LMFDB - Embedded newform 441.2.f.a.148.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$1$
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 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.a.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} +(-2.50000 - 4.33013i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(-2.50000 + 4.33013i) q^{13} +(1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(1.50000 - 2.59808i) q^{18} -1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{26} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{32} +8.66025i q^{33} +(1.50000 + 2.59808i) q^{34} +3.00000 q^{36} +3.00000 q^{37} +(0.500000 + 0.866025i) q^{38} +(7.50000 - 4.33013i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} -5.00000 q^{44} -3.00000 q^{45} +3.00000 q^{46} -1.73205i q^{48} +(2.00000 - 3.46410i) q^{50} +(4.50000 + 2.59808i) q^{51} +(2.50000 + 4.33013i) q^{52} -9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +5.00000 q^{55} +(1.50000 + 0.866025i) q^{57} +(0.500000 - 0.866025i) q^{58} -1.73205i q^{60} +(-7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(7.50000 - 4.33013i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-4.50000 - 7.79423i) q^{72} -3.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} -6.92820i q^{75} +(-0.500000 + 0.866025i) q^{76} +(-7.50000 - 4.33013i) q^{78} +(-4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(0.500000 - 0.866025i) q^{86} -1.73205i q^{87} +(7.50000 + 12.9904i) q^{88} +13.0000 q^{89} +(1.50000 + 2.59808i) q^{90} +(1.50000 + 2.59808i) q^{92} +(0.500000 - 0.866025i) q^{95} +(7.50000 - 4.33013i) q^{96} +(-4.50000 - 7.79423i) q^{97} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 + q^4 - q^5 - 6 * q^8 + 3 * q^9	$ 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 6 q^{8} + 3 q^{9} + 2 q^{10} - 5 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{15} + q^{16} - 6 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - 3 q^{23} + 9 q^{24} + 4 q^{25} + 10 q^{26} + q^{29} - 3 q^{30} - 5 q^{32} + 3 q^{34} + 6 q^{36} + 6 q^{37} + q^{38} + 15 q^{39} + 3 q^{40} - 5 q^{41} + q^{43} - 10 q^{44} - 6 q^{45} + 6 q^{46} + 4 q^{50} + 9 q^{51} + 5 q^{52} - 18 q^{53} - 9 q^{54} + 10 q^{55} + 3 q^{57} + q^{58} - 14 q^{61} + 14 q^{64} - 5 q^{65} + 15 q^{66} - 4 q^{67} - 3 q^{68} + 9 q^{69} - 24 q^{71} - 9 q^{72} - 6 q^{73} - 3 q^{74} - q^{76} - 15 q^{78} - 8 q^{79} - 2 q^{80} - 9 q^{81} + 10 q^{82} - 9 q^{83} + 3 q^{85} + q^{86} + 15 q^{88} + 26 q^{89} + 3 q^{90} + 3 q^{92} + q^{95} + 15 q^{96} - 9 q^{97} + 15 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 + q^4 - q^5 - 6 * q^8 + 3 * q^9 + 2 * q^10 - 5 * q^11 - 3 * q^12 - 5 * q^13 + 3 * q^15 + q^16 - 6 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - 3 * q^23 + 9 * q^24 + 4 * q^25 + 10 * q^26 + q^29 - 3 * q^30 - 5 * q^32 + 3 * q^34 + 6 * q^36 + 6 * q^37 + q^38 + 15 * q^39 + 3 * q^40 - 5 * q^41 + q^43 - 10 * q^44 - 6 * q^45 + 6 * q^46 + 4 * q^50 + 9 * q^51 + 5 * q^52 - 18 * q^53 - 9 * q^54 + 10 * q^55 + 3 * q^57 + q^58 - 14 * q^61 + 14 * q^64 - 5 * q^65 + 15 * q^66 - 4 * q^67 - 3 * q^68 + 9 * q^69 - 24 * q^71 - 9 * q^72 - 6 * q^73 - 3 * q^74 - q^76 - 15 * q^78 - 8 * q^79 - 2 * q^80 - 9 * q^81 + 10 * q^82 - 9 * q^83 + 3 * q^85 + q^86 + 15 * q^88 + 26 * q^89 + 3 * q^90 + 3 * q^92 + q^95 + 15 * q^96 - 9 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	−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
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$			1.73205i			0.707107i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.00000			0.316228
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	4.50000	+	2.59808i	0.918559	+	0.530330i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	5.00000			0.980581
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	−1.50000	−	0.866025i	−0.273861	−	0.158114i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$			8.66025i			1.50756i
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$		0			0
$36$	3.00000			0.500000
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	7.50000	−	4.33013i	1.20096	−	0.693375i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−5.00000			−0.753778
$45$	−3.00000			−0.447214
$46$	3.00000			0.442326
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		−	1.73205i		−	0.250000i
$49$		0			0
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	4.50000	+	2.59808i	0.630126	+	0.363803i
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	5.00000			0.674200
$56$		0			0
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$		0			0
$63$		0			0
$64$	7.00000			0.875000
$65$	−2.50000	−	4.33013i	−0.310087	−	0.537086i
$66$	7.50000	−	4.33013i	0.923186	−	0.533002i
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	−4.50000	−	7.79423i	−0.530330	−	0.918559i
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$		−	6.92820i		−	0.800000i
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$		0			0
$78$	−7.50000	−	4.33013i	−0.849208	−	0.490290i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.00000			0.552158
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		−	1.73205i		−	0.185695i
$88$	7.50000	+	12.9904i	0.799503	+	1.38478i
$89$	13.0000			1.37800			0.688999	−	0.724763i	$-0.258051\pi$
$89$	13.0000			1.37800			0.688999	+	0.724763i	$0.258051\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$		0			0
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	0.541890	−	0.840450i	$-0.317709\pi$
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	−0.998796	+	0.0490655i	$0.984376\pi$
$98$		0			0
$99$	7.50000	−	12.9904i	0.753778	−	1.30558i
$100$	4.00000			0.400000
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	−0.884941	−	0.465704i	$-0.845801\pi$
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	0.0391591	−	0.999233i	$-0.487532\pi$
$102$		−	5.19615i		−	0.514496i
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	−0.889607	−	0.456727i	$-0.849022\pi$
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	0.840341	+	0.542059i	$0.182355\pi$
$104$	7.50000	−	12.9904i	0.735436	−	1.27381i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	17.0000			1.64345			0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000			1.64345			0.821726	+	0.569883i	$0.193011\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$	−4.50000	−	2.59808i	−0.427121	−	0.246598i
$112$		0			0
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		−	1.73205i		−	0.162221i
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	1.00000			0.0928477
$117$	−15.0000			−1.38675
$118$		0			0
$119$		0			0
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−7.00000	+	12.1244i	−0.633750	+	1.09769i
$123$	7.50000	−	4.33013i	0.676252	−	0.390434i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$		−	1.73205i		−	0.152499i
$130$	−2.50000	+	4.33013i	−0.219265	+	0.379777i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$	7.50000	+	4.33013i	0.652791	+	0.376889i
$133$		0			0
$134$	4.00000			0.345547
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	9.00000			0.771744
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−4.50000	−	2.59808i	−0.383065	−	0.221163i
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	25.0000			2.09061
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−1.00000			−0.0830455
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$		0			0
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	3.00000			0.243332
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$		0			0
$155$		0			0
$156$		−	8.66025i		−	0.693375i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$	13.5000	+	7.79423i	1.07062	+	0.618123i
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$		0			0
$162$	9.00000			0.707107
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	2.50000	+	4.33013i	0.195217	+	0.338126i
$165$	−7.50000	−	4.33013i	−0.583874	−	0.337100i
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−9.50000	+	16.4545i	−0.735132	+	1.27329i	0.219533	+	0.975605i	$0.429547\pi$
$167$	−9.50000	+	16.4545i	−0.735132	+	1.27329i	−0.954665	+	0.297681i	$0.903787\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	−3.00000			−0.230089
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$	1.00000			0.0762493
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	−0.999293	−	0.0375896i	$-0.988032\pi$
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	0.467093	−	0.884208i	$-0.345301\pi$
$174$	−1.50000	+	0.866025i	−0.113715	+	0.0656532i
$175$		0			0
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$		0			0
$178$	−6.50000	−	11.2583i	−0.487196	−	0.843848i
$179$	19.0000			1.42013			0.710063	−	0.704138i	$-0.248666\pi$
$179$	19.0000			1.42013			0.710063	+	0.704138i	$0.248666\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$			24.2487i			1.79252i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$		0			0
$187$	7.50000	+	12.9904i	0.548454	+	0.949951i
$188$		0			0
$189$		0			0
$190$	−1.00000			−0.0725476
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	−10.5000	−	6.06218i	−0.757772	−	0.437500i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$			8.66025i			0.620174i
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−15.0000			−1.06600
$199$	−3.00000			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$200$	−6.00000	−	10.3923i	−0.424264	−	0.734847i
$201$	6.00000	−	3.46410i	0.423207	−	0.244339i
$202$	−8.50000	+	14.7224i	−0.598058	+	1.03587i
$203$		0			0
$204$	4.50000	−	2.59808i	0.315063	−	0.181902i
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$	1.00000			0.0696733
$207$	−9.00000			−0.625543
$208$	−5.00000			−0.346688
$209$	2.50000	+	4.33013i	0.172929	+	0.299521i
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$	18.0000	+	10.3923i	1.23334	+	0.712069i
$214$	−8.50000	−	14.7224i	−0.581048	−	1.00640i
$215$	−1.00000			−0.0681994
$216$			15.5885i			1.06066i
$217$		0			0
$218$	4.50000	+	7.79423i	0.304778	+	0.527892i
$219$	4.50000	+	2.59808i	0.304082	+	0.175562i
$220$	2.50000	−	4.33013i	0.168550	−	0.291937i
$221$	7.50000	−	12.9904i	0.504505	−	0.873828i
$222$			5.19615i			0.348743i
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$		0			0
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	−1.00000			−0.0665190
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$	1.50000	−	0.866025i	0.0993399	−	0.0573539i
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$	−1.50000	+	2.59808i	−0.0989071	+	0.171312i
$231$		0			0
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$	7.50000	+	12.9904i	0.490290	+	0.849208i
$235$		0			0
$236$		0			0
$237$			13.8564i			0.900070i
$238$		0			0
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	−0.514719	−	0.857359i	$-0.672104\pi$
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	0.999854	+	0.0170808i	$0.00543724\pi$
$240$	1.50000	+	0.866025i	0.0968246	+	0.0559017i
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	14.0000			0.899954
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−14.0000			−0.896258
$245$		0			0
$246$	−7.50000	−	4.33013i	−0.478183	−	0.276079i
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$		0			0
$249$			15.5885i			0.987878i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	28.0000			1.76734			0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000			1.76734			0.883672	+	0.468106i	$0.155064\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$	6.00000	+	10.3923i	0.376473	+	0.652071i
$255$	−4.50000	+	2.59808i	−0.281801	+	0.162698i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.0828783	+	0.996560i	$0.526411\pi$
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.821607	+	0.570055i	$0.806922\pi$
$258$	−1.50000	+	0.866025i	−0.0933859	+	0.0539164i
$259$		0			0
$260$	−5.00000			−0.310087
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	1.00000			0.0617802
$263$	−2.50000	−	4.33013i	−0.154157	−	0.267007i	0.778595	−	0.627527i	$-0.215933\pi$
$263$	−2.50000	−	4.33013i	−0.154157	−	0.267007i	−0.932752	+	0.360520i	$0.882599\pi$
$264$		−	25.9808i		−	1.59901i
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$		0			0
$267$	−19.5000	−	11.2583i	−1.19338	−	0.688999i
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$		−	5.19615i		−	0.316228i
$271$	−1.00000			−0.0607457			−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000			−0.0607457			−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−1.50000	−	2.59808i	−0.0909509	−	0.157532i
$273$		0			0
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$		−	5.19615i		−	0.312772i
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$	−9.00000			−0.539784
$279$		0			0
$280$		0			0
$281$	14.5000	+	25.1147i	0.864997	+	1.49822i	0.867050	+	0.498222i	$0.166013\pi$
$281$	14.5000	+	25.1147i	0.864997	+	1.49822i	−0.00205220	+	0.999998i	$0.500653\pi$
$282$		0			0
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	−0.0640654	−	0.997946i	$-0.520407\pi$
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	0.896279	−	0.443491i	$-0.146260\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	−1.50000	+	0.866025i	−0.0888523	+	0.0512989i
$286$	−12.5000	−	21.6506i	−0.739140	−	1.28023i
$287$		0			0
$288$	−15.0000			−0.883883
$289$	−8.00000			−0.470588
$290$	0.500000	+	0.866025i	0.0293610	+	0.0508548i
$291$			15.5885i			0.913812i
$292$	−1.50000	+	2.59808i	−0.0877809	+	0.152041i
$293$	−2.50000	+	4.33013i	−0.146052	+	0.252969i	−0.929765	−	0.368154i	$-0.879990\pi$
$293$	−2.50000	+	4.33013i	−0.146052	+	0.252969i	0.783713	+	0.621123i	$0.213323\pi$
$294$		0			0
$295$		0			0
$296$	−9.00000			−0.523114
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	3.00000			0.173785
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$	−6.00000	−	3.46410i	−0.346410	−	0.200000i
$301$		0			0
$302$	−2.50000	+	4.33013i	−0.143859	+	0.249171i
$303$			29.4449i			1.69156i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	14.0000			0.801638
$306$	−4.50000	+	7.79423i	−0.257248	+	0.445566i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	1.50000	−	0.866025i	0.0853320	−	0.0492665i
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	−22.5000	+	12.9904i	−1.27381	+	0.735436i
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−8.00000			−0.450035
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		−	15.5885i		−	0.874157i
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	−3.50000	+	6.06218i	−0.195656	+	0.338886i
$321$	−25.5000	−	14.7224i	−1.42327	−	0.821726i
$322$		0			0
$323$	3.00000			0.166924
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−20.0000			−1.10940
$326$	5.50000	+	9.52628i	0.304617	+	0.527612i
$327$	13.5000	+	7.79423i	0.746552	+	0.431022i
$328$	7.50000	−	12.9904i	0.414118	−	0.717274i
$329$		0			0
$330$			8.66025i			0.476731i
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	−9.00000			−0.493939
$333$	4.50000	+	7.79423i	0.246598	+	0.427121i
$334$	19.0000			1.03963
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$		0			0
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	0.926049	−	0.377403i	$-0.123183\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	−1.50000	+	0.866025i	−0.0814688	+	0.0470360i
$340$	−1.50000	−	2.59808i	−0.0813489	−	0.140900i
$341$		0			0
$342$	−1.50000	+	2.59808i	−0.0811107	+	0.140488i
$343$		0			0
$344$	−1.50000	−	2.59808i	−0.0808746	−	0.140079i
$345$			5.19615i			0.279751i
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$	−1.50000	−	0.866025i	−0.0804084	−	0.0464238i
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	0.999951	+	0.00987003i	$0.00314178\pi$
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	−0.491428	+	0.870918i	$0.663525\pi$
$350$		0			0
$351$	22.5000	+	12.9904i	1.20096	+	0.693375i
$352$	25.0000			1.33250
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	0.974456	−	0.224580i	$-0.0721011\pi$
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	−0.681720	+	0.731613i	$0.738768\pi$
$354$		0			0
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	6.50000	−	11.2583i	0.344499	−	0.596690i
$357$		0			0
$358$	−9.50000	−	16.4545i	−0.502091	−	0.869646i
$359$	−11.0000			−0.580558			−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000			−0.580558			−0.290279	+	0.956942i	$0.593748\pi$
$360$	9.00000			0.474342
$361$	−18.0000			−0.947368
$362$	−7.00000	−	12.1244i	−0.367912	−	0.637242i
$363$	21.0000	−	12.1244i	1.10221	−	0.636364i
$364$		0			0
$365$	1.50000	−	2.59808i	0.0785136	−	0.135990i
$366$	21.0000	−	12.1244i	1.09769	−	0.633750i
$367$	−1.50000	−	2.59808i	−0.0782994	−	0.135618i	0.824217	−	0.566274i	$-0.191616\pi$
$367$	−1.50000	−	2.59808i	−0.0782994	−	0.135618i	−0.902516	+	0.430656i	$0.858282\pi$
$368$	−3.00000			−0.156386
$369$	−15.0000			−0.780869
$370$	3.00000			0.155963
$371$		0			0
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	7.50000	−	12.9904i	0.387816	−	0.671717i
$375$	13.5000	+	7.79423i	0.697137	+	0.402492i
$376$		0			0
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	−0.500000	−	0.866025i	−0.0256495	−	0.0444262i
$381$	18.0000	+	10.3923i	0.922168	+	0.532414i
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	−0.282079	−	0.959391i	$-0.591024\pi$
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	0.971897	−	0.235408i	$-0.0756427\pi$
$384$		−	5.19615i		−	0.265165i
$385$		0			0
$386$	−10.0000			−0.508987
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	−9.00000			−0.456906
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$	7.50000	−	4.33013i	0.379777	−	0.219265i
$391$	4.50000	−	7.79423i	0.227575	−	0.394171i
$392$		0			0
$393$	1.50000	−	0.866025i	0.0756650	−	0.0436852i
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	8.00000			0.402524
$396$	−7.50000	−	12.9904i	−0.376889	−	0.652791i
$397$	−15.0000			−0.752828			−0.376414	−	0.926451i	$-0.622843\pi$
$397$	−15.0000			−0.752828			−0.376414	+	0.926451i	$0.622843\pi$
$398$	1.50000	+	2.59808i	0.0751882	+	0.130230i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	−6.00000	−	3.46410i	−0.299253	−	0.172774i
$403$		0			0
$404$	−17.0000			−0.845782
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$		0			0
$407$	−7.50000	−	12.9904i	−0.371761	−	0.643909i
$408$	−13.5000	−	7.79423i	−0.668350	−	0.385872i
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$	−2.50000	+	4.33013i	−0.123466	+	0.213850i
$411$		−	15.5885i		−	0.768922i
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$		0			0
$414$	4.50000	+	7.79423i	0.221163	+	0.383065i
$415$	9.00000			0.441793
$416$	−12.5000	−	21.6506i	−0.612863	−	1.06151i
$417$	−13.5000	+	7.79423i	−0.661098	+	0.381685i
$418$	2.50000	−	4.33013i	0.122279	−	0.211793i
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$	13.0000			0.632830
$423$		0			0
$424$	27.0000			1.31124
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		−	20.7846i		−	1.00702i
$427$		0			0
$428$	8.50000	−	14.7224i	0.410863	−	0.711636i
$429$	−37.5000	−	21.6506i	−1.81052	−	1.04530i
$430$	0.500000	+	0.866025i	0.0241121	+	0.0417635i
$431$	−9.00000			−0.433515			−0.216757	−	0.976226i	$-0.569548\pi$
$431$	−9.00000			−0.433515			−0.216757	+	0.976226i	$0.569548\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	1.50000	+	0.866025i	0.0719195	+	0.0415227i
$436$	−4.50000	+	7.79423i	−0.215511	+	0.373276i
$437$	1.50000	−	2.59808i	0.0717547	−	0.124283i
$438$		−	5.19615i		−	0.248282i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−15.0000			−0.715097
$441$		0			0
$442$	−15.0000			−0.713477
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$	−4.50000	+	2.59808i	−0.213561	+	0.123299i
$445$	−6.50000	+	11.2583i	−0.308130	+	0.533696i
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$	4.50000	−	2.59808i	0.212843	−	0.122885i
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	12.0000			0.565685
$451$	25.0000			1.17720
$452$	−0.500000	−	0.866025i	−0.0235180	−	0.0407344i
$453$			8.66025i			0.406894i
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$		0			0
$456$	−4.50000	−	2.59808i	−0.210732	−	0.121666i
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$	1.00000			0.0467269
$459$			15.5885i			0.727607i
$460$	−3.00000			−0.139876
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	0.997871	−	0.0652135i	$-0.0207728\pi$
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	−0.555412	+	0.831575i	$0.687440\pi$
$462$		0			0
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	−0.976607	−	0.215032i	$-0.931015\pi$
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	0.674526	+	0.738251i	$0.264348\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$	−7.50000	+	12.9904i	−0.346688	+	0.600481i
$469$		0			0
$470$		0			0
$471$	21.0000	−	12.1244i	0.967629	−	0.558661i
$472$		0			0
$473$	2.50000	−	4.33013i	0.114950	−	0.199099i
$474$	12.0000	−	6.92820i	0.551178	−	0.318223i
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$	−13.5000	−	23.3827i	−0.618123	−	1.07062i
$478$	−15.0000			−0.686084
$479$	12.5000	+	21.6506i	0.571140	+	0.989243i	0.996449	+	0.0841949i	$0.0268318\pi$
$479$	12.5000	+	21.6506i	0.571140	+	0.989243i	−0.425310	+	0.905048i	$0.639835\pi$
$480$			8.66025i			0.395285i
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$	5.50000	−	9.52628i	0.250518	−	0.433910i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	9.00000			0.408669
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	19.0000			0.860972			0.430486	−	0.902597i	$-0.358342\pi$
$487$	19.0000			0.860972			0.430486	+	0.902597i	$0.358342\pi$
$488$	21.0000	+	36.3731i	0.950625	+	1.64653i
$489$	16.5000	+	9.52628i	0.746156	+	0.430793i
$490$		0			0
$491$	−6.50000	+	11.2583i	−0.293341	+	0.508081i	−0.974598	−	0.223963i	$-0.928100\pi$
$491$	−6.50000	+	11.2583i	−0.293341	+	0.508081i	0.681257	+	0.732045i	$0.261434\pi$
$492$		−	8.66025i		−	0.390434i
$493$	−1.50000	−	2.59808i	−0.0675566	−	0.117011i
$494$	−5.00000			−0.224961
$495$	7.50000	+	12.9904i	0.337100	+	0.583874i
$496$		0			0
$497$		0			0
$498$	13.5000	−	7.79423i	0.604949	−	0.349268i
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	0.276683	+	0.960961i	$0.410765\pi$
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	−0.970558	+	0.240866i	$0.922569\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	28.5000	−	16.4545i	1.27329	−	0.735132i
$502$	−14.0000	−	24.2487i	−0.624851	−	1.08227i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$	−7.50000	−	12.9904i	−0.333416	−	0.577493i
$507$			20.7846i			0.923077i
$508$	−6.00000	+	10.3923i	−0.266207	+	0.461084i
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	0.342126	+	0.939654i	$0.388853\pi$
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	−0.984827	+	0.173537i	$0.944480\pi$
$510$	4.50000	+	2.59808i	0.199263	+	0.115045i
$511$		0			0
$512$	−11.0000			−0.486136
$513$			5.19615i			0.229416i
$514$	29.0000			1.27914
$515$	−0.500000	−	0.866025i	−0.0220326	−	0.0381616i
$516$	−1.50000	−	0.866025i	−0.0660338	−	0.0381246i
$517$		0			0
$518$		0			0
$519$			24.2487i			1.06440i
$520$	7.50000	+	12.9904i	0.328897	+	0.569666i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	3.00000			0.131306
$523$	−1.00000			−0.0437269			−0.0218635	−	0.999761i	$-0.506960\pi$
$523$	−1.00000			−0.0437269			−0.0218635	+	0.999761i	$0.506960\pi$
$524$	0.500000	+	0.866025i	0.0218426	+	0.0378325i
$525$		0			0
$526$	−2.50000	+	4.33013i	−0.109005	+	0.188803i
$527$		0			0
$528$	−7.50000	+	4.33013i	−0.326396	+	0.188445i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−9.00000			−0.390935
$531$		0			0
$532$		0			0
$533$	−12.5000	−	21.6506i	−0.541435	−	0.937793i
$534$			22.5167i			0.974391i
$535$	−8.50000	+	14.7224i	−0.367487	+	0.636506i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	−28.5000	−	16.4545i	−1.22987	−	0.710063i
$538$	1.50000	+	2.59808i	0.0646696	+	0.112011i
$539$		0			0
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	0.500000	+	0.866025i	0.0214768	+	0.0371990i
$543$	−21.0000	−	12.1244i	−0.901196	−	0.520306i
$544$	7.50000	−	12.9904i	0.321560	−	0.556958i
$545$	4.50000	−	7.79423i	0.192759	−	0.333868i
$546$		0			0
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	9.00000			0.384461
$549$	21.0000	−	36.3731i	0.896258	−	1.55236i
$550$	−20.0000			−0.852803
$551$	−0.500000	−	0.866025i	−0.0213007	−	0.0368939i
$552$	−13.5000	+	7.79423i	−0.574598	+	0.331744i
$553$		0			0
$554$	−9.50000	+	16.4545i	−0.403616	+	0.699084i
$555$	4.50000	−	2.59808i	0.191014	−	0.110282i
$556$	−4.50000	−	7.79423i	−0.190843	−	0.330549i
$557$	−37.0000			−1.56774			−0.783870	−	0.620925i	$-0.786757\pi$
$557$	−37.0000			−1.56774			−0.783870	+	0.620925i	$0.786757\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		−	25.9808i		−	1.09691i
$562$	14.5000	−	25.1147i	0.611646	−	1.05940i
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$564$		0			0
$565$	0.500000	+	0.866025i	0.0210352	+	0.0364340i
$566$	−28.0000			−1.17693
$567$		0			0
$568$	36.0000			1.51053
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	0.963849	+	0.266450i	$0.0858508\pi$
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	−0.251172	+	0.967943i	$0.580816\pi$
$570$	1.50000	+	0.866025i	0.0628281	+	0.0362738i
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	12.5000	−	21.6506i	0.522651	−	0.905259i
$573$			13.8564i			0.578860i
$574$		0			0
$575$	−12.0000			−0.500435
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	−31.0000			−1.29055			−0.645273	−	0.763952i	$-0.723257\pi$
$577$	−31.0000			−1.29055			−0.645273	+	0.763952i	$0.723257\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	−15.0000	+	8.66025i	−0.623379	+	0.359908i
$580$	−0.500000	+	0.866025i	−0.0207614	+	0.0359597i
$581$		0			0
$582$	13.5000	−	7.79423i	0.559593	−	0.323081i
$583$	22.5000	+	38.9711i	0.931855	+	1.61402i
$584$	9.00000			0.372423
$585$	7.50000	−	12.9904i	0.310087	−	0.537086i
$586$	5.00000			0.206548
$587$	−18.5000	−	32.0429i	−0.763577	−	1.32255i	−0.940996	−	0.338418i	$-0.890108\pi$
$587$	−18.5000	−	32.0429i	−0.763577	−	1.32255i	0.177419	−	0.984135i	$-0.443225\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−3.00000	−	1.73205i	−0.123404	−	0.0712470i
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	−15.0000			−0.615976			−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000			−0.615976			−0.307988	+	0.951390i	$0.599656\pi$
$594$	22.5000	+	12.9904i	0.923186	+	0.533002i
$595$		0			0
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$	4.50000	+	2.59808i	0.184173	+	0.106332i
$598$	−7.50000	+	12.9904i	−0.306698	+	0.531216i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$			20.7846i			0.848528i
$601$	−4.50000	−	7.79423i	−0.183559	−	0.317933i	0.759531	−	0.650471i	$-0.225428\pi$
$601$	−4.50000	−	7.79423i	−0.183559	−	0.317933i	−0.943090	+	0.332538i	$0.892095\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	−5.00000			−0.203447
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$	25.5000	−	14.7224i	1.03587	−	0.598058i
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	−7.00000	−	12.1244i	−0.283422	−	0.490901i
$611$		0			0
$612$	−9.00000			−0.363803
$613$	19.0000			0.767403			0.383701	−	0.923457i	$-0.374649\pi$
$613$	19.0000			0.767403			0.383701	+	0.923457i	$0.374649\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$			8.66025i			0.349215i
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$	−1.50000	−	0.866025i	−0.0603388	−	0.0348367i
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	0.999996	+	0.00279365i	$0.000889247\pi$
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	−0.497579	+	0.867419i	$0.665777\pi$
$620$		0			0
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		0			0
$623$		0			0
$624$	7.50000	+	4.33013i	0.300240	+	0.173344i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$		−	8.66025i		−	0.345857i
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	−9.00000			−0.358854
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	12.0000	+	20.7846i	0.477334	+	0.826767i
$633$	19.5000	−	11.2583i	0.775055	−	0.447478i
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$	13.5000	−	7.79423i	0.535310	−	0.309061i
$637$		0			0
$638$	−5.00000			−0.197952
$639$	−18.0000	−	31.1769i	−0.712069	−	1.23334i
$640$	−3.00000			−0.118585
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$			29.4449i			1.16210i
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	−0.990274	−	0.139134i	$-0.955568\pi$
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	0.615630	+	0.788035i	$0.288902\pi$
$644$		0			0
$645$	1.50000	+	0.866025i	0.0590624	+	0.0340997i
$646$	−1.50000	−	2.59808i	−0.0590167	−	0.102220i
$647$	−31.0000			−1.21874			−0.609368	−	0.792888i	$-0.708577\pi$
$647$	−31.0000			−1.21874			−0.609368	+	0.792888i	$0.708577\pi$
$648$	13.5000	−	23.3827i	0.530330	−	0.918559i
$649$		0			0
$650$	10.0000	+	17.3205i	0.392232	+	0.679366i
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		−	15.5885i		−	0.609557i
$655$	−0.500000	−	0.866025i	−0.0195366	−	0.0338384i
$656$	−5.00000			−0.195217
$657$	−4.50000	−	7.79423i	−0.175562	−	0.304082i
$658$		0			0
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	−0.999545	−	0.0301523i	$-0.990401\pi$
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	0.473660	−	0.880708i	$-0.342933\pi$
$660$	−7.50000	+	4.33013i	−0.291937	+	0.168550i
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−4.00000	+	6.92820i	−0.155464	+	0.269272i
$663$	−22.5000	+	12.9904i	−0.873828	+	0.504505i
$664$	13.5000	+	23.3827i	0.523902	+	0.907424i
$665$		0			0
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$	−3.00000			−0.116160
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$		−	32.9090i		−	1.27233i
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	−35.0000	+	60.6218i	−1.35116	+	2.34028i
$672$		0			0
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	−29.0000			−1.11704
$675$	18.0000	−	10.3923i	0.692820	−	0.400000i
$676$	−12.0000			−0.461538
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$	1.50000	+	0.866025i	0.0576072	+	0.0332595i
$679$		0			0
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$			5.19615i			0.199117i
$682$		0			0
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$	−3.00000			−0.114708
$685$	−9.00000			−0.343872
$686$		0			0
$687$	1.50000	−	0.866025i	0.0572286	−	0.0330409i
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	22.5000	−	38.9711i	0.857182	−	1.48468i
$690$	4.50000	−	2.59808i	0.171312	−	0.0989071i
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	4.00000			0.151838
$695$	4.50000	+	7.79423i	0.170695	+	0.295652i
$696$			5.19615i			0.196960i
$697$	7.50000	−	12.9904i	0.284083	−	0.492046i
$698$	9.50000	−	16.4545i	0.359580	−	0.622811i
$699$	−4.50000	−	2.59808i	−0.170206	−	0.0982683i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		−	25.9808i		−	0.980581i
$703$	−3.00000			−0.113147
$704$	−17.5000	−	30.3109i	−0.659556	−	1.14238i
$705$		0			0
$706$	5.50000	−	9.52628i	0.206995	−	0.358526i
$707$		0			0
$708$		0			0
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	0.916845	−	0.399244i	$-0.130727\pi$
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	−0.804178	+	0.594389i	$0.797394\pi$
$710$	−12.0000			−0.450352
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$	−39.0000			−1.46159
$713$		0			0
$714$		0			0
$715$	−12.5000	+	21.6506i	−0.467473	+	0.809688i
$716$	9.50000	−	16.4545i	0.355032	−	0.614933i
$717$	−22.5000	+	12.9904i	−0.840278	+	0.485135i
$718$	5.50000	+	9.52628i	0.205258	+	0.355518i
$719$	27.0000			1.00693			0.503465	−	0.864016i	$-0.332058\pi$
$719$	27.0000			1.00693			0.503465	+	0.864016i	$0.332058\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$		0			0
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$		−	19.0526i		−	0.708572i
$724$	7.00000	−	12.1244i	0.260153	−	0.450598i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$	−21.0000	−	12.1244i	−0.779383	−	0.449977i
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.860376	+	0.509661i	$0.170229\pi$
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.0111912	+	0.999937i	$0.496438\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−3.00000			−0.111035
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	21.0000	+	12.1244i	0.776182	+	0.448129i
$733$	13.5000	−	23.3827i	0.498634	−	0.863659i	−0.501365	−	0.865236i	$-0.667169\pi$
$733$	13.5000	−	23.3827i	0.498634	−	0.863659i	0.999999	+	0.00157675i	$0.000501894\pi$
$734$	−1.50000	+	2.59808i	−0.0553660	+	0.0958967i
$735$		0			0
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	20.0000			0.736709
$738$	7.50000	+	12.9904i	0.276079	+	0.478183i
$739$	−9.00000			−0.331070			−0.165535	−	0.986204i	$-0.552935\pi$
$739$	−9.00000			−0.331070			−0.165535	+	0.986204i	$0.552935\pi$
$740$	1.50000	+	2.59808i	0.0551411	+	0.0955072i
$741$	−7.50000	+	4.33013i	−0.275519	+	0.159071i
$742$		0			0
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	−0.695024	−	0.718986i	$-0.744606\pi$
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	0.970173	+	0.242415i	$0.0779397\pi$
$744$		0			0
$745$	−1.50000	−	2.59808i	−0.0549557	−	0.0951861i
$746$	−25.0000			−0.915315
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$	15.0000			0.548454
$749$		0			0
$750$		−	15.5885i		−	0.569210i
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	0.431390	+	0.902165i	$0.358023\pi$
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	−0.996993	+	0.0774878i	$0.975310\pi$
$752$		0			0
$753$	−42.0000	−	24.2487i	−1.53057	−	0.883672i
$754$	2.50000	+	4.33013i	0.0910446	+	0.157694i
$755$	5.00000			0.181969
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	6.00000	+	10.3923i	0.217930	+	0.377466i
$759$	−22.5000	−	12.9904i	−0.816698	−	0.471521i
$760$	−1.50000	+	2.59808i	−0.0544107	+	0.0942421i
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	−0.510551	−	0.859848i	$-0.670558\pi$
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	0.999925	+	0.0122260i	$0.00389175\pi$
$762$		−	20.7846i		−	0.752947i
$763$		0			0
$764$	−8.00000			−0.289430
$765$	9.00000			0.325396
$766$	−27.0000			−0.975550
$767$		0			0
$768$	−25.5000	+	14.7224i	−0.920152	+	0.531250i
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$		0			0
$771$	43.5000	−	25.1147i	1.56661	−	0.904485i
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	−31.0000			−1.11499			−0.557496	−	0.830179i	$-0.688238\pi$
$773$	−31.0000			−1.11499			−0.557496	+	0.830179i	$0.688238\pi$
$774$	3.00000			0.107833
$775$		0			0
$776$	13.5000	+	23.3827i	0.484622	+	0.839390i
$777$		0			0
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	2.50000	−	4.33013i	0.0895718	−	0.155143i
$780$	7.50000	+	4.33013i	0.268543	+	0.155043i
$781$	30.0000	+	51.9615i	1.07348	+	1.85933i
$782$	−9.00000			−0.321839
$783$	4.50000	−	2.59808i	0.160817	−	0.0928477i
$784$		0			0
$785$	−7.00000	−	12.1244i	−0.249841	−	0.432737i
$786$	−1.50000	−	0.866025i	−0.0535032	−	0.0308901i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$			8.66025i			0.308313i
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$		0			0
$792$	−22.5000	+	38.9711i	−0.799503	+	1.38478i
$793$	70.0000			2.48577
$794$	7.50000	+	12.9904i	0.266165	+	0.461011i
$795$	−13.5000	+	7.79423i	−0.478796	+	0.276433i
$796$	−1.50000	+	2.59808i	−0.0531661	+	0.0920864i
$797$	11.5000	−	19.9186i	0.407351	−	0.705552i	−0.587241	−	0.809412i	$-0.699786\pi$
$797$	11.5000	−	19.9186i	0.407351	−	0.705552i	0.994592	+	0.103860i	$0.0331193\pi$
$798$		0			0
$799$		0			0
$800$	−20.0000			−0.707107
$801$	19.5000	+	33.7750i	0.688999	+	1.19338i
$802$	3.00000			0.105934
$803$	7.50000	+	12.9904i	0.264669	+	0.458421i
$804$		−	6.92820i		−	0.244339i
$805$		0			0
$806$		0			0
$807$	4.50000	+	2.59808i	0.158408	+	0.0914566i
$808$	25.5000	+	44.1673i	0.897087	+	1.55380i
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	1.50000	+	0.866025i	0.0526073	+	0.0303728i
$814$	−7.50000	+	12.9904i	−0.262875	+	0.455313i
$815$	5.50000	−	9.52628i	0.192657	−	0.333691i
$816$			5.19615i			0.181902i
$817$	−0.500000	−	0.866025i	−0.0174928	−	0.0302984i
$818$	−14.0000			−0.489499
$819$		0			0
$820$	−5.00000			−0.174608
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$	−13.5000	+	7.79423i	−0.470867	+	0.271855i
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	1.50000	−	2.59808i	0.0522550	−	0.0905083i
$825$	−30.0000	+	17.3205i	−1.04447	+	0.603023i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−4.50000	+	7.79423i	−0.156386	+	0.270868i
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$			32.9090i			1.14160i
$832$	−17.5000	+	30.3109i	−0.606703	+	1.05084i
$833$		0			0
$834$	13.5000	+	7.79423i	0.467467	+	0.269892i
$835$	−9.50000	−	16.4545i	−0.328761	−	0.569431i
$836$	5.00000			0.172929
$837$		0			0
$838$	−9.00000			−0.310900
$839$	−18.5000	−	32.0429i	−0.638691	−	1.10625i	−0.985720	−	0.168391i	$-0.946143\pi$
$839$	−18.5000	−	32.0429i	−0.638691	−	1.10625i	0.347029	−	0.937854i	$-0.387190\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	0.500000	−	0.866025i	0.0172311	−	0.0298452i
$843$		−	50.2295i		−	1.72999i
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$	12.0000			0.412813
$846$		0			0
$847$		0			0
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	−42.0000	+	24.2487i	−1.44144	+	0.832214i
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$	−4.50000	+	7.79423i	−0.154258	+	0.267183i
$852$	18.0000	−	10.3923i	0.616670	−	0.356034i
$853$	−18.5000	−	32.0429i	−0.633428	−	1.09713i	−0.986846	−	0.161664i	$-0.948314\pi$
$853$	−18.5000	−	32.0429i	−0.633428	−	1.09713i	0.353418	−	0.935466i	$-0.385019\pi$
$854$		0			0
$855$	3.00000			0.102598
$856$	−51.0000			−1.74314
$857$	5.50000	+	9.52628i	0.187876	+	0.325412i	0.944542	−	0.328391i	$-0.106506\pi$
$857$	5.50000	+	9.52628i	0.187876	+	0.325412i	−0.756666	+	0.653802i	$0.773173\pi$
$858$			43.3013i			1.47828i
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	−0.874429	−	0.485153i	$-0.838764\pi$
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	0.857369	+	0.514701i	$0.172097\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$		0			0
$862$	4.50000	+	7.79423i	0.153271	+	0.265472i
$863$	−39.0000			−1.32758			−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000			−1.32758			−0.663788	+	0.747921i	$0.731052\pi$
$864$	22.5000	+	12.9904i	0.765466	+	0.441942i
$865$	14.0000			0.476014
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$		0			0
$869$	−20.0000	+	34.6410i	−0.678454	+	1.17512i
$870$		−	1.73205i		−	0.0587220i
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$	27.0000			0.914335
$873$	13.5000	−	23.3827i	0.456906	−	0.791384i
$874$	−3.00000			−0.101477
$875$		0			0
$876$	4.50000	−	2.59808i	0.152041	−	0.0877809i
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.0608407	−	0.998147i	$-0.480622\pi$
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.834001	−	0.551763i	$-0.186045\pi$
$878$		0			0
$879$	7.50000	−	4.33013i	0.252969	−	0.146052i
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	−7.50000	−	12.9904i	−0.252252	−	0.436914i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−14.5000	+	25.1147i	−0.486862	+	0.843270i	−0.999886	−	0.0151042i	$-0.995192\pi$
$887$	−14.5000	+	25.1147i	−0.486862	+	0.843270i	0.513024	+	0.858375i	$0.328525\pi$
$888$	13.5000	+	7.79423i	0.453030	+	0.261557i
$889$		0			0
$890$	13.0000			0.435761
$891$	45.0000			1.50756
$892$	19.0000			0.636167
$893$		0			0
$894$	−4.50000	−	2.59808i	−0.150503	−	0.0868927i
$895$	−9.50000	+	16.4545i	−0.317550	+	0.550013i
$896$		0			0
$897$			25.9808i			0.867472i
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$		0			0
$900$	6.00000	+	10.3923i	0.200000	+	0.346410i
$901$	27.0000			0.899500
$902$	−12.5000	−	21.6506i	−0.416204	−	0.720887i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$	−7.00000	+	12.1244i	−0.232688	+	0.403027i
$906$	7.50000	−	4.33013i	0.249171	−	0.143859i
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$	−3.00000			−0.0995585
$909$	25.5000	−	44.1673i	0.845782	−	1.46494i
$910$		0			0
$911$	−13.5000	−	23.3827i	−0.447275	−	0.774703i	0.550933	−	0.834550i	$-0.314272\pi$
$911$	−13.5000	−	23.3827i	−0.447275	−	0.774703i	−0.998208	+	0.0598468i	$0.980939\pi$
$912$			1.73205i			0.0573539i
$913$	−22.5000	+	38.9711i	−0.744641	+	1.28976i
$914$	−11.0000	+	19.0526i	−0.363848	+	0.630203i
$915$	−21.0000	−	12.1244i	−0.694239	−	0.400819i
$916$	0.500000	+	0.866025i	0.0165205	+	0.0286143i
$917$		0			0
$918$	13.5000	−	7.79423i	0.445566	−	0.257248i
$919$	17.0000			0.560778			0.280389	−	0.959886i	$-0.409536\pi$
$919$	17.0000			0.560778			0.280389	+	0.959886i	$0.409536\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$	42.0000	+	24.2487i	1.38395	+	0.799022i
$922$	9.50000	−	16.4545i	0.312866	−	0.541900i
$923$	30.0000	−	51.9615i	0.987462	−	1.71033i
$924$		0			0
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	13.0000			0.427207
$927$	−3.00000			−0.0985329
$928$	−5.00000			−0.164133
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$		0			0
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$		0			0
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$	−15.0000			−0.490552
$936$	45.0000			1.47087
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$		0			0
$939$		−	24.2487i		−	0.791327i
$940$		0			0
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	−0.957273	−	0.289187i	$-0.906615\pi$
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	0.729079	+	0.684429i	$0.239949\pi$
$942$	−21.0000	−	12.1244i	−0.684217	−	0.395033i
$943$	−7.50000	−	12.9904i	−0.244234	−	0.423025i
$944$		0			0
$945$		0			0
$946$	−5.00000			−0.162564
$947$	10.0000	+	17.3205i	0.324956	+	0.562841i	0.981504	−	0.191444i	$-0.0613171\pi$
$947$	10.0000	+	17.3205i	0.324956	+	0.562841i	−0.656547	+	0.754285i	$0.727984\pi$
$948$	12.0000	+	6.92820i	0.389742	+	0.225018i
$949$	7.50000	−	12.9904i	0.243460	−	0.421686i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		−	10.3923i		−	0.336994i
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	−13.5000	+	23.3827i	−0.437079	+	0.757042i
$955$	8.00000			0.258874
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$	−7.50000	+	4.33013i	−0.242441	+	0.139973i
$958$	12.5000	−	21.6506i	0.403857	−	0.699500i
$959$		0			0
$960$	10.5000	−	6.06218i	0.338886	−	0.195656i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	15.0000			0.483619
$963$	25.5000	+	44.1673i	0.821726	+	1.42327i
$964$	11.0000			0.354286
$965$	5.00000	+	8.66025i	0.160956	+	0.278783i
$966$		0			0
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$	21.0000	−	36.3731i	0.674966	−	1.16907i
$969$	−4.50000	−	2.59808i	−0.144561	−	0.0834622i
$970$	−4.50000	−	7.79423i	−0.144486	−	0.250258i
$971$	−57.0000			−1.82922			−0.914609	−	0.404341i	$-0.867501\pi$
$971$	−57.0000			−1.82922			−0.914609	+	0.404341i	$0.867501\pi$
$972$		−	15.5885i		−	0.500000i
$973$		0			0
$974$	−9.50000	−	16.4545i	−0.304400	−	0.527236i
$975$	30.0000	+	17.3205i	0.960769	+	0.554700i
$976$	7.00000	−	12.1244i	0.224065	−	0.388091i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		−	19.0526i		−	0.609234i
$979$	−32.5000	−	56.2917i	−1.03870	−	1.79909i
$980$		0			0
$981$	−13.5000	−	23.3827i	−0.431022	−	0.746552i
$982$	13.0000			0.414847
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$	−22.5000	+	12.9904i	−0.717274	+	0.414118i
$985$	−1.00000	+	1.73205i	−0.0318626	+	0.0551877i
$986$	−1.50000	+	2.59808i	−0.0477697	+	0.0827396i
$987$		0			0
$988$	−2.50000	−	4.33013i	−0.0795356	−	0.137760i
$989$	−3.00000			−0.0953945
$990$	7.50000	−	12.9904i	0.238366	−	0.412861i
$991$	−37.0000			−1.17534			−0.587672	−	0.809099i	$-0.699955\pi$
$991$	−37.0000			−1.17534			−0.587672	+	0.809099i	$0.699955\pi$
$992$		0			0
$993$			13.8564i			0.439720i
$994$		0			0
$995$	1.50000	−	2.59808i	0.0475532	−	0.0823646i
$996$	13.5000	+	7.79423i	0.427764	+	0.246970i
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$	31.0000			0.981288
$999$		−	15.5885i		−	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.a.148.1		2
3.2	odd	2		1323.2.f.b.442.1		2
7.2	even	3		441.2.g.a.67.1		2
7.3	odd	6		63.2.h.a.58.1	yes	2
7.4	even	3		441.2.h.a.373.1		2
7.5	odd	6		63.2.g.a.4.1	✓	2
7.6	odd	2		441.2.f.b.148.1		2
9.2	odd	6		1323.2.f.b.883.1		2
9.4	even	3		3969.2.a.f.1.1		1
9.5	odd	6		3969.2.a.a.1.1		1
9.7	even	3	inner	441.2.f.a.295.1		2
21.2	odd	6		1323.2.g.a.361.1		2
21.5	even	6		189.2.g.a.172.1		2
21.11	odd	6		1323.2.h.a.226.1		2
21.17	even	6		189.2.h.a.37.1		2
21.20	even	2		1323.2.f.a.442.1		2
28.3	even	6		1008.2.q.c.625.1		2
28.19	even	6		1008.2.t.d.193.1		2
63.2	odd	6		1323.2.h.a.802.1		2
63.5	even	6		567.2.e.b.487.1		2
63.11	odd	6		1323.2.g.a.667.1		2
63.13	odd	6		3969.2.a.d.1.1		1
63.16	even	3		441.2.h.a.214.1		2
63.20	even	6		1323.2.f.a.883.1		2
63.25	even	3		441.2.g.a.79.1		2
63.31	odd	6		567.2.e.a.163.1		2
63.34	odd	6		441.2.f.b.295.1		2
63.38	even	6		189.2.g.a.100.1		2
63.40	odd	6		567.2.e.a.487.1		2
63.41	even	6		3969.2.a.c.1.1		1
63.47	even	6		189.2.h.a.46.1		2
63.52	odd	6		63.2.g.a.16.1	yes	2
63.59	even	6		567.2.e.b.163.1		2
63.61	odd	6		63.2.h.a.25.1	yes	2
84.47	odd	6		3024.2.t.d.1873.1		2
84.59	odd	6		3024.2.q.b.2305.1		2
252.47	odd	6		3024.2.q.b.2881.1		2
252.115	even	6		1008.2.t.d.961.1		2
252.187	even	6		1008.2.q.c.529.1		2
252.227	odd	6		3024.2.t.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	7.5	odd	6
63.2.g.a.16.1	yes	2	63.52	odd	6
63.2.h.a.25.1	yes	2	63.61	odd	6
63.2.h.a.58.1	yes	2	7.3	odd	6
189.2.g.a.100.1		2	63.38	even	6
189.2.g.a.172.1		2	21.5	even	6
189.2.h.a.37.1		2	21.17	even	6
189.2.h.a.46.1		2	63.47	even	6
441.2.f.a.148.1		2	1.1	even	1	trivial
441.2.f.a.295.1		2	9.7	even	3	inner
441.2.f.b.148.1		2	7.6	odd	2
441.2.f.b.295.1		2	63.34	odd	6
441.2.g.a.67.1		2	7.2	even	3
441.2.g.a.79.1		2	63.25	even	3
441.2.h.a.214.1		2	63.16	even	3
441.2.h.a.373.1		2	7.4	even	3
567.2.e.a.163.1		2	63.31	odd	6
567.2.e.a.487.1		2	63.40	odd	6
567.2.e.b.163.1		2	63.59	even	6
567.2.e.b.487.1		2	63.5	even	6
1008.2.q.c.529.1		2	252.187	even	6
1008.2.q.c.625.1		2	28.3	even	6
1008.2.t.d.193.1		2	28.19	even	6
1008.2.t.d.961.1		2	252.115	even	6
1323.2.f.a.442.1		2	21.20	even	2
1323.2.f.a.883.1		2	63.20	even	6
1323.2.f.b.442.1		2	3.2	odd	2
1323.2.f.b.883.1		2	9.2	odd	6
1323.2.g.a.361.1		2	21.2	odd	6
1323.2.g.a.667.1		2	63.11	odd	6
1323.2.h.a.226.1		2	21.11	odd	6
1323.2.h.a.802.1		2	63.2	odd	6
3024.2.q.b.2305.1		2	84.59	odd	6
3024.2.q.b.2881.1		2	252.47	odd	6
3024.2.t.d.289.1		2	252.227	odd	6
3024.2.t.d.1873.1		2	84.47	odd	6
3969.2.a.a.1.1		1	9.5	odd	6
3969.2.a.c.1.1		1	63.41	even	6
3969.2.a.d.1.1		1	63.13	odd	6
3969.2.a.f.1.1		1	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} +(-2.50000 - 4.33013i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(-2.50000 + 4.33013i) q^{13} +(1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(1.50000 - 2.59808i) q^{18} -1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{26} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{32} +8.66025i q^{33} +(1.50000 + 2.59808i) q^{34} +3.00000 q^{36} +3.00000 q^{37} +(0.500000 + 0.866025i) q^{38} +(7.50000 - 4.33013i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} -5.00000 q^{44} -3.00000 q^{45} +3.00000 q^{46} -1.73205i q^{48} +(2.00000 - 3.46410i) q^{50} +(4.50000 + 2.59808i) q^{51} +(2.50000 + 4.33013i) q^{52} -9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +5.00000 q^{55} +(1.50000 + 0.866025i) q^{57} +(0.500000 - 0.866025i) q^{58} -1.73205i q^{60} +(-7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(7.50000 - 4.33013i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-4.50000 - 7.79423i) q^{72} -3.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} -6.92820i q^{75} +(-0.500000 + 0.866025i) q^{76} +(-7.50000 - 4.33013i) q^{78} +(-4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(0.500000 - 0.866025i) q^{86} -1.73205i q^{87} +(7.50000 + 12.9904i) q^{88} +13.0000 q^{89} +(1.50000 + 2.59808i) q^{90} +(1.50000 + 2.59808i) q^{92} +(0.500000 - 0.866025i) q^{95} +(7.50000 - 4.33013i) q^{96} +(-4.50000 - 7.79423i) q^{97} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 + q^4 - q^5 - 6 * q^8 + 3 * q^9	\( 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 6 q^{8} + 3 q^{9} + 2 q^{10} - 5 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{15} + q^{16} - 6 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - 3 q^{23} + 9 q^{24} + 4 q^{25} + 10 q^{26} + q^{29} - 3 q^{30} - 5 q^{32} + 3 q^{34} + 6 q^{36} + 6 q^{37} + q^{38} + 15 q^{39} + 3 q^{40} - 5 q^{41} + q^{43} - 10 q^{44} - 6 q^{45} + 6 q^{46} + 4 q^{50} + 9 q^{51} + 5 q^{52} - 18 q^{53} - 9 q^{54} + 10 q^{55} + 3 q^{57} + q^{58} - 14 q^{61} + 14 q^{64} - 5 q^{65} + 15 q^{66} - 4 q^{67} - 3 q^{68} + 9 q^{69} - 24 q^{71} - 9 q^{72} - 6 q^{73} - 3 q^{74} - q^{76} - 15 q^{78} - 8 q^{79} - 2 q^{80} - 9 q^{81} + 10 q^{82} - 9 q^{83} + 3 q^{85} + q^{86} + 15 q^{88} + 26 q^{89} + 3 q^{90} + 3 q^{92} + q^{95} + 15 q^{96} - 9 q^{97} + 15 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 + q^4 - q^5 - 6 * q^8 + 3 * q^9 + 2 * q^10 - 5 * q^11 - 3 * q^12 - 5 * q^13 + 3 * q^15 + q^16 - 6 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - 3 * q^23 + 9 * q^24 + 4 * q^25 + 10 * q^26 + q^29 - 3 * q^30 - 5 * q^32 + 3 * q^34 + 6 * q^36 + 6 * q^37 + q^38 + 15 * q^39 + 3 * q^40 - 5 * q^41 + q^43 - 10 * q^44 - 6 * q^45 + 6 * q^46 + 4 * q^50 + 9 * q^51 + 5 * q^52 - 18 * q^53 - 9 * q^54 + 10 * q^55 + 3 * q^57 + q^58 - 14 * q^61 + 14 * q^64 - 5 * q^65 + 15 * q^66 - 4 * q^67 - 3 * q^68 + 9 * q^69 - 24 * q^71 - 9 * q^72 - 6 * q^73 - 3 * q^74 - q^76 - 15 * q^78 - 8 * q^79 - 2 * q^80 - 9 * q^81 + 10 * q^82 - 9 * q^83 + 3 * q^85 + q^86 + 15 * q^88 + 26 * q^89 + 3 * q^90 + 3 * q^92 + q^95 + 15 * q^96 - 9 * q^97 + 15 * q^99

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