LMFDB - Embedded newform 441.2.e.b.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.e (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.2.e.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +(2.00000 + 3.46410i) q^{11} +2.00000 q^{13} +(0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +2.00000 q^{29} +(-2.50000 - 4.33013i) q^{32} -6.00000 q^{34} +(-3.00000 + 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-3.00000 + 5.19615i) q^{40} +2.00000 q^{41} -4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +8.00000 q^{55} +(-1.00000 + 1.73205i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +7.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{73} +(-3.00000 - 5.19615i) q^{74} +4.00000 q^{76} +(8.00000 - 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-1.00000 + 1.73205i) q^{82} -12.0000 q^{83} +12.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-6.00000 - 10.3923i) q^{88} +(7.00000 - 12.1244i) q^{89} +(-4.00000 - 6.92820i) q^{95} -18.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} + 2 q^{5} - 6 q^{8}+O(q^{10}) $ 2 * q - q^2 + q^4 + 2 * q^5 - 6 * q^8	$ 2 q - q^{2} + q^{4} + 2 q^{5} - 6 q^{8} + 2 q^{10} + 4 q^{11} + 4 q^{13} + q^{16} + 6 q^{17} + 4 q^{19} + 4 q^{20} - 8 q^{22} + q^{25} - 2 q^{26} + 4 q^{29} - 5 q^{32} - 12 q^{34} - 6 q^{37} + 4 q^{38} - 6 q^{40} + 4 q^{41} - 8 q^{43} - 4 q^{44} - 2 q^{50} + 2 q^{52} + 6 q^{53} + 16 q^{55} - 2 q^{58} - 12 q^{59} - 2 q^{61} + 14 q^{64} + 4 q^{65} - 4 q^{67} - 6 q^{68} - 6 q^{73} - 6 q^{74} + 8 q^{76} + 16 q^{79} - 2 q^{80} - 2 q^{82} - 24 q^{83} + 24 q^{85} + 4 q^{86} - 12 q^{88} + 14 q^{89} - 8 q^{95} - 36 q^{97}+O(q^{100}) $ 2 * q - q^2 + q^4 + 2 * q^5 - 6 * q^8 + 2 * q^10 + 4 * q^11 + 4 * q^13 + q^16 + 6 * q^17 + 4 * q^19 + 4 * q^20 - 8 * q^22 + q^25 - 2 * q^26 + 4 * q^29 - 5 * q^32 - 12 * q^34 - 6 * q^37 + 4 * q^38 - 6 * q^40 + 4 * q^41 - 8 * q^43 - 4 * q^44 - 2 * q^50 + 2 * q^52 + 6 * q^53 + 16 * q^55 - 2 * q^58 - 12 * q^59 - 2 * q^61 + 14 * q^64 + 4 * q^65 - 4 * q^67 - 6 * q^68 - 6 * q^73 - 6 * q^74 + 8 * q^76 + 16 * q^79 - 2 * q^80 - 2 * q^82 - 24 * q^83 + 24 * q^85 + 4 * q^86 - 12 * q^88 + 14 * q^89 - 8 * q^95 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$		0			0
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−4.00000			−0.852803
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$		0			0
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$		0			0
$40$	−3.00000	+	5.19615i	−0.474342	+	0.821584i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$		0			0
$58$	−1.00000	+	1.73205i	−0.131306	+	0.227429i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		0			0
$63$		0			0
$64$	7.00000			0.875000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	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	$-0.189818\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$		0			0
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		0			0
$88$	−6.00000	−	10.3923i	−0.639602	−	1.10782i
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	−18.0000			−1.82762			−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000			−1.82762			−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$	−6.00000			−0.582772
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$		0			0
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$	−4.00000	+	6.92820i	−0.381385	+	0.660578i
$111$		0			0
$112$		0			0
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$		0			0
$116$	1.00000	+	1.73205i	0.0928477	+	0.160817i
$117$		0			0
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$		0			0
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$	−9.00000	−	15.5885i	−0.771744	−	1.33670i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$		0			0
$145$	2.00000	−	3.46410i	0.166091	−	0.287678i
$146$	6.00000			0.496564
$147$		0			0
$148$	−6.00000			−0.493197
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$		0			0
$160$	−10.0000			−0.790569
$161$		0			0
$162$		0			0
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−6.00000	+	10.3923i	−0.460179	+	0.797053i
$171$		0			0
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	−0.610939	−	0.791677i	$-0.709208\pi$
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	0.991082	+	0.133250i	$0.0425415\pi$
$174$		0			0
$175$		0			0
$176$	4.00000			0.301511
$177$		0			0
$178$	7.00000	+	12.1244i	0.524672	+	0.908759i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$		0			0
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.00000	+	10.3923i	0.441129	+	0.764057i
$186$		0			0
$187$	−12.0000	+	20.7846i	−0.877527	+	1.51992i
$188$		0			0
$189$		0			0
$190$	8.00000			0.580381
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	9.00000	−	15.5885i	0.646162	−	1.11919i
$195$		0			0
$196$		0			0
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	0.880616	+	0.473831i	$0.157129\pi$
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	−0.0299585	+	0.999551i	$0.509538\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$		0			0
$202$	14.0000			0.985037
$203$		0			0
$204$		0			0
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$		0			0
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	16.0000			1.10674
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$		0			0
$217$		0			0
$218$	−18.0000			−1.21911
$219$		0			0
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$		0			0
$226$	−7.00000	+	12.1244i	−0.465633	+	0.806500i
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$		0			0
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$	−2.50000	−	4.33013i	−0.160706	−	0.278351i
$243$		0			0
$244$	−2.00000			−0.128037
$245$		0			0
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	0.101305	+	0.994855i	$0.467698\pi$
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	−0.912222	+	0.409695i	$0.865635\pi$
$258$		0			0
$259$		0			0
$260$	4.00000			0.248069
$261$		0			0
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	6.00000			0.362473
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	6.00000	−	10.3923i	0.359856	−	0.623289i
$279$		0			0
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$		0			0
$285$		0			0
$286$	−8.00000			−0.473050
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	2.00000	+	3.46410i	0.117444	+	0.203419i
$291$		0			0
$292$	3.00000	−	5.19615i	0.175562	−	0.304082i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$	−24.0000			−1.39733
$296$	9.00000	−	15.5885i	0.523114	−	0.906061i
$297$		0			0
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	8.00000			0.460348
$303$		0			0
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	2.00000	+	3.46410i	0.114520	+	0.198354i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	0.954810	−	0.297218i	$-0.0960589\pi$
$314$	2.00000			0.112867
$315$		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	$0.997978\pi$
$318$		0			0
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	7.00000	−	12.1244i	0.391312	−	0.677772i
$321$		0			0
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$		0			0
$328$	−6.00000			−0.331295
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$		0			0
$334$	4.00000	−	6.92820i	0.218870	−	0.379094i
$335$	−8.00000			−0.437087
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$	5.00000	+	8.66025i	0.268802	+	0.465578i
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$		0			0
$352$	10.0000	−	17.3205i	0.533002	−	0.923186i
$353$	−5.00000	−	8.66025i	−0.266123	−	0.460939i	0.701734	−	0.712439i	$-0.252409\pi$
$353$	−5.00000	−	8.66025i	−0.266123	−	0.460939i	−0.967857	+	0.251500i	$0.919076\pi$
$354$		0			0
$355$		0			0
$356$	14.0000			0.741999
$357$		0			0
$358$	4.00000			0.211407
$359$	16.0000	−	27.7128i	0.844448	−	1.46263i	−0.0416523	−	0.999132i	$-0.513262\pi$
$359$	16.0000	−	27.7128i	0.844448	−	1.46263i	0.886100	−	0.463494i	$-0.153404\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−13.0000	+	22.5167i	−0.683265	+	1.18345i
$363$		0			0
$364$		0			0
$365$	−12.0000			−0.628109
$366$		0			0
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$		0			0
$369$		0			0
$370$	−12.0000			−0.623850
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$		0			0
$376$		0			0
$377$	4.00000			0.206010
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$	2.00000			0.101797
$387$		0			0
$388$	−9.00000	−	15.5885i	−0.456906	−	0.791384i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	11.0000	−	19.0526i	0.554172	−	0.959854i
$395$	−16.0000	−	27.7128i	−0.805047	−	1.39438i
$396$		0			0
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	−0.998492	−	0.0549046i	$-0.982515\pi$
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	0.546795	+	0.837267i	$0.315848\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$		0			0
$404$	7.00000	−	12.1244i	0.348263	−	0.603209i
$405$		0			0
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	−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	$-0.349725\pi$
$410$	2.00000	+	3.46410i	0.0987730	+	0.171080i
$411$		0			0
$412$	8.00000			0.394132
$413$		0			0
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$	−5.00000	−	8.66025i	−0.245145	−	0.424604i
$417$		0			0
$418$	−8.00000	+	13.8564i	−0.391293	+	0.677739i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	38.0000			1.85201			0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000			1.85201			0.926003	+	0.377515i	$0.123221\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$		0			0
$424$	−9.00000	−	15.5885i	−0.437079	−	0.757042i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$		0			0
$428$	4.00000			0.193347
$429$		0			0
$430$	−4.00000	−	6.92820i	−0.192897	−	0.334108i
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$	−9.00000	+	15.5885i	−0.431022	+	0.746552i
$437$		0			0
$438$		0			0
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$	−24.0000			−1.14416
$441$		0			0
$442$	−12.0000			−0.570782
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$		0			0
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	7.00000	+	12.1244i	0.329252	+	0.570282i
$453$		0			0
$454$	−12.0000			−0.563188
$455$		0			0
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$		0			0
$460$		0			0
$461$	−10.0000			−0.465746			−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000			−0.465746			−0.232873	+	0.972507i	$0.574813\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	0.0627555	+	0.998029i	$0.480011\pi$
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	−0.895696	+	0.444667i	$0.853322\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	18.0000	+	31.1769i	0.828517	+	1.43503i
$473$	−8.00000	−	13.8564i	−0.367840	−	0.637118i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$		0			0
$478$	12.0000	−	20.7846i	0.548867	−	0.950666i
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	−2.00000			−0.0910975
$483$		0			0
$484$	−5.00000			−0.227273
$485$	−18.0000	+	31.1769i	−0.817338	+	1.41567i
$486$		0			0
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$		0			0
$490$		0			0
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$	4.00000	+	6.92820i	0.179969	+	0.311715i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	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
$505$	−28.0000			−1.24598
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$		0			0
$512$	−11.0000			−0.486136
$513$		0			0
$514$	−13.0000	−	22.5167i	−0.573405	−	0.993167i
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−16.0000			−0.697633
$527$		0			0
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$		0			0
$532$		0			0
$533$	4.00000			0.173259
$534$		0			0
$535$	−4.00000	−	6.92820i	−0.172935	−	0.299532i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$		0			0
$538$	6.00000			0.258678
$539$		0			0
$540$		0			0
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$		0			0
$544$	15.0000	−	25.9808i	0.643120	−	1.11392i
$545$	36.0000			1.54207
$546$		0			0
$547$	4.00000			0.171028			0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000			0.171028			0.0855138	+	0.996337i	$0.472747\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$		0			0
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$		0			0
$554$	22.0000			0.934690
$555$		0			0
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−1.00000	−	1.73205i	−0.0423714	−	0.0733893i	0.844062	−	0.536246i	$-0.180158\pi$
$557$	−1.00000	−	1.73205i	−0.0423714	−	0.0733893i	−0.886433	+	0.462856i	$0.846825\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	−11.0000	+	19.0526i	−0.464007	+	0.803684i
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	14.0000	−	24.2487i	0.588984	−	1.02015i
$566$	20.0000			0.840663
$567$		0			0
$568$		0			0
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	−0.741981	−	0.670421i	$-0.766114\pi$
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	0.951592	+	0.307364i	$0.0994469\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	−4.00000	+	6.92820i	−0.167248	+	0.289683i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	0.965701	+	0.259656i	$0.0836092\pi$
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	−0.257982	+	0.966150i	$0.583058\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$	4.00000			0.166091
$581$		0			0
$582$		0			0
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$	9.00000	+	15.5885i	0.372423	+	0.645055i
$585$		0			0
$586$	−7.00000	+	12.1244i	−0.289167	+	0.500853i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$		0			0
$590$	12.0000	−	20.7846i	0.494032	−	0.855689i
$591$		0			0
$592$	3.00000	+	5.19615i	0.123299	+	0.213561i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$	6.00000			0.245770
$597$		0			0
$598$		0			0
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.660006	+	0.751260i	$0.270554\pi$
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.320607	+	0.947212i	$0.396113\pi$
$600$		0			0
$601$	6.00000			0.244745			0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000			0.244745			0.122373	+	0.992484i	$0.460950\pi$
$602$		0			0
$603$		0			0
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$	−20.0000			−0.811107
$609$		0			0
$610$	−4.00000			−0.161955
$611$		0			0
$612$		0			0
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	0.999574	+	0.0291886i	$0.00929235\pi$
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	−0.474509	+	0.880251i	$0.657374\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$		0			0
$621$		0			0
$622$	−24.0000			−0.962312
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$		0			0
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$	−36.0000			−1.43541
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−24.0000	+	41.5692i	−0.954669	+	1.65353i
$633$		0			0
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−8.00000			−0.316723
$639$		0			0
$640$	−3.00000	−	5.19615i	−0.118585	−	0.205396i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	20.0000	+	34.6410i	0.786281	+	1.36188i	0.928231	+	0.372005i	$0.121330\pi$
$647$	20.0000	+	34.6410i	0.786281	+	1.36188i	−0.141950	+	0.989874i	$0.545337\pi$
$648$		0			0
$649$	24.0000	−	41.5692i	0.942082	−	1.63173i
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$		0			0
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		0			0
$664$	36.0000			1.39707
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−4.00000	−	6.92820i	−0.154765	−	0.268060i
$669$		0			0
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	−8.00000			−0.308837
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$		0			0
$676$	−4.50000	−	7.79423i	−0.173077	−	0.299778i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$		0			0
$680$	−36.0000			−1.38054
$681$		0			0
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$		0			0
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	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	$0.0424468\pi$
$692$	10.0000			0.380143
$693$		0			0
$694$	28.0000			1.06287
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	12.0000	+	20.7846i	0.452589	+	0.783906i
$704$	14.0000	+	24.2487i	0.527645	+	0.913908i
$705$		0			0
$706$	10.0000			0.376355
$707$		0			0
$708$		0			0
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$		0			0
$711$		0			0
$712$	−21.0000	+	36.3731i	−0.787008	+	1.36314i
$713$		0			0
$714$		0			0
$715$	16.0000			0.598366
$716$	2.00000	−	3.46410i	0.0747435	−	0.129460i
$717$		0			0
$718$	16.0000	+	27.7128i	0.597115	+	1.03423i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$		0			0
$721$		0			0
$722$	−3.00000			−0.111648
$723$		0			0
$724$	13.0000	+	22.5167i	0.483141	+	0.836825i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$		0			0
$729$		0			0
$730$	6.00000	−	10.3923i	0.222070	−	0.384636i
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	−0.982986	−	0.183679i	$-0.941199\pi$
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	0.650564	+	0.759452i	$0.274533\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.00000	−	13.8564i	0.294684	−	0.510407i
$738$		0			0
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	−0.980052	−	0.198741i	$-0.936315\pi$
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	0.317911	−	0.948120i	$-0.397019\pi$
$740$	−6.00000	+	10.3923i	−0.220564	+	0.382029i
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	−6.00000	−	10.3923i	−0.219823	−	0.380745i
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$		0			0
$748$	−24.0000			−0.877527
$749$		0			0
$750$		0			0
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$		0			0
$753$		0			0
$754$	−2.00000	+	3.46410i	−0.0728357	+	0.126155i
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	−6.00000	+	10.3923i	−0.217930	+	0.377466i
$759$		0			0
$760$	12.0000	+	20.7846i	0.435286	+	0.753937i
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$		0			0
$766$		0			0
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$		0			0
$772$	1.00000	−	1.73205i	0.0359908	−	0.0623379i
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	0.712241	−	0.701935i	$-0.247680\pi$
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	−0.964014	+	0.265852i	$0.914347\pi$
$774$		0			0
$775$		0			0
$776$	54.0000			1.93849
$777$		0			0
$778$	−6.00000			−0.215110
$779$	4.00000	−	6.92820i	0.143315	−	0.248229i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.00000			−0.142766
$786$		0			0
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	−0.929467	−	0.368906i	$-0.879732\pi$
$787$	−22.0000	−	38.1051i	−0.784215	−	1.35830i	0.145251	−	0.989395i	$-0.453601\pi$
$788$	−11.0000	−	19.0526i	−0.391859	−	0.678719i
$789$		0			0
$790$	32.0000			1.13851
$791$		0			0
$792$		0			0
$793$	−2.00000	+	3.46410i	−0.0710221	+	0.123014i
$794$	−9.00000	−	15.5885i	−0.319398	−	0.553214i
$795$		0			0
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	−26.0000			−0.920967			−0.460484	−	0.887668i	$-0.652324\pi$
$797$	−26.0000			−0.920967			−0.460484	+	0.887668i	$0.652324\pi$
$798$		0			0
$799$		0			0
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$		0			0
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	21.0000	+	36.3731i	0.738777	+	1.27960i
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$		0			0
$811$	−44.0000			−1.54505			−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000			−1.54505			−0.772524	+	0.634985i	$0.781006\pi$
$812$		0			0
$813$		0			0
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	22.0000			0.769212
$819$		0			0
$820$	4.00000			0.139686
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	−0.316691	−	0.948529i	$-0.602572\pi$
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	0.979795	−	0.200002i	$-0.0640949\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	−12.0000	+	20.7846i	−0.418040	+	0.724066i
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	0.961601	−	0.274450i	$-0.0884958\pi$
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	−0.718481	+	0.695546i	$0.755162\pi$
$830$	−12.0000	−	20.7846i	−0.416526	−	0.721444i
$831$		0			0
$832$	14.0000			0.485363
$833$		0			0
$834$		0			0
$835$	−8.00000	+	13.8564i	−0.276851	+	0.479521i
$836$	8.00000	+	13.8564i	0.276686	+	0.479234i
$837$		0			0
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	−8.00000			−0.276191			−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000			−0.276191			−0.138095	+	0.990419i	$0.544098\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−19.0000	+	32.9090i	−0.654783	+	1.13412i
$843$		0			0
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−9.00000	+	15.5885i	−0.309609	+	0.536259i
$846$		0			0
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	−3.00000	−	5.19615i	−0.102899	−	0.178227i
$851$		0			0
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	0.960461	−	0.278416i	$-0.0898092\pi$
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	−0.721345	+	0.692576i	$0.756476\pi$
$858$		0			0
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	−0.196887	−	0.980426i	$-0.563083\pi$
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	0.947518	−	0.319704i	$-0.103583\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$	24.0000			0.817443
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$		0			0
$865$	−10.0000	−	17.3205i	−0.340010	−	0.588915i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$		0			0
$869$	64.0000			2.17105
$870$		0			0
$871$	−4.00000	−	6.92820i	−0.135535	−	0.234753i
$872$	−27.0000	−	46.7654i	−0.914335	−	1.58368i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	0.157205	+	0.987566i	$0.449752\pi$
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	−0.933860	+	0.357640i	$0.883582\pi$
$878$	−12.0000	−	20.7846i	−0.404980	−	0.701447i
$879$		0			0
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	−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
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	−0.925332	−	0.379157i	$-0.876214\pi$
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	0.791026	+	0.611783i	$0.209547\pi$
$888$		0			0
$889$		0			0
$890$	28.0000			0.938562
$891$		0			0
$892$	−8.00000	−	13.8564i	−0.267860	−	0.463947i
$893$		0			0
$894$		0			0
$895$	−8.00000			−0.267411
$896$		0			0
$897$		0			0
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$		0			0
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	−8.00000			−0.266371
$903$		0			0
$904$	−42.0000			−1.39690
$905$	26.0000	−	45.0333i	0.864269	−	1.49696i
$906$		0			0
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	0.897318	−	0.441384i	$-0.145512\pi$
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	−0.830909	+	0.556408i	$0.812179\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$		0			0
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	−24.0000	−	41.5692i	−0.794284	−	1.37574i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	−10.0000			−0.330409
$917$		0			0
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$		0			0
$922$	5.00000	−	8.66025i	0.164666	−	0.285210i
$923$		0			0
$924$		0			0
$925$	−6.00000			−0.197279
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$		0			0
$928$	−5.00000	−	8.66025i	−0.164133	−	0.284287i
$929$	−13.0000	+	22.5167i	−0.426516	+	0.738748i	−0.996561	−	0.0828661i	$-0.973593\pi$
$929$	−13.0000	+	22.5167i	−0.426516	+	0.738748i	0.570045	+	0.821614i	$0.306926\pi$
$930$		0			0
$931$		0			0
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−18.0000	−	31.1769i	−0.588978	−	1.02014i
$935$	24.0000	+	41.5692i	0.784884	+	1.35946i
$936$		0			0
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$		0			0
$944$	−12.0000			−0.390567
$945$		0			0
$946$	16.0000			0.520205
$947$	22.0000	−	38.1051i	0.714904	−	1.23825i	−0.248093	−	0.968736i	$-0.579804\pi$
$947$	22.0000	−	38.1051i	0.714904	−	1.23825i	0.962997	−	0.269514i	$-0.0868629\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		0			0
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$	−16.0000			−0.516937
$959$		0			0
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−6.00000	−	10.3923i	−0.193448	−	0.335061i
$963$		0			0
$964$	−1.00000	+	1.73205i	−0.0322078	+	0.0557856i
$965$	−4.00000			−0.128765
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$	7.50000	−	12.9904i	0.241059	−	0.417527i
$969$		0			0
$970$	−18.0000	−	31.1769i	−0.577945	−	1.00103i
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$		0			0
$973$		0			0
$974$	−8.00000			−0.256337
$975$		0			0
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$		0			0
$979$	56.0000			1.78977
$980$		0			0
$981$		0			0
$982$	10.0000	−	17.3205i	0.319113	−	0.552720i
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$		0			0
$985$	−22.0000	+	38.1051i	−0.700978	+	1.21413i
$986$	−12.0000			−0.382158
$987$		0			0
$988$	8.00000			0.254514
$989$		0			0
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	48.0000			1.52170
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.e.b.226.1		2
3.2	odd	2		147.2.e.c.79.1		2
7.2	even	3		441.2.a.f.1.1		1
7.3	odd	6		441.2.e.a.361.1		2
7.4	even	3	inner	441.2.e.b.361.1		2
7.5	odd	6		63.2.a.a.1.1		1
7.6	odd	2		441.2.e.a.226.1		2
12.11	even	2		2352.2.q.e.961.1		2
21.2	odd	6		147.2.a.a.1.1		1
21.5	even	6		21.2.a.a.1.1	✓	1
21.11	odd	6		147.2.e.c.67.1		2
21.17	even	6		147.2.e.b.67.1		2
21.20	even	2		147.2.e.b.79.1		2
28.19	even	6		1008.2.a.l.1.1		1
28.23	odd	6		7056.2.a.p.1.1		1
35.12	even	12		1575.2.d.a.1324.2		2
35.19	odd	6		1575.2.a.c.1.1		1
35.33	even	12		1575.2.d.a.1324.1		2
56.5	odd	6		4032.2.a.h.1.1		1
56.19	even	6		4032.2.a.k.1.1		1
63.5	even	6		567.2.f.g.379.1		2
63.40	odd	6		567.2.f.b.379.1		2
63.47	even	6		567.2.f.g.190.1		2
63.61	odd	6		567.2.f.b.190.1		2
77.54	even	6		7623.2.a.g.1.1		1
84.11	even	6		2352.2.q.e.1537.1		2
84.23	even	6		2352.2.a.v.1.1		1
84.47	odd	6		336.2.a.a.1.1		1
84.59	odd	6		2352.2.q.x.1537.1		2
84.83	odd	2		2352.2.q.x.961.1		2
105.44	odd	6		3675.2.a.n.1.1		1
105.47	odd	12		525.2.d.a.274.1		2
105.68	odd	12		525.2.d.a.274.2		2
105.89	even	6		525.2.a.d.1.1		1
168.5	even	6		1344.2.a.g.1.1		1
168.107	even	6		9408.2.a.m.1.1		1
168.131	odd	6		1344.2.a.s.1.1		1
168.149	odd	6		9408.2.a.bv.1.1		1
231.131	odd	6		2541.2.a.j.1.1		1
273.194	even	6		3549.2.a.c.1.1		1
336.5	even	12		5376.2.c.r.2689.1		2
336.131	odd	12		5376.2.c.l.2689.1		2
336.173	even	12		5376.2.c.r.2689.2		2
336.299	odd	12		5376.2.c.l.2689.2		2
357.152	even	6		6069.2.a.b.1.1		1
399.341	odd	6		7581.2.a.d.1.1		1
420.299	odd	6		8400.2.a.bn.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.a.a.1.1	✓	1	21.5	even	6
63.2.a.a.1.1		1	7.5	odd	6
147.2.a.a.1.1		1	21.2	odd	6
147.2.e.b.67.1		2	21.17	even	6
147.2.e.b.79.1		2	21.20	even	2
147.2.e.c.67.1		2	21.11	odd	6
147.2.e.c.79.1		2	3.2	odd	2
336.2.a.a.1.1		1	84.47	odd	6
441.2.a.f.1.1		1	7.2	even	3
441.2.e.a.226.1		2	7.6	odd	2
441.2.e.a.361.1		2	7.3	odd	6
441.2.e.b.226.1		2	1.1	even	1	trivial
441.2.e.b.361.1		2	7.4	even	3	inner
525.2.a.d.1.1		1	105.89	even	6
525.2.d.a.274.1		2	105.47	odd	12
525.2.d.a.274.2		2	105.68	odd	12
567.2.f.b.190.1		2	63.61	odd	6
567.2.f.b.379.1		2	63.40	odd	6
567.2.f.g.190.1		2	63.47	even	6
567.2.f.g.379.1		2	63.5	even	6
1008.2.a.l.1.1		1	28.19	even	6
1344.2.a.g.1.1		1	168.5	even	6
1344.2.a.s.1.1		1	168.131	odd	6
1575.2.a.c.1.1		1	35.19	odd	6
1575.2.d.a.1324.1		2	35.33	even	12
1575.2.d.a.1324.2		2	35.12	even	12
2352.2.a.v.1.1		1	84.23	even	6
2352.2.q.e.961.1		2	12.11	even	2
2352.2.q.e.1537.1		2	84.11	even	6
2352.2.q.x.961.1		2	84.83	odd	2
2352.2.q.x.1537.1		2	84.59	odd	6
2541.2.a.j.1.1		1	231.131	odd	6
3549.2.a.c.1.1		1	273.194	even	6
3675.2.a.n.1.1		1	105.44	odd	6
4032.2.a.h.1.1		1	56.5	odd	6
4032.2.a.k.1.1		1	56.19	even	6
5376.2.c.l.2689.1		2	336.131	odd	12
5376.2.c.l.2689.2		2	336.299	odd	12
5376.2.c.r.2689.1		2	336.5	even	12
5376.2.c.r.2689.2		2	336.173	even	12
6069.2.a.b.1.1		1	357.152	even	6
7056.2.a.p.1.1		1	28.23	odd	6
7581.2.a.d.1.1		1	399.341	odd	6
7623.2.a.g.1.1		1	77.54	even	6
8400.2.a.bn.1.1		1	420.299	odd	6
9408.2.a.m.1.1		1	168.107	even	6
9408.2.a.bv.1.1		1	168.149	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +(2.00000 + 3.46410i) q^{11} +2.00000 q^{13} +(0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +2.00000 q^{29} +(-2.50000 - 4.33013i) q^{32} -6.00000 q^{34} +(-3.00000 + 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-3.00000 + 5.19615i) q^{40} +2.00000 q^{41} -4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +8.00000 q^{55} +(-1.00000 + 1.73205i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +7.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{73} +(-3.00000 - 5.19615i) q^{74} +4.00000 q^{76} +(8.00000 - 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-1.00000 + 1.73205i) q^{82} -12.0000 q^{83} +12.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-6.00000 - 10.3923i) q^{88} +(7.00000 - 12.1244i) q^{89} +(-4.00000 - 6.92820i) q^{95} -18.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} + 2 q^{5} - 6 q^{8}+O(q^{10}) \) 2 * q - q^2 + q^4 + 2 * q^5 - 6 * q^8	\( 2 q - q^{2} + q^{4} + 2 q^{5} - 6 q^{8} + 2 q^{10} + 4 q^{11} + 4 q^{13} + q^{16} + 6 q^{17} + 4 q^{19} + 4 q^{20} - 8 q^{22} + q^{25} - 2 q^{26} + 4 q^{29} - 5 q^{32} - 12 q^{34} - 6 q^{37} + 4 q^{38} - 6 q^{40} + 4 q^{41} - 8 q^{43} - 4 q^{44} - 2 q^{50} + 2 q^{52} + 6 q^{53} + 16 q^{55} - 2 q^{58} - 12 q^{59} - 2 q^{61} + 14 q^{64} + 4 q^{65} - 4 q^{67} - 6 q^{68} - 6 q^{73} - 6 q^{74} + 8 q^{76} + 16 q^{79} - 2 q^{80} - 2 q^{82} - 24 q^{83} + 24 q^{85} + 4 q^{86} - 12 q^{88} + 14 q^{89} - 8 q^{95} - 36 q^{97}+O(q^{100}) \) 2 * q - q^2 + q^4 + 2 * q^5 - 6 * q^8 + 2 * q^10 + 4 * q^11 + 4 * q^13 + q^16 + 6 * q^17 + 4 * q^19 + 4 * q^20 - 8 * q^22 + q^25 - 2 * q^26 + 4 * q^29 - 5 * q^32 - 12 * q^34 - 6 * q^37 + 4 * q^38 - 6 * q^40 + 4 * q^41 - 8 * q^43 - 4 * q^44 - 2 * q^50 + 2 * q^52 + 6 * q^53 + 16 * q^55 - 2 * q^58 - 12 * q^59 - 2 * q^61 + 14 * q^64 + 4 * q^65 - 4 * q^67 - 6 * q^68 - 6 * q^73 - 6 * q^74 + 8 * q^76 + 16 * q^79 - 2 * q^80 - 2 * q^82 - 24 * q^83 + 24 * q^85 + 4 * q^86 - 12 * q^88 + 14 * q^89 - 8 * q^95 - 36 * q^97

Introduction

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