LMFDB - Embedded newform 882.2.g.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(361,882)]

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([0, 4]))

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

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.g (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 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.2.g.a.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{10} +(-2.00000 + 3.46410i) q^{11} -4.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{19} +4.00000 q^{20} +4.00000 q^{22} +(-5.50000 + 9.52628i) q^{25} +(2.00000 + 3.46410i) q^{26} -2.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-2.00000 - 3.46410i) q^{40} +4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(4.00000 + 6.92820i) q^{47} +11.0000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-5.00000 + 8.66025i) q^{53} +16.0000 q^{55} +(1.00000 + 1.73205i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(8.00000 + 13.8564i) q^{65} +(-2.00000 + 3.46410i) q^{67} -8.00000 q^{71} +(-8.00000 + 13.8564i) q^{73} +(3.00000 - 5.19615i) q^{74} -4.00000 q^{76} +(4.00000 + 6.92820i) q^{79} +(-2.00000 + 3.46410i) q^{80} -12.0000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-4.00000 - 6.92820i) q^{89} +(4.00000 - 6.92820i) q^{94} +(8.00000 - 13.8564i) q^{95} -8.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 4 q^{5} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 4 * q^5 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 4 q^{5} + 2 q^{8} - 4 q^{10} - 4 q^{11} - 8 q^{13} - q^{16} + 4 q^{19} + 8 q^{20} + 8 q^{22} - 11 q^{25} + 4 q^{26} - 4 q^{29} + 8 q^{31} - q^{32} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 8 q^{43} - 4 q^{44} + 8 q^{47} + 22 q^{50} + 4 q^{52} - 10 q^{53} + 32 q^{55} + 2 q^{58} - 4 q^{59} - 4 q^{61} - 16 q^{62} + 2 q^{64} + 16 q^{65} - 4 q^{67} - 16 q^{71} - 16 q^{73} + 6 q^{74} - 8 q^{76} + 8 q^{79} - 4 q^{80} - 24 q^{83} - 4 q^{86} - 4 q^{88} - 8 q^{89} + 8 q^{94} + 16 q^{95} - 16 q^{97}+O(q^{100}) $ 2 * q - q^2 - q^4 - 4 * q^5 + 2 * q^8 - 4 * q^10 - 4 * q^11 - 8 * q^13 - q^16 + 4 * q^19 + 8 * q^20 + 8 * q^22 - 11 * q^25 + 4 * q^26 - 4 * q^29 + 8 * q^31 - q^32 + 6 * q^37 + 4 * q^38 - 4 * q^40 + 8 * q^43 - 4 * q^44 + 8 * q^47 + 22 * q^50 + 4 * q^52 - 10 * q^53 + 32 * q^55 + 2 * q^58 - 4 * q^59 - 4 * q^61 - 16 * q^62 + 2 * q^64 + 16 * q^65 - 4 * q^67 - 16 * q^71 - 16 * q^73 + 6 * q^74 - 8 * q^76 + 8 * q^79 - 4 * q^80 - 24 * q^83 - 4 * q^86 - 4 * q^88 - 8 * q^89 + 8 * q^94 + 16 * q^95 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.0599153	−	0.998203i	$-0.519083\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.00000	+	3.46410i	−0.632456	+	1.09545i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$	4.00000			0.852803
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		0			0
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	+	5.19615i	0.493197	+	0.854242i	0.999969	−	0.00783774i	$-0.00249486\pi$
$37$	3.00000	+	5.19615i	0.493197	+	0.854242i	−0.506772	+	0.862080i	$0.669162\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$		0			0
$40$	−2.00000	−	3.46410i	−0.316228	−	0.547723i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$		0			0
$46$		0			0
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$		0			0
$50$	11.0000			1.55563
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	0.286064	+	0.958211i	$0.407653\pi$
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	−0.972867	+	0.231367i	$0.925680\pi$
$54$		0			0
$55$	16.0000			2.15744
$56$		0			0
$57$		0			0
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	8.00000	+	13.8564i	0.992278	+	1.71868i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−8.00000	+	13.8564i	−0.936329	+	1.62177i	−0.164083	+	0.986447i	$0.552466\pi$
$73$	−8.00000	+	13.8564i	−0.936329	+	1.62177i	−0.772246	+	0.635323i	$0.780867\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$		0			0
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$		0			0
$82$		0			0
$83$	−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
$85$		0			0
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	0.572327	−	0.820025i	$-0.306041\pi$
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	−0.996326	+	0.0856373i	$0.972707\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	8.00000	−	13.8564i	0.820783	−	1.42164i
$96$		0			0
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$		0			0
$99$		0			0
$100$	−5.50000	−	9.52628i	−0.550000	−	0.952628i
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	−0.948207	−	0.317653i	$-0.897105\pi$
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	0.749199	+	0.662344i	$0.230438\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	10.0000			0.971286
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$	−8.00000	−	13.8564i	−0.762770	−	1.32116i
$111$		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
$118$	4.00000			0.368230
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−2.00000	+	3.46410i	−0.181071	+	0.313625i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	24.0000			2.14663
$126$		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
$129$		0			0
$130$	8.00000	−	13.8564i	0.701646	−	1.21529i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$		0			0
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$		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
$142$	4.00000	+	6.92820i	0.335673	+	0.581402i
$143$	8.00000	−	13.8564i	0.668994	−	1.15873i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$	16.0000			1.32417
$147$		0			0
$148$	−6.00000			−0.493197
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$		0			0
$155$	−32.0000			−2.57030
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	4.00000			0.316228
$161$		0			0
$162$		0			0
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	0.529454	−	0.848339i	$-0.322397\pi$
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	−0.999410	+	0.0343508i	$0.989064\pi$
$164$		0			0
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$		0			0
$176$	4.00000			0.301511
$177$		0			0
$178$	−4.00000	+	6.92820i	−0.299813	+	0.519291i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.0000	−	20.7846i	0.882258	−	1.52811i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−16.0000			−1.16076
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	−5.50000	+	9.52628i	−0.388909	+	0.673610i
$201$		0			0
$202$	4.00000			0.281439
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−16.0000			−1.10674
$210$		0			0
$211$	−28.0000			−1.92760			−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000			−1.92760			−0.963800	+	0.266627i	$0.914091\pi$
$212$	−5.00000	−	8.66025i	−0.343401	−	0.594789i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	−8.00000	−	13.8564i	−0.545595	−	0.944999i
$216$		0			0
$217$		0			0
$218$	−14.0000			−0.948200
$219$		0			0
$220$	−8.00000	+	13.8564i	−0.539360	+	0.934199i
$221$		0			0
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$		0			0
$226$	−7.00000	−	12.1244i	−0.465633	−	0.806500i
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$		0			0
$232$	−2.00000			−0.131306
$233$	−5.00000	−	8.66025i	−0.327561	−	0.567352i	0.654466	−	0.756091i	$-0.272893\pi$
$233$	−5.00000	−	8.66025i	−0.327561	−	0.567352i	−0.982027	+	0.188739i	$0.939560\pi$
$234$		0			0
$235$	16.0000	−	27.7128i	1.04372	−	1.80778i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$		0			0
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$		0			0
$244$	4.00000			0.256074
$245$		0			0
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		0			0
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	−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
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$		0			0
$260$	−16.0000			−0.992278
$261$		0			0
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	−0.715944	−	0.698158i	$-0.754003\pi$
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	0.962594	+	0.270947i	$0.0873367\pi$
$264$		0			0
$265$	40.0000			2.45718
$266$		0			0
$267$		0			0
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	0.0243472	+	0.999704i	$0.492249\pi$
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	−0.877942	+	0.478766i	$0.841084\pi$
$270$		0			0
$271$	−16.0000	−	27.7128i	−0.971931	−	1.68343i	−0.689713	−	0.724083i	$-0.742263\pi$
$271$	−16.0000	−	27.7128i	−0.971931	−	1.68343i	−0.282218	−	0.959350i	$-0.591070\pi$
$272$		0			0
$273$		0			0
$274$	10.0000			0.604122
$275$	−22.0000	−	38.1051i	−1.32665	−	2.29783i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	6.00000	+	10.3923i	0.359856	+	0.623289i
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$		0			0
$286$	−16.0000			−0.946100
$287$		0			0
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$		0			0
$292$	−8.00000	−	13.8564i	−0.468165	−	0.810885i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	16.0000			0.931556
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$		0			0
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$		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
$305$	−8.00000	+	13.8564i	−0.458079	+	0.793416i
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$		0			0
$310$	16.0000	+	27.7128i	0.908739	+	1.57398i
$311$	−16.0000	+	27.7128i	−0.907277	+	1.57145i	−0.0894452	+	0.995992i	$0.528509\pi$
$311$	−16.0000	+	27.7128i	−0.907277	+	1.57145i	−0.817832	+	0.575458i	$0.804824\pi$
$312$		0			0
$313$	12.0000	+	20.7846i	0.678280	+	1.17482i	0.975499	+	0.220006i	$0.0706077\pi$
$313$	12.0000	+	20.7846i	0.678280	+	1.17482i	−0.297218	+	0.954810i	$0.596059\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−8.00000			−0.450035
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		0			0
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$	−2.00000	−	3.46410i	−0.111803	−	0.193649i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	22.0000	−	38.1051i	1.22034	−	2.11369i
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$	−4.00000	−	6.92820i	−0.218870	−	0.379094i
$335$	16.0000			0.874173
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$		0			0
$341$	16.0000	+	27.7128i	0.866449	+	1.50073i
$342$		0			0
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000	−	3.46410i	−0.106600	−	0.184637i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	16.0000	+	27.7128i	0.849192	+	1.47084i
$356$	8.00000			0.423999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$		0			0
$364$		0			0
$365$	64.0000			3.34991
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$		0			0
$370$	−24.0000			−1.24770
$371$		0			0
$372$		0			0
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$		0			0
$375$		0			0
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	8.00000			0.412021
$378$		0			0
$379$	36.0000			1.84920			0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000			1.84920			0.924598	+	0.380945i	$0.124401\pi$
$380$	8.00000	+	13.8564i	0.410391	+	0.710819i
$381$		0			0
$382$		0			0
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		0			0
$385$		0			0
$386$	2.00000			0.101797
$387$		0			0
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	16.0000	−	27.7128i	0.805047	−	1.39438i
$396$		0			0
$397$	2.00000	+	3.46410i	0.100377	+	0.173858i	0.911840	−	0.410546i	$-0.134662\pi$
$397$	2.00000	+	3.46410i	0.100377	+	0.173858i	−0.811463	+	0.584404i	$0.801328\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	11.0000			0.550000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	−16.0000	+	27.7128i	−0.797017	+	1.38047i
$404$	−2.00000	−	3.46410i	−0.0995037	−	0.172345i
$405$		0			0
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	−12.0000	+	20.7846i	−0.593362	+	1.02773i	0.400414	+	0.916334i	$0.368866\pi$
$409$	−12.0000	+	20.7846i	−0.593362	+	1.02773i	−0.993776	+	0.111398i	$0.964467\pi$
$410$		0			0
$411$		0			0
$412$	8.00000			0.394132
$413$		0			0
$414$		0			0
$415$	24.0000	+	41.5692i	1.17811	+	2.04055i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	8.00000	+	13.8564i	0.391293	+	0.677739i
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	14.0000	+	24.2487i	0.681509	+	1.18041i
$423$		0			0
$424$	−5.00000	+	8.66025i	−0.242821	+	0.420579i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−4.00000			−0.193347
$429$		0			0
$430$	−8.00000	+	13.8564i	−0.385794	+	0.668215i
$431$	20.0000	−	34.6410i	0.963366	−	1.66860i	0.249424	−	0.968394i	$-0.419759\pi$
$431$	20.0000	−	34.6410i	0.963366	−	1.66860i	0.713942	−	0.700205i	$-0.246908\pi$
$432$		0			0
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$		0			0
$435$		0			0
$436$	7.00000	+	12.1244i	0.335239	+	0.580651i
$437$		0			0
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	16.0000			0.762770
$441$		0			0
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	−16.0000	+	27.7128i	−0.758473	+	1.31371i
$446$	−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
$451$		0			0
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	20.0000			0.938647
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$		0			0
$460$		0			0
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	0.536352	−	0.843995i	$-0.319802\pi$
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	−0.999097	+	0.0424970i	$0.986469\pi$
$468$		0			0
$469$		0			0
$470$	−32.0000			−1.47605
$471$		0			0
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$	−44.0000			−2.01886
$476$		0			0
$477$		0			0
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	−12.0000	−	20.7846i	−0.547153	−	0.947697i
$482$	−8.00000			−0.364390
$483$		0			0
$484$	5.00000			0.227273
$485$	16.0000	+	27.7128i	0.726523	+	1.25837i
$486$		0			0
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	−0.761052	−	0.648691i	$-0.775317\pi$
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	0.942309	+	0.334744i	$0.108650\pi$
$488$	−2.00000	−	3.46410i	−0.0905357	−	0.156813i
$489$		0			0
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	0.968500	−	0.249015i	$-0.0801067\pi$
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	−0.699903	+	0.714238i	$0.746773\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$		0			0
$502$	10.0000	+	17.3205i	0.446322	+	0.773052i
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$		0			0
$505$	16.0000			0.711991
$506$		0			0
$507$		0			0
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	2.00000	+	3.46410i	0.0886484	+	0.153544i	0.906940	−	0.421260i	$-0.138412\pi$
$509$	2.00000	+	3.46410i	0.0886484	+	0.153544i	−0.818292	+	0.574803i	$0.805079\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−4.00000	+	6.92820i	−0.176432	+	0.305590i
$515$	−16.0000	+	27.7128i	−0.705044	+	1.22117i
$516$		0			0
$517$	−32.0000			−1.40736
$518$		0			0
$519$		0			0
$520$	8.00000	+	13.8564i	0.350823	+	0.607644i
$521$	−16.0000	+	27.7128i	−0.700973	+	1.21412i	0.267153	+	0.963654i	$0.413917\pi$
$521$	−16.0000	+	27.7128i	−0.700973	+	1.21412i	−0.968125	+	0.250466i	$0.919416\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−8.00000			−0.348817
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−20.0000	−	34.6410i	−0.868744	−	1.50471i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	8.00000	−	13.8564i	0.345870	−	0.599065i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	28.0000			1.20717
$539$		0			0
$540$		0			0
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	0.886721	−	0.462304i	$-0.152977\pi$
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	−0.843728	+	0.536771i	$0.819644\pi$
$542$	−16.0000	+	27.7128i	−0.687259	+	1.19037i
$543$		0			0
$544$		0			0
$545$	−56.0000			−2.39878
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$		0			0
$550$	−22.0000	+	38.1051i	−0.938083	+	1.62481i
$551$	−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
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	−28.0000	−	48.4974i	−1.17797	−	2.04030i
$566$	28.0000			1.17693
$567$		0			0
$568$	−8.00000			−0.335673
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−18.0000	+	31.1769i	−0.753277	+	1.30471i	0.192950	+	0.981209i	$0.438194\pi$
$571$	−18.0000	+	31.1769i	−0.753277	+	1.30471i	−0.946227	+	0.323505i	$0.895139\pi$
$572$	8.00000	+	13.8564i	0.334497	+	0.579365i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−8.00000	+	13.8564i	−0.333044	+	0.576850i	−0.983107	−	0.183031i	$-0.941409\pi$
$577$	−8.00000	+	13.8564i	−0.333044	+	0.576850i	0.650063	+	0.759880i	$0.274743\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	−8.00000			−0.332182
$581$		0			0
$582$		0			0
$583$	−20.0000	−	34.6410i	−0.828315	−	1.43468i
$584$	−8.00000	+	13.8564i	−0.331042	+	0.573382i
$585$		0			0
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$	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
$589$	32.0000			1.31854
$590$	−8.00000	−	13.8564i	−0.329355	−	0.570459i
$591$		0			0
$592$	3.00000	−	5.19615i	0.123299	−	0.213561i
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	0.999965	−	0.00831589i	$-0.00264706\pi$
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	−0.507184	+	0.861838i	$0.669314\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	32.0000			1.30531			0.652654	−	0.757656i	$-0.273656\pi$
$601$	32.0000			1.30531			0.652654	+	0.757656i	$0.273656\pi$
$602$		0			0
$603$		0			0
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	−10.0000	+	17.3205i	−0.406558	+	0.704179i
$606$		0			0
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	16.0000			0.647821
$611$	−16.0000	−	27.7128i	−0.647291	−	1.12114i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	10.0000	+	17.3205i	0.403567	+	0.698999i
$615$		0			0
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$	16.0000	−	27.7128i	0.642575	−	1.11297i
$621$		0			0
$622$	32.0000			1.28308
$623$		0			0
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	12.0000	−	20.7846i	0.479616	−	0.830720i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$		0			0
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$		0			0
$634$	15.0000	−	25.9808i	0.595726	−	1.03183i
$635$	32.0000	+	55.4256i	1.26988	+	2.19950i
$636$		0			0
$637$		0			0
$638$	−8.00000			−0.316723
$639$		0			0
$640$	−2.00000	+	3.46410i	−0.0790569	+	0.136931i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		0			0
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$		0			0
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$	−44.0000			−1.72582
$651$		0			0
$652$	12.0000			0.469956
$653$	−23.0000	−	39.8372i	−0.900060	−	1.55895i	−0.827415	−	0.561591i	$-0.810189\pi$
$653$	−23.0000	−	39.8372i	−0.900060	−	1.55895i	−0.0726446	−	0.997358i	$-0.523144\pi$
$654$		0			0
$655$	24.0000	−	41.5692i	0.937758	−	1.62424i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	−0.454099	−	0.890951i	$-0.650039\pi$
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	0.998636	−	0.0522143i	$-0.0166279\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$		0			0
$670$	−8.00000	−	13.8564i	−0.309067	−	0.535320i
$671$	16.0000			0.617673
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	16.0000	−	27.7128i	0.612672	−	1.06118i
$683$	−22.0000	+	38.1051i	−0.841807	+	1.45805i	0.0465592	+	0.998916i	$0.485174\pi$
$683$	−22.0000	+	38.1051i	−0.841807	+	1.45805i	−0.888366	+	0.459136i	$0.848159\pi$
$684$		0			0
$685$	40.0000			1.52832
$686$		0			0
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	20.0000	−	34.6410i	0.761939	−	1.31972i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$	−4.00000			−0.152057
$693$		0			0
$694$	−12.0000			−0.455514
$695$	24.0000	+	41.5692i	0.910372	+	1.57681i
$696$		0			0
$697$		0			0
$698$	−6.00000	−	10.3923i	−0.227103	−	0.393355i
$699$		0			0
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		0			0
$703$	−12.0000	+	20.7846i	−0.452589	+	0.783906i
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$		0			0
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	0.963512	+	0.267664i	$0.0862517\pi$
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	−0.249952	+	0.968258i	$0.580415\pi$
$710$	16.0000	−	27.7128i	0.600469	−	1.04004i
$711$		0			0
$712$	−4.00000	−	6.92820i	−0.149906	−	0.259645i
$713$		0			0
$714$		0			0
$715$	−64.0000			−2.39346
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	8.00000	−	13.8564i	0.298557	−	0.517116i
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	0.998224	−	0.0595683i	$-0.0189724\pi$
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	−0.550700	+	0.834703i	$0.685639\pi$
$720$		0			0
$721$		0			0
$722$	−3.00000			−0.111648
$723$		0			0
$724$	10.0000	−	17.3205i	0.371647	−	0.643712i
$725$	11.0000	−	19.0526i	0.408530	−	0.707594i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$		0			0
$730$	−32.0000	−	55.4256i	−1.18437	−	2.05139i
$731$		0			0
$732$		0			0
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	0.826723	−	0.562609i	$-0.190202\pi$
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	−0.900595	+	0.434659i	$0.856869\pi$
$734$	16.0000			0.590571
$735$		0			0
$736$		0			0
$737$	−8.00000	−	13.8564i	−0.294684	−	0.510407i
$738$		0			0
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	−0.621374	−	0.783514i	$-0.713425\pi$
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	0.989230	+	0.146369i	$0.0467586\pi$
$740$	12.0000	+	20.7846i	0.441129	+	0.764057i
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	−20.0000	+	34.6410i	−0.732743	+	1.26915i
$746$	−11.0000	+	19.0526i	−0.402739	+	0.697564i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$751$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$	−32.0000			−1.16460
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−18.0000	−	31.1769i	−0.653789	−	1.13240i
$759$		0			0
$760$	8.00000	−	13.8564i	0.290191	−	0.502625i
$761$	−8.00000	−	13.8564i	−0.290000	−	0.502294i	0.683810	−	0.729661i	$-0.260322\pi$
$761$	−8.00000	−	13.8564i	−0.290000	−	0.502294i	−0.973809	+	0.227366i	$0.926989\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−12.0000	+	20.7846i	−0.433578	+	0.750978i
$767$	8.00000	−	13.8564i	0.288863	−	0.500326i
$768$		0			0
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	0.336323	+	0.941747i	$0.390817\pi$
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	−0.983738	+	0.179609i	$0.942517\pi$
$774$		0			0
$775$	44.0000	+	76.2102i	1.58053	+	2.73755i
$776$	−8.00000			−0.287183
$777$		0			0
$778$	6.00000			0.215110
$779$		0			0
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−16.0000			−0.571064
$786$		0			0
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$		0			0
$790$	−32.0000			−1.13851
$791$		0			0
$792$		0			0
$793$	8.00000	+	13.8564i	0.284088	+	0.492055i
$794$	2.00000	−	3.46410i	0.0709773	−	0.122936i
$795$		0			0
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$		0			0
$800$	−5.50000	−	9.52628i	−0.194454	−	0.336805i
$801$		0			0
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	−32.0000	−	55.4256i	−1.12926	−	1.95593i
$804$		0			0
$805$		0			0
$806$	32.0000			1.12715
$807$		0			0
$808$	−2.00000	+	3.46410i	−0.0703598	+	0.121867i
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	−0.214930	−	0.976629i	$-0.568952\pi$
$809$	21.0000	−	36.3731i	0.738321	−	1.27881i	0.953251	−	0.302180i	$-0.0977142\pi$
$810$		0			0
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$		0			0
$813$		0			0
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	−24.0000	+	41.5692i	−0.840683	+	1.45611i
$816$		0			0
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	24.0000			0.839140
$819$		0			0
$820$		0			0
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	0.765487	−	0.643451i	$-0.222498\pi$
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	−0.939989	+	0.341206i	$0.889165\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	−26.0000	+	45.0333i	−0.903017	+	1.56407i	−0.0794606	+	0.996838i	$0.525320\pi$
$829$	−26.0000	+	45.0333i	−0.903017	+	1.56407i	−0.823557	+	0.567234i	$0.808014\pi$
$830$	24.0000	−	41.5692i	0.833052	−	1.44289i
$831$		0			0
$832$	−4.00000			−0.138675
$833$		0			0
$834$		0			0
$835$	−16.0000	−	27.7128i	−0.553703	−	0.959041i
$836$	8.00000	−	13.8564i	0.276686	−	0.479234i
$837$		0			0
$838$	−14.0000	−	24.2487i	−0.483622	−	0.837658i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−3.00000	−	5.19615i	−0.103387	−	0.179071i
$843$		0			0
$844$	14.0000	−	24.2487i	0.481900	−	0.834675i
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$		0			0
$848$	10.0000			0.343401
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−52.0000			−1.78045			−0.890223	−	0.455525i	$-0.849452\pi$
$853$	−52.0000			−1.78045			−0.890223	+	0.455525i	$0.849452\pi$
$854$		0			0
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	−0.990533	−	0.137277i	$-0.956165\pi$
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	0.376381	−	0.926465i	$-0.377169\pi$
$860$	16.0000			0.545595
$861$		0			0
$862$	−40.0000			−1.36241
$863$	24.0000	+	41.5692i	0.816970	+	1.41503i	0.907905	+	0.419176i	$0.137681\pi$
$863$	24.0000	+	41.5692i	0.816970	+	1.41503i	−0.0909355	+	0.995857i	$0.528986\pi$
$864$		0			0
$865$	8.00000	−	13.8564i	0.272008	−	0.471132i
$866$	−4.00000	−	6.92820i	−0.135926	−	0.235430i
$867$		0			0
$868$		0			0
$869$	−32.0000			−1.08553
$870$		0			0
$871$	8.00000	−	13.8564i	0.271070	−	0.469506i
$872$	7.00000	−	12.1244i	0.237050	−	0.410582i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	0.673109	−	0.739543i	$-0.264958\pi$
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	−0.977018	+	0.213158i	$0.931625\pi$
$878$		0			0
$879$		0			0
$880$	−8.00000	−	13.8564i	−0.269680	−	0.467099i
$881$	−8.00000			−0.269527			−0.134763	−	0.990878i	$-0.543027\pi$
$881$	−8.00000			−0.269527			−0.134763	+	0.990878i	$0.543027\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$		0			0
$890$	32.0000			1.07264
$891$		0			0
$892$	−8.00000	+	13.8564i	−0.267860	+	0.463947i
$893$	−16.0000	+	27.7128i	−0.535420	+	0.927374i
$894$		0			0
$895$	−48.0000			−1.60446
$896$		0			0
$897$		0			0
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	−8.00000	+	13.8564i	−0.266815	+	0.462137i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$	14.0000			0.465633
$905$	40.0000	+	69.2820i	1.32964	+	2.30301i
$906$		0			0
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	−0.650868	−	0.759191i	$-0.725595\pi$
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	0.982913	+	0.184073i	$0.0589282\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$		0			0
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	24.0000	−	41.5692i	0.794284	−	1.37574i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	−4.00000			−0.132164
$917$		0			0
$918$		0			0
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	0.924922	+	0.380158i	$0.124130\pi$
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	−0.133235	+	0.991084i	$0.542536\pi$
$920$		0			0
$921$		0			0
$922$	−6.00000	−	10.3923i	−0.197599	−	0.342252i
$923$	32.0000			1.05329
$924$		0			0
$925$	−66.0000			−2.17007
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$		0			0
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	−0.927546	−	0.373709i	$-0.878086\pi$
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	0.140132	−	0.990133i	$-0.455247\pi$
$930$		0			0
$931$		0			0
$932$	10.0000			0.327561
$933$		0			0
$934$	−10.0000	+	17.3205i	−0.327210	+	0.566744i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$	16.0000	+	27.7128i	0.521862	+	0.903892i
$941$	6.00000	−	10.3923i	0.195594	−	0.338779i	−0.751501	−	0.659732i	$-0.770670\pi$
$941$	6.00000	−	10.3923i	0.195594	−	0.338779i	0.947095	+	0.320953i	$0.104003\pi$
$942$		0			0
$943$		0			0
$944$	4.00000			0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	−14.0000	−	24.2487i	−0.454939	−	0.787977i	0.543746	−	0.839250i	$-0.317006\pi$
$947$	−14.0000	−	24.2487i	−0.454939	−	0.787977i	−0.998685	+	0.0512727i	$0.983672\pi$
$948$		0			0
$949$	32.0000	−	55.4256i	1.03876	−	1.79919i
$950$	22.0000	+	38.1051i	0.713774	+	1.23629i
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−24.0000			−0.775405
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−12.0000	+	20.7846i	−0.386896	+	0.670123i
$963$		0			0
$964$	4.00000	+	6.92820i	0.128831	+	0.223142i
$965$	8.00000			0.257529
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$		0			0
$970$	16.0000	−	27.7128i	0.513729	−	0.889805i
$971$	−2.00000	−	3.46410i	−0.0641831	−	0.111168i	0.832148	−	0.554553i	$-0.187111\pi$
$971$	−2.00000	−	3.46410i	−0.0641831	−	0.111168i	−0.896331	+	0.443385i	$0.853777\pi$
$972$		0			0
$973$		0			0
$974$	−8.00000			−0.256337
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	7.00000	−	12.1244i	0.223950	−	0.387893i	−0.732054	−	0.681247i	$-0.761438\pi$
$977$	7.00000	−	12.1244i	0.223950	−	0.387893i	0.956004	+	0.293354i	$0.0947715\pi$
$978$		0			0
$979$	32.0000			1.02272
$980$		0			0
$981$		0			0
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	4.00000	−	6.92820i	0.127580	−	0.220975i	−0.795158	−	0.606402i	$-0.792612\pi$
$983$	4.00000	−	6.92820i	0.127580	−	0.220975i	0.922739	+	0.385426i	$0.125946\pi$
$984$		0			0
$985$	12.0000	+	20.7846i	0.382352	+	0.662253i
$986$		0			0
$987$		0			0
$988$	16.0000			0.509028
$989$		0			0
$990$		0			0
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$		0			0
$995$	−32.0000			−1.01447
$996$		0			0
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	−0.554554	−	0.832148i	$-0.687111\pi$
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	0.997938	+	0.0641836i	$0.0204443\pi$
$998$	6.00000	−	10.3923i	0.189927	−	0.328963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.g.a.361.1		2
3.2	odd	2		294.2.e.d.67.1		2
7.2	even	3	inner	882.2.g.a.667.1		2
7.3	odd	6		882.2.a.f.1.1		1
7.4	even	3		882.2.a.l.1.1		1
7.5	odd	6		882.2.g.f.667.1		2
7.6	odd	2		882.2.g.f.361.1		2
12.11	even	2		2352.2.q.y.1537.1		2
21.2	odd	6		294.2.e.d.79.1		2
21.5	even	6		294.2.e.e.79.1		2
21.11	odd	6		294.2.a.c.1.1	yes	1
21.17	even	6		294.2.a.b.1.1	✓	1
21.20	even	2		294.2.e.e.67.1		2
28.3	even	6		7056.2.a.a.1.1		1
28.11	odd	6		7056.2.a.ca.1.1		1
84.11	even	6		2352.2.a.b.1.1		1
84.23	even	6		2352.2.q.y.961.1		2
84.47	odd	6		2352.2.q.a.961.1		2
84.59	odd	6		2352.2.a.y.1.1		1
84.83	odd	2		2352.2.q.a.1537.1		2
105.59	even	6		7350.2.a.cj.1.1		1
105.74	odd	6		7350.2.a.br.1.1		1
168.11	even	6		9408.2.a.de.1.1		1
168.53	odd	6		9408.2.a.bo.1.1		1
168.59	odd	6		9408.2.a.b.1.1		1
168.101	even	6		9408.2.a.br.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.a.b.1.1	✓	1	21.17	even	6
294.2.a.c.1.1	yes	1	21.11	odd	6
294.2.e.d.67.1		2	3.2	odd	2
294.2.e.d.79.1		2	21.2	odd	6
294.2.e.e.67.1		2	21.20	even	2
294.2.e.e.79.1		2	21.5	even	6
882.2.a.f.1.1		1	7.3	odd	6
882.2.a.l.1.1		1	7.4	even	3
882.2.g.a.361.1		2	1.1	even	1	trivial
882.2.g.a.667.1		2	7.2	even	3	inner
882.2.g.f.361.1		2	7.6	odd	2
882.2.g.f.667.1		2	7.5	odd	6
2352.2.a.b.1.1		1	84.11	even	6
2352.2.a.y.1.1		1	84.59	odd	6
2352.2.q.a.961.1		2	84.47	odd	6
2352.2.q.a.1537.1		2	84.83	odd	2
2352.2.q.y.961.1		2	84.23	even	6
2352.2.q.y.1537.1		2	12.11	even	2
7056.2.a.a.1.1		1	28.3	even	6
7056.2.a.ca.1.1		1	28.11	odd	6
7350.2.a.br.1.1		1	105.74	odd	6
7350.2.a.cj.1.1		1	105.59	even	6
9408.2.a.b.1.1		1	168.59	odd	6
9408.2.a.bo.1.1		1	168.53	odd	6
9408.2.a.br.1.1		1	168.101	even	6
9408.2.a.de.1.1		1	168.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{10} +(-2.00000 + 3.46410i) q^{11} -4.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{19} +4.00000 q^{20} +4.00000 q^{22} +(-5.50000 + 9.52628i) q^{25} +(2.00000 + 3.46410i) q^{26} -2.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-2.00000 - 3.46410i) q^{40} +4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(4.00000 + 6.92820i) q^{47} +11.0000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-5.00000 + 8.66025i) q^{53} +16.0000 q^{55} +(1.00000 + 1.73205i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(8.00000 + 13.8564i) q^{65} +(-2.00000 + 3.46410i) q^{67} -8.00000 q^{71} +(-8.00000 + 13.8564i) q^{73} +(3.00000 - 5.19615i) q^{74} -4.00000 q^{76} +(4.00000 + 6.92820i) q^{79} +(-2.00000 + 3.46410i) q^{80} -12.0000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-4.00000 - 6.92820i) q^{89} +(4.00000 - 6.92820i) q^{94} +(8.00000 - 13.8564i) q^{95} -8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 4 q^{5} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 4 * q^5 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 4 q^{5} + 2 q^{8} - 4 q^{10} - 4 q^{11} - 8 q^{13} - q^{16} + 4 q^{19} + 8 q^{20} + 8 q^{22} - 11 q^{25} + 4 q^{26} - 4 q^{29} + 8 q^{31} - q^{32} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 8 q^{43} - 4 q^{44} + 8 q^{47} + 22 q^{50} + 4 q^{52} - 10 q^{53} + 32 q^{55} + 2 q^{58} - 4 q^{59} - 4 q^{61} - 16 q^{62} + 2 q^{64} + 16 q^{65} - 4 q^{67} - 16 q^{71} - 16 q^{73} + 6 q^{74} - 8 q^{76} + 8 q^{79} - 4 q^{80} - 24 q^{83} - 4 q^{86} - 4 q^{88} - 8 q^{89} + 8 q^{94} + 16 q^{95} - 16 q^{97}+O(q^{100}) \) 2 * q - q^2 - q^4 - 4 * q^5 + 2 * q^8 - 4 * q^10 - 4 * q^11 - 8 * q^13 - q^16 + 4 * q^19 + 8 * q^20 + 8 * q^22 - 11 * q^25 + 4 * q^26 - 4 * q^29 + 8 * q^31 - q^32 + 6 * q^37 + 4 * q^38 - 4 * q^40 + 8 * q^43 - 4 * q^44 + 8 * q^47 + 22 * q^50 + 4 * q^52 - 10 * q^53 + 32 * q^55 + 2 * q^58 - 4 * q^59 - 4 * q^61 - 16 * q^62 + 2 * q^64 + 16 * q^65 - 4 * q^67 - 16 * q^71 - 16 * q^73 + 6 * q^74 - 8 * q^76 + 8 * q^79 - 4 * q^80 - 24 * q^83 - 4 * q^86 - 4 * q^88 - 8 * q^89 + 8 * q^94 + 16 * q^95 - 16 * q^97

Introduction

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