LMFDB - Embedded newform 882.2.f.g.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.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:	$7.04280545828$
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 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.g.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +3.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} -1.00000 q^{26} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(-4.50000 + 2.59808i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +5.19615i q^{33} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{36} -1.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(1.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +9.00000 q^{45} +9.00000 q^{46} -1.73205i q^{48} +(2.00000 + 3.46410i) q^{50} +(4.50000 - 2.59808i) q^{51} +(-0.500000 + 0.866025i) q^{52} +3.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(1.50000 + 2.59808i) q^{58} +5.19615i q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(4.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-13.5000 - 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} -6.92820i q^{75} +(-3.50000 - 6.06218i) q^{76} +(1.50000 - 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} -3.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +3.00000 q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 - 0.866025i) q^{86} -5.19615i q^{87} +(-1.50000 + 2.59808i) q^{88} -3.00000 q^{89} +(4.50000 - 7.79423i) q^{90} +(4.50000 - 7.79423i) q^{92} +(-12.0000 - 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 - q^4 + 3 * q^5 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 2 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{11} + 3 q^{12} - q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 3 q^{18} + 14 q^{19} + 3 q^{20} - 3 q^{22} + 9 q^{23} + 3 q^{24} - 4 q^{25} - 2 q^{26} - 3 q^{29} - 9 q^{30} + 8 q^{31} + q^{32} - 3 q^{34} - 6 q^{36} - 2 q^{37} + 7 q^{38} + 3 q^{39} - 3 q^{40} + 3 q^{41} + q^{43} - 6 q^{44} + 18 q^{45} + 18 q^{46} + 4 q^{50} + 9 q^{51} - q^{52} + 6 q^{53} + 9 q^{54} + 18 q^{55} - 21 q^{57} + 3 q^{58} + 2 q^{61} + 16 q^{62} + 2 q^{64} + 3 q^{65} + 9 q^{66} + 4 q^{67} + 3 q^{68} - 27 q^{69} + 24 q^{71} - 3 q^{72} - 22 q^{73} - q^{74} - 7 q^{76} + 3 q^{78} + 16 q^{79} - 6 q^{80} - 9 q^{81} + 6 q^{82} - 9 q^{83} - 9 q^{85} - q^{86} - 3 q^{88} - 6 q^{89} + 9 q^{90} + 9 q^{92} - 24 q^{93} + 21 q^{95} - 3 q^{96} - q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 + 3 * q^5 - 2 * q^8 + 3 * q^9 + 6 * q^10 + 3 * q^11 + 3 * q^12 - q^13 - 9 * q^15 - q^16 - 6 * q^17 - 3 * q^18 + 14 * q^19 + 3 * q^20 - 3 * q^22 + 9 * q^23 + 3 * q^24 - 4 * q^25 - 2 * q^26 - 3 * q^29 - 9 * q^30 + 8 * q^31 + q^32 - 3 * q^34 - 6 * q^36 - 2 * q^37 + 7 * q^38 + 3 * q^39 - 3 * q^40 + 3 * q^41 + q^43 - 6 * q^44 + 18 * q^45 + 18 * q^46 + 4 * q^50 + 9 * q^51 - q^52 + 6 * q^53 + 9 * q^54 + 18 * q^55 - 21 * q^57 + 3 * q^58 + 2 * q^61 + 16 * q^62 + 2 * q^64 + 3 * q^65 + 9 * q^66 + 4 * q^67 + 3 * q^68 - 27 * q^69 + 24 * q^71 - 3 * q^72 - 22 * q^73 - q^74 - 7 * q^76 + 3 * q^78 + 16 * q^79 - 6 * q^80 - 9 * q^81 + 6 * q^82 - 9 * q^83 - 9 * q^85 - q^86 - 3 * q^88 - 6 * q^89 + 9 * q^90 + 9 * q^92 - 24 * q^93 + 21 * q^95 - 3 * q^96 - q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−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	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$			1.73205i			0.707107i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	3.00000			0.948683
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	−4.50000	−	2.59808i	−1.16190	−	0.670820i
$16$	−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
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.768613	+	0.639713i	$0.220947\pi$
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.169701	+	0.985496i	$0.445720\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−1.00000			−0.196116
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	−4.50000	+	2.59808i	−0.821584	+	0.474342i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$			5.19615i			0.904534i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	3.50000	−	6.06218i	0.567775	−	0.983415i
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−3.00000			−0.452267
$45$	9.00000			1.34164
$46$	9.00000			1.32698
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		−	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
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	9.00000			1.21356
$56$		0			0
$57$	−10.5000	+	6.06218i	−1.39076	+	0.802955i
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$			5.19615i			0.670820i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$	4.50000	+	2.59808i	0.553912	+	0.319801i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	−13.5000	−	7.79423i	−1.62521	−	0.938315i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$		−	6.92820i		−	0.800000i
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$		0			0
$78$	1.50000	−	0.866025i	0.169842	−	0.0980581i
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$	−3.00000			−0.335410
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	3.00000			0.331295
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	−4.50000	−	7.79423i	−0.488094	−	0.845403i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$		−	5.19615i		−	0.557086i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$	4.50000	−	7.79423i	0.474342	−	0.821584i
$91$		0			0
$92$	4.50000	−	7.79423i	0.469157	−	0.812605i
$93$	−12.0000	−	6.92820i	−1.24434	−	0.718421i
$94$		0			0
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$	−4.50000	−	7.79423i	−0.452267	−	0.783349i
$100$	4.00000			0.400000
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		−	5.19615i		−	0.514496i
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	0.344865	−	0.938652i	$-0.387925\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	9.00000			0.870063			0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000			0.870063			0.435031	+	0.900415i	$0.356737\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	−13.0000			−1.24517			−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000			−1.24517			−0.622587	+	0.782551i	$0.713918\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$	1.50000	−	0.866025i	0.142374	−	0.0821995i
$112$		0			0
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	0.996262	−	0.0863794i	$-0.0275297\pi$
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	−0.572938	+	0.819599i	$0.694196\pi$
$114$			12.1244i			1.13555i
$115$	−13.5000	+	23.3827i	−1.25888	+	2.18045i
$116$	3.00000			0.278543
$117$	−3.00000			−0.277350
$118$		0			0
$119$		0			0
$120$	4.50000	+	2.59808i	0.410792	+	0.237171i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	3.00000			0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$			1.73205i			0.152499i
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$	4.50000	−	2.59808i	0.391675	−	0.226134i
$133$		0			0
$134$	4.00000			0.345547
$135$	−13.5000	+	7.79423i	−1.16190	+	0.670820i
$136$	3.00000			0.257248
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	−13.5000	+	7.79423i	−1.14920	+	0.663489i
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−3.00000			−0.250873
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−9.00000			−0.747409
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$	−6.00000	−	3.46410i	−0.489898	−	0.282843i
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	−0.687741	−	0.725956i	$-0.741398\pi$
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	0.972567	+	0.232623i	$0.0747309\pi$
$152$	−7.00000			−0.567775
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$	−12.0000	+	20.7846i	−0.963863	+	1.66946i
$156$		−	1.73205i		−	0.138675i
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$	−4.50000	+	2.59808i	−0.356873	+	0.206041i
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−19.0000			−1.48819			−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000			−1.48819			−0.744097	+	0.668071i	$0.767120\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	−13.5000	+	7.79423i	−1.05097	+	0.606780i
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	−7.50000	−	12.9904i	−0.580367	−	1.00523i	−0.995436	−	0.0954356i	$-0.969576\pi$
$167$	−7.50000	−	12.9904i	−0.580367	−	1.00523i	0.415068	−	0.909790i	$-0.363758\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−9.00000			−0.690268
$171$	10.5000	−	18.1865i	0.802955	−	1.39076i
$172$	−1.00000			−0.0762493
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−4.50000	−	2.59808i	−0.341144	−	0.196960i
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	−1.50000	+	2.59808i	−0.112430	+	0.194734i
$179$	−21.0000			−1.56961			−0.784807	−	0.619740i	$-0.787238\pi$
$179$	−21.0000			−1.56961			−0.784807	+	0.619740i	$0.787238\pi$
$180$	−4.50000	−	7.79423i	−0.335410	−	0.580948i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$			3.46410i			0.256074i
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$	−12.0000	+	6.92820i	−0.879883	+	0.508001i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$	21.0000			1.52350
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	0.500000	+	0.866025i	0.0358979	+	0.0621770i
$195$			5.19615i			0.372104i
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−9.00000			−0.639602
$199$	25.0000			1.77220			0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000			1.77220			0.886102	+	0.463491i	$0.153403\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	−6.00000	−	3.46410i	−0.423207	−	0.244339i
$202$	−1.50000	−	2.59808i	−0.105540	−	0.182800i
$203$		0			0
$204$	−4.50000	−	2.59808i	−0.315063	−	0.181902i
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−13.0000			−0.905753
$207$	27.0000			1.87663
$208$	1.00000			0.0693375
$209$	10.5000	−	18.1865i	0.726300	−	1.25799i
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−18.0000	+	10.3923i	−1.23334	+	0.712069i
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$	3.00000			0.204598
$216$		−	5.19615i		−	0.353553i
$217$		0			0
$218$	−6.50000	+	11.2583i	−0.440236	+	0.762510i
$219$	16.5000	−	9.52628i	1.11497	−	0.643726i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$		−	1.73205i		−	0.116248i
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	−0.882281	−	0.470723i	$-0.843993\pi$
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	0.848799	+	0.528716i	$0.177326\pi$
$224$		0			0
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$	9.00000			0.598671
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$	10.5000	+	6.06218i	0.695379	+	0.401478i
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$	13.5000	+	23.3827i	0.890164	+	1.54181i
$231$		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	$0.468670\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$		0			0
$236$		0			0
$237$			27.7128i			1.80014i
$238$		0			0
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	0.910453	−	0.413613i	$-0.135733\pi$
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	−0.813426	+	0.581669i	$0.802400\pi$
$240$	4.50000	−	2.59808i	0.290474	−	0.167705i
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	−0.995809	−	0.0914555i	$-0.970848\pi$
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	0.577107	+	0.816668i	$0.304181\pi$
$242$	2.00000			0.128565
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−4.50000	+	2.59808i	−0.286910	+	0.165647i
$247$	−3.50000	−	6.06218i	−0.222700	−	0.385727i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		−	15.5885i		−	0.987878i
$250$	1.50000	−	2.59808i	0.0948683	−	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
$253$	27.0000			1.69748
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$	13.5000	+	7.79423i	0.845403	+	0.488094i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	−0.981901	−	0.189396i	$-0.939347\pi$
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	0.326929	−	0.945049i	$-0.393986\pi$
$258$	1.50000	+	0.866025i	0.0933859	+	0.0539164i
$259$		0			0
$260$	−3.00000			−0.186052
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$	15.0000			0.926703
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$		−	5.19615i		−	0.319801i
$265$	4.50000	+	7.79423i	0.276433	+	0.478796i
$266$		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	$-0.651177\pi$
$269$	−15.0000			−0.914566			−0.457283	+	0.889321i	$0.651177\pi$
$270$			15.5885i			0.948683i
$271$	−5.00000			−0.303728			−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−5.00000			−0.303728			−0.151864	+	0.988401i	$0.548528\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$		0			0
$274$	−4.50000	−	7.79423i	−0.271855	−	0.470867i
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$			15.5885i			0.938315i
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	−7.00000			−0.419832
$279$	24.0000			1.43684
$280$		0			0
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	−0.361895	−	0.932219i	$-0.617870\pi$
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	0.988273	−	0.152699i	$-0.0487965\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−31.5000	−	18.1865i	−1.86590	−	1.07728i
$286$	−1.50000	+	2.59808i	−0.0886969	+	0.153627i
$287$		0			0
$288$	3.00000			0.176777
$289$	−8.00000			−0.470588
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$		−	1.73205i		−	0.101535i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$	1.00000			0.0581238
$297$	13.5000	+	7.79423i	0.783349	+	0.452267i
$298$	9.00000			0.521356
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$	−6.00000	+	3.46410i	−0.346410	+	0.200000i
$301$		0			0
$302$	−3.50000	−	6.06218i	−0.201402	−	0.348839i
$303$			5.19615i			0.298511i
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	6.00000			0.343559
$306$	4.50000	+	7.79423i	0.257248	+	0.445566i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$	19.5000	+	11.2583i	1.10932	+	0.640464i
$310$	12.0000	+	20.7846i	0.681554	+	1.18049i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$	−1.50000	−	0.866025i	−0.0849208	−	0.0490290i
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$			5.19615i			0.291386i
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	−13.5000	+	7.79423i	−0.753497	+	0.435031i
$322$		0			0
$323$	−21.0000			−1.16847
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	4.00000			0.221880
$326$	−9.50000	+	16.4545i	−0.526156	+	0.911330i
$327$	19.5000	−	11.2583i	1.07835	−	0.622587i
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$		0			0
$330$			15.5885i			0.858116i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	9.00000			0.493939
$333$	−1.50000	+	2.59808i	−0.0821995	+	0.142374i
$334$	−15.0000			−0.820763
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−13.5000	−	7.79423i	−0.733219	−	0.423324i
$340$	−4.50000	+	7.79423i	−0.244047	+	0.422701i
$341$	24.0000			1.29967
$342$	−10.5000	−	18.1865i	−0.567775	−	0.983415i
$343$		0			0
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		−	46.7654i		−	2.51776i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	−4.50000	+	2.59808i	−0.241225	+	0.139272i
$349$	11.5000	−	19.9186i	0.615581	−	1.06622i	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	11.5000	−	19.9186i	0.615581	−	1.06622i	0.990282	−	0.139072i	$-0.0444119\pi$
$350$		0			0
$351$	4.50000	−	2.59808i	0.240192	−	0.138675i
$352$	3.00000			0.159901
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$		0			0
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$	1.50000	+	2.59808i	0.0794998	+	0.137698i
$357$		0			0
$358$	−10.5000	+	18.1865i	−0.554942	+	0.961188i
$359$	9.00000			0.475002			0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000			0.475002			0.237501	+	0.971387i	$0.423672\pi$
$360$	−9.00000			−0.474342
$361$	30.0000			1.57895
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	−3.00000	−	1.73205i	−0.157459	−	0.0909091i
$364$		0			0
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$	3.00000	+	1.73205i	0.156813	+	0.0905357i
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$	−9.00000			−0.469157
$369$	9.00000			0.468521
$370$	−3.00000			−0.155963
$371$		0			0
$372$			13.8564i			0.718421i
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$	−4.50000	+	2.59808i	−0.232379	+	0.134164i
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	10.5000	−	18.1865i	0.538639	−	0.932949i
$381$	6.00000	−	3.46410i	0.307389	−	0.177471i
$382$		0			0
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	1.00000			0.0507673
$389$	−13.5000	+	23.3827i	−0.684477	+	1.18555i	0.289124	+	0.957292i	$0.406636\pi$
$389$	−13.5000	+	23.3827i	−0.684477	+	1.18555i	−0.973601	+	0.228257i	$0.926697\pi$
$390$	4.50000	+	2.59808i	0.227866	+	0.131559i
$391$	−13.5000	−	23.3827i	−0.682724	−	1.18251i
$392$		0			0
$393$	−22.5000	−	12.9904i	−1.13497	−	0.655278i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	48.0000			2.41514
$396$	−4.50000	+	7.79423i	−0.226134	+	0.391675i
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	12.5000	−	21.6506i	0.626568	−	1.08525i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$	−6.00000	+	3.46410i	−0.299253	+	0.172774i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−3.00000			−0.149256
$405$	13.5000	−	23.3827i	0.670820	−	1.16190i
$406$		0			0
$407$	−1.50000	+	2.59808i	−0.0743522	+	0.128782i
$408$	−4.50000	+	2.59808i	−0.222783	+	0.128624i
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	−0.889392	−	0.457146i	$-0.848872\pi$
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	0.0487958	−	0.998809i	$-0.484462\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$			15.5885i			0.768922i
$412$	−6.50000	+	11.2583i	−0.320232	+	0.554658i
$413$		0			0
$414$	13.5000	−	23.3827i	0.663489	−	1.14920i
$415$	−27.0000			−1.32538
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	10.5000	+	6.06218i	0.514187	+	0.296866i
$418$	−10.5000	−	18.1865i	−0.513572	−	0.889532i
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$		0			0
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$	−5.00000			−0.243396
$423$		0			0
$424$	−3.00000			−0.145693
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$			20.7846i			1.00702i
$427$		0			0
$428$	−4.50000	−	7.79423i	−0.217516	−	0.376748i
$429$	4.50000	−	2.59808i	0.217262	−	0.125436i
$430$	1.50000	−	2.59808i	0.0723364	−	0.125290i
$431$	27.0000			1.30054			0.650272	−	0.759701i	$-0.274655\pi$
$431$	27.0000			1.30054			0.650272	+	0.759701i	$0.274655\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	13.5000	−	7.79423i	0.647275	−	0.373705i
$436$	6.50000	+	11.2583i	0.311294	+	0.539176i
$437$	31.5000	+	54.5596i	1.50685	+	2.60994i
$438$		−	19.0526i		−	0.910366i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	3.00000			0.142695
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	−1.50000	−	0.866025i	−0.0711868	−	0.0410997i
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	0.500000	+	0.866025i	0.0236757	+	0.0410075i
$447$	−13.5000	−	7.79423i	−0.638528	−	0.368654i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	12.0000			0.565685
$451$	9.00000			0.423793
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$			12.1244i			0.569652i
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$		0			0
$456$	10.5000	−	6.06218i	0.491708	−	0.283887i
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−13.0000			−0.607450
$459$		−	15.5885i		−	0.727607i
$460$	27.0000			1.25888
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		0			0
$463$	−20.5000	−	35.5070i	−0.952716	−	1.65015i	−0.739511	−	0.673145i	$-0.764943\pi$
$463$	−20.5000	−	35.5070i	−0.952716	−	1.65015i	−0.213205	−	0.977007i	$-0.568390\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		−	41.5692i		−	1.92773i
$466$	1.50000	−	2.59808i	0.0694862	−	0.120354i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	1.50000	+	2.59808i	0.0693375	+	0.120096i
$469$		0			0
$470$		0			0
$471$	33.0000	+	19.0526i	1.52056	+	0.877896i
$472$		0			0
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$	24.0000	+	13.8564i	1.10236	+	0.636446i
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	3.00000			0.137217
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	−0.898257	−	0.439470i	$-0.855166\pi$
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	0.829721	+	0.558179i	$0.188500\pi$
$480$		−	5.19615i		−	0.237171i
$481$	0.500000	+	0.866025i	0.0227980	+	0.0394874i
$482$	6.50000	+	11.2583i	0.296067	+	0.512803i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−3.00000			−0.136223
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−25.0000			−1.13286			−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000			−1.13286			−0.566429	+	0.824110i	$0.691675\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	28.5000	−	16.4545i	1.28881	−	0.744097i
$490$		0			0
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	0.525694	−	0.850674i	$-0.323806\pi$
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	−0.999552	+	0.0299272i	$0.990472\pi$
$492$			5.19615i			0.234261i
$493$	4.50000	−	7.79423i	0.202670	−	0.351034i
$494$	−7.00000			−0.314945
$495$	13.5000	−	23.3827i	0.606780	−	1.05097i
$496$	−8.00000			−0.359211
$497$		0			0
$498$	−13.5000	−	7.79423i	−0.604949	−	0.349268i
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$	22.5000	+	12.9904i	1.00523	+	0.580367i
$502$	−6.00000	+	10.3923i	−0.267793	+	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	−	23.3827i	0.600148	−	1.03949i
$507$			20.7846i			0.923077i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	0.748894	−	0.662690i	$-0.230585\pi$
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	−0.948353	+	0.317217i	$0.897252\pi$
$510$	13.5000	−	7.79423i	0.597790	−	0.345134i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$			36.3731i			1.60591i
$514$	−21.0000			−0.926270
$515$	19.5000	−	33.7750i	0.859273	−	1.48830i
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$		0			0
$518$		0			0
$519$		−	10.3923i		−	0.456172i
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	9.00000			0.393919
$523$	7.00000			0.306089			0.153044	−	0.988219i	$-0.451092\pi$
$523$	7.00000			0.306089			0.153044	+	0.988219i	$0.451092\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		0			0
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$	−4.50000	−	2.59808i	−0.195837	−	0.113067i
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$	9.00000			0.390935
$531$		0			0
$532$		0			0
$533$	1.50000	−	2.59808i	0.0649722	−	0.112535i
$534$		−	5.19615i		−	0.224860i
$535$	13.5000	+	23.3827i	0.583656	+	1.01092i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	31.5000	−	18.1865i	1.35933	−	0.784807i
$538$	−7.50000	+	12.9904i	−0.323348	+	0.560055i
$539$		0			0
$540$	13.5000	+	7.79423i	0.580948	+	0.335410i
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	−2.50000	+	4.33013i	−0.107384	+	0.185995i
$543$	3.00000	−	1.73205i	0.128742	−	0.0743294i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−19.5000	−	33.7750i	−0.835288	−	1.44676i
$546$		0			0
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	−9.00000			−0.384461
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	12.0000			0.511682
$551$	−10.5000	+	18.1865i	−0.447315	+	0.774772i
$552$	13.5000	+	7.79423i	0.574598	+	0.331744i
$553$		0			0
$554$	−0.500000	−	0.866025i	−0.0212430	−	0.0367939i
$555$	4.50000	+	2.59808i	0.191014	+	0.110282i
$556$	−3.50000	+	6.06218i	−0.148433	+	0.257094i
$557$	−9.00000			−0.381342			−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000			−0.381342			−0.190671	+	0.981654i	$0.561066\pi$
$558$	12.0000	−	20.7846i	0.508001	−	0.879883i
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		−	15.5885i		−	0.658145i
$562$	−10.5000	−	18.1865i	−0.442916	−	0.767153i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	−31.5000	+	18.1865i	−1.31939	+	0.761750i
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	1.50000	+	2.59808i	0.0627182	+	0.108631i
$573$		0			0
$574$		0			0
$575$	−36.0000			−1.50130
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	25.0000			1.04076			0.520382	−	0.853934i	$-0.325790\pi$
$577$	25.0000			1.04076			0.520382	+	0.853934i	$0.325790\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	21.0000	+	12.1244i	0.872730	+	0.503871i
$580$	4.50000	+	7.79423i	0.186852	+	0.323638i
$581$		0			0
$582$	−1.50000	−	0.866025i	−0.0621770	−	0.0358979i
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	11.0000			0.455183
$585$	−4.50000	−	7.79423i	−0.186052	−	0.322252i
$586$	−9.00000			−0.371787
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$		0			0
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$	−27.0000	+	15.5885i	−1.11063	+	0.641223i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−39.0000			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$		0			0
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$	−37.5000	+	21.6506i	−1.53477	+	0.886102i
$598$	−4.50000	−	7.79423i	−0.184019	−	0.318730i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$			6.92820i			0.282843i
$601$	−12.5000	+	21.6506i	−0.509886	+	0.883148i	0.490049	+	0.871695i	$0.336979\pi$
$601$	−12.5000	+	21.6506i	−0.509886	+	0.883148i	−0.999934	+	0.0114528i	$0.996354\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	−7.00000			−0.284826
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$	4.50000	+	2.59808i	0.182800	+	0.105540i
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	3.00000	−	5.19615i	0.121466	−	0.210386i
$611$		0			0
$612$	9.00000			0.363803
$613$	23.0000			0.928961			0.464481	−	0.885583i	$-0.346241\pi$
$613$	23.0000			0.928961			0.464481	+	0.885583i	$0.346241\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		−	15.5885i		−	0.628587i
$616$		0			0
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.819818	+	0.572624i	$0.194074\pi$
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.0859976	+	0.996295i	$0.472592\pi$
$618$	19.5000	−	11.2583i	0.784405	−	0.452876i
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	0.984738	+	0.174042i	$0.0556830\pi$
$620$	24.0000			0.963863
$621$	−40.5000	+	23.3827i	−1.62521	+	0.938315i
$622$	−24.0000			−0.962312
$623$		0			0
$624$	−1.50000	+	0.866025i	−0.0600481	+	0.0346688i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	5.00000	+	8.66025i	0.199840	+	0.346133i
$627$			36.3731i			1.45260i
$628$	−11.0000	+	19.0526i	−0.438948	+	0.760280i
$629$	3.00000			0.119618
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$	7.50000	+	4.33013i	0.298098	+	0.172107i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$	4.50000	+	2.59808i	0.178437	+	0.103020i
$637$		0			0
$638$	9.00000			0.356313
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$	3.00000			0.118585
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$			15.5885i			0.615227i
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	0.996379	+	0.0850262i	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$	−4.50000	+	2.59808i	−0.177187	+	0.102299i
$646$	−10.5000	+	18.1865i	−0.413117	+	0.715540i
$647$	21.0000			0.825595			0.412798	−	0.910823i	$-0.364552\pi$
$647$	21.0000			0.825595			0.412798	+	0.910823i	$0.364552\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$		0			0
$650$	2.00000	−	3.46410i	0.0784465	−	0.135873i
$651$		0			0
$652$	9.50000	+	16.4545i	0.372049	+	0.644407i
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	0.681137	−	0.732156i	$-0.261486\pi$
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	−0.974634	+	0.223803i	$0.928153\pi$
$654$		−	22.5167i		−	0.880471i
$655$	−22.5000	+	38.9711i	−0.879148	+	1.52273i
$656$	−3.00000			−0.117130
$657$	−16.5000	+	28.5788i	−0.643726	+	1.11497i
$658$		0			0
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	−0.893762	−	0.448542i	$-0.851943\pi$
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	0.835330	+	0.549749i	$0.185277\pi$
$660$	13.5000	+	7.79423i	0.525487	+	0.303390i
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	−4.50000	−	2.59808i	−0.174766	−	0.100901i
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	−27.0000			−1.04544
$668$	−7.50000	+	12.9904i	−0.290184	+	0.502613i
$669$		−	1.73205i		−	0.0669650i
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	−3.00000	−	5.19615i	−0.115814	−	0.200595i
$672$		0			0
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	0.302017	+	0.953302i	$0.402340\pi$
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	−0.976593	+	0.215096i	$0.930993\pi$
$674$	13.0000			0.500741
$675$	−18.0000	−	10.3923i	−0.692820	−	0.400000i
$676$	−12.0000			−0.461538
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	0.419380	+	0.907811i	$0.362247\pi$
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	−0.995877	+	0.0907112i	$0.971086\pi$
$678$	−13.5000	+	7.79423i	−0.518464	+	0.299336i
$679$		0			0
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$		−	5.19615i		−	0.199117i
$682$	12.0000	−	20.7846i	0.459504	−	0.795884i
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$	−21.0000			−0.802955
$685$	27.0000			1.03162
$686$		0			0
$687$	19.5000	+	11.2583i	0.743971	+	0.429532i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−1.50000	−	2.59808i	−0.0571454	−	0.0989788i
$690$	−40.5000	−	23.3827i	−1.54181	−	0.890164i
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	−0.0555386	−	0.998457i	$-0.517688\pi$
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	0.892458	−	0.451130i	$-0.148979\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	10.5000	−	18.1865i	0.398288	−	0.689855i
$696$			5.19615i			0.196960i
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	−11.5000	−	19.9186i	−0.435281	−	0.753930i
$699$	−4.50000	+	2.59808i	−0.170206	+	0.0982683i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		−	5.19615i		−	0.196116i
$703$	−7.00000			−0.264010
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−1.50000	−	2.59808i	−0.0564532	−	0.0977799i
$707$		0			0
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	36.0000			1.35106
$711$	−24.0000	−	41.5692i	−0.900070	−	1.55897i
$712$	3.00000			0.112430
$713$	−36.0000	+	62.3538i	−1.34821	+	2.33517i
$714$		0			0
$715$	−4.50000	−	7.79423i	−0.168290	−	0.291488i
$716$	10.5000	+	18.1865i	0.392403	+	0.679663i
$717$	−4.50000	−	2.59808i	−0.168056	−	0.0970269i
$718$	4.50000	−	7.79423i	0.167939	−	0.290878i
$719$	15.0000			0.559406			0.279703	−	0.960087i	$-0.409764\pi$
$719$	15.0000			0.559406			0.279703	+	0.960087i	$0.409764\pi$
$720$	−4.50000	+	7.79423i	−0.167705	+	0.290474i
$721$		0			0
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$		−	22.5167i		−	0.837404i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$	−3.00000	+	1.73205i	−0.111340	+	0.0642824i
$727$	−6.50000	+	11.2583i	−0.241072	+	0.417548i	−0.961020	−	0.276479i	$-0.910832\pi$
$727$	−6.50000	+	11.2583i	−0.241072	+	0.417548i	0.719948	+	0.694028i	$0.244166\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−33.0000			−1.22138
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	3.00000	−	1.73205i	0.110883	−	0.0640184i
$733$	−0.500000	−	0.866025i	−0.0184679	−	0.0319874i	0.856644	−	0.515908i	$-0.172546\pi$
$733$	−0.500000	−	0.866025i	−0.0184679	−	0.0319874i	−0.875112	+	0.483921i	$0.839212\pi$
$734$	−8.50000	−	14.7224i	−0.313741	−	0.543415i
$735$		0			0
$736$	−4.50000	+	7.79423i	−0.165872	+	0.287299i
$737$	12.0000			0.442026
$738$	4.50000	−	7.79423i	0.165647	−	0.286910i
$739$	23.0000			0.846069			0.423034	−	0.906114i	$-0.360965\pi$
$739$	23.0000			0.846069			0.423034	+	0.906114i	$0.360965\pi$
$740$	−1.50000	+	2.59808i	−0.0551411	+	0.0955072i
$741$	10.5000	+	6.06218i	0.385727	+	0.222700i
$742$		0			0
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	0.606590	−	0.795015i	$-0.292537\pi$
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	−0.991798	+	0.127815i	$0.959204\pi$
$744$	12.0000	+	6.92820i	0.439941	+	0.254000i
$745$	−13.5000	+	23.3827i	−0.494602	+	0.856675i
$746$	13.0000			0.475964
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$	9.00000			0.329073
$749$		0			0
$750$			5.19615i			0.189737i
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$		0			0
$753$	18.0000	−	10.3923i	0.655956	−	0.378717i
$754$	1.50000	−	2.59808i	0.0546268	−	0.0946164i
$755$	21.0000			0.764268
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	−40.5000	+	23.3827i	−1.47006	+	0.848738i
$760$	−10.5000	−	18.1865i	−0.380875	−	0.659695i
$761$	−22.5000	−	38.9711i	−0.815624	−	1.41270i	−0.908879	−	0.417061i	$-0.863060\pi$
$761$	−22.5000	−	38.9711i	−0.815624	−	1.41270i	0.0932544	−	0.995642i	$-0.470273\pi$
$762$		−	6.92820i		−	0.250982i
$763$		0			0
$764$		0			0
$765$	−27.0000			−0.976187
$766$	15.0000			0.541972
$767$		0			0
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$		0			0
$771$	31.5000	+	18.1865i	1.13444	+	0.654972i
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	−27.0000			−0.971123			−0.485561	−	0.874203i	$-0.661385\pi$
$773$	−27.0000			−0.971123			−0.485561	+	0.874203i	$0.661385\pi$
$774$	−3.00000			−0.107833
$775$	−32.0000			−1.14947
$776$	0.500000	−	0.866025i	0.0179490	−	0.0310885i
$777$		0			0
$778$	13.5000	+	23.3827i	0.483998	+	0.838310i
$779$	10.5000	+	18.1865i	0.376202	+	0.651600i
$780$	4.50000	−	2.59808i	0.161126	−	0.0930261i
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	−27.0000			−0.965518
$783$	−13.5000	−	7.79423i	−0.482451	−	0.278543i
$784$		0			0
$785$	33.0000	−	57.1577i	1.17782	−	2.04004i
$786$	−22.5000	+	12.9904i	−0.802548	+	0.463352i
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$		−	15.5885i		−	0.554964i
$790$	24.0000	−	41.5692i	0.853882	−	1.47897i
$791$		0			0
$792$	4.50000	+	7.79423i	0.159901	+	0.276956i
$793$	−2.00000			−0.0710221
$794$	6.50000	−	11.2583i	0.230676	−	0.399543i
$795$	−13.5000	−	7.79423i	−0.478796	−	0.276433i
$796$	−12.5000	−	21.6506i	−0.443051	−	0.767386i
$797$	−10.5000	−	18.1865i	−0.371929	−	0.644200i	0.617933	−	0.786231i	$-0.287970\pi$
$797$	−10.5000	−	18.1865i	−0.371929	−	0.644200i	−0.989862	+	0.142031i	$0.954637\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000			−0.141421
$801$	−4.50000	+	7.79423i	−0.159000	+	0.275396i
$802$	−27.0000			−0.953403
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$			6.92820i			0.244339i
$805$		0			0
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	22.5000	−	12.9904i	0.792038	−	0.457283i
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−33.0000			−1.16022			−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000			−1.16022			−0.580109	+	0.814539i	$0.696990\pi$
$810$	−13.5000	−	23.3827i	−0.474342	−	0.821584i
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	7.50000	−	4.33013i	0.263036	−	0.151864i
$814$	1.50000	+	2.59808i	0.0525750	+	0.0910625i
$815$	−28.5000	−	49.3634i	−0.998311	−	1.72913i
$816$			5.19615i			0.181902i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	−34.0000			−1.18878
$819$		0			0
$820$	9.00000			0.314294
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$	13.5000	+	7.79423i	0.470867	+	0.271855i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	6.50000	+	11.2583i	0.226438	+	0.392203i
$825$	−18.0000	−	10.3923i	−0.626680	−	0.361814i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−13.5000	−	23.3827i	−0.469157	−	0.812605i
$829$	−11.0000			−0.382046			−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000			−0.382046			−0.191023	+	0.981586i	$0.561180\pi$
$830$	−13.5000	+	23.3827i	−0.468592	+	0.811625i
$831$			1.73205i			0.0600842i
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$		0			0
$834$	10.5000	−	6.06218i	0.363585	−	0.209916i
$835$	22.5000	−	38.9711i	0.778645	−	1.34865i
$836$	−21.0000			−0.726300
$837$	−36.0000	+	20.7846i	−1.24434	+	0.718421i
$838$	9.00000			0.310900
$839$	7.50000	−	12.9904i	0.258929	−	0.448478i	−0.707026	−	0.707187i	$-0.749964\pi$
$839$	7.50000	−	12.9904i	0.258929	−	0.448478i	0.965955	+	0.258709i	$0.0832972\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	17.5000	+	30.3109i	0.603090	+	1.04458i
$843$			36.3731i			1.25275i
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$	36.0000			1.23844
$846$		0			0
$847$		0			0
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$	6.00000	+	3.46410i	0.205919	+	0.118888i
$850$	−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
$853$	−0.500000	+	0.866025i	−0.0171197	+	0.0296521i	−0.874458	−	0.485101i	$-0.838783\pi$
$853$	−0.500000	+	0.866025i	−0.0171197	+	0.0296521i	0.857339	+	0.514753i	$0.172116\pi$
$854$		0			0
$855$	63.0000			2.15455
$856$	−9.00000			−0.307614
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	−0.839268	−	0.543718i	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$		−	5.19615i		−	0.177394i
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	0.570064	−	0.821600i	$-0.306918\pi$
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	−0.996559	+	0.0828900i	$0.973585\pi$
$860$	−1.50000	−	2.59808i	−0.0511496	−	0.0885937i
$861$		0			0
$862$	13.5000	−	23.3827i	0.459812	−	0.796417i
$863$	−51.0000			−1.73606			−0.868030	−	0.496512i	$-0.834614\pi$
$863$	−51.0000			−1.73606			−0.868030	+	0.496512i	$0.834614\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	−18.0000			−0.612018
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$		0			0
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$		−	15.5885i		−	0.528498i
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$	13.0000			0.440236
$873$	1.50000	+	2.59808i	0.0507673	+	0.0879316i
$874$	63.0000			2.13101
$875$		0			0
$876$	−16.5000	−	9.52628i	−0.557483	−	0.321863i
$877$	−23.5000	−	40.7032i	−0.793539	−	1.37445i	−0.923763	−	0.382965i	$-0.874903\pi$
$877$	−23.5000	−	40.7032i	−0.793539	−	1.37445i	0.130224	−	0.991485i	$-0.458430\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$	13.5000	+	7.79423i	0.455344	+	0.262893i
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	1.50000	−	2.59808i	0.0504505	−	0.0873828i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−16.5000	−	28.5788i	−0.554016	−	0.959583i	−0.997979	−	0.0635387i	$-0.979761\pi$
$887$	−16.5000	−	28.5788i	−0.554016	−	0.959583i	0.443964	−	0.896045i	$-0.353572\pi$
$888$	−1.50000	+	0.866025i	−0.0503367	+	0.0290619i
$889$		0			0
$890$	−9.00000			−0.301681
$891$	−27.0000			−0.904534
$892$	1.00000			0.0334825
$893$		0			0
$894$	−13.5000	+	7.79423i	−0.451508	+	0.260678i
$895$	−31.5000	−	54.5596i	−1.05293	−	1.82373i
$896$		0			0
$897$			15.5885i			0.520483i
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−24.0000			−0.800445
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	−9.00000			−0.299833
$902$	4.50000	−	7.79423i	0.149834	−	0.259519i
$903$		0			0
$904$	−4.50000	−	7.79423i	−0.149668	−	0.259232i
$905$	−3.00000	−	5.19615i	−0.0997234	−	0.172726i
$906$	10.5000	+	6.06218i	0.348839	+	0.201402i
$907$	21.5000	−	37.2391i	0.713896	−	1.23650i	−0.249488	−	0.968378i	$-0.580262\pi$
$907$	21.5000	−	37.2391i	0.713896	−	1.23650i	0.963384	−	0.268126i	$-0.0864043\pi$
$908$	3.00000			0.0995585
$909$	−4.50000	−	7.79423i	−0.149256	−	0.258518i
$910$		0			0
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	0.337991	+	0.941149i	$0.390253\pi$
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	−0.984055	+	0.177866i	$0.943081\pi$
$912$		−	12.1244i		−	0.401478i
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$	−9.00000	+	5.19615i	−0.297531	+	0.171780i
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$		0			0
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	53.0000			1.74831			0.874154	−	0.485648i	$-0.161416\pi$
$919$	53.0000			1.74831			0.874154	+	0.485648i	$0.161416\pi$
$920$	13.5000	−	23.3827i	0.445082	−	0.770904i
$921$	−42.0000	+	24.2487i	−1.38395	+	0.799022i
$922$	4.50000	+	7.79423i	0.148200	+	0.256689i
$923$	−6.00000	−	10.3923i	−0.197492	−	0.342067i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	−41.0000			−1.34734
$927$	−39.0000			−1.28093
$928$	−3.00000			−0.0984798
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	−36.0000	−	20.7846i	−1.18049	−	0.681554i
$931$		0			0
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$	36.0000	+	20.7846i	1.17859	+	0.680458i
$934$	1.50000	−	2.59808i	0.0490815	−	0.0850117i
$935$	−27.0000			−0.882994
$936$	3.00000			0.0980581
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$		0			0
$939$		−	17.3205i		−	0.565233i
$940$		0			0
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	0.812975	−	0.582298i	$-0.197846\pi$
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	−0.910773	+	0.412908i	$0.864513\pi$
$942$	33.0000	−	19.0526i	1.07520	−	0.620766i
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$		0			0
$945$		0			0
$946$	−3.00000			−0.0975384
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	24.0000	−	13.8564i	0.779484	−	0.450035i
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$	14.0000	+	24.2487i	0.454220	+	0.786732i
$951$		−	31.1769i		−	1.01098i
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$		0			0
$956$	1.50000	−	2.59808i	0.0485135	−	0.0840278i
$957$	−13.5000	−	7.79423i	−0.436393	−	0.251952i
$958$	1.50000	+	2.59808i	0.0484628	+	0.0839400i
$959$		0			0
$960$	−4.50000	−	2.59808i	−0.145237	−	0.0838525i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	1.00000			0.0322413
$963$	13.5000	−	23.3827i	0.435031	−	0.753497i
$964$	13.0000			0.418702
$965$	21.0000	−	36.3731i	0.676014	−	1.17089i
$966$		0			0
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	31.5000	−	18.1865i	1.01193	−	0.584236i
$970$	−1.50000	+	2.59808i	−0.0481621	+	0.0834192i
$971$	−33.0000			−1.05902			−0.529510	−	0.848304i	$-0.677624\pi$
$971$	−33.0000			−1.05902			−0.529510	+	0.848304i	$0.677624\pi$
$972$		−	15.5885i		−	0.500000i
$973$		0			0
$974$	−12.5000	+	21.6506i	−0.400526	+	0.693731i
$975$	−6.00000	+	3.46410i	−0.192154	+	0.110940i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$		−	32.9090i		−	1.05231i
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$		0			0
$981$	−19.5000	+	33.7750i	−0.622587	+	1.07835i
$982$	−21.0000			−0.670137
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	−0.960489	−	0.278319i	$-0.910223\pi$
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	0.721276	+	0.692648i	$0.243556\pi$
$984$	4.50000	+	2.59808i	0.143455	+	0.0828236i
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$	−4.50000	−	7.79423i	−0.143309	−	0.248219i
$987$		0			0
$988$	−3.50000	+	6.06218i	−0.111350	+	0.192864i
$989$	9.00000			0.286183
$990$	−13.5000	−	23.3827i	−0.429058	−	0.743151i
$991$	−25.0000			−0.794151			−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000			−0.794151			−0.397076	+	0.917786i	$0.629975\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$		−	13.8564i		−	0.439720i
$994$		0			0
$995$	37.5000	+	64.9519i	1.18883	+	2.05911i
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	−6.50000	+	11.2583i	−0.205857	+	0.356555i	−0.950405	−	0.311014i	$-0.899332\pi$
$997$	−6.50000	+	11.2583i	−0.205857	+	0.356555i	0.744548	+	0.667568i	$0.232665\pi$
$998$	25.0000			0.791361
$999$		−	5.19615i		−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.g.295.1		2
3.2	odd	2		2646.2.f.a.883.1		2
7.2	even	3		882.2.e.c.655.1		2
7.3	odd	6		126.2.h.b.79.1	yes	2
7.4	even	3		882.2.h.i.79.1		2
7.5	odd	6		126.2.e.a.25.1	✓	2
7.6	odd	2		882.2.f.i.295.1		2
9.2	odd	6		7938.2.a.be.1.1		1
9.4	even	3	inner	882.2.f.g.589.1		2
9.5	odd	6		2646.2.f.a.1765.1		2
9.7	even	3		7938.2.a.b.1.1		1
21.2	odd	6		2646.2.e.g.2125.1		2
21.5	even	6		378.2.e.b.235.1		2
21.11	odd	6		2646.2.h.d.667.1		2
21.17	even	6		378.2.h.a.289.1		2
21.20	even	2		2646.2.f.d.883.1		2
28.3	even	6		1008.2.t.f.961.1		2
28.19	even	6		1008.2.q.a.529.1		2
63.4	even	3		882.2.e.c.373.1		2
63.5	even	6		378.2.h.a.361.1		2
63.13	odd	6		882.2.f.i.589.1		2
63.20	even	6		7938.2.a.t.1.1		1
63.23	odd	6		2646.2.h.d.361.1		2
63.31	odd	6		126.2.e.a.121.1	yes	2
63.32	odd	6		2646.2.e.g.1549.1		2
63.34	odd	6		7938.2.a.m.1.1		1
63.38	even	6		1134.2.g.c.163.1		2
63.40	odd	6		126.2.h.b.67.1	yes	2
63.41	even	6		2646.2.f.d.1765.1		2
63.47	even	6		1134.2.g.c.487.1		2
63.52	odd	6		1134.2.g.e.163.1		2
63.58	even	3		882.2.h.i.67.1		2
63.59	even	6		378.2.e.b.37.1		2
63.61	odd	6		1134.2.g.e.487.1		2
84.47	odd	6		3024.2.q.f.2881.1		2
84.59	odd	6		3024.2.t.a.289.1		2
252.31	even	6		1008.2.q.a.625.1		2
252.59	odd	6		3024.2.q.f.2305.1		2
252.103	even	6		1008.2.t.f.193.1		2
252.131	odd	6		3024.2.t.a.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	7.5	odd	6
126.2.e.a.121.1	yes	2	63.31	odd	6
126.2.h.b.67.1	yes	2	63.40	odd	6
126.2.h.b.79.1	yes	2	7.3	odd	6
378.2.e.b.37.1		2	63.59	even	6
378.2.e.b.235.1		2	21.5	even	6
378.2.h.a.289.1		2	21.17	even	6
378.2.h.a.361.1		2	63.5	even	6
882.2.e.c.373.1		2	63.4	even	3
882.2.e.c.655.1		2	7.2	even	3
882.2.f.g.295.1		2	1.1	even	1	trivial
882.2.f.g.589.1		2	9.4	even	3	inner
882.2.f.i.295.1		2	7.6	odd	2
882.2.f.i.589.1		2	63.13	odd	6
882.2.h.i.67.1		2	63.58	even	3
882.2.h.i.79.1		2	7.4	even	3
1008.2.q.a.529.1		2	28.19	even	6
1008.2.q.a.625.1		2	252.31	even	6
1008.2.t.f.193.1		2	252.103	even	6
1008.2.t.f.961.1		2	28.3	even	6
1134.2.g.c.163.1		2	63.38	even	6
1134.2.g.c.487.1		2	63.47	even	6
1134.2.g.e.163.1		2	63.52	odd	6
1134.2.g.e.487.1		2	63.61	odd	6
2646.2.e.g.1549.1		2	63.32	odd	6
2646.2.e.g.2125.1		2	21.2	odd	6
2646.2.f.a.883.1		2	3.2	odd	2
2646.2.f.a.1765.1		2	9.5	odd	6
2646.2.f.d.883.1		2	21.20	even	2
2646.2.f.d.1765.1		2	63.41	even	6
2646.2.h.d.361.1		2	63.23	odd	6
2646.2.h.d.667.1		2	21.11	odd	6
3024.2.q.f.2305.1		2	252.59	odd	6
3024.2.q.f.2881.1		2	84.47	odd	6
3024.2.t.a.289.1		2	84.59	odd	6
3024.2.t.a.1873.1		2	252.131	odd	6
7938.2.a.b.1.1		1	9.7	even	3
7938.2.a.m.1.1		1	63.34	odd	6
7938.2.a.t.1.1		1	63.20	even	6
7938.2.a.be.1.1		1	9.2	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +3.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} -1.00000 q^{26} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(-4.50000 + 2.59808i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +5.19615i q^{33} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{36} -1.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(1.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +9.00000 q^{45} +9.00000 q^{46} -1.73205i q^{48} +(2.00000 + 3.46410i) q^{50} +(4.50000 - 2.59808i) q^{51} +(-0.500000 + 0.866025i) q^{52} +3.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(1.50000 + 2.59808i) q^{58} +5.19615i q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(4.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-13.5000 - 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} -6.92820i q^{75} +(-3.50000 - 6.06218i) q^{76} +(1.50000 - 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} -3.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +3.00000 q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 - 0.866025i) q^{86} -5.19615i q^{87} +(-1.50000 + 2.59808i) q^{88} -3.00000 q^{89} +(4.50000 - 7.79423i) q^{90} +(4.50000 - 7.79423i) q^{92} +(-12.0000 - 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 - q^4 + 3 * q^5 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 2 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{11} + 3 q^{12} - q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 3 q^{18} + 14 q^{19} + 3 q^{20} - 3 q^{22} + 9 q^{23} + 3 q^{24} - 4 q^{25} - 2 q^{26} - 3 q^{29} - 9 q^{30} + 8 q^{31} + q^{32} - 3 q^{34} - 6 q^{36} - 2 q^{37} + 7 q^{38} + 3 q^{39} - 3 q^{40} + 3 q^{41} + q^{43} - 6 q^{44} + 18 q^{45} + 18 q^{46} + 4 q^{50} + 9 q^{51} - q^{52} + 6 q^{53} + 9 q^{54} + 18 q^{55} - 21 q^{57} + 3 q^{58} + 2 q^{61} + 16 q^{62} + 2 q^{64} + 3 q^{65} + 9 q^{66} + 4 q^{67} + 3 q^{68} - 27 q^{69} + 24 q^{71} - 3 q^{72} - 22 q^{73} - q^{74} - 7 q^{76} + 3 q^{78} + 16 q^{79} - 6 q^{80} - 9 q^{81} + 6 q^{82} - 9 q^{83} - 9 q^{85} - q^{86} - 3 q^{88} - 6 q^{89} + 9 q^{90} + 9 q^{92} - 24 q^{93} + 21 q^{95} - 3 q^{96} - q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 + 3 * q^5 - 2 * q^8 + 3 * q^9 + 6 * q^10 + 3 * q^11 + 3 * q^12 - q^13 - 9 * q^15 - q^16 - 6 * q^17 - 3 * q^18 + 14 * q^19 + 3 * q^20 - 3 * q^22 + 9 * q^23 + 3 * q^24 - 4 * q^25 - 2 * q^26 - 3 * q^29 - 9 * q^30 + 8 * q^31 + q^32 - 3 * q^34 - 6 * q^36 - 2 * q^37 + 7 * q^38 + 3 * q^39 - 3 * q^40 + 3 * q^41 + q^43 - 6 * q^44 + 18 * q^45 + 18 * q^46 + 4 * q^50 + 9 * q^51 - q^52 + 6 * q^53 + 9 * q^54 + 18 * q^55 - 21 * q^57 + 3 * q^58 + 2 * q^61 + 16 * q^62 + 2 * q^64 + 3 * q^65 + 9 * q^66 + 4 * q^67 + 3 * q^68 - 27 * q^69 + 24 * q^71 - 3 * q^72 - 22 * q^73 - q^74 - 7 * q^76 + 3 * q^78 + 16 * q^79 - 6 * q^80 - 9 * q^81 + 6 * q^82 - 9 * q^83 - 9 * q^85 - q^86 - 3 * q^88 - 6 * q^89 + 9 * q^90 + 9 * q^92 - 24 * q^93 + 21 * q^95 - 3 * q^96 - q^97 - 9 * q^99

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