52.7	even	12		1040.2.f.a.129.1		2
52.19	even	12		1040.2.f.b.129.1		2
65.4	even	6		845.2.b.a.339.2		2
65.7	even	12		325.2.c.e.51.1		2
65.9	even	6		845.2.b.b.339.1		2
65.17	odd	12		4225.2.a.m.1.1		1
65.19	odd	12		65.2.d.a.64.1	✓	2
65.22	odd	12		4225.2.a.h.1.1		1
65.24	odd	12		845.2.l.a.699.1		4
65.29	even	6	inner	845.2.n.b.484.1		4
65.32	even	12		325.2.c.e.51.2		2
65.33	even	12		325.2.c.b.51.2		2
65.34	odd	4		845.2.l.a.654.2		4
65.43	odd	12		4225.2.a.e.1.1		1
65.44	odd	4		845.2.l.b.654.2		4
65.48	odd	12		4225.2.a.k.1.1		1
65.49	even	6		845.2.n.a.484.2		4
65.54	odd	12		845.2.l.b.699.1		4
65.58	even	12		325.2.c.b.51.1		2
65.59	odd	12		65.2.d.b.64.1	yes	2
65.64	even	2		845.2.n.a.529.1		4
195.59	even	12		585.2.h.b.64.1		2
195.149	even	12		585.2.h.c.64.2		2
260.19	even	12		1040.2.f.a.129.2		2
260.59	even	12		1040.2.f.b.129.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.d.a.64.1	✓	2	65.19	odd	12
65.2.d.a.64.2	yes	2	13.7	odd	12
65.2.d.b.64.1	yes	2	65.59	odd	12
65.2.d.b.64.2	yes	2	13.6	odd	12
325.2.c.b.51.1		2	65.58	even	12
325.2.c.b.51.2		2	65.33	even	12
325.2.c.e.51.1		2	65.7	even	12
325.2.c.e.51.2		2	65.32	even	12
585.2.h.b.64.1		2	195.59	even	12
585.2.h.b.64.2		2	39.32	even	12
585.2.h.c.64.1		2	39.20	even	12
585.2.h.c.64.2		2	195.149	even	12
845.2.b.a.339.1		2	13.4	even	6
845.2.b.a.339.2		2	65.4	even	6
845.2.b.b.339.1		2	65.9	even	6
845.2.b.b.339.2		2	13.9	even	3
845.2.l.a.654.1		4	13.5	odd	4
845.2.l.a.654.2		4	65.34	odd	4
845.2.l.a.699.1		4	65.24	odd	12
845.2.l.a.699.2		4	13.2	odd	12
845.2.l.b.654.1		4	13.8	odd	4
845.2.l.b.654.2		4	65.44	odd	4
845.2.l.b.699.1		4	65.54	odd	12
845.2.l.b.699.2		4	13.11	odd	12
845.2.n.a.484.1		4	13.10	even	6
845.2.n.a.484.2		4	65.49	even	6
845.2.n.a.529.1		4	65.64	even	2
845.2.n.a.529.2		4	13.12	even	2
845.2.n.b.484.1		4	65.29	even	6	inner
845.2.n.b.484.2		4	13.3	even	3	inner
845.2.n.b.529.1		4	1.1	even	1	trivial
845.2.n.b.529.2		4	5.4	even	2	inner
1040.2.f.a.129.1		2	52.7	even	12
1040.2.f.a.129.2		2	260.19	even	12
1040.2.f.b.129.1		2	52.19	even	12
1040.2.f.b.129.2		2	260.59	even	12
4225.2.a.e.1.1		1	65.43	odd	12
4225.2.a.h.1.1		1	65.22	odd	12
4225.2.a.k.1.1		1	65.48	odd	12
4225.2.a.m.1.1		1	65.17	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.73205 - 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 + 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.73205 - 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 + 1.73205i) q^{6} +3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 - 1.86603i) q^{10} +(1.00000 - 1.73205i) q^{11} +2.00000i q^{12} +(-2.46410 - 3.73205i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{18} +(3.00000 + 5.19615i) q^{19} +(-0.133975 - 2.23205i) q^{20} +(-1.73205 + 1.00000i) q^{22} +(5.19615 + 3.00000i) q^{23} +(3.00000 - 5.19615i) q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000i q^{27} +(-3.00000 + 5.19615i) q^{29} +(0.267949 + 4.46410i) q^{30} +6.00000 q^{31} +(4.33013 - 2.50000i) q^{32} +(-3.46410 + 2.00000i) q^{33} +(0.500000 - 0.866025i) q^{36} +(-5.19615 - 3.00000i) q^{37} -6.00000i q^{38} +(-3.00000 + 6.00000i) q^{40} +(4.00000 - 6.92820i) q^{41} +(5.19615 - 3.00000i) q^{43} -2.00000 q^{44} +(0.133975 + 2.23205i) q^{45} +(-3.00000 - 5.19615i) q^{46} -8.00000i q^{47} +(-1.73205 + 1.00000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-0.598076 - 4.96410i) q^{50} -12.0000i q^{53} +(2.00000 - 3.46410i) q^{54} +(3.73205 - 2.46410i) q^{55} -12.0000i q^{57} +(5.19615 - 3.00000i) q^{58} +(1.00000 + 1.73205i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(-3.00000 - 5.19615i) q^{61} +(-5.19615 - 3.00000i) q^{62} -7.00000 q^{64} +4.00000 q^{66} +(10.3923 + 6.00000i) q^{67} +(-6.00000 - 10.3923i) q^{69} +(1.00000 + 1.73205i) q^{71} +(-2.59808 + 1.50000i) q^{72} -6.00000i q^{73} +(3.00000 + 5.19615i) q^{74} +(-1.19615 - 9.92820i) q^{75} +(3.00000 - 5.19615i) q^{76} +(1.86603 - 1.23205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-6.92820 + 4.00000i) q^{82} +4.00000i q^{83} -6.00000 q^{86} +(10.3923 - 6.00000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(-4.00000 + 6.92820i) q^{89} +(1.00000 - 2.00000i) q^{90} -6.00000i q^{92} +(-10.3923 - 6.00000i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(0.803848 + 13.3923i) q^{95} -10.0000 q^{96} +(5.19615 - 3.00000i) q^{97} +(6.06218 - 3.50000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^4 + 8 * q^5 + 4 * q^6 + 2 * q^9	\( 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{15} + 2 q^{16} + 12 q^{19} - 4 q^{20} + 12 q^{24} + 12 q^{25} - 12 q^{29} + 8 q^{30} + 24 q^{31} + 2 q^{36} - 12 q^{40} + 16 q^{41} - 8 q^{44} + 4 q^{45} - 12 q^{46} - 14 q^{49} + 8 q^{50} + 8 q^{54} + 8 q^{55} + 4 q^{59} - 8 q^{60} - 12 q^{61} - 28 q^{64} + 16 q^{66} - 24 q^{69} + 4 q^{71} + 12 q^{74} + 16 q^{75} + 12 q^{76} + 4 q^{80} + 22 q^{81} - 24 q^{86} - 16 q^{89} + 4 q^{90} - 16 q^{94} + 24 q^{95} - 40 q^{96} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^4 + 8 * q^5 + 4 * q^6 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^15 + 2 * q^16 + 12 * q^19 - 4 * q^20 + 12 * q^24 + 12 * q^25 - 12 * q^29 + 8 * q^30 + 24 * q^31 + 2 * q^36 - 12 * q^40 + 16 * q^41 - 8 * q^44 + 4 * q^45 - 12 * q^46 - 14 * q^49 + 8 * q^50 + 8 * q^54 + 8 * q^55 + 4 * q^59 - 8 * q^60 - 12 * q^61 - 28 * q^64 + 16 * q^66 - 24 * q^69 + 4 * q^71 + 12 * q^74 + 16 * q^75 + 12 * q^76 + 4 * q^80 + 22 * q^81 - 24 * q^86 - 16 * q^89 + 4 * q^90 - 16 * q^94 + 24 * q^95 - 40 * q^96 + 8 * q^99

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