LMFDB - Embedded newform 441.2.o.a.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

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([1, 3]))

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

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

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (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:	$3.52140272914$
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 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.293
Dual form			441.2.o.a.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -3.00000 q^{6} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -3.00000 q^{6} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +5.19615i q^{10} +(-1.50000 + 0.866025i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.50000 + 0.866025i) q^{13} +(4.50000 - 2.59808i) q^{15} +(2.50000 + 4.33013i) q^{16} +3.00000 q^{17} +(4.50000 + 2.59808i) q^{18} +5.19615i q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-4.50000 - 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-2.00000 - 3.46410i) q^{25} +3.00000 q^{26} -5.19615i q^{27} +(-4.50000 + 2.59808i) q^{29} +(4.50000 - 7.79423i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} +3.00000 q^{33} +(4.50000 - 2.59808i) q^{34} +3.00000 q^{36} +7.00000 q^{37} +(4.50000 + 7.79423i) q^{38} +(-1.50000 - 2.59808i) q^{39} +(-4.50000 - 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +1.73205i q^{44} -9.00000 q^{45} -9.00000 q^{46} -8.66025i q^{48} +(-6.00000 - 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(1.50000 - 0.866025i) q^{52} +8.66025i q^{53} +(-4.50000 - 7.79423i) q^{54} -5.19615i q^{55} +(4.50000 - 7.79423i) q^{57} +(-4.50000 + 7.79423i) q^{58} -5.19615i q^{60} +(12.0000 - 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-4.50000 + 2.59808i) q^{65} +(4.50000 - 2.59808i) q^{66} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(4.50000 + 7.79423i) q^{69} -3.46410i q^{71} +(-4.50000 + 2.59808i) q^{72} -5.19615i q^{73} +(10.5000 - 6.06218i) q^{74} +6.92820i q^{75} +(4.50000 + 2.59808i) q^{76} +(-4.50000 - 2.59808i) q^{78} +(-4.00000 - 6.92820i) q^{79} -15.0000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.19615i q^{82} +(7.50000 + 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(-1.50000 - 0.866025i) q^{86} +9.00000 q^{87} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{89} +(-13.5000 + 7.79423i) q^{90} +(-4.50000 + 2.59808i) q^{92} +(3.00000 + 5.19615i) q^{93} +(-13.5000 - 7.79423i) q^{95} +(-4.50000 - 7.79423i) q^{96} +(1.50000 - 0.866025i) q^{97} +(-4.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + 3 * q^9	$ 2 q + 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{13} + 9 q^{15} + 5 q^{16} + 6 q^{17} + 9 q^{18} + 3 q^{20} - 3 q^{22} - 9 q^{23} + 3 q^{24} - 4 q^{25} + 6 q^{26} - 9 q^{29} + 9 q^{30} - 6 q^{31} + 9 q^{32} + 6 q^{33} + 9 q^{34} + 6 q^{36} + 14 q^{37} + 9 q^{38} - 3 q^{39} - 9 q^{40} - 3 q^{41} - q^{43} - 18 q^{45} - 18 q^{46} - 12 q^{50} - 9 q^{51} + 3 q^{52} - 9 q^{54} + 9 q^{57} - 9 q^{58} + 24 q^{61} - 12 q^{62} - 2 q^{64} - 9 q^{65} + 9 q^{66} + 4 q^{67} + 3 q^{68} + 9 q^{69} - 9 q^{72} + 21 q^{74} + 9 q^{76} - 9 q^{78} - 8 q^{79} - 30 q^{80} - 9 q^{81} + 15 q^{83} - 9 q^{85} - 3 q^{86} + 18 q^{87} - 3 q^{88} + 6 q^{89} - 27 q^{90} - 9 q^{92} + 6 q^{93} - 27 q^{95} - 9 q^{96} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^13 + 9 * q^15 + 5 * q^16 + 6 * q^17 + 9 * q^18 + 3 * q^20 - 3 * q^22 - 9 * q^23 + 3 * q^24 - 4 * q^25 + 6 * q^26 - 9 * q^29 + 9 * q^30 - 6 * q^31 + 9 * q^32 + 6 * q^33 + 9 * q^34 + 6 * q^36 + 14 * q^37 + 9 * q^38 - 3 * q^39 - 9 * q^40 - 3 * q^41 - q^43 - 18 * q^45 - 18 * q^46 - 12 * q^50 - 9 * q^51 + 3 * q^52 - 9 * q^54 + 9 * q^57 - 9 * q^58 + 24 * q^61 - 12 * q^62 - 2 * q^64 - 9 * q^65 + 9 * q^66 + 4 * q^67 + 3 * q^68 + 9 * q^69 - 9 * q^72 + 21 * q^74 + 9 * q^76 - 9 * q^78 - 8 * q^79 - 30 * q^80 - 9 * q^81 + 15 * q^83 - 9 * q^85 - 3 * q^86 + 18 * q^87 - 3 * q^88 + 6 * q^89 - 27 * q^90 - 9 * q^92 + 6 * q^93 - 27 * q^95 - 9 * q^96 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	−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
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	−3.00000			−1.22474
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$			5.19615i			1.64317i
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	4.50000	−	2.59808i	1.16190	−	0.670820i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	4.50000	+	2.59808i	1.06066	+	0.612372i
$19$			5.19615i			1.19208i	0.802955	+	0.596040i	$0.203260\pi$
$19$			5.19615i			1.19208i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−4.50000	−	2.59808i	−0.938315	−	0.541736i	−0.0488832	−	0.998805i	$-0.515566\pi$
$23$	−4.50000	−	2.59808i	−0.938315	−	0.541736i	−0.889432	+	0.457068i	$0.848900\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	3.00000			0.588348
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	−4.50000	+	2.59808i	−0.835629	+	0.482451i	−0.855776	−	0.517346i	$-0.826920\pi$
$29$	−4.50000	+	2.59808i	−0.835629	+	0.482451i	0.0201471	+	0.999797i	$0.493587\pi$
$30$	4.50000	−	7.79423i	0.821584	−	1.42302i
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$	3.00000			0.522233
$34$	4.50000	−	2.59808i	0.771744	−	0.445566i
$35$		0			0
$36$	3.00000			0.500000
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	4.50000	+	7.79423i	0.729996	+	1.26439i
$39$	−1.50000	−	2.59808i	−0.240192	−	0.416025i
$40$	−4.50000	−	2.59808i	−0.711512	−	0.410792i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$			1.73205i			0.261116i
$45$	−9.00000			−1.34164
$46$	−9.00000			−1.32698
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		−	8.66025i		−	1.25000i
$49$		0			0
$50$	−6.00000	−	3.46410i	−0.848528	−	0.489898i
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	1.50000	−	0.866025i	0.208013	−	0.120096i
$53$			8.66025i			1.18958i	0.803882	+	0.594789i	$0.202764\pi$
$53$			8.66025i			1.18958i	−0.803882	+	0.594789i	$0.797236\pi$
$54$	−4.50000	−	7.79423i	−0.612372	−	1.06066i
$55$		−	5.19615i		−	0.700649i
$56$		0			0
$57$	4.50000	−	7.79423i	0.596040	−	1.03237i
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		−	5.19615i		−	0.670820i
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.999043	−	0.0437377i	$-0.0139266\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.50000	+	2.59808i	−0.558156	+	0.322252i
$66$	4.50000	−	2.59808i	0.553912	−	0.319801i
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	4.50000	+	7.79423i	0.541736	+	0.938315i
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$	−4.50000	+	2.59808i	−0.530330	+	0.306186i
$73$		−	5.19615i		−	0.608164i	−0.952646	−	0.304082i	$-0.901650\pi$
$73$		−	5.19615i		−	0.608164i	0.952646	−	0.304082i	$-0.0983496\pi$
$74$	10.5000	−	6.06218i	1.22060	−	0.704714i
$75$			6.92820i			0.800000i
$76$	4.50000	+	2.59808i	0.516185	+	0.298020i
$77$		0			0
$78$	−4.50000	−	2.59808i	−0.509525	−	0.294174i
$79$	−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	$0.981922\pi$
$80$	−15.0000			−1.67705
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$			5.19615i			0.573819i
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	0.903263	+	0.429087i	$0.141165\pi$
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	−0.0800311	+	0.996792i	$0.525502\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	−1.50000	−	0.866025i	−0.161749	−	0.0933859i
$87$	9.00000			0.964901
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$	−13.5000	+	7.79423i	−1.42302	+	0.821584i
$91$		0			0
$92$	−4.50000	+	2.59808i	−0.469157	+	0.270868i
$93$	3.00000	+	5.19615i	0.311086	+	0.538816i
$94$		0			0
$95$	−13.5000	−	7.79423i	−1.38507	−	0.799671i
$96$	−4.50000	−	7.79423i	−0.459279	−	0.795495i
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	−0.421912	−	0.906637i	$-0.638641\pi$
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	0.574214	+	0.818705i	$0.305308\pi$
$98$		0			0
$99$	−4.50000	−	2.59808i	−0.452267	−	0.261116i
$100$	−4.00000			−0.400000
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	−9.00000			−0.891133
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.116298	−	0.993214i	$-0.537103\pi$
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.918298	+	0.395890i	$0.870436\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	7.50000	+	12.9904i	0.728464	+	1.26174i
$107$		−	8.66025i		−	0.837218i	−0.908166	−	0.418609i	$-0.862518\pi$
$107$		−	8.66025i		−	0.837218i	0.908166	−	0.418609i	$-0.137482\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	19.0000			1.81987			0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000			1.81987			0.909935	+	0.414751i	$0.136131\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$	−10.5000	−	6.06218i	−0.996616	−	0.575396i
$112$		0			0
$113$	1.50000	+	0.866025i	0.141108	+	0.0814688i	0.568892	−	0.822412i	$-0.307372\pi$
$113$	1.50000	+	0.866025i	0.141108	+	0.0814688i	−0.427784	+	0.903881i	$0.640706\pi$
$114$		−	15.5885i		−	1.45999i
$115$	13.5000	−	7.79423i	1.25888	−	0.726816i
$116$			5.19615i			0.482451i
$117$			5.19615i			0.480384i
$118$		0			0
$119$		0			0
$120$	4.50000	+	7.79423i	0.410792	+	0.711512i
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	12.0000	−	20.7846i	1.08643	−	1.88175i
$123$	4.50000	−	2.59808i	0.405751	−	0.234261i
$124$	−3.00000	+	1.73205i	−0.269408	+	0.155543i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$			1.73205i			0.152499i
$130$	−4.50000	+	7.79423i	−0.394676	+	0.683599i
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$	1.50000	−	2.59808i	0.130558	−	0.226134i
$133$		0			0
$134$		−	6.92820i		−	0.598506i
$135$	13.5000	+	7.79423i	1.16190	+	0.670820i
$136$			5.19615i			0.445566i
$137$	10.5000	−	6.06218i	0.897076	−	0.517927i	0.0208253	−	0.999783i	$-0.493371\pi$
$137$	10.5000	−	6.06218i	0.897076	−	0.517927i	0.876250	+	0.481856i	$0.160037\pi$
$138$	13.5000	+	7.79423i	1.14920	+	0.663489i
$139$	7.50000	+	4.33013i	0.636142	+	0.367277i	0.783127	−	0.621862i	$-0.213624\pi$
$139$	7.50000	+	4.33013i	0.636142	+	0.367277i	−0.146985	+	0.989139i	$0.546957\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−3.00000			−0.250873
$144$	−7.50000	+	12.9904i	−0.625000	+	1.08253i
$145$		−	15.5885i		−	1.29455i
$146$	−4.50000	−	7.79423i	−0.372423	−	0.645055i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	−1.50000	−	0.866025i	−0.122885	−	0.0709476i	0.437298	−	0.899317i	$-0.355936\pi$
$149$	−1.50000	−	0.866025i	−0.122885	−	0.0709476i	−0.560182	+	0.828369i	$0.689269\pi$
$150$	6.00000	+	10.3923i	0.489898	+	0.848528i
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$	−9.00000			−0.729996
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$	9.00000	−	5.19615i	0.722897	−	0.417365i
$156$	−3.00000			−0.240192
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$	−12.0000	−	6.92820i	−0.954669	−	0.551178i
$159$	7.50000	−	12.9904i	0.594789	−	1.03020i
$160$	−13.5000	+	7.79423i	−1.06727	+	0.616188i
$161$		0			0
$162$			15.5885i			1.22474i
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$	−4.50000	+	7.79423i	−0.350325	+	0.606780i
$166$	22.5000	+	12.9904i	1.74634	+	1.00825i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$			15.5885i			1.19558i
$171$	−13.5000	+	7.79423i	−1.03237	+	0.596040i
$172$	−1.00000			−0.0762493
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	13.5000	−	7.79423i	1.02343	−	0.590879i
$175$		0			0
$176$	−7.50000	−	4.33013i	−0.565334	−	0.326396i
$177$		0			0
$178$	4.50000	−	2.59808i	0.337289	−	0.194734i
$179$		−	15.5885i		−	1.16514i	−0.812782	−	0.582568i	$-0.802048\pi$
$179$		−	15.5885i		−	1.16514i	0.812782	−	0.582568i	$-0.197952\pi$
$180$	−4.50000	+	7.79423i	−0.335410	+	0.580948i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−24.0000			−1.77413
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−10.5000	+	18.1865i	−0.771975	+	1.33710i
$186$	9.00000	+	5.19615i	0.659912	+	0.381000i
$187$	−4.50000	+	2.59808i	−0.329073	+	0.189990i
$188$		0			0
$189$		0			0
$190$	−27.0000			−1.95879
$191$	15.0000	−	8.66025i	1.08536	−	0.626634i	0.153024	−	0.988222i	$-0.451099\pi$
$191$	15.0000	−	8.66025i	1.08536	−	0.626634i	0.932338	+	0.361588i	$0.117765\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$	1.50000	−	2.59808i	0.107694	−	0.186531i
$195$	9.00000			0.644503
$196$		0			0
$197$			13.8564i			0.987228i	0.869681	+	0.493614i	$0.164324\pi$
$197$			13.8564i			0.987228i	−0.869681	+	0.493614i	$0.835676\pi$
$198$	−9.00000			−0.639602
$199$		−	8.66025i		−	0.613909i	−0.951724	−	0.306955i	$-0.900690\pi$
$199$		−	8.66025i		−	0.613909i	0.951724	−	0.306955i	$-0.0993100\pi$
$200$	6.00000	−	3.46410i	0.424264	−	0.244949i
$201$	−6.00000	+	3.46410i	−0.423207	+	0.244339i
$202$	−4.50000	−	2.59808i	−0.316619	−	0.182800i
$203$		0			0
$204$	−4.50000	+	2.59808i	−0.315063	+	0.181902i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−21.0000			−1.46314
$207$		−	15.5885i		−	1.08347i
$208$			8.66025i			0.600481i
$209$	−4.50000	−	7.79423i	−0.311272	−	0.539138i
$210$		0			0
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	7.50000	+	4.33013i	0.515102	+	0.297394i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	3.00000			0.204598
$216$	9.00000			0.612372
$217$		0			0
$218$	28.5000	−	16.4545i	1.93026	−	1.11444i
$219$	−4.50000	+	7.79423i	−0.304082	+	0.526685i
$220$	−4.50000	−	2.59808i	−0.303390	−	0.175162i
$221$	4.50000	+	2.59808i	0.302703	+	0.174766i
$222$	−21.0000			−1.40943
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	−0.341703	−	0.939808i	$-0.611004\pi$
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	0.643046	+	0.765828i	$0.277671\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	3.00000			0.199557
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	0.969533	+	0.244962i	$0.0787754\pi$
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	−0.272623	+	0.962121i	$0.587891\pi$
$228$	−4.50000	−	7.79423i	−0.298020	−	0.516185i
$229$	−7.50000	−	4.33013i	−0.495614	−	0.286143i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	−7.50000	−	4.33013i	−0.495614	−	0.286143i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	13.5000	−	23.3827i	0.890164	−	1.54181i
$231$		0			0
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$			5.19615i			0.340411i	0.985409	+	0.170206i	$0.0544432\pi$
$233$			5.19615i			0.340411i	−0.985409	+	0.170206i	$0.945557\pi$
$234$	4.50000	+	7.79423i	0.294174	+	0.509525i
$235$		0			0
$236$		0			0
$237$			13.8564i			0.900070i
$238$		0			0
$239$	1.50000	+	0.866025i	0.0970269	+	0.0560185i	0.547728	−	0.836656i	$-0.315493\pi$
$239$	1.50000	+	0.866025i	0.0970269	+	0.0560185i	−0.450701	+	0.892675i	$0.648826\pi$
$240$	22.5000	+	12.9904i	1.45237	+	0.838525i
$241$	−19.5000	+	11.2583i	−1.25611	+	0.725213i	−0.972315	−	0.233674i	$-0.924925\pi$
$241$	−19.5000	+	11.2583i	−1.25611	+	0.725213i	−0.283790	+	0.958886i	$0.591592\pi$
$242$			13.8564i			0.890724i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		−	13.8564i		−	0.887066i
$245$		0			0
$246$	4.50000	−	7.79423i	0.286910	−	0.496942i
$247$	−4.50000	+	7.79423i	−0.286328	+	0.495935i
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$		−	25.9808i		−	1.64646i
$250$	−4.50000	+	2.59808i	−0.284605	+	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	30.0000	−	17.3205i	1.88237	−	1.08679i
$255$	13.5000	−	7.79423i	0.845403	−	0.488094i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$	1.50000	+	2.59808i	0.0933859	+	0.161749i
$259$		0			0
$260$			5.19615i			0.322252i
$261$	−13.5000	−	7.79423i	−0.835629	−	0.482451i
$262$			15.5885i			0.963058i
$263$	−19.5000	+	11.2583i	−1.20242	+	0.694218i	−0.961093	−	0.276225i	$-0.910916\pi$
$263$	−19.5000	+	11.2583i	−1.20242	+	0.694218i	−0.241329	+	0.970443i	$0.577583\pi$
$264$			5.19615i			0.319801i
$265$	−22.5000	−	12.9904i	−1.38216	−	0.797993i
$266$		0			0
$267$	−4.50000	−	2.59808i	−0.275396	−	0.159000i
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$	27.0000			1.64317
$271$			12.1244i			0.736502i	0.929726	+	0.368251i	$0.120043\pi$
$271$			12.1244i			0.736502i	−0.929726	+	0.368251i	$0.879957\pi$
$272$	7.50000	+	12.9904i	0.454754	+	0.787658i
$273$		0			0
$274$	10.5000	−	18.1865i	0.634328	−	1.09869i
$275$	6.00000	+	3.46410i	0.361814	+	0.208893i
$276$	9.00000			0.541736
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	15.0000			0.899640
$279$		−	10.3923i		−	0.622171i
$280$		0			0
$281$	−16.5000	+	9.52628i	−0.984307	+	0.568290i	−0.903568	−	0.428445i	$-0.859062\pi$
$281$	−16.5000	+	9.52628i	−0.984307	+	0.568290i	−0.0807396	+	0.996735i	$0.525728\pi$
$282$		0			0
$283$	3.00000	+	1.73205i	0.178331	+	0.102960i	0.586509	−	0.809943i	$-0.300502\pi$
$283$	3.00000	+	1.73205i	0.178331	+	0.102960i	−0.408177	+	0.912903i	$0.633835\pi$
$284$	−3.00000	−	1.73205i	−0.178017	−	0.102778i
$285$	13.5000	+	23.3827i	0.799671	+	1.38507i
$286$	−4.50000	+	2.59808i	−0.266091	+	0.153627i
$287$		0			0
$288$			15.5885i			0.918559i
$289$	−8.00000			−0.470588
$290$	−13.5000	−	23.3827i	−0.792747	−	1.37308i
$291$	−3.00000			−0.175863
$292$	−4.50000	−	2.59808i	−0.263343	−	0.152041i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$		0			0
$296$			12.1244i			0.704714i
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$	−3.00000			−0.173785
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$		0			0
$302$	25.5000	+	14.7224i	1.46736	+	0.847181i
$303$			5.19615i			0.298511i
$304$	−22.5000	+	12.9904i	−1.29046	+	0.745049i
$305$			41.5692i			2.38025i
$306$	13.5000	+	7.79423i	0.771744	+	0.445566i
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$	10.5000	+	18.1865i	0.597324	+	1.03460i
$310$	9.00000	−	15.5885i	0.511166	−	0.885365i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	4.50000	−	2.59808i	0.254762	−	0.147087i
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.913356	−	0.407163i	$-0.866518\pi$
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.104065	+	0.994571i	$0.533185\pi$
$314$		0			0
$315$		0			0
$316$	−8.00000			−0.450035
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$		−	25.9808i		−	1.45693i
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$	−7.50000	+	12.9904i	−0.418609	+	0.725052i
$322$		0			0
$323$			15.5885i			0.867365i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		−	6.92820i		−	0.384308i
$326$	16.5000	−	9.52628i	0.913850	−	0.527612i
$327$	−28.5000	−	16.4545i	−1.57605	−	0.909935i
$328$	−4.50000	−	2.59808i	−0.248471	−	0.143455i
$329$		0			0
$330$			15.5885i			0.858116i
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	15.0000			0.823232
$333$	10.5000	+	18.1865i	0.575396	+	0.996616i
$334$		−	15.5885i		−	0.852962i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$	−15.0000	−	8.66025i	−0.815892	−	0.471056i
$339$	−1.50000	−	2.59808i	−0.0814688	−	0.141108i
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	6.00000			0.324918
$342$	−13.5000	+	23.3827i	−0.729996	+	1.26439i
$343$		0			0
$344$	1.50000	−	0.866025i	0.0808746	−	0.0466930i
$345$	−27.0000			−1.45363
$346$	9.00000	+	5.19615i	0.483843	+	0.279347i
$347$	3.00000	+	1.73205i	0.161048	+	0.0929814i	0.578358	−	0.815783i	$-0.303694\pi$
$347$	3.00000	+	1.73205i	0.161048	+	0.0929814i	−0.417310	+	0.908764i	$0.637027\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	−10.5000	+	6.06218i	−0.562052	+	0.324501i	−0.753969	−	0.656910i	$-0.771863\pi$
$349$	−10.5000	+	6.06218i	−0.562052	+	0.324501i	0.191917	+	0.981411i	$0.438530\pi$
$350$		0			0
$351$	4.50000	−	7.79423i	0.240192	−	0.416025i
$352$	−9.00000			−0.479702
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$		0			0
$355$	9.00000	+	5.19615i	0.477670	+	0.275783i
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$		0			0
$358$	−13.5000	−	23.3827i	−0.713497	−	1.23581i
$359$		−	22.5167i		−	1.18838i	−0.804323	−	0.594192i	$-0.797472\pi$
$359$		−	22.5167i		−	1.18838i	0.804323	−	0.594192i	$-0.202528\pi$
$360$		−	15.5885i		−	0.821584i
$361$	−8.00000			−0.421053
$362$		0			0
$363$	12.0000	−	6.92820i	0.629837	−	0.363636i
$364$		0			0
$365$	13.5000	+	7.79423i	0.706622	+	0.407969i
$366$	−36.0000	+	20.7846i	−1.88175	+	1.08643i
$367$	4.50000	−	2.59808i	0.234898	−	0.135618i	−0.377932	−	0.925834i	$-0.623365\pi$
$367$	4.50000	−	2.59808i	0.234898	−	0.135618i	0.612830	+	0.790215i	$0.290031\pi$
$368$		−	25.9808i		−	1.35434i
$369$	−9.00000			−0.468521
$370$			36.3731i			1.89095i
$371$		0			0
$372$	6.00000			0.311086
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.230291	−	0.973122i	$-0.426032\pi$
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.727603	−	0.685999i	$-0.240634\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$	4.50000	+	2.59808i	0.232379	+	0.134164i
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−13.5000	+	7.79423i	−0.692535	+	0.399835i
$381$	−30.0000	−	17.3205i	−1.53695	−	0.887357i
$382$	15.0000	−	25.9808i	0.767467	−	1.32929i
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	−0.957790	−	0.287469i	$-0.907186\pi$
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	0.727851	+	0.685736i	$0.240519\pi$
$384$	21.0000			1.07165
$385$		0			0
$386$		−	3.46410i		−	0.176318i
$387$	1.50000	−	2.59808i	0.0762493	−	0.132068i
$388$		−	1.73205i		−	0.0879316i
$389$	−31.5000	+	18.1865i	−1.59711	+	0.922094i	−0.605074	+	0.796170i	$0.706856\pi$
$389$	−31.5000	+	18.1865i	−1.59711	+	0.922094i	−0.992040	+	0.125924i	$0.959810\pi$
$390$	13.5000	−	7.79423i	0.683599	−	0.394676i
$391$	−13.5000	−	7.79423i	−0.682724	−	0.394171i
$392$		0			0
$393$	13.5000	−	7.79423i	0.680985	−	0.393167i
$394$	12.0000	+	20.7846i	0.604551	+	1.04711i
$395$	24.0000			1.20757
$396$	−4.50000	+	2.59808i	−0.226134	+	0.130558i
$397$		−	8.66025i		−	0.434646i	−0.976100	−	0.217323i	$-0.930268\pi$
$397$		−	8.66025i		−	0.434646i	0.976100	−	0.217323i	$-0.0697324\pi$
$398$	−7.50000	−	12.9904i	−0.375941	−	0.651149i
$399$		0			0
$400$	10.0000	−	17.3205i	0.500000	−	0.866025i
$401$	28.5000	+	16.4545i	1.42322	+	0.821698i	0.996573	−	0.0827195i	$-0.0263606\pi$
$401$	28.5000	+	16.4545i	1.42322	+	0.821698i	0.426649	+	0.904417i	$0.359694\pi$
$402$	−6.00000	+	10.3923i	−0.299253	+	0.518321i
$403$	−3.00000	−	5.19615i	−0.149441	−	0.258839i
$404$	−3.00000			−0.149256
$405$	−13.5000	−	23.3827i	−0.670820	−	1.16190i
$406$		0			0
$407$	−10.5000	+	6.06218i	−0.520466	+	0.300491i
$408$	4.50000	−	7.79423i	0.222783	−	0.385872i
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	0.344270	−	0.938871i	$-0.388126\pi$
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	−0.640951	+	0.767582i	$0.721460\pi$
$410$	−13.5000	−	7.79423i	−0.666717	−	0.384930i
$411$	−21.0000			−1.03585
$412$	−10.5000	+	6.06218i	−0.517298	+	0.298662i
$413$		0			0
$414$	−13.5000	−	23.3827i	−0.663489	−	1.14920i
$415$	−45.0000			−2.20896
$416$	4.50000	+	7.79423i	0.220631	+	0.382143i
$417$	−7.50000	−	12.9904i	−0.367277	−	0.636142i
$418$	−13.5000	−	7.79423i	−0.660307	−	0.381228i
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	−0.109483	−	0.993989i	$-0.534920\pi$
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	0.915561	−	0.402179i	$-0.131747\pi$
$420$		0			0
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	0.700306	−	0.713843i	$-0.253047\pi$
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	−0.968359	+	0.249561i	$0.919714\pi$
$422$		−	8.66025i		−	0.421575i
$423$		0			0
$424$	−15.0000			−0.728464
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$			10.3923i			0.503509i
$427$		0			0
$428$	−7.50000	−	4.33013i	−0.362526	−	0.209305i
$429$	4.50000	+	2.59808i	0.217262	+	0.125436i
$430$	4.50000	−	2.59808i	0.217009	−	0.125290i
$431$		−	15.5885i		−	0.750870i	−0.926849	−	0.375435i	$-0.877493\pi$
$431$		−	15.5885i		−	0.750870i	0.926849	−	0.375435i	$-0.122507\pi$
$432$	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	$-0.108043\pi$
$434$		0			0
$435$	−13.5000	+	23.3827i	−0.647275	+	1.12111i
$436$	9.50000	−	16.4545i	0.454967	−	0.788027i
$437$	13.5000	−	23.3827i	0.645793	−	1.11855i
$438$			15.5885i			0.744845i
$439$	27.0000	−	15.5885i	1.28864	−	0.743996i	0.310228	−	0.950662i	$-0.399595\pi$
$439$	27.0000	−	15.5885i	1.28864	−	0.743996i	0.978412	+	0.206666i	$0.0662612\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$	9.00000			0.428086
$443$	−27.0000	+	15.5885i	−1.28281	+	0.740630i	−0.977361	−	0.211579i	$-0.932139\pi$
$443$	−27.0000	+	15.5885i	−1.28281	+	0.740630i	−0.305448	+	0.952209i	$0.598806\pi$
$444$	−10.5000	+	6.06218i	−0.498308	+	0.287698i
$445$	−4.50000	+	7.79423i	−0.213320	+	0.369482i
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$	1.50000	+	2.59808i	0.0709476	+	0.122885i
$448$		0			0
$449$		−	34.6410i		−	1.63481i	−0.576063	−	0.817405i	$-0.695412\pi$
$449$		−	34.6410i		−	1.63481i	0.576063	−	0.817405i	$-0.304588\pi$
$450$		−	20.7846i		−	0.979796i
$451$		−	5.19615i		−	0.244677i
$452$	1.50000	−	0.866025i	0.0705541	−	0.0407344i
$453$		−	29.4449i		−	1.38344i
$454$	31.5000	+	18.1865i	1.47837	+	0.853536i
$455$		0			0
$456$	13.5000	+	7.79423i	0.632195	+	0.364998i
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	−0.383437	+	0.923567i	$0.625260\pi$
$458$	−15.0000			−0.700904
$459$		−	15.5885i		−	0.727607i
$460$		−	15.5885i		−	0.726816i
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	−22.5000	−	12.9904i	−1.04454	−	0.603063i
$465$	−18.0000			−0.834730
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	4.50000	+	2.59808i	0.208013	+	0.120096i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.50000	+	0.866025i	0.0689701	+	0.0398199i
$474$	12.0000	+	20.7846i	0.551178	+	0.954669i
$475$	18.0000	−	10.3923i	0.825897	−	0.476832i
$476$		0			0
$477$	−22.5000	+	12.9904i	−1.03020	+	0.594789i
$478$	3.00000			0.137217
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	−0.990060	−	0.140643i	$-0.955083\pi$
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	0.373230	−	0.927739i	$-0.378250\pi$
$480$	27.0000			1.23238
$481$	10.5000	+	6.06218i	0.478759	+	0.276412i
$482$	−19.5000	+	33.7750i	−0.888201	+	1.53841i
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$			5.19615i			0.235945i
$486$	13.5000	−	23.3827i	0.612372	−	1.06066i
$487$	−23.0000			−1.04223			−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000			−1.04223			−0.521115	+	0.853487i	$0.674484\pi$
$488$	12.0000	+	20.7846i	0.543214	+	0.940875i
$489$	−16.5000	−	9.52628i	−0.746156	−	0.430793i
$490$		0			0
$491$	−22.5000	−	12.9904i	−1.01541	−	0.586248i	−0.102639	−	0.994719i	$-0.532729\pi$
$491$	−22.5000	−	12.9904i	−1.01541	−	0.586248i	−0.912771	+	0.408471i	$0.866062\pi$
$492$		−	5.19615i		−	0.234261i
$493$	−13.5000	+	7.79423i	−0.608009	+	0.351034i
$494$			15.5885i			0.701358i
$495$	13.5000	−	7.79423i	0.606780	−	0.350325i
$496$		−	17.3205i		−	0.777714i
$497$		0			0
$498$	−22.5000	−	38.9711i	−1.00825	−	1.74634i
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	0.437955	+	0.898997i	$0.355703\pi$
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	−0.997532	+	0.0702185i	$0.977630\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−13.5000	+	7.79423i	−0.603136	+	0.348220i
$502$	−18.0000	+	10.3923i	−0.803379	+	0.463831i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	13.5000	−	7.79423i	0.600148	−	0.346496i
$507$			17.3205i			0.769231i
$508$	10.0000	−	17.3205i	0.443678	−	0.768473i
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	−0.224957	−	0.974369i	$-0.572224\pi$
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	0.956306	−	0.292366i	$-0.0944425\pi$
$510$	13.5000	−	23.3827i	0.597790	−	1.03540i
$511$		0			0
$512$			8.66025i			0.382733i
$513$	27.0000			1.19208
$514$			5.19615i			0.229192i
$515$	31.5000	−	18.1865i	1.38806	−	0.801394i
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$		0			0
$518$		0			0
$519$		−	10.3923i		−	0.456172i
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−45.0000			−1.97149			−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000			−1.97149			−0.985743	+	0.168259i	$0.946186\pi$
$522$	−27.0000			−1.18176
$523$			19.0526i			0.833110i	0.909110	+	0.416555i	$0.136763\pi$
$523$			19.0526i			0.833110i	−0.909110	+	0.416555i	$0.863237\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$		0			0
$526$	−19.5000	+	33.7750i	−0.850240	+	1.47266i
$527$	−9.00000	−	5.19615i	−0.392046	−	0.226348i
$528$	7.50000	+	12.9904i	0.326396	+	0.565334i
$529$	2.00000	+	3.46410i	0.0869565	+	0.150613i
$530$	−45.0000			−1.95468
$531$		0			0
$532$		0			0
$533$	−4.50000	+	2.59808i	−0.194917	+	0.112535i
$534$	−9.00000			−0.389468
$535$	22.5000	+	12.9904i	0.972760	+	0.561623i
$536$	6.00000	+	3.46410i	0.259161	+	0.149626i
$537$	−13.5000	+	23.3827i	−0.582568	+	1.00904i
$538$	22.5000	−	12.9904i	0.970044	−	0.560055i
$539$		0			0
$540$	13.5000	−	7.79423i	0.580948	−	0.335410i
$541$	−13.0000			−0.558914			−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000			−0.558914			−0.279457	+	0.960158i	$0.590154\pi$
$542$	10.5000	+	18.1865i	0.451014	+	0.781179i
$543$		0			0
$544$	13.5000	+	7.79423i	0.578808	+	0.334175i
$545$	−28.5000	+	49.3634i	−1.22081	+	2.11450i
$546$		0			0
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	0.994459	−	0.105123i	$-0.0335235\pi$
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	−0.588269	+	0.808666i	$0.700190\pi$
$548$		−	12.1244i		−	0.517927i
$549$	36.0000	+	20.7846i	1.53644	+	0.887066i
$550$	12.0000			0.511682
$551$	−13.5000	−	23.3827i	−0.575119	−	0.996136i
$552$	−13.5000	+	7.79423i	−0.574598	+	0.331744i
$553$		0			0
$554$	1.50000	+	0.866025i	0.0637289	+	0.0367939i
$555$	31.5000	−	18.1865i	1.33710	−	0.771975i
$556$	7.50000	−	4.33013i	0.318071	−	0.183638i
$557$		−	12.1244i		−	0.513725i	−0.966448	−	0.256863i	$-0.917311\pi$
$557$		−	12.1244i		−	0.513725i	0.966448	−	0.256863i	$-0.0826888\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$		−	1.73205i		−	0.0732579i
$560$		0			0
$561$	9.00000			0.379980
$562$	−16.5000	+	28.5788i	−0.696010	+	1.20553i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	−4.50000	+	2.59808i	−0.189316	+	0.109302i
$566$	6.00000			0.252199
$567$		0			0
$568$	6.00000			0.251754
$569$	−6.00000	+	3.46410i	−0.251533	+	0.145223i	−0.620466	−	0.784233i	$-0.713057\pi$
$569$	−6.00000	+	3.46410i	−0.251533	+	0.145223i	0.368933	+	0.929456i	$0.379723\pi$
$570$	40.5000	+	23.3827i	1.69636	+	0.979393i
$571$	−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	$0.933141\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$	−30.0000			−1.25327
$574$		0			0
$575$			20.7846i			0.866778i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$		−	39.8372i		−	1.65844i	−0.558920	−	0.829222i	$-0.688784\pi$
$577$		−	39.8372i		−	1.65844i	0.558920	−	0.829222i	$-0.311216\pi$
$578$	−12.0000	+	6.92820i	−0.499134	+	0.288175i
$579$	−3.00000	+	1.73205i	−0.124676	+	0.0719816i
$580$	−13.5000	−	7.79423i	−0.560557	−	0.323638i
$581$		0			0
$582$	−4.50000	+	2.59808i	−0.186531	+	0.107694i
$583$	−7.50000	−	12.9904i	−0.310618	−	0.538007i
$584$	9.00000			0.372423
$585$	−13.5000	−	7.79423i	−0.558156	−	0.322252i
$586$		−	15.5885i		−	0.643953i
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	0.563781	−	0.825925i	$-0.309346\pi$
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	−0.997162	+	0.0752860i	$0.976013\pi$
$588$		0			0
$589$	9.00000	−	15.5885i	0.370839	−	0.642311i
$590$		0			0
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$	17.5000	+	30.3109i	0.719246	+	1.24577i
$593$	39.0000			1.60154			0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000			1.60154			0.800769	+	0.598973i	$0.204424\pi$
$594$	13.5000	+	7.79423i	0.553912	+	0.319801i
$595$		0			0
$596$	−1.50000	+	0.866025i	−0.0614424	+	0.0354738i
$597$	−7.50000	+	12.9904i	−0.306955	+	0.531661i
$598$	−13.5000	−	7.79423i	−0.552056	−	0.318730i
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	0.863354	−	0.504598i	$-0.168359\pi$
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	−0.00531761	+	0.999986i	$0.501693\pi$
$600$	−12.0000			−0.489898
$601$	25.5000	−	14.7224i	1.04017	−	0.600541i	0.120286	−	0.992739i	$-0.461619\pi$
$601$	25.5000	−	14.7224i	1.04017	−	0.600541i	0.919881	+	0.392199i	$0.128285\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	17.0000			0.691720
$605$	−12.0000	−	20.7846i	−0.487869	−	0.845015i
$606$	4.50000	+	7.79423i	0.182800	+	0.316619i
$607$	13.5000	+	7.79423i	0.547948	+	0.316358i	0.748294	−	0.663367i	$-0.230873\pi$
$607$	13.5000	+	7.79423i	0.547948	+	0.316358i	−0.200346	+	0.979725i	$0.564207\pi$
$608$	−13.5000	+	23.3827i	−0.547497	+	0.948293i
$609$		0			0
$610$	36.0000	+	62.3538i	1.45760	+	2.52463i
$611$		0			0
$612$	9.00000			0.363803
$613$	47.0000			1.89831			0.949156	−	0.314806i	$-0.101939\pi$
$613$	47.0000			1.89831			0.949156	+	0.314806i	$0.101939\pi$
$614$	21.0000	+	36.3731i	0.847491	+	1.46790i
$615$			15.5885i			0.628587i
$616$		0			0
$617$	−4.50000	−	2.59808i	−0.181163	−	0.104595i	0.406676	−	0.913573i	$-0.366688\pi$
$617$	−4.50000	−	2.59808i	−0.181163	−	0.104595i	−0.587839	+	0.808978i	$0.700021\pi$
$618$	31.5000	+	18.1865i	1.26712	+	0.731570i
$619$	16.5000	−	9.52628i	0.663191	−	0.382893i	−0.130301	−	0.991475i	$-0.541594\pi$
$619$	16.5000	−	9.52628i	0.663191	−	0.382893i	0.793492	+	0.608581i	$0.208261\pi$
$620$		−	10.3923i		−	0.417365i
$621$	−13.5000	+	23.3827i	−0.541736	+	0.938315i
$622$		−	41.5692i		−	1.66677i
$623$		0			0
$624$	7.50000	−	12.9904i	0.300240	−	0.520031i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−18.0000	+	31.1769i	−0.719425	+	1.24608i
$627$			15.5885i			0.622543i
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	12.0000	−	6.92820i	0.477334	−	0.275589i
$633$	−7.50000	+	4.33013i	−0.298098	+	0.172107i
$634$		0			0
$635$	−30.0000	+	51.9615i	−1.19051	+	2.06203i
$636$	−7.50000	−	12.9904i	−0.297394	−	0.515102i
$637$		0			0
$638$		−	15.5885i		−	0.617153i
$639$	9.00000	−	5.19615i	0.356034	−	0.205557i
$640$		−	36.3731i		−	1.43777i
$641$	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	$0.256369\pi$
$642$			25.9808i			1.02538i
$643$	−10.5000	−	6.06218i	−0.414080	−	0.239069i	0.278462	−	0.960447i	$-0.410176\pi$
$643$	−10.5000	−	6.06218i	−0.414080	−	0.239069i	−0.692541	+	0.721378i	$0.743509\pi$
$644$		0			0
$645$	−4.50000	−	2.59808i	−0.177187	−	0.102299i
$646$	13.5000	+	23.3827i	0.531150	+	0.919979i
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$	−13.5000	−	7.79423i	−0.530330	−	0.306186i
$649$		0			0
$650$	−6.00000	−	10.3923i	−0.235339	−	0.407620i
$651$		0			0
$652$	5.50000	−	9.52628i	0.215397	−	0.373078i
$653$	34.5000	+	19.9186i	1.35009	+	0.779474i	0.988262	−	0.152771i	$-0.0488196\pi$
$653$	34.5000	+	19.9186i	1.35009	+	0.779474i	0.361828	+	0.932245i	$0.382153\pi$
$654$	−57.0000			−2.22888
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$	−15.0000			−0.585652
$657$	13.5000	−	7.79423i	0.526685	−	0.304082i
$658$		0			0
$659$	10.5000	−	6.06218i	0.409022	−	0.236149i	−0.281347	−	0.959606i	$-0.590781\pi$
$659$	10.5000	−	6.06218i	0.409022	−	0.236149i	0.690369	+	0.723457i	$0.257448\pi$
$660$	4.50000	+	7.79423i	0.175162	+	0.303390i
$661$	36.0000	+	20.7846i	1.40024	+	0.808428i	0.994417	−	0.105525i	$-0.0336523\pi$
$661$	36.0000	+	20.7846i	1.40024	+	0.808428i	0.405821	+	0.913953i	$0.366986\pi$
$662$	12.0000	+	6.92820i	0.466393	+	0.269272i
$663$	−4.50000	−	7.79423i	−0.174766	−	0.302703i
$664$	−22.5000	+	12.9904i	−0.873169	+	0.504125i
$665$		0			0
$666$	31.5000	+	18.1865i	1.22060	+	0.704714i
$667$	27.0000			1.04544
$668$	−4.50000	−	7.79423i	−0.174110	−	0.301568i
$669$	−9.00000			−0.347960
$670$	18.0000	+	10.3923i	0.695401	+	0.401490i
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		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	$0.644544\pi$
$674$			32.9090i			1.26761i
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$	−10.0000			−0.384615
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$	−4.50000	−	2.59808i	−0.172821	−	0.0997785i
$679$		0			0
$680$	−13.5000	−	7.79423i	−0.517701	−	0.298895i
$681$		−	36.3731i		−	1.39382i
$682$	9.00000	−	5.19615i	0.344628	−	0.198971i
$683$		−	8.66025i		−	0.331375i	−0.986178	−	0.165688i	$-0.947016\pi$
$683$		−	8.66025i		−	0.331375i	0.986178	−	0.165688i	$-0.0529844\pi$
$684$			15.5885i			0.596040i
$685$			36.3731i			1.38974i
$686$		0			0
$687$	7.50000	+	12.9904i	0.286143	+	0.495614i
$688$	2.50000	−	4.33013i	0.0953116	−	0.165085i
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$	−40.5000	+	23.3827i	−1.54181	+	0.890164i
$691$	−3.00000	+	1.73205i	−0.114125	+	0.0658903i	−0.555976	−	0.831198i	$-0.687655\pi$
$691$	−3.00000	+	1.73205i	−0.114125	+	0.0658903i	0.441851	+	0.897089i	$0.354322\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	6.00000			0.227757
$695$	−22.5000	+	12.9904i	−0.853474	+	0.492753i
$696$			15.5885i			0.590879i
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$	−10.5000	+	18.1865i	−0.397431	+	0.688370i
$699$	4.50000	−	7.79423i	0.170206	−	0.294805i
$700$		0			0
$701$		−	34.6410i		−	1.30837i	−0.756333	−	0.654187i	$-0.773011\pi$
$701$		−	34.6410i		−	1.30837i	0.756333	−	0.654187i	$-0.226989\pi$
$702$		−	15.5885i		−	0.588348i
$703$			36.3731i			1.37184i
$704$	1.50000	−	0.866025i	0.0565334	−	0.0326396i
$705$		0			0
$706$	31.5000	+	18.1865i	1.18552	+	0.684459i
$707$		0			0
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	18.0000			0.675528
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$			5.19615i			0.194734i
$713$	9.00000	+	15.5885i	0.337053	+	0.583792i
$714$		0			0
$715$	4.50000	−	7.79423i	0.168290	−	0.291488i
$716$	−13.5000	−	7.79423i	−0.504519	−	0.291284i
$717$	−1.50000	−	2.59808i	−0.0560185	−	0.0970269i
$718$	−19.5000	−	33.7750i	−0.727734	−	1.26047i
$719$	−9.00000			−0.335643			−0.167822	−	0.985817i	$-0.553673\pi$
$719$	−9.00000			−0.335643			−0.167822	+	0.985817i	$0.553673\pi$
$720$	−22.5000	−	38.9711i	−0.838525	−	1.45237i
$721$		0			0
$722$	−12.0000	+	6.92820i	−0.446594	+	0.257841i
$723$	39.0000			1.45043
$724$		0			0
$725$	18.0000	+	10.3923i	0.668503	+	0.385961i
$726$	12.0000	−	20.7846i	0.445362	−	0.771389i
$727$	10.5000	−	6.06218i	0.389423	−	0.224834i	−0.292487	−	0.956270i	$-0.594483\pi$
$727$	10.5000	−	6.06218i	0.389423	−	0.224834i	0.681910	+	0.731436i	$0.261149\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	27.0000			0.999315
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	−12.0000	+	20.7846i	−0.443533	+	0.768221i
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.392337	−	0.919822i	$-0.628333\pi$
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.992757	+	0.120137i	$0.961667\pi$
$734$	4.50000	−	7.79423i	0.166098	−	0.287690i
$735$		0			0
$736$	−13.5000	−	23.3827i	−0.497617	−	0.861897i
$737$			6.92820i			0.255204i
$738$	−13.5000	+	7.79423i	−0.496942	+	0.286910i
$739$	−7.00000			−0.257499			−0.128750	−	0.991677i	$-0.541096\pi$
$739$	−7.00000			−0.257499			−0.128750	+	0.991677i	$0.541096\pi$
$740$	10.5000	+	18.1865i	0.385988	+	0.668550i
$741$	13.5000	−	7.79423i	0.495935	−	0.286328i
$742$		0			0
$743$	−10.5000	−	6.06218i	−0.385208	−	0.222400i	0.294874	−	0.955536i	$-0.404722\pi$
$743$	−10.5000	−	6.06218i	−0.385208	−	0.222400i	−0.680082	+	0.733136i	$0.738056\pi$
$744$	−9.00000	+	5.19615i	−0.329956	+	0.190500i
$745$	4.50000	−	2.59808i	0.164867	−	0.0951861i
$746$		−	64.0859i		−	2.34635i
$747$	−22.5000	+	38.9711i	−0.823232	+	1.42588i
$748$			5.19615i			0.189990i
$749$		0			0
$750$	9.00000			0.328634
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	0.301373	+	0.953506i	$0.402555\pi$
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	−0.976447	+	0.215757i	$0.930778\pi$
$752$		0			0
$753$	18.0000	+	10.3923i	0.655956	+	0.378717i
$754$	−13.5000	+	7.79423i	−0.491641	+	0.283849i
$755$	−51.0000			−1.85608
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−30.0000	+	17.3205i	−1.08965	+	0.629109i
$759$	−13.5000	−	7.79423i	−0.490019	−	0.282913i
$760$	13.5000	−	23.3827i	0.489696	−	0.848179i
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	−0.0932544	−	0.995642i	$-0.529727\pi$
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	0.908879	−	0.417061i	$-0.136940\pi$
$762$	−60.0000			−2.17357
$763$		0			0
$764$		−	17.3205i		−	0.626634i
$765$	−27.0000			−0.976187
$766$			15.5885i			0.563234i
$767$		0			0
$768$	28.5000	−	16.4545i	1.02841	−	0.593750i
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$770$		0			0
$771$	4.50000	−	2.59808i	0.162064	−	0.0935674i
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	51.0000			1.83434			0.917171	−	0.398493i	$-0.130467\pi$
$773$	51.0000			1.83434			0.917171	+	0.398493i	$0.130467\pi$
$774$		−	5.19615i		−	0.186772i
$775$			13.8564i			0.497737i
$776$	1.50000	+	2.59808i	0.0538469	+	0.0932655i
$777$		0			0
$778$	−31.5000	+	54.5596i	−1.12933	+	1.95606i
$779$	−13.5000	−	7.79423i	−0.483688	−	0.279257i
$780$	4.50000	−	7.79423i	0.161126	−	0.279078i
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−27.0000			−0.965518
$783$	13.5000	+	23.3827i	0.482451	+	0.835629i
$784$		0			0
$785$		0			0
$786$	13.5000	−	23.3827i	0.481529	−	0.834033i
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.221162	−	0.975237i	$-0.570985\pi$
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.955161	+	0.296087i	$0.904318\pi$
$788$	12.0000	+	6.92820i	0.427482	+	0.246807i
$789$	39.0000			1.38844
$790$	36.0000	−	20.7846i	1.28082	−	0.739483i
$791$		0			0
$792$	4.50000	−	7.79423i	0.159901	−	0.276956i
$793$	24.0000			0.852265
$794$	−7.50000	−	12.9904i	−0.266165	−	0.461011i
$795$	22.5000	+	38.9711i	0.797993	+	1.38216i
$796$	−7.50000	−	4.33013i	−0.265830	−	0.153477i
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	−0.124576	−	0.992210i	$-0.539757\pi$
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	0.921567	−	0.388219i	$-0.126909\pi$
$798$		0			0
$799$		0			0
$800$		−	20.7846i		−	0.734847i
$801$	4.50000	+	7.79423i	0.159000	+	0.275396i
$802$	57.0000			2.01274
$803$	4.50000	+	7.79423i	0.158802	+	0.275052i
$804$			6.92820i			0.244339i
$805$		0			0
$806$	−9.00000	−	5.19615i	−0.317011	−	0.183027i
$807$	−22.5000	−	12.9904i	−0.792038	−	0.457283i
$808$	4.50000	−	2.59808i	0.158309	−	0.0914000i
$809$			1.73205i			0.0608957i	0.999536	+	0.0304478i	$0.00969334\pi$
$809$			1.73205i			0.0608957i	−0.999536	+	0.0304478i	$0.990307\pi$
$810$	−40.5000	−	23.3827i	−1.42302	−	0.821584i
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$	10.5000	−	18.1865i	0.368251	−	0.637830i
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	−16.5000	+	28.5788i	−0.577970	+	1.00107i
$816$		−	25.9808i		−	0.909509i
$817$	4.50000	−	2.59808i	0.157435	−	0.0908952i
$818$	−12.0000			−0.419570
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−6.00000	+	3.46410i	−0.209401	+	0.120898i	−0.601033	−	0.799224i	$-0.705244\pi$
$821$	−6.00000	+	3.46410i	−0.209401	+	0.120898i	0.391632	+	0.920122i	$0.371911\pi$
$822$	−31.5000	+	18.1865i	−1.09869	+	0.634328i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	10.5000	−	18.1865i	0.365785	−	0.633558i
$825$	−6.00000	−	10.3923i	−0.208893	−	0.361814i
$826$		0			0
$827$			24.2487i			0.843210i	0.906780	+	0.421605i	$0.138533\pi$
$827$			24.2487i			0.843210i	−0.906780	+	0.421605i	$0.861467\pi$
$828$	−13.5000	−	7.79423i	−0.469157	−	0.270868i
$829$			36.3731i			1.26329i	0.775258	+	0.631644i	$0.217620\pi$
$829$			36.3731i			1.26329i	−0.775258	+	0.631644i	$0.782380\pi$
$830$	−67.5000	+	38.9711i	−2.34296	+	1.35271i
$831$		−	1.73205i		−	0.0600842i
$832$	−1.50000	−	0.866025i	−0.0520031	−	0.0300240i
$833$		0			0
$834$	−22.5000	−	12.9904i	−0.779111	−	0.449820i
$835$	13.5000	+	23.3827i	0.467187	+	0.809191i
$836$	−9.00000			−0.311272
$837$	−9.00000	+	15.5885i	−0.311086	+	0.538816i
$838$		−	57.1577i		−	1.97448i
$839$	19.5000	+	33.7750i	0.673215	+	1.16604i	0.976987	+	0.213298i	$0.0684204\pi$
$839$	19.5000	+	33.7750i	0.673215	+	1.16604i	−0.303773	+	0.952745i	$0.598246\pi$
$840$		0			0
$841$	−1.00000	+	1.73205i	−0.0344828	+	0.0597259i
$842$	−16.5000	−	9.52628i	−0.568628	−	0.328297i
$843$	33.0000			1.13658
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	30.0000			1.03203
$846$		0			0
$847$		0			0
$848$	−37.5000	+	21.6506i	−1.28776	+	0.743486i
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$	−18.0000	−	10.3923i	−0.617395	−	0.356453i
$851$	−31.5000	−	18.1865i	−1.07981	−	0.623426i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	−0.833012	−	0.553255i	$-0.813386\pi$
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	0.0626267	+	0.998037i	$0.480052\pi$
$854$		0			0
$855$		−	46.7654i		−	1.59934i
$856$	15.0000			0.512689
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	0.537867	−	0.843029i	$-0.319230\pi$
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	−0.999019	+	0.0442921i	$0.985897\pi$
$858$	9.00000			0.307255
$859$	43.5000	+	25.1147i	1.48420	+	0.856904i	0.999839	−	0.0179638i	$-0.00571836\pi$
$859$	43.5000	+	25.1147i	1.48420	+	0.856904i	0.484362	+	0.874868i	$0.339052\pi$
$860$	1.50000	−	2.59808i	0.0511496	−	0.0885937i
$861$		0			0
$862$	−13.5000	−	23.3827i	−0.459812	−	0.796417i
$863$		−	43.3013i		−	1.47399i	−0.675897	−	0.736996i	$-0.736244\pi$
$863$		−	43.3013i		−	1.47399i	0.675897	−	0.736996i	$-0.263756\pi$
$864$	13.5000	−	23.3827i	0.459279	−	0.795495i
$865$	−18.0000			−0.612018
$866$	−12.0000	−	20.7846i	−0.407777	−	0.706290i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$		0			0
$869$	12.0000	+	6.92820i	0.407072	+	0.235023i
$870$			46.7654i			1.58549i
$871$	6.00000	−	3.46410i	0.203302	−	0.117377i
$872$			32.9090i			1.11444i
$873$	4.50000	+	2.59808i	0.152302	+	0.0879316i
$874$		−	46.7654i		−	1.58186i
$875$		0			0
$876$	4.50000	+	7.79423i	0.152041	+	0.263343i
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	27.0000	−	46.7654i	0.911206	−	1.57825i
$879$	−13.5000	+	7.79423i	−0.455344	+	0.262893i
$880$	22.5000	−	12.9904i	0.758475	−	0.437906i
$881$	54.0000			1.81931			0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000			1.81931			0.909653	+	0.415369i	$0.136347\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	4.50000	−	2.59808i	0.151351	−	0.0873828i
$885$		0			0
$886$	−27.0000	+	46.7654i	−0.907083	+	1.57111i
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	−0.712203	−	0.701974i	$-0.752302\pi$
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	0.964028	+	0.265799i	$0.0856358\pi$
$888$	10.5000	−	18.1865i	0.352357	−	0.610300i
$889$		0			0
$890$			15.5885i			0.522526i
$891$		−	15.5885i		−	0.522233i
$892$		−	5.19615i		−	0.173980i
$893$		0			0
$894$	4.50000	+	2.59808i	0.150503	+	0.0868927i
$895$	40.5000	+	23.3827i	1.35377	+	0.781597i
$896$		0			0
$897$			15.5885i			0.520483i
$898$	−30.0000	−	51.9615i	−1.00111	−	1.73398i
$899$	18.0000			0.600334
$900$	−6.00000	−	10.3923i	−0.200000	−	0.346410i
$901$			25.9808i			0.865545i
$902$	−4.50000	−	7.79423i	−0.149834	−	0.259519i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$	−25.5000	−	44.1673i	−0.847181	−	1.46736i
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268820\pi$
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	−0.979531	+	0.201291i	$0.935486\pi$
$908$	21.0000			0.696909
$909$	4.50000	−	7.79423i	0.149256	−	0.258518i
$910$		0			0
$911$	4.50000	−	2.59808i	0.149092	−	0.0860781i	−0.423598	−	0.905850i	$-0.639233\pi$
$911$	4.50000	−	2.59808i	0.149092	−	0.0860781i	0.572690	+	0.819772i	$0.305900\pi$
$912$	45.0000			1.49010
$913$	−22.5000	−	12.9904i	−0.744641	−	0.429919i
$914$	39.0000	+	22.5167i	1.29001	+	0.744785i
$915$	36.0000	−	62.3538i	1.19012	−	2.06135i
$916$	−7.50000	+	4.33013i	−0.247807	+	0.143071i
$917$		0			0
$918$	−13.5000	−	23.3827i	−0.445566	−	0.771744i
$919$	−29.0000			−0.956622			−0.478311	−	0.878191i	$-0.658751\pi$
$919$	−29.0000			−0.956622			−0.478311	+	0.878191i	$0.658751\pi$
$920$	13.5000	+	23.3827i	0.445082	+	0.770904i
$921$	21.0000	−	36.3731i	0.691974	−	1.19853i
$922$	−22.5000	−	12.9904i	−0.740998	−	0.427815i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$		0			0
$925$	−14.0000	−	24.2487i	−0.460317	−	0.797293i
$926$		−	1.73205i		−	0.0569187i
$927$		−	36.3731i		−	1.19465i
$928$	−27.0000			−0.886318
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$	−27.0000	+	15.5885i	−0.885365	+	0.511166i
$931$		0			0
$932$	4.50000	+	2.59808i	0.147402	+	0.0851028i
$933$	−36.0000	+	20.7846i	−1.17859	+	0.680458i
$934$	4.50000	−	2.59808i	0.147244	−	0.0850117i
$935$		−	15.5885i		−	0.509797i
$936$	−9.00000			−0.294174
$937$		−	13.8564i		−	0.452669i	−0.974050	−	0.226335i	$-0.927326\pi$
$937$		−	13.8564i		−	0.452669i	0.974050	−	0.226335i	$-0.0726743\pi$
$938$		0			0
$939$	36.0000			1.17482
$940$		0			0
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$		0			0
$943$	13.5000	−	7.79423i	0.439620	−	0.253815i
$944$		0			0
$945$		0			0
$946$	3.00000			0.0975384
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.463186	−	0.886261i	$-0.346706\pi$
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.999118	+	0.0419998i	$0.0133729\pi$
$948$	12.0000	+	6.92820i	0.389742	+	0.225018i
$949$	4.50000	−	7.79423i	0.146076	−	0.253011i
$950$	18.0000	−	31.1769i	0.583997	−	1.01151i
$951$		0			0
$952$		0			0
$953$		−	20.7846i		−	0.673280i	−0.941634	−	0.336640i	$-0.890710\pi$
$953$		−	20.7846i		−	0.673280i	0.941634	−	0.336640i	$-0.109290\pi$
$954$	−22.5000	+	38.9711i	−0.728464	+	1.26174i
$955$			51.9615i			1.68144i
$956$	1.50000	−	0.866025i	0.0485135	−	0.0280093i
$957$	−13.5000	+	7.79423i	−0.436393	+	0.251952i
$958$	−40.5000	−	23.3827i	−1.30850	−	0.755460i
$959$		0			0
$960$	−4.50000	+	2.59808i	−0.145237	+	0.0838525i
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	21.0000			0.677067
$963$	22.5000	−	12.9904i	0.725052	−	0.418609i
$964$			22.5167i			0.725213i
$965$	3.00000	+	5.19615i	0.0965734	+	0.167270i
$966$		0			0
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	−0.591991	−	0.805945i	$-0.701658\pi$
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	0.993964	+	0.109707i	$0.0349913\pi$
$968$	−12.0000	−	6.92820i	−0.385695	−	0.222681i
$969$	13.5000	−	23.3827i	0.433682	−	0.751160i
$970$	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
$974$	−34.5000	+	19.9186i	−1.10545	+	0.638233i
$975$	−6.00000	+	10.3923i	−0.192154	+	0.332820i
$976$	60.0000	+	34.6410i	1.92055	+	1.10883i
$977$	36.0000	+	20.7846i	1.15174	+	0.664959i	0.949311	−	0.314338i	$-0.101783\pi$
$977$	36.0000	+	20.7846i	1.15174	+	0.664959i	0.202431	+	0.979297i	$0.435116\pi$
$978$	−33.0000			−1.05522
$979$	−4.50000	+	2.59808i	−0.143821	+	0.0830349i
$980$		0			0
$981$	28.5000	+	49.3634i	0.909935	+	1.57605i
$982$	−45.0000			−1.43601
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	−0.989122	−	0.147100i	$-0.953006\pi$
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	0.367168	−	0.930155i	$-0.380327\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	−36.0000	−	20.7846i	−1.14706	−	0.662253i
$986$	−13.5000	+	23.3827i	−0.429928	+	0.744656i
$987$		0			0
$988$	4.50000	+	7.79423i	0.143164	+	0.247967i
$989$			5.19615i			0.165228i
$990$	13.5000	−	23.3827i	0.429058	−	0.743151i
$991$	−47.0000			−1.49300			−0.746502	−	0.665383i	$-0.768268\pi$
$991$	−47.0000			−1.49300			−0.746502	+	0.665383i	$0.768268\pi$
$992$	−9.00000	−	15.5885i	−0.285750	−	0.494934i
$993$		−	13.8564i		−	0.439720i
$994$		0			0
$995$	22.5000	+	12.9904i	0.713298	+	0.411823i
$996$	−22.5000	−	12.9904i	−0.712940	−	0.411616i
$997$	−7.50000	+	4.33013i	−0.237527	+	0.137136i	−0.614040	−	0.789275i	$-0.710457\pi$
$997$	−7.50000	+	4.33013i	−0.237527	+	0.137136i	0.376512	+	0.926412i	$0.377123\pi$
$998$			43.3013i			1.37068i
$999$		−	36.3731i		−	1.15079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.a.293.1		2
3.2	odd	2		1323.2.o.b.881.1		2
7.2	even	3		441.2.s.a.374.1		2
7.3	odd	6		441.2.i.a.68.1		2
7.4	even	3		63.2.i.a.5.1	✓	2
7.5	odd	6		63.2.s.a.59.1	yes	2
7.6	odd	2		441.2.o.b.293.1		2
9.2	odd	6		441.2.o.b.146.1		2
9.7	even	3		1323.2.o.a.440.1		2
21.2	odd	6		1323.2.s.a.962.1		2
21.5	even	6		189.2.s.a.17.1		2
21.11	odd	6		189.2.i.a.152.1		2
21.17	even	6		1323.2.i.a.1097.1		2
21.20	even	2		1323.2.o.a.881.1		2
28.11	odd	6		1008.2.ca.a.257.1		2
28.19	even	6		1008.2.df.a.689.1		2
63.2	odd	6		441.2.i.a.227.1		2
63.4	even	3		567.2.p.a.404.1		2
63.5	even	6		567.2.p.a.80.1		2
63.11	odd	6		63.2.s.a.47.1	yes	2
63.16	even	3		1323.2.i.a.521.1		2
63.20	even	6	inner	441.2.o.a.146.1		2
63.25	even	3		189.2.s.a.89.1		2
63.32	odd	6		567.2.p.b.404.1		2
63.34	odd	6		1323.2.o.b.440.1		2
63.38	even	6		441.2.s.a.362.1		2
63.40	odd	6		567.2.p.b.80.1		2
63.47	even	6		63.2.i.a.38.1	yes	2
63.52	odd	6		1323.2.s.a.656.1		2
63.61	odd	6		189.2.i.a.143.1		2
84.11	even	6		3024.2.ca.a.2609.1		2
84.47	odd	6		3024.2.df.a.17.1		2
252.11	even	6		1008.2.df.a.929.1		2
252.47	odd	6		1008.2.ca.a.353.1		2
252.151	odd	6		3024.2.df.a.1601.1		2
252.187	even	6		3024.2.ca.a.2033.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.a.5.1	✓	2	7.4	even	3
63.2.i.a.38.1	yes	2	63.47	even	6
63.2.s.a.47.1	yes	2	63.11	odd	6
63.2.s.a.59.1	yes	2	7.5	odd	6
189.2.i.a.143.1		2	63.61	odd	6
189.2.i.a.152.1		2	21.11	odd	6
189.2.s.a.17.1		2	21.5	even	6
189.2.s.a.89.1		2	63.25	even	3
441.2.i.a.68.1		2	7.3	odd	6
441.2.i.a.227.1		2	63.2	odd	6
441.2.o.a.146.1		2	63.20	even	6	inner
441.2.o.a.293.1		2	1.1	even	1	trivial
441.2.o.b.146.1		2	9.2	odd	6
441.2.o.b.293.1		2	7.6	odd	2
441.2.s.a.362.1		2	63.38	even	6
441.2.s.a.374.1		2	7.2	even	3
567.2.p.a.80.1		2	63.5	even	6
567.2.p.a.404.1		2	63.4	even	3
567.2.p.b.80.1		2	63.40	odd	6
567.2.p.b.404.1		2	63.32	odd	6
1008.2.ca.a.257.1		2	28.11	odd	6
1008.2.ca.a.353.1		2	252.47	odd	6
1008.2.df.a.689.1		2	28.19	even	6
1008.2.df.a.929.1		2	252.11	even	6
1323.2.i.a.521.1		2	63.16	even	3
1323.2.i.a.1097.1		2	21.17	even	6
1323.2.o.a.440.1		2	9.7	even	3
1323.2.o.a.881.1		2	21.20	even	2
1323.2.o.b.440.1		2	63.34	odd	6
1323.2.o.b.881.1		2	3.2	odd	2
1323.2.s.a.656.1		2	63.52	odd	6
1323.2.s.a.962.1		2	21.2	odd	6
3024.2.ca.a.2033.1		2	252.187	even	6
3024.2.ca.a.2609.1		2	84.11	even	6
3024.2.df.a.17.1		2	84.47	odd	6
3024.2.df.a.1601.1		2	252.151	odd	6

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

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -3.00000 q^{6} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -3.00000 q^{6} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +5.19615i q^{10} +(-1.50000 + 0.866025i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.50000 + 0.866025i) q^{13} +(4.50000 - 2.59808i) q^{15} +(2.50000 + 4.33013i) q^{16} +3.00000 q^{17} +(4.50000 + 2.59808i) q^{18} +5.19615i q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-4.50000 - 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-2.00000 - 3.46410i) q^{25} +3.00000 q^{26} -5.19615i q^{27} +(-4.50000 + 2.59808i) q^{29} +(4.50000 - 7.79423i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} +3.00000 q^{33} +(4.50000 - 2.59808i) q^{34} +3.00000 q^{36} +7.00000 q^{37} +(4.50000 + 7.79423i) q^{38} +(-1.50000 - 2.59808i) q^{39} +(-4.50000 - 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +1.73205i q^{44} -9.00000 q^{45} -9.00000 q^{46} -8.66025i q^{48} +(-6.00000 - 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(1.50000 - 0.866025i) q^{52} +8.66025i q^{53} +(-4.50000 - 7.79423i) q^{54} -5.19615i q^{55} +(4.50000 - 7.79423i) q^{57} +(-4.50000 + 7.79423i) q^{58} -5.19615i q^{60} +(12.0000 - 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-4.50000 + 2.59808i) q^{65} +(4.50000 - 2.59808i) q^{66} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(4.50000 + 7.79423i) q^{69} -3.46410i q^{71} +(-4.50000 + 2.59808i) q^{72} -5.19615i q^{73} +(10.5000 - 6.06218i) q^{74} +6.92820i q^{75} +(4.50000 + 2.59808i) q^{76} +(-4.50000 - 2.59808i) q^{78} +(-4.00000 - 6.92820i) q^{79} -15.0000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.19615i q^{82} +(7.50000 + 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(-1.50000 - 0.866025i) q^{86} +9.00000 q^{87} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{89} +(-13.5000 + 7.79423i) q^{90} +(-4.50000 + 2.59808i) q^{92} +(3.00000 + 5.19615i) q^{93} +(-13.5000 - 7.79423i) q^{95} +(-4.50000 - 7.79423i) q^{96} +(1.50000 - 0.866025i) q^{97} +(-4.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + 3 * q^9	\( 2 q + 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{13} + 9 q^{15} + 5 q^{16} + 6 q^{17} + 9 q^{18} + 3 q^{20} - 3 q^{22} - 9 q^{23} + 3 q^{24} - 4 q^{25} + 6 q^{26} - 9 q^{29} + 9 q^{30} - 6 q^{31} + 9 q^{32} + 6 q^{33} + 9 q^{34} + 6 q^{36} + 14 q^{37} + 9 q^{38} - 3 q^{39} - 9 q^{40} - 3 q^{41} - q^{43} - 18 q^{45} - 18 q^{46} - 12 q^{50} - 9 q^{51} + 3 q^{52} - 9 q^{54} + 9 q^{57} - 9 q^{58} + 24 q^{61} - 12 q^{62} - 2 q^{64} - 9 q^{65} + 9 q^{66} + 4 q^{67} + 3 q^{68} + 9 q^{69} - 9 q^{72} + 21 q^{74} + 9 q^{76} - 9 q^{78} - 8 q^{79} - 30 q^{80} - 9 q^{81} + 15 q^{83} - 9 q^{85} - 3 q^{86} + 18 q^{87} - 3 q^{88} + 6 q^{89} - 27 q^{90} - 9 q^{92} + 6 q^{93} - 27 q^{95} - 9 q^{96} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^13 + 9 * q^15 + 5 * q^16 + 6 * q^17 + 9 * q^18 + 3 * q^20 - 3 * q^22 - 9 * q^23 + 3 * q^24 - 4 * q^25 + 6 * q^26 - 9 * q^29 + 9 * q^30 - 6 * q^31 + 9 * q^32 + 6 * q^33 + 9 * q^34 + 6 * q^36 + 14 * q^37 + 9 * q^38 - 3 * q^39 - 9 * q^40 - 3 * q^41 - q^43 - 18 * q^45 - 18 * q^46 - 12 * q^50 - 9 * q^51 + 3 * q^52 - 9 * q^54 + 9 * q^57 - 9 * q^58 + 24 * q^61 - 12 * q^62 - 2 * q^64 - 9 * q^65 + 9 * q^66 + 4 * q^67 + 3 * q^68 + 9 * q^69 - 9 * q^72 + 21 * q^74 + 9 * q^76 - 9 * q^78 - 8 * q^79 - 30 * q^80 - 9 * q^81 + 15 * q^83 - 9 * q^85 - 3 * q^86 + 18 * q^87 - 3 * q^88 + 6 * q^89 - 27 * q^90 - 9 * q^92 + 6 * q^93 - 27 * q^95 - 9 * q^96 + 3 * q^97 - 9 * q^99

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