LMFDB - Embedded newform 525.2.t.e.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.e.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{11} +1.73205i q^{12} -3.46410i q^{13} +(3.00000 + 3.46410i) q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} +5.19615i q^{18} +(-6.00000 - 3.46410i) q^{19} +(3.00000 + 3.46410i) q^{21} -6.00000 q^{22} +(-1.50000 - 0.866025i) q^{23} +(1.50000 - 2.59808i) q^{24} +(3.00000 - 5.19615i) q^{26} +5.19615i q^{27} +(0.500000 + 2.59808i) q^{28} -1.73205i q^{29} +(-3.00000 + 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} -6.00000 q^{33} +10.3923i q^{34} +(-1.50000 + 2.59808i) q^{36} +(2.00000 - 3.46410i) q^{37} +(-6.00000 - 10.3923i) q^{38} +(3.00000 - 5.19615i) q^{39} -3.00000 q^{41} +(1.50000 + 7.79423i) q^{42} -1.00000 q^{43} +(-3.00000 - 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(7.50000 - 4.33013i) q^{48} +(5.50000 + 4.33013i) q^{49} +10.3923i q^{51} +(3.00000 - 1.73205i) q^{52} +(-4.50000 + 7.79423i) q^{54} +(1.50000 - 4.33013i) q^{56} +(-6.00000 - 10.3923i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-4.50000 - 2.59808i) q^{61} -6.00000 q^{62} +(1.50000 + 7.79423i) q^{63} -1.00000 q^{64} +(-9.00000 - 5.19615i) q^{66} +(-6.50000 - 11.2583i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.50000 - 2.59808i) q^{69} -6.92820i q^{71} +(4.50000 - 2.59808i) q^{72} +(-3.00000 + 1.73205i) q^{73} +(6.00000 - 3.46410i) q^{74} -6.92820i q^{76} +(-9.00000 + 1.73205i) q^{77} +(9.00000 - 5.19615i) q^{78} +(8.00000 - 13.8564i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(-1.50000 + 4.33013i) q^{84} +(-1.50000 - 0.866025i) q^{86} +(1.50000 - 2.59808i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-1.50000 + 2.59808i) q^{89} +(3.00000 - 8.66025i) q^{91} -1.73205i q^{92} -6.00000 q^{93} +9.00000 q^{96} +10.3923i q^{97} +(4.50000 + 11.2583i) q^{98} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} + q^{4} + 3 q^{6} + 5 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 + q^4 + 3 * q^6 + 5 * q^7 + 3 * q^9	$ 2 q + 3 q^{2} + 3 q^{3} + q^{4} + 3 q^{6} + 5 q^{7} + 3 q^{9} - 6 q^{11} + 6 q^{14} + 5 q^{16} + 6 q^{17} - 12 q^{19} + 6 q^{21} - 12 q^{22} - 3 q^{23} + 3 q^{24} + 6 q^{26} + q^{28} - 6 q^{31} + 9 q^{32} - 12 q^{33} - 3 q^{36} + 4 q^{37} - 12 q^{38} + 6 q^{39} - 6 q^{41} + 3 q^{42} - 2 q^{43} - 6 q^{44} - 3 q^{46} + 15 q^{48} + 11 q^{49} + 6 q^{52} - 9 q^{54} + 3 q^{56} - 12 q^{57} + 3 q^{58} - 9 q^{61} - 12 q^{62} + 3 q^{63} - 2 q^{64} - 18 q^{66} - 13 q^{67} - 6 q^{68} - 3 q^{69} + 9 q^{72} - 6 q^{73} + 12 q^{74} - 18 q^{77} + 18 q^{78} + 16 q^{79} - 9 q^{81} - 9 q^{82} + 18 q^{83} - 3 q^{84} - 3 q^{86} + 3 q^{87} + 6 q^{88} - 3 q^{89} + 6 q^{91} - 12 q^{93} + 18 q^{96} + 9 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^3 + q^4 + 3 * q^6 + 5 * q^7 + 3 * q^9 - 6 * q^11 + 6 * q^14 + 5 * q^16 + 6 * q^17 - 12 * q^19 + 6 * q^21 - 12 * q^22 - 3 * q^23 + 3 * q^24 + 6 * q^26 + q^28 - 6 * q^31 + 9 * q^32 - 12 * q^33 - 3 * q^36 + 4 * q^37 - 12 * q^38 + 6 * q^39 - 6 * q^41 + 3 * q^42 - 2 * q^43 - 6 * q^44 - 3 * q^46 + 15 * q^48 + 11 * q^49 + 6 * q^52 - 9 * q^54 + 3 * q^56 - 12 * q^57 + 3 * q^58 - 9 * q^61 - 12 * q^62 + 3 * q^63 - 2 * q^64 - 18 * q^66 - 13 * q^67 - 6 * q^68 - 3 * q^69 + 9 * q^72 - 6 * q^73 + 12 * q^74 - 18 * q^77 + 18 * q^78 + 16 * q^79 - 9 * q^81 - 9 * q^82 + 18 * q^83 - 3 * q^84 - 3 * q^86 + 3 * q^87 + 6 * q^88 - 3 * q^89 + 6 * q^91 - 12 * q^93 + 18 * q^96 + 9 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.50000	+	2.59808i	0.612372	+	1.06066i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		−	1.73205i		−	0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$			1.73205i			0.500000i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	3.00000	+	3.46410i	0.801784	+	0.925820i
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$			5.19615i			1.22474i
$19$	−6.00000	−	3.46410i	−1.37649	−	0.794719i	−0.384759	−	0.923017i	$-0.625715\pi$
$19$	−6.00000	−	3.46410i	−1.37649	−	0.794719i	−0.991736	+	0.128298i	$0.959049\pi$
$20$		0			0
$21$	3.00000	+	3.46410i	0.654654	+	0.755929i
$22$	−6.00000			−1.27920
$23$	−1.50000	−	0.866025i	−0.312772	−	0.180579i	0.335394	−	0.942078i	$-0.391130\pi$
$23$	−1.50000	−	0.866025i	−0.312772	−	0.180579i	−0.648166	+	0.761499i	$0.724464\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$		0			0
$26$	3.00000	−	5.19615i	0.588348	−	1.01905i
$27$			5.19615i			1.00000i
$28$	0.500000	+	2.59808i	0.0944911	+	0.490990i
$29$		−	1.73205i		−	0.321634i	−0.986984	−	0.160817i	$-0.948587\pi$
$29$		−	1.73205i		−	0.321634i	0.986984	−	0.160817i	$-0.0514129\pi$
$30$		0			0
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$	−6.00000			−1.04447
$34$			10.3923i			1.78227i
$35$		0			0
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	−6.00000	−	10.3923i	−0.973329	−	1.68585i
$39$	3.00000	−	5.19615i	0.480384	−	0.832050i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	1.50000	+	7.79423i	0.231455	+	1.20268i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−3.00000	−	1.73205i	−0.452267	−	0.261116i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	7.50000	−	4.33013i	1.08253	−	0.625000i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$			10.3923i			1.45521i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$		0			0
$56$	1.50000	−	4.33013i	0.200446	−	0.578638i
$57$	−6.00000	−	10.3923i	−0.794719	−	1.37649i
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	0.183442	−	0.983030i	$-0.441276\pi$
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	−0.759608	+	0.650381i	$0.774609\pi$
$62$	−6.00000			−0.762001
$63$	1.50000	+	7.79423i	0.188982	+	0.981981i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$		−	6.92820i		−	0.822226i	−0.911584	−	0.411113i	$-0.865140\pi$
$71$		−	6.92820i		−	0.822226i	0.911584	−	0.411113i	$-0.134860\pi$
$72$	4.50000	−	2.59808i	0.530330	−	0.306186i
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	−0.665180	−	0.746683i	$-0.731645\pi$
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	0.314057	+	0.949404i	$0.398312\pi$
$74$	6.00000	−	3.46410i	0.697486	−	0.402694i
$75$		0			0
$76$		−	6.92820i		−	0.794719i
$77$	−9.00000	+	1.73205i	−1.02565	+	0.197386i
$78$	9.00000	−	5.19615i	1.01905	−	0.588348i
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−4.50000	−	2.59808i	−0.496942	−	0.286910i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	−1.50000	+	4.33013i	−0.163663	+	0.472456i
$85$		0			0
$86$	−1.50000	−	0.866025i	−0.161749	−	0.0933859i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$	3.00000	−	8.66025i	0.314485	−	0.907841i
$92$		−	1.73205i		−	0.180579i
$93$	−6.00000			−0.622171
$94$		0			0
$95$		0			0
$96$	9.00000			0.918559
$97$			10.3923i			1.05518i	0.849500	+	0.527589i	$0.176904\pi$
$97$			10.3923i			1.05518i	−0.849500	+	0.527589i	$0.823096\pi$
$98$	4.50000	+	11.2583i	0.454569	+	1.13726i
$99$	−9.00000	−	5.19615i	−0.904534	−	0.522233i
$100$		0			0
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$	−9.00000	+	15.5885i	−0.891133	+	1.54349i
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	0.705038	−	0.709170i	$-0.250930\pi$
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	−0.261640	+	0.965166i	$0.584263\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$		0			0
$107$	−4.50000	−	2.59808i	−0.435031	−	0.251166i	0.266456	−	0.963847i	$-0.414147\pi$
$107$	−4.50000	−	2.59808i	−0.435031	−	0.251166i	−0.701488	+	0.712681i	$0.747481\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$		0			0
$111$	6.00000	−	3.46410i	0.569495	−	0.328798i
$112$	10.0000	−	8.66025i	0.944911	−	0.818317i
$113$			6.92820i			0.651751i	0.945413	+	0.325875i	$0.105659\pi$
$113$			6.92820i			0.651751i	−0.945413	+	0.325875i	$0.894341\pi$
$114$		−	20.7846i		−	1.94666i
$115$		0			0
$116$	1.50000	−	0.866025i	0.139272	−	0.0804084i
$117$	9.00000	−	5.19615i	0.832050	−	0.480384i
$118$		0			0
$119$	3.00000	+	15.5885i	0.275010	+	1.42899i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−4.50000	−	7.79423i	−0.407411	−	0.705656i
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$	−3.00000	−	1.73205i	−0.269408	−	0.155543i
$125$		0			0
$126$	−4.50000	+	12.9904i	−0.400892	+	1.15728i
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−3.00000	−	5.19615i	−0.261116	−	0.452267i
$133$	−12.0000	−	13.8564i	−1.04053	−	1.20150i
$134$		−	22.5167i		−	1.94514i
$135$		0			0
$136$	9.00000	−	5.19615i	0.771744	−	0.445566i
$137$	18.0000	−	10.3923i	1.53784	−	0.887875i	0.538879	−	0.842383i	$-0.318848\pi$
$137$	18.0000	−	10.3923i	1.53784	−	0.887875i	0.998965	−	0.0454914i	$-0.0144854\pi$
$138$		−	5.19615i		−	0.442326i
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	6.00000	+	10.3923i	0.501745	+	0.869048i
$144$	15.0000			1.25000
$145$		0			0
$146$	−6.00000			−0.496564
$147$	4.50000	+	11.2583i	0.371154	+	0.928571i
$148$	4.00000			0.328798
$149$	−19.5000	−	11.2583i	−1.59750	−	0.922318i	−0.991967	−	0.126500i	$-0.959626\pi$
$149$	−19.5000	−	11.2583i	−1.59750	−	0.922318i	−0.605536	−	0.795818i	$-0.707041\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$	−9.00000	+	15.5885i	−0.727607	+	1.26025i
$154$	−15.0000	−	5.19615i	−1.20873	−	0.418718i
$155$		0			0
$156$	6.00000			0.480384
$157$	3.00000	−	1.73205i	0.239426	−	0.138233i	−0.375487	−	0.926828i	$-0.622524\pi$
$157$	3.00000	−	1.73205i	0.239426	−	0.138233i	0.614913	+	0.788595i	$0.289191\pi$
$158$	24.0000	−	13.8564i	1.90934	−	1.10236i
$159$		0			0
$160$		0			0
$161$	−3.00000	−	3.46410i	−0.236433	−	0.273009i
$162$	−13.5000	+	7.79423i	−1.06066	+	0.612372i
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	13.5000	+	7.79423i	1.04780	+	0.604949i
$167$	−21.0000			−1.62503			−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000			−1.62503			−0.812514	+	0.582941i	$0.801902\pi$
$168$	6.00000	−	5.19615i	0.462910	−	0.400892i
$169$	1.00000			0.0769231
$170$		0			0
$171$		−	20.7846i		−	1.58944i
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	4.50000	−	2.59808i	0.341144	−	0.196960i
$175$		0			0
$176$			17.3205i			1.30558i
$177$		0			0
$178$	−4.50000	+	2.59808i	−0.337289	+	0.194734i
$179$	−9.00000	+	5.19615i	−0.672692	+	0.388379i	−0.797096	−	0.603853i	$-0.793631\pi$
$179$	−9.00000	+	5.19615i	−0.672692	+	0.388379i	0.124404	+	0.992232i	$0.460298\pi$
$180$		0			0
$181$			5.19615i			0.386227i	0.981176	+	0.193113i	$0.0618586\pi$
$181$			5.19615i			0.386227i	−0.981176	+	0.193113i	$0.938141\pi$
$182$	12.0000	−	10.3923i	0.889499	−	0.770329i
$183$	−4.50000	−	7.79423i	−0.332650	−	0.576166i
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$		0			0
$186$	−9.00000	−	5.19615i	−0.659912	−	0.381000i
$187$	−18.0000	−	10.3923i	−1.31629	−	0.759961i
$188$		0			0
$189$	−4.50000	+	12.9904i	−0.327327	+	0.944911i
$190$		0			0
$191$	9.00000	+	5.19615i	0.651217	+	0.375980i	0.788922	−	0.614493i	$-0.210639\pi$
$191$	9.00000	+	5.19615i	0.651217	+	0.375980i	−0.137705	+	0.990473i	$0.543973\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	0.924853	+	0.380325i	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$	−9.00000	+	15.5885i	−0.646162	+	1.11919i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			3.46410i			0.246807i	0.992357	+	0.123404i	$0.0393809\pi$
$197$			3.46410i			0.246807i	−0.992357	+	0.123404i	$0.960619\pi$
$198$	−9.00000	−	15.5885i	−0.639602	−	1.10782i
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	−0.272026	−	0.962290i	$-0.587694\pi$
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	0.697355	+	0.716726i	$0.254360\pi$
$200$		0			0
$201$		−	22.5167i		−	1.58820i
$202$			25.9808i			1.82800i
$203$	1.50000	−	4.33013i	0.105279	−	0.303915i
$204$	−9.00000	+	5.19615i	−0.630126	+	0.363803i
$205$		0			0
$206$	4.50000	+	7.79423i	0.313530	+	0.543050i
$207$		−	5.19615i		−	0.361158i
$208$	−15.0000	−	8.66025i	−1.04006	−	0.600481i
$209$	24.0000			1.66011
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$	6.00000	−	10.3923i	0.411113	−	0.712069i
$214$	−4.50000	−	7.79423i	−0.307614	−	0.532803i
$215$		0			0
$216$	9.00000			0.612372
$217$	−9.00000	+	1.73205i	−0.610960	+	0.117579i
$218$			8.66025i			0.586546i
$219$	−6.00000			−0.405442
$220$		0			0
$221$	18.0000	−	10.3923i	1.21081	−	0.699062i
$222$	12.0000			0.805387
$223$			3.46410i			0.231973i	0.993251	+	0.115987i	$0.0370030\pi$
$223$			3.46410i			0.231973i	−0.993251	+	0.115987i	$0.962997\pi$
$224$	13.5000	−	2.59808i	0.902007	−	0.173591i
$225$		0			0
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$	6.00000	−	10.3923i	0.397360	−	0.688247i
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$		0			0
$231$	−15.0000	−	5.19615i	−0.986928	−	0.341882i
$232$	−3.00000			−0.196960
$233$	−3.00000	−	1.73205i	−0.196537	−	0.113470i	0.398502	−	0.917167i	$-0.369530\pi$
$233$	−3.00000	−	1.73205i	−0.196537	−	0.113470i	−0.595039	+	0.803697i	$0.702863\pi$
$234$	18.0000			1.17670
$235$		0			0
$236$		0			0
$237$	24.0000	−	13.8564i	1.55897	−	0.900070i
$238$	−9.00000	+	25.9808i	−0.583383	+	1.68408i
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	−6.00000	+	3.46410i	−0.386494	+	0.223142i	−0.680640	−	0.732618i	$-0.738298\pi$
$241$	−6.00000	+	3.46410i	−0.386494	+	0.223142i	0.294146	+	0.955761i	$0.404965\pi$
$242$	1.50000	−	0.866025i	0.0964237	−	0.0556702i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		−	5.19615i		−	0.332650i
$245$		0			0
$246$	−4.50000	−	7.79423i	−0.286910	−	0.496942i
$247$	−12.0000	+	20.7846i	−0.763542	+	1.32249i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$	13.5000	+	7.79423i	0.855528	+	0.493939i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	−6.00000	+	5.19615i	−0.377964	+	0.327327i
$253$	6.00000			0.377217
$254$	24.0000	+	13.8564i	1.50589	+	0.869428i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$	−1.50000	−	2.59808i	−0.0933859	−	0.161749i
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$		0			0
$261$	4.50000	−	2.59808i	0.278543	−	0.160817i
$262$	−18.0000	+	10.3923i	−1.11204	+	0.642039i
$263$	−1.50000	+	0.866025i	−0.0924940	+	0.0534014i	−0.545534	−	0.838089i	$-0.683673\pi$
$263$	−1.50000	+	0.866025i	−0.0924940	+	0.0534014i	0.453040	+	0.891490i	$0.350340\pi$
$264$			10.3923i			0.639602i
$265$		0			0
$266$	−6.00000	−	31.1769i	−0.367884	−	1.91158i
$267$	−4.50000	+	2.59808i	−0.275396	+	0.159000i
$268$	6.50000	−	11.2583i	0.397051	−	0.687712i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	6.00000	+	3.46410i	0.364474	+	0.210429i	0.671042	−	0.741420i	$-0.265847\pi$
$271$	6.00000	+	3.46410i	0.364474	+	0.210429i	−0.306568	+	0.951849i	$0.599181\pi$
$272$	30.0000			1.81902
$273$	12.0000	−	10.3923i	0.726273	−	0.628971i
$274$	36.0000			2.17484
$275$		0			0
$276$	1.50000	−	2.59808i	0.0902894	−	0.156386i
$277$	13.0000	+	22.5167i	0.781094	+	1.35290i	0.931305	+	0.364241i	$0.118672\pi$
$277$	13.0000	+	22.5167i	0.781094	+	1.35290i	−0.150210	+	0.988654i	$0.547995\pi$
$278$	−9.00000	+	15.5885i	−0.539784	+	0.934934i
$279$	−9.00000	−	5.19615i	−0.538816	−	0.311086i
$280$		0			0
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$		0			0
$283$	27.0000	−	15.5885i	1.60498	−	0.926638i	0.614514	−	0.788906i	$-0.289352\pi$
$283$	27.0000	−	15.5885i	1.60498	−	0.926638i	0.990470	−	0.137732i	$-0.0439811\pi$
$284$	6.00000	−	3.46410i	0.356034	−	0.205557i
$285$		0			0
$286$			20.7846i			1.22902i
$287$	−7.50000	−	2.59808i	−0.442711	−	0.153360i
$288$	13.5000	+	7.79423i	0.795495	+	0.459279i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−9.00000	+	15.5885i	−0.527589	+	0.913812i
$292$	−3.00000	−	1.73205i	−0.175562	−	0.101361i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$	−3.00000	+	20.7846i	−0.174964	+	1.21218i
$295$		0			0
$296$	−6.00000	−	3.46410i	−0.348743	−	0.201347i
$297$	−9.00000	−	15.5885i	−0.522233	−	0.904534i
$298$	−19.5000	−	33.7750i	−1.12960	−	1.95653i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	−2.50000	−	0.866025i	−0.144098	−	0.0499169i
$302$			3.46410i			0.199337i
$303$			25.9808i			1.49256i
$304$	−30.0000	+	17.3205i	−1.72062	+	0.993399i
$305$		0			0
$306$	−27.0000	+	15.5885i	−1.54349	+	0.891133i
$307$		−	22.5167i		−	1.28509i	−0.766246	−	0.642547i	$-0.777878\pi$
$307$		−	22.5167i		−	1.28509i	0.766246	−	0.642547i	$-0.222122\pi$
$308$	−6.00000	−	6.92820i	−0.341882	−	0.394771i
$309$	4.50000	+	7.79423i	0.255996	+	0.443398i
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$	−9.00000	−	5.19615i	−0.509525	−	0.294174i
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	6.00000			0.338600
$315$		0			0
$316$	16.0000			0.900070
$317$	15.0000	+	8.66025i	0.842484	+	0.486408i	0.858108	−	0.513470i	$-0.171640\pi$
$317$	15.0000	+	8.66025i	0.842484	+	0.486408i	−0.0156238	+	0.999878i	$0.504973\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	−4.50000	−	7.79423i	−0.251166	−	0.435031i
$322$	−1.50000	−	7.79423i	−0.0835917	−	0.434355i
$323$		−	41.5692i		−	2.31297i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	12.0000	−	6.92820i	0.664619	−	0.383718i
$327$			8.66025i			0.478913i
$328$			5.19615i			0.286910i
$329$		0			0
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$	12.0000			0.657596
$334$	−31.5000	−	18.1865i	−1.72360	−	0.995123i
$335$		0			0
$336$	22.5000	−	4.33013i	1.22748	−	0.236228i
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$	1.50000	+	0.866025i	0.0815892	+	0.0471056i
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	18.0000	−	31.1769i	0.973329	−	1.68585i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$			1.73205i			0.0933859i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	−16.5000	+	9.52628i	−0.885766	+	0.511397i	−0.872555	−	0.488515i	$-0.837539\pi$
$347$	−16.5000	+	9.52628i	−0.885766	+	0.511397i	−0.0132111	+	0.999913i	$0.504205\pi$
$348$	3.00000			0.160817
$349$		−	8.66025i		−	0.463573i	−0.972767	−	0.231786i	$-0.925543\pi$
$349$		−	8.66025i		−	0.463573i	0.972767	−	0.231786i	$-0.0744570\pi$
$350$		0			0
$351$	18.0000			0.960769
$352$	−9.00000	+	15.5885i	−0.479702	+	0.830868i
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$	−3.00000			−0.159000
$357$	−9.00000	+	25.9808i	−0.476331	+	1.37505i
$358$	−18.0000			−0.951330
$359$	−21.0000	−	12.1244i	−1.10834	−	0.639899i	−0.169939	−	0.985455i	$-0.554357\pi$
$359$	−21.0000	−	12.1244i	−1.10834	−	0.639899i	−0.938398	+	0.345556i	$0.887690\pi$
$360$		0			0
$361$	14.5000	+	25.1147i	0.763158	+	1.32183i
$362$	−4.50000	+	7.79423i	−0.236515	+	0.409656i
$363$	1.50000	−	0.866025i	0.0787296	−	0.0454545i
$364$	9.00000	−	1.73205i	0.471728	−	0.0907841i
$365$		0			0
$366$		−	15.5885i		−	0.814822i
$367$	−13.5000	+	7.79423i	−0.704694	+	0.406855i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	−13.5000	+	7.79423i	−0.704694	+	0.406855i	0.104399	+	0.994535i	$0.466708\pi$
$368$	−7.50000	+	4.33013i	−0.390965	+	0.225723i
$369$	−4.50000	−	7.79423i	−0.234261	−	0.405751i
$370$		0			0
$371$		0			0
$372$	−3.00000	−	5.19615i	−0.155543	−	0.269408i
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$	−18.0000	−	31.1769i	−0.930758	−	1.61212i
$375$		0			0
$376$		0			0
$377$	−6.00000			−0.309016
$378$	−18.0000	+	15.5885i	−0.925820	+	0.801784i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$	24.0000	+	13.8564i	1.22956	+	0.709885i
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	−10.5000	−	18.1865i	−0.535826	−	0.928078i
$385$		0			0
$386$			38.1051i			1.93950i
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	−9.00000	+	5.19615i	−0.456906	+	0.263795i
$389$	24.0000	−	13.8564i	1.21685	−	0.702548i	0.252606	−	0.967569i	$-0.418712\pi$
$389$	24.0000	−	13.8564i	1.21685	−	0.702548i	0.964242	+	0.265022i	$0.0853791\pi$
$390$		0			0
$391$		−	10.3923i		−	0.525561i
$392$	7.50000	−	9.52628i	0.378807	−	0.481150i
$393$	−18.0000	+	10.3923i	−0.907980	+	0.524222i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$		0			0
$396$		−	10.3923i		−	0.522233i
$397$	21.0000	+	12.1244i	1.05396	+	0.608504i	0.923755	−	0.382983i	$-0.125103\pi$
$397$	21.0000	+	12.1244i	1.05396	+	0.608504i	0.130204	+	0.991487i	$0.458437\pi$
$398$	12.0000			0.601506
$399$	−6.00000	−	31.1769i	−0.300376	−	1.56080i
$400$		0			0
$401$	−16.5000	−	9.52628i	−0.823971	−	0.475720i	0.0278131	−	0.999613i	$-0.491146\pi$
$401$	−16.5000	−	9.52628i	−0.823971	−	0.475720i	−0.851784	+	0.523893i	$0.824479\pi$
$402$	19.5000	−	33.7750i	0.972572	−	1.68454i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	−7.50000	+	12.9904i	−0.373139	+	0.646296i
$405$		0			0
$406$	6.00000	−	5.19615i	0.297775	−	0.257881i
$407$			13.8564i			0.686837i
$408$	18.0000			0.891133
$409$	19.5000	−	11.2583i	0.964213	−	0.556689i	0.0667458	−	0.997770i	$-0.478738\pi$
$409$	19.5000	−	11.2583i	0.964213	−	0.556689i	0.897467	+	0.441081i	$0.145405\pi$
$410$		0			0
$411$	36.0000			1.77575
$412$			5.19615i			0.255996i
$413$		0			0
$414$	4.50000	−	7.79423i	0.221163	−	0.383065i
$415$		0			0
$416$	−9.00000	−	15.5885i	−0.441261	−	0.764287i
$417$	−9.00000	+	15.5885i	−0.440732	+	0.763370i
$418$	36.0000	+	20.7846i	1.76082	+	1.01661i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$	−30.0000	−	17.3205i	−1.46038	−	0.843149i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	18.0000	−	10.3923i	0.872103	−	0.503509i
$427$	−9.00000	−	10.3923i	−0.435541	−	0.502919i
$428$		−	5.19615i		−	0.251166i
$429$			20.7846i			1.00349i
$430$		0			0
$431$	9.00000	−	5.19615i	0.433515	−	0.250290i	−0.267328	−	0.963606i	$-0.586141\pi$
$431$	9.00000	−	5.19615i	0.433515	−	0.250290i	0.700843	+	0.713316i	$0.252807\pi$
$432$	22.5000	+	12.9904i	1.08253	+	0.625000i
$433$		−	13.8564i		−	0.665896i	−0.942945	−	0.332948i	$-0.891957\pi$
$433$		−	13.8564i		−	0.665896i	0.942945	−	0.332948i	$-0.108043\pi$
$434$	−15.0000	−	5.19615i	−0.720023	−	0.249423i
$435$		0			0
$436$	−2.50000	+	4.33013i	−0.119728	+	0.207375i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$	−9.00000	−	5.19615i	−0.430037	−	0.248282i
$439$	−6.00000	−	3.46410i	−0.286364	−	0.165333i	0.349937	−	0.936773i	$-0.386203\pi$
$439$	−6.00000	−	3.46410i	−0.286364	−	0.165333i	−0.636301	+	0.771441i	$0.719536\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$	36.0000			1.71235
$443$	−13.5000	−	7.79423i	−0.641404	−	0.370315i	0.143751	−	0.989614i	$-0.454084\pi$
$443$	−13.5000	−	7.79423i	−0.641404	−	0.370315i	−0.785155	+	0.619299i	$0.787417\pi$
$444$	6.00000	+	3.46410i	0.284747	+	0.164399i
$445$		0			0
$446$	−3.00000	+	5.19615i	−0.142054	+	0.246045i
$447$	−19.5000	−	33.7750i	−0.922318	−	1.59750i
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$			12.1244i			0.572184i	0.958202	+	0.286092i	$0.0923563\pi$
$449$			12.1244i			0.572184i	−0.958202	+	0.286092i	$0.907644\pi$
$450$		0			0
$451$	9.00000	−	5.19615i	0.423793	−	0.244677i
$452$	−6.00000	+	3.46410i	−0.282216	+	0.162938i
$453$			3.46410i			0.162758i
$454$			20.7846i			0.975470i
$455$		0			0
$456$	−18.0000	+	10.3923i	−0.842927	+	0.486664i
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$		0			0
$459$	−27.0000	+	15.5885i	−1.26025	+	0.727607i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$	−18.0000	−	20.7846i	−0.837436	−	0.966988i
$463$	−29.0000			−1.34774			−0.673872	−	0.738848i	$-0.735370\pi$
$463$	−29.0000			−1.34774			−0.673872	+	0.738848i	$0.735370\pi$
$464$	−7.50000	−	4.33013i	−0.348179	−	0.201021i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	10.5000	−	18.1865i	0.485882	−	0.841572i	−0.513986	−	0.857798i	$-0.671832\pi$
$467$	10.5000	−	18.1865i	0.485882	−	0.841572i	0.999868	+	0.0162260i	$0.00516512\pi$
$468$	9.00000	+	5.19615i	0.416025	+	0.240192i
$469$	−6.50000	−	33.7750i	−0.300142	−	1.55958i
$470$		0			0
$471$	6.00000			0.276465
$472$		0			0
$473$	3.00000	−	1.73205i	0.137940	−	0.0796398i
$474$	48.0000			2.20471
$475$		0			0
$476$	−12.0000	+	10.3923i	−0.550019	+	0.476331i
$477$		0			0
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$		0			0
$481$	−12.0000	−	6.92820i	−0.547153	−	0.315899i
$482$	−12.0000			−0.546585
$483$	−1.50000	−	7.79423i	−0.0682524	−	0.354650i
$484$	1.00000			0.0454545
$485$		0			0
$486$	−27.0000			−1.22474
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$	−4.50000	+	7.79423i	−0.203705	+	0.352828i
$489$	12.0000	−	6.92820i	0.542659	−	0.313304i
$490$		0			0
$491$		−	38.1051i		−	1.71966i	−0.510581	−	0.859830i	$-0.670569\pi$
$491$		−	38.1051i		−	1.71966i	0.510581	−	0.859830i	$-0.329431\pi$
$492$		−	5.19615i		−	0.234261i
$493$	9.00000	−	5.19615i	0.405340	−	0.234023i
$494$	−36.0000	+	20.7846i	−1.61972	+	0.935144i
$495$		0			0
$496$			17.3205i			0.777714i
$497$	6.00000	−	17.3205i	0.269137	−	0.776931i
$498$	13.5000	+	23.3827i	0.604949	+	1.04780i
$499$	7.00000	−	12.1244i	0.313363	−	0.542761i	−0.665725	−	0.746197i	$-0.731878\pi$
$499$	7.00000	−	12.1244i	0.313363	−	0.542761i	0.979088	+	0.203436i	$0.0652110\pi$
$500$		0			0
$501$	−31.5000	−	18.1865i	−1.40732	−	0.812514i
$502$	−27.0000	−	15.5885i	−1.20507	−	0.695747i
$503$	15.0000			0.668817			0.334408	−	0.942428i	$-0.391463\pi$
$503$	15.0000			0.668817			0.334408	+	0.942428i	$0.391463\pi$
$504$	13.5000	−	2.59808i	0.601338	−	0.115728i
$505$		0			0
$506$	9.00000	+	5.19615i	0.400099	+	0.230997i
$507$	1.50000	+	0.866025i	0.0666173	+	0.0384615i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	22.5000	−	38.9711i	0.997295	−	1.72737i	0.434992	−	0.900434i	$-0.356751\pi$
$509$	22.5000	−	38.9711i	0.997295	−	1.72737i	0.562303	−	0.826931i	$-0.309915\pi$
$510$		0			0
$511$	−9.00000	+	1.73205i	−0.398137	+	0.0766214i
$512$		−	8.66025i		−	0.382733i
$513$	18.0000	−	31.1769i	0.794719	−	1.37649i
$514$		0			0
$515$		0			0
$516$		−	1.73205i		−	0.0762493i
$517$		0			0
$518$	18.0000	−	3.46410i	0.790875	−	0.152204i
$519$	−18.0000	+	10.3923i	−0.790112	+	0.456172i
$520$		0			0
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$	9.00000			0.393919
$523$	−21.0000	−	12.1244i	−0.918266	−	0.530161i	−0.0351845	−	0.999381i	$-0.511202\pi$
$523$	−21.0000	−	12.1244i	−0.918266	−	0.530161i	−0.883081	+	0.469220i	$0.844535\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−3.00000			−0.130806
$527$	−18.0000	−	10.3923i	−0.784092	−	0.452696i
$528$	−15.0000	+	25.9808i	−0.652791	+	1.13067i
$529$	−10.0000	−	17.3205i	−0.434783	−	0.753066i
$530$		0			0
$531$		0			0
$532$	6.00000	−	17.3205i	0.260133	−	0.750939i
$533$			10.3923i			0.450141i
$534$	−9.00000			−0.389468
$535$		0			0
$536$	−19.5000	+	11.2583i	−0.842272	+	0.486286i
$537$	−18.0000			−0.776757
$538$			5.19615i			0.224022i
$539$	−24.0000	−	3.46410i	−1.03375	−	0.149209i
$540$		0			0
$541$	−14.5000	+	25.1147i	−0.623404	+	1.07977i	0.365444	+	0.930834i	$0.380917\pi$
$541$	−14.5000	+	25.1147i	−0.623404	+	1.07977i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	6.00000	+	10.3923i	0.257722	+	0.446388i
$543$	−4.50000	+	7.79423i	−0.193113	+	0.334482i
$544$	27.0000	+	15.5885i	1.15762	+	0.668350i
$545$		0			0
$546$	27.0000	−	5.19615i	1.15549	−	0.222375i
$547$	1.00000			0.0427569			0.0213785	−	0.999771i	$-0.493195\pi$
$547$	1.00000			0.0427569			0.0213785	+	0.999771i	$0.493195\pi$
$548$	18.0000	+	10.3923i	0.768922	+	0.443937i
$549$		−	15.5885i		−	0.665299i
$550$		0			0
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$	−4.50000	+	2.59808i	−0.191533	+	0.110581i
$553$	32.0000	−	27.7128i	1.36078	−	1.17847i
$554$			45.0333i			1.91328i
$555$		0			0
$556$	−9.00000	+	5.19615i	−0.381685	+	0.220366i
$557$	15.0000	−	8.66025i	0.635570	−	0.366947i	−0.147336	−	0.989087i	$-0.547070\pi$
$557$	15.0000	−	8.66025i	0.635570	−	0.366947i	0.782906	+	0.622140i	$0.213736\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$			3.46410i			0.146516i
$560$		0			0
$561$	−18.0000	−	31.1769i	−0.759961	−	1.31629i
$562$	6.00000	−	10.3923i	0.253095	−	0.438373i
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$		0			0
$565$		0			0
$566$	54.0000			2.26979
$567$	−18.0000	+	15.5885i	−0.755929	+	0.654654i
$568$	−12.0000			−0.503509
$569$	6.00000	+	3.46410i	0.251533	+	0.145223i	0.620466	−	0.784233i	$-0.286943\pi$
$569$	6.00000	+	3.46410i	0.251533	+	0.145223i	−0.368933	+	0.929456i	$0.620277\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$	9.00000	+	15.5885i	0.375980	+	0.651217i
$574$	−9.00000	−	10.3923i	−0.375653	−	0.433766i
$575$		0			0
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	−21.0000	+	12.1244i	−0.874241	+	0.504744i	−0.868755	−	0.495241i	$-0.835080\pi$
$577$	−21.0000	+	12.1244i	−0.874241	+	0.504744i	−0.00548605	+	0.999985i	$0.501746\pi$
$578$	−28.5000	+	16.4545i	−1.18544	+	0.684416i
$579$			38.1051i			1.58359i
$580$		0			0
$581$	22.5000	+	7.79423i	0.933457	+	0.323359i
$582$	−27.0000	+	15.5885i	−1.11919	+	0.646162i
$583$		0			0
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$		0			0
$586$	−36.0000	−	20.7846i	−1.48715	−	0.858604i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$	−7.50000	+	9.52628i	−0.309295	+	0.392857i
$589$	24.0000			0.988903
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	−10.0000	−	17.3205i	−0.410997	−	0.711868i
$593$	24.0000	−	41.5692i	0.985562	−	1.70704i	0.346149	−	0.938179i	$-0.387489\pi$
$593$	24.0000	−	41.5692i	0.985562	−	1.70704i	0.639413	−	0.768864i	$-0.279178\pi$
$594$		−	31.1769i		−	1.27920i
$595$		0			0
$596$		−	22.5167i		−	0.922318i
$597$	12.0000			0.491127
$598$	−9.00000	+	5.19615i	−0.368037	+	0.212486i
$599$	−12.0000	+	6.92820i	−0.490307	+	0.283079i	−0.724702	−	0.689063i	$-0.758022\pi$
$599$	−12.0000	+	6.92820i	−0.490307	+	0.283079i	0.234395	+	0.972141i	$0.424689\pi$
$600$		0			0
$601$		−	20.7846i		−	0.847822i	−0.905704	−	0.423911i	$-0.860657\pi$
$601$		−	20.7846i		−	0.847822i	0.905704	−	0.423911i	$-0.139343\pi$
$602$	−3.00000	−	3.46410i	−0.122271	−	0.141186i
$603$	19.5000	−	33.7750i	0.794101	−	1.37542i
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$		0			0
$606$	−22.5000	+	38.9711i	−0.914000	+	1.58309i
$607$	1.50000	+	0.866025i	0.0608831	+	0.0351509i	0.530133	−	0.847915i	$-0.322142\pi$
$607$	1.50000	+	0.866025i	0.0608831	+	0.0351509i	−0.469249	+	0.883066i	$0.655475\pi$
$608$	−36.0000			−1.45999
$609$	6.00000	−	5.19615i	0.243132	−	0.210559i
$610$		0			0
$611$		0			0
$612$	−18.0000			−0.727607
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	19.5000	−	33.7750i	0.786956	−	1.36305i
$615$		0			0
$616$	3.00000	+	15.5885i	0.120873	+	0.628077i
$617$		−	34.6410i		−	1.39459i	−0.716782	−	0.697297i	$-0.754386\pi$
$617$		−	34.6410i		−	1.39459i	0.716782	−	0.697297i	$-0.245614\pi$
$618$			15.5885i			0.627060i
$619$	−21.0000	+	12.1244i	−0.844061	+	0.487319i	−0.858643	−	0.512575i	$-0.828692\pi$
$619$	−21.0000	+	12.1244i	−0.844061	+	0.487319i	0.0145814	+	0.999894i	$0.495358\pi$
$620$		0			0
$621$	4.50000	−	7.79423i	0.180579	−	0.312772i
$622$			41.5692i			1.66677i
$623$	−6.00000	+	5.19615i	−0.240385	+	0.208179i
$624$	−15.0000	−	25.9808i	−0.600481	−	1.04006i
$625$		0			0
$626$		0			0
$627$	36.0000	+	20.7846i	1.43770	+	0.830057i
$628$	3.00000	+	1.73205i	0.119713	+	0.0691164i
$629$	24.0000			0.956943
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−24.0000	−	13.8564i	−0.954669	−	0.551178i
$633$	−30.0000	−	17.3205i	−1.19239	−	0.688428i
$634$	15.0000	+	25.9808i	0.595726	+	1.03183i
$635$		0			0
$636$		0			0
$637$	15.0000	−	19.0526i	0.594322	−	0.754890i
$638$			10.3923i			0.411435i
$639$	18.0000	−	10.3923i	0.712069	−	0.411113i
$640$		0			0
$641$	10.5000	−	6.06218i	0.414725	−	0.239442i	−0.278093	−	0.960554i	$-0.589702\pi$
$641$	10.5000	−	6.06218i	0.414725	−	0.239442i	0.692818	+	0.721113i	$0.256369\pi$
$642$		−	15.5885i		−	0.615227i
$643$		−	17.3205i		−	0.683054i	−0.939872	−	0.341527i	$-0.889056\pi$
$643$		−	17.3205i		−	0.683054i	0.939872	−	0.341527i	$-0.110944\pi$
$644$	1.50000	−	4.33013i	0.0591083	−	0.170631i
$645$		0			0
$646$	36.0000	−	62.3538i	1.41640	−	2.45328i
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	0.894004	−	0.448059i	$-0.147885\pi$
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	−0.835033	+	0.550200i	$0.814551\pi$
$648$	13.5000	+	7.79423i	0.530330	+	0.306186i
$649$		0			0
$650$		0			0
$651$	−15.0000	−	5.19615i	−0.587896	−	0.203653i
$652$	8.00000			0.313304
$653$	27.0000	+	15.5885i	1.05659	+	0.610023i	0.924487	−	0.381212i	$-0.124493\pi$
$653$	27.0000	+	15.5885i	1.05659	+	0.610023i	0.132104	+	0.991236i	$0.457827\pi$
$654$	−7.50000	+	12.9904i	−0.293273	+	0.507964i
$655$		0			0
$656$	−7.50000	+	12.9904i	−0.292826	+	0.507189i
$657$	−9.00000	−	5.19615i	−0.351123	−	0.202721i
$658$		0			0
$659$		−	41.5692i		−	1.61931i	−0.586908	−	0.809653i	$-0.699655\pi$
$659$		−	41.5692i		−	1.61931i	0.586908	−	0.809653i	$-0.300345\pi$
$660$		0			0
$661$	28.5000	−	16.4545i	1.10852	−	0.640005i	0.170075	−	0.985431i	$-0.445599\pi$
$661$	28.5000	−	16.4545i	1.10852	−	0.640005i	0.938446	+	0.345426i	$0.112266\pi$
$662$	−15.0000	+	8.66025i	−0.582992	+	0.336590i
$663$	36.0000			1.39812
$664$		−	15.5885i		−	0.604949i
$665$		0			0
$666$	18.0000	+	10.3923i	0.697486	+	0.402694i
$667$	−1.50000	+	2.59808i	−0.0580802	+	0.100598i
$668$	−10.5000	−	18.1865i	−0.406257	−	0.703658i
$669$	−3.00000	+	5.19615i	−0.115987	+	0.200895i
$670$		0			0
$671$	18.0000			0.694882
$672$	22.5000	+	7.79423i	0.867956	+	0.300669i
$673$	−4.00000			−0.154189			−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000			−0.154189			−0.0770943	+	0.997024i	$0.524564\pi$
$674$	48.0000	+	27.7128i	1.84889	+	1.06746i
$675$		0			0
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	−18.0000	+	10.3923i	−0.691286	+	0.399114i
$679$	−9.00000	+	25.9808i	−0.345388	+	0.997050i
$680$		0			0
$681$			20.7846i			0.796468i
$682$	18.0000	−	10.3923i	0.689256	−	0.397942i
$683$	−34.5000	+	19.9186i	−1.32011	+	0.762163i	−0.983745	−	0.179570i	$-0.942529\pi$
$683$	−34.5000	+	19.9186i	−1.32011	+	0.762163i	−0.336361	+	0.941733i	$0.609196\pi$
$684$	18.0000	−	10.3923i	0.688247	−	0.397360i
$685$		0			0
$686$	1.50000	+	32.0429i	0.0572703	+	1.22341i
$687$		0			0
$688$	−2.50000	+	4.33013i	−0.0953116	+	0.165085i
$689$		0			0
$690$		0			0
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$	−12.0000			−0.456172
$693$	−18.0000	−	20.7846i	−0.683763	−	0.789542i
$694$	−33.0000			−1.25266
$695$		0			0
$696$	−4.50000	−	2.59808i	−0.170572	−	0.0984798i
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$	7.50000	−	12.9904i	0.283879	−	0.491693i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$		0			0
$701$			25.9808i			0.981280i	0.871362	+	0.490640i	$0.163237\pi$
$701$			25.9808i			0.981280i	−0.871362	+	0.490640i	$0.836763\pi$
$702$	27.0000	+	15.5885i	1.01905	+	0.588348i
$703$	−24.0000	+	13.8564i	−0.905177	+	0.522604i
$704$	3.00000	−	1.73205i	0.113067	−	0.0652791i
$705$		0			0
$706$		0			0
$707$	7.50000	+	38.9711i	0.282067	+	1.46566i
$708$		0			0
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	−0.987421	−	0.158114i	$-0.949459\pi$
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	0.630641	+	0.776075i	$0.282792\pi$
$710$		0			0
$711$	48.0000			1.80014
$712$	4.50000	+	2.59808i	0.168645	+	0.0973670i
$713$	6.00000			0.224702
$714$	−36.0000	+	31.1769i	−1.34727	+	1.16677i
$715$		0			0
$716$	−9.00000	−	5.19615i	−0.336346	−	0.194189i
$717$	−9.00000	+	15.5885i	−0.336111	+	0.582162i
$718$	−21.0000	−	36.3731i	−0.783713	−	1.35743i
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	9.00000	+	10.3923i	0.335178	+	0.387030i
$722$			50.2295i			1.86935i
$723$	−12.0000			−0.446285
$724$	−4.50000	+	2.59808i	−0.167241	+	0.0965567i
$725$		0			0
$726$	3.00000			0.111340
$727$			5.19615i			0.192715i	0.995347	+	0.0963573i	$0.0307191\pi$
$727$			5.19615i			0.192715i	−0.995347	+	0.0963573i	$0.969281\pi$
$728$	−15.0000	−	5.19615i	−0.555937	−	0.192582i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$	4.50000	−	7.79423i	0.166325	−	0.288083i
$733$	15.0000	+	8.66025i	0.554038	+	0.319874i	0.750749	−	0.660588i	$-0.229693\pi$
$733$	15.0000	+	8.66025i	0.554038	+	0.319874i	−0.196711	+	0.980461i	$0.563026\pi$
$734$	−27.0000			−0.996588
$735$		0			0
$736$	−9.00000			−0.331744
$737$	39.0000	+	22.5167i	1.43658	+	0.829412i
$738$		−	15.5885i		−	0.573819i
$739$	−19.0000	−	32.9090i	−0.698926	−	1.21058i	−0.968839	−	0.247691i	$-0.920328\pi$
$739$	−19.0000	−	32.9090i	−0.698926	−	1.21058i	0.269913	−	0.962885i	$-0.413005\pi$
$740$		0			0
$741$	−36.0000	+	20.7846i	−1.32249	+	0.763542i
$742$		0			0
$743$			46.7654i			1.71566i	0.513938	+	0.857828i	$0.328186\pi$
$743$			46.7654i			1.71566i	−0.513938	+	0.857828i	$0.671814\pi$
$744$			10.3923i			0.381000i
$745$		0			0
$746$	−6.00000	+	3.46410i	−0.219676	+	0.126830i
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$		−	20.7846i		−	0.759961i
$749$	−9.00000	−	10.3923i	−0.328853	−	0.379727i
$750$		0			0
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$		0			0
$753$	−27.0000	−	15.5885i	−0.983935	−	0.568075i
$754$	−9.00000	−	5.19615i	−0.327761	−	0.189233i
$755$		0			0
$756$	−13.5000	+	2.59808i	−0.490990	+	0.0944911i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	24.0000	+	13.8564i	0.871719	+	0.503287i
$759$	9.00000	+	5.19615i	0.326679	+	0.188608i
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	24.0000	+	41.5692i	0.869428	+	1.50589i
$763$	2.50000	+	12.9904i	0.0905061	+	0.470283i
$764$			10.3923i			0.375980i
$765$		0			0
$766$	31.5000	−	18.1865i	1.13814	−	0.657106i
$767$		0			0
$768$		−	32.9090i		−	1.18750i
$769$			41.5692i			1.49902i	0.661991	+	0.749512i	$0.269712\pi$
$769$			41.5692i			1.49902i	−0.661991	+	0.749512i	$0.730288\pi$
$770$		0			0
$771$		0			0
$772$	−11.0000	+	19.0526i	−0.395899	+	0.685717i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		−	5.19615i		−	0.186772i
$775$		0			0
$776$	18.0000			0.646162
$777$	18.0000	−	3.46410i	0.645746	−	0.124274i
$778$	48.0000			1.72088
$779$	18.0000	+	10.3923i	0.644917	+	0.372343i
$780$		0			0
$781$	12.0000	+	20.7846i	0.429394	+	0.743732i
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$	9.00000			0.321634
$784$	32.5000	−	12.9904i	1.16071	−	0.463942i
$785$		0			0
$786$	−36.0000			−1.28408
$787$	22.5000	−	12.9904i	0.802038	−	0.463057i	−0.0421450	−	0.999112i	$-0.513419\pi$
$787$	22.5000	−	12.9904i	0.802038	−	0.463057i	0.844183	+	0.536054i	$0.180086\pi$
$788$	−3.00000	+	1.73205i	−0.106871	+	0.0617018i
$789$	−3.00000			−0.106803
$790$		0			0
$791$	−6.00000	+	17.3205i	−0.213335	+	0.615846i
$792$	−9.00000	+	15.5885i	−0.319801	+	0.553912i
$793$	−9.00000	+	15.5885i	−0.319599	+	0.553562i
$794$	21.0000	+	36.3731i	0.745262	+	1.29083i
$795$		0			0
$796$	6.00000	+	3.46410i	0.212664	+	0.122782i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$	18.0000	−	51.9615i	0.637193	−	1.83942i
$799$		0			0
$800$		0			0
$801$	−9.00000			−0.317999
$802$	−16.5000	−	28.5788i	−0.582635	−	1.00915i
$803$	6.00000	−	10.3923i	0.211735	−	0.366736i
$804$	19.5000	−	11.2583i	0.687712	−	0.397051i
$805$		0			0
$806$			20.7846i			0.732107i
$807$			5.19615i			0.182913i
$808$	22.5000	−	12.9904i	0.791547	−	0.457000i
$809$	16.5000	−	9.52628i	0.580109	−	0.334926i	−0.181068	−	0.983471i	$-0.557955\pi$
$809$	16.5000	−	9.52628i	0.580109	−	0.334926i	0.761177	+	0.648544i	$0.224622\pi$
$810$		0			0
$811$		−	45.0333i		−	1.58133i	−0.612247	−	0.790667i	$-0.709734\pi$
$811$		−	45.0333i		−	1.58133i	0.612247	−	0.790667i	$-0.290266\pi$
$812$	4.50000	−	0.866025i	0.157919	−	0.0303915i
$813$	6.00000	+	10.3923i	0.210429	+	0.364474i
$814$	−12.0000	+	20.7846i	−0.420600	+	0.728500i
$815$		0			0
$816$	45.0000	+	25.9808i	1.57532	+	0.909509i
$817$	6.00000	+	3.46410i	0.209913	+	0.121194i
$818$	39.0000			1.36360
$819$	27.0000	−	5.19615i	0.943456	−	0.181568i
$820$		0			0
$821$	36.0000	+	20.7846i	1.25641	+	0.725388i	0.972375	−	0.233426i	$-0.0749938\pi$
$821$	36.0000	+	20.7846i	1.25641	+	0.725388i	0.284034	+	0.958814i	$0.408327\pi$
$822$	54.0000	+	31.1769i	1.88347	+	1.08742i
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	0.993831	−	0.110910i	$-0.0353764\pi$
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	−0.592966	+	0.805228i	$0.702043\pi$
$824$	4.50000	−	7.79423i	0.156765	−	0.271525i
$825$		0			0
$826$		0			0
$827$		−	22.5167i		−	0.782981i	−0.920182	−	0.391491i	$-0.871960\pi$
$827$		−	22.5167i		−	0.782981i	0.920182	−	0.391491i	$-0.128040\pi$
$828$	4.50000	−	2.59808i	0.156386	−	0.0902894i
$829$	−12.0000	+	6.92820i	−0.416777	+	0.240626i	−0.693698	−	0.720266i	$-0.744020\pi$
$829$	−12.0000	+	6.92820i	−0.416777	+	0.240626i	0.276920	+	0.960893i	$0.410686\pi$
$830$		0			0
$831$			45.0333i			1.56219i
$832$			3.46410i			0.120096i
$833$	−6.00000	+	41.5692i	−0.207888	+	1.44029i
$834$	−27.0000	+	15.5885i	−0.934934	+	0.539784i
$835$		0			0
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	−9.00000	−	15.5885i	−0.311086	−	0.538816i
$838$		0			0
$839$	−30.0000			−1.03572			−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000			−1.03572			−0.517858	+	0.855467i	$0.673270\pi$
$840$		0			0
$841$	26.0000			0.896552
$842$	52.5000	+	30.3109i	1.80927	+	1.04458i
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$		0			0
$846$		0			0
$847$	2.00000	−	1.73205i	0.0687208	−	0.0595140i
$848$		0			0
$849$	54.0000			1.85328
$850$		0			0
$851$	−6.00000	+	3.46410i	−0.205677	+	0.118748i
$852$	12.0000			0.411113
$853$		−	20.7846i		−	0.711651i	−0.934552	−	0.355826i	$-0.884200\pi$
$853$		−	20.7846i		−	0.711651i	0.934552	−	0.355826i	$-0.115800\pi$
$854$	−4.50000	−	23.3827i	−0.153987	−	0.800139i
$855$		0			0
$856$	−4.50000	+	7.79423i	−0.153807	+	0.266401i
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$	−18.0000	+	31.1769i	−0.614510	+	1.06436i
$859$	24.0000	+	13.8564i	0.818869	+	0.472774i	0.850026	−	0.526740i	$-0.176586\pi$
$859$	24.0000	+	13.8564i	0.818869	+	0.472774i	−0.0311570	+	0.999515i	$0.509919\pi$
$860$		0			0
$861$	−9.00000	−	10.3923i	−0.306719	−	0.354169i
$862$	18.0000			0.613082
$863$	−7.50000	−	4.33013i	−0.255303	−	0.147399i	0.366887	−	0.930265i	$-0.380424\pi$
$863$	−7.50000	−	4.33013i	−0.255303	−	0.147399i	−0.622190	+	0.782866i	$0.713757\pi$
$864$	13.5000	+	23.3827i	0.459279	+	0.795495i
$865$		0			0
$866$	12.0000	−	20.7846i	0.407777	−	0.706290i
$867$	−28.5000	+	16.4545i	−0.967911	+	0.558824i
$868$	−6.00000	−	6.92820i	−0.203653	−	0.235159i
$869$			55.4256i			1.88019i
$870$		0			0
$871$	−39.0000	+	22.5167i	−1.32146	+	0.762948i
$872$	7.50000	−	4.33013i	0.253982	−	0.146637i
$873$	−27.0000	+	15.5885i	−0.913812	+	0.527589i
$874$			20.7846i			0.703050i
$875$		0			0
$876$	−3.00000	−	5.19615i	−0.101361	−	0.175562i
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	−0.458606	−	0.888640i	$-0.651651\pi$
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	0.998888	−	0.0471555i	$-0.0150156\pi$
$878$	−6.00000	−	10.3923i	−0.202490	−	0.350723i
$879$	−36.0000	−	20.7846i	−1.21425	−	0.701047i
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$	−22.5000	+	28.5788i	−0.757614	+	0.962300i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	18.0000	+	10.3923i	0.605406	+	0.349531i
$885$		0			0
$886$	−13.5000	−	23.3827i	−0.453541	−	0.785557i
$887$	4.50000	−	7.79423i	0.151095	−	0.261705i	−0.780535	−	0.625112i	$-0.785053\pi$
$887$	4.50000	−	7.79423i	0.151095	−	0.261705i	0.931630	+	0.363407i	$0.118387\pi$
$888$	−6.00000	−	10.3923i	−0.201347	−	0.348743i
$889$	40.0000	+	13.8564i	1.34156	+	0.464729i
$890$		0			0
$891$		−	31.1769i		−	1.04447i
$892$	−3.00000	+	1.73205i	−0.100447	+	0.0579934i
$893$		0			0
$894$		−	67.5500i		−	2.25921i
$895$		0			0
$896$	−21.0000	−	24.2487i	−0.701561	−	0.810093i
$897$	−9.00000	+	5.19615i	−0.300501	+	0.173494i
$898$	−10.5000	+	18.1865i	−0.350390	+	0.606892i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$		0			0
$902$	18.0000			0.599334
$903$	−3.00000	−	3.46410i	−0.0998337	−	0.115278i
$904$	12.0000			0.399114
$905$		0			0
$906$	−3.00000	+	5.19615i	−0.0996683	+	0.172631i
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$	−22.5000	+	38.9711i	−0.746278	+	1.29259i
$910$		0			0
$911$		−	24.2487i		−	0.803396i	−0.915772	−	0.401698i	$-0.868420\pi$
$911$		−	24.2487i		−	0.803396i	0.915772	−	0.401698i	$-0.131580\pi$
$912$	−60.0000			−1.98680
$913$	−27.0000	+	15.5885i	−0.893570	+	0.515903i
$914$	−12.0000	+	6.92820i	−0.396925	+	0.229165i
$915$		0			0
$916$		0			0
$917$	−24.0000	+	20.7846i	−0.792550	+	0.686368i
$918$	−54.0000			−1.78227
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	19.5000	−	33.7750i	0.642547	−	1.11292i
$922$	−45.0000	−	25.9808i	−1.48200	−	0.855631i
$923$	−24.0000			−0.789970
$924$	−3.00000	−	15.5885i	−0.0986928	−	0.512823i
$925$		0			0
$926$	−43.5000	−	25.1147i	−1.42950	−	0.825321i
$927$			15.5885i			0.511992i
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	−18.0000	−	45.0333i	−0.589926	−	1.47591i
$932$		−	3.46410i		−	0.113470i
$933$			41.5692i			1.36092i
$934$	31.5000	−	18.1865i	1.03071	−	0.595082i
$935$		0			0
$936$	−9.00000	−	15.5885i	−0.294174	−	0.509525i
$937$			48.4974i			1.58434i	0.610299	+	0.792171i	$0.291049\pi$
$937$			48.4974i			1.58434i	−0.610299	+	0.792171i	$0.708951\pi$
$938$	19.5000	−	56.2917i	0.636698	−	1.83799i
$939$		0			0
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$	9.00000	+	5.19615i	0.293236	+	0.169300i
$943$	4.50000	+	2.59808i	0.146540	+	0.0846050i
$944$		0			0
$945$		0			0
$946$	6.00000			0.195077
$947$	22.5000	+	12.9904i	0.731152	+	0.422131i	0.818843	−	0.574017i	$-0.194616\pi$
$947$	22.5000	+	12.9904i	0.731152	+	0.422131i	−0.0876916	+	0.996148i	$0.527949\pi$
$948$	24.0000	+	13.8564i	0.779484	+	0.450035i
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$		0			0
$951$	15.0000	+	25.9808i	0.486408	+	0.842484i
$952$	27.0000	−	5.19615i	0.875075	−	0.168408i
$953$			6.92820i			0.224427i	0.993684	+	0.112213i	$0.0357940\pi$
$953$			6.92820i			0.224427i	−0.993684	+	0.112213i	$0.964206\pi$
$954$		0			0
$955$		0			0
$956$	−9.00000	+	5.19615i	−0.291081	+	0.168056i
$957$			10.3923i			0.335936i
$958$			10.3923i			0.335760i
$959$	54.0000	−	10.3923i	1.74375	−	0.335585i
$960$		0			0
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−12.0000	−	20.7846i	−0.386896	−	0.670123i
$963$		−	15.5885i		−	0.502331i
$964$	−6.00000	−	3.46410i	−0.193247	−	0.111571i
$965$		0			0
$966$	4.50000	−	12.9904i	0.144785	−	0.417959i
$967$	−23.0000			−0.739630			−0.369815	−	0.929105i	$-0.620579\pi$
$967$	−23.0000			−0.739630			−0.369815	+	0.929105i	$0.620579\pi$
$968$	−1.50000	−	0.866025i	−0.0482118	−	0.0278351i
$969$	36.0000	−	62.3538i	1.15649	−	2.00309i
$970$		0			0
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	−9.00000	+	25.9808i	−0.288527	+	0.832905i
$974$		−	55.4256i		−	1.77595i
$975$		0			0
$976$	−22.5000	+	12.9904i	−0.720207	+	0.415812i
$977$	21.0000	−	12.1244i	0.671850	−	0.387893i	−0.124928	−	0.992166i	$-0.539870\pi$
$977$	21.0000	−	12.1244i	0.671850	−	0.387893i	0.796777	+	0.604273i	$0.206537\pi$
$978$	24.0000			0.767435
$979$		−	10.3923i		−	0.332140i
$980$		0			0
$981$	−7.50000	+	12.9904i	−0.239457	+	0.414751i
$982$	33.0000	−	57.1577i	1.05307	−	1.82397i
$983$	28.5000	+	49.3634i	0.909009	+	1.57445i	0.815444	+	0.578836i	$0.196493\pi$
$983$	28.5000	+	49.3634i	0.909009	+	1.57445i	0.0935651	+	0.995613i	$0.470174\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$		0			0
$986$	18.0000			0.573237
$987$		0			0
$988$	−24.0000			−0.763542
$989$	1.50000	+	0.866025i	0.0476972	+	0.0275380i
$990$		0			0
$991$	−17.0000	−	29.4449i	−0.540023	−	0.935347i	−0.998902	−	0.0468483i	$-0.985082\pi$
$991$	−17.0000	−	29.4449i	−0.540023	−	0.935347i	0.458879	−	0.888499i	$-0.348251\pi$
$992$	−9.00000	+	15.5885i	−0.285750	+	0.494934i
$993$	−15.0000	+	8.66025i	−0.476011	+	0.274825i
$994$	24.0000	−	20.7846i	0.761234	−	0.659248i
$995$		0			0
$996$			15.5885i			0.493939i
$997$	−6.00000	+	3.46410i	−0.190022	+	0.109709i	−0.591993	−	0.805943i	$-0.701659\pi$
$997$	−6.00000	+	3.46410i	−0.190022	+	0.109709i	0.401971	+	0.915652i	$0.368325\pi$
$998$	21.0000	−	12.1244i	0.664743	−	0.383790i
$999$	18.0000	+	10.3923i	0.569495	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.e.26.1		2
3.2	odd	2		525.2.t.a.26.1		2
5.2	odd	4		525.2.q.b.299.1		4
5.3	odd	4		525.2.q.b.299.2		4
5.4	even	2		105.2.s.a.26.1	✓	2
7.3	odd	6		525.2.t.a.101.1		2
15.2	even	4		525.2.q.a.299.2		4
15.8	even	4		525.2.q.a.299.1		4
15.14	odd	2		105.2.s.b.26.1	yes	2
21.17	even	6	inner	525.2.t.e.101.1		2
35.3	even	12		525.2.q.a.374.2		4
35.4	even	6		735.2.s.e.521.1		2
35.9	even	6		735.2.b.b.146.2		2
35.17	even	12		525.2.q.a.374.1		4
35.19	odd	6		735.2.b.a.146.2		2
35.24	odd	6		105.2.s.b.101.1	yes	2
35.34	odd	2		735.2.s.c.656.1		2
105.17	odd	12		525.2.q.b.374.2		4
105.38	odd	12		525.2.q.b.374.1		4
105.44	odd	6		735.2.b.a.146.1		2
105.59	even	6		105.2.s.a.101.1	yes	2
105.74	odd	6		735.2.s.c.521.1		2
105.89	even	6		735.2.b.b.146.1		2
105.104	even	2		735.2.s.e.656.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.a.26.1	✓	2	5.4	even	2
105.2.s.a.101.1	yes	2	105.59	even	6
105.2.s.b.26.1	yes	2	15.14	odd	2
105.2.s.b.101.1	yes	2	35.24	odd	6
525.2.q.a.299.1		4	15.8	even	4
525.2.q.a.299.2		4	15.2	even	4
525.2.q.a.374.1		4	35.17	even	12
525.2.q.a.374.2		4	35.3	even	12
525.2.q.b.299.1		4	5.2	odd	4
525.2.q.b.299.2		4	5.3	odd	4
525.2.q.b.374.1		4	105.38	odd	12
525.2.q.b.374.2		4	105.17	odd	12
525.2.t.a.26.1		2	3.2	odd	2
525.2.t.a.101.1		2	7.3	odd	6
525.2.t.e.26.1		2	1.1	even	1	trivial
525.2.t.e.101.1		2	21.17	even	6	inner
735.2.b.a.146.1		2	105.44	odd	6
735.2.b.a.146.2		2	35.19	odd	6
735.2.b.b.146.1		2	105.89	even	6
735.2.b.b.146.2		2	35.9	even	6
735.2.s.c.521.1		2	105.74	odd	6
735.2.s.c.656.1		2	35.34	odd	2
735.2.s.e.521.1		2	35.4	even	6
735.2.s.e.656.1		2	105.104	even	2

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{11} +1.73205i q^{12} -3.46410i q^{13} +(3.00000 + 3.46410i) q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} +5.19615i q^{18} +(-6.00000 - 3.46410i) q^{19} +(3.00000 + 3.46410i) q^{21} -6.00000 q^{22} +(-1.50000 - 0.866025i) q^{23} +(1.50000 - 2.59808i) q^{24} +(3.00000 - 5.19615i) q^{26} +5.19615i q^{27} +(0.500000 + 2.59808i) q^{28} -1.73205i q^{29} +(-3.00000 + 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} -6.00000 q^{33} +10.3923i q^{34} +(-1.50000 + 2.59808i) q^{36} +(2.00000 - 3.46410i) q^{37} +(-6.00000 - 10.3923i) q^{38} +(3.00000 - 5.19615i) q^{39} -3.00000 q^{41} +(1.50000 + 7.79423i) q^{42} -1.00000 q^{43} +(-3.00000 - 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(7.50000 - 4.33013i) q^{48} +(5.50000 + 4.33013i) q^{49} +10.3923i q^{51} +(3.00000 - 1.73205i) q^{52} +(-4.50000 + 7.79423i) q^{54} +(1.50000 - 4.33013i) q^{56} +(-6.00000 - 10.3923i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-4.50000 - 2.59808i) q^{61} -6.00000 q^{62} +(1.50000 + 7.79423i) q^{63} -1.00000 q^{64} +(-9.00000 - 5.19615i) q^{66} +(-6.50000 - 11.2583i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.50000 - 2.59808i) q^{69} -6.92820i q^{71} +(4.50000 - 2.59808i) q^{72} +(-3.00000 + 1.73205i) q^{73} +(6.00000 - 3.46410i) q^{74} -6.92820i q^{76} +(-9.00000 + 1.73205i) q^{77} +(9.00000 - 5.19615i) q^{78} +(8.00000 - 13.8564i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(-1.50000 + 4.33013i) q^{84} +(-1.50000 - 0.866025i) q^{86} +(1.50000 - 2.59808i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-1.50000 + 2.59808i) q^{89} +(3.00000 - 8.66025i) q^{91} -1.73205i q^{92} -6.00000 q^{93} +9.00000 q^{96} +10.3923i q^{97} +(4.50000 + 11.2583i) q^{98} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} + q^{4} + 3 q^{6} + 5 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 + q^4 + 3 * q^6 + 5 * q^7 + 3 * q^9	\( 2 q + 3 q^{2} + 3 q^{3} + q^{4} + 3 q^{6} + 5 q^{7} + 3 q^{9} - 6 q^{11} + 6 q^{14} + 5 q^{16} + 6 q^{17} - 12 q^{19} + 6 q^{21} - 12 q^{22} - 3 q^{23} + 3 q^{24} + 6 q^{26} + q^{28} - 6 q^{31} + 9 q^{32} - 12 q^{33} - 3 q^{36} + 4 q^{37} - 12 q^{38} + 6 q^{39} - 6 q^{41} + 3 q^{42} - 2 q^{43} - 6 q^{44} - 3 q^{46} + 15 q^{48} + 11 q^{49} + 6 q^{52} - 9 q^{54} + 3 q^{56} - 12 q^{57} + 3 q^{58} - 9 q^{61} - 12 q^{62} + 3 q^{63} - 2 q^{64} - 18 q^{66} - 13 q^{67} - 6 q^{68} - 3 q^{69} + 9 q^{72} - 6 q^{73} + 12 q^{74} - 18 q^{77} + 18 q^{78} + 16 q^{79} - 9 q^{81} - 9 q^{82} + 18 q^{83} - 3 q^{84} - 3 q^{86} + 3 q^{87} + 6 q^{88} - 3 q^{89} + 6 q^{91} - 12 q^{93} + 18 q^{96} + 9 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 + q^4 + 3 * q^6 + 5 * q^7 + 3 * q^9 - 6 * q^11 + 6 * q^14 + 5 * q^16 + 6 * q^17 - 12 * q^19 + 6 * q^21 - 12 * q^22 - 3 * q^23 + 3 * q^24 + 6 * q^26 + q^28 - 6 * q^31 + 9 * q^32 - 12 * q^33 - 3 * q^36 + 4 * q^37 - 12 * q^38 + 6 * q^39 - 6 * q^41 + 3 * q^42 - 2 * q^43 - 6 * q^44 - 3 * q^46 + 15 * q^48 + 11 * q^49 + 6 * q^52 - 9 * q^54 + 3 * q^56 - 12 * q^57 + 3 * q^58 - 9 * q^61 - 12 * q^62 + 3 * q^63 - 2 * q^64 - 18 * q^66 - 13 * q^67 - 6 * q^68 - 3 * q^69 + 9 * q^72 - 6 * q^73 + 12 * q^74 - 18 * q^77 + 18 * q^78 + 16 * q^79 - 9 * q^81 - 9 * q^82 + 18 * q^83 - 3 * q^84 - 3 * q^86 + 3 * q^87 + 6 * q^88 - 3 * q^89 + 6 * q^91 - 12 * q^93 + 18 * q^96 + 9 * q^98 - 18 * q^99

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