LMFDB - Embedded newform 882.2.h.e.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} -3.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(2.50000 - 4.33013i) q^{13} +(4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} -3.00000 q^{23} +(1.50000 - 0.866025i) q^{24} +4.00000 q^{25} +(2.50000 + 4.33013i) q^{26} -5.19615i q^{27} +(1.50000 + 2.59808i) q^{29} +5.19615i q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 + 2.59808i) q^{34} -3.00000 q^{36} +(3.50000 + 6.06218i) q^{37} -5.00000 q^{38} -8.66025i q^{39} +3.00000 q^{40} +(-4.50000 + 7.79423i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{45} +(1.50000 - 2.59808i) q^{46} +1.73205i q^{48} +(-2.00000 + 3.46410i) q^{50} -5.19615i q^{51} -5.00000 q^{52} +(1.50000 - 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} -9.00000 q^{55} +(7.50000 + 4.33013i) q^{57} -3.00000 q^{58} +(6.00000 + 10.3923i) q^{59} +(-4.50000 - 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(7.50000 - 12.9904i) q^{65} -5.19615i q^{66} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-4.50000 + 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} -7.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(2.50000 - 4.33013i) q^{76} +(7.50000 + 4.33013i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(1.50000 + 2.59808i) q^{83} +(4.50000 - 7.79423i) q^{85} +11.0000 q^{86} +(4.50000 + 2.59808i) q^{87} -3.00000 q^{88} +(7.50000 + 12.9904i) q^{89} +(4.50000 + 7.79423i) q^{90} +(1.50000 + 2.59808i) q^{92} +(-6.00000 - 3.46410i) q^{93} +(7.50000 + 12.9904i) 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} + 6 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 + 6 * q^5 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} + 6 q^{5} + 2 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} + 5 q^{13} + 9 q^{15} - q^{16} + 3 q^{17} + 3 q^{18} + 5 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 3 q^{24} + 8 q^{25} + 5 q^{26} + 3 q^{29} - 4 q^{31} - q^{32} - 9 q^{33} + 3 q^{34} - 6 q^{36} + 7 q^{37} - 10 q^{38} + 6 q^{40} - 9 q^{41} - 11 q^{43} + 3 q^{44} + 9 q^{45} + 3 q^{46} - 4 q^{50} - 10 q^{52} + 3 q^{53} + 9 q^{54} - 18 q^{55} + 15 q^{57} - 6 q^{58} + 12 q^{59} - 9 q^{60} + 2 q^{61} + 8 q^{62} + 2 q^{64} + 15 q^{65} + 4 q^{67} - 6 q^{68} - 9 q^{69} + 3 q^{72} + 11 q^{73} - 14 q^{74} + 12 q^{75} + 5 q^{76} + 15 q^{78} - 8 q^{79} - 3 q^{80} - 9 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{85} + 22 q^{86} + 9 q^{87} - 6 q^{88} + 15 q^{89} + 9 q^{90} + 3 q^{92} - 12 q^{93} + 15 q^{95} - 3 q^{96} - q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 + 6 * q^5 + 2 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 3 * q^12 + 5 * q^13 + 9 * q^15 - q^16 + 3 * q^17 + 3 * q^18 + 5 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 + 3 * q^24 + 8 * q^25 + 5 * q^26 + 3 * q^29 - 4 * q^31 - q^32 - 9 * q^33 + 3 * q^34 - 6 * q^36 + 7 * q^37 - 10 * q^38 + 6 * q^40 - 9 * q^41 - 11 * q^43 + 3 * q^44 + 9 * q^45 + 3 * q^46 - 4 * q^50 - 10 * q^52 + 3 * q^53 + 9 * q^54 - 18 * q^55 + 15 * q^57 - 6 * q^58 + 12 * q^59 - 9 * q^60 + 2 * q^61 + 8 * q^62 + 2 * q^64 + 15 * q^65 + 4 * q^67 - 6 * q^68 - 9 * q^69 + 3 * q^72 + 11 * q^73 - 14 * q^74 + 12 * q^75 + 5 * q^76 + 15 * q^78 - 8 * q^79 - 3 * q^80 - 9 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^85 + 22 * q^86 + 9 * q^87 - 6 * q^88 + 15 * q^89 + 9 * q^90 + 3 * q^92 - 12 * q^93 + 15 * 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−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
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$			1.73205i			0.707107i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$	4.50000	−	2.59808i	1.16190	−	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	4.00000			0.800000
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$			5.19615i			0.948683i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−5.00000			−0.811107
$39$		−	8.66025i		−	1.38675i
$40$	3.00000			0.474342
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	4.50000	−	7.79423i	0.670820	−	1.16190i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$			1.73205i			0.250000i
$49$		0			0
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		−	5.19615i		−	0.727607i
$52$	−5.00000			−0.693375
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	−9.00000			−1.21356
$56$		0			0
$57$	7.50000	+	4.33013i	0.993399	+	0.573539i
$58$	−3.00000			−0.393919
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−4.50000	−	2.59808i	−0.580948	−	0.335410i
$61$	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	$0.125799\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	7.50000	−	12.9904i	0.930261	−	1.61126i
$66$		−	5.19615i		−	0.639602i
$67$	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	$0.754762\pi$
$68$	−3.00000			−0.363803
$69$	−4.50000	+	2.59808i	−0.541736	+	0.312772i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$	−7.00000			−0.813733
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$		0			0
$78$	7.50000	+	4.33013i	0.849208	+	0.490290i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$		0			0
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$	11.0000			1.18616
$87$	4.50000	+	2.59808i	0.482451	+	0.278543i
$88$	−3.00000			−0.319801
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$	4.50000	+	7.79423i	0.474342	+	0.821584i
$91$		0			0
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$		0			0
$95$	7.50000	+	12.9904i	0.769484	+	1.33278i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$		0			0
$99$	−4.50000	+	7.79423i	−0.452267	+	0.783349i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	−5.00000			−0.492665			−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000			−0.492665			−0.246332	+	0.969185i	$0.579225\pi$
$104$	2.50000	−	4.33013i	0.245145	−	0.424604i
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	0.958952	+	0.283567i	$0.0915178\pi$
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	−0.233900	+	0.972261i	$0.575149\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$	10.5000	+	6.06218i	0.996616	+	0.575396i
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−7.50000	+	4.33013i	−0.702439	+	0.405554i
$115$	−9.00000			−0.839254
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	−7.50000	−	12.9904i	−0.693375	−	1.20096i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	−2.00000			−0.181818
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$			15.5885i			1.40556i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−16.5000	−	9.52628i	−1.45274	−	0.838742i
$130$	7.50000	+	12.9904i	0.657794	+	1.13933i
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$	4.50000	+	2.59808i	0.391675	+	0.226134i
$133$		0			0
$134$	−4.00000			−0.345547
$135$		−	15.5885i		−	1.34164i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$		−	5.19615i		−	0.442326i
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	−0.740308	−	0.672268i	$-0.765320\pi$
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	0.952355	+	0.304991i	$0.0986536\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.50000	+	12.9904i	−0.627182	+	1.08631i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	−3.00000			−0.245770			−0.122885	−	0.992421i	$-0.539215\pi$
$149$	−3.00000			−0.245770			−0.122885	+	0.992421i	$0.539215\pi$
$150$			6.92820i			0.565685i
$151$	11.0000			0.895167			0.447584	−	0.894242i	$-0.352285\pi$
$151$	11.0000			0.895167			0.447584	+	0.894242i	$0.352285\pi$
$152$	2.50000	+	4.33013i	0.202777	+	0.351220i
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$		0			0
$155$	−6.00000	−	10.3923i	−0.481932	−	0.834730i
$156$	−7.50000	+	4.33013i	−0.600481	+	0.346688i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$		−	5.19615i		−	0.412082i
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$	9.00000			0.707107
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	0.313304	−	0.949653i	$-0.398564\pi$
$164$	9.00000			0.702782
$165$	−13.5000	+	7.79423i	−1.05097	+	0.606780i
$166$	−3.00000			−0.232845
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	−0.802135	−	0.597143i	$-0.796303\pi$
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	4.50000	+	7.79423i	0.345134	+	0.597790i
$171$	15.0000			1.14708
$172$	−5.50000	+	9.52628i	−0.419371	+	0.726372i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	−4.50000	+	2.59808i	−0.341144	+	0.196960i
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	18.0000	+	10.3923i	1.35296	+	0.781133i
$178$	−15.0000			−1.12430
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$	−9.00000			−0.670820
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$		−	3.46410i		−	0.256074i
$184$	−3.00000			−0.221163
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$	6.00000	−	3.46410i	0.439941	−	0.254000i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$	−15.0000			−1.08821
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	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	$-0.334758\pi$
$194$	1.00000			0.0717958
$195$		−	25.9808i		−	1.86052i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	−0.963001	−	0.269498i	$-0.913142\pi$
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	0.714893	+	0.699234i	$0.246476\pi$
$200$	4.00000			0.282843
$201$	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
$205$	−13.5000	+	23.3827i	−0.942881	+	1.63312i
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$	2.50000	+	4.33013i	0.173344	+	0.300240i
$209$	−7.50000	−	12.9904i	−0.518786	−	0.898563i
$210$		0			0
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$	−3.00000			−0.206041
$213$		0			0
$214$	−15.0000			−1.02538
$215$	−16.5000	−	28.5788i	−1.12529	−	1.94906i
$216$		−	5.19615i		−	0.353553i
$217$		0			0
$218$	3.50000	+	6.06218i	0.237050	+	0.410582i
$219$		−	19.0526i		−	1.28745i
$220$	4.50000	+	7.79423i	0.303390	+	0.525487i
$221$	−7.50000	−	12.9904i	−0.504505	−	0.873828i
$222$	−10.5000	+	6.06218i	−0.704714	+	0.406867i
$223$	8.50000	+	14.7224i	0.569202	+	0.985887i	0.996645	+	0.0818447i	$0.0260811\pi$
$223$	8.50000	+	14.7224i	0.569202	+	0.985887i	−0.427443	+	0.904042i	$0.640586\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	−9.00000			−0.597351			−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000			−0.597351			−0.298675	+	0.954355i	$0.596545\pi$
$228$		−	8.66025i		−	0.573539i
$229$	−17.0000			−1.12339			−0.561696	−	0.827344i	$-0.689851\pi$
$229$	−17.0000			−1.12339			−0.561696	+	0.827344i	$0.689851\pi$
$230$	4.50000	−	7.79423i	0.296721	−	0.513936i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−13.5000	−	23.3827i	−0.884414	−	1.53185i	−0.846383	−	0.532574i	$-0.821225\pi$
$233$	−13.5000	−	23.3827i	−0.884414	−	1.53185i	−0.0380310	−	0.999277i	$-0.512109\pi$
$234$	15.0000			0.980581
$235$		0			0
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$			13.8564i			0.900070i
$238$		0			0
$239$	−13.5000	+	23.3827i	−0.873242	+	1.51250i	−0.0146191	+	0.999893i	$0.504654\pi$
$239$	−13.5000	+	23.3827i	−0.873242	+	1.51250i	−0.858623	+	0.512607i	$0.828680\pi$
$240$			5.19615i			0.335410i
$241$	−23.0000			−1.48156			−0.740780	−	0.671748i	$-0.765544\pi$
$241$	−23.0000			−1.48156			−0.740780	+	0.671748i	$0.765544\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	25.0000			1.59071
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	4.50000	+	2.59808i	0.285176	+	0.164646i
$250$	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
$253$	9.00000			0.565825
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$		−	15.5885i		−	0.976187i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.0000			−0.935674			−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000			−0.935674			−0.467837	+	0.883815i	$0.654967\pi$
$258$	16.5000	−	9.52628i	1.02725	−	0.593080i
$259$		0			0
$260$	−15.0000			−0.930261
$261$	9.00000			0.557086
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$	−9.00000			−0.554964			−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000			−0.554964			−0.277482	+	0.960731i	$0.589500\pi$
$264$	−4.50000	+	2.59808i	−0.276956	+	0.159901i
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$		0			0
$267$	22.5000	+	12.9904i	1.37698	+	0.794998i
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$	13.5000	+	7.79423i	0.821584	+	0.474342i
$271$	−6.50000	−	11.2583i	−0.394847	−	0.683895i	0.598235	−	0.801321i	$-0.295869\pi$
$271$	−6.50000	−	11.2583i	−0.394847	−	0.683895i	−0.993082	+	0.117426i	$0.962536\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$	−12.0000			−0.723627
$276$	4.50000	+	2.59808i	0.270868	+	0.156386i
$277$	−7.00000			−0.420589			−0.210295	−	0.977638i	$-0.567442\pi$
$277$	−7.00000			−0.420589			−0.210295	+	0.977638i	$0.567442\pi$
$278$	2.50000	+	4.33013i	0.149940	+	0.259704i
$279$	−12.0000			−0.718421
$280$		0			0
$281$	−1.50000	−	2.59808i	−0.0894825	−	0.154988i	0.817810	−	0.575488i	$-0.195188\pi$
$281$	−1.50000	−	2.59808i	−0.0894825	−	0.154988i	−0.907293	+	0.420500i	$0.861855\pi$
$282$		0			0
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	0.960076	−	0.279741i	$-0.0902485\pi$
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	−0.722300	+	0.691580i	$0.756915\pi$
$284$		0			0
$285$	22.5000	+	12.9904i	1.33278	+	0.769484i
$286$	−7.50000	−	12.9904i	−0.443484	−	0.768137i
$287$		0			0
$288$	−3.00000			−0.176777
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−9.00000			−0.528498
$291$	−1.50000	−	0.866025i	−0.0879316	−	0.0507673i
$292$	−11.0000			−0.643726
$293$	−13.5000	+	23.3827i	−0.788678	+	1.36603i	0.138098	+	0.990419i	$0.455901\pi$
$293$	−13.5000	+	23.3827i	−0.788678	+	1.36603i	−0.926777	+	0.375613i	$0.877432\pi$
$294$		0			0
$295$	18.0000	+	31.1769i	1.04800	+	1.81519i
$296$	3.50000	+	6.06218i	0.203433	+	0.352357i
$297$			15.5885i			0.904534i
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	−7.50000	+	12.9904i	−0.433736	+	0.751253i
$300$	−6.00000	−	3.46410i	−0.346410	−	0.200000i
$301$		0			0
$302$	−5.50000	+	9.52628i	−0.316489	+	0.548176i
$303$	4.50000	−	2.59808i	0.258518	−	0.149256i
$304$	−5.00000			−0.286770
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	9.00000			0.514496
$307$	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
$309$	−7.50000	+	4.33013i	−0.426660	+	0.246332i
$310$	12.0000			0.681554
$311$	−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	$-0.404886\pi$
$312$		−	8.66025i		−	0.490290i
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$	4.50000	+	2.59808i	0.252347	+	0.145693i
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	3.00000			0.167705
$321$	22.5000	+	12.9904i	1.25583	+	0.725052i
$322$		0			0
$323$	15.0000			0.834622
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	10.0000	−	17.3205i	0.554700	−	0.960769i
$326$	17.0000			0.941543
$327$		−	12.1244i		−	0.670478i
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$		0			0
$330$		−	15.5885i		−	0.858116i
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	1.50000	−	2.59808i	0.0823232	−	0.142588i
$333$	21.0000			1.15079
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	−0.293783	−	0.955872i	$-0.594914\pi$
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	0.974701	−	0.223513i	$-0.0717525\pi$
$338$	12.0000			0.652714
$339$			25.9808i			1.41108i
$340$	−9.00000			−0.488094
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	−7.50000	+	12.9904i	−0.405554	+	0.702439i
$343$		0			0
$344$	−5.50000	−	9.52628i	−0.296540	−	0.513623i
$345$	−13.5000	+	7.79423i	−0.726816	+	0.419627i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		−	5.19615i		−	0.278543i
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$	−22.5000	−	12.9904i	−1.20096	−	0.693375i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	9.00000			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$354$	−18.0000	+	10.3923i	−0.956689	+	0.552345i
$355$		0			0
$356$	7.50000	−	12.9904i	0.397499	−	0.688489i
$357$		0			0
$358$	−1.50000	−	2.59808i	−0.0792775	−	0.137313i
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$	4.50000	−	7.79423i	0.237171	−	0.410792i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−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
$367$	1.00000			0.0521996			0.0260998	−	0.999659i	$-0.491691\pi$
$367$	1.00000			0.0521996			0.0260998	+	0.999659i	$0.491691\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	13.5000	+	23.3827i	0.702782	+	1.21725i
$370$	−21.0000			−1.09174
$371$		0			0
$372$			6.92820i			0.359211i
$373$	17.0000			0.880227			0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000			0.880227			0.440113	+	0.897942i	$0.354938\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$	−4.50000	+	2.59808i	−0.232379	+	0.134164i
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	7.50000	−	12.9904i	0.384742	−	0.666392i
$381$	−24.0000	+	13.8564i	−1.22956	+	0.709885i
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	15.0000			0.766464			0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000			0.766464			0.383232	+	0.923652i	$0.374811\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$	14.0000			0.712581
$387$	−33.0000			−1.67748
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	9.00000			0.456318			0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000			0.456318			0.228159	+	0.973624i	$0.426729\pi$
$390$	22.5000	+	12.9904i	1.13933	+	0.657794i
$391$	−4.50000	+	7.79423i	−0.227575	+	0.394171i
$392$		0			0
$393$	−4.50000	+	2.59808i	−0.226995	+	0.131056i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−12.0000	+	20.7846i	−0.603786	+	1.04579i
$396$	9.00000			0.452267
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	0.957839	+	0.287307i	$0.0927599\pi$
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	−0.230105	+	0.973166i	$0.573907\pi$
$398$	−3.50000	−	6.06218i	−0.175439	−	0.303870i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$	−6.00000	+	3.46410i	−0.299253	+	0.172774i
$403$	−20.0000			−0.996271
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$	−13.5000	−	23.3827i	−0.670820	−	1.16190i
$406$		0			0
$407$	−10.5000	−	18.1865i	−0.520466	−	0.901473i
$408$		−	5.19615i		−	0.257248i
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$	−13.5000	−	23.3827i	−0.666717	−	1.15479i
$411$	4.50000	−	2.59808i	0.221969	−	0.128154i
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$		0			0
$414$	−4.50000	−	7.79423i	−0.221163	−	0.383065i
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$	−5.00000			−0.245145
$417$		−	8.66025i		−	0.424094i
$418$	15.0000			0.733674
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	−0.900337	−	0.435194i	$-0.856680\pi$
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	0.827057	+	0.562118i	$0.190013\pi$
$420$		0			0
$421$	15.5000	+	26.8468i	0.755424	+	1.30843i	0.945163	+	0.326598i	$0.105902\pi$
$421$	15.5000	+	26.8468i	0.755424	+	1.30843i	−0.189740	+	0.981834i	$0.560764\pi$
$422$	−2.50000	−	4.33013i	−0.121698	−	0.210787i
$423$		0			0
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$		0			0
$428$	7.50000	−	12.9904i	0.362526	−	0.627914i
$429$			25.9808i			1.25436i
$430$	33.0000			1.59140
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	13.5000	+	7.79423i	0.647275	+	0.373705i
$436$	−7.00000			−0.335239
$437$	−7.50000	−	12.9904i	−0.358774	−	0.621414i
$438$	16.5000	+	9.52628i	0.788400	+	0.455183i
$439$	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
$442$	15.0000			0.713477
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$		−	12.1244i		−	0.575396i
$445$	22.5000	+	38.9711i	1.06660	+	1.84741i
$446$	−17.0000			−0.804973
$447$	−4.50000	+	2.59808i	−0.212843	+	0.122885i
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	6.00000	+	10.3923i	0.282843	+	0.489898i
$451$	13.5000	−	23.3827i	0.635690	−	1.10105i
$452$	15.0000			0.705541
$453$	16.5000	−	9.52628i	0.775238	−	0.447584i
$454$	4.50000	−	7.79423i	0.211195	−	0.365801i
$455$		0			0
$456$	7.50000	+	4.33013i	0.351220	+	0.202777i
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	−0.127469	−	0.991843i	$-0.540685\pi$
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	0.922695	−	0.385530i	$-0.125981\pi$
$458$	8.50000	−	14.7224i	0.397179	−	0.687934i
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$	4.50000	+	7.79423i	0.209814	+	0.363408i
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$		0			0
$463$	−17.5000	+	30.3109i	−0.813294	+	1.40867i	0.0972525	+	0.995260i	$0.468995\pi$
$463$	−17.5000	+	30.3109i	−0.813294	+	1.40867i	−0.910546	+	0.413407i	$0.864339\pi$
$464$	−3.00000			−0.139272
$465$	−18.0000	−	10.3923i	−0.834730	−	0.481932i
$466$	27.0000			1.25075
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$	−7.50000	+	12.9904i	−0.346688	+	0.600481i
$469$		0			0
$470$		0			0
$471$	21.0000	+	12.1244i	0.967629	+	0.558661i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	16.5000	+	28.5788i	0.758671	+	1.31406i
$474$	−12.0000	−	6.92820i	−0.551178	−	0.318223i
$475$	10.0000	+	17.3205i	0.458831	+	0.794719i
$476$		0			0
$477$	−4.50000	−	7.79423i	−0.206041	−	0.356873i
$478$	−13.5000	−	23.3827i	−0.617476	−	1.06950i
$479$	9.00000			0.411220			0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000			0.411220			0.205610	+	0.978634i	$0.434082\pi$
$480$	−4.50000	−	2.59808i	−0.205396	−	0.118585i
$481$	35.0000			1.59586
$482$	11.5000	−	19.9186i	0.523811	−	0.907267i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−1.50000	−	2.59808i	−0.0681115	−	0.117973i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	−0.265260	−	0.964177i	$-0.585458\pi$
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	0.967632	−	0.252367i	$-0.0812090\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−25.5000	−	14.7224i	−1.15315	−	0.665771i
$490$		0			0
$491$	19.5000	−	33.7750i	0.880023	−	1.52424i	0.0287085	−	0.999588i	$-0.490861\pi$
$491$	19.5000	−	33.7750i	0.880023	−	1.52424i	0.851314	−	0.524656i	$-0.175806\pi$
$492$	13.5000	−	7.79423i	0.608627	−	0.351391i
$493$	9.00000			0.405340
$494$	−12.5000	+	21.6506i	−0.562402	+	0.974108i
$495$	−13.5000	+	23.3827i	−0.606780	+	1.05097i
$496$	4.00000			0.179605
$497$		0			0
$498$	−4.50000	+	2.59808i	−0.201650	+	0.116423i
$499$	11.0000			0.492428			0.246214	−	0.969216i	$-0.420813\pi$
$499$	11.0000			0.492428			0.246214	+	0.969216i	$0.420813\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		−	5.19615i		−	0.232147i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	−4.50000	+	7.79423i	−0.200049	+	0.346496i
$507$	−18.0000	−	10.3923i	−0.799408	−	0.461538i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	27.0000			1.19675			0.598377	−	0.801215i	$-0.295813\pi$
$509$	27.0000			1.19675			0.598377	+	0.801215i	$0.295813\pi$
$510$	13.5000	+	7.79423i	0.597790	+	0.345134i
$511$		0			0
$512$	1.00000			0.0441942
$513$	22.5000	−	12.9904i	0.993399	−	0.573539i
$514$	7.50000	−	12.9904i	0.330811	−	0.572981i
$515$	−15.0000			−0.660979
$516$			19.0526i			0.838742i
$517$		0			0
$518$		0			0
$519$		−	10.3923i		−	0.456172i
$520$	7.50000	−	12.9904i	0.328897	−	0.569666i
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	0.779301	−	0.626650i	$-0.215574\pi$
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	−0.932345	+	0.361569i	$0.882241\pi$
$524$	1.50000	+	2.59808i	0.0655278	+	0.113497i
$525$		0			0
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	−12.0000			−0.522728
$528$		−	5.19615i		−	0.226134i
$529$	−14.0000			−0.608696
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$	36.0000			1.56227
$532$		0			0
$533$	22.5000	+	38.9711i	0.974583	+	1.68803i
$534$	−22.5000	+	12.9904i	−0.973670	+	0.562149i
$535$	22.5000	+	38.9711i	0.972760	+	1.68487i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$			5.19615i			0.224231i
$538$	10.5000	+	18.1865i	0.452687	+	0.784077i
$539$		0			0
$540$	−13.5000	+	7.79423i	−0.580948	+	0.335410i
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	13.0000			0.558398
$543$	15.0000	−	8.66025i	0.643712	−	0.371647i
$544$	−3.00000			−0.128624
$545$	10.5000	−	18.1865i	0.449771	−	0.779026i
$546$		0			0
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	0.724157	−	0.689635i	$-0.242229\pi$
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	−0.959320	+	0.282321i	$0.908896\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	−7.50000	+	12.9904i	−0.319511	+	0.553409i
$552$	−4.50000	+	2.59808i	−0.191533	+	0.110581i
$553$		0			0
$554$	3.50000	−	6.06218i	0.148701	−	0.257557i
$555$	31.5000	+	18.1865i	1.33710	+	0.771975i
$556$	−5.00000			−0.212047
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$	6.00000	−	10.3923i	0.254000	−	0.439941i
$559$	−55.0000			−2.32625
$560$		0			0
$561$			15.5885i			0.658145i
$562$	3.00000			0.126547
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$	−22.5000	+	38.9711i	−0.946582	+	1.63953i
$566$	−8.00000			−0.336265
$567$		0			0
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$	−22.5000	+	12.9904i	−0.942421	+	0.544107i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	15.0000			0.627182
$573$			20.7846i			0.868290i
$574$		0			0
$575$	−12.0000			−0.500435
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	5.50000	−	9.52628i	0.228968	−	0.396584i	−0.728535	−	0.685009i	$-0.759798\pi$
$577$	5.50000	−	9.52628i	0.228968	−	0.396584i	0.957503	+	0.288425i	$0.0931316\pi$
$578$	−8.00000			−0.332756
$579$	−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
$584$	5.50000	−	9.52628i	0.227592	−	0.394200i
$585$	−22.5000	−	38.9711i	−0.930261	−	1.61126i
$586$	−13.5000	−	23.3827i	−0.557680	−	0.965930i
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	−0.974668	−	0.223659i	$-0.928200\pi$
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	0.293640	−	0.955916i	$-0.405133\pi$
$588$		0			0
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$	−36.0000			−1.48210
$591$	−9.00000	+	5.19615i	−0.370211	+	0.213741i
$592$	−7.00000			−0.287698
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	0.565792	−	0.824548i	$-0.308570\pi$
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	−0.996976	+	0.0777165i	$0.975237\pi$
$594$	−13.5000	−	7.79423i	−0.553912	−	0.319801i
$595$		0			0
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$			12.1244i			0.496217i
$598$	−7.50000	−	12.9904i	−0.306698	−	0.531216i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	6.00000	−	3.46410i	0.244949	−	0.141421i
$601$	−0.500000	−	0.866025i	−0.0203954	−	0.0353259i	0.855648	−	0.517559i	$-0.173159\pi$
$601$	−0.500000	−	0.866025i	−0.0203954	−	0.0353259i	−0.876043	+	0.482233i	$0.839826\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	−5.50000	−	9.52628i	−0.223792	−	0.387619i
$605$	−6.00000			−0.243935
$606$			5.19615i			0.211079i
$607$	43.0000			1.74532			0.872658	−	0.488332i	$-0.162394\pi$
$607$	43.0000			1.74532			0.872658	+	0.488332i	$0.162394\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$		0			0
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$			46.7654i			1.88576i
$616$		0			0
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$		−	8.66025i		−	0.348367i
$619$	19.0000			0.763674			0.381837	−	0.924230i	$-0.375291\pi$
$619$	19.0000			0.763674			0.381837	+	0.924230i	$0.375291\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$			15.5885i			0.625543i
$622$	24.0000			0.962312
$623$		0			0
$624$	7.50000	+	4.33013i	0.300240	+	0.173344i
$625$	−29.0000			−1.16000
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	−22.5000	−	12.9904i	−0.898563	−	0.518786i
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$	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	$0.449096\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$			8.66025i			0.344214i
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$	−48.0000			−1.90482
$636$	−4.50000	+	2.59808i	−0.178437	+	0.103020i
$637$		0			0
$638$	9.00000			0.356313
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−45.0000			−1.77739			−0.888697	−	0.458496i	$-0.848388\pi$
$641$	−45.0000			−1.77739			−0.888697	+	0.458496i	$0.848388\pi$
$642$	−22.5000	+	12.9904i	−0.888004	+	0.512689i
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	−0.424555	−	0.905402i	$-0.639569\pi$
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	0.996379	−	0.0850262i	$-0.0270974\pi$
$644$		0			0
$645$	−49.5000	−	28.5788i	−1.94906	−	1.12529i
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	−0.894004	−	0.448059i	$-0.852115\pi$
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	0.835033	+	0.550200i	$0.185449\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−18.0000	−	31.1769i	−0.706562	−	1.22380i
$650$	10.0000	+	17.3205i	0.392232	+	0.679366i
$651$		0			0
$652$	−8.50000	+	14.7224i	−0.332886	+	0.576575i
$653$	9.00000			0.352197			0.176099	−	0.984373i	$-0.443652\pi$
$653$	9.00000			0.352197			0.176099	+	0.984373i	$0.443652\pi$
$654$	10.5000	+	6.06218i	0.410582	+	0.237050i
$655$	−9.00000			−0.351659
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$	−16.5000	−	28.5788i	−0.643726	−	1.11497i
$658$		0			0
$659$	−19.5000	−	33.7750i	−0.759612	−	1.31569i	−0.943049	−	0.332655i	$-0.892055\pi$
$659$	−19.5000	−	33.7750i	−0.759612	−	1.31569i	0.183436	−	0.983032i	$-0.441278\pi$
$660$	13.5000	+	7.79423i	0.525487	+	0.303390i
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$	−22.5000	−	12.9904i	−0.873828	−	0.504505i
$664$	1.50000	+	2.59808i	0.0582113	+	0.100825i
$665$		0			0
$666$	−10.5000	+	18.1865i	−0.406867	+	0.704714i
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$	−3.00000			−0.116073
$669$	25.5000	+	14.7224i	0.985887	+	0.569202i
$670$	−12.0000			−0.463600
$671$	−3.00000	+	5.19615i	−0.115814	+	0.200595i
$672$		0			0
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	−0.952343	+	0.305028i	$0.901334\pi$
$674$	12.5000	+	21.6506i	0.481482	+	0.833951i
$675$		−	20.7846i		−	0.800000i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	−22.5000	−	12.9904i	−0.864107	−	0.498893i
$679$		0			0
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	−13.5000	+	7.79423i	−0.517321	+	0.298675i
$682$	−12.0000			−0.459504
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	−0.355920	−	0.934516i	$-0.615832\pi$
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	0.987275	−	0.159022i	$-0.0508342\pi$
$684$	−7.50000	−	12.9904i	−0.286770	−	0.496700i
$685$	9.00000			0.343872
$686$		0			0
$687$	−25.5000	+	14.7224i	−0.972886	+	0.561696i
$688$	11.0000			0.419371
$689$	−7.50000	−	12.9904i	−0.285727	−	0.494894i
$690$		−	15.5885i		−	0.593442i
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	7.50000	−	12.9904i	0.284491	−	0.492753i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	13.5000	+	23.3827i	0.511349	+	0.885682i
$698$	−5.00000			−0.189253
$699$	−40.5000	−	23.3827i	−1.53185	−	0.884414i
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	22.5000	−	12.9904i	0.849208	−	0.490290i
$703$	−17.5000	+	30.3109i	−0.660025	+	1.14320i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$		0			0
$708$		−	20.7846i		−	0.781133i
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$	−22.5000	+	38.9711i	−0.841452	+	1.45744i
$716$	3.00000			0.112115
$717$			46.7654i			1.74648i
$718$	15.0000			0.559795
$719$	19.5000	+	33.7750i	0.727227	+	1.25959i	0.958051	+	0.286599i	$0.0925247\pi$
$719$	19.5000	+	33.7750i	0.727227	+	1.25959i	−0.230823	+	0.972996i	$0.574142\pi$
$720$	4.50000	+	7.79423i	0.167705	+	0.290474i
$721$		0			0
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$	−34.5000	+	19.9186i	−1.28307	+	0.740780i
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$		−	3.46410i		−	0.128565i
$727$	2.50000	+	4.33013i	0.0927199	+	0.160596i	0.908655	−	0.417548i	$-0.137111\pi$
$727$	2.50000	+	4.33013i	0.0927199	+	0.160596i	−0.815935	+	0.578144i	$0.803777\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	16.5000	+	28.5788i	0.610692	+	1.05775i
$731$	−33.0000			−1.22055
$732$	−3.00000	+	1.73205i	−0.110883	+	0.0640184i
$733$	−41.0000			−1.51437			−0.757185	−	0.653201i	$-0.773426\pi$
$733$	−41.0000			−1.51437			−0.757185	+	0.653201i	$0.773426\pi$
$734$	−0.500000	+	0.866025i	−0.0184553	+	0.0319656i
$735$		0			0
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−27.0000			−0.993884
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	0.00311943	+	0.999995i	$0.499007\pi$
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$740$	10.5000	−	18.1865i	0.385988	−	0.668550i
$741$	37.5000	−	21.6506i	1.37760	−	0.795356i
$742$		0			0
$743$	−1.50000	+	2.59808i	−0.0550297	+	0.0953142i	−0.892228	−	0.451585i	$-0.850859\pi$
$743$	−1.50000	+	2.59808i	−0.0550297	+	0.0953142i	0.837198	+	0.546899i	$0.184192\pi$
$744$	−6.00000	−	3.46410i	−0.219971	−	0.127000i
$745$	−9.00000			−0.329734
$746$	−8.50000	+	14.7224i	−0.311207	+	0.539027i
$747$	9.00000			0.329293
$748$	9.00000			0.329073
$749$		0			0
$750$		−	5.19615i		−	0.189737i
$751$	29.0000			1.05823			0.529113	−	0.848552i	$-0.322525\pi$
$751$	29.0000			1.05823			0.529113	+	0.848552i	$0.322525\pi$
$752$		0			0
$753$	−18.0000	+	10.3923i	−0.655956	+	0.378717i
$754$	−7.50000	+	12.9904i	−0.273134	+	0.473082i
$755$	33.0000			1.20099
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$	13.5000	−	7.79423i	0.490019	−	0.282913i
$760$	7.50000	+	12.9904i	0.272054	+	0.471211i
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$		−	27.7128i		−	1.00393i
$763$		0			0
$764$	12.0000			0.434145
$765$	−13.5000	−	23.3827i	−0.488094	−	0.845403i
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$	60.0000			2.16647
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	−0.500000	+	0.866025i	−0.0180305	+	0.0312297i	−0.874900	−	0.484304i	$-0.839073\pi$
$769$	−0.500000	+	0.866025i	−0.0180305	+	0.0312297i	0.856869	+	0.515534i	$0.172406\pi$
$770$		0			0
$771$	−22.5000	+	12.9904i	−0.810318	+	0.467837i
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$	16.5000	−	28.5788i	0.593080	−	1.02725i
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$	−0.500000	−	0.866025i	−0.0179490	−	0.0310885i
$777$		0			0
$778$	−4.50000	+	7.79423i	−0.161333	+	0.279437i
$779$	−45.0000			−1.61229
$780$	−22.5000	+	12.9904i	−0.805629	+	0.465130i
$781$		0			0
$782$	−4.50000	−	7.79423i	−0.160920	−	0.278721i
$783$	13.5000	−	7.79423i	0.482451	−	0.278543i
$784$		0			0
$785$	21.0000	+	36.3731i	0.749522	+	1.29821i
$786$		−	5.19615i		−	0.185341i
$787$	22.0000	+	38.1051i	0.784215	+	1.35830i	0.929467	+	0.368906i	$0.120268\pi$
$787$	22.0000	+	38.1051i	0.784215	+	1.35830i	−0.145251	+	0.989395i	$0.546399\pi$
$788$	3.00000	+	5.19615i	0.106871	+	0.185105i
$789$	−13.5000	+	7.79423i	−0.480613	+	0.277482i
$790$	−12.0000	−	20.7846i	−0.426941	−	0.739483i
$791$		0			0
$792$	−4.50000	+	7.79423i	−0.159901	+	0.276956i
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	−29.0000			−1.02917
$795$		−	15.5885i		−	0.552866i
$796$	7.00000			0.248108
$797$	−13.5000	+	23.3827i	−0.478195	+	0.828257i	−0.999687	−	0.0249984i	$-0.992042\pi$
$797$	−13.5000	+	23.3827i	−0.478195	+	0.828257i	0.521493	+	0.853256i	$0.325375\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	45.0000			1.59000
$802$	−13.5000	+	23.3827i	−0.476702	+	0.825671i
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$		−	6.92820i		−	0.244339i
$805$		0			0
$806$	10.0000	−	17.3205i	0.352235	−	0.610089i
$807$		−	36.3731i		−	1.28039i
$808$	3.00000			0.105540
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$	27.0000			0.948683
$811$	−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
$813$	−19.5000	−	11.2583i	−0.683895	−	0.394847i
$814$	21.0000			0.736050
$815$	−25.5000	−	44.1673i	−0.893226	−	1.54711i
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	27.5000	−	47.6314i	0.962103	−	1.66641i
$818$	22.0000			0.769212
$819$		0			0
$820$	27.0000			0.942881
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.181250	−	0.983437i	$-0.441986\pi$
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.761056	−	0.648686i	$-0.224681\pi$
$822$			5.19615i			0.181237i
$823$	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	$0.587782\pi$
$824$	−5.00000			−0.174183
$825$	−18.0000	+	10.3923i	−0.626680	+	0.361814i
$826$		0			0
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$	9.00000			0.312772
$829$	20.5000	−	35.5070i	0.711994	−	1.23321i	−0.252113	−	0.967698i	$-0.581125\pi$
$829$	20.5000	−	35.5070i	0.711994	−	1.23321i	0.964107	−	0.265513i	$-0.0855412\pi$
$830$	−9.00000			−0.312395
$831$	−10.5000	+	6.06218i	−0.364241	+	0.210295i
$832$	2.50000	−	4.33013i	0.0866719	−	0.150120i
$833$		0			0
$834$	7.50000	+	4.33013i	0.259704	+	0.149940i
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$	−18.0000	+	10.3923i	−0.622171	+	0.359211i
$838$	−1.50000	−	2.59808i	−0.0518166	−	0.0897491i
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	−0.976987	−	0.213298i	$-0.931580\pi$
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	0.303773	−	0.952745i	$-0.401754\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−31.0000			−1.06833
$843$	−4.50000	−	2.59808i	−0.154988	−	0.0894825i
$844$	5.00000			0.172107
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$		0			0
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	12.0000	+	6.92820i	0.411839	+	0.237775i
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$	−10.5000	−	18.1865i	−0.359935	−	0.623426i
$852$		0			0
$853$	8.50000	+	14.7224i	0.291034	+	0.504086i	0.974055	−	0.226313i	$-0.0726672\pi$
$853$	8.50000	+	14.7224i	0.291034	+	0.504086i	−0.683020	+	0.730400i	$0.739334\pi$
$854$		0			0
$855$	45.0000			1.53897
$856$	7.50000	+	12.9904i	0.256345	+	0.444002i
$857$	33.0000			1.12726			0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000			1.12726			0.563629	+	0.826028i	$0.309405\pi$
$858$	−22.5000	−	12.9904i	−0.768137	−	0.443484i
$859$	−11.0000			−0.375315			−0.187658	−	0.982235i	$-0.560090\pi$
$859$	−11.0000			−0.375315			−0.187658	+	0.982235i	$0.560090\pi$
$860$	−16.5000	+	28.5788i	−0.562645	+	0.974530i
$861$		0			0
$862$	1.50000	+	2.59808i	0.0510902	+	0.0884908i
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	0.709675	−	0.704529i	$-0.248842\pi$
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	−0.964978	+	0.262332i	$0.915509\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$	−13.5000	+	7.79423i	−0.457693	+	0.264249i
$871$	20.0000			0.677674
$872$	3.50000	−	6.06218i	0.118525	−	0.205291i
$873$	−3.00000			−0.101535
$874$	15.0000			0.507383
$875$		0			0
$876$	−16.5000	+	9.52628i	−0.557483	+	0.321863i
$877$	−43.0000			−1.45201			−0.726003	−	0.687691i	$-0.758624\pi$
$877$	−43.0000			−1.45201			−0.726003	+	0.687691i	$0.758624\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$			46.7654i			1.57736i
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−7.50000	+	12.9904i	−0.252252	+	0.436914i
$885$	54.0000	+	31.1769i	1.81519	+	1.04800i
$886$		0			0
$887$	39.0000			1.30949			0.654746	−	0.755849i	$-0.272776\pi$
$887$	39.0000			1.30949			0.654746	+	0.755849i	$0.272776\pi$
$888$	10.5000	+	6.06218i	0.352357	+	0.203433i
$889$		0			0
$890$	−45.0000			−1.50840
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	8.50000	−	14.7224i	0.284601	−	0.492943i
$893$		0			0
$894$		−	5.19615i		−	0.173785i
$895$	−4.50000	+	7.79423i	−0.150418	+	0.260532i
$896$		0			0
$897$			25.9808i			0.867472i
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$	−12.0000			−0.400000
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$	13.5000	+	23.3827i	0.449501	+	0.778558i
$903$		0			0
$904$	−7.50000	+	12.9904i	−0.249446	+	0.432054i
$905$	30.0000			0.997234
$906$			19.0526i			0.632979i
$907$	17.0000			0.564476			0.282238	−	0.959344i	$-0.408923\pi$
$907$	17.0000			0.564476			0.282238	+	0.959344i	$0.408923\pi$
$908$	4.50000	+	7.79423i	0.149338	+	0.258661i
$909$	4.50000	−	7.79423i	0.149256	−	0.258518i
$910$		0			0
$911$	−4.50000	−	7.79423i	−0.149092	−	0.258234i	0.781800	−	0.623529i	$-0.214302\pi$
$911$	−4.50000	−	7.79423i	−0.149092	−	0.258234i	−0.930892	+	0.365295i	$0.880968\pi$
$912$	−7.50000	+	4.33013i	−0.248350	+	0.143385i
$913$	−4.50000	−	7.79423i	−0.148928	−	0.257951i
$914$	17.0000	+	29.4449i	0.562310	+	0.973950i
$915$		−	10.3923i		−	0.343559i
$916$	8.50000	+	14.7224i	0.280848	+	0.486443i
$917$		0			0
$918$	13.5000	−	7.79423i	0.445566	−	0.257248i
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	0.874154	−	0.485648i	$-0.161416\pi$
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	−0.857661	+	0.514216i	$0.828083\pi$
$920$	−9.00000			−0.296721
$921$	42.0000	−	24.2487i	1.38395	−	0.799022i
$922$	−9.00000			−0.296399
$923$		0			0
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$	−17.5000	−	30.3109i	−0.575086	−	0.996078i
$927$	−7.50000	+	12.9904i	−0.246332	+	0.426660i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$	18.0000	−	10.3923i	0.590243	−	0.340777i
$931$		0			0
$932$	−13.5000	+	23.3827i	−0.442207	+	0.765925i
$933$	−36.0000	−	20.7846i	−1.17859	−	0.680458i
$934$	3.00000			0.0981630
$935$	−13.5000	+	23.3827i	−0.441497	+	0.764696i
$936$	−7.50000	−	12.9904i	−0.245145	−	0.424604i
$937$	34.0000			1.11073			0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000			1.11073			0.555366	+	0.831606i	$0.312578\pi$
$938$		0			0
$939$		−	24.2487i		−	0.791327i
$940$		0			0
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$	−21.0000	+	12.1244i	−0.684217	+	0.395033i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−33.0000			−1.07292
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$	12.0000	−	6.92820i	0.389742	−	0.225018i
$949$	−27.5000	−	47.6314i	−0.892688	−	1.54618i
$950$	−20.0000			−0.648886
$951$			51.9615i			1.68497i
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	9.00000			0.291386
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$	27.0000			0.873242
$957$	−13.5000	−	7.79423i	−0.436393	−	0.251952i
$958$	−4.50000	+	7.79423i	−0.145388	+	0.251820i
$959$		0			0
$960$	4.50000	−	2.59808i	0.145237	−	0.0838525i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−17.5000	+	30.3109i	−0.564223	+	0.977262i
$963$	45.0000			1.45010
$964$	11.5000	+	19.9186i	0.370390	+	0.641534i
$965$	−21.0000	−	36.3731i	−0.676014	−	1.17089i
$966$		0			0
$967$	24.5000	−	42.4352i	0.787867	−	1.36463i	−0.139404	−	0.990236i	$-0.544519\pi$
$967$	24.5000	−	42.4352i	0.787867	−	1.36463i	0.927271	−	0.374390i	$-0.122148\pi$
$968$	−2.00000			−0.0642824
$969$	22.5000	−	12.9904i	0.722804	−	0.417311i
$970$	3.00000			0.0963242
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	0.563914	−	0.825833i	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$			15.5885i			0.500000i
$973$		0			0
$974$	15.5000	+	26.8468i	0.496652	+	0.860227i
$975$		−	34.6410i		−	1.10940i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$	25.5000	−	14.7224i	0.815400	−	0.470771i
$979$	−22.5000	−	38.9711i	−0.719103	−	1.24552i
$980$		0			0
$981$	−10.5000	−	18.1865i	−0.335239	−	0.580651i
$982$	19.5000	+	33.7750i	0.622270	+	1.07780i
$983$	21.0000			0.669796			0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000			0.669796			0.334898	+	0.942254i	$0.391298\pi$
$984$			15.5885i			0.496942i
$985$	−18.0000			−0.573528
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$		0			0
$988$	−12.5000	−	21.6506i	−0.397678	−	0.688798i
$989$	16.5000	+	28.5788i	0.524669	+	0.908754i
$990$	−13.5000	−	23.3827i	−0.429058	−	0.743151i
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	−0.998991	−	0.0449040i	$-0.985702\pi$
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	0.538384	+	0.842700i	$0.319035\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$			34.6410i			1.09930i
$994$		0			0
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$		−	5.19615i		−	0.164646i
$997$	−41.0000			−1.29848			−0.649242	−	0.760582i	$-0.724914\pi$
$997$	−41.0000			−1.29848			−0.649242	+	0.760582i	$0.724914\pi$
$998$	−5.50000	+	9.52628i	−0.174099	+	0.301549i
$999$	31.5000	−	18.1865i	0.996616	−	0.575396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.e.67.1		2
3.2	odd	2		2646.2.h.f.361.1		2
7.2	even	3		882.2.e.h.373.1		2
7.3	odd	6		882.2.f.e.589.1		2
7.4	even	3		882.2.f.a.589.1		2
7.5	odd	6		126.2.e.b.121.1	yes	2
7.6	odd	2		126.2.h.a.67.1	yes	2
9.2	odd	6		2646.2.e.e.2125.1		2
9.7	even	3		882.2.e.h.655.1		2
21.2	odd	6		2646.2.e.e.1549.1		2
21.5	even	6		378.2.e.a.37.1		2
21.11	odd	6		2646.2.f.i.1765.1		2
21.17	even	6		2646.2.f.e.1765.1		2
21.20	even	2		378.2.h.b.361.1		2
28.19	even	6		1008.2.q.e.625.1		2
28.27	even	2		1008.2.t.c.193.1		2
63.2	odd	6		2646.2.h.f.667.1		2
63.4	even	3		7938.2.a.bd.1.1		1
63.5	even	6		1134.2.g.f.163.1		2
63.11	odd	6		2646.2.f.i.883.1		2
63.13	odd	6		1134.2.g.d.487.1		2
63.16	even	3	inner	882.2.h.e.79.1		2
63.20	even	6		378.2.e.a.235.1		2
63.25	even	3		882.2.f.a.295.1		2
63.31	odd	6		7938.2.a.r.1.1		1
63.32	odd	6		7938.2.a.c.1.1		1
63.34	odd	6		126.2.e.b.25.1	✓	2
63.38	even	6		2646.2.f.e.883.1		2
63.40	odd	6		1134.2.g.d.163.1		2
63.41	even	6		1134.2.g.f.487.1		2
63.47	even	6		378.2.h.b.289.1		2
63.52	odd	6		882.2.f.e.295.1		2
63.59	even	6		7938.2.a.o.1.1		1
63.61	odd	6		126.2.h.a.79.1	yes	2
84.47	odd	6		3024.2.q.a.2305.1		2
84.83	odd	2		3024.2.t.f.1873.1		2
252.47	odd	6		3024.2.t.f.289.1		2
252.83	odd	6		3024.2.q.a.2881.1		2
252.187	even	6		1008.2.t.c.961.1		2
252.223	even	6		1008.2.q.e.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	63.34	odd	6
126.2.e.b.121.1	yes	2	7.5	odd	6
126.2.h.a.67.1	yes	2	7.6	odd	2
126.2.h.a.79.1	yes	2	63.61	odd	6
378.2.e.a.37.1		2	21.5	even	6
378.2.e.a.235.1		2	63.20	even	6
378.2.h.b.289.1		2	63.47	even	6
378.2.h.b.361.1		2	21.20	even	2
882.2.e.h.373.1		2	7.2	even	3
882.2.e.h.655.1		2	9.7	even	3
882.2.f.a.295.1		2	63.25	even	3
882.2.f.a.589.1		2	7.4	even	3
882.2.f.e.295.1		2	63.52	odd	6
882.2.f.e.589.1		2	7.3	odd	6
882.2.h.e.67.1		2	1.1	even	1	trivial
882.2.h.e.79.1		2	63.16	even	3	inner
1008.2.q.e.529.1		2	252.223	even	6
1008.2.q.e.625.1		2	28.19	even	6
1008.2.t.c.193.1		2	28.27	even	2
1008.2.t.c.961.1		2	252.187	even	6
1134.2.g.d.163.1		2	63.40	odd	6
1134.2.g.d.487.1		2	63.13	odd	6
1134.2.g.f.163.1		2	63.5	even	6
1134.2.g.f.487.1		2	63.41	even	6
2646.2.e.e.1549.1		2	21.2	odd	6
2646.2.e.e.2125.1		2	9.2	odd	6
2646.2.f.e.883.1		2	63.38	even	6
2646.2.f.e.1765.1		2	21.17	even	6
2646.2.f.i.883.1		2	63.11	odd	6
2646.2.f.i.1765.1		2	21.11	odd	6
2646.2.h.f.361.1		2	3.2	odd	2
2646.2.h.f.667.1		2	63.2	odd	6
3024.2.q.a.2305.1		2	84.47	odd	6
3024.2.q.a.2881.1		2	252.83	odd	6
3024.2.t.f.289.1		2	252.47	odd	6
3024.2.t.f.1873.1		2	84.83	odd	2
7938.2.a.c.1.1		1	63.32	odd	6
7938.2.a.o.1.1		1	63.59	even	6
7938.2.a.r.1.1		1	63.31	odd	6
7938.2.a.bd.1.1		1	63.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} -3.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(2.50000 - 4.33013i) q^{13} +(4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} -3.00000 q^{23} +(1.50000 - 0.866025i) q^{24} +4.00000 q^{25} +(2.50000 + 4.33013i) q^{26} -5.19615i q^{27} +(1.50000 + 2.59808i) q^{29} +5.19615i q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 + 2.59808i) q^{34} -3.00000 q^{36} +(3.50000 + 6.06218i) q^{37} -5.00000 q^{38} -8.66025i q^{39} +3.00000 q^{40} +(-4.50000 + 7.79423i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{45} +(1.50000 - 2.59808i) q^{46} +1.73205i q^{48} +(-2.00000 + 3.46410i) q^{50} -5.19615i q^{51} -5.00000 q^{52} +(1.50000 - 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} -9.00000 q^{55} +(7.50000 + 4.33013i) q^{57} -3.00000 q^{58} +(6.00000 + 10.3923i) q^{59} +(-4.50000 - 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(7.50000 - 12.9904i) q^{65} -5.19615i q^{66} +(2.00000 + 3.46410i) q^{67} -3.00000 q^{68} +(-4.50000 + 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} -7.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(2.50000 - 4.33013i) q^{76} +(7.50000 + 4.33013i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(1.50000 + 2.59808i) q^{83} +(4.50000 - 7.79423i) q^{85} +11.0000 q^{86} +(4.50000 + 2.59808i) q^{87} -3.00000 q^{88} +(7.50000 + 12.9904i) q^{89} +(4.50000 + 7.79423i) q^{90} +(1.50000 + 2.59808i) q^{92} +(-6.00000 - 3.46410i) q^{93} +(7.50000 + 12.9904i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} + 6 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 + 6 * q^5 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} + 6 q^{5} + 2 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} + 5 q^{13} + 9 q^{15} - q^{16} + 3 q^{17} + 3 q^{18} + 5 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 3 q^{24} + 8 q^{25} + 5 q^{26} + 3 q^{29} - 4 q^{31} - q^{32} - 9 q^{33} + 3 q^{34} - 6 q^{36} + 7 q^{37} - 10 q^{38} + 6 q^{40} - 9 q^{41} - 11 q^{43} + 3 q^{44} + 9 q^{45} + 3 q^{46} - 4 q^{50} - 10 q^{52} + 3 q^{53} + 9 q^{54} - 18 q^{55} + 15 q^{57} - 6 q^{58} + 12 q^{59} - 9 q^{60} + 2 q^{61} + 8 q^{62} + 2 q^{64} + 15 q^{65} + 4 q^{67} - 6 q^{68} - 9 q^{69} + 3 q^{72} + 11 q^{73} - 14 q^{74} + 12 q^{75} + 5 q^{76} + 15 q^{78} - 8 q^{79} - 3 q^{80} - 9 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{85} + 22 q^{86} + 9 q^{87} - 6 q^{88} + 15 q^{89} + 9 q^{90} + 3 q^{92} - 12 q^{93} + 15 q^{95} - 3 q^{96} - q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 + 6 * q^5 + 2 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 3 * q^12 + 5 * q^13 + 9 * q^15 - q^16 + 3 * q^17 + 3 * q^18 + 5 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 + 3 * q^24 + 8 * q^25 + 5 * q^26 + 3 * q^29 - 4 * q^31 - q^32 - 9 * q^33 + 3 * q^34 - 6 * q^36 + 7 * q^37 - 10 * q^38 + 6 * q^40 - 9 * q^41 - 11 * q^43 + 3 * q^44 + 9 * q^45 + 3 * q^46 - 4 * q^50 - 10 * q^52 + 3 * q^53 + 9 * q^54 - 18 * q^55 + 15 * q^57 - 6 * q^58 + 12 * q^59 - 9 * q^60 + 2 * q^61 + 8 * q^62 + 2 * q^64 + 15 * q^65 + 4 * q^67 - 6 * q^68 - 9 * q^69 + 3 * q^72 + 11 * q^73 - 14 * q^74 + 12 * q^75 + 5 * q^76 + 15 * q^78 - 8 * q^79 - 3 * q^80 - 9 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^85 + 22 * q^86 + 9 * q^87 - 6 * q^88 + 15 * q^89 + 9 * q^90 + 3 * q^92 - 12 * q^93 + 15 * q^95 - 3 * q^96 - q^97 - 9 * q^99

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