LMFDB - Embedded newform 882.2.g.b.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 42)
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.b.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +4.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(-2.00000 + 3.46410i) q^{25} +(-2.00000 - 3.46410i) q^{26} -9.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.50000 - 2.59808i) q^{40} -10.0000 q^{43} +(1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{47} +4.00000 q^{50} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-5.00000 - 8.66025i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +6.00000 q^{71} +(1.00000 - 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} +4.00000 q^{76} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} -9.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 - 5.19615i) q^{94} +(-6.00000 + 10.3923i) q^{95} +1.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{8} - 3 q^{10} + 3 q^{11} + 8 q^{13} - q^{16} - 4 q^{19} + 6 q^{20} - 6 q^{22} - 4 q^{25} - 4 q^{26} - 18 q^{29} - q^{31} - q^{32} - 8 q^{37} - 4 q^{38} - 3 q^{40} - 20 q^{43} + 3 q^{44} + 6 q^{47} + 8 q^{50} - 4 q^{52} - 3 q^{53} - 18 q^{55} + 9 q^{58} - 3 q^{59} - 10 q^{61} + 2 q^{62} + 2 q^{64} - 12 q^{65} + 10 q^{67} + 12 q^{71} + 2 q^{73} - 8 q^{74} + 8 q^{76} + q^{79} - 3 q^{80} - 18 q^{83} + 10 q^{86} + 3 q^{88} - 6 q^{89} + 6 q^{94} - 12 q^{95} + 2 q^{97}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^8 - 3 * q^10 + 3 * q^11 + 8 * q^13 - q^16 - 4 * q^19 + 6 * q^20 - 6 * q^22 - 4 * q^25 - 4 * q^26 - 18 * q^29 - q^31 - q^32 - 8 * q^37 - 4 * q^38 - 3 * q^40 - 20 * q^43 + 3 * q^44 + 6 * q^47 + 8 * q^50 - 4 * q^52 - 3 * q^53 - 18 * q^55 + 9 * q^58 - 3 * q^59 - 10 * q^61 + 2 * q^62 + 2 * q^64 - 12 * q^65 + 10 * q^67 + 12 * q^71 + 2 * q^73 - 8 * q^74 + 8 * q^76 + q^79 - 3 * q^80 - 18 * q^83 + 10 * q^86 + 3 * q^88 - 6 * q^89 + 6 * q^94 - 12 * q^95 + 2 * 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
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		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	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	−3.00000			−0.639602
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$		0			0
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$		0			0
$50$	4.00000			0.565685
$51$		0			0
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	1.00000			0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$		0			0
$83$	−9.00000			−0.987878			−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000			−0.987878			−0.493939	+	0.869496i	$0.664443\pi$
$84$		0			0
$85$		0			0
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	3.00000			0.291386
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	4.50000	+	7.79423i	0.429058	+	0.743151i
$111$		0			0
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$		0			0
$118$	3.00000			0.276172
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	−0.500000	−	0.866025i	−0.0449013	−	0.0777714i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−6.00000	+	10.3923i	−0.526235	+	0.911465i
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		0			0
$133$		0			0
$134$	−10.0000			−0.863868
$135$		0			0
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	6.00000	−	10.3923i	0.501745	−	0.869048i
$144$		0			0
$145$	13.5000	+	23.3827i	1.12111	+	1.94183i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	8.00000			0.657596
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$		0			0
$154$		0			0
$155$	3.00000			0.240966
$156$		0			0
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$	0.500000	−	0.866025i	0.0397779	−	0.0688973i
$159$		0			0
$160$	3.00000			0.237171
$161$		0			0
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$		0			0
$165$		0			0
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000			−0.226134
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	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
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.0000	+	20.7846i	−0.882258	+	1.52811i
$186$		0			0
$187$		0			0
$188$	−6.00000			−0.437595
$189$		0			0
$190$	12.0000			0.870572
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	−0.500000	−	0.866025i	−0.0358979	−	0.0621770i
$195$		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
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−18.0000			−1.26648
$203$		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
$209$	−12.0000			−0.830057
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	15.0000	+	25.9808i	1.02299	+	1.77187i
$216$		0			0
$217$		0			0
$218$	14.0000			0.948200
$219$		0			0
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$		0			0
$222$		0			0
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.5000	−	23.3827i	0.896026	−	1.55196i	0.0634974	−	0.997982i	$-0.479775\pi$
$227$	13.5000	−	23.3827i	0.896026	−	1.55196i	0.832529	−	0.553981i	$-0.186892\pi$
$228$		0			0
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$		0			0
$232$	−9.00000			−0.590879
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		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
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	−0.500000	+	0.866025i	−0.0317500	+	0.0549927i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	27.0000			1.70422			0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000			1.70422			0.852112	+	0.523359i	$0.175321\pi$
$252$		0			0
$253$		0			0
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$		0			0
$260$	12.0000			0.744208
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$		0			0
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$		0			0
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	0.983312	−	0.181928i	$-0.0582339\pi$
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	−0.649211	+	0.760609i	$0.724901\pi$
$272$		0			0
$273$		0			0
$274$	−18.0000			−1.08742
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	1.00000	+	1.73205i	0.0599760	+	0.103882i
$279$		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
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−12.0000			−0.709575
$287$		0			0
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	13.5000	−	23.3827i	0.792747	−	1.37308i
$291$		0			0
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	33.0000			1.92788			0.963940	−	0.266119i	$-0.0857413\pi$
$293$	33.0000			1.92788			0.963940	+	0.266119i	$0.0857413\pi$
$294$		0			0
$295$	9.00000			0.524000
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−1.00000			−0.0575435
$303$		0			0
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−15.0000	+	25.9808i	−0.858898	+	1.48765i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$		0			0
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−15.5000	−	26.8468i	−0.876112	−	1.51747i	−0.855574	−	0.517681i	$-0.826795\pi$
$313$	−15.5000	−	26.8468i	−0.876112	−	1.51747i	−0.0205381	−	0.999789i	$-0.506538\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$		0			0
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.00000	+	13.8564i	−0.443760	+	0.768615i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		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	$-0.351905\pi$
$332$	4.50000	−	7.79423i	0.246970	−	0.427764i
$333$		0			0
$334$	−3.00000	−	5.19615i	−0.164153	−	0.284321i
$335$	−30.0000			−1.63908
$336$		0			0
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$		0			0
$341$	1.50000	+	2.59808i	0.0812296	+	0.140694i
$342$		0			0
$343$		0			0
$344$	−10.0000			−0.539164
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	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
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	−9.00000	−	15.5885i	−0.477670	−	0.827349i
$356$	6.00000			0.317999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	0.924932	+	0.380131i	$0.124121\pi$
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	−0.133263	+	0.991081i	$0.542545\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	4.00000	+	6.92820i	0.210235	+	0.364138i
$363$		0			0
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	−0.999989	−	0.00473247i	$-0.998494\pi$
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	0.504093	+	0.863649i	$0.331827\pi$
$368$		0			0
$369$		0			0
$370$	24.0000			1.24770
$371$		0			0
$372$		0			0
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$		0			0
$375$		0			0
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$	−36.0000			−1.85409
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$		0			0
$382$		0			0
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$		0			0
$386$	−19.0000			−0.967075
$387$		0			0
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	−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
$395$	1.50000	−	2.59808i	0.0754732	−	0.130723i
$396$		0			0
$397$	−2.00000	−	3.46410i	−0.100377	−	0.173858i	0.811463	−	0.584404i	$-0.198672\pi$
$397$	−2.00000	−	3.46410i	−0.100377	−	0.173858i	−0.911840	+	0.410546i	$0.865338\pi$
$398$	−20.0000			−1.00251
$399$		0			0
$400$	4.00000			0.200000
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	9.00000	+	15.5885i	0.447767	+	0.775555i
$405$		0			0
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$		0			0
$411$		0			0
$412$	−8.00000			−0.394132
$413$		0			0
$414$		0			0
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$		0			0
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	−7.00000	−	12.1244i	−0.340755	−	0.590204i
$423$		0			0
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	3.00000			0.145010
$429$		0			0
$430$	15.0000	−	25.9808i	0.723364	−	1.25290i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$		0			0
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$		0			0
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	−0.929631	−	0.368492i	$-0.879874\pi$
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	0.145692	−	0.989330i	$-0.453459\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$		0			0
$448$		0			0
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−27.0000			−1.26717
$455$		0			0
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	−2.00000	+	3.46410i	−0.0934539	+	0.161867i
$459$		0			0
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$468$		0			0
$469$		0			0
$470$	−18.0000			−0.830278
$471$		0			0
$472$	−1.50000	+	2.59808i	−0.0690431	+	0.119586i
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	16.0000			0.734130
$476$		0			0
$477$		0			0
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	−16.0000	−	27.7128i	−0.729537	−	1.26360i
$482$	1.00000			0.0455488
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−1.50000	−	2.59808i	−0.0681115	−	0.117973i
$486$		0			0
$487$	−20.5000	+	35.5070i	−0.928944	+	1.60898i	−0.143851	+	0.989599i	$0.545949\pi$
$487$	−20.5000	+	35.5070i	−0.928944	+	1.60898i	−0.785093	+	0.619378i	$0.787385\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$		0			0
$490$		0			0
$491$	33.0000			1.48927			0.744635	−	0.667472i	$-0.232624\pi$
$491$	33.0000			1.48927			0.744635	+	0.667472i	$0.232624\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	1.00000			0.0449013
$497$		0			0
$498$		0			0
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	0.842774	−	0.538267i	$-0.180921\pi$
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	−0.887540	+	0.460730i	$0.847588\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	−13.5000	−	23.3827i	−0.602534	−	1.04362i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−54.0000			−2.40297
$506$		0			0
$507$		0			0
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	0.897352	−	0.441315i	$-0.145488\pi$
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	−0.830866	+	0.556473i	$0.812154\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$	12.0000	−	20.7846i	0.528783	−	0.915879i
$516$		0			0
$517$	18.0000			0.791639
$518$		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	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$		0			0
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	−9.00000			−0.393167
$525$		0			0
$526$	6.00000			0.261612
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$	5.00000	−	8.66025i	0.215967	−	0.374066i
$537$		0			0
$538$	21.0000			0.905374
$539$		0			0
$540$		0			0
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	−0.997587	−	0.0694205i	$-0.977885\pi$
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	0.438674	−	0.898646i	$-0.355448\pi$
$542$	5.50000	−	9.52628i	0.236245	−	0.409189i
$543$		0			0
$544$		0			0
$545$	42.0000			1.79908
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$		0			0
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	18.0000	+	31.1769i	0.766826	+	1.32818i
$552$		0			0
$553$		0			0
$554$	8.00000			0.339887
$555$		0			0
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$		0			0
$559$	−40.0000			−1.69182
$560$		0			0
$561$		0			0
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$		0			0
$565$		0			0
$566$	−14.0000			−0.588464
$567$		0			0
$568$	6.00000			0.251754
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	−0.945573	−	0.325409i	$-0.894498\pi$
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	0.190974	−	0.981595i	$-0.438835\pi$
$570$		0			0
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	11.5000	−	19.9186i	0.478751	−	0.829222i	−0.520952	−	0.853586i	$-0.674423\pi$
$577$	11.5000	−	19.9186i	0.478751	−	0.829222i	0.999703	+	0.0243645i	$0.00775624\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	−27.0000			−1.12111
$581$		0			0
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$		0			0
$586$	−16.5000	−	28.5788i	−0.681609	−	1.18058i
$587$	21.0000			0.866763			0.433381	−	0.901211i	$-0.357320\pi$
$587$	21.0000			0.866763			0.433381	+	0.901211i	$0.357320\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$	−4.50000	−	7.79423i	−0.185262	−	0.320883i
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−12.0000	−	20.7846i	−0.492781	−	0.853522i	0.507184	−	0.861838i	$-0.330686\pi$
$593$	−12.0000	−	20.7846i	−0.492781	−	0.853522i	−0.999965	+	0.00831589i	$0.997353\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$		0			0
$598$		0			0
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$		0			0
$601$	−11.0000			−0.448699			−0.224350	−	0.974509i	$-0.572026\pi$
$601$	−11.0000			−0.448699			−0.224350	+	0.974509i	$0.572026\pi$
$602$		0			0
$603$		0			0
$604$	0.500000	+	0.866025i	0.0203447	+	0.0352381i
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$		0			0
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	0.786212	−	0.617957i	$-0.212039\pi$
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	−0.928272	+	0.371901i	$0.878706\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	30.0000			1.21466
$611$	12.0000	+	20.7846i	0.485468	+	0.840855i
$612$		0			0
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		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
$619$	−17.0000	+	29.4449i	−0.683288	+	1.18349i	0.290684	+	0.956819i	$0.406117\pi$
$619$	−17.0000	+	29.4449i	−0.683288	+	1.18349i	−0.973972	+	0.226670i	$0.927216\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$		0			0
$622$	24.0000			0.962312
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$		0			0
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$		0			0
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	0.500000	+	0.866025i	0.0198889	+	0.0344486i
$633$		0			0
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	−7.50000	−	12.9904i	−0.297628	−	0.515508i
$636$		0			0
$637$		0			0
$638$	27.0000			1.06894
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$		0			0
$649$	4.50000	+	7.79423i	0.176640	+	0.305950i
$650$	16.0000			0.627572
$651$		0			0
$652$	−16.0000			−0.626608
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$		0			0
$655$	13.5000	−	23.3827i	0.527489	−	0.913637i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$		0			0
$664$	−9.00000			−0.349268
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$		0			0
$670$	15.0000	+	25.9808i	0.579501	+	1.00372i
$671$	−30.0000			−1.15814
$672$		0			0
$673$	29.0000			1.11787			0.558934	−	0.829212i	$-0.311211\pi$
$673$	29.0000			1.11787			0.558934	+	0.829212i	$0.311211\pi$
$674$	3.50000	+	6.06218i	0.134815	+	0.233506i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	0.986695	+	0.162581i	$0.0519817\pi$
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	−0.352549	+	0.935793i	$0.614685\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	1.50000	−	2.59808i	0.0574380	−	0.0994855i
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	−0.355920	−	0.934516i	$-0.615832\pi$
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	0.987275	−	0.159022i	$-0.0508342\pi$
$684$		0			0
$685$	−54.0000			−2.06323
$686$		0			0
$687$		0			0
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−12.0000			−0.455514
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$		0			0
$700$		0			0
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	−16.0000	+	27.7128i	−0.603451	+	1.04521i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−9.00000	+	15.5885i	−0.337764	+	0.585024i
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$	−36.0000			−1.34632
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		0			0
$721$		0			0
$722$	−3.00000			−0.111648
$723$		0			0
$724$	4.00000	−	6.92820i	0.148659	−	0.257485i
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$		0			0
$729$		0			0
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$		0			0
$732$		0			0
$733$	−5.00000	−	8.66025i	−0.184679	−	0.319874i	0.758789	−	0.651336i	$-0.225791\pi$
$733$	−5.00000	−	8.66025i	−0.184679	−	0.319874i	−0.943468	+	0.331463i	$0.892458\pi$
$734$	19.0000			0.701303
$735$		0			0
$736$		0			0
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$		0			0
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.119677	+	0.992813i	$0.538186\pi$
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.799962	+	0.600050i	$0.795147\pi$
$740$	−12.0000	−	20.7846i	−0.441129	−	0.764057i
$741$		0			0
$742$		0			0
$743$	−42.0000			−1.54083			−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000			−1.54083			−0.770415	+	0.637542i	$0.779951\pi$
$744$		0			0
$745$	27.0000	−	46.7654i	0.989203	−	1.71335i
$746$	−4.00000	+	6.92820i	−0.146450	+	0.253660i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$		0			0
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$	−3.00000			−0.109181
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−4.00000	−	6.92820i	−0.145287	−	0.251644i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−9.00000	+	15.5885i	−0.325183	+	0.563234i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$		0			0
$769$	19.0000			0.685158			0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000			0.685158			0.342579	+	0.939489i	$0.388700\pi$
$770$		0			0
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$	1.00000			0.0358979
$777$		0			0
$778$	6.00000			0.215110
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.0000			0.428298
$786$		0			0
$787$	25.0000	−	43.3013i	0.891154	−	1.54352i	0.0526599	−	0.998613i	$-0.483230\pi$
$787$	25.0000	−	43.3013i	0.891154	−	1.54352i	0.838494	−	0.544911i	$-0.183437\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$		0			0
$790$	−3.00000			−0.106735
$791$		0			0
$792$		0			0
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$	−2.00000	+	3.46410i	−0.0709773	+	0.122936i
$795$		0			0
$796$	10.0000	+	17.3205i	0.354441	+	0.613909i
$797$	−33.0000			−1.16892			−0.584460	−	0.811423i	$-0.698694\pi$
$797$	−33.0000			−1.16892			−0.584460	+	0.811423i	$0.698694\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	12.0000	−	20.7846i	0.423735	−	0.733930i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$	4.00000			0.140894
$807$		0			0
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		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
$817$	20.0000	+	34.6410i	0.699711	+	1.21194i
$818$	25.0000			0.874105
$819$		0			0
$820$		0			0
$821$	−1.50000	−	2.59808i	−0.0523504	−	0.0906735i	0.838663	−	0.544651i	$-0.183338\pi$
$821$	−1.50000	−	2.59808i	−0.0523504	−	0.0906735i	−0.891013	+	0.453978i	$0.850005\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$		0			0
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$		0			0
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	−0.898665	−	0.438636i	$-0.855462\pi$
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	0.829202	+	0.558949i	$0.188795\pi$
$830$	13.5000	−	23.3827i	0.468592	−	0.811625i
$831$		0			0
$832$	4.00000			0.138675
$833$		0			0
$834$		0			0
$835$	−9.00000	−	15.5885i	−0.311458	−	0.539461i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$		0			0
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$		0			0
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$	3.00000			0.103020
$849$		0			0
$850$		0			0
$851$		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
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$		0			0
$859$	25.0000	+	43.3013i	0.852989	+	1.47742i	0.878498	+	0.477746i	$0.158546\pi$
$859$	25.0000	+	43.3013i	0.852989	+	1.47742i	−0.0255092	+	0.999675i	$0.508121\pi$
$860$	−30.0000			−1.02299
$861$		0			0
$862$	−12.0000			−0.408722
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		0			0
$865$	−27.0000	+	46.7654i	−0.918028	+	1.59007i
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$		0			0
$868$		0			0
$869$	3.00000			0.101768
$870$		0			0
$871$	20.0000	−	34.6410i	0.677674	−	1.17377i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	−0.998888	−	0.0471555i	$-0.984984\pi$
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	0.458606	−	0.888640i	$-0.348349\pi$
$878$	17.5000	−	30.3109i	0.590596	−	1.02294i
$879$		0			0
$880$	4.50000	+	7.79423i	0.151695	+	0.262743i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$		0			0
$885$		0			0
$886$	−16.5000	+	28.5788i	−0.554328	+	0.960125i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$		0			0
$890$	18.0000			0.603361
$891$		0			0
$892$	−9.50000	+	16.4545i	−0.318084	+	0.550937i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	−36.0000			−1.20335
$896$		0			0
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	4.50000	−	7.79423i	0.150083	−	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$		0			0
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	13.5000	+	23.3827i	0.448013	+	0.775982i
$909$		0			0
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	−13.5000	+	23.3827i	−0.446785	+	0.773854i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$		0			0
$916$	4.00000			0.132164
$917$		0			0
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$		0			0
$921$		0			0
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	24.0000			0.789970
$924$		0			0
$925$	32.0000			1.05215
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$		0			0
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$		0			0
$932$	24.0000			0.786146
$933$		0			0
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$		0			0
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$		0			0
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	−0.783309	−	0.621633i	$-0.786469\pi$
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	0.930004	+	0.367549i	$0.119803\pi$
$942$		0			0
$943$		0			0
$944$	3.00000			0.0976417
$945$		0			0
$946$	30.0000			0.975384
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−8.00000	−	13.8564i	−0.259554	−	0.449561i
$951$		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
$958$	−18.0000			−0.581554
$959$		0			0
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	−16.0000	+	27.7128i	−0.515861	+	0.893497i
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.0161039	−	0.0278928i
$965$	−57.0000			−1.83489
$966$		0			0
$967$	−1.00000			−0.0321578			−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000			−0.0321578			−0.0160789	+	0.999871i	$0.505118\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	−1.50000	+	2.59808i	−0.0481621	+	0.0834192i
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$		0			0
$973$		0			0
$974$	41.0000			1.31372
$975$		0			0
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$		0			0
$982$	−16.5000	−	28.5788i	−0.526536	−	0.911987i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$	16.0000			0.509028
$989$		0			0
$990$		0			0
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$		0			0
$994$		0			0
$995$	−60.0000			−1.90213
$996$		0			0
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	−1.00000	+	1.73205i	−0.0316544	+	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.g.b.361.1		2
3.2	odd	2		294.2.e.f.67.1		2
7.2	even	3	inner	882.2.g.b.667.1		2
7.3	odd	6		882.2.a.g.1.1		1
7.4	even	3		882.2.a.k.1.1		1
7.5	odd	6		126.2.g.b.37.1		2
7.6	odd	2		126.2.g.b.109.1		2
12.11	even	2		2352.2.q.m.1537.1		2
21.2	odd	6		294.2.e.f.79.1		2
21.5	even	6		42.2.e.b.37.1	yes	2
21.11	odd	6		294.2.a.a.1.1		1
21.17	even	6		294.2.a.d.1.1		1
21.20	even	2		42.2.e.b.25.1	✓	2
28.3	even	6		7056.2.a.g.1.1		1
28.11	odd	6		7056.2.a.bz.1.1		1
28.19	even	6		1008.2.s.n.289.1		2
28.27	even	2		1008.2.s.n.865.1		2
63.5	even	6		1134.2.h.p.541.1		2
63.13	odd	6		1134.2.e.p.865.1		2
63.20	even	6		1134.2.h.p.109.1		2
63.34	odd	6		1134.2.h.a.109.1		2
63.40	odd	6		1134.2.h.a.541.1		2
63.41	even	6		1134.2.e.a.865.1		2
63.47	even	6		1134.2.e.a.919.1		2
63.61	odd	6		1134.2.e.p.919.1		2
84.11	even	6		2352.2.a.n.1.1		1
84.23	even	6		2352.2.q.m.961.1		2
84.47	odd	6		336.2.q.d.289.1		2
84.59	odd	6		2352.2.a.m.1.1		1
84.83	odd	2		336.2.q.d.193.1		2
105.47	odd	12		1050.2.o.b.499.2		4
105.59	even	6		7350.2.a.ce.1.1		1
105.62	odd	4		1050.2.o.b.949.1		4
105.68	odd	12		1050.2.o.b.499.1		4
105.74	odd	6		7350.2.a.cw.1.1		1
105.83	odd	4		1050.2.o.b.949.2		4
105.89	even	6		1050.2.i.e.751.1		2
105.104	even	2		1050.2.i.e.151.1		2
168.5	even	6		1344.2.q.v.961.1		2
168.11	even	6		9408.2.a.bm.1.1		1
168.53	odd	6		9408.2.a.db.1.1		1
168.59	odd	6		9408.2.a.bu.1.1		1
168.83	odd	2		1344.2.q.j.193.1		2
168.101	even	6		9408.2.a.d.1.1		1
168.125	even	2		1344.2.q.v.193.1		2
168.131	odd	6		1344.2.q.j.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.b.25.1	✓	2	21.20	even	2
42.2.e.b.37.1	yes	2	21.5	even	6
126.2.g.b.37.1		2	7.5	odd	6
126.2.g.b.109.1		2	7.6	odd	2
294.2.a.a.1.1		1	21.11	odd	6
294.2.a.d.1.1		1	21.17	even	6
294.2.e.f.67.1		2	3.2	odd	2
294.2.e.f.79.1		2	21.2	odd	6
336.2.q.d.193.1		2	84.83	odd	2
336.2.q.d.289.1		2	84.47	odd	6
882.2.a.g.1.1		1	7.3	odd	6
882.2.a.k.1.1		1	7.4	even	3
882.2.g.b.361.1		2	1.1	even	1	trivial
882.2.g.b.667.1		2	7.2	even	3	inner
1008.2.s.n.289.1		2	28.19	even	6
1008.2.s.n.865.1		2	28.27	even	2
1050.2.i.e.151.1		2	105.104	even	2
1050.2.i.e.751.1		2	105.89	even	6
1050.2.o.b.499.1		4	105.68	odd	12
1050.2.o.b.499.2		4	105.47	odd	12
1050.2.o.b.949.1		4	105.62	odd	4
1050.2.o.b.949.2		4	105.83	odd	4
1134.2.e.a.865.1		2	63.41	even	6
1134.2.e.a.919.1		2	63.47	even	6
1134.2.e.p.865.1		2	63.13	odd	6
1134.2.e.p.919.1		2	63.61	odd	6
1134.2.h.a.109.1		2	63.34	odd	6
1134.2.h.a.541.1		2	63.40	odd	6
1134.2.h.p.109.1		2	63.20	even	6
1134.2.h.p.541.1		2	63.5	even	6
1344.2.q.j.193.1		2	168.83	odd	2
1344.2.q.j.961.1		2	168.131	odd	6
1344.2.q.v.193.1		2	168.125	even	2
1344.2.q.v.961.1		2	168.5	even	6
2352.2.a.m.1.1		1	84.59	odd	6
2352.2.a.n.1.1		1	84.11	even	6
2352.2.q.m.961.1		2	84.23	even	6
2352.2.q.m.1537.1		2	12.11	even	2
7056.2.a.g.1.1		1	28.3	even	6
7056.2.a.bz.1.1		1	28.11	odd	6
7350.2.a.ce.1.1		1	105.59	even	6
7350.2.a.cw.1.1		1	105.74	odd	6
9408.2.a.d.1.1		1	168.101	even	6
9408.2.a.bm.1.1		1	168.11	even	6
9408.2.a.bu.1.1		1	168.59	odd	6
9408.2.a.db.1.1		1	168.53	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +4.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(-2.00000 + 3.46410i) q^{25} +(-2.00000 - 3.46410i) q^{26} -9.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.50000 - 2.59808i) q^{40} -10.0000 q^{43} +(1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{47} +4.00000 q^{50} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-5.00000 - 8.66025i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +6.00000 q^{71} +(1.00000 - 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} +4.00000 q^{76} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} -9.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 - 5.19615i) q^{94} +(-6.00000 + 10.3923i) q^{95} +1.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{8} - 3 q^{10} + 3 q^{11} + 8 q^{13} - q^{16} - 4 q^{19} + 6 q^{20} - 6 q^{22} - 4 q^{25} - 4 q^{26} - 18 q^{29} - q^{31} - q^{32} - 8 q^{37} - 4 q^{38} - 3 q^{40} - 20 q^{43} + 3 q^{44} + 6 q^{47} + 8 q^{50} - 4 q^{52} - 3 q^{53} - 18 q^{55} + 9 q^{58} - 3 q^{59} - 10 q^{61} + 2 q^{62} + 2 q^{64} - 12 q^{65} + 10 q^{67} + 12 q^{71} + 2 q^{73} - 8 q^{74} + 8 q^{76} + q^{79} - 3 q^{80} - 18 q^{83} + 10 q^{86} + 3 q^{88} - 6 q^{89} + 6 q^{94} - 12 q^{95} + 2 q^{97}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^8 - 3 * q^10 + 3 * q^11 + 8 * q^13 - q^16 - 4 * q^19 + 6 * q^20 - 6 * q^22 - 4 * q^25 - 4 * q^26 - 18 * q^29 - q^31 - q^32 - 8 * q^37 - 4 * q^38 - 3 * q^40 - 20 * q^43 + 3 * q^44 + 6 * q^47 + 8 * q^50 - 4 * q^52 - 3 * q^53 - 18 * q^55 + 9 * q^58 - 3 * q^59 - 10 * q^61 + 2 * q^62 + 2 * q^64 - 12 * q^65 + 10 * q^67 + 12 * q^71 + 2 * q^73 - 8 * q^74 + 8 * q^76 + q^79 - 3 * q^80 - 18 * q^83 + 10 * q^86 + 3 * q^88 - 6 * q^89 + 6 * q^94 - 12 * q^95 + 2 * q^97

Introduction

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